Elsevier

Journal of International Economics

Volume 108, September 2017, Pages 300-314
Journal of International Economics

Optimal monetary policy in open economies revisited

https://doi.org/10.1016/j.jinteco.2017.07.006Get rights and content

Abstract

This paper revisits optimal monetary policy in open economies, in particular, focusing on the noncooperative policy game under local currency pricing in a two-country dynamic stochastic general equilibrium model. We first derive the quadratic loss functions which noncooperative policy makers aim to minimize. Then, we show that noncooperative policy makers face extra trade-offs regarding stabilizing real marginal costs induced by deviations from the law of one price under local currency pricing, and that optimal monetary policy seeks to stabilize CPI inflation rates and more so under noncooperation than it does under cooperation. As a result of the increased number of stabilizing objectives, welfare gains from cooperation emerge even when two countries face only technology shocks. Still, gains from cooperation are not large, implying that frictions other than nominal rigidities are necessary to strongly recommend cooperation as an important policy framework to increase global welfare.

Introduction

In a world of integrated trade in goods and assets, sovereign nations become more and more interdependent. The prolonged recession after the Global Financial Crisis again reminds policy makers in major economies of the depth and scope of such interrelations. Understanding the nature of cross-country spillovers of shocks and policy impacts comes back to center stage in policy discussions. Should central banks cooperate in order to internalize the possible externality from policy reactions? Is there any gain from such cooperation? And if so, how large might it be?

The desirability of policy cooperation, namely whether there exist gains from cooperation, has been one of the central issues in macroeconomics. The root of the discussion can be traced way back to Hume (1752), who first noticed possible policy spillovers among countries. Since then, there have been a vast number of studies investigating the nature of policy games in open economies. Recently, many have studied optimal monetary policy in open economies using micro-founded, open-economy sticky-price models based on the so-called New Open Economy Macroeconomics (hereafter, NOEM) initiated by Obstfeld and Rogoff, 1995, Svensson and van Wijnbergen, 1989. Contrary to traditional studies using the Mundell-Fleming model, correct welfare can be computed with the NOEM models. Thus, comparison of different policies becomes possible without resort to ad hoc criteria.

This paper revisits optimal monetary policy in open economies in a new direction, which is a noncooperative game under local currency pricing (hereafter, LCP). The motivations behind seeking optimal noncooperative monetary policy under LCP are twofold: one is positive and the other is normative. The former arises because exchange rate pass-through is imperfect. There are numerous empirical studies which point out significant deviation from the law of one price. To name a few, Isard (1977), among early studies on this issue, presents evidence that “the law of one price is flagrantly and systematically violated.” Knetter (1993) reports that “Japanese and German exporters use destination-specific markup adjustment to stabilize local-currency prices of exports.” Goldberg and Knetter (1997) offer a comprehensive survey of early literature on empirical evidence that “the local currency prices of foreign products do not respond fully to exchange rates.” Engel (1999) shows that “relative prices of nontraded goods appear to account for almost none of the movement of U.S. real exchange rates,” implying that there are significant fluctuations in the relative prices of traded goods. A recent study by Atkeson and Burstein (2008) provides new evidence using individual prices: “the terms of trade for manufactured goods are significantly less volatile than the manufacturing PPI-based real exchange rate; and that the CPI-based real exchange rate for goods has roughly the same volatility as the manufacturing PPI-based real exchange rate.” These two findings support their modeling strategy to put emphasis on “the decisions of individual firms to price-to-market.”

The latter motivation will be discussed in detail in the next subsection, and is illustrated diagrammatically in Table 1. Optimal monetary policy in open economies has been investigated under many different settings in the NOEM, such as under cooperation or noncooperation, producer currency pricing (hereafter, PCP) or LCP, and with or without home bias. Consequently, our understanding of how monetary policy should be conducted in an interconnected world is deepened. There is, however, one last missing piece, which has not yet been analyzed in a theoretical dynamic stochastic general equilibrium (hereafter, DSGE) model. That is, how optimal noncooperative monetary policy under LCP should be conducted, or whether there are any gains from cooperation under LCP. These are the questions to which we aim to give answers in this paper.

For this purpose, we first solve the equilibrium conditions under monopolistic competition, sticky prices and LCP in a two-country model. The Ramsey (deterministic) steady states under both cooperative and noncooperative regimes are at globally efficient levels and identical to those under the flexible-price equilibrium. Thus, the exact welfare comparison between cooperation and noncooperation becomes possible. Then, we approximate welfare around this deterministic steady state up to the second order. In a noncooperative regime, even if the steady state is efficient thanks to the optimal subsidy, linear terms cannot be eliminated. Following Sutherland, 2002, Benigno and Woodford, 2005, Benigno and Benigno, 2006, we take a second-order approximation to the structural equations to substitute out the linear terms with only second-order terms. Correct welfare metrics up to the second-order approximation are thus obtained.

Our loss functions under LCP show that noncooperative policy makers naturally aim to stabilize variables whose fluctuations are to be minimized by cooperative policy makers as analyzed in Engel (2011), including output, producer price index (hereafter, PPI) inflation rates, import price inflation rates, and deviations from the law of one price.1 In addition, they also seek to stabilize fluctuations in real marginal costs that firms face when setting prices in both domestic and export markets. These additional objectives are unique to the noncooperative game and therefore the sources for potential gains from cooperation, which are absent in previous studies on optimal monetary policy in open economies.2

Then, in order to clarify the nature of optimal monetary policy in open economies, we compare impulse responses under optimal monetary policies among three cases: (1) PCP; (2) cooperative regime and LCP; (3) noncooperative regime and LCP. Note that in our setting with only technology shocks, optimal cooperative as well as noncooperative policies result in identical allocations and prices under PCP.

Fluctuations in consumer price index (hereafter, CPI) inflation rates become smaller under LCP than under PCP. This is because the violation of the law of one price induces inefficient price dispersions within producer as well as export prices, as emphasized by Engel (2011). As a result, the “inward-looking” policy that focuses on stabilization of PPI inflation rates is no more optimal under LCP. In addition, under LCP, noncooperative policy makers stabilize CPI inflation rates more than cooperative central banks do. This larger stabilization motive arises from the unique objectives in the loss functions under noncooperation. Inability to cooperate constrains the dynamics toward more efficient outcomes. Reactions of domestic output to a domestic technology shock become smaller under noncooperation. Without any frictions, global welfare increases when production in the country with favorable efficiency shocks increases. This difference in the responses of output creates room for cooperative policies to improve global welfare.

We also compute the welfare gain from cooperation under LCP by solving the nonlinear Ramsey problem. Welfare gains from cooperation are largest with log utility even though both countries become insular in structural equations under PCP. Still, welfare gains computed from nonlinear Ramsey problems are not sizable with only technology shocks. Within the reasonable range of parameter calibration, the welfare cost stemming from the inability to cooperate can only be, at most, 0.04% in consumption units, in response to one standard deviation of technology shocks. Corsetti (2008) remarks that in early leading studies, the quantitative assessment of welfare gains from cooperation is found far from sufficient to justify cooperation, and whether this result still holds in richer models is a critical research question. Our paper finds that given only price rigidities, sizable welfare gains may not arise from cooperation.

First, we classify previous studies of optimal monetary policy in open economies by three dimensions.3 The first dimension regards assumptions about nominal rigidities, that is, either one-period ahead price setting or staggered price setting à la Calvo (1983). In early studies using one-period ahead price setting, analytical solutions can be obtained with money supply as the control variable of monetary policy. With staggered price setting, central banks maximize correctly approximated social welfare up to the second order subject to the linearly approximated structural equations. The second dimension is about export price setting, namely PCP or LCP. In the former, export prices fully reflect exchange rate fluctuations, while not at all in the latter. The third dimension is whether monetary policy in open economies is conducted in a cooperative or noncooperative manner.

Table 1 offers a taxonomy of previous studies on optimal monetary policy in open economies. Regarded as the beginning of the NOEM framework for monetary policy analysis in open economies, Obstfeld and Rogoff (1995) develop a micro-founded two-country model with PCP and a one-period in advance price setting rule. Monetary expansion in any country increases social welfare globally. Thus, there is no scope for policy cooperation. Corsetti and Pesenti (2001) extend the model of Obstfeld and Rogoff (1995) by assuming different elasticities of substitution within and across goods categories.4 A domestic monetary expansion can be either beggar-thy-neighbor or beggar-thyself depending on the elasticity of substitution, giving rise to national policy makers' incentives to manipulate the terms of trade in favor of their own welfare. Obstfeld and Rogoff (2002) assume the existence of the nontradable sector for their examination of international cooperation under PCP. When nominal stickiness has little interaction with real distortions, welfare gains from cooperation are relatively small.

Devereux and Engel (2003) assume LCP while keeping the price setting in the period-by-period basis. The flexible exchange rate regime is no longer optimal under LCP. Distortions stemming from the violation of the law of one price should be corrected by restricting the fluctuations of nominal exchange rates. Corsetti and Pesenti (2005a) propose a unifying approach to model the exchange rate pass-through in which PCP and LCP are two extreme cases of the parameterization. No welfare gains from cooperation are found under either complete or no exchange rate pass-through. In general cases with partial exchange rate pass-through they argue that a country can do better than “keeping one's house in order”.

Clarida et al., 2002, Benigno and Benigno, 2003 (Benigno and Benigno, 2003, Benigno and Benigno, 2006) all assume the staggered price adjustment rule à la Calvo (1983) and obtain quadratic loss functions under cooperation as well as noncooperation under PCP. Clarida et al. (2002) choose output as policy variables. The linear terms in the second-order approximation of the utility function are eliminated by strategic use of a sales subsidy. As a result, Ramsey steady states become different between cooperation and noncooperation. On the other hand, they are set to be identical in Benigno and Benigno (Benigno and Benigno, 2003, Benigno and Benigno, 2006). Benigno and Benigno (2003) derive the quadratic loss function under noncooperation using the fact that price stability turns out to be optimal monetary policy. Benigno and Benigno (2006) make use of second-order approximations of the structural equations to substitute out those linear terms following Sutherland, 2002, Benigno and Woodford, 2005. Besides the methodological differences, these three studies also take on different focuses on the implications of optimal policy analysis. Specifically, Clarida et al. (2002) appraise the potential gains from cooperation arising from internalizing the terms-of-trade externalities. Benigno and Benigno (2003) explore the theoretical conditions under which flexible-price allocations are optimal, and cooperative and noncooperative allocations coincide under PCP. Finally, Benigno and Benigno (2006) show how to design simple rules for noncooperative policy makers to achieve cooperative allocations in the linear-quadratic framework.

Engel (2011) incorporates the staggered price setting rule for optimal monetary analysis under LCP and the cooperative regime. Home bias in consumption preferences is also assumed. With home bias, central banks face a trade-off between the costs of currency misalignment and the stabilization of asymmetric output fluctuations. The derived quadratic global loss function highlights international relative price misalignments stemming from the violation of the law of one price under LCP. Thus, optimal cooperative policy under LCP should trade off these misalignments with inflation and output goals, and should target CPI inflation rates rather than just PPI inflation rates. Our paper is an extension of Engel (2011) to the noncooperative game, providing the final block of the class of the NOEM literature as summarized in Table 1.

Several recent studies provide new insights on different dimensions of the monetary policy game. Corsetti et al. (2010) review previous studies on optimal monetary policy in open economies with incomplete financial markets. The targeting rules, which central banks in open economies should follow, may allow deviations from allocations and prices under optimal risk sharing. Senay and Sutherland (Senay and Sutherland, 2007, Senay and Sutherland, 2013) show that the timing of trading in asset markets relative to policy decisions matters to optimal policy design in open economies. If policy decisions are made before asset trading takes place, information about the policy decision must be incorporated in the risk sharing condition. In above-mentioned studies on optimal monetary policy in open economies, the opposite timing assumption is usually but implicitly assumed. There, the risk sharing condition becomes independent of policy making. Although the differences in optimal policies between cooperation and noncooperation are not discussed in Senay and Sutherland (Senay and Sutherland, 2007, Senay and Sutherland, 2013), the timing of asset trading offers new insights on possible gains from cooperation. Engel (2016) is among the first attempts to investigate these issues altogether, namely the differences between cooperation and noncooperation under both complete and incomplete markets, where state contingent assets are traded after policy making.5 It is shown that “optimal policy, even under complete financial markets and cooperation, does not try to minimize spillovers.” The spillovers under optimal policy are different between cooperation and noncooperation.

The rest of the paper is organized as follows. Section 2 specifies the model and derives equilibrium conditions. Section 3 sets up optimal policy problems in both nonlinear and linear-quadratic frameworks. Quadratic loss functions under LCP and noncooperation are derived. Section 4 compares impulse responses under both games and computes welfare costs stemming from noncooperation. Section 5 concludes.

Section snippets

The model

The model is close to the one considered in Engel (2011). There are two countries of equal size, Home and Foreign, each populated with a continuum of households with population size normalized to unity. Agents in the two countries consume both home goods and foreign goods but have a symmetric home bias. Households supply labor services to firms within their own country via a competitive labor market. Households are also the owner of domestic firms. Firms maximize profits in a monopolistically

Optimal monetary policy in open economies

In this section, we first set up the Ramsey problem. Optimal monetary policy under noncooperation is derived in an open-loop Nash equilibrium. Then, we derive the quadratic loss functions which central banks aim to minimize by the second-order approximation to social welfare around the Ramsey steady state.

Results

In this section, we first draw impulse responses of the two countries to a positive technology shock to the home country. The dynamics are obtained under the optimal monetary policy in Section 3.2. We consider cooperative and noncooperative games under both PCP and LCP. As discussed in previous section, cooperative and noncooperative allocations and prices coincide under PCP. We then compute welfare gains from cooperation using the Ramsey policy problem presented in Section 3.1.

Conclusion

This paper finds that there exist gains from cooperation with optimal monetary policy under LCP in response to technology shocks. A two-country DSGE model is developed in the paper and a linear-quadratic approach is adopted to obtain the quadratic loss functions of noncooperative policy makers. The paper shows that noncooperative policy makers under LCP face extra trade-offs regarding stabilizing real marginal costs induced by deviations from the law of one price. Optimal monetary policy seeks

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    We thank the Editor, Charles Engel and two anonymous referees for many useful comments. We also have benefited from discussions with Kosuke Aoki, Pierpaolo Benigno, Richard Dennis, Mick Devereux, Jinill Kim, Warwick McKibbin and seminar participants at the Australian National University and the University of Melbourne. Fujiwara is grateful for financial support from JSPS KAKENHI Grant-in-Aid for Scientific Research (A) Grant Number 15H01939. Wang is grateful for financial support from Australian Research Council Discovery Project 160102654.

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