Estimation of wage inequality in the UK by quantile regression with censored selection

Arellano and Bonhomme (2017) proposed a quantile selection model to study the evolution of wage inequality in the UK, which specifies a binary selection equation and requires an exclusion restriction. In this paper we propose a quantile selection model with a more informative censored selection equation. Following Heckman (1974, 1979), Heckman and Sedlacek (1990), and Blundell et al. (2003), among others, the employment selection equation could be equivalently modeled by an hours worked equation through a censored selection. In our model, both the outcome and selection equations are specified as semiparametric quantile regressions, and no exclusion restriction is needed. We propose a quantile selection estimator that was applied to study wage inequality using the same data as in Arellano and Bonhomme (2017). Among our major findings based on our method, after adjusting for sample selection, (i) there is significant negative selection among males, in contrast to the finding of significant positive selection by Arellano and Bonhomme (2017); (ii) similar to Arellano and Bonhomme (2017), we also find positive selection for females, but our selection effects are more significant than those of Arellano and Bonhomme (2017) (See Section 5 for more details); (iii) the gender wage gap has remained large and accounting for selection leads to much smaller reduction in the gender wage gap over time, compared with the observed wage distribution and that of Arellano and Bonhomme (2017).