  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.
