The aim of this paper is to analyze the conditions under which optimal or sub-optimal equilibria obtain in a competitive credit market of risk-neutral optimizing agents where firms borrow from banks and information is asymmetric. Each firm has a heterogeneous endowment of quality and of a production technology, whose input can be financed by means of a bank loan only. The firm’s output, which is increasing in the amount of the loan and is indexed by firm quality and technology, depends on an individual random component, thus varying across firms. As quality is unobservable by banks, an ex ante asymmetric information problem arises on the side of the lenders, which prevents banks from designing debt contracts contingent on firms’ quality, and raises adverse selection effects. We assume that firm’s technology can either be observable or not by lenders. In the former case, the adverse selection effect is due to the unobservabilty of quality only, while in the latter it is due to the combined interaction of both unobservable quality and technology. We do not consider either moral hazard or ex post asymmetric information problems: each firm cannot change its quality or technological type after having signed a debt contract, and banks observe firms’ end-of-period returns at no cost. Credit market equilibria with loans of variable size and firm signaling can emerge, with either separating or pooling contracts, and are characterized by a rich set ofover- and under-financing equilibria, whereby under-financing often implies credit rationing equilibria.
Several models of credit market equilibria with asymmetric information have been proposed in the past, starting with Jaffee and Russell (1976) and followed by Stiglitz and Weiss (1981) (henceforth S-W) and Stiglitz and Weiss (1992), De Meza and Webb (1987) (D-W), Milde and Riley (1988) (M-R), Innes (1991). S-W analyzed banks’ financing of loans of fixed size with equal expected firm returns but different riskiness across firms in accordance with the mean preserving spread principle (Rothschild and Stiglitz (1970)), and obtained pooling equilibria with type-II credit rationing. D-W too referred to the case of fixed size loans for firms of different quality. They considered both the case of loans to firms whose expected returns are equal and actual returns differ, which replicated the results reached by S-W, and the case of loans to firms whose returns are equal and the probability of success are different, which leads to a pooling equilibrium with over-financing of higher quality firms. Conversely, M-R and Innes (1991) considered loans of variable size and standard debt contracts contingent on realized firm returns. In their models, the variable size of the loan allows for borrowers’ signaling, thus generating self-selection and separating equilibria for firms of different but unobservable quality. While Innes (1991) also obtains pooling equilibria with over and under-financing, both signaling and separating equilibria weaken the occurrence of type-I credit rationing.
As the latter models highlight, when the size of the loan is allowed to vary, differences in firms’ returns can be due both to differences in firms’ quality and to differences in the loan size. Moreover, the variable loan size can imply the non-existence of Nash equilibria and the consequent reference to other concepts of equilibrium (e.g. Riley or Wilson equilibria). In M-R, for instance, each firm is endowed with a production function which depends on the amount of the loan and on a firm-specific quality parameter unobservable by lenders, and firms’ returns are increasing in quality. The borrowers’ signaling stems from the relation between quality, loan size and output. M-R depict three different cases based either on different production technologies, which are known to both the firms and the banks, or on different orderings of the random returns. In the first case, the production function is multiplicative in the quality parameter so that the loan size is increasing in quality, and hence higher quality firms can signal their type by demanding larger loans; in the second case, the production function is additive in the quality parameter so that the loan size is invariant to quality, and hence higher quality firms can signal their type by accepting smaller loans 1 ; in the third case, firms projects have different riskiness but the same expected return, for any given amount of loan, so that lower quality firms with higher returns in case of success require larger loans. Under a Riley equilibrium construction, given asymmetric information, the latter two cases imply under-financing whereas the former case implies over-financing of firms of higher quality, and separating second-best equilibria.
In this paper we take two analytical steps forward with respect to M-R and Innes. First, we treat M-R’s three separate cases within a general and unified setting in which firms’ returns depend not only on an unobservable quality parameter but also on a technological one, and in which the Wilson equilibrium construction replaces Riley’s one. More specifically, we argue that different ways of organizing production activities can have different implications in terms of firms’ quality and can lead, in a three-stage Wilson contracting game, to a set of equilibria which is richer than those deriving from M-R’s cases. Secondly, we do not resort to the strong informational assumption that each firm’s technological parameter is always observable by banks, thus obtaining a new set of possible equilibria, as opposed to the set of equilibria that arise when technology is observable (like in M-R and Innes). In both cases we reach under-financing equilibria and type-I credit rationing which are stronger than those obtained by M-R.
For this purpose, as quality is not observable, we assume that firm realized returns have the monotone likelihood ratio property (MLRP) with respect to quality, in the sense of Milgrom (1981). The rationale for assuming this MLRP
for the firm profit densities is that of exploiting the monotonicity property implied by the definition of quality. In the literature on credit rationing, two different quality definitions are used. With the first definition, higher quality implies a better profit distribution in the sense of first order stochastic dominance (e.g. Chan and Kanatas (1985), Besanko and Thakor (1987)). With the second, lower quality implies a mean preserving spread or higher risk in the sense of second order stochastic dominance (e.g. Stiglitz and Weiss (1981, 1986), Bester (1985)). In both cases higher quality means better outcomes, which is what matters for the monotonicity property of the definition of quality we need. However, these two definitions of quality imply different relations between quality and the amount of loans, so that, as M-R have shown in their models, we have to specify these relations on an a-priori basis. In this paper we argue that this basis can be given by the way we look at how firms organize their production activities. Hence, we say that if internal economies of scale and/or transaction costs prevail, a larger size of the loan demanded will signal a higher firm quality, while if external economies of scale and/or organizational costs prevail a larger size of the loan demanded will signal a lower firm quality.
The MLRP tool has a crucial role to play also in the building up of the model when technology is assumed to be non-observable by banks. In this case, we do not simply assume that firm realized profits have the MLRP with respect to quality but we assume that the loan size has the MLRP with respect to quality and technology together. This assumption implies that banks are able to order all loan applicants, which have unobservable quality and productive organization, on the basis of their marginal rate of substitution (MRS) between the loan size and the interest rate factor. In particular, banks know that the high-quality firms with prevailing internal economies of scale have the greatest MRS , followed by the low-quality firms with prevailing external economies of scale, the low-quality firms with prevailing internal economies of scale and, finally, by the high-quality firms with prevailing external economies of scale.
The paper is organized as follows. In Sections 2A and 2B, we characterize the main features of borrowers and lenders in order to specify the debt contract. This last specification requires the definition of a three-stage pure strategy game between banks and entrepreneurs which leads to Wilson equilibria (Section 2C). Together with the entrepreneurs’ indifference curves and the banks iso-profit curves, we can thus specify the set of contracts designed by banks and chosen by entrepreneurs (Section 2D). The introduction of the assumption that firm realized profits have the MLRP with respect to quality completes the setting of the model by defining the possible relations between the technological parameter, the quality of the firm and the size of its demand for loans (Section 2E). This setting is sufficient to determine the set of equilibria which can obtain when the technological parameter is observable by banks and when either internal or external economies of scale prevail (Section 3A). When the technological parameter is firms’ private knowledge, the assumption of the MLRP with respect to quality and technology together is required. The previous setting of the model and this new MLRP determine the set of equilibria which can obtain when banks do not observe the technological parameter and make it possible to compare these equilibria with the previous ones (Section 3B). In the final Section we sum up the main results of the paper and we suggest how further research avenues could address a number of problems still unsolved.
Download
PDF Ebook Loan Size and Credit Market Equilibria Under Asymmetric Information
