Optimal Lending and Investment with Default Risk

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Intellectual meritThere is growing concern about the risk of default and its implications for the structuring of lending contracts. Default and breach of contract appear to be quite pervasive and costly in a wide variety of situations ranging from firm lending, sovereign debt and opportunistic quit behavior. In all these cases, the financing agents (lenders, firms) may fail to share returns to the investments to cover their costs while the borrower/worker may find alternative uses for their capital and resources. How should contracts bedesigned in the presence of default risk? How does the risk of default constrain lending and investment? These are the main questions addressed in this proposal. More specifically, the purpose of this proposal is to consider optimal financing in dynamic settings in the presence of default risk. We consider an environment where default/inefficient separations occur with positive probability under the optimal contract. Financing is constrained by voluntary repayment: the borrower can, at any moment, walk away for some outside opportunity. The value of the outside opportunity is random and private information. This is the key difference with the existing literature and implies that default actually occurs with positive probability as part of the optimal contract. Our approach thus provides contract theoretic foundations for endogenous default and implications for the time profile of borrowing constraints and investment. We place no ad hoc assumptions on contracting, but impose the constraints arising from the agent's private information and lack of commitment. Our model allows for a few different economic interpretations. The most obvious is the financing of a firm, where the lender is an entrepreneur undertaking an investment project and the borrower is a bank seeking to finance this project. Alternatively, one can apply the model to human capital investments and on-the-job training. The borrower in this case is a worker accumulating skills while working at a firm. The firm helps finance this investment but is concerned about retaining the worker. Or similarly, a researcher in an R&D lab that may quit benefiting elsewhere from ideas developed in the lab. Finally, the model can be applied to an international context by interpreting the borrower as a sovereign government seeking to finance its government spending, including public investments, from foreign investors. In all these situations, the risk of default/separation constrains the possibilities of investment. In turn, theaccumulation of capital is likely to have an impact on outside opportunities and consequently on default risk. An optimal dynamic contract considers this optimal tradeoff over time. The approach we propose has the additional advantage of providing a very tractable framework. The optimal dynamic contract is the solution to a problem that can be easily characterized for simple cases and very easily computed more generally. This contrasts with existing dynamic models of default that are extensively used in the sovereign debt literature- that are very difficult to characterize and carry a very high computational burden.Broader impactThe research proposed provides a novel and very tractable framework to study problems of lending and investment with default risk. There is a large literature ranging from Finance, consumer theory, labor economics and international economics to which the model applies. Our research will thus provide a theoretical framework to look at evidence in this area. Moreover, it will help better understand the structuring of contracts to mitigate default risk while taking advantage of investment opportunities. From a methodological point of view, the modeling approach (continuous time/Poisson arrivals) is also quite novel in the dynamic contracts literature and proved to have considerable advantages over the standard (discrete time) approach. Future research in this area will find this approach useful.