Hypothesis tests when decomposing differences in the first moment

Recently the Oaxaca decomposition for wage differentials has been extended to study the differences in the first moment. For example, this type of decomposition can be used to study differences in labor market participation rates by race, where the participation equation may be estimated by logit or probit. This paper develops a simple test for the significance of characteristics and coefficients effects in a decomposition analysis of differences in the first moment at aggregate and individual variable levels. In order to derive the test statistics, the asymptotic variances of the characteristics and coefficients effects at both aggregate and individual variable levels are calculated using the well-known delta method. The significance test for the Oaxaca decomposition is incorporated as a special case of this proposed test.