Estimation and Testing in Panel Data with Cross-Section Dependence
Abstract: This thesis makes a contribution the econometrics of panel data with cross-section dependence (CSD). It consists of five self-contained papers. The most popular approach to account for CSD is to attribute the co-movements of observed variables across entities to unobserved common factors and to estimate these factors via simple cross-section averages of the data. The chapters in this thesis investigate the properties of regression estimators that are based on this approach and suggest new tests that rely on cross-sectionaverages to capture the impact of latent common factors.Chapter two points out a problem with the Common Correlated Effects (CCE) estimator of Pesaran (2006) that appears in the empirically relevant case when the number of factors is strictly less than the number of observables used in their estimation. Specifically, the use of too many observables causes the second moment matrix of the estimated factors to become asymptotically singular, an issue that has not yet been appropriately accounted for. We show that the dominating method of proving the asymptotic properties of the CCE estimator breaks down in this case and suggest a more general method of proof.Chapter three develops PANICCA, an approach to panel unit root testing that combines the merits of the two most popular approaches for testing for a unit root in panel data with CSD. We take over the separate treatment of idiosyncratic and common components inherent in the PANIC framework which allows todetermine the source of nonstationarity specifically. In order to decompose the observed data into its two components, we use cross-section averages of all available variables, a simple, yet powerful approach with good small sample properties.Chapter four considers models where the impact of latent factors converges to zero as the number of individuals tends to infinity. These so-called weak factors constitute a setting for which the two dominating regression estimators for panel data with CSD are not explicitly conceived for. We investigate theasymptotic properties of these two estimators and set up minimal conditions for the factor strength under which asymptotic normality and consistency can be proven.Chapter five suggests a Hausman test statistic based on the difference between Pesaran’s (2006) CCE estimator and the OLS estimator. Under the null hypothesis of no cross-section dependence, this difference has a higher rate of convergence than the estimators themselves. As an immediate consequence, the test statistic diverges at a higher rate than the popular CD test of Pesaran (2004) when the data are crosssectionally correlated, thus leading to a test with higher power.Chapter six provides a simple and user-friendly way of measuring the contribution of different markets on developments in the fundamental price of an asset. We note that standard models for price discovery can be represented in the form of a common factor model and use a decomposition based on cross-section averages to separate idiosyncratic and common components of the observed price series.
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