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Avoiding costly default with state-contingent contracts:

issues of market power and moral hazard

Marcus Miller and Lei Zhang

Houblon Norman Fellows at the Bank of England1* December, 2013

Abstract

To reduce the severity of sovereign debt problems, the CIEPR report on Revisiting Sovereign Bankruptcy advocates statutory change. The focus of recent proposals from economists at the Bank of England and the Bank of Canada, however, is on promoting contractual innovations, the issuance of state-contingent securities in particular.

In this paper, where Stone-Geary preferences are used to capture ‗inability to pay‘, we discuss how the maturity-extension clauses of ‗sovereign cocos‘ can support the competitive equilibrium for solvent but illiquid debtors. But if the status quo is advantageous to powerful creditors, is this not an innovation they will resist?

Secondly, we analyse the proposal for GDP bonds in terms of ―completing the market‖ by adding Arrow securities. When debtor moral hazard is introduced, however, a puzzle emerges: how to price such securities if ‗hidden actions‘ by the debtor can change state probabilities?

*The views expressed here are those of the authors and do not represent those of the Bank or the Monetary Policy Committee.

1 For comments and discussion, we thank Ken Binmore, Martin Brooke, Oliver Bush, Alex Pienkowski and Dania Thomas, but remain responsible for the views expressed and errors made; and we are grateful to Efthymia Mantellou for research assistance, funded by ESRC/CAGE.

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2 ―If debt contracts embodied more risk-sharing between debtors and creditors, or were

written in ways that made countries less vulnerable to rollover crises or exchange rate movements, debt crises would be both less frequent and less severe.

Sturzenegger and Zettelmeyer (2006)

1 Introduction

According to Revisiting Sovereign Bankruptcy, co-written by lawyers and economists and issued by Brookings, there are three reasons why sovereign debt problems have become more salient over the last decade. First because they are no longer confined to emerging markets, but involve North Atlantic economies too – especially in the Euro area; second because the use of debt swaps may be jeopardised by the recent US court ruling giving ‗holdout creditors‘ the right to interfere with payments to those that have accepted a debt swap; and finally because distorted incentives and/or policy mistakes lead to ‗overborrowing‘ ex ante. Such factors, they conclude, ‗create a much stronger case for an orderly sovereign bankruptcy regime than ten years ago‘ CIEPR (2013).

But what if – to strike a more optimistic note – crises are a spur for financial innovation? This is the perspective taken in Brooke et al. (2013) ―Sovereign default and State-Contingent Debt,‖ a Financial Stability Paper No. 27, co-authored by economists at the Bank of England and Bank of Canada which studies contractual changes that may help avoid costly default. They are quick to concede that experience of EMEs shows evidence of the high costs of sovereign default, including substantial deadweight losses. In fact, they cite evidence that‘ sovereign debt crises in EMEs have led to median output losses of at least 5% in levels terms‘, De Paoli et al. (2009); and, since these periods of low growth seem last for about a decade, it would appear that the output cost of crisis cumulate to about one fifth of one year‘s GDP.

They also claim, however, that the contractual nature of sovereign debt and of procedures for crisis resolution have evolved in response: this is shown in Table 1, where the last line refers to innovations proposed by the authors.

Date Event Subsequent Development

1980s Latin American Debt Crisis Baker Plan for liquidity provision/ Brady swap for debt relief

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3 2001/2002 Argentine default Pari Passu principle

2008/9 North Atlantic Financial Crisis

Proposal for state-contingent debt: Cocos and GDP bonds

Table 1 Debt crises and changes in contracts and procedures

It should be noted, however, that the paper by Brooke et al. focuses on how to handle

liquidity shocks, rather than how to achieve debt write downs for insolvent sovereigns, which is the key feature of the Brookings study.

In what follows we begin with liquidity issues which can affect a sovereign debtor who is solvent but nevertheless exposed to balance sheet pressures which, in the absence of external support, may lead to default and substantial deadweight losses. After highlighting the two proposals for state-contingent debt in Brooke et al. (2013), a ‗toy‘ model of an endowment economy with some initial short term debt is used to illustrate the risk of default from a liquidity shock; and how Cocos and may help to avoid them. Issues of market power, coordination failure and asymmetric information are then discussed.

What if the liquidity shock panic was driven by the risk of an adverse shift in future

fundamentals that might lead to future default? In this case Arrow Securities can be used by the debtor to avoid default, essentially by buying insurance against the adverse shock. But pricing problems arise if there is moral hazard.

2 Highlights from the paper by Brooke et al. (2013)

2.1 Sovereign Cocos

The proposal is for bonds which ‗automatically extend in repayment maturity when a country receives official sector emergency liquidity assistance. (Italics added) Activation of the maturity extension would not require approval by the existing bondholders. If the entire debt stock of a country were to contain these clauses, the entire amortisation profile of the sovereign would shift into the future when a crisis occurs and official sector assistance was provided. The details of this automatic private sector bail-in would be defined ex ante in the bond‘s legal documentation.‘

While acknowledging that that state-contingent rollovers had been advocated earlier by others – by Buiter and Sibert (1999) and, in the context of Euro area bonds, by Weber et al. (2011) – the key innovative feature they propose is to use the provision of official liquidity

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4 support as the trigger for ‗bailing-in‘ private creditors. A possible boiler plate is provided, as follows.

Feature Design

Trigger for maturity extension: when the sovereign receives emergency liquidity from the official sector – for example when the sovereign draws upon credit from the IMF or the ESM.

Length of maturity extension: should match that of typical official sector support programmes – around three years for an IMF programme.

Bonds covered: all sovereign and sovereign-guaranteed debt

(bonds and loans) would include this clause. Treasury bills with an original maturity of one year or less would be excluded Coupon payments: will continue at their original level and

frequency. ‗Amortising bonds‘ would have the principal (but not coupon) payments postponed

Number of maturity extensions: Only one per coco. But any sovereign cocos issued after the trigger event would be unaffected – these could

be triggered in the normal way Table 2 Proposed design features of a sovereign coco

It is argued that this may reduce creditor moral hazard as creditors ‗could no longer anticipate full repayment by the official sector in times of crisis‘. Without an IMF/ESM ‗put‘, creditors will have to share more of the downside risk and should, for that reason, take more care in lending.

2.2 GDP bonds

The second proposal involving state-contingent instruments in the paper by the Central bankers is to recommend issuing GDP bonds in place of plain vanilla bonds, effectively a pre-emptive debt equity swap.

‗While sovereign cocos are primarily designed to tackle liquidity crises, GDP-linked bonds help reduce the likelihood of solvency crises. And both are state-contingent instruments, which can be defined in bond contracts at issuance. [The contracts to include] the following features: first, the bond‘s principal would be directly indexed to nominal GDP; and second, the coupon on this bond is paid as a fixed proportion of this principal, and therefore also

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5 varies with nominal GDP. GDP-linked bonds are not a new idea. Shiller (1993 and 2003) argues that these bonds would allow households and companies to take an ‗equity stake‘ in a country‘s economic performance, helping risk diversification and hedging.

Barro (1995) focuses on the benefits to the government, in particular, the ability to use GDP-linked bonds as a means to smooth taxes through time. Others, including Chamon and Mauro (2005) and Ruban, Poon and Vonatsos (2008) demonstrate how GDP-linked bonds can reduce the credit risk on sovereign debt.

GDP-linked bonds can reduce the likelihood of sovereign default through two related means. First, they reduce the size of increases in sovereign debt related to contractions in GDP. Second, GDP-linked bonds can raise the maximum sustainable debt level of the sovereign, providing countries with more ‗fiscal space‘ in times of crisis, Barr et al. (2012).

3. A ‘toy’ model of debt and default

As do the authors of FSP No 27, we assume that debtors are greatly concerned to avoid default because of the deadweight and other costs of so doing. Yue (2010) discusses recent evidence of how the balance of power shifts towards the creditors in such circumstances. From an anthropological perspective, Graeber (2010) stresses that severe treatment of defaulting debtors has been highly persistent for millennia2.

We use a highly-stylised model of a sovereign who is solvent but has considerable short term debt exposure to illustrate some key aspects of these proposals. Stone-Geary utility functions – where a minimum level of consumption is required for subsistence – are used to explain default triggered by ‗inability to pay‘. This formulation yields a sharp contrast between competitive equilibrium and one where a creditor with market power can take advantage of the debtor‘s lack of a viable outside option.

Specification

Consider an endowment economy which lasts for two periods with two players (a creditor and a sovereign debtor). There is no uncertainty in period one, and uncertainty in period two is captured by

2Widespread evidence of ‗fair‘ responses in the ‗ultimatum game‘ might lead one to expect creditors to treat defaulting debtors with more compassion; but default may be seen as a serious violation of cooperative behaviour which is evolutionarily efficient, Binmore (2010).

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two possible states: High or Low with probability of and . Assume that the debtor has

inherited a given level of one period debt of which needs to be serviced (amortised or rolled over at interest) in period 1.

Endowments

The endowment structure is shown in the following table:

Period t=1 t=2

State and state probability Creditor

Debtor

Table 3. Endowment structure

Endowment is not storable and .

Stone-Geary Preferences

Preferences of the two players are assumed to be identical with period utility of and a discount factor of . Each player has a subsistence level of consumption at where . The life-time utility of a player is given by

where , , , and subscripts denote time period and superscripts the states. We assume that consumption at any time and state is at least the level of subsistence,

Unless otherwise stated, we assume (i) Perfect information.

(ii) Initial debt is large enough to trigger current period default if there is no rollover, i.e., . (So the debtor‘s initial endowment is insufficient to cover subsistence and paying off the debt in period one)

(iii) The debt is small enough so that the debtor is solvent in two periods (to be specified later).

Each agent chooses a consumption profile to maximise expected utility subject their endowments, the rate of interest and Arrow prices, if applicable. . (Here we assume away any strategic interaction between players, so decisions are made taking the interest rate as given.)

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In Section 3.1 we start with the case of no uncertainty, and in Section 3.2, we examine a case where the debtor can share risks by issuing state-contingent securities, whose prices are determined in competitive markets.( In the Annex we look at a two period bond.)

To simplify the presentation, we scale all endowment and consumption relative to the subsistence level of consumption. Measured in this way the endowment structure becomes:

Period t=1 t=2

Player/State H L

Creditor 1 1 1

Debtor 1 1

Table 4. Rescaled endowments.

The rescaled consumption is defined as

Now we can rewrite utility function in terms of ―discretionary consumption‖

with subsistence constraints ; and the high initial debt assumption, .

3.1 Competitive equilibrium without uncertainty

To set the scene, we start with the simple case where the debtor is illiquid but solvent, i.e. , there is no uncertainty in the debtor‘s endowment in period 2 ( , and both agents are ‗price-takers‘.

Both debtor and creditor take the interest rate as given and

(1) subject to

, or , as appropriate, and (2, 3)

implying an Euler equation for each player

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8 So the two budget constraints (2, 3) and the Euler equations (4, 5) determine the consumption profile for the two agents given the interest rate; which in competitive equilibrium is

determined by the market clearing in period 1:

. (6)

3.2 Liquidity shocks and sovereign cocos – a graphical treatment

In this section we look at the case with log utility. As shown in Figure 1, where the dimensions of the Edgeworth box measure the total endowments in each period (namely

), the Stone-Geary utility functions only apply to consumption above subsistence, so the logarithmic utility curves are measured from the origins indicated by and , with reference to the debtor and creditor respectively. In the absence of any initial debt, the ―no-trade equilibrium‖ would be at A in the middle of the diagram, where the slope of the budget line (tangent to the indifference curves for both parties) is the gross interest rate which with constant endowments is simply

(7) As the agents have parallel linear Engle curves, redistribution will not affect the interest rate, it will merely redistribute consumption from debtor to creditor, giving stationary

consumption for the creditor at the level

(8) and for the debtor at the level

. (9)

As the debtor is solvent, i.e. , the rollover implied by these choices of consumption improve both player‘s welfare.

As can be seen from Figure 1, where the initial endowment is indicated at (as the debt is all short term), the debtor is illiquid and cannot pay off the entire debt in period 1 as this would take consumption below subsistence. This poses no problem for market

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9 equilibrium3, however, as the creditor effectively rolls over the short-term debt by choice, as shown by the competitive equilibrium at where the budget line has been shifted left to

and the debtor amortises a little over half the debt in period 1. In fact, as can be seen from the consumption choices (8) and (9), the debtor amortises the debt by two equal payments of ), so the amount of the debt rollover in period 1 is

. (10)

Figure 1. A liquidity shock that triggers default.

But what if this voluntary rolling over ceases – for reasons of market panic perhaps or doubts about the solvency of the debtor – i.e. there is a liquidity or ‗balance sheet‘ shock which has no impact on the endowments but shifts the equilibrium abruptly to E? The debtor will be forced to default and face the costs that incurs.

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As Milton Friedman would doubtless have predicted, given his views on how the anonymity of markets prevents discrimination.

E 1 L L R s 2 s b a Default OB C OC Subsistence for Borrower Subsistence for Creditor

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10 If, in the face of this shock, the sovereign were to apply and qualify for official emergency liquidity4 then the ―sovereign cocos‖ proposed by Brooke et al. (2013) would effectively reverse the liquidity shock and shift the equilibrium back to . Action taken by the official sector resembles that of a central bank which provides liquidity in the case of a bank run; but here it is the creditors that provide liquidity to the sovereign. In the terminology of Corsetti et al. (2006), one could say that official lending effectively acts as a catalyst for private lending. 3.3 Creditor Market Power

There are, of course, important issues to be borne in mind often missing from market equilibrium models; issues involving market power or market dislocation, for example, and asymmetric information. Take the case of market power where the creditor has a monopoly in the supply of credit.

In the circumstances described, with a solvent but illiquid debtor, it is obvious that the ‗take it or leave it‘ offer from a maximizing creditor would be , where the debt is rolled over but only at the cost of the debtor losing all discretionary consumption in both periods. It might of course be that the option of outright default could put a limit on creditor power. In other words, the benefits the creditor can extract from the ‗take it or leave it‘ offer would be limited to the costs of a financial crisis to the debtor. But for convenience we proceed on the

assumption that the debtor sees outright default as a more costly option.

What if the creditor acts as a market monopolist offering rollover credit at interest rates higher than the competitive market rate? Given Stone-Geary preferences, we find that a monopoly creditor will also achieve the same result! To find the monopoly outcome we first determine the debtor‘s offer curve by solving

s.t. (11)

and the Euler condition with log utility. Solving for and as functions of the interest rate set by the creditor:

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(11)

11 (13) By substitution we obtain the offer curve explicitly as

(14) This is shown in Figure 2 starting from the origin ( ; passing through the

competitive equilibrium where and (15)

and tending asymptotically to as .

Figure 2. The Debtor’s Offer Curve and Monopoly Equilibrium

Given this offer curve above, the monopoly creditor will choose the origin in the figure above by setting . This is obvious when one inserts the offer curve into the earlier Figure 1 where the indifference curve of the creditor is shown passing through . What is striking is how, instead of proceeding from the initial endowment to the competitive equilibrium as would be the case for the creditor, the offer curve for the debtor starts from

, before heading to . This simply reflects the fact that a sole supplier facing an illiquid Oligopoly Outcomes Debtor’s Endowment Competitive Equilibrium Monopoly Equilibrium

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12 debtor with no outside option can raise the cost of credit until it reduces the ―continuation value‖ of the debtor to subsistence.

Assuming imperfect competition, with Cournot Oligopoly in the supply of credit will yield outcomes on the offer curve tending towards as a number of oligopolist increases without limit (Miller et al., 2013). Such oligopoly outcomes are of course less likely to trigger the option of outright default by the debtor.

One implication of such strategic behaviour is that the cost of credit will rise in liquidity crisis with a corresponding transfer of resources to the creditor.5 Another is that tough creditors will not see reducing the dead-weight cost of crisis as being in their interest: it will give the debtor a more attractive outside option. By the same token, such creditors will presumably resist the inclusion of rollover clauses in sovereign debt!

Domestic credit markets provide analogous evidence of market power being used in this way. Recently, for example, a British bank has been accused of market manipulation for cutting off credit to various SMEs so as to drive them into the arms of its restructuring unit, which purchased their collateral assets at knock down prices (Tomlinson, 2013). There are similar accounts of predatory behaviour by banks in the US Great Depression.6

Creditor coordination and moral hazard

What if the liquidity shock has a negative impact on the net worth of the borrower, reducing its capacity to pay? In circumstances where the supply of credit is not coordinated but delivered by many individual agents, each acting to minimise its losses, this could in principle result in a ‗debt run‘ leading to a self-fulfilling solvency crisis, as discussed in Sachs (1984). The wide-spread use of sovereign cocos would presumably avoid coordination problems of this sort. 7

What of incentive effects of rollovers on debtor behaviour, effects that may not be directly observable or contractible? There is enormous literature dealing with debtor and creditor moral hazard and we do not propose to add to it. It is worth noting that institutional features may be important in terms of revealing hidden actions giving appropriate incentives.

5Could this be an element of what Hausmann and Sturzenegger (2007a, b) refer to as ―dark matter‖ – the capitalized value of return privileges obtained by powerful creditors?

6See also Allen and Gale‘s (2006) discussion of ―cash-in-the-market‖ pricing, and multiple equilibria in asset markets with limited participation.

7 See Sturzenegger and Zettelmeyer (2006) for discussion of an alternative contingent loan scheme proposed

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13 As regards debtor moral hazard, for example, some argue that automatic rollovers without conditionality give local elites the opportunity to arrange things so that they receive non-contractible benefits while the creditors take a haircut, Ghosal and Miller (2003). But Corsetti et al. (2006), in their model of ‗the IMF‘s catalytic approach‘ argue that the time provided by a rollover may allow a benevolent government to implement policies that enhance its

capacity to pay its creditors. The different predictions here depend largely on the involvement of agent with powers of discovery and conditionality. The potential debtor moral hazard effect of the ‗sovereign coco‘ is presumably offset because it is emergency lending by the IMF and/or ESM which acts as a trigger for maturity extension.

3.4 Risk of Insolvency: GDP Bonds as Arrow Securities

In this section, we turn to case of exogenous endowment shocks with known probability. We analyse the proposal for GDP bonds in terms of ―completing the market‖ by adding Arrow securities to secure efficient risk sharing. This offers an interpretation of the proposed GDP bonds.

Let p and q be the Arrow prices for date 2 High and Low state consumption measured in date 1 consumption. The creditor‘s problem is then

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subject to

, (17)

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Which has two first order conditions

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With log utility, one can show that

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The debtor‘s problem is the same as that of the creditor‘s, except the budget constraint being replaced by

, (24)

Solvency requires

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The demand functions of the debtor under log utility are then

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(26)

. (27)

Using market-clearing conditions in period 2

one obtains the Arrow prices as

(26) (27) Given (26) and (27), all consumption allocation can be backed out.

What is the rollover in this case?

Using (10), we get the amount of debt that is rolled over is

(28) in exchange for period 2 repayment, in the high state, of

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15 and in the low state, of

The key points can be illustrated using a crudely adjusted version of the earlier figure, where the endowment shock appears as a reduction of the size of the Edgeworth box , see Figure 2 (where , for simplicity, only discretionary consumption is plotted).

Given the risk of default in the lower state and the consequences that may follow, the debtor could ensure no default by saving sufficiently in period 1, i.e. by reducing period 1

consumption to the point shown as . (This form of self-insurance is hardly optimal, however, as it would involve great consumption variance in period 2 – some more savings in period 1 would prove worthwhile. )

Figure 3. Avoiding default by precautionary saving; or by issuing Arrow Securities Δ

b

E

Default

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16 The obvious alternative to self-insurance is a risk-sharing contract where the creditor

provides insurance against the adverse shock, as discussed above. In terms of Figure 2 required savings by the debtor will diminish as indicated at the point which lies to the right of , with state contingent repayments in the second period are indicated by , .

In outline, such risk-sharing contracts seem to correspond to the issuance of GDP, bonds as proposed by Brooke et al. (2013) for sovereign debtors.

3.5 Risk-sharing by Arrow securities: discussion

With Arrow securities and GDP bonds the debtor effectively buys insurance cover against bad outcomes. As with insurance contracts in general, however, moral hazard issues will arise: might the debtor not behave differently in the presence of such insurance?

For this purpose it is tempting to extend the analysis of the previous section by allowing for costly effort on the part of the debtor to reduce the probability of the bad outcome. This is relatively straightforward for non-contingent, plain vanilla long term debt.

Take the case where the debtor can choose either High or Low effort. With High effort, the probability of High state is larger than that resulted from Low effort, . But exerting High effort costs the debtor in terms of its utility (where the utility cost of Low effort is normalized to zero). Does the issuance of a long term debt affect the debtor‘s incentive to put in effort?

Since the debt contract is not state contingent, creditor‘s behavour will depend only on the interest rate and not on state probability. So whether High or Low effort is an equilibrium will depend on debtor‘s utility with respect to these two effort levels.

Applying the envelope theorem to debtor‘s utility function (gross of effort cost), one can show that

where and are two positive Lagrange multipliers (because budget constraints of the debtor are binding). It can be shown from the market clearing condition that <0, i.e., increasing effort reduces the equilibrium interest rate. As ,

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and , so . Hence, excluding the effort cost, increasing the

effort level improves debtor‘s utility.

Consequently whether the High effort level will be an equilibrium outcome or not simply depends on whether it is efficient, i.e.,

So presence of longer term debt contract does not per se create debtor moral hazard even if effort level is not observable.

Before proceeding further to analyse the case of state-contingent Arrow securities, it is crucial to note that one is dealing with an environment in which, by definition, the action of a large agent changes state probabilities. One might well expect a loss of Pareto efficiency in such a case – a sort of ―pecuniary externality‖ perhaps where state prices are affected by the action (or inaction) of the debtor? In fact, the problem may be more serious. Magill, Quinzii and Rochet (2012), in an illustration with discrete choice of effort which affects state

probability, demonstrate that Arrow prices do not exist.

They begin with a criticism of the state-space formulation of the Arrow-Debreu paradigm as follows:

The Arrow-Debreu model is however of far more limited applicability than the literature […] would have us believe, and this for two reasons. The first is that the Arrow-Debreu (AD) model is based on assumptions about the way productive

uncertainty within firms can be described and the nature of the markets on which firms are supposed to operate which are difficult, if not impossible, to match to anything we observe, or could even imagine observing, in the real world. The conditions that would need to be satisfied are the following:

(1) it must be possible to make a complete enumeration of primitive causes (states of nature) which, when combined with the actions (investment) of the firms, serve to explain the firms' different possible outcomes;

(2) these primitive causes must:

(i) have probabilities which are exogenous and independent of the actions of the firms;

(ii) be known and understood, not only by the manager of each firm, but by all agents in the economy;

(iii) be sufficiently simple to describe and verify to form the basis for contracts traded on markets. In the standard Arrow-Debreu model these contracts are (promises to make) forward delivery of goods contingent on the primitive causes (states of nature).

Secondly, even if all these conditions could be satisfied, on which Arrow (1971) raised serious doubts, he also argued that the technical conditions required to obtain existence

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18 of an equilibrium may be violated by the unavoidable presence of indivisibilities or non convexities. Magill et al. (2012, p. 2)

They go on to consider a case of discrete action where an industrial product can be good or bad depending, in discrete fashion, on the non-verifiable effort of the producers.

For example consider the problem faced by an automobile company like Toyota which needs to design and implement the production of a new model or improve on the design and production of an existing model. It can hire engineers to design the various

components of the car, test the prototypes, and set up a factory to produce and assemble all the components. At the end of the period of design and production, cars get

produced which are either ―good‖ (no flaws) or ―bad‖ (have flaws in the functioning of some parts leading for example to unintended acceleration). […] The contingencies which condition the outcome of the production process are numerous and difficult to describe. Furthermore, whatever the difficulties involved in their enumeration, they are very much ―internal‖ to the firm, and are hence unlikely to be observable and verifiable by outsiders. However the precise description of these contingencies is an essential ingredient of the Arrow-Debreu model since it assumes that prices are based on these contingencies. Magill et al. (2012, p. 14)

The authors then proceed to prove that in such a case Arrow-Debreu prices do not exist: In the informal discussion preceding the description of the AD model we expressed doubts about the realism of the market structure based on states of nature. We now show that even if we accepted the strong assumption that such markets can be put in place, it would not suffice to solve the inefficiency, since this economy has no Arrow-Debreu equilibrium. Magill et al. (2012, p. 14)

As yet, we have not been able to solve for the Arrow prices even in our toy model when it is expanded to introduce unobserved effort on the part of the debtor. Is it simply a matter of trying harder; or is it mission impossible even in this primitive setting? While output increases for high effort in any given state (and likewise for low effort), there is no simple correlation between the unobserved effort and output: and with discrete choice of effort it seems to satisfy the conditions for which this non-existence theorem is proved. If so, the impossibility result should apply here too!

If it is correct to interpret GDP bonds as Arrow securities, how can they be priced? Maybe the interpretation of GDP bonds as Arrow-Debreu securities is a blind alley that leads nowhere? Is there an alternative approach that will work in these circumstances?

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19 4. Conclusion

We should emphasize, in conclusion, that the two reports we have mentioned deal with different aspects of sovereign debt problems. That by the Central Bankers, on which we have focussed, is explicitly limited to handling problems facing a solvent debtor - by providing maturity extensions in the face of liquidity shock and by providing insurance against shocks to net wealth. The CIEPR report, on the other hand, is more concerned with sovereigns who have ‗over-borrowed‘ and need a debt write-down for sustainability; and the focus is on the institutional changes required to achieve this - by aggregating across creditors and protecting the debtor‘s assets from seizure by vultures, for example.

Although the paper by Brooke et al. (2013) emphasises the positive benefits of contractual evolution, it is nevertheless true that institutions play an important part, certainly for

sovereign cocos where the institutional trigger which plays a vital role. This may also be true of GDP bonds, if the problems of pricing go deeper than GDP revisions, as we discuss above. Could it be that institutional monitoring of policy effort is a necessary condition for proper pricing of contracts like this that include elements of macroeconomic insurance?

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20 Buiter, W., H. and A., C. Sibert (1999), ―UDROP: a contribution to the new international financial architecture‖, International Finance, 2 (2), pp. 227-247.

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22 Annex

A1. Rollover to a debt contract with uncertainty

Let the market determined gross real interest rate be , the creditor‘s problem is as follows (A1) Subject to

(A2)

(A3)

where the rollover measured in terms of period one consumption is

(A4)

The first order condition for optimality to (A1)-(A2) is

(A5)

Note that (A2) and (A5) determine creditor‘s demand functions. Using log utility, these result in

. (A6)

Similarly, the problem faced by the debtor is

(A7) Subject to

(A8)

, (A9)

(23)

23 Assume

(A11) so the debtor is solvent ex ante.

The first order condition to (A7)—(A9) is

With log utility, one can solve for period 1 consumption of the debtor:

References

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