Regression with discrete covariates

Abstract

In this chapter, we outline how to construct nonparametric estimators for a regression model in the presence of discrete regressors. Estimating a regression model when either all of the covariates are discrete or there is mixed data is relatively straightforward, given our earlier discussion in Chapter 5. The key is that we must use kernels appropriate for smoothing discrete data, as discussed in Chapter 7. As with density estimation we will need to modify the kernel weights. Aside from this modification from the continuous-only setting, the intuition and construction of the estimators follow. We feel that you will have little trouble following the arguments in this chapter (assuming you understand the previous chapters). We leave our treatment of estimation with a discrete left-hand-side variable for the presentation of semiparametric methods (Chapter 9).