Nonparametric Estimation in Panel Data Models with Heterogeneity and Time Varyingness

Panel data subject to heterogeneity in both cross-sectional and time-serial directions are commonly encountered across social and scientific fields. To address this problem, we propose a class of time-varying panel data models with individual-specific regression coefficients and interactive common factors. This results in a model capable of describing heterogeneous panel data in terms of time-varyingness in the time-serial direction and individual-specific coefficients among crosssections. Another striking generality of this proposed model relies on its compatibility with endogeneity in the sense of interactive common factors. Model estimation is achieved through a novel duple least-squares (DLS) iteration algorithm, which implements two least-squares estimation recursively. Its unified ability in estimation is nicely illustrated according to flexible applications on various cases with exogenous or endogenous common factors. Established asymptotic theory for DLS estimators benefits practitioners by demonstrating effectiveness of iteration in eliminating estimation bias gradually along with iterative steps. We further show that our model and estimation perform well on simulated data in various scenarios as well as an OECD healthcare expenditure dataset. The time-variation and heterogeneity among cross-sections are confirmed by our analysis.