Two-step Estimation of Network Formation Models with Unobserved Heterogeneities and Strategic Interactions

TL;DR

This paper develops a two-step estimation method for network formation models considering unobserved heterogeneities and strategic interactions, using a static game framework and data from a large network.

Contribution

It introduces a novel two-step estimator that accounts for unobserved heterogeneity and strategic interactions in network formation models, with proven consistency and asymptotic normality.

Findings

First-step estimator is uniformly consistent at rate N^{-1/4}.

Second-step estimator converges to a normal distribution at the same rate.

Method effectively estimates model parameters and unobserved fixed effects.

Abstract

In this paper, I characterize the network formation process as a static game of incomplete information, where the latent payoff of forming a link between two individuals depends on the structure of the network, as well as private information on agents' attributes. I allow agents' private unobserved attributes to be correlated with observed attributes through individual fixed effects. Using data from a single large network, I propose a two-step estimator for the model primitives. In the first step, I estimate agents' equilibrium beliefs of other people's choice probabilities. In the second step, I plug in the first-step estimator to the conditional choice probability expression and estimate the model parameters and the unobserved individual fixed effects together using Joint MLE. Assuming that the observed attributes are discrete, I showed that the first step estimator is uniformly consistent with rate $N^{-1/4}$, where $N$ is the total number of linking proposals. I also show that the second-step estimator converges asymptotically to a normal distribution at the same rate.