Alternatives to Inflation Targeting in
Low Interest Rate Environments
Keynote Speech by Carl E. Walsh
The challenges of a low interest rate, low inflation environment have
led to calls to re-examine the basic framework of flexible inflation
targeting (IT). Interest in alternatives such as price-level targeting(PLT) and average inflation targeting (AIT) arises from the way inwhich these policy regimes cause inflation expectations to work as
automatic stabilizers, a factor that can be of major importance if
the central bank is constrained at the ELB. I show that the performance of PLT deteriorates significantly relative to IT and AIT in thepresence of wage rigidities, shocks to productivity, and deviations
from rational expectations. A central bank able to credibly commit
to the optimal policy consistent with PLT is likely to face a muchhigher probability of needing balance sheet policies to implement
policy than would be the case under IT or AIT. These results suggest
it is too early to count IT out in the competition over policy design.
Keywords: Optimal monetary policy; Inflation targeting; Price-leveltargeting; Average inflation targeting
JEL Classification: E52, E58

Distinguished Professor of Economics, University of California, Santa Cruz (E-mail:walshc@ucsc.edu)..............................................................................................................
This paper is based on a keynote address delivered at the 2019 BOJ-IMES Conference
on Central Bank Design under a Continued Low Inflation and Interest Rate Environment,
Tokyo, Japan, May 29–30, 2019. I would like to thank conference participants for helpfulcomments and Alan Ledesma for excellent research assistance and helpful discussions.
The views expressed in this paper are those of the author and do not necessarily reflect theoﬃcial views of the Bank of Japan.

MONETARY AND ECONOMIC STUDIES / NOVEMBER 2019
DO NOT REPRINT OR REPRODUCE WITHOUT PERMISSION

41

Figure 1 Inflation and 10-yr. Government Bond Rates in Japan and the U.S.,
2000/Q1–2019/Q1

Source: Federal Reserve Bank of St. Louis.

I. Introduction
Ten years ago, in June 2009, the Great Recession in the U.S. oﬃcially ended. Far
from marking a return to normalcy however, the last decade has brought to prominencemonetary policy challenges for the U.S. and the euro zone that Japan has faced formore than two decades. These challenges are reflected in the diﬃculty central banks
have had in reaching their inflation targets from below and the fear that the new normal
involves a low natural real rate of interest and low inflation, implying there will be little
room to cut nominal rates in a recession. These challenges are particularly pressing inJapan. Figure 1 shows the past 20 years of CPI inflation (less food and energy) andthe 10-year government bond rate for Japan and the U.S. With the exception of therise in 2014 due to the increase in the consumption tax, the inflation rate in Japan has
remained below 1% and has averaged essentially zero over this period, compared to an
average inflation rate of 2.1% over the same period in the U.S. The cumulative eﬀect
on the price level in the two countries is illustrated in Figure 2, which shows the CPI(less food and energy) in each country, expressed as an index equal to 100 in 1970/Q1.
This environment has prompted re-evaluations of the widely held monetary policy
consensus that characterized the academic and policy community on the cusp of the
Global Financial Crisis. This consensus involved agreement on the importance of (1)a commitment to price stability, defined in practice as a low and stable rate of inflation (commonly 2% among major economies), (2) the use of a short-term interest rate
as the primary instrument of policy, and (3) a commitment to transparent communications about the objectives of policy.1 Put into practice, this consensus provided theunderpinning of flexible inflation targeting (IT) which came to exemplify best practices................................
1. See Goodfriend (2007) for a discussion of this consensus.

42 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2019

Alternatives to Inflation Targeting in Low Interest Rate Environments

Figure 2 Consumer Price Indexes (Less Food and Energy) for Japan and U.S.

Source: Federal Reserve Bank of St. Louis.

in monetary policy. To a large degree, IT has survived the financial crisis intact. For
example, Stan Fischer in drawing the lessons of the Global Financial Crisis for monetary policy concluded: “How to summarize all these conclusions? Simply: flexible
inflation targeting is the best way of conducting monetary policy.”2 At the time Fischer
wrote, the continuing persistent decline in the natural rate of interest was less clear, but
the recent evidence suggests that real rates will continue to remain low.3 Thus, IT may
no longer provide the best design for monetary policy in the environment faced by the
Bank of Japan, the U.S. Federal Reserve and other central banks.
In 2010, Blanchard, Dell’Ariccia, and Mauro (2010) launched the debate over policy design, albeit still within the context of flexible inflation targeting, by proposingthat the 2% inflation target adopted by many central banks be doubled to 4%. An increase in the inflation target, by lifting average levels of nominal rates further fromthe eﬀective lower bound (ELB) on nominal rates, would make hitting the ELB lesscommon and provide more room for monetary policy to cut interest rates if necessary
in responding to contractionary shocks. Evaluating such a proposal involves assessing
the benefits—less frequent episodes at the ELB and a more stable macro economy—against the costs—higher steady-state inflation. Such a calculation parallels the evaluation of any insurance: are the annual costs of the insurance arising from higher average
inflation less than the expected benefits of less frequent episodes at the ELB? In any
case, no major central bank has raised its inflation target.4
As an alternative to raising the inflation target, attention has also focused on replacing IT. The proposed alternatives are all designed to generate endogenous movements................................
2. Fischer (2013, p. 14) emphasis in original.
3. See Holston, Laubach, and Williams (2017).
4. Billi (2011), Coibion, Gorodnichenko, and Wieland (2012) and others suggest optimal inflation, even in theface of the ELB, is still quite low.

43

in inflation expectations that would help achieve the central bank’s inflation and real
objectives. Such alternatives may be particularly relevant in environments of discretionary policymaking in which policymakers’ statements about future policy are not of
suﬃcient credibility to move private sector expectations. And they may be especiallyvaluable when policy actions are constrained by the eﬀective lower bound on nominalinterest rates.5
In this paper, I examine two of the primary candidates to replace inflation
targeting—price-level targeting (PLT) and average inflation targeting (AIT). Both PLT
and AIT have received attention recently, but much of this literature—see, for example,
Bernanke, Kiley, and Roberts (2019) or Mertens and Williams (2019)—examines
whether, in a regime of inflation targeting, the central bank should include the pricelevel or a measure of average inflation in an instrument rule that helps guide policy. In
my view, this type of analysis does not provide a meaningful evaluation of price-leveltargeting. If a central bank finds an instrument rule a useful guide for implementing a
policy designed to achieve its inflation target, then the policy framework is still one of
inflation targeting, whatever variables might appear in the reference instrument rule.
In contrast, I evaluate PLT and AIT as targeting frameworks, with each altering thegoals of monetary policy. A regime of inflation targeting establishes the inflation target
as the objective of monetary policy, and the appropriate way to evaluate alternatives to
IT is to consider the implications of assigning objectives other than inflation, the pricelevel for example, to the central bank. This is the approach adopted to evaluating PLT,
speed limit policies, nominal income policies and other policy frameworks in Svensson(1999), Jensen (2002), Walsh (2003), Vestin (2006), Nessén and Vestin (2005), Cateau
et al. (2009), Billi (2017), Bodenstein and Zhao (2019b), and Nakata, Schmidt, andYoo (2018), among others.6 For each framework I assume a flexible regime in which
deviations from the price level or average inflation target are traded oﬀ against ensuring
greater stability in the real economy. With this approach, PLT and AIT are treatedequivalently to IT as frameworks for monetary policy.
A second and crucial aspect of the specification of the policy framework is deciding
whether to model policy as conducted with commitment or with discretion. The workthat treats policymakers as implementing a pre-specified instrument rule assumes anability to commit to the rule; the assumption implicit in the inflation targeting literatureis that the central bank can commit to its goals.7 The literature on IT often assumes
that, given the goals of the central bank, actual policy is implemented with discretion,
while the Ramsey policy that maximizes social welfare provides a benchmark against
which to compare IT. I follow this tradition, but I also evaluate outcomes under IT, PLT,
and AIT when the central bank can implement a commitment policy. The commitment
solution is of interest because central banks do seem purposefully committed to behaving in ways consistent with past statements about policy actions, as evidenced, forexample, by the eﬀects of forward guidance.8 Work by Kurozumi (2008), Kurozumi................................
5. I will take it as given that there is some eﬀective lower bound on nominal rates. For proposals to remove any
lower bound, see, for example, Goodfriend (2016), Bordo and Levin (2019), and Lilley and Rogoﬀ (2019).
6. Billi (2017), Bodenstein and Zhao (2019b), and Nakata, Schmidt, and Yoo (2018) are distinguished by theirfocus on the implications of the ELB.
7. See Walsh (2015) for a discussion of using goals versus rules in evaluating central bank performance.
8. See, for example, the work by Swanson (2018).

44 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2019

Alternatives to Inflation Targeting in Low Interest Rate Environments(2012), and Nakata (2018) suggests commitment equilibria may be sustainable in New
Keynesian (NK) models even absent a formal commitment mechanism. And it may befeasible for policymakers to commit to time-inconsistent actions if those actions canbe justified on the grounds that they help achieve the ultimate goals to which the central bank is (publicly) committed. In a rule-based approach, it may be harder to justify
time-inconsistent responses to variables such as the past price level, as called for underapproaches that add the price level to an instrument rule, if the actual goal the central
bank is committed to is an inflation target and not the price level.
Even with commitment, alternative policy regimes may still diﬀer from the Ramsey policy if the central bank’s objectives diﬀer from the model-consistent measure ofsocial welfare. In fact, central banks are not asked to maximize social welfare; instead,they are assigned more limited objectives, such as price stability.9 Price stability may
contribute to social welfare, but the latter is vastly broader than the former. I assume
that in each targeting regime, the central bank focuses on a dual mandate that involves
stabilizing a measure of real economic activity and a nominal variable (the price levelor a measure of inflation), even if other variables appear in the model-consistent definition of social welfare.
The alternatives to IT I consider address the challenges of low inflation and a low
natural rate by generating endogenous movements in expectations that act as automaticstabilizers. The idea of monetary policy as an automatic stabilizer is not new, and wascentral to the classic analysis of the instrument choice problem by Poole (1970). In
Poole’s analysis, the choice was between using a monetary aggregate or a nominal interest rate as the policy instrument. The timing was such that the policymaker had to
set the instrument before observing current shocks. When shocks occurred, the variablechosen as the instrument, either the interest rate or the monetary aggregate, remained
unchanged, while the other responded endogenously. And it was this endogenous response that governed the automatic stabilizing (or destabilizing eﬀects) of monetary
policy.10
Poole’s framework oﬀered two key insights. First, the policy choice aﬀects the way
economic activity and inflation respond to shocks. Second, the optimal choice of the
instrument will depend on the nature of the shocks of greatest concern. In the simple Poole example, if aggregate demand shocks are the major source of volatility, themonetary aggregate is the better instrument choice; if money demand shocks are ofprimary concern, the interest rate is the better choice. This last insight is particularly
relevant: if low inflation and low interest rates are currently the major concerns, thenpolicy frameworks, such as IT, developed in an environment of high inflation and highinterest rates may no longer be appropriate in the new policy environment. New designs for monetary policy need to be examined, and the notion of creating automaticstabilizers through the choice of monetary policy design oﬀers a useful perspective forsuch an examination.
If the goals of the central bank involve the price level or average inflation, pol................................
9. As noted by O’Flaherty (1990), when you call a plumber to fix a leak, you don’t want her to arrive and begin
to bake a cake, even if, in the moment, you’d prefer a piece of cake to having the leak fixed.
10. See Friedman (1990) for a survey of the instrument choice problem. See also Walsh (1990), or Chapter 12,
section 3.1 of Walsh (2017).

45

icy will respond to past target misses, something that is not true to the same extent
under inflation targeting.11 Responding to past target misses aﬀects private sector expectations about future inflation. Because PLT and AIT regimes are designed to makeexpectations react in a stabilizing fashion, they are very much in line with the emphasison expectations in modern macro models and the importance of inflation expectations
when policy is constrained by the ELB. As Woodford (2005) noted even before thefinancial crisis, “For not only do expectations about policy matter, but, at least undercurrent conditions, very little else matters.”
Managing expectations is crucial when, as at the eﬀective lower bound for nominal interest rates, direct actions such as changing the central bank’s normal instrument
may not be feasible. Yet the search for frameworks in which expectations act as automatic stabilizers predates the period when major central banks (other than the Bankof Japan) were concerned with the ELB. For example, Svensson (1999) and Vestin(2006) showed that price-level targeting could, in an environment of discretionary policy making, dominate inflation targeting by inducing movements in expectations thatmimicked those generated under an optimal commitment policy. Under PLT, any shortfall of prices from target would generate expectations of the higher future inflationnecessary to regain the target price level. And at the ELB, a rise in expected inflation
is desirable. Reifschneider and Williams (2000) showed how instrument rules that respond to cumulated past target misses could perform well. Similarly, average inflation
targeting (AIT), unlike simple IT, ensures that a temporary decline in inflation relative
to target would generate expectations of the higher future inflation need to achieve thetarget for average inflation.
The rest of the paper is organized as follows. In section II, I argue that the relative performance of diﬀerent targeting regimes is altered once one moves beyond thevery simple textbook version of the New Keynesian model, specifically by introducing
wage stickiness. In the face of wage rigidity and productivity shocks, IT and AIT defined over 4 to 16 quarters perform similarly and marginally outperform PLT. I carryout the analysis under both discretion and commitment when the central bank has adual mandate defined in terms of minimizing the volatility of a measure of inflation or
the price level and a measure of real economic activity (an output gap). By interpreting the interest rate in the model as a shadow rate along the lines of Wu and Zhang(2017), I compare how frequently balance sheet policies would be required to implement optimal policy under each regime. While PLT is designed to make expectations
act like automatic stabilizers, policymakers seem to place great store on anchoring
expectations, so in section III, I contrast the performance of PLT, IT and AIT when
expectations are anchored, while in section IV, I compare outcomes when expectations
are assumed to follow an ad hoc partial adjustment model that allows for deviations
from rational expectations. Conclusions are summarized in the final section.

................................
11. If the inflation process is purely forward looking, optimal discretion in an IT regime does not respond tolagged inflation and therefore does not respond to past target misses. This is no longer true if current inflation
depends in part on lagged inflation.

46 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2019

Alternatives to Inflation Targeting in Low Interest Rate Environments

II. Alternatives to Flexible Inflation Targeting
How do IT, PLT and AIT compare? To address this question, and to evaluate alternative
policy regimes consistently, I interpret the design of a policy regime to consist of a loss
function adopted (or assigned) to the central bank. For example, flexible IT is modeled
as a regime in which the policymakers minimizes a dual loss function in inflation πt
and an output gap xt of the form
Lt =

∞

1  i 2
β πt+i + λ x x2t+i .
Et
2 i=0

(1)

This loss function is then minimized, subject to the structural constraints that characterize the macroeconomy, under either discretion or commitment. Hence, there is acommitment to the objective function, but implementation of policy may or may not
involve credible promises of future policy actions by the central bank. In either case,the assumption is that policymakers act systematically to pursue well-defined objectives; they do not commit to mechanically follow a simple instrument rule such as a
Taylor rule.
Similarly alternative policy regimes such as PLT or AIT are evaluated as regimes
in which the objective assigned to a central bank is a loss function of the form
Ltj =

∞

1  i 2
β nt+i + λ j,x x2t+i ,
Et
2 i=0

(2)

where nt equals either pt or πkt , where pt is the log price level and πkt denotes the kperiod average inflation rate, defined as
πkt ≡

 
1
(pt − pt−k ) .
kMore generally, the goals of a central bank targeting the price-level would include
2
2


pt − pTt rather than πt − πT , where pTt is the target for the price level and πT is
the inflation target. I normalize both the log price level target and the inflation target tozero.
While the U.S. Federal Reserve has had an explicit dual mandate of price stability
and maximum sustainable employment, most inflation targeting central banks whose
formal goals are defined in terms of price stability act as “flexible inflation targeters,”in that deviations from the inflation target are tolerated in order to limit volatility inreal economic activity.12 I therefore interpret alternative regimes such as price leveltargeting or average inflation targeting as similarly involving a degree of flexibility, as
reflected in the loss function given by (2).
................................
12. As of February 2019, the Reserve Bank of New Zealand also has a dual mandate which calls for monetary
policy to “keep inflation between 1 and 3 percent over the medium term, with a focus on keeping inflation nearthe 2 percent mid-point; and support maximum sustainable employment.” (https://www.rbnz.govt.nz/news/2
019/02/new-rbnz-monetary-policy-committee-remit-reiterates-focus-on-price-stability-and-employment)

47

Figure 3 Estimated Shadow Interest Rates for Japan, the U.S., and the Euro Area,
Jan. 1995–May 2019

Source: Krippner (2016). Data downloaded from https://www.rbnz.govt.nz/research-and-publications/research-programme/additional-research/measures-of-the-stance-of-united-states-monetary-policy/comparison-of-international-monetary-policy-measures.

While recent discussions of alternative policy frameworks have stressed their importance in mitigating the consequences of ELB episodes, I consider these policy
frameworks when the ELB is ignored. In part, this is because the underlying intuition concerning the potential value of PLT under discretion in New Keynesian models
predates any concern, at least in the U.S. and European context, with the ELB. In addition, Swanson and Williams (2014) and Swanson (2018) question the extent to which
the ELB constrained the Federal Reserve, while Wu and Xia (2016) and Wu and Zhang(2017) argue that the net impact of interest rate and balance sheet policies can be measured by a shadow interest rate that, as seen in Figure 3, was significantly negative forJapan, the U.S. and the euro area.13
Therefore, I interpret the policy interest rate that is implied under optimal policyin the comparisons of IT, PLT and AIT regimes as a shadow rate that can take on
positive and negative values. Implementing negative values of the shadow rate would
require using unconventional policies such as quantitative easing or other balance sheet
policies. The frequency with which the shadow rate is negative under the diﬀerent
regimes then provides some insights into the extent to which balance sheet policies
would need to be relied on. This issue is discussed further in section D.
If central banks can credibly commit to a policy regime (IT or PLT) but conduct
meeting-by-meeting policy in a discretionary fashion, then the case for PLT appears
strong. In a basic NK model, it outperforms IT away from the ELB (Vestin [2006]) and................................
13. Ichiue and Ueno (2018) provide an alternative measure of the U.S. shadow rate based on survey measured of
expectations.

48 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2019

Alternatives to Inflation Targeting in Low Interest Rate Environments

at the ELB. This makes PLT look like a win–win choice, avoiding the insurance relatedtrade-oﬀ of balancing better performance at the ELB against poorer performance awayfrom the ELB. The first step, therefore, is to extend the analysis of PLT by Vestin(2006) and AIT by Nessén and Vestin (2005) to the case of commitment and to a(slightly) richer model.
To evaluate policy regimes, I employ a standard log-linearized New Keynesianmodel, based on Erceg, Henderson, and Levin (2000), that incorporates sticky prices
and sticky wages.14 Outcomes in which the central bank minimizes (2) will be ranked
based on the model-consistent measure of social welfare. As is well-known, a loss
function such as (2) with nt = πt does not coincide with the standard quadratic approximation to social welfare in the Erceg, Henderson, and Levin (2000) model. As thoseauthors showed, a welfare cost is also generated by fluctuations in the rate of wage
inflation, a factor missing from (2). The quadratic loss function that provides a secondorder approximation to the welfare of the representative agent in the Erceg, Henderson,and Levin (2000) model, assuming an eﬃcient steady state, isLt =∞ 2 
1  i 2
β πt+i + λ x x2t+i + λw πwt+i ,
Et
2 i=0

(3)

where λ x and λw are functions of the model’s structural parameters.15 However, nocentral bank has explicitly targeted wage inflation, and I take a loss function that depends on targets related to price inflation (or the price level) and real economic activity(represented by the output gap) as the relevant objective of the central bank. That is,I maintain the dual mandate form of the social loss function by assuming the central
bank seeks to minimize (2) even when the true social loss function includes a termin wage inflation. Assigning an objective that diﬀers from social welfare introduces a
distortion and will therefore lead to a cost relative to the fully optimal commitment policy. By evaluating PLT and AIT under commitment, I can assess the implications of thecosts associated with what might be called a “misspecification” of the central bank’s
objectives. Such misspecification is relevant to consider as part of the rationale for delegating a targeting regime is as a means of assessing the central bank’s performance(see Walsh [2015]). Performance measures need to be relatively simple to promotetransparency and accountability, while social welfare is inherently more complex anddiﬃcult to assess in practice.
A. The Model and Its Calibration
The Erceg, Henderson, and Levin (2000) model represents the standard benchmark
New Keynesian model with nominal price and wage rigidities. It has been employed
by Galí (2013) and Billi and Galí (2019) to investigate the eﬀects of wage flexibility, by
Nakata, Schmidt, and Yoo (2018) to evaluate speed limit policies, and by Bodenstein
and Zhao (2019b) who examine price-level and speed limit policies.
The calibration of the structural parameters of the model follows that employed in................................
14. The version of the model I use follows the presentation of Galí (2015). For recent evaluations of policy
regimes using this model, see Bodenstein and Zhao (2019a) and Nakata (2018).
15. See Erceg, Henderson, and Levin (2000) or Galí (2015) for details.

49

Table 1 Parameters
Discount factor
CRRA
Inverse labor supply elasticity
Demand elasticity: goods
Demand elasticity: labor
Calvo parameter: prices
Calvo parameter: wages
Persistence of productivity shock
Persistence of markup shock

β
σ
η
θp
θw
φp
φw
ρz
ρu

0.995
0.65
5
9
4. 5
0.75
0.75
0. 8
0

Billi and Galí (2019) with the exception of the value of σ, the inverse elasticity of intertemporal substitution, as explained below. I include an i.i.d. price markup shock, as
in Nakata, Schmidt, and Yoo (2018) and Bodenstein and Zhao (2019a), and a persistent productivity shock that aﬀects both the natural rate of interest and the economy’s
eﬃcient level of output. The persistence of the productivity shock is taken to be 0.8,
following Billi and Galí (2019). I calibrate the standard deviations of these two shocks
to match the standard deviation of U.S. output and inflation over the 1960/Q1–2019/Q1
period under optimal discretionary inflation targeting when both prices and wages are
sticky.16 Under optimal policy unconstrained by the ELB, demand shocks play no roleand σ, the inverse elasticity of intertemporal substitution, only influences the volatilityof the nominal interest rate required to implement the optimal policy. I calibrate σ tomatch the fraction of quarters the federal funds rate was less than or equal to 25 basis
points, the eﬀective lower bound in the U.S. During 1960/Q1–2019/Q1, this fraction
was equal to 0.118, and this is matched when σ = 0.65. Setting σ = 1, a more standard
value, implies greater volatility of the policy rate and would generate a higher frequency at the ELB in the model than observed in the U.S. data. Values of the structuralparameters used in the calibration exercises are given in Table 1.
B. Results with Sticky Prices Only
Arguments in favor of a price level target rather than an inflation rate target emphasis
the manner in which a credible price-level targeting regime causes inflation expectations to adjust automatically so as to contribute to stabilizing the economy. This was
first demonstrated in a standard, sticky price NK model by Vestin (2006). When inflation is forward-looking, as implied in sticky-price models, a negative cost shock thatpushes the price level below its target path will generate expectations of higher future
inflation, as this will be necessary if the price level is to return to target. This rise in expected future inflation acts to boost current inflation, limiting the impact of the inflation
shock and allowing current inflation to be stabilized with a smaller rise in economic
activity. This mechanism is particularly important at the ELB, as shown by Eggertsson
and Woodford (2003), a situation in which, in a policy regime of discretion, the adjustment of inflation expectations may be the primary channel by which monetary policy
can stimulate the economy.
................................
16. I match the standard deviation of HP filtered log real GDP and the inflation rate as measured by the GDP
deflator. Their respective standard deviations are 2.32 and 0.58.

50 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2019

Alternatives to Inflation Targeting in Low Interest Rate Environments

Table 2 Social Loss: Flexible Wages

Policy
(1)
IT
4Q
8Q
12Q
16Q
PLT

Discretion
Loss Loss/LossR
(2)
(3)
0.706
1.274
0.937
1.691
1.155
2.086
1.265
2.283
1.332
2.414
0.562
1.014

Commitment
Loss Loss/LossR
(4)
(5)
0.554
1.000
0.879
1.586
1.091
1.969
1.203
2.171
1.227
2.305
0.600
1.083

Note: Loss as percent of steady-state consumption. LossR is loss under the Ramsey policy.

Regimes that focus on average inflation also generate stabilizing movements in expectations by ensuring the central bank reacts to past actual inflation. If the objective
is to stabilize inflation averaged over several periods, then a temporary fall (rise) in
inflation below (above) target will generate expectations of higher (lower) future inflation. Regimes of average inflation targeting have been analyzed by Nessén and Vestin(2005). Both PLT and AIT regimes ensure policy continues to respond to past target
misses in ways that are similar to optimal commitment policies.
Table 2 reports the results for inflation targeting, average inflation targeting withaverage inflation defined over 4 to 16 quarters, and price-level targeting (PLT) when
the only shocks arise from stochastic fluctuations in the price markup (cost shocks) andonly prices are sticky.17 Loss is expressed as a percent of steady-state consumption.
Also reported is the loss under each policy relative to LossR , the loss under the Ramsey
policy that minimizes social loss under commitment. Given that social loss depends
only on output gap and inflation volatility when wages are flexible (λw = 0 in thesocial loss function (3)), the central bank’s objective (2) coincides with social loss. In
this case, inflation targeting under discretion generates a loss that is approximately 27%
larger than achieved by the Ramsey policy, while loss under PLT is less than 2% higher
than under the Ramsey outcome. The diﬀerent forms of average inflation targeting
actually perform worse than traditional inflation targeting, with loss increasing in thelength of the averaging period.18
Figure 4 illustrates the responses to a negative i.i.d. cost shock under the diﬀerent
regimes. As is well-known, the Ramsey policy restores the price level to its pre-shock
value, as does price level targeting (see the figure in the lower right). The variations on
inflation targeting all fail to do so. The lower left panel of the figure (labeled pi_exp)
reports expected future inflation Et πt+1 under each policy. For an i.i.d. shock, expected................................
17. I did not consider average inflation targets defined over more than 16 quarters. Issues of communicating
policy to the public are crucial for monetary policy, and there may be diﬃculty in demonstrating a credible
commitment to targeting average inflation if the average is defined over a very long period.
18. As Vestin (2006) and Nessén and Vestin (2005) showed, performance of these targeting regimes can be
improved by allowing the weight placed on output gap stabilization to diﬀer from the value places on x2t in
the social loss function. I maintain the same λx for the diﬀerent regimes, which for my calibration implies
PLT comes very close to the Ramsey outcome. Most policy-focused discussion of alternative regimes havefocused on the definition of the nominal target and have not emphasized any need to alter the “flexibility” ofa new regime.

51

Figure 4 Response under Discretion of the Output Gap (x), Inflation (pi), Expected
Inflation (pi_exp) and the Price Level (p) to a Negative i.i.d. Cost Shock in
the Sticky Price, Flexible Wage Model

inflation is simply zero under IT, as both inflation and the output gap return immediately to their steady state values. Expected inflation under PLT mirrors its behavior
under the Ramsey policy.
The fourth and fifth columns of Table 2 illustrates the performance of the alternatives if the central bank can credibly commit to minimizing the present discounted
value of its loss function (2). Normally, assigning the central bank an objective that
diﬀers from social welfare is a means of overcoming a distortion that arises when thecentral bank carries out policy in a discretionary fashion. However, it is also plausible
to view central banks, particularly those with successful experience as inflation targeters, as having gained a great deal of credibility. If the central bank commits to an
objective such as (2), it is of interest to see how economic performance is aﬀected if
policymakers’ statements about future policy come to be credible. With only sticky
prices, inflation targeting under commitment coincides with the Ramsey policy. However, notice that the optimal commitment policy under PLT generates outcomes that are
8.4% worse than under IT. AIT under commitment performs much more poorly thaneither IT or PLT.
Figure 5 shows the response under commitment to a temporary cost shock. Compared to the Ramsey policy and IT (which are identical), PLT generates expectations
that the price level will overshoot (see the lower right subfigure), producing somewhat
less inflation variability than the Ramsey policy, while the various forms of AIT produce smaller movements in the output gap and significantly greater inflation volatility.
Table 3 shows how the components of social loss arising from variability in its

52 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2019

Alternatives to Inflation Targeting in Low Interest Rate Environments

Figure 5 Response under Commitment of the Output Gap (x), Inflation (pi), Expected
Inflation (pi_exp) and the Price Level (p) to a Negative i.i.d. Cost Shock in
the Sticky Price, Flexible Wage Model

Table 3 Standard Deviations: Flexible Wages

Policy
IT
4Q
8Q
12Q
16Q
PLT

Discretion
σπ2
σx2
1.035 1.211
1.826 0.381
2.064 0.201
2.166 0.138
2.229 0.104
1.111 0.897

Commitment
σπ2
σx21.000 1.000
1.755 0.424
1.997 0.263
2.107 0.198
2.175 0.158
1.176 0.895

Note: Standard deviations expressed relative to values under the Ramsey policy.

components, the variance of inflation and the output gap, vary under the diﬀerent policy
regimes. Values are reported relative to their values under the Ramsey policy. Under
discretion, IT generates more volatility in both inflation and the output gap than the
Ramsey policy (under commitment, IT and Ramsey coincide in the sticky price model).
Average inflation targeting performs worse than either IT or PLT; as the length of theaveraging period increases, inflation becomes increasingly volatile, while the varianceof the output gap falls so that under discretion with 16 quarter averaging, σ2x is lessthan 16% of its value under the Ramsey policy. Relative to Ramsey, discretionary PLT
generates more volatility in inflation but a more stable output gap, so that social loss
is similar to the Ramsey result (Table 2). PLT performs somewhat worse if the central
bank can implement PLT under commitment, primarily because of the more volatile53

Table 4 Social Loss: Sticky Prices and Wages

Policy
(1)
IT
4Q
8Q
12Q
16Q
PLT

Discretion
Loss Loss/LossR
(2)
(3)
1.484
1.037
1.479
1.034
1.475
1.031
1.471
1.029
1.468
1.027
1.651
1.155

Commitment
Loss Loss/LossR
(4)
(5)
1.482
1.036
1.460
1.021
1.460
1.021
1.456
1.018
1.454
1.017
2.673
1.869

Note: Loss as percent of steady-state consumption. LossR is loss under the Ramsey policy.

inflation that results.
The results in Tables 2 and 3 assume the weight λ x from the social loss functionis also the weight on the output gap in the central bank’s objective function. It is clear
from Table 3 that outcomes could be improved under average inflation targeting and
PLT by having the central bank place relative less weight on output gap stabilization,
as both forms of policy excessively stabilize the output gap.19 For IT, both inflation andthe output gap are more variable under discretion, so whether more or less weight on
inflation objectives is less clear, though Clarida, Galí, and Gertler (1999) show that,for a serially correlated inflation shock, welfare is improved if a weight less than λ x is
placed on x2t in the central bank’s loss function (i.e., if a Rogoﬀ [1985] conservative
central banker is appointed).
C. Results with Sticky Prices and Wages
While models with sticky prices but flexible wages provide useful platforms for gaining
insights into many policy issues, policy models that are taken to the data generally
incorporate sticky prices and wages. When wages are sticky, productivity shocks aswell as cost shocks will aﬀect the output gap, price inflation, and wage inflation. In
addition, the social loss function will depend on the volatility of wage inflation, priceinflation and the output gap. Because the dual mandate loss function (2) ignores wage
inflation, the alternative regimes will be distorted relative to the Ramsey policy even
if the central bank is able to implement the commitment policy associated with its
targeting regime.
Table 4 shows that adding sticky wages increases social loss under all regimes, but,importantly, PLT generates the largest loss among the alternatives regimes. Now, 16quarter average inflation targeting (the longest horizon considered here) does the best,though the diﬀerences across all regimes is small. Figure 6 shows the response to anegative i.i.d. cost shock when wages as well as prices are sticky. Recall that when
only prices were sticky, it was the way expected inflation moved that gave PLT its
advantage over IT. When wages are also sticky, inflation expectations move similarly
under all the regimes, unlike the case shown in Figure 4. The fact that expected inflation
rises after a negative cost shock even under IT eliminates the sharp contrast between................................

19. Nessén and Vestin (2005) show that this depends on the value of λx in the social loss function.

54 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2019

Alternatives to Inflation Targeting in Low Interest Rate Environments

Figure 6 Response under Discretion of the Output Gap (x), Inflation (pi), Expected
Inflation (pi_exp), Wage Inflation (piw), the Price Level (p), and the Real
Wage Level (w) to a Negative i.i.d. Cost Shock in the Sticky Price, Sticky
Wage Model

Table 5 Standard Deviations: Sticky Prices and Wages

Policy
IT
4Q
8Q
12Q
16Q
PLT

σπ2
1.017
1.017
1.017
1.016
1.016
0.965

Discretion
σx2
σπ2w
0.748 1.493
0.270 1.445
0.173 1.372
0.127 1.305
0.097 1.246
3.968 4.070

Commitment
σπ2
σx2
σπ2w
0.989 1.767 2.704
1.002 0.935 1.956
1.005 0.717 1.784
1.007 0.592 1.597
1.008 0.500 1.432
0.940 7.458 9.124

Note: Standard deviations expressed relative to values under the Ramsey policy.

IT and PLT seen in the model with flexible wages.
Even though all the alternatives now yield approximately the same social loss, thecomponents of loss diﬀer, as shown in Table 5. Output gap volatility is much higher
under PLT, while IT and the various AIT regimes stabilize the output gap much morethan occurs under the Ramsey policy. I have used the same weight on x2t in (2) as in thesocial loss function. Clearly, outcomes under PLT would be improved if the weight on
the output gap were increased relative to λ x , that is, if PLT were made more flexible,
while the variants of inflation targeting could be improved if less weight were put on
x2t .20................................
20. In a model with sticky prices but flexible wages, Vestin (2006) and Nessén and Vestin (2005) optimize the55Figure 7 Response under Discretion of the Output Gap (x), Inflation (pi), Expected
Inflation (pi_exp), Wage Inflation (piw), the Price Level (p), and the Real
Wage Level (w) to a Persistent Productivity Shock in the Sticky Price, Sticky
Wage Model

The deterioration in PLT when sticky wages are added is also apparent in Figure 7,
which shows the impulse responses to a persistent productivity shock. The top left
panel shows the extreme volatility of the output gap, while the lower left panel showsthat while PLT ensures the price level is stationary, the Ramsey policy and all the
inflation related regimes allow for a much slower return of the price level to its initiallevel. Because a shift in productivity requires a persistent change in real wages, andbecause both wages and prices are sticky, PLT forces too much of the adjustment tofall on wages.
The combination of sticky wages and persistent productivity shocks leads to a hugeincrease in the volatility of the output gap and wage inflation under PLT relative to theRamsey outcome (Table 5). The large increase in the variability of the output gap andwage inflation under PLT explains why it performs worse than IT under both discretionand commitment. The fact that this translates into a relatively modest deterioration in
PLT as measured by social loss in Table 4 is due to the small weight placed on output
gap volatility in the social loss function and the small variance of wage inflation under
the Ramsey policy.21..........................................................................................................................................
jvalue of λx for PLT and average inflation targeting. Bodenstein and Zhao (2019b) does so for PLT and speed
limit policies in a model with sticky prices and wages.
21. These results might appear to conflict with those of Bodenstein and Zhao (2019b) who find, in a basic NK
model with sticky prices and wages, that PLT does better than IT under discretion but worse under commitment: I find IT performs better in both cases. Several aspects could account for the diﬀerent conclusions,
including diﬀerences in the parameter calibrations and in the specification of the exogenous shock processes.

56 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2019

Alternatives to Inflation Targeting in Low Interest Rate Environments

Table 6 ELB Episodes: Discretion, Sticky Prices and Wages
Policy
IT
4Q
8Q
12Q
16Q
PLT
RamseyFrequency
11.8%
9.6%
9.8%
9.9%
9.8%
9.4%
8.9%

Mean duration
1.844
2.341
2.279
2.250
2.279
2.186
2.171

Maximum duration
9
9
9
9
9
7
9

Note: Duration measured in quarters.

D. The Policy Rate as a Shadow Rate
The results reported so far have ignored the eﬀective lower bound constraint on thenominal policy rate. In the linearized model, the nominal interest rate it appears as
a deviation from its steady state value, implying the ELB constraint takes the formit ≥ −rn , where rn is the steady-state real rate, given that the implicit inflation target in
the model equals zero.22 If the model’s it is interpreted not as the policy rate itself but asa shadow interest rate, along the lines of the shadow rate NK model of Wu and Zhang(2017), then the outcomes reported in Tables 2–5 would require the use of balance
sheet policies whenever it < −rn . In fact, the eﬀectiveness of balance sheet policies
is widely debated. To illustrate the range of views, Eberly, Stock, and Wright (2019)conclude that forward guidance and balance sheet policies “were able to oﬀset perhaps
one percentage point of the zero lower bound constraint” (p. 2), while Debortoli, Galí,and Gambetti (2019), using responses of U.S. macro variables to shocks obtained froman estimated VAR, argue the evidence is consistent with the hypothesis of that the ELB
is irrelevant, suggesting unconventional monetary policies have been able to substituted
fully for conventional policies. Examining the frequency with which it < −rn provides
some insight into how often balance sheet policies would be required to implement the
optimal policy under the alternative targeting regimes.
Table 6 provides evidence on how frequently the ELB constraint is violated undereach of the alternative policy regimes. Recall that the model has been calibrated tomatch the frequency of the ELB observed in the U.S. under a counterfactual policyof optimal discretionary inflation targeting. All other regimes lead to less frequent
occurrences of it < −rn , with the constraint binding 8.9% of the time under the Ramsey
policy and between 9.4% and 9.9% for the other regimes. PLT leads to the lowest
frequency at the ELB, while IT has the highest frequency. Thus, both PLT and AIT
reduce the frequency of ELB episodes relative to IT. When the model is simulated..........................................................................................................................................
Bodenstein and Zhao also optimize the weight on x2t for IT and PLT. They find, as I do, that IT outperforms
PLT in the face of persistent productivity shocks. The fact that PLT does better than IT when both cost shocks
and productivity shocks are present in their model may arise from the diﬀerent specifications of the shocks
volatilities. Bodenstein and Zhao parameterize the shock processes based on their estimation of the Smets
and Wouters (2007) model. Employing these estimates for the shock processes in the simple sticky price andwage NK model I employ implies volatilities for output and inflation that are much greater than observed in
the data. I set the shock processes so that simple model matches U.S. output and inflation volatility.
22. Alternatively, if one assumed
indexation to the inflation target πT by “non-adjusting” firms, the completenT
constraint would be it ≥ − r + π .

57

Table 7 ELB Episodes: Commitment, Sticky Prices and Wages
Policy
IT
4Q
8Q
12Q
16Q
PLT
RamseyFrequency
8.3%
8.4%
9.1%
9.5%
9.6%
18.7%
8.9%

Mean duration
2.184
2.211
2.116
2.159
2.233
2.253
2.171

Maximum duration
9
9
9
9
9
7
9

Note: Duration measured in quarters.

Table 8 Loss and ELB Outcomes When β = 0.998
Policy
IT
4Q
8Q
12Q
16Q
PLT
RamseyLoss/LossR
1.038
1.035
1.032
1.029
1.027
1.152
1.000

Frequency
34.0%
31.3%
31.2%
31.7%
31.6%
31.8%
30.9%

Mean duration
2.371
3.330
3.216
3.302
3.258
3.495
3.090

Maximum duration
12
12
12
12
12
22
12

Note: Duration measured in quarters.

under the alternative policies, the maximum duration of an ELB episode was 9 quarters
for all regimes except PLT, under which the maximum duration was 7 quarters.23
Table 7 reports characteristics of ELB episodes when the central bank has developed credibility for its policy regime, enabling it to implement the optimal commitment
policy. Moving from optimal discretion to optimal commitment reduces the probabilityof ELB under IT and AIT, with the largest reductions occurring for the shorter duration regimes (i.e., IT and 4-quarter AIT). The major diﬀerence under commitment isthat implementing a credible PLT policy more than doubles the probability of beingat the ELB, with this probability rising from 9.4% under discretion to 18.7% undercommitment.
E. A Lower Natural Rate
The results under sticky prices and wages employed a benchmark calibration in which
the steady-state level of the nominal interest rate, given that the implicit inflation target
underlying the Calvo inflation equation was zero, equals the steady-state real interest
rate. This steady-state rate, when expressed at an annual rate, was 400(β−1 − 1) =2.01%. An increase in β would lower the steady-state nominal rate and result in an increase in the frequency with which the shadow rate would be negative. Table 8 reports
outcomes when β is increased to 0.998, reducing the steady-state nominal interest rate
to 0.80% and leading to more frequent occurrences of a negative shadow rate. The column labeled Loss/LossR reports social loss relative to loss under the optimal Ramsey................................
23. Each regime is simulated using the same stochastic realizations of the exogenous shocks.

58 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2019

Alternatives to Inflation Targeting in Low Interest Rate Environments

policy for the diﬀerent policy regimes. Comparing this to Table 4 shows that reducing
the steady-state real interest rate has little eﬀect on the relative performance of IT, AITand PLT if one assumes balance sheet policies can be used to implement the optimal
shadow rate policy. A lower steady-state real rate significantly increases the frequency
with which the shadow rate would be negative for all policies regimes, but the increaseis similar across all policy regimes (compare with Table 6). Mean and maximum durations also increase, but for the latter, the major diﬀerence that stands out in comparing
Tables 6 and 8 is the eﬀect under PLT. The maximum duration of an ELB episodeunder PLT, which was 7 quarters under the benchmark calibration, increases to 22
quarters when the steady-state value for the nominal interest rate falls. If, as suggested
by Eberly, Stock, and Wright (2019), balance sheet and forward guidance policies areable to oﬀset only a fraction of the ELB constraint, then the high fraction of periods inwhich the shadow rate is below the eﬀective lower bound under all the policy regimes,
even when the central bank is able to fully commit, suggests that none of the alternatives would eliminate the need to rely on balance sheet policies. The potential for
long-duration spells at the ELB under PLT certainly warrants further study.
F. Summary on Outcomes with Rational Expectations
To summarize these results, price-level targeting is often promoted as superior to inflation targeting because of the way expectations serve as an automatic stabilizer under
PLT even in an environment of discretionary policymaking. This intuition is based on
simple New Keynesian models with sticky prices and flexible wages, and is shown
clearly in Figure 4. Incorporating sticky wages and persistent productivity shocks dramatically alters the relative ranking of PLT, IT and AIT. Sticky wages introduce alagged endogenous variable, the real wage, into the model. As shown by Walsh (2003)
in a model with flexible wages but lagged inflation in the inflation adjustment equation,
the performance of PLT deteriorates relative to IT as the lagged endogenous variable
becomes more important. And Figure 6 shows that expected inflation under all the inflation regimes mimics the behavior of expected inflation under the Ramsey policy; all
the regimes lead to movements of expected inflation that help stabilize the economy.
And when persistent productivity shocks are included, a PLT regime, defined here as aflexible regime that cares about output gap volatility but not wage inflation, generates
excessive volatility in the output gap and wage inflation that is costly from the perspective of social welfare. In contrast to PLT, IT and the various AIT regimes perform
similarly when wages are sticky. Of the variants of IT considered, 16-quarter average
inflation targeting led to the best outcomes in terms of social loss, though the gain fromswitching from IT to 16-quarter AIT was small. Despite the fact that IT dominates PLT
and in turn is dominated by AIT based on social loss when policy is implemented withdiscretion, IT would require greater reliance on balance sheet policies for its implementation, as episodes at the ELB were more frequent though of shorter duration thanfor the other regimes.
These results for both markup (cost) and productivity shocks do suggest that under the alternative policies considered, the mean duration of ELB episodes is relatively
short, significantly less than 2.5 quarters under all policies. This short duration seems
inconsistent with the decade long experience of Japan, and with that of the U.S., where

59the Federal Reserves’ traditional policy instrument remained below 25 basis points
for 7 years. And both countries have experienced low real economic growth, inflation below target, and extremely low, even negative interest rates in the case of Japan,
outcomes that call into question the basic New Keynesian macro framework that has
dominated policy analysis of the ELB.

III. Anchored Expectations
Adopting a policy such as price-level targeting or average inflation targeting that explicitly seeks to produce stabilizing movements in inflation expectations would be a
distinct shift from the focus on “anchoring” expectations that has been common among
policymakers. This emphasis on anchoring reflects one of the legacies of the 1970s and1980s, when many countries struggled with the task of reducing inflation and thenmaintaining it at low levels. The fear was that a shock that pushed up inflation, or aninterest rate cut designed to oﬀset an anticipated negative shock to demand, might leadthe public to expect higher inflation. If they did, the monetary authorities would be
faced with the choice of contracting the real economy to prevent inflation from risingor validating expectations by tolerating a rise in inflation to avoid a contraction in real
activity. Anchoring expectations would, in eﬀect, anchor the short-run Phillips curve.
Having fought to anchor inflation expectations, it was perhaps not surprising thateven during the recessions following the global financial crisis, few, if any, policymakers proposed letting inflation rise temporarily above target, though that is what theoretical models of optimal policy suggest they should have done. The fear of unanchoring
expectations was too great.24 I think there is little disagreement about the importanceof anchoring longer-term inflation expectations at the central bank’s target. However,suggestions for alternative policy regimes such as PLT and AIT eﬀectively want tokeep inflation expectations anchored in the longer-term while unanchoring them in themedium- to short-run, thereby allowing expectations to work as automatic stabilizers.
Should expectations be used by policymakers as short-run automatic stabilizers,
or should they strive to ensure expectations remain anchored? The answer depends
on the gains from managing expectations and the costs of anchoring inflation expectations. In a simple NK model with sticky prices, a credible, discretionary regime ofprice-level targeting causes expectations to move in a manner that closely replicates anoptimal commitment equilibrium under rational expectations, thereby improving overa discretionary regime of inflation targeting (see Table 2). However, in the same simple
NK model, discretionary inflation targeting exactly replicates the optimal commitment
equilibrium if expectations are completely anchored. An open question is whether thegains from having anchored expectations might mitigate any advantage of price-leveltargeting.
................................
24. For example, in July 2008 during testimony before the House Committee on Financial Services, Federal
Reserve Chairman Bernanke stressed that the Fed would prevent a rise in inflation as the economy recovers
from the current recession, stating “.... that it is important to assure the public and the markets that theextraordinary policy measures we have taken in response to the financial crisis and the recession can bewithdrawn in a smooth and timely manner as needed, thereby avoiding the risk that policy stimulus could
lead to a future rise in inflation.” See the discussion in Walsh (2009).

60 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2019

Alternatives to Inflation Targeting in Low Interest Rate Environments

Table 9 Social Loss: Anchored Expectations, Sticky Prices
Policy
(1)
IT
4Q
8Q
12Q
16Q
PLT

RE/Ramsey
(2)
1.274
1.691
2.086
2.283
2.414
1.014

AE/Ramsey
(3)
1.000
1.670
2.003
2.142
2.215
1.250

AE/RE
(4)
1.000
1.258
1.224
1.195
1.169
1.571

Note: RE (AE) denotes outcomes under rational (anchored) expectations.

To address this question, I begin by contrasting two extremes: rational expectations
and fixed expectations. The latter corresponds to the case in which inflation expectations are so firmly anchored that they do not respond at all in the short-run.25 Results forthe sticky price, flexible wage model with i.i.d. cost shocks are reported in Table 9.26
The second column repeats the results under rational expectations from Table 2. The
third column reports loss when inflation expectations are completely anchored, andthe fourth column shows the ratio of the loss with anchored expectations to that withrational expectations. In both columns (2) and (3), losses under rational expectations(RE) and anchored expectations (AE) are expressed relative to outcomes under theRamsey policy. Values greater than one in column (3) measure the cost of having inflation expectations remain completely anchored. Column (4) shows loss with anchored
expectations relative to the loss under rational expectations. Because future expected
inflation remains at zero under inflation targeting and the Ramsey policy when expected
future inflation remains at zero, the column (3) value for IT equals one. Not surprisingly, column (4) shows that anchoring expectations leads to the largest rise in loss
under price-level targeting, illustrating how the endogenous movement of expectations
plays a major stabilization role under PLT. This contribution to stabilizing the economy is absent when expectations of inflation are anchored. For similar reasons, average
inflation targeting operates, in part, by inducing stabilizing movements in expected inflation, so when expectations are anchored, AIT regimes perform more poorly, though
the deterioration of AIT is less than that experienced by PLT.
The importance of rational expectations for the performance of PLT is even more
pronounced when wages, as well as prices, are sticky, as shown in Table 10.27 With
price and wage inflation expectations anchored, social loss increases 13% to 14% under the IT and AIT policies (relative to outcomes under rational expectations—see lastcolumn of Table 10). For PLT, however, social loss rises by over 300% and is almost................................

25. The basic model contains Et πt+1 and Et xt+1 . The discussions surrounding monetary policy have focused ininflation expectations, and so I consider alternative assumptions about expectations of inflation while continuing to assume expectations about future economic activity coincide with model consistent expectations.
Et xt+1 appears in the aggregate expenditure condition arising from household consumption choices. It may bereasonable to assume households have more informed expectations about their own consumption plans thanthey do about aggregate inflation.
26. Recall that all of the policies prevent the productivity shock from aﬀecting either the output gap or inflation
when wages are flexible.
27. I assume expectations of both price and wage inflation are anchored.

61

Table 10 Social Loss: Anchored Expectations, Sticky Prices and Wages
Policy
IT
4Q
8Q
12Q
16Q
PLT

RE/Ramsey
1.037
1.034
1.031
1.029
1.027
1.155

AE/Ramsey
1.000
1.002
1.002
1.002
1.003
4.037

AE/RE
1.128
1.134
1.137
1.140
1.143
4.092

Note: RE (AE) denotes outcomes under rational (anchored) expectations.

Table 11 Standard Deviation: Anchored Expectations, Sticky Prices and Wages
Policy
IT
4Q
8Q
12Q
16Q
PLT
Ramseyσπ (AE)/σπ (RE)
1.070
1.071
1.072
1.073
1.074
1.101
1.088

σx (AE)/σx (RE)
0.882
0.841
0.876
0.959
1.073
5.103
0.617

σπw (AE)/σπw (RE)
0.300
0.285
0.296
0.310
0.323
1.575
0.415

Note: RE (AE) denotes outcomes under rational (anchored) expectations. Standard deviations expressed relative to values with rational expectations.

Table 12 ELB Episodes: Anchored Expectations
Policy
IT
4Q
8Q
12Q
16Q
PLT
RamseyFrequency
9.5%
6.2%
5.9%
5.7%
5.8%
28.1%
8.7%

Mean duration
1.696
2.000
2.034
1.966
1.933
5.204
1.776

Maximum duration
8
6
6
5
5
27
8

Note: Duration measured in quarters.

four times larger than achieved under IT. Table 11 shows the variances of the inflation
rate, the output gap, and wage inflation under anchored expectations relative to rational
expectations. Inflation volatility is increased when expectations are anchored for all
regimes. Anchoring expectations decreases output gap volatility for IT and AIT except
for 16-quarter AIT. Output gap volatility rises very significantly under PLT when expectations are anchored, while wage inflation volatility decreases when expectations
are anchored for all regimes except PLT.
Table 12 provides information on the frequency and duration of episodes at the
ELB under discretion in the model with sticky prices and wages when expectations
are firmly anchored. In comparison to the case under rational expectations (see Table 6), anchoring expectations reduces the frequency, mean duration, and maximum

62 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2019

Alternatives to Inflation Targeting in Low Interest Rate Environments

duration of ELB episodes under IT and AIT relative to the case in which expectations
are formed rationally. This is not the case, however, under PLT. The frequency of ELB
periods rises from 9.4% to 28.1% when expectations are anchored, the mean duration
rises from 2.2 quarters to 5.2 quarters, and the maximum duration in the simulation increases from 7 quarters to 27 quarters. The deterioration of outcomes under PLT when
expectations are anchored is not surprising. PLT works under rational expectations bygenerating endogenous movements in expectations that serve as an automatic stabilization mechanism. When expectations are anchored, they cannot act as automaticstabilizers, leading to a marked decline in the performance of PLT.

IV. Partial Adjustment of Expectations
Completely anchored expectations is an extreme assumption. In his Keynote address
at the 2017 BOJ-IMES Conference, Gertler (2017) showed how the power of forward
guidance was greatly aﬀected if expectations adjust only gradually to changes in thecentral bank’s target inflation rate. In this section, I investigate how deviations fromrational expectations aﬀect the performance of alternative targeting regimes.
I adopt a very simple ad-hoc model to capture the evolution of expectations. Let πetdenote expectations of next period’s rate of inflation. Suppose expected future inflation
follows a partial adjustment model given by
πet − πet−1 = δ1 π̄t − πet−1 ,

(4)

where
π̄t = δ2 Et πt+1 + (1 − δ2 ) πt−1 ,for 0 ≤ δ1 , δ2 ≤ 1. According to (4), expected future inflation is updated based on
deviations of π̄t from past expectations, where π̄t is a hweighted average of the fully
rational expectation of future inflation and lagged inflation. This specification nests a
number of special cases. For example, if δ1 = δ2 = 1, πet = Et πt+1 and expectations are
fully model consistent and coincide with rational expectations. If δ1 = 1 but δ2 = 0,then πet = πt−1 and expectations are backward-looking, equal to lagged inflation. For
δ1 = 1 and 0 < δ2 < 1, expectations equal a weighted average of Et πt+1 and πt−1 .
For a given δ2 , variations in δ1 aﬀect the degree of updating, with smaller values ofδ1 implying πet displays more inertial behavior. Completely anchored expectations arecaptured by setting δ1 = δ2 = 0.28 When wages as well as prices are sticky, I assume a................................
28. An alternative, closer to Gertler (2017) would be
πet = δ1 πt − πet−1 + δ2 πet−1 .
Gertler assumes δ1 = 0.125 and δ2 = 0.95. He assumed expectations of trend inflation, which I have assumed
to be zero, evolve asπ̄et = 0.5 πt − π̄et−1 + π̄et−1 .

63Figure 8 Performance Relative to IT When Expectations Follow (4)Note: Sticky price, flexible wage model denoted by sp. Sticky price, sticky wage model denoted by sw.

similar process for expected future wage inflation.29 Because expectations of nominal
variables such as inflation and wage inflation have been the central focus of policy
discussions, I continue to assume rational expectations apply to agent’s expectations of
future income.
Consider first results when only prices are sticky. The upper left subfigure of Figure 8 shows the loss under PLT as a percent of the loss under IT for values of δ1 andδ2 with each parameter running from zero to one. The right front corner in the figure
corresponds to rational expectations (δ1 = δ2 = 1). As δ1 declines, expectations display more inertia, while as δ2 declines, less weight is placed on the model-consistentexpectation of πt+1 . For high values of both δ1 and δ2 , including the case of rational
expectations, PLT outperforms IT. However, as either δ1 or δ2 decline, IT eventually
dominates PLT. However, when sticky wages are introduced (and assuming a similar process to (4) for expectations of future wage inflation), IT dominates PLT for all
combinations of δ1 and δ2 , as shown in the upper right subfigure of Figure 8.
The lower row of Figure 8 compares 4-quarter average inflation targeting and 16quarter average inflation targeting to IT when prices and wages are sticky and priceand wage inflation expectations are given by (4). In contrast to PLT, average inflation
targeting leads to better macro outcomes except when expectations are very inertial andrelatively insensitive to either lagged inflation or the model-consistent expectations of
future inflation (i.e., when δ1 is very small). With rational expectations, both versions of
AIT dominate IT, though the diﬀerences are small relative to the case of PLT (compare
the scales for the sticky prices and wages model in the top right subfigure with thescales in the subfigures in the bottom row). Except for very small values of δ1 , AIT
generates lower social loss regardless of the value of δ2 , that is, regardless of whether................................
29. Allowing price inflation expectations to follow (4) while wage inflation expectations remain rational does not
aﬀect the basic conclusions.

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Alternatives to Inflation Targeting in Low Interest Rate Environments

expectations respond to the true, rational expectation of future inflation or to lagged
actual inflation. Thus, IT and especially AIT seem more robust to the type of deviations
from rational expectations considered here than is true of PLT.

V. Conclusions
The intuition for why discretionary optimal policies under PLT and AIT would dominate IT was developed before concerns about the ELB were considered and was basedon a New Keynesian model with sticky prices. Extending that model to incorporate
sticky wages and shocks to productivity leads to significant deterioration in the performance of PLT, primarily because, when both prices and wages are sticky, inflation
expectations under IT and AIT behave much as they do under PLT. And in the face of
persistent productivity shocks, PLT causes large swings in the output gap as it returns
the price level to target much faster than occurs under the optimal Ramsey policy, IT
or AIT.
Rather than emphasize the use of inflation expectations as automatic stabilizers,
policymakers usually stress the importance of anchoring expectations. Not surprisingly,
both PLT and AIT do more poorly when expectations are truly anchored. I also examine
the relative performance of the alternatives in a case in which expectations deviate fromrational expectations is a simple but ad hoc manner. In this case, IT generally dominates
PLT, while AIT generally dominates IT.
Whether alternative policy regimes such as IT, PLT or AIT are evaluated under theassumption of discretion or commitment, with rational expectations, anchored expectations or partially anchored expectations, incorporating sticky wages makes a critical
diﬀerence for how regimes are ranked. This result aligns with those of Bodenstein andZhao (2019a) who suggest that in the face of model uncertainty concerning the labormarket, a robust policy is one designed to do well in a sticky price and sticky wage
model. And while the model I have used is admittedly simple, much of the intuition
for the potential superiority of PLT comes from even simpler models, models that incorporate only sticky prices as in Vestin (2006) or New Keynesian models of the ELB
developed by Eggertsson and Woodford (2003) that are being increasingly questioned
as models of the ELB.
Several aspects of the analysis reported here are important to keep in mind, and fiveaspects are particularly important to highlight. First, even when alternatives to rational
expectations were examined, a maintained assumption was that private agents believed
the central bank was committed to its goals (be they price-level targeting or average
inflation targeting). This ignores the issue of how the economy transitions from one
policy regime to a new one.30 One advantage of a regime defined in terms of goals isthat it may be easier to communicate and explain policy actions in terms of a goal thanin terms of an instrument rule of the type often used to characterize alternative policies.
Second, I have treated the weight given to stabilizing the output gap as the sameunder all policy regimes. Performance of each can be improved if λ x is optimized foreach policy alternative. Much of the discussion over alternatives to IT have focused................................
30. An exception in the literature that does consider learning during the transition to PLT is Cateau et al. (2009).

65

on the nominal variable on which policy should focus rather than on the appropriate
weight to place on any real objectives. For that reason, I have treated λ x as the sameacross regimes. If, for example, productivity shocks are believed to be important, than
the results from the simple model suggest a PLT regime would need to place muchgreater weight on stabilizing the volatility of the output gap than is the case under IT.31
Third, the results were based on a simple NK model that lacks the features commonly included in versions that are taken to the data. These features, such as habit persistence, wage and price indexation, capital and capital adjustment costs, as well as the
specification of the shocks included in the model will aﬀect the relative performance of
diﬀerent regimes. For example, Bodenstein and Zhao (2019b) obtain findings that aremuch more favorable to PLT (and even more so to the speed-limit policies introducedin Walsh [2003]) in a model that incorporates these data-friendly features. However,the basic intuition for PLT and AIT is based on the simple sticky price, flexible wage
NK model. The finding that allowing for sticky wages and productivity shocks canalter the ranking of the various policies is a useful reminder that intuition about howa policy handles a particular shock may not carry over if other shocks are important.
This lesson is one that should be familiar from the analysis of Poole (1970).
Fourth, the analysis has not imposed an eﬀective lower bound on the nominal interest rate, interpreting the policy interest rate in the model as a shadow rate that would
require the use of unconventional policy tools to implement. Such tools are unlikely tobe this eﬀective. In this case, the results on the frequency with which the shadow ratewould be negative under diﬀerent policy alternatives may provide some evidence on
how often each regime would need to resort to unconventional policies.
Finally, the analysis has been conducted within the framework of a New Keynesian model. The experience of major economies with long periods at the ELB and thestruggles in Japan and the eurozone with getting inflation up to their targets may require
re-examining not just monetary policy frameworks, but the core theoretical model andthe assumption of rational expectations that have provide the insights that shape muchof our understanding of monetary policy.

................................
31. The issue of the optimal weight to put on output stabilization is not ignored by Nessén and Vestin (2005),
Vestin (2006), or Bodenstein and Zhao (2019b).

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Alternatives to Inflation Targeting in Low Interest Rate Environments

References
Bernanke, Ben S., Michael T. Kiley, and John M. Roberts, “Monetary Policy Strategies for a LowRate Environment,” American Economic Association Papers and Proceedings, 109, 2019,
pp. 421–426.
Billi, Roberto M., “Optimal Inflation for the US Economy,” American Economic Journal: Macroeconomics, 3(3), 2011, pp. 29–52.
, “A Note on Nominal GDP Targeting and the Zero Lower Bound,” Macroeconomic Dynamics, 21(8), 2017, pp. 2138–2157.
, and Jordi Galí, “Gains from Wage Flexibility and the Zero Lower Bound,” Sveriges Riksbank
Working Paper Series No. 367, Sveriges Riksbank, 2019.
Blanchard, Olivier, Giovanni Dell’Ariccia, and Paolo Mauro, “Rethinking Macroeconomic Policy,”
Journal of Money, Credit and Banking, 42(S1), 2010, pp. 199–215.
Bodenstein, Martin, and Junzhu Zhao, “Employment, Wages and Optimal Monetary Policy,” Journalof Monetary Economics, 2019a (forthcoming).
, and, “On Targeting Frameworks and Optimal Monetary Policy,” Journal of Money,
Credit and Banking, 2019b (forthcoming).
Bordo, Michael D., and Andrew T. Levin, “Digital Cash: Principles & Practical Steps,” NBER Working Paper No. 25455, National Bureau of Economic Research, 2019.
Cateau, Gino, Oleksiy Kryvtsov, Malik Shukayev, and Alexander Ueberfeldt, “Adopting Price-Level
Targeting under Imperfect Credibility in ToTEM,” Bank of Canada Working Paper No. 200917, Bank of Canada, 2009.
Clarida, Richard, Jordi Galí, and Mark Gertler, “The Science of Monetary Policy: A New Keynesian
Perspective,” Journal of Economic Literature, 37(4), 1999, pp. 1661–1707.
Coibion, Olivier, Yuriy Gorodnichenko, and Johannes Wieland, “The Optimal Inflation Rate in New
Keynesian Models: Should Central Banks Raise Their Inflation Targets in Light of the Zero
Lower Bound?” Review of Economic Studies, 79(4), 2012, pp. 1371–1406.
Debortoli, Davide, Jordi Galí, and Luca Gambetti, “On the Empirical (Ir)Relevance of the Zero
Lower Bound Constraint,” NBER Working Paper No. 25820, National Bureau of Economic
Research, 2019.
Eberly, Janice C., James H. Stock, and Jonathan H. Wright, “The Federal Reserve’s Current Framework for Monetary Policy: A Review and Assessment,” paper presented at the Federal Reserve Bank of Chicago conference on “Monetary Policy Strategy, Tools, and Communication
Practices,” in Chicago, June 4–5, 2019.
Eggertsson, Gauti B., and Michael Woodford, “The Zero Bound on Interest Rates and Optimal Monetary Policy,” Brookings Papers on Economic Activity, 2003(1), 2003, pp. 139–211.
Erceg, Christopher J., Dale W. Henderson, and Andrew T. Levin, “Optimal Monetary Policy with
Staggered Wage and Price Contracts,” Journal of Monetary Economics, 46(2), 2000, pp. 281–
313.
Fischer, Stanley, “Introduction: Central Bank Lessons from the Global Crisis,” in Jacob Braude, Zvi
Eckstein, Stanley Fischer, and Karnit Flug, eds. The Great Recession: Lessons for Central
Bankers, Cambridge: The MIT Press, 2013, pp. 1–18.
Friedman, Benjamin M., “Targets and Instruments of Monetary Policy,” in Benjamin M. Friedman,and Frank H. Hahn, eds. Handbook of Monetary Economics, North-Holland: Elsevier, 1990,
pp. 1185–1230.
Galí, Jordi, “Notes for a New Guide to Keynes (I): Wages, Aggregate Demand, and Employment,”
Journal of the European Economic Association, 11(5), 2013, pp. 973–1003.
, Monetary Policy, Inflation, and the Business Cycle: An Introduction to the New Keynesian
Framework and Its Applications, 2nd edition, Princeton: Princeton University Press, 2015.
Gertler, Mark, “Rethinking the Power of Forward Guidance: Lessons from Japan,” Monetary andEconomic Studies, 35, Institute for Monetary and Economic Studies, Bank of Japan, 2017,
pp. 39–58.
Goodfriend, Marvin, “How the World Achieved Consensus on Monetary Policy,” Journal of Eco-67

nomic Perspectives, 21(4), 2007, pp. 47–68.
, “The Case for Unencumbering Interest Rate Policy at the Zero Bound,” paper presented
at the Federal Reserve Bank of Kansas City’s Economic Policy Symposium on “Designing
Resilient Monetary Policy Frameworks for the Future,” in Jackson Hole, August 25–27, 2016.
Holston, Kathryn, Thomas Laubach, and John C. Williams, “Measuring the Natural Rate of Interest:
International Trends and Determinants,” Journal of International Economics, 108(S1), 2017,
pp. S59–S75.
Ichiue, Hibiki, and Yoichi Ueno, “A Survey-based Shadow Rate and Unconventional Monetary Policy
Eﬀects,” IMES Discussion Paper No. 2018-E-5, Institute for Monetary and Economic Studies,Bank of Japan, 2018.
Jensen, Henrik, “Targeting Nominal Income Growth or Inflation?” American Economic Review,
92(4), 2002, pp. 928–956.
Krippner, Leo, “Documentation for Measures of Monetary Policy,” mimeo, Reserve Bank of New
Zealand, 2016.
Kurozumi, Takushi, “Optimal Sustainable Monetary Policy,” Journal of Monetary Economics, 55(7),2008, pp. 1277–1289.
, “Sustainability, Flexibility, and Inflation Targeting,” Economics Letters, 114(1), 2012,
pp. 80–82.
Lilley, Andrew, and Kenneth Rogoﬀ, “The Case for Implementing Eﬀective Negative Interest Rate
Policy,” paper presented at the Hoover Institution and Stanford University conference on“Strategies for Monetary Policy: A Policy Conference,” on May 3, 2019.
Mertens, Thomas M., and John C. Williams, “Monetary Policy Frameworks and the Eﬀective Lower
Bound on Interest Rates,” American Economic Association Papers and Proceedings, 109,
2019, pp. 427–432.
Nakata, Taisuke, “Reputation and Liquidity Traps,” Review of Economic Dynamics, 28, 2018,
pp. 252–268.
, Sebastian Schmidt, and Paul Yoo, “Speed Limit Policy and Liquidity Traps,” Finance andEconomics Discussion Series No. 2018-050, Board of Governors of the Federal Reserve System, 2018.
Nessén, Marianne, and David Vestin, “Average Inflation Targeting,” Journal of Money, Credit andBanking, 37(5), 2005, pp. 837–863.
O’Flaherty, Brendan, “The Care and Handling of Monetary Authorities,” Economics and Politics,
2(1), 1990, pp. 25–44.
Poole, William, “Optimal Choice of Monetary Policy Instruments in a Simple Stochastic Macro
Model,” Quarterly Journal of Economics, 84(2), 1970, pp. 197–216.
Reifschneider, David, and John C. Williams, “Three Lessons for Monetary Policy in a Low-Inflation
Era,” Journal of Money, Credit and Banking, 32(4), 2000, pp. 936–966.
Rogoﬀ, Kenneth, “The Optimal Degree of Commitment to an Intermediate Monetary Target,” Quarterly Journal of Economics, 100(4), 1985, pp. 1169–1189.
Smets, Frank, and Rafael Wouters, “Shocks and Frictions in US Business Cycles: A Bayesian DSGE
Approach,” American Economic Review, 97(3), 2007, pp. 586–606.
Svensson, Lars E. O., “Price-Level Targeting versus Inflation Targeting: A Free Lunch?” Journal of
Money, Credit and Banking, 31(3), 1999, pp. 277–295.
Swanson, Eric T., “The Federal Reserve is Not Very Constrained by the Lower Bound on NominalInterest Rates,” NBER Working Paper No. 25123, National Bureau of Economic Research,2018.
, and John C. Williams, “Measuring the Eﬀect of the Zero Lower Bound on Medium- andLonger-Term Interest Rates,” American Economic Review, 104(10), 2014, pp. 3154–3185.
Vestin, David, “Price-Level versus Inflation Targeting,” Journal of Monetary Economics, 53(7), 2006,
pp. 1361–1376.
Walsh, Carl E., “Issues in the Choice of Monetary Policy Operating Procedures,” in William S. Haraf,
and Phillip Cagan, eds. Monetary Policy for a Changing Financial Environment, Washington,
D.C.: AEI Press, 1990, pp. 8–37.

68 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2019

Alternatives to Inflation Targeting in Low Interest Rate Environments, “Speed Limit Policies: The Output Gap and Optimal Monetary Policy,” American Economic
Review, 93(1), 2003, pp. 265–278.
, “Using Monetary Policy to Stabilize Economic Activity,” paper presented at the Federal
Reserve Bank of Kansas City’s Economic Policy Symposium on “Financial Stability andMacroeconomic Policy,” in Jackson Hole, August 20–22, 2009.
, “Goals and Rules in Central Bank Design,” International Journal of Central Banking,11(S1), 2015, pp. 295–352.
, Monetary Theory and Policy, 4th edition, Cambridge: The MIT Press, 2017.
Woodford, Michael, “Central Bank Communication and Policy Eﬀectiveness,” paper presented at theFederal Reserve Bank of Kansas City’s Economic Policy Symposium on “The Greenspan Era:
Lessons for the Future,” in Jackson Hole, August 25–27, 2005.
Wu, Jing Cynthia, and Fan Dora Xia, “Measuring the Macroeconomic Impact of Monetary Policy at
the Zero Lower Bound,” Journal of Money, Credit and Banking, 48(2–3), 2016, pp. 253–291.
, and Ji Zhang, “A Shadow Rate New Keynesian Model,” Journal of Economic Dynamics andControl, 107, 2019 (forthcoming).

69

70 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2019