A Partially Linear Kernel Estimator for Categorical Data

We extend Robinson's (1988) partially linear estimator to admit the mix of datatypes typically encountered by applied researchers, namely, categorical (nominal and ordinal) and continuous. We also relax the independence assumption that is prevalent in this literature and allow for β-mixing time-series data. We employ Li, Ouyang, and Racine's (2009) categorical and continuous data kernel method, and extend this so that a mix of continuous and/or categorical variables can appear in the nonparametric part of a partially linear time-series model. The estimator appearing in the linear part is shown to be -consistent, which is of course the case for Robinson's (1988) estimator. Asymptotic normality of the nonparametric component is also established. A modest Monte Carlo simulation demonstrates that the proposed estimator can outperform existing nonparametric, semiparametric, and popular parametric specifications that appear in the literature. An application using Survey of Income and Program Participation (SIPP) data to model a dynamic labor supply function is undertaken that provides a robustness check and demonstrates that the proposed method is capable of outperforming popular parametric specifications that have been used to model this dataset.