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Limit theorems for network dependent random variables?
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DOI：10.1016/j.jeconom.2020.05.019.png)
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This paper is concerned with cross-sectional dependence arising because observations are interconnected through an observed network. Following (Doukhan and Louhichi, 1999), we measure the strength of dependence by covariances of nonlinearly trans -formed variables. We provide a law of large numbers and central limit theorem for network dependent variables. We also provide a method of calculating standard errors robust to general forms of network dependence. For that purpose, we rely on a network heteroskedasticity and autocorrelation consistent (HAC) variance estimator, and show its consistency. The results rely on conditions characterized by tradeoffs between the rate of decay of dependence across a network and network's denseness. Our approach can accommodate data generated by network formation models, random fields on graphs, conditional dependency graphs, and large functional-causal systems of equations. (C) 2020 Elsevier B.V. All rights reserved.
Keyword:
Network dependence
Random fields
Central limit theorem
Networks
Law of large numbers
Cross-sectional dependence
Spatial processes
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