International Lending with Moral Hazard and Risk of Repudiation

Atkeson opens by noting that international lending has occurred “in a succession of waves of lending followed by a lack of lending” over the past 150 years, and that a simple full-information, full-enforcement credit-market model predicts each country should receive a net capital inflow when its output is low relative to world output and a net outflow when the reverse holds – “the predicted pattern… is not the pattern that is typically observed” (Sec. 1). Instead, debt crises recur in which countries suffer a net capital outflow precisely when domestic output is low, “despite evidence of efficient investments that go unexploited in the borrowing country,” and through the mid-1980s many Third World debtors were net creditors to the developed world even as their output fell sharply relative to trend.

Lemma 2.1 (Appendix) shows that under full information and full contract enforcement, the risk-neutral lender effectively rents the borrower’s stochastic investment technology at the rate equating its marginal rate of transformation to the risk-averse borrower’s marginal rate of substitution, and the optimal allocation gives the borrower a constant consumption level each period (the state variable Q = Y - d is constant through time at its initial value). This is the frictionless risk-sharing benchmark against which the paper’s two successive frictions – repudiation risk, then moral hazard – are measured.

Lemma 2.1 in the repudiation-constrained setting (attributed to Worrall 1987) shows that when the borrower’s output has finite support and debt service can be made fully state-contingent, the repudiation-constrained Pareto-optimal contract still achieves complete consumption smoothing for the borrower in finite time – borrowing is initially restricted, but once the borrower has accumulated a sufficiently large deposit with lenders (sufficient that losing it deters any future repudiation), full consumption smoothing is reached and maintained thereafter. Atkeson states explicitly that this implies “repudiation risk is an important constraint on international lending in the short run, [but] this risk itself does not satisfactorily explain the recurrence of debt crises over the long run” (Sec. 1) – establishing that the paper’s title problem (recurrent debt crises) requires a second friction beyond repudiation risk, which motivates the introduction of moral hazard.

The environment has a single infinitely lived, risk-averse borrower who owns a stochastic-returns storage technology, and an overlapping sequence of short-lived, risk-neutral lenders (each lender born in period t is active in t and t+1) who have access to perfect capital markets (Sec. 2). The borrower’s investment choice I_t (from a feasible set) each period determines the probability distribution (density g(Y’; I), satisfying the monotone-likelihood-ratio property and convexity-of-distribution-function condition) over next period’s output; crucially, the borrower’s investment level is unobservable to lenders, so consumption may be “disguised as investment” (e.g., through overemployment of labor whose shadow value is obscured, or outright fraud in project execution). Lenders can indirectly discipline the borrower only by withholding future credit, and because the borrower can always fall back on the autarkic payoff (solving the borrower’s own optimal consumption/investment problem absent any contract), the worst punishment lenders can impose is permanent exclusion from credit markets – shown (Sec. 3) to be sustainable in a perfect equilibrium via a chain of lenders each refusing credit if all future lenders plan to do the same.

The FC problem maximizes the borrower’s expected utility subject to feasibility, individual rationality (for both lenders and the borrower), immunity from the threat of repudiation (the continuation allocation must remain individually rational in every contingency), and incentive compatibility of the investment choice (Sec. 3, eq. FC). Atkeson’s stated technical contribution is to generalize the self-generation and factorization results of Abreu, Pearce, and Stacchetti (1986a) – originally developed for repeated Cournot oligopoly and repeated principal-agent problems – to an environment with a persistent state variable (the borrower’s net output Q, which carries history dependence forward) and with the specific incentive-compatibility structure of this moral-hazard problem (Sec. 4). Proposition 1 (Self-Generation) and Proposition 2 (Factorization) together establish that the set of payoffs attainable under the full dynamic program equals the set of payoffs generated by a simpler static “admissibility” problem parameterized by a continuation-value function, reducing the search for the constrained-optimal allocation to a straightforward recursive (Bellman-equation) problem.

Proposition 3 shows that the continuation value function at which the recursive program is solved is necessarily equal (almost everywhere) to the overall value function V evaluated at the next period’s state – formally, that “the provision of incentives for the borrower to invest is achieved completely through the design of the repayment schedule and not through variation in the plan for lending as a function of the current state” (Sec. 5). This is a specific and non-obvious result: a priori it was unclear whether the optimal scheme would punish suspected underinvestment via higher debt service, reduced new lending, or some alternating reward/punishment-phase structure (as arises in the related Cournot-collusion and principal-agent literatures, where optimal schemes put positive probability on price wars or on the agent being fired). Atkeson shows that for low realizations of output, the optimal punishment lowers the state Q so far that the continuation value exactly equals the autarkic value – the same continuation payoff a borrower gets from outright repudiation – but the allocation that supports it is different: net repayments and gross lending both continue to be observed (a “debt crisis”), rather than the complete absence of transactions that follows actual repudiation.

Under the assumption that the expected value of debt-service repayments is increasing in investment (which holds when the repayment schedule is upward-sloping, i.e., embodies risk-sharing) and that the likelihood ratio g_I(Y’;I)/g(Y’;I) is sufficiently negative at the lowest output realization (satisfied by the paper’s example family of distributions), Atkeson shows that the first-order condition on the repayments schedule forces the Lagrange multiplier on the repudiation-immunity constraint to bind for low output realizations, which in turn forces the state variable (output net of repayments plus new loans) to be strictly below gross output for those realizations – “this implies that the borrower must make a net transfer of capital to the lender when low income is realized” (Sec. 5, end). The Conclusion states this as the paper’s headline result: “the optimal lending program in this environment with moral hazard necessarily specifies that the borrower must make a net transfer of capital to the lenders when low output is realized” – i.e., debt crises of exactly the kind the Introduction identifies as empirically puzzling are shown to be a necessary feature of efficient (constrained-optimal) risk-sharing, not evidence of market failure, once moral hazard over investment is added to repudiation risk.

The working paper explicitly marks its planned Section 6 as “(Forthcoming)”: “I solve this dynamic program in an example economy which displays debt crises (Section 6 forthcoming),” and the Section 6 heading itself appears in the text followed immediately by “I solve this dynamic program in an example economy in section 6 (forthcoming)” – i.e., at the time this draft (NBER-adjacent Minneapolis Fed Working Paper 381, November 1987) circulated, the worked numerical example illustrating the model’s behavior (including the paper’s stated interest in whether the critical output threshold triggering a crisis is decreasing in the state, which would generate persistence of crises, versus increasing, which would make them more transient) had not yet been written. This record’s Layer 2 is accordingly grounded in the paper’s proven propositions (1 through 3, and the repayments-schedule argument of Section 5) rather than in any specific numerical results, since those results are not present in the source text obtained. The published 1991 Econometrica version is understood to contain a completed worked example; a reader wanting the specific quantitative illustration of crisis persistence should consult the published version directly.

Atkeson concludes that “we should interpret the observation of debt crises as an essential feature of the proper functioning of international credit markets” rather than as a symptom of dysfunction, warning that “if governments were to intervene in these markets to relieve the burden of debt crises on borrowing countries on a consistent basis, then the incentive structure that supports international lending in the first place would be undermined.” The paper offers one qualification: if international agencies such as the IMF can assist in monitoring debtor countries’ actual investment and consumption decisions, such monitoring could reduce the burden of debt crises by directly relaxing the information friction (making investment less private) rather than by overriding the incentive scheme that friction makes necessary.