Functional Coefficient Estimation with Both Categorical and Continuous Data∗

We propose a local linear functional coefficient estimator that admits a mix of discrete and continuous data for stationary time series. Under weak conditions our estimator is asymptotically normally distributed. A small set of simulation studies is carried out to illustrate the finite sample performance of our estimator. As an application, we estimate a wage determination function that explicitly allows the return to education to depend on other variables. We find evidence of the complex interacting patterns among the regressors in the wage equation, such as increasing returns to education when experience is very low, high return to education for workers with several years of experience, and diminishing returns to education when experience is high. Compared with the commonly used parametric and semi-parametric methods, our estimator performs better in both goodness-of-fit and in yielding economically interesting interpretation.