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Federal Reserve Bank of Chicago
Constrained Discretion and
Central Bank Transparency
Francesco Bianchi and Leonardo Melosi
October 2016
WP 2016-15
Constrained Discretion and Central Bank Transparencyy
Francesco Bianchi
Leonardo Melosi
Duke University
Federal Reserve Bank of Chicago
CEPR and NBER
October 2016
Abstract
We develop and estimate a general equilibrium model to quantitatively assess the e¤ects and
welfare implications of central bank transparency. Monetary policy can deviate from active in‡ation
stabilization and agents conduct Bayesian learning about the nature of these deviations. Under
constrained discretion, only short deviations occur, agents’ uncertainty about the macroeconomy
remains contained, and welfare is high. However, if a deviation persists, uncertainty accelerates and
welfare declines. Announcing the future policy course raises uncertainty in the short run by revealing that active in‡ation stabilization will be temporarily abandoned. However, this announcement
reduces policy uncertainty and anchors in‡ationary beliefs at the end of the policy. For the U.S.,
enhancing transparency is found to increase welfare. The same result is found when we relax the
assumption of perfectly credible announcements.
Keywords: Policy announcement, Bayesian learning, reputation, forward guidance, macroeconomic risk, uncertainty, in‡ation expectations, Markov-switching models, likelihood estimation.
JEL classi…cation: E52, D83, C11.
y We
wish to thank Martin Eichenbaum, Cristina Fuentes-Albero, Jordi Galí, Pablo Guerron-Quintana,
Yuriy Gorodnichenko, Narayana Kocherlakota, Frederick Mishkin, Matthias Paustian, Jon Steinsson, Mirko
Wiederholt, Michael Woodford, and Tony Yates for helpful comments. We also thank seminar participants
at the NBER Summer Institute, Columbia University, UC Berkeley, Duke University, the SED conference in
Cyprus, the Bank of England, the ECB Conference “Information, Beliefs and Economic Policy,”the Midwest
Macro Meetings 2014, and the Philadelphia Fed. Part of this paper was written while Leonardo Melosi was
visiting the Bank of England, whose hospitality is gratefully acknowledged. The views in this paper are solely
the responsibility of the authors and should not be interpreted as re‡ecting the views of the Bank of England
or that of the Federal Reserve Bank of Chicago or any other person associated with the Federal Reserve
System. Francesco Bianchi gratefully acknowledges …nancial support from the National Science Foundation through grant SES-1227397. Correspondence to: Francesco Bianchi, francesco.bianchi@duke.edu, and
Leonardo Melosi, lmelosi@frbchi.org.
1
Introduction
The last two decades have witnessed two major breakthroughs in the practice of central
banking worldwide. First, most central banks have adopted a monetary policy framework
that Bernanke and Mishkin (1997) have termed constrained discretion. Bernanke (2003)
explains that under constrained discretion, the central bank retains some ‡exibility in deemphasizing in‡ation stabilization so as to pursue alternative short-run objectives such as
unemployment stabilization. However, such ‡exibility is constrained to the extent that
the central bank should maintain a strong reputation for keeping in‡ation and in‡ation
expectations …rmly under control. Second, many countries have taken remarkable steps to
make their central bank more transparent (Bernanke et al. 1999 Mishkin 2002 and Campbell
et al. 2012).
As a result of these changes, the following questions are crucial for modern monetary
policymaking. First, for how long can a central bank de-emphasize in‡ation stabilization
before the private sector starts fearing a return to a period of high and volatile in‡ation as in
1970s? Second, does transparency play an essential role for e¤ective monetary policymaking?
Should a central bank be explicit about the future course of monetary policy? The recent
…nancial crisis has triggered a prolonged period of accommodative monetary policy that
some members of the Federal Open Market Committee fear could lead to a disanchoring of
in‡ation expectations (as an example, see Plosser 2012.) Thus, these questions are at the
center of the current policy debate.
To address these questions, we develop and estimate a model in which the anti-in‡ationary
stance of the central bank can change over time and agents face uncertainty about the nature
of deviations from active in‡ation stabilization. When monetary policy alternates between
prolonged periods of active in‡ation stabilization (active regime) and short periods during
which the emphasis on in‡ation stabilization is reduced (short-lasting passive regime), the
model captures the monetary approach described as constrained discretion. However, the
central bank can also engage in prolonged deviations from the active regime of the type
1
observed in the 1970s (long-lasting passive regime). Agents in the model are fully rational
and able to infer if monetary policy is active or not. However, when the passive rule prevails,
they are uncertain about whether the central bank is engaging in a short-lasting or in a
long-lasting deviation from the active regime. The central bank can then follow two possible
communication strategies: Transparency or no transparency. Under no transparency, the
nature of the deviation is not revealed. Under transparency, the duration of short-lasting
deviations is announced.
Under no transparency, when passive monetary policy prevails, agents conduct Bayesian
learning in order to infer the likely duration of the deviation from active monetary policy.
Given that the behavior of the monetary authority is unchanged across the two passive
regimes, the only way for rational agents to learn about the nature of the deviation consists
of keeping track of the number of consecutive deviations. As agents observe more and more
realizations of the passive rule, they become increasingly convinced that the long-lasting
passive regime is occurring. As a result, the more the central bank deviates from active
in‡ation stabilization, the more agents become discouraged about a quick return to the
active regime. We solve the model by keeping track of the joint evolution of policymakers’
behavior and agents’beliefs, using the methods developed in Bianchi and Melosi (2016a).
In the model, social welfare is shown to be a function of agents uncertainty about future
in‡ation and future output gaps. In standard models, monetary policy a¤ects agents’welfare
by in‡uencing the unconditional variances of the endogenous variables. In our nonlinear
setting, policy actions exert dynamic e¤ects on uncertainty. Therefore, welfare evolves over
time in response to the short-run ‡uctuations of uncertainty. To our knowledge, this feature
is new in the literature and allows us to study changes in the macroeconomic risk due to
policy actions and communication strategies and the associated welfare implications.
We measure uncertainty taking into account agents’beliefs about the evolution of monetary policy. As long as the number of deviations from the active regime is low, the increase
in uncertainty is very modest and stays in line with the levels implied by the active regime.
2
This is because agents regard the early deviations as temporary. However, as the number
of deviations increases and fairly optimistic agents become fairly pessimistic about a quick
return to active policies, uncertainty starts increasing and eventually converges to the values
implied by the long-lasting passive regime. As a result, for each horizon, our measure of
uncertainty is now higher than its long-run value. This is because agents take into account
that while in the short run a prolonged period of passive monetary policy will prevail, in
the long run the economy will surely visit the active regime again. Therefore, an important
result arises: Deviations from the active regime that last only a few periods have no disruptive consequences on welfare because they do not have a large impact on agents’uncertainty
regarding future monetary policy. Instead, if a central bank deviates from the active regime
for a prolonged period of time, the disanchoring of agents’uncertainty occurs, causing sizable
welfare losses.
The model under the assumption of no transparency is …tted to U.S. data. We identify
prolonged deviations from active monetary policy in the 1960s and the 1970s in line with
previous contributions to the literature. However, we also …nd that the Federal Reserve has
recurrently engaged in short-lasting passive policies since the early 1980s, supporting the view
that constrained discretion has been the predominant approach to U.S. monetary policy in
the past three decades. In the analysis, we abstract from the reasons why the Federal Reserve
has engaged in such deviations. In fact, we consider these recurrent deviations as a given
of our analysis. This approach provides us with a parsimonious, reduced-form framework to
estimate the Federal Reserve’s behaviors in the data. Given these estimated behaviors, we
evaluate how quickly agents’beliefs respond to policymakers’behaviors and announcements,
what this implies for the evolution of uncertainty and welfare, and what the potential gains
are from reducing the uncertainty about the future conduct of monetary policy.
The paper introduces a practical de…nition of reputation: A central bank has a strong
reputation if it is less likely to engage in long-lasting deviations from active policies. We
…nd useful to distinguish two related concepts: long-run reputation and short-run reputation.
3
Long-run reputation depends on how frequently the central bank has historically deviated
from active policies and for how long. This measure of reputation maps into the estimated
transition matrix, which controls the unconditional probability of observing long spans of
passive monetary policy and deeply a¤ects the unconditional level of uncertainty in the
macroeconomy. Short-run reputation captures agents’beliefs about the conduct of monetary
policy in the near future. This second measure of reputation corresponds to a precise statistic:
the expected number of consecutive deviations from active monetary policy. To avoid having
to constantly distinguish between the two measures of reputation, this last statistic is dubbed
pessimism, as it captures how pessimistic agents are about observing a switch to active policy.
We often use the term reputation to refer to long-run reputation.
While our de…nition of reputation is not exactly as the one used in theory studies (Kydland and Prescott 1977 Barro and Gordon 1983 Faust and Svensson 2001 and Galí and
Gertler 2007), it suits well Bernanke’s de…nition of constrained discretion and has the important advantage of being measurable in the data. Bernanke (2003) explains that for
constrained discretion to work e¤ectively, the central bank has to “establish a strong commitment to keeping in‡ation low and stable.”In our paper, the strength of this commitment
is called long-run reputation. If the Federal Reserve engages in prolonged periods of passive
policies, agents become more pessimistic about a return to the active regime. As pessimism
increases, so do in‡ation volatility and uncertainty. In Bernanke’s parlance, the Federal
Reserve’s “discretion” can become “constrained” in that short-run reputation deteriorates
after a prolonged deviation from active policy.
The fact that the Federal Reserve conducted a prolonged spell of passive policy in the
1970s has contributed to lowering its reputation in our estimated model. Nevertheless, even
though the Federal Reserve’s reputation is not immaculate, the Federal Reserve is found to
bene…t from its strong reputation. Based on the estimates, pessimism and, hence, agents’
uncertainty about future in‡ation change vary sluggishly in response to deviations from active
monetary policy. This …nding has the important implication that the Federal Reserve can
4
conduct passive policies for a fairly large number of years before the disanchoring of in‡ation
expectations and an overall increase in macroeconomic uncertainty occur. However, very
prolonged deviations from active policy lead agents to become wary that the central bank
has switched to 1970s-type of policies, causing detrimental e¤ects on welfare.
While this result implies that the Federal Reserve can successfully implement constrained
discretion even without transparency, our …ndings suggest that increasing transparency
would improve welfare. The estimated model suggests that the welfare gains from transparency range between 0.54% to 3.74% of steady-state consumption. A transparent central
bank systematically announces the duration of any short-lasting deviation from the active
regime beforehand, whereas in the case of a long-lasting deviation the exact duration is not
known. The implications of such a communication strategy vary based on the nature of
the deviation. When the central bank engages in a short-lasting deviation, announcing its
duration immediately removes the fear of the 1970s. Under no transparency, instead, agents
are not informed about the exact nature of the observed deviation. As a result, whenever a
short deviation occurs, ex-ante agents cannot rule out the possibility of a long-lasting deviation of the kind that characterized the 1970s. As a result, ex-post, agents turn out to have
overstated the persistence of the observed deviation. How large this e¤ect is depends on the
central bank’s reputation.
The model allows us to highlight an important trade-o¤ associated with transparency.
First, in the short run, being transparent reduces welfare because agents are told that passive
monetary policy will prevail for a while and thereby future shocks are expected to have larger
e¤ects. Second, as time goes by, agents know that the prolonged period of passive monetary
policy is coming to an end. This leads to a reduction in the level of uncertainty at every
horizon with an associated improvement in welfare. Notice, that this is exactly the opposite
of what occurs when no announcement is made: Agents, in the case of no transparency,
become more and more discouraged about the possibility of moving to the active regime
and uncertainty increases. To our knowledge, this is the …rst paper that studies this critical
5
trade-o¤ associated with central bank’s announcements through the lens of an estimated
dynamic stochastic general equilibrium (DSGE) model. Furthermore, our results are robust
to relaxing the assumption that the central bank never lies about the duration of passive
monetary policy.
This paper makes three main contributions to the existing literature. First, we show how
to model recurrent policymakers’ announcements about the central bank’s future reaction
function in an estimated DSGE model.1 Second, we show how to characterize and compute
social welfare in a Markov switching DSGE model with Bayesian learning and announcements. Interestingly, in our nonlinear framework, welfare captures the macroeconomic risk
perceived by the agents as a function of the expected or announced policy decisions. Finally,
we estimate a microfounded general equilibrium model with changes in policymakers’behavior and Bayesian learning. To the best of our knowledge, this is the …rst paper that estimates
a DSGE model with Markov-switching structural parameters and Bayesian learning. Our
learning mechanism implies that agents’beliefs are not invariant to the duration of a certain
policy. Therefore, the model captures a very intuitive idea: Agents in the late 1970s were
arguably more pessimistic about a quick return to the active regime than they had been
in the early 1970s. This feature was not present in previous contributions such as Bianchi
(2013) and Davig and Doh (2014a).
This paper is part of a broader research agenda that aims to model the evolution of
agents’beliefs in general equilibrium models (Bianchi and Melosi 2014, 2016b). Our modeling
framework goes beyond the assumption of anticipated utility that is often used in the learning
literature.2 Such an assumption implies that agents forecast future events assuming that their
beliefs will never change in the future. Instead, agents in our models know that they do not
know. Therefore, when forming expectations, they take into account that their beliefs will
evolve according to what they will observe in the future.
1
The importance of this type of forward guidance has been recognized by some members of the FOMC.
See, for instance, Mester (2014)
2
For some prominent examples see Marcet and Sargent (1989a, 1989b), Cho, Williams, and Sargent (2002)
, and Evans and Honkapohja (2001, 2003).
6
Schorfheide (2005) considers an economy in which agents use Bayesian learning to infer
changes in a Markov-switching in‡ation target. In that paper agents solve a …ltering problem
to disentangle a persistent component from a transitory component. The learning mechanism
is treated as external to the model, implying that the model needs to be solved in every period
in order to re‡ect the change in agents’beliefs regarding the two components. Consequently,
when agents form their beliefs, they do not take into account how their beliefs will change.
Furthermore, the method developed in Schorfheide (2005) cannot be immediately extended
to models in which agents learn about changes in the stochastic properties of the model’s
structural parameters. Eusepi and Preston (2010) study monetary policy communication in
a model where agents face uncertainty about the value of model parameters. Cogley, Matthes
and Sbordone (2011) address the problem of a newly appointed central bank governor who
wants to disin‡ate. Unlike in the last two papers, in our paper regime changes are recurrent,
agents learn about the regime in place as opposed to Taylor rule parameters, we do not
assume anticipated utility, and we conduct likelihood-based estimation.
Our paper also shows that when discrete regime changes are combined with a learning mechanism, a smooth evolution of expectations and uncertainty arises. Therefore, we
implicitly connect the literature on discrete regime changes to the literature that models parameter instability as slow-moving processes.3 Our work is also linked to papers that study
the transmission of nominal disturbances in general equilibrium models with information
frictions, such as Gorodnichenko (2008), Mackowiak and Wiederholt (2009), Mankiw and
Reis (2006), Melosi (2014a, forthcoming), and Nimark (2008). Finally, this paper is connected with the literature that studies the macroeconomic e¤ects of forward guidance (Del
Negro, Giannoni, and Patterson 2012; Campbell et al. forthcoming). The key innovation of
our paper is that forward guidance is about the central bank’s reaction function, whereas in
that literature, communication is about future deviations from the monetary policy rule.
3
See, among others, Sims and Zha (2006), Bianchi (2013), Bianchi and Ilut (2013), Davig and Doh
(2014a), Liu, Waggoner, and Zha (2011) for the …rst body of literature and then Primiceri (2005), Cogley
and Sargent (2005), Fernandez-Villaverde and Rubio-Ramirez (2008), and Justiniano and Primiceri (2008)
for the second body of the literature.
7
This paper is organized as follows. In Section 2, we introduce the baseline model. In
Section 3, we show how to solve the model under the assumption of no transparency and
transparency. In Section 4, the model under the assumption of no transparency is …tted to
U.S. data. In Section 5, we assess the welfare implications of introducing transparency. In
Section 6, we extend the analysis to imperfectly credible announcements. In Section 7, we
assess the robustness of our results. Section 8 concludes.
2
The Model
The model is built on Coibion, Gorodnichenko and Wieland (2012), who develop a prototypical New-Keynesian DSGE model with trend in‡ation and partial price indexation. We
make two main departures from this standard framework. First, we assume that households
and …rms have incomplete information, in a sense to be made clear shortly. Second, we
assume parameter instability in the monetary policy rule.4
Households: The representative household maximizes expected utility:
E
hP
1
t=0
t
n
ln Ct+j
( + 1)
1
R
1+1=
Nit+j
i
o
di jF0 ;
where Ct is composite consumption and Nit is labor worked in industry i. The parameter
2 (0; 1) is the discount factor, the parameter
0 is the Frisch elasticity of labor supply.
E [ jF0 ] is the expectation operator conditioned on information of private agents available
at time 0. The information set Ft contains the history of all model variables but not the
history of policy regimes
p
t
that, as we shall show, determine the parameter value of the
central bank’s reaction function.
4
Extending the analysis to state-of-the-art monetary DSGE models such as Christiano, Eichenbaum, and
Evans (2005) and Smets and Wouters (2007) would be interesting, but it would also imply a signi…cant
increase in computational time. Furthermore, we do not have reasons to believe that the main results would
change. Bianchi (2013) estimates a version of the Christiano, Eichenbaum, and Evans (2005) model and
…nds a sequence of regime changes similar to the one that we recover in this paper.
8
The ‡ow budget constraint of the representative household in period t reads
Ct + Bt =Pt
R1
0
(Nit Wit =Pt ) di + Bt 1 Rt 1 =Pt + Divt =Pt + Tt =Pt ;
where Bt is the stock of one-period government bonds in period t, Rt is the gross nominal
interest rate, Pt is the price of the …nal good, Wit is the nominal wage earned from labor in
industry i, Tt is real transfers, and Divt are pro…ts from ownership of …rms.
Composite consumption in period t is given by the Dixit-Stiglitz aggregator
Ct =
R1
1 1="
C
0 it
di
"
" 1
;
where Cit is consumption of a di¤erentiated good i in period t and " > 1 determines the
elasticity of substitution between consumption goods. The price level is given by
Pt =
R1
P 1 " di
0 it
1=(1 ")
:
(1)
In every period t, the representative household chooses a consumption vector, labor
supply, and bond holdings subject to the sequence of the ‡ow budget constraints and a noPonzi-scheme condition. The representative household takes as given the nominal interest
rate, the nominal wages, nominal aggregate pro…ts, nominal lump-sum taxes, and the prices
of all consumption goods.
Firms: There is a continuum of monopolistically competitive …rms of mass one. Firms
are indexed by i. Firm i supplies a di¤erentiated good i. Firms face Calvo-type nominal
rigidities and the probability of re-optimizing prices in any given period is given by 1
independent across …rms. We allow for partial price indexation to steady-state in‡ation by
…rms that do not re-optimize their prices, with the parameter ! 2 (0; 1) capturing the degree
of indexation. Those …rms that are allowed to re-optimize their price choose their price Pit
9
so as to maximize:
P1
k
k=0
k!
Et Qt;t+k
Wit+k Nit+k jFt ;
Pit Yit+k
where Qt;t+k is the stochastic discount factor measuring the time t utility of one unit of
consumption good available at time t + k,
is the gross steady-state in‡ation rate, Nit
is amount of labor hired, and Yit is the amount of di¤erentiated good produced by …rm i.
Firms are endowed with an identical technology of production: Yit = Zt Nit : The variable
Zt captures exogenous shifts of the marginal costs of production and is assumed to follow a
stationary …rst-order autoregressive process in log-di¤erence:
ln zt = (1
where zt
z ) ln z
+
z
ln zt
1
+
Zt =Zt 1 : We refer to the innovations
z zt ;
zt
zt
N (0; 1) ;
as technology shocks. Firms face a
downward-sloping demand function in every period, Yit = (Pit =Pt )
"
Yt ; where Pit denotes
the price …rm i sells its good at time t. Aggregate labor input is de…ned as
Z
Nt =
1
1 1="
di
Nit
"
" 1
:
0
Policymakers: There are a monetary authority and a …scal authority. Government
consumption is de…ned as Gt = (1
1=gt ) Yt , with the variable gt following a stationary
…rst-order autoregressive process:
ln gt = 1
where
gt
g
ln g +
g
ln gt
1
+
g gt ;
gt
N (0; 1) ;
(2)
is an i.i.d. government expenditure shock. The …scal authority always follows a
Ricardian …scal policy and collects a lump-sum tax. The aggregate resource constraint reads
Yt = Ct + Gt :
10
The monetary authority sets the nominal interest rate Rt according to the Taylor rule
p
r; t
Rt = Rt
where
t
= Pt =Pt
The variable
rt
1
1
h
p
; t
t=
(Yt = (zYt 1 ))
p
y; t
i1
p
r; t
e
r rt
;
(3)
N (0; 1) ;
rt
denotes the gross in‡ation rate and Yt is aggregate output in period t.
captures nonsystematic exogenous deviations of the nominal interest rate
p
t
Rt from the rule. The variable
controls the policy regime that determines the policy
coe¢ cients of the rule re‡ecting the emphasis of the central bank on in‡ation stabilization
relative to output gap stabilization.
2.1
Policy Regimes
We model changes in the central bank’s emphasis on in‡ation and output stabilization by
introducing a three-regime Markov-switching process
p
t
that evolves according to this matrix:
2
p12 p13
6 p11
6
Pp = 6
6 1 p22 p22 0
4
1 p33 0 p33
3
7
7
7:
7
5
(4)
The realized regime determines the monetary policy parameters of the central bank’s reaction
function. In symbols,
R
(
p
t
= j) ;
(
p
t
= j) ;
p
t
(
R
y
(
= j) ;
p
t
(
= j) =
p
t
= j) ;
P
P
R;
y
;
(
p
t
P
y
, if j = 2 or j = 3: Under Regime
= j) =
A
R;
A
;
A
y
, if j = 1 and
1 (the active regime), the central bank’s main emphasis is on stabilizing in‡ation and the
Taylor principle is satis…ed:
(
p
t
= 1) =
A
1. Under Regime 2 (the short-lasting passive
regime), the central bank de-emphasizes in‡ation stabilization, but only for short periods
of time (on average). The same parameter combination also characterizes Regime 3 (the
long-lasting passive regime). Therefore,
(
p
t
= 1) =
A
P
=
(
p
t
= 2) =
(
p
t
= 3).
However, under Regime 3, deviations are generally more prolonged. In other words, Regime
2 is less persistent than Regime 3: p22 < p33 . Therefore, the two passive regimes do not
11
di¤er in terms of response to in‡ation
P
and the output gap
P
y,
but only in terms of their
relative persistence.
The three policy regimes are meant to capture the recurrent changes in the Federal Reserve’s attitude toward in‡ation and output stabilization in the postwar period. A number
of empirical works (Clarida, Galí, and Gertler 2000 Lubik and Schorfheide 2004) have documented that the Federal Reserve de-emphasized in‡ation stabilization for prolonged periods
of time in the 1970s. Furthermore, as argued by Bernanke (2003), while the Federal Reserve
has been mostly focused on actively stabilizing in‡ation starting from the early 1980s, it
has also occasionally engaged in short-lasting policies whose objective was not to stabilize
in‡ation in the short run. This monetary policy approach has been dubbed constrained discretion. We introduce this three-regime structure so as to give the model enough ‡exibility
to explain both the long-lasting passive monetary policy of the 1970s, as well as the recurrent
and short-lasting passive policies of the post-1970s.
The probabilities p11 , p12 , p22 govern the evolution of monetary policy when the central
bank follows constrained discretion. The larger p12 is vis-a-vis p11 , the more frequent the
short-lasting deviations are. The larger p22 is, the more persistent the short-lasting deviations
are. The probability p13 controls how likely it is that constrained discretion is abandoned
in favor of a prolonged deviation from the active regime. The ratio p12 = (1
p11 ) captures
the relative probability of a short-lasting deviation conditional on having deviated to passive
regimes and can be interpreted as a measure of central bank’s long-run reputation. This
is because this composite parameter controls how likely it is that the central bank will
abandon constrained discretion the moment it starts deviating from the active regime. As it
will become clear later on, central bank’s long-run reputation has deep implications for the
general equilibrium properties of the macroeconomy. This is because agents are fully rational
and form expectations while taking into account the possibility of regime changes, implying
that their beliefs matter for the way shocks propagate through the economy. Therefore,
the proposed de…nition of central bank reputation has the important advantage of being
12
measurable in the data, even over a relatively short period of time.
2.2
Communication Strategies
It can be shown that regime changes do not a¤ect the steady-state equilibrium, but only
the way the economy propagates around it. Since technology Zt follows a random walk, we
normalize all the nonstationary real variable by the level of technology. We then log-linearize
the model around the steady-state equilibrium in which the steady-state in‡ation does not
have to be zero.5
Once log-linearized around the steady state, the imperfect information model can be
solved under di¤erent assumptions on what the central bank communicates about the future
monetary policy course. The central bank’s communication a¤ects agents’information set
Ft . We consider two cases: no transparency and transparency. If the central bank is not
transparent, it never announces the duration of passive policies. We call this approach no
transparency. We make a minimal departure from the assumption of perfect information
by assuming that agents can observe the history of all the endogenous variables and the
history of the structural shocks but not the policy regimes
p
t.
It should be noted that agents
are always able to infer if monetary policy is currently active or passive. However, when
monetary policy is passive, agents cannot immediately …gure out whether (short-lasting)
Regime 2 or (long-lasting) Regime 3 is in place. To see why, recall that the two passive
regimes are observationally equivalent to agents, given that
p
and
p
y
are the same across
the two regimes. Therefore, agents conduct Bayesian learning in order to infer which one of
the two regimes is in place. In the next section we will discuss how agents’beliefs evolve as
agents observe more and more deviations from the active regime.
Under transparency all the information held by the central bank is communicated to
agents. We assume that the central bank knows for how long it will be deviating from
active monetary policy when conducting short-lasting deviations. Long-lasting deviations
5
The log-linearized equations and a detailed discussion on how nonzero steady-state in‡ation a¤ects the
agents’behaviors in the model is in the online appendix.
13
are intended to capture structural changes in the way monetary policy is conducted (e.g.,
the type of a newly appointed central banker). Therefore, their duration is always unknown
to the central bank and, hence, cannot be announced. Notice that under transparency,
rational agents immediately infer when such a structural change in the conduct of monetary
policy has occurred. If a transparent central bank starts deviating from active policy without
announcing the duration of such a passive policy, this deviation must be a long lasting one.6
A transparent central bank announces the duration of short-lasting passive policies, revealing to agents exactly when monetary policy will switch back to the active regime. Agents
form their beliefs by taking into account that the central bank will systematically announce
the duration of every short-lasting passive policy. We assume that the central bank’s announcements are truthful and are believed as such by rational agents. In Section 6, we will
consider the case in which the announcements made by the central bank are not always
truthful. In Section 7.2, we will study the case in which the central bank can only announce
the likely duration of passive policies
3
that is, the type of passive regime.
Beliefs Dynamics and Model Solution
Here we provide a brief discussion of how to solve the model under the two di¤erent communication strategies. More details are provided in the online appendix.
No Transparency: To solve the model under no transparency we use the methods developed in Bianchi and Melosi (2016a). Denote the number of consecutive deviations from the
active regime at time t as
t
2 f0; 1; :::g, where
at time t. Conditional on having observed
t
t
= 0 means that monetary policy is active
1 consecutive deviations from the active
regime at time t, agents believe that the central bank will keep deviating in the next period,
6
Our results still hold if one allows the central bank to announce the duration of the long-lasting deviations
as well.
14
t + 1; with probability:
prob f
t+1
6= 0j
Equation (5) makes it clear that
p22 (p12 =p13 ) (p22 =p33 ) t + p33
:
(p12 =p13 ) (p22 =p33 ) t + 1
t
6= 0g =
(5)
t
is a su¢ cient statistic for the probability of being in the
passive regime next period. This equation captures the dynamics of agents’ beliefs about
observing yet another period of passive policy in the next period, which is the key state
variable we use to solve the model under no transparency.
It should be also observed that equation (5) has a number of properties that are quite
insightful to the key mechanism of the model at hand. The probability of observing yet
another period of passive policy in the next period is a weighted average of the probabilities
p22 and p33 , with weights that vary with the number of consecutive periods of passive policy
t.
(
t
When agents observe the central bank deviating from the active regime for the …rst time
= 1), the weights for the probabilities p22 and p33 are p12 = (1
p11 ) and p13 = (1
p11 ),
respectively. These weights re‡ect the central bank’s long-run reputation. When its long-run
reputation is high, it is very unlikely that the central bank engages in a long-lasting passive
policy. Therefore, as the …rst period of passive policy is observed, agents are con…dent that
the economy has entered the short-lasting passive regime (Regime 2). If the central bank
keeps deviating from the active regime, agents will eventually become convinced of being in
the long-lasting passive regime (Regime 3). After a su¢ ciently long-lasting passive policy,
the probability of observing an additional deviation in the next period degenerates to the
persistence of the long-lasting passive regime (Regime 3). Hence, p33 is the upper bound for
the probability that agents attach to staying in the passive regime next period. It follows that
for any e > 0, there exists an integer
for any
t
>
such that p33 prob f
t+1
6= 0j
t
=
g < e: Therefore,
, agents’beliefs can be e¤ectively approximated using the properties of the
long-lasting passive regime.
Endowed with these results, we can solve the model under no transparency by expanding
15
the number of regimes in order to take into account the evolution of agents’ beliefs. Now
each regime is characterized by the central bank’s behavior and the number of observed
consecutive deviations from active policy at any time t;
set of regimes indexed by
t
2 f0; 1; :::;
t:
The transition matrix for this new
g can be derived by equation (5), as shown in the
online appendix. Now regimes are de…ned in terms of the observed consecutive durations,
t,
which, unlike the primitive set of policy regime
p
t
2 f1; 2; 3g, belongs to the agents’
information set Ft . Hence, we can solve this model by applying any of the methods developed
to solve Markov-switching rational expectations models with perfect information, such as
Davig and Leeper (2007); Farmer, Waggoner and Zha (2011); and Foerster et al. (2013). We
use Farmer, Waggoner, and Zha (2011).
It is worth emphasizing that this way of recasting the learning process allows us to
tractably model the behavior of agents that know that they do not know. In other words,
agents are aware of the fact that their beliefs will change in the future according to what they
observe in the economy. This represents a substantial di¤erence from the anticipated utility
approach, in which agents form expectations without taking into account that their beliefs
about the economy will change over time. Furthermore, our approach di¤ers from the one
traditionally used in the learning literature in which agents form expectations according to a
reduced-form law of motion that is updated recursively (for example, using discounted least
squares regressions). The advantage of adaptive learning is the extreme ‡exibility given that,
at least in principle, no restrictions need to be imposed on the type of parameter instability
characterizing the model. However, such ‡exibility does not come without a cost, given that
agents are not really aware of the model they live in.
Transparency: When the central bank is transparent, the exact duration of every shortlasting deviation from active policy is truthfully announced. In this model the number of
announced short-lasting deviations from active policy yet to be carried out
a
t
is a su¢ cient
statistic that captures the dynamics of beliefs after an announcement. Since the exact
16
duration of long-lasting passive policies is not announced, we also have to keep the longlasting passive regime as one of the possible regimes. Regimes are ordered from the smallest
number of announced deviations (zero or the active policy) to the largest one ( a ). The
long-lasting passive regime, whose conditional persistence is p33 , is ordered as the last regime.
eA . The online appendix
The evolution of the regimes is controlled by the transition matrix P
explains how to build such a transition matrix. As in the case of no transparency, we recast
the MS-DSGE model under transparency as a Markov-switching rational expectations model
with perfect information, in which the short-lasting passive regime is rede…ned in terms of
the number of announced deviations from the active regimes yet to be carried out,
a
t.
This
rede…ned set of regimes belongs to the agents’information set Ft under transparency. This
result allows us to solve the model under transparency by applying any of the methods
developed to solve Markov-switching rational expectations models of perfect information.
4
Empirical Analysis
In order to put discipline on the parameter values, the model under no transparency is …tted
to U.S. data. We believe that the model with a non-transparent central bank is better
suited to capture the Federal Reserve communication strategy in our sample that ranges
from the mid-1950s to just prior to the Great Recession. We then use the results to quantify
the Federal Reserve’s reputation and the potential gains from making the Federal Reserve’s
monetary policy more transparent.
4.1
Data and Estimation
For observables, we use three series of U.S. quarterly data: the annualized Gross Domestic
Product (GDP) growth rate, the annualized quarterly in‡ation (GDP de‡ator), and the
federal funds rate (FFR). The sample spans from 1954:Q4 through 2009:Q3. Table 1 reports
the prior and the posterior distribution of model parameters. The model is estimated by using
17
Name
A
A
y
A
R
P
P
y
P
R
p11
p22 =p33
p33
p12 =(1 p11 )
"
!
g
z
100 ln z
100 ln
100 g
100 m
100 z
100 r
Median
Posterior
5%
95%
Type
Prior
Mean
Std.
3.0993
0.6947
0.6864
1.3365
0.4034
0.6925
0.9497
0.7070
0.9689
0.9536
0.9998
7.7764
0.6569
0.9189
0.9974
0.9496
0.3690
0.4808
0.7433
2.5499
3.1215
1.4827
0.6009
2.5299
0.5368
0.5186
1.0426
0.2541
0.5864
0.8955
0.5114
0.9403
0.9003
0.8469
4.3259
0.3562
0.8734
0.9955
0.9260
0.1435
0.3144
0.5571
1.8268
1.7974
1.0278
0.4531
3.7031
0.9126
0.7778
1.6032
0.6384
0.7774
0.9776
0.8915
0.9868
0.9883
1.1788
13.1161
0.8799
0.9496
0.9986
0.9682
0.5959
0.6368
0.9115
3.8237
5.8893
2.2091
08799
N
G
B
G
G
B
B
B
B
B
G
G
B
B
B
B
B
N
N
IG
IG
IG
IG
2.5
0.25
0.5
0.9
0.25
0.5
0.9
0.8
0.95
0.95
1
8
0.5
0.5
0.99
0.5
0.5
0.4
0.5
2
2
2
0.5
0.5
0.15
0.2
0.3
0.15
0.2
0.05
0.1
0.025
0.025
0.1
3
0.2
0.2
0.005
0.2
0.2
0.125
0.125
1
1
1
0.2
Table 1: Posterior modes, means, and 90% error bands of the model parameters. Type N,
G, B, and IG stand for Normal, Gamma, Beta, and Inversed Gamma density, respectively.
Dir stands for the Dirichelet distribution
a Gibbs sampling algorithm in which both the regime sequence and the model parameters
are sampled. The algorithm is similar to the one used in Bianchi (2013). Convergence is
checked by using the Brooks-Gelman-Rubin potential reduction scale factor. The …ve chains
consist of 270; 000 draws each and 1 of every 1; 000 draws is saved.
The parameter values are quite standard with the central bank responding fairly aggressively to in‡ation when monetary policy is active. The central bank is also responding more
aggressively to output under active policy. The response of the FFR to in‡ation in the passive
regimes is estimated to be around 1.33, with 90% error bands spanning the interval between
1.04 and 1.60. This implies that many draws for the passive regime are well above 1, which is
the threshold that is generally associated with the Taylor principle and active monetary policy. However, in a model like the one considered in this paper, the threshold for determinacy
18
is a¤ected by the absence of full indexation to trend in‡ation, as pointed out by Coibion and
Gorodnichenko (2011). Once the determinacy region is properly adjusted, around 5% of the
draws associated with the passive monetary policy rule fall in fact into the passive region
and 30% of them are within 0.25 from the passive region. We still refer to this rule as passive
to the extent that in‡ation stabilization is de-emphasized. Furthermore, other studies that
use richer models instead of the prototypical …xed-parameter three-equation new-Keynesian
model also …nd a sizable probability that the response of monetary policy to in‡ation was
not violating the Taylor principle in the 1970s (see, for example, Bianchi (2013) and Davig
and Doh (2014b)).
The posterior median of the elasticity of substitution " implies a net markup equal to
approximately 13%. The Calvo parameter implies a fairly large degree of nominal rigidities
as is common when small-scale models are estimated. The Frisch elasticity of labor supply
is close to one. The probability of being in the short-lasting passive regime conditional on
having switched to passive policies, p12 = (1
p11 ), plays a critical role in the model. As
noticed in Section 2, this parameter value relates to the strength of the Federal Reserve’s
long-run reputation. This parameter is found to be fairly close to one, con…rming that
the Federal Reserve has a strong reputation. This number means that as agents observe
a deviation from the active regime, they expect that the Federal Reserve is conducting a
short-lasting passive policy with a probability of 95:36%.
Recall that in the estimated model, regimes are indexed with respect to the number of
consecutive periods of passive policy,
t.
We have a total of
+ 1 regimes, where
depends
on the speed of learning and can be larger than 100. Reporting the regime probabilities for
such a large number of regimes is not practical. A most e¤ective approach is to report the
estimated expected number of consecutive deviations from active policy over the sample. As
explained above, the higher the number of expected consecutive deviations, the larger is
the posterior probability mass associated with the long-lasting passive regime. Furthermore,
this statistic re‡ects agents’beliefs, and it is, therefore, critical to understand the e¤ects of
19
Expected Number of Consecutive Deviations
20
10
0
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
Figure 1: The gray shaded areas mark periods of passive monetary policy based on the regime sequence
associated with the posterior mode based on the Gibbs sampling algorithm. The blue solid line reports the
corresponding expected number of consecutive deviations from the active regime.
central bank communication on social welfare, as we will show later.
The shaded areas in Figure 1 show the periods of passive monetary policy based on the
regime sequence associated with the posterior mode. The solid line reports the corresponding
expected number of consecutive deviations from the active regime. This can be considered
a measure of agents’pessimism because, as we will show later in the paper, a larger number
of expected consecutive deviations determines an increase in uncertainty and, as a result,
a decline in agents’welfare. The …gure highlights that short-lasting deviations from active
policy only imply a modest increase in this statistic. In contrast, at the end of the 1970s
and early 1980s the number of expected consecutive deviations approaches its highest value,
(1
p33 ) 1 , re‡ecting the fact that most of the posterior probability is shifted toward regimes
associated with passive policies of fairly long duration. The expected duration of passive
policy grows gradually throughout the 1970s and reaches relatively high levels at the end of
this decade. This suggests that agents slowly changed their expectations about future policy
as they observed more and more periods of passive policy in the 1970s. After the 1970s, a
large posterior probability is attributed to either the active regime or passive policies of very
short realized duration. This is captured by the number of expected deviations from active
policy being either close to zero, when the active regime prevails, or else slightly positive,
20
No Transparency
Transparency
50
40
Pessimism
40
30
30
20
20
10
10
10
20
30
40
50
10
Consecutive Periods of Passive Policy
20
30
40
50
Consecutive Period of Passive Policy
Figure 2: Pessimism on the vertical axis is measured as the expected number of consecutive deviations.
1
On the left plot the two horizontal lines denote the smallest lower bound (1 p22 ) and upper bound of
1
pessimism (1 p33 ) . These statistics are computed at the posterior mode.
but below 10 quarters, i.e., 2 years and a half, when short-lasting deviations occur during
the 2001 recession and in correspondence with the most recent recession. This is the essence
of constrained discretion we want to study in this paper.
Finally, we want to evaluate whether there is empirical support for our benchmark model
with no transparency. To this end, we estimate an alternative model in which parameters are
not allowed to change and then compare the two models by using Bayesian model comparison.
We …nd that the data strongly favor the Markov-switching speci…cation, despite the larger
number of parameters. In fact, the model with …xed parameters can attain a higher posterior
probability only if one attaches extremely low prior probabilities (< 1:39E 11) to this model.
4.2
Communication and Beliefs Dynamics
Regime changes in monetary policy and communication strategies critically a¤ect social
welfare and the macroeconomic equilibrium by in‡uencing agents’pessimism about future
monetary policy. In this paper, we use the word pessimism to precisely mean agents’expec-
21
tations about the duration of an observed passive policy. A high level of pessimism means
that agents expect an observed passive policy to last for fairly long
expected duration of the long-lasting passive regime: (1
that is, close to the
p33 ) 1 . While expecting a longer
lasting deviation from the active regime is not necessarily welfare decreasing, we will show
that expecting a prolonged period of passive policy impairs social welfare in the estimated
model.
We measure pessimism by computing the number of expected consecutive periods of
passive monetary policy conditional on the observed duration of passive policy
0. The
evolution of this variable is tightly linked to the estimated transition matrix, that in turn
captures the central bank’s long-run reputation. Let us consider the case in which the
central bank decides to engage in passive policies lasting 50 consecutive periods. While
such a long deviation from the active regime is not so likely, this example illustrates how
transparency a¤ects pessimism relative to no transparency. Figure 2 reports the evolution of
pessimism under no transparency (left graph) and under transparency (right graph) at the
posterior mode. The two horizontal lines mark the smallest lower bound and upper bound for
pessimism. The former is given by the expected duration of the short-lasting passive Regime
(1
p22 ) 1 . The smallest lower bound is attained at the …rst period of passive policy only
if the conditional probability of a short-lasting deviation is one: p12 = (1
p11 ) = 1. The left
graph shows that the intercept of the solid line is quite close to the bottom dashed line,
implying that agents expect that the Federal Reserve is engaging in a short-lasting deviation
as the …rst period of passive policy is observed. This result is due to the fact that the Federal
Reserve’s reputation is estimated to be fairly high (p12 = (1
p11 ) = 0:9536).
The upper bound for pessimism is given by the expected duration of the long-lasting
passive policy (1
p33 )
1
and is attained only after a very large number of consecutive
deviations from the active regime. Such a gradual increase in pessimism suggests that the
Federal Reserve can enjoy a great deal of leeway in deviating from active monetary policy in
order to stabilize alternative short-lasting objectives. This result is again due to the strong
22
reputation of the Federal Reserve. If the reputation coe¢ cient p12 = (1
p11 ) were close to
zero, then the expected number of consecutive deviations would experience a larger jump
and, hence, the convergence to the upper bound would be faster.
As shown in the right graph, pessimism follows an inverse path under transparency.
Unlike the case of no transparency, agents’ pessimism is very high at the initial stages of
the deviation from active policy, but it decreases as the time goes by. This result comes
from assuming that agents are fully rational and the announcement is truthful. As the 50
periods of passive monetary policy are announced (t = 0), an immediate rise in pessimism
occurs. As the number of periods of passive policy yet to be carried out decreases, agents’
pessimism declines accordingly. At the end of the policy (t = 50), pessimism reaches its
lowest level, with agents expecting to return to the active regime with a probability of one
in the following period. It should be noted that at the end of the announced deviation,
transparency allows the central bank to lower agents’ pessimism below the smallest lower
bound attainable under no transparency: This result emerges because the central bank is
able to inform agents about the exact period in which passive policy will be terminated.
This assumption will be relaxed in Section 7.2.
To sum up, Figure 2 allows us to isolate two important e¤ects of transparency on agents’
pessimism about future monetary policy: (i) transparency raises pessimism at the beginning
of the policy and (ii) transparency anchors down pessimism at the end of the policy. As we
shall show, these two e¤ects play a critical role for the welfare implications of transparency.
5
Welfare Implications of Transparency
In this section, we assess the welfare implications of introducing transparency. Before proceeding, it is worth emphasizing that the regime changes considered in this paper do not
a¤ect the steady state, but only the way the economy ‡uctuates around the steady state.
The period welfare function can then be obtained by taking a log-quadratic approximation
23
of the representative household’s utility function around the deterministic steady state:
P1
Wi (st (i)) =
h=1
h
[
0
+
1 vari
(^
yt+h jst (i)) +
2 vari
(^ t+h jst (i))] ;
(6)
where vari ( ) with i 2 fT; N g stands for the stochastic variance associated with agents’
forecasts of in‡ation conditional on transparency (T ) or no transparency (N ) and the output
gap at horizon h. The coe¢ cients
i,
i 2 f0; 1; 2g are functions of the model’s parameters
and are de…ned in the online appendix. The subscript i refers to the communication strategy:
i = N stands for the case of no transparency, while i = T denotes transparency. Finally, st (i)
denotes the policy regime: st (i = N ) 2 f0; 1; :::;
g=
t
and st (i = T ) 2 f0; 1; :::;
a
+ 1g =
a 7
t.
The term
0
captures the steady-state e¤ects from positive trend in‡ation. These e¤ects
stem from positive trend in‡ation raising cross-sectional steady-state dispersion in prices that
in turn leads to ine¢ cient allocations of resources across industries (Coibion, Gorodnichenko,
and Wieland, 2012). These steady-state e¤ects are eliminated if price indexation is perfect
(! = 1). The term
1
is directly related to the increasing disutility of labor supply. Since
households’costs of supplying labor are convex, the expected disutility from labor rises with
the volatility of output around its steady state. As discussed in Coibion, Gorodnichenko, and
Wieland, 2012, the magnitude of this coe¢ cient is invariant to the level of trend in‡ation
The term
2
.
captures the e¤ects of price dispersion on social welfare. Positive trend in‡ation
generates some price dispersion. The increased price dispersion following an in‡ationary
shock becomes now more costly because of the higher initial price dispersion due to positive
trend in‡ation. Higher nominal rigidities ( ) lead to stronger e¤ects of price dispersion on
welfare (
2 ).
It should be noted that zero trend in‡ation (
= 1) or positive trend in‡ation
with perfect indexation (! = 1) would imply that the steady-state costs of positive trend
in‡ation go to zero (
7
Recall st (i = T ) =
announced.
a
0
= 0). A detailed derivation of the welfare function can be found
+ 1 denotes the long-lasting passive regime, whose exact realized duration is not
24
in Coibion, Gorodnichenko, and Wieland, 2012. These welfare coe¢ cients
0,
1,
and
2
depends on the government-purchase-to-output ratio in steady state, which we assume to be
equal to 22%.
It can be shown that conditional on a price markup shock, the active regime is associated
with a lower volatility of in‡ation but a higher volatility of the output gap compared with
deviating to passive policies. This result captures the monetary policy trade-o¤ due to
these ine¢ cient shocks, which is a well-known feature in the context of linear DSGE models.
However, conditional on the other three shocks (i.e., the discount factor shock
technology shock
zt ,
and the monetary shock
rt ),
g;t ,
the
active policy always leads to a lower level
of both volatilities and, hence, to an unambiguously higher welfare.
Equation (6) makes it explicit that social welfare depends on agents’uncertainty about
future in‡ation and future output gaps. It should be noted that agents’uncertainty in any
given period captures the macroeconomic risk associated with the observed policy regime
and communication strategy, st (i). Unlike standard New Keynesian models with …xed parameters, where welfare is merely a function of the unconditional variance of in‡ation and the
output gap, our model allows us to study the dynamic e¤ects of policy actions and forwardlooking communication on welfare. To the best of our knowledge, this is the …rst paper that
studies this feature using a structural model. Furthermore, the learning mechanism plays
an important role in our welfare analysis by linking the concept of a central bank’s long-run
reputation to a central bank’s ability to control the dynamics of the macroeconomic risk
associated with policy actions. This last point will be the focus of the next session.
To assess the desirability of transparency, we compute the model predicted welfare
gains/losses from transparency as follows:
We =
P
a +1
a =0
p T ( a ) WT ( a )
P
=0
pN ( ) WN ( )
(7)
where pT ( a ) stands for the vector of ergodic probabilities of a passive policy of announced
25
duration
a
and pN ( ) stands for the vector of ergodic probabilities of a passive policy of
observed duration . It is important to emphasize that welfare gains from transparency are
not conditioned on a particular shock or policy path. Instead, the welfare gain is measured
by the unconditional long-run change in welfare that arises if the central bank systematically
announces the duration of any short-lasting deviation from active monetary policy.
Uncertainty about future output gaps turn out to play only a minor role for social welfare,
since the estimated value of the slope of the Phillips curve is very small and the elasticity
of substitution among goods " is quite large. Such a ‡at Phillips curve is a standard …nding
when DSGE models are estimated using U.S. data and the estimated value of the elasticity of
substitution is in line with the results of previous studies and with micro data on U.S. …rms’
average pro…tability. The estimated value of these two parameters causes the estimated
coe¢ cient for the in‡ation risk in the welfare function (
coe¢ cients (
0
and
1)
2)
to be bigger than the other two
by several orders of magnitude. Therefore, welfare turns out to be
tightly related to agents’uncertainty about future in‡ation, which, as we shall show, depends
on the time-varying level of pessimism about observing a future switch to active monetary
policy. For the sake of brevity, in what follows we do not discuss the evolution of uncertainty
about output gaps.
5.1
Evolution of Uncertainty
We have shown that agents’uncertainty about future in‡ation crucially a¤ects social welfare
in the estimated model. In this section, we will show how uncertainty is tightly linked to
agents’pessimism about observing active monetary policy in the future. As shown in Section
4.2, transparency has two e¤ects on pessimism: (i) pessimism rises at the beginning of the
policy (henceforth, the short-run e¤ect of transparency on pessimism) and (ii) pessimism is
anchored down at the end of the policy (henceforth, the anchoring e¤ect of transparency on
pessimism). As we shall show, these two e¤ects play a critical role for the welfare implications
of enhancing a central bank’s transparency.
26
To illustrate how uncertainty responds to pessimism under the two communication strategies, we consider the case in which the Federal Reserve conducts a 40-quarter-long deviation
from active monetary policy.8 While such a long-lasting realization of the short-lasting
regime is implausible, this example allows us to highlight the key implications of the two
communication strategies on welfare. The upper panel of Figure 3 shows the evolution of
uncertainty about in‡ation at di¤erent horizons h under no transparency (left panel) and
under transparency (right panel). At each point in time, the evolution of agents’uncertainty
is measured by the h-period ahead standard deviation of in‡ation given the communication
i
hp
p
vari ( t+h jst (i))
vari ( t+h jst (i) = 0) , where
strategy that is, sdi ( t+h j t ) = 100
i 2 fN; T g captures the communication strategy.9 We analytically compute the conditional
standard deviations taking into account regime uncertainty by using the methods described
in Bianchi (2016).
As shown in the upper left graph, when the central bank does not announce its policy
course beforehand, uncertainty about future in‡ation is fairly low at the beginning of the
policy because agents interpret the …rst deviations from active policy as short-lasting. As
more and more periods of passive policy are observed, agents become progressively more
convinced that the observed deviation may have a long-lasting nature and uncertainty about
future in‡ation gradually takes o¤. Uncertainty rises because expecting a longer spell of
passive policies raises concerns about the central bank’s ability to control the in‡ationary
consequences of future shocks. Note that the increase in uncertainty occurs at every horizon
because agents expect passive monetary policy to prevail for many periods ahead. It is
worth emphasizing that the pattern of agents’uncertainty over time mimics the evolution
of pessimism depicted in Figure 2. Since higher uncertainty leads to bigger welfare losses,
the progressive disanchoring of uncertainty about future in‡ation is a reason of concern for
8
The analysis is conducted for an economy at the steady-state and, hence, without conditioning on a
particular shock. The exercise is conditioned only on the policy path and intends to facilitate the exposition
of the welfare implications of transparency in the next section.
9
The graphs plot the results for h from 1 to 60: At horizon h = 0, uncertainty is zero as agents observe
current in‡ation.
27
Transparency
Uncertainty
Uncertainty
No Transparency
0.6
0.4
0.2
60
40
20
10
Horizon
20
40
30
0.4
0.2
60
40
20
10
Horizon
Time
20
40
30
Time
0.6
Uncertainty
0.6
Uncertainty
0.6
0.5
0.4
Perf.Inf.Bounds
10 deviations
20 deviations
40 deviations
0.3
0.2
0.5
0.4
Perf.Inf.Bounds
10 deviations
20 deviations
40 deviations
0.3
0.2
10
20
30
40
50
60
10
Horizon
20
30
40
50
60
Horizon
Figure 3: Upper graphs: Evolution of uncertainty about in‡ation at di¤erent horizons (h) over 40 periods of
passive policy (time) under no transparency (left graph) and under transparency (right graph). The vertical
axis reports the standard deviations in percentage points at the posterior mode. Lower graphs: Dynamics
of uncertainty across horizons after having observed (left plot) or announced (right plot) 10, 20, and 40
consecutive quarters of passive policy. The gray areas denote the bounds for the dynamics of uncertainty
about in‡ation across horizons when agents know the nature of the observed passive policy. The upper
(lower) bound is when the passive policy is of the short-lasting (long-lasting) type. Parameter values are set
at the posterior mode.
a nontransparent central bank.
The lower left panel shows the dynamics of uncertainty across di¤erent horizons when
10, 20, and 40 quarters of deviations are observed under no transparency. The gray area
captures the dynamics of uncertainty across horizons in the case of perfect information
that is, the case in which agents know whether the passive regime in place is short- or longlasting. Thus, the lower- (upper-) bound of the gray area captures the uncertainty when
agents know for certain that the short- (long-) lasting passive regime is in place. After
40 consecutive deviations from active policy have been observed, uncertainty evolves as if
agents knew with certainty that the central bank is conducting a long-lasting policy (the
28
black dashed-dotted line). After observing so many deviations, agents are certain that this
is a long-lasting passive policy and cannot become more uncertain about future in‡ation.
Therefore, the dynamics of uncertainty when agents perfectly know that the nature of passive
policy is long-lasting represents an upper bound for agents’uncertainty.
The dynamics of uncertainty conditional on a short-lasting passive policy under perfect
information constitute a lower bound for uncertainty under no-transparency. Once the central bank starts deviating, the higher the central bank’s long-run reputation p12 = (1
p11 ) is,
the closer the dynamics of uncertainty to this lower bound are. The lower left graph shows
that the evolution of uncertainty remains close to the lower bound even after ten consecutive
periods of passive policy. This result re‡ects the high reputation of the Federal Reserve.
The right upper graph of Figure 3 shows the dynamics of uncertainty about future in‡ation in the case of transparency. Comparing the upper graphs (the scale of the z-axes
are identical) illustrates that uncertainty is higher under transparency at the beginning of a
40-period long passive policy. This is captured by the pronounced hump-shaped dynamics
of short- and medium-horizon uncertainty. This result is driven by the short-run e¤ect of
transparency on pessimism. The announcement commits the central bank to follow a passive
policy for the next 40 periods, causing agents to expect larger consequences from the shocks
that will materialize during the implementation of the announced policy path. The lower
right graph compares the dynamics of uncertainty after announcing the passive policy of increasing durations (10, 20, and 40 quarters) with the upper and lower bounds for the case of
no transparency (the gray area). After announcing 40 quarters of passive policy, uncertainty
is above the gray area at short and medium horizons, implying that uncertainty becomes
higher than the upper bound for the case of no transparency. This overreaction of short-run
uncertainty is driven by the short-run e¤ect of transparency on pessimism and contributes
to lowering the welfare gains from transparency.
Compared with uncertainty in the case of no transparency, uncertainty in the case of
transparency is larger at the beginning of the policy at both short and medium horizons.
29
However, 40-quarter-ahead in‡ation uncertainty appears to be smaller in the case of transparency. This result is due to the anchoring e¤ect of transparency on pessimism. While
agents know that monetary policy will be passive for 40 quarters, they also take into account
that there will be a switch to the active regime in 40 quarters. Announcing the timing of
the return to active monetary policy determines a fall in uncertainty in correspondence with
the horizons that coincide with the announced date. In the upper right graph of Figure 3,
such a decline in uncertainty shows up as a valley in the surface representing the level of
uncertainty. As we shall show, this feature of transparency has the e¤ect of raising social
welfare by systematically anchoring agents’uncertainty at the end of the announced deviations from the active regime. Furthermore, at long horizons, uncertainty is always lower
under transparency. In fact, the lower right graph shows that in the case of transparency
long-horizon uncertainty is lower than the lower bound for the no-transparency case even
when very persistent passive policies are announced. This result is due to the anchoring e¤ect
of transparency on pessimism and contributes to raising welfare gains from transparency.
To sum up, under the no transparency, uncertainty increases across all horizons as the
policy is implemented while under transparency, uncertainty decreases over time because
agents are aware that the end of the prolonged period of passive monetary policy is approaching. These opposite patterns for uncertainty under the two communication strategies
are due to the anchoring e¤ect of transparency on pessimism.
It should be noted that the evolution of uncertainty conditional on being in the active
regime is not the same across the two alternative communication strategies. This is because
transparency determines an overall reduction in uncertainty that manifests itself also under
the active regime, even if under the active regime no announcement is made. A transparent
central bank enjoys lower uncertainty even when monetary policy is active because agents
understand that should a short-lasting passive policy of any duration be implemented in the
future, the central bank will announce its duration beforehand. As it will soon become clear,
such a communication strategy is e¤ective in reducing uncertainty by removing the fear of
30
Welfare Gains From Transparency
Ergodic prob (left scale)
Welfare gains from transparency (right scale)
0.6
3.75
3.7
0.4
3.65
0.2
3.6
0
0
5
10
15
20
25
30
35
Observed Periods of Passive Policy
Figure 4: The solid line shows the dynamics of the welfare gains from transparency as a function of the
observed periods of passive policy ( t ). The bars show the ergodic probability of observing the periods of
passive policy on the x-axis ( t ). Parameter values are set at the posterior mode.
a long-lasting deviation for the frequent short-lasting deviations and creating an anchoring
e¤ect for the sporadic long-lasting deviations. Since the active regime occurs often, its
weight for the welfare calculation in equation (7) is rather large, implying that welfare gains
conditional on being in the active regime will critically a¤ect the welfare-based ranking of
the two alternative communication strategies.
5.2
Welfare Gains from Transparency
To assess the overall welfare gains from transparency, we use equation (7), which combines
the welfare associated with the policy regimes (
t
for the case of no transparency and
a
t
for
the case of transparency) and their ergodic probabilities.10 To facilitate the comparison, we
rede…ne the regimes under transparency
a
t
in terms of observed periods of passive policy
t
and recompute welfare in the case of transparency associated with these new set of regimes.
The line in Figure 4 shows the welfare gains from transparency associated with having
10
This is a long-run welfare measure. The online appendix shows the evolution of welfare under transparency and no transparency as passive policies of di¤erent length are implemented.
31
observed passive policies for
t
periods based on the posterior mode estimates. The bars
report the ergodic probabilities of regimes
t.
Only short deviations from active policy are
plausible for the U.S. The line shows that for passive policies of plausible durations, transparency raises welfare, implying that the model predicted welfare gains from transparency
We in equation (7) are positive. Interestingly, the welfare gains from transparency for
observed deviations
t
gradually decline as the number of observed deviations increases.
This result stems from the fact that announcing longer and longer deviations progressively
strengthens the short-run e¤ect of transparency on pessimism. This, in turn, raises the risk
of macroeconomic instability, as shown in Figure 3.
We …nd that the gains from transparency are roughly 3.74% of steady-state consumption
for the U.S. economy, with a 70% posterior credible interval covering the range 1:74% 5:30%.
. This result implies that the anchoring e¤ect of transparency dominates the short-run
e¤ects. In other words, transparency is welfare improving because it allows the central bank
to e¤ectively sweep away the fear of a return to the 1970s-type of passive policies. This
explains why when the central bank conducts an active policy (
t
= 0), the welfare gains
from transparency are not zero. They are, in fact, positive, capturing the welfare gains from
expecting that the central bank will systematically and truthfully announce the duration of
any future short-lasting passive policy.
5.3
In‡ation Uncertainty in the Data
One property of the estimated model is that beliefs change gradually as more and more
periods of passive policy are observed. If we assume that for an alternative model, agents
perfectly know the realization of policy regimes (perfect information), their beliefs would
respond abruptly as the central bank changes its attitude toward in‡ation stabilization. In
this section, we want to test the diverging predictions of these two models on the dynamics
of in‡ation uncertainty in the 1970s, which both models identify as a period in which a
32
Inflation Uncertainty
1
Data: D'Amico Orphanides (2014)
Model with Learning
Model with Perfect Information
0.9
0.8
0.7
0.6
0.5
1970
1972
1974
1976
1978
1980
Figure 5: Long-Run Trend of Uncertainty about Future In‡ation Predicted by the Model with Learning
and the Perfect Information Model. The dynamics of in‡ation uncertainty resulting only from policy actions.
The dynamics of uncertainty predicted by the two models is rescaled so that in 1968:Q4, in‡ation uncertainty
is equal to the least square constant estimated using uncertainty in the data.
long-lasting passive policy was implemented.11 This test is intended to empirically validate
the learning mechanism put forward in the paper.12 We focus on uncertainty about in‡ation
because this variable is the key driver of social welfare in the estimated model.
Figure 5 compares the dynamics of one-year-ahead in‡ation uncertainty measured by
D’Amico and Orphanides (2014) from the Survey of Professional Forecasters, with the trend
in the one-year-ahead in‡ation uncertainty predicted by the estimated Markov-switching
model with learning (no transparency) and by the estimated Markov-switching model with
11
We focus on the 1970s for two reasons. First, our model does not have interesting predictions for
uncertainty during periods characterized by active monetary policy because the central bank’s reputation
is immediately rebuilt once monetary policy moves back to the active regime. As a result, the dynamics
of uncertainty is ‡at, like in a perfect information model. Second, the dynamics of beliefs during periods
of active policy or short-lasting passive policy are very similar to the ones that would arise under perfect
information, making it hard to distinguish our benchmark model from the alternative model with perfect
information over sample periods that do not include the 1970s.
12
Comparing the marginal likelihood of the estimated model with that of the same model with perfect
information leads to inconclusive results. It is likely that estimating the models with a data set that includes
in‡ation expectations may help us select one of the two models. However, reliable survey-based expectations
data are available only from the early 1970s onward. Yet, using the entire sample is key to estimating
the properties of the active regime and those of the transition matrix. Using uncertainty as an observable
variable is computationally very challanging as uncertainty follows a nonlinear law of motion, requiring MC
…ltering to evaluate the likelihood.
33
perfect information. In the latter model, agents perfectly know which type of policy regime
is in place. The model with perfect information predicts a sharp rise in in‡ation uncertainty
as monetary policy switches to the long-lasting passive policy. After the switch to passive
policy, the perfect information model predicts that long-run uncertainty stays put at this
higher level throughout the 1970s. In contrast, the model with learning predicts a smaller
rise in uncertainty as monetary policy becomes passive in the late 1960s and a gradual run-up
in in‡ation uncertainty in the subsequent years. This gradual increase in uncertainty is due
to the prolonged period of passive policy that caused agents to become progressively more
convinced that this policy had a long-lasting nature. The data (the dotted line) suggest that
in‡ation uncertainty grew slowly in the 1970s, favoring the dynamics predicted by the model
with learning. Since uncertainty is not an observable in our estimation, the comparison in
Figure 5 constitutes an external validation exercise.
6
Imperfectly Credible Announcements
In this section we study the consequences of imperfectly credible announcements. Let us
consider the case in which the central bank systematically announces the duration of shortlasting deviations, but it lies if the duration is longer than
. To model this idea, we
assume that the duration of passive policies is drawn accordingly with the Markov-switching
process implied by the primitive matrix P, de…ned in Section 3. If the drawn duration of
the passive policy
is smaller than or equal to , the central bank announces
drawn duration of the passive policy
a number of consecutive deviations
is discovered after
a
a
= . If the
is larger than , the central bank lies and announces
a
between 1 and . Note that the central bank’s lie
+ 1 periods, and at this point, rational agents know that the policy
will stay passive for sure until
a.
For any period of the short-lasting passive policy
observed after , agents have to learn the persistence of the regime in place as they do in
the no-transparency case.
34
We also assume that if the central bank lies, it is more likely to announce a fairly large
number of deviations in order to deceive the lie for longer. This property also implies that
the longer the announced deviation, the more likely it is that the central bank has lied and
will keep deviating from active policy at the end of the announced passive policy. Thus, the
probability of returning to an active policy declines as the horizon of the announced policy
increases. The central bank does not announce long-lasting deviations, which is consistent
with how we have de…ned transparency throughout this paper.
A detailed description of how to specify the transition matrix for the regimes in the case
of imperfectly credible announcements is provided in the online appendix. In what follows,
we assume that the central bank always lies if the number of deviations is larger than
= 4:
We then assume a mapping f ( a ) to control the probability that the central bank announces
a
periods of passive policy conditional on having lied ( > ): f ( a ) = f:1; :2; :3; :4g for
a
= f1; 2; 3; 4g, respectively. This mapping implies that if the central bank lies, it is four
times more likely that a four-quarter deviation from active policy is announced relative to a
one-quarter deviation. This last assumption causes the probability of returning to an active
policy to decline as the horizon of the announced policy increases.
It turns out that this speci…cation does not substantially change the main results of
the paper. Even if the central bank can lie, transparency is still welfare improving. In
fact, limiting the number of periods of passive policy the central bank truthfully announces,
leads to a slight increase in the welfare gains from transparency. For the sake of illustrating
the key mechanism, Figure 6 shows the dynamics of welfare as a 20-period passive policy
is implemented under three di¤erent announcements. In all cases, the announcements are
made by the central bank at the beginning of the period of passive policy.13 The solid
blue line corresponds to the benchmark model and captures the dynamics of welfare in the
13
This example is about a very longed passive policy ( = 20 > ) and hence it is very unrealistic for
countries such as the U.S, in which the average duration of a short-lasting passive policy is three quarters.
Nevertheless, this numerical example allows us to isolate two key e¤ects of lying about passive policies with
duration > on the welfare gains from transparency. It can be shown that for a given transition matrix
P, the magnitude of these two e¤ects becomes smaller and smaller as grows.
35
Transparency: 20-Quarter Passive Policy
Truthful Announcement
Untruthful Announcement: 1 Quarter
Untruthful Announcement: 4 Quarters
Welfare
-102
-104
-106
-108
-110
2
4
6
8
10
12
14
16
18
20
Time
Figure 6: Welfare evolution as a 20-quarter deviation from the active policy is implemented under imperfectly credible announcements.
case in which the central bank truthfully announces the duration of the passive policy. The
dot-dashed line and the solid line with circles capture the dynamics of welfare in the case
in which the central bank announces that the passive policy will last one quarter and four
quarters, respectively.
This plot illustrates that lying about the duration of passive policies raises welfare in the
short run. These gains stem from preventing the sudden rise in pessimism that occurs at
the beginning of an announced passive policy. Nevertheless, lying eventually back…res. Once
agents realize that the announcement was in fact a lie, welfare experiences a discrete drop.
After that, it starts following a pattern similar to the one prevailing under no transparency.
Of course, relaxing the assumption that announcements are fully credible has also a third
e¤ect on the welfare gains from transparency. This has to do with the fact that agents
question the veracity of central bank’s announcements even when the central bank is, in fact,
telling the truth. This e¤ect contributes to lowering the welfare gains from transparency. For
the U.S., the positive short-run e¤ects on the welfare gains from transparency dominate the
other two negative e¤ects. Consequently, our results suggest that even if the central bank is
36
Welfare gains
from transparency
6.5
6
5.5
5
4.5
4
2
4
6
8
10
12
14
16
18
20
Realized Duration of Passive Policy
Figure 7: Average per-period welfare gains from transparency associated with passive policies of given
realized durations. Parameter values are set at their posterior mode.
unable to make perfectly credible announcements, transparency still determines an increase
in welfare and this gain might be even larger than under perfectly credible announcements.
7
Robustness
In this section we conduct a series of robustness exercises. In Section 7.1 we investigate
whether transparency is welfare increasing for passive policies of every plausible duration.
In Section 7.2, we relax the assumption that the central bank knows exactly the realized
duration of the ongoing passive policy.
7.1
Short-Run Bene…ts from Transparency
In the previous sections, we have showed that enhancing a central bank’s transparency would
raise welfare. The computation of expected welfare gains from transparency is obtained
using the ergodic distribution of the policy regimes and, hence, captures the long-run gains.
However, it remains to be seen if the central bank is better o¤ following transparency for
any possible duration of the short-lasting deviations. In other words, are there short-lasting
37
deviations for which the central bank would rather be nontransparent?
We …nd that the positive gains from transparency occur for every plausible duration of
the passive policy. To see this, the solid line of Figure 7 shows the dynamics of the average
per-period welfare gains from transparency associated with the short-lasting passive policy
of various durations. The important result is that welfare gains are positive for all plausible
durations of short-lasting passive policies. This …nding suggests that the central bank is
better o¤ by announcing passive policies of every plausible duration. Quite interestingly, this
plot suggests that the central bank is better o¤ even if it has to announce passive policies
of fairly long durations. This is an important result that implies that the overall reduction
in uncertainty that occurs owing to introducing transparency overcomes any short-run loss
associated with announcing a prolonged deviation from active policy.
It should be noted the di¤erence between the welfare gains from transparency in Figure 4
and those of Figure 7. Figure 4 reports the welfare gains from having announced the duration
of the ongoing passive policy when
t
deviations out of the announced
a
t
t
have been
observed. Figure 7 shows the average per-period welfare gains, should the Federal Reserve
decide to announce a passive policy of a certain duration. The latter measure evaluates the
average welfare gains from transparency across periods of policy implementation, whereas
the former measure, combined with the ergodic probability distribution of the deviations,
captures the expected bene…t from being transparent over the long run.
7.2
Limited Information
We have modeled transparency as a communication strategy in which the central bank shares
all the information about the policy regime to households and …rms. Since we assume that
the central bank knows the exact duration of its short-lasting passive policies, transparency
implies that such information is shared with the public. In this section, we relax the assumption that the central bank knows the exact duration of passive policies. Rather, we
assume that the central bank knows only the expected duration of the deviations from the
38
active regime
that is, the bank perfectly knows only if the passive policy is short-lasting or
long-lasting. Thus, now under transparency the central bank truthfully announces whether
it will be conducting a short-lasting or a long-lasting passive policy.14
We …nd that under limited information, welfare gains from transparency are always
positive for policies of any plausible duration.15 Compared with the case in which the central
bank announces the exact duration of the short-lasting passive policies, the magnitude of
the welfare gains from transparency is smaller as the central bank knows less about the
duration of the policy it is implementing. In fact, the model predicted welfare gains from
transparency amount to 0.54% of steady-state consumption. Thus, our analysis suggests
that the welfare gains from transparency are positive and are quanti…ed to range from 0.54%
to 3.74% depending on how much informed the central bank is regarding the duration of
passive policies.
8
Concluding Remarks
We have developed a general equilibrium model in which the central bank can deviate from
active in‡ation stabilization. Agents observe when monetary policy becomes passive, but
they face uncertainty regarding the nature of these deviations. Importantly, when observing
passive policy, they cannot rule out the possibility of a return to the 1970s-type of passive
policies. The longer the deviation from active policy is, the more pessimistic about the
evolution of future monetary policy agents become. This implies that as the central bank
keeps deviating, uncertainty increases and welfare deteriorates.
When the model is …tted to U.S. data, we …nd that the Federal Reserve bene…ts from
a strong reputation. As a result, policymakers can deviate for a prolonged period of time
from active monetary policy before losing control over agents’ uncertainty about future
14
Therefore, the model boils down to a Markov-switching model with perfect information given that now
the history of policy regimes pt 2 f1; 2; 3g belongs to the agents’information set.
15
We plot the welfare gains from transparency conditional on the observed periods of passive policy as
well as the distribution of these periods in the online appendix.
39
in‡ation. Nevertheless, increasing transparency about the central bank’s future behaviors
would improve welfare by anchoring agents’ pessimism following exceptionally prolonged
periods of passive monetary policy and by removing the fear of a return to the 1970s following
the frequent short-lasting deviations.
A limitation of the current analysis is that agents learn only the persistence of passive
policies, while the active regime is fully revealing. This implies that agents’expectations are
completely revised as soon as the central bank returns to the active regime. In Bianchi and
Melosi (2016a) we develop a more general methodology that could be used to study a model
in which agents have to learn about the likely duration of both passive and active policies.
This extension would add further realism to the model because it would make the cost of
losing reputation more persistent. While we regard the estimation of a model with richer
learning dynamics as an important direction for future research, at this stage estimating
a model of this type is computationally challenging. Furthermore, we believe that such an
extension is unlikely to a¤ect the main conclusions of this paper. This is because announcing
the return to a long-lasting period of active monetary policy would still have the e¤ect of
anchoring agents’pessimism and uncertainty.
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Dynamics, 8(2): 392–419.
Sims, Christopher A., and Tao Zha. 2006. “Were There Regime Switches in U.S. Monetary Policy?” American Economic Review, 96(1): 54–81.
Smets, Frank, and Rafael Wouters. 2007. “Shocks and Frictions in US Business Cycles:
A Bayeasian DSGE Approach.”American Economic Review, 97(3): 586–606.
45
Online Appendix
Not For Publication
46
A
The Log-Linearized Model
Since technology Zt follows a random walk, we normalize all the nonstationary real variable by the level of technology. We then log-linearize the model around the steady-state
equilibrium in which the steady-state in‡ation does not have to be zero. Let us denote logdeviations of the detrended variable xt from its own steady-state value x with x
bt
ln (xt =x).
The log-linearized model can be expressed as follows:16
y^t = E (^
yt+1 jFt )
r^t
Et (^ t+1 jFt )
^t
zz
+ 1
g
(8)
g^t
1^
bt
^t =
(9)
1
^bt = (1 + "= )
d^t = (1
1
+1
2)
+
2
h
h
d^t
Et (^
yt+1 jFt )
Et (^
yt+1 jFt )
e^t +
y^t +
y^t +
(10)
m m;t
2
"
^t
zz
+1
^t
R
i
+ 1 Et (^ t+1 jFt ) +
2 Et
d^t+1 jFt
(11)
(12)
i
^ t + "Et (^ t+1 jFt ) + 1 Et (^
y^t + z z^t R
et+1 jFt )
i
h
p (
p ^t +
p
y
^
+
z
^
)
+ r r;t
t
t
y; t
; t
R; t
(13)
e^t =
1
r^t =
R;
r^t
1
+ 1
g^t =
^t 1
gg
+
g gt
(15)
z^t =
^t 1
zz
+
z zt ;
(16)
where
1
p
t
(! 1)(1 ")
and
2
(1 !)["( 1 +1)]
(14)
and ^bt denotes the optimal reset price
of …rms. Following Coibion, Gorodnichenko and Wieland (2012), we add an i.i.d. cost-push
shock
m;t
to the Phillips curve. If one abstracts from imperfect information, this model
is very similar to the model studied by Coibion and Gorodnichenko (2011) and Coibion,
Gorodnichenko and Wieland (2012).
Equation (9) suggests that in‡ation, ^ t , is less sensitive to changes in the re-optimizing
price, ^bt , as steady-state in‡ation rises. Coibion, Gorodnichenko and Wieland (2012) explain
that this e¤ect has to do with the fact that, with positive steady-state in‡ation, …rms that
16
The detailed derivations of these equations are in an appendix, which is available upon request.
47
reset their price have higher prices than others and receive a smaller share of expenditures,
thereby reducing the sensitivity of in‡ation to these price changes. Indexation of prices
tends to o¤set this e¤ect, with full indexation completely restoring the usual relationship
between reset prices and in‡ation. However, equations (10)-(13) suggest that higher trend
in‡ation
makes …rms more forward-looking in their price-setting decisions by raising the
importance of expected future marginal costs and in‡ation and by inducing them to respond
to expected future output growth and interest rate. The increased coe¢ cient on expectations
of future in‡ation, which re‡ects the expected future depreciation of the reset price and the
associated losses, plays a critical role. Coibion, Gorodnichenko and Wieland (2012) explain
that in response to an in‡ationary shock, a …rm that can reset its price will expect higher
in‡ation today and in the future as other …rms update their prices in response to the shock.
Given this expectation, the more forward-looking a …rm is, the greater the optimal reset
price must be in anticipation of other …rms raising their prices in the future. Thus, reset
prices become more responsive to current shocks with higher
. Coibion, Gorodnichenko
and Wieland (2012) argue that this e¤ect dominates the reduced sensitivity of in‡ation to
the reset price in equation (9).
B
Solving the Model with No Transparency
It is very important to emphasize that the evolution of agents’beliefs about the future conduct of monetary policies plays a critical role in the Markov-switching model with learning.
In fact, three policy regimes
p
t
are not a su¢ cient statistic for the dynamics of the endoge-
nous variables in the model with learning. Instead, agents expect di¤erent dynamics for the
next period’s endogenous variables depending on their beliefs about a return to the active
regime.
To account for agents learning, we expand the number of regimes and rede…ne them as
a combination between the central bank’s behaviors and agents’beliefs. Bianchi and Melosi
48
(2016a) show that the Markov-switching model with learning described previously can be
recast in terms of an expanded set of (
+ 1) > 3 new regimes, where
t
t
> 0 is de…ned
by the following convergence theorem. For any e > 0, there exists an integer
prob f
p33
t+1
6= 0j
t
=
g < e: Therefore, that for any
, agents’ beliefs can be
>
t
such that
e¤ectively approximated using the properties of the long-lasting passive regime (Regime 3).
These new set of regimes constitute a su¢ cient statistics for the endogenous variables in the
model as they capture the evolution of agents’beliefs about observing a switch to the active
regime in the next period. The
[(
p
t
= 1;
t
= 0) ; (
p
t
+ 1 regimes are given by
6= 1;
t
= 1) ; (
p
t
6= 1;
t
= 2) ; :::; (
and the transition matrix Pep is de…ned using equation (5)
2
p11
6
6
6
6
6
6
6
e
Pp = 6
6
6
6
6
6 1
6
4
1
1
p12 p22 +p13 p33
p12 +p13
1
p12 p222 +p13 p233
p12 p22 +p13 p33
p22 (p12 =p13 )(p22 =p33 )
(p12 =p13 )(p22 =p33 )
1
t
=
)] ;
that is,
3
0
::: 0
0
0
p12 p22 +p13 p33
p12 +p13
::: 0
0
0
..
.
0
..
.
:::
..
.
0
..
.
0
..
.
0
0
0
0
p22 (p12 =p13 )(p22 =p33 )
(p12 =p13 )(p22 =p33 )
2
0
0
0
0
p22 (p12 =p13 )(p22 =p33 )
(p12 =p13 )(p22 =p33 )
1
2
2
6= 1;
p12 + p13
..
.
p22 (p12 =p13 )(p22 =p33 )
(p12 =p13 )(p22 =p33 )
p
t
+p33
+1
1
+p33
+1
2
+p33
+1
1
+p33
+1
(17)
Equation (5) measures the probability that monetary policy remains passive in period
t + 1 conditional on having observed
Realize that
prob f
t+1
t+1
6= 0j
t
t
consecutive periods of passive policy at time t.
6= 0 can be true only if either
p
t+1
= 2 or
p
t+1
= 3. Hence, the probability,
6= 0g, in the main text, can be obtained by using the law of total probability
49
7
7
7
7
7
7
7
7:
7
7
7
7
7
7
5
as follows:
prob f
t+1
6= 0j
t
p
t
6= 0g = prob f
+prob f
= 2j
p
t
t
6= 0g prob
= 3j
p
t+1
p
t+1
6= 0g prob
t
p
t
= 2j
= 3j
= 2;
p
t
t
= 3;
6= 0
t
(18)
6= 0 ;
where we have used the fact that p23 = p32 = 0 to simplify the expression. Note that the
Markovian property of the process implies that
prob
p
t+1
= 2j
p
t
= 2;
t
6= 0
= p22 ;
(19)
prob
p
t+1
= 2j
p
t
= 2;
t
6= 0
= p33 :
(20)
(21)
p13 p33t
;
p12 p22t + p13 p33t
(22)
The Bayes’theorem allows us to write:
prob f
p
t
= 2j
t
p12 p22t
6 0g =
=
;
p12 p22t + p13 p33t
prob f
p
t
= 3j
t
6= 0g =
where p12 (p13 ) is the probability that switching to the passive block was originally due to
a switch to the short-lasting (long-lasting) passive regime
p
t
=2(
p
t
= 2) and p22t (p33t ) is
the probability that the short-lasting (long-lasting) passive regime lasts for
t
consecutive
periods conditional on the original switch to the short-lasting (long-lasting) passive regime.
Replacing this results into equation (18) leads to
prob f
t+1
6= 0j
t
6= 0g =
p12 p22t +1 + p13 p33t +1
:
p12 p22t + p13 p33t
Dividing both sides by p13 p33t delivers equation (5) in the main text.
50
(23)
C
Welfare Function
The period welfare function can then be obtained by taking a log-quadratic approximation
of the representative household’s utility function around the deterministic steady state:
P1
Wi (st (i)) =
h
h=1
[
0
+
1 vari
(^
yt+h jst (i)) +
2 vari
(^ t+h jst (i))] ;
(24)
where vari ( ) with i 2 fT; N g stands for the stochastic variance associated with agents’
forecasts of in‡ation conditional on transparency (T ) or no transparency (N ) and the output
gap at horizon h. The coe¢ cients
i,
i 2 f0; 1; 2g are functions of the model’s parameters
and are de…ned in the online appendix. The subscript i refers to the communication strategy:
i = N stands for the case of no transparency, while i = T denotes transparency. Finally, st (i)
denotes the policy regime: st (i = N ) 2 f0; 1; :::;
g=
t
and st (i = T ) 2 f0; 1; :::;
a
+ 1g =
a 17
t.
The coe¢ cients
1
0
1
1
1
2
1
g
g
1
1+
2
=
1 gy
1 2
"
2
=
3
(1 gy )
where
17
1
1
0;
and
1
2
1
1+
1+
Q0y
2
are de…ned as follows:
Q0y
(1
ln x
Q0y +
"2 (1 +
2
) 1+
2 (1 gy )
1
)
1
ln (x )2
1
Q1y "
1
1 + 1+
1
1+
"
1
"
Q0y Q1y
1+
1
"
1
"
Q1y ln x
1) ="]; the steady-state government purchase share gy is set equal to
log [("
Recall st (i = T ) =
announced.
1,
a
+ 1 denotes the long-lasting passive regime, whose exact realized duration is not
51
;
0.22; and
"
x
Q0y
h
0
1
1
1
0:5 " " 1
" 1 2
"
1 + ("
1) Q1p (1
1
1) (1
("
1
(1 !)(" 1)
1 0:5
h
1 + 0:5
) b + Q0p
!) Q1p
" 1 2
"
" 1 2
"
#
2
i3
(1
!)
0:5 (1
")2
1 + 0:5 (1
")2
1
0
) M2 +
(1
1
0:5 (1
Q0p
(1 !)"( 1 +1)
1
1
Q1y
i2 ;
1 + 0:5
0
3
+"
(1 ")
(! 1)(1 ")
1 + 0:5 (1
")
")2
2;
1
Q1p
2
3;
where the cross-sectional price dispersion in the nonstochastic steady state is given by
2
2 (1 !)
2
(1 )
=
and the cross-sectional dispersion of output in the nonstochastic steady state is
= "2 . The log of the optimal reset price in the nonstochastic steady state is given by
1
1
b = log
D
(! 1)(1
1
)
1
and M
t
bt b
log(
)
=
(" 1)(1 !)
1
(" 1)(1 !)
.
Transition Matrix under Transparency
When the central bank is transparent, the exact duration of every short-lasting deviation
from active policy is truthfully announced. In this model the number of announced shortlasting deviations from active policy yet to be carried out
a
t
is a su¢ cient statistic that
captures the dynamics of beliefs after an announcement. Since the exact duration of longlasting passive policies is not announced, we also have to keep the long-lasting passive regime
as one of the possible regimes. Regimes are ordered from the smallest number of announced
deviations (zero, or active policy) to the largest one ( a ). The long-lasting passive regime,
whose conditional persistence is p33 , is ordered as the last regime. Notationally, regime
a
t
=
a
+ 1 denotes the long-lasting passive regime. Hence, we rede…ne the set of policy
regimes in terms of this variable with the following mapping to the parameter values of the
52
policy rule:
a
t
r(
where
a
t
a
= j) ;
(
a
t
= j) ;
y(
a
t
2
A
r;
6
= j) = 4
P
P
r ;
A
P
y
;
;
A
y
3
, if j = 0
, if 1
a
j
7
5
+1
(25)
is a large number at which we truncate the rede…ned set of regimes. The regimes
2 f0; 1; :::;
a
0
[e
p10
e20
e30
e1A is a 1
A; p
A; p
A ] , where p
a
a
+ 1g are governed by the (
(
a
+ 2)
(
a
eA =
+ 2) transition matrix P
+ 2) vector whose j-th element is p11 if j = 1; p12 pj22 2 p21 if
+ 1 (the probability that the realized short-lasting passive policy will last exactly
2
j
j
1 consecutive periods conditional on being in the active regime); and p13 if j =
a
+ 2.
This vector pe1A captures the probability of remaining in the active regime; switching to a
short-lasting passive regime of duration 1 up to
regime
a;
and switching to the long-lasting passive
a
all conditional on being currently in the active regime. The
pe2A is de…ned as I a ; 0
a
2
, where I
a
a
is a
a
identity matrix and 0
(
a
2
a
+ 1) matrix
is
a
2 null
matrix. This submatrix captures the transition while the announced deviation from active
policy is carried out. pe3A is de…ned as a 1
j = 1; zero if 2
j
a
(
+ 1; and p33 if j =
a
+ 2) vector whose j-th element is (1
a
eA captures
+ 2. The last row of the matrix P
p33 ) if
the probability of staying in the long-lasting passive regime or switching to the active regime,
conditional on being currently in the long-lasting passive regime. To ensure that the …rst row
Pa 1 1
sums up to one, we set pe1A ( a ) = 1 p11
eA (j) p13 , which, e¤ectively, becomes the
j=1 p
probability for the central bank to announce a deviation longer than
a
to be large enough so that pe1A ( a )
a
periods. We choose
0 and the approximation error becomes negligible.18
Let us make a simple example to illustrate how to construct the transition matrix gov-
erning the evolution of the policy regimes in the case of transparency. To serve the purpose
of this simple example, let us truncate the maximum number of announced deviations at
a
= 3 periods. We need to construct a total of
18
a
+ 2 = 5 regimes. The …rst regime is
Since p22 < 1, it can be easily shown that the larger the truncation
error.
53
a,
the lower the approximation
A
r;
active
P
r ;
P
;
P
y
A
;
A
y
and all of the other regimes (from the second to the …fth) are passive
. The 5
eA can be constructed as follows:
5 transition matrix P
2
6
6
6
6
6
A
e =6
P
6
6
6
6
4
p11
1
p12 p21 p12 p22 p21 p12 p222 p21 p13
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
p33
3
7
7
0 7
7
7
0 7
7:
7
7
0 7
5
p33
Let assume that at time t the central bank announces it will implement a three-period passive
policy (i.e.,
a
t
= 3). The system will move to the fourth regime in period t + 1, to third
regime in period t + 2, to the second regime in period t + 3, and then back to the active
regime (i.e., the …rst regime) in period t + 4.
Similarly to the case of no transparency, we have recast the MS-DSGE model under
transparency as a Markov-switching rational expectations model with perfect information,
in which the short-lasting passive regime is rede…ned in terms of the number of announced
deviations from the active regimes yet to be carried out,
a
t.
This rede…ned set of regimes
belongs to the agents’information set Ft in the case of transparency. This result allows us
to solve the model under transparency by applying any of the methods developed to solve
Markov-switching rational expectations models of perfect information.
E
Transformation of Regimes under Transparency
In Figure 4 we express welfare under transparency in terms of number of observed deviations from the active regime. This corresponds to the de…nition of policy regime under no
transparency. This is done in order to facilitate the analysis of how the welfare gains from
transparency varies with passive policies of duration :
First of all, the probability that
periods of deviation from the active regime are due
54
to the implementation of a short-lasting passive policy (primitive Regime 2) is de…ned as
follows:
P( ) =
p12 pi22 1
:
i 1
p12 p22
+ p13 pi33 1
Furthermore, we compute the probability that i consecutive periods of passive policy has
been announced conditional on having observed
i period of short-lasting passive policy
as follows:
i 1
p12 p22
p21
for any
1
p12 pj22 1 p21
j=
(i) = P
i
a+
+
a
:
Note that the numerator captures the probability that a deviation of duration i is realized
and, hence, announced (recall all announcements are truthful). The denominator is the
probability of (announcing) a short-lasting passive policy lasting
the truncation
periods or longer (up to
).
The welfare associated with a policy that has been deviating for
1 consecutive periods
under transparency is given by19
f
WT ( ) = P ( )
a
X
(j + ) WT (
a
= j) + [1
p ( )] WT (
a
=
a
+ 1) :
(26)
j=0
Note the di¤erence from WT ( a ) in equation (6), which is the welfare function de…ned
in terms of policy regimes for the case of transparency (i.e.,
a
the number of announced
deviations yet to be carried out). WT ( a ) is the welfare under transparency associated
with a announcing
a
periods of passive policy. f
WT ( ; ) is the welfare under transparency
associated with having observed
consecutive periods of passive policy. We can show that
this recasting of policy regimes leads to a negligible approximation error as
X
=0
19
The Regime
a
pN ( ) f
WT ( )
a +1
X
pT ( a ) WT ( a ) :
a =0
+ 1 denotes the long-lasting passive regime (
55
p
= 3).
The welfare gains from transparency can be alternatively computed as follows
X
f
We
h
pN ( )
=0
f
WT ( )
i
WN ( ) :
This formula can be used to compute the welfare gains from transparency that are identical to
those obtained by using the formula (7) in the main text (up to some very tiny computational
h
i
f
error). Figure 4 plots the conditional welfare gains from transparency WT ( ) WN ( )
for 1
.
We analyze the welfare gains from transparency under limited information (i.e., the
welfare in the perfect information case) by the central bank in Section 7.1. To do so, we …rst
compute the long-run welfare under perfect information as follows
f
WP ( ) =
( ) WP (
p
= 2) + [1
( )] WP (
p
= 3) ; for 1
where Wp denotes the welfare under perfect information and
of policy regimes. The weight
p12 p22 1
;
p12 p22 1 + p13 p33 1
which captures the probability that the observed
stems from a short-lasting passive policy (
p
t
= 1 or
2 f1; 2; 3g, the primitive set
is de…ned as follows:
( )=
the active regime,
p
t
;
p
consecutive deviations from active policy
= 2). For
= 0 (i.e., conditional on being in
= 0), the welfare f
WP (0) = WP
p
=1 .
This computation gives almost identical welfare gains from transparency to the alternative computation on the right-hand-side of the following expression:
X
=0
pN ( ) f
WP ( )
X
p
t 2f1;2;3g
56
p ( pt ) WP ( pt ) :
Four-Quarter Passive Policy
Eight-Quarter Passive Policy
-108
Welfare
Welfare
-108
-109
-110
-111
-109
-110
-111
-112
1
2
3
4
2
Time
Twelve-Quarter Passive Policy
4
6
8
Time
Forty-Quarters Passive Policy
-108
Welfare
Welfare
-110
-110
-112
No transparancy
Transparency
-114
2
4
6
-115
-120
8
10
12
Time
10
20
30
Time
Figure 8: Evolution of welfare Wi (st (i)) de…ned in equation (6) as a passive policy of duration 4 (upperleft graph), 8 (upper right graph), 12 (lower left graph), and 40 quarters (lower right graph) is implemented
under no transparency (i = N ), the blue dashed line, and under transparency (i = T ), the red solid line.
Parameter values are set at the posterior mode.
F
Welfare Dynamics: a Numerical Example
For the sake of illustrating the dynamics of welfare, let us consider passive policies of duration 4, 8, 12, and 40 quarters.20 Figure 8 shows the dynamics of welfare Wi (st (i)), de…ned
in equation (6), over time as these policies are implemented under the two communication
schemes: no transparency i = N and transparency i = T . Welfare under transparency (red
solid line) is always higher than welfare under no transparency (blue dashed line) at every
time during the implementation of passive policies of four-, eight-, and twelve-quarter duration. Nonetheless, welfare under transparency is lower than welfare under no transparency
at the very early stage of a 40-quarter-long passive policy. Larger gains from transparency,
measured by the vertical distance between the two lines, are reaped at the end of this pro20
This is a numerical example and is made for the sake of illustrating the evolution of welfare. We pick
fairly prolonged deviations from the active regime so as to make these dynamics more visible in the graphs.
Such long-lasting passive policies have low probability of occuring based on our estimates.
57
Price Indexation
=0.0
Price Indexation
=0.5
6.55
29.6
6.5
Welfare gains
from transparency
Welfare gains
from transparency
29.4
29.2
29
28.8
6.45
6.4
6.35
28.6
6.3
28.4
28.2
6.25
0
10
20
30
0
Observed Periods of Passive Policy
10
20
30
Observed Periods of Passive Policy
Figure 9: The graphs report the dynamics of the welfare gains from transparency as a function of the
observed periods of passive policy ( t ) under no price indexation (left graph) and under partial price indexation, ! = 0:5, (right graph). The other parameter values are set at the posterior mode.
longed passive policy. As discussed earlier, when the announcement is made, agents become
suddenly more pessimistic and, hence, being transparent may lower welfare compared to not
being transparent at the beginning of the policy.
However, transparency lowers pessimism as the passive policy is implemented because
agents expect fewer and fewer periods of passive policy ahead. Therefore, welfare generally
increases as the passive policy is implemented. In contrast welfare is downward sloping
under no transparency because the central bank does not communicate the duration of
passive policies; agents’pessimism gradually grows, progressively lowering welfare.
G
Lower Price Indexation
Figure 9 shows the welfare gains from transparency conditional on observing a given number
of periods of (short-lasting) passive policy. A quick comparison of these plots with Figure
58
4 shows that welfare gains from transparency are higher when price indexation is lower.
Interestingly, the pattern of these gains with respect to the observed duration of passive
policy is qualitatively very similar to that in the estimated model (Figure 4).
H
Imperfectly Credible Announcements
To solve the model in which the central bank’s announcements are only partially credible,
we rede…ne the structure of the three regimes (i.e., active, short-lasting passive, and longlasting passive) into a new set of 2regimes
A
; A
y
6
follows:
( t = i) ; y ( t = i) = 4
P
; Py
set of regimes
t
t
determining
3 the Taylor rule parameters as
, if i = 1 7
5 . The evolution of the rede…ned
, if i > 1
eA . To simplify the description of this
is governed by the transition matrix P
matrix, let us consider the case in which
= 4 and
59
= 7 (i.e., the truncation for the model
eA reads:
with no transparency). The transition matrix P
2
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
4
0
pa2
0 0
pa3
0 0 0
pa4
0
0
0
p11
0
0
0
pa1
0
0
0
0
0
0
0
0 0
0
0 0 0
0
1
0
0
0
1
0
0
0
0
0
0 0
0
0 0 0
0
0
0
0
0
0
1
0
0
0
0
0 0
0
0 0 0
0
0
0
0
1
(1)
0
0
(1)
0
0
0
0 0
0
0 0 0
0
0
0
0
1
(2)
0
(2)
0
0
0
0
0 0
0
0 0 0
0
0
0
0
0
0
0
0
1
0
0 0
0
0 0 0
0
0
0
0
(3)
0
0
0
0
0
0 0
0
0 0 0
0
0
0
0
0
0
0
0
0
0
0
1 0
0
0 0 0
0
0
0
0
0
0
0
0
0
0
0
0 1
0
0 0 0
0
0
0
0
0
0
0
0
0
0
0 0
0
0 0 0
0
(4)
0
0
0
0
0
0
0
0
0
0 0
0
1 0 0
0
0
0
0
0
0
0
0
0
0
0
0 0
0
0 1 0
0
0
0
0
0
0
0
0
0
0
0
0 0
0
0 0 1
0
0
0
0
pe56
0
0
0
0
0
0
0 0
0
0 0 0
0
0
0
pe67
0
0
0
0
0
0
0 0
0
0 0 0
0
0
pe56
pe78
0
0
0
0
0
0
0 0
0
0 0 0
0
0
0
pe88
0
0
0
0
0
0
0 0
0
0 0 0
0
0
0
0
1
(3)
1
1
1
1
1
(4)
0
pe67
0
0
3
p13 7
7
0 7
7
7
7
0 7
7
7
0 7
7
7
0 7
7
7
7
0 7
7
7
0 7
7
7
0 7
7
7
7
0 7
7
7
0 7
7
7
0 7
7
7
7
0 7
7
7
0 7
7
7
0 7
7
7
7
0 7
7
7
0 7
7
7
pe78 7
7
5
pe88
where we denote the probability (conditional on being in the active regime) of announcing
= i consecutive periods of passive monetary policy with pai . Note that this probability
a
is de…ned as paa =
a
+ f ( a ), where
i
denotes the probability that the duration of the
passive policy (conditional on being in the active regime) is shorter than i periods
a
p12 p22a 1 p21 , and
that is,
denotes the probability (conditional on being in the active regime)
that the central bank lies when making an announcement. This probability is de…ned as
60
follows:
prob ( > ) = p12
X
i=
i
a
where p12 is the probability of switching to the short-lasting passive regime conditional on
being in the active regime. f ( a ) is a monotonically increasing (deterministic) function
that determines the probability that the central bank announces
a
consecutive periods of
passive policy conditional on having lied ( > ). A monotonically increasing function f
captures the property that when the central bank lies, it is more likely that a a relatively
longer deviation from active policy is announced. Furthermore, the probability that the
announcement made turns out to be untrue after having observed the announced number of
deviations
a
is denoted by
( a ) = = (1
p12 ) f ( a ). Recall that probabilities p~ij are the
probabilities in the transition matrix in the case of no transparency.
Note that after
a
+ 1 periods the central bank’s lie is discovered and agents know that
the policy will stay passive until
passive policy after
a.
Moreover, for any period of the short-lasting
agents have to learn the persistence of the regime in place as they do
eA is a
in the no-transparency world. This is why the lower-right submatrix of the matrix P
the submatrix of the transition matrix P; which is the matrix that capture the evolution of
policy regimes under no transparency. Note that in the case of an untruthful announcement
agents start learning after having already observed + 1 periods of passive monetary policy.
So the learning based on counting the number of consecutive periods of passive policy starts
from
I
+1
that is, 5 periods in this example.
Limited Information
The upper graph of Figure 10 shows the welfare gains from transparency associated with
observing di¤erent durations of passive policies. The lower graph reports the ergodic probability of observing passive policies of di¤erent durations where zero duration means active
61
Welfare gains
from transparency
0.55
0.545
0.54
0
5
10
15
20
25
30
35
Ergodic Prob.
Observed Periods of Passive Policy
0.6
0.4
0.2
0
0
5
10
15
20
25
30
35
Observed Periods of Passive Policy
Figure 10: The upper graphs report the dynamics of the welfare gains from transparency as a function of
the observed periods of passive policy ( t ) when the central bank is assumed to have limited information.
The lower graph reports the ergodic probability of observing the periods of passive policy on the x-axis.
Parameter values are set at their posterior mode.
policy.21 The important result that emerges from this graph is that welfare gains from
transparency are always positive for policies of any plausible duration.
Computing the upper graph requires to transform the primitive regimes, pt 2 f1; 2; 3g ; into the set of
regimes used for the case of no transparency, which are de…ned in terms of the observed durations of passive
policies t . The details of this transformation are provided in Appendix E.
21
62
Working Paper Series
A series of research studies on regional economic issues relating to the Seventh Federal
Reserve District, and on financial and economic topics.
The Urban Density Premium across Establishments
R. Jason Faberman and Matthew Freedman
WP-13-01
Why Do Borrowers Make Mortgage Refinancing Mistakes?
Sumit Agarwal, Richard J. Rosen, and Vincent Yao
WP-13-02
Bank Panics, Government Guarantees, and the Long-Run Size of the Financial Sector:
Evidence from Free-Banking America
Benjamin Chabot and Charles C. Moul
WP-13-03
Fiscal Consequences of Paying Interest on Reserves
Marco Bassetto and Todd Messer
WP-13-04
Properties of the Vacancy Statistic in the Discrete Circle Covering Problem
Gadi Barlevy and H. N. Nagaraja
WP-13-05
Credit Crunches and Credit Allocation in a Model of Entrepreneurship
Marco Bassetto, Marco Cagetti, and Mariacristina De Nardi
WP-13-06
Financial Incentives and Educational Investment:
The Impact of Performance-Based Scholarships on Student Time Use
Lisa Barrow and Cecilia Elena Rouse
WP-13-07
The Global Welfare Impact of China: Trade Integration and Technological Change
Julian di Giovanni, Andrei A. Levchenko, and Jing Zhang
WP-13-08
Structural Change in an Open Economy
Timothy Uy, Kei-Mu Yi, and Jing Zhang
WP-13-09
The Global Labor Market Impact of Emerging Giants: a Quantitative Assessment
Andrei A. Levchenko and Jing Zhang
WP-13-10
Size-Dependent Regulations, Firm Size Distribution, and Reallocation
François Gourio and Nicolas Roys
WP-13-11
Modeling the Evolution of Expectations and Uncertainty in General Equilibrium
Francesco Bianchi and Leonardo Melosi
WP-13-12
Rushing into the American Dream? House Prices, the Timing of Homeownership,
and the Adjustment of Consumer Credit
Sumit Agarwal, Luojia Hu, and Xing Huang
WP-13-13
1
Working Paper Series (continued)
The Earned Income Tax Credit and Food Consumption Patterns
Leslie McGranahan and Diane W. Schanzenbach
WP-13-14
Agglomeration in the European automobile supplier industry
Thomas Klier and Dan McMillen
WP-13-15
Human Capital and Long-Run Labor Income Risk
Luca Benzoni and Olena Chyruk
WP-13-16
The Effects of the Saving and Banking Glut on the U.S. Economy
Alejandro Justiniano, Giorgio E. Primiceri, and Andrea Tambalotti
WP-13-17
A Portfolio-Balance Approach to the Nominal Term Structure
Thomas B. King
WP-13-18
Gross Migration, Housing and Urban Population Dynamics
Morris A. Davis, Jonas D.M. Fisher, and Marcelo Veracierto
WP-13-19
Very Simple Markov-Perfect Industry Dynamics
Jaap H. Abbring, Jeffrey R. Campbell, Jan Tilly, and Nan Yang
WP-13-20
Bubbles and Leverage: A Simple and Unified Approach
Robert Barsky and Theodore Bogusz
WP-13-21
The scarcity value of Treasury collateral:
Repo market effects of security-specific supply and demand factors
Stefania D'Amico, Roger Fan, and Yuriy Kitsul
Gambling for Dollars: Strategic Hedge Fund Manager Investment
Dan Bernhardt and Ed Nosal
Cash-in-the-Market Pricing in a Model with Money and
Over-the-Counter Financial Markets
Fabrizio Mattesini and Ed Nosal
WP-13-22
WP-13-23
WP-13-24
An Interview with Neil Wallace
David Altig and Ed Nosal
WP-13-25
Firm Dynamics and the Minimum Wage: A Putty-Clay Approach
Daniel Aaronson, Eric French, and Isaac Sorkin
WP-13-26
Policy Intervention in Debt Renegotiation:
Evidence from the Home Affordable Modification Program
Sumit Agarwal, Gene Amromin, Itzhak Ben-David, Souphala Chomsisengphet,
Tomasz Piskorski, and Amit Seru
WP-13-27
2
Working Paper Series (continued)
The Effects of the Massachusetts Health Reform on Financial Distress
Bhashkar Mazumder and Sarah Miller
WP-14-01
Can Intangible Capital Explain Cyclical Movements in the Labor Wedge?
François Gourio and Leena Rudanko
WP-14-02
Early Public Banks
William Roberds and François R. Velde
WP-14-03
Mandatory Disclosure and Financial Contagion
Fernando Alvarez and Gadi Barlevy
WP-14-04
The Stock of External Sovereign Debt: Can We Take the Data at ‘Face Value’?
Daniel A. Dias, Christine Richmond, and Mark L. J. Wright
WP-14-05
Interpreting the Pari Passu Clause in Sovereign Bond Contracts:
It’s All Hebrew (and Aramaic) to Me
Mark L. J. Wright
WP-14-06
AIG in Hindsight
Robert McDonald and Anna Paulson
WP-14-07
On the Structural Interpretation of the Smets-Wouters “Risk Premium” Shock
Jonas D.M. Fisher
WP-14-08
Human Capital Risk, Contract Enforcement, and the Macroeconomy
Tom Krebs, Moritz Kuhn, and Mark L. J. Wright
WP-14-09
Adverse Selection, Risk Sharing and Business Cycles
Marcelo Veracierto
WP-14-10
Core and ‘Crust’: Consumer Prices and the Term Structure of Interest Rates
Andrea Ajello, Luca Benzoni, and Olena Chyruk
WP-14-11
The Evolution of Comparative Advantage: Measurement and Implications
Andrei A. Levchenko and Jing Zhang
WP-14-12
Saving Europe?: The Unpleasant Arithmetic of Fiscal Austerity in Integrated Economies
Enrique G. Mendoza, Linda L. Tesar, and Jing Zhang
WP-14-13
Liquidity Traps and Monetary Policy: Managing a Credit Crunch
Francisco Buera and Juan Pablo Nicolini
WP-14-14
Quantitative Easing in Joseph’s Egypt with Keynesian Producers
Jeffrey R. Campbell
WP-14-15
3
Working Paper Series (continued)
Constrained Discretion and Central Bank Transparency
Francesco Bianchi and Leonardo Melosi
WP-14-16
Escaping the Great Recession
Francesco Bianchi and Leonardo Melosi
WP-14-17
More on Middlemen: Equilibrium Entry and Efficiency in Intermediated Markets
Ed Nosal, Yuet-Yee Wong, and Randall Wright
WP-14-18
Preventing Bank Runs
David Andolfatto, Ed Nosal, and Bruno Sultanum
WP-14-19
The Impact of Chicago’s Small High School Initiative
Lisa Barrow, Diane Whitmore Schanzenbach, and Amy Claessens
WP-14-20
Credit Supply and the Housing Boom
Alejandro Justiniano, Giorgio E. Primiceri, and Andrea Tambalotti
WP-14-21
The Effect of Vehicle Fuel Economy Standards on Technology Adoption
Thomas Klier and Joshua Linn
WP-14-22
What Drives Bank Funding Spreads?
Thomas B. King and Kurt F. Lewis
WP-14-23
Inflation Uncertainty and Disagreement in Bond Risk Premia
Stefania D’Amico and Athanasios Orphanides
WP-14-24
Access to Refinancing and Mortgage Interest Rates:
HARPing on the Importance of Competition
Gene Amromin and Caitlin Kearns
WP-14-25
Private Takings
Alessandro Marchesiani and Ed Nosal
WP-14-26
Momentum Trading, Return Chasing, and Predictable Crashes
Benjamin Chabot, Eric Ghysels, and Ravi Jagannathan
WP-14-27
Early Life Environment and Racial Inequality in Education and Earnings
in the United States
Kenneth Y. Chay, Jonathan Guryan, and Bhashkar Mazumder
WP-14-28
Poor (Wo)man’s Bootstrap
Bo E. Honoré and Luojia Hu
WP-15-01
Revisiting the Role of Home Production in Life-Cycle Labor Supply
R. Jason Faberman
WP-15-02
4
Working Paper Series (continued)
Risk Management for Monetary Policy Near the Zero Lower Bound
Charles Evans, Jonas Fisher, François Gourio, and Spencer Krane
Estimating the Intergenerational Elasticity and Rank Association in the US:
Overcoming the Current Limitations of Tax Data
Bhashkar Mazumder
WP-15-03
WP-15-04
External and Public Debt Crises
Cristina Arellano, Andrew Atkeson, and Mark Wright
WP-15-05
The Value and Risk of Human Capital
Luca Benzoni and Olena Chyruk
WP-15-06
Simpler Bootstrap Estimation of the Asymptotic Variance of U-statistic Based Estimators
Bo E. Honoré and Luojia Hu
WP-15-07
Bad Investments and Missed Opportunities?
Postwar Capital Flows to Asia and Latin America
Lee E. Ohanian, Paulina Restrepo-Echavarria, and Mark L. J. Wright
WP-15-08
Backtesting Systemic Risk Measures During Historical Bank Runs
Christian Brownlees, Ben Chabot, Eric Ghysels, and Christopher Kurz
WP-15-09
What Does Anticipated Monetary Policy Do?
Stefania D’Amico and Thomas B. King
WP-15-10
Firm Entry and Macroeconomic Dynamics: A State-level Analysis
François Gourio, Todd Messer, and Michael Siemer
WP-16-01
Measuring Interest Rate Risk in the Life Insurance Sector: the U.S. and the U.K.
Daniel Hartley, Anna Paulson, and Richard J. Rosen
WP-16-02
Allocating Effort and Talent in Professional Labor Markets
Gadi Barlevy and Derek Neal
WP-16-03
The Life Insurance Industry and Systemic Risk: A Bond Market Perspective
Anna Paulson and Richard Rosen
WP-16-04
Forecasting Economic Activity with Mixed Frequency Bayesian VARs
Scott A. Brave, R. Andrew Butters, and Alejandro Justiniano
WP-16-05
Optimal Monetary Policy in an Open Emerging Market Economy
Tara Iyer
WP-16-06
Forward Guidance and Macroeconomic Outcomes Since the Financial Crisis
Jeffrey R. Campbell, Jonas D. M. Fisher, Alejandro Justiniano, and Leonardo Melosi
WP-16-07
5
Working Paper Series (continued)
Insurance in Human Capital Models with Limited Enforcement
Tom Krebs, Moritz Kuhn, and Mark Wright
WP-16-08
Accounting for Central Neighborhood Change, 1980-2010
Nathaniel Baum-Snow and Daniel Hartley
WP-16-09
The Effect of the Patient Protection and Affordable Care Act Medicaid Expansions
on Financial Wellbeing
Luojia Hu, Robert Kaestner, Bhashkar Mazumder, Sarah Miller, and Ashley Wong
WP-16-10
The Interplay Between Financial Conditions and Monetary Policy Shock
Marco Bassetto, Luca Benzoni, and Trevor Serrao
WP-16-11
Tax Credits and the Debt Position of US Households
Leslie McGranahan
WP-16-12
The Global Diffusion of Ideas
Francisco J. Buera and Ezra Oberfield
WP-16-13
Signaling Effects of Monetary Policy
Leonardo Melosi
WP-16-14
Constrained Discretion and Central Bank Transparency
Francesco Bianchi and Leonardo Melosi
WP-16-15
6
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