The Incidental Parameters Problem in Testing for Remaining Cross-section Correlation

In this paper we consider the properties of the Pesaran (2004, 2015a) CD test for cross-section correlation when applied to residuals obtained from panel data models with many estimated parameters. We show that the presence of period-specific parameters leads the CD test statistic to diverge as length of the time dimension of the sample grows. This result holds even if cross-section dependence is correctly accounted for and hence constitutes an example of the Incidental Parameters Problem. The relevance of this problem is investigated both for the classical Time Fixed Effects estimator as well as the Common Correlated Effects estimator of Pesaran (2006). We suggest a weighted CD test statistic which re-establishes standard normal inference under the null hypothesis. Given the widespread use of the CD test statistic to test for remaining cross-section correlation, our results have far reaching implications for empirical researchers.Comment: 84 pages, 11 table

A Linear Estimator for Factor-Augmented Fixed-T Panels With Endogenous Regressors

A novel method-of-moments approach is proposed for the estimation of factor-augmented panel data models with endogenous regressors when T is fixed. The underlying methodology involves approximating the unobserved common factors using observed factor proxies. The resulting moment conditions are linear in the parameters. The proposed approach addresses several issues which arise with existing nonlinear estimators that are available in fixed T panels, such as local minima-related problems, a sensitivity to particular normalization schemes, and a potential lack of global identification. We apply our approach to a large panel of households and estimate the price elasticity of urban water demand. A simulation study confirms that our approach performs well in finite samples