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