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The Zero Bound on Interest Rates and Optimal Monetary Policy
GAUTI B. EGGERTSSON
MICHAEL WOODFORD
オーバーナイト名目金利のゼロ下限が存在する場合における適切な金融政策はどのようなものであるかについては最近注目のトピックになっている。日本ではコールレート（アメリカにおけるフェデラルファンドレートと同等のオーバナイトキャッシュレートのこと）は1995年10月から50ベーシスポイント以下となっている。そして、ここ4年間ではほとんどの間ほぼゼロになっている（図1参照）。よって日本銀行はその期間中ずっと名目金利を引き下げる余地を持っていなかった。この間、日本の成長率は低迷したままで、物価は下落し続けた。これは金融緩和の必要性を意味する。しかし通常の救済方法---短期名目金利を低める---は明らかに利用不可能であった。マネタリーベースの盛んな拡大はこれらの状況下では需要を刺激する効果はほとんどなかったように見える。図1が示すように、マネタリーベースは1990年代始めからGDP比で2倍にもなった。
#ref(eggertsson woodford 2003.gif)
In the United States, meanwhile, the federal funds rate has now been reduced to only 1 percent, and signs of recovery remain exceedingly frag- ile. This has led many to wonder if this country might not also soon find itself in a situation where interest rate policy is no longer available as a tool for macroeconomic stabilization. A number of other countries face similar questions. John Maynard Keynes first raised the question of what can be done to stabilize the economy when it has fallen into a liquidity trap—when interest rates have fallen to a level below which they cannot be driven by further monetary expansion—and whether monetary policy can be effective at all under such circumstances. Long treated as a mere theoretical curiosity, Keynes's question now appears to be one of urgent practical importance, but one with which theorists have become unfamiliar.
The question of how policy should be conducted when the zero bound is reached—or when the possibility of reaching it can no longer be ignored—raises many fundamental issues for the theory of monetary pol- icy. Some would argue that awareness of the possibility of hitting the zero bound calls for fundamental changes in the way policy is conducted even before the bound has been reached. For example, Paul Knigman refers to deflation as a "black hole,"' from which an economy cannot expect to escape once it has entered. A conclusion often drawn from this pes- simistic view of the efficacy of monetary policy in a liquidity trap is that it is vital to steer far clear of circumstances in which deflationary expecta- tions could ever begin to develop—for example, by targeting a suffi- ciently high positive rate of inflation even under normal circumstances. Others are more sanguine about the continuing effectiveness of monetary policy even when the zero bound is reached. For example, it is often argued that deflation need not be a black hole, because monetary policy can affect aggregate spending, and hence inflation, through channels other than centra] bank control of short-term nominal interest rates. Thus there has been much recent discussion, with respect to both Japan and the United States—of the advantages of vigorous expansion of the monetary base even without any further reduction in interest rates, of the desirabil- ity of attempts to shift longer-term interest rates through central bank pur- chases of longer-maturity government securities, and even of the desirability of central bank purchases of other kinds of assets.
Yet if these views are correct, they challenge much of the recent con- ventional wisdom regarding the conduct of monetary policy, both within central banks and among academic monetary economists. That wisdom has stressed a conception of the problem of monetary policy in terms ofthe appropriate adjustment of an operating target for overnight interest rates, and the prescriptions formulated for monetary policy, such as the celebrated Taylor rule,^ are typically cast in these terms. Indeed, some have argued that the inability of such a policy to prevent the economy from falling into a deflationary spiral is a critical flaw of the Taylor rule as a guide to policy.
Similarly, concern over the possibility of entering a liquidity trap is sometimes presented as a serious objection to another currently popular monetary policy prescription, namely, inflation targeting. The definition of a policy prescription in terms of an inflation target presumes that there is in fact some level of the nominal interest rate that can allow the target to be hit (or at least projected to be hit, on average). But, some argue, if the zero interest rate bound is reached under circumstances of deflation, it will not be possible to hit any higher inflation target, because further interest rate decreases are not possible. Is there, in such circumstances, any point in having an inflation target? The Bank of Japan has frequently offered this argument as a reason for resisting inflation targeting. For example, Kunio Okina, director of the Institute for Monetary and Eco- nomic Studies at the Bank of Japan, was quoted as arguing that "because short-term interest rates are already at zero, setting an inflation target of, say, 2 percent wouldn't carry much credibility."''
We seek to shed light on these issues by considering the consequences of the zero lower bound on nominal interest rates for the optimal conduct of monetary policy, in the context of an explicitly intertemporal equilib- rium model of the monetary transmission mechanism. Although our model is extremely simple, we believe it can help clarify some of the basic issues just raised. We are able to consider the extent to which the zero bound represents a genuine constraint on attainable equilibrium paths for inflation and real activity, and the extent to which open-market purchases of various kinds of assets by the central bank can mitigate that constraint. We are also able to show how the existence of the zero bound changes the character of optimal monetary policy, relative to the policy rules that would be judged optimal in its absence or in the case of real disturbances small enough for the bound never to matter under an optimal policy.
To preview our results, we find that the zero bound does represent an important constraint on what monetary stabilization policy can achieve, at least when certain kinds of real disturbances are encountered in an envi- ronment of low inflation. We argue that the possibility of expanding the monetary base through central bank purchases of a variety of types of assets does little if anything to expand the set of feasible paths for infla- tion and real activity that are consistent with equilibrium under some (fully credible) policy commitment.
Hence the relevant trade-offs can correctly be studied by simply con- sidering what alternative anticipated state-contingent paths of the short- term nominal interest rate can achieve, taking into account the constraint that this rate must be nonnegative at all times. Doing so, we find that the zero interest rate bound can indeed be temporarily binding, and when it is, it inevitably results in lower welfare than could be achieved in the absence of such a constraint,'
Nonetheless, we argue that the zero bound restricts possible stabiliza- tion outcomes under sound policy tc a much more modest degree than the deflation pessimists presume. Even though the set of feasible equilib- rium outcomes corresponds to those that can be achieved through alter- native interest rate policies, monetary policy is far from powerless to mitigate the contractionary effects of the kind of disturbances that would make the zero bound a binding constraint. The key to dealing with this sort of situation in the least damaging way is to create the right kind of expectations regarding how monetary policy will be used after the con- straint is no longer binding, and the central bank again has room to maneuver. We use our intertemporal equilibrium model to characterizethe kind of expectations regarding future policy that it would be desir- able to create, and we discuss a form of price-level targeting rule that— if credibly committed to—should bring about the constrained-optimal equilibrium. We also discuss, more informally, how other types of policy actions could help increase the credibility of the central bank's announced commitment to this kind of future policy.
Our analysis will be recognized as a development of several key themes in Paul Krugman's treatment of the same topic in these pages a few years ago.* Like Krugman, we give particular emphasis to the role of expectations regarding future policy in determining the severity of the distortions that result from hitting the zero bound. Our primary contribu- tion, relative to Krugman's earlier treatment, will be the presentation of a more fully dynamic analysis. For example, our assumption of staggered pricing, rather than Krugman's simple hypothesis of prices that are fixed for one period, allows for richer (and at least somewhat more realistic) dynamic responses to disturbances. In our model, unlike in Krugman's, a real disturbance that lowers the natural rate of interest can cause output to remain below potential for years (as shown in figure 2 later in the paper), rather than only for a single "period," even when the average frequency of price adjustments is more than once a year. These richer dynamics are also important for a realistic discussion of the kind of policy commitment that can help to reduce economic contraction during a liquidity trap. In our model a commitment to create subsequent inflation involves a com- mitment to keep interest rates low for some time in the future, whereas in Krugman's model a commitment to a higher future price level does not involve any reduction in future nominal interest rates. We are also better able to discuss such questions as how the creation of inflationary expec- tations while the zero bound is binding can be reconciled with maintain- ing the credibility of the central bank's commitment to long-run price stability.
Our dynamic analysis also allows us to further clarify the several ways in which the central bank's management of private sector expectations can be expected to mitigate the effects of the zero bound. Krugman emphasizes the fact that increased expectations of inflation can lower the real interest rate implied by a zero nominal interest rate. This might sug- gest, however, that the central bank can affect the economy only insofar as it affects expectations regarding a variable that it cannot influence except quite indirectly; it might also suggest that the only expectations that should matter are those regarding inflation over the relatively short horizon corresponding to the tenn of the nominal interest rate that has fallen to zero. Such interpretations easily lead to skepticism about the practical effectiveness of the expectations channel, especially if inflation is regarded as being relatively "sticky" in the short run. Our model is instead one in which expectations affect aggregate demand through sev- eral channels.
First of all. it is not merely short-term real interest rates that matter for current aggregate demand; our model of intertemporal substitution in spending implies that the entire expected future path of short-term real rates should matter, or alternatively that very long term real rates should matter.^ This means that the creation of inflation expectations, even with regard to inflation that should not occur until at least a year into the future, should also be highly relevant to aggregate demand, as long as it is not accompanied by correspondingly higher expected future nominal interest rates. Furthermore, the expected future path of nominal interest rates matters, and not just their current level, so that a commitment to keep nominal interest rates low for a longer period of time should stimulate aggregate demand, even when current interest rates cannot be lowered further, and even under the hypothesis that inflation expectations would remain unaffected. Because the central bank can clearly control the future path of short-term nominal interest rates if it has the will to do so, any failure of such a commitment to be credible will not be due to skep- ticism about whether the central bank is able to follow through on its commitment.
The richer dynamics of our model are also important for the analysis of optimal policy. Krugman mainly addresses the question of whether mon- etary policy is completely impotent when the zero bound binds, and he argues for the possibility of increasing real activity in the liquidity trap by creating expectations of inflation. Although we agree with this conclu- sion, it does not answer the question of whether, or to what extent, it would be desirable to create such expectations, given the well-founded reasons that the central bank should have to not prefer inflation at a later time. Nor is Krugman's model well suited to address such a question, insofar as it omits any reason for even an extremely high subsequent infla- tion to be deemed harmful. Our staggered-pricing model instead implies that inflation (whether anticipated or not) does create distortions, justify- ing an objective function for stabilization policy that trades off inflation stabilization and output gap stabilization in terms that are often assumed to represent actual central bank concerns. We characterize optimal policy in such a setting and show that it does indeed involve a commitment to history-dependent policy of a sort that should result in higher inflation expectations in response to a binding zero bound. We can also show to what extent it should be optimal to create such expectations, assuming that this is possible. We find, for example, that it is not optimal to commit to so much future inflation that the zero bound ceases to bind, even though this is one possible type of equilibrium; this is why the zero bound does remain a relevant constraint, even under an optimal policy commitment.
***Conclusion
We have argued that the key to dealing with a situation in which mon- etary policy is constrained by the zero lower bound on short-term nominal interest rates is the skillful management of expectations regarding the future conduct of policy. By "management of expectations" we do not mean that the central bank should imagine that, if it uses sufficient guile, it can lead the private sector to believe whatever the central bank wishes it to believe, no matter what it actually does. Instead we have assumed that there is no point in the central bank trying to get the private sector to expect something that the central bank does not itself intend to bring about. But we do contend that it is highly desirable for a central bank to be able to commit itself in advance to a course of action that is desirable because of the benefits that flow from its being anticipated, and then to work to make that commitment credible to the private sector.
In the context of a simple optimizing model of the monetary transmis- sion mechanism, we have shown that a purely forward-looking approach to policy—which allows for no possibility of committing future policy to respond to past conditions—can lead to quite bad outcomes in the event of a temporary decline in the natural rate of interest, regardless of the kind of policy pursued at the time of the disturbance. We have also character- ized optimal policy, under the assumption that credible commitment is possible, and shown that it involves a commitment to eventually bring the general price level back up to a level even higher than would have pre- vailed had the disturbance never occurred. Finally, we have described a type of history-dependent price-level targeting mle with the following properties: that a commitment to base interest rate policy on this mle determines the optimal equilibrium, and that the same foim of targeting mle continues to describe optimal policy regardless of which of a large number of types of disturbances may affect the economy.
Given the role of private sector anticipation of history-dependent pol- icy in realizing a desirable outcome, it is important for central banks to develop effective methods of signaling their policy commitments to the private sector. An essential precondition for this, certainly, is for the cen- tral bank itself to clearly understand the kind of history-dependent behav- ior to which it should be seen to be committed. It can then communicate its thinking on the matter and act consistently with the principles that it wishes the private sector to understand. Simply conducting policy in accordance with a mle may not suffice to bring about an optimal, or nearly optimal, equilibrium, but it is the place to start.
The Zero Bound on Interest Rates and Optimal Monetary Policy
GAUTI B. EGGERTSSON
MICHAEL WOODFORD
オーバーナイト名目金利のゼロ下限が存在する場合における適切な金融政策はどのようなものであるかについては最近注目のトピックになっている。日本ではコールレート（アメリカにおけるフェデラルファンドレートと同等のオーバナイトキャッシュレートのこと）は1995年10月から50ベーシスポイント以下となっている。そして、ここ4年間ではほとんどの間ほぼゼロになっている（図1参照）。よって日本銀行はその期間中ずっと名目金利を引き下げる余地を持っていなかった。この間、日本の成長率は低迷したままで、物価は下落し続けた。これは金融緩和の必要性を意味する。しかし通常の救済方法---短期名目金利を低める---は明らかに利用不可能であった。マネタリーベースの盛んな拡大はこれらの状況下では需要を刺激する効果はほとんどなかったように見える。図1が示すように、マネタリーベースは1990年代始めからGDP比で2倍にもなった。
#ref(eggertsson woodford 2003.gif)
アメリカでは同時期にフェデラルファンドレートはわずか1％にまで引き下げられ、回復の兆しは極めて弱い。このため多くの人々がアメリカも金利政策がマクロ経済の安定化ツールとして無効になってしまう状況に陥るのではないかと危惧している。他の多くの国も同じような問題に直面している。ジョン・メイナード・ケインズは金利がこれ以上の金融緩和のできない水準にまで下がってしまうという流動性の罠に陥った時にどのような政策が経済の安定化のために用いることができるか、また金融政策がこのような状況でわずかでも有効であるかを問うた最初の経済学者である。長い間より理論的な好奇心として扱われてきたテーマであるが、ケインズの問いは現在緊急の実際的な重要性を帯びてきたが、それは理論家達にとって既になじみのないものになってしまっていた。
The question of how policy should be conducted when the zero bound is reached—or when the possibility of reaching it can no longer be ignored—raises many fundamental issues for the theory of monetary pol- icy. Some would argue that awareness of the possibility of hitting the zero bound calls for fundamental changes in the way policy is conducted even before the bound has been reached. For example, Paul Knigman refers to deflation as a "black hole,"' from which an economy cannot expect to escape once it has entered. A conclusion often drawn from this pes- simistic view of the efficacy of monetary policy in a liquidity trap is that it is vital to steer far clear of circumstances in which deflationary expecta- tions could ever begin to develop—for example, by targeting a suffi- ciently high positive rate of inflation even under normal circumstances. Others are more sanguine about the continuing effectiveness of monetary policy even when the zero bound is reached. For example, it is often argued that deflation need not be a black hole, because monetary policy can affect aggregate spending, and hence inflation, through channels other than centra] bank control of short-term nominal interest rates. Thus there has been much recent discussion, with respect to both Japan and the United States—of the advantages of vigorous expansion of the monetary base even without any further reduction in interest rates, of the desirabil- ity of attempts to shift longer-term interest rates through central bank pur- chases of longer-maturity government securities, and even of the desirability of central bank purchases of other kinds of assets.
Yet if these views are correct, they challenge much of the recent con- ventional wisdom regarding the conduct of monetary policy, both within central banks and among academic monetary economists. That wisdom has stressed a conception of the problem of monetary policy in terms ofthe appropriate adjustment of an operating target for overnight interest rates, and the prescriptions formulated for monetary policy, such as the celebrated Taylor rule,^ are typically cast in these terms. Indeed, some have argued that the inability of such a policy to prevent the economy from falling into a deflationary spiral is a critical flaw of the Taylor rule as a guide to policy.
Similarly, concern over the possibility of entering a liquidity trap is sometimes presented as a serious objection to another currently popular monetary policy prescription, namely, inflation targeting. The definition of a policy prescription in terms of an inflation target presumes that there is in fact some level of the nominal interest rate that can allow the target to be hit (or at least projected to be hit, on average). But, some argue, if the zero interest rate bound is reached under circumstances of deflation, it will not be possible to hit any higher inflation target, because further interest rate decreases are not possible. Is there, in such circumstances, any point in having an inflation target? The Bank of Japan has frequently offered this argument as a reason for resisting inflation targeting. For example, Kunio Okina, director of the Institute for Monetary and Eco- nomic Studies at the Bank of Japan, was quoted as arguing that "because short-term interest rates are already at zero, setting an inflation target of, say, 2 percent wouldn't carry much credibility."''
We seek to shed light on these issues by considering the consequences of the zero lower bound on nominal interest rates for the optimal conduct of monetary policy, in the context of an explicitly intertemporal equilib- rium model of the monetary transmission mechanism. Although our model is extremely simple, we believe it can help clarify some of the basic issues just raised. We are able to consider the extent to which the zero bound represents a genuine constraint on attainable equilibrium paths for inflation and real activity, and the extent to which open-market purchases of various kinds of assets by the central bank can mitigate that constraint. We are also able to show how the existence of the zero bound changes the character of optimal monetary policy, relative to the policy rules that would be judged optimal in its absence or in the case of real disturbances small enough for the bound never to matter under an optimal policy.
To preview our results, we find that the zero bound does represent an important constraint on what monetary stabilization policy can achieve, at least when certain kinds of real disturbances are encountered in an envi- ronment of low inflation. We argue that the possibility of expanding the monetary base through central bank purchases of a variety of types of assets does little if anything to expand the set of feasible paths for infla- tion and real activity that are consistent with equilibrium under some (fully credible) policy commitment.
Hence the relevant trade-offs can correctly be studied by simply con- sidering what alternative anticipated state-contingent paths of the short- term nominal interest rate can achieve, taking into account the constraint that this rate must be nonnegative at all times. Doing so, we find that the zero interest rate bound can indeed be temporarily binding, and when it is, it inevitably results in lower welfare than could be achieved in the absence of such a constraint,'
Nonetheless, we argue that the zero bound restricts possible stabiliza- tion outcomes under sound policy tc a much more modest degree than the deflation pessimists presume. Even though the set of feasible equilib- rium outcomes corresponds to those that can be achieved through alter- native interest rate policies, monetary policy is far from powerless to mitigate the contractionary effects of the kind of disturbances that would make the zero bound a binding constraint. The key to dealing with this sort of situation in the least damaging way is to create the right kind of expectations regarding how monetary policy will be used after the con- straint is no longer binding, and the central bank again has room to maneuver. We use our intertemporal equilibrium model to characterizethe kind of expectations regarding future policy that it would be desir- able to create, and we discuss a form of price-level targeting rule that— if credibly committed to—should bring about the constrained-optimal equilibrium. We also discuss, more informally, how other types of policy actions could help increase the credibility of the central bank's announced commitment to this kind of future policy.
Our analysis will be recognized as a development of several key themes in Paul Krugman's treatment of the same topic in these pages a few years ago.* Like Krugman, we give particular emphasis to the role of expectations regarding future policy in determining the severity of the distortions that result from hitting the zero bound. Our primary contribu- tion, relative to Krugman's earlier treatment, will be the presentation of a more fully dynamic analysis. For example, our assumption of staggered pricing, rather than Krugman's simple hypothesis of prices that are fixed for one period, allows for richer (and at least somewhat more realistic) dynamic responses to disturbances. In our model, unlike in Krugman's, a real disturbance that lowers the natural rate of interest can cause output to remain below potential for years (as shown in figure 2 later in the paper), rather than only for a single "period," even when the average frequency of price adjustments is more than once a year. These richer dynamics are also important for a realistic discussion of the kind of policy commitment that can help to reduce economic contraction during a liquidity trap. In our model a commitment to create subsequent inflation involves a com- mitment to keep interest rates low for some time in the future, whereas in Krugman's model a commitment to a higher future price level does not involve any reduction in future nominal interest rates. We are also better able to discuss such questions as how the creation of inflationary expec- tations while the zero bound is binding can be reconciled with maintain- ing the credibility of the central bank's commitment to long-run price stability.
Our dynamic analysis also allows us to further clarify the several ways in which the central bank's management of private sector expectations can be expected to mitigate the effects of the zero bound. Krugman emphasizes the fact that increased expectations of inflation can lower the real interest rate implied by a zero nominal interest rate. This might sug- gest, however, that the central bank can affect the economy only insofar as it affects expectations regarding a variable that it cannot influence except quite indirectly; it might also suggest that the only expectations that should matter are those regarding inflation over the relatively short horizon corresponding to the tenn of the nominal interest rate that has fallen to zero. Such interpretations easily lead to skepticism about the practical effectiveness of the expectations channel, especially if inflation is regarded as being relatively "sticky" in the short run. Our model is instead one in which expectations affect aggregate demand through sev- eral channels.
First of all. it is not merely short-term real interest rates that matter for current aggregate demand; our model of intertemporal substitution in spending implies that the entire expected future path of short-term real rates should matter, or alternatively that very long term real rates should matter.^ This means that the creation of inflation expectations, even with regard to inflation that should not occur until at least a year into the future, should also be highly relevant to aggregate demand, as long as it is not accompanied by correspondingly higher expected future nominal interest rates. Furthermore, the expected future path of nominal interest rates matters, and not just their current level, so that a commitment to keep nominal interest rates low for a longer period of time should stimulate aggregate demand, even when current interest rates cannot be lowered further, and even under the hypothesis that inflation expectations would remain unaffected. Because the central bank can clearly control the future path of short-term nominal interest rates if it has the will to do so, any failure of such a commitment to be credible will not be due to skep- ticism about whether the central bank is able to follow through on its commitment.
The richer dynamics of our model are also important for the analysis of optimal policy. Krugman mainly addresses the question of whether mon- etary policy is completely impotent when the zero bound binds, and he argues for the possibility of increasing real activity in the liquidity trap by creating expectations of inflation. Although we agree with this conclu- sion, it does not answer the question of whether, or to what extent, it would be desirable to create such expectations, given the well-founded reasons that the central bank should have to not prefer inflation at a later time. Nor is Krugman's model well suited to address such a question, insofar as it omits any reason for even an extremely high subsequent infla- tion to be deemed harmful. Our staggered-pricing model instead implies that inflation (whether anticipated or not) does create distortions, justify- ing an objective function for stabilization policy that trades off inflation stabilization and output gap stabilization in terms that are often assumed to represent actual central bank concerns. We characterize optimal policy in such a setting and show that it does indeed involve a commitment to history-dependent policy of a sort that should result in higher inflation expectations in response to a binding zero bound. We can also show to what extent it should be optimal to create such expectations, assuming that this is possible. We find, for example, that it is not optimal to commit to so much future inflation that the zero bound ceases to bind, even though this is one possible type of equilibrium; this is why the zero bound does remain a relevant constraint, even under an optimal policy commitment.
***Conclusion
We have argued that the key to dealing with a situation in which mon- etary policy is constrained by the zero lower bound on short-term nominal interest rates is the skillful management of expectations regarding the future conduct of policy. By "management of expectations" we do not mean that the central bank should imagine that, if it uses sufficient guile, it can lead the private sector to believe whatever the central bank wishes it to believe, no matter what it actually does. Instead we have assumed that there is no point in the central bank trying to get the private sector to expect something that the central bank does not itself intend to bring about. But we do contend that it is highly desirable for a central bank to be able to commit itself in advance to a course of action that is desirable because of the benefits that flow from its being anticipated, and then to work to make that commitment credible to the private sector.
In the context of a simple optimizing model of the monetary transmis- sion mechanism, we have shown that a purely forward-looking approach to policy—which allows for no possibility of committing future policy to respond to past conditions—can lead to quite bad outcomes in the event of a temporary decline in the natural rate of interest, regardless of the kind of policy pursued at the time of the disturbance. We have also character- ized optimal policy, under the assumption that credible commitment is possible, and shown that it involves a commitment to eventually bring the general price level back up to a level even higher than would have pre- vailed had the disturbance never occurred. Finally, we have described a type of history-dependent price-level targeting mle with the following properties: that a commitment to base interest rate policy on this mle determines the optimal equilibrium, and that the same foim of targeting mle continues to describe optimal policy regardless of which of a large number of types of disturbances may affect the economy.
Given the role of private sector anticipation of history-dependent pol- icy in realizing a desirable outcome, it is important for central banks to develop effective methods of signaling their policy commitments to the private sector. An essential precondition for this, certainly, is for the cen- tral bank itself to clearly understand the kind of history-dependent behav- ior to which it should be seen to be committed. It can then communicate its thinking on the matter and act consistently with the principles that it wishes the private sector to understand. Simply conducting policy in accordance with a mle may not suffice to bring about an optimal, or nearly optimal, equilibrium, but it is the place to start.
