Liquidity, Moral Hazard and Inter-Bank Market Collapse
Summary (4 min read)
1. Introduction
- The financial market turmoil that has been under way since the summer of 2007 hit the core of the global financial system, the interbank market for liquidity.
- While this paper does not endeavor to account for all the features of the recent crisis, be it hard evidence or casual stories about the motivations of market players, it argues that a proper modeling of the collapse in the market for liquidity involves a close look at incentives to provision/hoard liquidity and moral hazard mechanisms in the interbank market.
- This relaxes the moral-hazard-induced liquidity constraint, raising the demand for liquidity and thereby the price of liquidity on the interbank market, which in turn raises incentives to provision liquidity ex ante.
- A common feature of this literature is that bank holdings of liquidity are not necessarily optimal.
2. Timing and Technology Assumptions
- Banks are risk neutral and maximize expected profits.
- At date 0, each bank has a unit capital endowment and two investment possibilities.
- 6The alternative arrangement under which banks would sign ex ante insurance contracts against liquidity shock is not possible here.
- Distressed banks reinvest their own liquidity plus borrowed funds in their illiquid project and deliver some effort.
3. The First-Best Allocation
- To derive the first-best allocation, the authors remove two assumptions regarding market imperfections.
- First, date 0 allocation between liquid and illiquid assets is now verifiable.
- Moreover, each distressed project in which k is reinvested yields an expected return keR(e).
- Put differently, the expected return to illiquid investments without any ex ante liquidity provision (1 − q)R is very large.
- The social planner then prefers to maximize illiquid investments.
4.1 Distressed Banks’ Optimal Demand for Liquidity
- The authors can then derive the following proposition.
- Having determined optimal borrowing and effort conditional on reinvestment, the authors can now examine whether distressed banks prefer to reinvest in their illiquid assets or to give up their illiquid project and lend their liquid holdings on the interbank market.
- Expected profits π′b from lending liquid assets on the interbank market are simply π′b = eirli because the repayment probability of distressed banks is ei.
- Given the assumption R(ei) ≥ r, d∗i is always positive and profits from reinvestment πb are always larger than profits from lending liquid assets on the interbank market.
4.2 Intact Banks’ Optimal Supply of Liquidity
- When a distressed bank delivers low effort el, the interest rate r it is charged cannot be larger than μR—otherwise, the distressed bank would not borrow—and by assumption the authors have elμR < 1.
- To make sure that the distressed bank delivers high effort eh, intact lending banks impose a liquidity constraint.
- The volume of liquidity the distressed bank can then borrow verifies the incentive constraint: eh((li + di)R − dir) ≥ el((li + di)μR − dir).
- Denoting [x]+ = max(x; 0), this condition simplifies as a borrowing constraint: di ≤ d(li) ≡ ψR [r − ψR]+ li. (9) In this case, a distressed bank’s total borrowing from the interbank market is a positive function of its ex ante liquidity provision.
5. The Decentralized Equilibrium
- In the previous section, the authors derived the optimal date 1 decision rules for intact and distressed banks in terms of lending, borrowing, and effort.
- Based on these results, the authors now turn to the optimal date 0 liquidity provision policy in order to characterize the different equilibria of the economy.
- Recall that ex ante liquidity provisions are observable, so that the size of illiquid projects as well as reinvestment needs, assuming a shock has occurred, are also observable.
- The implementation of a borrowing constraint by intact banks on distressed banks requires the additional (implicit yet standard) assumption that total interbank borrowing is observable by lenders.
- The following two subsections are devoted to laying down the conditions under which each of these two situations can be an equilibrium.
5.1 The Full-Reinvestment Equilibrium
- 1.1 Optimal Ex Ante Liquidity Provision with Full Reinvestment.
- The equilibrium with distressed banks achieving full reinvestment exists if and only if two conditions are met:.
- The authors can then derive the following proposition.
- This drives up the interbank market interest rate, which provides incentives for banks to provision liquidity ex ante.
- The full-reinvestment equilibrium is therefore more likely when the liquidity shock is more likely, a property the authors refer to as the virtue of bad times.
5.2 The Credit-Rationing Equilibrium
- In the equilibrium described in the previous subsection, distressed banks are able to carry out full reinvestment thanks to their relatively large ex ante liquidity provision.
- The function ∂Eπi∂li is potentially nonmonotonic in the interest rate on the interbank market.
- The authors can then derive the following proposition.
- When the liquidity shock is less likely, banks provision less liquidity ex ante and invest more in illiquid assets.
- Credit rationing reduces the demand for liquidity and thereby depresses the return on ex ante liquidity provision for intact banks.
5.3 Multiple Equilibria and the General Equilibrium Externality
- When ex ante liquidity provisioning is low, then both liquidity supply and liquidity demand are relatively low.
- Hence, with little provisioning, the demand for liquidity is also low.
- The expected return on ex ante liquidity provisioning is then high.
- Outside this region the equilibrium is unique.
- The multiple equilibria property can be examined in a diagram representing aggregate liquidity supply Ls and aggregate 10The interbank-market-collapse equilibrium could be eliminated if banks could sign contracts contingent on the volume of date 0 liquidity provisioning.
6.1 Aggregate Shocks
- While this model shows that the fragility of the market for liquidity does not necessarily stem from the presence of aggregate shocks, it can easily be extended to allow for such shocks.
- Suppose, for instance, that the individual probability q to face a liquidity shock can take different values, F denoting the cumulative distribution function for q.
- Then when q < q, which happens with probability F (q), the interbank market collapse is the unique equilibrium and therefore happens with probability one.
- On the one hand, it raises the return to illiquid investments and hence raises banks’ incentives to invest in illiquid assets.
- As a consequence, the probability q below which the market-collapse equilibrium exists tends to decrease.
6.2 Interim Liquidation of Illiquid Assets
- Let us assume instead that distressed banks can liquidate (part of) their illiquid projects with a strictly positive liquidation value.
- Hence, its profit conditional on reinvestment being successful is (li +ρvi +di)R−rdi, while eh is both the effort the distressed bank undertakes and the probability that reinvestment is successful.
- Second, the distressed bank cannot liquidate more than a fraction α of its illiquid project.
- Moreover, interim liquidation could well happen at the same time or even after distressed banks borrow on the interbank market.
- When the share α of illiquid assets that distressed banks can liquidate is sufficiently low, there is still a credit-rationing equilibrium in which some liquidity is traded on the interbank market as opposed to the previous credit-rationing equilibrium where a total collapse of the interbank market takes place.
7. Policy Implications
- In this section the authors investigate whether and how policy can avoid a collapse of the interbank market.
- First the authors look at ex post interventions, i.e., policies that take place after the interbank market has collapsed.
- Then the authors focus on ex ante interventions, i.e., interventions aiming at preventing the collapse of the interbank market.
7.1 Ex Post Interventions
- There are basically two types of interventions that can take place after the interbank market has collapsed: liquidity injections and changes in interest rates which modify the return on the liquid technology.
- It can also influence the cost of liquidity by modifying short-term interest rates.
- In other words, unless the central bank has access to a monitoring technology that market participants do not have access to, liquidity injections are doomed to fail.
- Given that banks make no ex ante liquidity provision in the equilibrium with a market collapse, the reduction in interest rates does not modify distressed banks’ borrowing capacity, which remains at zero.
- Hence, interest rate cuts are most effective when banks have made relatively large ex ante liquidity provisions.
7.2 Ex Ante Interventions
- A regulator can affect the banks’ date 0 allocation of capital by imposing a liquidity ratio, requiring that banks invest at least some fraction of their portfolio in liquid assets.
- Yet imposing a liquidity ratio is equivalent to writing such a contingent contract between the regulator and banks, stating that the bank would be shut down if the share of liquid assets was lower than a given threshold.
- Imposing such a regulation in this type of model therefore ends up giving discretion to the regulator, which can be costly for reasons outside the scope of this paper (e.g., in terms of capture of the regulator by the regulated agents).
- In particular, the central bank can raise the return to liquid assets between date 0 and date 1 to raise banks’ incentives to invest in liquid assets and thereby prevent the collapse of the interbank market at date 1.
- Given that the right-hand side of the above inequality is decreasing in the interest rate r, the above inequality always holds if it holds for the lowest possible interest rate, i.e., when ehr = 1.
8. Conclusion
- The model the authors analyzed in this paper provides a framework for analyzing the occurrence of liquidity crises and discussing policy responses to situations of interbank market collapse.
- When banks achieve full reinvestment, they always provision the first-best volume of liquidity, and the equilibrium interest rate on the interbank market is r∗ = min{r1; r2}.
- There may be two types of such equilibria.
- The equilibrium with zero ex ante liquidity provision and interbank market collapse is therefore the only equilibrium, when it exists, in the credit-rationing regime.
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...…IBM is critical for the efficiency and effectiveness of the whole financial system, monetary policy implementations, and credit supply to the real economy (e.g. Acharya, Gromb and Yorulmazer, 2012; Freixas, Martin and Skeie, 2011; Kharroubi and Vidon, 2009, and Montagna and Lux, 2017)....
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Q2. What future works have the authors mentioned in the paper "Liquidity, moral hazard, and interbank market collapse" ?
These are possible research avenues for future work. However, since by assumption the authors have eh ≥ 1 − q, this condition can not be satisfied. There may be two types of such equilibria. Having determined banks ’ date 1 decisions, the authors can turn to banks ’ date 0 problem, which writes as max l ( 1 − q ) [ ( 1 − l ) R + [ ( 1 − l ) β + l ] max { ehr ; 1 } ] + qehr R [ 1 − ψ ] r − ψR ( l + ρα ( 1 − l ) ).