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Decomposing Differences in Arithmetic Means: A Doubly-Robust Estimation Approach

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  • Boris Kaiser

Abstract

When decomposing differences in average economic outcome between two groups of individuals, it is common practice to base the analysis on logarithms if the dependent variable is nonnegative. This paper argues that this approach raises a number of undesired statistical and conceptual issues because decomposition terms have the interpretation of approximate percentage differences in geometric means. Instead, we suggest that the analysis should be based on the arithmetic means of the original dependent variable. We present a flexible parametric decomposition framework that can be used for all types of continuous (or count) nonnegative dependent variables. In particular, we derive a propensity-score-weighted estimator for the aggregate decomposition that is "doubly robust", that is, consistent under two separate sets of assumptions. A comparative Monte Carlo study illustrates that the proposed estimator performs well in a many situations. An application to the union wage gap in the United States finds that the importance of the unexplained union wage premium is much smaller than suggested by the standard log-wage decomposition.

Suggested Citation

  • Boris Kaiser, 2013. "Decomposing Differences in Arithmetic Means: A Doubly-Robust Estimation Approach," Diskussionsschriften dp1308, Universitaet Bern, Departement Volkswirtschaft.
    • Handle: RePEc:ube:dpvwib:dp1308
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    Cited by:

    1. Słoczyński, Tymon & Wooldridge, Jeffrey M., 2018. "A General Double Robustness Result For Estimating Average Treatment Effects," Econometric Theory, Cambridge University Press, vol. 34(1), pages 112-133, February.
    2. Gail Pacheco & Bill Cochrane, 2015. "Decomposing the temporary-permanent wage gap in New Zealand," Working Papers 2015-07, Auckland University of Technology, Department of Economics.

    More about this item

    Keywords

    Oaxaca-Blinder; Decomposition Methods; Quasi-Maximum-Likelihood; Doubly Robust Estimation; Arithmetic and Geometric Means; Inverse Probability Weighting;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials

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