We present a simple way to estimate the effects of changes in a vector of observable variables X on a limited dependent variable Y when Y is a general nonseparable function of X and unobservables, and X is independent of the unobservables. We treat models in which Y is censored from above, below, or both. The basic idea is to first estimate the derivative of the conditional mean of Y given X at x with respect to x on the uncensored sample without correcting for the effect of x on the censored population. We then correct the derivative for the effects of the selection bias. We discuss nonparametric and semiparametric estimators for the derivative. We also discuss the cases of discrete regressors and of endogenous regressors in both cross section and panel data contexts.

We examine changes in the characteristics of American youth between the late 1970s and the late 1990s, with a focus on characteristics that matter for labor market success. The current generation is more skilled than the previous one. Blacks and Hispanics have gained relative to whites, and women have gained relative to men. However, the skill distribution has widened overall. Shifts in parental education generate many of the observed changes. We also provide speculative estimates suggesting that if recent trends in technology and the supply of human capital continue, wage inequality will increase substantially by 2025.