ثبات و قوانین سیاست های پولی اقتصاد کلان در سراسر جهان

We study the interaction of multiple large economies in dynamic stochastic general equilibrium. Each economy has a monetary policymaker that attempts to control the economy through the use of a linear nominal interest rate feedback rule. The main results show how the determinacy of worldwide equilibrium depends on the joint behavior of policymakers worldwide. The results also show how indeterminacy exposes all economies to endogenous volatility, even ones where monetary policy may be judged appropriate from a closed economy perspective. Two quantitative cases are discussed. In the 1970s, worldwide equilibrium was characterized by a two-dimensional indeterminacy, despite US adherence to a version of the Taylor principle. In the last 15 years, worldwide equilibrium was still characterized by a one-dimensional indeterminacy, leaving all economies exposed to endogenous volatility. This analysis provides a rationale for a type of international policy coordination, and the gains to coordination in the sense of avoiding indeterminacy may be large.

It has been widely documented that the 1970s and early 1980s were characterized by substantially more macroeconomic volatility than the later 1980s or the 1990s in the major industrialized economies.1 In an influential paper, Clarida et al. (2000) explored the possibility that the earlier era might be viewed as a sunspot equilibrium induced by poor monetary policy. Their empirical results suggested that US policymakers did not obey the Taylor principle 2 during this era, and their theoretical findings suggested that failure to obey the Taylor principle can be associated with indeterminacy of rational expectations equilibrium and the possibility of sunspot equilibria. Under this interpretation, the volatility observed during the 1970s was facilitated by poor policy. 3 A natural question is how the Clarida et al. (2000) analysis may be altered in an open economy setting. With several large economies interacting, determinacy of the resulting world equilibrium hinges on the joint actions of world policymakers. It is not very clear a priori how the determinacy conditions might be influenced by the nature of policy in each of the countries, the nature of the economic interactions between the economies, or the relative size of the economies involved. The principal goal in this paper is to explore an international version of the Clarida et al. (2000) argument. One of the recent extensions of the standard New Keynesian model to multiple, large industrialized economies is employed for this purpose. The primary goal is to understand how the monetary policies in the various economies impinge on the determinacy of worldwide equilibrium. In the closed economy literature, indeterminacy of rational expectations equilibrium has been viewed as an outcome to be avoided if at all possible. This is because indeterminacy is associated with the existence of, at least potentially, quite volatile rational expectations equilibria in which the volatility is unrelated to the fundamental disturbances buffeting the economy.4 The same view of the worldwide equilibrium is adopted for this paper. But because there are multiple policymakers in the international setting, interest also centers on the implications that might be drawn for international monetary policy coordination. The coordination can be designed primarily to avoid indeterminacy of worldwide equilibrium. 1.1. Main findings The analysis shows how determinacy of worldwide equilibrium depends on the joint behavior of the world's policymakers in the model. The conditions for determinacy that apply in the open economy setting are shown to be related to certain conditions that are available from known closed economy analyses. The open economy setting puts a relatively sharp upper bound on how aggressive each policymaker can be in its policy rule with respect to inflation deviations in order to remain consistent with determinacy. This finding is consistent with some of the related small open economy literature and suggests that analyses of major industrialized economies in closed economy settings—surely the bulk of the analysis to date in the large and rapidly growing New Keynesian literature—may be misleading from the perspective of the discussion of which types of monetary policy rules are consistent with equilibrium determinacy. One focus of the paper is the idea that policymakers in a large economy may be able to take a simple unilateral action to guarantee determinacy of worldwide equilibrium. For example, the monetary authority in a large economy might be able to adopt a policy rule of a specific sort that effectively coordinates expectations worldwide and renders worldwide equilibrium determinate, even in a situation where monetary policy in partner economies would be, by itself, inappropriate for generating a determinate worldwide equilibrium. However, it turns out that the scope for one country to take a simple unilateral action to guarantee determinacy of world equilibrium is limited. It can be done, to be sure, in certain situations, but generally speaking if a foreign economy is pursuing a policy sufficiently inconsistent with determinacy, domestic policymakers would have no simple options that would render worldwide equilibrium determinate.5 Instead, they would have to suffer with indeterminacy and the potential for endogenous volatility, or try to persuade the policymakers in the foreign economy to change their approach to policymaking. One may have the intuition, as we did, that policymakers in a large economy could adopt policies and influence macroeconomic adjustment to shocks in such a way as to avoid the worst types of exposure to endogenous volatility, but such is not the case in the economy here. This and related results are discussed further in the main text. When worldwide equilibrium is indeterminate, all countries are exposed to endogenous volatility. One aim of the paper is to try to understand how this volatility plays out across the world economy. Sunspot equilibria are simulated for several calibrated, three-country cases, and the extent to which endogenous volatility originating in one country can be transmitted across borders is verified in each case. The dimension of indeterminacy can be as large as nine in a three country model, a clear change from the closed economy analysis. This means that multiple sunspot processes can be operating simultaneously, and in this sense the world economy can be exposed to endogenous volatility originating from many sources. One finding is that even economies in which policymakers are pursuing what may be viewed as an appropriate policy—a policy rule consistent with determinacy when viewed from a closed economy perspective—are exposed to additional volatility in the sunspot equilibrium. Those pursuing inappropriate policies fare even worse. This finding suggests that policymakers from large economies running what appears from a closed economy perspective to be very reasonable monetary policies may still have much to fear from the potential for endogenous volatility worldwide. This concern would be especially pronounced in cases where a large partner economy was pursuing a monetary policy inconsistent with worldwide equilibrium determinacy. The model analyzed here is not rich enough to match international data in a completely convincing way,6 but in keeping with the provocative analysis of Clarida et al. (2000), the paper ends with a consideration of some empirical estimates of monetary policy rules for the three largest economies in the 1970s, an era sometimes associated with indeterminacy, and in the 1990s, an era often described approvingly as being associated with better monetary policy worldwide. Using these estimates, our global perspective suggests that the earlier era was characterized by a two-dimensional indeterminacy in the worldwide equilibrium. The US can actually be viewed as following a rule conducive to equilibrium determinacy, but still, because the partner countries were not, the world equilibrium would still have been indeterminate, leaving the US as well as all other countries exposed to endogenous volatility. For the more recent era, worldwide equilibrium is characterized by a one-dimensional indeterminacy, so that the world economy is still exposed to endogenous volatility. The point is to emphasize that calculations like these would clearly depend on joint policymaker behavior in the large economies, and may not be evaluated effectively in a closed economy model. These findings have implications for concepts of international monetary policy coordination. The theoretical, fully optimal cooperative worldwide monetary policy has been worked out for this model.7 But the present paper is written from a positive perspective, and the empirical findings suggest that not every industrialized country has employed at each moment in time a monetary policy rule consistent with determinacy of worldwide equilibrium. Some have, to be sure, but others have not, and according to the estimates the major economies have not simultaneously pursued policy sufficient to induce determinacy of worldwide equilibrium. One implication may be that the world's policymakers should not be content to let each large economy pursue monetary policy unilaterally. Coordination in our model most likely means direct discussions with foreign policymakers in an attempt to convince them to follow a policy rule which will, in joint operation with other monetary policies, generate a unique rational expectations equilibrium worldwide. Viewed from this perspective, the gains from international monetary policy coordination may be large. 1.2. Recent related literature A number of papers have addressed determinacy issues and the connection to monetary policy for small open economies. De Fiore and Liu (2005) study a small open economy version of Cooley and Hansen (1989). They find that monetary policy rules associated with determinacy in the closed economy may not be associated with determinacy in the open economy. The analysis here produces similar results for a model with large economies interacting. The De Fiore and Liu (2005) findings contrast with earlier work by Carlstrom and Fuerst (1999) for a small open economy, which suggested that determinacy conditions were largely unaffected by trade openness. But Carlstrom and Fuerst (1999) did not have the terms of trade effects that play an important role in De Fiore and Liu (2005) and in the present paper. Zanna (2003) also works in a small open economy setting, in continuous time and under alternative assumptions relative to the present paper. He finds that the degree of openness and the degree of exchange rate pass-through are key factors for generating a determinate equilibrium under a given monetary policy rule. Linnemann and Schabert (2004) work in continuous time as well and with a somewhat different small open economy model. They also find that equilibrium determinacy generally depends on the degree of trade openness. Batini et al. (2004) discuss indeterminacy issues in a symmetric two-bloc model related to ours. The model used by Batini et al. (2004) is a more elaborate, two-country version of the n-country model employed here. The focus of Batini et al. (2004) is to use root-locus methods to analyze how equilibrium determinacy is related to the forecast horizon of policymakers that react to expected inflation alone with policy inertia. They find, in agreement with the present paper, that there is an upper bound on how aggressive policymakers can be if the goal is to generate determinacy of worldwide equilibrium, and they also argue that longer forecast horizons tend to be associated with indeterminacy. The forecast horizon is fixed at one in the present model to maintain comparability to Clarida et al. (2000). The related paper by Batini et al. (2006) contains an analysis of optimally robust monetary policy rules in a closely related environment. Bullard and Schaling (2006) discuss both determinacy and learnability in a two country model similar to the one used here, but from a purely theoretical perspective, and considering a wide variety of monetary policy rules, including targeting rules and situations of asymmetric policy. Also, the learning issue is not examined in this paper. For a closed economy analysis of that question, see Honkapohja and Mitra (2004). There is a large literature on international monetary policy cooperation. Benigno and Benigno (2006), for instance, work in a context similar to the one used here, and show that in general there are theoretical gains from international policy cooperation. This type of result also occurs in this model, as discussed by Clarida et al. (2002). Benigno and Benigno (2008) discuss strategic aspects of monetary policy cooperation, showing how the optimal cooperative allocations can be implemented when each country follows an inflation targeting regime. Similar themes are contained in Obstfeld and Rogoff (2002). They study a symmetric two-country model related to the one in this paper, and find plausible conditions under which the Nash equilibrium of a game in which each participant is choosing a monetary policy rule approximates the fully optimal cooperative equilibrium. Corsetti and Pesenti (2005) also work in a model related to the one in this paper, and find that the degree of exchange rate exposure is a key determinant of whether purely inward-looking policies or ones that involve international cooperation are to be preferred. There is also a large literature on the estimation of Taylor-type monetary policy rules which cannot be effectively summarized here. One related line of research stems from Orphanides (2001), who has argued that monetary policy rules should be estimated using only data available to policymakers at the time that policy actions are being decided. Orphanides (2004) re-estimates the Clarida et al. (2000) policy rules using real-time data. He argues that the real-time estimates are consistent with the Federal Reserve abiding by the Taylor principle, so that there was no risk of indeterminacy. Real time data are not used in this paper to obtain the estimates across three countries and two time periods. However, the baseline estimates are consistent with Orphanides (2004) for the US in the 1970s, in that a sufficiently strong reaction to deviations of inflation from target is obtained that one would conclude that the policy rule in use was consistent with equilibrium determinacy, if the economy was closed. The two-dimensional indeterminacy for this period is due to monetary policy in the partner economies, not the US. Lubik and Schorfheide (2004) estimate closed economy, one-dimensional sunspot equilibria directly based on subsamples of US postwar data. It would be interesting to apply this methodology to the multi-economy, multi-dimensional setting here. Belaygorod et al. (2006) extend the Lubik and Schorfheide closed economy analysis to a fully dynamic, full sample approach in which the economy can switch between determinacy and indeterminacy. Beyer and Farmer (2004) discuss identification in the Lubik and Schorfheide (2004) context. 1.3. Organization The next section discusses the model used in this paper. The following section turns to a discussion of determinacy conditions for worldwide equilibrium, and relates these conditions to analogous findings in closed economy settings. The subsequent section explores how all variables worldwide can be volatile as part of a sunspot equilibrium, even in those countries which, from a closed economy perspective, are pursuing policies consistent with determinacy of rational expectations equilibrium. The final section turns to estimates of policy rules in the spirit of Clarida et al. (2000). These estimates are combined with a simple calibration, which suggests that worldwide equilibrium was indeterminate in the 1970s and in fact remains indeterminate today.

We show how international monetary policy considerations impinge on determinacy conditions for worldwide rational expectations equilibrium, an international version of a famous result due to Clarida et al. (2000). Failure to achieve determinacy has been considered a severe shortcoming in the closed economy new Keynesian literature, and such a failure can be viewed the same way in the international context. The difference is that in the international context, determinacy is influenced jointly, most importantly by the large policymakers on the world scene. This paper considered a simple, n-economy version of the new Keynesian model discussed in Clarida et al. (2002). This particular international version is certainly not the only one available, but has the distinct advantage that it collapses to the standard, simple new Keynesian model widely studied following Woodford (2003) when any of the economies becomes completely closed. The analysis indicates that the degree of openness of each economy has clear effects on determinacy conditions, a finding that is consistent with previous studies. The analysis has shown how the closed economy case is consistent with known findings from the literature, and also how these conditions are altered as an economy becomes more open. Clear upper limits were found on how aggressive a policymaker can be with respect to inflation in the monetary policy rule. This limit would exist in the closed economy case but only at extreme values which would seem to be unlikely to impinge on actual policy. One finding is then that policymakers for large economies in this model can neither be too passive nor too aggressive with respect to deviations of inflation from target if they wish to remain consistent with determinacy of worldwide rational expectations equilibrium. Some of the tradeoffs that exist between the policy rule adopted by one nation versus that adopted by another were also explored. One finding is that there is little or no scope for a large country to render the worldwide equilibrium determinate via simple, unilateral action in cases where a partner country is pursuing a policy sufficiently inconsistent with determinacy. The paper also investigated the extent to which sunspot shocks originating in a single country may be transmitted across borders in a worldwide sunspot equilibrium. The general finding is that all variables in all countries are more volatile in such an equilibrium. The strength of this effect depends on the source of the sunspot shock, the degree of openness of each of the economies, and the monetary policy rules in effect in each economy. One generality is that sunspot volatility originating in a relatively small economy following a policy which is inconsistent with determinacy of worldwide equilibrium has muted effects on large economy volatility. Sunspot shocks originating in a large country following a policy which is inconsistent with worldwide determinacy, on the other hand, have large effects on the partner economies. Both of these results are in accord with a great deal of intuition about poor policies being followed in large versus small countries. In keeping with the original closed economy analysis of Clarida et al. (2000), monetary policy rules were estimated for three large economies, and determinacy conditions for worldwide equilibrium were assessed using these estimates. The baseline estimates suggest that the 1970s were associated with a two-dimensional indeterminacy of worldwide rational expectations equilibrium, and thus that endogenous volatility was a distinct possibility during that era. Interestingly, the US policy can be viewed as reasonable according to these estimates, as a version of the Taylor principle is met. But in conjunction with partner country policies in Germany and Japan, worldwide equilibrium was indeterminate. For the more recent 1990–2004 era, the estimates suggest a one-dimensional indeterminacy of worldwide equilibrium. Thus, while policy has generally been better in the more recent era, the world economy has still been exposed to the threat of endogenous volatility. A long-standing debate in monetary policy circles concerns possible welfare gains from international monetary policy coordination. At issue is the extent to which policymakers in large economies such as the United States, the Euro area, and Japan should adjust policy in reaction to economic events outside their own borders. In the multiple country version of the new Keynesian model studied here, each large policymaker can contribute, but only contribute, importantly to the determinacy of worldwide equilibrium. Failure to ensure determinacy worldwide would open the door to unnecessary equilibrium fluctuations in the world rational expectations equilibrium. These unnecessary fluctuations would affect all economies. The poor macroeconomic performance potentially associated with indeterminacy could reduce the welfare of households worldwide dramatically as the magnitude of the unnecessary equilibrium fluctuations could, in principle, be quite large. Policymakers in major economies may want to coordinate to avoid such an outcome. This is a very different reason for international policy coordination than those that are normally advanced, but one that may warrant further study.