TY  - RPRT
        AU  - Poirier, Alexandre
AU  - Sloczynski, Tymon
        TI  - Quantifying the Internal Validity of Weighted Estimands
        PY  - 2025/Mar/
        PB  - Institute of Labor Economics (IZA)
        CY  - Bonn
        T2  - IZA Discussion Paper
        IS  - 17805
        UR  - https://www.iza.org/publications/dp17805
        AB  - 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.
        KW  - weakly causal estimands
KW  - two-way fixed effects
KW  - two-stage least squares
KW  - treatment effects
KW  - representativeness
KW  - ordinary least squares
KW  - internal validity
KW  - weighted estimands
        ER  -