Estimation of Panel Data Models with Cross-Sectionally Heteroskedastic Data

Panel data models with cross-sectionally heteroskedastic data often suffer from the well-known incidental parameters problem. Some recent studies have proposed that the structural parameters (common parameters to all of the cross-sectional entities) can be consistently estimated if they are estimated jointly with the cross-sectionally weighted averages of the incidental parameters. In this paper, we provide a sufficient condition under which the proposed methods can yield consistent and asymptotically normal estimates of the structural parameters. With the condition, we show that the unrestricted factor IV method proposed by Robertson and Sarafidis (2015, Journal of Econometrics) and the transformed likelihood method of Hayakawa and Pesaran (2015, Journal of Econometrics) can consistently estimate the structural parameters in the panel data models with unknown common factors or dynamic panel models with fixed individual entity-specific effects