School officials and legislators have long been concerned with the possibility of declining teacher quality (see e.g., Sean Corcoran et al., 2002). Beginning in the 1960's, states began testing prospective teachers in a direct effort to ensure that teachers meet minimum standards for basic skills and subject knowledge. By 1999, 41 states required applicants to pass some sort of standardized certification test. As a theoretical matter, however, the impact of such testing is ambiguous. Test requirements may establish a minimum achievement standard, as their proponents hope. On the other hand, testing and other certification requirements may deter some qualified applicants from teaching if these requirements are perceived as costly. This is the barriers-to-entry story first noted in the occupational licensing context by Milton F. Friedman and Simon Kuznets (1945). Another concern with job applicant testing is the possibility of an adverse impact on minority candidates, who usually do worse on tests (see David Autor and David Scarborough [2003] for a recent study). Paralleling increased state involvement in teacher certification is the increase in teachers' educational credentials, especially in public schools. For example, in 1971, over two-thirds of public-school teachers had a B.A., while only 27 percent had a master's or education specialist's degree. By 1991, however, over half of public school teachers (52.6 percent) had a master's or education specialist's degree. In contrast, the proportion of private-school teachers

The problem of when to control for continuous or high-dimensional discrete covariate vectors arises in both experimental and observational studies. Large-cell asymptotic arguments suggest that full control for covariates or stratification variables is always efficient, even if treatment is assigned independently of covariates or strata. Here, we approximate the behavior of different estimators using a panel-data-type asymptotic sequence with fixed cell sizes and the number of cells increasing to infinity. Exact calculations in simple examples and Monte Carlo evidence suggest this generates a substantially improved approximation to actual finite-sample distributions. Under this sequence, full control for covariates is dominated by propensity-score matching when cell sizes are small, the explanatory power of the covariates conditional on the propensity score is low, and/or the probability of treatment is close to 0 or 1. Our panel-asymptotic framework also provides an explanation for why propensity-score matching can dominate covariate matching even when there are no empty cells. Finally, we introduce a random-effects estimator that provides finite-sample efficiency gains over both covariate matching and propensity-score matching.

The Metropolitan Council for Educational Opportunity (Metco) is a desegregation program that sends students from Boston schools to more affluent suburbs. Metco increases the number of blacks and reduces test scores in receiving districts. School-level data for Massachusetts and micro data from a large district show no impact of Metco on the scores of white non-Metco students. But the micro estimates show some evidence of an effect on minority third graders, especially girls. Instrumental variables estimates for third graders are imprecise but generally in line with ordinary least squares estimates. Given the localized nature of these results, we conclude that peer effects from Metco are modest and short lived.