We study a competitive market for risk-sharing, in which risk-tolerant providers of risk protection, who face frictional costs in holding capital, offer coverage over a range of risk classes to risk-averse agents. We distinguish monoline and multiline industry structures and characterize when each structure is optimal. Markets for which the risks are limited in number, asymmetric or correlated will be served by monoline structures, whereas markets characterized by a large number of essentially independent risks will be served by many multiline firms. Our results are consistent with observed structures within insurance, and also have general implications for the financial services industry.

THE Federal Home Loan Bank Board (FHLBB), a government regulatory agency for member Savings and Loan Associations (SLA), provides advance loans (advances) to members. Advances are considered a major policy tool for the FHLBB in stabilizing deposit, mortgage, and housing markets. Indeed, the FHLBB has characterized advances as providing 'a central credit resource, capable of expanding and contracting to meet the needs of its member institutions for housing credit.' Debt issues in the government agency capital market are the primary source for FHLBB funds.2 The quantity of advances outstanding has grown from $5.3 billion at year-end 1968 to $32.7 billion at year-end 1978, and with considerable variation in between. A key issue in evaluating the role of advances has been whether or not the FHLBB uses nonprice rationing in allocating advance loans. Without nonprice rationing, the FHLBB sets the interest charge for the advances and member SLAs determine the quantity of loans they wish to borrow. In this case, an appraisal of FHLBB policy is relatively straightforward and can be based on the level of the advances rate. With nonprice rationing, in contrast, an appraisal of FHLBB policy is more complicated because the unobserved availability of advances must also be considered. The relevance of this issue is underscored by a recent report of the existence of nonprice rationing.3 Existing econometric models of the advances market treat the question of nonprice rationing in different ways. Hendershott (1977) has the quantity of advances determined by SLA demand without regard to interest rates, so there is neither price nor nonprice rationing. As a consequence, advances policy is viewed as purely passive. Kearl and Rosen (197-4) have the quantity of advances determined by a FHLBB reaction function, again with no role for interest rates, so they have a pure nonprice rationing system. In the MPS model (see Gramlich and Jaffee (1972)) both the quantity and interest rate for advances are set exogenously by the FHLBB, which then implies a combination of interest rate and nonprice rationing. Finally, Silber (1973), in the most sophisticated of the studies, has two versions, one with interest rate and one with nonprice rationing. The version with interest rate clearing has a FHLBB reaction function determining the interest rate and an SLA demand function determining the quantity. The version with nonprice rationing has the FHLBB determine the quantity of advances and no equation for the interest rate, in much the same spirit as Kearl and Rosen. The treatment of rationing in these models is not satisfactory. First, the models specify a priori the presence or absence of rationing, but without providing a test of the hypothesis that rationing takes place. Second, among the rationing models, the specifications are deficient in assuming either that only rationing occurs (Kearl and Rosen, and Silber) or that price and nonprice rationing always occur together (the MPS model). In this paper we develop a model based on optimizing behavior on the part of the FHLBB. Whether market clearing or nonprice rationing behavior obtains in a given time period depends on both economic conditions and the nature of the FHLBB's objective function. As a polar case, the general model collapses into an ordinary market clearing simultaneous equation model and we are able to offer statistical evidence as to which model is to be preferred. In section II.A we develop a market clearing model and in II. B a rationing model. A geometric interpretation is given in section II.C. Section III provides the empirical specification for impleReceived for publication November 6, 1978. Revision accepted for publication July 12, 1979. * We are indebted to NSF Grant SOC77-07680 and the Federal Home Loan Bank Board for support, to Naoyaki Yoshino for helpful comments, and to David Romer for expert research assistance. An earlier version of this paper was presented at the Econometric Society Meetings, Vienna, September 1977. 1 FHLBB Journal, April 1972, p. 24. 2 See Jaffee (1976) for a recent survey of FHLBB structure and policies. 3 Wall Street Journal, May 4, 1979, p. 18.

The recent financial crisis has revealed significant externalities and systemic risks that arise from the interconnectedness of financial intermediaries’ risk portfolios. We develop a model in which the negative externality arises because intermediaries’ actions to diversify that are optimal for individual intermediaries may prove to be suboptimal for society. We show that the externality depends critically on the distributional properties of the risks. The optimal social outcome involves less risk-sharing, but also a lower probability for massive collapses of intermediaries. We derive the exact conditions under which risk-sharing restrictions create a socially preferable outcome. Our analysis has implications for regulation of financial institutions and risk management.

Oliver D. Hart, Dwight M. Jaffee; On the Application of Portfolio Theory to Depository Financial Intermediaries12, The Review of Economic Studies, Volume 4

We develop a model for markets for catastrophic risk. The model explains why insurance providers may choose not to offer insurance for catastrophic risks and not to participate in reinsurance markets, even though there is a large enough market capacity to reach full risk sharing through diversification in a reinsurance market. This is a “nondiversification trap.” We show that nondiversification traps may arise when risk distributions have heavy left tails and insurance providers have limited liability. When they are present, there may be a coordination role for a centralized agency to ensure that risk sharing takes place.

[This paper is concerned with the econometric problems associated with estimating supply and demand schedules in disequilibrium markets. The general problem is that in the absence of an equilibrium condition the ex ante demand and supply quantities cannot in general be equated to the observed quatity traded in the market. Four methods of estimation, differing primarily in their use of information on price-setting behavior, are developed in this paper. The first method is a generalization of an earlier meothd developed by R. Quandt and is based upon the maximization of a likelihood function. The method does not require any specific assumption about price-setting behavior, and it allows the sample separation (into demand and supply regimes) to be estimated along with the coefficient estimates. The second and third methods use the change in price as a qualitative proxy in determining the sample separation. The fouth method uses the change in price as a quantitative proxy for the amount of excess demand (supply) in the market. In the final section of the paper the four methods are used to estimate a a model of the housing and mortgage market in an effort to gauge the potential usefulness of each of the methods.]