[Paper Review] Multiple Treatments with Strategic Substitutes

Jorge Balat, Sukjin Han|Bristol Research (University of Bristol)|Jun 1, 2023

Economic Policies and Impacts4 citations

TL;DR

This paper develops a nonparametric identification and estimation framework for average treatment effects (ATEs) in models with multiple treatments arising from strategic interaction, such as oligopolistic entry or peer effects. By exploiting monotonicity in equilibria and excluded instruments that counteract strategic substitution, it derives bounds on ATEs without parametric assumptions or large support conditions, applying the method to show that airline presence increases pollution non-linearly in U.S. cities.

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 of complete information and strategic substitutability, 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 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 (ATE’s) under nonparametric shape restrictions and the existence of excluded exogenous variables. We show that the 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.

Motivation & Objective

• To address identification of treatment effects when treatments result from strategic interaction among agents.
• To overcome challenges from simultaneity and lack of monotonicity in selection due to multiple equilibria.
• To develop bounds on average treatment effects (ATEs) without parametric restrictions or large support assumptions.
• To incorporate excluded instruments that counteract strategic substitution to resolve multiple equilibria.
• To apply the framework to real-world data on airline entry and air pollution in U.S. cities.

Proposed method

• Proposes a model where agents play a complete-information discrete game, with equilibrium actions (binary treatments) determining a nonseparable outcome.
• Establishes a monotonic pattern in equilibria based on the number of treatments selected, enabling identification under shape restrictions.
• Derives nonparametric bounds on ATEs using shape restrictions and the existence of excluded exogenous variables.
• Introduces instrument variation that compensates for strategic substitution to resolve multiple equilibria.
• Uses exclusion restrictions and monotonicity in equilibrium selection to identify treatment effects without large support assumptions.
• Applies the framework to a structural model of airline entry and local air pollution, estimating heterogeneous effects.

Experimental results

Research questions

• RQ1 How can treatment effects be identified when treatments are determined by strategic interaction among agents?
• RQ2 What conditions allow for nonparametric bounds on average treatment effects in models with multiple equilibria?
• RQ3 How can excluded instruments that counteract strategic substitution improve identification in such models?
• RQ4 What is the nature of the causal effect of airline presence on local air pollution in U.S. cities?
• RQ5 How does the treatment effect of airline entry on pollution vary with the number of airlines present?

Key findings

• The causal effect of each additional airline on air pollution is positive, indicating that airline presence increases pollution levels.
• The effect of airline entry on pollution increases with the number of firms but at a decreasing rate, indicating diminishing returns.
• The model identifies bounds on average treatment effects without requiring parametric assumptions or large support conditions.
• Instrumental variables that counteract strategic substitution are essential for resolving multiple equilibria and enabling identification.
• The monotonic pattern in equilibria based on treatment count enables nonparametric identification under shape restrictions.
• Empirical application to U.S. city-level data confirms that airline entry has a significant and non-linear impact on local air pollution.