Essays on Cross-Sectional and Network Dependence
Cross-sectional dependence is a common phenomenon in economic data. It has attracted increasing attention recently and puts forward new challenges. This dissertation consists of three chapters that deal with several important econometric problems that arise when crosssectional dependence is present. Chapter 1: We apply Stein’s method to investigate the normal approximation for both non-degenerate and degenerate U-statistics with cross-sectionally dependent underlying processes in the Wasserstein metric. We show that the convergence rates depend on the mixing rates, the sparsity of the cross-sectional dependence, and the moments of the kernel functions. Conditions are derived for central limit theorems to hold as corollaries. Chapter 2: We apply the limiting distribution theory for degenerate U-statistics, discussed in the previous chapter, to kernel smoothing based nonparametric specification tests, allowing for cross-sectional dependence in the underlying processes. This theory is then used to generalise the classical Fama-MacBeth regression test. Chapter 3: We generalise the tapering estimators for high-dimensional covariance matrices to allow for more complex and practical dependence structures, whilst allowing for measurement errors in the observations of the structure. We establish the convergence rate of such estimators under weak conditions on the measurement errors and we argue that it is often beneficial to include auxiliary structural information even if it is measured with errors.
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