Functional Differencing in Networks

TL;DR

This paper adapts the functional differencing method to network data, enabling estimation of models with heterogeneous agents in both dense and sparse networks without restrictive assumptions.

Contribution

It extends Bonhomme's (2012) functional differencing approach to network settings, allowing for flexible heterogeneity and network structures in economic models.

Findings

Derives valid moment restrictions for network models

Applicable to both dense and sparse networks

Demonstrates with linear and nonlinear employer-employee models

Abstract

Economic interactions often occur in networks where heterogeneous agents (such as workers or firms) sort and produce. However, most existing estimation approaches either require the network to be dense, which is at odds with many empirical networks, or they require restricting the form of heterogeneity and the network formation process. We show how the functional differencing approach introduced by Bonhomme (2012) in the context of panel data, can be applied in network settings to derive moment restrictions on model parameters and average effects. Those restrictions are valid irrespective of the form of heterogeneity, and they hold in both dense and sparse networks. We illustrate the analysis with linear and nonlinear models of matched employer-employee data, in the spirit of the model introduced by Abowd, Kramarz, and Margolis (1999).