Asymptotic Theory for Dynamic Heterogeneous Panels with Cross-Sectional Dependence and Its Applications

This paper considers dynamic heterogeneous panels with cross-sectional dependence (DHP+CSD), where the dependence is modeled using a factor structure. Dynamics, heterogeneity and cross-sectional dependence are pervasive characteristics of most data sets and it is therefore essential for empirically realistic models to allow for the three features. It is also well-known that the persistence of aggregate series may not reflect the true persistence of its underlying series when the disaggregated data exhibit the three characteristics. In this regard, the estimation of DHP+CSD models is indispensable for examining the reliability of the existing analysis based on aggregate series. The main contribution of this paper is that it addresses the three issues in estimation all at the same time. To cope with the challenges in estimation arising from the greater flexibility of the model, we adopt an iterative principal component method and develop an asymptotic theory under large N and large T . The proposed estimator is shown to be √ T -consistent under non-stringent conditions and to perform well in finite samples. We apply the developed estimator to two empirical contexts. In the first application, we estimate the heterogeneous dynamics of sectoral real exchange rates to examine the role of aggregation bias in explaining the purchasing power parity puzzle. In the second application, we estimate the intrinsic persistence of the sectoral New Keynesian Phillips curves to investigate the degree of the forward-looking nature of price setting. Both applications illustrate that the DHP+CSD estimator can shed new light on the true nature of disaggregated data sets by extending the existing empirical models in meaningful ways.