Estimating a Continuous Treatment Model with Spillovers: A Control Function Approach

TL;DR

This paper develops a control function method to identify and estimate the effects of continuous treatments with spillovers in social networks, addressing endogeneity and providing a practical estimation procedure.

Contribution

It introduces a nonparametric identification framework and a semiparametric estimation method for treatment spillovers in network settings.

Findings

Successfully identifies causal effects in a network spillover model.

Provides a three-step estimation procedure for practical application.

Empirically demonstrates the impact of unemployment on crime rates.

Abstract

We study a continuous treatment effect model in the presence of treatment spillovers through social networks. We assume that one's outcome is affected not only by his/her own treatment but also by a (weighted) average of his/her neighbors' treatments, both of which are treated as endogenous variables. Using a control function approach with appropriate instrumental variables, we show that the conditional mean potential outcome can be nonparametrically identified. We also consider a more empirically tractable semiparametric model and develop a three-step estimation procedure for this model. As an empirical illustration, we investigate the causal effect of the regional unemployment rate on the crime rate.