Academic journal article Economic Quarterly - Federal Reserve Bank of Richmond

Banks and Liquidity Creation: A Simple Exposition of the Diamond-Dybvig Model

Academic journal article Economic Quarterly - Federal Reserve Bank of Richmond

Banks and Liquidity Creation: A Simple Exposition of the Diamond-Dybvig Model

Article excerpt

(ProQuest-CSA LLC: ... denotes formulae omitted.)

Banks make loans that cannot be sold quickly at a high price. Banks issue demand deposits that allow depositors to withdraw at any time. This mismatch of liquidity, in which a bank's liabilities are more liquid than its assets, has caused problems for banks when too many depositors attempt to withdraw at once (a situation referred to as a bank run). Banks have followed policies to stop runs, and governments have instituted deposit insurance to prevent runs. Diamond and Dybvig (1983) develop a model to explain why banks choose to issue deposits that are more liquid than their assets and to understand why banks are subject to runs. The model has been widely used to understand bank runs and other types of financial crises, as well as ways to prevent such crises. This article uses narrative and numerical examples to provide a straightforward explanation of the ideas in Diamond and Dybvig (1983).

Diamond and Dybvig (1983) argue that an important function of banks is to create liquidity, that is, to offer deposits that are more liquid than the assets that they hold. Investors who have a demand for liquidity will prefer to invest via a bank, rather than hold assets directly. Before discussing the methods by which banks might create liquidity, it is important to understand why there is a demand for liquidity by consumers or producers. I begin with the consumer demand for liquidity. Investors demand liquidity because they are uncertain about when they need to consume and, thus, how long they wish to hold assets. As a result, they care about the value of liquidating their assets on several possible dates, rather than on a single date.

Creating deposits that are more liquid than the assets held by banks can be viewed as an insurance arrangement in which depositors share the risk of liquidating an asset early at a loss. This model explains an important function of banks. It also shows that offering these demand deposits subjects the banks to bank runs if too many depositors withdraw.

Creating liquid deposits is one important function of financial intermediaries like banks. Another function is monitoring borrowers and enforcing loan covenants. The latter function is modeled in Diamond (1984), and is described in a simple framework in Diamond (1996).


This section first analyzes some important reasons for the demand for more liquid assets by investors who are consumers. It then provides an alternative motivation for a demand for liquid assets by entrepreneurs. When the assets that investors can hold directly are illiquid, there is a demand for creating more liquid assets.

An illiquid asset is one in which the proceeds available from physical liquidation or a sale on some date are less than the present value of its payoff on some future date. In the extreme, a totally illiquid asset isworthless (cannot be sold or physically liquidated for a positive amount) on some date but has a positive value on a later date. The lower the fraction of the present value of the future cash flow that can be obtained today, the less liquid is the asset.

Consider the following asset on three dates, T = 0, T = 1, and T = 2. If one invests one unit at date 0, it will be worth r2 at date 2, but only r1 < r2 at date 1. The lower r1/r2 is (holding constant market discount rates), the less liquid is the asset.

The Uncertain Horizon of Investors

Investors face an uncertain horizon to hold the asset. Each will need to consume either at date T = 1 or T = 2. However, as of date 0, an investor does not know at which date he will need to consume. Each begins with 1 with which to invest on date T = 0. An investor cannot buy direct insurance against his need for liquidity, because the need is private information and, thus, is not due to some observable event such as a hurricane. However, contracts can be designed that indirectly provide this insurance. …

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