This article addresses the issue of specification of econometric selectivity models and suggests approaches for the correction of selectivity bias. Our approaches provide ways to specify selectivity models without the assumption of multinormal distribution. Some flexible function forms for the correction of selectivity bias in the regression equation are derived. All the models considered can be estimated by simple consistent two stage methods. Our approaches provide simple procedures for the testing of selectivity bias without imposing restrictive distributional assumptions and also tests for the normality assumption.

This paper investigates asymptotic properties of the maximum likelihood estimator and the quasi-maximum likelihood estimator for the spatial autoregressive model. The rates of convergence of those estimators may depend on some general features of the spatial weights matrix of the model. It is important to make the distinction with different spatial scenarios. Under the scenario that each unit will be influenced by only a few neighboring units, the estimators may have -rate of convergence and be asymptotically normal. When each unit can be influenced by many neighbors, irregularity of the information matrix may occur and various components of the estimators may have different rates of convergence.

[The model considered is a two-equations model consisting of a binary choice equation and a regression equation. Tests for the bivariate normal distribution are derived for the truncated samples case and the censored samples case. The tests are Lagrangean multiplier tests for testing the bivariate normal distribution within the bivariate Edgeworth series of distributions. Simple intuitive interpretations for the statistics are provided.For the truncated case, the test compares with the estimated differences between some sample moments of order (r,s) for which r + s extgreater 2 and the corresponding hypothesized moments of the disturbances. For the censored case, the test is equivalent to the testing of some sample semi-invariants for which r + s extgreater 2 are zeros.]

During the recent years, there is substantial interest in the econometric models with qualitative and censored dependent variables. The important contributions on these topics by Amemiya [1973J, McFadden [1973J and Heckman [1974J among others stimulate the recent

A class of statistical models which generate simultaneous equation models with both discrete and continuous endogenous variables is introduced. This class of models can also be regarded as a new class of switching simultaneous equation models which are of general interest. Identification and estimation problems are investigated. Several simple consistent two stage methods are proposed. The consistency of those estimators is proved. Two step maximum likelihood procedures are then developed. -Author

This article provides general formulas for the computation of opportunity costs (or forgone earnings) of unchosen alternatives in sample selection models with polychotomous choices. With observed choice probabilities and outcomes of alternatives chosen by some individuals, the opportunity costs for individuals who do not choose those alternatives can be evaluated. For the probability indexed sample selection models with legit choice probabilities, which include the polychotomous choice model of Lee (1983), the formulas are simple and reveal restrictions implicitly imposed on those models. These formulas can be useful for empirical studies.

[This paper considers the problem of specifying and estimating demand systems for samples which contain a significant proportion of observation with zero consumption of one or more goods. Our approach uses virtual prices, which are dual to the Kuhn-Tucker conditions, to select the set of goods consumed--the demand regime--and to transform binding nonnegativity constraints into nonbinding constraints. It has the advantage of permitting the use of indirect cost and utility functions such as the translog, and the analytic decomposition of demand effects for goods at the nonnegativity limit.]