In the previous chapter, we showed that banks create value by offering liquid deposits backed by illiquid assets. The optimal deposit contract \((c_1^*, c_2^*)\) satisfies \(u'(c_1^*) = R \cdot u'(c_2^*)\) and delivers higher expected utility than either autarky or market trading. We also showed that this contract requires trading restrictions to prevent patient depositors from exploiting the front-loading (Jacklin, 1987).
But there is a darker consequence of these same features. The very structure that enables liquidity creation — liquid liabilities backed by illiquid assets — makes banks vulnerable to self-fulfilling panics. If depositors believe the bank will fail, their collective withdrawal can cause the bank to fail, even when the bank is fundamentally solvent.
The same features that make banking valuable also make it fragile:
This creates a coordination problem among depositors: each depositor’s optimal action depends on what they believe other depositors will do.
Recall the Diamond-Dybvig environment from the previous chapter:
The key question is: who withdraws at \(t=1\)?
In the previous chapter, we simply assumed that only the 25 impatient depositors withdraw. But depositor types are private information — the bank cannot verify who is truly impatient. The contract offers every depositor the option to withdraw \(c_1^* = 1.28\) at \(t=1\) or wait for \(c_2^*\) at \(t=2\). Patient depositors must choose whether to wait.
Suppose all depositors expect that only impatient types will withdraw. Then:
Since \(c_2^* = 1.813 > 1.28 = c_1^*\), patient depositors prefer to wait. Their expectation is confirmed — this is a Nash equilibrium.
Now suppose all depositors expect that everyone will withdraw at \(t=1\). What happens?
If all 100 depositors attempt to withdraw \(c_1^* = 1.28\):
The bank can pay at most \(\lfloor 100/1.28 \rfloor = 78\) depositors before exhausting its assets. Depositors 79 through 100 receive nothing.
If a patient depositor believes everyone else will withdraw, she faces a choice:
Withdrawing is the rational choice. But when all patient depositors reason this way, the bank is indeed liquidated. The fear of a run causes the run.
Following Diamond (2007) and Tirole (2006), let \(\hat{\lambda}\) denote the fraction of depositors who actually withdraw at \(t=1\). This includes all impatient depositors plus any patient depositors who run, so \(\hat{\lambda} \geq \lambda\).
We can write \(\hat{\lambda} = \lambda + (1 - \lambda)x\), where \(x\) is the fraction of patient depositors who choose to withdraw.
Payoff to an early withdrawer:
\[ \text{Early payoff} = \min\left(c_1^*, \frac{1}{\hat{\lambda}}\right) \]
If \(\hat{\lambda} c_1^* \leq 1\), the bank can meet all withdrawal requests and each early withdrawer gets \(c_1^*\). If \(\hat{\lambda} c_1^* > 1\), the bank runs out of assets and the last withdrawers get nothing. On average, each early withdrawer gets \(1/\hat{\lambda}\).
Payoff to a late withdrawer (waits until \(t=2\)):
\[ \text{Late payoff} = \max\left(\frac{(1 - \hat{\lambda} c_1^*)R}{1 - \hat{\lambda}}, \; 0\right) \]
After paying the early withdrawers, the bank has \(1 - \hat{\lambda} c_1^*\) units of the illiquid asset remaining. These mature at \(t=2\) and are worth \(R\) each. The \((1 - \hat{\lambda})\) remaining depositors share the proceeds.
With \(c_1^* = 1.28\), \(R = 2\), and \(\lambda = 1/4\):
Figure (adapted from Tirole, 2006, Figure 12.2). The payoffs to early and late withdrawers as a function of \(\hat{\lambda}\), the fraction of depositors who withdraw at \(t=1\). The x-axis begins at \(\hat{\lambda} = \lambda\) (only impatient depositors withdraw):
The curves cross at the unstable equilibrium (\(\hat{\lambda}^* = 0.5625\)). Any perturbation away from this point pushes toward either the good equilibrium (\(\hat{\lambda} = \lambda\)) or the run equilibrium (\(\hat{\lambda} = 1\)).
The game among depositors exhibits strategic complementarities: my incentive to run increases when more other depositors run. As \(\hat{\lambda}\) rises:
This is what makes the run self-fulfilling. Once enough depositors are expected to run, every depositor prefers to run.
Following Diamond (2007), the tipping point occurs when the early and late payoffs are equal:
\[ c_1^* = \frac{(1 - \hat{\lambda} c_1^*)R}{1 - \hat{\lambda}} \]
Solving for the critical \(\hat{\lambda}\):
\[ c_1^*(1 - \hat{\lambda}) = (1 - \hat{\lambda} c_1^*)R \] \[ c_1^* - c_1^* \hat{\lambda} = R - \hat{\lambda} c_1^* R \] \[ c_1^* - R = \hat{\lambda} c_1^* - \hat{\lambda} c_1^* R = \hat{\lambda} c_1^*(1 - R) \] \[ \hat{\lambda}^* = \frac{R - c_1^*}{c_1^*(R - 1)} \]
With \(c_1^* = 1.28\) and \(R = 2\):
\[ \hat{\lambda}^* = \frac{2 - 1.28}{1.28(2 - 1)} = \frac{0.72}{1.28} = 0.5625 \]
So if more than 56.25% of depositors are expected to withdraw, the run becomes self-fulfilling. Since only 25% are truly impatient, this means the run is triggered when more than roughly 42% of patient depositors decide to withdraw.
The depositor game has exactly three equilibria:
Good equilibrium (\(\hat{\lambda} = \lambda = 0.25\)): Only impatient depositors withdraw. Patient depositors wait because \(c_2^* = 1.813 > 1.28 = c_1^*\). This is the DD optimal allocation.
Unstable equilibrium (\(\hat{\lambda} = \hat{\lambda}^* = 0.5625\)): Patient depositors are indifferent between withdrawing and waiting. Any perturbation pushes toward one of the stable equilibria.
Run equilibrium (\(\hat{\lambda} = 1\)): All depositors withdraw. The bank is liquidated. Everyone gets less than in the good equilibrium.
Because moving away from a good equilibrium requires a large change in beliefs. Starting from the good equilibrium (\(\hat{\lambda} = 0.25\)), a small increase in \(\hat{\lambda}\) (say to 0.27) does not change the incentives — patient depositors still prefer to wait. It takes a coordinated shift in beliefs to push \(\hat{\lambda}\) past the tipping point of 0.5625.
This is why Diamond (2007) emphasizes that initiating a run requires “something that all (or nearly all) depositors see (and believe that others see)” — a newspaper story, a social media post, or even a long line at the bank.
The multiple equilibria result raises a natural question: what determines which equilibrium prevails?
Diamond and Dybvig (1983) do not provide a theory of equilibrium selection. Instead, they note that runs can be triggered by publicly observable signals — anything that causes depositors to coordinate on the bad equilibrium:
Sunspots: Arbitrary events that serve as coordination devices. Even a completely irrelevant signal can trigger a run if depositors believe others will respond to it.
News about bank fundamentals: A newspaper report that the bank’s assets have declined in value. Even if depositors know the report is inaccurate, they may run if they believe others will run based on the report.
Observable queues: As Diamond (2007) notes, “it would make sense for a bank to have a large lobby (or fast bank tellers), because if a line to withdraw extended out to the street, passersby may conclude that a run is in progress.”
The sunspot approach has been criticized as making the model “empirically vacuous and untestable” (Gorton, 1988) — if runs are driven by arbitrary signals, the model makes no predictions about when runs occur or which banks are vulnerable. This criticism points to a deeper question: are bank runs driven by coordination failure (as in DD) or by bad fundamentals? And can we distinguish the two empirically?
The DD model generates panic-based runs — runs that occur even though the bank is fundamentally solvent. But in practice, many runs appear to be triggered by genuine bad news about bank fundamentals. This has led to an important debate in the literature.
In the DD model, depositors have no information about the quality of the bank’s assets — runs are purely driven by coordination failure. An alternative class of models takes the opposite view: depositors run because they learn bad news about the bank’s fundamentals.
The basic idea: Suppose depositors receive a signal (public or private) about the return on the bank’s assets. If the signal indicates that the bank’s loans are performing poorly — say, because borrowers are defaulting or the economy is entering a recession — then each depositor rationally concludes that the bank may not be able to honor its obligations at \(t=2\). Withdrawing early is then the individually optimal response, regardless of what other depositors do.
Key models in this tradition:
Chari and Jagannathan (1988): Some depositors observe a signal about the bank’s asset quality. Uninformed depositors observe the length of the withdrawal queue and try to infer the signal. A long queue could mean many depositors received bad news, or it could simply mean many depositors have legitimate liquidity needs. This inference problem can lead uninformed depositors to withdraw even when the bank is healthy — a run driven by information extraction rather than coordination failure.
Jacklin and Bhattacharya (1988): Depositors receive private information about the return on the bank’s assets. Those with bad news withdraw early to avoid losses. The bank must liquidate assets to meet withdrawals, which can make it insolvent even if the bad news was only partially correct. Here, runs serve a disciplining function — they penalize banks that have made poor investment decisions.
Allen and Gale (1998): Bank runs can be part of an optimal risk-sharing arrangement. When depositors observe that the economy is in a bad state, a run forces liquidation of bank assets, transferring resources from long-term projects to depositors who need them now. In their framework, runs are an efficient response to aggregate shocks, not a market failure.
In a fundamental-based run, the dominant strategy for each depositor is to withdraw once bad news arrives. Even if a depositor knew for certain that no one else would withdraw, she would still prefer to withdraw because the bank’s assets are impaired. This is a dominant strategy equilibrium — beliefs about other depositors’ actions are irrelevant.
In a panic-based run (DD), withdrawal is only optimal if enough other depositors also withdraw. The bank is fundamentally solvent, and a patient depositor who waits would receive \(c_2^* > c_1^*\) if others also wait. Running is only rational as a response to the belief that others will run. This is a coordination game with multiple equilibria.
Fundamental runs:
Panic-based runs (DD):
Gorton (1988) documented that historical U.S. bank run episodes were consistently preceded by deteriorating bank fundamentals. This was initially interpreted as evidence against the panic-based view.
However, as Goldstein (2013) argues, this interpretation is incorrect:
A prerequisite for panic-based runs is weaker fundamentals. Strategic complementarities among depositors amplify the effect of bad news. The fact that runs are associated with bad fundamentals does not rule out the existence of panic-based dynamics — it is exactly what the theory predicts.
The key question is not whether fundamentals matter, but whether coordination failure makes the response to fundamentals larger than it would be in the absence of strategic complementarities.
Goldstein and Pauzner (2005) provide an elegant resolution to both problems — the multiplicity of equilibria and the fundamentals-vs.-panic debate — by introducing incomplete information into the DD framework using the global games methodology (Carlsson and van Damme, 1993; Morris and Shin, 1998).
In the standard DD model, depositors have common knowledge of the bank’s fundamentals. Everyone knows the bank is solvent, everyone knows that everyone knows, and so on. Under common knowledge, both the good and the bad equilibrium are sustainable, and the model cannot predict which one will prevail.
This is not just a theoretical inconvenience. It means the DD model cannot answer basic questions: Which banks are more likely to experience runs? What bank characteristics make runs more likely? How does policy affect the probability of a run? The model has multiple equilibria and no mechanism to select among them.
Goldstein and Pauzner embed the DD bank run game into an environment with uncertain fundamentals. The key elements:
Bank fundamentals \(\theta\): The bank’s asset return is no longer a known constant \(R\). Instead, the return depends on a fundamental \(\theta\) drawn from a continuous distribution on \([\theta_L, \theta_H]\). Higher \(\theta\) means better asset quality.
The deposit contract: As in DD, the bank offers a demand deposit contract with \(c_1^*\) to early withdrawers. The late withdrawer’s payoff depends on both the fraction who withdraw early (\(\hat{\lambda}\)) and the realized fundamental:
\[ \text{Late payoff}(\hat{\lambda}, \theta) = \max\left(\frac{(1 - \hat{\lambda} c_1^*) R(\theta)}{1 - \hat{\lambda}}, \; 0\right) \]
Private signals: Each depositor \(i\) observes a noisy private signal about the bank’s health:
\[ x_i = \theta + \epsilon_i \]
where the \(\epsilon_i\) are drawn independently from a distribution with small variance \(\sigma^2\). Each depositor knows her own signal but not those of others. Crucially, depositors do not have common knowledge of \(\theta\).
Dominance regions: There exist extreme values of fundamentals where behavior is pinned down regardless of others’ actions:
The interesting region is \(\theta \in [\underline{\theta}, \overline{\theta}]\), where the bank is solvent in the good equilibrium but would fail in a run — exactly the DD multiple-equilibria region.
The key insight is that with private signals, the game is no longer one of common knowledge. Consider the reasoning of a depositor who observes signal \(x_i\):
Step 1: Dominance at the extremes. A depositor who receives a very low signal (near \(\theta_L\)) knows the bank is almost certainly insolvent. She withdraws regardless of what others do. A depositor with a very high signal knows the bank is safe and waits.
Step 2: Iterated elimination. A depositor with a signal just above \(\underline{\theta}\) knows that depositors with slightly lower signals will withdraw (by Step 1). She therefore expects some withdrawals. Given the strategic complementarities in the bank run game, this makes her more inclined to withdraw as well. So she also withdraws.
Step 3: Contagion propagates upward. A depositor with a signal slightly higher knows that the depositors in Step 2 will withdraw (because they expect the Step 1 depositors to withdraw). This further increases the expected number of withdrawals, making her even more inclined to withdraw. The reasoning cascades upward through the signal space.
Step 4: The cascade stops. At some critical signal \(x^*\), the reasoning stops — depositors above \(x^*\) find it optimal to wait despite knowing that some others will withdraw. This pins down the unique threshold.
The key difference from DD is not the noise per se, but the destruction of common knowledge. In DD, depositors know the bank is solvent, they know that others know, they know that others know that others know, and so on. This infinite chain of mutual knowledge supports both equilibria.
With private signals, this chain breaks. A depositor who receives a middling signal \(x_i\) is uncertain whether other depositors received signals above or below the dominance threshold. She is uncertain about what others believe about what others believe. This higher-order uncertainty is what unravels the multiplicity and pins down a unique equilibrium.
In the limit as signals become precise (\(\sigma \to 0\)), the threshold strategy implies that the bank’s fate is determined by a critical fundamental \(\theta^*\) that lies within the intermediate region \([\underline{\theta}, \overline{\theta}]\):
The threshold \(\theta^*\) thus splits the old DD multiple-equilibria region into two: a panic run region \([\underline{\theta}, \theta^*]\) where coordination failure causes the bank to fail, and a no-run region \([\theta^*, \overline{\theta}]\) where fundamentals are strong enough to sustain confidence. Together with the dominance regions, this gives three regions:
\(\theta < \underline{\theta}\) (Insolvent): The bank’s assets are so impaired that it cannot honor its obligations even if no patient depositor withdraws. Runs here are purely fundamental-based — they would occur regardless of coordination.
\(\underline{\theta} < \theta < \theta^*\) (Panic run region): The bank is solvent — it could survive if depositors coordinated on the good equilibrium. But the private information structure prevents coordination, and the bank fails due to self-fulfilling withdrawals. These are panic-based runs triggered by weak (but not fatal) fundamentals.
\(\theta > \theta^*\) (No run): Fundamentals are strong enough that the bank survives despite the coordination problem. Patient depositors wait.
The global games framework resolves the debate between the fundamental and panic views of bank runs. It shows that both forces operate simultaneously:
The probability of a run is \(\Pr(\theta < \theta^*)\), which is well-defined and depends on the bank’s characteristics. This makes the model empirically testable.
The central result of Goldstein and Pauzner (2005) is a comparative static on the threshold \(\theta^*\):
Banks that offer more generous demand deposit contracts (higher \(c_1^*\) relative to the liquidation value of assets) have a higher threshold \(\theta^*\). This means:
Intuitively, when the bank promises more to early withdrawers, the remaining assets for late withdrawers are smaller if others withdraw. This strengthens the strategic complementarities among depositors: each depositor’s payoff from waiting is more sensitive to the actions of others. The stronger the complementarities, the larger the region where panic-based runs can occur.
This generates a sharp, testable prediction: banks with greater liquidity mismatch should exhibit greater fragility, controlling for fundamentals. Specifically, the sensitivity of deposit outflows to bad performance should be stronger for banks that perform more liquidity transformation. This prediction is tested empirically by Chen, Goldstein, Huang, and Vashishtha (2022), which we discuss in the next chapter.
A central empirical challenge is that fundamental-based and panic-based runs look similar ex post — both involve large deposit outflows following bad news. The GP model suggests a way to distinguish them:
If runs are purely fundamental-based, the response of deposits to bad performance should depend only on the severity of the bad news. The bank’s liability structure (how much liquidity it creates) should be irrelevant — depositors withdraw because assets are bad, not because they fear a coordination failure.
If panic dynamics are present, the response should be amplified by liquidity mismatch. Banks with greater maturity transformation should exhibit a stronger sensitivity of outflows to the same fundamental shock, because the strategic complementarities are stronger.
This is the identification strategy of Chen et al. (2022): they test whether the interaction between performance shocks and liquidity mismatch predicts deposit outflows. Finding that it does — and that the effect operates through uninsured deposits, not insured ones — provides evidence that the panic channel is empirically relevant.
Understanding whether runs are panic-based, fundamental-based, or (as the GP model suggests) both, is essential for designing the right policy response.
The policy implications depend critically on what triggers the run:
If runs are purely panic-based: A credible announcement of government support is sufficient. Deposit insurance and lender-of-last-resort policies eliminate the bad equilibrium at no cost — off the equilibrium path, the guarantee is never invoked.
If runs are purely fundamental-based: Government support constitutes a bailout of a failing institution. Ex ante policies like capital requirements and supervisory oversight are more appropriate. Runs serve a disciplining function, and eliminating them may encourage excessive risk-taking.
If both forces operate (as in Goldstein-Pauzner): Policy must address both the panic region (through liquidity backstops) and the insolvency region (through prudential regulation). The optimal policy mix depends on the relative size of each region.
Suppose the bank announces in advance: “We will suspend withdrawals once a fraction \(\lambda\) of deposits have been withdrawn.”
Then patient depositors know that no matter how many people try to withdraw, the bank will always have enough assets to pay \(c_2^*\) at \(t=2\):
\[ r_2(\lambda) = \frac{(1 - \lambda c_1^*)R}{1 - \lambda} = c_2^* > c_1^* \]
Since waiting always dominates withdrawing, no patient depositor runs. The run equilibrium is eliminated.
In this case, suspension is a threat that need not be carried out — the mere announcement prevents the run.
Historical practice: Before the establishment of deposit insurance, banks in the United States regularly suspended convertibility during panics (Gorton, 1985). Between 1814 and 1907, the American banking system suspended convertibility eight times (Tirole, 2006).
Limitations of suspension:
Aggregate uncertainty: If the fraction of impatient depositors \(\lambda\) fluctuates and cannot be observed, the bank cannot set the suspension threshold perfectly. Some truly impatient depositors may be prevented from withdrawing.
Moral hazard: Suspension can be exploited by poorly managed banks. A bank whose assets have genuinely declined in value might suspend convertibility to prevent legitimate withdrawals, shielding its management from market discipline (Tirole, 2006). This is the fundamental-run problem: suspension is effective against panic but can be abused to mask insolvency.
Political unpopularity: When suspension actually occurs, it is deeply unpopular with depositors who genuinely need their funds.
A government deposit insurance scheme promises to pay every depositor the contractually specified amount — \(c_1^*\) for early withdrawers, \(c_2^*\) for late withdrawers — regardless of how many depositors withdraw.
If depositors believe the guarantee is credible, there is no reason to run. Each patient depositor knows she will receive \(c_2^* > c_1^*\) at \(t=2\) no matter what. The run equilibrium is eliminated.
Why the government? Diamond (2007) emphasizes that deposit insurance requires taxation authority — the ability to take resources without prior contracts. A private insurer might itself face a run (or would need to hold enough liquid assets to cover systemic events, which defeats the purpose of liquidity creation). The government can provide a credible guarantee against large losses “that are usually off the equilibrium path without holding reserves to back up their promise.”
Advantages over suspension:
Costs and trade-offs:
Moral hazard: If deposits are fully insured, depositors have no incentive to monitor the bank’s risk-taking. Banks may take excessive risks, knowing that losses are borne by the insurance fund (Barth, Caprio, and Levine, 2006).
Fiscal cost: When a bank does fail, the insurance fund (and ultimately taxpayers) bears the loss.
Coverage limits: In practice, deposit insurance covers up to a limit (currently $250,000 in the U.S.). Uninsured deposits remain vulnerable to runs.
The U.S. established the Federal Deposit Insurance Corporation (FDIC) in 1933, following the bank failures of the Great Depression. Key features:
The existence of FDIC insurance has virtually eliminated retail bank runs in the U.S. However, runs on uninsured deposits remain a significant risk, as demonstrated by the 2023 failure of Silicon Valley Bank.
The global games perspective on deposit insurance: In the Goldstein-Pauzner framework, deposit insurance reduces \(\theta^*\) — it shrinks the panic region by weakening the strategic complementarities among depositors. Davila and Goldstein (2023) show that the optimal level of insurance balances the benefit of a smaller panic region against the moral hazard cost of insulating depositors from risk. Their key finding: as long as bank failures happen in equilibrium and public funds are costly, unlimited deposit insurance is not optimal.
A third mechanism, emphasized by Tirole (2006), is a credit line with the central bank or another financial institution. If patient depositors know that the bank can borrow to meet withdrawal demands without liquidating long-term assets, there is no reason to run.
This is the principle behind central bank discount window lending: the central bank stands ready to lend to solvent but illiquid banks against good collateral, providing liquidity during panics. The principle dates to Bagehot (1873), who argued that in a crisis, the central bank should “lend freely, at a high rate, on good collateral.”
Limitation: A credit line from a private institution can protect against a run on a single bank, but not against a systemic run on the entire banking sector. Only the central bank (with money creation authority) can provide liquidity in a system-wide crisis (Tirole, 2006).
The Bagehot boundary: The Bagehot principle — lend to solvent but illiquid banks — maps directly onto the GP framework. The central bank should provide liquidity to banks in the panic region (\(\underline{\theta} < \theta < \theta^*\)), where the bank is solvent but failing due to coordination failure. It should not provide liquidity to banks in the insolvency region (\(\theta < \underline{\theta}\)), where the run reflects genuine asset impairment. The difficulty, of course, is distinguishing the two in real time.
The global games framework also clarifies the role of other regulatory tools:
Capital requirements improve the bank’s ability to absorb losses, effectively raising \(\underline{\theta}\) (expanding the solvency region). They may also reduce \(\theta^*\) by making the bank less leveraged and thus less fragile to coordination failures.
Transparency has ambiguous effects. Better information about bank fundamentals (smaller \(\sigma\)) makes the threshold sharper but does not eliminate the panic region. In some cases, more precise public information can actually increase fragility by coordinating depositors on negative signals (Morris and Shin, 2002). Private signals, by contrast, reduce the scope for coordination and may reduce fragility.
Bank runs are an inherent consequence of liquidity creation: The same maturity transformation that makes banking valuable also creates the possibility of self-fulfilling panics (Diamond and Dybvig, 1983)
Multiple equilibria: The DD model has a good equilibrium (only impatient depositors withdraw) and a bad equilibrium (everyone withdraws). The bad equilibrium is self-fulfilling because of strategic complementarities among depositors
The tipping point: Runs become self-fulfilling once expected withdrawals exceed a critical threshold. In Diamond’s numerical example, the threshold is \(\hat{\lambda}^* = 0.5625\)
Fundamental vs. panic-based runs: Fundamental runs are driven by bad news about bank assets (dominant strategy); panic runs are driven by coordination failure among depositors (multiple equilibria). In practice, both forces operate simultaneously
Global games resolution: Goldstein and Pauzner (2005) show that introducing private information into the DD model generates a unique equilibrium with a threshold \(\theta^*\) that depends on liquidity mismatch. Banks with greater maturity transformation have a larger panic region and are more fragile. The model can be tested empirically by examining whether liquidity mismatch amplifies the sensitivity of deposit outflows to bad performance
Anti-run policies must address both panic and fundamentals:
Diamond, D. W., & Dybvig, P. H. (1983). Bank runs, deposit insurance, and liquidity. Journal of Political Economy, 91(3), 401-419.
Diamond, D. W. (2007). Banks and liquidity creation: A simple exposition of the Diamond-Dybvig model. Federal Reserve Bank of Richmond Economic Quarterly, 93(2), 189-200.
Tirole, J. (2006). The Theory of Corporate Finance. Princeton University Press. Chapter 12.3.
Chari, V. V., & Jagannathan, R. (1988). Banking panics, information, and rational expectations equilibrium. Journal of Finance, 43(3), 749-761.
Jacklin, C. J., & Bhattacharya, S. (1988). Distinguishing panics and information-based bank runs: Welfare and policy implications. Journal of Political Economy, 96(3), 568-592.
Allen, F., & Gale, D. (1998). Optimal financial crises. Journal of Finance, 53(4), 1245-1284.
Gorton, G. (1988). Banking panics and business cycles. Oxford Economic Papers, 40(4), 751-781.
Goldstein, I., & Pauzner, A. (2005). Demand deposit contracts and the probability of bank runs. Journal of Finance, 60(3), 1293-1328.
Carlsson, H., & van Damme, E. (1993). Global games and equilibrium selection. Econometrica, 61(5), 989-1018.
Morris, S., & Shin, H. S. (1998). Unique equilibrium in a model of self-fulfilling currency attacks. American Economic Review, 88(3), 587-597.
Morris, S., & Shin, H. S. (2002). Social value of public information. American Economic Review, 92(5), 1521-1534.
Goldstein, I. (2013). Empirical literature on financial crises: Fundamentals vs. panic. In The Evidence and Impact of Financial Globalization (ed. G. Caprio), pp. 523-534. Academic Press.
Chen, Q., Goldstein, I., Huang, Z., & Vashishtha, R. (2022). Liquidity transformation and fragility in the US banking sector. Journal of Finance, 77(4), 2001-2057.
Bagehot, W. (1873). Lombard Street: A Description of the Money Market. London: Henry S. King & Co.
Gorton, G. (1985). Bank suspension of convertibility. Journal of Monetary Economics, 15(2), 177-193.
Barth, J. R., Caprio, G., & Levine, R. (2006). Rethinking Bank Regulation: Till Angels Govern. Cambridge University Press.
Davila, E., & Goldstein, I. (2023). Optimal deposit insurance. Journal of Political Economy, 131(7), 1676-1730.