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Choices by Poor Households when the Interest Rate for Deposits Differs from the Interest Rate for Loans

Poor households try to save and to borrow to smooth consumption in the face of low and uncertain streams of income. They are constrained by credit limits and by the spread between the price paid for loans (borrowing) and the price earned for deposits (saving). Models of household choices that include all these facts are intractable. I use orthogonal polynomial projection methods to solve a Bellman equation of this model for a household with an infinite horizon and with rational expectations over uncertain future income. I use changes in the optimal choices of the household and in the long-run distribution of its consumption to suggest the effects of reduced costs of access to formal financial services. As the spread narrows, there is less disintermediation—households are more likely to borrow or to save. Still, sometimes the best choice is neither to save nor to borrow. This means that the long-run distribution of consumption has more than one mode. Simulations of the optimal decision rule suggest that favorable interest rates help poor households to increase and to smooth consumption. The model formalizes some of the ways in which access to formal financial services can improve the welfare of poor households. Authors’ Note This is an earlier version of a paper that appears in pp. 348-355 in G.H. Peters and Joachim Von Braun (eds) Food Security, Diversification, and Resource Management: Refocusing the Role of Agriculture? Proceedings of the Twenty-third International Conference of Agriculture Economists, Aldershot: Ashgate, ISBN 1-84014-04405.