The standard analysis of price controls assumes that goods are efficiently allocated, even when there are shortages. But if shortages mean that goods are randomly allocated across the consumers that want them, the welfare costs from misallocation may be greater than the undersupply costs. We develop a framework to empirically test for misallocation. The methodology compares consumption patterns for demographic subgroups in rent-controlled and free-market places. We find that in New York City, which is rent-controlled, an economically and statistically significant fraction of apartments appears to be misallocated across demographic subgroups.