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Quantifying the Internal Validity of Weighted Estimands

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  • Alexandre Poirier
  • Tymon S{l}oczy'nski

Abstract

In this paper we study a class of weighted estimands, which we define as parameters that can be expressed as weighted averages of the underlying heterogeneous treatment effects. The popular ordinary least squares (OLS), two-stage least squares (2SLS), and two-way fixed effects (TWFE) estimands are all special cases within our framework. Our focus is on answering two questions concerning weighted estimands. First, under what conditions can they be interpreted as the average treatment effect for some (possibly latent) subpopulation? Second, when these conditions are satisfied, what is the upper bound on the size of that subpopulation, either in absolute terms or relative to a target population of interest? We argue that this upper bound provides a valuable diagnostic for empirical research. When a given weighted estimand corresponds to the average treatment effect for a small subset of the population of interest, we say its internal validity is low. Our paper develops practical tools to quantify the internal validity of weighted estimands.

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  • Alexandre Poirier & Tymon S{l}oczy'nski, 2024. "Quantifying the Internal Validity of Weighted Estimands," Papers 2404.14603, arXiv.org, revised May 2025.
    • Handle: RePEc:arx:papers:2404.14603
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    1. Andrew Baker & Brantly Callaway & Scott Cunningham & Andrew Goodman-Bacon & Pedro H. C. Sant'Anna, 2025. "Difference-in-Differences Designs: A Practitioner's Guide," Papers 2503.13323, arXiv.org.

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    More about this item

    JEL classification:

    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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