Chapter 56
COMPUTATIONALLY INTENSIVE METHODS FOR
INTEGRATION IN ECONOMETRICS*
JOHN GEWEKE
University of Iowa
MICHAEL KEANE
New York University
Contents
Abstract 3465
Keywords 3465
1 Introduction 3466
2 Monte Carlo methods of integral approximation 3468
2.1 Independence sampling 3470
2.2 The Gibbs sampler 3472
2.3 The Hastings-Metropolis algorithm 3474
2.4 Some Markov chain Monte Carlo theory 3476
2.5 Metropolis within Gibbs 3479
2.6 Assessing numerical accuracy in Markov chain Monte Carlo 3479
3 Approximate solution of discrete dynamic optimization problems 3481
4 Classical simulation estimation of the multinomial probit model 3494
5 Univariate latent linear models 3506
5.1 An overview of the univariate latent linear model 3507
5.1 1 Distribution of disturbances 3507
5.1 2 Observable outcomes 3508
5.1 3 Prior distributions 3508
5.1 4 Existence of the posterior 3509
5.1 5 MCMC algorithm for inference 3510
5.1 6 Marginal likelihoods 3511
5.2 Some evidence from artificial data 3511
5.2 1 Parameter posterior moments 3512
5.2 2 Marginal likelihood approximations 3516
5.3 Some evidence from real data 3518
6 Multivariate latent linear models 3518
6.1 An overview of the multivariate latent linear model 3519
6.1 1 Linear restrictions in the multivariate latent linear model 3519
6.1 2 Distribution of disturbances 3520
6.1 3 Observed outcomes 3521
6.1 4 Prior distributions 3522
6.1 5 Existence of the posterior distribution 3524
6.1 6 MCMC algorithm for inference 3524
6.1 7 Marginal likelihoods 3525
6.2 Some evidence from artificial data 3525
6.2 1 Multivariate linear model 3525
6.2 2 Degenerate multivariate linear model 3528
6.2 3 Multiple discrete choice model 3528
6.2 4 Continuous selection model 3530
6.2 5 Discrete choice selection model 3533
6.2 6 Marginal likelihood approximations 3535
6.2 7 Prospects for applications and future development 3537
7 Bayesian inference for a dynamic discrete choice model 3538
Appendix A The full univariate latent linear model 3548
Appendix B The full multivariate latent linear model 3555
References 3564