This paper considers panel data models in the presence of two sources of cross-sectional depen-dence: endogenous spatial interactions and common effects. It derives identification conditions and proposes a number of estimators for the joint model. The estimation approach replaces the unobserved common factors with cross-sectional averages and utilizes instrumental variables and quadratic moment conditions in order to cope with the endogenous spatial effects. The proposed estimators are shown to be consistent as long as N is large, irrespective of the size of T. The asymptotic distributions of these estimators are free of nuisance parameters, provided that T is of a smaller order of magnitude than N, as (N, T) → ∞ jointly. Compared with the maximum likelihood approach, the number of latent factors need not be estimated, and more general forms of serial correlation in the disturbances are permitted. A wide range of Monte Carlo exercises lend further support to the theoretical results regarding identification and estimation.
A detailed empirical application to real house price changes reveals that significant spatial dependence exists across MSAs in the US, and it demonstrates the importance of adequately
35See Appendix B and the Online Supplement for a more detailed characterization and comparison of different spatial weights matrices.
36We have also considered the Durbin terms, but they are found to be insignificant.
removing common effects when analyzing the strength of spatial interconnections. The study also identifies significant effects of population and income growth on house price growth. Besides geographical proximity, we also consider spatial weights based on migration flows and on pairwise correlations of de-factored house price changes. The main findings remain valid under the different measures of connections. These empirical results highlight the need to consider the spatial spillover effects in housing markets when making policy and business decisions.
An important next step for future research is to incorporate rich spatio-temporal dynamics into the model specifications. Such extensions provide a full characterization of how an economic phenomenon transmits across space and over time, and they enable us to distinguish between short-term and long-term spillover effects. Another possible extension of the model is to include slope heterogeneity, which is especially relevant for studies covering different countries, regions, and industries. The present paper is also related to the recent study by Pesaran and Yang (2016), who consider networks with dominant units and common factors. The identification and estimation of these models, in which the spatial weights matrix may have unbounded column sums, are of practical importance and worth further investigation.
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