下载Complete and Incomplete Econometric Models
1 Introduction 7
2 The Bayesian paradigm 11
2.1 Complete models . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Model comparison and averaging . . . . . . . . . . . . . . . . . 16
2.3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4 Model evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4.1 Prior predictive analysis . . . . . . . . . . . . . . . . . . 22
2.4.2 Posterior predictive analysis . . . . . . . . . . . . . . . . 24
3 Prior Predictive Analysis and Model Evaluation 27
3.1 Data and models . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.1.2 A Gaussian model . . . . . . . . . . . . . . . . . . . . . 29
3.1.3 A GARCH model . . . . . . . . . . . . . . . . . . . . . . 31
3.1.4 A stochastic volatility model . . . . . . . . . . . . . . . . 33
3.2 Prior predictive analysis . . . . . . . . . . . . . . . . . . . . . . 36
3.2.1 Features (or checking functions) . . . . . . . . . . . . . . 36
3.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2.3 Prior predictive analysis of variance . . . . . . . . . . . . 42
3.3 Comparison with an incomplete model . . . . . . . . . . . . . . 45
3.3.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3.2 Application . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.4 Appendix: A Gaussian copula for evaluating predictive densities
of vector functions of interest . . . . . . . . . . . . . . . . . . . 51
4 Incomplete structural models 53
4.1 The essential elements of DSGE models . . . . . . . . . . . . . . 54
4.1.1 An example: General equilibrium models of the equity
premium . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.1.2 The Mehra-Prescott and Rietz models . . . . . . . . . . 56
4.1.3 The Labadie and Tsionas models . . . . . . . . . . . . . 57
4.2 Strong econometric interpretation . . . . . . . . . . . . . . . . . 58
4.3 Weak econometric interpretation . . . . . . . . . . . . . . . . . . 60
4.3.1 Formalizing the weak econometric interpretation . . . . . 60
4.3.2 Illustration in the equity premium model . . . . . . . . . 62
4.3.3 Di¢ culties with the weak econometric interpretation . . 65
4.4 Minimal econometric interpretation . . . . . . . . . . . . . . . . 66
4.4.1 Formal development . . . . . . . . . . . . . . . . . . . . 67
4.4.2 Illustration in the equity premium model . . . . . . . . . 69
CONTENTS 3
4.5 Implications for structural modeling . . . . . . . . . . . . . . . . 72
5 An incomplete model space 75
5.1 Context and motivation . . . . . . . . . . . . . . . . . . . . . . 75
5.1.1 Log scoring . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.1.2 Linear pooling . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2 Pools of two models . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.3 Examples of two-model pools . . . . . . . . . . . . . . . . . . . 82
5.4 Pools of multiple models . . . . . . . . . . . . . . . . . . . . . . 86
5.5 Multiple-model pools: An example . . . . . . . . . . . . . . . . 91
5.6 Pooling and model improvement . . . . . . . . . . . . . . . . . . 93
5.7 Consequences of an incomplete model space . . . . . . . . . . . 95