Negative Weights are No Concern in Design-Based Specifications

Kirill Borusyak and Peter Hull

No 32017, NBER Working Papers from National Bureau of Economic Research, Inc

Abstract: Recent work shows that popular partially-linear regression specifications can put negative weights on some treatment effects, potentially producing incorrectly-signed estimands. We counter by showing that negative weights are no problem in design-based specifications, in which low-dimensional controls span the conditional expectation of the treatment. Specifically, the estimands of such specifications are convex averages of causal effects with “ex-ante” weights that average the potentially negative “ex-post” weights across possible treatment realizations. This result extends to design-based instrumental variable estimands under a first-stage monotonicity condition, and applies to “formula” treatments and instruments such as shift-share instruments.

JEL-codes: C21 C26 (search for similar items in EconPapers)
Date: 2024-01
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Published as Kirill Borusyak & Peter Hull, 2024. "Negative Weights Are No Concern in Design-Based Specifications," AEA Papers and Proceedings, vol 114, pages 597-600.

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