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.

We study the consequences of an exogenous upsurge in coca prices and cultivation in Colombia, where most coca leaf is now harvested. This shift generated only modest economic gains in rural areas, primarily in the form of increased self-employment earnings and increased labor supply by teenage boys. The rural areas that saw accelerated coca production subsequently became considerably more violent, while urban areas were affected little. These findings are consistent with the view that the Colombian civil conflict is fueled by the financial opportunities that coca provides and that rent-seeking by combatants limits the economic gains from coca.