The Macroeconomics of the Great Recession

Transcrição

The Macroeconomics of the Great Recession
Implications for models of the labor market and central banking
DISSERTATION
of the University of St. Gallen,
School of Management,
Economics, Law, Social Sciences
and International Affairs
to obtain the title of
Doctor of Philosophy in Economics and Finance
submitted by
Johannes Fritz
from
Austria.
Approved on the application of
Prof. Dr. Uwe Sunde
and
Prof. Dr. Leo Kaas
Dissertation no. 4269
Studentendruckerei der Universität Zürich, 2014
The University of St. Gallen, School of Management, Economics, Law, Social Sciences and
International Affairs hereby consents to the printing of the present disseration, without hereby
expressing any opinon on the views herein expressed.
St. Gallen, May 14, 2014
The President:
Prof. Dr. Thomas Bieger
i
Danke!
Eine Dissertation zu schreiben ist ein Privileg und ich bin dankbar nach meinem politikwissenschaftlichen Studium dieses anspruchsvolle, volkswirtschaftliche Doktorat absolvieren zu
dürfen. Auf dem Weg zum vorliegenden Buch haben mir zahlreiche Menschen geholfen. Ihnen
möchte ich vorweg gerne und von Herzen danken.
Mit der Betreuung meiner Arbeit nahm Prof. Dr. Uwe Sunde die inhaltliche Hauptlast auf sich.
Für seinen guten und geduldigen Rat an entscheidenden Punkten meiner Forschungsarbeit bin
ich ihm sehr dankbar. Besonders schätze ich seine Flexibilität und Neugier, die es mir erlaubte
mich erst geographisch und dann inhaltlich immer weiter von ihm zu entfernen.
Neben Uwes gutem Rat durfte ich mehrfach die Hilfe anderer Forscher in Anspruch nehmen.
Im Verlauf der Arbeit aber insbesondere zuletzt begleitete mich Prof. Dr. Reto Föllmi mit treffenden Kommentaren. Ebenfalls danke ich Prof. Dr. Leo Kaas für seine Korrekturen und
die anregende Diskussion im Rahmen meiner Verteidigung. Für die wertvollen Wegweiser bei
meinen verschiedenen methodischen Ausflügen bin ich Prof. Dr. Daniel Buncic, Prof. Dr.
Jochen Mankart, Prof. Dr. Celine Poilly, Dr. Alexander Rathke, Dr. Samad Sarferaz und Prof.
Dr. Kozo Ueda sehr dankbar.
Besonders erwähnen möchte ich an dieser Stelle meinen Freund und Koautor Daniel Kienzler.
Zusammen sind wir durch einen besonders schwierigen und unerwartet langwierigen Abschnitt
unserer Promotionen gegangen. Es spricht sehr für ihn und unsere Zusammenarbeit, dass
wir durchgehend und zuletzt lachen konnten. Ich freue mich schon auf den ein oder anderen
«Mainzer Moment» auf dem Weg zur Publikation unseres Artikels.
Sehr dankbar bin ich Prof. Simon Evenett, Ph.D., für eine intellektuell anspruchsvolle und abwechslungsreiche Assistenzstelle am Schweizer Institut für Aussenwirtschaft und Angewandte
Wirtschaftsforschung (HSG-SIAW). Seine Unterstützung ist insbesondere in der Zeit nach meiner
Abgabe besonders wertvoll und gibt mir Zeit zur beruflichen Orientierung. Während meiner Arbeit genoss ich ausserdem die unerschöpfliche Hilfsbereitschaft von Gabriela Schmid und das
freundliche Miteinander am Institut.
Ich hatte das grosse Glück zeitgleich mit zwei fantastischen Institutskollegen ins Doktoratsstudium
zu starten. In jeder Phase und Dimension sind Florian Habermacher und Martin Wermelinger
famose Weggefährten. Mit Prof. Dr. Mark Schelker kam kurz darauf ein wichtiger, weitsichtiger
Ratgeber bei den verschiedensten Entscheidungen hinzu. Ebenfalls nicht missen möchte ich
die Zeit mit den zahlreichen Doktoratskollegen von den ich Thomas Davoine, Dario Fauceglia,
Berit Gerritzen, Jürg Müller, Uli Schetter, Fabian Schnell, Andreas Steinmayr und Jürg Vollenweider hier besonders danken möchte.
ii
Durch ihre vielschichtige Unterstützung hat meine Familie den entscheidenden Anteil am Erfolg
dieser Dissertation. Es waren meine Eltern Helene und Willi Fritz, die mich auf diesen Weg
brachten und sich niemals darüber beschwerten, dass ich ihn nun erst nach dem vollen Parcours wieder verlasse. Meine Schwestern Bernadette und Valeria sind Beispiel und Rückhalt
im Umgang mit schwierigen Situationen.
Die zentrale Stütze dieser Dissertation ist aber Jovanka Ruoss, die oft genug ein abwesendes,
zauderndes Gegenüber ertragen und aufbauen musste. Ich freue mich sehr darauf zusammen
mit ihr und unseren Kindern Alija Sophia und Naim Elias die Früchte dieser Arbeit ernten zu
dürfen.
Zürich im Juli 2014
Johannes Fritz
iii
Contents
Zusammenfassung
viii
Synopsis
ix
I
The comovement of output and job growth in the United States
1
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1
Motivation and outline of this chapter . . . . . . . . . . . . . . . . . . . . . . . . .
2
2
Relevant literature and data selection
. . . . . . . . . . . . . . . . . . . . . . . .
4
3
Evidence from dynamic correlations . . . . . . . . . . . . . . . . . . . . . . . . .
7
4
Evidence from Vector Autoregressions . . . . . . . . . . . . . . . . . . . . . . . .
13
5
Accounting for output growth dynamics in recent recoveries . . . . . . . . . . . .
28
6
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
A
Data used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
B
Gibbs sampling procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
C
VAR estimated using frequentist methods . . . . . . . . . . . . . . . . . . . . . .
37
D
Impulse response analysis for the alternative ordering . . . . . . . . . . . . . . .
40
E
Estimated recoveries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
F
Estimated recessions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
II
Amplification and propagation in the search & matching model of the labor market 44
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
1
Motivation and outline of this chapter . . . . . . . . . . . . . . . . . . . . . . . . .
45
2
Stylized facts about the comovement of employment and output in the United
States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
3
Amplification and propagation in the canonical DMP model . . . . . . . . . . . .
50
4
Extensions to improve amplification . . . . . . . . . . . . . . . . . . . . . . . . . .
60
5
Improving propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
iv
III
6
Empirical performance of model combinations . . . . . . . . . . . . . . . . . . . .
76
7
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
83
A
The economic importance of business cycle frequencies . . . . . . . . . . . . . .
85
B
Model calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
The role of bank financing costs for the transmission of monetary policy
91
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
91
1
Motivation and outline of this chapter
. . . . . . . . . . . . . . . . . . . . . . . .
92
2
Descriptive model outline and relevant literature . . . . . . . . . . . . . . . . . . .
93
3
Model economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
4
Calibration strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6
Bank funding costs and lending rates to the real economy: Evidence from the
euro zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
A
Data description and additional estimations . . . . . . . . . . . . . . . . . . . . . 140
B
Derivation of the external finance premia equations . . . . . . . . . . . . . . . . . 146
C
Derivation of the steady state values . . . . . . . . . . . . . . . . . . . . . . . . . 148
References
150
Curriculum Vitae
157
v
List of Tables
I.1
The long-run response of job growth to employment growth innovations . . . . .
10
I.2
Cumulative impulse responses to a common shock . . . . . . . . . . . . . . . . .
15
I.3
Estimation results
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
II.1 Volatilities and correlations in the canonical DMP model . . . . . . . . . . . . . .
59
II.2 Relative volatilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
II.3 Crosscorrelations in the amplification extensions . . . . . . . . . . . . . . . . . .
66
II.4 Autocorrelations in the amplification extensions . . . . . . . . . . . . . . . . . . .
67
II.5 Variable responses to the common shock in the amplification extensions . . . . .
68
II.6 Volatilities and correlations in the propagation extensions . . . . . . . . . . . . .
75
II.7 Variable responses to the common shock in the propagation extensions . . . . .
76
II.8 Volatilities and correlations in the combined models . . . . . . . . . . . . . . . . .
80
II.9 Autocorrelations of the combined models: t-statistics . . . . . . . . . . . . . . . .
81
II.10 Variable responses to the common shock in the combined models: t-statistics . .
82
II.11 List of parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
II.12 Stand-alone models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
II.13 Model combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
III.1 Calibration of the real economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
III.2 Calibration of the financial sector . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
III.3 Interest rate rules and associated welfare results.
. . . . . . . . . . . . . . . . . 130
III.4 Lending rates and borrowing cost in the eurozone in the Great Recession . . . . 136
III.5 Elasticity of bank borrowing cost with respect to the leverage ratio . . . . . . . . 138
III.6 Summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
III.7 Lending rates and borrowing cost in the eurozone, different specifications . . . . 142
III.8 Lending rates and borrowing cost in the eurozone, different specifications (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
III.9 Bank EFP and leverage ratio, different specifications . . . . . . . . . . . . . . . . 144
III.10Bank EFP and leverage ratio, different specifications (continued) . . . . . . . . . 145
vi
List of Figures
I.1
US recoveries since 1948 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
I.2
The evolution of US jobs and real GDP growth . . . . . . . . . . . . . . . . . . .
6
I.3
Dynamic correlation of output and job growth . . . . . . . . . . . . . . . . . . . .
7
I.4
Window estimates and marginal impact analysis . . . . . . . . . . . . . . . . . .
11
I.5
Adjusting for 1977-1982 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
I.6
Impulse responses to a common shock before and after 1984 . . . . . . . . . . .
14
I.7
Estimated moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
I.8
Impulse response analysis for the common shock . . . . . . . . . . . . . . . . . .
24
I.9
Cumulative impulse responses for the common shock . . . . . . . . . . . . . . .
26
I.10 Shock decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
I.11 Job growth in US recoveries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
I.12 Job losses in US recessions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
I.13 Evolution of IRFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
I.14 Impulse response analysis for the common shock . . . . . . . . . . . . . . . . . .
41
I.15 Estimated job growth in US recoveries . . . . . . . . . . . . . . . . . . . . . . . .
42
I.16 Estimated job losses in US recessions . . . . . . . . . . . . . . . . . . . . . . . .
43
II.1 Auto- and crosscorrelation of employment and output
. . . . . . . . . . . . . . .
48
II.2 Impulse Response Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
II.3 Auto- and crosscorrelation of employment and output in the canonical DMP model 57
II.4 Impulse Response Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
II.5 Auto- and crosscorrelation in the amplification extensions . . . . . . . . . . . . .
65
II.6 Impulse response functions in the amplification extensions . . . . . . . . . . . . .
66
II.7 Auto- and crosscorrelation in the propagation extensions . . . . . . . . . . . . . .
73
II.8 Impulse response functions in the propagation extensions . . . . . . . . . . . . .
74
II.9 Auto- and crosscorrelation in the combined models . . . . . . . . . . . . . . . . .
78
II.10 Impulse response functions in the combined models . . . . . . . . . . . . . . . .
79
II.11 Frequency estimates of output and employment . . . . . . . . . . . . . . . . . . .
86
III.1 Monetary policy shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
vii
III.2 Exogenous spending shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
III.3 Preference shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
III.4 Risk shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
III.5 Impulse response functions to an exogenous spending shock. . . . . . . . . . . . 121
III.6 Impulse response functions to a risk shock. . . . . . . . . . . . . . . . . . . . . . 122
III.7 Impulse response functions to a preference shock. . . . . . . . . . . . . . . . . . 123
III.8 Responses of firm bankruptcy rates and loan losses to different shocks. . . . . . 125
III.9 Impulse response functions for a bank net worth shock. . . . . . . . . . . . . . . 127
III.10Welfare surface for different combinations of the policy reaction parameters . . . 131
III.11Loss surface for different combinations of the central bank’s reaction parameters 132
viii
Zusammenfassung
Diese Dissertation besteht aus zwei separaten Teilen: Die ersten beiden Kapitel behandeln
das Miteinander von Arbeitsmarkt- und Wirtschaftsdynamik. Das dritte Kapitel enthält einen
theoretischen Beitrag zur Durchsetzung von Geldpolitik angesichts maroder Geschäftsbanken.
Arbeitsmarktdynamik und Konjunktur
Im empirischen Beitrag dieser Dissertation untersuche ich die gemeinsame Dynamik von Jobwachstum und Konjunkturentwicklung in den USA. Ich stelle eine leichte Verzögerung des Jobwachstums bei Konjunkturbewegungen seit den späten 1980ern fest. Seither reagiert das Jobwachstum auf einen gemeinsamen Schock erst nach 1-2 Quartalen mit dem maximalen Ausschlag. Zuvor war dieser maximale Ausschlag gleichzeitig mit dem des BIPs gemessen worden.
Allerdings ist die kumulative Reaktion des Jobwachstums auf einen gemeinsamen Shock von
vergleichbarer Grösse für den gesamten Beobachtungszeitraum. Angewandt auf die letzten
drei Wirtschaftsaufschwünge folgere ich, dass der Begriff „jobless recoveries“ treffender durch
„delayed recoveries“ ersetzt würde.
Im theoretischen Beitrag des Arbeitsmarktteils überprüfe ich, ob das Search & Matching Modell
von Diamond, Mortensen und Pissarides die oben beschriebene Dynamik abbilden kann. Ich
simuliere dazu eine Reihe von Modellvarianten, die auf bestehende Probleme des Modells
antworten. Es wird gezeigt, dass Modellerweiterungen mit Fixkosten für die Jobausschreibung
und geglätteter Lohnfestlegung realistischere Dynamiken erzeugen.
Durchsetzung der Geldpolitik bei flexiblen Bankfinanzierungskosten
Zusammen mit Daniel Kienzler entwickelte ich ein Neokeynesianisches Modell in dem Banken
sich nicht ausschliesslich zum Zentralbankzins finanzieren können. Stattdessen modellieren
wir einen variablen Keil zwischen Bankfinanzierungskosten und dem Zentralbankzins. Die
Grösse und Richtung dieses Keils hängt ab von der Bilanzgesundheit der Geschäftsbanken.
Diese Bilanzen werden beeinflusst von der Konjunktur indem Kreditverluste kontrazyklisch variieren. Wir finden, dass der Effekt von flexiblen Bankfinanzierungskosten in regulären Konjunkturschwankungen minimal ist. Einzig grosse, direkte Schocks auf das Eigenkapital können die
Bankfinanzierungskosten bedeutsam vom Zentralbankzins entkoppeln.
ix
Synopsis
The selection of topics covered in this thesis truly illustrate why I enrolled in a PhD in economics
in the first place. When I was about to finish my master’s degree in international relations, Bear
Sterns had just sought shelter under the wings of JP Morgan Chase and the global financial
crisis was in its early stages. While I followed the events and commentary with great interest, I
soon realized my lack of tools to grasp the economic issues at hand. The methods and theory
studied in the pursuit of this doctorate have narrowed this gap. In line with the initial motivation
for my PhD studies, the two threads of this thesis have little in common but their (re-)emergence
as pressing public policy issues within the past five years.
Labor market dynamics in the United States and macroeconomic models
The first thread is motivated from a curiosity for the discussion of «jobless recoveries» in the
United States. The iconic chart of this discussion is a diagram showing the evolution of US job
numbers after the economy has left a recession behind itself (see figure I.1 on page 2 for a
reproduction). In recoveries between 1948 and 1982, jobs grew out of the recession’s trough
relatively quickly, resembling the shape of a forward slash «/». In stark contrast, the labor market
gains have been nonexistent, a «_»-shape, after the three recessions since 1990.
The first two chapters of this thesis approach the topic from a wide angle. Although attempts
are made to reconnect to the discussion on «jobless recoveries», both chapters are concerned
with the comovement of output and employment growth in general. The first chapter analyzes
the evolving pattern of output and employment growth in the United States across all stages of
the business cycle, not only recoveries. While labor market growth after the three most recent
US recessions has been anemic by historical standards, the same applies to the dynamics of
real GDP growth. To discern whether the unsatisfactory labor market performance is a mere
byproduct of sluggish output growth, this chapter investigates how the relative timing and the
relative magnitude of US jobs and real GDP growth have evolved over time.
Built on consistent results from different time series methods, this chapter concludes that the
comovement between real GDP and job growth has grown delayed and somewhat jobless since
the late 1980s. Since then, the unconditional crosscorrelogram of output and employment
growth has widened significantly and a conditional correlation has emerged at the first outputemployment-lead. While the intertemporal correlation of the the two variables has widened,
the long-term response of employment growth to innovations in output growth has remained
unchanged.
Evidence from a Bayesian time-varying parameter vector autoregression with stochastic volatility also supports that the response of job growth has grown more persistent over the last 30
x
years. In the same period, a hump shape emerged with its peak lagging that of the output
growth response by 1-2 quarters. Prior to the 1980s, the largest response of job growth was
observable in tandem with that of GDP in the initial period of the shock. However, the observed
total response of job growth for a given common shock has decreased when measured over
time horizons of less than two years. Transplanting these findings into the three most recent recoveries suggests that their perceived joblessness can partly be explained by a general change
in the comovement pattern.
In parallel with the empirical analysis, I turned to a standard macroeconomic model of the labor
market for guidance on what changes may affect the comovement of output and employment.
Concerned with the intertemporal dimension of the problem analyzed in the empirical section,
I realized that the standard model is not sufficiently realistic to directly derive a theory-guided
conjecture on what may cause the observed changes. The second chapter of this thesis thus
turned into an attempt to reconcile the standard model with US observations.
Previous research by Shimer (2005) and Fujita and Ramey (2007) has shown that the canonical
search & matching model by Diamond, Mortensen and Pissarides exhibits unsatisfactory low
amplification and propagation properties. For common specifications of the underlying shock
process, the canonical model neither produces realistic volatilities in key variables nor do the
shocks remain in the model for a sufficient amount of periods. The second chapter revisits
solutions proposed for the amplification as well as the propagation problem of the canonical
search & matching model. It is shown that extensions of the model with a combination of
vacancy creation costs plus either smoothed wage setting or fixed hiring costs results in realistic
comovement of output and employment. However, an impulse response analysis suggests that
the underlying mechanism needs further consideration.
Flexible bank financing costs and the transmission of monetary policy
The second thread of this thesis is a response to recent developments in the euro zone. While
I was advancing in my thesis, the developments in the euro zone took a strong turn for the
worse. Only a year after European policy makers after had declared premature victory in 2011,
European Central Bank officials raised concerns that its monetary stance may not influence
lending rates to the real economy in a sufficiently equal manner throughout the euro zone.
A prime culprit for this disturbance might be the unequal evolution of bank financing costs in
different parts of the area, the officials conjectured. The final chapter of this thesis investigates
to what extent such a development can be replicated in a macroeconomic model.
Teaming up for the third chapter of our theses in 2012, Daniel Kienzler and I developed a New
Keynesian model in which banks do not necessarily finance at the monetary policy rate. Instead,
we propose a variable wedge between bank financing costs and the central bank’s policy rate.
The sign and size of this wedge depends on balance sheet conditions in the banking sector.
xi
The balance sheet conditions, in turn, can be influenced by deteriorating bank net worth arising
from loan losses in economic downturns.
This setup allows us to study scenarios in which the transmission of monetary policy is hampered in the sense that endogenous policy rate movements are not fully passed through to bank
financing costs and hence credit costs for the real economy. The effects of this impairment on
aggregate variables are small for shocks that emanate in the real sector and endogenously
trigger a deterioration in bank net worth but sizable for a direct impact on bank net worth. An
optimal policy rule in the presence of leverage-sensitive bank financing costs demands that the
central bank responds to tightening bank financing conditions with an interest rate decrease.
1
Chapter I. The comovement of output and job
growth in the United States
Abstract
In the context of recent discussions over «jobless recoveries», this chapter analyzes the evolving pattern
of output and employment growth in the United States. While labor market growth after the three most
recent US recessions has been anemic by historical standards, the same applies to the dynamics of real
GDP growth. To discern whether the unsatisfactory labor market performance is a mere byproduct of
sluggish output growth, this chapter investigates how the relative timing and the relative magnitude of
US jobs and real GDP growth have evolved over time.
This chapter concludes that the comovement between real GDP and job growth has grown delayed
and somewhat jobless since the late 1980s. Since then, the unconditional crosscorrelogram of output
and employment growth has widened significantly and a conditional correlation has emerged at the first
output-employment-lead. While the intertemporal correlation of the the two variables has widened, the
long-term response of employment growth to innovations in output growth has remained unchanged.
Evidence from a Bayesian time-varying parameter vector autoregression with stochastic volatility supports that the response of job growth has become more persistent over the last 30 years. In the same
period, a hump shape emerged with its peak lagging that of the output growth response by 1-2 quarters.
Prior to the 1980s, the largest response of job growth was observable in tandem with that of GDP in the
initial period of the shock. However, the observed total response of job growth for a given common shock
has decreased when measured over time horizons of less than two years. Transplanting these findings
into the three most recent recoveries suggests that their perceived joblessness can partly be explained
by a general change in the comovement pattern.
2
1 Motivation and outline of this chapter
1
In the aftermath of the Great Recession of 2008/09, the relative dynamics of output and labor market growth have attracted considerable public attention. Academic commentators and
media pundits alike put the spotlight on historically low absolute values of job creation and diagnosed a «jobless recovery». The term «jobless recovery» not only applies to the most recent
experience. Also in the two prior recessions, the labor market recoveries have followed a similar
pattern as figure I.1a illustrates.1
Fig. I.1: US recoveries since 1948
(a) jobs
(b) real GDP
Note: All recoveries have been indexed at the NBER-defined trough of the recession. Each value represents the
ratio of the observed level over its value in the NBER-defined trough.
However, while labor market growth after the three most recent US recessions has been anemic
by historical standards, the same applies to the dynamics of real GDP growth (figure I.1b). In
line with the empirical literature on the «Great Moderation», a period of decreased volatility
in US macroeconomic variables, real GDP growth after the three most recent US recessions
has fallen short of the dynamic upswings observed after prior recessions. In principle, it is
well possible that the unsatisfactory labor market dynamics are perfectly in line with the muted
output recovery.
In the light of reduced dynamics in both variables, this chapter investigates how the «comovement», operationalized as the relative timing and the relative magnitude of growth in the US
jobs and real GDP growth, has evolved over time. The analysis seeks to establish whether in
comparison to prior episodes, the recent US labor market and output growth have been either
1
In line with the phrasing of a «jobless» recovery, the labor market data used in this chapter stems from the BLS
Current Employment Statistics (CES). The CES use establishment data to capture the number of jobs (=occupied
positions) in the United States (see data selection section below). The CES makes no correction for individuals
with more than one job, and thus does not literally capture employment. Still, for the sake of better readability, I will
use the words «jobs», «labor market» or «employment» interchangeably throughout this chapter.
3
(i) slow, (ii) delayed, (iii) prolonged, or truly (iv) jobless. In the terminology of this chapter, «slow
growth» is defined as a symmetric slowdown in both labor market and GDP growth. According
to this «slow growth hypothesis», the US is witnessing a period of generally anemic growth with
no significant change in the relative dynamics of employment and GDP. Shifts in the relative dynamics of the two variables point at either the «delayed» or the «prolonged growth hypothesis».
The «delayed growth hypothesis» would be supported by an emerging timing gap between upswings in GDP and upswings in the labor market. If the «prolonged growth hypothesis» were
true, job growth would show increased persistence in response to GDP growth. Finally, if one
were to find a significantly lower amount of labor market growth following a comparable positive
impulse on GDP growth, the «jobless growth hypothesis» would hold.
This chapter concludes that the comovement between real GDP and job growth has grown
delayed and somewhat jobless since the late 1980s. Since then, the unconditional crosscorrelogram of output and employment growth has widened significantly and a conditional correlation
has emerged at the first output-employment-lead. While the intertemporal correlation of the
the two variables has widened, the long-term response of employment growth to innovations in
output growth has remained unchanged.
Evidence from a Bayesian time-varying parameter vector autoregression with stochastic volatility also supports that the response of job growth has grown more persistent over the last 30
years. In the same period, a hump shape emerged with its peak lagging that of the output
growth response by 1-2 quarters. Prior to the 1980s, the largest response of job growth was
observable in tandem with that of GDP in the initial period of the shock. However, the observed
total response of job growth for a given common shock has decreased when measured over
time horizons of less than two years. Transplanting these findings into the three most recent recoveries suggests that their perceived joblessness can partly be explained by a general change
in the comovement pattern.
The rest of this chapter is structured as follows. The next section positions this work in the
relevant literature and discusses the data selection. In section 3, an analysis of the dynamic
correlations between the two variables reveals an increased persistence of output fluctuations
in subsequent employment growth. To enrich this evidence, the results from a Bayesian vector
autoregression with time-varying parameters and stochastic volatility are discussed in section
4. Reconnecting this discussion of the general pattern to the recent perception of «jobless
recoveries», section 5 accounts for the role of the observed changes in the anemic job growth
dynamics. Section 6 concludes.
2 Relevant literature and data selection
2
4
Relevant literature and data selection
Related literature
The existing literature on jobless recoveries is focused on the most recent recoveries after US
recessions. The authors define a «jobless recovery» as a continued decline or stagnation of
employment, despite a continued increase in real GDP after the NBER-defined trough of the
recession. Given this focus on few recovery episodes, little systematic analysis besides simple
comparisons is used as evidence for the apparent phenomenon.
Most discussions of jobless recoveries focus exclusively on job creation without systematically
controlling for the evolution of real GDP (e.g. Aaronson, Rissman, and Sullivan, 2004; Berger,
2012; Groshen and Potter, 2003). Other authors account for the apparent declines in both
employment and output growth through the use of simple duration statistics that capture the
time between the trough and a pre-recessionary level of either variable (e.g. Jaimovich and Siu,
2012; Morin, 2013; Schreft and Singh, 2003; Schreft, Singh, and Hodgson, 2005). To give a
comparative measure of recovery speed, Jaimovich and Siu (2012), for instance, choose to
count the time until half the employment or half the output lost in the recession have been
re-gained. From a mean comparison across three pre- and three post-1990 recessions, the authors conclude that employment recoveries have become markedly slower while the slowdown
in output recoveries has been meager. Another approach to control for the dynamics of GDP
growth is provided by Schreft and Singh (2003). The authors take into account the slower recovery in real GDP. They apply Okun’s Law to receive a rule-of-thumb estimate for the warranted
employment growth given the meager pace of output.2 According to this estimate, post-1990
recoveries create less jobs than predicted by Okun’s Law.
Most relevant to the research in this chapter, Gordon (2010a,b) provides a split-sample analysis
of the stability of Okun’s Law. His conclusion is based on a regression of growth rates of cyclical
components. He splits the sample in 1986 and finds an increased procyclicality of the employment participation rate in the more recent period. As Gordon’s finding is seemingly at odds
with claims of a jobless recovery, one needs to note that it refers to the employment rate rather
than the absolute employment figures. Absent strong fluctuations in labor force participation,
the implication of larger procyclicality in the employment rate is stronger job creation for a given
impulse of output. However, it is evident from US data that labor force participation has fallen
in the recent recessions and only recovered slowly thereafter, if at all. Pending further analysis,
the two findings of a jobless recovery and a stronger procyclicality of the employment rate are
thus not at odds with each other.
2
In its original formulation, Okun’s law stated that for every annual percentage point deviation of output growth
from its trend growth rate, there shall be a rise in the employment-population ratio by a third of a percentage point
(Okun, 1962).
5
In the recent literature on the subject, only Galí, Smets, and Wouters (2012) provide an openly
skeptic view of the evidence on jobless recoveries. After a motivational analysis, they conclude
that recent recoveries are merely slow in the sense that both output and employment recover
only gradually after 1990. As with other studies mentioned above, the basis of their conclusion
is a simple difference-in-means analysis of cumulative 4- or 8-quarter growth rates for output,
employment and productivity. Unsurprisingly, the means of the first two variables are lower
in the post 1990 sample. However, the mean cumulative growth rate of productivity remains
unchanged (or lower) across samples, which contradicts what one would expect in a fully jobless
recovery where output would grow with a constant or decreasing proportion of labor.
In an extension of this literature, this chapter contains an in-depth study of the comovement of
output and employment in the United Sates. In its analysis of the two variables regardless of
the stage of the business cycle, this chapter takes a step back from the discussion over «jobless recoveries». The chapter reconnects to the discussion on «jobless recoveries» in its final
section where it identifies the extent to which the phenomenon can be explained by the general
comovement changes uncovered in prior sections. In terms of methodology, this chapter takes
a wide angle starting with simple correlations and standard regression analysis before following
the pioneering work on Bayesian methods by Primiceri (2005). As will be discussed further
below, a Bayesian approach is particularly useful for an analysis of the evolution in the comovement of output and employment growth as it allows for an efficient estimation of time-varying
coefficients under stochastic volatility.
Data issues and selection
The study of the US labor market begins with the choice of the relevant employment survey.
The US Bureau of Labor Statistics conducts two monthly surveys on the employment situation
in the country. The Current Population Survey (CPS) collects information on the employment
status of the members in approximately 60’000 households. The Current Employment Statistics
(CES) surveys 160’000 businesses and government agencies for the number of occupied jobs
in the establishment. Unfortunately, the two surveys have diverged in the late 1990s, even after
correcting for differences in their occupational coverage.3 In the context of jobless recoveries,
this divergence received additional attention as the household survey reports positive albeit
slow employment growth after the 2001 recession (Aaronson, Rissman, and Sullivan, 2004).
However, on the ground of apparently superior data collection, the literature largely uses the
establishment survey CES.4
3
See e.g. Bowler and Morisi (2006); Nardone, Bowler, Kropf, Kirkland, and Wetrogan (2003) for the in-depth
discussion of the discrepancies and Aaronson, Rissman, and Sullivan (2004); Bachmann (2009) for its relevance
in the discussion of jobless recoveries.
4
Jaimovich and Siu (2012) are a notable exception. The prime motivation for their deviation is the additional
use of income data which is only available for the CPS survey.
6
This study concentrates on the comovement in the non-agricultural private sector. The data
on real GDP are the seasonally adjusted, quarterly figures for real non-farm business GDP as
reported by the Bureau of Economic Analysis (table 1.3.6. «Real Gross Value Added by Sector,
Chained Dollars»). The data on jobs is generated from seasonally adjusted, monthly figures for
total private employment as reported by the Bureau of Labor Statistics in its Current Employment Statistics (CES) (BLS ID CES0500000001). The monthly jobs data have been aggregated
to quarters through a simple average. In line with the literature on the Great Moderation, all data
is used in growth rates i.e. log first differences (see e.g. Stock and Watson, 2003). The data has
not been filtered due to methodological concerns about both band pass and Hodrick-Prescott
filters as forcefully expressed by Gordon (2010b) as well as Berger (2012).
Figure I.2 reproduces the visual evidence as well as the summary statistics for the two variables.
Evidently, the more recent realizations of jobs and output growth have come in substantially
below their prior magnitudes. The Great Moderation literature suggests a break in the volatility
of various US macroeconomic variables around the mid-1980s, with 1984 being the consensus
estimate. In line with this literature, both displayed series suffer a visible drop in volatility across
the two sub-samples. The standard deviations fall to 50 resp. 60 percent of their initial values.
The remainder of this chapter seeks to identify whether this drop has been accompanied by a
shift in the relative timing of the dynamics of job and real GDP growth. The analysis starts with
a consideration of the dynamic correlations between the two series.
Fig. I.2: The evolution of US jobs and real GDP growth
standard deviation
pre 1984
post 1984
post 1984
pre 1984
job growth
real GDP growth
0.0090
0.0161
0.5626
0.0055
0.0082
0.6781
0.6121
0.5079
1.2053
σn
σy
7
3 Evidence from dynamic correlations
3
Evidence from dynamic correlations
The analysis of comovement is often reduced to the contemporaneous period, namely the correlation coefficient. Given the inter-temporal dimension of the research object, this chapter
also takes the comovement of real output and job growth for leading and lagging periods into
account. In his motivational section, Bachmann (2009) cites the unconditional dynamic correlogram between output and employment as evidence for the changed relative dynamics of
the two series. Replicating his work in figure I.3a, the increased persistence of the correlation
across periods is clearly distinguishable. Prior to 1984, output and jobs growth correlated the
most in the contemporaneous period. The correlation of contemporaneous output growth with
subsequent quarters of job growth decreased rapidly and vanished after 3 quarters.
The width of the correlogram increases significantly after 1984. In the more recent sample, contemporaneous output growth correlates significantly with job growth over a year later. Furthermore, the peak correlation has shifted from present job growth to job growth in the subsequent
quarter. At first glance, this seems to support the delayed job growth hypothesis. While output
and job growth patterns were centered around the present period prior to 1984, the relative
dynamics of job growth seem to have shifted backwards.
While unconditional dynamic correlations illustrate the aggregate comovement pattern, they
are less informative for the distinction between the different hypothesis introduced above. Figure I.3a merely implies that the past, present and future fluctuations of job growth move more
alike those of contemporaneous output growth after 1984. Absent further controls it is unclear
whether this increased resemblance is due to a prolonged resonance of job growth to innovations in output growth. For instance, the observed increase in the dynamic correlations could
also be the result of an increased persistence of either variable to its individual shocks. Given
the strong contemporaneous correlation, this increased persistence results in higher correlations at the leads and lags.
Fig. I.3: Dynamic correlation of output and job growth
(a) unconditional
(b) conditional
8
To identify changes in the comovement of employment and output growth, one thus has to
control for interim realizations of both variables between the contemporaneous period and the
lead or lag of interest. Partial correlation coefficients offer a simple means to control for the
correlation explained by in-between realizations of output and employment growth.5
The results, displayed in figure I.3b, support the notion of a prolonged comovement between
current output and future employment growth. However, the change is less pronounced than the
unconditional correlations would let us to believe. The main difference between the two periods
is the partial correlation coefficient for the first lag. It increases into statistical significance only
after 1984. Based on this finding it seems that current job growth mirrors preceding quarter’s
GDP growth, even after controlling for the auto- and the contemporaneous correlation of both
variables.
In principle, this evidence is in line with both the «delayed growth» and the «prolonged growth»
hypotheses. Nothing has been inferred with respect to the relative magnitudes involved. The
only hint with respect to the relative magnitudes so far are the summary statistics presented in
figure I.2. The apparent concurrency of a higher relative standard deviation and the increased
inter-temporal correlation of output and job growth points at the «prolonged growth hypothesis».
According to these estimates, job growth following upswings in GDP growth materializes in full
only with a delay, but is potentially stronger in total than prior to 1984.
The long-term response of employment
To better identify the overall strength of job growth, one needs a measure of cumulative job
growth following an innovation to real GDP growth. This chapter follows the method of Gordon
(2010b) for the estimation of a long-term employment response. The basis for this calculation
is equation (1). The long-run responses of employment growth to innovations in output growth
are computed as the ratio of the of the sum of the output-related coefficients over one minus
the
P4
j=0 βj
sum of the job growth related coefficients in a simple regression equation, i.e. LRE = 1−P4 α .
i=1
5
i
The method for the calculation of the partial correlation coefficients follows Greene (2008). In principle, the
partial correlation is calculated from purged values of the variables of interest, say contemporaneous output growth
∆yt and employment growth two quarters ago ∆nt−2 . As we seek to control for in-between realizations of output
and job growth, we regress each variable on these in-between realizations. The error terms yielded by this regression represent the components of the variable of interest that cannot be explained by our control variables. The
correlation of these purged values is thus the partial correlation of contemporaneous output and past job growth.
The exemplary estimation equations are:
∆yt
∆nt−2
= α0 + α1 ∆yt−1 + α2 ∆yt−2 + α3 ∆nt + α4 ∆nt−1 + yt
= β0 + β1 ∆yt−1 + β2 ∆yt−2 + β3 ∆nt + β4 ∆nt−1 + nt
9
∆nt = α0 +
4
X
i=1
αi ∆nt−i +
4
X
βj ∆yt−j + γ (nt−1 − φyt−1 ) + t
(1)
j=0
The equation is estimated for the sample split in 1984. Besides controlling for output and
employment growth over the past year, the equation also contains an error correction term. As
is standard for single equation Error Correction Models (ECM), this term consists of the levels
from the tested variables. In the estimations, the term featured the expected negative sign which
implies a mean-reversion mechanism. However, the magnitudes involved are small, indicating
that cointegration is not an issue in the differenced data.6 Unsurprisingly, a re-estimation of the
equation without the error correction term yielded identical results.
As is evident from table I.1, the long-run response of job growth to output growth has hardly
changed across samples. While the long-run response is a bit larger after 1984, the difference
is too small to provide more support for the «prolonged growth hypothesis». Furthermore, note
how the coefficients for real GDP have evolved across samples. The estimated magnitude
of the coefficient of current real GDP has decreased while that of the first lag has increased
and turned significant. Adding to the above observations of increased conditional correlations
and relative standard deviations, the evolution of the long-run response suggests that the US
witnesses a delayed response of the labor market to innovations in real GDP growth after 1984,
albeit at a similar cumulative magnitude.
6
Augmented Dickey Fuller tests confirm this claim. The tests cannot reject the null hypothesis of a unit root
in the levels of the real GDP and the jobs series. However, they reject the null at 1-percent significance for the
differenced data.
Furthermore, using the Engle-Granger method does not indicate cointegration for employment and output levels.
Regressing the former onto the latter yields a non-stationary error term. If the two variables were cointegrated i.e.
subject to a common stochastic drift, then the error term had to be stationary.
10
Tab. I.1: The long-run response of job growth to employment growth innovations
job growth
last quarter
2 quarters ago
3 quarters ago
4 quarters ago
RGDP growth
this quarter
last quarter
2 quarters ago
3 quarters ago
4 quarters ago
job level, last quarter
RGDP level, last quarter
Constant
Observations
R-squared
pre 1984
post 1984
0.502***
(0.093)
-0.209**
(0.102)
0.172*
(0.099)
-0.058
(0.073)
0.724***
(0.097)
-0.068
(0.119)
0.041
(0.119)
0.004
(0.080)
0.326***
(0.025)
0.047
(0.039)
0.069*
(0.037)
0.035
(0.035)
-0.016
(0.030)
-0.006
(0.011)
0.006
(0.006)
0.026
(0.077)
143
0.844
0.148***
(0.024)
0.114***
(0.028)
0.014
(0.030)
-0.024
(0.029)
-0.001
(0.028)
-0.016***
(0.006)
0.006**
(0.003)
0.122***
(0.045)
118
0.908
long-run response of job growth
pre 1984
.777
post 1984
.839
Robustness to sample selection
The split-sample estimates suggest a period of delayed growth since 1984. However, the split
in 1984 itself has only been assumed following the literature on the Great Moderation. To
evaluate the robustness of the finding with respect to the timing of the split, we re-estimate
the dynamic correlations using rolling sub-samples of the data. Results from these window
estimates suggest that the relevant correlations become unstable in the in the late 1980s and
evolve until the onset of the Great Recession in 2007. This is broadly in line with the suggested
split in 1984.
11
To characterize its evolution in more detail, the top panels in figure I.4 provide the result for
the rolling estimates of the correlations of interest using different window widths. Evidently, the
contemporaneous correlation is largely stable from 1947 until about 1990. It then falls to a lowpoint of around half its original magnitude right before the most recent downturn in 2007. As for
the conditional correlation of contemporaneous real GDP growth with the subsequent period’s
job growth, the opposite evolution is observable. It starts to increase from about the late 1980s
until a peak again right before the outbreak of 2007. In general, it appears that this conditional
correlation has been far less stable than that of the contemporaneous growth rates.
Fig. I.4: Window estimates and marginal impact analysis
(a) contemporaneous correlation
(b) conditional correlation, 1 quarter Output-Jobs
lead
(c) normalized marginal impact
While rolling estimations are a useful tool to assess the stability of a relationship, it is difficult
to interpret the importance of the observed changes. The apparent variation in the correlations
is driven by adding new information, but also by discarding old information. It is thus hard to
identify whether the newly added information is different from the existing data.
12
To better compare the value of the newly added observation to the existing estimate, this chapter
proposes a marginal impact analysis. This marginal impact analysis starts from a sub-sample
estimate for the moment in question. Here we use data from 1947-Q1 to 1959-Q4 and take
the estimated correlation as the basis for the marginal impact analysis. To measure the impact
of the marginal observation, the remainder of the sample is added sequentially, quarter-byquarter. The resulting difference in the correlation estimate yields the impact of the marginal
observation.
An ever increasing sample size biases the impact measure against the newly added observation. To compensate for the increasing weight of already added observations, each measured change is weighted by the number of observations included up until the prior period i.e.
M It = [ln (ρt ) − ln (ρt−1 )] Tt . For the sake of better legibility, the results are normalized by the
absolute value of the largest impact.
The marginal impact analysis yields different results for the two relevant moments (figure I.4,
lower panel). For one, the contemporaneous correlation seems to fall slowly, but almost continuously since the early 1980s. Upward and downward movements of the estimated correlation
were roughly in balance prior to 1984. After 1984, downward corrections, albeit meager ones,
outnumber upward shifts by two to one. While this decrease is persistent, the small magnitudes
involved suggest a gradual erosion rather than a one-time shift. This implies that any change in
the contemporaneous correlation observed in a sample split at 1984 is largely due to dropping
the earlier observations from the estimation.
Dropping the earlier observations also seems to explain the evolution of the conditional correlation at the first output-jobs lead. As is apparent from the lower panel of figure I.4, the variation
is much less systematic than that of the contemporaneous correlation. The marginal impact
of newly added observations pushes the updated estimate in either direction before and after
1984. This suggest that there is much less of a trend in the observed changes compared to
that in the contemporaneous correlation.
In particular, note that the visible increase in the rolling estimation coincides with the exit of observations that had a strongly negative impact. As is evident from the purple line in figure I.4c,
the mid to late 1970s provided a series of strong downward corrections in the estimated conditional correlation. Once those observations are dropped, the window estimate of the conditional
correlation starts to rise in figure I.4b, (red line: 1987, green: 1992, blue: 1997).
Given these particularly low realizations, it is necessary to verify the stated results. The interim
conclusion in favor of the «delayed growth hypothesis» was based on an apparently increased
conditional correlation at the first output-jobs lead, and a stable long-run response of employment to innovations in output. To see whether the late 1970s depress the pre-1984 estimate
to an extent that allows for the emergence of the observed pre/post-1984 difference, the above
calculations are repeated for the sample 1947-Q1 to 1976-Q4. The results of this re-estimation
are reported in figure I.5 and indicate that the above conclusion of delayed job growth remains
13
4 Evidence from Vector Autoregressions
warranted. Excluding the data from 1977-Q1 to 1983-Q4 does not meaningfully affect the results.
Fig. I.5: Adjusting for 1977-1982
(a) Conditional correlations of output and jobs
growth
(b) long-run response to output innovations
long-run response of job growth
pre 1984
.777
1947-1976
.768
post 1984
.839
4
Evidence from Vector Autoregressions
While the use of the above techniques is informative, vector autoregressions (VARs) provide
powerful tools to enrich the evidence. In particular, impulse response functions (IRFs) give an
intuitive format for the interpretation of observed changes in the comovement. To motivate this
tool, figure I.6 on the next page depicts the impulse response of the bi-variate VAR estimated
for the split sample.7 The decrease in the initial impulse reflects the reduced volatility of both
variables after 1984. Besides the fall in the absolute magnitudes, two changes in the IRF
structure are noteworthy.
For one, the shape of the IRF of job growth after an impulse on real GDP growth has developed
a hump shape. Before 1984, the estimates suggest an equally strong response in the first two
quarters which fades out into insignificance after a total of 5 periods. In line with the «delayed
growth hypothesis», the maximum response of job growth following a shock to real GDP growth
now occurs in the subsequent two quarters. Both quarters show a response that is significantly
7
The VAR is specified as follows. The included variables are job and real GDP growth. I order real GDP growth
first which implies that innovations in job growth do not affect real GDP growth in the contemporaneous period
(for a discussion of this issue, see the ordering section in the main text below). The VAR is estimated with a lag
length p = 3, to ensure no auto-correlation based on a Lagrange Multiplier test. The literature and the Schwarz
Information Criterion (SBIC) suggest using only two lags. Varying the lag length did not change the reported
results. The reported confidence intervals are calculated from a parametric bootstrap with 999 repetitions.
See Appendix C on page 37 for the result tables. A rolling estimate of this VAR is available in Appendix C.
14
larger than the point estimate for the initial response of job growth. Furthermore, the response
persistence is extended to 7 quarters. No such change of shape is evident for the real GDP
response.
Fig. I.6: Impulse responses to a common shock before and after 1984
(a) real GDP growth
(b) job growth
The second noteworthy change concerns the disappearing counter-reaction in the second year
following the initial shock. The point estimates of both IRFs produced from the earlier sample
suggest that the response changes its sign in both variables after a few quarters. While these
sign switches largely remain statistically insignificant, they do affect the estimated cumulative
impulse response.
The cumulative impulse response is one measure of total growth following an innovation in the
GDP equation. As the name implies, cumulative impulse responses are calculated by summation across an arbitrary lag length of the IRF. Comparing this measure of total growth provides a
means to discuss the job-intensity of output growth. As is apparent from table I.2, it is vital where
one stops the accumulation. While there is no change in the relative cumulative responses of
job growth to real GDP growth over the entire estimation period (16 quarters), one does see
relatively less job growth over periods smaller than 8 quarters after 1984. Thus, output growth
may appear jobless after 1984 if one fails to take into account the apparent correction in the
second year following the initial shock.
15
Tab. I.2: Cumulative impulse responses to a common shock
cumulative
response
after 4 quarters
pre 1984
post 1984
after 8 quarters
pre 1984
post 1984
after 16 quarters
pre 1984
post 1984
job
growth
real GDP
growth
job
real GDP
0.0137
0.0061
0.0195
0.0118
0.703
0.514
0.0120
0.0095
0.0123
0.0131
0.976
0.728
0.0114
0.0105
0.0139
0.0130
0.818
0.810
A Bayesian VAR with time-varying parameters and stochastic volatility
Frequentist methods may not be at their best in the task at hand. As indicated in the above
sections, at least some of the coefficients in the VAR fitted to US data are bound to gradually
evolve over time. Holding the coefficients constant, even only for a sub-sample, comes with
a loss of granularity for the object of this study. Furthermore, the volatility in the variables of
interest has witnessed a considerable decrease in the 1980s as the literature on the Great
Moderation emphasizes. If one fails to take into account the variance of the volatility, estimates
may produce excessively volatile coefficients (Sims, 2001). For an accurately specified model
of the US economy, it is thus necessary to add stochastic volatility.
Estimating a VAR model with time-varying coefficients as well as stochastic volatility using frequentist methods would stretch the capacity of the data set. The unobserved evolution of the
parameters and the volatility demands the use of filtering methods such as the Kalman filter
to recover them from the observed time series. Even though this is theoretically feasible also
for models with high dimensionality, it is undesirable because of the potential properties of the
resulting likelihood function and the practical feat of maximizing it in the first place.
As shown by Primiceri (2005), Bayesian methods enable researchers to estimate such a system
more efficiently. Essentially, the Bayesian procedure allows for a split of the high dimensional
problem into sub-problems of smaller dimension. Compared to deriving the joint posterior outright, it is often easier to characterize the distribution of the relevant parameters conditional
on each other. Under certain regularity conditions, this joint posterior can then be derived by
repeated sampling of the parameters conditional on each other using a Gibbs sampler (Greenberg, 2008).
16
Bayesian methods are particularly useful for the inspection of the evolution and the transmission of shocks. The estimation process of a Bayesian VAR allows the generation of impulse
response functions at every point in the data set. As stressed by Primiceri, the Gibbs sampling method used in this estimation is a smoothing method and thus allows us to estimate the
parameters of interest based on the information contained in the entire data set. The impulse
responses generated from time-varying coefficients thus capture the evolution of the propagation mechanism more accurately than frequentist methods such as window estimates.
The implementation of the Bayesian VAR follows the pioneering and widely applied model of
Primiceri (2005). Before presenting the results, the next section will describe the model. The
prior assumptions are discussed thereafter.
Description of the Bayesian VAR model
The model below is conceptually identical to those of Benati and Mumtaz (2007); Galí and Gambetti (2009); Primiceri (2005); Rathke and Sarferaz (2010), among others. A brief description of
the sampling procedure is relegated to Appendix B on page 33.
The estimated VAR model with time-varying coefficients and stochastic volatility is described in
equation (2). The endogenous variables are captured by the (2×1)-vector Yt ≡ [∆RGDPt , ∆JOBSt ]0 ,
the time-varying intercept is denoted A0,t and the time-varying coefficients are given by the matrix Ai,t for i = 1, ..., p. The results presented in the following section are built from an estimation
with three lags (p = 3) in line with the specification of the frequentist model used above.
Yt = A0,t +
p
X
Ai,t Yt−i + ut
(2)
i=1
ut ∼ N (0, Ωt )
Volatility is stochastic, follows a Gaussian distribution with zero mean and a time-varying covariance matrix Ωt . It is assumed that the error term ut is a function of t ∼ N (0, 1). To provide room
for stochastic volatilities, but keep the model solvable by standard procedures, the time-varying
covariance matrix is modeled as Ωt = Bt Σt Bt0 , where Σt is a diagonal matrix of time-varying
standard deviation and Bt is a lower triangular matrix with ones on the diagonal.
One can thus rewrite
Yt = A0,t +
p
X
i=1
Ai,t Yt−i + Bt−1 Σt t
(3)
17
Denote At = [A0,t , ..., Ap,t ] and αt = vec (A0t ), the off-diagonal elements of the matrix Bt are
denoted βt , and let the vector of the diagonal elements on Σt be given by σt . As is common in
this literature8 , the states are characterized as independent, driftless random walks:
αt = αt−1 + ωt
(4)
βt = βt−1 + υt
(5)
σt = σt−1 + ηt
(6)
Under this specification, the relationships between output and employment change with the
arrival of new information in an unpredictable way. Primiceri points out that assuming a random
walk process for the state equations has the undesirable implication that these coefficients can
reach any upper or lower bound as time advances. However, he discards this possibility with a
reference to the limited sample size.
The gains of using a random walk process compared to other models lie in its ability to replicate also gradual parameter shifts as well as in the lower number of estimated coefficients.
Including an autoregressive parameter into the above equations would demand the estimation
of 17 additional coefficients. An alternative to random walks would be Markov switching models.
However, these models are best suited for strong parameter shifts and entail a loss of flexibility
due to the necessary pre-specification of the possible number of states. Also, the number of
estimated coefficients increases by a factor of the assumed breaks.
The final assumption in the model setup concerns the variance covariance matrices. This
chapter follows Primiceri in assuming a block-diagonal structure for the variance covariance
matrix V of all innovations. The shocks are thus assumed to be independent of each other which
economizes on the number of estimated parameters. Second and again following Primiceri, it is
vital to assume a block diagonal structure of S in order to be able to use algorithms for Normal
linear state space models as described in Appendix B. This block diagonal structure implies
that the coefficients of the contemporaneous relations among variables evolve independently in
each equation. According to Primiceri (2005), generalizing S to non-zero off-diagonal elements
did not meaningfully affect the results.
8
see e.g. Benati and Mumtaz, 2007; Benati and Lubik, 2013; Canova and Gambetti, 2009; Cogley and Sargent,
2002, 2005; Galí and Gambetti, 2009; Primiceri, 2005; Rathke and Sarferaz, 2010.
18
The variance covariance matrix is thus given by:





t
ωt
υt
ηt






 ∼ N (0, V ) , V = 


In 0 0 0
0 Q 0 0
0 0 S 0
0 0 0 W





(7)
Priors and identification
The calibration strategy of this chapter follows Benati and Mumtaz (2007); Cogley and Sargent
(2005); Galí and Gambetti (2009) and Primiceri (2005). The priors are thus a mix of sample
moments recovered from a training period, and outright assumptions.
The prior densities of the coefficients are motivated by the estimation of a non-variant VAR on a
sub-period of the sample. The training sample used here covers data from 1947-Q1 to 1957-Q4
(40 observations). The results of this estimation are denoted with the subscript «OLS».
α0 ∼ N (α̂OLS , V (α̂OLS ))
β0 ∼ N β̂OLS , |β̂OLS |
σ0 ∼ N (σ̂OLS , In )
Besides these data-driven priors, it is necessary to specify the variance covariance matrix without any training observations. Here, I follow the Galí and Gambetti (2009) with somewhat tighter
priors than those used by Primiceri (2005).
Q0 ∼ IW (.005 × V (α̂OLS ) , 40)
S0 ∼ IW .001 × V β̂OLS , 2
2 .01 1
,
W0 ∼ IG
2 2
The specification of Q0 , S0 and W0 seeks to minimize the impact of the priors, thus allowing for
the sample information to drive the evolution of the states. To this end, the least informative
priors with an almost flat probability distribution are selected. For the inverse Wishart distribution, the least informative priors specify the minimal degrees of freedom (see e.g. Cogley and
Sargent, 2002). For Q0 , this is the number of sample observations and equals 40 in this paper.
For S0 , the proper minimum is its dimension and equal to 2. As shown by Kass and Natarajan
19
(2006), using the variances from the first stage estimates provides a good specification for the
scale parameter of an inverse Wishart distribution. To reduce the drift of the coefficients, I follow
Galí and Gambetti and scale said estimates by .005 and .001 respectively. Finally, for W0 which
follows an inverse Gamma distribution, I adopt Cogley and Sargent (2005) and insert a single
degree of freedom (which translates into the scale parameter of 12 displayed above). Under this
specification, the sample information also receives decisive weight as it rules out finite moments
for W0 .
The final specification issue for this model concerns the identification strategy used in the interpretation of the shocks. Given that the present model is estimated with two non-stationary
variables that are not cointegrated, a structural interpretation based on long-term restrictions
as pioneered by Blanchard and Quah (1989) is unwarranted. Recall that for a identification
strategy in the spirit of Blanchard & Quah, at least one of the variables needs to be stationary.
Furthermore, the bi-variate setup rules out identification via sign restrictions as proposed more
recently by Uhlig (2005). We thus turn to the original, recursive identification proposed by Sims
(1980) and also used by Primiceri (2005) which imposes an ordering on the shocks affecting
the two equations.
When imposing an ordering in a bi-variate VAR, one has to exclude one out of three possible innovation sources. In principle, current output and job growth could be affected by a combination
of output-specific, job-specific or common shocks. By definition, output-specific shocks affect
only output growth in the impact period and transmit into job growth only in subsequent quarters
via the VAR coefficients. The reverse is true for job-specific shocks. The only shock that affects
both output and job growth upon impact is the common shock. It is this common shock which
is of particular interest in this chapter. However, to identify the response to a common shock,
one has to exclude either the job-specific or the output-specific shock. Put differently, one has
to make the assumption whether (i) all shocks to real GDP growth to some degree also transmit
into job growth in the same period, or whether (ii) all shocks to job growth to some degree also
transmit into real GDP growth in the same period.
The estimation in this presented in this chapter builds on the recursive VAR identification with
output growth ordered first.9 A shock to output is always accompanied by a shock to job growth
within the same quarter albeit with possibly different (and time-varying) absolute magnitude.
This shock is referred to as the common shock below, as it yields responses in both output and
jobs growth. With output growth ordered first, a shock to job growth need not have instanta9
To assess the robustness of the results to the order selection, those for the alternative ordering are discussed
in Appendix D on page 40. If one allows for the combination of a common and a GDP-specific shock, one can
also discern the falling volatility in the later part of the sample and the increased duration of the job response.
The notable exception to this pattern is that the hump shape described in the main text below does not emerge in
the 1980s. Rather than increasing from the impact period to the subsequent period as observed in the main text,
the job response only declines more gradually in the later part of the sample. The more gradual decline is in line
with the delay in job growth attested in the main text, although the finding is less pronounced under the alternative
ordering.
20
neous ramifications for output growth. Those that do are counted under the common shock.
Those that do not are relegated to the job-specific shock. Note that the proposed identification
scheme is agnostic about the composition of each shock along the common types found in the
theoretic literature e.g. technology, monetary policy or risk shocks.10
Designating the second shock to be job- rather than output-specific aligns well with the timing of the search and matching model of the labor market established through the work of
Peter Diamond, Dale Mortensen and Christopher Pissarides (DMP).11 In the DMP setup, aggregate shocks such as the productivity shock affect both end-of-period measures for output
and employment. However, the canonical DMP demands that a shock on output transmits
into employment instantly. Shocks on output always affect the hiring volume of firms and thus
end-of-period employment. This is in line with the interpretation of yt as a common shock of
unknown composition.
Furthermore, job-specific shocks only affect output with a lag of one quarter.12 The reason
for this delay is the introduction of the so-called «matching function». Interpretable as the
production function of the labor market, the matching function describes the combination of
unemployed and vacancies into job matches i.e. successful hires. In the timing of the DMP
model, successful matches in period t are counted as part of the work force at the end of
the period but only produce output from period t + 1 onwards. Employment is thus turned
into a state variable. Shocks on productivity or otherwise only affect the hiring activity in the
contemporaneous period, but not the production-relevant workforce of that period. Interpreted
in light of the DMP-model, the job shocks nt identified in this chapter are disturbances to the
hiring process e.g. changes in the efficiency of the matching function.
Results
As a first result, figure I.7 presents the estimated standard deviations of both variables. Evidently, the volatility of both series has declined over the past 60 years, and it did so in a vastly
similar pattern. In line with the literature on the Great Moderation, the drop in volatility around
10
This agnostic stance overcomes a particular difficulty of strict structural interpretations concerning time-varying
parameter VARs. As elaborated by Primiceri (2005), the presence of time-varying coefficients and stochastic
volatility does not allow for the imposition of strong restrictions in the sense of Blanchard and Quah. In a time
invariant setup, the additive shock εt is the only innovation to the system. However, in time-varying parameter
VAR with stochastic volatility there are at least three independent sources of shocks as the variance covariance
matrix given by equation (7) implies. The core issue with respect to a structural interpretation is that shocks to
the regression coefficients are allowed to correlate across equations. Innovations to the coefficients in the jobs
equation may thus affect the coefficients in the output equation. There thus exists a source of uncertainty that is
not easily separable and cannot be fully orthogonalized as would be necessary for a strict structural interpretation
of the estimation results.
11
A detailed exposition of the model can be found in the following chapter of this thesis on page 50.
12
A potential exception to this pattern is a separation rate shock which, depending on its exact timing could also
be designed to affect current output. Note that under the proposed identification scheme, a respectively timed
separation rate shock would be subsumed under the common shock, yt .
21
1984 is pronounced and persistent. The spike towards the end of both series reflects the turmoil during the most recent downturn. In sum, it appears that the fit of the VAR has increased
over the sample. Past realizations of the two variables now account for a greater proportion of
the observed values in the later part of the sample.
The similarity of the described pattern across variables is clearly visible in figure I.7. Compared
to its initial estimate for 1955, the volatility of job growth seems to have declined somewhat
more than that of real GDP growth. However, the differences are meager as the all but constant
relative standard deviation implies.
A description of the evolution of the comovement of output and employment growth would be
incomplete with a comparison of the trends underlying each series. Given the reliance on
unfiltered data, this trend is best captured by the unconditional mean which can be recovered
from the VAR estimation using
E (Yt ) = (I − A1,t − A2,t − A3,t )−1 A0,t .
(8)
From this estimation, a decline in expected growth is observable for both variables (see bottomleft panel of figure I.7). However, the estimates towards the end of the sample suggest that
this decline may only be temporary. Two aspects about this pattern are noteworthy. First, the
decline in expected growth only starts about a decade after the onset of the Great Moderation,
namely in the mid-1990s. Second, the ratio of the two means remains largely stable except for
the first decade of the new millennium (bottom-right panel of figure I.7).
This timing is inconsistent with general explanations of «jobless growth» or «jobless recoveries»
that rely on diverging trend growth. The presented estimates of the unconditional means neither
suggest a gradual divergence of job and real GDP growth, nor a persistent drop in their relative
magnitude. Of the three «jobless recoveries» diagnosed so far in the United States, only that
of 2001 falls within the period of diverging trend growth. For the other two, both relative and
absolute expected means are close to their historical values.
22
Fig. I.7: Estimated moments
(a) absolute standard deviation
(b) indexed and relative standard deviation
(c) absolute mean
(d) indexed and relative mean
Impulse response analysis
The main tool for the analysis of the evolution of the comovement between output and job
growth used in this section are impulse response functions. Capitalizing on the advantages of
Bayesian methods, the top panel of figure I.8 displays estimates of the responses to a common
shock for all periods that remain in the estimation sample.13 With respect to the response
of real GDP growth, the structure has not changed over time while the magnitudes involved
clearly have. Across the entire sample, the response in the initial periods shows the strongest
impact. The innovation to real GDP growth then quickly subsides to only a quarter of the initial
magnitude before it vanishes entirely after about four quarters. This pattern has remained
broadly unchanged across the 1984 split samples as I.8d reveals.
The mentioned decline in the initial response is also evident in the evolution of the job growth
IRFs (I.8b). In contrast to real GDP growth however, also the structure of the job growth response seems to have shifted somewhat. After the middle of the 1980s, the IRFs of job growth
13
To allow for a clearer presentation, figure I.8a and (b) only display one IRF per year. The four quarterly
estimates have been compressed by a simple average.
23
take a more pronounced hump shape (I.8e). It seems that impulses from a common shock only
develop their peak impact after one or two quarters, rather than in the initial period. This finding
is in line with the increased conditional correlation at the first output-jobs lead uncovered above.
Furthermore, the post-1984 IRFs suggests that the common shock propagates longer in job
growth than in the prior sample.
To characterize the apparent change in the structure of the job growth response, I.8c presents
a variant of the original chart (b). To illustrate the emergence of the hump shape, the figure
has been rotated around the y-axis such that the reader now looks «into» the IRF with the
initial response at the surface of the chapter. The second variation over the original chart is
a normalization of the IRF. The base of this normalization is the initial response of real GDP
growth in the given year. Thus a value of .5 on the y-axis implies that the employment response
was half of the initial impact on real GDP growth.
The resulting figure I.8c reveals two changes to the comovement of output and employment
growth. For one, the initial response of job growth to a given common shock has declined
since the mid-1980s. This contrasts particularly strongly with substantial initial responses of job
growth throughout the 1970s and early 1960s. For two, the emerging hump shape is clearly visible after 1990 although not unprecedented. It seems that over the last 20 years, the response
of job growth to has built up over a few quarters before it reached its peak.
24
Fig. I.8: Impulse response analysis for the common shock
(a) Evolution real GDP growth
(b) Evolution job growth
(c) Responses of job growth, normalized by initial innovation to
real GDP growth
(d) Average normalized response of real GDP(e) Average normalized response of job
growth
growth
25
Cumulative impulse responses
With continued support for the increased persistence of the job growth response, the question
remains whether there is a degree of joblessness accompanying the changed comovement.
The counterpart to Gordon’s long-term responses used in the above section are cumulative
impulse responses. The evolution of this measure is depicted in figure I.9. Acknowledging the
role of accumulated duration, the cumulative impulse responses have been calculated again for
4, 8 and 16 quarters.
Unsurprisingly given the importance of the initial responses, the evolution of the cumulative
IRFs broadly mirrors that of the standard deviations reported above. Again, the 1970s stand
out as a period in which employment and output growth were particularly strongly aligned. For a
brief period, the cumulative response of employment closely matched that of output. In general,
the relative cumulative impulse responses appear volatile but lack any observable direction.
In line with the long run response estimate presented above for the sample split in 1984, no
clear decline in the relative cumulative responses is evident if one sums up over 16 quarters
(figure I.9b). If one only looks at response periods shorter than 2 years, the drop in the relative
standard deviation across samples is about 14 percentage points. This would imply that output
growth has grown less job-intensive in the more recent period. However, the observed volatility
of the cumulative job growth response demands a more detailed discussion. The final section
of this chapter attempts such an individual assessment for the most recent recovery episodes.
26
Fig. I.9: Cumulative impulse responses for the common shock
(a) cumulative response of job growth at differ-(b) cumulative response of real GDP growth at
ent lag length
different lag length
(c) Relative cumulative impulse response:
jobs over GDP
cumulative
response
after 4 quarters
pre 1984
post 1984
after 8 quarters
pre 1984
post 1984
after 16 quarters
pre 1984
post 1984
job
growth
real GDP
growth
job
real GDP
0.0128
0.0054
0.0202
0.0110
0.636
0.495
0.0150
0.0084
0.0178
0.0118
0.847
0.707
0.0138
0.0091
0.0169
0.0117
0.813
0.779
In sum, the evidence gathered in this section also supports the delayed growth hypothesis. The
evolution of the IRF of job growth suggests that the job response has shifted from the impact
period to subsequent quarters. From the late 1980s onwards, the job response peaks at the
second lag and fades out more gradually than in earlier periods. Overall, the sum cumulative
response indicates that a given measure of GDP growth is still accompanied by a comparable
amount of job growth, also in the later part of the sample. However, in line with the delayed
growth hypothesis, some of this growth has shifted towards later periods.
27
Shock decomposition
The responses to the common shock show an evolution of the employment-output nexus over
time. Overall, the nexus is still intact in terms of the relative magnitudes of job and GDP growth
as indicated by the cumulative responses. However, the relationship between output and employment growth in the US has stretched out inter-temporally. Rather than an immediate and
strong response, the peak transmission into job growth has become delayed by up to two quarters throughout the 1990s and remained so since.
Besides the transmission of the shocks, the VAR also allows the study of the shock decomposition over time. Using the above model, the shocks were decomposed into a common shock and
a job-specific shock. Figure I.10 depicts the evolution of these shocks throughout the sample.
Fig. I.10: Shock decomposition
(a) Evolution of shock standard deviations
(b) indexed and relative shock standard deviations
Note: Time series in panel (b) are indexed at the start of the estimation period (1957-Q3=1).
The relative size refers to the ratio of the job-specific over the common shock standard deviation magnitudes (as
depicted in panel (a)).
According to this decomposition, the decrease in volatility observed above for both job and
output growth is largely the mirror image of the declining magnitude of the common shock.
Being the more volatile of the two shocks, a sharp drop in the standard deviation of the common
shock is clearly observable at the beginning of the 1980s.
By comparison, the evolution of the job-specific shock is more gradual albeit hardly less pronounced. After the volatility reduces to less than half its initial size by the late 1990s, its standard
deviation stabilizes thereafter. Overall, the relative size of the two shocks fluctuates in a narrow
band around its historic mean (see the green line in I.10b).
28
5 Accounting for output growth dynamics in recent recoveries
This combination of the stable relative size with the delayed transmission of the common shock
into job growth suggests that job growth fluctuations are more independent from those of output
growth in the later part of the sample. Given that the initial response of job growth to a common
shock has decreased throughout the 1990s, the job-specific shock carries relatively more weight
over the short-term. As the cumulative response of job growth to a common shock is roughly
constant throughout the sample, this change in the composition washes out over the long run.
5
Accounting for output growth dynamics in recent recoveries
To reconnect the above findings to the debate about «jobless recoveries», this section seeks to
assess to what extent the observed changes in the comovement account for the recent recoveries with apparently anemic job growth. To identify how much job growth would be warranted
given the observed real GDP growth and past estimates of job growth, the job series is interpolated based on the coefficients obtained in the above VAR-estimation.14 The coefficients used
in this exercise are those of the jobs equation estimated at the NBER trough of each recession.
By construction, the coefficients obtained from the VAR are estimated over all stages of the
business cycle. The estimated growth rate one receives from multiplying the coefficients with
the associated past growth rate observations can thus be interpreted as a trend growth rate
conditional on the recent past.
In total, the interpolation stretches over 12 quarters and starts at the NBER-identified trough.
The obtained estimates are then multiplied with the job level observed in the trough to generate
an estimated evolution of the job level throughout the recovery. The observed job level at the
trough is the numeraire for the results depicted below.
Furthermore, a counterfactual is constructed to assess the role of the changes in the comovement for the job dynamics in the post-1990 recoveries. To gauge how much jobs would have
resulted from the observed output dynamics under historic comovement, the interpolation is
14
An estimate for job growth in period t is constructed as follows. Denote the observed value of real GDP growth
by ∆yt . The estimated of job growth is denoted ∆n̂t . The coefficients βi,trough are taken from the job equation
of the VAR in the previous section. The coefficients are kept at the level estimated for the trough of the studied
recession. Then
∆n̂t
= β0,trough +
3
X
i=1
βi,trough ∆yt−i +
3
X
β3+j,trough ∆n̂t−j .
j=1
The resulting estimates of job growth are then multiplied with the level of jobs observed at the trough to construct
the evolution of the employment level throughout the recovery.
Note that the estimate contains only realized values of real GDP growth. Due to the lag length, the estimates for
the first three quarters of the recovery contain realized values of job growth.
For the counterfactuals, I replace the coefficients estimated in the post-1990 troughs with a simple average of the
coefficients estimated for the pre-1990 troughs.
29
repeated for the post-1990 recoveries using averaged coefficients of the pre-1990 troughs.15
Fig. I.11: Job growth in US recoveries
(a) average pre-1990
(b) 1991-Q1
(c) 2001-Q4
(d) 2009-Q2
Note: Values normalized by the number of jobs observed in the trough of the recession.
A comparison with the observed evolution of jobs reveals that the bi-variate model tends to
underestimate the amount of job growth in recoveries (see figure figure I.11).16 This is un15
See figure I.15 in the Appendix on page 42 for individual graphs of the pre-1990 recoveries.
Two sources can account for the estimation inaccuracy. For one, the estimated shock correlation for the job
and output equation may adjust too rigidly. It is conceivable that an extreme common shock transmits differently
than one of average size. A recessionary common shock may for instance transmit into job growth at a magnitude
comparable to that of output growth, while on average the relative magnitude fluctuates around .2. One could
implement this assumption by increasing the prior variability of the β’s in the VAR. While a robustness exercise in
this spirit is sensible in principle, one is at risk of producing an assumed result.
The second source for the estimation inaccuracy may lie in the model specification. The model may be extended
to reflect the mean reversion of output and job growth. As elaborated in footnote 6 on page 9, the Engle-Granger
test did not find evidence for the cointegration of output and jobs. Regressing the former onto the latter yields a
non-stationary error term. If the two variables were cointegrated i.e. subject to a common stochastic drift, the error
term had to be stationary.
The correct specification of the VAR is thus one in first differences rather than to estimate their relationship as
a Vector Error Correction Model (VECM). Ruling out VECM, the model could be extended to include a variable
reflecting the opportunity for «catch-up growth». A possible extension could be a measure of the output gap
with the conjecture that the variable’s fluctuations around their means reflect the distance of the output level from
its trend. Further possibilities include attempts to decompose the job-specific shock directly. For instance, prior
vacancy creation activity or measures of skill mismatch in the job offering and unemployment composition may
account for part of the observed job growth in subsequent quarters.
16
30
surprising given the above interpretation of the estimates as a trend growth conditional on the
recent past. For the pre-1990 recoveries and that of 2009, observed job growth is considerably
larger than implied by the estimates. The difference accumulates to employment levels that
are around four percentage points higher in US data than in the fictional series. This larger
than conditional trend growth may be rationalized as «catch-up» job growth necessary for the
economy to return to its pre-recessionary growth path. It seems however, that this catch-up
growth remained absent during the recoveries of 1991 and 2001 where the fit of the model is
remarkable.17 These recoveries were fully in line with the conditional trend estimate at the time.
Still, they were less dynamic than their predecessors in the sense that the positive shocks, i.e.
catch-up growth, did not materialize.
According to the counterfactuals, the instability in the comovement has played a role in the
recent lackluster recovery dynamics of job growth. Using the average pre-1990 coefficients for
interpolation lifts the estimated series considerably (see dashed lines in the figures I.11b-d). In
the counterfactuals, job growth turns positive more quickly than in the original estimate and the
observed series. The stronger dynamics accumulate to a difference of about four percentage
points in the employment level after three years for the last two recessions. The difference is
not as pronounced in the recovery of 1991, which suggests that changes in the comovement of
output and job growth cannot explain the perceived weakness of the labor market at the time.
Rationalizing the good fit of the estimates for the 1991 and 2001 recovery as missing catchup growth begs the question whether such catch-up growth was warranted in the first place.
To assess the room for catch-up growth, figure I.12 compares the model’s prediction for all
recessions with the respective observed values. For all recessions, the estimate generated in
the above manner remains above the observed value. This negative deviation from conditional
trend growth is in line with lower job creation or net job losses observed in recessions.
17
Of the pre-1990 recoveries, only that of 1961 shows a similar fit (see figure I.15c on page 42).
31
Fig. I.12: Job losses in US recessions
(b) 1991-Q1
(c) 2001-Q4
(d) 2009-Q2
Note: Values normalized by the number of jobs observed at the peak prior to the recession.
The figures for the recessions of 1991 and 2001 support the notion that the missing catch-up
growth in the recovery is connected to fewer job losses in the first place. Both recessions were
relatively short with a duration of 2 quarters. The gap between the estimate and the observed
value at the trough is narrower in the 1991 and 2001 recessions than during any other US
recession.18 There were thus less negative shocks on job growth during the recessions of 1990
and 2001, thus leaving less room for positive shocks in order to return to the historic trend.
In sum, this exercise suggests that delayed job growth justifies the perception of different job
growth dynamics for two of the last three recoveries. Judging from the estimates, job growth
in the recovery of 1991 is largely in line with the lackluster real output growth observed in
the period and little room for catch-up job growth. The counterfactual job growth estimates
using pre-1990 coefficients yield a similar result and the absences of positives shocks can be
explained by comparative mildness of the recession. While the recession of 2001 was also mild,
the changes in the coefficients do manifest themselves in a considerable difference between
the estimate and the counterfactual. Under the comovement observed prior to 1990, the labor
market would have rebounded more quickly. This is also true for the most recent recovery in
18
See figure on page 43 in the appendix for the corresponding graphs of all individual pre-1990 recessions. For
recessions of similar durations as those in 1990/2001, see the graphs for the recessions of 1958 and 1961.
6 Conclusion
32
which past dynamics would have provided for a faster job recovery, especially if one expects
some degree of catch-up growth after the severe job losses during the recession.
6
Conclusion
This chapter studied the evolution of output and job growth in the United States. In the context
of a public debate over «jobless recoveries», it provided evidence for the evolving job-intensity
of US real GDP growth and the associated timing in job creation. The findings of this chapter
suggest that the response of the labor market has increased in duration, but became delayed
compared to observations prior to the 1980s. A joint analysis of unconditional and partial correlations with a measure for the long-term response of job growth revealed an emerging persistence of job growth into the first lag after an impulse to real GDP growth albeit with a comparable
cumulative response.
This finding is in line with evidence from impulse response analysis. According to the presented estimates, job growth now peaks in the first or second quarter following the respective
impulse on real GDP, rather than immediately as observed in the prior period. The analysis
also suggested that relative job growth has remained constant when measured over a longer
time horizon. However, the short-term response within the first two years after the impulse has
declined post 1980.
Estimating a counterfactual path for the recent recoveries revealed that the anemic labor market
response can in part be accounted for with the changed comovement of output and employment. If the comovement of output and job growth as captured by the VAR-coefficients had
remained at its pre-1990 average, the recoveries of 2001 and 2009 would have been accompanied with a higher degree of job growth. However, the first «jobless recovery» of 1991 can
largely be explained by lackluster real GDP growth and little room for catch-up job growth.
This chapter only discussed an aggregate phenomenon without making an attempt to propose
or evaluate the underlying causes. In particular, the restriction of the VAR analysis to a common
shock of unknown composition provides the ground for more detailed inquiries on the different
underlying factors driving the aggregate result. Furthermore, while this chapter focused on the
US labor market, a similar analysis may be of interest for various advanced economies that
have reported unsatisfactory job growth after the recent recession.
A Data used
A
33
Data used
The data on real GDP is the seasonally adjusted, quarterly figures for real non-farm business
GDP as reported by the Bureau of Economic Analysis (table 1.3.6. «Real Gross Value Added
by Sector, Chained Dollars»).
The data on jobs is generated from seasonally adjusted, monthly figures for total private employment as reported by the Bureau of Labor Statistics in its Current Employment Statistics
(BLS ID CES0500000001).
The data on employment is generated from seasonally adjusted, monthly figures for total private
employment as reported by the Bureau of Labor Statistics in its Current Population Survey.
The data on unemployment is generated from seasonally adjusted, monthly figures as reported
by the Bureau of Labor Statistics in its Current Employment Statistics (FRED ID UNEMPLOY).
All monthly data have been aggregated to quarters through a simple average.
B
Gibbs sampling procedure
As shown by Primiceri (2005), the proposed model can be evaluated using a Markov Chain
Monte Carlo algorithm, namely the Gibbs sampler. The procedure of iterative draws from the
underlying conditional distributions yields the sought posterior distribution. Given the available
extensive description of the procedure in Primiceri (2005), it is repeated only briefly below.
Summary
The steps of the sampling procedure used in this chapter can be summarized as follows:
1. Initialize bT , ΣT , sT and V as specified in the prior declaration above.
2. Draw aT from p aT |Y T , bT , ΣT , V .
3. Draw bT from p Y T |Y T , aT , ΣT , V .
4. Draw ΣT from p ΣT |Y T , aT , bT , sT , V .
5. Draw V by sampling its components, the hyperparamters Q, W and S from p Q, W, S|Y T , bT , ΣT =
= p Q|Y T , aT , bT , ΣT × p W |Y T , aT , bT , ΣT ×
×p S1 |Y T , aT , bT , ΣT × ... × p Sn−1 |Y T , aT , bT , ΣT .
6. Re-start from (2).
B Gibbs sampling procedure
34
This procedure differs from that proposed in Primiceri (2005) in the estimation of the volatility
states (Step 4). Instead we use the sampling procedure proposed by Jacquier, Polson, and
Rossi (1994) and popularized by Cogley and Sargent (2005). Doing so, we avoid an issue
related to the draw sequence of Primiceri (2005) pointed out in a recent corrigendum (Primiceri
and Del Negro, 2013). This avoidance comes at the cost of lost estimation efficiency. As pointed
out by Kim, Shephard, and Chib (1998), the method of Jacquier, Polson, and Rossi (1994)
generates substantial auto-correlation between the draws which biases inference. Similar to
Galí and Gambetti (2009), this auto-correlation is addressed by discarding every 39 out of 40
draws.
In sum, the stated procedure has been reiterated 50’000 times. The first 10’000 draws have
been discarded as a burn-in period. Of the remaining draws only every 40th is kept in the sample
to account for the mentioned auto-correlation. The stated results have thus been produced from
1’000 draws.
35
Description of each step
Draw the coefficient states aT from p aT |Y T , bT , ΣT , V
Recall that the observation equation of our model is given by
Yt = A0,t +
p
X
Ai,t Yt−i + Bt−1 Σt t
(9)
i=1
Conditional on bT , ΣT and V and our prior assumptions, the innovations in this equations have
known variance and follow a Normal distribution. Under these conditions, the algorithm put forth
by Carter and Kohn (1994) can be used to generate draws of aT .
Draw the error covariances bT from p bT |Y T , aT , ΣT , V
Once we have an observation for aT , one can observe the error term of the VAR equation which
is given by
0
Ŷt = Yt − Zt−1
⊗ In at
(10)
Using the above equations for the observation equation and the state equation for the error
covariances, we can write
Yt =
0
Zt−1
⊗ In at + ut
ut = Bt−1 Σt t
Bt Ŷt = Σt t
(11)
Recall that Bt is assumed to be lower triangular with ones on the main diagonal. Carrying
out the multiplication on the left-hand side of equation 11 yields a matrix with the values of
Ŷt on the diagonal and the products of individual elements with these values below. One can
then separate the diagonal elements from those below through the introduction of an additional
matrix Lt into Ŷt + Lt bt . Thus rewriting the system of equations 11 as
36
(12)
Ŷt = Lt bt + Σt t
where:

Lt
Ŷ[1,..,i],t
=
=
0
···
..
.

 −Ŷ1,t


 0
−Ŷ[1,2],t

 ..
..
.
 .
0
···
h
i
Ŷ1,t , Ŷ2,t , ..., Ŷi,t
···
0

···
...
0
..
.
..
0








0
.
−Ŷ[1,...,n−1],t
Unfortunately, this
is non-linear as the matrix Lt includes realizations of Ŷt which implies
h system
i
that the vector Ŷt , b̂t is not jointly normal. This problem can be circumvented using the assumption of a block-diagonal structure of the covariance matrix S for innovations on bt . Given
that innovations are uncorrelated across equations, one can apply Carter & Kohn equationby-equation rather than for the system a whole. Thanks to the structure of Lt , the dependent
variable of each equation Ŷi,t is not included in the controls on the right-hand-side.
Drawing the state of innovation volatility ΣT from p ΣT |Y T , aT , bT , V .
Following Cogley and Sargent (2005), this chapter applies the uni-variate algorithm developed
by Jacquier, Polson, and Rossi (1994). Given the previous draws of aT , bT and the data, each
element of the orthogonalized covariance matrix is observable. Using the orthogonalized covariance matrix implies that the estimated volatilities are mutually independent, which essential
for the individual application of the algorithm by Jacquier et al. to each element of the covariance
matrix.
Drawing the error covariance matrix V
The final draw concerns the innovations in the transition equations for aT , bT and σ T . As the
realizations of these variables have been drawn in the preceding steps, the innovations in the
transition equations are now observable. The assumed prior distribution for these innovations
was inverse Wishart. Given zero correlation between the transition equations, the posterior
distributions of Q, W and S are also inverse Wishart.
C VAR estimated using frequentist methods
C
37
VAR estimated using frequentist methods
The VAR is specified as follows. The included variables are job and real GDP growth. I order
real GDP growth first which implies that innovations in job growth do not affect real GDP growth
in the contemporaneous period (for a discussion of this issue, see the ordering section in the
main text below). The VAR is estimated with a lag length p = 3, to ensure no auto-correlation
based on a Lagrange Multiplier test. The literature and the Schwarz Information Criterion (SBIC)
suggest using only two lags. Varying the lag length did not change the reported results. The
reported confidence intervals are calculated from a parametric bootstrap with 999 repetitions.
38
Tab. I.3: Estimation results
GDP equation
real GDP growth
last period
2 periods ago
3 periods ago
job growth
last period
2 periods ago
3 periods ago
Constant
Job equation
real GDP growth
last period
2 periods ago
3 periods ago
job growth
last period
2 periods ago
3 periods ago
Constant
Observations
pre 1984
post 1984
-0.042
(0.121)
0.29
(0.108)
0.124
(0.099)
0.164
(0.103)
0.014
(0.113)
-0.102
(0.107)
1.082
(0.278)
-1.304
(0.315)
-0.184
(0.245)
0.008
(0.002)
0.666
(0.358)
0.533
(0.455)
-0.713
(0.29)
0.001
(0.001)
0.02
(0.053)
0.175
(0.047)
0.084
(0.043)
0.131
(0.03)
0.005
(0.033)
-0.042
(0.031)
0.885
(0.121)
-0.642
(0.138)
0.041
(0.107)
0.001
(0.001)
0.881
(0.104)
0.012
(0.132)
-0.102
(0.084)
-0.0001
(0.0003)
144
118
To assess the robustness of the stated pattern with respect to the cut-off, the VAR is reestimated in a rolling fashion. The window width is 20 years (80 observations). The above
VAR is estimated for each window. Figure I.13 on the next page presents the evolution of the
39
IRFs. Evidently, the hump shape of the job growth response emerges once observations from
the 1990s enter the sample and those from the 1970s exit. The observed pattern resembles
that produced by Bayesian estimates in the main text closely. The main difference lies in the
timing of the hump-shape emergence. While the Bayesian estimates suggest its occurrence
in the late 1980s, the rolling estimation with a window of 20 years dates this change into the
mid-1990s.
Fig. I.13: Evolution of IRFs
(a) Evolution of real GDP response
(b) Evolution of job response
D Impulse response analysis for the alternative ordering
D
40
Impulse response analysis for the alternative ordering
This section presents the results for the alternative ordering of the variables. It is thus assume
that the common shock is nt , while yt includes only output-specific shocks. The latter innovations only transmit into job growth in future periods.
The impulse responses to the common shock produce a similar pattern under the alternative
ordering (see figure I.14). Again one can identify the falling volatility in the later part of the
sample and the increased duration of the job response. The notable exception to this pattern
is that the hump shape described in the main text does not emerge in the 1980s. Rather than
increasing from the impact period to the subsequent period as observed in the main text, the
job response declines more gradually in the later part of the sample. The more gradual decline
is in line with the delay in job growth attested in the main text, although the finding is less
pronounced under the alternative ordering.
41
D Impulse response analysis for the alternative ordering
Fig. I.14: Impulse response analysis for the common shock
(a) Evolution real GDP growth
(b) Evolution job growth
(c) Average normalized response of real GDP(d) Average normalized response of job
growth
growth
(e) Response of real GDP growth: Recoveries
(f) Response of job growth: Recoveries
42
E Estimated recoveries
E
Estimated recoveries
Fig. I.15: Estimated job growth in US recoveries
(b) 1958-Q2
(c) 1961-Q1
(d) 1970-Q4
(e) 1975-Q1
(f) 1982-Q4
43
F Estimated recessions
F
Estimated recessions
Fig. I.16: Estimated job losses in US recessions
(b) 1958-Q2
(c) 1961-Q1
(d) 1970-Q4
(e) 1975-Q1
(f) 1982-Q4
44
Chapter II. Amplification and propagation in the
search & matching model of the labor market
Abstract
This chapter investigates whether the current vintage of search & matching models of the labor market
is able to replicate the observed comovement of output and employment in US data. Previous research
by Shimer (2005) and Fujita and Ramey (2007) has shown that the canonical search & matching model
exhibits unsatisfactory low amplification and propagation properties. For common specifications of the
underlying shock process, the canonical model neither produces realistic volatilities in key variables nor
do the shocks remain in the model for a sufficient amount of periods.
The contribution of this chapter is an analysis of the comovement of output and employment implied by
the DMP model. To this end, it revisits solutions proposed for the amplification as well as the propagation
problem of the canonical search & matching model. It is shown that extensions of the model with a
combination of vacancy creation costs plus either smoothed wage setting or fixed hiring costs results in
realistic comovement of output and employment. However, an impulse response analysis suggests that
either additional model extensions or alternative shock sources are called for.
1
45
The evidence gathered in the previous chapter of this thesis suggests that the relationship between output and employment growth has evolved in the United States. The patterns have
evolved in the late 1980s, early 1990s. To receive guidance on what might explain this development, this chapter analyzes the comovement of output and employment within a standard
macroeconomic model of the labor market.
The focus of this chapter is the canonical model of Diamond, Mortensen and Pissarides (DMP)
as described in Pissarides (2000). While being the work horse model for macroeconomic analysis of the labor market, the empirical accuracy of the DMP model has been questioned in
two distinct dimensions. First came the discovery of the «unemployment volatility puzzle» by
Shimer (2005) and also Hall (2005a). As these authors showed, the canonical DMP model
implies unrealistic volatilities of its two central variables, vacancies and unemployment. Their
ratio, referred to as «labor market tightness» in the literature, shows only a fraction of the volatility observed in US data. The amplification of the productivity shock that drives the canonical
model is thus not strong enough with respect to labor market variables. Below, this stream of
the literature will be referred to as the «amplification problem» of the DMP model.
Within the quest for possible answers to the amplification problem, Fujita and Ramey (2007)
uncovered a further empirical inaccuracy of the DMP model. According to their work, the propagation within the DMP model is too low relative to the data. Comparing the persistence of
productivity with that of employment as well as labor market tightness, Fujita and Ramey show
that the latter variables return to their steady states too quickly. Productivity shocks do not propagate sufficiently long in the standard specification of the DMP model. Below, this dimension of
the empirical criticism will be referred to as the «propagation problem».
The contribution of this chapter is to evaluate the empirical accuracy of extensions to the DMP
model with respect to the comovement of employment and output. The selected models include
proposed solutions to the amplification or the propagation problem of the canonical model as
well as combinations thereof. In their critique, Fujita and Ramey (2007) demonstrate that a
new form of vacancy creation costs improves the propagation dynamics of the DMP model.
The authors also solve the amplification problem through a simple recalibration of the canonical
model parameters along the lines of Hagedorn and Manovskii (2008a). However, Costain and
Reiter (2008) and Hall and Milgrom (2008) have shown that such a recalibration is unwarranted.
These papers showed that a calibration along these lines implies grossly unrealistic elasticities
of unemployment and labor supply with respect to non-work benefits. The solution to the amplification problem incorporated in Fujita and Ramey’s solution of the propagation problem thus
needs to be reconsidered.
This chapter acknowledges the three critiques of Shimer (2005), Fujita and Ramey (2007) as
well as Costain and Reiter (2008). The critique of Costain and Reiter is addressed through the
2 Stylized facts about the comovement of employment and output in the United States
46
use of an altered version of the vacancy creation cost model of Fujita and Ramey later in this
chapter. In contrast to Fujita and Ramey, this chapter does not rely on recalibration to address
the amplification problem. Instead, this chapter introduces various wage setting regimes into
the model of Fujita and Ramey. The wage setting regimes tested below include a real rigidity
in the form of a wage norm as in Hall (2005a) and Faia (2008), staggered wage setting as
in Gertler and Trigari (2009) as well as an alternative specification of the wage bargain as
in Hall and Milgrom (2008). As a final extension, a re-specification of the hiring cost as in
Pissarides (2009) is implemented. The latter non-wage extension of the canonical DMP model
is included as the evidence of wage rigidities is contested (see e.g. Pissarides, 2009; Rogerson
and Shimer, 2011). By combining these various solutions, this analysis provides a helpful basis
to distinguish the viability of proposed solutions to improve the empirical accuracy of the DMP
model. The performance of the enumerated models will be evaluated against US data on the
comovement of employment and output.
To set the stage, the following section provides the stylized facts for the comovement of employment and output in the United States. The rest of this chapter proceeds with an exposition
of the canonical DMP model in section 3 and the review of its unsatisfactory amplification as
well as propagation properties thereafter. Addressing the lack of amplification first, the selected
solutions along the wage setting regime and the alternative hiring costs are described in section
4. The evaluation of these extensions reveals their failure to increase the internal propagation
of the DMP model. The extension of the DMP with vacancy creation costs is modeled in section
5 and results are presented in section 5. Section 6 directly proceeds to the empirical evaluation
of the combined models. Section 7 concludes.
2
Stylized facts about the comovement of employment and output in
the United States
To inform the analysis, this section briefly describes the comovement between real GDP and
employment for the United States. The evidence is based on the entire post-World War II
sample i.e. 1948 to 2012. This sample duration contrasts with the analysis of the first chapter
that described the changing dynamics within this period. The main reason for the comparison
with the full sample lies in the relation of this chapter with the existing literature. Below, I test a
variety of different models that have been calibrated to the entire post-war data set, rather than
a subset. In order to use established model parameters, I follow these authors and conduct a
model evaluation for the entire period.
As this chapter evaluates a series of macroeconomic models empirically, it follows the business
cycle literature and uses only the cyclical components of HP-filtered data for the analysis.19
19
See appendix A on page 85 for evidence from spectral analysis showing that substantial variation occurs within
47
The first stylized facts on the comovement are the auto- and unconditional crosscorrelations of
employment and output. Finally, the impulse response functions from a vector autoregression
(VAR) specified as in the previous chapter are estimated.
The autocorrelation of both series is remarkably similar (see upper panels in figure II.1 on the
next page). Both real GDP and employment show a significant and positive autocorrelation
up to the third lag.20 Of the two, the autocorrelation of employment is more pronounced. It is
significantly larger than that of output for the first two lags. The autocorrelation then re-emerges
into significance for lags seven to 12. However, for these more distant periods it is of smaller
magnitude and barely significant at the 95 percent level.
Turning to the comovement, the evolution of the two time series is close to symmetric in the
short term (see lower panel in figure II.1). The fluctuations of employment around its mean
closely resemble those of real GDP in the present as well as the two subsequent periods. The
correlation of the two time series ranges between .8 and .9 in this time window. In total, the
positive correlation between output and employment remains statistically significant until the
fifth quarter. In accordance with the negative autocorrelation observed in both series for more
distant quarters, their comovement is also characterized by a significant negative correlation
at a lead of employment to real GDP of 4 quarters or more. As the comovement is strongest
around contemporaneity, the evaluation of the macroeconomic models will focus on the window
from the second lead to the sixth lag of employment.
the filter frequencies.
The data on real GDP is the seasonally adjusted, quarterly figures for real non-farm business GDP as reported
by the Bureau of Economic Analysis (table 1.3.6. «Real Gross Value Added by Sector, Chained Dollars»). The data
on employment is generated from seasonally adjusted, monthly figures for total private employment as reported by
the Bureau of Labor Statistics in its Current Employment Statistics (BLS ID CES0500000001). Monthly data have
been aggregated to quarters through a simple average.
All data are HP-filtered with a punishment term λHP = 1600.
The data are available from 1948 to 2012, which yields a total of 256 observations per series.
20
Statistical significance has been computed using Huber-White standard errors.
48
Fig. II.1: Auto- and crosscorrelation of employment and output
(a) Autocorrelation of employment
(b) Autocorrelation of output
(c) Crosscorrelation of employment and output
Note: Dotted lines depict the confidence bounds at the 95 percent level using Huber-White standard errors.
Besides the crosscorrelation of employment and output, this chapter also uses impulse response functions to evaluate the realism of the tested models. These impulse response functions are based on a third-order, bi-variate Vector Autoregression including the cyclical components of jobs and output data.21
The individual analysis of employment and output has implications for the lessons that can be
drawn from the impulse responses generated from the described VAR. The focus of Shimer
(2005) and Fujita and Ramey (2007) is the accuracy of the DMP model within the domain of
productivity-induced changes of the US economy. They stress that the canonical DMP model
is inaccurate even if one focuses exclusively on the dynamics explained by movements in productivity. To make their argument, these studies need to dissect the stylized facts observed in
US data for the component that is attributable to changes in productivity.22
21
For the data description see footnote 19. The VAR is estimated using three lags for each variable. Other
lag lengths do not affect the qualitative results. Consistent with the model, the initial impulse is assumed to stem
from a common shock on real GDP and job growth. The complete ordering is GDP, employment; thus allowing
for a shock that affects jobs exclusively. The depicted impulse responses are orthogonalized using a Cholesky
decomposition.
22
In his contribution, Shimer (2005) does not take this limitation into account. In particular, he mistakenly com-
49
However, an individual analysis of employment and output makes it impossible to identify a
productivity shock econometrically as productivity is commonly defined as the ratio of these
two variables. The conclusions drawn below thus concern the overall empirical accuracy of the
evaluated models with respect to US data. The results gauge to what extent the observed comovement in US output and employment can be explained by this simple vintage of productivitydriven DMP models.
Figure II.2 depicts the responses of GDP and employment to a shock on the GDP equation
(referred to as the «common shock» above). As is expected from the strong autocorrelation,
the initial impulse remains significant within GDP for up to five quarters. Employment shows a
different reaction pattern. The initial shock unfolds its full impact only with a lag of two quarters. Overall the boost for employment from a positive common shock remains significant for
the subsequent seven quarters and is hump-shaped. To discern the relative magnitudes of
the responses, figure II.2 also includes the impulse responses relevant for the comovement of
employment and output normalized by the size of the initial shock. As is evident from the lowerright hand panel, the estimated peak of the employment response is approximately 60 percent
the size of the initial response of output.
pares the relative volatility of the uv -ratio as observed in the data with that generated by the model, and then draws
conclusions with respect to the empirical accuracy of the model within its domain. However, the domain of the
DMP model is the share of the observed volatility that can be attributed to a productivity shock. In this case, the
volatility of the uv -ratio has to be adjusted using the correlation between the uv -ratio and productivity. As will be
discussed below, the unemployment volatility puzzle survives this shortcoming in quality. Among the authors who
have pointed this out are e.g. Mortensen and Nagypál (2007) as well as Pissarides (2009).
3 Amplification and propagation in the canonical DMP model
50
Fig. II.2: Impulse Response Functions
(a) Impact of GDP impulse on GDP, absolute
(b) Impact of GDP impulse on employment, absolute
(c) Impact of GDP impulse on GDP, normalized
(d) Impact of GDP impulse on employment, normalized
Dotted lines depict the confidence bounds at the 95 percent level.
Figures (c) and (d) are normalized by the initial response of real GDP growth.
Going into the model analysis, the stylized facts developed in this section are fourfold. First,
both employment and output are autocorrelated for a duration of up to one year with employment being the slightly more persistent of the two series. Second, the crosscorrelation of the
two variables is positive and significant for a total of eight quarters with a peak between contemporaneous output and employment in the subsequent period. Third, impulse responses
show that a common shock remains in the system for about five quarters and shows significant
internal propagation within both employment and output. Finally, the common shock moves
employment in the same direction as output, but with a peak that lags that of output by two
quarters and is about 60 percent its magnitude.
3
Amplification and propagation in the canonical DMP model
This section derives the canonical version of the DMP model as outlined in Pissarides (2000)
and explains the unemployment volatility puzzle in more detail. The lack of amplification and
51
propagation is then shown in a first model performance analysis at the end of this section.
Model exposition
The core novelty of the search and matching model of the labor market is the introduction of a
production function for the labor market. Rather than physical output, this production function
describes the combination of vacancies vt and unemployed ut into successful job matches mt .
For the canonical model, the matching function is assumed to be Cobb-Douglas. The CobbDouglas weight of the vacancies is given by η.
m (ut , vt ) = χu1−η
vtη
t
f (θt )
m (ut , vt )
=
q (θt ) =
vt
θt
m (ut , vt )
f (θt ) =
= q (θt ) θt
ut
In the DMP model, the matching function is combined with its components for a selection of
useful metrics. The key combination is the vacancy-unemployment ratio, a measure of labor
market tightness, is denoted θt = uvtt . In further combinations, the variable q (θt ) denotes the
probability of filling a vacancy from the perspective of the firm, and f (θt ) gives the probability of
finding a job from the perspective of an unemployed, respectively.
In its basic setup, the DMP model only distinguishes between employed and unemployed
agents. There is no inactive labor force. The evolution of the employment share is determined
by the work force that did not fall prey to the constant separation rate s plus the newly hired
workers mt−1 . Hired workers thus start productive work only in the subsequent period.
nt = 1 − u t
nt = (1 − s) nt−1 + mt−1
Using these definitions one can write the law of motion for unemployment:
ut = [1 − f (θt−1 )] ut−1 + snt−1
The matching function is a central innovation of the DMP model. The insight that matches have
to be «produced» from searching workers and enterprises and the entailing probabilistic rather
52
than automatic matching of the two gives rise to a surplus from a match. This surplus then
serves as the object of the wage bargain between the two parties.
Using Bellman equations, Jt denotes the value of a filled position for the firm and Vt that of a
vacant position.
Jt
= pt − wt + βEt {(1 − s) Jt+1 + sVt+1 }
Vt
= −c + βEt {q (θt ) Jt+1 + (1 − q (θt )) Vt+1 }
(13)
The contemporaneous value of a filled position is the surplus of the output value over the wage
cost pt − wt . Advertising vacancies costs the firm c each period. The discounted future values
are the sum of the values over all potential future states weighted by their probability. The
probability that a filled job remains occupied is given by the constant separation rate s. The
probability of finding a suitable candidate is given by q (θt ).
The analogous value functions for the worker are those of having a job Wt or being unemployed
Ut . Here, the contemporaneous payoff is either the wage wt or the non-work benefit b. The
potential future states and the assigned probabilities are as described for the firm.
Wt
= wt + βEt {(1 − s) Wt+1 + sUt+1 }
Ut
= b + βEt {q (θt ) θt Wt+1 + [1 − q (θt ) θt ] Ut+1 }
A match between a searching firm and a searching worker thus creates a surplus St = Wt −
Ut + Jt − Vt . This surplus from a match over continued search is what firms and workers can
bargain over in wage negotiations.
In the canonical DMP model, the resulting wage wt is modeled as the Nash bargaining solution.
It is thus a weighted sum over the minimum wage a worker can accept wtw and the maximum
wage a firm can afford wtf . In the canonical DMP model, the worker’s threat point is simply the
non-work benefit, while for the firm it is the sum over output and vacancy posting costs. The
weight assigned to these outcomes reflects the bargaining power of the worker and is denoted
by α.
wt = max (Jt − Vt )1−α (Wt − Ut )α
wt
wt = αwtf + (1 − α) wtw
wt = α (pt + cv θt ) + (1 − α) b
(14)
The last central equation of the DMP model sketched out here is the «job creation condition».
Free entry of profit-maximizing firms ensures that the value of an open position Vt is equal to
53
its creation cost. In the canonical model, vacancy creation itself is costless. One can thus use
Vt = 0 to rewrite equation 13. Substituting the above Bellman equations yields the canonical
specification of the job creation condition.
c
= βEt [Jt+1 ]
q (θt )
c
c
= βEt pt+1 − wt+1 + (1 − s)
q (θt )
q (θt+1 )
(15)
Productivity follows the common AR(1) process log (pt ) = ρlog (pt−1 ) + t .
The «unemployment volatility puzzle»
In two separate pieces, Shimer (2005) and Hall (2005b) revealed that the canonical DMP
model is unable to produce realistic relative volatilities for key variables. By simulating the
canonical version, Shimer showed that the search and matching model implies that the vacancyunemployment ratio ( uv -ratio) has approximately the same volatility as average labor productivity.
This is in stark contrast to the twenty-fold relative volatility of the uv -ratio that Shimer finds in US
data.
The magnitude of this gap has been convincingly questioned by Mortensen and Nagypál (2007).
Shimer compares aggregate US data to the moments found in a model driven solely by a productivity shock. Shimer’s large estimate thus relies on the assumption that all observed volatility
in the American uv -ratio stems from changes in productivity. If one relaxes this assumption, the
estimate for the relative volatility of the uv -ratio in the US reduces to 7.56 compared to 1.75 found
in the model (see also Hall (2005b) and Pissarides (2009)). Although the gap between model
and reality is thus not as wide as suggested by Shimer, the DMP model volatilities of vacancies
and unemployment are nonetheless unsatisfactory.
For Shimer, the wage dynamics are the central culprit for the lack of uv -volatility. As he shows
for shocks to productivity and for shocks to separation rates, little of the initial impulse feeds
through to the employment decision of the firm. Flexible wages absorb all the pressure. In
the canonical characterization, wage adjustments almost completely offset productivity shocks
and also mitigate the negative impact of of an extension along varying separation rates. To
see this, recall that the first component in the canonical wage equation (equation 14 above)
includes pt as well as θt and is highly pro-cyclical. Wages thus absorb a substantial part of the
changes in productivity. With this buffer in place, unemployment and vacancies turn out to be
relatively stable in the DMP model, while wages tend to be too volatile according to Shimer’s
interpretation. In the analysis below, we will refer to the unemployment volatility puzzle as the
«amplification problem» as the aim of this literature is to amplify the volatility of unemployment
and vacancies.
54
Model calibration, simulation and results
This section concludes with a first analysis of amplification and propagation within the DMP
model. Besides the comovement statistics, the standard deviations of vacancies and unemployment relative to that of productivity are calculated. The model will serve as a benchmark for
the proposed solutions analyzed below. However, I calibrate this baseline models relying on the
parameter values of Pissarides (2009) rather than those of Shimer (2005).23 The calibration of
Pissarides (2009) is more representative of the literature than Shimer’s as it builds on the data
and insights from various papers mentioned below.
As Pissarides elaborates in his description, this calibration is based on the data of Shimer
(2005) for the monthly separation rate s = .036, mean labor market tightness θ = .72, the
unemployment rate u = 0.057 and the monthly job-finding probability f (θ) = .594. Based on
the empirical values of labor market tightness and the job-finding probability f (θ) = χθ1−η ,
Pissarides derives the scale parameter of the matching function χ = .7.
The appeal in using Pissarides rather than Shimer’s calibration lies in the increased generality of
the values used for the matching function elasticities, the labor bargaining weight and the nonwork benefit. Following work by Pissarides and Petrongolo (2001) as well as Hosios (1990),
many authors assume the matching function elasticities of η = 1 − η = .5 and to equalize this
to the bargaining weight of labor α = 1 − η = .5. In his piece, Shimer acknowledges that his
specification of α = 1−η = .72 is an upper bound to the estimates of Pissarides and Petrongolo,
but cites the inexisting welfare implications of this choice as reason to pursue with them.
The final deviation of Pissarides from Shimer’s calibration concerns the non-work benefit b.
Here, Shimer uses a value of b = .4 which is equal to about two fifths of the steady state
wage. Again, Shimer acknowledges this value to be at the boundary of the common range, but
proposes a narrow interpretation of these benefits as unemployment insurance payments to rationalize the value. As later shown by Hagedorn and Manovskii (2008a) and elaborated further
by Costain and Reiter (2008), the volatility of unemployment is very sensitive to the choice of the
non-work benefit value. In their recalibration of the model, Hagedorn and Manovskii revealed
that using a non-work benefit value close to the steady state wage increases the volatility of
the v-u-ratio to its value in US data. Pissarides here sides with Hall and Milgrom (2008) and
assumes a positive time value of unemployment spells. In his calibration, Pissarides uses their
value of non-work benefits b = .71 which is considerably higher than that of Shimer albeit it
a little lower than the benchmark estimate of b = .745 calculated by Costain and Reiter. This
chapter will also use a b = .71 as it is the middle ground between Costain and Reiter’s estimate
and the value used by Fujita and Ramey (b = .65).
The final parameter to be set in the baseline model is the periodic hiring cost c. Using the above
values in the equilibrium conditions yields a c = .356, which is again higher than the value used
23
For an overview of all calibrations used in this chapter, see appendix B on page 87.
55
by Shimer (2005). However, if one takes into account the different steady state hiring probabilities q (θ) implied by the two calibration strategies, the expected total recruitment costs c/q (θ)
are almost identical (43% or 47% of monthly output for Pissarides or Shimer respectively).
To allow for the comparison of the model dynamics, each model in this chapter is subject to the
same productivity shock process. This process is calibrated to match the moments reported
by Shimer (2005) and uses a persistence parameter of ρp = .97, in line with the estimates for
the US economy provided by e.g. Fujita and Ramey (2007); Faia (2008) or Gertler and Trigari
(2009).
Simulation method
For the evaluation, each model is simulated for a productivity shock process and analyzed applying the identical methods as those used for the US data above. Each simulation is repeated
10’000 times yielding a total of 10’000 different time series. To make the evaluation of different
models as comparable as possible, the same 10’000 sequences of productivity shocks are used
in all simulations.
The simulation has a duration of 1’256 quarters. The first 1’000 observations of this simulated
time series are discarded in order to start the evaluation outside the model’s steady state. The
remaining time series of 256 observations is equivalent to the sample duration used in the
VAR estimation above. Before the statistical analysis, the generated time series are filtered
à la Hodrick and Prescott (1981) with a smoothing parameter of λHP = 10 600. The cyclical
components of each time series are then analyzed for the implied auto- and crosscorrelations.
Furthermore, impulse response functions are generated from a VAR specified as the one used
in the empirical section.
A model’s performance relative to US data is then evaluated using the mean of each comovement measure across all 10’000 time series. To gauge the proximity of the simulated series
to the data, a simple t-test is performed using the standard errors of each estimate. These
standard errors are calculated from the variation found across the 10’000 time series. The null
hypothesis is that the empirical and theoretical comovement measure are the same.
For the purpose of this chapter, the t-statistics are calculated as a means to compare the performance of the various models against each other. Given the simplicity of the DMP model with
productivity as the only shock source, the observation that it does not fit US data perfectly is
not surprising. The aim for the tested models rather is to generate patterns that are in line with
the empirical moments. To compare the accuracy across different models that generate similar
patterns, the t-statistics provide a useful metric.
56
Simulation results for the canonical DMP model
The simulation of the canonical DMP model reproduces the amplification problem identified by
Shimer (see table II.1d). The relative volatilities of unemployment, vacancies and labor market
tightness are only around 20 percent of the magnitude observed in US data.24
Turning to the first two stylized facts enumerated above, the canonical model produces broadly
similar autocorrelations but fails to generate the wide crosscorrelation observed in the data
(see figure II.3). The autocorrelation for output while slightly low at the early lags produces a
better fit than that found for employment. The autocorrelation found for the model’s employment
series remains significantly below the corresponding US observation for the first three quarters.
The slightly subdued autocorrelation in both variables brings about less encouraging results
for the intertemporal comovement. The model’s crosscorrelation does not show the width of
the peak observed above. In US data, the peak ranges from contemporaneity to the second
output-employment lead with a peak at the first lead. The canonical DMP model on the other
hand produces a peak at contemporaneity which quickly levels off after the second outputemployment lead.
24
The US observations given in the table refer to the data set described above. Productivity is defined as the
ratio of the output over the employment series used above.
The stated relative standard deviations may be interpreted as elasticities of the variable in the numerator with
respect to productivity. Following Pissarides (2009), the stated statistics are the coefficient from a regression of
the numerator variable on productivity, alas the relative standard deviation multiplied by the correlation of the two
series.
57
Fig. II.3: Auto- and crosscorrelation of employment and output in the canonical DMP model
An analysis of the model’s impulse responses to a common shock reveals a meager response
of employment as a potential culprit behind this shortfall (see figure II.4). The response of
employment is falls considerably short when compared to US data. While it is significantly
different from zero up until four quarters after the shock to output, the magnitude of this reaction
is greatly at odds with the data. At its peak, the reaction of employment is only 10 percent of the
size of the initial output response compared to a relative magnitude of 60 percent found in US
data. Furthermore, the response of employment peaks at the first lag and returns to the steady
state quickly thereafter which is not the broad hump shape found in the data. By contrast, the
response of output is barely distinguishable from the empirical observation for the first two years
after the impulse.
The discrepancy between the observed and the simulated response of employment to a common shock can stem from two sources. First, as will be further discussed in the model extensions below, the structure of the model plays a role. Adding e.g. hiring costs increases the
volatility assigned to the common shock by the estimated VAR. Thus, further extensions may
also alleviate the lacking response of employment to the common shock. Second, the discrepancy can also be due to the shock source in the DMP model. According to this interpretation,
58
the productivity shock alone cannot account for the observed employment and output dynamics.
Additional drivers for the DMP model may thus be called for.
Fig. II.4: Impulse Response Functions
(a) Impact of common shock on GDP
(b) Impact of common shock on employment, including US data
Dotted lines depict the confidence bounds at the 95 percent level.
In sum, the performance of the canonical DMP model is mixed. The individual persistence of
output as captured by the autocorrelation and the impulse response albeit a bit too low is largely
in line with the data. The comovement of the two variables is unsatisfactory in two respects.
The crosscorrelation between output and employment peaks too early and dies off too fast.
The impulse responses suggests that the employment dynamics may lie behind this shortfall,
although it remains unclear whether the shock process or the model structure is accountable
for this discrepancy.
59
Tab. II.1: Volatilities and correlations in the canonical DMP model
(b) Variable responses to the
common shock in the
canonical DMP model
(a) Auto- and crosscorrelations
autocorrelation
lag
0
1
2
3
4
5
6
7
8
y
n
-
-
Lag
crosscorrelation
leading n
leading y
0
14.57***
(1)
1
2.13**
3.82***
1.68**
1.53*
(0.98)
(1)
(0.95)
(0.94)
1.81**
3.08***
1.59*
4.21***
(0.97)
(1)
(0.94)
(1)
0.93
2.09**
2.18***
4.27***
(0.82)
(0.98)
(0.99)
(1)
0.15
1.04
2.71***
3.68***
(0.56)
(0.85)
(1)
(1)
0.49
0.14
2.93***
2.99***
(0.69)
(0.56)
(1)
(1)
0.68
0.48
2.70***
2.40***
(0.75)
(0.69)
(1)
(0.99)
0.71
0.91
2.18***
1.74**
(0.76)
(0.82)
(0.99)
(0.96)
0.42
1.07
1.43*
1.02
(0.66)
(0.86)
(0.92)
(0.85)
2
3
4
5
6
7
8
output
employment
0.01
(0.5)
0.15
(0.88)
1.62**
(0.95)
1.63*
(0.95)
1.52*
(0.94)
1.18
(0.88)
0.15
(0.56)
1.30*
(0.9)
2.94***
(1)
105.51***
(1)
68.21***
(1)
59.93***
(1)
54.18***
(1)
46.57***
(1)
41.03***
(1)
31.89***
(1)
18.40***
(1)
1.67***
(0.95)
(c) Variable volatilities
DMP σi
DMP
US
σi
σp
σi
σp
u
v
v
u
p
0.026
0.034
0.057
0.016
1.60
2.08
3.49
1
2.35
4.29
6.65
1
Note in tables (a) and (b): The first row yields the number of standard deviations between the model’s and the observed value using the
standard deviation of the model output. The second row includes the associated p-value.
4 Extensions to improve amplification
4
60
Extensions to improve amplification
Following Shimer’s diagnosis that wages are too flexible, re-modeling the wage dynamics became an early source of solutions to the «unemployment volatility puzzle». In the original DMP
model, wages are the outcome of a Nash bargain over the complete bargaining set. The agreed
wage is thus a weighted average of the threat points for the firm and the worker. In case the
two parties cannot agree on a wage, both the firm and worker have to return to the labor market
and search anew. Below, a variety of proposed rigidities to the canonical wage setting mechanism are described. These include adaptive and smoothed wage setting as well as alternative
disagreement payoffs.25
More recently, the solution of the «unemployment volatility puzzle» through tamed wage fluctuations has received strong criticism. For instance, the friction parameters needed to generate
smoothed or adaptive wages are difficult to identify empirically. The authors can thus choose
within a wide range of possible rigidity parameters, which allows for considerable discretion
with respect to the model dynamics. In a more fundamental critique to these solution attempts,
Pissarides (2009) presents evidence for the strong procyclicality of wages. In his interpretation,
the wages relevant for the DMP model are those of the newly hired. The microeconometric
evidence he presents suggests that these wages evolve in tandem with the business cycle. A
more recent study by Haefke, Sonntag, and Rens (2012) supports this finding. Solutions to the
«unemployment volatility puzzle» thus need to preserve the wage dynamics of the original DMP
model.
While the critique of Pissarides is powerful, it does not fully invalidate the use of models with
wage rigidities in this literature. In a response to this criticism, Gertler and Trigari question that
the evidence on the cyclicality of new wages is sufficiently sharp to support Pissarides’ claim. In
their view, the data rarely match firms to workers making it impossible to compare new workers’
wages to those of existing workers. Furthermore, the cyclicality of job quality is not controlled
for. It thus remains possible that the observed cyclicality of the wages of new hires is due to
different job quality composition available over the business cycle. A wage rigidity tying the pay
of new hires to that of the existing work force may still exist. The analysis below thus remains
centered on alternative wage regimes. However acknowledging the mentioned criticism, the
final model evaluated below does not affect wage fluctuations but rather uses alternative hiring
costs as proposed by Pissarides (2009).
25
The evaluated models do not include alternative wage setting via flexible bargaining weights. As Brügemann
and Moscarini (2010) as well as Costain and Reiter (2008) show, only an inverse relationship between the bargaining power of the worker and aggregate productivity sufficiently improves the realism of the DMP model. In
such a specification, the contracted wage becomes rigid over the business cycle as the counter-cyclical weight
of the workers mitigates wage pressures. Neither of the two cited articles offers a convincing explanation why
a worker’s bargaining power should increase in recessions. As it seems counter-intuitive that workers are in a
stronger bargaining position during a downturn, this line of research is not further pursued here.
61
Alternative wage regimes
Smoothed and adaptive wages
Hall (2005b) provides the useful distinction «smoothed» and «adaptive» wages. In a smoothed
wage regime, wages are set periodically as a weighted average of the current Nash-bargaining
wage and a time-invariant wage norm. Faia (2008) is one study using this setup and the rigidity parameter used in this evaluation follows her calibration strategy. Shimer (2004) and Hall
(2005b) demonstrate the increased amplification of DMP models using a fixed wage that does
not change over time. This extreme form of a wage norm is not considered here as it its only
useful to gauge the amplification potential of wage norms, but does not constitute an empirically
plausible re-specification of the DMP model.
The adaptive wage regime considered by Hall corresponds to the nominal wage rigidity of
Gertler and Trigari (2009). In this setup, wages are pinned down as a weighted average of
the current Nash-bargaining wage and the wage contracted in the previous period. Incorporating these wage regimes into the canonical wage equation yields equation 16. The weight of
the wage norm w̄ is given by (1 − γ), the wage-negotiation frequency by π and wtc denotes the
outcome of the original Nash bargaining solution without rigidities.
wt = π [γwtc + (1 − γ) w̄] + (1 − π) wt−1
(16)
In the simulations below, adaptive and smoothed wages will be simulated in turn.
Changing the disagreement payoff
The final re-specification category related to wage-setting is the specification of the disagreement outcome. In the original DMP model, the agents return to the labor market and start anew.
Hall and Milgrom (2008) remove this assumption and replace it with a continued bargain. As
the return to the labor market bears new search and advertising costs as well as a new waiting
period, both parties to the bargain have an incentive prolong the negotiation. In the view of Hall
and Milgrom, continued negotiation is thus the more likely consequence of disagreement in the
first period.
Instead of renewed search, Hall and Milgrom assume the delay is equal to cost ι for the firm
and to the non-market benefit b for the worker. Substituting the disagreement outcome in this
fashion alters the boundaries of the bargaining set. The previous outside option, renewed
search, is replaced by a time-invariant disagreement payoff. As the former payoff is pro-cyclical,
its substitution makes wages less sensitive to changes in aggregate productivity. One can
calculate the new wage wtHM using the surpluses from immediate agreement for both firm (F)
and worker (W).
62
StF = pt − wtHM + β (1 − s) Et {Jt+1 } − [−ι + β (1 − s) Et {Jt+1 }]
= pt − wtHM + ι
StW = wtHM + β (1 − s) Et {Wt+1 } − [b + β (1 − s) Et {Wt+1 }]
= wtHM − b
Using these surpluses in the Nash bargaining process as above, one receives the following
wage:
α pt − wtHM + ι = (1 − α) wtHM − b
wtHM = (1 − α) b + α (pt + ι)
(17)
Note that this wage equation differs from the original one only in the second component on
the right hand side. The current degree of labor market tightness θt is no longer part of the
wage bargain. With labor market tightness being pro-cyclical, its removal implies a less shockabsorbing wage than that of the canonical DMP model.
Alternative hiring costs
In an effort to maintain the wage flexibility of the canonical model, Pissarides (2009) proposes a
re-specification of the labor turnover cost. In the canonical from of the DMP, total labor turnover
costs are modeled as a periodic cost for open vacancies. The cost of a vacancy creation is thus
proportional to the likelihood of contracting a new worker. In the canonical model, this likelihood
and aggregate productivity are inversely related. If aggregate productivity increases, the chance
of hiring a worker falls and the expected duration of an advertised position increases. The
proportionality of vacancy costs to the duration of the opening thus dampens vacancy creation.
To alleviate this nexus, Pissarides (2009) disentangles the overall matching cost into a smaller
periodic component and a larger one-time cost that materializes once a new worker is hired. As
he shows, this rearrangement greatly increases the relevant volatilities in the DMP model.
The introduction of a fixed hiring cost H alters the value of an open vacancy for the firm, which
then feeds through into both the wage equation and the job creation condition. Note that in
contrast to the different wage setting regimes discussed above, the direct effect of this decomposition on the volatility of the wages is unclear as also the fixed hiring cost H is weighted by
the the pro-cyclical job-finding probability f (θt ).
63
Vt = −c + βEt {q (θt ) (Jt+1 − H) + (1 − q (θt )) Vt+1 }
wt = (1 − α) b + α [cθt + pt + f (θt ) βH]
c
c
+ H = βEt pt+1 − wt+1 + (1 − s)
+ βH
q (θt )
q (θt+1 )
(18)
(19)
The simulation strategy for the extended DMP models is identical to the one explained above.
The calibration of the wage extensions analyzed in this chapter does not affect the standard
parameters of the DMP model laid out above. Thus, the standard parameters used in this
section are identical to the ones described above. Following Gertler and Trigari (2009), I assume
that wages are renegotiated every nine months on average in the adaptive wage extension of
the model. For the disagreement payoff extension, I use the estimates of Hall and Milgrom
(2008) for the firm’s disagreement cost ι and the probability that a negotiation terminates without
a final agreement. The calibration is more difficult for the smoothed wage regime. Faia (2008)
uses a value for this rigidity of γ = .6 which she motivates from estimates by Smets and Wouters
(2003). Following Faia’s lead, I use data from Smets and Wouters (2007) which is estimated on
US rather than euro zone data and use γ = .7, a value that has also been reported as plausible
for US data by Blanchard and Galí (2010).
The calibration of the parameters used in the cost extension is not entirely independent from
the parameters chosen for the standard model. As mentioned above, the hiring cost extension
of Pissarides (2009) allows for a decomposition of the periodic hiring cost c into a itself and a
fixed hiring cost H. Pissarides himself provides the values of H = .3 and c = .11 as a preferred
decomposition of the total hiring cost.
The proposed extensions outperform the canonical model in various respects. By design, the
relative volatilities are far more realistic than those found in the benchmark simulation above
(see table II.2). The hiring cost extension as proposed by Pissarides (2009) provides the best
fit overall with all moments within relatively few standard deviations from those found in US
data. The volatility of unemployment slightly overshoots, while those of vacancies and labor
market tightness are too small. Looking at individual variable performances, the smoothed
wage and adaptive wage extensions do well for the volatilities of both vacancies and labor
market tightness. The hiring cost model provides the most realistic unemployment volatility for
the tested models.
64
Tab. II.2: Relative volatilities
σi
σp
canonical
smoothed
adaptive
disagreement
hiring cost
US
σi
σp
mean
u
t-statistic
v
v
u
u
v
v
u
1.6
2.08
3.49
78.45***
62.80***
6423.64***
(0.01)
(0.035)
(0)
(1)
(1)
(1)
2.86
3.76
6.26
4.03***
2.48***
1.28*
(0.13)
(0.21)
(0.31)
(1)
(0.99)
(0.9)
3.11
4.71
7.02
5.18***
1.34**
1.01
(0.15)
(0.31)
(0.36)
(1)
(0.91)
(0.84)
1.85
2.41
4.04
9.89***
21.35***
22.17***
(0.05)
(0.09)
(0.12)
(1)
(1)
(1)
2.63
3.45
5.74
3.56***
5.83***
4.76***
(0.08)
(0.14)
(0.19)
(1)
(1)
(1)
2.35
4.29
6.65
Note:
In the «mean» column, the standard errors are stated in brackets in every other row. In the t-statistic column, every other row contains the
p-value in brackets.
With one exception, the visual examination of the simulated auto- and crosscorrelations does
not reveal substantial differences between the canonical model and the amplification extensions
(see figure II.5). The tested models largely reveal the same shortcomings identified above,
namely too little persistence in employment and too narrow a peak in the crosscorrelation of
output with employment. The exception from this pattern is the adaptive wage extension. With
the introduction of staggered wage setting, the persistence of employment decreases substantially and the autocorrelation turns negative well ahead of the data. The lack of employment
persistence is also visible in the crosscorrelation of output and employment. For the adaptive
wage extension, the peak of the crosscorrelation is in the present rather than at the first lag,
and the fall from this peak to zero correlation is completed already after the second rather than
the sixth quarter.
65
Fig. II.5: Auto- and crosscorrelation in the amplification extensions
With respect to the impulse responses, the hiring cost extension of Pissarides again slightly
outperforms the rest (see figure II.6). With the exception of overshooting slightly at the first
lag of the impulse response of output, Pissarides’ hiring cost model as well as the smoothed
wage extension match the observed patterns better than the other extensions considered here.
However, while the impulse response of employment is better than that of the canonical model,
the Pissarides and the smoothed wage model are still more than 20 standard deviations away
from the observed pattern. While the hump-shaped response of employment is reproduced to a
greater extent, the magnitude of the peak response of employment remains around 20 percent
of the initial shock to output compared to the 60 percent found in the data.
66
Fig. II.6: Impulse response functions in the amplification extensions
(a) Impact of common shock on output
(b) Impact of common shock on employment
Confidence bounds omitted for better legibility.
Tab. II.3: Crosscorrelations in the amplification extensions
t-statistics
model
canonical
smoothed
adaptive
disagreement
hiring cost
Output-Employment Lead
-2
-1
0
1
2
3
4
5
6
1.59*
1.68**
14.57***
1.53*
4.21***
4.27***
3.68***
2.99***
2.40***
(0.94)
(0.95)
(1)
(0.94)
(1)
(1)
(1)
(1)
(0.99)
1.64**
1.77**
12.76***
0.28
4.34***
4.31***
3.70***
2.99***
2.38***
(0.95)
(0.96)
(1)
(0.61)
(1)
(1)
(1)
(1)
(0.99)
2.09**
1.98***
10.33***
13.44***
12.33***
12.35***
10.92***
8.03***
5.03***
(0.98)
(0.98)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
1.59*
1.66**
14.27***
1.02
4.28***
4.29***
3.69***
2.99***
2.39***
(0.94)
(0.95)
(1)
(0.85)
(1)
(1)
(1)
(1)
(0.99)
1.64**
1.79**
14.44***
0.79
4.27***
4.28***
3.68***
2.98***
2.39***
(0.95)
(0.96)
(1)
(0.78)
(1)
(1)
(1)
(1)
(0.99)
Note:
The first row yields the number of standard deviations between the model’s and the observed value using the standard deviation of the model
output. The second row includes the associated p-value.
67
Tab. II.4: Autocorrelations in the amplification extensions
(a) Autocorrelation of output: t-statistics
lag
1
2
3
4
5
6
7
8
canonical
smoothed
adaptive
disagreement
hiring cost
3.82***
3.55***
7.48***
3.72***
3.62***
(1)
(1)
(1)
(1)
(1)
3.08***
2.91***
7.45***
3.02***
2.95***
(1)
(1)
(1)
(1)
(1)
2.09**
2.02***
6.32***
2.07**
2.03**
(0.98)
(0.98)
(1)
(0.98)
(0.98)
1.04
1.03
4.09***
1.03
1.02
(0.85)
(0.85)
(1)
(0.85)
(0.85)
0.14
0.17
1.57*
0.15
0.16
(0.56)
(0.57)
(0.94)
(0.56)
(0.56)
0.48
0.43
0.39
0.46
0.45
(0.69)
(0.67)
(0.65)
(0.68)
(0.67)
0.91
0.85
1.69
0.88
0.86
(0.82)
(0.8)
(0.95)
(0.81)
(0.81)
1.07
1.02
2.42***
1.06
1.04
(0.86)
(0.85)
(0.99)
(0.85)
(0.85)
(b) Autocorrelation of employment: t-statistics
lag
1
2
3
4
5
6
7
8
canonical
smoothed
adaptive
disagreement
hiring cost
2.13**
1.97**
2.77***
2.10**
1.99**
(0.98)
(0.98)
(1)
(0.98)
(0.98)
1.81**
1.73**
2.52***
1.80**
1.74**
(0.97)
(0.96)
(0.99)
(0.96)
(0.96)
0.93
0.88
1.55*
0.92
0.89
(0.82)
(0.81)
(0.94)
(0.82)
(0.81)
0.15
0.13
0.59
0.15
0.14
(0.56)
(0.55)
(0.72)
(0.56)
(0.55)
0.49
0.49
0.27
0.49
0.49
(0.69)
(0.69)
(0.61)
(0.69)
(0.69)
0.68
0.67
0.65
0.68
0.67
(0.75)
(0.75)
(0.74)
(0.75)
(0.75)
0.71
0.68
0.83
0.71
0.69
(0.76)
(0.75)
(0.8)
(0.76)
(0.75)
0.42
0.39
0.63
0.41
0.39
(0.66)
(0.65)
(0.74)
(0.66)
(0.65)
Note: The first row yields the number of standard deviations between the model’s and the observed value using the standard deviation of the
model output. The second row includes the associated p-value.
68
Tab. II.5: Variable responses to the common shock in the amplification extensions
(a) t-statistics for the output response
Lag
0
1
2
3
4
5
6
7
8
canonical
smoothed
adaptive
disagreement
hiring cost
0.01
1.95**
2.55***
1.14
1.70**
(0.5)
(0.97)
(0.99)
(0.87)
(0.95)
0.15
0.91
1.18
0.23
0.77
(0.88)
(0.36)
(0.24)
(0.82)
(0.44)
1.62**
0.95
1.47*
1.46*
1.06
(0.95)
(0.83)
(0.93)
(0.93)
(0.86)
1.63**
1.23
2.33***
1.73**
1.38*
(0.95)
(0.89)
(0.99)
(0.96)
(0.92)
1.52*
1.45*
1.56*
1.76**
1.54*
(0.94)
(0.93)
(0.94)
(0.96)
(0.94)
1.18
1.01
0.97
1.18
1.06
(0.88)
(0.84)
(0.83)
(0.88)
(0.86)
0.15
0.06
0.42
0.04
0.05
(0.56)
(0.52)
(0.66)
(0.52)
(0.52)
1.30*
1.55*
0.31
1.66**
1.57*
(0.9)
(0.94)
(0.62)
(0.95)
(0.94)
2.94***
3.35***
1.26*
3.56***
3.37***
(1)
(1)
(0.9)
(1)
(1)
(b) t-statistics for the employment response
Lag
0
1
2
3
4
5
6
7
8
canonical
smoothed
adaptive
disagreement
hiring cost
105.51***
21.81***
13.61***
52.73***
29.12***
(1)
(1)
(1)
(1)
(1)
68.21***
17.08***
16.30***
41.52***
22.49***
(1)
(1)
(1)
(1)
(1)
59.93***
21.47***
25.76***
42.27***
25.53***
(1)
(1)
(1)
(1)
(1)
54.18***
21.47***
29.97***
40.33***
24.91***
(1)
(1)
(1)
(1)
(1)
46.57***
21.88***
28.96***
39.25***
25.02***
(1)
(1)
(1)
(1)
(1)
41.03***
21.04***
26.29***
35.80***
23.57***
(1)
(1)
(1)
(1)
(1)
31.89***
16.88***
23.68***
27.58***
18.61***
(1)
(1)
(1)
(1)
(1)
18.40***
9.88***
13.83***
15.71***
10.78***
(1)
(1)
(1)
(1)
(1)
1.67*
0.99
3.14***
1.16
1.00
(0.95)
(0.84)
(1)
(0.88)
(0.84)
Note: The first row yields the number of standard deviations between the model’s and the observed value using the standard deviation of the
model output. The second row includes the associated p-value.
5 Improving propagation
5
69
Improving propagation
The above analysis showed that the comovement of employment and output is dissimilar to that
found in US data. Dismal shock persistence has been pointed out by Cogley and Nason (1995)
and Fujita and Ramey (2007) for RBC and DMP models respectively. The two papers provide
different solutions to the propagation problem, but only one will be considered here.
In their seminal work on RBC models, Cogley and Nason showed that the propagation problem
may be alleviated with the introduction of convex labor adjustment costs. While a modification
of the DMP model along this line has been proposed by Gertler and Trigari (2009), it will not
be evaluated here. As pointed out by Lawrence Christiano and Thijs van Rens, this extension
cannot be considered a search model of the labor market (van Rens, 2008). Replacing the
linear vacancy posting cost c with a quadratic labor adjustment cost removes the «congestion
externality» from the DMP model. With this externality removed from the model dynamics, this
extension can only be considered as a partial equilibrium version of the DMP model.
The mentioned congestion externality arises as follows. In the canonical model, firms do not
take into account the negative effect of posting a vacancy on the aggregate hiring probability. However, additional vacancy posting by a firm entails a congestion externality for all hiring
firms as the aggregate probability for finding a suitable worker decreases with each additional
vacancy on the market. In the specification using quadratic instead of linear labor-force adjustment costs, firms can directly choose their desired hiring rate, rather than the mass of posted
vacancies. The congestion externality ceases to matter. Without this feedback, Christiano and
van Rens categorize Gertler and Trigari’s contribution as a partial equilibrium model of the labor market. It cannot be used to make statements about the amplification problem of the DMP
model. Hence, its evaluation is outside the scope of this chapter.
An extension of the DMP model that maintains the congestion externality is proposed by Fujita and Ramey (2007). In their model, the introduction of a vacancy creation cost turns the
vacancy stock into a state variable and so increases the propagation of productivity shocks
across periods.
Vacancy creation cost
Fujita and Ramey (2007) motivate their model with the observation of unsatisfactory low persistence of productivity shocks in the DMP model compared to US data. To make good on this
discrepancy, they propose to turn vacancies into a state variable, rather than a choice variable
as it is in the canonical model. In the canonical model, firms have to decide on the mass of
70
vacancies they post each period anew. There is thus no explicit vacancy stock in the original
model, although qualitatively, the repeated re-posting of similar masses amounts to an implicit
vacancy stock. The assumption that Fujita and Ramey (2007) utilize to make the vacancy stock
explicit is the indefinite lifetime of a posted vacancy. In their specification, firms cannot decide
to withdraw an existing vacancy. They can only refrain from posting additional new vacancies.
To partially offset the assumption of infinite vacancy posting durations, Fujita and Ramey (2007)
decompose the canonical separation rate into two types of separations, one of which also affects open vacancies. In this decomposition, they distinguish «normal» separations through
firing from «obsolescence» separations through the disappearance of the firm. The normal
separation rate affects only existing jobs. It is assumed that normally separated relationships
lead both parties to return to the labor market. Workers and firms will search for a new match
from the beginning of the following period.
The case is different for separation due to obsolescence. Obsolescence separations occur
through firm exit and may affect both existing jobs and open vacancies. Existing positions
lost due to obsolescence are not (re-)posted as new vacancies by the firm in the next period.
Neither are open vacancies of firms that suffer an obsolescence shock. To account for this
distinction, the generalized aggregate separation rate s here consists of the two components ς o
for disappearing firms and ς n for normal separations.
s = ς o + (1 − ς o ) ς n
The introduction of the separation types has consequences for the value functions as the probability of switching one’s state have changed.
Jt = pt − wt + (1 − ς o ) βEt {(1 − ς n ) Jt+1 + ς n Vt+1 }
(20)
Vt = −c + (1 − ς o ) βEt {q (θt ) Jt+1 + [1 − q (θt )] Vt+1 }
(21)
Wt = wt + βEt {(1 − ς n ) (1 − ς o ) Wt+1 + (ς n + (1 − ς n ) ς o ) Ut+1 }
Ut = b + βEt {(1 − ς o ) f (θt ) Wt+1 + [1 − (1 − ς o ) f (θt )] Ut+1 }
To turn vacancies into a state variable, Fujita and Ramey (2007) introduce a fixed cost of vacancy creation. That is, firms must pay a fixed amount K proportional to the mass of new
vacancies ht that they seek to post in the job market. The vacancy creation cost does not apply
to vacancies posted after normal separations. Existing firms that return to the labor market after
suffering a normal separation shock only need to pay the periodic vacancy cost c. Note that this
specification has consequences for the interpretation of K. As the canonical DMP model consists only of single-worker firms, creating a entirely new vacancy is synonymous with starting
71
a new firm. In this light, K may contain a variety of costs and is not restricted to preparations
for the hiring process. As is discussed further below, this wide interpretation of K may provide
some rationale for the calibration put forth by the authors.
The introduction of a new vacancy variable ht and the decomposed separation rate changes the
laws of motion for unemployment and vacancies. The evolution of unemployment only reflects
the respecified separation rate. The new law of motion for vacancies reflects both innovations
of Fujita and Ramey. For a given period, vacancies consist of newly and deliberately created
advertisements ht plus the quasi-automatic re-posted vacancies from normal separation and
the stock of unfilled vacancies from the prior period. The latter is given by the share [1 − q (θt )]
of vacancies that could not be matched in the previous period. Note that both the vacancy stock
and the re-posted vacancies due to normal separations are subject to the obsolesce rate.
vt = ht + (1 − ς o ) (ς n nt−1 + [1 − q (θt−1 )] vt−1 )
ut = [1 − (1 − ς o ) f (θt )] ut−1 + [ς o + (1 − ς o ) ς n ] nt−1
The wage equation and the job creation condition reflect the introduction of a fixed hiring costs.
The value of an open vacancy is equal to its marginal cost. In the canonical model, that cost
was zero and thus Vt = 0. In the model of Fujita and Ramey (2007), this becomes Vt = Kht .
The wage equation and the job creation condition are as follows.
wt = α (pt + θt c) + (1 − α) b − α (1 − θt ) {Kht − (1 − ς o ) βEt {Kht+1 }}
Kht = −c + (1 − ς o ) βEt {q (θt ) Jt+1 + [1 − q (θt )] Kht+1 }
(22)
(23)
To align the model’s standard parameters with those of the models tested in the previous sections, I slightly deviate from the calibration provided by Fujita and Ramey. The first specification
that Fujita and Ramey provide includes a non-work benefit b = .9 in line with the calibration of
Hagedorn and Manovskii (2008b). As noted by Costain and Reiter (2008), such a calibration
is unwarranted as it implies an unrealistically large sensitivity of hiring with respect to marginal
changes in labor market policy as captured by non-work benefits b. The second calibration
provided by Fujita and Ramey, pins b = .65 which is in line with other values used in the literature. To align this model with the calibration used above, I slightly deviate from this second
specification and choose b = .71 in line with Pissarides (2009).26
26
For details, please see the full calibration description in Appendix B on page 87.
72
Fujita and Ramey explain that the periodic cost c anchors the assumed value of the vacancy
creation cost. Following their calibration strategy, I receive a K = 73.78 for the parameters
defined above. Finalizing the vacancy cost extension, I use the decomposition of the steady
state separation rate offered by Fujita and Ramey. Using equilibrium conditions, the authors
choose the obsolescence and normal separation rates to match Shimer’s separation data (i.e
the s = .036 used above).
Two problems arise with this calibration. First, as is noted by the authors and visible from the
results below, the amplification problem re-emerges. Fujita and Ramey’s extensions needs the
high non-work benefit to sufficiently amplify the volatility of unemployment and vacancies. The
second problem that arises is that the sum of total costs associated with hiring balloons with
decreasing value for the non-work benefit. The total expected costs of hiring are given by the
c
+ K · ht . Their baseline calibration with b = .9 allows Fujita and Ramey to choose
sum κt = q(θ)
comparatively small values for c = .13 and K = 26.94. In sum, the total expected hiring cost
κ1 = .158 + .647 = .805 i.e. 80 percent of annual output. Evidently, the linear vacancy cost c,
while in line with calibrated magnitudes used in the literature, is of negligible importance for the
steady state hiring costs. However, the cost associated with the novel vacancy creation K · ht
amount to roughly 65 percent of steady state output. As was indicated above, the interpretation
of Kht as the total costs incurred through firm creation may rationalize this magnitude.
Unfortunately, the size of these firm creation costs increases substantially in the second calibration. With a non-work benefit of b = .71, both the linear vacancy posting cost and the vacancy
creation cost increase, to c = .356 and K = 73.78, respectively.27 Using these values, the total
expected cost of vacancy creation κ2 = .432 + 1.284 = 1.715 i.e. 170 percent of annual output
seems hard to rationalize even with the wide interpretation. Fortunately, the combination of
the model of Fujita and Ramey with that of Pissarides (2009) proposed below may solve this
problem.
Before we turn to this combination, the results of the unrealistic calibration are briefly analyzed
nonetheless. In sum, the extension of Fujita and Ramey produces the intended increase of the
shock persistence in the DMP model. However, the volatility of the key variables is a third to
half the volatility found in US data and thus lower than that of the canonical model tested above
(table II.6c).
As intended by Fujita and Ramey, the extension of the DMP model with a vacancy creation
cost increases the model’s internal propagation substantially (figure II.7). The improvement is
especially pronounced in the autocorrelation of employment which compares well to the data
for the first three lags, but overshoots thereafter. This overshooting is also evident in the crosscorrelation. While Fujita and Ramey’s extension nicely reproduces its location, the peak of the
crosscorrelation is too wide when compared to the data. However, this overshoot is minimal
27
In the second specification offered by Fujita and Ramey (b=.65), the respective values are c = .46 and K =
94.30.
73
when compared to the underperformance with respect to propagation of the canonical DMP
model.
The lack of amplification found for the labor market variables also translates into lower impulse
responses (figure II.8). The vacancy cost extension of the model marginally reduces the fit of
the IRF with respect to output. Similarly, the peak of the response of employment falls to around
7 percent of the initial output response, worse than the 10 percent observed in the canonical
model.
Fig. II.7: Auto- and crosscorrelation in the propagation extensions
74
Fig. II.8: Impulse response functions in the propagation extensions
(a) Impact of common shock on output
75
Tab. II.6: Volatilities and correlations in the propagation extensions
(a) Autocorrelations: t-statistics
output
lag
employment
canonical
vacancy cost
canonical
vacancy cost
3.82***
0.48
2.13**
1.88**
(1)
(0.68)
(0.98)
(0.97)
3.08***
0.15
1.81**
1.50*
(1)
(0.56)
(0.97)
(0.93)
2.09*
0.26
0.93
0.63
(0.98)
(0.6)
(0.82)
(0.74)
1.04
0.63
0.15
0.08
(0.85)
(0.74)
(0.56)
(0.53)
1
2
3
4
5
6
7
8
0.14
0.81
0.49
0.64
(0.56)
(0.79)
(0.69)
(0.74)
0.48
0.78
0.68
0.75
(0.69)
(0.78)
(0.75)
(0.77)
0.91
0.65
0.71
0.70
(0.82)
(0.74)
(0.76)
(0.76)
1.07
0.42
0.42
0.35
(0.86)
(0.66)
(0.66)
(0.64)
(b) Crosscorrelations: t-statistics
model
canonical
vacancy cost
-2
-1
0
1
2
3
4
5
6
1.59*
1.68**
14.57***
1.53*
4.21***
4.27***
3.68***
2.99***
2.40***
(0.94)
(0.95)
(1)
(0.94)
(1)
(1)
(1)
(1)
(0.99)
0.68
1.82**
2.44***
3.01***
2.77***
1.08
0.73
0.61
0.41
(0.75)
(0.97)
(0.99)
(1)
(1)
(0.86)
(0.77)
(0.73)
(0.66)
(c) Relative volatilities
σi
σp
canonical
vacancy cost
US
σi
σp
mean
u
t-statistic
v
v
u
u
v
v
u
1.6
2.08
3.49
78.45***
62.80***
6423.64***
(0.01)
(0.035)
(0)
(1)
(1)
(1)
1.06
1.28
2.29
33.50***
89.40***
55.79***
(0.04)
(0.03)
(0.08)
(1)
(1)
(1)
2.35
4.29
6.65
Note in tables (a) and (b): The first row yields the number of standard deviations between the model’s and the observed value using the
standard deviation of the model output. The second row includes the associated p-value.
Note in table (c): In the «mean» column, the standard errors are stated in brackets in every other row. In the t-statistic column, every other row
contains the p-value in brackets.
76
6 Empirical performance of model combinations
Tab. II.7: Variable responses to the common shock in the propagation extensions
t-statistics
lag
0
1
2
3
4
5
6
7
8
output
employment
canonical
vacancy cost
canonical
vacancy cost
0.01
0.23
105.51***
292.40***
(0.5)
(0.59)
(1)
(1)
0.15
0.74
68.21***
153.89***
(0.88)
(0.46)
(1)
(1)
1.62**
2.25***
59.93***
100.62***
(0.95)
(0.99)
(1)
(1)
1.63**
1.95**
54.18***
73.97***
(0.95)
(0.97)
(1)
(1)
1.52*
1.34*
46.57***
54.51***
(0.94)
(0.91)
(1)
(1)
1.18
0.83
41.03***
37.90***
(0.88)
(0.8)
(1)
(1)
0.15
0.23
31.89***
24.33***
(0.56)
(0.59)
(1)
(1)
1.30*
0.60
18.40***
12.33***
(0.9)
(0.72)
(1)
(1)
2.94***
1.43*
1.67**
0.38
(1)
(0.92)
(0.95)
(0.65)
Note:
The first row yields the number of standard deviations between the model’s and the observed value using the standard deviation of the model
output. The second row includes the associated p-value.
6
Empirical performance of model combinations
The above evaluation confirmed that the inclusion of amplification or propagation extensions
improves the empirical fit of the DMP model only within the domain the extensions were initially designed for. This section inspects a variety of combinations of the above models with
respect to their empirical properties. Of all considered amplification extensions, the alternative
disagreement payoff suggested by Hall and Milgrom (2008) did worst. To economize on space,
it is not further considered in this section. The remaining combinations are between the vacancy creation cost extension of Fujita and Ramey and (i) the adaptive wage model of Gertler
and Trigari, (ii) the smoothed wage model of Faia, and (iii) the hiring cost model of Pissarides.
77
Calibration of model combinations
In line with the introduction of the wage rigidities into the canonical model described above, I
enter the rigidity parameters used above into this calibration without further alterations.
The procedure is different for the combination of the vacancy creation cost model with the
hiring cost model of Pissarides. The combination of Fujita and Ramey’s model with the hiring
cost extension of Pissarides allows a circumvention of the calibration problem discussed above.
Recall that largely due to high values for the vacancy/firm creation cost K, the model of Fujita
and Ramey yielded unrealistically high costs for the establishment of a new vacancy. The
introduction of the hiring cost H results in a decrease in the vacancy creation cost. The reason
for this decrease is that both papers rely on a fixed relationship between the linear vacancy cost
c and the introduced fixed cost H or K, respectively. For given values of c, different values of H
and K result.
To explore the relationship between H ,K and c, two calibrations will be evaluated below. The
first calibration uses a c = .11 found among the suggested calibrations in both papers. In this
setup, the vacancy creation cost parameter is set at K = 22.91 and the total steady state hiring
c
+ mH + Kh = .699, already lower than the κ1 = .805 and κ2 = 1.715 found
cost κ.11 = q(θ)
above. The second calibration exploits the inverse relationship between H and c. In his model,
Pissarides seeks to decompose the original linear vacancy cost c = .356 into a larger fixed cost
H and a smaller linear cost c. Thus for a higher H one can include a lower c. The highest fixed
hiring cost value deemed credible by Pissarides is H = .4 which implies c = .02. Using this
lower c, allows to reduce the vacancy creation cost to K = 4.17, only a fifth of its previous value.
Accordingly, the total steady state hiring cost falls to κ.02 = .473. In the evaluation below, this
latter specification will be referred to as the hiring cost combination with a low K. The calibration
with K = 22.91 is referred to as the hiring cost combination with a high K.
Simulation results
The simulation reveals improved variable volatilities for the combined models compared to their
individual components (see table II.8b). The combination with the smoothed wage works best at
amplifying the volatility of unemployment, vacancies and labor market tightness. The hiring cost
combination with a low K also performs well including a labor market tightness volatility within a
mere 1.1 standard deviations of its empirical counterpart. In both combinations, unemployment
is too volatile when compared to US data, while vacancies and the uv -ratio are somewhat too
inert.
With respect to the comovement, again the smoothed wage and the hiring cost combination
perform best among the tested models (see figure II.9). The crosscorrelation between employment and output produced by the hiring cost model with a high K are impressively close to the
78
data. Only for the first lag, the null hypothesis of equal estimates in the simulated and the US
data is rejected (table II.8a). As most models, the hiring cost combination with a high K slightly
overshoots at this position.
Fig. II.9: Auto- and crosscorrelation in the combined models
Finally looking at the impulse responses, basically all models hit the empirical estimate of the
output response (figure II.10). Again, the smoothed and hiring cost specification outperform,
but only marginally along this metric. Unfortunately, the comparatively small response of employment to a common shock remains for all combinations. In this dimension, the hiring cost
model that already proved the most accurate stand-alone extension exhibits the best employment response. The best specification in the IRFs is the hiring cost extension with a low K.
79
Fig. II.10: Impulse response functions in the combined models
(a) Impact of common shock on GDP
In sum, the combinations proposed in this section outperform the stand-alone varieties evaluated in this chapter. The realism of the generated auto- and crosscorrelation of output and
employment is substantially improved especially for combinations including a smoothed wage
or the hiring cost with different values of K. The main caveat to this upbeat conclusion is the
unsatisfactory impulse response of employment. Here, the overall realism still falls short with
respect to the response of employment to the common shock.
80
Tab. II.8: Volatilities and correlations in the combined models
(a) Crosscorrelations: t-statistics
model
canonical
adaptive
smoothed
hiring cost, high K
hiring cost, low K
-2
-1
0
1
2
3
4
5
6
1.59*
1.68**
14.57***
1.53*
4.21***
4.27***
3.68***
2.99***
2.40***
(0.94)
(0.95)
(1)
(0.94)
(1)
(1)
(1)
(1)
(0.99)
1.20
0.57
1.56*
8.22***
3.59***
4.93***
4.76***
4.57***
4.48***
(0.88)
(0.72)
(0.94)
(1)
(1)
(1)
(1)
(1)
(1)
0.30
1.42*
2.16**
1.89**
2.45***
1.24
0.97
0.84
0.61
(0.62)
(0.92)
(0.98)
(0.97)
(0.99)
(0.89)
(0.83)
(0.8)
(0.73)
0.22
0.61
0.10
8.21***
0.60
1.00
1.01
0.84
0.78
(0.59)
(0.73)
(0.54)
(1)
(0.73)
(0.84)
(0.84)
(0.8)
(0.78)
0.97
0.57
3.70***
8.82***
2.15**
2.83***
2.48***
2.04**
1.72**
(0.83)
(0.72)
(1)
(1)
(0.98)
(1)
(0.99)
(0.98)
(0.96)
(b) Relative volatilities
σi
σp
canonical
adaptive
smoothed
hiring cost, high K
hiring cost, low K
US
σi
σp
mean
t-statistic
u
v
v
u
u
v
v
u
1.6
2.08
3.49
78.45***
62.80***
6423.64***
(0.01)
(0.035)
(0)
(1)
(1)
(1)
2
2.58
4.4
5.93***
21.63***
17.35***
(0.06)
(0.08)
(0.13)
(1)
(1)
(1)
2.44
3.08
5.36
0.65
6.81***
4.01***
(0.15)
(0.18)
(0.32)
(0.74)
(1)
(1)
2.08
2.58
4.52
3.39***
18.28***
12.38***
(0.08)
(0.09)
(0.17)
(1)
(1)
(1)
2.97
3.67
6.4
6.18***
4.44***
1.13
(0.1)
(0.14)
(0.22)
(1)
(1)
(0.87)
2.35
4.29
6.65
Note in table (a): The first row yields the number of standard deviations between the model’s and the observed value using the standard
deviation of the model output. The second row includes the associated p-value.
Note in table (b): In the «mean» column, the standard errors are stated in brackets in every other row. In the «t-statistic» column, every other
row contains the p-value in brackets.
output
lag
1
2
3
4
5
6
7
8
hiring cost
low
canonical
adaptive
employment
hiring cost
smoothed
high
canonical
adaptive
smoothed
hiring cost
high
hiring cost
low
3.82***
2.59***
0.10
1.42*
2.47***
2.13**
1.65**
1.35*
1.63**
1.56*
(1)
(1)
(0.54)
(0.92)
(0.99)
(0.98)
(0.95)
(0.91)
(0.95)
(0.94)
3.08***
2.42***
0.22
1.05
2.00**
1.81**
1.41*
1.01
1.33*
1.37*
(1)
(0.99)
(0.59)
(0.85)
(0.98)
(0.97)
(0.92)
(0.84)
(0.91)
(0.91)
2.09**
2.08**
0.57
0.54
1.33*
0.93
0.67
0.21
0.54
0.62
(0.98)
(0.98)
(0.72)
(0.71)
(0.91)
(0.82)
(0.75)
(0.58)
(0.7)
(0.73)
1.04
1.65**
0.88
0.02
0.61
0.15
0.09
0.39
0.11
0.01
(0.85)
(0.95)
(0.81)
(0.51)
(0.73)
(0.56)
(0.53)
(0.65)
(0.54)
(0.51)
0.14
1.26*
1.00
0.34
0.01
0.49
0.38
0.84
0.62
0.54
(0.56)
(0.9)
(0.84)
(0.63)
(0.51)
(0.69)
(0.65)
(0.8)
(0.73)
(0.71)
0.48
0.91
0.90
0.49
0.37
0.68
0.45
0.84
0.70
0.64
(0.69)
(0.82)
(0.82)
(0.69)
(0.64)
(0.75)
(0.67)
(0.8)
(0.76)
(0.74)
0.91
0.45
0.71
0.54
0.61
0.71
0.42
0.69
0.63
0.60
(0.82)
(0.67)
(0.76)
(0.71)
(0.73)
(0.76)
(0.66)
(0.75)
(0.74)
(0.73)
1.07
0.03
0.42
0.48
0.70
0.42
0.14
0.26
0.28
0.28
(0.86)
(0.51)
(0.66)
(0.68)
(0.76)
(0.66)
(0.56)
(0.6)
(0.61)
(0.61)
Tab. II.9: Autocorrelations of the combined models: t-statistics
Note:
The first row yields the number of standard deviations between the model’s and the observed value using the standard deviation of the model output. The second row includes the associated
p-value.
81
output
lag
0
1
2
3
4
5
6
7
8
employment
canonical
adaptive
smoothed
hiring cost
high
hiring cost
low
canonical
adaptive
smoothed
hiring cost
high
hiring cost
low
0.01
0.65
0.79
0.73
1.30*
105.51***
123.56***
79.49***
99.48***
44.88***
(0.5)
(0.74)
(0.79)
(0.77)
(0.9)
(1)
(1)
(1)
(1)
(1)
0.15
0.18
0.02**
0.04**
0.78
68.21***
62.40***
37.67***
50.86***
23.79***
(0.88)
(0.86)
(0.98)
(0.97)
(0.44)
(1)
(1)
(1)
(1)
(1)
1.62**
1.36*
1.35*
1.43*
0.82
59.93***
43.85***
28.01***
39.14***
22.07***
(0.95)
(0.91)
(0.91)
(0.92)
(0.79)
(1)
(1)
(1)
(1)
(1)
1.63**
1.71**
1.05
1.25
0.90
54.18***
35.58***
22.38***
32.25***
20.48***
(0.95)
(0.96)
(0.85)
(0.89)
(0.82)
(1)
(1)
(1)
(1)
(1)
1.52*
1.53*
0.69
1.01
0.94
46.57***
30.83***
17.20***
25.89***
18.03***
(0.94)
(0.94)
(0.76)
(0.84)
(0.83)
(1)
(1)
(1)
(1)
(1)
1.18
0.77
0.38
0.72
0.75
41.03***
25.86***
12.50***
20.05***
15.62***
(0.88)
(0.78)
(0.65)
(0.76)
(0.77)
(1)
(1)
(1)
(1)
(1)
0.15
0.03
0.07
0.14
0.11
31.89***
19.28***
8.26***
14.48***
12.44***
(0.56)
(0.51)
(0.53)
(0.56)
(0.54)
(1)
(1)
(1)
(1)
(1)
1.30*
0.75
0.67
0.72
0.90
18.40***
11.32***
4.17***
8.27***
7.57***
(0.9)
(0.77)
(0.75)
(0.77)
(0.82)
(1)
(1)
(1)
(1)
(1)
2.94***
1.27*
1.28*
1.64**
2.01***
1.67**
3.09***
0.09
0.91
1.20
(1)
(0.9)
(0.9)
(0.95)
(0.98)
Note:
(0.95)
(1)
(0.54)
(0.82)
(0.89)
Tab. II.10: Variable responses to the common shock in the combined models: t-statistics
The first row yields the number of standard deviations between the model’s and the observed value using the standard deviation of the model output. The second row includes the associated
p-value.
82
7 Conclusion
7
83
Conclusion
As pointed out in previous work, the amplification and propagation implied by the canonical
DMP model do not compare well to the moments found in US data. This chapter re-visited
these findings and suggested combinations of the proposals to solve each problem in order to
reap a more satisfactory performance in both dimensions.
The main finding of this chapter is that largely preserved versions of the canonical DMP model
can generate both improved amplification and propagation properties. The extensions necessary to achieve this outcome are the introduction of a fixed vacancy creation cost as in Fujita
and Ramey (2007) in combination with either a smoothed wage regime (Faia, 2008) or a fixed
cost of hiring (Pissarides, 2009). The latter solution is particularly promising as it resolves a
calibration issue found in the original specification of the model by Fujita and Ramey.
Two avenues of future research remain. For one, while the generated crosscorrelation of output
and employment corresponded well with that found in US data, the analysis of the impulse
responses yielded an unsatisfactory low response of employment to a common shock. This
suggests that while the combined models do generate a realistic comovement of output and
employment, the mechanism that gives rise to these moments may not be the one driving
the output-employment nexus in the US economy. Alterations to the simulated model could
either include further extensions of the labor market structure or the inclusion of additional
shock sources. The second avenue of future research concerns alternative means to increase
vacancy persistence. The assumed lifespan of vacancies as well as the associated creation
cost implied in the model of Fujita and Ramey are difficult to assess empirically. To provide for
a more robust analysis, extensions that rely on more verifiable parameters may provide further
insights.
The labor market part of this thesis concludes with this chapter. Juxtaposing the results of
the two chapters provides further guidance for future research. As exercised in this chapter,
macroeconomic models are traditionally benchmarked by matching the moments observed in
aggregate data and replicating selected impulse responses. In this chapter, the benchmark
was based on US data taken from the entire existing sample spanning from 1948 - 2013. Using
the entire sample is warranted in an environment where the relationships between the relevant
variables can be thought of as constant or roughly constant.
However, this stability may not be taken for granted in the relationship between output and
employment dynamics, as argued in the first chapter. The evolution documented there calls for
models with yet stronger propagation than those studied in the analysis based on 1948 - 2013
data. The models studied in this chapter did already display the sought hump shape of the
employment response, albeit at an insufficient magnitude and width. In line with this shortfall,
the unconditional crosscorrelation used in the model evaluation has to increase in width by
strengthening in more distant quarters.
7 Conclusion
84
The model extensions analyzed in this chapter also offer tentative guidance on what may be
driving the observed differences in the comovement of output and employment. As we have
seen, the introduction of different hiring costs increased the fit of the model as did the introduction of a wage rigidity in the form of a wage norm. The combined hiring and vacancy creation
costs were particularly effective in increasing the propagation of the DMP model. In the quest to
understand a changed comovement in output and employment, future research may thus start
with a consideration of how hiring costs and wage rigidities may have increased over the past
30 years.
A The economic importance of business cycle frequencies
A
85
The economic importance of business cycle frequencies
A frequency-domain analysis of employment and output establishes the economic significance
of filtered data as commonly used in the literature and in the chapter above (see figure II.11
on the following page). First, employment and output have a large proportion of their variance
within the business cycle frequencies of 6 to 32 quarters. Second, the comovement of the two
variables is also largely concentrated within this frequency band. Thus models informed by
filtered data should be able to capture the stylized facts on the comovement of employment and
output.
To analyze the variance of output and employment in the frequency domain, the spectrum of
each variable is estimated using Parzen windows. To provide the reader with more information
on the sensitivity of the spectral estimates to the choice of the window width, a range of estimates is presented in figure II.11. The solid red line represents the preferred estimate. The
spectra of output and employment both show a broad peak between 8 and 32 quarters with the
highest concentration at around 12 to 16 quarters (figures II.11a and II.11b). In sum, more than
half of each variable’s variation occurs at business cycle frequencies.
Turning to comovement of the two, spectral analysis offers three tools for the analysis. First,
the coherence which is the frequency domain equivalent to the squared correlation. Second,
the gain offers the frequency equivalent for the regression coefficient in the time domain. Third,
an estimate of the phase yields insights into whether the variables move simultaneously or at
a lag. As is evident from figure II.11c, the association of employment and output is strongest
at business cycle frequencies. In this frequency band, output growth is the more volatile of the
two variables as is indicated by the gain values around .8. The negative value of the phase
suggests that output growth slightly leads employment growth at business cycle frequencies.
86
A The economic importance of business cycle frequencies
Fig. II.11: Frequency estimates of output and employment
(a) Spectrum of output
(b) Spectrum of employment
(c) Coherence of employment and output
(d) Gain
(e) Phase
B Model calibration
B
87
Model calibration
The models tested in this chapter are calibrated using the same parameters for the standard
DMP model. To allow for the comparison of the model dynamics, each model is subject to the
same productivity shock process. This process is calibrated to match the moments reported
by Shimer (2005) and uses a persistence parameter of ρp = .97, in line with the estimates for
the US economy provided by e.g. Fujita and Ramey (2007); Faia (2008) or Gertler and Trigari
(2009).
For the simulations, I choose to follow the calibration of Pissarides (2009) whose strategy is
more representative of the literature than Shimer’s as it builds on the data and insights from
various papers mentioned above. As Pissarides elaborates in his description, this calibration is
based on the data of Shimer (2005) for the monthly separation rate s = .036, mean labor market tightness θ = .72, the unemployment rate u = 0.057 and the monthly job-finding probability
f (θ) = .594. Based on the empirical values of labor market tightness and the job-finding probability f (θ) = χθ1−η , Pissarides derives the scale parameter of the matching function χ = .7.
The appeal in using Pissarides rather than Shimer’s calibration lies in the increased generality of
the values used for the matching function elasticities, the labor bargaining weight and the nonwork benefit. Following work by Pissarides and Petrongolo (2001) as well as Hosios (1990),
many authors assume the matching function elasticities of η = 1 − η = .5 and to equalize this
to the bargaining weight of labor α = 1 − η = .5. In his piece, Shimer acknowledges that his
specification of α = 1−η = .72 is an upper bound to the estimates of Pissarides and Petrongolo,
but cites the inexisting welfare implications of this choice as reason to pursue with them.
The final deviation of Pissarides from Shimer’s calibration concerns the non-work benefit b.
Here, Shimer uses a value of b = .4 which is equal to about two fifths of the steady state
wage. Again, Shimer acknowledges this value to be at the boundary of the common range, but
proposes a narrow interpretation of these benefits as unemployment insurance payments to rationalize the value. As later shown by Hagedorn and Manovskii (2008a) and elaborated further
by Costain and Reiter (2008), the volatility of unemployment is very sensitive to the choice of the
non-work benefit value. In their recalibration of the model, Hagedorn and Manovskii revealed
that using a non-work benefit value close to the steady state wage increases the volatility of
the v-u-ratio to its value in US data. Pissarides here sides with Hall and Milgrom (2008) and
assumes a positive time value of unemployment spells. In his calibration, Pissarides uses their
value of non-work benefits b = .71 which is considerably higher than that of Shimer albeit it
a little lower than the benchmark estimate of b = .745 calculated by Costain and Reiter. This
chapter will also use a b = .71 as it is the middle ground between Costain and Reiter’s estimate
and the value used by Fujita and Ramey (b = .65).
The final parameter to be set in the baseline model is the periodic hiring cost c. Using the above
values in the equilibrium conditions yields a c = .356, which is again higher than the value used
B Model calibration
88
by Shimer (2005). However, if one takes into account the different steady state hiring probabilities q (θ) implied by the two calibration strategies, the expected total recruitment costs c/q (θ)
are almost identical (43% or 47% of monthly output for Pissarides or Shimer respectively).
The calibration of the wage extensions analyzed in this chapter do not affect the standard parameters of the DMP model laid out above. Following Gertler and Trigari (2009), I assume that
wages are on average renegotiated every nine months on average in the adaptive wage extensions of the model. For the disagreement payoff extension, I use the estimates of Hall and
Milgrom (2008) for the firm’s disagreement cost ι and the probability that a negotiation terminates without a final agreement. The calibration is more difficult for the smoothed wage regime.
Faia (2008) uses a value for this rigidity of γ = .6 which she motivates from estimates by Smets
and Wouters (2003). Following Faia’s lead, I use data from Smets and Wouters (2007) which is
estimated on US rather than euro zone data and use γ = .7, a value that has also been reported
as plausible for US data by Blanchard and Galí (2010).
The calibration of the parameters used in the cost extensions is not entirely independent from
the parameters chosen for the standard model. The hiring cost extension of Pissarides (2009)
allows for a decomposition of the periodic hiring cost c into a itself and a fixed hiring cost H.
Pissarides himself provides the values of H = .3 and c = .11 as a preferred decomposition
of the total hiring cost. As for the vacancy creation cost, Fujita and Ramey explain that the
periodic cost c anchors the assumed value of the vacancy creation cost. Following their calibration strategy, I receive a K = 73.78 for the parameters defined above. Finalizing the vacancy
cost extension, I use the decomposition of the steady state separation rate offered by Fujita
and Ramey. Using equilibrium conditions, the authors choose the obsolescence and normal
separation rates to match Shimer’s separation data (i.e the s = .036 used above).
Turning to the combined models, I use the described calibration for the vacancy creation cost
model as the basis. In line with the introduction of the wage rigidities into the canonical model
described above, I enter the rigidity parameters into this calibration without further alterations.
The procedure is different for the combination of the vacancy creation cost model with the hiring
cost model of Pissarides. The cited possibility to decompose the periodic cost allows one to
downsize the vacancy creation cost K. Exploiting this opportunity, I calibrate two versions of
this combination. In the specification with a high K, I use the c = .11 and H = .3 as in the
original simulation of the Pissarides model. This combination implies a K = 22.91, already
substantially lower than the 73.78 used above. To receive intuition on the effects of alternative
hiring cost decomposition, I also simulate a calibration with a low K. Here, I use the maximal
value for H = .4 deemed credible by Pissarides. The associated periodic hiring cost of c = .02
yields a vacancy creation cost of 4.17.
B Model calibration
Tab. II.11: List of parameters
symbol
interpretation
symbol
interpretation
α
worker bargaining power
ρ
AR(1)-coefficient of productivity shock
η
matching function elasticity w.r.t vt
σ
standard deviation of productivity shock
χ
matching function scaling parameter
γ
wage smoothing parameter
b
non-work benefit
π
share of adjusted wages
c
periodic vacancy posting cost
ι
firm disagreement payoff
β
discount factor
Π
share of terminated negotiations
s
separation rate
H
fixed hiring cost
ςo
obsolesce rate
K
fixed vacancy creation cost
ςn
normal separation rate
Tab. II.12: Stand-alone models
simulation period = monthly
α
η
b
c
β
χ
s
ρ
σ
γ
π
ι
Π
H
K
ςo
ςn
canonical
.5
.5
.71
.356
.9531/12
.7
.036
.97
.008
-
-
-
-
-
-
-
-
smoothed wage
.5
.5
.71
.356
.9531/12
.7
.036
.97
.008
0.7
-
-
-
-
-
-
-
adaptive wage
.5
.5
.71
.356
.9531/12
.7
.036
.97
.008
-
1/9
-
-
-
-
-
-
.356
.9531/12
.7
.036
.97
.008
-
-
.23
.165
-
-
-
-
.11
.9531/12
.7
.036
.97
.008
-
-
-
-
.3
-
-
-
.356
.9531/12
.7
-
.97
.008
-
-
-
-
-
73.78
.021
.018
disagreement payoff
hiring cost
vacancy creation cost
.5
.5
.5
.5
.5
.5
.71
.71
.71
89
π
ι
Π
H
K
ςo
ςn
0.7
-
-
-
-
73.78
.021
.018
-
1/9
-
-
-
73.78
.021
.018
.008
-
-
.23
.165
-
73.78
.021
.018
.97
.008
-
-
-
-
.4
4.17
.021
.018
.97
.008
-
-
-
-
.3
22.91
.021
.018
simulation period = monthly
α
η
b
c
β
χ
ρp
σp
γ
smoothed wage
.5
.5
.71
.356
.9531/12
.7
.97
.008
adaptive wage
.5
.5
.71
.356
.9531/12
.7
.97
.008
.356
.9531/12
.7
.97
.02
.9531/12
.7
.11
.9531/12
.7
disagreement payoff
hiring cost with low K
hiring cost with high K
.5
.5
.5
.5
.5
.5
.71
.71
.71
B Model calibration
Tab. II.13: Model combinations
90
91
Chapter III. The role of bank financing costs for the
transmission of monetary policy
joint work with Daniel Kienzler
Abstract
Recently, policy makers have conjectured that the monetary policy stance is not transmitted undisturbed
to bank financing costs and hence to lending rates for the real economy. We present a New Keynesian
model with a variable wedge between bank financing costs and the central bank’s policy rate. The
sign and size of this wedge depends on balance sheet conditions in the banking sector. The balance
sheet conditions, in turn, can be influenced by deteriorating bank net worth arising from loan losses in
economic downturns. This setup allows us to study scenarios in which the transmission of monetary
policy is hampered in the sense that endogenous policy rate movements are not fully passed through
to bank financing costs and hence credit costs for the real economy. The effects of this impairment on
aggregate variables are small for shocks that emanate in the real sector and endogenously trigger a
deterioration in bank net worth but sizable for a direct impact on bank net worth. An optimal policy rule
in the presence of leverage-sensitive bank financing costs demands that the central bank responds to
tightening bank financing conditions with an interest rate decrease.
1
92
In this chapter we present a macroeconomic model with a variable wedge between bank financing costs and the central bank’s policy rate. The sign and size of this wedge depends on balance
sheet conditions in the banking sector. The balance sheet conditions, in turn, can be influenced
by deteriorating bank net worth arising from loan losses in economic downturns. This setup
allows us to study scenarios in which the transmission of monetary policy is hampered in the
sense that endogenous policy rate movements are not fully passed through to bank financing
costs and hence credit costs for the real economy.
The motivation for modeling such a scenario comes from recent developments in the euro area.
European Central Bank (ECB) President Mario Draghi has repeatedly expressed his concern
about "[...] the proper transmission of [the] policy stance to the real economy [...]" (ECB, 2012b).
In his view, "[o]ne reason [...] is that the cost of bank credit to firms is inevitably linked to the
cost of market funding for the banks themselves. If there are fears about potential destructive
scenarios, the cost of funding for banks can be affected [...]. [...] It is that distortion in financing
costs that hinders the smooth functioning of credit markets and the transmission of monetary
policy" (ECB, 2012a).
According to this view, a model that seeks to reproduce the possibility of an impaired transmission mechanism in this vein has to incorporate banks whose financing costs can deviate from
the monetary policy rate. Conventional macroeconomic models are not able to do so either because there is no financial sector or because the financial sector does not involve autonomous
financial intermediaries. In the latter case, bank financing costs always equal the risk-less policy
rate, for the relation between banks and their funding sources is frictionless. The transmission
of monetary policy thus cannot be disrupted by assumption. This is the case, for example, in
the financial accelerator model of Bernanke, Gertler, and Gilchrist (1999) (BGG henceforth),
one of the most widely used framework for credit frictions in the literature.
In our model, we introduce a financial friction that makes depositors demand a compensation for
the perceived riskiness of banks. The perceived riskiness of banks is captured by the banking
sector’s leverage ratio. Accordingly, aggregate bank financing costs fluctuate around the riskless rate depending on the leverage ratio of the banking system. By incorporating risk concerns
into bank financing conditions, our model allows for a meaningful analysis of impediments in
the monetary policy transmission process. Another feature of our model is that we allow for
endogenous loan losses on behalf of banks. This provides a mechanism for connecting bank
balance sheets to aggregate economic conditions.
Our focus is on scenarios where the monetary authority reacts endogenously to deteriorating economic conditions. In contrast, an exogenous policy rate cut induces better economic
conditions. This implies different consequences of endogenous and exogenous policy rate
movements for the banking sector’s leverage ratio and hence the monetary policy transmission
2 Descriptive model outline and relevant literature
93
process.
The model suggests that leverage-sensitive bank financing costs can be an effective disturbance for the transmission of monetary policy. If the central bank cuts interest rates in a recession, the contemporaneous deterioration of banks’ balance sheets - and hence the increasing
risk component in bank financing costs - has the potential to render the pass-through of policy
rates to bank financing costs less effective or even counteract policy rate movements. This, in
turn, tightens lending conditions in the real sector, thus reducing investment and output beyond
the reductions that would occur without leverage-sensitive bank financing costs. However, for
shocks originating in the real sector like exogenous spending shocks, preference shocks and
shocks to the riskiness of credit-financed intermediate firms, we find that the effects on aggregate outcomes are small. We explain this finding with the small amount of endogenously
generated loan losses, implying that bank net worth deteriorates only little after real sector
shocks. In contrast, a shock that depletes bank net worth directly has a sizable impact on aggregate outcomes. In light of the recent developments in several European banking sectors, we
consider this shock empirically relevant.
The potential impediment of the monetary policy transmission mechanism in the presence of
leverage-sensitive bank financing costs raises the question if the central bank can mitigate
the impediment by reacting to bank financing conditions. Therefore, we consider a policy rule
that allows the central bank to react to bank financing conditions and examine whether an
optimal rule assigns a non-zero weight on the associated reaction coefficient. We find that it is
optimal for the central bank to negatively respond to bank financing conditions. That is, if bank
financing conditions tighten, the central bank should lower the policy rate. We also find that a
strong reaction to inflation is the most important component of monetary policy. This result is
in line with the literature on optimal monetary policy which assigns a superior role to inflation
stabilization.
The rest of this chapter is organized as follows. The next section provides a verbal outline
of the model and sets it in the context of the related literature. A detailed description of the
model follows in section 3. Section 4 presents the calibration strategy and section 5 describes
the model results. Section 6 presents empirical evidence from the euro zone for two core
assumption underlying our model, namely the association between bank financing costs and
lending rates to the real economy as well as the sensitivity of bank financing costs to the bank
leverage ratio. Section 7 concludes and discusses avenues for future research.
2
Descriptive model outline and relevant literature
This chapter presents a New Keynesian model with leverage-sensitive bank financing costs.
To reflect the research object - the influence of bank financing costs on the transmission of
94
monetary policy - our model needs a credit-constrained private sector, a credit-constrained
banking sector and depositors as the ultimate source of funds.
The basis of our work is the model in BGG. In line with their setup, the intermediate goods
producer is an autonomous agent of the model who consumes on his own right. We assume
that intermediate good producers need to source external finance to realize their investments.
The only source of external finance for them is the banking sector. To this end, intermediate
goods producers and banks engage in a credit contract. This credit contract is characterized
by a financial friction. The intermediate goods sector is the only client of the banking sector.
We thus do not differentiate between different asset classes for the banks (e.g. loans, bonds,
equities etc.) or distinguish different loan varieties (e.g. non-financial company loans, consumer
loans, mortgages). Furthermore, as in BGG the only depositor in our setup is the household.
We thus abstract from other existing bank funding sources such as interbank lending or debt
instruments.
We extend BGG’s model in two ways. First, we model banks as entities that are independent
from households. Thus besides households and intermediate goods producers, our model contains a third autonomous agent who consumes on his own right. In our model economy, banks
channel household savings to intermediate goods producers. In the process, banks accumulate their own net worth and engage in a credit contract with households which determines the
terms of household deposits. In contrast, BGG assume that banks are merely a veil; they are
ultimately a part of the household and play no active role in the economy.
Establishing an independent banking sector which enters a credit contract with households allows us to introduce a BGG-type friction between depositors and banks into the model. This is
an additional friction to the canonical friction between banks and intermediate goods producers. This friction is vital for the central mechanism of the model, namely the deviation of bank
financing costs from the risk-free policy rate. Our conjecture is that bank financing cost are
a function of the perceived riskiness of the banking system. This riskiness is captured by the
bank leverage ratio.
Our second deviation from the original BGG model concerns the credit contract between the
banks and the intermediate goods producers. BGG assume that the intermediate goods sector
fully insures the banking sector against any loss from loan default. The insurance is modeled
as a state-contingent credit contract between the bank and the intermediate goods sector. This
contract is signed in the period of loan origination and contains a lending rate for each possible
state of the economy in the following period when the loan is repaid. Thus for example in an
economic downturn with higher debt default, the surviving intermediate good producers pay a
higher lending rate on their pre-existing loans in order to cover the bankruptcy costs of their
former colleagues.
In our model, we maintain this insurance structure in the credit contract between the bank and
the depositor. In the spirit of a deposit insurance scheme, banks guarantee the risk-less rate
95
to the households through the described state-contingent contract. However, contrary to BGG
we do not assume this insurance scheme to hold between banks and the intermediate good
sector. In our model, the banks and the intermediate good producers agree on a non-state
contingent lending rate in the period of loan origination. The consequence of this change is that
the bank is now exposed to aggregate risk. If its assumptions about future economic conditions
turn out to be too optimistic, part of its loan book turns sour. This loss transmits into a reduction
of bank net worth and an increase in the bank leverage ratio. Given that our model features
leverage-sensitive depositors, bank financing costs will increase.
In sum, this setup provides the basis for the sought feedback between an economic downturn,
bank balance sheet and lending rates to the real sector. The rise in bank financing costs is
endogenous.
We are not the first who emphasize the role of banks in the economy. One branch of the
literature that features a meaningful banking sector is built on the model of Holmstrom and
Tirole (1997).28 The key difference between this strand of the literature and our work lies in
the nature of the financial friction and resulting implications for bank borrowing costs. Following
Holmstrom and Tirole (1997), the presence of moral hazard on the side of the borrower reduces
their capacity to take on debt. However, this constraint only works along the borrowing quantity,
but not along the cost of credit. While lenders will adjust the loan volume, the lending rate is
always equal to the risk-free rate. This specification is thus unsuitable for our purposes as bank
financing costs remain insensitive to the leverage ratio of the bank.
Several authors extended the work of BGG with a banking sector. The model closest to ours
is the one in Hirakata, Sudo, and Ueda (2009, HSU hereafter).29 In what they refer to as
"chained credit contracts", HSU feature a model where banks play a dual role as both lenders
and debtors. Both relationships are subject to a financial frictions built on the the costly state
verification mechanism put forth in BGG. Contrary to this chapter, HSU assume that banks are
the monopolistic supplier of loans to a group of entrepreneurs. Given its status as a monopolist,
banks are at the core of the HSU model and solve the maximization problem for all agents in
the financial market.
The most important difference between this chapter and HSU concerns the nature of the debt
contract between banks and intermediate goods producers. HSU maintain the state-contingent
nature of all credit contracts. In their model, entrepreneurs thus insure banks against all aggregate risk. However, the absence of bank losses implies that the variation of bank funding costs
is only a function of final loan demand, rather than the health of the bank balance sheet. Hence,
the model is incapable of generating loan volume reductions or lending rate increases due to
decreasing bank net worth. In the HSU model, the causality goes into the opposite direction.
28
See e.g. Chen (2001), Aikman and Paustian (2006), and Meh and Moran (2004, 2010), or Gertler and Karadi
(2011) and Gertler and Kiyotaki (2010) for single-friction versions.
29
See also Hirakata, Sudo, and Ueda (2013), Hirakata, Sudo, and Ueda (2011) and Ueda (2012) for applications
of this model. See Badarau and Levieuge (2011) for a similar two-country model.
96
There, a decreased loan demand reduces bank revenues and thus bank net worth. Given their
full insurance through the entrepreneurs, it is impossible in this setup to generate bank losses
endogenously.
The specification of non-contingent interest rates in the credit contract between banks and the
producing sector used in this chapter has been proposed by Benes and Kumhof (2011, BK
hereafter). In their model, lending rates between banks and the real economy are set in the
contracting period and cannot be altered thereafter. Given this deviation, banks still operate
under a zero-profit condition ex ante. However, once the aggregate state is realized, banks
stand to make a profit or a loss ex post. Due to this alteration, it is possible that banks take
a loss that impairs their ability to repay depositors. In order to induce flows from risk-averse
households, one has to find a safety net to credibly ensure that households will be made whole
in the next period.
The way BK approach this issue is to impose capital adequacy requirements for banks. If banks
breach the capital adequacy regulation, they have to pay a penalty. The threat of the penalty
entices banks to hold an equity buffer in excess of the statutory minimum.30 BK choose the
penalty such that the buffer is big enough to ensure that banks on average never deplete their
net worth to an extent that would endanger the repayment of deposits. There is thus no need
for depositors to punish their bank for risky behavior.
The implementation of capital adequacy rules is unsuitable for this chapter as bank financing
costs are not sensitive to the leverage ratio in this scenario. Contrary to BK, we thus introduces a BGG-type financial contract between households and banks subject to costly state
verification. As the deposit rate is state-contingent this contract can be interpreted as imposing
a deposit insurance scheme: Banks acknowledge that a share of their sector may fail to deliver
the promised interest rate and thus goes bankrupt. However, non-bankrupt banks will adjust
interest payments ex-post such that the average interest earned on all deposits is equivalent to
the risk-free rate.
The benefit of imposing the canonical BGG credit contract for the relationship between depositors and banks is that it implies deposit rates which reflect the leverage of the bank. The
concern stated by BK that it is impracticable for depositors to monitor banks may be mitigated
by a wider interpretation of who constitutes bank creditors. A substantial share of bank funding
stems from professional investors such as money market funds or buyers of debt securities. In
our view, it is thus warranted to create a model in which bank financing costs depend on bank
leverage.
30
See Kollmann, Enders, and Müller (2011) for a similar setup in an two-country model with one global bank and
a single financial friction.
97
3 Model economy
3
Model economy
Households
Households supply labor hH
t to intermediate goods firms. Households maximize the expected
sum of discounted period utility functions subject to their real budget constraint:
(
max
D
t
t
ct ,hH
t ,P
Et
∞
X
t=0
)
1+ν h
β t ζtc log (ct ) − ψ t
1+ν
s.t.
Dt
Rt−1 Dt−1 Πcap
WtH H
Πret
=
ht − gt +
+ t + t ,
(λt ) ct +
Pt
Pt
πt Pt−1
Pt
Pt
where β is the household’s discount factor, ζtc is a demand shock, ψ is a scaling parameter for
the disutility of labor and ν is the elasticity of labor supply. The right hand side of the budget constraint represents household income. WtH is the nominal wage, gt are government expenditures
which are financed via lump sum real taxes (see description of government sector below) and
πt is the inflation rate. Being the owner of both the retailer and the capital good producer, the
household is the final recipient of their nominal profits Πcap
and Πret
t
t . Moreover, the household
receives the nominal gross risk-free interest rate Rt−1 for nominal deposits Dt−1 made in the
prior period. Deposits are the only savings vehicle available to the households in this economy.
For expositional clarity, we assume that deposits are administered by designated household
members called «investors». Investors deposit household savings at banks under the condition
to generate the nominal gross risk-free interest rate for the household. The left hand side of the
budget constraint shows that households can use their income for consuming retail goods or
making deposits. Denoting the Lagrange multiplier as λt the equilibrium conditions are
1
= λt
ct
ν
WtH
ψ hH
=
λ
t
t
Pt
ζtc
(24)
(25)
λt = βRt Et
λt+1
πt+1
(26)
Banks
As mentioned in the model outline, banks are the second autonomous agent in this model.
Banks take deposits from investors. Banks finance nominal loans Lt to intermediate firms using
98
3 Model economy
nominal deposits and nominal bank net worth NtB .31 The bank balance sheet is thus
Lt = NtB + Dt .
(27)
To avoid confusion, it is useful to discuss the timing convention of this model explicitly at this
point. Note that all loans Lt originated in period t are used to finance capital purchases kt in
period t. As is common in the literature, capital is used in production only in period t + 1. We
chose to denote all variables in this model with a time subscript that identifies their «settlement
period» i.e. the period in which their final magnitude has been decided. As neither loan nor
capital volumes can be adjusted after the transaction at the end of period t, we denote them kt
and Lt . However, as the return to a unit of capital and a unit of bank loans is only known after
the realization of aggregate uncertainty at the beginning of the next period, we denote these
B
k
returns by Rt+1
and Rt+1
, respectively. Also observe that a capital letter identifies a nominal
variable and real variables are written in small type.
Following BGG, we assume that households are risk averse and banks are risk neutral. In order
to entice deposit flows, banks have to guarantee investors a return equal to the risk-free rate
Rt of the depositing period. Banks make this guarantee by proposing a state-contingent debt
D 32
. On this menu,
contract that includes a menu of ex-post nominal gross deposit rates Rt+1
one deposit rate is chosen for every possible state of the economy. The chosen deposit rate
ensures a return equal to the current risk-free rate for the households. Banks thus fully insure
the household against all risk in the economy.
In particular, banks insure the depositors against aggregate and bank-specific risk. For reasons
B
that will be explained below, the return on banking Rt+1
, the gross interest earned on a unit of
loans, fluctuates with aggregate risk. Furthermore, bank-specific risk arises through a partial
default of the banking sector in every state of the economy. The share of defaulting banks
fluctuates with aggregate risk, but is positive in all states of the economy.
We introduce this bank-specific risk by transplanting the setup of BGG into the relationship between investors and banks. In our model, banks receive a periodic i.i.d. draw of idiosyncratic
productivity χjt . Across the continuum of banks that make up the banking sector, this idiosyncratic productivity is log-normally distributed with time-invariant mean E (χt ) = 1 and variance
σχ . The individual productivity draw is private information to the bank.
31
We present the relations for banks in aggregate terms right away. As Christiano, Motto, and Rostagno (2013)
and Fernández-Villaverde (2010) explain, this is possible because the contract relations are such that all banks
choose the same deposit rate and amount of deposits irrespective of their individual net worth. For details, see
footnote 33.
32
Note that while the menu of possible deposit rates is contracted in period t, the final deposit rate is only settled
after aggregate uncertainty vanishes at the beginning of the following period. In line with the rationale of the timing
D
convention explained above, we thus denote the return on deposits made in period t with Rt+1
.
99
3 Model economy
After idiosyncratic productivity has been drawn and aggregate uncertainty is realized, banks
decide whether to default on their depositors or not. Banks that receive a draw that does not
allow them to repay their depositors in full have no choice but to declare bankruptcy immediately.
Declaring default demands handing over all assets to the depositors. However note that as long
as the idiosyncratic productivity of the defaulting bank is private information, the defaulting bank
may in principle transfer only a fraction of their assets to the depositors. Banks that received
a draw that allows them to honor their debts in full also have the choice to declare default and
transfer a chosen volume of assets to the depositors. Denoting the idiosyncratic productivity of
the marginal defaulting bank by χ̄t+1 , one can express its value as
B
D
χ̄t+1 Rt+1
Lt ≥ Rt+1
Dt ,
(28)
i.e. the observed cut-off productivity of banks χ̄t+1 is at least as high as the idiosyncratic productivity needed to generate bank revenues equal to the amount of deposit repayments. When
this equation holds with equality, only those banks default which received an insufficient idiosyncratic productivity draw.
As shown by Townsend (1979), a simple setup reduces the default choice to an intuitive outcome. For one, we assume that by paying an auditing cost µB , depositors can learn the idiosyncratic productivity, and thus the total revenue, of the defaulted bank. For two, we assume that
the depositor of the defaulted bank may repossess all assets found in the audit. An audited bank
is thus left with zero assets, while the auditing depositor receives the net value of repossessed
assets minus auditing cost. As established by Townsend, the outcome of this setup is that only
insolvent banks declare default and depositors always audit defaulted banks. Hence, equation
(28) holds with strict equality. We may thus interpret χ̄t+1 as the cut-off value for the minimum
idiosyncratic productivity needed by a bank to generate sufficient revenues to compensate its
depositors.
Positive bank default reflects on the deposit rates agreed upon in the debt contract between
investor and bank. When the contract is signed in period t, the realized value of the return on
banking is still unknown as it is a function of the aggregate state of the economy in period t + 1.
To ensure sufficient deposit revenues, banks propose a contract with a menu of deposit rates
that satisfy the investor’s participation constraint i.e.
ˆ
Rt Dt = [1 −
D
Fχ (χ̄t+1 )] Rt+1
Dt
+ 1−µ
B
Fχ (χ̄t+1 )
0
χ̄t+1
χt+1 f (χ̄t+1 )
B
dχt+1 Rt+1
Lt , (29)
Fχ (χ̄t+1 )
where Fχ (χ̄t+1 ) is the default probability for banks and fχ is the probability density function of χ.
100
3 Model economy
The left hand side of equation (29) represents the payoff demanded by investors. The first
component on the right hand side is the total interest payment reaped from the solvent fraction
of banks, 1 − Fχ (χ̄t+1 ). The second component on the right hand side is the repossession
value from the fraction of Fχ (χ̄t+1 ) bankrupt banks less the monitoring costs. As in the original
BGG model, we assume that the monitoring cost µB is proportional to the size of repossessed
D
after
assets. For this equation to hold ex post, banks will choose the ex post deposit rate Rt+1
aggregate uncertainty - and hence the return on banking - is realized in period t + 1. One can
rationalize such a contract as a deposit insurance scheme that shields bank creditors from bank
default.
Before we characterize the maximization problem of the banking sector, it is useful to introduce
additional notation. Let 1 − Ψ (χ̄t+1 ) denote the share of total bank revenue that remains in the
banking sector after all deposits have been repaid. This share is constructed as one minus the
share of bank revenues spent on depositor repayment or lost in bank default. Furthermore, let
M (χ̄t+1 ) be the share of total bank assets belonging to defaulted banks. Then,
ˆ
1 − Ψ (χ̄t+1 ) = 1 − χ̄t+1
ˆ
M (χ̄t+1 ) =
ˆ
∞
f (χ) dχ +
χ̄t+1
χ̄t+1
χf (χ) dχ
(30)
0
χ̄t+1
χf (χ) dχ.
(31)
0
Recall that for the investor, a share µB of repossessed bank assets is lost as auditing cost. Using
B
Lt .
the above definitions, the net proceeds of the investor are thus given by Ψ (χ̄t+1 ) − µB M (χ̄t+1 ) Rt+1
In turn, the share of aggregate bank returns that goes to the bank can be expressed as
B
Lt .
[1 − Ψ (χ̄t+1 )] Rt+1
Plugging in (27), (30) and (31), the investor’s participation constraint (29) can be expressed as
B
Ψ (χ̄t+1 ) − µB M (χ̄t+1 ) Rt+1
Lt = Rt Lt − NtB .
(32)
Using these parsimonious expressions, one can express the maximization problem of the banking sector as
s.t.
ΥB
t
B
Lt
max Et [1 − Ψ (χ̄t+1 )] Rt+1
χ̄t+1 ,Lt
B
Ψ (χ̄t+1 ) − µB M (χ̄t+1 ) Rt+1
Lt = Rt Lt − NtB .
Banks thus maximize the expected share of the aggregate return on banking subject to the
101
3 Model economy
participation constraint of the investor. The first-order conditions for this problem are
Et
B
Rt+1
Rt
0
B
0
Ψ0 (χ̄t+1 ) − ΥB
= 0
t Ψ (χ̄t+1 ) − µ M (χ̄t+1 )
B
Rt+1 [1 − Ψ (χ̄t+1 )] + ΥB
Ψ (χ̄t+1 ) − µB M (χ̄t+1 ) − 1
= 0.
t
Rt
(33)
(34)
and the participation constraint 32.33
We conclude the description of the banking sector with the evolution of bank net worth. In our
model, bank net worth stems from two sources. The main source of bank net worth are the net
revenues generated from the application of the solution to the above maximization problem. The
nominal net revenues of the banking sector are equivalent to the term in the objective function.
For expositional parsimony, we denote nominal bank net revenues by VtB , i.e.
B
VtB = [1 − Ψ (χ̄t )] RtB Lt−1 = RtB Lt−1 − Rt−1 (Lt−1 − Nt−1
) − µB M (χ̄t ) RtB Lt−1 .
(35)
While net revenues from their lending activity are the main source of bank net worth, a further
source of funds is needed for technical reasons as explained by BGG. To be able to solve the
model, it is necessary that banks enter their first lending activity with own net worth. In order
to provide them with start-up capital, we assume that banks inelastically supply labor hB ≡ 1
for the production of intermediate goods. Thus, besides their respective profits from lending
activities, banks generate a small nominal wage income WtB . The determination of this wage is
explained in section 3. As will be elaborated in the calibration section, we choose the a share
of labor stemming from the banking sector as well as the magnitude of the associated wage
payments to be negligible in order to avoid a significant distortion of the model dynamics.
The final assumption necessary for a smooth solution of the model concerns the lifespan of
the average bank. To avoid scenarios in which banks accumulate sufficient net worth to be
self-financing, we make use of BGG’s assumption of a constant exit rate.34 In our model, banks
33
The banking sector is composed of a continuum of banks. We present the model relations in aggregate terms
right away. As Fernàndez-Villaverde (2010) explains, this is possible because the contract relations are such that
all banks choose to charge the same deposit rate and take the same amount of deposits irrespective of their
individual net worth. To see this, note that we can express equation 32 as
RB
Ψ (χ̄t+1 ) − µB M (χ̄t+1 ) t+1
Rt
L −N B
=
(κt − 1)
κt
where κt = NLBt and κt = tN B t . Thus, banks will have the same leverage ratio κt irrespective of their level of
t
t
net worth and the maximization problem of banks can be written down in terms of the leverage ratio. We apply the
same reasoning later on for the intermediate goods producers and present their sector in aggregate terms right
away as well.
34
In the original BGG model, this assumption is made only with respect to the real sector. See Gertler and
Karadi (2011) or Gertler and Kiyotaki (2010) for models that also feature a constant exit rate for banks. One may
rationalize such an assumption as banking sector that is myopic relative to the ever-enduring household.
102
3 Model economy
survive a period only with probability γ B < 1. Banks that do not survive the period consume
their net revenue. Banks’ real consumption cB
t is thus represented by
cB
=
t
1 − γB
VtB
.
Pt
(36)
The evolution of banks’ nominal net worth NtB is thus the sum of remaining net revenues plus
the wage income
B
NtB = γ B VtB + WtB + N
t .
(37)
B
35
We will
Note that the net worth equation is completed by N
t , an exogenous net worth shock.
use this exogenous net worth shock below to illustrate the consequences of a direct impact on
bank net worth.
Intermediate good producers
In this economy, all real output is generated by the third autonomous agent, the intermediate
good producers. As will be explained below, the intermediate good producers are the ultimate
borrowers in our model.36
Intermediate firms combine labor ht and capital kt to produce intermediate goods xt . They
purchase capital from capital producers at a nominal price Qt and use it for production in the
next period. The production technology takes the usual Cobb-Douglas form, i.e.
xt = at ktα h1−α
,
t
(38)
where at is aggregate productivity and follows the process with disturbance a,t ∼ N(0, σa ) and
steady state value a = 1.
a ρa
at
t−1
=
ea,t .
a
a
35
(39)
This specification resembles that of Gilchrist and Leahy (2002) as well as Hirakata, Sudo, and Ueda (2013).
See e.g. Christiano, Motto, and Rostagno (2008) for an exogenous decease in net worth induced by a shock on
the survival rate γ B .
36
We present the relations for intermediate firms in aggregate terms right away. As Christiano, Motto, and
Rostagno (2013) and Fernández-Villaverde (2010) explain, this is possible because the contract relations are such
that all intermediate goods producers choose the same interest rate and amount of loans irrespective of their
individual net worth.
103
3 Model economy
Intermediate firms sell their output to retail firms in a competitive environment at the nominal
. Thus, the real
price Px,t . Accordingly, real marginal costs in the economy are px,t = PPx,t
t
xt
marginal return to capital from producing intermediate goods in period t is px,t α kt−1
. Taking
into account that capital to be used in t + 1 is bought at price Qt and undepreciated capital is
sold after production at price Qt+1 , we can express the ex post nominal gross return to capital
purchased in period t as
k
Rt+1
where qt =
of capital.
Qt
Pt
= πt+1
px,t+1 α xt+1
+ (1 − δ) qt+1
kt
qt
(40)
is the real price of capital, πt+1 is the inflation rate and δ is the depreciation rate
The remaining structure of this sector resembles that of banks discussed above. To finance
their capital purchases, intermediate firms use their end-of-period nominal net worth NtI and
nominal loans Lt from banks. The balance sheet equation of intermediate firms thus reads
Qt kt = NtI + Lt
(41)
As with banks, intermediate good producers are subject to aggregate and idiosyncratic uncertainty. Aggregate uncertainty enters the intermediate good sector via the productivity shock that
determines the production volume in each period. The relative performance of an intermediate good producer is further determined by a periodic i.i.d. draw of idiosyncratic productivity
ωt . Across the continuum of all intermediate good producers, idiosyncratic productivity is lognormally distributed with time-invariant mean E(ωt ) = 1. In contrast to the banking sector,
2
we assume that the variance of intermediate good producer risk is time-variant, V(ωt ) = σω,t
.
The cumulative density function of ωt is denoted Fω and the standard deviation σω,t follows the
stochastic process
σω,t+1
=
σω
σω,t
σω
ρσω
eσω ,t+1
(42)
where σω ,t+1 is a shock to the riskiness of intermediate firms. The assumption of time-varying
intermediate good producer risk has been empirically validated by Christiano, Motto, and Rostagno (2013). Intuitively, the authors describe a risk shock as fluctuating degrees of uncertainty
surrounding the payoffs of business investment. When uncertainty is high i.e. the dispersion of
ωt is increased, credit is only extended at a higher price and a lower volume. Having estimated
104
3 Model economy
their model using US data, Christiano et al. find that such fluctuations in risk may be the most
important shock driving the business cycle.
The debt contract between banks and intermediate good producers deviates from that described earlier in one crucial aspect. In contrast to the existing literature, we do not assume
that intermediate good producers take on all risk in the economy to insure banks (and as a
consequence depositors). In our setup, banks and intermediate good producers agree on a
non-state contingent contract. That is, the lending rate for a unit of loans originated in period t
is also settled at a unique value in the same period. Denote this non-contingent nominal gross
interest rate RtL . Under the Townsend setup discussed in detail above, the cut-off equation is
thus slightly different with idiosyncratic productivity and lending rate settled in different periods.
k
ω̄t+1 Rt+1
Qt kt = RtL Lt
(43)
As a result of this deviation, banks in our model also carry part of the risk borne only by intermediate good producers in the alternative setup. This participation in aggregate risk is why the
B
is uncertain at the time of loan origination, as indicated above.
return on bank Rt+1
We can now determine the return on banking. A share of 1 − Fω (ω̄t+1 ) intermediate firms pay
back their loans plus interest, while a share Fω (ω̄t+1 ) does not and the bank repossesses a
fraction 1 − µI of the remaining assets. However, since the contract between the banks and
the intermediate firms does not involve state-contingent lending rates, this return is uncertain
for the banks. Banks sign the contract with the intermediate good producer in expectation of a
cut-off value Et {ω̄t+1 }. We thus write
B Et Rt+1
Lt = Et [1 − Fω (ω̄t+1 )] RtL Lt +
ˆ ω̄t+1
ωt+1 fω (ω̄t+1 )
k
I
dωRt+1 Qt kt
+Et 1 − µ Fω (ω̄t+1 )
Fω (ω̄t+1 )
0
(44)
where fω is the probability density function of ω. This expectation will only be validated in one
case. In all other realizations of the aggregate shock, the ex post value of ω̄t+1 will turn out to be
either above or below the bank’s expectation. The consequence of this deviation is that banks
suffer a revenue short fall when a negative aggregate shock hits the economy. Denoting this
short fall ∆t , it can be expressed as
∆t =
B
Rt − Et−1 RtB Lt−1 .
(45)
105
3 Model economy
Given that the banking sector guarantees a fixed repayment amount to depositors, a revenue
short fall eats directly into bank net worth NtB and thus affects bank leverage. We will return to
this variable in the results section below.
Finalizing the characterization of the intermediate good producer’s problem, we make use of
the analogous equations as in the previous section. Define the share of gross revenues kept
by the intermediate firms as 1 − Γ (ω̄t+1 ) and the share of gross revenue lost in bankruptcy as
G (ω̄t+1 ). We can express these two variables as
ˆ
Γ (ω̄t+1 ) = ω̄t+1
ˆ
ˆ
∞
ω̄t+1
ω̄t+1
ωt+1 fω (ωt+1 ) dωt+1
fω (ωt+1 ) dωt+1 +
ω̄t+1
ωt+1 fω (ωt+1 ) dωt+1
G (ω̄t+1 ) =
(46)
0
(47)
0
Using these definitions, we can express the share of intermediate firms’ gross revenue ceded
to the bank as Γ (ω̄t+1 ) − µI G (ω̄t+1 ). Using (41) and (43) in (44) yields
B k Et Rt+1
Qt kt − NtI = Et Γ (ω̄t+1 ) − µI G (ω̄t+1 ) Rt+1
Qt kt
(48)
The optimization problem for the intermediate firm is thus
s.t.
k
max Et [1 − Γ (ω̄t+1 )] Rt+1
Qt kt
kt ,ω̄t+1
k B ΥIt Et Γ (ω̄t+1 ) − µI G (ω̄t+1 ) Rt+1
Qt kt = Et Rt+1
Qt kt − NtI
The equilibrium conditions are
Et
k
Rt+1
B
Rt+1
Γ0 (ω̄t+1 ) − ΥIt Γ0 (ω̄t+1 ) − µI G0 (ω̄t+1 ) = 0
(49)
k
Rt+1 [1 − Γ (ω̄t+1 )] + ΥIt
Γ (ω̄t+1 ) − µI G (ω̄t+1 ) − 1
= 0
(50)
B
Rt+1
k B I
Et Γ (ω̄t+1 ) − µI G (ω̄t+1 ) Rt+1
Qt kt = Et Rt+1
Qt kt − N(51)
t
As with the bank, intermediate good producer net worth stems from two sources. The main
source of equity is the net revenue VtI from intermediate good production i.e.
VtI = [1 − Γ (ω̄t )] Rtk Qt−1 kt−1
I
= Rtk Qt−1 kt−1 − RtB Qt−1 kt−1 − Nt−1
− µI Fω (ω̄t ) E (ω|ω < ω̄t ) Rtk Qt−1 kt−1
(52)
106
3 Model economy
The first term on the right-hand side represents total revenues of the intermediate goods sector.
The second and third term are the value of the total debt repayment to banks and the value lost
in bankruptcy, respectively. For the reasons expressed above, intermediate firms survive a
period only with probability γ I < 1. Intermediate firms that do not survive the period consume
their net revenues, which yields intermediate firms’ consumption cIt
cIt =
1 − γI
VtI
.
Pt
(53)
The second source of funds is necessary to equip new intermediate good producers with startup capital. Again we assume that these funds are generated from work at (other) intermediate
good producers with a constant labor supply hI ≡ 1. We can thus write the law of motion for
intermediate firm net worth as
NtI = γ I VtI + WtI .
(54)
The derivation of the wage payments concludes the description of the intermediate good sector.
As households an banks are the only other sources of labor for the intermediate good sector,
total labor input is given by
ht =
hH
t
1−ΩI −ΩB
hIt
ΩI
hB
t
ΩB
(55)
where ΩB and ΩI are the shares of bankers and intermediate good producers in the total labor
supply. Assuming a competitive labor market, the wages of the agents are equal to the marginal
product of their labor services. Thus, the wage expressions are
WtH
Pt
WtI
Pt
WtB
Pt
xt
= (1 − α) 1 − ΩI − ΩB px,t H
ht
xt
= (1 − α) ΩI px,t I
h
xt
= (1 − α) ΩB px,t B ,
h
(56)
(57)
(58)
External finance premia
In the described setup, banks and intermediate good producers cannot fully self-finance their
desired quantity of assets. This implies that in equilibrium, the marginal return of an additional
107
3 Model economy
unit of assets is equal to the marginal cost of external finance.37 The marginal cost of exter k nal finance of the intermediate good producer is thus given by Et Rt+1
; that of the bank by
B Et Rt+1 .
The marginal cost of external finance fluctuates with the leverage ratios of the borrowers. As in
BGG, we can combine equations (32), (33) and (34) to obtain
Et
B
Rt+1
= Φ
B
Lt
NtB
where ΦB is an increasing function in the bank leverage ratio
and (50) can be combined to give
Et
k
Rt+1
= Φ
I
Qt kt
NtI
(59)
Rt ,
Lt
.Similarly,
NtB
equations (48), (49)
B Et Rt+1
where ΦI is an increasing function in the intermediate firm leverage ratio
(60)
Qt k t
.The
NtI
appendices
37
k
In this paper, we refer to Et Rt+1
as the «cost of external finance». We deduce this terminology from two
passages in the handbook article by Bernanke, Gertler and Gilchrist (BGG). The first passage makes explicit
reference to «the cost of external finance» and is taken from the model description. The second passage is part of
k
the calibration section and, in our reading, implicitly equalizes Et Rt+1
with the term «cost of external finance».
BGG introduce the term «cost of external finance» on page 1354, in the paragraph below equation (3.9):
j N
k
Rt+1 , s (·) < 0.
(3.9)
E Rt+1 = s Q Kt+1
j
t
t−1
For an entrepreneur who is not fully self-financed, in equilibrium the return to capital will be equated
to the marginal cost of external finance. Thus Equation (3.9) expresses the equilibrium condition that
the ratio s of the cost of external finance to the safe rate - which we have called the discounted return
to capital but may be equally well interpreted as the external finance premium - depends inversely
on the share of the firm’s capital investment that is financed by the entrepreneur’s own net worth.
[emphasis added]
We deduce our terminology from the above paragraph in two steps: From the first sentence of the above quotation,
we deduce that the «cost of external finance» is written on the RHS of equation (3.9). In equilibrium, it is equal
to the expected
return on assets on the LHS of equation (3.9) which is, as you write, the primary interpretation of
k
E Rt+1
.
From the second sentence of the above quotation we deduce that the expected return on capital can also be
interpreted as the cost of external finance. BGG write «[...] the ratio s of the cost of external finance to the safe
rate [...] depends inversely on the share of the firm’s capital investment that is financedby the entrepreneur’s
own
j
k
E (Rt+1
Nt+1
)
net worth». We interpret this statement as a re-arrangement of (3.9) into Rt+1 = s Q K j
. In our reading,
t
t−1
the first part of thesecond sentence («the ratio s of the cost of external finance to the safe rate») refers to the
k
numerator E Rt+1
and the denominator Rt+1 respectively.
Furthermore, we build our interpretation on the calibration strategy of BGG. In their description of the calibration
strategy, BGG write on page 1368:
Specifically, we choose parameters to imply the following three steady state outcomes: (1) a risk
spread, Rk − R, equal to two hundred basis points, approximately the historical average spread
between the prime lending rate and the six-month Treasury bill rate; [...]
k
This calibration strategy equalizes steady state E Rt+1
with «the prime lending rate». Although BGG do not go
into further detail about what constitutes the data on the prime lending rate, we believe this data is consistent with
what one would refer to as «the cost of external
finance».
k
In our reading, BGG thus refer to E Rt+1
as «the cost of external finance».
108
3 Model economy
on pages on page 146 and on page 146 give details on the derivation of the expressions for the
external finance premia. The intuition for these representations is that asymmetric information
between lenders and borrowers increases the agency costs for lower values of the borrower’s
net worth, thereby increasing the premium that borrowers have to pay to their lenders.
We further adopt the terminology of the original BGG model and refer to the external finance
B
Et {Rt+1
Et {Rk }
}
for banks.
for intermediate firms, and ef pB =
premia as ef pI = E Rt+1
B
R
t
t { t+1 }
Capital producer
Capital producers are perfectly competitive. They buy back undepreciated capital from intermediate firms after intermediate goods production. Moreover, they buy the quantity it of final goods
as inputs to capital production. Capital producers sell capital for the real price qt to intermediate
goods firms.
As is standard in the literature,
convex capital adjustment costs. In particular, an
we assume
2
it
investment of it yields it − ϕ2k kt−1
− δ kt−1 units of new physical capital kt . Thus, the law of
motion for capital is
kt
ϕk
= (1 − δ) kt−1 + it −
2
it
kt−1
2
−δ
kt−1
(61)
Πcap
The capital producer’s real profits Pt t are the revenue from capital sales to the intermediate
goods producer net of her costs from repurchasing undepreciated capital and buying investment
goods:
Πcap
t
= qt (kt − (1 − δ) kt−1 ) − it
Pt
(62)
Using the law of motion for capital, we can eliminate kt from the profit expression:
Πcap
t
Pt
"
= q t it −
ϕk
2
it
kt−1
2
−δ
#
kt−1 − it
Hence, the capital producer’s maximization problem in each period is:
Πcap
max t .
it
Pt
(63)
109
3 Model economy
The first-order condition is
it
−δ .
1 = qt 1 − ϕ k
kt−1
(64)
Retailer
There is a continuum of monopolistically competitive retailers in the economy indexed by i. They
buy the homogeneous intermediate goods at real price px,t and transform them one-to-one into
differentiated retail goods xt (i). The agents in the economy do not use the differentiated retail
´1
θ
θ−1
goods separately but a Dixit-Stiglitz aggregator of the differentiated goods yt ≡ 0 [ct (i) θ di] θ−1 ,
where θ > 1 is the elasticity of substitution between retail goods. We call yt final goods. Choosing the optimal expenditure level for each of the differentiated retail goods implies a demand
function of the form
xt (i) =
´
1
0
Pt (i)
Pt
−θ
1−θ
(65)
yt .
1
1−θ
Pt (i) di
Pt (i) is the price of retail good i and Pt =
is the aggregate price level in the
economy. Retailers take (65) as a constraint in their profit maximization problem.
Retail goods are sold for real price PPt (i)
. Due to their market power, retailers can choose the
t
price of their retail goods but price changes are subject to adjustment costs as in Rotemberg
(1982). Firm i maximizes its discounted profit stream subject to the demand function for retail
good i:
(
max
Pt (i)
s.t.
∞
X
"
2 #)
−θ
λ
P
(i)
P
(i)
ϕ
P
(i)
p
t+1
t
t
t
Et
βt
− π yt
yt − px,t xt (i) −
λ
P
P
2
P
(i)
t
t
t
t−1
t=0
−θ
Pt (i)
yt = xt (i) ,
Pt
θ
i θ−1
´1h
θ−1
, and
where π represents steady state inflation, yt ≡ 0 xt (i) θ di
Rotemberg price adjustment costs. The first-order condition reads
0 = (1 − θ) yt + px,t θyt − ϕp (πt − π) πt yt + βEt
ϕp
2
Pt (i)
Pt−1 (i)
−π
2
λt+1
ϕp (πt+1 − π) πt+1 yt+1 .
λt
yt are
(66)
110
3 Model economy
Fiscal policy, monetary policy, shocks and resources
We assume that government expenditures fluctuate around their steady state share of total
output. We will use this fluctuation to represent the demand shock in the model evaluation
below. The parameter τ̄ is the steady state fraction of government expenditure in total output.
All government expenditures are fully financed by lump-sum taxes τt yt from the household in
each period.
gt = τt yt
τ ρg
τt
t−1
=
eg,t
τ̄
τ̄
(67)
Monetary policy follows the standard Taylor rule
Rt
=
R
Rt−1
R
ρR "
π t φp
π
φy #1−ρR
yt
eR,t ,
y
(68)
where R and y are the steady state values of the nominal gross interest rate and output, respectively.That is, the central bank reacts to deviations of inflation and output from their respective
steady states. Moreover, as is common in the literature, we assume interest rate smoothing on
behalf of the central bank, where ρR is the smoothing parameter. φπ and φy are the reaction parameters for output and inflation deviations, respectively. Monetary policy is in principle subject
to R,t , a transitory monetary policy shock with zero persistence and mean zero. However, we
only use this shock for an illustrational exercise in the results section and do not conduct any
simulations based on its specification.
Final goods are consumed by households, invested by capital goods producers or purchased by
the government. Moreover, part of the final goods are lost in monitoring activities. The resource
constraint is
ωp
(πt − 1)2 yt +
2
+µB F (χ̄t ) E (χ|χ < χ̄t ) RtB lt−1 + µI F (ω̄t ) E (ω|ω < ω̄t ) Rtk qt−1 kt−1 ,
yt = ct + cIt + cB
t + g t + it +
where lt =
Lt
.
Pt
(69)
4 Calibration strategy
4
111
Calibration strategy
The model calibration contains four distinct parameter sets: (1) standard parameters (e.g. discount or depreciation rates), (2) financial sector steady state values (e.g. leverage ratios, external finance premia), (3) financial sector parameters for which we do not have data, but derive
them via the model’s equilibrium equations (e.g. the idiosyncratic risk dispersion), and (4) the
variation and persistence of exogenous shocks. This section describes the derivation of each
parameter set in turn.38 Tables III.1 and III.2 contain an overview of the model parameters as
well as their sources.
standard parameters
The standard parameters of our model include household preferences, parameters associated
with intermediate goods production, adjustment costs and the monetary policy rule. For these
parameters, we rely on estimates from other authors and used widely in DSGE models. In this
spirit, we choose the depreciation rate, the discount rate, the capital intensity of production as
well as the curvature of the households disutility from labor following Smets and Wouters (2003).
In a seminal contribution, these authors have estimated these parameters from euro zone data
using as DSGE model. The main difference between their and our model structure lies the
shape of the financial sector. We view this difference as of minor relevance for the standard
parameter estimates. The estimates for the standard parameters reflect long-run relationships
in the data which should be largely invariant to the exact shape of the model economy’s financial
sector.
As explained in the model description, we split total labor supply into three segments i.e. household, intermediate good producer and banking sector labor supply. As described above, intermediate good and banking sector labor is introduced to ensure positive steady state net worth
of these agents. Following BGG, we assign a miniscule value for the proportions of the labor
force stemming from these two sectors to ensure that this income source does not affect the
model dynamics. Furthermore, choosing small values for these proportions is also called for as
there exists an inverse relationship between the average lifespan of banks as well as intermediate good producer labor income and their respective labor incomes. As further explained in the
description of the indirect parameters below, we choose to lower their share of the labor force
in order to increase the survival rate of banks.
For the adjustment costs, we use a common value for the price adjustment costs found in
the literature of ϕP = 100. As shown by Keen and Wang (2007), this price adjustment cost
resembles the dynamics generated by a price setting frequency of .25 i.e. a quarter of retail
38
A detailed derivation of the steady state values of all variables can be found in Appendix C.
112
firms may reset their prices every period. Furthermore, we take the capital adjustment cost
parameter ϕk = 17 from Carrillo and Poilly (2013), whose functional form corresponds to that
used in our model. The elasticity of substation between retail goods θ = 11 is also taken from
these authors.39
Concluding the description of the calibrated standard parameters, we specify the monetary
policy rule using standard values of the literature. In this specification, monetary policy is highly
persistent (ρR = .9) and largely tailored to deviations of inflation from the steady state (φP = 1.5;
φy = .125).
financial sector steady state values
Besides the described common parameters found in New Keynesian models, our model also
includes a series of parameters related to the financial sector. To calculate those, we follow
the calibration strategy of BGG. The calibration of the parameters builds on three steady state
observations for each borrower: (i) the leverage ratio, (ii) the bankruptcy rate and (iii) the external finance premium. Our economy features two borrowers, banks and intermediate good
producers.
The leverage ratio of the intermediate good sector is taken from recent empirical work by
Kalemli-Ozcan, Sorensen, and Yesiltas (2012). Using firm-level data from the ORBIS database,
they find a leverage ratio of 4.5 for European non-financial companies. For the bank leverage
ratio in our model, we use data from the ECB and estimate a leverage ratio of 18.40 KalemliOzcan, Sorensen, and Yesiltas also report European median bank leverage to vary between
17.5 and 15 in their sample. Given that the empirical section at the end of this paper is based
on euro zone data, we choose to simulate our model with the value taken from ECB data.41
To the best of our knowledge, there is not aggregate data for firm and bank bankruptcy in the
euro zone. We thus rely on BGG for the assumed firm bankruptcy rate of 3 percent p.a. (.75
percent per quarter). The bankruptcy rate for banks is taken from FDIC data.42 We find an
annual bank bankruptcy rate of .554 percent (.14 percent per quarter).
Finally, we rely again on the mentioned ECB data to construct the costs of external finance for
both the bank and the intermediate good producer. Namely, we take the average value of the
39
Testing alternative specification for these parameters revealed that the model dynamics remain largely unaffected by their choice. For robustness, we simulated models with ϕp = 200 or θ = 6 (≈ Calvo price adjustment
frequency of 1/9) and ϕk = 10. The quantitative effects of these changes were miniscule and the qualitative
findings unaffected by these alterations.
40
The data is further described in section 6 on page 133. See Appendix A for a data sources.
41
A robustness simulation with a bank leverage ratio of 10 (the leverage ratio used by HSU) did not meaningfully
affect our results.
42
Calculated as the average ratio of «Number of Failed Institutions» to «Total Number of Banks (incl. savings
and commercial)» taken from the FDIC’s Historical Trends Series. Annual data covering 1990 to 2012.
113
lending rate to non-financial companies as the costs of external finance for the intermediate
good producer and the average interest rate on deposits with fixed maturity as a measure of
bank financing costs. As further explained in the empirical section below, neither measure is a
perfect description of external funding costs, but we are unaware of more accurate and publicly
available data sets. To construct a measure of the external finance premium, we use as the
risk-less rate the average yield on German government bonds with a remaining maturity of one
year. The bond data corresponding to the duration of the used ECB data has been taken from
the Bundesbank.43
financial sector parameters
As shown by BGG, using the leverage ratio, the bankruptcy rate and the external finance premium for each borrower allows the calculation of the remaining parameters in the financial
sector i.e. the auditing costs, the survival rates, the cuf-off values and the dispersion of idiosyncratic risk. To calculate these values, we use the steady state equilibrium conditions for each
borrower as well as the included definitions. We used Matlab to solve this problem numerically
and obtained only a single solution. For illustration, we repeat the mentioned equations below.
Γ0 (ω̄) − ΥI Γ0 (ω̄) − µI G0 (ω̄) = 0
k
Rk
I R
I
[1 − Γ (ω̄)] + Υ
Γ (ω̄) − µ G (ω̄) − 1 = 0
RB
RB
Γ (ω̄) − µI G (ω̄) Rk Qk = RB Qk − N I
N I = γ I [1 − Γ (ω̄)] Rk Qk + W I
(70)
(71)
(72)
(73)
Ψ0 (χ̄) − ΥB Ψ0 (χ̄) − µB M 0 (χ̄) = 0
B
RB
B R
B
[1 − Ψ (χ̄)] + Υ
Ψ (χ̄) − µ M (χ̄) − 1 = 0
R
R
Ψ (χ̄) − µB M (χ̄) RB L = R L − N B
(74)
N B = γB V B + W B
(77)
(75)
(76)
The mean and standard deviation of the idiosyncratic risks are based on two assumptions. As in
BGG, we assume idiosyncratic risk to be log-normally distributed and assume a time-invariant
expected value E (ω) = E (χ) = 1. To ensure this expected value, the mean of the log-normal
2
distribution becomes a function of its standard deviation i.e. µω = − σ2ω . The steady state
bankruptcy rates F (ω̄) and F (χ̄) are then used to derive the value of σω and σχ , respectively.
43
Yields on German sovereign bonds with a remaining time to maturity of 1 year, monthly values taken from the
Bundesbank (Database ID: BBK01.WZ3400).
114
Following this approach we obtain auditing costs in the real economy of 9 percent, which is a
the lower end of the credible range discussed by Carlstrom and Fuerst (1997). We also receive
a firm survival rate of 97 percent, or an average firm lifespan of 7.5 years. For the banks, we
receive higher auditing costs (16 percent). A side-effect of this calibration strategy are myopic
banks. Using the above values, we obtain an average lifespan of 5 years for the banking sector.
This value is lower than that used in related models, e.g. Gertler and Karadi (2011) or Ueda
(2012) who operate with bank lifespans of 8 to 9 years.
Unfortunately, the current model and the boundaries set by the observable calibration values
do not allow for longer bank lifespans. The model implies that bank exit is a function of the
leverage ratio and the wage earned outside the banking system (see equation 73 above). The
leverage ratio of 18 is considerably higher than that used e.g. by Ueda (bank capital ratio of 10
percent) or Gertler and Karadi (25 percent). If we were to use their leverage ratios, the lifespan
of the banking system would increase to 8 resp. 13 years.
exogenous shocks
Below, we compare our model to a model in which policy rate movements transmit undisturbed
into bank financing costs. Thus, the focus lies on the differences between model responses to
the same shock. For the presentation below, we choose the shock size such that real output
falls by one percent upon impact in our model. With two exceptions, we base the persistence of
our exogenous driving forces on the estimates from Smets and Wouters (2003). As Smets and
Wouters do not feature a risk shock comparable to our specification, we use the persistence
found in Christiano, Motto, and Rostagno (2013) for the shock on intermediate good producer
risk. The second exception is the persistence of the monetary policy shock which we assume
to be zero. The reason for this assumption is that we only use the monetary policy shock to
illustrate the transmission of monetary policy in an otherwise undisturbed state of our model
economy. We choose to illustrate this with a one-off shock to the monetary policy rate that,
which reverts to the value implied by the Taylor Rule in the next quarter.
We acknowledge that the shock specification is not ideal. Smets and Wouters have estimated a
model that featured ten different shock sources and abstracted from a financial sector. To make
a model-founded statement about monetary policy in the euro area, one needed to estimate
the model on euro zone data in order to decompose the aggregate shocks into the sources we
use in our model. This is beyond the scope of our paper. Rather, we base our calibration on
euro area data where available in order to make a general inquiry about the significance of our
model extension. This approach is in line with those of the related models cited above, e.g.
HSU, Carillo and Poilly (2013) or Gertler and Karadi (2011).44
44
If the new mechanism offered high explanatory power, a more careful shock calibration would be called for
in order to deduce specific policy recommendations. As our results below only indicate a marginal role of the
115
Tab. III.1: Calibration of the real economy
Symbol
Description
Household
β
Discount rate
ν
Curvature of disutility of labor
ψ
Disutility weight of labor
Intermediate good producer
δ
Depreciation rate
α
Power on capital in production function
Ω
Proportion of household labor
I
Ω
Proportion of intermediate labor
B
Ω
Proportion of bank labor
Capital good producer
ϕk
Capital adjustment costs
Retailer
θ
Elasticity of substitution retail goods
ϕP
Price adjustment costs
Monetary policy rule
ρR
Policy smoothing parameter
φP
Policy weight on inflation
φy
Policy weight on output gap
Steady state values used in calibration
Household labor supply
h̄H
I
B
h ,h
Intermediate/bank labor supply (fixed)
τ̄
Government share of output
Π̄
Inflation
Shock specification
ρa / σ,a
Technology shock
c
ρζ / σ,c
Demand shock
ρg / σ,g
Government expenditure shock
ρσω / σσ,ω
Risk shock to intermediates
ρm
Monetary policy shock
Value
Source
.99
2.5
1.11
Smets & Wouters (2003)
Implied by steady state
.025
.33
.997
.0015
.0015
BGG (1999)
own, based on BGG
own, based on BGG
17
Carillo & Poilly (2013)
11
100
Carillo & Poilly (2013)
Standard
.95
1.5
.125
Standard
Standard
Standard
1
1
.2
1
Normalized
Normalized
OECD data
Standard
.81 / .0825
.83 / .021
.94 / .0673
.97 / .213
0
Smets & Wouters (2003) / see text
Christiano et al. (2013) / see text
see model description
proposed mechanism, we refrain from undertaking the model estimation ourselves.
116
5 Results
Tab. III.2: Calibration of the financial sector
Symbol
Description
Intermediate good producer
Q̄k̄
N̄ I
F ¯(¯)
ω
¯PI
EF
I
µ
γI
¯
ω̄
σω
Banks
Q̄k̄
N̄ I
F (¯¯χ)
¯PB
EF
B
µ
γB
¯
χ̄
σω
5
Value
Source
Steady state leverage ratio
Steady state bankruptcy rate
4.5
.0075
Kalemli-Ozcan, Sorensen, and Yesiltas (2012)
BGG (1999)
Steady state EFP
Auditing cost
Survival rate
Steady state cut-off value
Idiosyncratic risk dispersion
1.015.25
.0903
.9672
.7756
.1023
ECB data
Implied by long-run moments
Steady state leverage ratio
Steady state bankruptcy rate
18
.0014
ECB data
FDIC data
Steady state EFP
Auditing cost
Survival rate
Steady state cut-off value
Idiosyncratic risk dispersion
1.009.25
.1616
.9518
.9518
.0197
ECB data
Results
Transmission of monetary policy
The purpose of this chapter is to examine how the presence of leverage-sensitive bank financing
costs affects the transmission of monetary policy. In particular, we are interested in whether the
model can reproduce a scenario described in section 1. In that scenario, the transmission of
monetary policy during recessions is impaired in the sense that policy rate cuts are not fully
passed through to bank financing costs and hence loan rates for the real economy.
B In our model, the study of the bank’s marginal cost of external finance Et Rt+1
suffices to
infer whether the transmission of monetary policy into the real economy is impaired. To see
this, recall that central bank policy seeks to affect the real economy’s external financing costs
conditional on borrower risk. By altering the policy rate, the central bank seeks to induce a
similar move in the average lending rate for each risk category. Note that if the risk-composition
of the borrowers evolves during changes in the monetary policy rate, one need not necessarily
observe a reflection of the policy rate change in the average lending rates. It is thus unwarranted
to deduce the transmission of monetary policy from the evolution of the average marginal cost
k of external finance for intermediate good producers Et Rt+1
.
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The expression for the marginal cost of external finance of intermediate good producers, repeated in equation (78) below, neatly disentangles these sources
for an observed change in
I Qt kt
can be interpreted as the
the average lending rate to the real economy. The term Φ
NtI
markup that banks charge over their own marginal financing costs. This markup is solely a
function of borrower risk, represented by the leverage ratio QNt kI t . Any difference between the
t
bank’s marginal financing cost and the lending rate to the real economy is due to borrower risk.
Et
k
Rt+1
= Φ
I
Qt kt
NtI
B Et Rt+1
(78)
B The term Et Rt+1
, the bank’s marginal cost of external finance, anchors the marginal cost of
external finance in the real economy. It is the level from which the markup reflecting borrower
risk is applied. A monetary policy that is concerned with altering the real economy’s financing
B . If the
costs conditional on borrower risk is thus implicitly concerned with the level of Et Rt+1
B level of Et Rt+1 does not fully adapt to changes in monetary policy, the lending rates to the
real economy cannot fully reflect the policy change either. Thus, to study the transmission of
monetary policy, we analyze the evolution of the bank’s financing costs.
As described in section 2, the independence of bank financing costs is a fundamental difference
from standard New Keynesian models. In the canonical models, the bank financing costs and
B the policy rate are identical, i.e. Et Rt+1
= Rt . In these models, the banking system is a
neutral veil and monetary policy always transmits undisturbed.
For our analysis, it is important to distinguish between an exogenously and an endogenously
induced movement in monetary policy. Consider a decrease in the policy rate. If the decrease
is exogenous, real output booms and bank financing costs unambiguously decrease due to a
lower policy rates and the better aggregate state of the economy which translates into less debt
default on bank loans.
However, if the policy rate cut is endogenous, it is the reaction to a recessionary state of the
economy. In this case, bank financing costs receive a decreasing impulse from monetary policy
but an increasing impulse from the recessionary aggregate state of the economy. It is through
these opposing signals that our model has the potential to describe a scenario in which the
monetary policy transmission into bank financing costs, and hence into the financing costs of
the real economy, is impaired.
To illustrate this, figure III.1 displays the responses of the policy rate Rt , bank financing costs
B Et Rt+1
and their ratio ef pB to an exogenous policy rate decrease. The vertical axes show
basis point deviations from the steady state, plotted for the first quarter when the shock occurs
as well as the subsequent quarters along the horizontal axes. As the policy rate decreases,
bank financing costs also decrease. The simultaneous fall in the ef pB implies that the decrease
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in bank financing costs is stronger than that in the policy rate. The additional decrease is due
to the described expansionary effect of the exogenous rate cut.
Fig. III.1: Monetary policy shock
(a) Policy rate reaction
(b) Bank financing costs reaction
(c) ef pB reaction
In contrast, figures III.2, III.4 and III.3 show the reactions of the policy rate, bank financing
costs and the external finance premium for banks to a recessionary exogenous spending, risk
and preference shock, respectively. The decrease in the policy rate is thus an endogenous
reaction of a central bank following a Taylor rule. Again, basis point deviations from steady state
are shown on the vertical and quarters are shown on the horizontal axis. In the cases of an
exogenous spending shock (figure III.2) and a preference shock (figure III.3), a decrease in the
policy rate is accompanied by a weaker decrease in the bank financing costs and consequently
an increasing external finance premium of banks. In the case of a risk shock (figure III.4), we
see that a decrease in the policy rate is even accompanied by an increase in bank financing
costs and thus a strong increase in the external finance premium for banks. In all cases, the
transmission of monetary policy is impaired in that the policy rate reductions are not passed on
to bank financing costs in full or at all. Note that this scenario cannot be reproduced in traditional
models featuring a financial accelerator mechanism. In these models, the bank financing costs
are always equal to the risk free rate in the economy.
Fig. III.2: Exogenous spending shock
(c) ef pB reaction
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Fig. III.3: Preference shock
(c) ef pB reaction
Fig. III.4: Risk shock
(c) ef pB reaction
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120
Does the impaired transmission of monetary policy matter for aggregate
outcomes?
Having shown that the transmission of monetary policy can be impaired by the presence of
leverage-sensitive bank financing costs, this section asks what the effect of this mechanism is
for aggregate outcomes. To this end, we need to compare the outcomes of our model with those
of a model in which policy rate movements transmit undisturbed into bank financing costs. Similar to Faia and Monacelli (2007), removing the financial friction between banks and investors by
setting µB = 0 provides such a model. Without monitoring costs there is no asymmetric information because investors can always observe the return on banking costlessly. Consequently,
there is no variable spread between the risk-free rate and the bank financing costs.
For an exogenous spending, risk, and preference shock, the top rows of figures III.5, III.6 and
III.7 show the reaction of output and investment in the model with and without a variable spread
between the risk-free rate and the bank financing costs, respectively. To illustrate the role of
bank financing costs, the bottom row shows the external finance premia for banks and intermediate firms, respectively. For output and investment, the vertical axis shows percentage
deviations from steady state, while for the finance premia it shows annualized basis point deviations from the steady state. The shock sizes are scaled so as to induce an initial one percent
reduction in output.
The graphs for the external finance premium of banks visualize the difference between the
two model specifications. While in the model with leverage-sensitive bank financing costs the
external finance premium for banks increases with a contractionary shock, it stays constant in
the model without leverage-sensitive bank financing costs. Thus, the external finance premium
for intermediate firms increases by more in the model with variable spread between the policy
rate and bank financing costs. As a consequence, the decrease in investment and output is
stronger.
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Fig. III.5: Impulse response functions to an exogenous spending shock.
Note: The solid line represents the model with a hampered transmission of the policy rate to bank financing costs
while the dashed line represents the model with an undisturbed transmission.
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Fig. III.6: Impulse response functions to a risk shock.
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Fig. III.7: Impulse response functions to a preference shock.
As is apparent in the presented impulse response functions the additional amplification in the
real sector in the model with a leverage-sensitive external finance premium for banks is relatively
small. This is a direct consequence of the relatively small variation in the external finance
premium for banks. For the exogenous spending and the preference shock, it increases by
approximately six basis points, while for the risk shock the increase is roughly 25 basis points.
The small movements in the external finance premium for banks are the consequence of the
shocks’ small impact on loan losses and hence bank net worth. Bank financing costs are a
function of the leverage ratio, i.e. the ratio of total bank assets over bank net worth. In contrast to the existing literature, our model provides an endogenous mechanism that strengthens
the link between the health of bank balance sheet and aggregate economic performance. This
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mechanism is introduced via a non-state-contingent debt contract between banks and intermediate firms. As explained in section 2, banks in our model have to set interest rate at the time of
loan origination and are not insured against aggregate uncertainty. In recessions, banks suffer
a revenue shortfall due to increased loan default. Denote this shortfall ∆t . We interpret ∆t as a
loss as it directly reduces bank net worth relative to its steady state level.
∆t =
Et−1 RtB − RtB Lt−1 ,
NtB = γ B [Et−1 {Vt } − ∆t ] + WtB .
If banks expected a bigger payoff from their lending activities than actually materialized, losses
are positive. This is the case when a negative shock hits the economy and not as many intermediate firms can pay back their loans as expected due to bankruptcy. The loan losses, in
turn, deplete banks’ net worth, increasing the leverage ratio. If these losses are small, so is the
variation in the leverage ratio and thus in the external finance premium for banks.
To illustrate this point, figure III.8 shows the reactions of firm bankruptcy rates and loan losses to
an exogenous spending, risk, and preference shock, respectively. For the exogenous spending
and preference shocks, the quarterly firm bankruptcy rate only increases by 0.2 percentage
points, i.e. from 0.75 percent to about 0.95 percent. Consequently, loan losses only amount
to roughly 0.5 percent of bank net worth. The risk shock evokes a bigger response in the firm
bankruptcy rate and loan losses, but still only 5 percent of banks’ net worth depletes.
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125
Fig. III.8: Responses of firm bankruptcy rates and loan losses to different shocks.
Note: Firm bankruptcy rates are expressed in percentage point deviations from steady state. Loan losses are
expressed as percent of bank net worth.
Consequences of a direct impact on bank net worth
The loan losses resulting from the demand shocks covered in section 5 are small compared to
empirical observations for some European countries in the last couple of years. For example,
the Bank of Spain reports that the Spanish banking sector’s realized total losses since 2009
amount to more than a third of initial bank equity.45 According to the World Bank’s World Development Indicators, 16% and 19 % of total bank loans in Ireland were non-performing in 2011
and 2012, respectively. Although it is clear that this is not equivalent to bank losses, it indicates substantial valuation adjustment on loan portfolios. The housing sector plays a major role
in these loan losses, as noted for example by Lane (2011) for Ireland and the IMF (2013) for
Spain.
To assess how a depletion of bank net worth of a similar magnitude as described above af45
See table 4.7 ("Equity, valuation adjustments and impairment allowances") of the Bank of Spain’s Statistical
Bulletin. Unfortunately, similar data from other national central banks could not be found.
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126
fects the transmission of monetary policy, we employ an exogenous shock to bank net worth.46
The net worth shock can be regarded as a proxy for loan losses incurred by a housing sector
downturn and ensuing losses from mortgages and loans to real estate developers. We use
a net worth shock that inflicts a loss of roughly 1 percent of total assets on the banking system. We consider this magnitude as conservative in light of the reported evidence. Due to
our steady state bank leverage ratio of 18 (i.e. a capital-asset-ratio of 5.6 percent), this loss
depletes 20 percent of bank equity in the initial period. There a no further exogenous losses in
the subsequent period as the shock has zero persistence.
Figure III.9 depicts the impulse responses of this exercise. A shock to bank net worth has
little effect on an economy without leverage-sensitive bank financing costs (dashed lines). For
the model with leverage-sensitive bank financing costs, the policy rate decreases due to the
contractionary shock. However, this decrease is strongly counteracted by an increase in bank
financing costs.
According to the IRF, the bank financing costs increase by about .3 percent (28 basis points) in
quarterly terms on impact. Over the first year following the shock, banks suffered an average
quarterly markup of about 20 basis points. Instead of the assumed steady state mark up of
25 basis points over the risk free rate (1 percent at annual rates), these banks are thus faced
approximately 45 basis points (1.9 percent at annual rates). The increases in the external
finance premium for the intermediate good sector are of similar magnitude, albeit from a higher
base. In the steady state, the intermediate goods sector finances itself at a markup of 60 basis
points over the quarterly risk free rate. After the net worth shock to the banking sector, the total
markup averages about 90 basis points per quarter in the first year, or 3.6 percent at annual
rates.
This strong response of the lending rate transmits into investment activity. The contraction
there is considerable, being roughly 3.5 percent off its equilibrium value in the initial period after
the shock. It also fails to recover in full over the depicted time span of 3 years. The reaction
of output, half a percent off the steady state value, is more moderate although the resulting
recession grosses more than 2 percent of steady state output throughout the first year.
This shows that a variable spread between the policy rate and bank financing costs can have
considerable consequences for aggregate variables if the effect of the macroeconomic disturbance on the bank leverage ratio is big enough.
46
Ueda (2012) also uses net worth shocks in his model.
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Fig. III.9: Impulse response functions for a bank net worth shock.
Note: The shock depletes 20 percent of the respective steady state net worth. Responses of output and investment
are expressed as percent deviations from steady state. The policy rate, bank financing costs, and external finance
premia are expressed as annualized basis point deviations from steady state.
Welfare implications of flexible bank financing costs
The last two sections showed that leverage-sensitive bank financing costs have effects on the
transmission of monetary policy and, for large deviations from the steady state, also on aggregate outcomes. Therefore, the question arises if the central bank can achieve better welfare
results if it reacts to bank financing conditions. When the economy is in a recession and the external finance premium for banks increases - signaling a hampered transmission from the policy
rate to bank financing costs - a negative reaction of the policy rate to the external finance premium could compensate for the disturbance in monetary policy transmission. As was evident
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from the responses to a monetary shock, a decrease in the policy rate improves banking sector conditions and hence reduces the leverage-dependent spread between the bank financing
costs and the policy rate.
To evaluate whether a reaction to bank financing costs on behalf of the central bank can increase welfare in the economy, we employ the welfare cost concept suggested by SchmittGrohe and Uribe (2007). In particular, we compare the conditional welfare generated by the
Ramsey optimal policy with the conditional welfare generated by alternative monetary policies
which - besides the common components inflation and output - take into account the external
finance premium for banks.
The Ramsey policy is obtained by maximizing the expected sum of discounted period utility
functions subject to the equilibrium conditions of the competitive economy.47 The alternative
policies are represented by different values of the coefficients φπ , φy and φB in the policy rule
Rt
=
R
Rt−1
R
ρR "
π t φp
π
φy φB #1−ρR
yt
ef pB
t
,
y
ef pB
(79)
where ef pB denotes the steady state value of the external finance premium for banks.
Let fr0 be the welfare of the Ramsey policy conditional on the state in period 0 being the deterministic steady state,
fr0 = E0
(∞
X
t=0
βt
(hr )1+ν
log crt − ψ t
1+ν
)
,
(80)
)
a 1+ν
(h )
.
β t log cat − ψ t
1+ν
(81)
and let the conditional welfare of an alternative policy be
(
fa0 = E0
∞
X
t=0
The welfare costs ϑ of a particular alternative policy are defined as the share of the consumption
process in the Ramsey monetary policy regime that the household is willing to forgo in order to
reach the same conditional welfare in the alternative regime as in the Ramsey regime. Thus, ϑ
is defined as
(∞
)
r 1+ν
X (h
)
fa0 = E0
β t log ((1 − ϑ)crt ) − ψ t
.
(82)
1
+
ν
t=0
47
We only use the household’s utility function for our normative analysis. The fact that banks and intermediate
goods producers also consume is not taken into account. We may neglect banks and intermediate goods producers because they are risk neutral agents. Their risk neutrality implies that their mean consumption is not affected by
the volatility of our model. Thus, taking into account the consumption of banks and intermediate goods producers
would alter the absolute level of welfare in every monetary policy regime by the same amount. However, it would
not affect the welfare ranking among the regimes (this argument has first been put forth by Faia and Monacelli,
2007). We thus only include household utility in the welfare analysis.
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Note that we can write
fs0
(hs )1+ν
+ E0
= log(cs0 ) − ψ 0
1+ν
(∞
X
t=1
)
s 1+ν
)
(h
t
β t log (cst ) − ψ
1+ν
(83)
for s ∈ {r, a} and hence, using (82),
fa0 − fr0 = log (1 − ϑ) + log (cr0 ) − log (cr0 ) +
(∞
)
(∞
)
(∞
)
X
X
X
+E0
β t log(1 − ϑ) + E0
β t log(crt ) − E0
β t log(crt ) . (84)
t=1
t=1
P
t
Noting that E0 { ∞
t=1 β log(1 − ϑ)} =
β
(1
1−β
t=1
− ϑ), and solving (84) for ϑ we get48
ϑ = 1 − exp [(1 − β)(fa0 − fr0 )]
(85)
Similar to Faia and Monacelli (2007), we first evaluate some ad-hoc rules to see what role the
central bank’s reaction to the external finance premium for bank plays for standard values of
the inflation and output coefficient. Table III.3 shows these rules. In particular, we look at (i) a
rule that only reacts to inflation; (ii) a rule that reacts to inflation and positively to the external
finance premium for banks; (iii) a rule that reacts to inflation and negatively to the external
finance premium for banks; (iv) a standard Taylor rule; (v) a standard Taylor rule plus a positive
reaction on the external finance premium for banks; (vi) a standard Taylor rule plus a negative
reaction on the external finance premium for banks.
The first three data columns in table III.3 show the specifics of these interest rate rules. Data
column four in table III.3 shows the conditional welfare as described in 81, while data column
five shows the welfare loss of switching from the optimal policy to the respective policy rule as a
percentage of steady state consumption (equation 85). As is apparent in table III.3, the addition
48
We rely on a second-order approximation of the model to compute ϑ. As explained in Schmitt-Grohe and Uribe
(2007) and Faia and Monacelli (2007), a first-order approximation of the model cannot be used to conduct welfare
rankings of different policies since in this case the expected value of an endogenous variable equals its steady
state value. Comparing two variables with the same steady state thus would indicate a welfare difference of zero.
Instead, when using a second-order approximation, the expected value of an endogenous variable equals the
steady state of that variable plus a constant "correction-term" which depends on the model’s volatility. For further
details see Schmitt-Grohe and Uribe (2007). Furthermore, as the welfare results depend on volatility, we cannot
use the calibration of the shocks’ standard deviation used in section 5. There, we chose the standard deviations
to yield a one percent initial decrease in output for comparison purposes. As the implied shock sizes are big in
this case, there would be implausibly large welfare gains from switching to the optimal policy. For the welfare
considerations in this section we therefore employ standard deviations of the shocks that are commonly described
in the literature as being empirically relevant. Please see the calibration section for a detailed description of the
shock specification used here. Note that the qualitative welfare results do not change for the shock sizes used in
section 5.
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Tab. III.3: Interest rate rules and associated welfare results.
Rule
φπ
φy
φB
Welfare ϕ ∗ 100
Rule with inflation only (RI)
1.5
0
0
-8.6095
1.92
RI plus positive reaction to BFC (RI and φB > 0)
1.5
0 0.3 -10.1100
3.38
RI plus negative reaction to BFC (RI and φB < 0)
1.5
0 -0.3
-7.6727
0.99
Standard Taylor rule (STR)
1.5 0.125
0
-7.3018
0.63
STR plus positive reaction to BFC (STR and φB > 0) 1.5 0.125 0.3
-7.6378
0.96
STR plus negative reaction to BFC (STR and φB < 0) 1.5 0.125 -0.3
-7.1001
0.43
Note: φπ , φy and φB are the reaction coefficients in the policy rule 79. The welfare column shows the conditional
welfare obtained from 81 and ϕ ∗ 100 describes the percentage of steady state consumption lost from switching to
a non-optimal policy.
of a negative reaction to the external finance premium for banks in an otherwise unaltered policy
rule increases welfare, while the addition of a positive reaction to the external finance premium
for banks decreases welfare. Moreover, comparing rows one and four, two and five, and three
and six, respectively, we see that a reaction to output in an otherwise unchanged policy rule
improves welfare results. This is because demand shocks - causing movement of output and
inflation in the same direction - play a significant role in our model.
To check whether the welfare improving negative reaction to the external finance premium only
picks up policy rate movements that could equally well be evoked by a higher output coefficient
in the policy rule, we do the following. For a policy rule which only reacts to inflation and
output, we fix the inflation coefficient at its usual value of 1.5 and search for the value of the
output coefficient which maximizes conditional welfare (which is 0.3). We then add to this rule
a negative reaction to the external finance premium for banks and note that welfare increases.
Moreover, increasing the output coefficient after the addition of the reaction to the external
finance premium still results in decreasing welfare. Hence, reacting negatively to the external
finance premium for banks yields welfare improvements that cannot be achieved by a stronger
positive reaction to output.
To gain more general insights into the role of the external finance premium in the policy rule,
we fix the output coefficient to 0.3 and search for the optimal coefficients for inflation and the
finance premium jointly.49 The welfare surface emerging from this exercise is displayed in figure
III.10. For a given value of the output coefficient, the optimal coefficients for inflation and the
external finance premium of banks are 3 and -1.5. The main result emerging from figure III.10 is
that there is a positive effect of responding to the external finance premium of banks for all levels
of the inflation coefficient. The other important message from figure III.10 is the important role
for inflation stabilization: First, the highest welfare levels are reached for an inflation coefficient
49
For the inflation coefficient, we search over the interval [1;3]. We choose one as the lower bound since this
value ensures the abidance of the Taylor principle. For the upper bound, a value of φpi > 3 only yields minimal
welfare gains. This upper bound can also be found in the literature, for example in Schmitt-Grohe and Uribe (2007).
For the coefficient of the external finance premium for banks, we search in the interval [-5;1.5]. Looking at figure
III.10, it is clear that welfare is decreasing beyond these bounds.
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131
on the upper bound of our search interval. Second, we see that the reaction to bank financing
conditions is less welfare-improving for higher values of the inflation coefficient. The important
role for inflation stabilization is in line with much of the literature on optimal monetary policy.
Fig. III.10: Welfare surface for different combinations of the policy reaction parameters
Note: The figure depicts different combinations of the parameters on inflation and the external finance premium
for banks. The output coefficient is fixed at 0.3.
Figure III.11 shows the welfare losses relative to the optimal policy as a percentage share of
the optimal consumption process (computed as shown in equation (85)) for different combinations of the coefficients for inflation and the external finance premium for banks. The optimal
monetary policy rule comes very close to the Ramsey-optimal policy, with welfare losses close
zero. Figure III.11 also indicates the welfare costs that arise from deviating from the optimal
combination of parameters. These can be substantial for highly negative or positive values of
the parameter for the external finance premium of banks. For φB = 0 — that is, if the central
bank does not react at all to bank financing conditions — the welfare costs from deviating from
the optimal parameter amount to approximately 0.3% of the optimal consumption process if the
inflation reaction parameter is fixed at its optimal value.
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Fig. III.11: Loss surface for different combinations of the central bank’s reaction parameters
Note: The figure depicts different combinations of the parameters on inflation and the external finance premium
for banks. The welfare loss is expressed as percentage share of the optimal consumption process. The output
coefficient is fixed at 0.3.
Discussion: Motivation for unconventional monetary policy
The last section showed that in an economy where the monetary policy transmission is impaired
by developments in the banking sector, conventional monetary policy - the central bank setting
the interest rate - can improve welfare results by reacting to bank financing conditions. However,
the following question arises: If the transmission of monetary policy is disturbed in the banking
sector should the central bank try to circumvent this transmission channel altogether? In this
sense, our model may provide a motivation for unconventional monetary policies, that is, policies
where the central bank lends directly in private credit markets.
A model that can reproduce such a scenario is the one by Gertler and Karadi (2011). They rely
on a model with a single financial friction in the form of moral hazard/costly enforcement: At the
beginning of a period a bank can steal a fraction of its assets (and hence household deposits)
at the cost of the household forcing the bank into bankruptcy. In this case the household can
recover the fraction of assets that has not been embezzled but recovering the embezzled funds
is too costly. This kind of friction, similarly as the BGG framework, induces tightening lending
standards in downturns that depend on bank balance sheet conditions. In contrast, the central
bank can intermediate funds between the household and the real economy without frictions
because it can commit to honor its debt by assumption. However, the central bank is less
6 Bank funding costs and lending rates to the real economy: Evidence from the euro zone
133
efficient in lending to the real economy than banks. In a downturn, the costs of the banks’
balance sheet constraint can exceed the central bank’s efficiency costs of intermediating funds.
Thus, unconventional monetary policy can yield welfare gains.
Because we use a different credit market framework we cannot directly examine whether a
deterioration of bank balance sheets warrants specific unconventional monetary policies. However, the result that severely deteriorated bank balance sheet decrease the effectiveness of the
core monetary policy instrument in principle makes room for other, unconventional instruments.
Challenged by the hampered transmission of the policy rate, a monetary authority can react in
two ways. First, it can employ additional instruments to reach its goal. The purchase of asset
backed securities or government bonds belong to this strategy. With the purchase of asset
backed securities, central banks can ease borrowing conditions for, say, mortgages or loans
to small and medium enterprises. With the purchase of government bonds, central bank can
lower the slope of the yield curve which implies a lower opportunity cost for bank lending on
long-term lending and should result in lower borrowing rates for the real economy at large.
The second strategy against the decreased effectiveness of the policy rate instrument is to
directly tackle its source, namely the deterioration of bank balance sheets. Multiple policies of
the recent past come to mind. Besides outright capital injections, the practice of paying interest
on reserves or the ECB’s Long-Term Refinancing Operations (LTROs) can be interpreted as
measures to rebuild bank balance sheets and/or ease bank financing conditions.
In principle, the dynamics of our model thus warrant the observed and discussed crisis measures of the ECB in the recent past. In its current setup, our model is unsuited for a detailed
comparison of the stated unconventional monetary policies with conventional policy rate setting.
We leave this issue for future research.
6
Bank funding costs and lending rates to the real economy: Evidence
from the euro zone
Association between bank funding costs and lending rates to the real economy
One main implication of our model in section 3 is that higher bank funding costs are transmitted
into higher lending rates to the real economy. That is, banks do not bear the full increase in
funding costs themselves, but pass at least some of the increase on to their borrowers. Lacking detailed microeconomic data, it is impossible to establish causality. However, we can use
aggregate data provided by the ECB to provide suggestive evidence of the positive association
between bank funding costs and lending rates.50
50
See the Appendix on page 142 for a detailed description of the data.
134
Our econometric model is guided by the distinction between three components in real sector
lending rates. Average lending rates to the real economy include a component reflecting the
monetary policy rate, the average borrower and business cycle risk, as well as bank financing
costs. To control for the first determinant in the lending rate toward the real sector, we include
the ECB interest rate for Main Refinancing Operations (MROs). According to the ECB, these
operations account for the bulk of central bank related liquidity in the euro zone’s banking system and the associated interest rate is the one commonly referred to as policy rate in public
discourse.
Controlling for the second component in the lending rate towards the real sector is more difficult.
To control for business-cycle related risks we include annualized rates of real GDP growth at
the national level. Unfortunately, we are unaware of comprehensive data that can control for
the risk composition of the borrowers in any given quarter. Absent any further information, the
estimation below is carried out under the assumption that the composition of the borrowers
varies in proportion with the business cycle. The annualized rates of real GDP growth thus
serve to capture both the average borrower and business cycle risk.
The measure of bank funding costs, in line with our theoretical model, are average interest rates
on deposits with fixed maturity, which account for roughly 15 percent of euro zone bank liabilities.51 In line with the conjecture of the ECB, our dependent variable are average lending rates
to non-financial companies (NFCs). As banks may not change the terms of existing contracts,
only the interest rates on new business are used in the estimations.
Finally, we include the slope of the yield curve to account for maturity mismatch. The observed
interest rates on bank lending correspond to long-term loans, while the bank financing costs
relate to short-term funding. We control for the expected long-term evolution of interest rates
using the difference between long-term and short-term rates at the national level. The measure
51
In our sample, deposits with fixed maturity account for roughly 15 percent of bank liabilities inside the eurozone.
A further 20 percent of bank liabilities stem from overnight deposits and deposits redeemable at notice. While
interest rate data on the latter are unavailable, overnight deposits do not deviate from the central bank policy rate.
This is unsurprising as elusive overnight deposits yield little bargaining power to the depositor. He has thus no
means to express risk-concerns through the interest rate, but will rather move his funds elsewhere.
In our view, the missing volatility of overnight deposit rates leaves the validity of our conjecture intact. In a homogenous agent model, the claim that bank funding costs may deviate from the central bank policy rate demands
that a significant proportion of its creditors show the desired behavior. Arguably, the remaining sources of bank
funding do have the necessary bargaining power to demand higher interest rates for their funds. Besides capital
and reserves, a further 50 percent of bank liabilities stems from inter-bank lending, debt securities or moneymarket funds. In our view it is a credible assumption that this class of professional investors is able to express
any risk concerns through higher interest rate demands. Following this claim, about 65 percent of bank liabilities
originate from risk-sensitive sources.
We chose to leave the claim of risk-sensitive professional investors unsupported by further data. Unfortunately,
representative euro zone-wide data about interest rates on inter-bank lending, lending from money market funds
or in the form of debt securities is either not publicly available, or its generation demands disproportionate effort.
For evidence of recent price-differentiation in bank debt securities in the Eurozone see Gilchrist and Mojon (2013).
For evidence of price-differentiation in secured and unsecured inter-bank and money market lending in Europe see
e.g. Kraenzlin and von Scarpatetti (2011), Afonso, Kovner, and Schoar (2011), Heijmans, Heuver, and Walraven
(2011).
135
of national long-term rates is the yield on central government bonds with a residual maturity of
10 years. As the short-term rate, we employ the ECB policy rate. As stated, our measure of the
slope of the yield curve is constructed as the difference between the two.
To account for national inflation differentials, country-specific measures of the Harmonized Index of Consumer Prices (HICP) are the final control variable added to our econometric model.
The estimation is based on national, quarterly data from eurozone member countries since
2003-Q1 or upon entry into the currency union. To allow for an interpretation of the coefficients
as changes in percentage points, the data are transformed to a common base.52
To assess the robustness of the coefficients, we re-estimate the model with either country fixed
effects, year fixed effects, or both. Also, the estimations are performed for the contemporaneous
values of the independent variables as well as their first lag. We deem the latter specification
more reliable as it avoids endogeneity concerns and is a more accurate description of the
agent’s information set. Our preferred specification includes the independent variables at their
first lag as well as all mentioned fixed effects (see equation 4 in table III.4).53
As this chapter is concerned with recession scenarios, the above estimation is repeated for a
split sample. To this end, we include a binary dummy variable that is equal to one for observations more recent than 2008-Q3, and equal to zero otherwise. To account for differences
between the years prior and after the onset of the Great Recession, this dummy variable is
interacted with all independent variables of our baseline model. Country and year fixed effects
remain included without interaction.
To account for serial correlation in the error term, we employ a Prais-Winsten estimator for all
specifications. The Durbin-Watson statistics pre and post this transformation are reported at
the bottom of the table. Recall that a statistic close to 2 implies no serial correlation in the
error term. Furthermore, we generalize the estimation to account for heteroskedasticity. The
asterisks mark the conventional degrees of significance.
52
All variables have been transformed into decimals i.e. 4% interest is included as .04 and likewise for real GDP
and inflation.
53
To economize on space, the table including all tested specifications can be found in the Appendix. The estimation equation and further data description is also relegated to the Appendix starting on page 142. For comparability,
we include the specification including the contemporaneous values for the independent variables in this section.
136
Tab. III.4: Lending rates and borrowing cost in the eurozone in the Great Recession
Dependent: Lending rate to NFCs
(1)
(2)
(3)
(4)
Borrowing cost, this quarter
0.718***
(0.061)
Borrowing cost, last quarter
0.297***
(0.065)
Constant
0.016***
(0.002)
0.793***
(0.066)
-0.126
(0.082)
0.326***
(0.056)
-0.053
(0.089)
0.004
(0.018)
-0.010
(0.032)
-0.008*
(0.004)
-0.009
(0.010)
0.048
(0.037)
0.045
(0.043)
0.008***
(0.003)
0.013***
(0.003)
Observations
Country fixed effects
Year fixed effects
R-squared
Adj. R-squared
Degrees of freedom
Durbin-Watson statistic, post
Durbin-Watson statistic, pre
559
yes
yes
0.883
0.877
528
1.718
0.348
559
yes
yes
0.884
0.876
522
1.800
0.439
Coefficient on interaction term
ECB policy rate, this quarter
0.282***
(0.031)
Inflation, this quarter
-0.009
(0.018)
Real GDP growth, this quarter
-0.014**
(0.006)
Yield curve slope, this quarter
0.086***
(0.019)
Crisis dummy
Constant
0.019***
(0.002)
0.522***
(0.065)
-0.208***
(0.079)
0.636***
(0.059)
-0.387***
(0.091)
0.042**
(0.017)
0.002
(0.026)
-0.010*
(0.005)
0.029***
(0.009)
0.173***
(0.054)
-0.040
(0.060)
0.019***
(0.003)
0.007***
(0.002)
Observations
Year fixed effects
R-squared
Adj. R-squared
Degrees of freedom
553
yes
yes
0.838
0.829
522
1.761
0.510
553
yes
yes
0.855
0.845
516
2.013
0.493
ECB policy rate, last quarter
0.383***
(0.066)
Inflation, last quarter
0.041**
(0.018)
Real GDP growth, last quarter
0.006
(0.006)
0.157***
(0.021)
Crisis dummy
In line with the model mechanisms in section 3, the results reported in table III.4 confirm bank
funding costs to be a relevant determinant of lending rates to NFCs. The coefficient for interest
paid on deposits with fixed maturity is positive, of considerable magnitude and strongly significant. In the specification with lagged independent variables, which includes our preferred one,
bank funding costs turn out to have the strongest of all tested associations with lending rates
to NFCs. The stated pattern carries over to the estimation including the crisis dummy and its
interaction.
137
Note that our preferred specification (equation 4) points towards significant differences across
the two tested periods. While ECB policy rates and bank funding costs appear to be of roughly
equal importance prior to the Great Recession, their influence drops significantly during the crisis. That is, since the beginning of the financial crisis lending rates to NFCs were less sensitive
to bank funding conditions, be it funding from the central bank or from depositors.
It is also informative to look at the evolution of the coefficient on the ECB policy rates. According
to this estimate, lending rates have lost some association with ECB policy rates since 2008-Q3.
The sum of the individual coefficient and its interaction with the crisis dummy is only about two
thirds the value of the pre-crisis estimate. Contrary to the fading influence of monetary policy
rates, the significant association between bank financing cost and lending rates remains intact.
The sum of the individual coefficient and the crisis dummy matches the pre-crisis estimate
closely. This evidence suggests that bank lending rates remain sensitive to bank funding costs
in the deposit market as well as the ECB policy rate throughout the studied period.
Sensitivity of bank funding costs to the leverage ratio
The second main implication of our model in section 3 is the sensitivity of bank funding conditions to the bank leverage ratio. Recall that in our model banks need to pay a markup over the
risk-free rate that depends on their leverage ratio i.e. the ratio of total assets over equity. To test
this implication, we make use of a reduced form equation for the external finance premium (the
ratio of financing costs to the risk free rate) as in BGG. According to their model, the sensitivity
of the external finance premium to the leverage ratio can be approximated by the parameter ν
in
log (EF Pt ) = ν [log (assetst ) − log (equityt )] .
Our estimation is based on this reduced form. Using the above described sources, we employ
log values of quarterly aggregate bank balance sheet data and the ratio of bank funding costs
over the ECB policy rate. In line with the reduced form of BGG there are no further independent
variables, nor is there a constant included in the estimation. To assess robustness, country
and year fixed effects are included. As above, we interact a crisis dummy with the independent
variable to identify differences before and after 2008-Q3. Note however that only this interaction
term is included. In order to preserve the reduced form, the crisis dummy is not included individually. As above, we estimate by OLS and correct for serial correlation and heteroskedasticity
in the error term.
The results in table III.5 provide support for the a positive association of bank financing conditions and the leverage ratio.54 The estimates of the sensitivity are positive and significant,
54
See the Appendix on page 142 for further results, the estimation equation and data description.
138
7 Conclusion
although less pronounced when controlling for country- and year-specific effects. The estimates are of similar magnitude whether the leverage ratio is included with its contemporaneous
value or at its first lag. According to our estimates, the elasticity is significantly larger since
2008-Q3. Depending on the specification, the elasticity of the bank EFP to the leverage ratio
has tripled or even only emerged during the more recent period. The relevance of leverage for
the bank EFP has also increased sharply in the second sample. While only 5 percent of the
variation in bank external financing costs could be explained by leverage prior to 2008-Q3, the
inclusion of the interaction term raises its explanatory power to 36 percent overall.
Tab. III.5: Elasticity of bank borrowing cost with respect to the leverage ratio
Dependent: Bank EFP (log)
(5)
(6)
(7)
(8)
leverage ratio (log), this period
0.202***
(0.036)
0.096***
(0.019)
0.021
(0.045)
-0.019
(0.052)
leverage ratio (log), last period
0.199***
(0.011)
Observations
Year fixed effects
R-squared
Adj. R-squared
Degrees of freedom
7
585
no
no
0.048
0.0461
584
1.463
0.0889
568
no
no
0.366
0.363
566
1.669
0.178
(9)
(10)
(11)
(12)
0.250***
(0.039)
0.119***
(0.021)
0.195***
(0.010)
0.066
(0.046)
0.023
(0.044)
0.190***
(0.008)
568
no
no
0.061
0.0593
567
1.424
0.0877
568
no
no
0.365
0.363
566
1.673
0.178
568
yes
yes
0.414
0.385
541
2.024
0.734
568
yes
yes
0.583
0.562
540
1.938
0.521
0.191***
(0.008)
585
yes
yes
0.434
0.407
558
2.043
0.728
568
yes
yes
0.585
0.563
540
1.939
0.521
Conclusion
Recently, policy makers have conjectured that monetary policy is not transmitted undisturbed to
bank financing costs and hence to lending rates for the real economy. To shed light on the plausibility of such a scenario we construct a business cycle model with a financial contract between
households, represented by investors, and banks as well as between banks and intermediate
firms. Unlike conventional financial accelerator models, the banking sector is an independent
agent in our model whose refinancing costs vary with its leverage ratio. Moreover, contrary to
existing models, banks can incur losses due to a non-state-contingent lending rate between
banks and intermediate firms.
7 Conclusion
139
Our model can reproduce a scenario where policy rate cuts due to a depressed economy are
not transmitted fully or at all to bank financing costs and hence the real economy. However,
the movements in bank financing costs induced by real sector shocks - such as an exogenous
spending, a risk or a preference shock - are not big enough so as to have a significant impact
on investment or aggregate output.
Further analysis suggested that the increases in loan default rates associated with these shocks
do not result in sizable endogenous losses for the banking system. Hence, the exposure of bank
net worth to aggregate downturns is small. By contrast, a shock which exogenously depletes
bank net worth directly by a significant amount shows that leverage-sensitive bank financing
costs have the potential to cause a significant economic downturn.
In the presence of leverage sensitive bank financing costs, it is optimal for the central bank
to decrease interest rates if bank financing conditions tighten. In this way, it can mitigate the
incomplete transmission of movements in the policy rates to bank financing costs. Our analysis
of optimal policy rules also shows that inflation stabilization remains of high importance for
welfare.
We also presented suggestive evidence for two of our main model implications. First, aggregate
euro area data confirm a positive relationship between bank financing costs and lending rates to
the real economy. Second, bank financing costs are positively related to the bank leverage ratio.
The relevance of the latter relationship seems to be more pronounced in economic downturns.
Future research could focus on an endogenous mechanism associated with large bank net
worth decreases. One possibility is to incorporate additional asset classes such as housing
finance, which turned out to be of particular relevance in the recent episode. Another possibility
is to increase the sensitivity of bank funding costs to the the state of the aggregate economy
more generally. In the structure of our model, this sensitivity can be increased by increasing
the cyclicality and/or magnitude of intermediate good producer default; or augmenting the riskconsciousness of the depositors.
A Data description and additional estimations
A
140
Data description and additional estimations
data description and summary statistics
The data used in the motivation of this chapter consist of observations on the national level for
all eurozone members. The time series start on 1. January 2003 as deposit rate date is not
available for prior periods. For countries that have joined the monetary union after 1. January
2003, only observations after the relevant entrance date were included. The data on real GDP
is only available until and including 2012Q4 thus limiting the time span of the econometric
analysis.
Real GDP and inflation have been transformed into annual growth rates.
No further transformations have been applied to the data.
Bank assets: Country-specific, quarterly values for total assets and stated composition taken
from the ECB MFI balance sheet statistics.
Bank liabilities: Country-specific, quarterly values for total assets and stated composition taken
from the ECB MFI balance sheet statistics.
Bank EFP: Country-specific, quarterly values calculated as the ratio of funding costs over the
ECB MRO rate.
Bank leverage: Country-specific, quarterly values calculated as total liabilities over «capital and
reserves».
ECB MRO rate: Quarterly values for official MRO rates taken from Eurostat (Database ID:
irt_cb_q).
Funding cost: Country-specific, annualized agreed percentage rate on new business in deposits with agreed maturity sourced from non-financial corporations, households or nonprofit institutions. Deposits of all maturities included. Monthly data taken from Eurostat
(Database ID: irt_rtl_dep_m).
Inflation: Country-specific, simple averages of monthly values for Harmonized Index of Consumer Prices (HICP) taken from Eurostat (Database ID: prc_hicp_midx).
Lending rate: Country-specific, annualized agreed percentage rate on new business in loans
to non-financial companies. Loans of all maturities included. Monthly data taken from
Eurostat (Database ID: irt_rtl_lnfc_m).
Real GDP: Country-specific, quarterly values of seasonally adjusted data taken from Eurostat
(Database ID: namq_gdp_c).
141
Slope of the yield curve: Country-specific, quarterly values for central government bond yields
with a residual maturity around 10 years taken from Eurostat (Database ID: irt_euryld_q).
The slope of the yield curve is constructed as the difference between the bond yields and
the ECB policy rate.
Tab. III.6: Summary statistics
Variable
N
Mean
Std. Dev
Min
Max
bank EFP
bank leverage ratio
lending rate
funding cost
ECB MRO rate
inflation
real GDP growth
yield curve slope
585
585
585
585
585
585
567
576
1.794889
15.80932
0.0466261
0.0278033
0.0197094
0.0232645
0.0321111
.0240618
1.027908
5.295728
0.0126601
0.0087905
0.011142
0.0132375
0.0402423
.0263604
0.6571429
4.87264
0.0207
0.0064
0.0075
-0.0275013
-0.106617
-.0007
6.031111
29.1174
0.0784333
0.0543333
0.0425
0.064561
0.1386239
.244
estimation equations and additional results
association between bank borrowing cost and lending rates
The full estimation equation is
L
D
GOV
Ri,t
= β0 + β1 Ri,t(−1)
+ β2 Rt(−1) + β3 πi,t(−1) + β4 ∆yi,t(−1) + β5 Ri,t(−1)
+
D
+β6 crisis × Ri,t(−1) + β7 crisis × Rt(−1) + β8 crisis × πi,t(−1) +
GOV
+β9 crisis × ∆yi,t(−1) + β10 crisis × Ri,t(−1)
+
+β11 countryi + β12 yearj + i,t
The following table displays the results for the different specifications tested here. All model
use the stated Prais-Winsten estimator and differ along the inclusion of country and year fixed
effects.
142
Tab. III.7: Lending rates and borrowing cost in the eurozone, different specifications
Borrowing cost, this quarter
ECB policy rate, this quarter
Inflation, this quarter
Real GDP growth, this quarter
Constant
Observations
Year fixed effects
R-squared
Adj. R-squared
Degrees of freedom
(13)
(14)
(15)
(16)
0.868***
(0.069)
0.321***
(0.038)
0.012
(0.017)
0.008
(0.006)
0.067***
(0.025)
0.015***
(0.003)
0.836***
(0.053)
0.322***
(0.037)
0.016
(0.018)
0.008
(0.006)
0.070***
(0.021)
0.009***
(0.002)
0.718***
(0.066)
0.295***
(0.029)
-0.011
(0.018)
-0.013**
(0.006)
0.088***
(0.020)
0.024***
(0.003)
0.718***
(0.061)
0.282***
(0.031)
-0.009
(0.018)
-0.014**
(0.006)
0.086***
(0.019)
0.016***
(0.002)
559
no
no
0.734
0.732
553
1.990
0.106
559
yes
no
0.864
0.859
538
1.888
0.421
559
no
yes
0.789
0.783
543
1.769
0.0934
559
yes
yes
0.883
0.877
528
1.718
0.348
143
Tab. III.8: Lending rates and borrowing cost in the eurozone, different specifications (continued)
Borrowing cost, last quarter
ECB policy rate, last quarter
Inflation, last quarter
Real GDP growth, last quarter
Yield curve slope, last quarter
Constant
Observations
Year fixed effects
R-squared
Adj. R-squared
Degrees of freedom
(17)
(18)
(19)
(20)
0.048
(0.070)
0.700***
(0.066)
0.050***
(0.016)
0.004
(0.006)
0.167***
(0.022)
0.026***
(0.002)
0.087
(0.073)
0.705***
(0.061)
0.046***
(0.017)
0.002
(0.007)
0.177***
(0.021)
0.016***
(0.002)
0.275***
(0.072)
0.367***
(0.068)
0.047**
(0.019)
0.009
(0.006)
0.144***
(0.022)
0.030***
(0.002)
0.297***
(0.065)
0.383***
(0.066)
0.041**
(0.018)
0.006
(0.006)
0.157***
(0.021)
0.019***
(0.002)
553
no
no
0.672
0.669
547
1.740
0.115
553
yes
no
0.825
0.818
532
1.683
0.369
553
no
yes
0.700
0.692
537
1.788
0.117
553
yes
yes
0.838
0.829
522
1.761
0.510
144
association between bank borrowing cost and leverage ratio
The full estimation equation is
log
D
Ri,t
Rt
!
= β0 log
liabilitiesi,t(−1)
capitali,t(−1)
liabilitiesi,t(−1)
+ β1 crisis × log
+
capitali,t(−1)
+β2 countryi + β3 yearj + i,t
The following table displays the results for the different specifications tested here. All model
use the stated Prais-Winsten estimator and differ along the inclusion of country and year fixed
effects.
Tab. III.9: Bank EFP and leverage ratio, different specifications
Dependent: Bank EFP
(21)
(22)
(23)
(24)
(25)
(26)
(27)
(28)
leverage ratio (log), this period
0.202***
(0.036)
0.142
(0.107)
0.094***
(0.020)
0.021
(0.045)
0.096***
(0.019)
0.199***
(0.011)
-0.024
(0.061)
0.206***
(0.011)
0.053***
(0.018)
0.190***
(0.009)
-0.019
(0.052)
0.191***
(0.008)
585
no
no
0.048
0.0461
584
1.463
0.0889
585
yes
no
0.073
0.0450
568
1.463
0.121
585
no
yes
0.258
0.243
574
2.022
0.390
585
yes
yes
0.434
0.407
558
2.043
0.728
568
no
no
0.366
0.363
566
1.669
0.178
568
yes
no
0.442
0.423
550
1.674
0.277
568
no
yes
0.494
0.483
556
1.929
0.294
568
yes
yes
0.585
0.563
540
1.939
0.521
Observations
Year fixed effects
R-squared
Adj. R-squared
Degrees of freedom
145
Tab. III.10: Bank EFP and leverage ratio, different specifications (continued)
Dependent: Bank EFP
(29)
(30)
(31)
(32)
(33)
(34)
(35)
(36)
leverage ratio (log), last period
0.250***
(0.039)
0.342***
(0.123)
0.131***
(0.020)
0.066
(0.046)
0.119***
(0.021)
0.195***
(0.010)
0.080
(0.056)
0.202***
(0.011)
0.068***
(0.017)
0.189***
(0.009)
0.023
(0.044)
0.190***
(0.008)
568
no
no
0.061
0.0593
567
1.424
0.0877
568
yes
no
0.080
0.0514
551
1.434
0.122
568
no
yes
0.247
0.232
557
1.989
0.387
568
yes
yes
0.414
0.385
541
2.024
0.734
568
no
no
0.365
0.363
566
1.673
0.178
568
yes
no
0.430
0.411
550
1.673
0.278
568
no
yes
0.492
0.481
556
1.929
0.293
568
yes
yes
0.583
0.562
540
1.938
0.521
Observations
Year fixed effects
R-squared
Adj. R-squared
Degrees of freedom
146
B Derivation of the external finance premia equations
B
Derivation of the external finance premia equations
Equation for the bank-investor contract
The calculations below are re-arrangements of the FOCs from the bank’s problem. For convenience, these FOCs are repeated here:
Et
B
Rt+1
Rt
0
B
0
Ψ0 (χ̄t+1 ) − ΥB
= 0
(86)
t Ψ (χ̄t+1 ) − µ M (χ̄t+1 )
B
Rt+1 [1 − Ψ (χ̄t+1 )] + ΥB
Ψ (χ̄t+1 ) − µB M (χ̄t+1 ) − 1
= 0
(87)
t
Rt
B
Lt = Rt Lt − NtB (88)
Ψ (χ̄t+1 ) − µB M (χ̄t ) Rt+1
From equation (86), we receive an expression for ΥB
t :
ΥB
=
t
Ψ0 (χ̄t+1 )
Ψ0 (χ̄t+1 ) − µB M 0 (χ̄t+1 )
(89)
where
Ψ0 (χ̄t+1 ) = 1 − Fχ (χ̄t+1 )
(90)
M 0 (χ̄t+1 ) = χ̄t+1 fχ (χ̄t+1 )
(91)
Furthermore, we can re-arrange (88) to Ψ (χ̄t+1 ) − µB M (χ̄t ) =
(87). We receive:
(
Et
Rt (Lt −NtB )
B L
Rt+1
t
, and plug it into
"
#)
B
B R L − NB
Rt+1
R
t
t
t+1 t
[1 − Ψ (χ̄t+1 )] + ΥB
−1
= 0
t
B
Rt
Rt
Rt+1 Lt
B
NtB
Rt+1
[1 − Ψ (χ̄t+1 )]
= E t ΥB
Et
t
Rt
Lt
(92)
which commonly expressed as
Lt
NtB
= Et


ΥB
t


B
 Rt+1
[1 − Ψ (χ̄t+1 )] 
Rt
=φ
B
B
Rt+1
, χ̄t+1
Rt
(93)
The external finance premium equation presented above is the inverted form of equation (93):The
function ΦB (.) referred to in the main text is thus defined as
147
B Derivation of the external finance premia equations
Et
B
Rt+1
= Φ
B
Lt
, χ̄t+1 Rt .
NtB
Evidently ΦB (.) is determined also by the expected share of defaulting banks Et {χ̄t+1 }. Loglinearizing the model reveals, that the influence of expected default remains constant for fluctuations around the non-stochastic steady state.
Equation for the bank-entrepreneur contract
The calculations below are re-arrangements of the FOCs from the intermediate firm’s problem.
For convenience, these FOCs are repeated here:
Et
k
Rt+1
B
Rt+1
Γ0 (ω̄t+1 ) − ΥIt Γ0 (ω̄t+1 ) − µI G0 (ω̄t+1 ) = 0
(94)
k
Rt+1 [1 − Γ (ω̄t+1 )] + ΥIt
Γ (ω̄t+1 ) − µI G (ω̄t+1 ) − 1
= 0
(95)
B
Rt+1
k B I
Et Γ (ω̄t+1 ) − µI G (ω̄t+1 ) Rt+1
Qt kt = Et Rt+1
Qt kt − N(96)
t
From equation (94), we get ΥIt =
ogous to the previous section.
Γ0 (ω̄t+1 )
,
Γ0 (ω̄t+1 )−µI G0 (ω̄t+1 )
and the definition of its components is anal-
Again, we re-arrange the participation constraint to Et
Γ (ω̄t+1 ) − µI G (ω̄t+1 ) =
B
Et {Rt+1
}(Qt kt −NtI )
k
Et {Rt+1
}Qt kt
and use this in (95):
(
Et
"
#)
B I
k
k
E
R
Q
k
−
N
Rt+1
R
t t
t+1
t
t+1 t
k [1 − Γ (ω̄t+1 )] + ΥIt
−1
= 0
B
B
Rt+1
Rt+1
Et Rt+1 Qt kt
k
I NtI
Rt+1
[1
−
Γ
(ω̄
)]
=
E
(97)
Et
Υt
t+1
t
B
Qt kt
Rt+1
With the same manipulations as above, we can write:
Et
K
Rt+1
= Φ
I
Qt kt
NtI
B .
Et Rt+1
148
C Derivation of the steady state values
C
Derivation of the steady state values
The steady state values for the variables of the model are computed as follows, using the
parameter values given in table III.1 on page 115.
1. Using steady state inflation Π = 1 and the discount factor β, one can solve for the risk-free
rate R = Πβ .
2. The steady state values of the return on capital and the return on banking are calculated
using the calibrated premia i.e. E RB = RB = ef pB · R and E Rk = Rk = ef pi · RB .
3. To maintain a constant capital stock in the steady state, it must be that i = δk . Using this
insight in the equilibrium condition of the capital good producer, yields the steady state
price of capital q = 1−ϕ 1 i −δ = 1.
[ k ( k )]
4. With final output as the numeraire good, the price of intermediate goods is given by the
inverse of the markup i.e. Px = θ−1
.
θ
5. To receive a ratio of steady state output to capital, we re-arrange the definition of the return
k
Y
= R P−1+δ
.
to capital K
xα
6. Given the calibration assumption of hh = 1, total labor input is given by h = 1.
7. The production function can be re-arranged (first take it to the power
α
1−α
.
Y α ) to find the value for steady state output Y = h K
Y
8. The steady state value of the capital stock thus is K =
K
Y
Y
1
,
1−α
then multiply by
.
9. The steady state value of intermediate net worth is thus given by N I =
NI
K.
QK
10. This allows us to calculate the steady state loan volume L = QK − N I .
11. This in turn gives steady state bank net worth using the calibrated leverage ratio N B =
NB
L.
L
12. Here come steady state deposits D = L − N B .
13. The steady state revenues are calculated using the calibrated values for cut-off productivity i.e. V I = [1 − Γ (ω̄)] Rk K and V B = [1 − Ψ (χ̄)] RB L.
14. Wages are given by their marginal product wj = (1 − α) Ωj px Y .
15. This yields the survival rates γ B =
N B −wB
VB
and γ I =
N I −wI
.
VI
16. Which is all we need for bank and intermediate good producer consumption C j = (1 − γ j ) V j .
149
17. Investment and government consumption are given by I = δK and G = τ Y .
18. Household consumption can than be computed via the budget constraint C = Y − C I −
C B − G − I − µB F (χ̄) RB L − µI F (ω̄) Rk QK.
19. What remains are the Lagrange multiplier of the household Λ = C −σ .
20. The final piece is the disutility weight of labor ψ =
(1−α)ΩΛpx Y
1+ν
(hh )
.
150
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157
C URRICULUM V ITAE
J OHANNES F RITZ
B ORN
C ITIZENSHIP
A DDRESS
E DUCATION
2009 - 2014
11 June 1982 in Oberstdorf, Germany
Austrian
Waffenplatzstrasse 69, 8002 Zürich, Switzerland
PhD in Economics and Finance, specialization in Economics
University of St.Gallen, Switzerland.
2010
Swiss Program for Beginning Doctoral Students in Economics
Study Center Gerzensee, Foundation of the Swiss National Bank
2006 - 2009
Master of Arts in International Affairs and Governance
University of St.Gallen, Switzerland
2006 - 2009
Master of Arts in International Management (CEMS)
University of St.Gallen and ESADE Business School, Barcelona, Spain
2003 - 2006
Bachelor of Arts in International Affairs
University of St.Gallen, Switzerland
2001 - 2003
Prediploma in Economics
University of Hamburg, Germany
2001
Abitur
Gertrud-von-LeFort-Gymnasium, Oberstdorf, Germany
P ROFESSIONAL
2013
158
Consultant to the United Nations Economic and Social Commission
United Nations ESCAP, Bangkok (working off-site from Zurich)
2008 - 2012
Research assistant and editor of the Global Trade Alert Initiative
Chair of Prof. Simon Evenett, PhD, University of St.Gallen
Swiss Institute for International Economics and Applied Economic Research
prior
Internships in the editorial and sales departments of different media houses
e.g. Axel Springer (Hamburg), Austrian Public Radio (ORF, Vienna),
and G+J (Hamburg).

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