The Endogeneity of Union Status: An Empirical Test

Abstract

An unsettled issue in the literature relating to the relative wage effect of unions is the appropriate treatment of union status in a wage determination model. In the context of a three-equation model determining union membership and union- and nonunion-sector wage rates, this paper presents an instrumental variables (IV) procedure for estimating the parameters of the wage equations and a test of the exogeneity of union status using the Hausman specification test. An advantage of our IV procedure in comparison to the widely used inverse Mill's ratio procedure is that our procedure is a distribution-free estimator, whereas the inverse Mill's ratio estimator hinges in the assumption that the error term of the choice equation is normally distributed. Using data for a sample of middle-aged white workers, we estimate the parameters of the union and nonunion wage equations with both procedures. On the key question of the endogeneity of union status, the Hausman test decisively rejects the null hypothesis of exogeneity. The inverse Mill's ratio procedure, in contrast, provides coefficient estimates on the selectivity terms that fail to indicate evidence of sample selectivity in either sector.

Keywords: Discrete Endogenous Variables, Union Status, Wage Equations

JEL Classification: J30,J31,J50,C35