Reflections on Monetary Policy in the Open Economy

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Previous articleNext article FreeReflections on Monetary Policy in the Open EconomyRichard H. ClaridaRichard H. ClaridaColumbia University and NBER Search for more articles by this author PDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinked InRedditEmailQR Code SectionsMoreI. IntroductionA perennial topic of discussion among scholars and policy makers is how best to think about a benchmark for macroeconomics as it applies to monetary policy. Should the benchmark for policy analysis be the open economy with international interest rate linkages and flexible exchange rates (after all, major economies are in fact open with flexible exchange rates), or should it be the closed economy in which such linkages and exchange rate adjustments are assumed away? Of course, few if any policy makers would seek to guide policy by ignoring capital flows and exchange rates, but in many cases it appears as though the starting point for analysis is the closed‐economy macro model, these days a variant of the dynamic new Keynesian model.Those who start from a closed‐economy framework often have questions about how “openness” influences the analysis. How does the neutral real interest depend on “global” developments? Is the Phillips curve trade‐off between inflation and domestic output better or worse in the open versus the closed economy? Is “potential GDP” a function of global developments, or only of domestic resources available and domestic productivity? Perhaps most important, how—if at all—does openness influence the optimal monetary policy rule? Is a Taylor rule the right monetary policy for an open economy?In 2002 Jordi Gali, Mark Gertler, and I published a paper in the Journal of Monetary Economics that developed a benchmark (at least in our way of thinking) dynamic two‐country optimizing macro model of optimal monetary policies in the open economy. Our focus in that paper was deriving optimal policy rules in the two‐country model and assessing the gains from international monetary policy cooperation. In that paper, we emphasized the following implications of the model:• Optimal monetary policy in each open economy can be written as a Taylor rule, linear in the “domestic” equilibrium real interest rate and the gap between domestic inflation and the inflation target.• In general, there are gains to international monetary policy cooperation. Optimal monetary policy under cooperation can be written as a Taylor rule in which the domestic as well as the foreign inflation gap enters the reaction function, as well as the equilibrium real interest rate.• Optimal policy features a flexible exchange rate, and the nominal exchange rate under optimal discretionary policy has a unit root as does the domestic price level, and they are cointegrated. Optimal monetary policy produces a “random walk” nominal exchange rate because under discretion, the central bank cannot credibly commit to a price‐level target (but can achieve only a stationary inflation rate). This paper provides some intuition for these results and develops some further insights into monetary policy in the open economy. The approach I pursue is to “inspect the mechanism” of the two‐country Clarida et al. (2002) optimizing model by focusing on the three main building blocks that can be derived from it: the “open‐economy” IS curve, the open‐economy Phillips curve, and the open‐economy Taylor rule. Because these building blocks are derived from a two‐country optimizing model, we can use them to gain insight into how special the “special case” of the closed‐economy framework is, which does appear to be the starting point for much contemporary monetary policy analysis.The plan of the paper is as follows. In Section II, I describe the basic structure of the two‐country model. In Sections III, IV, and V, I derive and assemble the building blocks of the model: the open‐economy IS curve, the open‐economy Phillips curve, and the open‐economy policy rule. I illustrate and discuss in detail how openness affects the analysis and highlight an interesting empirical implication of the model, namely, that under inflation targeting, bad news about inflation can be good news for the nominal exchange rate, even though in the long run purchasing power parity (PPP) holds so that ultimately bad news about inflation is bad news for the exchange rate. In Section VI, I propose and implement a new approach for calibrating forward‐looking Taylor rules that makes use of real‐time financial data on inflation‐indexed government bonds and break‐even inflation in lieu of the instrumental variable/generalized method of moments (GMM) approach introduced in Clarida et al. (1998). I apply this approach to the Fed and European Central Bank (ECB) reaction functions since 2000 and find that it accounts well for Fed policy with much less emphasis on interest rate smoothing than in prior work. For the ECB, the results are encouraging but less clear‐cut owing to the limited issuance of inflation‐indexed bonds during much of the sample. Section VII offers some concluding remarks.II. Review of the Theoretical Two‐Country ModelA. Essence of the ModelThe complete model is presented in Clarida et al. (2002) and is sketched out in this section. There are two countries, producing differentiated tradable final goods from a continuum of intermediate labor varieties. Households share identical Cobb‐Douglas preferences over a consumption index $$C_{t}$$ of home and foreign varieties. A key parameter is γ, which is the share of home spending on foreign goods. The larger γ is, the more open the home economy, which is the economy I shall focus on for the purposes of this discussion. The law of one price holds and there is producer currency pricing. Under these assumptions (see Cole and Obstfeld 1991; Corsetti and Pesenti 2001) the complete markets allocation can be achieved through endogenous adjustments in the equilibrium terms of trade, denoted by $$S_{t}$$, that clear the world goods market.Household utility takes the standard form where $$1/ \sigma $$ is the intertemporal elasticity of substitution of consumption, and $$N_{t}( h) $$ is labor supply. I focus on the benchmark case with $$\sigma > 1$$. However, as I discuss below, this assumption is not innocuous.Firms produce final output from a variety of intermediate inputs $$Y_{t}( f) $$: Each intermediate input $$Y_{t}( f) =A_{t}N_{t}( f) $$ is produced from a variety of labor inputs and an exogenous productivity shock $$A_{t}$$, where Note that each household (and each input producer) has market power because labor varieties (and intermediate inputs) are heterogeneous and imperfectly substitutable. However, while we assume that money wages are flexible, intermediate goods prices are sticky.Firms will set prices as a markup over marginal cost. Real marginal cost is just the real product wage scaled by productivity $$MC_{t}=( 1-\tau ) ( W_{t}/ P_{H,t}) A^{-1}_{t}$$. In our open economy this can be written as where $$P_{t}$$ is the consumer price index (CPI), τ is a wage subsidy, and $$k=( 1-\gamma ) ^{( 1-\gamma ) }\gamma ^{\gamma }$$. From the first‐order condition for labor supply we have where $$1+\mu ^{w}_{t}=\eta _{t}/ ( \eta _{t}-1) $$ is a wage markup. With flexible wages, all workers are paid the same wage and work the same hours, so the h indicator is redundant and will be suppressed below.B. Some Equilibrium ConditionsThe following equilibrium conditions hold in both the flexible‐price and sticky‐price equilibrium. In equilibrium current accounts are in balance period by period, and the consumption index satisfies where $$Y^{*}_{t}$$ is foreign output. The equilibrium terms of trade that brings this about is In equilibrium, the amount of home output produced will depend on labor supply, productivity, and the dispersion across firms in the prices of intermediate goods: where $$V_{t}$$ is an index of price dispersion across intermediate input sellers: From all this it follows that equilibrium real marginal cost in the open economy $$MC_{t}$$ can be written as where and Marginal cost spillovers. The sign of the effect of foreign output on home marginal cost is given by κ0. Under our assumption that $$\sigma > 1$$, κ0 is positive and, thus, so is the spillover from foreign output to domestic marginal cost. A rise in foreign output improves the home terms of trade, and this, by increasing the purchasing power of home wages, will tend to lower home marginal cost with an elasticity of γ. But the improvement in the home terms of trade will also raise the consumption index and lower the marginal utility of work, and thus raise marginal cost with an elasticity of γσ. In the benchmark case $$\sigma > 1$$, this income effect from a foreign output expansion dominates the substitution effect and marginal cost spillovers are positive. However, if $$\sigma < 1$$, the substitution effect dominates and a rise in foreign output lowers home marginal cost. In the knife‐edge case $$\sigma =1$$, there are no international spillovers to home marginal cost.Although our focus will be on the sticky‐price equilibrium, it is useful to solve for the flexible‐price equilibrium, the case in which all firms can change their price every period. In this case, $$P_{H,t}$$ will be common across firms and will be a constant markup over nominal marginal cost, so that real marginal cost will be constant and equal to $$\overline{MC}=1/ ( 1+\mu ^{p}) $$, where an overbar represents the flexible‐price equilibrium and $$1+\mu ^{p}=\xi / ( \xi -1) $$. Every firm will choose the same price, so $$V_{t}=1$$ and we have Using (9), which always holds, and the expression for real marginal cost, which holds under flexible prices, we can solve for the “natural” level of home output consistent with a given level of foreign output and the mean level of the wage markup: Thus in the open economy the natural rate of output is a function of foreign output unless $$\sigma =1$$. When $$\sigma > 1$$, a rise in foreign output, with home productivity held constant, raises home marginal cost, and this lowers home natural output because the income effect from the terms of trade gain lowers the flexible‐price labor supply. Moreover, this effect is larger the more open the economy. Note, however, that if the source of the rise in foreign output is a productivity shock that is positively correlated with home productivity, the reduced‐form correlation between home natural output and foreign output can be positive even for the case $$\sigma > 1$$.III. The Open‐Economy IS CurveIn this model, as in many other new open‐economy macro models, the path for optimal consumption must satisfy an Euler equation of the form where $$r_{t}$$ is the nominal interest rate, πt is domestic inflation, and lowercase letters for all other variables denote log deviations from the nonstochastic steady state. We note that $$\pi ^{\mathrm{CPI}\,}_{t+1}=\pi _{t+1}+\gamma \Delta s_{t+1}$$. How do we turn this into an open‐economy IS curve? We start by recognizing that with balanced trade $$y_{t}=c_{t}+\gamma s_{t}$$ and substitute out for $$c_{t}$$ and $$c_{t+1}$$. We obtain an Euler equation in $$y_{t}$$: The terms of trade plays several roles. As in static models, a terms of trade worsening boosts exports and increases demand for domestic output. But an anticipated terms of trade worsening raises expected inflation and lowers the consumption real interest rate for any given nominal interest rate. Consider the special case in which $$E_{t}y_{t+1}=\rho y_{t}$$ and $$E_{t}s_{t+1}=\rho s_{t}$$ (which in fact will be the case under optimal monetary policy with an exogenous home cost push shock, no foreign cost push shock, and constant productivity as shown in Clarida et al. [2002]). In this case the open‐economy IS curve can be written as This is form of the IS curve often found in traditional overshooting literature. We note that with the benchmark case $$\sigma > 1$$, a rise in $$s_{t}$$ that increases the relative price of foreign goods in terms of home goods will boost aggregate demand for home output. Of course, a rise in the real interest rate reduces aggregate demand for home output.In this particular model, we have more structure, so we can say more about the open‐economy IS curve. We know that $$s_{t}=y_{t}-y^{*}_{t}$$. So we can substitute out for $$s_{t}$$. Defining the log domestic output gap $$\tilde{y}_{t}=y_{t}-\overline{y}_{t}$$, we obtain where is the domestic natural real interest rate, with where it will be recalled that $$\kappa _{0}=\gamma ( \sigma -1) $$. In our benchmark case, $$\sigma > 1$$ and $$\kappa _{0}> 0$$. Also note for the benchmark case that σ0 is decreasing in γ, the parameter that indexes openness.There is a lot going on here, so let us take stock. We have derived an open‐economy IS curve in terms of the domestic output gap and the gap between the domestic real interest rate and the appropriate natural real interest rate. How is this an open‐economy IS curve? First, as discussed above, the natural rate of output in the open economy depends on the level of foreign output, and thus the domestic output gap does depend on foreign output.Second, the slope of the open‐economy IS curve depends on how open the economy is. In our benchmark case $$\sigma > 1$$, the semielasticity of aggregate demand for domestic output with respect to the real interest rate is increasing in openness. In other words, in our benchmark case, a more open economy has a flatter IS curve, so that the central bank gets more bang out of every basis point buck by which it changes the policy rate.Third, the appropriate natural or neutral real interest rate depends on foreign output growth as well as home output growth: In the special case $$\sigma =1$$, this reduces to the standard growth model in which the neutral real interest rate is equal to the domestic growth rate in potential output. In the benchmark case with $$\sigma > 1$$, κ0 is positive, and the neutral domestic real interest rate is positively correlated with foreign growth. Moreover, the more open the economy, the more important the effect of foreign output growth on the domestic real interest rate.IV. The Open‐Economy Phillips CurveWe assume as in Calvo that prices of domestic intermediate goods are sticky and that a constant fraction $$1-N$$ of firms can change price every period. The optimal price chosen at date t is given by where $$Q_{t,t+j}$$ is the standard stochastic discount factor. With this standard staggered price model, the domestic price index evolves according to From this it follows that domestic inflation (producer price index [PPI] inflation) evolves according to where $$\delta =( 1-N) ( 1-\beta N) / N$$.Thus domestic inflation in the open economy is driven by the present value of log real marginal cost. But what is log real marginal cost in the open economy? One way to express log real marginal cost is simply As is evident from this equation, other things equal, an improvement in the home terms of trade, a fall in $$s_{t}$$, lowers real marginal cost and is thus disinflationary. Moreover, the more open the economy, the larger the effect of the terms of trade on real marginal cost and thus on inflation.Given the structure of our model, it is possible to express real marginal cost as a function of home output, foreign output, and productivity: However, from the definition of domestic natural output, we know that $$\overline{y}_{t}=\kappa ^{-1}[ ( 1+\phi ) a_{t}-\kappa _{0}y^{*}_{t}] $$. It follows that in equilibrium, the log of real marginal cost can be written as where it will be recalled that $$\kappa =\sigma ( 1-\gamma ) +\gamma +\phi $$.The open‐economy Phillips curve follows immediately: where $$\lambda =\delta \kappa $$. We see that, in our benchmark case with $$\sigma > 1$$, the more open economy has a flatter Phillips curve in terms of domestic (PPI) inflation.1 The intuition is as follows. The more open the economy, the smaller the impact of a change in domestic output on the domestic consumption index and thus the marginal utility of consumption, so this tends to reduce the impact of domestic output on marginal cost. However, the more open the economy, the greater the impact on marginal cost of the terms of trade change that follows from a change in output. In our benchmark case, the income effect of the rise in output outweighs the induced effect of the terms of trade change, resulting in a flatter open‐economy Phillips curve. In practice, many central banks target CPI, not PPI, inflation. The Phillips curve expressed in terms of CPI inflation will contain an additional term γΔe reflecting the assumed full pass‐though of the exchange rate to import prices. The impact of a shock on a CPI open‐economy Phillips curve will depend on the nature of the shock, for example, a productivity shock as opposed to a cost push shock, as well as σ. Potentially also, the slope of the CPI Phillips curve will depend on the credibility of the inflation target (which in this paper is assumed credible) as well as on the policy rule (e.g., to the extent that money growth or interest rates lean against the exchange rate).V. Completing the Model: Policy Rules for the Open EconomyCombining our IS and Phillips curve and terms of trade equations, we have where the home country takes foreign output as given. To close the model, we need to specify a path for the home nominal interest rate.As is customary in this literature, we assume that the central bank maximizes Clarida et al. (2002) show that this quadratic approximation to the social welfare function in the open economy can be derived as in Woodford (2003) and that at a social optimum $$\alpha =\lambda / \xi $$ or Thus, in our benchmark case, we see that a more open economy places a smaller weight on output stabilization and thus a larger weight on inflation stabilization. This follows directly from the fact that the more open economy has a flatter Phillips curve under our benchmark case.Under discretion, optimal policy must satisfy the following first‐order conditions: with $$\Psi =[ ( 1-\beta \rho ) +\lambda \xi ] ^{-1}$$, where ρ is the exogenous autocorrelation in shocks to the markup.2 One way to write the optimal monetary policy in the open economy is as a forward‐looking Taylor rule, with We see immediately that for our benchmark case with σ0 decreasing in γ, in a more open economy the central bank needs to lean less against the wind for any given inflation shock. This is so even though the more open economy places a greater weight on inflation stabilization. The intuition for this result is that for our benchmark case of $$\sigma > 1$$, the more open economy has a flatter IS curve, which means that the central bank gets more bang out of every basis point: In effect, a given rise in the real interest rate affects aggregate demand through two channels, exports and domestic consumption. Under a Taylor rule, an inflation shock is met by a rise in the ex ante real policy rate, and this induces a real appreciation and an improvement in the terms of trade.While there is a unique way to write the optimal policy rule as a function of the model’s state variables $$\{ a_{t},\,a^{*}_{t},\,u_{t},\,u^{*}_{t}\} $$, there are several ways to express the policy rule in terms of endogenous variables so that (30) is by no means unique. For example, we can also write the optimal policy rule as where we assume for expositional convenience that $$\pi ^{*}=0$$. Thus, while in our open‐economy framework it is possible to write the optimal policy rule without explicitly including the nominal exchange rate, there is an equivalent way to express the rule that includes the nominal exchange rate of depreciation as well as the growth rate differential between the home and foreign country. The intuition is as follows. A nominal rate of depreciation equal to the growth differential will produce a terms of trade

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