  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.
