Self-Fulfilling Debt Crises

The paper builds a dynamic, stochastic general equilibrium model in which a government that cannot commit to repay must roll one-period debt over each period, and uses it to answer two questions: when is a purely belief-driven default possible, and what should a government do about the risk. The mechanism is a liquidity crunch: because the government issues new debt before retiring the old, “the liquidity crunch induced by the inability to sell new debt can lead to a self-fulfilling default,” so if lenders refuse to buy at any positive price the government may find default optimal, confirming their refusal. The answer to the first question is the paper’s central object, the crisis zone: if fundamentals – “the level of the government’s debt, its maturity structure, and the private capital stock” – lie in a particular range, “the probability of default is determined by the beliefs of market participants.” The zone is bounded below by the largest debt the government would still repay even with no access to new borrowing (the no-lending condition) and above by the largest debt consistent with repayment when it can borrow (the participation constraint). Crises are coordinated by a sunspot uniform on [0,1], whose cutoff is simultaneously the crisis probability, and the consequences inside the zone are real rather than merely financial: consumers, anticipating a crisis with probability π, set a capital stock satisfying β(1−π)+παf′(k^π) = 1, so “the country’s economic activity is depressed in proportion to the probability that a crisis will take place,” while bankers pay only β(1−π) per unit of debt. The answer to the second question is that only preemptive policy works. Reacting once a crisis has begun is useless: pegging the interest rate on government debt, as Calvo (1988) suggested, “simply results in a refusal of the private agents to buy government debt,” and lengthening the maturity of the debt being issued is irrelevant to a crisis today because “it is the maturity structure of the prevailing debt, and not that of the debt being issued, that determines whether or not a crisis is possible.” What does work is reducing the debt below the crisis-zone floor – which triggers “an investment boom in period T−1” and, in period T, rising consumption and government spending – or lengthening maturity in advance, for which Proposition 4 shows that for any debt level in the zone there is a maturity long enough to preclude crises. Two results cut against intuition. Making default costlier raises both bounds of the zone without necessarily closing it, so “the consequences of the acquisition of some additional credibility can be to make the effects of a crisis much worse.” And the governments most exposed are the well-behaved ones: “a government that cares sufficiently more about private than government consumption or is sufficiently farsighted is guaranteed to have a crisis zone.” The model is motivated by Mexico in 1994-95, where the debt/GDP ratio looked responsible but average maturity had become very short, and where the government could sell neither dollar-indexed tesobonos nor peso debt – a pattern “hard to explain on the basis of currency risk, but easy to explain on the basis of default risk.”

Timothy Kehoe | Macro Paper Warehouse

Self-Fulfilling Debt Crises