Even as increased demand and misallocation of housing are established consequences of rent controls, there is limited research on how household demand responds to rent subsidies. In a setting with heterogenous households and wide-spread rent controls, a likely consequence is overconsumption of housing that results in a less-than-optimal household-apartment matching. Data from Stockholm, Sweden, with both household and apartment characteristics is analyzed. There is considerable variation in how much apartments are subsidized, household size, and income. On average, regulated rents are 36.1% lower than estimated market rents. Apartment size is regressed on both household characteristics at the time of moving-in, and a measure of the rent subsidy. Controlling for household size, age(s), income, and location, it is found that the average difference between an estimated counterfactual market rent and the regulated rent results in an average household renting an apartment that is 15.9% larger compared to if paying market rent. When regressing the number of rooms, rather than apartment size, the results are consistent. The average annual subsidy per square meter will, on average, result in households renting an apartment with .28 additional rooms. The observed behavior is a consequence of ineffective targeting of rent subsidies. The shift in demand will amplify housing shortages and decrease access to housing and therefore contradict the policy goals. Estimates of housing consumption in a counterfactual setting with market rents, yields a 20.6% larger renter population housed in the existing housing stock.