We develop a framework for estimating the otpimal expenditure of agents subject to unobserved liquidity constraints. Our framework allows us to estimate credit ceilings as well as preferences parameters. We apply the framework to data on net resource transfers from private lenders to twenty-nine sovereign debtors during 1973-1993. We obtain reasonable estimates of the discount factor, elasticity of marginal utility of expenditure, and the credit ceilings for most countries. Our estimated credit ceilings rise quite regularly with income across the countries of our sample, and are positively associated with a country's trade, in line with several theoretical arguments. Our estimates imply that slightly less than half the countries in our sample were liguidity constrained during the 1970s. The fraction rose to around 80 per cent in the mid 1980s and subsequently declined.