Determination of Participation Decision, Hiring Decision, and Wages in a Double Selection Framework: Male-Female Wage Differentials in the U.S. Labor Market Revisited

Article excerpt


The magnitude of the male-female wage differential is known to be highly sensitive to the specification of the wage equations used. An important source of misspecification is the failure to correct the sample selection bias that results from estimating the wage equation obtained through two sequential decisions: the worker's decision to participate in the labor market and the employer's decision to hire. Estimation of the wage equation ignoring this double selection process leads to biased estimates, and consequently the resulting male-female wage differentials are likely to be misleading. Following a double selection approach and using a sample from the National Longitudinal Survey of Youth, this article examines the determinants of not only the wage equation but also the worker's participation and the employer's hiring decisions in both male and female samples. The study further demonstrates that the unexplained male--female wage differential remains underestimated when the roles of both selection decision s are ignored in the estimation of wage equations. (JEL J71)


Research on male-female wage differentials in the U.S. labor market suggests that males receive higher wages than otherwise identical female workers. Decomposing these differentials into explained and unexplained parts by using Oaxaca-Blinder residual difference technique (Oaxaca, 1973; Blinder, 1973), several authors during the last two decades have demonstrated that large percentages of the male-female wage differentials remain unexplained by observed worker characterstics (Blau et al., 1998). These unexplained differentials are often attributed to the presence of wage discrimination against females. It is important to note that the unexplained differential does not necessarily measure the magnitude of discrimination. How-ever, in the presence of a positive unexplained differential, the possibility of gender discrimination cannot completely be ruled out (Blau et al., 1998, 193).

It is already known in the literature that the Oaxaca-Blinder residual difference approach is highly sensitive to the specification of the wage equation. In fact, the size of the unexplained differential may change drastically due to inclusion or exclusion of relevant explanatory variables, and consequently, a positive unexplained differential may even fail to indicate the presence of discrimination unless the problem of misspecification is completely resolved.

An important source of misspecification of the wage equation is the sample selection bias (Heckman, 1979; Lee, 1978). Because wages are not available for all workers in the sample, the wage equation is usually estimated from a censored sample that includes employed workers only. The expected value of the error term of the wage equation in such a sample is not necessarily zero, and consequently ordinary least squares (OLS) estimates are biased. This bias is widely known in the literature as the selectivity bias. Heckman (1979) demonstrates that this bias arises due to omitted variable misspecification and can be corrected by including a selectivity variable as an explanatory variable in the wage regression.

After the publication of a series of path-breaking papers by both Heckman and Lee on the correction of selectivity bias in the late 1970s, several researchers used their two-step approach to estimate male and female wage equations and wage differentials (Blau and Beller, 1988; Wright and Ermisch, 1991). Their findings suggest that the size of the unexplained differential changes significantly when the selectivity variable is included in the wage equation as a regressor. Under the original Heckman-Lee formulation, the wage sample is assumed to result from a single censoring process, and consequently the selectivity bias is corrected by including one selectivity variable generated by a first stage univariate probit. However, the problem of sample selection may still remain unresolved if, in fact, the wage sample is generated through multiple selection rules. …