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We analyze the role of selection bias in generating the 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 the 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 have increased wages at all quantiles while the impact of the structural effects varies by time period and quantile. Changes in the role of selection only appear at the lower quantiles of the wage distribution. The evidence suggests that there is positive selection in the 1970s which diminishes until the later 1990s. This reduces wages at lower quantiles and increases wage inequality. Post 2000 there appears to be an increase in positive sorting which reduces the selection effects on wage inequality., Comment: 52 pages, 19 figures, change of title with respect to version v4

We consider identification and estimation of nonseparable sample selection models with censored selection rules. We employ a control function approach and discuss different objects of interest based on (1) local effects conditional on the control function, and (2) global effects obtained from integration over ranges of values of the control function. We derive the conditions for the identification of these different objects and suggest strategies for estimation. Moreover, we provide the associated asymptotic theory. These strategies are illustrated in an empirical investigation of the determinants of female wages in the United Kingdom., Comment: 53 pages, 4 tables, 5 figures

We examine the impact of annual hours worked on annual earnings by decomposing changes in the real annual earnings distribution into composition, structural and hours effects. We do so via a nonseparable simultaneous model of hours, wages and earnings. Using the Current Population Survey for the survey years 1976--2019, we find that changes in the female distribution of annual hours of work are important in explaining movements in inequality in female annual earnings. This captures the substantial changes in their employment behavior over this period. Movements in the male hours distribution only affect the lower part of their earnings distribution and reflect the sensitivity of these workers' annual hours of work to cyclical factors., Comment: 44 pages, 20 figures, includes web appendix

We develop a distribution regression model under endogenous sample selection. This model is a semi-parametric generalization of the Heckman selection model. It accommodates much richer effects of the covariates on outcome distribution and patterns of heterogeneity in the selection process, and allows for drastic departures from the Gaussian error structure, while maintaining the same level tractability as the classical model. The model applies to continuous, discrete and mixed outcomes. We provide identification, estimation, and inference methods, and apply them to obtain wage decomposition for the UK. Here we decompose the difference between the male and female wage distributions into composition, wage structure, selection structure, and selection sorting effects. After controlling for endogenous employment selection, we still find substantial gender wage gap -- ranging from 21\% to 40\% throughout the (latent) offered wage distribution that is not explained by composition. We also uncover positive sorting for single men and negative sorting for married women that accounts for a substantive fraction of the gender wage gap at the top of the distribution., 85 pages, 4 tables, 40 figures, includes supplement

Many applications involve a censored dependent variable and an endogenous independent variable. Chernozhukov et al. (2015) introduced a censored quantile instrumental variable estimator (CQIV) for use in those applications, which has been applied by Kowalski (2016), among others. In this article, we introduce a Stata command, cqiv, that simplifes application of the CQIV estimator in Stata. We summarize the CQIV estimator and algorithm, we describe the use of the cqiv command, and we provide empirical examples., Comment: 12 pages, 1 table, associated software can be found at https://ideas.repec.org/c/boc/bocode/s457478.html. arXiv admin note: text overlap with arXiv:1104.4580. We have updated the command to report standard errors and bootstrap percentile-t confidence intervals

We propose strategies to estimate and make inference on key features of heterogeneous effects in randomized experiments. These key features include best linear predictors of the effects using machine learning proxies, average effects sorted by impact groups, and average characteristics of most and least impacted units. The approach is valid in high dimensional settings, where the effects are proxied (but not necessarily consistently estimated) by predictive and causal machine learning methods. We post-process these proxies into estimates of the key features. Our approach is generic, it can be used in conjunction with penalized methods, neural networks, random forests, boosted trees, and ensemble methods, both predictive and causal. Estimation and inference are based on repeated data splitting to avoid overfitting and achieve validity. We use quantile aggregation of the results across many potential splits, in particular taking medians of p-values and medians and other quantiles of confidence intervals. We show that quantile aggregation lowers estimation risks over a single split procedure, and establish its principal inferential properties. Finally, our analysis reveals ways to build provably better machine learning proxies through causal learning: we can use the objective functions that we develop to construct the best linear predictors of the effects, to obtain better machine learning proxies in the initial step. We illustrate the use of both inferential tools and causal learners with a randomized field experiment that evaluates a combination of nudges to stimulate demand for immunization in India., 81 pages, 8 figures, 17 tables, includes Online Appendix

We derive fixed effects estimators of parameters and average partial effects in (possibly dynamic) nonlinear panel data models with individual and time effects. They cover logit, probit, ordered probit, Poisson and Tobit models that are important for many empirical applications in micro and macroeconomics. Our estimators use analytical and jackknife bias corrections to deal with the incidental parameter problem, and are asymptotically unbiased under asymptotic sequences where $N/T$ converges to a constant. We develop inference methods and show that they perform well in numerical examples., Comment: 84 pages, 10 tables, includes supplementary appendix; Relative to the published version we corrected some expressions in Theorem 4.2 here