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We analyze the role of selection bias in generating changes in the observed distribution of female hourly wages in the United States using CPS data for the years 1975 to 2020. We account for selection bias from the employment decision by modeling the distribution of the number of working hours and estimating a nonseparable model of wages. We decompose changes in the wage distribution into composition, structural, and selection effects. Composition effects increased wages at all quantiles while the impact of the structural effects varied by time period and quantile. Changes in the role of selection only appeared at the lower quantiles of the wage distribution. The evidence suggests that there was positive selection in the 1970s, which diminished until the later 1990s. This reduced wages at lower quantiles and increased wage inequality. Post 2000 there appears to be an increase in positive sorting, which reduced the selection effects on wage inequality. [ABSTRACT FROM AUTHOR]

Counterfactual distributions are important ingredients for policy analysis and decomposition analysis in empirical economics. In this article, we develop modeling and inference tools for counterfactual distributions based on regression methods. The counterfactual scenarios that we consider consist of ceteris paribus changes in either the distribution of covariates related to the outcome of interest or the conditional distribution of the outcome given covariates. For either of these scenarios, we derive joint functional central limit theorems and bootstrap validity results for regression-based estimators of the status quo and counterfactual outcome distributions. These results allow us to construct simultaneous confidence sets for function-valued effects of the counterfactual changes, including the effects on the entire distribution and quantile functions of the outcome as well as on related functionals. These confidence sets can be used to test functional hypotheses such as no-effect, positive effect, or stochastic dominance. Our theory applies to general counterfactual changes and covers the main regression methods including classical, quantile, duration, and distribution regressions. We illustrate the results with an empirical application to wage decompositions using data for the United States. As a part of developing the main results, we introduce distribution regression as a comprehensive and flexible tool for modeling and estimating the entire conditional distribution. We show that distribution regression encompasses the Cox duration regression and represents a useful alternative to quantile regression. We establish functional central limit theorems and bootstrap validity results for the empirical distribution regression process and various related functionals. [ABSTRACT FROM AUTHOR]