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Article Excerpt
Summary. We show that it is sometimes efficient for a bank to commit to a policy that keeps information about its risky assets private. Our model, based upon Diamond-Dybvig (1983), has the feature that banks acquire information about their risky assets before depositors acquire it. A bank has the option of using contracts where the middle-period return on deposits is contingent on this information, but by doing so it must also reveal the information. We derive the conditions on depositors' preferences and banking technology for which a bank would prefer to keep information secret even though it must then use a non-contingent deposit contract.
Keywords and Phrases: Deposit contracts, Interim information.
JEL Classification Numbers: D8, G21, G28.
1 Introduction
In the 1980's, poor credit risks caused the failure of many Savings & Loans. In response to these failures, the U.S. government enacted legislation devised to prevent such crises. The Financial Institutions Reform, Recovery, and Enforcement Act of 1989 and the Federal Deposit Insurance Corporation Improvement Act of 1991 made changes to banking laws designed to reduce moral-hazard problems and prevent losses from federal insurance. (1)
Part of these laws limit the ability of a bank to keep information private by creating a minimum capital requirement, imposing a new examination standard for bank assets, and implementing a risk-based insurance scheme. A minimum capital requirement entails accurate measurements of a bank's capital. Likewise, a risk-based insurance scheme is based on both a bank's capital and the riskiness of a bank's investments. These changes require altering both the examination standard and accounting methods of bank assets. Furthermore, they increase revelation about a bank's assets as do other moves to have banks mark loans at market value rather than book value. (2) Thus, these laws could theoretically reveal more information. Moreover, Morgan (2002) finds empirical evidence that banks indeed have information to reveal. (3) This leads us to the main question of the paper: Could this increase of information about a bank's assets have unintended adverse effects?
This question of whether an increase in information can lead to a decrease in welfare appears in other contexts. Hirshleifer (1971) shows that an increase of information may hurt efficiency in an exchange economy (the breadth of examples was recently expanded by Schlee, 2001). Verrecchia (1982) then shows such may be the case in insurance markets. (4) Eckwert and Zilcha (2003) study when additional information may hurt in a production economy. In a different setting, Maskin and Tirole (1990, 1992) analyze a principal-agent model where an informed principal does strictly better by not revealing his information. In another context, Kaplan and Zamir (2000) show that in an auction a seller can exploit this "information property" by giving buyers additional information making the outcome of the auction worse for the buyers and better for the seller with an overall welfare loss.
To ask this question in a banking context, we use a version of the Diamond-Dybvig model (1983) with a risky investment where the bank and depositors are asymmetrically informed about the return on investment in the middle period. While similar environments have been analyzed in the literature (see Gorton, 1985; Jacklin and Bhattacharya, 1988; Alonso, 1996; Hazlett, 1997), our model is tailored toward the question we wish to answer.
As in Diamond-Dybvig, we have three periods in which initially depositors don't know whether they will enjoy only the middle period good or enjoy both the middle and last period goods. The former are the impatient depositors, while the latter are the patient depositors. Each depositor's type is private information and discovered only in the middle period. A bank has access to an illiquid constant-returns-to-scale investment technology. This technology offers a safe middle-period return and an uncertain last-period return. A key assumption is that in the middle period, only the bank learns the risky last-period return. In the initial period, a bank offers a deposit contract that specify payments to depositors. A bank also has the ability to make the middle-period payments (not just the last-period payments) contingent upon the bank's information. However, a bank writing such contingent contracts implicitly reveals its information--depositors cannot be ignorant of the same information on which their received payments are based. The only way for a bank to keep its information private is to write contracts with a non-contingent middle-period payment. Thus, we permit a bank to choose whether to reveal its information and offer contingent contracts or not to reveal its information and offer non-contingent contracts (a third option of revealing its information and offering a non-contingent contract is weakly dominated by the second).
This dilemma of the bank allows us to answer our question in the following line of reasoning. If a bank always chooses to reveal its information with a contingent contract, then forcing a bank to reveal its information will have no effect. However, if there is a case when a bank chooses to offer a non-contingent contract and doing so leads to a strictly better outcome, then the same contract with information revealed will result that when the return is low, the patient depositors would claim to be impatient depositors. Thereby, the bank would be forced to offer the inferior, contingent contract. Thus, forcing a bank to disclose information will have an adverse effect.
We find such a case by first finding the technological conditions under which the patient depositors' incentive constraints will bind. Then, by showing that if these constraints are indeed binding and the depositors are moderately risk averse (the degree of relative risk aversion is between 1 and 2), then the bank will conceal its information by offering non-contingent contracts.
The format of this paper is as follows. Section 2 describes the model. The solution concept is defined and the reduced social planner's problem is derived in Section 3. Results are analyzed in Section 4 and the conclusions are discussed in Section 5. The proofs of all the lemmas and properties are listed in the Appendix.
2 Model
The environment, similar to Diamond-Dybvig (1983) (henceforth DD), is described in this section.
Time periods, goods, depositors and preferences
There are three time periods, 0, 1, and 2 (referred to as initial, middle, and last), and one good for each period. Let [c.sub.t] denote an allocation of time t good and c = ([c.sub.0], [c.sub.1], [c.sub.2]) denote an allocation bundle. There is a continuum with measure one of ex-ante identical depositors. Each depositor is endowed with one unit of time good. At time 1, depositors privately discover their type, either impatient (i) or patient (p). Impatient depositors enjoy only the time 1 good ([u.sub.i](c) = u([c.sub.1])), while the patient depositors enjoy both the time 1 good and the time 2 good ([u.sub.p](c) = u([c.sub.1] + [c.sub.2])). The utility function, u, is twice differentiable, increasing and strictly concave. Each depositor has an equal chance of being either type and there is no aggregate uncertainty in depositor types.
The bank and savings technologies
We start by looking at a single bank with the depositors' best interests in mind...
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