We develop a framework for estimating the optimal expenditure of agents subject to unobserved liquidity constraints. Our framework allows us to estimate credit ceilings as well as preference 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 ceiling 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 slilghtly less than half the countries in our sample were liquidity constrained during the 1970s. The fraction rose to around 80 per cent in the mid 1980s, and subsequently declined.