Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/316760 
Year of Publication: 
2025
Series/Report no.: 
IZA Discussion Papers No. 17805
Publisher: 
Institute of Labor Economics (IZA), Bonn
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.
Subjects: 
weakly causal estimands
two-way fixed effects
two-stage least squares
treatment effects
representativeness
ordinary least squares
internal validity
weighted estimands
JEL: 
C20
C21
C23
C26
Document Type: 
Working Paper

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