Optimal allotment policy in central bank open market operations1

This article derives a central bank's optimal liquidity supply towards a money market with an unrestricted lending facility. We show that when the effect of liquidity on market rates is not too small, and the monetary authority is concerned with both interest rates and liquidity conditions, then the optimal allotment policy may entail a ‘discontinuous’ reaction to initial conditions. In particular, the model predicts a threshold level of liquidity below which the central bank will not bail out the banking system. An estimation of the liquidity effect for the euro area suggests that the discontinuity might have contributed to the Eurosystem's tight response to occurrences of underbidding during the period June 2000 through March 2004.     

Systemic banks and the lender of last resort

We propose a model where systemic and non-systemic banks are exposed to liquidity shortfalls so that a lender of last resort policy is required. We find that it is socially optimal to override the decision of the central bank by the unconditional provision of liquidity support when the shortfall is large enough, i.e. in crisis times. The existence of systemic banks provides a rationale for the central bank to act as lender of last resort for non-systemic banks in a larger range of their liquidity shortfalls. However, the impact of systemic risk on the optimal allocation of the lender of last resort responsibilities for systemic banks depends on the relative size of counteracting effects.     

Rediscounting under Aggregate Risk with Moral Hazard

Freeman (1999) proposes a model in which discount window lending and open‐market operations have different effects. This is important because in most of the literature these policies are indistinguishable. However, Freeman's argument that the central bank should absorb losses associated with default to provide risk sharing stands in stark contrast to the concern that central banks should limit their exposure to credit risk. We extend Freeman's model by introducing moral hazard. With moral hazard, the central bank should avoid absorbing losses and Freeman's argument breaks down. However, we show that policies resembling discount window lending and open‐market operations can still be distinguished in this new framework. The optimal policy is for the central bank to make a restricted number of creditors compete for funds. By restricting the number of agents, the central bank can limit the moral hazard problem. By making them compete with each other, the central bank can exploit market information that reveals the state of the economy.     

Funding liquidity risk: Definition and measurement

Funding liquidity risk has played a key role in all historical banking crises. Nevertheless, a measure for funding liquidity risk based on publicly available data remains so far elusive. We address this gap by showing that aggressive bidding at central bank auctions reveals funding liquidity risk. We can extract an insurance premium from banks’ bids which we propose as a measure of funding liquidity risk. Using a unique data set consisting of all bids in all auctions for the main refinancing operation conducted at the ECB between June 2005 and October 2008 we find that funding liquidity risk is typically stable and low, with occasional spikes especially around key events during the recent crisis. We also document downward spirals between funding liquidity risk and market liquidity. As measurement without clear definitions is impossible, we initially provide definitions of funding liquidity and funding liquidity risk.     

流动性、银行间市场摩擦与借贷便利类货币政策工具

通过内生引入流动性短缺银行(拆入行)对流动性盈余银行(拆出行)的流动性需求机制,本文构建了一个包含银行间市场的DSGE模型,对借贷便利类货币政策工具的传导机制和传导效果进行了理论和实证研究。研究表明:(1)负向冲击会同时增加拆入行和拆出行对流动性的预防性需求,在经济形势不确定的情形下,拆出行不会很快恢复对拆入行的流动性供给,引起银行间市场流动性缺口放大和市场失灵。(2)由于仅依赖银行间市场自发回归稳态的过程太过缓慢,需要央行进行流动性干预。借贷便利类工具可以通过引导贷款市场定价和流动性效应这两个渠道来影响银行融资可得性,进而降低银行间市场流动性风险对宏观经济的负面影响。(3)借贷便利类货币政策工具的影响效果边际递减,央行可根据借贷便利操作的收益和成本,制定最佳的反应程度参数。     

流动性、银行间市场摩擦与借贷便利类货币政策工具

通过内生引入流动性短缺银行(拆入行)对流动性盈余银行(拆出行)的流动性需求机制,本文构建了一个包含银行间市场的DSGE模型,对借贷便利类货币政策工具的传导机制和传导效果进行了理论和实证研究。研究表明:(1)负向冲击会同时增加拆入行和拆出行对流动性的预防性需求,在经济形势不确定的情形下,拆出行不会很快恢复对拆入行的流动性供给,引起银行间市场流动性缺口放大和市场失灵。(2)由于仅依赖银行间市场自发回归稳态的过程太过缓慢,需要央行进行流动性干预。借贷便利类工具可以通过引导贷款市场定价和流动性效应这两个渠道来影响银行融资可得性,进而降低银行间市场流动性风险对宏观经济的负面影响。(3)借贷便利类货币政策工具的影响效果边际递减,央行可根据借贷便利操作的收益和成本,制定最佳的反应程度参数。     

Collective Risk Management in a Flight to Quality Episode

Severe flight to quality episodes involve uncertainty about the environment, not only risk about asset payoffs. The uncertainty is triggered by unusual events and untested financial innovations that lead agents to question their worldview. We present a model of crises and central bank policy that incorporates Knightian uncertainty. The model explains crisis regularities such as market‐wide capital immobility, agents' disengagement from risk, and liquidity hoarding. We identify a social cost of these behaviors, and a benefit of a lender of last resort facility. The benefit is particularly high because public and private insurance are complements during uncertainty‐driven crises.     

Optimal pricing of intraday liquidity

This paper presents a general equilibrium model where intraday liquidity is needed because the timing of payments is uncertain. A necessary and sufficient condition for an equilibrium to be efficient is that the nominal intraday interest rate be zero, even when the overnight rate is strictly positive. Because a market for liquidity may not achieve efficiency, this creates a role for the central bank. I allow for the possibility of moral hazard and study policies commonly used by central banks to reduce their exposure to risk. I show collateralized lending achieves the efficient allocation, while, for certain parameters, caps cannot prevent moral hazard.     

On the efficiency of bilateral interbank insurance

This paper studies banks’ incentives to engage in liquidity cross-insurance. In contrast to previous literature we view interbank insurance as the outcome of bilateral (and non-exclusive) contracting between pairs of banks and ask whether this outcome is socially efficient. Using a simple model of interbank insurance we find that this is indeed the case when insurance takes place through pure transfers. This is even though liquidity support among banks sometimes breaks down, as observed in the crisis of 2007–2008. However, when insurance is provided against some form of repayment (such as is the case, for example, with credit lines), banks have a tendency to insure each other less than the socially efficient amount. We show that efficiency can be restored by introducing seniority clauses for interbank claims or through subsidies that resemble government interbank lending guarantees.     

Credit line takedown and endogenous bank capital

This paper investigates the implications of the uncertain timing and usage of loan commitments for the optimal level of bank capital. We use trended Brownian motion to proxy the stochastic takedown of credit lines. Relying on “time to first passage” mathematics, we derive a probability density function for the time to depletion of the bank credit line as well as the likelihood for the time to exhausting the sources of liquidity that fund the loan takedown. Armed with these analytical results, we solve for the optimal level of bank capital within a simultaneous equation framework in order to capture the interrelationships of the endogenous variables. The optimality conditions produce a system of integral differential equations which refuse to yield reduced form solutions and provide no immediate intuition. Therefore, the maximizing values of the bank’s decision variables were simulated over a host of realistic scenarios. We document the comparative static behavior of the bank’s decision variables when equity is unencumbered by capital requirements and, also, examine the impact of the same parametric changes on bank behavior when equity is a fixed proportion of lending. Further simulations produce the expected time to liquidity depletion under different capital requirement schemes.     

Reserve Requirements,Liquidity Risk,and Bank Lending Behavior

Although reserve requirements (RR) have been used in emerging markets to smooth credit cycles, the transmission mechanism remains blurry. Using bank‐level data, we unveil the interaction of RR with bank lending. We identify a new channel that works through a decline in banks’ liquid assets and loan supply due to an increase in RR. “Quantitative tightening” through RR raises the short‐term funding needs of the banking system, which is met by collateralized central bank lending, thus depleting banks’ unencumbered liquid assets. Our results suggest that such a shift in bank liquidity is associated with a significant change in lending.     

Getting the Right Mix of Capital and Cash Requirements in Prudential Bank Regulation*

Cash reserve requirements are useful as a broadly conceived prudential tool, not just as a narrowly focused means of limiting the risks associated with illiquidity. Indeed, illiquidity risk is neither a necessary nor a sufficient condition for establishing bank liquidity requirements. The primary means of mitigating the systemic costs of bank illiquidity risk is the creation of an effective lender of last resort (LOLR). But instead of focusing narrowly on bank funding risks when designing liquidity requirements, regulators should consider tradeoffs among capital requirements, liquidity requirements, and LOLR policies for achieving the broader prudential goal of limiting bank default risk. When considering the optimal tradeoff between capital ratios and cash ratios as prudential requirements, five “frictions” are identified that favor the use of one or the other: (1) the adverse‐selection costs of raising equity (which favors the use of cash); (2) the opportunity cost of forgone abnormal profits (or “quasi rents”) from lending (which favors the use of capital); (3) the limited verifiability of loan outcomes (which favors the use of cash); (4) the moral hazard that results from costly or postponed loss recognition, given the incentive for risk shifting in bad states (which favors the use of cash); and (5) the prospect of changes in the risk environment (which favors cash since it creates greater option value for maintaining targeted default risk with lower adjustment costs in the face of changing loan risk or illiquidity risk). When viewed from the perspective of achieving the main prudential goal of controlling default risk at a minimum social cost, capital requirements have some limitations that favor liquidity requirements, and vice versa. And thus the optimal regulatory policy will combine liquidity and capital requirements.     

The effect of bank capital on lending: Does liquidity matter?

This paper uses a sample of quarterly observations of insured US commercial banks to examine whether the effect of bank capital on lending differs depending upon the level of bank liquidity. We find that the effect of an increase in bank capital on credit growth, defined as growth rate of net loans and unused commitments, is positively associated with the level of bank liquidity only for large banks and that this positive relationship has been more substantial during the recent financial crisis period. This result suggests that bank capital exerts a significantly positive effect on lending only after large banks retain sufficient liquid assets.     

Liquidity Coinsurance and Bank Capital

Banks can deal with their liquidity risk by holding liquid assets (self‐insurance), by participating in interbank markets (coinsurance), or by using flexible financing instruments, such as bank capital (risk sharing). We use a simple model to show that undiversifiable liquidity risk, that is, the liquidity risk that banks are unable to coinsure on interbank markets, represents an important risk factor affecting their capital structures. Banks facing higher undiversifiable liquidity risk hold more capital. We posit that, empirically, banks that are more exposed to undiversifiable liquidity risk are less active on interbank markets. Therefore, we test for the existence of a negative relationship between bank capital and interbank market activity and find support in a large sample of U.S. commercial banks.     

Bank liabilities channel

The financial intermediation sector is important not only for channeling resources from agents in excess of funds to agents in need of funds (lending channel). By issuing liabilities it also creates financial assets held by other sectors of the economy for insurance or liquidity purpose. When the intermediation sector creates less liabilities or their value falls, agents are less willing to engage in activities that are individually risky but desirable in aggregate (bank liabilities channel). The paper shows how financial crises driven by self-fulfilling expectations about the liquidity of the banking sector are transmitted to the real sector of the economy. Since the government could also create financial assets by borrowing, the paper analyzes how public debt affects the issuance of liabilities by the financial intermediation sector.     

Bank risk and monetary policy

We find evidence of a bank lending channel operating in the euro area via bank risk. Financial innovation and the wider use of new ways of transferring credit risk have tended to diminish the informational content of standard bank balance sheet indicators. We show that bank risk conditions, as perceived by financial market investors, need to be considered, together with the other indicators (i.e., size, liquidity and capitalization), traditionally used in the bank lending channel literature to assess banks’ ability and willingness to supply new loans. Using a large sample of European banks, we find that banks characterized by lower expected default frequency are able to offer a larger amount of credit and to better insulate their loan supply from monetary policy changes.     

Risk Overhang and Loan Portfolio Decisions: Small Business Loan Supply before and during the Financial Crisis

We estimate a structural model of bank portfolio lending and find that the typical U.S. community bank reduced its business lending during the global financial crisis. The decline in business credit was driven by increased risk overhang effects (consistent with a reduction in the liquidity of assets held on bank balance sheets) and by reduced loan supply elasticities suggestive of credit rationing (consistent with an increase in lender risk aversion). Nevertheless, we identify a group of strategically focused relationship banks that made and maintained higher levels of business loans during the crisis.     

Liquidity and transparency in bank risk management

Banks may be unable to refinance short-term liabilities in case of solvency concerns. To manage this risk, banks can accumulate a buffer of liquid assets, or strengthen transparency to communicate solvency. While a liquidity buffer provides complete insurance against small shocks, transparency covers also large shocks but imperfectly. Due to leverage, an unregulated bank may choose insufficient liquidity buffers and transparency. The regulatory response is constrained: while liquidity buffers can be imposed, transparency is not verifiable. Moreover, liquidity requirements can compromise banks’ transparency choices, and increase refinancing risk. To be effective, liquidity requirements should be complemented by measures that increase bank incentives to adopt transparency.     

The price of liquidity: The effects of market conditions and bank characteristics

We study the prices that individual banks pay for liquidity (captured by borrowing rates in repos with the central bank and benchmarked by the overnight index swap) as a function of market conditions and bank characteristics. These prices depend in particular on the distribution of liquidity across banks, which is calculated over time using individual bank-level data on reserve requirements and actual holdings. Banks pay more for liquidity when positions are more imbalanced across banks, consistent with the existence of short squeezing. We also show that small banks pay more for liquidity and are more vulnerable to squeezes. Healthier banks pay less but, contrary to what one might expect, banks in formal liquidity networks do not. State guarantees reduce the price of liquidity but do not protect against squeezes.     

Impact of regulatory interactions on bank capital structure

This article examines a bank's optimal capital structure and risk-taking decisions in a regulated environment. We focus on the interactive nature of the Fed's collateralized discount window lending and the FDIC's deposit insurance. Such regulatory interactions are shown to have nonlinear and nonuniform impacts on the bank's leverage and risk-taking decisions. Thus, bank moral hazard problems may persist, even when banks are charged risk-adjusted deposit insurance premia and are also subject to market discipline through subordinate debt. Our analysis yields several new policy implications about the design and pricing of bank regulations.