Non-parametric regression for binary dependent variables

Finite-sample properties of non-parametric regression for binary dependent variables are analyzed. Non parametric regression is generally considered as highly variable in small samples when the number of regressors is large. In binary choice models, however, it may be more reliable since its variance is bounded. The precision in estimating conditional means as well as marginal effects is investigated in settings with many explanatory variables (14 regressors) and small sample sizes (250 or 500 observations). The Klein-Spady estimator, Nadaraya-Watson regression and local linear regression often perform poorly in the simulations. Local likelihood logit regression, on the other hand, is 25 to 55% more precise than parametric regression in the Monte Carlo simulations. In an application to female labour supply, local logit finds heterogeneity in the effects of children on employment that is not detected by parametric or semiparametric estimation. (The semiparametric estimator actually leads to rather similar results as the parametric estimator.)