This paper concerns the problem of optimally allocating scarce indivisible resources among a target group of individuals based on experimental data for a sample drawn from the same population. For a wide class of social welfare functions, the problem can be set up as a mathematical program with estimated components. The paper develops asymptotic statistical inference on the estimated value function which depends on uniqueness of the population solution. This work complements the "set identification" literature in econometrics by conducting inference on the optimized value of the criterion function and the "treatment choice" literature by allowing aggregate resource constraints. A key methodological contribution is to show that applicability of these techniques extends beyond linear maximands like the mean to other important policy objectives like outcome quantiles which, though nonlinear, are proved to be quasi-convex in the allocation probabilities. I apply the methods on data from Dartmouth’s random assignment of freshmen to dorm rooms, where Sacerdote (2001) had detected significant contextual peer effects. Segregation by previous academic achievement and by race are seen to minimize mean enrolment into sororities and maximize mean enrolment into fraternities. Segregation has no effect on mean and median freshman year GPA but increases the higher and decreases the lower percentiles of the GPA distribution for both men and women. Efficiency loss due to political constraints on allocations (e.g. race-blindness) is shown to be significant and also larger for women for whom peer effects are more nonlinear.

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