The paper derives a general Central Limit Theorem (CLT) and asymptotic distributions for sample moments related to panel data models with large n. The results allow for the data to be cross sectionally dependent, while at the same time allowing the regressors to be only sequentially rather than strictly exogenous. The setup is sufficiently general to accommodate situations where cross sectional dependence stems from spatial interactions and/or from the presence of common factors. The latter leads to the need for random norming.
Limit Theory for Panel Data Models with Cross Sectional Dependence and Sequential ExogeneityGuido Kuersteiner and Ingmar Prucha ,
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Journal of Econometrics