Sample Selection Issues and Applications

Abstract

In many occasions of regression analysis, researchers may encounter the problem of a non-random sample that leads to a biased estimator when using the OLS method. This study thus examines some related issues of sample selection bias due to non-random sampling. We first explain the source of bias caused by non-random sampling and then demonstrate that the direction of such bias in most cases cannot be ascertained based on prior information. By treating the sample selection as informative sampling, we can formulate the sample selection bias issue as an omitted variable problem in the regression model. Heckman (1979) proposed a two-stage estimation procedure to correct for selection bias. The first stage applies the Probit model to produce the estimated value of the inverse Mill’s ratio and then includes it into the second-stage regression model as an explanatory variable to yield unbiased estimators. As the sample selection rule may not always be derived from a yes–no choice, our study further utilizes Lee’s (1983) extension by applying the Multinomial Logit model into the first-stage estimation procedure to allow for its application with multi-choice sample selection rule. Since the pioneer works related to sample selection issues are mostly in the field of labor economics, we give two examples of an empirical study in labor economics to respectively demonstrate applications of the Probit correction approach and Multinomial Logit correction approach. Finally, we point out that the problem of a non-random sample is not limited to applications in economics. In the past 20 years, quite a few researchers have taken into account the issue of sample selection for studies of finance and management issues.