RDP 2019-10: Emergency Liquidity Injections 1. Introduction

If financial intermediaries in liquidity distress are to be bailed out, how should it be done? In late 2008 policymakers were forced to decide quickly. The world's largest banking systems experienced a rapid decline of funding liquidity, alongside fire sales and a drying up of market liquidity for many securities. Financial intermediaries (henceforth ‘banks’) with insufficient cash or high-quality liquid assets (HQLA) then had difficulty meeting their short-term liabilities. Governments and central banks (i.e. authorities) were aware that bailouts could damage banks' incentives to manage liquidity risk (e.g. Bernanke 2008), but nonetheless responded with massive liquidity injections, because avoiding imminent bank failures was a higher priority.

Trillions of US dollars worth of emergency liquidity was provided to banks around the world through a range of policies. The largest provisions were implemented with secured lending (i.e. repo) via central banks' market operations and with government guarantees on banks' unsecured debt issuance. Capital injections and secondary market securities purchases were also relied upon to varying degrees.[1] To prepare policymakers for future crises, a range of research papers have analysed these policies for saving banks, but secured lending, arguably the most-used policy in the 2008 liquidity crisis, has received little comparison with other injection policies. Moreover, policy comparisons tend to emphasise the near-term effects on the financial system, whereas in the longer term, effects on incentives may be just as consequential.

This paper addresses these gaps by considering alternative policies in a banking crisis model that incorporates a range of features from the literature. Banks choose their asset-side liquidity risk by allocating their portfolio across highly liquid and less-liquid securities (e.g. Diamond and Dybvig 1983). The prospect of a funding liquidity shock encourages banks to hold some highly liquid securities (Hanson et al 2015), but they hold too few due to fire sale externalities (Stein 2012). Subsequently, if there is no funding liquidity shock, the riskier securities pay positive returns; if there is a shock, banks must cover a randomly drawn cash outflow. When banks' liquid securities are insufficient to meet the outflow, they sell their less-liquid securities, which can temporarily put downward pressure on market liquidity and the securities price (e.g. Brunnermeier and Pedersen 2009; Diamond and Rajan 2011). A ‘banking crisis’ eventuates if the price falls to the point that banks cannot handle the liquidity shock, characterised primarily by an inability to liquidate assets at ‘fair’ values. Its probability is endogenous because the maximum manageable liquidity shock is decreasing in banks' liquidity risk-taking (e.g. Goldstein and Pauzner 2005). In a banking crisis, the authority injects scarce liquidity to prevent bank failures, calibrating its policy to maximise its objectives of low ex ante liquidity risk-taking and high ex post bank profits (e.g. Farhi and Tirole 2012).

This relatively simple crisis anatomy yields some important characteristics of liquidity injections that have not been highlighted by previous papers. The main underlying result is that lending to banks against securities as collateral, rather than unsecured, can mitigate fire selling in illiquid securities markets. Both the secured and unsecured lending policies can put an upper bound on fire sale price depression at the interest rate charged, by offering banks a cheaper source of liquidity than securities sales. However, low interest rates on emergency lending also incentivise liquidity risk-taking and make a crisis more probable. Secured lending presents an additional means of constraining fire selling, because banks cannot liquidate securities that they are providing as collateral. In other words, collateral obligations force banks to treat emergency borrowing and securities sales as substitutes. If the lending policy gives banks more liquidity for their securities than sales – by, for example, not pricing fire sale effects into the collateral valuation – then higher liquidity needs imply more borrowing and less selling. That is, the more scarce is liquidity, the greater is the role played by the authority's balance sheet, which is immune to illiquidity, in replacing the liquidity provision function of securities markets.

Ashcraft, Gârleanu and Pedersen (2011) also argue that liquidity injections through secured lending can raise market prices for securities, but they highlight different mechanisms. In their model, the central bank can expand secured lending by reducing its haircuts, which raises securities prices by lowering the cost of funding securities purchases. That is, lower haircuts permit banks to fund a higher proportion of their purchases by borrowing against the purchased securities, and this funding is cheaper for banks than using their own capital. The mechanism can be thought of as a loosening of constraints on banks' demand for securities. In contrast, the model presented here emphasises the policy's capability to tighten constraints on the supply of securities available to fire selling banks. Both models show that low haircuts are beneficial for banks that need liquidity; this paper additionally demonstrates that ideal haircuts are not so low that the policy economically resembles unsecured lending.

Moreover, the authority can better achieve its objectives if its emergency lending is secured rather than unsecured because mitigation of fire sale prices positively affects banks' post-crisis profits. Importantly, this benefit does not raise incentives for liquidity risk-taking. Instead, it offsets fire sale externalities driven by banks' failure to acknowledge how their own securities sales contribute to price depression. The banks that benefit most from higher securities prices are those whose market participation is least constrained by collateral requirements; that is, those that took less liquidity risk and have less emergency borrowing to collateralise. The result is that, compared to an unsecured lending policy, a secured lending policy can leave banks more profitable post-crisis without generating a higher ex ante likelihood of a crisis occurring.

The model presents several additional implications for emergency lending policies. ‘Penalising’ interest rates on emergency lending have been recommended by previous literature for two reasons: (i) to incentivise banks to miminise their borrowing from the authority (e.g. Bagehot 1920); and (ii) to disincentivise banks from taking liquidity risk ex ante (e.g. Fischer 1999). This paper demonstrates an equivalency between the two. Achieving (ii) requires that liquidity risk-taking be costly at the margin, and since the marginal effect of taking liquidity risk is to increase the probability of requiring emergency lending, objective (ii) requires that emergency borrowing is more expensive than private sources of liquidity. The same condition determines which liquidity source banks prefer to exhaust first, tying it to objective (i).

A second implication for emergency lending policies is that secured lending can force banks to borrow more from the authority than unsecured lending, because banks' liquidity acquisition through securities sales is constrained by their need to provide collateral. Relative to an unsecured policy, this amplifies the disincentive effect of penalising interest rates, but also means more expansion of the authority's balance sheet.[2] A third implication is that haircuts under a secured lending policy should be sufficiently loose; specifically, they should permit banks to extract more liquidity from their collateral than they can get in the private market. Otherwise, the policy provides little benefit to banks that face failure due to insufficient access to liquidity (Allen and Carletti (2008) make a similar recommendation). Authorities appear to have followed this principle in 2008 and 2009, by expanding collateral eligibility to securities whose markets had dried up.[3]

Another way the authority can save banks is by buying their securities at a higher price than the private market is willing to pay. The price paid must be generous enough to transfer banks the amount of liquidity they need, so, for a given quantity of securities held by banks, it is increasing in the extent of banks' liquidity deficiency. Accordingly, if banks coordinate on a relatively high level of liquidity risk, then conditional on a crisis they are more liquidity deficient and receive a more favourable policy. Banks' liquidity risk choices are therefore strategic complements. Farhi and Tirole (2012) demonstrate a similar result in a model in which different forms of liquidity injections are equivalent, showing that policies that aim to disincentivise ex ante liquidity risk-taking are not credible. In the model presented here, lending policies that permit banks to repay the loans after conditions improve are more credible than a securities purchase policy.

This paper's portrayal of a liquidity crisis is key to the credibility difference between policies. The core market imperfection is a temporarily limited supply of cash, which causes unexploited arbitrage opportunities in the securities market and an implicit inability for banks to borrow against other non-marketable assets at any interest rate. A similar perspective of liquidity is presented by several of the citations above (Diamond and Rajan 2011; Stein 2012; Hanson et al 2015). A consequence is that banks can benefit from borrowing even if it is costly, because it can save them from failing if they can delay the costly repayment until the availability of cash improves. Alternatively, if banks' access to liquidity is directly tied to the sale price of their marketable assets (as in this paper's securities purchase policy) or determined by the interest rate at which their non-marketable assets can be pledged (as in Farhi and Tirole (2012)), then banks can only be saved by being offered generous terms. The policy implication is that in the type of liquidity crisis this paper models, emergency lending policies, if for sufficiently long terms, can simultaneously provide liquidity support and be penalising, so penalising terms can be credible.

This paper contributes to the literature on crisis interventions by providing an ex ante and ex post analysis of a range of policies for preventing illiquidity-driven bank failures. A variety of insightful papers model crisis interventions, although the focus typically differs in either or both of the following: i) illiquidity-driven bank failures are not possible or not undesirable; or ii) the policy objectives do not include the incentives generated. Acharya and Yorulmazer (2008) and Acharya, Shin and Yorulmazer (2011) show how asset purchase policies can be designed to generate prudent incentives, with an authority that credibly permits bank failures. He and Krishnamurthy (2013) compare the ex post effects of lending, asset purchase and capital injection policies on liquidity-affected asset prices. Farhi and Tirole (2012) and Philippon and Schnabl (2013) consider policies aimed at stimulating bank lending, without the possibility of bank failures. The former compare the ex post implications of system-wide and bank-specific funding subsidisations, and the latter analyse the optimal design for a capital injection policy. Tirole (2012) and Choi, Santos and Yorulmazer (2019) analyse how various policy formulations can jump start frozen asset markets. This paper also contributes to the recent literature on how central banks' collateral frameworks affect banks' securities portfolio decisions (Nyborg 2017; Cassola and Koulischer 2019).

This paper has seven sections. Section 2 presents the model framework. Sections 3, 4 and 5 analyse unsecured lending, secured lending and asset purchase policies, emphasising points of comparison. Section 6 draws insights from extensions that relax some of the model assumptions and considers a policy that injects capital into banks. Section 7 concludes. Appendix A discusses the liquidity injection policies implemented in Europe and the United States in 2008 and 2009. Proofs of the model results are in Appendix B.


Appendix A provides examples of the various policies. [1]

Unsecured lending policies commonly take the form of government guarantees on banks' unsecured debt issuance, for a pro rata fee that in this paper is interpreted as an interest rate premium. With this type of policy the authority essentially experiences an increase in off-balance sheet contingent liabilities. Still, the authority's exposure to borrowing banks is essentially the same as if it lent directly to banks itself. [2]

The model also illustrates that no matter how loose the haircuts, the authority's counterparty risk is more collateralised than a policy of guaranteeing banks' unsecured debt. [3]