Decomposing differences in arithmetic means: a doubly robust estimation approach

When decomposing differences in average economic outcomes 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 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 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 many situations. An application to the union wage gap in the USA finds that the importance of the unexplained union wage premium is much smaller than suggested by the standard log-wage decomposition.