Equivalence of the standard and the modified switching regression models

Ophem (1993) employed a switching regression model with earnings entering the choice equation to investigate earnings differentials between the public and private sectors. Ophem also described a ''modified switching regression model'' in which only the equation for unknown earnings is substituted into the choice equation. He argued the coefficients in the choice equation can be identified in the modified switching regression model without exclusion restrictions and estimates from the modified switching regression model are more efficient than estimates from the standard switching regression model. We show that there are flaws in Ophem's analysis which invalidate his claims.