Identification, Estimation, and Inference in Two-Sided Interaction Models

TL;DR

This paper introduces a new model for two-sided interactions that captures complementarities with a single parameter, proposes an estimator for this parameter, and demonstrates its effectiveness through theoretical results and an empirical application.

Contribution

The paper develops the Tukey model for two-sided interactions, establishing identification conditions, and proposes a cycle-based estimator that works with sparse networks.

Findings

The Tukey model is identified under mild conditions.

The cycle-based estimator is consistent and asymptotically normal.

Empirical application shows the model captures meaningful complementarities.

Abstract

This paper studies a class of models for two-sided interactions, where outcomes depend on latent characteristics of two distinct agent types. Models in this class have two core elements: the matching network, which records which agent pairs interact, and the interaction function, which maps latent characteristics of these agents to outcomes and determines the role of complementarities. I introduce the Tukey model, which captures complementarities with a single interaction parameter, along with two extensions that allow richer complementarity patterns. First, I establish an identification trade-off between the flexibility of the interaction function and the density of the matching network: the Tukey model is identified under mild conditions, whereas the more flexible extensions require dense networks that are rarely observed in applications. Second, I propose a cycle-based estimator for the Tukey interaction parameter and show that it is consistent and asymptotically normal even when the network is sparse. Third, I use its asymptotic distribution to construct a formal test of no complementarities. Finally, an empirical illustration shows that the Tukey model recovers economically meaningful complementarities.