Welfare reform evaluators currently have several ways to approach crossover. For example, MDRC researchers generally include crossover cases in the sample and estimate impacts using an original experimental/control status variable, without any accompanying sensitivity analyses. Abt Associates, Inc., in its work on the Michigan evaluation, excluded all migrants and other crossover cases from the research sample and employed a weighting scheme to make the reduced sample representative of the original research sample.
We recommend that evaluators studying the impacts of a welfare reform initiative include crossover cases in the analysis sample whenever the available outcome data permit. This approach minimizes sample selection bias and avoids the need for reweighting. Including crossover cases in the research sample also makes it unnecessary for the evaluator to identify presumed crossover-type cases for systematic deletion from the sample. By not deleting crossover cases, original experimental cases remain comparable with original control cases. Because cases that subsequently cross over remain in the research sample, impact estimates over time will apply to the same sample of cases.
In addition to including crossover cases in the analysis sample, it is important that evaluators identify the extent to which crossover behavior occurs for the experimental and control groups. As noted earlier, there are at least four ways of measuring crossover. The preferred measure will depend on the nature of the intervention being evaluated. Evaluators need to be clear about how they define crossover; they may also want to consider the sensitivity of crossover rate estimates to the way in which crossover is defined.
As long as the incidence of crossover is low, any sort of statistical correction should generate impact estimates similar to the uncorrected impact estimates. However, if the incidence of crossover is high, it is important that welfare reform evaluations provide sufficient information to compare results obtained using different approaches and methodologies.
When generating estimates of the impacts of welfare reform, we recommend that the primary focus be on impacts estimated using the original experimental/control status of research cases (with regression adjustments applied to increase the precision of these estimates). This approach always provides a lower bound on the true impact estimate. In contrast, the Bloom procedure is less precise and provides downwardly biased estimates if impacts are greater for crossover-type cases than noncrossover-type cases, and upwardly biased estimates if impacts are greater for noncrossover-type cases than crossover-type cases. Knowing the Bloom-corrected impact estimate for each outcome may still be valuable for sensitivity analyses, so we recommend that these estimates be included in appendixes to the impact study reports.