Asymmetric monetary policy and the effective lower bound

Accepted Manuscript

Asymmetric Monetary Policy and the Effective Lower Bound Christopher Gust, David Lopez-Salido, Steve Meyer ´ PII: DOI: Reference:

S1090-9443(17)30150-3 10.1016/j.rie.2017.05.005 YREEC 728

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Research in Economics

Received date: Revised date: Accepted date:

1 May 2017 21 May 2017 21 May 2017

Please cite this article as: Christopher Gust, David Lopez-Salido, Steve Meyer, Asymmetric Monetary ´ Policy and the Effective Lower Bound, Research in Economics (2017), doi: 10.1016/j.rie.2017.05.005

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Asymmetric Monetary Policy and the Effective Lower Bound David L´opez-Salido April 28, 2017

Abstract

Steve Meyer∗

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Christopher Gust

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We use the canonical New Keynesian model to study optimal discretionary policy when the nominal interest rate is constrained by the effective lower bound (ELB). We show that policymakers who seek to minimize a (symmetric) quadratic loss function involving deviations of inflation and output from targets will achieve an average inflation rate below target due to the contractionary effects associated with hitting the ELB. We also characterize optimal discretionary policy for policymakers who view output losses as asymmetric: they place weight on the output gap when output is below potential but place little or no weight on the gap when output is above potential. In comparison to optimal policy using the symmetric loss function, the average inflation rate is higher and closer to the central banks target. Moreover, in response to contractionary demand shocks that push the nominal interest rate to the effective lower bound, policymakers with an asymmetric loss function adopt a policy rate path that remains at the ELB longer but eventually rises more quickly than the path adopted by a policymaker with a symmetric loss function.

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Keywords: zero lower bound, optimal monetary policy, asymmetric loss function, time-consistent policy

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JEL classification: E32, E52

∗

We thank Bill English, Etienne Gagnon, Brian Madigan, and Bob Tetlow for useful comments and suggestions. The views expressed in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System.

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1

Introduction

Although policy rates in the United States and some other economies are modestly above their effective lower bound (ELB), this bound—whether slightly positive, zero, or slightly negative—is likely to

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remain an important consideration for monetary policymakers going forward. Recent research including Hamilton et al. (2015), Laubach and Williams (2015), and Mertens and Johannsen (2015) has emphasized a secular downward trend in real interest rates and more specifically a downward trend in the natural real rate of interest—the real rate of interest consistent with the economy operating at potential. Indeed, policymakers have cited estimates that the natural rate currently is near zero and have raised the possibility that factors such as sluggish productivity growth and demographic trends

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may keep it near zero.1 Inasmuch as many central banks in the “advanced economies” are aiming for inflation in the vicinity of 2 percent, a persistently low natural real interest rate would imply a persistently low level of the nominal policy rate (relative to historical norms) even when the economy is operating near potential with inflation near target. That outcome, in turn, would mean that central banks would have less room than typically was the case in the past to cut their policy rates in order

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to provide monetary stimulus when necessary.

To illustrate this point, Figure 1 displays post-World War II easing cycles undertaken by the Federal

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Reserve. For the 12 easing episodes shown, the federal funds rate declined by an average of slightly more than 4 percentage points with the easing occurring over a two year period on average. Rate decreases

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have historically ended before the federal funds rate target hit the effective lower bound. But, this was not the case for the most recent easing cycle and may prove less likely going forward. In particular,

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as shown in Figure 2, FOMC participants and private sector forecasters view the longer-run value of the federal funds rate as having declined below 3.5 percent, suggesting that there will be less room for reducing rates during a future easing cycle than during past episodes.2 Thus, the effective lower bound

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will likely remain a key factor in the design of current and future monetary policy strategies. In this paper, we use the canonical New Keynesian (NK) model to study such strategies, focusing on

optimal discretionary monetary policy. Under such a policy, policymakers do not commit to pursuing time-inconsistent policies that they would regret when it subsequently becomes necessary to live up to the commitment. This time-inconsistency problem is particularly large at the ELB: the effectiveness of 1

See Gagnon et al. (2016) for evidence that demographics have lowered the natural rate and Fernald (2014) and Gordon (2016) for evidence that trend productivity has slowed. 2 For similar calculations, see Haldane (2015) and English (2015).

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an optimal commitment-based strategy requires keeping the interest rate at the effective lower bound for long periods of time and depends crucially on convincing the private sector that policymakers would not re-optimize and would continue to follow the same policy strategy long into the future. We view such policies as very difficult to implement in practice because the private sector is likely to doubt that

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policymakers would follow through on such long-horizon commitments.3 Accordingly, we focus only on optimal monetary policy under discretion.

The loss function that policymakers minimize plays a key role in our analysis. We study loss functions consistent with policymakers having an inflation objective of 2 percent. Some observers have suggested that a higher inflation objective, either temporarily or permanently, could help ease the

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constraint generated by the lower bound on nominal interest rates (see, for instance, Blanchard et al. (2010); echoing Summers (1991)). However, some policymakers have argued that a change in the inflation goal could be misunderstood or could undermine the credibility of the central bank. Because of the substantial communications and credibility problems that a change in the objective could raise, policymakers will need to carefully balance the potential gains against the costs and risks before taking

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such a step. In this note, we take as given the FOMC’s existing statement regarding its longer-run goals and use loss functions that we view as consistent with that statement.

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We first consider a relatively standard symmetric loss function involving the squared deviations of output from potential and inflation from a 2 percent target.4 In our model, the economy is buffeted by two shocks: cost-push shocks that present a tradeoff to policymakers in terms of stabilizing inflation or

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the output gap, and shocks to the natural real interest rate that occasionally push the nominal interest rate to the ELB. In those circumstances, the nominal interest rate consistent with maintaining full

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output or employment can fall to a level below the ELB, and we show that policymakers, acting under discretion, will end up achieving, over time, an average inflation rate below the central bank’s stated

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target and an average level of output that falls below potential. The inability of the policymaker to accommodate, through reductions in the nominal interest rate, shocks that reduce the equilibrium real rate underlies this failure of not being able to achieve the central bank’s dual objectives for inflation and real activity. We next consider the implications of a nonstandard assumption about policymakers’ views of how 3

See Levin et al. (2010) for a more detailed discussion of this point. Evans et al. (2015) and Gust et al. (2015) also study optimal policy under discretion at the ELB using this loss function. 4

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the costs of output exceeding potential compare to the costs of output falling short of potential. Specifically, we consider a loss function in which the costs associated with output below potential have the standard quadratic form but there are no direct costs to output above potential. Deviations of inflation from target have the standard quadratic form. This asymmetric loss function can be

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interpreted as a simple representation of the views of some policymakers that the costs associated with output and employment falling short of potential by some amount might be appreciably larger than the costs associated with output and employment exceeding potential to the same extent. When people become unemployed, for example, their job skills and human capital can deteriorate, particularly if they suffer a prolonged spell of unemployment. There is no obvious counterpart to this cost when

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the unemployment rate is temporarily below its long-run equilibrium level. Indeed, some have argued that there are benefits rather than costs to “running the economy hot” for a while, particularly after a prolonged period during which the economy operates below potential.

We show that, in the context of our model, average inflation will exceed the target rate if policymakers seek to minimize this asymmetric loss function in a hypothetical environment where the

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effective lower bound constraint can be ignored. But, when the ELB binds occasionally, policymakers who seek to minimize this asymmetric loss function can expect to achieve average inflation that is closer

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to their 2 percent target. This outcome occurs because policy under the asymmetric loss function eases considerably more in response to shocks that put downward pressure on inflation or output than it tightens in response to shocks that put upward pressure on inflation or output. This asymmetric re-

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sponse helps counteract the downward bias to inflation arising from the presence of the ELB constraint, and we show, in the context of the canonical NK model, that policymakers who seek to minimize the

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asymmetric loss function achieve an average inflation rate closer to target than policymakers who seek to minimize the standard, symmetric loss function. As a result, longer-run inflation expectations will

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be more closely anchored to the inflation objective under the asymmetric loss function. The asymmetric loss function also has important implications for how policy rates return to their

longer-run values following an episode at the ELB. In response to contractionary demand shocks that push the nominal interest rate to the zero lower bound, policy under the asymmetric loss function calls for a nominal rate path that remains at the ELB longer than under the symmetric loss function but eventually rises more quickly. This deferral in tightening is helpful in bringing inflation back up to target, as inflation remains permanently below target under the symmetric loss function. However, policy

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under the asymmetric loss function also heightens the risk that inflation will overshoot policymakers’ target and remain high in the future, requiring a more aggressive pace of rate hikes after the policy rate departs from the ELB.

A New Keynesian Model

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2

Our analysis builds on Woodford (2003) and Gali (2008) who use the canonical New Keynesian (NK) model to characterize optimal monetary policy under discretion. The model has two key equations: an IS equation that relates output to the real interest rate (that is, the nominal short-term rate adjusted by

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expected inflation) and expected future output, and a Phillips curve relationship that relates inflation to the output gap and expected future inflation. Formally, these equations can be written as:

n o ybt = Et {b yt+1 } − σEt bit − π bt+1 − rte

(2)

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π bt = βEt {b πt+1 } + κb yt + µt ,

(1)

where Et represents the expectation conditional on time t information; ybt = log( yyt ) and π bt = log( ΠΠt )

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refer to the log deviations of output and inflation from their values in nonstochastic steady state; and bit

represents the log of the (gross) short-term nominal interest rate in deviations from its non-stochastic

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¯ steady state–that is, bit = log( iit ), where i = log( Π β ) and Π is the target inflation rate of the central

bank.5 The parameter β represents households’ rate of time discounting, σ captures the elasticity of

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output to changes in the real interest rate, and κ is the slope of the New Keynesian Phillips curve. These parameters are related to preferences and the degree of price stickiness, respectively. The variables rte and µt represent exogenous shocks to the (efficient) natural rate of interest and the firm’s marginal

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cost, respectively. A decrease in rte represents an exogenous factor that induces a temporary rise in households’ propensity to save, and reduces current aggregate household demand for goods. An increase in µt corresponds to an exogenous cost-push shock that increases inflation for given levels of output and expected future inflation; therefore, it introduces a trade-off between inflation and output. Because of the presence of cost-push shocks, µt , the “divine coincidence” property discussed in Blanchard and Gali (2007) is not present in our model. Thus, it will not be optimal for the policymaker to pursue a 5

See Gust, Johannsen, and L´ opez-Salido (2015) for the derivation of these expressions. See also Gali (2008).

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policy in which the ex ante real rate equals the efficient real interest rate.

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Optimal Discretionary Policy

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We now discuss the optimal monetary policy when the policymaker is unable to credibly commit to future policy actions, and when the nominal interest rate is sometimes constrained by the effective lower bound. We first consider the (standard) case in which the central bank losses are quadratic in deviations of output and inflation from their targets. We then consider the case in which a policymaker has asymmetric preferences over losses stemming from the output gap.

Symmetric Loss Function

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3.1

We build on Eggertsson and Woodford (2003) who first introduced the effective lower bound constraint into the linear-quadratic framework originally studied by Rotemberg and Woodford (1997) and Clarida, Gali, and Gertler (1999). We first assume that the monetary authority seeks to minimize the following quadratic loss function,

∞

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1 X t 2 E0 β π bt + λb yt2 , 2

(3)

t=0

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where β is the discount factor, λ is a trade-off parameter and Et represents the expectation conditional on time t information. The monetary authority is constrained by the private sector equilibrium

log(it ) ≥ 0,

(4)

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conditions, equations (1) and (2), as well as by the effective lower bound on the nominal interest rate:

which can also be written as bit ≥ − log(i).

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The nonlinearity introduced by the effective lower bound places an important constraint on optimal

policy, as it prevents the optimal real rate from being set equal to the economy’s efficient real rate. Moreover, at the effective lower bound, any shock will create a trade-off between inflation and output stabilization for the optimal discretionary policymaker. To see this, note that under discretion, it is not possible for the policymaker to affect private sector’s expectations, and the first-order condition

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characterizing optimal policy can be written as: λb yt = −κb πt − γt

(5)

condition is log(it ) · γt = 0.

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where γt denotes the Lagrange multiplier of equation (4). In addition, the complementary-slackness

(6)

Away from the effective lower bound, the Lagrange multiplier γt = 0, and hence the optimal discretionary policy gives rise to the following optimality condition or targeting rule,

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κ ybt = − π bt . λ

(7)

Using the terminology of Clarida, Gali, and Gertler (1999), this targeting rule implies a leanagainst-the-wind policy response. If inflation is above the target π bt > 0, as a result of a supply shock, this policy depends on the ratio

κ λ,

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then the optimal policy pushes the output gap into negative territory (b yt < 0). The aggressiveness of

where κ measures the gain in terms of reduced inflation obtained

from each unit of lost output(the slope of the Phillips curve) and λ reflects the trade-off between π b

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and yb. Importantly, this lean-against-the-wind policy is stronger if the weight on the output gap in a policymaker’s loss function is smaller.

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Assuming that the ELB constraint never binds and that the cost-push shock, µt , is iid, the full solution can be easily characterized. In that case, the expressions for inflation and output under the

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optimal policy are: π bt = λδµt , ybt = −κδµt , with δ = (λ + κ2 )−1 . Accordingly the current value of the

cost push shock can be used to characterize the tradeoff between inflation and output. Furthermore, as λ → 0, the volatility of inflation approaches zero, and σy → σµ . Also, as λ → ∞, the volatility

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of the output gap converges to zero and σπ → σµ . The instrument rule that supports optimal policy

can be written as: ˆit = rte +

σκ bt . λ π

Furthermore, with no cost-push shocks, the optimal discretionary

policy consists of setting the actual real rate equal to the efficient real rate, rte . In these circumstances,

inflation is equal to target and the output gap is closed at every date (i.e., π bt = ybt = 0).

However, the presence of the effective lower bound will change this prescription. At the effective

lower bound, the equilibrium under discretion implies that the targeting rule characterizing optimal

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policy is affected by the Lagrange multiplier associated with that constraint: κ 1 ybt = − π bt − γt . λ λ

(8)

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In normal times, optimal policy under discretion imposes that the output gap moves proportionately with the inflation gap; however, at the effective lower bound, a tightening in the constraint implies a larger decline in the output gap or inflation gap, since γt > 0. That is, the presence of the effective lower bound worsens the trade-off between inflation and the output gap, because − κ1 γt represents the extra loss in terms of current output due to the effective lower bound. Substituting expression (8) into

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expression (2) yields: (λ + κ2 )b πt = λβEt {b πt+1 } − κγt π bt = − λβ , λ+κ2

j=0

βej Et γt+j = −



κ  γt + λ + κ2

∞ X j=0



βej Et γt+j  ,

and for simplicity we have assumed that µt = 0 ∀t. If the nominal rate is currently

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where βe =

κ λ + κ2

∞ X

at the ELB or expected to be there in the future, then inflation will be below target. Moreover, for a

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given path of the Lagrange multipliers on the ELB constraint, this downward bias to inflation will be greater, the more a policymaker cares about inflation stabilization relative to stabilizing real activity

Asymmetric Loss Function

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3.2

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(i.e., the lower is the value of λ).

Policymakers may not view positive and negative deviations from longer-run values as equally costly, and we now consider the implications of a loss function for policymakers who disproportionally dislike

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output below potential and are tolerant of movements in output above potential. Formally, policymakers minimize the loss function,

∞

1 X t 2 E0 β π bt + I(b yt ) , 2 t=0

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(9)

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where I(b y ) is an indicator function defined as:

 λb yt2

ybt ≥ 0

ybt < 0.

(10)

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I(b yt ) =

  0

Figure 3 plots the period t losses stemming from variations in the output gap under this loss function and compares it to the case in which losses are symmetric. Policymakers might regard the cost of an increase in output above potential as considerably smaller than an equal-sized decrease below potential for a variety of reasons. For instance, high unemployment could lead to skill deterioration and thus

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to persistently low output, a channel that may not be relevant for economies operating at or below the natural rate. Similarly, some policymakers might perceive the anticipated costs of systematically undershooting the inflation objective as disproportionately large because of an increased likelihood of outsized disruptions to economic activity stemming from the lower bound on nominal interest rates or from downward nominal price and wage rigidities.

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In the absence of the effective lower bound, the optimal rate of inflation is given by:

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bt = π

  0

 − λ yb κ t

ybt ≥ 0

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ybt < 0.

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If inflation rises due to an increase in the cost-push shock, µt , then policymakers who view output losses as asymmetric, just like their counterparts who view output losses symmetrically, will lean against the wind and act to push output below potential. However, policymakers with an asymmetric loss function

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will lean against the wind to a much larger extent if µt falls, in order to push inflation back up to target, since they are willing to tolerate as large a rise in output above potential as necessary in order

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to achieve this objective. As a result, policymakers with an asymmetric loss function have an easing bias relative to their counterparts with a symmetric loss function. In the absence of the ELB, this easing bias will lead to an average inflation rate above the central bank’s target. In the presence of the ELB, this easing bias can counteract the downward pressures on the average

inflation rate created by that constraint. The ELB alters the optimal discretionary inflation rate, since

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in that case we have: bt = π

  − 1 γt κ

 − λ yb − 1 γ κ t κ t

ybt ≥ 0

(12)

ybt < 0

the inability to lower the nominal rate reduces inflation by − κ1 γt .

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Results

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If the economy is in a recession (b yt < 0) with the nominal rate at the effective lower bound (γt > 0),

We solve the model using a global solution method that does not impose perfect foresight or certainty

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equivalence and thus is well suited to characterizing optimal policy under uncertainty in the presence of the occasionally binding ELB constraint and the asymmetry in policymakers’ loss function.6 To illustrate how optimal policy is affected by the ELB and the asymmetric loss function, we use relatively standard values for the parameters of the model. The time discount factor, β, is chosen to be consistent with a quarterly model and is set equal to 0.9975. As a result, the steady state real rate equals 1 percent

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¯ is chosen to be consistent with a 2 percent on an annual basis. The central bank’s inflation target, Π, annual rate. The parameter κ which governs the slope of the Phillips curve, is set equal to 0.01, and

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σ = 1 (i.e., log preferences in consumption). We choose λ = 0.065, which implies that policymakers place equal weight on deviations of annualized inflation and output from their target values. We set the parameters describing the shocks as follows. The natural rate shock, rte , follows a normally-distributed

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AR(1) process with an autocorrelation coefficient, ρr , equal to 0.85 and with a standard deviation, σr , of 0.325. The markup shock is also an AR(1) process with an autocorrelation coefficient, ρµ , equal to

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0.3 and with a standard deviation, σµ , of 0.1. Table 1 shows the unconditional mean and variance for inflation and the output gap under the

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symmetric and asymmetric loss functions. The first column shows that, in the absence of the ELB constraint, the average annualized rate of inflation is equal to 2 percent while on average the output gap is equal to zero when policymakers seek to minimize the symmetric loss function. Both output and inflation fluctuate in response to the cost-push shock in that case but those fluctuations are negligible, and hence the value of expected present discounted sum of losses, computed using either the symmetric or asymmetric loss function, is small. In comparison, a policymaker who seeks to minimize 6 That is, the policymakers are mindful of the risks that current and future shocks might impose on policy actions, including those associated with the effective lower bound binding.

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the asymmetric loss function in the hypothetical economy without an ELB constraint achieves much larger losses than a policymaker minimizing the symmetric loss function, even if the losses are computed under the asymmetric loss function. These larger losses reflect that a policymaker with an asymmetric loss function eases more aggressively to counteract low inflation than she tightens to counter high

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inflation, generating private sector beliefs that expected future inflation will be high on average (e.g., Barro and Gordon (1983)). As a consequence, average inflation at 2.9 percent ends up well above the policymaker’s objective.

These unconditional outcomes change considerably when the policy rate is constrained by the zero lower bound. In this case, a policymaker who minimizes the symmetric loss function ends up achieving

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an average inflation rate 30 basis points below target, reflecting that the economy suffers occasional spells at the ELB where the real interest rates cannot be lowered sufficiently and output and inflation fall below their targets. With average inflation and output falling below target, the unconditional average value of the policymakers’ loss function rises from 2 percent to 5 percent as a result of the ELB constraint.

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One might expect that a policymaker who only cared about deviations of inflation from target would be able to achieve an average inflation rate closer to 2 percent. However, a policymaker who cares only

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about inflation ends up responding less aggressively to a shock that lowers the natural real rate and so reduces both output and inflation relative to a policymaker who cares about both inflation and real activity. Accordingly, the final column of Table 1 shows that the inflation rate for this policymaker is

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even lower, averaging only a little over 1.5 percent. A policymaker who seeks to minimize the asymmetric loss function when the ELB occasionally

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binds does much better at keeping inflation close to target: the average inflation rate for this policymaker is just a tad over 2 percent. This inflation outcome results because the easing bias implied by the

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asymmetric loss function effectively offsets the disinflationary pressure stemming from the inability of policymakers to lower the policy rate due to the effective lower bound constraint. A policymaker acting to minimize the asymmetric loss function achieves average losses almost on par with a policymaker minimizing the symmetric loss function even when the losses are computed using the symmetric function. This result arises because the asymmetric policy generates private sector beliefs that expected future inflation will remain near 2 percent despite the deflationary effects of the ELB constraint, greatly improving the average outcomes for inflation according to either loss functions. The only reason that

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policymakers with the asymmetric loss function achieve greater losses under the symmetric loss function is that they are willing to accept higher output gap volatility whenever output is above potential. Figure 4 shows the associated unconditional distributions of inflation, the output gap, and the real rate for the symmetric and asymmetric loss functions when the ELB occasionally binds. For

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the policymaker with asymmetric preferences, the likelihood of inflation below target is substantially reduced relative to a policymaker with symmetric preferences. However, the likelihood of inflation above target is considerably higher. This shifting in the distribution of inflation risks reflects that a policymaker with an asymmetric loss function eases much more aggressively in response to shocks that reduce inflation than a policymaker with a symmetric loss function. Consequently, the nominal rate

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is more frequently at the ELB and the distribution of real rates under the asymmetric loss function shows a large mass of outcomes of rates near −2 percent and is generally shifted to the left relative to the distribution associated with the symmetric loss function.

Figure 5 displays the response of the economy to a fall in the efficient or natural real rate, rte that is large enough to cause the nominal rate to reach the effective lower bound under both optimal discretion

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with asymmetric preferences and optimal discretion with symmetric preferences. We assume that the initial expected fall in the natural real rate is equal to -2.25 percent after which it is expected to revert

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back to its mean value of 1 percent with an AR(1) coefficient of 0.85. Because the model is nonlinear, the effects of the shock depend on the economy’s initial conditions, which for the canonical NK model include only the two exogenous shocks; we assume that the lagged values of the two shocks are equal

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to their means of zero. As a result, the economy can be viewed as initially being at its non-stochastic steady state in which inflation is at target and output is at potential prior to the large shock to the

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efficient real rate. In the simulation, the shocks that hit the economy at each date are uncertain and the dashed line shows the median paths of variables under policy with the asymmetric loss function while

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the shaded region shows the 32nd and 67th percentile uncertainty bands stemming from fluctuations in the efficient real rate. The dashed red lines show the median paths and uncertainty bands associated with the variables under policy with the symmetric loss function. Figure 5 highlights two notable properties of optimal policy under the asymmetric loss function

after the nominal interest rate begins to rise from its initial position at the ELB towards an eventual median value of 3 percent. First, policymakers minimizing the asymmetric loss function are successful at keeping the median path of inflation close to target (top-right panel) while the median path of

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output only falls temporarily below potential (top-left panel). In contrast, policymakers minimizing the symmetric loss function have very little chance of achieving inflation at or above target, as all outcomes between the 32nd and 67th percentile lie below the central bank’s inflation target. Second, the median path of the nominal interest rate prescribed by a policymaker with an asymmetric loss

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function stays at the ELB longer than the median path prescribed by a policymaker with a symmetric loss function (bottom-left panel). However, after departing from the ELB, the median path for the policy rate prescribed by the policymaker with the asymmetric loss function rises more quickly than the path prescribed by the policymaker with a symmetric loss function.

Conclusion

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In this paper, we demonstrate that, if monetary policy is constrained by the effective lower bound (ELB), optimal policymakers minimizing a standard quadratic loss function involving deviations of inflation and output from targets under discretion systematically undershoot their inflation target. This

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result suggests that the ELB is a particularly pernicious constraint on policymakers who are unable or unwilling to influence private sector expectations through credible commitments. As an alternative, we consider policymakers with an asymmetric loss function that places weight on deviations of output

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below potential but no weight on deviations above potential. In the context of the canonical NK model, we show that policymakers who minimize such an asymmetric loss function are able to achieve better

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inflation outcomes than policymakers with a symmetric loss function. This result suggests that policies that systematically ease more in circumstances when inflation is low than they tighten when inflation is

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high can be an effective way of mitigating the undershooting of inflation caused by the ELB. However, our results also imply that there are costs to systematically responding in this way: policymakers need to be mindful of upside inflationary risks posed by such a reaction function, especially as the policy

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rate moves away from the ELB and the likelihood of being constrained diminish.

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References [1] Blanchard,Olivier and Jordi Gal´ı (2007), “Real Wage Rigidities and the New Keynesian Model,” Journal of Money, Credit, and Banking, Vol. 39, No. 1, Supplement, pp.36–65. [2] Barro, Robert J. and David B. Gordon (1983), “A Positive Theory of Monetary Policy in a Natural Rate Model,” The Journal of Political Economy, Vol. 91, No. 4 (Aug., 1983), pp. 589–610

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[3] Carney, Mark (2016), “Redeeming an unforgiving world,” at the 8th Annual Institute of International Finance G20 Conference, Shanghai, February 26. [4] Clarida, Richard, Jordi Gali, and Mark Gertler (1999), “The Science of Monetary Policy: A New Keynesian Perspective,” Journal of Economic Literature, Vol. XXXVII, pp. 1661–1707. [5] Eggertsson, Gauti, and Michael Woodford (2003), “The Zero Bound on Interest Rates and Optimal Monetary Policy,” Brookings Papers on Economic Activity, No. 1, pp.139–233.

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[6] English, William (2015),“Notes on the Risk of a Return to the Effective Lower Bound,” Federal Reserve Board. [7] English, William B., J. David Lopez-Salido, and Robert J. Tetlow (2015), “The Federal Reserve’s Framework for Monetary Policy: Recent Changes and New Questions,” IMF Economic Review, vol. 63 (April), pp. 22-70.

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[8] Charles Evans, Jonas Fisher, Francio Gourio, and Spencer Krane (2015), “Risk management for monetary policy near the zero lower bound,” Brookings Papers on Economic Activity,March 2015. [9] John Fernald (2014), “Productivity and Potential Output Before, During, and After the Great Recession” NBER Macroeconomics Annual, Jonathan Parker and Michael Woodford eds.

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[10] Gagnon, Etienne, David Lopez-Salido and Benjamin K. Johannsen (2016), “Family Composition, Life Expectancy, and the Equilibrium Real Interest Rate,” Federal Reserve Board, May 15, 2016.

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[11] Gali, Jordi (2008), Monetary Policy, Inflation and the Business Cycle: An Introduction to the New Keynesian Framework, Princeton University Press.

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[12] Gordon, Robert J. (2016), The Rise and Fall of American Growth:The U.S. Standard of Living since the Civil War, Princeton University Press. [13] Haldane, Andrew (2015), “Stuck,” Speech to be given to the Open University, London, on 30 June 2015

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[14] Hamilton, James D., Ethan S. Harris, Jan Hatzius, and Kenneth D. West (2015), “The Equilibrium Real Funds Rate: Past, Present, and Future,” presented at the US Monetary Policy Forum, New York, February 27, 2015. [15] Johannsen, Benjamin K. and Elmar Mertens (2016), “A Time Series Model of Interest Rates with the Effective Lower Bound,” FEDS Working Paper 2016-033. [16] Gust, Christopher, Benjamin K. Johannsen and David Lopez-Salido (2015), “ Monetary Policy, Incomplete Information, and the Zero Lower Bound,” FEDS Working Paper 2015-099. [17] Laubach, Thomas and John Williams (2015), “Measuring the Natural Rate of Interest Redux,” Federal Reserve Bank of San Francisco, Working Paper 2015-16. 13

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[18] Andrew T. Levin, David Lopez-Salido, Edward Nelson, and Tack Yun (2010), “Limitations on the effectiveness of forward guidance at the zero lower bound,” International Journal of Central Banking, March 2010.

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[19] Rotemberg, Julio and Michael Woodford (1997),“An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy,” NBER Macroeconomics Annual, Ben Bernanke and J. Rotemberg, eds. [20] Summers, Lawrence (1991), “Panel Discussion: Price Stability: How Should Long-Term Monetary Policy Be Determined?” Journal of Money, Credit and Banking 23:3, Part 2 (August), pp. 625631. [21] Michael Woodford (2003), Interest rate and prices, Princeton University Press, 2003

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[22] Yellen, Janet (2015), “Normalizing Monetary Policy: Prospects and Perspectives” at the “The New Normal Monetary Policy,” a research conference sponsored by the Federal Reserve Bank of San Francisco, San Francisco, California, March 27, 2015.

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[23] Yellen, Janet (2016), “The Outlook, Uncertainty, and Monetary Policy,” at the Economic Club of New York, New York, New York. March 29, 2016

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Table 1: Selected Unconditional Moments under Optimal Discretion for Alternative Loss Functions

2 2 0.32

1.71 1.71 0.38

Output Gap Mean Median Variance

0 0 0.01

-0.29 0 0.59

Prob(it = 0) Symmetric Losses Asymmetric Losses

0.02 0.01

AC

CE

PT

ED

M

26.2 0.0503 0.0358

15

λ=0 Constrained

2.94 2.92 0.31

2.04 2.02 0.35

1.54 1.57 0.37

0.25 -0.04 3.02

0.22 -0.01 1.06

-0.15 0.01 1.89

52.5 0.057 0.0236

53.9 0.0987 0.0599

AN US

Annual Inflation Mean Median Variance

Asymmetric Loss Function Unconstrained Constrained

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Symmetric Loss Function Unconstrained Constrained

0.1718 0.0370

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0

1967

−2

1958 1974 1972

−6

−4

AN US

1963

1971

1976

−8

Percentage points

Easings: Pre−1979

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Figure 1: Federal Reserve Easing Cycles

20

40

60

M

0

80

100

ED

PT

−2 −4

1999

2015

2004

−6

1987

CE

Percentage points

0

NA Easings: Post−1982

AC

−8

1994

0

20

40

60

Months since start of easing

16

80

100

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Class II FOMC –

Survey Expectations of the Long−Run Federal Funds Rate

Figure 2: Survey Expectations of Longer-Run Federal Funds Rate

Survey Expectations of Longer-Run Federal Funds Rate PointEstimates Estimates SEP Point Percent

5.0

M

AN US

PDS (median) SEP (median) Blue Chip (mean)

2010

4.0

3.5

3.0

ED PT 2009

4.5

2.5

2.0 2011

2012

2013

2014

2015

2016

AC

CE

Note: The lines show survey expectations of the long-run federal funds rate. The black line shows the median response from the Primary Dealer Survey, the red show the median response from FOMC participants in the Summary of Economic Projections, and the blue line shows the mean forecast from Blue Chip Financial Forecasts the Blue Chip survey. Percent Mean 8

6

17

Nov. 24 4

2

2012 2013 2014 2015 Note: The light shaded area represents the 10th and 90 of responses, while the dark shaded area represents the 25th and 75th percentiles.

Primary Dealer Surveys

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Figure 3: A Comparison of Alternative Loss Functions

0.045

Asymmetric Quadratic

0.04

AN US

0.035

0.03

Loss

0.025

M

0.02

ED

0.015

0.005

−0.15

−0.1

−0.05

AC

CE

0 −0.2

PT

0.01

18

0 Output Gap

0.05

0.1

0.15

0.2

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Figure 4: Unconditional Outcomes under Optimal Discretion for Alternative Loss Functions

Inflation 1

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0.8 0.6 0.4 0.2

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

0.8

1

AN US

0

Output Gap

12 10 8

M

6 4

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

Real Interest Rate Symmetric Preferences Asymmetric Preferences

CE

1.5

−0.8

PT

0 −1

ED

2

1

AC

0.5

0 −3

−2

−1

0

1

19

2

3

4

5

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Figure 5: The Effects of a Large Fall in the Natural Real Rate

Output Gap

Inflation

0.2

2.2

2 Annual Percent

−0.2 −0.4

−0.8 −1 −1.2 0

5

10 Quarters

15

Nominal Rate

1.4

20

0

5

10 Quarters

15

20

15

20

M

3

4 3

ED

Annual Percent

1.6

Real Rate

5

2

5

10 Quarters

15

2 1 0 −1 −2

20

AC

CE

0

PT

1 0

1.8

AN US

−0.6

Annual Percent

Percent Deviations

0

20

0

5

10 Quarters