Comparing the Incomparable? Issues of Lacking Common Support, Functional-Form Misspecification, and Insufficient Sample Size in Decompositions

Abstract

Decompositions make it possible to investigate whether gaps between groups in certain outcomes would remain if groups had comparable characteristics. In practice, however, such a counterfactual comparability is difficult to establish in the presence of lacking common support, functional-form misspecification, and insufficient sample size. In this article, the authors show how decompositions can be undermined by these three interrelated issues by comparing the results of a regression-based Kitagawa-Blinder-Oaxaca decomposition and matching decompositions applied to simulated and real-world data. The results show that matching decompositions are robust to issues of common support and functional-form misspecification but demand a large number of observations. Kitagawa-Blinder-Oaxaca decompositions provide consistent estimates also for smaller samples but require assumptions for model specification and, when common support is lacking, for model-based extrapolation. The authors recommend that any decomposition benefits from using a matching approach first to assess potential problems of common support and misspecification.