Construction and Bayesian estimation of DSGE models for the Euro area [Elektronische Ressource] / vorgelegt von Ernest Pytlarczyk
240 Pages
English
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Construction and Bayesian estimation of DSGE models for the Euro area [Elektronische Ressource] / vorgelegt von Ernest Pytlarczyk

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240 Pages
English

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Construction and Bayesian Estimation of DSGE Models for theEuro AreaDISSERTATIONzur Erlangung des akademischen Gradeseines Doktorsder Wirtschafts- und Sozialwissenschaften(Dr. rer. pol.)des Departments Wirtschaftswissenschaftender Universität Hamburgvorgelegt vonMSc Ernest Pytlarczykaus WarschauHamburg, den 13. Dezember 2006Mitglieder der Promotionskommission:Vorsitzender: Prof. Dr. Georg HasenkampErstgutachter: Prof. Dr. Bernd LuckeZweitgutachter: Prof. Dr. Michael FunkeDas wissenschaftliche Gespräch fand am 16. Mai 2007 statt.iACKNOWLEDGEMENTSManypeoplehavehelpedmeinvariouswayswhileIwasworkingonthisthesis. Greatestthanksare due to Bernd Lucke, my supervisor, for his comments, helpful advice, guidance and continuoussupport. Special thanks go to Matthias Paustian for cooperation on the joint research project andsuggestions on earlier drafts of my thesis. I am also grateful to Heinz Herrmann, the head of theBundesbank research centre, for giving me the opportunity to conduct part of my research at theBundesbank. I would also like to thank Michel Juillard and Stephane Adjemian, both affiliatedwithCEPREMAP as wellas WolfgangLemkeand MichaelKrause from the Bundesbank and KeithKüster from the ECB for discussing my research and subsequent working papers.

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Construction and Bayesian Estimation of DSGE Models for the
Euro Area
DISSERTATION
zur Erlangung des akademischen Grades
eines Doktors
der Wirtschafts- und Sozialwissenschaften
(Dr. rer. pol.)
des Departments Wirtschaftswissenschaften
der Universität Hamburg
vorgelegt von
MSc Ernest Pytlarczyk
aus Warschau
Hamburg, den 13. Dezember 2006Mitglieder der Promotionskommission:
Vorsitzender: Prof. Dr. Georg Hasenkamp
Erstgutachter: Prof. Dr. Bernd Lucke
Zweitgutachter: Prof. Dr. Michael Funke
Das wissenschaftliche Gespräch fand am 16. Mai 2007 statt.
iACKNOWLEDGEMENTS
ManypeoplehavehelpedmeinvariouswayswhileIwasworkingonthisthesis. Greatestthanks
are due to Bernd Lucke, my supervisor, for his comments, helpful advice, guidance and continuous
support. Special thanks go to Matthias Paustian for cooperation on the joint research project and
suggestions on earlier drafts of my thesis. I am also grateful to Heinz Herrmann, the head of the
Bundesbank research centre, for giving me the opportunity to conduct part of my research at the
Bundesbank. I would also like to thank Michel Juillard and Stephane Adjemian, both affiliated
withCEPREMAP as wellas WolfgangLemkeand MichaelKrause from the Bundesbank and Keith
Küster from the ECB for discussing my research and subsequent working papers.
I also greatly benefited from comments and discussions of seminar participants and colleagues
at the University of Hamburg, Deutsche Bundesbank, the University of Frankfurt, CEPREMAP
in Paris, Georgetown University in Washington DC, the National Bank of Poland, Institut für
Wirtschaftsforschung Halle and the Centre for European Integration Studies in Bonn.
Finally, I would like to express my thanks to my friends and companions at the Universities
of Hamburg and Frankfurt, in particular Beatriz, Timo, Atilim, Olaf, Stefan, Jacopo, Omar, and
Theofanis who all took time to provide helpful comments on various draft chapters and articles.
Financial support through a doctoral scholarship from the DAAD is greatly acknowledged.
On a personal level I owe gratitude to my wife, my parents and my grandparents for their
steady and kind encouragement.
iiTo my wife
Niniejszą pracę dedykuję mojej żonie.
iiiContents
1 Introduction 1
1.1 Objective of the study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Summary of the chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Bayesian estimation of DSGE models 4
2.1 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Basic concepts of Bayesian analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Estimation procedure: an overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 DSGE framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4.1 Model solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4.2 Setting up a state space framework . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.3 Using the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5 Prior distributions in DSGE model estimation . . . . . . . . . . . . . . . . . . . . . 16
2.6 Computation of the data likelihood . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.6.1 Problem of filtering and prediction . . . . . . . . . . . . . . . . . . . . . . . 17
2.6.2 Prediction, and likelihood of linear Gaussian models . . . . . . . . 18
2.7 Approximations of the posterior distribution . . . . . . . . . . . . . . . . . . . . . . 20
2.7.1 Posterior simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.7.2 Numerical optimization of the posterior . . . . . . . . . . . . . . . . . . . . 27
2.8 Model evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.8.1 Model-data fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.8.2 Robustness of the results and identification issues . . . . . . . . . . . . . . . 32
3 Sticky contracts or sticky information? Evidence from an estimated Euro area
DSGE model 35
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Outline of the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.2 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2.3 Market clearing, monetary policy and exogenous processes . . . . . . . . . . 40
3.3 Staggered wage and price setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.1 Calvo set up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.2 Sticky information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.4 Equilibrium and linearized equations . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4.1 Log-linearized versions of sticky information price and wage equations . . . 45
3.5 Empirical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.5.1 The data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.5.2 Calibrated parameters and priors . . . . . . . . . . . . . . . . . . . . . . . . 47
3.6 Results for the baseline model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.6.1 Empirical properties of the seminal closed-economy DSGE model . . . . . . 48
iv3.6.2 Model comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.6.3 Extension I: Increasing the truncation point . . . . . . . . . . . . . . . . . . 57
3.6.4 II: Departing from exponential decay . . . . . . . . . . . . . . . . 61
3.7 Alternative model comparison method - models of heterogenous price and wage setters 62
3.7.1 The nested Calvo - sticky information model . . . . . . . . . . . . . . . . . 63
3.7.2 Hybrid sticky information with backward looking agents . . . . . . . . . . . 65
3.7.3 Estimation results for heterogenous agents models . . . . . . . . . . . . . . 65
3.8 Overall discussion of model dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4 Transmission of economic fluctuations in an estimated two-region DSGE model
for the Euro area 90
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.2 Related literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.3 Theoretical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.3.1 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.3.2 Households and preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.3.3 Relative prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.3.4 Fiscal authority . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.3.5 Market clearing conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.3.6 Monetary authority . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.4 Macroeconomic equilibrium and model solution . . . . . . . . . . . . . . . . . . . . 107
4.4.1 Model in stationary variables . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.4.2 Solution method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.5 Data consideration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.6 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.6.1 Evaluation of the posterior . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.6.2 Calibrated parameters and specification of the priors . . . . . . . . . . . . . 118
4.7 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.7.1 Posterior estimates of the parameters . . . . . . . . . . . . . . . . . . . . . . 120
4.7.2 Modification I: Estimation based on detrended data . . . . . . . . . . . . . 125
4.7.3 Mo II: Excluding the nominal exchange rate from the set of observ-
ables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
4.7.4 Empirical performance of the model . . . . . . . . . . . . . . . . . . . . . . 130
4.7.5 Role of frictions and open economy mechanisms . . . . . . . . . . . . . . . . 131
4.8 International spillover effects within the Euro area . . . . . . . . . . . . . . . . . . 132
4.8.1 Variance decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.8.2 Evidence from reduced-form models . . . . . . . . . . . . . . . . . . . . . . 136
4.8.3 Impulse responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
4.9 Out-of-sample forecasting experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 144
4.9.1 Design of the experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
4.9.2 Empirical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
4.10 Conclusions and direction of further research . . . . . . . . . . . . . . . . . . . . . 149
A Steady state 206
A.1 The two-region model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
B The stationary log-linearized system 209
B.1 The two-region model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
vC Derivation of wage and price equations 214
C.1 The New-Keynesian Phillips Curve with a time varying markup . . . . . . . . . . . 214
C.2 Wage equation with a time varying markup . . . . . . . . . . . . . . . . . . . . . . 216
C.3 The Phillips curve in the presence of non-zero steady state inflation 219
C.4 Wage equation in the presence of non-zero steady state inflation and the balanced
growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
D Data description 228
D.1 The area-wide model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
D.2 The two-region model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
viList of Figures
3.1 Age distributions of information sets J =12 . . . . . . . . . . . . . . . . . . . . . . 53
3.2 Impulse response to monetary shock . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.3 response to markup shock . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.4 Replicated autocorrelations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.5 Age distributions of information sets J =24 . . . . . . . . . . . . . . . . . . . . . . 58
3.6 Impulse response to monetary shock . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.7 response to technology shock . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.8 Impulse response to price markup shock . . . . . . . . . . . . . . . . . . . . . . . . 60
3.9 response to wage shock . . . . . . . . . . . . . . . . . . . . . . . . 60
3.10 Age distribution of information sets: price setting . . . . . . . . . . . . . . . . . . . 67
3.11 Age of sets: wage . . . . . . . . . . . . . . . . . . . 68
3.12 Replicated autocorrelations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.13 Comparison of cross-covariances of the DSGE model and the data . . . . . . . . . . 84
3.14 Estimated impulse responses: Technology shock . . . . . . . . . . . . . . . . . . . . 85
3.15 resp Monetary shock . . . . . . . . . . . . . . . . . . . . . 86
3.16 Estimated impulse responses: Labor supply shock . . . . . . . . . . . . . . . . . . . 87
3.17 resp Price markup shock . . . . . . . . . . . . . . . . . . 88
3.18 Estimated impulse responses: Wage shock . . . . . . . . . . . . . . . . . . 89
4.1 Estimates of the nominal exchange rate, baseline model vs. perfect risk sharing model128
4.2 Posterior and prior distributions, structural parameters . . . . . . . . . . . . . . . 177
4.3 P and prior shocks . . . . . . . . . . . . . . . . . . 177
4.4 Observed data and one-step forecasts, model estimated with log-differences . . . . 178
4.5ed data and model with detrended data . . . . 178
4.6 Annual hours worked per full time employed . . . . . . . . . . . . . . . . . . . . . . 179
4.7 Sequential posterior mode estimates, the two-region DSGE model . . . . . . . . . . 179
4.8tial p mode the tw model (cont.) . . . . . . 180
4.9 Sequential posterior mode estimates, the area-wide DSGE model . . . . . . . . . . 180
4.10 Response to Home stationary technology shock . . . . . . . . . . . . . . . . . . . . 181
4.11 Response to Foreign tec shock . . . . . . . . . . . . . . . . . . . 181
4.12 Response to a common component on the stationary technology shock . . . . . . . 182
4.13 Response to a unit-root technology shock . . . . . . . . . . . . . . . . . . . . . . . 182
4.14 Response to an asymmetric technology shock . . . . . . . . . . . . . . . . . . . . . 183
4.15 Response to Home preference shock . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
4.16 Response to Foreign shock . . . . . . . . . . . . . . . . . . . . . . . . . . 184
4.17 Response to a common component on the preference shock . . . . . . . . . . . . . . 184
4.18 Response to Home investment shock . . . . . . . . . . . . . . . . . . . . . . . . . . 185
4.19 Response to Foreign invt shock . . . . . . . . . . . . . . . . . . . . . . . . . 185
4.20 Response to a common component on the investment shock . . . . . . . . . . . . . 186
4.21 Response to Foreign negative labor supply shock . . . . . . . . . . . . . . . . . . . 186
4.22 Response to Fe labor shock . . . . . . . . . . . . . . . . . . . 187
vii4.23 Response to a common component on the negative labor supply shock . . . . . . . 187
4.24 Response to Home government spending shock . . . . . . . . . . . . . . . . . . . . 188
4.25 Response to Foreign govt sp shock . . . . . . . . . . . . . . . . . . . 188
4.26 Response to a common component on the government spending shock . . . . . . . 189
4.27 Response to Home Phillips curve shock . . . . . . . . . . . . . . . . . . . . . . . . . 189
4.28 Response to curve shock . . . . . . . . . . . . . . . . . . . . . . . . . 190
4.29 Response to Home CPI equation shock . . . . . . . . . . . . . . . . . . . . . . . . . 190
4.30 Response to Foreign CPI shock . . . . . . . . . . . . . . . . . . . . . . . . 191
4.31 Response to Home inflation target shock under flexible exchange rate regime . . . . 191
4.32 Response to Foreign target shock under exchange rate . . . 192
4.33 Response to a common component on the inflation target shock under flexible ex-
change rate regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
4.34 Response to a common inflation target shock in EMU . . . . . . . . . . . . . . . . 193
4.35 Response to Home interest rate shock under flexible exchange rate regime . . . . . 193
4.36 Response to Foreign interest rate shock under exchange rate . . . . 194
4.37 Responsetoacommoncomponentontheinterestrateshockunderflexibleexchange
rate regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
4.38 Response to a common interest rate shock in EMU . . . . . . . . . . . . . . . . . . 195
4.39 Response to UIP shock under flexible exchange rate regime . . . . . . . . . . . . . 195
viiiList of Tables
3.1 Prior parameter distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2 Comparison of second moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.3 ofts (cont.) . . . . . . . . . . . . . . . . . . . . . . . . 50
3.4 In-sample accuracy of the seminal DSGE model . . . . . . . . . . . . . . . . . . . 51
3.5 Log of marginal densities: baseline models . . . . . . . . . . . . . . . . . . . . . . . 51
3.6 Posterior distribution: Calvo model with indexation and truncated Mankiw-Reiss
model with J =12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.7 Standard deviations and autocorrelation of the models and the data . . . . . . . . 55
3.8 Root mean squared error: Calvo, standard sticky information . . . . . . . . . . . . 56
3.9 Log of marginal densities: mixed models . . . . . . . . . . . . . . . . . . . . . . . . 56
3.10 Posterior distribution: Truncated Mankiw-Reiss model with J =12 and J =24. . 58
3.11 Different parameterizations of the sticky information model . . . . . . . . . . . . . 62
3.12 Comparison of marginal densities for heterogenous agents models . . . . . . . . . . 66
3.13 Estimated shares of sticky information agents . . . . . . . . . . . . . . . . . . . . . 66
3.14 Posterior distribution: Calvo model with indexation (Smets and Wouters 2003),
standard Calvo model without indexation . . . . . . . . . . . . . . . . . . . . . . . 73
3.15 Posterior Calvo model estimated without price markup shock, Calvo
model estimated without wage markup shock . . . . . . . . . . . . . . . . . . . . . 74
3.16 Posterior distribution: Mixed model - sticky information prices and Calvo wages,
Mixed model - sticky information prices and Calvo wages estimated without price
markup shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.17 Posterior distribution: Mixed model - Calvo prices and sticky information wages,
Mixed model - Calvo prices and sticky information wages estimated without wage
markup shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.18 Posterior distribution, parsimonious parameterization: standard sticky information
and nested Calvo - sticky information model . . . . . . . . . . . . . . . . . . . . . . 77
3.19 Posterior intermediateparameterizationI:standardstickyinformation,
nested Calvo - sticky information and hybrid sticky information model . . . . . . . 78
3.20 Posterior distribution, intermediate II: standard sticky informa-
tion, nested Calvo - sticky information and hybrid sticky information model . . . . 79
3.21 Variance decomposition: Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.22 V Nominal interest rate . . . . . . . . . . . . . . . . . . . . 81
3.23 Variance decomposition: Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.24 V Wage inflation . . . . . . . . . . . . . . . . . . . . . . . . 82
3.25 Variance decomposition: Real wage . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.26 V Employment . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.1 Weights used in aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.2 Prior and posterior distributions, baseline model . . . . . . . . . . . . . . . . . . . 124
4.3 Prior and p model (cont.) . . . . . . . . . . . . . . . 125
4.4 Estimation based on detrended data, prior and posterior distributions . . . . . . . 126
ix