This paper considers a general form of network dependence where dependence between two sets of random variables becomes weaker as their distance in a networkgets longer. We show that such network dependence cannot be embedded as a random field on a lattice in a Euclidean space with a fixed dimension when the maximum clique increases in size as the network grows. This paper applies Doukhan and Louhichi (1999) 's weak dependence notion to network dependence by measuring dependence strength by the covariance between nonlinearly transformed random variables. While this approach covers examples such as strong mixing random fields on a graph and conditional dependency graphs, it is most useful when dependence arises through a large functional-causal system of equations. The main results of our paper include the law of large numbers , and the central limit theorem  . We also propose a heteroskedasticity-autocorrelation consistent variance estimator and prove its consistencyunder regularity conditions. The finite sample performance of this latter estimator is investigated through a Monte Carlo simulation study .
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 transformed 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 .
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considers a general form of network dependence where dependence between two sets of random variables becomes weaker as their distance in a networkgets longer. We show that such network dependence cannot be embedded as a random field on a lattice in a Euclidean space with a fixed dimension when the maximum clique increases in size as the network grows. This paper applies
is concerned with cross-sectional dependence arising because observations are interconnected through an observed network. Following
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's weak dependence notion to network dependence by measuring dependence strength by the covariance between nonlinearly transformed random variables. While this approach covers examples such as strong mixing random fields on a graph and conditional dependency graphs, it is most useful when dependence arises through a large functional-causal system of equations. The main results of our paper include the
, we measure the strength of dependence by covariances of nonlinearly transformed variables. We provide a
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, and the
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for network dependent variables
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propose a heteroskedasticity-autocorrelation consistent variance estimator and prove its consistencyunder regularity conditions. The finite sample performance of this latter estimator is investigated through a Monte Carlo simulation study
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