Estimation of Varying Coefficient models in Stata

Non-parametric regressions are a powerful statistical tool to model relationships between dependent and independent variables with minimal assumptions on the underlying functional forms. However, these types of models have two main weaknesses: First, their added flexibility also creates a curse of dimensionality, even with a modest set of independent variables. Second, while the above weakness can be addressed using larger samples, procedures available for model selection, in particular cross-validation, are computationally intensive in large samples. An alternative is to use semiparametric regression modeling combining the flexibility of non-parametric with the structure of standard models. In this presentation, I’m introducing a set of programs that aim to estimate a semiparametric model known as varying coefficient models. The proposed modules estimate linear models where the coefficients for the independent variables are assume to be a smooth function of a single running z, using a local linear kernel estimation. The current set of modules can be used to: 1) Estimate the optimal bandwidth for the semiparametric model using CV, 2) Estimate the model(s) using a predefined set of reference points, with three alternatives standard errors estimations 3) Obtain the model predictions as well as a set of diagnosis and specification tests, 4) Plot all the coefficients, and rate of change, respect to the running variable for the selected points of reference.