A Simple Model of Credit Rationing with Information Externalities: A General
Equilibrium Approach
AKM Rezaul Hossain
University of Connecticut
and
Stephen Ross
University of Connecticut
Stiglitz and Weiss (S-W) [1983] show how credit rationing1 may occur as a result of
adverse selection in the credit markets. This theoretical paper considers a simple model of
credit rationing similar of S-W and incorporate information externalities into the model to
understand how credit market may behave when the market is characterized by both imperfect
information and information externalities. Specifically, Lang and Nakamura (L-N) [1993]
hypothesis for information externalities in the context of mortgage credit market is
incorporated into a traditional credit-rationing model. Although L-N model describes
information externalities that are specific to mortgage markets, the model introduced in this
paper is applicable to any other market characterized by information externalities and credit
rationing.
According to L-N model, total loan volume supplied in a neighborhood generates
valuable public information for every lender in the neighborhood regardless of the volume of
loan supplied by any individual lender. Information generated through loan volume – or
through L-N process - helps lender understand the equity risk associated with the properties in
the neighborhood. Specifically, increased loan volume in the neighborhood reduces the error2
associated with appraised value. Improved assessment of the market value of the property
allows lenders to distinguish observable risks, which increases lenders’ profit at any given interest
rate, and leads to increased supply of loans. A larger supply of loans, on the other hand, leads to greater
information and therefore, additional loans in the next period. Majority of the empirical studies
[Calem 1996, Ling and Wachter 1998, Avery et. al. 1999, Harrison 2001] find evidence
1
S-W defines credit rationing as a situation where (a) among observationally equivalent credit applicants some
receive credit and others do not or (b) there are identifiable groups of applicants who, with a given supply of
credit, are unable to obtain loans at any interest rate, even though with a larger supply of credit they would.
supporting pubic nature of this information and consequent information externalities affecting
underwriting decision of lenders.
L-N process would have important implications in a credit-rationing model. Increased supply of
loans in the L-N model would lead to increased neighborhood-specific information, which would affect
equilibrium interest rate offered in a credit rationing model. Equilibrium interest rate, in turn, will affect
loan supply in the neighborhood. The combination of these two propositions leads to a general
equilibrium model that is likely to exhibit multiple equilibria. This essay describes the properties of this
general equilibrium model. In other words, L-N process can be described as follows:
I=f(Ls), where Ls = loan volume and
I = Information level about the equity risk
Here, information is a function of loan volume. Credit rationing equilibrium can be
described as:
Ls=g(r*(I)), where r* = Equilibrium interest rate in a credit rationing model
Here, information affects equilibrium interest rate, which affects the loan supply. The
general equilibrium of credit market with information externalities can be described as follows:
I*=f(g(r*(I*)))
In the general equilibrium, we obtain a set, possibly a multiple set of equilibrium interest rate
(r*) and information level (I*) that are consistent with each other.
Since S-W model, credit rationing remained an active area of research in both
theoretical and empirical fronts. Numerous theoretical works have been done to understand the
existence and equilibrium properties of a credit rationing. Bester [1985] shows screening on
the part of lenders may eliminate adverse selection and resulting credit rationing. Similarly,
Besanko and Thakor [1987] show that by offering different types of credit contracts lender can
separate risk types of borrowers and eliminates credit rationing. Recently, Ben-Shahar and
Feldman [2001] show how two types of contracts and strategic pricing may allow lenders to
separate between risk types and eliminate credit rationing. In this paper, we show one of the
sufficient conditions for the disappearance of credit rationing in the neighborhoods in the
2
Divergence between actual market value and assessed value of the property.
presence of information externalities. One of the other key theoretical result of this paper
suggests that external information increases the accuracy of the lenders’ assessment about
equity risks associated with the housing properties in the neighborhoods and, contrary to usual
intuition, this increased accuracy may increase the interest rates in the market, but reduce the
credit rationing. This counter-intuitive result follows from the increased ability of lender to
raise interest rates as losses from default fall with increasing lender information. This paper
also looks at the general equilibrium properties of mortgage credit market and describes the
effect of several parameters in the model including cost of fund rate, loss of rate of return
parameter due to high risk borrowers and shift parameter between high risk and low risk
borrowers. This general equilibrium model describes the credit market more fully than either
S-W or L-N model. Consequently, the results of this general equilibrium model cannot be
obtained by considering one model alone. For example, our model predicts that a reduction of
the cost of fund rate in the neighborhood characterized by credit rationing would raise rate of
return for lenders, but may not change the equilibrium level of interest rate, loan supply and
level of credit rationing.
Credit rationing in the context of mortgage market had remained an important public
policy issue. There currently is no model that carefully incorporates credit rationing with the
underwriting decision of a mortgage lender. By incorporating information externalities into
credit rationing model, we obtain result that have important policy implications. This paper
shows important trade offs between several policy parameters in a rich general equilibrium set
up. Furthermore, we expect that this simple model can be used as a building block in future
theoretical and empirical studies in understanding complex issues affecting credit market
including default risk that varies with borrower heterogeneity, multiple neighborhoods and
sorting of borrowers across neighborhoods.
Reference:
R. B. Avery, P. E. Beeson, and M. S. Sniderman, “Neighborhood information and home
mortgage lending,” Journal of Urban Economics, 45, pp. 287-310, 1999.
H. Bester, “Screening vs. Rationing in Credit Markets with Imperfect Information,” The
American Economic Review, Volume 75, No. 4, pp. 850-855, 1985.
D. Ben-Shahar and D. Feldman, “Signaling-Screening Equilibrium in the Mortgage Market,”
Working paper, Arison School of business, The Interdisciplinary Center, Herzliya, Israel.
D. Besanko and A. Thakor, “Collateral and Rationing: Sorting Equilibria in Monopolist and
Competitive Credit markets,” International Economic Review, 28(3), pp. 671-689, 1987.
P. S Calem, “Mortgage credit availability in low- and moderate-income minority neighborhoods: are
information externalities critical?” Journal of Real Estate Finance and Economics, 13, 71-89, 1996
D. M. Harrison, “Importance of Lender Heterogeneity in Mortgage Lending ” Journal of Urban
Economics, 49, pp. 285-309, 2001
W. W. Lang and L. I. Nakamura, “A Model of Redlining.” Journal of Urban Economics, 33,
pp. 223-234, 1993
E. Y. Lin, “Information, Neighborhood Characteristics, and Home Mortgage Lending.” Journal
of Urban Economics, 49, pp. 337-355, 2001
D. C. Ling and S. M. Wachter, “Information externalities and home mortgage underwriting,,” Journal
of Urban Economics, 44, pp. 317-332, 1998.