Microfoundations and the Causal Interpretation of Price-Exposure Designs

TL;DR

This paper examines the use of commodity price exposure designs for causal inference, highlighting identification challenges, proposing solutions, and demonstrating their importance through an empirical application in the Amazon.

Contribution

It provides a formal characterization of price-exposure estimands, derives conditions for causal interpretation, and introduces a new standard error estimator to improve inference accuracy.

Findings

Standard inference procedures overreject in price-exposure designs.

New standard error estimator reduces overrejection issues.

Application shows main effects are statistically insignificant with improved inference.

Abstract

This paper studies regional exposure designs that use commodity prices as instruments to study local effects of aggregate shocks. Unlike standard shift share designs that leverage differential exposure to many shocks, the price exposure relies on exogenous variation from a single shock, leading to challenges for both identification and inference. We motivate the design using a multi sector labor model. Under the model and a potential outcomes framework, we characterize the 2SLS and TWFE estimands as weighted averages of region and sector specific effects plus contamination terms driven by the covariance structure of prices and by general-equilibrium output responses. We derive conditions under which these estimands have a clear causal interpretation and provide simple sensitivity analysis procedures for violations. Finally, we show that standard inference procedures suffer from an overrejection problem in price-exposure designs. We derive a new standard error estimator and show its desirable finite-sample properties through Monte Carlo simulations. In an application to gold mining and homicides in the Amazon, the price exposure standard errors are roughly twice as large as conventional clustered standard errors, making the main effect statistically insignificant.