# Testing for Externalities in Network Formation Using Simulation

## TL;DR

This paper introduces a simulation-based exact testing method for detecting interdependencies in network formation preferences, accounting for heterogeneity, and demonstrates its application on a real-world risk-sharing network.

## Contribution

It develops a novel simulation approach for testing network externalities that conditions on agent heterogeneity, improving accuracy over previous methods.

## Key findings

- Nyakatoke network transitivity exceeds expectations based on degree heterogeneity
- The method accurately estimates null distributions for complex network tests
- Demonstrates practical application on real-world network data

## Abstract

We discuss a simplified version of the testing problem considered by Pelican and Graham (2019): testing for interdependencies in preferences over links among N (possibly heterogeneous) agents in a network. We describe an exact test which conditions on a sufficient statistic for the nuisance parameter characterizing any agent-level heterogeneity. Employing an algorithm due to Blitzstein and Diaconis (2011), we show how to simulate the null distribution of the test statistic in order to estimate critical values and/or p-values. We illustrate our methods using the Nyakatoke risk-sharing network. We find that the transitivity of the Nyakatoke network far exceeds what can be explained by degree heterogeneity across households alone.