The lead article in Volume 23, Issue 5 of the Review of Finance is Credit Market Competition and Liquidity Crises by Elena Carletti and Agnese Leonello. This paper finds that – contrary to common concerns – greater competition in the banking industry can reduce the risk of financial crises.
The Double-Edged Sword of Competition
In most industries, competition is believed to be socially beneficial – it benefits customers through greater product choice and lower prices, suppliers through higher input costs, and workers through enhanced wages. And because the prices customers pay are close to the costs of production, allocative efficiency rises. Indeed, last issue’s lead article documented a sharp decline in competition across most industries in the US, and argued that it’s a cause for concern.
But for banking, the effect of competition might be different. What’s special about the banking industry is the danger of excessive risk-taking. Of course, in any industry, a firm could take too much risk, but if it backfires, the losses are largely confined to the bank’s investors and employees. If a bank fails, the impact can be systemic, as evidenced by the financial crisis. The concern is that, if competition in banking is high, profits from “business as usual” will be low – encouraging banks to gamble through risky lending activities (e.g. sub-prime loans).
But credit risk – lending to risky customers who subsequently default – isn’t the only reason banks go bankrupt. As famously shown by Diamond and Dybvig (1983), even if a bank is fundamentally healthy – its loans are safe – it may still go bankrupt due to liquidity risk. Banks lend long-term (e.g. loans to entrepreneurs) but finance themselves short-term (via bank deposits that can be withdrawn at any time). If many depositors suddenly choose to withdraw, the bank needs to cash in its long-term loans. But even though the loans are fundamentally healthy – the entrepreneurs won’t default – they’re illiquid. Ordinary people, and even many institutional investors (e.g. equity mutual funds) don’t hold second-hand bank loans. There’s only a limited set of other investors who the bank can sell them to, so it can’t raise enough to finance its depositors’ withdrawals, and so goes bankrupt. Indeed, Northern Rock (2007), Laiki Bank (2013) and Banco Popular (2017) are examples of banks that went bust primarily due to illiquidity.
This Paper’s Approach
Elena and Agnese’s goal is to understand how competition affects liquidity crises. Now one approach might be to do so empirically – to study the link between competition and liquidity crises in the data. But there are many challenges with this. First, it’s hard to pinpoint whether a banking failure was due to liquidity or credit. Second, it’s hard to pinpoint the effect of competition on banking failures. One might look across several countries and see whether the ones with more frequent and more severe financial crises have greater banking competition. But these countries will differ in many dimensions, not just banking competition.
So Elena and Agnese study this question theoretically – they construct a model of bank lending and liquidity risk, then change the level of banking competition and see how it affects the frequency of liquidity crises. The advantage of a theoretical approach is that they can change competition while holding everything else constant. This is a similar approach to a flight simulator or city simulator.
The Model
The model has three periods, 0, 1, and 2. At time 0, banks raise funds from households. They can invest these funds in two places. One is reserves (such as Treasury bills), which are liquid and can be cashed in at time 1 for their full value. The second is loans to entrepreneurs, which give a higher return than reserves. Critically, the higher the amount of bank competition, the more banks are willing to offer loans to entrepreneurs, so the return to loans is lower.
To isolate the effect of liquidity risk, the authors deliberately remove credit risk from their model. The loans are risk-free, in that the entrepreneurs can always pay back the loan in full at time 2. But the twist is that repayment only occurs at time 2 – the entrepreneurs use the loans to set up businesses, which only have long-term payoffs. At time 1, some households need to withdraw. If the bank doesn’t have enough reserves to meet the withdrawals, it will have to sell some of its loans. Since the only purchasers of these loans are other banks, who themselves may be cash-strapped, this is a fire sale – selling banks will fetch far less than the loans’ time 2 values. One of the paper’s technical contributions is to derive these fire sale prices endogenously (known as cash-in-the-market pricing). These prices depend on the number of other banks and their cash needs (which in turn depends on their own depositor withdrawals and how many reserves they chose to hold).
There are two possible equilibria. The safe equilibrium is where all banks play it safe. While they still make some loans, they hold enough reserves so that, even if there are large depositor withdrawals, they can meet them using their reserves and there are never any fire sales. In the risky equilibrium, some banks play it safe, but others take risk by investing most of their funds in loans. If depositor withdrawals are low, the bank stays solvent and makes more money than if it played it safe, due to the higher return on loans than reserves. But if depositor withdrawals are high (i.e. there is a liquidity shock), the bank goes bankrupt. In equilibrium, these two forces exactly offset, so banks are indifferent between the risky and safe strategies.
Which equilibrium will arise in reality? Critically, it depends on the level of banking competition – the motivation for constructing the model. If banking competition is low, then the return to loans is high. Then, if the probability of liquidity shocks is also low, many banks think it’s worth it to play the risky strategy – they get attractive returns in good times, and while they go bankrupt in bad times, these times are rare. So we get the risky equilibrium. This equilibrium is bad for society – while bankruptcies are indeed rare, they still take place, and the costs to society are much greater than to the bank, so it didn’t take them into account when choosing the risky strategy.
In contrast, when banking competition is high, then the return to loans is low, so it’s not worth it for any bank to play the risky strategy. We get the safe equilibrium, where there’s never any bankruptcy. So, in contrast to some credit risk models, where competition increases the probability of crises, the authors show that competition reduces the risk of liquidity crises.
Further Results
While the goal of the paper was to study the effect of competition on liquidity crises, the model derives additional results over and above the initial motivation. One is how liquidity risk (the probability of a liquidity shock) affects the frequency of crises. Simple intuition might suggest that, the likelier the liquidity shock, the likelier a crisis. But this intuition ignores the fact that banks rationally respond to the probability of a liquidity shock. When the liquidity shock is more likely, banks are more tempted to play it safe, and so we end up in the safe equilibrium where bankruptcies never occur.
Combining this result with the first one leads to an interesting twist. Recall that competition generally increases financial solvency. But if liquidity risk is so low, then even competition isn’t strong enough to avert the risk of financial crises. Even if the return to loans isn’t much higher than the return to reserves (due to fierce competition), the risk of withdrawals is so low that some banks still take the risky strategy. This has implications for policymakers – competition, while valuable, should not be the only tool to increase financial stability.
Another interesting result is the link between crises and aggregate credit (the amount of lending across the banking sector). This link might seem to be obvious – the greater the amount of lending, the greater the risk of bankruptcies. Indeed, the financial crisis is often attributed to over-lending. But the authors show that it’s not obvious – it depends on the probability of liquidity shocks. If this probability is high, then in the risky equilibrium, most banks play it safe and only a few lend – aggregate lending is lower than if we were in the safe equilibrium. So there is less aggregate creditin a world with crises than one without. Only if the probability of liquidity shocks is low do we get the “natural” result that the risky equilibrium has more aggregate credit than the safe one.
The key to this twist is that aggregate credit depends not only on an individual bank’s lending activity, but how many banks play the risky versus the safe strategy. In the safe equilibrium, each individual bank makes few loans, but because every bank does so, aggregate lending can be high. In the risky equilibrium, some banks make large loans. But there might not be many of them, and because the safe banks make very few loans (fewer than in the safe equilibrium – they want to hold reserves so that they can buy loans from risky banks at fire-sale prices), aggregate credit may be lower.