Nonparametric Estimation in Panel Data Models with Heterogeneity and Time-Varyingness

In this paper, we consider a class of time-varying panel data models with individual-specific regression coefficients and common factors where both the serial correlation and cross-sectional dependence among error terms can be present. Based on an initial estimator of factors, we propose a unified semiparametric profile method to estimate the time--varying slope coefficients and the factor loadings simultaneously for each individual. It can be applied in different cases with observable or unobservable factors. To address the curse of dimensionality, we establish asymptotic properties for summary statistics: the mean group estimators of both regression coefficients and loadings with large N and T. The finite sample performance of the proposed estimators are assessed by both simulated data examples and an empirical study on an OECD health care expenditure dataset