Centre for Development Economics
Department of Economics, Delhi School of Economics


A Theory of Progressive Lending


Dyotona Das Gupta

(Delhi School of Economics)

Thursday, February 20, 2020, at 3:05 P.M.

Venue: New Seminar Room (Room no. 116, First Floor)

Department of Economics, Delhi School of Economics

All are cordially invited

Microfinance Institutions (MFIs) lend to poor clients without any collateral, using a strategy of progressive lending where borrowers are eligible to borrow more in the future, conditional on repaying current loans. This helps sustain high repayment rates. We develop a theory of such progressive lending, extending a standard Ramsey growth model of a representative agent to incorporate dynamic repayment incentives. The agent has an exogenous initial wealth, preferences for smoothing consumption over time, access to a concave production technology in autarky and is able to save at an interest rate equal to the rate of time discount. The associated problem of default (well known since Bulow-Rogoff (1989)) is overcome by bundling the loan contract with `aid’ provided by the MFI which raises the borrower’s productivity, conditional on past repayment. We characterize the optimal dynamic contract which maximizes the agent’s payoff, subject to a breakeven constraint for the MFI, and show it involves progressive lending where the borrower never defaults on the equilibrium path. For agents with initial wealth above a critical threshold, the first-best is sustainable with a stationary contract. For other poorer agents, there is perpetual but shrinking underinvestment which tends to disappear in the long run: their loan sizes, investments and wealth grow over time eventually approaching the levels for the agent at the first-best threshold. The gaps in production and wealth between rich and poor agents narrow over time, but full long-run convergence does not obtain: those with initial wealth above the threshold remain wealthier in the long run. Poor agents with higher impatience or preferences for consumption smoothing experience slower growth.


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