COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1668R Estimating Derivatives in Nonseparable Models Joseph G. Altonji, Hidehiko Ichimura and Taisuke Otsu July 2008 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. |
