🤖 AI Summary
This study addresses the challenge of disentangling treatment effects from unknown interference—such as spillovers—in panel data settings. The authors propose an identification strategy that does not require pre-specifying an exposure mapping or classifying affected units. By imposing pre-treatment fit constraints to bound donor weights and incorporating application-specific linear restrictions, they construct a sharp identified set for the treatment effect. Their approach integrates convex combination scaling, linear constraint modeling, bootstrap calibration, and confidence set inversion, enabling compatibility testing under only general assumptions. An empirical application to Arizona’s Legal Workers Act yields a 95% confidence identified set containing both positive and negative values, indicating that the sign of the treatment effect cannot be determined with the available data.
📝 Abstract
When comparison units may also respond to treatment, panel comparisons reflect both the treatment effect and spillovers. If the interference pattern is unknown, observed outcomes alone do not separate the two. I characterize what can nevertheless be learned from panel outcomes under general restrictions, without requiring an exposure mapping or prior classification of affected donors. The framework scales validity bounds for every convex donor weight by its fit before treatment and combines these bounds with prespecified restrictions tailored to the application. The validity bounds constrain the treatment effect relative to spillovers, while the additional restrictions determine its possible values. Together these restrictions yield a sharp identified set. When the additional restrictions have a finite linear representation, checking whether a proposed treatment effect is compatible with the model reduces exactly to asking whether a finite linear system has a solution. Bootstrap calibration tests this condition. Inverting these tests uniformly controls, in large samples, the probability of falsely excluding each compatible value. In an application to the Legal Arizona Workers Act, the resulting 95 percent inversion sets contain effects of both signs across all reported specifications, leaving the sign of the treatment effect unresolved.