We prove central limit theorems for models of network formation and network processes with homophilous agents. The results hold under large-network asymptotics, enabling inference in the typical setting where the sample consists of a small set of large networks. We first establish a general central limit theorem under high-level `stabilization' conditions that provide a useful formulation of weak dependence , particularly in models with strategic interactions. The result delivers a square root n rate of convergence and a closed-form expression for the asymptotic variance. Then using techniques in branching process theory, we derive primitive conditions for stabilization in the following applications: static and dynamic models of strategic network formation , network regressions, and treatment effects with network spillovers. Finally, we suggest some practical methods for inference .
We develop a methodology for proving central limit theorems in network models with strategic interactions and homophilous agents. We consider an asymptotic framework in which the size of the network tends to infinity, which is useful for inference in the typical setting in which the sample consists of a single large network. In the presence of strategic interactions, network moments are generally complex functions of network components, where a node's component consists of all alters to which it is directly or indirectly connected. We find that a modification of "exponential stabilization" conditions from the stochastic geometry literature provides a useful formulation of weak dependence for moments of this type. Our first contribution is to prove a CLT for a large class of network moments satisfying stabilization and a moment condition. Our second contribution is a methodology for deriving primitive sufficient conditions for stabilization using results in branching process theory. We apply the methodology to static and dynamic models of network formation and discuss how it can be used more broadly .
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prove
develop a methodology for proving
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for models of network formation and network processes with
in network models with strategic interactions and
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The results hold under large-network asymptotics, enabling
We consider an asymptotic framework in which the size of the network tends to infinity, which is useful for
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where
in which
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small set of large networks. We first establish a general central limit theorem under high-level `stabilization' conditions that provide
single large network. In the presence of strategic interactions, network moments are generally complex functions of network components, where a node's component consists of all alters to which it is directly or indirectly connected. We find that a modification of "exponential stabilization" conditions from the stochastic geometry literature provides
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, particularly in models with strategic interactions. The result delivers a square root n rate of convergence and a closed-form expression for the asymptotic variance. Then using techniques in branching process theory, we derive primitive
for moments of this type. Our first contribution is to prove a CLT for a large class of network moments satisfying stabilization and a moment condition. Our second contribution is a methodology for deriving primitive sufficient
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in the following applications:
using results in branching process theory. We apply the methodology to
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strategic network formation , network regressions, and treatment effects with network spillovers. Finally, we suggest some practical methods for inference
network formation and discuss how it can be used more broadly