EC3115 Monetary Economics

Transcription

1 EC3115 :: L.18 : Financial crises Almaty, KZ :: 18 March 2016 EC3115 Monetary Economics Lecture 18: Financial crises Anuar D. Ushbayev International School of Economics Kazakh-British Technical University Tengri Partners Merchant Banking & Private Equity a.ushbayev@tengripartners.com Almaty, Kazakhstan, 18 March 2016

2 EC3115 :: L.18 : Financial crises - 2 / Relevant reading Book treatment F. Mishkin. (2013). The Economics of Money, Banking and Financial Markets, 10 th edition, Pearson Education, Chapters 9, 10. F. Allen and D. Gale. (2007). Understanding Financial Crises, Oxford University Press, Chapters 2 and 3. Must-read articles D. Diamond and P. Dybvig. (1983). Bank Runs, Deposit Insurance, and Liquidity, Journal of Political Economy, Vol. 91, No. 3, pp T. Hellmann, K. Murdock and J. Stiglitz. (2000). Liberalization, Moral Hazard in Banking and Prudential Regulation: Are Capital Requirements Enough?, American Economic Review, Vol. 90, No. 1, pp T. Adrian and H. Shin. (2010). Liquidity and leverage, Journal of Financial Intermediation, Vol. 19, No. 3, pp

3 EC3115 :: L.18 : Financial crises - 3 / Must-read articles (cont.) T. Adrian, E. Moench and H. Shin. (2010). Macro Risk Premium and Intermediary Balance Sheet Quantities, IMF Economic Review, Vol. 58, No. 1, pp M. Miller and J. Stiglitz. (2010). Leverage and Asset Bubbles: Averting Arma- geddon with Chapter 11?, Economic Journal, Vol. 120, No. 544, pp C. Borio. (2014). The financial cycle and macroeconomics: what have we learnt?, Journal of Banking & Finance, Vol. 45, pp M. Miller and Zhang, L. (2015). The Hedgehog and the Fox: From DSGE to Macro-Pru. The Manchester School, Vol. 83, pp

4 EC3115 :: L.18 : Financial crises - 4 / Recalling Minsky: crises are endogenous Can It a Great Depression happen again? And if It can happen why didn t It occur in the years since World War II? These are questions that naturally follow from both the historical record and the comparative success of the past thirtyfive years. To answer these questions it is necessary to have an economic theory which makes great depressions one of the possible states in which our type of capitalist economy can find itself. Hyman Minsky, (1982), Inflation, Recession and Economic Policy, Brighton: Wheatsheaf. Minsky s view [was] that economics should include the possibility of severe crises, not as the result of external shocks, but as events that emerge from within the system [...] Martin Wolf 1, (2014), The Shifts and the Shocks, Penguin Books. 1 Associate editor and chief economics commentator at the Financial Times.

5 EC3115 :: L.18 : Financial crises - 5 / Stylized account of financial crises Section 1 Stylized account of financial crises

6 EC3115 :: L.18 : Financial crises - 6 / Stylized account of financial crises Introduction Financial crises are major disruptions in financial markets characterized by sharp declines in asset prices and firm failures. Beginning in August 2007, defaults in the subprime mortgage market (for borrowers with weak credit records) sent a shudder through the financial markets, leading to the worst financial crisis since the Great Depression. In Congressional testimony, Alan Greenspan, former Chairman of the Fed, described the financial crisis as a once-in-a-century credit tsunami. Wall Street firms and commercial banks suffered hundreds of billions of dollars of losses. Households and businesses found they had to pay higher rates on their borrowings and it was much harder to get credit. All over the world, stock markets crashed, with the U.S market falling by 40% from its peak.

7 EC3115 :: L.18 : Financial crises - 7 / Stylized account of financial crises Many financial firms, including commercial banks, investment banks, and insurance companies, went belly up. Why did this financial crisis occur? Why have financial crises been so prevalent throughout U.S. history, as well as in so many other countries, and what insights do they provide on the current crisis? Why are financial crises almost always followed by severe contractions in economic activity?

8 EC3115 :: L.18 : Financial crises - 8 / Stylized account of financial crises Typical sequence of events according to Mishkin (2013) Stage 1: Initiation of Financial Crisis. Mismanagement of Financial Innovation/Liberalization. Asset-Price Boom and Bust. Increase in Uncertainty. Stage 2: Banking Crisis. Bank panic. Fire sales and further asset price declines. Bank insolvency. If the economic decline from Stages 1 and 2 is severe, then also: Stage 3: Debt Deflation. Significant decline in the price level. Substantial decline in real net worth of borrowers.

9 EC3115 :: L.18 : Financial crises - 9 / Stylized account of financial crises Sequence of events in financial crises in advanced economies

10 EC3115 :: L.18 : Financial crises - 10 / Stylized account of financial crises Some models that can produce endogenous crises Pecuniary externalities in the credit markets: Demand-side (collateral and credit constraints): Kiyotaki and Moore (1997). Supply-side (externalities and asset bubbles): Hyun Song Shin et al. 2007, Banking crises: Liquidity crises (financial panics as bank runs): Diamond and Dybvig (1983). Solvency crises (asymmetric information, moral hazard and imprudent gambling): Hellman, Murdock and Stiglitz (2000). NB: very frequently hard to disentangle illiquidity and insolvency in the real world.

11 EC3115 :: L.18 : Financial crises - 11 / Models of externalities in the credit markets Section 2 Models of externalities in the credit markets

12 EC3115 :: L.18 : Financial crises - 12 / Models of externalities in the credit markets Pecuniary externalities Demand side: These externalities arise when price movements that are meant to clear particular markets, have unintended side-effects, possibly because of balance sheet rules or conventions. In Kiyotaki and Moore (1997), for example, the balance sheet rule is that because of moral hazard - loans need to be fully collateralised. But this can generate accelerator effects and/or fire-sale externalities in face of macroeconomic technology shocks. Supply-side: For Adrian and Shin (2007), the balance sheet rule is that financial intermediaries be adequately capitalised i.e. have enough of their own skin in the game to prevent excess risk-taking. But through their effects on the equity base of the intermediaries, asset price changes can be greatly amplified, and risk premia compressed. This can generate boom- bust cycles.

13 EC3115 :: L.18 : Financial crises - 13 / Models of externalities in the credit markets Micro-macro link in models of externalities The link between micro and macro that emerges in these models may be roundabout; but it is nonetheless powerful: at the micro-level there is a moral hazard/principal-agent problem (borrowers won t repay; intermediaries will gamble). gives rise to a balance sheet rule to check the moral hazard involved, but this can cause macro-problems if the balance sheets are subject to a correlated shock (a positive technology shock, for example). While these micro-prudential rules work well for idiosyncratic shocks, they can generate significant pecuniary externalities when shocks are correlated. Since the above involves an externality it cannot be left to market forces to handle: it calls for macro-prudential policy measures. For the financial accelerators in certain models, these pecuniary externalities operate directly through balance-sheet pressures on borrowers or lenders.

14 EC3115 :: L.18 : Financial crises - 14 / Models of externalities in the credit markets Millenium bridge: financial innovation can make the world a riskier place An analogy popularized by Hyun Shin may help illustrate: the saga of the Millennium Bridge across the River Thames when first opened to pedestrians in The chosen structure was not rigid; it was somewhat elastic so it could move with gusts of wind; and, for planning purposes, it had been assumed that the pedestrian traffic of office workers and tourists would not be walking in step. On opening day, as pedestrians first flocked across the bridge, they were indeed out of step: but not when gusts of wind caused the structure to sway. Walkers in each direction, thrown sideways onto the same foot at the same time, fell into step and the bridge, picking up the harmony, began to sway so badly that it had to be closed that day and for many months thereafter as it underwent serious restructuring. The alarming swaying motion was the unintended consequence of choosing a flexible structure that, with pedestrian traffic, acted to amplify the effect of random gusts. Marcus Miller and Lei Zhang, (2015), The Hedgehog and the Fox: From DSGE to Macro-Pru, The Manchester School, Vol. 83, pp

15 EC3115 :: L.18 : Financial crises - 15 / Models of externalities in the credit markets Kiyotaki and Moore (1997) recap Even without financial intermediaries, a credit-constrained market economy- where collateral is used to handle repudiation risk-can exhibit credit cycles and collapsing asset prices, thanks to the externalities acting via the price of collateral. Highly productive small business entrepreneurs wish to raise outside finance to acquire fixed capital assets (which they employ with constant marginal productivity) but they face an agency problem because the human capital used in the business is inalienable. Recourse is had to issuing debt backed by physical collateral, priced to reflect its productivity outside the entrepreneurial sector (i.e. in the hands of the deep pocket lenders, who face declining marginal productivity). In the face of uncorrelated, idiosyncratic productivity shocks, individual agents adversely affected can sell capital and pay down debt without affecting asset prices.

16 EC3115 :: L.18 : Financial crises - 16 / Models of externalities in the credit markets Demand-side pro-cyclicality: a financial accelerator However, in the face of an adverse macroeconomic shock to entrepreneurial productivity, the borrowing constraint can lead to fire-sales which affect the price of the collateral and trigger yet further sales, i.e. there is a pecuniary externality. This is in sharp contrast with the first best economy where all agents are unconstrained in the credit market, and prices and production are unaffected by net worth. How this externality can impact on asset allocation in the model of Kiyotaki and Moore (1997) can be seen schematically in figure below, where fixed capital (e.g. land, used by the entrepreneurs as collateral) is measured on the horizontal axis and its price on the vertical (with holdings by entrepreneurs shown measured from the origin, the remainder being held by the uncon- strained deep pockets ).

17 EC3115 :: L.18 : Financial crises - 17 / Models of externalities in the credit markets Financial accelerator in Kiyotaki-Moore (1997): effect of a temporary positive aggregate technology shock

18 EC3115 :: L.18 : Financial crises - 18 / Models of externalities in the credit markets Consider the impact of a temporary aggregate productivity shock from initial equilibrium at E, where highly leveraged small business entrepreneurs hold the stock k of fixed assets at price q. Thanks to the immediate increase in net worth easing their credit position, small businesses can collectively acquire the additional amount of collateral EA. But, like the swaying of the Millennium Bridge when hit by a gust of wind, this initial shock will be amplified as the extra demand pushes up the price of collateral-enabling these entrepreneurs to go yet further on the acquisition trail. The effect of this financial accelerator is shown the movement from A to B, which can be many times as large as the initial shock. Like the bridge settling down when the wind stops gusting, however, the allocation of assets will absent further shocks move gradually back to equilibrium, as shown by the arrow from B to E.

19 EC3115 :: L.18 : Financial crises - 19 / Models of externalities in the credit markets Bubbles What ensures that the number of individuals certified to be creditworthy combined with those with cash resources generates a demand for current resources equal to current supplies? The conventional answer is that prices (interest rates) adjust to ensure that markets clear. We know that something is wrong with that answer because sometimes markets do not clear. There is unemployment. There may be excess demand for goods, leading to inflation. [...] Indeed, [...] markets by themselves may be destabilizing: an excess supply of credit leads to high levels of employment/inflation, enhancing the likelihood of loan repayment, and encouraging more lending activity. The reliance on collateral too may lead to a destabilizing dynamic: in a boom, collateral values rise, allowing more credit, to support even higher asset prices. Market economies have repeatedly been characterized by such collateral-based lending bubbles. Joseph Stiglitz, (2013), Selected Works of Joseph E. Stiglitz: Volume II: Information and Economic Analysis: Applications to Capital, Labor, and Product Markets, Oxford University Press.

20 EC3115 :: L.18 : Financial crises - 20 / Models of externalities in the credit markets Miller and Stiglitz (2010) What happens if the initial productivity shock is negative? In this case, the accelerator goes into reverse and asset prices have to fall until the balance- sheet-driven demand for liquidity by small businesses is matched by the supply of liquidity by the residual buyers the agents with deep pockets. Is there not a risk that highly leveraged borrowers trying to pay down their debts by disposing of assets in a fire-sale will become insolvent in the process? To illustrate, consider the case where the shock is the ending of an asset bubble (rather than an adverse shift of productivity). Imagine a growing asset bubble as indicated in figure below by the arrow pointing upwards from E with small businesses expanding their borrowing in line with rising collateral values until it bursts.

21 EC3115 :: L.18 : Financial crises - 21 / Models of externalities in the credit markets Black holes, boom and bust in Miller-Stiglitz (2010): asset price bubble and bankruptcy

22 EC3115 :: L.18 : Financial crises - 22 / Models of externalities in the credit markets In this case, DD and D D can be interpreted as schedules for the disposal of fixed assets needed to match the fall in net worth following the ending of the asset bubble at B or at B, respectively. Note that when the bubble bursts, asset prices overshoot equilibrium on the way down. If the bubble is large enough, however, they will not recover. With a whole segment of the market productive small businesses losing control of the productive asset, the price of capital falls to Z, based on the marginal product of deep pockets (which falls to β 0 < α) as they are now the only producers and face declining marginal productivity). Assuming only productivity shocks, Kiyotaki and Moore (1997) ignore the possibility that overshooting might be severe enough to render the illiquid agents insolvent.

23 EC3115 :: L.18 : Financial crises - 23 / Models of externalities in the credit markets With bursting asset bubbles, however, the risk of widespread insolvency seems much more plausible. The region to the left of the solvency condition is labelled a Black Hole in the figure above by analogy with those regions of the cosmos where stars have collapsed and (almost) nothing can escape. You could alternatively modify this framework so that the borrowing is done by financial intermediaries, risk-neutral bankers who raise finance from households and invest in risky projects; and he shows how the externality involved can be thought of in terms of bankers under-valuing liquidity. Banks who think that in adverse conditions they can sell assets fail to realize that with correlated shocks these sales will help push prices down: a social planner would anticipate this and take on less risk.

24 EC3115 :: L.18 : Financial crises - 24 / Models of externalities in the credit markets Correlation of shocks The lesson is that when these idiosyncratic shocks become highly correlated crisis can occur totally endogenously. In advanced economies, the correlation commonly comes from co-movements in the value of the assets acquired by borrowers. In emerging market crises, the correlation often came from liability dollarisation. Because loans issued in local currency were not trusted ( original sin ), agents were constrained to borrow in dollars. A shock to the exchange rate would then generate a correlated shock.

25 EC3115 :: L.18 : Financial crises - 25 / Models of externalities in the credit markets Supply-side pro-cyclicality: endogenous risk premia Consider now the pro-cyclicality coming from balance-sheet pressures operating on the supply-side of the credit market. There is obvious potential for pro-cyclical behaviour of financial intermediaries who actively manage their balance sheet subject to a Value-at-Risk (VaR) constraint. The argument is essentially that a change in the market value of assets already held allows the leveraged financial sector to change its supply of loans by a multiple of the initial shock to its balance sheet. A positive shock to asset values, for example, will raise the equity proportion of the intermediary s balance sheet and reduce the leverage. To restore the profit-maximizing debt/equity ratio, the intermediary can take on additional debt and make additional loans.

26 EC3115 :: L.18 : Financial crises - 26 / Models of externalities in the credit markets Adrian and Shin (2010) Construct simplified balance sheets for various agents in the economy and explore their different balance sheet management behaviour, and the consequences of this behaviour. Leverage of a financial firm is typically procyclical. When the securities price goes up, the upward adjustment of leverage entails purchases of securities that are even larger than that for the case of constant leverage. If there is the possibility of feedback, then the adjustment of leverage and price changes will reinforce each other in an amplification of the financial cycle.

27 EC3115 :: L.18 : Financial crises - 27 / Models of externalities in the credit markets If financial markets are not perfectly liquid so that greater demand for the asset tends to put upward pressure on its price, then there is the potential for a feedback effect in which stronger balance sheets feed greater demand for the asset, which in turn raises the asset s price and lead to stronger balance sheets. The mechanism works exactly in reverse in downturns. If financial markets are not perfectly liquid so that greater supply of the asset tends to put downward pressure on its price, then there is the potential for a feedback effect in which weaker balance sheets lead to greater sales of the asset, which depresses the asset s price and lead to even weaker balance sheets.

28 EC3115 :: L.18 : Financial crises - 28 / Models of externalities in the credit markets Adrian and Shin (2010) a look at the data Using data drawn from the U.S. flow of funds accounts for the period ( ) Adrian and Shin (2010) find the following patterns: Households and non-financial firms. Passive balance sheet management increase in asset value not matched by increase in debt. Households counter-cyclical leverage ratio. Non-financial firms counter-cyclical-to-neutral leverage ratio. Financial intermediaries. Active balance sheet management increase in asset value matched by increase in debt. Commercial banks constant leverage ratio. Investment banks procyclical leverage ratio

29 EC3115 :: L.18 : Financial crises - 29 / Models of externalities in the credit markets Households passive balance sheets Increase in asset value not matched by increase in debt. Leverage falls.

30 EC3115 :: L.18 : Financial crises - 30 / Models of externalities in the credit markets Non-financial firms somewhat active balance sheets Increase in asset value partly matched by increase in debt. Leverage falls slightly.

31 EC3115 :: L.18 : Financial crises - 31 / Models of externalities in the credit markets Commercial banks active balance sheets Increase in asset value matched by increase in debt. Leverage approximately constant.

32 EC3115 :: L.18 : Financial crises - 32 / Models of externalities in the credit markets Investment banks and brokers very active balance sheets For security brokers and dealers (including investment banks), increase in asset value more than matched by increase in debt. Leverage rises.

33 EC3115 :: L.18 : Financial crises - 33 / Models of externalities in the credit markets Adrian, Moench and Shin (2010) As a consequence of the above behaviour, financial intermediaries that amplify real shocks in this fashion can lead to a boom/bust cycle. To show this, Adrian et al. (2010) indicate how active balance-sheet management can lead to a compression of the risk premium after a positive shock. The figure below shows how the price of risky assets is determined before the shock. On the horizontal axis is the amount of the risky asset, with valuations plotted on the vertical axis, where q is the expected pay-off, and p the market price. The straight line represents the demand schedule of a representative, mean variance, unlevered investor (measured from the right of the figure), while the kinked line is the demand schedule for VaR-constrained, active intermediaries (measured from the left)- with the convex portion of the schedule indicating where the VaR constraint is binding.

34 EC3115 :: L.18 : Financial crises - 34 / Models of externalities in the credit markets Determination of risk premium The equilibrium price is shown as p < q; and, in a one period setting, the expected yield from the risky security is given by r = q/p 1, referred to as the risk premium.

35 EC3115 :: L.18 : Financial crises - 35 / Models of externalities in the credit markets Effect of a positive shock to returns Risk premium falls in response to a positive shock to the fundamental of the risky security, as demand from both sectors is raised but there is an amplified response from the leveraged institutions as a result of marked-to-market gains on their balance sheets and (crucially) the balance sheet quantity adjustments entailed by it.

36 EC3115 :: L.18 : Financial crises - 36 / Models of externalities in the credit markets Boom and bust A way of capturing the seeds of a downturn in a balance sheet expansion by the financial sector is to assume that the quality improvement discussed above was mistaken. We can illustrate what happens when the mistake is realized, so that both schedules return to their original positions. The passive investors will of course suffer a capital loss, but the leveraged investors may well take a bigger hit, as shown in the figure below, leading to insolvency if mark-to-market losses exceed their equity base. Two possibilities are shown: first the extreme case where all leveraged investors go broke leaving assets solely in the hands of passive investors (with equilibrium shown on the left hand axis); the other (shown in the middle of the diagram) is where some of the leveraged investors have gone out of business.

37 EC3115 :: L.18 : Financial crises - 37 / Models of externalities in the credit markets Boom and Bust in Adrian-Moench-Shin (2010): mis-priced risky assets get corrected In both cases, we get a substantial collapse of asset prices relative to their starting level. (We assume there is no new entry when the asset prices go up; but there is exit when asset prices go down.)

38 EC3115 :: L.18 : Financial crises - 38 / The Diamond-Dybvig model Section 3 The Diamond-Dybvig model

39 EC3115 :: L.18 : Financial crises - 39 / The Diamond-Dybvig model The intuition Before we look more closely at the bank run model itself, let s consider a simple illustration. Suppose that financial market structure comprises a single bank and many depositors. The bank takes in deposits from depositors and invests prudently in (loans to) long term projects. As the bank s liabilities are short term while its assets are long term, this mismatch of maturity means that the bank is very likely to have a liquidity problem when a large enough number of depositors demand their money before the bank s long term assets mature. The example below shows that in this setup a bank run could indeed be an equilibrium outcome.

40 EC3115 :: L.18 : Financial crises - 40 / The Diamond-Dybvig model Assume that there are n depositors and each deposits 1 in the bank. Suppose that the maturity of deposits is one period. A depositor can earn (1 + i) at the end of period one if they stay with the bank for this period (where i is the deposit rate). Alternatively, if the depositor withdraws his funds before maturity, they can demand only the face value of 1. The bank has a reserve ratio of R < 1, and invests the rest of the deposited funds in long term projects with a maturity of one period and with sufficient returns to payoff all depositors. The bank can thus satisfy some liquidity demand before maturity, but if all depositors decide to withdraw before maturity, the bank has to liquidate its long term assets (with a liquidation value of 0 in our simple example).

41 EC3115 :: L.18 : Financial crises - 41 / The Diamond-Dybvig model This would generally not be sufficient to payoff all demand deposits and so the bank goes bankrupt in this case. In the simple case we will look at here, each depositor can only get back R < 1. The payoff matrix below looks at the behaviour of one depositor (say j) when all other depositors behaviour is given exogenously: All other depositors Withdraw Stay Depositor j Withdraw R, R 1, 1 + i Stay 0, R + R n i, 1 + i

42 EC3115 :: L.18 : Financial crises - 42 / The Diamond-Dybvig model The below matrix shows that there are two Nash equilibria: if all other depositors decide to withdraw before maturity, depositor j will withdraw; if all other depositors stay with the bank, depositor j will stay. The first equilibrium is a bank run and the second is Pareto efficient. All other depositors Withdraw Stay Depositor j Withdraw R, R 1, 1 + i Stay 0, R + R n i, 1 + i

43 EC3115 :: L.18 : Financial crises - 43 / The Diamond-Dybvig model Allen and Gale (2007) in more detail Now we turn to explore the Diamond-Dybvig (1983) model following the notation and exposition of Allen and Gale (2007). The Diamond-Dybvig framework characterises banks as socially efficient, but fragile institutions because there s a coordination problem among depositors. Uncertainty about preferences is one way of modelling the demand for liquidity. Assume a consumer has an endowment of one unit of good at date 0 and nothing at future dates: consumption is to take place in the future, at dates 1 and 2, but the consumer is uncertain at which date 1. Let λ be the probability of being an early consumer with preference U c 1, and 1 λ the probability of being a late consumer with preference U c 2. 1 A simple way of modelling the potential of a liquidity shock.

44 EC3115 :: L.18 : Financial crises - 44 / The Diamond-Dybvig model Using the above the expected utility is given by: E [U] = λu c 1 + (1 λ) U c2 One possible strategy (storage) for the consumer is to keep access to this endowment in either period 1 or period 2. Allows one unit of the good at date t to be converted into one unit at time t + 1. This is convenient, but not very productive. The alternative is a long asset (investment) is to give up access to endowment in period 1 so as to get higher return in period 2. Allows one unit of the good at date 0 to be converted into R > 1 units of the good at time 2. This is productive, but illiquid.

45 EC3115 :: L.18 : Financial crises - 45 / The Diamond-Dybvig model Other things being equal, the consumer will want to earn the highest return possible on his investments. But if he is uncertain about the timing of his consumption, we will also care about liquidity, the possibility of realizing the value of this asset at short notice. We can think of λ as measuring the degree of a consumer s liquidity preference. If λ is 1, the consumer s liquidity preference will be high, since he cannot wait until date 2 to earn the higher return on the long asset. If λ is 0, he will have no preference for liquidity, since he can hold the long asset without inconvenience. For λ between 0 and 1, the consumer s uncertainty about the timing of his consumption poses a problem.

46 EC3115 :: L.18 : Financial crises - 46 / The Diamond-Dybvig model If the consumer knew that he was a late consumer, he would invest in the long asset because it gives a higher return. If he knew that he was an early consumer, he would hold only the short asset in spite of its lower return. Since the consumer is uncertain about his type, he will regret holding the short asset if he turns out to be a late consumer and he will regret holding the long asset if he turns out to be an early consumer. The optimal portfolio for the consumer to hold will depend on both his risk aversion and his liquidity preference and on the return to the long asset (the slope of the yield curve). The higher return [on the long asset] can be interpreted as the reward for the inconvenience of holding illiquid assets and as a reflection of the greater productivity of roundabout methods of production.

47 EC3115 :: L.18 : Financial crises - 47 / The Diamond-Dybvig model Timeline in the Diamond-Dybvig model

48 EC3115 :: L.18 : Financial crises - 48 / The Diamond-Dybvig model Autarky (Robinson Crusoe) What should Robinson Crusoe do? Will surely depend on his tastes. These are rather special. Recall that his expected utility from the consumption stream c 1, c 2 is: E [U] = λu c 1 + (1 λ) U c2 Recall that he has an initial endowment of one unit of the good at date 0, and let θ be the fraction of the wealth invested in the short asset (and (1 θ) in the long asset). Then his consumption at date 1 is given by c 1 = θ whereas his consumption at date 2 is c 2 = θ + (1 θ) R

49 EC3115 :: L.18 : Financial crises - 49 / The Diamond-Dybvig model The consumer s decision problem is then to choose θ to maximize: E [U] = λu (θ) + (1 λ) U (θ + (1 θ) R) If there is an interior solution, the optimal value of θ satisfies: E [U] = λu (θ) + (1 λ) U (θ + (1 θ) R) (1 R) = 0 θ If we, for example, choose to use log-utility such that then the above FOC becomes: λ θ + U (c) = ln c 1 λ (1 R) = 0 θ + (1 θ) R θ = λr R 1

50 EC3115 :: L.18 : Financial crises - 50 / The Diamond-Dybvig model Autarky equilibrium: most likely (1,1) Point A represents storing everything. Point L represents investing everything. Shading shows all the consumption possibilities.

51 EC3115 :: L.18 : Financial crises - 51 / The Diamond-Dybvig model Risk pooling As we have seen already, the consumer s attempt to provide for his future consumption needs is bound to lead to regret as long as he cannot perfectly foresee his type. If he could ensure against his liquidity shock, he could do better. Suppose that there are a number of consumers on the island (but so far no bank), all of whom are ex-ante identical and subject to the same shock, that is, they all have a probability λ of being early consumers. If we assume further that their liquidity shocks are independent, then the law of large numbers assures us that there will be no aggregate uncertainty. Whatever happens to the individual consumer, the fraction of the total population who become early consumers will be λ for certain. This suggests the potential for pooling risks and providing a better combination of returns and liquidity.

52 EC3115 :: L.18 : Financial crises - 52 / The Diamond-Dybvig model The social planner Suppose a financial institution were to take charge of the problem of investing the endowments of a large number of consumers and providing for their consumption. The financial institution would take the endowments at date 0 and invest a fraction θ in the short asset and a fraction θ in the long asset. At date 1 it would provide consumption equal to c 1 units of the good to early consumers and at date 2 it would provide c 2 units of the good to late consumers. The important difference between the financial institution and the individual consumers is that the company faces no uncertainty: it knows for sure that a fraction λ of its clients will be early consumers. Consequently, it knows for sure what the demand for the consumption good will be at date 1 and date 2.

53 EC3115 :: L.18 : Financial crises - 53 / The Diamond-Dybvig model At date 1 it needs to provide λc 1 per capita and at date 2 it needs to provide (1 λ) c 2 per capita. Because the return to the short asset is lower than the return to the long asset, the financial institution will hold the minimum amount of the short asset it needs to provide for the early consumers consumption at date 1, that is, θ = λc 1 and it will hold the rest of the portfolio in the long asset. The company s decision problem is thus max λu c 1 + (1 λ) U c2 s.t. λc 1 = θ (1 λ) c 2 = (1 θ) R Substituting for c 1 and c 2 in the objective function gives: θ (1 θ) R λu + (1 λ) U λ 1 λ

54 EC3115 :: L.18 : Financial crises - 54 / The Diamond-Dybvig model The FOC for maximizing the above expression with respect to θ is: U c 1 U c 2 R = 0 U c 1 U c 2 = R Notice that the terms involving the liquidity preference parameter λ have cancelled out. In terms of the earlier example with log-utility, the FOC would imply that that: c 2 = c 1 R θ = λ

55 EC3115 :: L.18 : Financial crises - 55 / The Diamond-Dybvig model Market without intermediaries We can add the option of selling assets in order to realize their value in a liquid form. In fact, one of the main purposes of asset markets is to provide liquidity to agents who may be holding otherwise illiquid assets. Again suppose that there are a number of consumers on the island (but so far no bank), all of whom are ex-ante identical and subject to the same shock, that is, they all have a probability λ of being early consumers. They can do better than Crusoe on his own, as follows. Each can make investments in line with the identical population parameters (λ, 1 λ) (e. g. all invest half of the endowment if there is a 50% chance of being a late consumer).

56 EC3115 :: L.18 : Financial crises - 56 / The Diamond-Dybvig model Assume there is a market in which the consumer can switch between the short and long assets at one to one after he discovers his true type. Then, if he discovers that he is an early consumer, he can sell his holding of the long asset at the prevailing price and consume the proceeds. Earlier consumers can get 1 and late consumers get R by trading on learning their type, The portfolio choice at date 0 is irrelevant and thus expected utility is higher: E [U] = λu (1) + (1 λ) U (R)

57 EC3115 :: L.18 : Financial crises - 57 / The Diamond-Dybvig model Trading at the end of period 1 improves on autarky: see market equilibrium at N.

58 EC3115 :: L.18 : Financial crises - 58 / The Diamond-Dybvig model Complete markets Now consider an economy with markets for individual contingencies that would signal the correct value of each asset to the market, in particular the value of liquidity. Suppose at time zero there are contingent securities available so the consumer can purchase date 1 consumption at price q 1 if he is an early type and at q 2 if he is late. Note that these prices are measured in terms of the good at date 0. Assuming the implicit price of goods at date 2 in terms of goods at date 1 is p, the budget constraint for an individual at date 0 is: q 1 λc 1 + q 2 p (1 λ) c 2 1 The left hand side represents the present value (at date 0) of expected consumption (since there is no aggregate uncertainty, each individual only pays for the expected value of his demand for goods at each date).

59 EC3115 :: L.18 : Financial crises - 59 / The Diamond-Dybvig model With probability λ he demands c 1 units of date-1 consumption and the present value of λc 1 is q 1 λc 1. Similarly,with probability (1 λ) he demands c 2 units of date-2 consumption and the present value of (1 λ) c 2 is q 2 p (1 λ) c 2. The individual chooses a consumption bundle c 1, c 2 to maximize the expected utility: E [U] = λu c 1 + (1 λ) U c2 subject to the budget constraint: Forming the Lagrangean q 1 λc 1 + q 2 p (1 λ) c 2 1 = λu c 1 + (1 λ) U c2 + µ 1 q1 λc 1 q 2 p (1 λ) c 2 (where µ > 0).

60 EC3115 :: L.18 : Financial crises - 60 / The Diamond-Dybvig model Differentiating gives the FOCs: = λu c 1 µq1 λ µ = U c1 c 1 = (1 λ) U c 2 µq2 p (1 λ) µ = U c2 c 2 q 2 p Solving the above gives: U c 1 = U c2 q 1 q 2 p U c 1 U c 2 = q 1 q 2 p q 1

61 EC3115 :: L.18 : Financial crises - 61 / The Diamond-Dybvig model Since we assume that the investment technology exhibits constant returns to scale, the equilibrium prices must satisfy two no-arbitrage conditions. 1. To provide one unit of the good at date 1, it is necessary to invest 1 unit in the short asset at date 0. Thus, there are zero profits from investing in the short asset if and only if q 1 = Similarly, to provide one unit of the good at date 2, it is necessary to invest 1/R units in the long asset at date 0. Thus, there are zero profits from investing in the long asset if and only if q 2 p = 1/R. i.e. the Arrow prices are given by λ and (1 λ) /R. This implies that U c 1 U c 2 = R which is the condition required for efficient risk sharing.

62 EC3115 :: L.18 : Financial crises - 62 / The Diamond-Dybvig model The banking solution A bank,by pooling the depositors investments,can provide insurance against the preference shock and allow early consumers to share the higher returns of the long asset. The bank takes one unit from each agent at time 0 and invests it in a portfolio of x units of the short asset and y units of the long asset. Since the law of large numbers assures us that there will be no aggregate uncertainty, by exploiting it the bank offers each consumer a non-stochastic consumption profile, which can be interpreted as a deposit contract where the depositor has the right to withdraw either at date 1 or at date 2, but not both. Assume that, with free entry and competition, banks will maximize the ex-ante expected utility of the typical depositor subject to a zero-profit (feasibility) constraint. In fact, the bank is in exactly the same position as the social central planner discussed previously.

63 EC3115 :: L.18 : Financial crises - 63 / The Diamond-Dybvig model At date 0 the bank faces a budget constraint: x + y = 1 At date 1, the bank faces a budget constraint λc 1 y Recalling that it is never optimal to carry consumption over from date 1 to date 2 by holding the short asset, we can write the budget constraint for the bank at the date 2 as: (1 λ) c 2 Rx So the bank will maximize: E [U] = λu c 1 + (1 λ) U c2 subject to constraints: x + y 1 at date 0 λc 1 y at date 1 (1 λ) c 2 Rx at date 2

64 EC3115 :: L.18 : Financial crises - 64 / The Diamond-Dybvig model Assuming the latter two constraints are satisfied with equality, the problem can be written to choose c 1 and c 2 to max the Lagrangean: = λu c 1 + (1 λ) U c2 µ 1 y x = λu c 1 + (1 λ) U c2 µ 1 λc 1 As seen above, for µ > 0 this implies U c 1 U c 2 = R 1 λ c 2 Note that U c 1 = RU c2 implies that c1 c 2 as R > 1 and U c i < 0. Hence the solution to this problem achieves the first-best allocation for consumers, just like a social planner who maximizes λu c 1 + (1 λ) U c2 subject to the resource constraint that (1 λ) c 2 = R 1 λc 1. R

65 EC3115 :: L.18 : Financial crises - 65 / The Diamond-Dybvig model Banking solution: competitive banking Note that the set of possible contracts, shown below as the Banks No-profit Constraint, is obtained as: (1 λ) c 2 R 1 λc 1 = 0 c 2 = R 1 λc 1 1 λ The Competitive Equilibrium (C) will be where the expected utility curves are tangent to this constraint, and represents the demand for liquidity insurance at the fair odds price. The Offer Curve shows what depositors would like at different prices for liquidity.

66 EC3115 :: L.18 : Financial crises - 66 / The Diamond-Dybvig model Competitive banking is inter-temporally efficient, i.e. U c 1 = RU c 2

67 EC3115 :: L.18 : Financial crises - 67 / The Diamond-Dybvig model Bank runs Suppose that c 1, c 2 is the optimal deposit contract and x, y is the optimal portfolio for the bank. In the absence of aggregate uncertainty, the portfolio x, y provides just the right amount of liquidity at each date assuming that the early consumers are the only ones to withdraw at date 1 and the late consumers all withdraw at date 2. This is an equilibrium in the sense that the bank is maximizing its objective, the welfare of the typical depositor, and the early and late consumers are timing their withdrawals to maximize their consumption. So far, we have treated the long asset as completely illiquid: there is no way that it can be converted into consumption at date 1. Suppose, instead, that there exists a liquidation process, so that if the long-term asset is liquidated prematurely at date 1, one unit of the long asset yields r 1 units of the good.

68 EC3115 :: L.18 : Financial crises - 68 / The Diamond-Dybvig model Under the assumption that the long asset can be prematurely liquidated, with a loss of (R r) per unit, there exists another equilibrium if we also assume that the bank is required to liquidate whatever assets it has in order to meet the demands of the consumers who withdraw at date 1. To see this, suppose that all depositors,whether they are early or late consumers,decide to withdraw at date 1. The liquidated value of the bank s assets at date 1 is r x + y x + y = 1 so the bank cannot possibly pay all of its depositors more than one unit at date 1. In the event that c 1 > r x + y, the bank is insolvent and will be able to pay only a fraction of the promised amount.

69 EC3115 :: L.18 : Financial crises - 69 / The Diamond-Dybvig model Because all assets will be used up trying to pay those who withdraw at period 1, anyone who waits for second period will get nothing. Given a late consumer thinks all others will withdraw, it is optimal for him to withdraw at date 1 and save the proceeds until date 2. Thus, bank runs are an equilibrium phenomenon. The rows in the matrix below correspond to the decision of an individual late consumer and the columns to the decision of all the other late consumers. All other late consumers Run No run One late customer Run No run r x + y, r x + y 0, r x + y c1, c 2 c2, c 2

70 EC3115 :: L.18 : Financial crises - 70 / The Diamond-Dybvig model Note: this is not a 2 2 game; the choice of column represents the actions of all but one late consumer. The ordered pairs are the payoffs for the distinguished late consumer (the first element) and the typical late consumer (the second element). It is clear that if c 2 > c 1 > r x + y > 0, then there are two equilibria of this coordination game. One is socially efficient, one is a failure to coordinate expectations: All other late consumers Run No run One late customer Run No run r x + y, r x + y 0, r x + y c1, c 2 (c 2, c 2 )

71 EC3115 :: L.18 : Financial crises - 71 / The Diamond-Dybvig model Liquidity preference various equilibria A. Autarky B. Market equilibrium without contingent contracts and canking equilibrium with log preferences C. Banking equilibrium with extreme risk aversion Note: banking equilibria are drawn for λ = 0.5 and assume no bank run. But the efficiency property U c 1 /U c 2 = R is independent of λ.

72 EC3115 :: L.18 : Financial crises - 72 / The Diamond-Dybvig model Avoiding bank runs 1. Lender of last resort (as implemented by the Bank of England). In 1873 Walter Bagehot laid out three principles for central bank intervention: a). Lend freely at a penalty rate against good collateral. b). Value assets at between panic and pre-panic values. c). Institutions without good collateral should be allowed to fail. 2. Deposit Insurance. The was no central bank in the US from 1836 until after a succession of bank panics the Federal Reserve System was established in The banking panic of 1933 led to the Glass-Steagall Act of that year, which introduced Deposit Insurance and required the separation of commercial and investment banking operations. (The FDIC was set up in 1934.)

73 EC3115 :: L.18 : Financial crises - 73 / The Diamond-Dybvig model Avoiding bank runs (cont.) 3. Suspension of convertibility ( Bank holiday ). If banks refuse to allow depositors to withdraw, once the proportion of withdrawals is equal to the proportion of early consumers, then late consumers will not have an incentive to withdraw. In the 1930s some US States ordered the closure of banks until panic was over. 4. Interbank market. Banks borrow from each other to meet withdrawals. Can absorb some mild shocks to individual institutions but cannot resolve systemic panic. 5. Narrow banking. Hold more liquidity so as to meet bank runs implies providing less liquidity insurance than regular fractional banking.

74 EC3115 :: L.18 : Financial crises - 74 / The Hellman-Murdock-Stiglitz model Section 4 The Hellman-Murdock-Stiglitz model

75 EC3115 :: L.18 : Financial crises - 75 / The Hellman-Murdock-Stiglitz model The intuition Let s now consider the possibility that instead of investing in loans for small and medium enterprises or for households, banks might take on riskier bets, e.g. by mergers and acquisitions. (That is, they may gamble.) Typically gambling leads to ruin... but what if losses are borne by someone else? Why would bankers gamble? Answer: incentives. If banks can take on risk where the owner/manager keeps the upside (profit) of the gamble, but does not have to pay the downside (loss), then there will be an economic incentive to gamble (take on extra risk). In practical terms, think of bonuses for executives that are paid in good times when positive payoffs received; but not clawed back when losses occur. Think also of limited liability for corporations, so shareholders can get a share of big profits in good times but their liability to losses is limited (to their initial investment).

76 EC3115 :: L.18 : Financial crises - 76 / The Hellman-Murdock-Stiglitz model Thus we come to the question of prudential regulation of banks. As bank deposits are assumed to be insured, depositors themselves have no incentive to monitor the use of their funds. How do HMS (2000) derive the minimum prudential capital requirement needed to stop gambling? 1. First, consider the capacity of prudent banks to pay interest, and how it declines as they have to put more equity into the business. 2. Then look at the pressure that competition will put on banks to gamble, by seeing how much a gambling bank can pay as interest. 3. If banks can pay higher interest by gambling than by investing prudently, it is assumed that they will choose to do so or, if not, that they are taken over by others who will! 4. Finally, see how increasing equity requirements can tip the scales against gambling - because it forces the owner/managers to put their own skin in the game.

77 EC3115 :: L.18 : Financial crises - 77 / The Hellman-Murdock-Stiglitz model First: prudent investing Assuming each bank operates with 1 unit of depositors funds and k units of their own money, and invests 1 + k units in a prudent asset yielding a gross return of α, then the per period profits when the bank invests in the prudent asset is π P = α (1 + k) ρk r where ρ is the opportunity cost of own funds (with ρ > α) and r is the gross interest paid to depositors i.e. one plus the usual deposit rate. In a zero profit competitive equilibrium, setting π P = 0 one finds the interest rate consistent with prudent investment will be: r P = α (1 + k) ρk Assuming assuming ρ > α, this will decline with the capital requirement k.

78 EC3115 :: L.18 : Financial crises - 78 / The Hellman-Murdock-Stiglitz model Next: gambling in HMS model What about the competitive pressure to pay high rates? HMS show that, in the absence of capital requirements, all banks will gamble; but that prudential requirements which force banks to bear some of the downside risk tend to reduce gambling. They also show how deposit rate ceilings can increase franchise value and check gambling. Consider an alternative, risky investment which pays γ > α in the good state and 0 in the bad state, where θ, the probability of the good state, is low enough so that the expected return is less than on the safe asset. Switching resources to this use is clearly socially inefficient. But the temptation to do this arises because banks (go bankrupt and) write off losses in the bad state.

79 EC3115 :: L.18 : Financial crises - 79 / The Hellman-Murdock-Stiglitz model For low k, the gambling return, calculated as π G = θ γ (1 + k) r ρk exceeds the return available by investing in the safe asset and the interest rate paid becomes ρ r G = γ (1 + k) k θ But as banks that gamble and fail are closed down, this high interest rate will only be paid if the gamble succeeds. So in the terminology of Akerlof and Shiller the bank is phishing for phools (if deposits are insured, the taxpayer will have to pay.)

80 EC3115 :: L.18 : Financial crises - 80 / The Hellman-Murdock-Stiglitz model Finally: No Gambling Condition for competitive banks The No Gambling Condition, NGC, requires that the bank make less expected profit in gambling than by acting prudently. Where the two schedules intersect defines the minimum capital adequacy ratio. This is designed to stop gambling by forcing the owner/manager to absorb the losses incurred by gambling and not pass them on to other parties. For k k, the fact that gambling banks can afford to offer higher interest rates indicates the incentive to gamble if capital requirements are too low.

81 EC3115 :: L.18 : Financial crises - 81 / The Hellman-Murdock-Stiglitz model Minimum capital adequacy ratio (assuming banks are competitive) See the line labelled r P in the below:

82 EC3115 :: L.18 : Financial crises - 82 / The Hellman-Murdock-Stiglitz model Social costs of gambling banks Incentive effects are important for domestic financial systems. Assume that monitoring the banks is costly; and that the prudential capital ratio is too low to stop gambling. Then, if all banks behave alike, the (expected) social costs are the misallocation of resources invested throughout the entire banking system, measured by the excess of the return on the prudent asset over the risky alternative times the resources involved. If banks are competitive they will not bear this cost: it will either fall on the deposit insurance corporation or be funded by a transfer from taxpayers required to bail out the banks.

83 EC3115 :: L.18 : Financial crises - 83 / The Hellman-Murdock-Stiglitz model Hellman, Murdock & Stiglitz (2000) in more detail A model of deposit insurance, capital requirements and banking franchise value. HMS (2000) construct a dynamic model to consider the effect of competition in the banking industry with and without deposit insurance. They show that, under limited liability, intense competition induces banks to invest in risky assets. Assumptions Risk neutral banks compete a la Bertrand in the deposit market. Banks set deposit rate r, and each receives insured deposits D. 0 < k < 1 is the capital ratio per unit of deposits. Sequence of events in one period: Deposit mobilisation. Asset allocation: investing in safe or risky project. Realisation of returns from project. Monitoring by regulatory agency.

84 EC3115 :: L.18 : Financial crises - 84 / The Hellman-Murdock-Stiglitz model Model setup N banks operate for T periods. Each period every bank i N offers interest rate r i while other banks offer interest rates r i (r i is a vector composed of N 1 elements). As a result, bank i receives an amount of deposits equal to D r i, r i, where D ( ) is increasing in r i and decreasing in r i. The volume of deposits depends only on the rate offered and not on the probability that banks are able to repay the deposits, because depositors are insured. A bank has two alternatives uses for the funds raised with the deposits. The bank can invest in a prudent asset with return α, or in a risky asset that returns γ with probability θ and returns 0 with probability 1 θ, where γ > α > θγ.

85 EC3115 :: L.18 : Financial crises - 85 / The Hellman-Murdock-Stiglitz model If the risky asset is chosen and the return happens to be 0, the bank fails and the license to run the bank is taken away by the regulator. When a bank loses its license, it loses its franchise value (= discounted value of future profits), but bank stakeholders get to keep the part of their capital that they did not invest in the bank (= owners enjoy limited liability).

86 EC3115 :: L.18 : Financial crises - 86 / The Hellman-Murdock-Stiglitz model Initial funds: Deposits D r i, r i ri, r i Capital requirement k (per unit deposit). Total funds: (1 + k) D r i, r i Opportunity cost of bank s own capital ρ (per unit deposit). k is exogenously given determined by the regulatory regime.

87 EC3115 :: L.18 : Financial crises - 87 / The Hellman-Murdock-Stiglitz model Investment projects: Assumptions: Returns Good state Bad state Safe (prudent) α α Risky (gamble) γ 0 Probability θ 1 θ Risky project is attractive: γ > α But it worse than the safe project on average: Bank s own capital is costly: θγ + (1 θ) 0 = θγ < α ρ > α

88 EC3115 :: L.18 : Financial crises - 88 / The Hellman-Murdock-Stiglitz model Expected profits per period (risk neutral banks): Return from prudent investment for banks invested in the safe project (given the deposit rate r): π P = α (1 + k) r i ρk D r i, r i Note that we have1 + k because banks use own capital k plus 1 unit of deposit funds. Expected return from gambling for bank invested in the risky project (given the deposit rate r): π G = θ γ (1 + k) r i ρk D r i, r i + (1 θ) ρk D ri, r i = θ γ (1 + k) r i ρk D ri, r i

89 EC3115 :: L.18 : Financial crises - 89 / The Hellman-Murdock-Stiglitz model Mechanics of the model Each bank chooses its best deposit rates, given its investment and other banks rates. Banks will thus choose strategies corresponding to the infinitely repeated static Nash equilibrium. The timing of the stage game works as follows: Banks simultaneously choose their own level of capital and offer a deposit rate. Depositors then choose the bank in which to place their funds. Banks then choose their asset portfolio. Finally, returns are realized, and the regulator inspects the balance sheet of the bank. Symmetric Nash equilibrium: dπ P dr i = dπ G dr i = 0 r i=r i

90 EC3115 :: L.18 : Financial crises - 90 / The Hellman-Murdock-Stiglitz model Best responses: Prudent bank: Gambling bank: r P (k) = ɛ α (1 + k) ρk 1 + ɛ r G (k) = γ (1 + k) ρk θ ɛ 1 + ɛ Interest elasticity of deposit: ɛ = d ln D d ln r i = r i D dd dr i Perfect competition ɛ

91 EC3115 :: L.18 : Financial crises - 91 / The Hellman-Murdock-Stiglitz model Deposit rates and capital requirements under perfect competition

92 EC3115 :: L.18 : Financial crises - 92 / The Hellman-Murdock-Stiglitz model Asset allocation Value function (present discounted profits, δ is the discount factor) For prudent banks: For gambling banks: V P = V G = t=0 δ t π P = π P 1 δ t=0 δ t θ t π G = π G 1 δθ where we note that the discount factor on the gambling asset is effectively δθ as the bank only earns π G in period t if the gambling assets of previous periods returned γ (i.e. the bank never failed before that period and thus continued to exist with probability θ in every period).

93 EC3115 :: L.18 : Financial crises - 93 / The Hellman-Murdock-Stiglitz model No gambling condition For it to be optimal for banks to stay prudent, we must have: π P V P = 1 δ π G 1 δθ = V G πp (1 δθ) π G 1 δ πp (1 δθ) π P π G π P 1 δ (1 δθ) V P (1 δ) V P π G π P (1 θ) δv P }{{} loss of franchise value π G π P }{{} one period gain from gambling The interpretation of the above is that the current gain from deviating from the prudent strategy to a gambling one must be below the present value of the franchise value that will be lost in the next period should the gamble fail. That is why we discount V P by the one-period discount factor δ (0, 1], an event that occurs with probability 1 θ.

94 EC3115 :: L.18 : Financial crises - 94 / The Hellman-Murdock-Stiglitz model No gambling threshold deposit interest rate From the above we can derive a threshold level of the deposit interest rest, showing the border between gambling and no-gambling, with the property that for any deposit rate r less that or equal to this threshold value ˆr (k), the bank will choose the prudent strategy: πp π G π P (1 θ) δv P = (1 θ) δ 1 δ δ (1 θ) π G 1 + π P 1 δ θ γ (1 + k) r ρk }{{} =π G θ γ (1 + k) r ρk α (1 + k) r ρk δ (1 θ) 1 + }{{} 1 δ =π P α (1 + k) r ρk 1 δθ 1 δ

95 EC3115 :: L.18 : Financial crises - 95 / The Hellman-Murdock-Stiglitz model θγ (1 + k) θ r ρk α (1 + k) r ρk 1 δθ 1 δ (1 δ) θγ (1 + k) (1 δθ) α (1 + k) (1 δ) θ r (1 δ) ρk (1 δθ) r (1 δθ) ρk r (1 δθ (1 δ) θ) (1 δθ) α (1 + k) ρk (1 δ) θγ (1 + k) + (1 δ) ρk r (1 θ) α (1 + k) δθα (1 + k) ρk + +δθρk (1 δ) θγ (1 + k) + (1 δ) ρk r (1 θ) α (1 + k) δθα (1 + k) ρk (1 δθ 1 + δ) (1 δ) θγ (1 + k) + (1 δ) α (1 + k) (1 δ) α (1 + k)

96 EC3115 :: L.18 : Financial crises - 96 / The Hellman-Murdock-Stiglitz model r (1 θ) (1 δ) (1 + k) α θγ δ (1 θ) ρk + δ (1 θ) α (1 + k) which reduces to: α θγ r ˆr (k) (1 δ) (1 + k) + δ α (1 + k) ρk 1 θ Note that the above function r slopes up for δ close to 1. When the bank is farsighted (as δ 1), the bank can pay out a deposit interest rate that approaches the bank s net return on assets α (1 + k) ρk and still choose to invest in the prudent asset. This is sensible because as δ 1 the bank only cares about average per-period returns, so the bank would never engage in a gambling activity that returns a finite positive one-period rent at the risk of losing all future returns. Once the bank is less than perfectly farsighted, however, the bank must earn a sufficiently large positive profit each period so that its franchise value at risk is greater than the expected returns from gambling.

97 EC3115 :: L.18 : Financial crises - 97 / The Hellman-Murdock-Stiglitz model Minimum capital adequacy ratio (with and without deposit rate ceiling)

98 EC3115 :: L.18 : Financial crises - 98 / The Hellman-Murdock-Stiglitz model Minimum capital requirements under perfect competition (ɛ ) No gambling threshold level of deposit rate is shown as the schedule labelled r, NGC in the figure above (which slopes up for high i.e. for sufficiently myopic banks). Where the two schedules intersect defines the minimum capital adequacy ratio. For k k as competition drives the rates up to r G banks will find it more profitable to gamble. k = k : ˆr (k) = r P (k) θ γ α r = (1 θ) θ γ α, k = r α α

99 EC3115 :: L.18 : Financial crises - 99 / The Hellman-Murdock-Stiglitz model Effect of premature liberalization Assume initially that there is a capital requirement of k 0 < k but the quality of bank portfolio is maintained by the imposition of a deposit rate ceiling r 0 (see point I in the figure below). The franchise value so generated is sufficient to prevent gambling. If the deposit rate ceiling is abolished without increasing the capital requirement, there will be gambling as r k 0 < rg. Note that the credible announcement of future liberalisation can trigger gambling even with a deposit rate ceiling in place. As T goes to infinity, this converges to the HMS s standard NGC but as T tends to one, the NGC becomes steeper.

100 EC3115 :: L.18 : Financial crises / The Hellman-Murdock-Stiglitz model So we have: Pre-liberalization: capital requirement + regulation Q k < k and r r 0 Post-liberalization: perfect competition (capital requirement but no regulation Q) π P = π G = 0 Assume that at time t = 0, it is announced that liberalisation will take place in period T and that it is fully credible. This will immediately reduces franchise values, and they will fall steadily towards zero as the date of liberalisation gets closer.

101 EC3115 :: L.18 : Financial crises / The Hellman-Murdock-Stiglitz model Pre-announced liberalization The revised time-dependent NGC can be written: where T 1 V L P = t=0 π G π P = (1 θ) δ 1 δ T 1 V P δ t π P δ t π P = V P δ T 1 V P = t=t 1 δ T 1 V P }{{} reduced franchise value so π G π P (1 θ) δ 1 δ T 1 V P r ˆr (k) 1 ˆr (k) δ T 1 δ T α (1 + k) ρk so the NGC swivels down as the period of pre-announcement shortens. Therefore, ˆr (k) rotates anti-clock-wise around (k, r ) relative to ˆr (k).

102 EC3115 :: L.18 : Financial crises / The Hellman-Murdock-Stiglitz model The effect of announcing future liberalisation

103 EC3115 :: L.18 : Financial crises / The Hellman-Murdock-Stiglitz model In the case shown in the figure above, the initial jump in NGC when future liberalisation is announced does not trigger gambling. But, as time passes, the NGC swivels downward and gambling will commence before liberalisation takes place. With shorter pre-announcement, gambling might even take place simultaneously with the announcement. Area between the old and the new NGC in the bottom left corner indicates that policy which would ensure prudent behaviour without liberalisation now becomes destabilising. Note also that for δ < 1, r A (0) < r (0) and r A (k ) = r (k ) where k is minimum capital requirement to prevent gambling in the absence of deposit ceiling.

104 EC3115 :: L.18 : Financial crises / The Hellman-Murdock-Stiglitz model Note: To find min value of k to stop gambling with competition: π G = 0 implies r G = γ (1 + k) k ρ θ π P = 0 implies r P = α (1 + k) ρk set r G = r P and solve for k as follows: ρ γ (1 + k) k = α (1 + k) ρk θ ρ γ α (1 + k) = θ ρ k ρ γ α = θ ρ + α γ k k = γ α ρ ρ + α γ θ

105 EC3115 :: L.18 : Financial crises / The Hellman-Murdock-Stiglitz model Regulations Two regulations are potential candidates to solve this market failure. 1. Minimum capital requirements: banks are required to invest an amount of their own capital that cannot be smaller than a set share of the deposits; 2. Deposit-rate controls: a cap on the interest rate that banks can offer. The argument in favor of minimum capital requirements seems intuitive. The more capital, the more skin in the game or the more of the cost of gambling or downside risk is borne by the bank, inducing prudent behavior. This capital-at-stake effect should therefore induce no-gambling. It turns out that this is not necessarily true. If investing the capital of the bank shareholders was a profitable choice, minimum capital requirements would be ineffective.

106 EC3115 :: L.18 : Financial crises / The Hellman-Murdock-Stiglitz model Minimum capital requirements are effective only if bank shareholders have alternative uses of capital that return on average more than α. In this case, minimum capital requirements reduce current and future profits and hence reduce the franchise value. A reduced franchise value in turn reduces the incentive to choose the prudent asset. Therefore either minimum capital requirements have no effects on the investment choice, or have two effects on the choice of investment and these two effects go in opposite directions. Deposit-rate controls are instead a way to curb the effect of competition for deposits. Deposit-rate controls increase the franchise value (I) and increase the expected payoff from a prudent investment more than they increase the payoff from a gambling investment (II). Both effect (I) and (II) ensure that the no gambling condition is satisfied by a larger set of parameters.

107 EC3115 :: L.18 : Financial crises / Claudio Borio modelling and policy suggestions Section 5 Claudio Borio modelling and policy suggestions

108 EC3115 :: L.18 : Financial crises / Claudio Borio modelling and policy suggestions The financial cycle: analytical challenges Analytically, modelling the financial cycle requires capturing three key features. 1. The booms should not just precede but cause the busts: busts are fundamentally endogenous, the result of the vulnerabilities and distortions built up during the boom. 2. The busts should generate debt and capital stock overhangs the natural legacy of the preceding unsustainable expansion. 3. And potential output should not just be identified with non-inflationary output: as the previous evidence indicates, output may be on an unsustainable trajectory even if inflation is stable.

109 EC3115 :: L.18 : Financial crises / Claudio Borio modelling and policy suggestions How could one best capture these features? Most likely, one would need to: Drop rational (model-consistent) expectations. Allow for state-varying risk tolerance, ie. for attitudes towards risk that vary with the state of the economy, wealth, and balance sheets. And last but not least, capture more deeply the monetary nature of our economies: the banking sector does not just allocate given resources but creates purchasing power out of thin air. In all probability, all this may require us to rediscover the merits of disequilibrium analysis.

110 EC3115 :: L.18 : Financial crises / Claudio Borio modelling and policy suggestions The financial cycle: policy challenges Dealing with the financial crisis calls for policies that are more symmetrical across booms and busts. Policies need to lean against the booms and tackle the debt-asset quality problems head on during the bust. A medium-term focus is essential. During the boom, the key question is how to address the build-up of financial imbalances. For prudential policy, it means containing the procyclicality of the financial system through macroprudential measures (Borio 2009). For fiscal policy, it means extra prudence, fully recognising the hugely flattering effect of financial booms on the fiscal accounts: potential output and growth are overestimated; financial booms are tax revenue-rich; large contingent liabilities needed to address the bust. For monetary policy, it means leaning against the build-up of financial imbalances even if short-term inflation remains subdued.

111 EC3115 :: L.18 : Financial crises / Claudio Borio modelling and policy suggestions During the bust, the key question is how to address the balance-sheet recession that follows, ie. how to prevent a stock problem from becoming a persistent and serious flow problem, in the form of anaemic output and expenditures. After having stabilised the system (crisis management phase), it is necessary to move swiftly to tackle the over-indebtedness and asset-quality problems head on (crisis resolution phase). The crisis resolution phase is critical and less well understood. For prudential policy, it means repairing banks balance sheets aggressively through the full recognition of losses, asset disposals, recapitalisations subject to strict conditionality, and the reduction of operational excess capacity necessary for sustainable profitability. This is what the Nordic countries did and what Japan failed to do following the bust in their respective financial cycles in the early 1990s; it is what partly explains their subsequent divergent economic performance.

112 EC3115 :: L.18 : Financial crises / Claudio Borio modelling and policy suggestions For fiscal policy, it means creating the fiscal space needed to use the sovereign s balance sheet to support private-sector balance-sheet repair while avoiding a sovereign crisis down the road. This can be done through bank recapitalisations, including via temporary public-sector ownership and selective debt relief for the non-financial sector (eg. households). In fact, contrary to received wisdom, pump-priming where it can be afforded may well be less effective in a balance-sheet recession, as agents tend to save the extra money to repay debt, resulting in a low multiplier. By contrast, by relieving debt burdens and asset-quality problems, the alternative use of fiscal space could set the basis for a self-sustaining recovery.

113 EC3115 :: L.18 : Financial crises / Claudio Borio modelling and policy suggestions For monetary policy, it means recognising its limitations and avoiding overburdening it. Monetary tools are blunt when overindebted sectors are unwilling to borrow, and banking system strains impair the transmission chain. As a result, when policymakers press harder on the gas pedal, the engine revs up without traction. Over time, this enhances any side effects that policy may have. These include the possibility of delaying balance-sheet adjustment, such as by facilitating evergreening; of undermining the profitability of banks, by compressing interest margins; of masking market signals; and of raising political-economy concerns, not least because of the quasi-fiscal nature of the large-scale deployment of central bank balance sheets. The risk is that policies that do not address aggressively the balance-sheet problems can buy time but also make it easier to waste it. This can prolong weakness and delay a strong, self-sustaining recovery. It is as if the economy operated in a state of suspended animation.

114 EC3115 :: L.18 : Financial crises / Claudio Borio modelling and policy suggestions The longer-term risk is that policies that fail to recognise the financial cycle will be too asymmetric and generate a serious bias over time. Failing to tighten policy in a financial boom but facing strong, if not overwhelming, incentives to loosen it during the bust would erode both the economy s defences and the authorities room for manoeuvre. In the end, policymakers would be left with a much bigger problem on their hands and without the ammunition to deal with it a new form of time inconsistency. The root causes here are horizons that are too short and a failure to appreciate the cumulative impact of flows on stocks. This could entrench instability in the system over successive cycles.

115 EC3115 :: L.18 : Financial crises / Claudio Borio modelling and policy suggestions Cure: addressing the bust What if unable to build up buffers and constrain the boom sufficiently? Need to address its legacy: a balance sheet recession (capital stock and debt overhangs; possibly a banking crisis). Key issue. Prevent a major stock problem from becoming a major and persistent flow problem (weak expenditures and output). Constraint 1: Room for manoeuvre is very limited. Buffers depleted. Constraint 2: Effectiveness of tools is limited. Not just because of tighter credit-supply constraints. But even more important credit-demand constraints. No-one wishes to borrow: agents give priority to debt reduction (MP and FP are less effective). Excessive capital weighs down on investment.

116 EC3115 :: L.18 : Financial crises / Claudio Borio modelling and policy suggestions Cure: crisis management and resolution Distinguish. Crisis management: prevent implosion of system. Crisis resolution: establish basis for self-sustained recovery. Should move swiftly from the first to the second. Crisis management. Priority is to shore up confidence. Aggressive MP is key (interest rates, liquidity, etc). Where necessary, provide (short-term) public guarantees. Crisis resolution. Priority is balance-sheet repair. Address debt overhang/asset quality nexus. Recognise the limitations of traditional countercyclical MP and FP. Buy time but make it easier to waste it. Risk bigger problems down the road.

117 EC3115 :: L.18 : Financial crises / Claudio Borio modelling and policy suggestions Cure: policies for crisis resolution Prudential policy. Ensure full loss recognition. Recapitalise financial institutions. Promote removal of excess capacity in financial sector. Fiscal policy. Make room to shore up private-sector balance sheets. Calls for substitution of public for private-sector debt (eg, debt relief). Buck for buck much better use of public money than pump-priming. Monetary policy. Recognise unintended side-effects of (interest-rate and balance-sheet policy), which can Mask underling balance-sheet weaknesses/delay loss recognition. Numb incentives to reduce excess supply in financial sector and encourage wrong risk-taking. Undermine earnings capacity of financial sector. Atrophy financial markets as central bank takes over intermediation.

118 EC3115 :: L.18 : Financial crises / Claudio Borio modelling and policy suggestions Limitations of policies: evidence? Recent preliminary empirical evidence. Financial bust/balance-sheet recessions are indeed different. Approach: 24 countries since mid-1960s; 73 recessions; 29 financial crises. Distinguish recessions (downturns) without and with financial crises. Control for various factors (severity downturn, etc). Findings: traditional macroeconomic policies are less effective. In normal recessions, the more accommodative monetary policy in the downturn, the stronger the subsequent recovery. but this relationship is no longer apparent if a financial crisis occurs (Graph a,b). Similar results for fiscal policy. And in recessions with financial crises, in contrast to normal ones, the faster the debt reduction in the downturn, the stronger the subsequent recovery.

119 EC3115 :: L.18 : Financial crises / Claudio Borio modelling and policy suggestions Graph a: monetary policy is less effective in financial-crisis downturns

120 EC3115 :: L.18 : Financial crises / Claudio Borio modelling and policy suggestions Graph b: monetary policy is less effective in financial-crisis downturns