Estimating the Variance of Decomposition Effects

Abstract

We derive the asymptotic variance of the Blinder-Oaxaca decomposition effects. We show that the delta method approach that builds on the assumption of fixed regressors understates true variability of the decomposition effects when regressors are stochastic. Our proposed variance estimator takes randomness of regressors into consideration. Our approach is applicable to both the linear and nonlinear decompositions, for the latter of which only a bootstrap method is an option. As our derivation follows the general framework of m-estimation, it is straightforward to extend to the cluster-robust variance estimator. We demonstrate the finite-sample performance of our variance estimator with a Monte Carlo study and present a real-data application