Rational and Self-Fulfilling Balance-of-Payments Crises

The paper’s thesis is that “balance-of-payments crises may indeed be purely self-fulfilling events rather than the inevitable result of unsustainable macroeconomic policies” (Introduction). The “recent balance-of-payments literature, beginning with the work of Krugman (1979),” holds that when asset holders have perfect foresight and a peg must eventually be abandoned, “profit maximization dictates that a sharp attack on the central bank’s reserves occur at some point on the economy’s path” – a rational, inevitable response to persistently conflicting internal and external policy targets. Obstfeld’s contribution is to show that under certain expectations about post-crisis policy, “even a permanently viable regime may break down, and the economy will possess multiple equilibria corresponding to different subjective assessments of the probability of collapse” – these are not irrational attacks, but “reflect…an indeterminacy of equilibrium that may arise when agents expect a speculative attack to cause a sharp change in government macroeconomic policies” (Introduction, Abstract).

The model (Section I) is “the simple linear one developed by Flood and Garber (1984a)”: a small open economy with perfect capital mobility, purchasing-power parity (P_t = S_t·P_t), uncovered interest parity, and linear money demand m_t = a − αi_t with money supply equal to reserves plus domestic credit, R_t + D_t.* Domestic credit follows a stationary AR(1) process D_t = D̄ + v_t, v_t = ρv_{t-1} + ε_t with 0 < ρ < 1 (Eqs. 1-4); reserves have a lower bound R̲, and the innovations are assumed bounded tightly enough that “the fixed exchange rate can, with probability one, persist indefinitely” absent any policy-regime change.

Obstfeld shows that if the stationary credit rule continues to be followed regardless of the exchange-rate regime, “domestic credit does not grow steadily and an exchange-rate collapse can never occur.” The argument is a no-arbitrage one: if a run were hypothesized to occur at date T, the resulting floating rate S_T (computed from the saddle-path solution, Eq. 6) would lie below the fixed rate S̄ with probability one, since v_T is bounded above the level that would make the shadow rate exceed the peg. “Because no one will wish to participate in the attack, it cannot occur at time T” — an investor who foresaw this appreciation would rather wait to buy foreign assets more cheaply after others dislodge the peg, so nobody attacks, and “equilibrium runs are probability-zero events” — domestic and foreign interest rates must then always coincide.

When domestic credit instead grows monotonically (D_t = D_{t-1} + η_t, η_t > 0 with probability one, Eq. 7), Obstfeld notes Flood and Garber’s informal claim that the exchange rate must float once the shadow floating rate S̃_t exceeds the peg S̄, but argues their stated rationale — that S̃_t > S̄ merely “offers speculators an opportunity to profit at official expense” — “merely shows that if a run is expected, it will pay for all to join in,” without itself proving no other equilibrium path is possible. Using Salant’s (1983) precise definition of an equilibrium exchange-rate function S(D), Obstfeld proves a Theorem: there is a critical domestic-credit level D̄ such that S(D) > S̄ if and only if D_t > D̄, where D̄ is defined by the point at which the shadow floating rate exactly equals the peg (Section I) — formalizing, and correcting a logical gap in, the earlier “shadow exchange rate” collapse-timing result.

The self-fulfilling example (Section II) assumes the public believes that “if a crisis occurs at any time T, the central bank allows the exchange rate to float forever and switches to the domestic-credit growth rule” of steady monetary expansion (Eq. 7) — i.e., that policy will turn inflationary specifically because of (not merely coincident with) a crisis. Obstfeld motivates this with real-world channels: once reserves hit R̲, the central bank can no longer borrow externally, and “the sharp rise in official net foreign indebtedness caused by the loss of reserves to private speculators” may force a turn to inflationary finance, a pattern he connects to Argentina’s and Chile’s early-1980s experience (citing Díaz-Alejandro 1984). Under this expectation, a run at T becomes advantageous whenever the realized shock exceeds a threshold, v_T > C (Eq. 11), “Because p > 0, inequality (11) may hold even under the boundedness assumption on ε made in section I” — i.e., a crisis becomes possible under exactly the credit-shock realizations that, absent the expected regime switch, would never have threatened the peg.

Obstfeld introduces an exogenous “sunspot” lottery: with probability π a “crisis state” occurs in which a run happens if and only if v_T exceeds the threshold C, and with probability 1−π no crisis state occurs at all. Setting π = 0 recovers the baseline no-run equilibrium of Section I. The paper shows there exists a strictly positive threshold π̄ such that “the crisis probabilities π in the interval [0, π̄) define a continuum of possible stochastic equilibria for the economy in which the exchange rate is fixed if state 1 has never occurred” — proved formally in the Appendix by showing reserves never fall below R̲ in the no-crisis-realized path for π below this bound. Each value of π in this range is a genuine self-fulfilling equilibrium: agents who believe a run is more likely (higher π) rationally demand less domestic currency, which is itself consistent with, and reinforces, that belief.

For π > 0, the domestic nominal interest rate exceeds the world rate even while the exchange rate remains fixed, because E_t[S_{t+1}] is a probability-weighted average of the peg and the (higher) rate expected to prevail after a collapse (Eq. 12), so “E_t[S_{t+1}] ≥ S̄, and so i_t = i + E_t[(S_{t+1}/S_t) − 1] ≥ i.”** Moreover, because domestic credit shocks are serially correlated, a positive shock to domestic credit raises the probability that next period’s shock will trigger a run, so “an increase in v_t causes a rise in next period’s expected exchange rate, and thus a rise in the interest rate i_t” (Eq. 13: d(E_t[S_{t+1}])/dv_t = α⁻¹πβ’q(v) > 0) — meaning “a positive domestic-credit shock may actually reduce money demand, occasioning a more-than-offsetting reserve loss,” the paper’s formal account of why reserve losses and interest-rate spikes typically intensify together in the run-up to an actual crisis.

Obstfeld draws a direct parallel to Diamond and Dybvig’s (1983) bank-run model, where “there are two equilibria: one in which agents have confidence in the solvency of financial intermediaries, and one in which lack of confidence leads to a run,” both self-fulfilling because “banks fail if, and only if, there is a run.” He notes an important disanalogy, however: “balance-of-payments crises, unlike bank runs, need not be self-ratifying. The stability of a pegged-rate regime hinges on the anticipated response of the authorities” — it is specifically the belief that policy will turn inflationary after a crisis that creates the multiplicity, not the crisis mechanics themselves. The randomization device linking crisis probability to a sunspot is credited to Blanchard’s (1979) bubble-crash model and to the “extrinsic uncertainty” concept of Cass and Shell (1983). The paper distinguishes its mechanism explicitly from an alternative source of indeterminacy that Flood and Garber (1984a) themselves raise — nonstationary speculative bubbles in the post-collapse floating rate — noting “the example studied in this paper explicitly assumes that the floating exchange rate depends entirely on its fundamental determinants” (Eq. 6, ruling out bubbles by the saddle-path solvency condition), so the indeterminacy here is purely about which fundamentals-based equilibrium path obtains, not about bubble components layered on top of one.

Obstfeld contrasts his result with papers like Obstfeld and Rogoff (1983, 1984) on fractional monetary backing and Diamond and Dybvig (1983) on deposit insurance, which show that “anticipated government policies can block the emergence of certain sub-optimal competitive equilibria.” His closing methodological point: “In a sense, the present paper turns that argument on its head. Expected government actions may lead to undesired outcomes in economies that would function correctly otherwise” (Section III) — i.e., an anticipated policy response that is contingent on a crisis can itself be the source of an otherwise-absent crisis, rather than only ever serving as a backstop against one.

This summary is grounded in the paper’s own NBER working-paper draft (Working Paper No. 1486, November 1984), the direct precursor to the March 1986 American Economic Review publication; the working paper’s abstract, structure (Sections I-III plus appendix), and results match the published article (confirmed via JSTOR’s listing of the published title, author, journal, volume 76(1), and page range 72-81), so the two are treated here as the same paper under normal pre-publication revision.