This book introduces a new generation of statistical econometrics. After linear models leading to analytical expressions for estimators, and non-linear models using numerical optimization algorithms, the availability of high- speed computing has enabled econometricians to consider econometric models without simple analytical expressions. The previous difficulties presented by the presence of integrals of large dimensions in the probability density functions or in the moments can be circumvented by a simulation-based approach.
Author(s): Christian Gouriéroux, Alain Monfort
Series: Oup/Core Lecture Series
Publisher: Oxford University Press, USA
Year: 1997
Language: English
Pages: 185
Contents......Page 8
1.1 Introduction......Page 12
1.2.1 Parametric conditional models......Page 13
1.2.2 Estimators defined by the optimization of a criterion function......Page 14
1.2.3 Properties of optimization estimators......Page 17
1.3 Potential Applications of Simulated Methods......Page 18
1.3.1 Limited dependent variable models......Page 19
1.3.2 Aggregation effect......Page 21
1.3.3 Unobserved heterogeneity......Page 22
1.3.4 Nonlinear dynamic models with unobservable factors......Page 23
1.3.5 Specification resulting from the optimization of some expected criterion......Page 25
1.4.2 How to simulate?......Page 26
1.4.3 Partial path simulations......Page 29
2.1 Path Calibration or Moments Calibration......Page 30
2.1.2 Moment calibration......Page 31
2.2.1 The static case......Page 32
2.2.2 The dynamic case......Page 33
2.3.1 Simulators......Page 35
2.3.2 Definition of the MSM estimators......Page 38
2.3.3 Asymptotic properties of the MSM......Page 40
2.3.4 Optimal MSM......Page 42
2.3.5 An extension of the MSM......Page 45
2A.1 Consistency......Page 48
2A.2 Asymptotic normality......Page 49
3.1 Simulated Maximum Likelihood Estimators (SML)......Page 52
3.1.2 Asymptotic properties......Page 53
3.1.3 Study of the asymptotic bias......Page 55
3.1.4 Conditioning......Page 56
3.1.5 Estimators based on other simulators......Page 59
3.2.1 Pseudo-maximum likelihood (PML) methods......Page 61
3.2.2 Simulated PML approaches......Page 66
3.3.1 Corrections based on the first order conditions......Page 67
3.3.2 Corrections based on the objective function......Page 68
3A.1 Definition of the algorithm......Page 69
3A.2 Properties of the algorithm......Page 70
4.1.1 Instrumental model......Page 72
4.1.2 Estimation based on the score......Page 73
4.1.3 Extensions to other estimation methods......Page 75
4.2.1 The dimension of the auxiliary parameter......Page 77
4.2.2 Which moments to match?......Page 78
4.2.3 Asymptotic properties......Page 80
4.3.1 Estimation of a moving average parameter......Page 82
4.3.2 Application to macroeconometrics......Page 86
4.3.3 The efficient method of moment......Page 87
4.4.1 Second order expansion......Page 88
4.4.2 Indirect information and indirect identification......Page 93
Appendix 4A: Derivation of the Asymptotic Results......Page 95
4A.1 Consistency of the estimators......Page 96
4A.2 Asymptotic expansions......Page 97
4B.1 Computation of II (θ)......Page 100
4B.2 Another expression of I[sup(P)] (θ)......Page 102
5.1.1 Discrete choice model......Page 104
5.1.2 Simulated methods......Page 105
5.1.3 Different simulators......Page 107
5.2.1 Approximations of a multivariate normal distribution in a neighbourhood of the no correlation hypothesis......Page 111
5.2.2 The use of the approximations when correlation is present......Page 113
5.3.1 Constrained and conditional moments of a multivariate Gaussian distribution......Page 114
5.3.2 Simulators for constrained moments......Page 115
5.3.3 Simulators for conditional moments......Page 118
5.4.1 Labour supply and wage equation......Page 123
5.4.2 Test of the rational expectation hypothesis from business survey data......Page 124
Appendix 5A: Some Monte Carlo Studies......Page 126
6.1.1 The principle......Page 130
6.1.2 Comparison between indirect inference and full maximum likelihood methods......Page 132
6.1.3 Specification of the volatility......Page 136
6.2.1 Moment conditions deduced from the infinitesimal operator......Page 144
6.2.2 Method of simulated moments......Page 148
6.3.1 Discrete time factor models......Page 149
6.3.2 State space form and Kitagawa's filtering algorithm......Page 150
6.3.3 An auxiliary model for applying indirect inference on factor ARCH models......Page 152
6.3.4 SML applied to a stochastic volatility model......Page 153
Appendix 6A: Form of the Infinitesimal Operator......Page 154
7.1.1 Static disequilibrium models......Page 156
7.1.2 Dynamic disequilibrium models......Page 159
7.2.1 Markovian vs. non-Markovian models......Page 162
7.2.2 A switching state space model and the partial Kalman filter......Page 163
7.2.3 Computation of the likelihood function......Page 164
References......Page 170
O......Page 184
W......Page 185
