Partial Time‐Varying Regression Modelling Under General Heterogeneity

Abstract

This paper studies a semiparametric time‐varying regression model in which a subset of regressors is associated with fixed parameters, while the remaining regressors have parameters that evolve smoothly over time. We propose a closed‐form semiparametric Frisch‐Waugh‐Lovell estimator for the fixed parameters, and a non‐parametric kernel type estimator for the time‐varying parameters, and establish their theoretical properties in a highly heterogeneous regression setting. The estimator of the fixed regression parameter attains the parametric rate of convergence. Despite the presence of substantial heterogeneity in both regressors and regression noise, asymptotic normality is established for individual components of the fixed and time‐varying parameters. The resulting standard error estimators take the same form as those in White (1980), while being theoretically justified under considerably weaker assumptions. The theoretical findings are supported by Monte Carlo simulations demonstrating good finite‐sample performance and are further illustrated through an empirical forecasting application.