The Diamond-Dybvig model was born in 1983 by the joint studies of Philip Dybvig and Douglas Diamond. The two had begun parallel projects in the early 80s, both motivated to better understand the involvement of financial intermediaries, in particular banks, in the dynamics of the Great Depression. Their theoretical model defined the role of banks in the economy and why these are vulnerable to the so-called bank runs and have had a huge impact in the regulation of financial intermediaries since its publishing. Moreover, the academic debate that developed on the Diamond-Dybvig paper helped to further understand this intricate world and enhance economic policy. Because of their huge contribution to the progress of the economic subject, the two academics have been awarded with the Nobel prize in Economic Sciences in 2022.
This article tries to explain the dynamics that determined the SVB bank crisis with the approach of economists.
The first important aspect to define is the features of the commercial banking sector in the Diamond-Dybvig world.
First, the banking sector transforms liquid assets (deposits of depositors) into illiquid assets (long term loans and investments).
The second important aspect we assume is that news regarding the banking sector influence how depositors perceive the stability of the bank, and that this news are spread very quickly between people.
Lastly, the bank doesn’t know the creditworthiness of the depositor, so the bank doesn’t know who is a “good” or a “bad” depositor but can estimate the percentage of presence of each type of depositor; we’ll get back on this point in a while.
The crucial aspect of the model is the relationship between bank and debtor. It is assumed that the bank must offer the possibility to participate in profits of a long-term investment to everyone through deposits, without knowing whether he/she is a good or a bad customer, the bank must allow everyone to withdraw money before the maturity of the investment and to receive part of the investment’s profits if they stay until the end of the investment.
In the model’s framework, there are three time periods (0,1,2) and many identical households, which can be of Type 1 or Type 2. Type 1 consumers want to consume in period 1, while Type 2 consumers want to consume in period 2.
Consumers can subscribe a deposit contract where households transfer their consumption goods in period 0 to the banking sector as deposits. Banks provide the option to cancel the contract and withdraw the investment either in period 1 or 2. Banks invest the percentage amount I in some long-run projects and (1-I) in short-run projects. Moreover, the banks’ investment opportunities include a liquid short-term investment alternative, where banks invest a percentage of deposits into short-term investments that can be readily converted to cash without losing value. These investments are terminated either in period 1 or period 2 and yield no return for the depositor. The illiquid long-term investment alternative is intended for high-return investments that require a longer time period to yield returns, ideally terminated in period 2 with a return R>1. Hence, withdrawing deposits in T=1 represents an opportunity cost for the depositors. Terminating investments in period 1 is possible but costly, since termination of long-term assets will yield only a liquidation value L<1. The bank will do so only if forced to, which is the situation we will analyse soon.
At time 0, households are endowed with one unit of goods. Households don’t know yet if they are of Type 1 or 2. They will be of Type 1 with probability or of Type 2 with probability . At time 1, households receive a private signal indicating if they are of Type 1 or Type 2. This is a case of adverse selection, entailing a situation in which the household possesses information unknown to the bank, namely, if it is Type 1 or Type 2.
The bank will invest I in the long run and (1-I) in the short run. The return from the short-term investment (1-I) must be high enough to finance consumption in period 1, which will occur with probability . The reflux from the long-term investment I needs to be high enough to finance consumption in period 2, which will occur with probability (1- ).
The optimal allocation is a balanced division of households among Type 1 and Type 2. From the perspective of the household, it is better to split in short-term and long-term investments based on their real needs.
The bank acts in the best interest of the depositors, so its investment decisions are taken to maximise the wellness (utility) of its clients. There exists a combination (C1*, C2*) which leads to an optimum. This Nash equilibrium is the one in which Type 1 depositors withdraw their funds in T1 and Type 2 depositors withdraw in T2. The banking sector offers an “altruistic” deposit contract, so that households can realise their utility maximum. It offers the possibility to gain a positive return and also to have the sum back prior to the end of the investment if needed. However, in the setup of the Diamond-Dybvig model, it may be the case that a banking crisis may emerge due to different equilibria situations.
A bank run can occur following a change in the expectations of Type 2 depositors, who then withdraw their deposits in period 1, since they are allowed to do so. However, in T1, the bank has only the liquidity from the short-term investment (1-I) . The liquidity position is only large enough to provide Type 1 households with liquidity. The proportion of Type 1 households is equal to , so the bank needs funds to match the demand for liquidity from Type 1 households. If some Type 2 investors also withdraw deposits due to an expected instability of the banking sector, the bank will indeed run into a liquidity problem. Due to the liquidity problem, banks will terminate long-term investments prematurely, and the system crashes because, as assumed, long-term investments yield a return L<1.
Households can only secure their deposits by arriving at the bank early in the bank run. Consequently, the banking system can slide into a vicious circle of anticipated and actual instability.
There exist two possible scenarios with respect to the stability of the banking sector: the first equilibrium is when Type 2 households believe in the stability of the banking sector and do not withdraw their deposit in T1. The second equilibrium is when Type 2 households do not believe in the stability of the banking sector and withdraw their deposits in T1, causing a bank run.
Although it is difficult to imagine in reality, this model only allows two possible equilibria: the “good” equilibrium in which only Type 1 agents run to the bank, and the “bad” one in which all the agents run to the bank.
This demonstrates that the expectations of Type 2 households determine the equilibrium. Indeed, their expectations are called “Self-fulfilling prophecies,” meaning that what they believe will actually happen.
The solution that the Diamond-Dybvig model proposed to counter bank runs was to give to central banks the function of “Lender of Last Resort”. LLR refers to an arrangement whereby a central bank provides funding to banks that are close to the collapse and are struggling to secure fundings. Diamond and Dybvig proposed that central banks be LLR to provide a service similar to deposit insurance and as in the previous case, adopting the solution would always prevent bank runs in the model but not in reality.
In the DD model, the central bank could use money from taxpayers and money creation to purchase commercial banks assets at prices above their liquidating value in T=1, thus improving the trust in the financial system stability and maintaining a stable equilibrium that reduces likelihood of bank runs. The theory seems to be in line with practical applications of this policy. Indeed, bank runs have occurred less frequently since the FED assigned to the central bank of the USA the role of LLR. This decision was followed also by ECB, hence decreasing bank runs in EU area too.
However, a criticism has been levied against LLR: being backed by a LLR, banks may take on excessive risk, assuming that they will be saved if a crisis occurs.
The collapse of SVB gives an example of the mechanics of a bank run proposed by the DD model. The bank had accumulated billions in uninsured short-term deposits from start-ups, which it invested in long-term, high-credit-rated securities. As interest rates rose, the value of these securities fell. Depositors, realising the situation, began withdrawing their funds. As seen shortly earlier, this is the mechanism of self-fulfilling prophecies: the bank was healthy, but the propagated fear of investors caused a bank run.
The surge in withdrawals forced SVB to sell large amounts of long-term securities at a loss, worsening its financial troubles and creating a vicious cycle of panic, concluded with SVB’s collapse. One of the main problems was the fact that many of the bank’s depositors were corporations and startups, that had accounts of millions of dollars (for example Spotify), and these deposits exceeded by far the insurance limit of $250,000 (see Ch.5).
This banking crisis in the U.S. spread fear among global investors, causing widespread panic and concerns about the stability of other banks. The crisis reached Europe, where banking stocks plummeted, and risk premiums rose. Credit Suisse, one of Europe’s largest banks, faced severe challenges, including a major drop in its share price and issues securing liquidity from its main shareholder. This led to its acquisition by UBS, a Swiss investment bank.
These urgent circumstances required quick action from financial institutions and governments. U.S. regulators took control of failing banks, and the Federal Reserve provided emergency liquidity to stabilise the situation. Furthermore, the government insured all deposits of SVB and Signature Bank customers to reassure the public and prevent a potential panic spread to other financial institutions.
The crisis pointed out the need for vigilance and awareness of banking system risks. Officials now face the complex task of managing the acquired banks and their risky assets, such as treasuries, municipal debt, and commercial mortgage-backed securities.
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