Smooth varying-coefficient models in Stata

Abstract

Nonparametric regressions are powerful statistical tools that can be used to model relationships between dependent and independent variables with minimal assumptions on the underlying functional forms. Despite their potential benefits, these models have two weaknesses: The added flexibility creates a curse of dimensionality, and procedures available for model selection, like crossvalidation, have a high computational cost in samples with even moderate sizes. An alternative to fully nonparametric models is semiparametric models that combine the flexibility of nonparametric regressions with the structure of standard models. In this article, I describe the estimation of a particular type of semiparametric model known as the smooth varying-coefficient model (Hastie and Tibshirani, 1993, Journal of the Royal Statistical Society, Series B 55: 757–796), based on kernel regression methods, using a new set of commands within vc_pack. These commands aim to facilitate bandwidth selection and model estimation as well as create visualizations of the results.