Correcting Sample Selection Bias for Bivariate Logistic Distribution of Disturbances

• NCJ Number: 91853
• Author(s): C S Ray; R A Berk; W T Bielby
• Date Published: 1981
• Length: 38 pages
• Grant Number(s): 80-IJ-CX-0037
• Agencies: NIJ-Sponsored
• Publication Type: Program/Project Evaluation

Annotation

In the past decade, Amemiya, Heckman, and others have examined the properties of OLS estimators obtained from the non-randomly selected subsample; this paper applies their analyses to random disturbances that have a bivariate logistic distribution instead of bivariate normal.

Abstract

The study considers two alternative formulations suggested by Gumbel (1961). Each of these two distribution functions yields logistic marginals; however, the implied estimation procedures are quite different. In one instance, the corrected model yields homoscedastic errors. In the other, although heteroscendasticity surfaces, the variance function is parametrically known, enabling the search for the optimal value within the admissible range of the parameter. In Section I, the two bivariate distribution functions are outlined. Sections II and III present consistent estimators of the parameters of one equation, using each of the distribution functions. Section IV indicates that the estimator derived is consistent and that the distribution of the estimates is asymptotically normal, so that despite non-normality of equation disturbances, the standard statistical tests apply in large samples. Finally, in Section V, simulation results compare the instrument used by Heckman in his probit model and the one implied in this study's logistic model. The model is applied to a study of the employment experiences of ex-offenders (Rossi, Berk, and Leniham, 1980). Thirteen references are provided. (Author summary modified)