Monetary Policy and Exchange Rate Volatility in a Small Open Economy

The paper is among the first to embed Calvo staggered price-setting – rather than the one-period-advance price-setting common in the earlier new open economy macroeconomics literature – into a small open economy model with monetary policy specified endogenously as an interest-rate rule, rather than as an exogenous money-supply process (Sec. 1). The authors argue this modeling choice both permits richer, more persistent dynamic effects of monetary policy than one-period pricing allows, and accords much better with how modern central banks actually conduct policy, making the framework directly suitable for evaluating and comparing alternative interest-rate rules – the express purpose of the paper.

The paper shows that the small open economy’s equilibrium dynamics can be written as exactly the same two-equation system as the closed-economy Calvo model – a New Keynesian Phillips curve, πH,t = βEt{πH,t+1} + καxt, and a dynamic IS curve, xt = Et{xt+1} − (1/σα)(rt − Et{πH,t+1} − rrt) – differing from the closed-economy case only in that (a) the composite coefficients κα and σα depend on the degree of openness α and the elasticities of substitution (η, γ), and (b) the natural rate of interest rrt generally depends on expected world output growth as well as domestic productivity (Sec. 3.3, eq. 36-37). The closed economy is nested exactly as the α = 0 limit. This equivalence is what lets the authors “invoke” existing closed-economy results on equilibrium determinacy (via Bullard and Mitra 2002) and welfare (via Rotemberg and Woodford 1999) rather than re-deriving them from scratch.

Under the paper’s assumption of complete international financial markets, the real exchange rate is proportional to the terms of trade, qt = (1−α)st, and the international risk-sharing (Backus-Smith) condition pins domestic consumption to world consumption and the terms of trade, ct = c*t + (1/σ)st (adjusting for α when η ≠ 1) (Sec. 2.1.2-2.1.3, eq. 12-18). This means that whenever a shock or a policy rule moves the terms of trade, it mechanically reallocates consumption between the domestic economy and the rest of the world through the insurance markets, a channel absent from incomplete-markets or one-period-pricing frameworks and central to how the paper’s monetary rules end up affecting welfare.

Optimality of strict domestic inflation targeting (DIT) is derived only for the special case of log utility and unit elasticities of substitution between goods of different origin (σ = η = γ = 1), and only once an employment subsidy is introduced that offsets not just firms’ market power but also the open economy’s separate incentive to manipulate its terms of trade to its own advantage (Sec. 4). The paper notes explicitly, following Corsetti and Pesenti (2001), that an open economy’s monetary authority has an additional temptation beyond the market-power distortion present even in a closed economy: because domestic and foreign goods are imperfect substitutes, and prices are sticky, monetary policy can influence the terms of trade in a way that benefits domestic consumers at the rest of the world’s expense. Only after this second distortion is also neutralized via the subsidy does full stabilization of domestic prices exactly replicate the flexible-price efficient allocation, ruling out any long-run inflation or deflation bias.

Setting rt = rrt directly is consistent with the optimal zero-inflation, zero-output-gap equilibrium, but that equilibrium is not unique under such a passive rule: the model instead admits a continuum of other, self-fulfilling (“sunspot”) equilibria in a neighborhood of the optimum, exactly as in the analogous closed-economy indeterminacy result (Sec. 4.1.1, Appendix C). The paper shows uniqueness can be restored by having the central bank instead commit to an active Taylor-type feedback rule, rt = rrt + φππH,t + φxxt, satisfying the Bullard and Mitra (2002) determinacy condition κα(φπ − 1) + (1−β)φx > 0; once determinacy is restored, the feedback terms vanish in equilibrium (since inflation and the output gap are zero at every date), so the credible threat of responding to deviations is what achieves the optimum, without the response ever actually needing to be exercised.

The paper compares a domestic-inflation-based Taylor rule (DITR, rt = ρ + φππH,t), a CPI-inflation-based Taylor rule (CITR, rt = ρ + φππt), and a strict exchange rate peg (PEG, et = 0 for all t), and finds that the three regimes can be ranked by the volatility they imply for the nominal exchange rate and terms of trade, with the ranking essentially inverted for domestic inflation and the nominal depreciation rate (Sec. 5, 5.1.3, Table 1). In the paper’s baseline calibration, the standard deviation of the terms of trade falls from 1.60% under the optimal DIT benchmark to 1.53% under DITR, 1.43% under CITR, and 1.17% under PEG, while the standard deviation of domestic inflation rises from 0.00% (DIT, by construction, since the optimal policy fully stabilizes domestic prices and the output gap) to 0.27% under both DITR and CITR and 0.36% under PEG; the standard deviation of the nominal depreciation rate falls from 0.95% (DIT) through 0.86% (DITR) and 0.53% (CITR) to exactly 0.00% under PEG, by construction.

A CPI-based rule reacts to a broader price index that includes the terms of trade, so stabilizing CPI inflation partly requires muting the terms-of-trade adjustment itself, which in turn requires a fall in domestic prices, a more contractionary interest-rate response, and a negative output gap, whereas a domestic-inflation rule leaves the terms of trade freer to adjust in line with the optimal policy’s own (natural) terms-of-trade path (Sec. 5.1.2, Fig. 1). Following a domestic productivity shock, the paper’s calibrated impulse responses show the terms of trade depreciating on impact and then reverting immediately to steady state under DITR, closely mirroring the optimal policy, whereas under CITR the terms-of-trade response is more muted initially and follows a hump-shaped path, driven by the initial rise in both nominal and real interest rates needed to help stabilize the CPI. The paper explicitly characterizes CITR as “a hybrid regime, somewhere between a domestic inflation-based Taylor rule and an exchange rate peg.”

Under a peg, the nominal exchange rate cannot adjust at all, and because domestic prices are sticky, they cannot fully compensate for the exchange rate’s constancy, so the terms of trade end up excessively stable relative to what the optimal, flexible policy would deliver – an “excess smoothness” of the real exchange rate that the paper explicitly connects to the empirical finding in Mussa (1986) that real exchange rates are much smoother under fixed than under floating nominal exchange rate regimes (Sec. 5.1.3). Because relative prices then fail to absorb shocks (such as a rise in domestic productivity) sufficiently quickly, the burden of adjustment falls disproportionately on domestic quantities and prices themselves, producing the largest output-gap and domestic-inflation volatility of the three regimes, and, correspondingly, the peg’s substantially larger welfare losses relative to either Taylor rule.

Across every calibration the paper considers, an exchange rate peg implies “a substantially larger deviation from the first best” (in percentage units of steady-state consumption) than either Taylor rule, while the two Taylor rules – domestic-inflation-based and CPI-based – imply “very similar welfare losses” to each other, pointing to a “substantial irrelevance” in which inflation index the rule targets, at least under the paper’s assumption of complete exchange-rate pass-through (Sec. 5.1.3, Table 2). At the benchmark calibration, the paper notes that welfare losses under all three regimes are “quantitatively small,” as is typical in this class of models; but lowering the steady-state markup (which raises the weight the loss function places on inflation variability) and/or lowering the elasticity of labor supply (which raises the weight placed on output-gap variability) substantially magnifies the losses, especially for the peg – with the largest welfare loss in the paper’s reported set of calibrations occurring in the scenario combining both a low markup and a low labor-supply elasticity, where the peg’s loss becomes “non-trivial” relative to the optimum.

The sign of the domestic response to a world output shock is ambiguous in general, depending on a composite parameter Θ (≡ ω − 1, where ω ≡ σγ + (1−α)(ση−1)); it is exactly zero, however, in the special case ω = 1, which includes σ = η = γ = 1, so that under the paper’s own welfare-optimal parameterization a change in world output leaves domestic output, the terms of trade, and domestic marginal cost entirely unchanged (Sec. 4.1.2, eq. 34-35). More generally, the paper shows that greater openness α lowers the terms-of-trade adjustment needed to absorb a given change in relative domestic output whenever ση > 1, dampening the resulting effect on marginal cost and inflation – so the framework does not support a simple “openness always amplifies shocks” or “openness always dampens shocks” statement; the sign depends on the underlying elasticities of substitution.

The baseline calibration sets σ = η = γ = 1 (the special, welfare-tractable case), a Frisch labor-supply elasticity of 1/3 (φ = 3), a steady-state markup of 1.2 (implying an elasticity of substitution across varieties ε = 6), Calvo price stickiness θ = 0.75 (an average one-year interval between price resets), a discount factor β = 0.99 (a 4% annual steady-state real return), an openness parameter α = 0.4 (calibrated to Canada’s import/GDP ratio, with Canada treated as a prototype small open economy), and a Taylor-rule inflation coefficient φπ = 1.5 (Sec. 5.1.1, Table calibration). Exogenous domestic productivity and world output are each fit to AR(1) processes on HP-filtered quarterly data over 1963:1-2002:4 – Canadian labor productivity for domestic productivity (persistence 0.66) and U.S. GDP as the proxy for world output (persistence 0.86), with innovations correlated at 0.3 – grounding the model’s quantitative comparisons in an empirically calibrated small open economy rather than a purely illustrative parameterization.

The authors explicitly flag four directions left for future work: deriving the welfare function and optimal policy outside the special log-utility, unit-elasticity case; building a genuine two-country version of the model to study spillovers, coordination, and exchange-rate stabilization agreements (issues the single small-open-economy setup cannot address, since the rest of the world is exogenous to it); adding sticky nominal wages alongside sticky prices, which the closed-economy literature (Erceg, Henderson and Levin 2000) shows introduces an additional policy trade-off that could overturn strict domestic-inflation targeting’s optimality; and relaxing the paper’s assumption of complete exchange-rate pass-through, which local-currency-pricing models elsewhere in the literature show can materially change the desirability of CPI-based versus domestic-inflation-based rules (Sec. 6). These four gaps were subsequently addressed by a large body of open-economy New Keynesian and, later, heterogeneous-agent open-economy work – including the companion papers this batch also covers – that builds directly on this paper’s canonical small-open-economy framework.