Intertemporal Price Speculation and the Optimal Current-Account Deficit

The model is an infinite-horizon optimizing framework for a small open economy of identical, immortal households with constant-relative-risk-aversion preferences over an exportable good (x) and an importable good (m), who hold a single internationally traded bond with a fixed face value denominated in units of the importable good (Sec. I). The subjective discount rate is assumed equal to the constant world interest rate r, and the economy is a price-taker in both goods and in the capital market. The paper states plainly that “the only available asset is an internationally-traded bond which carries a fixed face value equal to one unit of the importable good” – foreign debt is denominated in the import good rather than in exports, a choice the paper justifies by appeal to industrializing economies with dollar-denominated debt facing dollar-priced imports.

A temporary decline in output triggers a current-account deficit that grows throughout the low-output period and returns to zero the moment output recovers, as households borrow to hold consumption and utility constant at their new, lower permanent-income level (Sec. II). Because the shock operates purely through the household’s intertemporal budget constraint and not through any relative price, “the induced external asset path is not dependent on the risk aversion parameter R characterizing the curvature of the utility function” – the economy smooths a flat path of lower utility by borrowing while income is low and repaying once it recovers.

A temporary deterioration in the terms of trade also produces a current-account deficit, but the paper shows this deficit reflects both an ordinary desire to smooth consumption and an additional, purely speculative motive created by the import-indexed debt. Because the real value of existing debt (measured in the home consumption basket) is expected to fall once the terms of trade recover, “there is an incentive to shift consumption toward that period” while the terms of trade – and hence the effective real interest rate on debt – are temporarily unfavorable: households borrow not only to smooth away the temporary loss of real income but to exploit the anticipated capital loss on their own debt.

Unlike the flat utility path induced by a pure output shock, a terms-of-trade shock produces a path of utility that is constant within each regime but drops discretely the instant the terms of trade revert to normal, because consumption is pinned to the (constant) shadow value of wealth within each regime, and the paper shows “only at time T, when the terms of trade revert to p from p prime, can consumption and utility change discretely” (Sec. III) – and proves this jump at T is strictly negative.

The paper shows that for a sufficiently short-lived terms-of-trade deterioration, instantaneous utility can rise at the very moment the shock is revealed, even though the shock lowers lifetime welfare overall, because the initial jump in utility depends on an income effect (negative) and a price/speculative effect (positive), and the paper proves the shadow-value variation driving the income effect vanishes as the shock’s duration shrinks, concluding “there are time periods T sufficiently short that the derivative is positive” – so for short enough shocks the positive speculative effect dominates.

The cumulative deficit run while the terms of trade are poor is smaller the more risk-averse the household is. The paper’s own interpretation is that “as the measure of risk aversion R increases, the smoothing motive becomes more important relative to the speculative motive and the cumulative current-account deficit run while the terms of trade are poor declines” (Sec. III) – greater curvature of the utility function makes it costlier, in welfare terms, to shift consumption toward the low-terms-of-trade period purely to exploit the anticipated capital loss on debt.

The entire speculative channel depends on foreign debt being denominated in the good the country imports; the paper is explicit that reversing this assumption would reverse the sign of the effect. “If bonds were indexed instead to exports, an expected future terms-of-trade improvement would raise rather than lower the perceived cost of borrowing abroad during a spell of low export prices; and this rise in the relevant real interest rate would reinforce rather than oppose the income effect” (Sec. III) – so the speculative motive would push the current account in the same direction as the income effect rather than against it. The paper defends import-indexation as the more realistic assumption for economies with dollar-denominated debt and dollar-priced imports.

The paper credits Dornbusch (1983) with an identical central point – that the interest rate relevant to consumption decisions is the cost of borrowing expressed in the home consumption basket – but notes that “Dornbusch does not study the impact of terms-of-trade disturbances” and that the analytical techniques used here differ, allowing the economy’s equilibrium to be expressed “in closed form as a function of the expected future paths of the relevant exogenous variables” (Introduction). The paper also distinguishes itself from the author’s own prior work (Obstfeld 1980, 1982) and from Svensson and Razin (1983), which analyze permanent, unanticipated relative-price shocks in a model where subjective time preference drives saving; this paper instead assumes constant time preference equal to the world interest rate and focuses on transitory shocks.

The paper acknowledges its assumption of perfect foresight is a significant restriction: introducing a second, export-indexed bond into a fully specified two-country equilibrium implies a no-arbitrage relation that “severely restricts the possible terms-of-trade paths that can be analyzed,” ruling out the kind of anticipated, discrete terms-of-trade shift the paper studies (Sec. III). A fully satisfactory treatment of the two-country, general-equilibrium case, the paper notes, “requires an explicitly stochastic model of the type explored by Lucas (1982).”