Chapter 27 LIMITED DEPENDENT VARIABLES This chapter discusses classical estimation methods for limited dependent variable (LDV) models that employ Monte Carlo simulation techniques to overcome computational problems in such models. | Chapter 27 LIMITED DEPENDENT VARIABLES PHOEBUS J. DHRYMES Columbia University Contents 0. Introduction 1568 1. Logit and probit 1568 . Generalities 1568 . Why a general linear model GLM formulation is inappropriate 1570 . A utility maximization motivation 1572 . Maximum likelihood estimation 1575 . Goodness of fit 1579 2. Truncated dependent variables 1585 . Generalities 1585 . Why simple OLS procedures fail 1586 . Estimation of parameters by ML methods 1589 . An initial consistent estimator 1590 . Limiting properties and distribution of the ML estimator 1595 . Goodness of fit 1603 3. Sample selectivity 1604 . Generalities 1604 . Inconsistency of least squares procedures 1606 . The LF and ML estimation 1610 . An initial consistent estimator 1613 . Limiting distribution of the ML estimator 1619 . A test for selectivity bias 1625 References 1626 Handbook of Econometrics Volume III Edited by Z. Griliches and . Intriligator Elsevier Science Publishers BV 1986 1568 P. J. Dhrymes 0. Introduction This is intended to be an account of certain salient themes of the Limited Dependent Variable LDV literature. The object will be to acquaint the reader with the nature of the basic problems and the major results rather than recount just who did what when. An extended bibliography is given at the end that attempts to list as many papers as have come to my attention - even if only by title. By LDV we will mean instances of dependent . variables to be explained in terms of some economic model or rationalizing scheme for which a their range is intrinsically a finite discrete set and any attempt to extend it to the real fine or the appropriate multivariable generalization not only does not lead to useful simplification but befouls any attempt to resolve the issues at hand b even though their range may be the real half line or the appropriate multivariable generalization their behavior is conditioned on another process
