How We Might Model a Credit Squeeze, and Draw Some Policy Implications for Responding to It

Sinclair, Peter J. N. Working Paper How We Might Model a Credit Squeeze, and Draw Some Policy Implications for Responding to It Economics Discussion Papers, No. 2008-40 Provided in Cooperation with: Kiel Institute for the World Economy – Leibniz Center for Research on Global Economic Challenges Suggested Citation: Sinclair, Peter J. N. (2008) : How We Might Model a Credit Squeeze, and Draw Some Policy Implications for Responding to It, Economics Discussion Papers, No. 2008-40, Kiel Institute for the World Economy (IfW), Kiel This Version is available at: https://hdl.handle.net/10419/27476 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by-nc/2.0/de/deed.en Discussion Paper Nr. 2008-40 | December 16, 2008 | http://www.economics-ejournal.org/economics/discussionpapers/2008-40 How We Might Model a Credit Squeeze, and Draw Some Policy Implications for Responding to It Peter Sinclair University of Birmingham Abstract This paper endeavours to illustrate the consequences of a credit squeeze by inserting a standard model of retail banks into some familiar macroeconomic models. Some possible policy conclusions are drawn about the benefits of incentives to increase lending at these times, and to reduce it in much better times. Paper submitted to the special issue “Learning from the Financial Crisis” JEL: D53, D86, G32 Keywords: Credit famine; credit crunch Correspondence: Peter Sinclair, Department of Economics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, United Kingdom; e-mail: [email protected] Without incriminating anyone in any error, I should like to record my gratitude for their valuable comments to Peter Andrews, Clive Briault, Willem Buiter, Max Corden, Shelagh Heffernan, Ian McDonald, Marcus Miller, and participants at the September 2008 CDMA Conference at St Andrews, and seminar audiences at the University of Birmingham, the Reserve Bank of Australia, the Deutsche Bundesbank, the Bank of England and the Bank of Thailand, at which early versions of this paper or related research papers were presented. © Author(s) 2008. Licensed under a Creative Commons License - Attribution-NonCommercial 2.0 Germany 2 1 Introduction The financial crisis of 2008 provokes three kinds of questions. First, how and why did it start? Second, how is it best fought now? And third, how are repetitions best prevented? Answers to these three questions are interwoven in many different ways. The main focus of this paper is on the second and the third questions. But to explore how best to combat it and to stop any recurrences, we must start by deciding how best to analyse it. At the heart of the crisis lies a breakdown of trust. Trust lies at the heart of the financial system; when it snaps, grave effects must ensue. First, some banks began to distrust some of their debtors whose loans had previously seemed relatively sound, and packaged in bundles certified as such by credit rating agencies. Next came the fall of the second domino. Some banks got wind of this. So they started to lose trust in some of the other banks, in particular those thought to be over-exposed to these newly suspect loans. The third stage was a cascade of scepticism about almost any bank that sought to borrow from another. What had been a quite regular, if intermittent, business practice, was now taken as a signal of possible impending insolvency. The interbank loan markets seized up; perceived counterparty risks rose sharply; and an immense shadow fell upon credit default swaps and various other financial derivatives. 2 Background A year after the “repricing” of risk had begun in the wholesale markets, the collapse of Lehman Brothers in September 2008 marked the onset of a grim struggle for survival on the part of thousands of financial institutions across the world. The stage was now set for distrust to spread to the general public. We now witnessed distrust of many of the retail banks. What had been presaged in October 2007 in the United Kingdom’s first bank run for over 150 years, by depositors in Northern Rock, turned 3 into a hasty rearrangement of customers’ accounts across banks to maximize shelter under deposit insurance ceilings, and, in some cases, it led to a flight to cash. Many banks now faced three simultaneous threats. One was deposit withdrawal. The second was the unavailability of (or at best sharply increased interest rates on) any interbank borrowings they had made. And the third was the rapid deterioration of loan income, net of provisioning. So they attempted to pay back their most short term debt as a matter of desperate urgency. And when loans exceeded deposits, as it did for many banks, narrowing the gap for which financing had suddenly become so expensive meant trimming the loan portfolio as rapidly as possible. Credit rationing afflicted weaker banks, and they in turn transmitted it to their retail borrowers. Where contracts allowed, retail loan rates were already swollen by augmented risk premia, and to allow for increased default probabilities and losses given default, and deteriorating collateral values following the principles of the Bernanke-Gertler financial accelerator. Now they jumped further, as the lender encouraged borrowers to switch suppliers. Overdraft ceilings were sometimes reduced unilaterally without discussion. Thus corporate borrowers facing imminent rollover of their debts faced the prospect of sharply increased interest rates, at best. At worst, they could receive demand for repayment in full. Some would find they could not find another source for loans. When this happened, bankruptcy would often follow. Although central banks were to cut policy rates sharply, variable rate loan rates would tend to fall by less, and a large gap opened up between the marginal costs of external finance to those who could still borrow (or had yet to face roll over) on the one side, and those denied credit on the other. For those in the latter group, external finance became prohibitively expensive. Keynes’s “unsatisfied borrowers” would morph, therefore, from fringe to dense throng. And those corporate borrowers still lucky enough to be outside it, would wait anxiously, to see if their short term loans would be renewed, and began to disengage quickly from planned spending on projects or staff, in case they were not. Many households would then anticipate that their future labour income was 4 vulnerable, and cut back on various discretionary expenditures. These developments marked the start of the transformation from financial crisis to economic recession. 3 Banks The very simplest model of a retail bank, a starting point for analysing the macroeconomic effects of the financial crisis, can be adapted from Klein’s (1971) portrayal of a banking monopoly3. Suppose there are n independent banks, each of them choosing its own levels of loans and deposits to maximize its profits, taking its rivals’ quantity decisions as given. This is therefore a Counot model of simultaneous oligopsony for deposits and oligopoly in loans. For simplicity, loans are homogeneous, and deposits are homogeneous; there is no discrimination in either of these markets; there are uniform and constant marginal costs of managing loans of C, and of managing deposits of c; and B represents an official interest rate set by the monetary authorities, which every bank takes as given - and treats as a single number. Banks’ liabilities consist solely of the deposits they attract, and their loans and their holdings of short term claims against the monetary authority, all bearing the interest rate B, are strictly positive. The (industry-wide) demand for loans decreases smoothly as the market-determined rate of interest on them, R, rises; the supply of deposits rises smoothly with the market-determined deposit rate, r. I assume for convenience at this point that there are no defaults on loans, or no limits on the values B can take, that deposits will exceed loans, and that all banks will behave alike. With the banks behaving in an identical fashion, resulting outcomes will be symmetric. There are three types of outcome. One is the Cournot equilibrium. This will give us an almost4 analytical solution for the pair of retail rates: the deposit rate will equal n cB r ε 1 1+ − =, and the loan rate will be n CB R η 1 1− + =, where ε is the elasticity of industry wide deposits to r, and η (defined as a positive number) is the 3 Another paper on this subject, written almost at the same time and with a very similar approach, is by Monti (1972). Both models build on Edgeworth’s original insight (1886) that certain aspects of banking gave rise to increasing returns, thus making room for an imperfectly competitive industrial structure. 4 An exact solution is available when the two elasticities in the formulae are constants. 5 elasticity of industry wide loans to R5. If all the banks collude, however, and new entrants that might otherwise be tempted in are kept out of the picture, then the effective number of independent banks is unity. In that case, a collusive equilibrium will generate the largest equilibrium spread between the two retail rates, and the lowest volume of industry loans and deposits. The formulae continue to hold, with this restriction. The loan rate is clearly much higher than in the Cournot equilibrium, and the deposit rate much lower, especially when the number of banks is large. The largest volumes, and the smallest spread, c+C, would be observed in the opposite extreme. This covers the cases of textbook perfect competition (where n is effectively infinite, and the formula still holds) and also in Bertrand competition between two or more banks (when banks set their two rates independently, taking each others’ rates as given, and here the formulae do not hold). This would happen, too, even in monopoly-monopsony under the conditions of perfect contestability (no sunk costs, parity of technology and factor prices between an incumbent and a novice, and consumers able to switch banks faster than incumbents can reprice products; and again the formulae fail here). This spread would go to vanishing point if marginal administrative costs are negligible. In the Cournot or collusion cases, industry-level loan demand and deposit supply will need to be sufficiently well behaved – linearity or log linearity would of course suffice but nothing so restrictive is necessary - to rule out any possible instances of multiple equilibrium that might otherwise arise. The retail rate spread between loan and deposit rates increases with the two marginal cost terms, and decreases as the number of independent banks rises, or as loan demand or deposit supply becomes more elastic to its particular interest rate. As a first step, we might model the consequences of the credit crunch as triggered by a spontaneous, exogenous jump in the loan rate-deposit rate spread, traceable in turn to a sudden, exogenous change in the required direction by any one or more of these relevant parameters. Within the confines of our assumptions, perhaps the most appropriate way of modelling the crunch would be by supposing that C, the marginal cost associated with managing loans, had jumped sharply. Loan rates would rise by the full extent of the marginal cost jump in the third case of perfect competition (or 5 These results come from assuming that, under conditions stated above, bank i sets its quantities of loans ( ) and deposits to maximize i li diiii drcdBCR )()()( + − − + − ll . 6 Bertrand equilibrium or perfect contestability), or in the other cases, if industry loan demand happened to be semi-logarithmic6 (more generally, the loan rate could go up by more or less than one for one with C). A few points about generalizations could be made at this point. First, defaults. Let ψ and λ respectively be the default rate, and the rate of loss given default (LGD), with )(Ra φ ψλ =, say. Presumably )(R φ increases with the loan rate R for reasons explained by Stiglitz and Weiss (1981): a higher loan rate deters better risks more than riskier lenders, and induces remaining borrowers to take more risk in ways that the bank cannot directly observe or prevent. With ξ the elasticity of φ to R, the loan rate solution will now satisfy ]) 1 1)(1/[()( n a n aCBR η φξ η φ −−−−= . Here, the loan rate rises in response to an exogenous rise in the default or LGD rates (as reflected in parameter a) or if their product becomes more elastic in R. Had individual banks been price setters rather than quantity setters, on the other hand, loan rates may be tempered, rather than augmented, by their perceptions of how higher interest can trigger these moral hazard and adverse selection effects – and in such circumstances credit rationing might result. But within the setup above, it is straightforward to see how an exogenous deterioration in expected defaults (and/or in losses given default) must, all else equal, boost loan rates. Second, banks may not behave symmetrically. The monopoly – collusion solution is threatened by the incentive it provides for an individual cartel member to break ranks, and increase lending and deposit taking if he thinks he can get away with it. If one bank defects, and the others stick together, we move straight to Cournot duopoly / duopsony, with the formulae registering a rise in n from 1 to 2. If m banks defect, we see the interest rate spread shrinking further, with the formulae amending n to m+1. And complete fragmentation of the cartel takes us further, all the way to Cournot with n banks. Defection may be deterred if the cartel can credibly threaten, not just to identify the defector, but also to punish him, by flooding the market. Further, the cartel may be sustained if the rate of discount a potential defector applies to 6 That is, if the logarithm of industry loan demand were linear in the loan rate. In this special case, the loan rate will exceed B+C by a constant that is inversely proportional to n. 7 subsequent profits (which will be squeezed by such punishment) is sufficiently low. One strategy for a bank facing possible extinction (and thus exhibiting a high discount rate) may therefore be to attempt to expand its loans (and / or its deposits) rapidly. And if it is unsure about how and when its rivals will react to such moves, and the payoff to its decision takers is bounded below, this form of aggression could take on the character of a highly appealing “gamble for resurrection”. Regulators may of course intervene to try to prevent this, not least because such action could imperil the financial stability of other financial institutions. But this issue reminds us that financial crises could be attended, at least initially or temporarily, by credit feasts and not just credit famines, and by moves towards lower rather than higher loan rates. A recent instance of an interesting, but rather different kind of financial crisis model exhibiting loan rate reductions, and the breakdown of a cartel, is provided by Gorton and He (2008). Cournot equilibrium may itself also be infected by asymmetric behaviour. In a Stackelberg leadership equilibrium, one bank, the “leader”, has learnt that its rivals’ loan and deposit quantities are not given, but tend to fall when the leader takes on new business. The leader exploits this information, and now produces more than his rivals, in the belief that they will respond by yielding some profitable business to him. When industry loan demand and deposit supply are (approximately) linear, the leader’s quantities resemble those of a pair of the other, “follower” banks, and the retail rate spread inches down a bit, in the direction of greater competition. If two or more try to “lead”, the spread may collapse to the perfect competition level, or conceivably (for a while, out of equilibrium) below it. Asymmetry in market shares will also arise when behaviour is symmetric but costs are not. Smaller banks will be smaller because they suffer from higher costs. A third concern relates to the fact that the range of values that the retail rates may take may be bounded. There is presumably a zero lower bound to the monetary authorities’ nominal policy rate. Our formulae should be unproblematic when expected inflation is zero, because nominal and real interest rates converge. If not, one will wish to restrict their definition to real interest rates ruling in the retail markets. If so, this is how B will be defined. The zero lower bound to the nominal policy rate implies a lower bound to the real policy rate, too. Furthermore, because 8 currency offers a zero nominal return by definition, and because currency and bank deposits will generally be rather good substitutes, it is difficult to imagine that banks could pay a negative nominal rate on deposits for more than a brief period in unconventional circumstances (such was seen in Switzerland on deposits of foreign origin for a brief spell in 1978). Extending their earlier paper (2005), He, Huang and Wright (2008) propose a theoretical model of bank deposits motivated by the (higher) risk of theft of cash in which negative nominal rates on deposits could happen, and might indeed be optimal. But evidence of Japanese money market and bank deposit interest rates in the periodic zero bound episodes earlier this century (e.g. Baba et al, 2006) testifies to a concertina effect where the gap between r and B gets very severely squashed. 4 Modelling the Credit Squeeze – The Short Run, and a Possible Policy Response Suppose, for simplicity, that final expenditure by firms and households is partly paid for out of current income, and partly out of loans from banks, at a real rate R. Assume no foreign trade or fiscal activity, and let expectations of inflation be zero, so that nominal and real interest rates are equal. This will give us a very simple IS curve. Suppose that the monetary authorities set the policy rate at B, a “neutral” rate, supplying base money to meet demand for which the relevant opportunity cost is the rate on deposits, r. That will imply a simple LM curve. We might write these down in linear form as )( 1 wByy + −+= γ β α (1) m/p = )( 2 wBy −−+ ς ε δ (2) where y, and m/p denote real income and real balances of base money, all Greek parameters are positive (with 1 < β ) and and denote mark-up and mark-down from the central bank’s policy rate, B. If retail banking had been costless, perfectly competitive and completely devoid of risk, the two retail rates would lie at B. This is a basic textbook ISLM system, with the LM curve horizontal. 1 w2 w 15 (but it will be zero if they only cross at a negative rate of growth, an impossibility if it implies negative rates of training or invention). So it is now a simple matter to examine the consequences of capital market imperfections, if one assumes that the Ramsey, positive link refers to the behaviour of households who observe a (real) deposit rate r, with the other, non-positive link relating to the (real) borrowing rate, R. The implication is unmistakeable: a bigger wedge between the two real rates can only reduce the growth rate. And if the wedge is permanent, so will be the reduction in the rate of growth. For a given R-r gap, growth is the more impaired, the flatter these two relationships (if the rate of growth is placed on the horizontal axis). 6 Concluding Remarks – Some Policy Implication for the Longer Run If the key issue is one of a breakdown in trust of and by banks, this should ideally be addressed at source. Tinbergen’s rule is that if you have two targets, you should have two instruments. It is surely asking too much of the monetary authorities’ policy rate that it should be used for both macroeconomic stabilization and combatting fits of overoptimism or distrust on the part of participants in the financial markets. Just because distrust clogs up lending channels, and a credit famine may have very serious, though gradual, impact on inflation and real income, cannot imply that policy rate cuts – helpful, even invaluable as they may well be in such circumstances - are the ideal sole instrument for trying to deal with the source of the problem. Pigou’s solution to a problem of underprovision of a good or service from a social welfare standpoint11 was to urge a subsidy; overprovision should, he thought, be restrained by a tax. What might a Pigouvian solution therefore look like? First one would need to determine what overprovision or underprovision might mean, and how they could be quantified. One measure would be deviation from a mean value of corporate bond (or “debenture”) yields drawn from a wide index. One could construct an index of the prices (ideally adjusted to remove the influence of coupons) of (unindexed) corporate bonds, which were due to be redeemed within say 2 years, or approximately in one year’s time, stretching back over a long period. The mean 11 See Pigou (1954) and references therein. What follows in the present paper is a specific suggestion that builds , on Pigouvian lines, upon the proposal by de Fiore and Tristani (2008) for careful monitoring of credit spreads . 16 annualized yield to maturity could then be readily calculated, and compared with annualized yields of (unindexed) government bonds at similar maturities. The historical mean difference in the means would be, let us say, 150 basis points. This could then be compared with the actual difference in yields on a quarterly, monthly or even daily basis. Where the difference was historically low, say below the 90% confidence interval around the mean, a tax could be imposed on the nominal quarterly growth of a licensed or chartered bank’s lending, of perhaps £2 per £100 lent. This tax would become payable in conditions presumed to correspond to excessive optimism. It could be thought of as an advance charge that took the place of appropriate, forward looking provisioning. Where the difference was high, above the 90% confidence interval, the nominal growth in a bank’s lending would attract a symmetric subsidy. The scheme should be self financing if the long run yield difference proved stationary, and any changes in tax treatment that might alter it could be allowed for by amending the trigger points for subsidy and tax. Basing the tax/subsidy regime on the corporate versus government yield difference would be much less liable to manipulation than say on the gap between the central bank’s policy rate and a measure of interbank rates at a similar maturity. The costs of administering the scheme would be sharply lessened by the fact that it would only be expected to operate, by construction, one tenth of the time. The scheme could be enriched, if thought useful, by relating the size of the tax and the subsidy to the actual size of the difference, when this strayed outside the confidence interval, but care would be needed to correct for the skewness of the yield difference if long-run breakeven was to be achieved: the tax/subsidy schedules would need to be non-linear. If it were thought useful to narrow the confidence interval around the mean beyond which taxes or subsidies became payable, this could also be easily achieved, though at some extra administrative cost. The main aim of such a measure would be to redress the procyclical bias in existing regulatory arrangements, and, if possible, actually reverse it when certain thresholds were reached. But the system could be tailored to meet other needs. For example, if equilibrium correction econometric regressions12 revealed that the price of houses was more than x% away from values implied by fundamentals, or more than some 12 Of the kind pioneered in the housing context by Hendry (1983). 17 unacceptable number of standard deviations from fundamentals, the tax / subsidy regime could apply to the growth of mortgages13. This would not necessarily be an alternative to other stabilization devices, such as varying rates of stamp duty for housing transactions, or setting regulations on maximum loan-to-value ratios; it could be complementary with them. And while it is surely true that a credit famine will be accompanied by the likelihood of an abnormally large volume of credit rationing (in housing markets and well beyond), a phenomenon that transcends he simple models studied in this paper, fighting the famine by inducements to lend offer at least some reasonable hope of alleviating it. Alternatives to these proposals – or possibly complements - would be to focus on the growth of credit per se, or on the credit/GDP ratio. One could regress nominal credit aggregates on nominal GDP, over time, and perhaps a set of other variables. First one would need to see whether credit (or any of its aggregates) was cointegrated with GDP. Of course it should be, but this should be checked, and over short or atypical periods a negative answer is conceivable. Once cointegration was assured, the next task would be to pinpoint any trend in the ratio, and any other variables that theory would suggest, and evidence confirmed, entered a well identified cointegrating relationship. (There might well be none of these other variables). New cointegrating equations would be run, and, one would hope, just a single one would emerge. The next stage would involve stipulating a credit growth rule: This could be target annual credit growth = inflation target + GDP growth trend + any annual time trend. If actual credit growth overran the target for a sufficiently long interval or by a sufficiently large amount, penalties on banks raising credit growth at or above this overall rate would be imposed. And a long enough or large enough sequence of below-target credit growth would trigger subsidies on banks with lending growth at or above this rate. A second variant would be to penalize banks for raid lending growth when the credit-?GDP ratio was significantly above trend, and reward them when it was significantly below. Of these two, the first would probably be superior, for two reasons: first, a trigger that focussed on growth rates would lead to earlier 13 Goodhart and Hoffman (2008) provide a valuable review of the role of house prices in the moneycredit-interest nexus, and policy implications that may follow, and Gorton (2008) gives an excellent account of the role of mortgages in sowing the seeds of the current crisis. For the general argument for monitoring credit and asset prices, and the need for policy to react to them from time to time, Borio and Lowe (2004) are magisterial and persuasive. 18 intervention, and second, innovation that took the form of non-transient intercept shifts on the ratio would be much less likely to set off destabilizing policy responses. Perhaps it is also time, as suggested by Dodge (2008), to consider reviving reserve and/or liquidity ratios on banks in those jurisdictions where they had fallen been dropped or had fallen into desuetude. Much of the trouble in 2007 was characterized by banks (like Northern Rock, HBOS and Bradford and Bingley in the UK) that had gambled on an “external finance strategy” and borrowed heavily on money markets to supplement their deposit base.. A minimum liquidity ratio would simply prohibit such behaviour (a milder sanction would be to insist on evidence of well spread and lengthy maturity on these loans, or insurance against inter-bank markets drying up, on pain of threat of massive fines or to suspend a banking licence). And to prevent banks rushing like Gadarene swine to the opposite extreme of hoarding liquidity as many did in late 2008, one could envisage a maximum liquidity ratio, which might be reduced all the way to zero – or even belowin exceptional conditions. 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Prescott (1989), Recursive Methods in Economic Dynamics, Harvard University Press. Please note: You are most sincerely encouraged to participate in the open assessment of this discussion paper. You can do so by posting your comments. Please go to: http://www.economics-ejournal.org/economics/discussionpapers/2008-40 The Editor © Author(s) 2008. Licensed under a Creative Commons License - Attribution-NonCommercial 2.0 Germany