Essays on Panel Data with Multidimensional Unobserved Heterogeneity

Abstract: This thesis contributes to econometric methodology in terms of estimation and inference in static panel data models with unobserved multidimensional heterogeneity. When not properly accounted for, unobserved heterogeneity may introduce bias into the parameter estimates associated with covariates of interest, such as treatment indicators or determinants of macroeconomic indicators. A common way of representing such heterogeneity is through an interactive effects structure estimated by factor-augmented regression models. One of the workhorse methods in this literature is the common correlated effects (CCE) estimator of Pesaran (2006). A major inconvenience with this method is that its statistical properties are derived under the assumption that both the cross-section dimension, $N$, and the time dimension, $T$, of the panel are large, a condition that is rarely met by datasets used in empirical practice. In the first chapter, we develop a new theory that establishes the asymptotic properties of the CCE estimator in panel datasets with small time dimension $T$. We show that many of the previously derived large-$T$ results continue to hold.The second chapter investigates the well-known dummy variable trap in the framework of factor-augmented regressions. The problem of multicollinearity among regressors has been extensively discussed in the fixed effects literature but has gone largely unnoticed in the case of interactive effects. We consider the challenging case when some regressors are asymptotically collinear with the interactive effects. In this setting we develop the relevant asymptotic theory.In the third chapter, we show that fixed effects demeaning in linear panel data regressions is more useful than commonly thought, in that it enables consistent and asymptotically normal estimation of interactive effects models with heterogeneous slope coefficients for panels where $T$ is small and only $N$ is large. As an illustration, we consider the problem of estimating the average treatment effect in the presence of unobserved time-varying heterogeneity. The last chapter reviews the use of panel cointegration tests in studies on the existence of a long-run equilibrium relation between insurance market activity and economic output. I point out consequences for the validity of empirical findings when violating theoretically motivated conditions on the relative dimensions of the panel dataset under consideration. The bulk of existing evidence relies on Pedroni’s (2004) residual-based panel cointegration test procedure. I demonstrate how this test procedure tends to over-reject the null hypothesis of no cointegration leading to potentially false conclusions if the data set does not meet the theoretical restrictions on the panel size.

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