There are numerous potential estimators that might be brought to bear on policy questions such as the one studied in Chapter 6; but the proposal of new estimators is not a task to be taken lightly (Achen 2002). Probit and logit, though not perfect, have withstood the test of time. However, the distributional assumption implicit in these models might give us a false sense of where the effects are the largest. Although it is not useful in all circumstances, including some of those studied in Chapter 6, the bounds approach offers a simple, straightforward, and transparent means by which the probit assumptions can be tested. As reported in Chapter 6, the evidence from the results presented subsequently is insufficient to reject the assumptions maintained in the probit models.

In this appendix, I revert back to the exogenous selection assumption. As was shown in Chapter 3, the magnitude of the effects is influenced by whether one runs probit using the traditional or the difference in difference set up. However, my interest here is in comparing the relative size of the effects across levels of educational attainment. As will be demonstrated, the pattern of results across levels of education is the same whether probit is run on the difference in difference model or the traditional model; under each approach, by assumption, the effect will be the largest for those with an initial probability of voting = 0.5. Additionally, when estimating effects conditional on individual characteristics, the bounds approach requires that the sample be split accordingly, with the procedure run separately for each subgroup.