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Article Excerpt
Summary. We consider a simple model of lending and borrowing combining two informational problems: adverse selection and costly state verification. Our analysis highlights the interaction between these two informational problems. We notably show that the higher the monitoring cost, the less discriminating the optimal menu of contracts is.
Keywords and Phrases: Debt contracts, Diversity of opinions, Screening, Costly monitoring, Pooling.
JEL Classification Numbers: C7, D8, G3.
1 Introduction
In this paper, we consider a simple model of borrowing and lending in the presence of ex-ante and ex-post asymmetric information. We model the ex-post asymmetric information problem as a costly state verification problem, that is, a borrower freely observes the return of his risky investment while a lender has to pay a monitoring cost (see Townsend, 1979). As for the ex-ante asymmetric information, we suppose that a lender and a borrower have different and privately known opinions about the possible returns of the risky investment. Differences in opinions might be explained by (un-modelled) differences in private information or, more simply, differences in subjective beliefs. Moreover, following, among others, Boyd and Smith (1993), we suppose that a borrower offers an incentive-compatible menu of contracts to a lender; hence, our problem turns out to be a screening problem together with a costly monitoring problem. It is precisely the aim of the paper to shed light on the interaction between the screening and the costly monitoring problems for the structure of optimal contracts.
Since a general analysis of the contracting problem is extremely complex, if not out of reach, this paper thus adopts specific assumptions, which give rise to closed-form solutions. For instance, we restrict ourselves to a special class of contracts, so-called secured simple debt contracts, and suppose that the distribution of project return is uniform. As a consequence, we obtain that, at the optimum, the borrower offers at most two contracts [[delta].bar] and [bar.[delta]]. In turn, this extreme case of bunching enables us to focus on two types of optima: pooling and separating optima. We then analyze under which conditions pooling or separating solutions prevail.
We notably show that the more costly the monitoring, the less discriminating the optimal menu of contracts is. More precisely, there exists a threshold [gamma]* such that if the monitoring cost is above [gamma]*, the borrower offers a unique contract while for lower monitoring costs, the borrower offers two contracts. In particular, absent away the costly state verification problem (i.e., a zero monitoring cost), the optimal menu of contracts always features two contracts. We also show that, for monitoring costs lower than [gamma]*, there exist opinions of the lender that should be offered the contract [bar.[delta]] in a world without adverse selection, and are offered the contract [[delta].bar] in a world with adverse selection. However, for monitoring costs greater than [gamma]*, the borrower offers the same contract whether there is adverse selection or not. Thus, for high monitoring costs, the costly state verification effect dominates the adverse selection effect.
In a related paper, Boyd and Smith (1993) also consider a model with adverse selection and costly state verification problems, and prove the optimality of simple debt contracts. However, their model differs as they suppose that the borrower (the principal) is privately informed of both his ability (his type) to undertake a project and the realized return of the project. Hence, their problem is essentially a signalling problem together with a costly monitoring problem while our problem is a screening problem together with a costly monitoring problem.
In Section 2, we present the model. Section 3 solves for the optimal menu of contracts and presents some comparative statics.
2 The model
We consider a two-period economy with a unique borrower and a unique lender. The lender is endowed with a single unit of a good that might be used for both investment and consumption while the borrower has no initial endowment. They are assumed to be risk-neutral and to care only about second period consumption. Moreover, the borrower has access to an investment project requiring exactly one unit of the investment good to be undertaken. The project returns [omega] in the second period with [omega] a realization of the random variable [~.[omega]]. The opportunity cost is set to r.
Ex-post asymmetric information. The borrower freely observes the project return [omega] in the second period while the lender has to pay an utility cost of [gamma] to perfectly monitor the realized return [omega].
Ex-ante asymmetric information. The borrower and the lender have different, privately known, opinions (subjective beliefs) about the likelihood of exogenous factors, such as technology, consumers' taste, etc., which influence the project return. For instance, the lender might have (un-modelled) private information about the returns of...
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