Sovereign debt: Ignorance can be bliss

e e

consumption in eve For their result

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J.P. Thomas, Sovereign debt

reputational debt contracts. In their model ‘reputation’ is used in its alternative game theoretic sense to refer to beliefs about the type of government in a model of incomplete information. If there is some prior probability that the country’s government is honest - that is, will adhere to the contractual terms - then an equilibrium with lending can be sustained. If the government is involved in multiple trust relationships, even a small p&&ility of honesty can sustain large amounts of lending because reneging on one contract will reveal the government’s type and so lead to loss of trust in other contracts. The argument given in this paper, by contrast, in no way relies upon any probability of the government being honest. The form of hidden information assumed here is information about the country’s utility from net imports [the model formally resembles that of Green (198’7)]. The country wants to borrow in bad states to consumption smooth, and is prepared to sacrifice some consumption in good states to do this. Because the state of the world each period is not observable to the lender, a simple insurance contract will not be incentive compatible as the country -wou’ldannounce the bad state each period. Nevertheless long-term incentive compatible contracts which offer some insurance exist: one is constructed below. The key feature of such a contract is that potential insurance is offered today in return for a worsening of future terms: this delivers incentive compatibility. The main question looked at below is whether this contract is robust against reneging by the country and investment in single period cash-in-advance contracts. Such contracts cannot be state-contingent since the country would always announce the state whrch maximised its transfer. Because of this, a sequence of cash-in-advance contracts may not be able to offer the same amount of consu states as a long-term incentive compatible contract, and thus m An example is constructed where this is so, and conse uently where a reputational debt contract can exist.’ Specifically, an example will be given of a debt-contract which the debtor country never has an incentive to repudiate and yet for which the !GA of debt is always positive. Since the aim is to show the possibili contract the example will be kept as simple as possible: the re from the argument how a more general model could be co * The contract which will be constructed little resemblance to a standard ‘debt’ contract in the usual meaning of the

J.P. Thomas,sovmeli~ dt?bt

information no form CY:

ntract can exkS

and good, being independently and identically distributed wit p and (1 -p) respectively. The country’s utility in each state and its net imports X, which are used only for co no investment opportunities. In the bad state utility is given by

and in the good state by

c

-2

x<-30

- loo

u,(x)= i

1

0

-3osx<

-20

x>-20, =

where 2~ 1Mk4 The country maximises e another other than through int

391

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JR

Thomas, Sovereign debt

some form of political instability. 5 2 is a parameter which will be determined below: the idea is that it will be chosen to be sufficiently large to generate a strong consumption smoothing motive; the cash-in-advance contracts will not be able to offer as much smoothing= There exists a !arge nu mber of financial institutions, each of which is riskneutral and discounts with fkt,~r SC aho (so the ‘world’ interest rate is l/a- :I). The state of the world is private information to the country, altholucwk -with outside institutions are observable. (Equivalently &AA trcanaaAnn@ CAUllUUUCPVI~O net imports are observable, so it is possible to deduce if there are financial transactions with other institutions.) Contracts are assumed to be enforceable upon the institution. Consequent upon repudiation the country loses its reputation for keeping to contracts in general. It will be assumed for the moment that institutions will then only be prepared to enter into cash-in-advance contracts which in no way depend for their profitability upon the country’s behaviour. tally, since there is no public!y observable state upon which su can be conditioned, these cash-in-advance contracts must, under competition, be simple loan contracts paying the interest rate (l/u- 1). Consider a contract of the following form offered by one of the institutions. The contract has two states, high and low, starting in the high state. In the high state the transfer of resources to the country from the institution is 100 if the country announces a bad year, -20 otherwise. In the low state the transfer is 90 if a bad year is announced, -20 otherwise. If the bad state is announced, the contract next period is in its low state, otherwise it pjyliiibe in its high state. The cotltract is deemed to be repudiated as soon as the country fails any payment or makes any transaction with any other institution. I claim that this contract can offer the institution a positive profit - correspond to positive debt - while being incentive compatible and immune from repudiation. Each period the country has three choices: to tell the truth, to lie, or to renege. If the last option is taken, it is clearly best to announce the brad state to maximise the current transfer. First it will be shown that a strategy for the country that involves reneging is not as good as a truth-telling strategy. Four cases have to be considered to determine the pay-off fro repudiation, depending on the state of nature and state of the contract. tart with the high state of the contract and th,p good state of the world, at time t. announcing the bad state, the country can invest 120 in a on (thus breaking the contract) with no sacrifice nf c::rrc~~~ ~?ility, current utility loss of 100. (Any la investment would involve a current utility loss of Z, hich will be show elow to be an inferior strate q’s rather

than

the

I.P. Thmnus, Sowreign debt

393

ion.) Consider the next two riods t+l and t-1-2. occurs twice, then incurring a loss of 2 is unavoidable at t-12, or 130 was invested, if 130 -90 01

(

>

L9Q. a

Since utility is non-positive, an up to t is given by - a2p2Z if (1) hold Next, consider utility from a strategy o uth-telling and ad contract. Utility is either zero or - 1 (when the bad state occurs consecutively) so utility is certainly no lower than much higher. Clearly Z can be chosen large enoug la?ger than the upper bound on repudiation utility. We must also consider repudiation from the three other state combinations. In each case utility from repudiation can be no hi high-good combination because the starting point is les same upper bound on utility applies. To summarise: if (1) holds and -a2p2Zs

- 1

1-a),

(2)

then truth-telling is better than repudiation. We must check that truth-telling is worthwhile, i.e. that the contract is incentive compatible. Announcing the bad state in the nation has no current benefit (since the resources gained cann and do not increase uti ty) but must reduce fut low-good combination. n the low-bad combin state at t leads to a loss of current utility of (2% 1 an zero while future utihty under tr - 1G3q’(l-a), the future gain is n truth telling pays if

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J.P. Thomas, Sovereign debt

The average transfer from the country each period in the future is no less ), while than 20(1-p)- lOOp,with discounted value (a/(1-a))(20(1-p)-1 (from the high-ba state). So debt is the minimum transfer today is always positive at every date-state event provided -lOO+(a/(l-a))(20(1-p)-lOQp)>

(4

resumably the financial institution would only offer such a c xpected discounted value of transfers to it is non-negative initially. Conpositive all the dition (4) is stronger: it is a sufficient condition for debt to time. Are there parameter values such that (l)-(4) hold simultaneously? holds for a > IO/12 provided p is chosen to be small enough, while (1) also holds for such values of CLThen observe that for any given values for p, (2) and (3) hold for Z large enough. Thus there are parameters such t 11 1 b # &O repudiate, even though contract exists which the country has no incent+ ‘debt’ is always positive? We have considered only simple cash-in-advance loans at the interest rate. It may be asked if after loss of reputation there is not some incentive compatible contract which could be offered and which provides better insurance than a simple loan and which nevertheless involves the fin institution in m ~e~~~~~~~o~ risk? The answer must be negative. To overturn the argument given here for the reputation contract it is necessary to sho that some alternative contract(s) can be entered into which avoids a possibfe utility loss of within two periods of repudiation. Such a contract the possibility of receiving at least 90 in both periods, an

ve

in fact

to repudiate.

s

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J.P. Thomas, Sovereign debt

eferences Atkeson, A.B., 1391, International lending with moral hazard and risk of repudiation, Econometrica 59, 1069-1389. Bulow, J. and K. Rogoff, 1989, Sovereign debt: Is to forgive to forget?, American Economic Review ?9,43-50. Cole, H. and P. Kehoe, 1991, Reputation with multiple relationships: Reviving reputation models of debt, Mimeo. (Federal Reserve Bank of Minneapolis, Minneapolis, MN). Eaton, J. and M. Gersovitx, 1981, Debt with potential repudiation: Theoretical and empirical analysis, Review of Economic Studies 48,289-309. Fudenberg, D. and D. Levine, 1989, Monopoly and credibility in asset markets: An example, Working paper (Massachusetts Institute of Technology, Cambridge, MA). Green, E., 1987, Lending and the smoothing of uninsurable income, in Contractual Arrangements for Intertemporal Trade, E. Prescott and N. Wallace, eds. (University of Minnesota Press, Minneapolis, MN). Grossman, H. and J. Van Huyk, 1988, Sovereign debt as a contingent claim: Excusable default, repudiation and reputation, American Economic Review 78, 1088-1097. Manuelli, R., 1986, A general equilibrium model of international credit markets, Mimeo. (Stanford University, Stanford, CA). Thomas, J. and T. Worrall, 1990, Income fluctuation and rsymmetric information: An example of a repeated principal-agent problem, Journal of Ecouomic Theory 51, 367-390