  Generalizing estimates of causal effects from an experiment to a target
population is of interest to scientists. However, researchers are usually
constrained by available covariate information. Analysts can often collect much
fewer variables from population samples than from experimental samples, which
has limited applicability of existing approaches that assume rich covariate
data from both experimental and population samples. In this article, we examine
how to select covariates necessary for generalizing experimental results under
such data constraints. In our concrete context of a large-scale development
program in Uganda, although more than 40 pre-treatment covariates are available
in the experiment, only 8 of them were also measured in a target population. We
propose a method to estimate a separating set -- a set of variables affecting
both the sampling mechanism and treatment effect heterogeneity -- and show that
the population average treatment effect (PATE) can be identified by adjusting
for estimated separating sets. Our algorithm only requires a rich set of
covariates in the experimental data, not in the target population, by
incorporating researcher-specific constraints on what variables are measured in
the population data. Analyzing the development experiment in Uganda, we show
that the proposed algorithm can allow for the PATE estimation in situations
where conventional methods fail due to data requirements.
