Internal vs. external validity in studies with incomplete populations

Researchers working with administrative data rarely have access to the entire universe of units they need to estimate effects and make statistical inferences. Examples are varied and come from different disciplines. In social program evaluation, it is common to have data on all households who received the program, but only partial information on the universe of households who applied or could have applied for the program. In studies of voter turnout, information on the total number of citizens who voted is usually complete, but data on the total number of voting-eligible citizens is unavailable at low levels of aggregation. In criminology, information on arrests by race is available, but the overall population that could have potentially been arrested is typically unavailable. And in studies of drug overdose deaths, we lack complete information about the full population of drug users.

In all these cases, a reasonable strategy is to study treatment effects and descriptive statistics using the information that is available. This strategy may lack the generality of a full-population study, but may nonetheless yield valuable information for the included units if it has sufficient internal validity. However, the distinction between internal and external validity is complex when the subpopulation of units for which information is available is not defined according to a reproducible criterion and/or when this subpopulation itself is defined by the treatment of interest. When this happens, a useful approach is to consider the full range of conclusions that would be obtained under different possible scenarios regarding the missing information. I discuss a general strategy based on partial identification ideas that may be helpful to assess sensitivity of the partial-population study under weak (non-parametric) assumptions, when information about the outcome variable is known with certainty for a subset of the units. I discuss extensions such as the inclusion of covariates in the estimation model and different strategies for statistical inference.

Co-sponsored with the Political Science Department, Statistics Department and the Center for Social Statistics 

Bayesian Population Projections with Migration Uncertainty

The United Nations recently issued official probabilistic population projections for all countries for the first time, using a Bayesian hierarchical modeling framework developed by our group at the University of Washington. These take account of uncertainty about future fertility and mortality, but not international migration. We propose a Bayesian hierarchical autoregressive model for obtaining joint probabilistic projections of migration rates for all countries, broken down by age and sex. Joint trajectories for all countries are constrained to satisfy the requirement of zero global net migration. We evaluate our model using out-of-sample validation and compare point projections to the projected migration rates from a persistence model similar to the UN's current method for projecting migration, and also to a state of the art gravity model. We also resolve an apparently paradoxical discrepancy between growth trends in the proportion of the world population migrating and the average absolute migration rate across countries. This is joint work with Jonathan Azose and Hana Ševčíková.

Co-sponsored with the Center for Social Statistics 

Covariate Selection for Generalizing Experimental Results

Researchers are often interested in generalizing the average treatment effect (ATE) estimated in a randomized experiment to non-experimental target populations. Researchers can estimate the population ATE without bias if they adjust for a set of variables affecting both selection into the experiment and treatment heterogeneity.Although this separating set has simple mathematical representation, it is often unclear how to select this set in applied contexts. In this paper, we propose a data-driven method to estimate a separating set. Our approach has two advantages. First, our algorithm relies only on the experimental data. As long as researchers can collect a rich set of covariates on experimental samples, the proposed method can inform which variables they should adjust for. Second, we can incorporate researcher-specific data constraints. When researchers know certain variables are unmeasurable in the target population, our method can select a separating set subject to such constraints, if one is feasible. We validate our proposed method using simulations, including naturalistic simulations based on real-world data.

Co-Sponsored with The Center for Social Statistics