11

Discrete Choice Modeling

William Greene

Abstract
We detail the basic theory for models of discrete choice. This encompasses methods of estimation
and analysis of models with discrete dependent variables. Entry level theory is presented for the
practitioner. We then describe a few of the recent, frontier developments in theory and practice.

11.1 Introduction 474
11.2 Specification, estimation and inference for discrete choice models 475
11.2.1 Discrete choice models and discrete dependent variables 476
11.2.2 Estimation and inference 478
11.2.3 Application 479
11.3 Binary choice 480
11.3.1 Regression models 481
11.3.2 Estimation and inference in parametric binary choice models 483
11.3.2.1 Parameter estimation 483
11.3.2.2 Residuals and predictions 485
11.3.2.3 Marginal effects 486
11.3.2.4 Hypothesis tests 487
11.3.2.5 Specification tests 488
11.3.2.6 The fit of the model 489
11.3.3 A Bayesian estimator 490
11.3.3.1 Gibbs sampler for the binomial probit model 492
11.3.4 Semiparametric models 492
11.3.5 Endogenous right-hand-side variables 494
11.3.6 Panel data models 496
11.3.6.1 Panel data modeling frameworks 496
11.3.6.2 Fixed effects model 496
11.3.6.3 Random effects models and estimation 499
11.3.6.4 Dynamic models 502
11.3.6.5 Parameter heterogeneity: random parameters and latent class
models 503
11.3.7 Application 504
11.4 Bivariate and multivariate binary choice 510
11.4.1 Bivariate binary choice 510
11.4.2 Recursive simultaneous equations 511

473