Community colleges serve close to half of the undergraduate students in the United States and tuition at two-year public/non-profit colleges is mostly a public expenditure. We measure the effect of decreased course availability on grades, degree attainment, and transfer to four-year colleges using a regression discontinuity from course enrollment queues due to oversubscribed courses. Using a panel from a large California community college and the National Student Clearinghouse we find that in the short run students substitute unavailable courses with others. We find no significant effects on later outcomes, given the precision of our tests, however we cannot rule out economically significant effects.

We show that stratifying on the conditional expectation of the outcome given baseline variables is optimal in matched-pair randomized experiments. The assignment minimizes the variance of the post-treatment difference in mean outcomes between treatment and controls. Optimal pairing depends only on predicted values of outcomes for experimental units, where the predicted values are the conditional expectations. After randomization, both frequentist inference and randomization inference depend only on the actual strata chosen and not on estimated predicted values. This gives experimenters a way to use big data (possibly more covariates than the number of experimental units) ex-ante while maintaining simple post-experiment inference techniques. Optimizing the randomization with respect to one outcome allows researchers to credibly signal the outcome of interest prior to the experiment. Inference can be conducted in the standard way by regressing the outcome on treatment and strata indicators. We illustrate the application of the methodology by running simulations based on a set of field experiments. We find that optimal designs have mean squared errors 23% less than randomized designs, on average. In one case, mean squared error is 43% less than randomized designs.

It is standard practice in empirical work to allow for clustering in the error covariance matrix if the explanatory variables of interest vary at a more aggregate level than the units of observation. Often, however, the structure of the error covariance matrix is more complex, with correlations varying in magnitude within clusters, and not vanishing between clusters. Here we explore the implications of such correlations for the actual and estimated precision of least squares estimators. We show that with equal sized clusters, if the covariate of interest is randomly assigned at the cluster level, only accounting for non-zero covariances at the cluster level, and ignoring correlations between clusters, leads to valid standard errors and confidence intervals. However, in many cases this may not suffice. For example, state policies exhibit substantial spatial correlations. As a result, ignoring spatial correlations in outcomes beyond that accounted for by the clustering at the state level, may well bias standard errors. We illustrate our findings using the 5% public use census data. Based on these results we recommend researchers assess the extent of spatial correlations in explanatory variables beyond state level clustering, and if such correlations are present, take into account spatial correlations beyond the clustering correlations typically accounted for.