Nonparametric Time-Varying Coefficient Models for Panel Data

The collection rate of contributions to public pension (CRCP), expressed as the ratio of the actual contributions to the expected contributions from insurers, is a key component of the public pension system in China. Recent years have seen various patterns of change in CRCPs at the provincial level. In order to study the drastic changes in a short time and understand their underlying implications, we propose a nonparametric time-varying coefficients model for longitudinal data with pre-specified finite time points, also known as panel data. By utilizing a penalized least squares method, the proposed method enables estimation of a large number of parameters, which can exceed the sample size. The resulting estimator is shown to be efficient, robust, and computationally feasible. Furthermore, it possesses desirable theoretical properties such as n(1/2)-consistency, asymptotic normality, and the oracle property.