We investigate the empirical significance of borrowing constraints in the market for consumer loans. We set up a theoretical model of consumer loan demand, which in the presence of credit rationing implies restrictions on the elasticities of loan demand with respect to the interest rate and the maturity of the loan. We estimate these elasticities and test the theoretical implications using micro data from the Consumer Expenditure Survey (1984-1995) on auto loan contracts. The econometric specification that we employ accounts for important features of the data: selection, censoring, and simultaneity. Our results suggest that credit constraints are binding for some groups in the population, in particular for young and low-income households.