Exchange Rate Dynamics Redux

“Until now, thinking on open economy macroeconomics has been largely schizophrenic. When it comes to analyzing exchange rate dynamics, an empirically-minded economist abandons modern current account models which, while theoretically coherent, fail to address the awkward reality of sticky nominal prices. In this paper we develop an analytically tractable two-country model that marries a full account of dynamics to a supply framework based on monopolistic competition and sticky prices” (Abstract, p. 624). The paper explicitly aims to bridge the rigor of the intertemporal current-account approach (Sachs 1981, Obstfeld 1982, Frenkel and Razin 1987) with the descriptive plausibility of the classic Keynesian contributions of Fleming (1962), Mundell (1963, 1964), and Dornbusch (1976).

A continuum of monopolistically-competitive producers, indexed on [0,1] for Home and [n,1] for Foreign, each face a downward-sloping world demand curve; with log utility over consumption, real balances, and disutility of effort, the symmetric zero-net-foreign-asset steady state has closed-form solutions for output y0 and real balances M0/P0 as functions of the elasticity of demand theta, the markup, and the disutility-of-effort curvature kappa (Sec. 2.3, eqs. 21-22). Eq. (21) is analogous to the output equation of the static closed-economy monopolistic-competition model of Blanchard and Kiyotaki (1987): monopoly power pushes output below its competitive level, approached only as theta tends to infinity.

Log-linearizing the model around the symmetric steady state, the paper derives two schedules relating the exchange rate E-hat to the relative consumption differential C-hat minus C-hat: the MM schedule (eq. 52), E-hat = (M-hat minus M-hat) minus (1/(sigma times epsilon)) times (C-hat minus C-hat*), from the relative money-demand/Euler-equation conditions, and the GG schedule (eq. 54), from the short-run goods-market/output relationship – their intersection pins down the short-run equilibrium exchange rate and relative consumption jointly** (Sec. 3.2.2, Figure 1). The paper explicitly compares this apparatus to the textbook Mundell-Fleming diagram: “the MM schedule is analogous to the Mundell-Fleming model’s LM schedule, while GG is analogous to its IS schedule,” stressing the similarity is “superficial and partial.”

For a permanent unanticipated home money-supply increase, E-hat = (M-hat minus M-hat) minus (1/(sigma epsilon)) times (C-hat minus C-hat), and because relative consumption rises (eq. 56), the exchange rate depreciates by strictly LESS than the money-supply change: “the exchange rate rises less than the relative home money supply. … in the long run as well”** (Sec. 3.2.2, eqs. 52 and 54). The reason is that the shock permanently improves the home long-run terms of trade (eq. 58): higher long-run wealth from running a current-account surplus leads home residents to substitute out of work into leisure, raising the relative price of home goods – since E-hat equals E-hat’ (the exchange rate jumps immediately to its new long-run level, with no further expected depreciation), this result “does not mean… the model would behave exactly like a flexible-price model” – the exchange-rate and consumption responses are jointly, not separately, determined.

“The only effect of the money shock on U^R and U^R comes from the general increase in world demand in the initial period, dQ-hat, and both countries share the benefits equally” (eqs. 62-63); “thus, the only effect of unanticipated monetary expansion on U^R and U^R is the general increase in world demand in the initial period, and both countries share the benefits equally”** (Sec. 3.3). The mechanism: a monetary expansion in a monopolistically-competitive economy with preset prices raises welfare “familiar from the static closed-economy analyses of Akerlof and Yellen (1985a,b) and Blanchard and Kiyotaki (1987)” because price exceeds marginal cost at the optimum, so a first-order aggregate-demand stimulus coordinates the economy closer to efficient production; terms-of-trade and current-account effects, “long central to the international policy coordination literature,” turn out to be “of strictly second-order importance.” The paper connects this directly to Eichengreen and Sachs’s (1985) revisionist claim that competitive devaluations in the 1930s raised net world aggregate demand rather than being purely a beggar-thy-neighbor transfer.

A permanent, unanticipated rise in home government spending raises the relative demand for home money, so E-hat is given by the same MM equation as for money shocks but with a different GG-schedule intercept reflecting the discounted path of government spending differentials (Sec. 3.4, eq. following Figure 2). The home currency depreciates immediately to its new long-run level (E-hat equals E-hat’ as before), and because individuals smooth consumption intertemporally even against a permanent tax increase, “for a permanent increase in domestic government spending… the home country actually runs a surplus” (Sec. 3.4) – contrary to the standard flexible-price-economy result that permanent government-spending changes have no current-account effect at all.

A monetary expansion at home or abroad lowers the world real interest rate in proportion to the increase in the “world money supply,” n times M-hat plus (1-n) times M-hat (eqs. 59-60, Sec. 3.2.3); only the money-demand parameters epsilon and beta enter this result, since intertemporal consumption-smoothing washes out the role of monopoly-power and effort-curvature parameters.* For government spending, the paper derives (eq. 65, Sec. 3.4) that only INNOVATIONS in future government spending affect the real interest rate; temporary current spending increases, being demand-determined under sticky prices, raise global output one-for-one without changing the path of output available for private consumption, so the real rate is unaffected – in contrast to the standard flexible-price result of permanently higher spending leaving the real rate unchanged.

An appendix sketches a small-open-economy variant with a monopolistically-competitive nontraded sector (preset prices) alongside a perfectly competitive, flexibly-priced tradable sector; solving for the response to a permanent unanticipated home money-supply increase gives E-hat equal to [(beta plus (1-beta) times epsilon)/(1 plus (1-beta)(1 minus alpha plus alpha epsilon))] times M-hat, which EXCEEDS the long-run change in the exchange rate (so the nominal rate overshoots its long-run level) whenever epsilon is greater than 1 (Appendix, eq. 79). “One can understand the role of epsilon in overshooting by noting that in this model, 1/epsilon is the consumption elasticity of money demand” – genuine Dornbusch-style overshooting is recoverable once nontraded goods are reintroduced, showing the baseline model’s no-overshooting result is a feature of its specific all-traded-goods setup, not a general property of sticky-price optimizing models.

The conclusion states the model “can be extended in a number of dimensions, including the addition of nontraded goods, pricing to market behavior, home bias in government spending, labor market distortions, and so on,” and that a natural way to portray a productivity shock would be as a shift in the effort-curvature parameter kappa, with “standard techniques” sufficient to generate a fully stochastic version of the model (Conclusion and Extensions sections) – a research agenda the authors and others (including the paper’s own successor, “New Directions for Stochastic Open Economy Models,” 2000) subsequently pursued.