Edgeworth expansion based correction of selectivity bias in models of double selection

Abstract

Edgeworth expansions are known to be useful for approximating probability distributions and moments. In our case, we exploit the expansion in the context of models of double selection embedded in a trivariate normal structure. We assume bivariate normality among the random disturbance terms in the two selection equations but allow the distribution of the disturbance term in the outcome equation to be free. This sets the stage for a control function approach to correction of selectivity bias that affords tests for the more common trivariate normality specifi-cation. Other recently proposed methods for handling multiple outcomes are Multinomial Logit based selection correction models. An empirical example is presented to document the differ-ences among the results obtained from our selectivity correction approach, trivariate normality specification and Multinomial Logit based selection correction models.