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Negative Weights are No Concern in Design-Based Specifications

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Listed:
  • Kirill Borusyak
  • Peter Hull

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.

Suggested Citation

  • Kirill Borusyak & Peter Hull, 2024. "Negative Weights are No Concern in Design-Based Specifications," NBER Working Papers 32017, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:32017
    Note: LS TWP
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    More about this item

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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