Bayesian Estimation of DSGE Models

283 Pages·2016·6.05 MB·english

by  Edward P. Herbst, Frank Schorfheide

Bayesian Estimation
of DSGE Models
Edward P. Herbst and Frank Schorfheide
PrincetonUniversityPress
PrincetonandOxford
© 2016 by Edward P. Herbst and Frank Schorfheide.
Published by Princeton University Press, 41 William Street,
Princeton,NewJersey08540
In the United Kingdom: Princeton University Press, 6 Oxford
Street,Woodstock,OxfordshireOX201TW
press.princeton.edu
AllRightsReserved
LibraryofCongressCataloging-in-PublicationData
Herbst,EdwardP.,1984-
BayesianestimationofDSGEmodels/
EdwardP.Herbst,FrankSchorfheide.
pagescm.–(TheEconometricandTinbergenInstitutes
lectures)Includesbibliographicalreferencesandindex.
ISBN978-0-691-16108-2(hardcover:alk.paper)
1.Equilibrium(Economics)–Mathematicalmodels.2.Bayes-
ianstatisticaldecisiontheory.3.Stochasticanalysis.
4.Econometrics.
I.Schorfheide,Frank.II.Title.
HB145.H4672015
339.501’519542–dc23 2015023799
PrintedintheUnitedStatesofAmerica
Contents
Figures xi
Tables xiii
Series Editors’ Introduction xv
Preface xvii
I IntroductiontoDSGEModelingandBayes-
ian Inference 1
1 DSGE Modeling 3
1.1 ASmall-ScaleNewKeynesianDSGEModel 4
1.2 OtherDSGEModelsConsideredinThisBook 11
2 Turning a DSGE Model into a Bayesian Model 14
2.1 Solvinga(Linearized)DSGEModel 16
2.2 TheLikelihoodFunction 19
2.3 Priors 22
3 A Crash Course in Bayesian Inference 29
3.1 ThePosteriorofaLinearGaussianModel 31
3.2 BayesianInferenceandDecisionMaking 35
3.3 ANon-GaussianPosterior 43
3.4 ImportanceSampling 46
3.5 Metropolis-HastingsAlgorithms 52
II Estimation of Linearized DSGE Models 63
4 Metropolis-Hastings Algorithms for DSGE Models 65
4.1 ABenchmarkAlgorithm 67
4.2 TheRWMH-VAlgorithmatWork 69
4.3 ChallengesDuetoIrregularPosteriors 77
4.4 AlternativeMHSamplers 81
4.5 ComparingtheAccuracyofMHAlgorithms 87
4.6 EvaluationoftheMarginalDataDensity 93
5 Sequential Monte Carlo Methods 100
5.1 AGenericSMCAlgorithm 101
5.2 FurtherDetailsoftheSMCAlgorithm 109
5.3 SMCfortheSmall-ScaleDSGEModel 125
6 Three Applications 130
6.1 AModelwithCorrelatedShocks 131
6.2 TheSmets-WoutersModelwithaDiffusePrior 141
6.3 TheLeeper-Plante-TraumFiscalPolicyModel 150
III Estimation of Nonlinear DSGE Models 161
7 From Linear to Nonlinear DSGE Models 163
7.1 NonlinearDSGEModelSolutions 164
7.2 AddingNonlinearFeaturestoDSGEModels 167
8 Particle Filters 171
8.1 TheBootstrapParticleFilter 173
8.2 AGenericParticleFilter 182
8.3 AdaptingtheGenericFilter 185
8.4 AdditionalImplementationIssues 191
8.5 Adaptingst−1 Draws 198
8.6 ApplicationtotheSmall-ScaleDSGEModel 204
8.7 ApplicationtotheSWModel 212
8.8 ComputationalConsiderations 216
9 Combining Particle Filters with MH Samplers 218
9.1 ThePFMHAlgorithm 218
9.2 ApplicationtotheSmall-ScaleDSGEModel 222
9.3 ApplicationtotheSWModel 224
9.4 ComputationalConsiderations 229
10 Combining Particle Filters with SMC Samplers 231
10.1 AnSMC2 Algorithm 231
10.2 ApplicationtotheSmall-ScaleDSGEModel 237
10.3 ComputationalConsiderations 239
Appendix 241
A Model Descriptions 241
A.1 Smets-WoutersModel 241
A.2 Leeper-Plante-TraumFiscalPolicyModel 247
B Data Sources 249
B.1 Small-ScaleNewKeynesianDSGEModel 249
B.2 Smets-WoutersModel 249
B.3 Leeper-Plante-TraumFiscalPolicyModel 251
Bibliography 257
Index 271
Figures
3.1 PosteriorDistributionforSet-IdentifiedModel 45
3.2 ImportanceSamplingApproximations 51
3.3 PerformanceofDiscreteMHAlgorithm 60
4.1 ObservablesfortheSmall-ScaleModel 70
4.2 ConvergenceofMonteCarloAverage 71
4.3 EffectofScalingonAccuracy 74
4.4 ImpulseResponsesofExogenousProcesses 76
4.5 ImpulseResponsesofEndogenousVariables 77
4.6 PosteriorsforStylizedState-SpaceModel 80
4.7 AutocorrelationFunctionsandIneff.Factors 90
4.8 Small-SampleVarianceversusHACEstimates 92
5.1 SMCEvolutionofParticles 105
5.2 SMCPosteriorApproximation 108
5.3 AdaptionofSMCAlgorithm 115
5.4 ConvergenceofSMCApproximation 124
5.5 EffectofλonInefficiencyFactors 126
5.6 EffectofTuningonInaccuracy 127
6.1 Corr.Shocks:Priors/Posteriorsofρgz,ρzg 134
6.2 Corr.Shocks:ImpulseResponses(Part1) 135
6.3 Corr.Shocks:ImpulseResponses(Part2) 136
6.4 Corr.Shocks:PosteriorProbabilityApprox. 139
6.5 Corr.Shocks:MarginalDataDensityApprox. 140
6.6 SWModel:PrecisionofQuantileApprox.(1) 149
6.7 SWModel:PrecisionofQuantileApprox.(2) 151
6.8 LPTModel:OutputResponseParameters 158
6.9 LPTModel:TaxComovementParameters 159
6.10 LPTModel:ResponsetoLaborTaxInnovation 160
8.1 Small-ScaleModel:Log-Likelihood,Filteredgˆt 207
8.2 Small-Scale Model: Log-Likelihood Approxima-
tionErrors(Part1) 208
8.3 Small-Scale Model: Log-Likelihood Approxima-
tionErrors(Part2) 210
8.4 Small-ScaleModel:GreatRecession 212
8.5 SWModel:Log-LikelihoodApprox.Errors 215
8.6 SWModel:Filteredgˆt 217
9.1 AutocorrelationofPFMHDraws 224
Tables
2.1 ConditionalDistributionsforKalmanFilter 23
2.2 PriorDistribution 27
4.1 PosteriorEstimatesofDSGEModelParameters 72
4.2 RunTimesandTuningConstants 89
4.3 MH-BasedMarginalDataDensityEstimates 99
5.1 Resampling:AncestorsandOffsprings 116
5.2 SMC-BasedMarginalDataDensityEstimates 128
6.1 CorrelatedShocks:AlgorithmConfiguration 138
6.2 CorrelatedShocks:MarginalDataDensity 140
6.3 SWModel:PosteriorQuantiles 144
6.4 SWModel:AlgorithmConfiguration 147
6.5 LPT Model: Prior Distributions for Fiscal Rule
Parameters 155
6.6 LPTModel:CommonPriorDistributions 156
6.7 LPTModel:SMCConfiguration 156
6.8 LPTModel:PosteriorMoments(Part1) 157
8.1 Small-ScaleModel:ParameterValues 205
8.2 Small-ScaleModel:PFSummaryStatistics 209
8.3 SWModel:ParameterValues 214
8.4 SWModel:PFSummaryStatistics 216
9.1 Small-ScaleModel:PFMHAccuracy 223
9.2 SWModel:PFMHAccuracy 226
10.1 SMC2 ParticleSystemafterStagen 233
10.2 Small-ScaleModel:SMC2 Accuracy 238
A-1 SWModel:DiffusePrior 245
A-2 SWModel:OriginalPrior 246
A-3 LPTModel:PosteriorMoments(Part2) 248
Series Editors’ Introduction
TheEconometricandTinbergenInstitutesLecturesdealwith
topics in econometrics with important policy implications.
The lectures cover a wide range of topics and are not con-
finedtoanyoneareaorsub-discipline.Leadinginternational
scientists in the field of econometrics in which applications
play a major role are invited to give three-day lectures on a
topictowhichtheyhavecontributedsignificantly.
TheriseintheuseanddevelopmentofDynamicStochastic
GeneralEquilibrium(DSGE)modelsformacroeconomicfore-
casting and policy analysis has been spectacular in the past
twentyyearsinacademiaandprofessionalorganizations.The
present book written by Ed Herbst and Frank Schorfheide,
leading researchers in this field, is very timely. It contains a
clear introduction using basic New Keynesian Phillips curve
modelsandcontinuestoexploretheinherentnonlinearstruc-
ture of DSGE models. It covers a range of very novel simula-
tionbasedBayesianalgorithmstohandlesuchmodels.Here
the reader is taken to the frontiers of modern science in the
fieldofDSGEmodeling.
This book no doubt stimulates further research in the
DSGE class of models to analyze such modern economic is-
sues as slow and imbalanced international growth, risk of
deflation,andinterconnectednessbetweenrealandfinancial
sectors. This leads to the specification of a more appropriate
and effective mix of fiscal and monetary policy to battle the
issuesmentioned.
The editors of the series are indebted to the Tinbergen In-
stituteforcontinuedsupport.
HermanK.vanDijkandPhilipHansFranses
EconometricandTinbergenInstitutes
ErasmusSchoolofEconomics