Distribution regression with censored selection

Chernozhukov, Fernández-Val, and Luo (2023, CFL (2023) hereafter) considered a distribution regression model subject to sample selection with a binary selection mechanism. In this paper, we show how to identify and estimate a semi-parametric distribution regression model subject to a censored selection rule. With censored selection, we do not need to impose the usual outcome exclusion restriction or exclusion of the level of the latent selection variable from the selection sorting function for model identification, unlike CFL (2023). We propose new semiparametric estimators and corresponding inference procedures for model parameters and related functional parameters. We apply our method to investigate wage inequality in the UK for the period 1978–2000 using the Family Expenditure Survey (FES) data. Our findings reveal that (i) the selection sorting exclusion and outcome exclusion restrictions imposed by CFL (2023) are rejected; (ii) there is negative selection into work at most quantile levels for females, but not for males; (iii) in contrast to CFL (2023), our selection sorting effect pattern does not offer clear evidence on assortative matching or glass ceiling in the UK labor market; (iv) the latent gender wage gaps after correcting for selection bias are about 25%–50% of CFL (2023)’s estimates, and are also significantly smaller than the observed wage gaps; (v) similar to CFL (2023), there exists some strong evidence on gender discrimination in the UK labor market.