Bayesian Inference in the Social Sciences

352 Pages·2014·16.431 MB·English

by  Ivan Jeliazkov, Xin-She Yang

Bayesian Inference
in the Social Sciences

Bayesian Inference
in the Social Sciences
Edited by
Ivan Jeliazkov
Department of Economics
University of California, Irvine
California, USA
Xin-She Yang
School of Science and Technology
Middlesex University
London, UK
WILEY
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Library of Congress Cataloging-in-Publication Data:
Bayesian inference in the social sciences / edited by Ivan Jeliazkov, Department of Economics,
University of California, Irvine, California, USA, Xin-She Yang, School of Science and
Technology, Middlesex University, London, United Kingdom,
pages cm
Includes bibliographical references and index.
ISBN 978-1-118-77121-1 (hardback)
1. Social sciences—Statistical methods. 2. Bayesian statistical decision theory. I. Jeliazkov, Ivan,
1973- II. Yang, Xin-She.
HA29.B38345 2014
519.5'42—dc23 2014011437
Printed in the United States of America.
10 9 8 7 6 5 4 3 21
CONTENTS
Preface xiii
1 Bayesian Analysis of Dynamic Network Regression with Joint
Edge/Vertex Dynamics 1
Zack W. Almquist and Carter T. Butts
1.1 Introduction 1
1.2 Statistical Models for Social Network Data 2
1.2.1 Network Data and Nomenclature 2
1.2.2 Exponential Family Random Graph Models 3
1.2.3 Temporal Models for Network Data 7
1.3 Dynamic Network Logistic Regression with Vertex Dynamics 11
1.3.1 Bayesian Inference for DNR Parameters 11
1.3.2 Bayesian Estimation of DNR with Vertex Dynamics 13
1.4 Empirical Examples and Simulation Analysis 14
1.4.1 Blog Data 14
1.4.2 Beach Data 14
1.4.3 Case Analysis: Static Vertex Set 15
1.4.4 Bayesian DNR with Vertex Dynamics 19
v
X vi CONTENTS
1.5 Discussion 25
1.6 Conclusion 26
Bibliography 27
2 Ethnic Minority Rule and Civil War: A Bayesian Dynamic Multilevel
Analysis 35
Xun Pang
2.1 Introduction: Ethnic Minority Rule and Civil War 36
2.2 EMR: Grievance and Opportunities of Rebellion 37
2.3 Bayesian GLMM-AR(p) Model 38
2.3.1 General Model Specification 39
2.3.2 Parameter Estimation 40
2.3.3 Bayesian Model Comparison 42
2.4 Variables, Model, and Data 43
2.5 Empirical Results and Interpretation 46
2.6 Civil War: Prediction 51
2.6.1 Predictive Probabilities of Civil War 51
2.6.2 Receiver-Operating Characteristic Curve 53
2.7 Robustness Checking: Alternative Measures of EMR 56
2.8 Conclusion 58
Bibliography 59
3 Bayesian Analysis of Treatment Effect Models 63
Mingliang Li and Justin L. Tobias
3.1 Introduction 64
3.2 Linear Treatment Response Models Under Normality 65
3.2.1 Instruments and Identification 66
3.3 Nonlinear Treatment Response Models 69
3.3.1 A General Nonlinear Representation 70
3.4 Other Issues and Extensions: Non-Normality, Model
Selection, and Instrument Imperfection 74
3.4.1 Non-Normality 74
3.4.2 Model Comparison 76
3.4.3 Instrument Imperfection 79
3.5 Illustrative Application 81
3.6 Conclusion 85
Bibliography 86
4 Bayesian Analysis of Sample Selection Models 91
CONTENTS vii
Martijn van Hasselt
4.1 Introduction 91
4.2 Univariate Selection Models 93
4.2.1 General Framework 93
4.2.2 Likelihoods 94
4.2.3 Bayesian Inference 95
4.3 Multivariate Selection Models 97
4.3.1 Motivation 97
4.3.2 Heckman's Selection Model 98
4.3.3 Heckman's Selection Model: Bayesian Inference 99
4.3.4 A Model with Tobit Selection 103
4.3.5 Alternative Specifications 105
4.3.6 Endogeneity 107
4.4 Semiparametric Models 107
4.5 Conclusion 110
Bibliography 111
5 Modern Bayesian Factor Analysis 115
Hedibert Freitas Lopes
5.1 Introduction 115
5.2 Normal Linear Factor Analysis 117
5.2.1 Parsimony 118
5.2.2 Identifiability 118
5.2.3 Invariance 120
5.2.4 Posterior Inference 121
5.2.5 Number of Factors 123
5.3 Factor Stochastic Volatility 125
5.3.1 Factor Stochastic Volatility 126
5.3.2 Financial Index Models 127
5.4 Spatial Factor Analysis 129
5.4.1 Spatially Hierarchical Factor Analysis 130
5.4.2 Spatial Dynamic Factor Analysis 132
5.5 Additional Developments 134
5.5.1 Prior and Posterior Robustness 134
5.5.2 Mixture of Factor Analyzers 134
5.5.3 Factor Analysis in Time Series Modeling 136
5.5.4 Factor Analysis in Macroeconometrics 136
5.5.5 Term Structure Models 137
viii CONTENTS
5.5.6 Sparse Factor Structures 138
5.6 Modern non-Bayesian factor analysis 139
5.7 Final Remarks 139
Bibliography 141
6 Estimation of Stochastic Volatility Models with Heavy Tails and
Serial Dependence 155
Joshua C.C. Chan and Cody Y.L. Hsiao
6.1 Introduction 155
6.2 Stochastic Volatility Model 156
6.2.1 Auxiliary Mixture Sampler 158
6.2.2 Precision Sampler for Linear Gaussian State Space
Models 159
6.2.3 Empirical Example: Modeling AUD/USD Returns 163
6.3 Moving Average Stochastic Volatility Model 164
6.3.1 Estimation 165
6.3.2 Empirical Example: Modeling PHP/USD Returns
During Crisis 167
6.4 Stochastic Volatility Models with Heavy-Tailed Error
Distributions 169
6.4.1 Estimation 170
6.4.2 Empirical Example: Modeling Daily Returns on
the Silver Spot Price 172
Bibliography 175
7 From the Great Depression to the Great Recession: A Model-
Based Ranking of U.S. Recessions 177
Rui Liu and Ivan Jeliazkov
7.1 Introduction 177
7.2 Methodology 180
7.2.1 Model 180
7.2.2 Estimation Framework 181
7.3 Results 184
7.4 Conclusions 194
Appendix: Data 194
Bibliography 196
8 What Difference Fat Tails Make: A Bayesian MCMC Estimation
of Empirical Asset Pricing Models 199