Time-Varying Panel Data Models with an Additive Factor Structure

Motivated by many key features of real data from economics and finance, we study a semiparametric panel data model with time-varying regression coefficients associated with an additive factor structure. In our model, factor loadings are unknown functions of observable variables which can capture time-variant and heterogeneous covariate information. A profile marginal integration (PMI) method is proposed to estimate unknown coefficient functions, factors and their loadings jointly in a single step, which can result in estimators with closed forms. Asymptotic distributions for the proposed profile estimators are established. Two empirical applications on US stock returns and OECD health care expenditure are provided. Thorough numerical results demonstrate the finite sample performance of our estimation and its advantage over traditional models in the relevant literature.