When Do Covariates Matter? And Which Ones, and How Much?
40 Pages Posted: 26 Jun 2009 Last revised: 16 Sep 2014
Date Written: August 28, 2014
Authors often add covariates to a base model sequentially either to test a particular coefficient’s “robustness” or to account for the “effects” on this coefficient of adding covariates. This is problematic, due to sequence-sensitivity when added covariates are intercorrelated. Using the omitted variables bias formula, I construct a conditional decomposition that accounts for various covariates’ role in moving base regressors’ coefficients; I also provide a consistent covariance formula. I illustrate this conditional decomposition with NLSY data in an application that exhibits sequence-sensitivity. Related extensions include IV, the fact that my decomposition nests the Oaxaca-Blinder decomposition, and a Hausman-test result.
Keywords: decompositions, black-white wage gap, omitted variables
JEL Classification: C01, C13, C20, J31, J71
Suggested Citation: Suggested Citation