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Source: Eller College of Management, University of Arizona
Resulting in 1 citation.
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Gelbach, Jonah B. |
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When Do Covariates Matter? And Which Ones, and How Much? Working Paper, Eller College of Management, University of Arizona, June 2009. Also: http://www.econ.ubc.ca/seminars/gelbach.pdf Cohort(s): NLSY79 Publisher: Department of Economics, Eller College of Management, University of Arizona Keyword(s): Racial Differences; Variables, Independent - Covariate; Wage Gap Permission to reprint the abstract has not been received from the publisher. Many authors add variables sequentially to their covariate sets when using linear estimators to investigate the effect of a variable of interest X1, on some outcome y. One justification for this practice involves robustness: if estimates of the coefficient on X1 are stable across specifications, then researchers conclude that their findings are robust. A second justification involves accounting: by measuring the difference in X1's estimated coefficient as they add sets of covariates to the specification, researchers sometimes claim to have measured the effects of covariate variation on this coefficient. In this paper, I show that sequential covariate addition can be very misleading. The relationship between X1 and a given covariate set may be sensitive to the order in which other covariates have been added. This sensitivity is especially problematic for accounting exercises, as I show using the canonical example of the black-white wage gap. The paper's main contribution is to show how to use the population and sample omitted variables bias formulas to define an economically and econometrically meaningful conditional decomposition that explains how much various covariates account for sensitivity in the estimated coefficient on X1. I illustrate the conditional decomposition using NLSY data on the black-white wage gap, with interesting empirical results. I also discuss a number of extensions, including: instrumental variables estimators; the fact that my decomposition nests the Oaxaca-Blinder decomposition; and using the properties of the omitted variables bias formula to construct a Hausman test for cross-specification differences in coefficient estimates under the null that X1 and X2 are uncorrelated. I also provide asymptotic variance formulas in an appendix, as well as a link to Stata code that implements my estimators. |
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Bibliography Citation
Gelbach, Jonah B. "When Do Covariates Matter? And Which Ones, and How Much?" Working Paper, Eller College of Management, University of Arizona, June 2009. |