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Building on recent advances in inverse probability weighted identification and estimation of counterfactual distributions, the authors examine the history of wage earnings for women and their potential wage distributions in the United States. These potentials are two counterfactuals, what if women received men’s market “rewards” for their own “skills,” and what if they received the women’s rewards but for men’s characteristics? Using the Current Population Survey data from 1976 to 2013, the authors analyze the entire counterfactual distributions to separate the “structure” and human capital “composition” effect. In contrast to Maasoumi and Wang (2019), the reference outcome in these decompositions is women’s observed earnings distribution, and inverse probability methods are employed, rather than the conditional quantile approaches. The authors provide decision theoretic measures of the distance between two distributions, to complement assessments based on mean, median, or particular quantiles. We assess uniform rankings of alternate distributions by tests of stochastic dominance in order to identify evaluations robust to subjective measures. Traditional moment-based measures severely underestimate the declining trend of the structure effect. Nevertheless, dominance rankings suggest that the structure (“discrimination”?) effect is bigger than human capital characteristics.

Since its introduction by Chari, Kehoe, and McGrattan (2007), Business Cycle Accounting (BCA) exercises have become widespread. Much attention has been devoted to the results of such exercises and to methodological departures from the baseline methodology. Little attention has been paid to identification issues within these classes of models. In this chapter, the authors investigate whether such issues are of concern in the original methodology and in an extension proposed by Šustek (2011) called Monetary Business Cycle Accounting. The authors resort to two types of identification tests in population. One concerns strict identification as theorized by Komunjer and Ng (2011) while the other deals both with strict and weak identification as in Iskrev (2010). Most importantly, the authors explore the extent to which these weak identification problems affect the main economic takeaways and find that the identification deficiencies are not relevant for the standard BCA model. Finally, the authors compute some statistics of interest to practitioners of the BCA methodology.