Multiple Treatments with Strategic Interaction

TL;DR

This paper develops a nonparametric framework to identify and estimate the effects of strategic treatments in models with multiple equilibria, applying it to airline and pollution data.

Contribution

It introduces a novel approach to handle multiple equilibria in strategic interaction models without parametric assumptions, using shape restrictions and exogenous variation.

Findings

Airline presence increases pollution levels.

The effect of airlines on pollution grows with more firms but at a decreasing rate.

Instrumental variables help address multiple equilibria issues.

Abstract

We develop an empirical framework to identify and estimate the effects of treatments on outcomes of interest when the treatments are the result of strategic interaction (e.g., bargaining, oligopolistic entry, peer effects). We consider a model where agents play a discrete game with complete information whose equilibrium actions (i.e., binary treatments) determine a post-game outcome in a nonseparable model with endogeneity. Due to the simultaneity in the first stage, the model as a whole is incomplete and the selection process fails to exhibit the conventional monotonicity. Without imposing parametric restrictions or large support assumptions, this poses challenges in recovering treatment parameters. To address these challenges, we first establish a monotonic pattern of the equilibria in the first-stage game in terms of the number of treatments selected. Based on this finding, we derive bounds on the average treatment effects (ATEs) under nonparametric shape restrictions and the existence of excluded exogenous variables. We show that instrument variation that compensates strategic substitution helps solve the multiple equilibria problem. We apply our method to data on airlines and air pollution in cities in the U.S. We find that (i) the causal effect of each airline on pollution is positive, and (ii) the effect is increasing in the number of firms but at a decreasing rate.