Estimation of Panel Interactive Fixed Effects Model with Diversified Projections and Under Smooth Threshold Effects

Abstract

This dissertation focuses on the estimation and inferential issues of panel data models with a multiplication form of time and individual fixed effects, named interactive fixed effects. This flexible form is attractive in controlling the unobserved heterogeneity since it also captures the potential cross-sectional dependence among the data caused by the unobserved common shocks. This dissertation contributes to the existing studies by providing a new estimation method and also considering smooth transition threshold effects, discussed in Chapters 2 and 3, respectively.

Specifically, Chapter 2 proposes a new estimation approach with a combination of cross-sectional projections and a simple profile least squares method. Our method enjoys some merits, such as robustness to the pervasive conditions on factors, stationarity condition on data, or overestimating the number of factors. Under some regularity conditions, we prove that the estimator is consistent and has an asymptotic normal distribution. We run Monte Carlo simulations to investigate the finite sample properties of the proposed estimator and find its superior performance under the setup similar to real data. We also apply our method to the study of the nexus of GDP growth and financial development and find that the estimates from our approach are more reasonable in terms of the economic theory.

Chapter 3 deals with the estimation of panel data models when both interactive fixed effects and smooth transition threshold effects exist. We propose to adopt the nonlinear least squares method to estimate the parameters of interest and the principal component method for factor estimation. The asymptotic theories of the estimated parameters of interest are derived. We also conduct Monte Carlo simulations to demonstrate the good finite sample performance of the proposed estimator.