We develop a reliable Bayesian inference for the RIF-regression model of Firpo, Fortin and Lemieux (Econometrica, 2009) in which we first estimate the log wage distribution by a mixture of normal densities. This approach is pursued so as to provide better estimates in the upper tail of the wage distribution as well as valid confidence intervals for the Oaxaca-Blinder decomposition. We apply our method to a Mincer equation for analysing the recent changes in the U.S. wage structure and in earnings inequality. Our analysis uses data from the CPS Outgoing Rotation Group (ORG) from 1992 to 2009. We find first that the largest part (around 77% on average) of the recent changes in the U.S. wage inequality is explained by the wage structure effect and second that the earnings inequality is rising more at the top end of the wage distribution, even in the most recent years. The decline in the unionisation rate has a small impact on total wage inequality while differences in returns to education and gender discrimination are the dominant factors accounting for these recent changes.
