Stabilizing Expectations at the Zero Lower Bound:
Experimental Evidence
Jasmina Arifovic∗
Luba Petersen†
October 2015
Abstract
Can monetary or fiscal policy stabilize expectations during a deflationary episode? We
study expectation formation near the zero lower bound using a learning-to-forecast
laboratory experiment. Monetary policy targets inflation around a constant or statedependent target. Subjects’ expectations significantly over-react to stochastic aggregate demand shocks and historical information leading many economies to experience
severe deflationary traps. Neither quantitative nor qualitative communication of statedependent inflation targets reduce the duration or severity of economic crises. A stronger
initial recovery of fundamentals or supplementary anticipated fiscal stimulus stabilizes
expectations and increases the speed of macroeconomic recovery.
JEL classifications: C92, E2, E52, D50, D91
Keywords: monetary policy, expectations, zero lower bound, learning to forecast, communication, laboratory experiment
∗
Department of Economics, Simon Fraser University, e-mail: arifovic@sfu.ca
Department of Economics, Simon Fraser University, e-mail: lubap@sfu.ca. This paper has benefited from
insightful discussions with Klaus Adam, Jess Benhabib, Camille Cornand, and Frank Heinemann. We also
thank seminar participants at TU-Berlin/Humboldt University, the June 2014 CEF Meetings in Oslo, the 2014
North American Economic Science Association Meetings, Workshop on Experiments in Monetary Policy at
the University of Lyon - GATE in November 2014, Monash University, the 2015 ASSA Meetings in Boston,
the 2015 Barcelona GSE Summer Forum on Central Bank Design and the 2015 Expectations in Dynamic
Macroeconomics Models Conference in Oregon for useful comments. Finally we would like to thank Andriy
Baranskyy for excellent research assistance and the Social Science and Humanities Research Council of Canada
for generous financial support.
†
1
Introduction
How should monetary and fiscal policy be conducted when nominal interest rates are close
to zero? This question is important as, once interest rates reach zero and cannot be reduced
further (often referred to as the zero lower bound (ZLB)), central banks lose an important tool
for stimulating the economy. A negative demand shock could turn the situation dire because,
close to the ZLB, a central bank may not be able to lower interest rates sufficiently to stimulate
the economy during a recession. If the recession is persistent and severe, households and firms
may rationally form pessimistic expectations that the central bank will be unable to provide
sufficient stimulus. The existence of the ZLB has the potential to generate prolonged selffulfilling macroeconomic crisis often referred to as a liquidity trap.
Macroeconomists and policy makers generally agree that policies that create inflationary
expectations would alleviate the severity and duration of liquidity traps. For example, Eggertsson and Woodford (2003, 2004) show that creating inflationary expectations by promising
to keep nominal interest rates low through increased inflation targets even after the economy
has recovered can reduce the length of a liquidity trap. To reinforce the central bank’s commitment to higher future inflation, the state-dependent inflation target would be adjusted upward
when inflation fails to achieve past targets. Such a policy has the potential to successfully alleviate recessions if agents form rational expectations and the central bank can credibly commit
to a long-run price level target. If agents instead form adaptive expectations, accommodative
monetary policy must be combined with significant fiscal stimulus to stimulate expectations
and economic activity at the zero lower bound (e.g. Evans et al. 2008).
The goal of this paper is to identify how alternative policies influence individual and aggregate expectation formation at the zero lower bound. This is an empirically challenging
task as the policies and communication strategies we are interested in studying have not
been implemented by central banks. Moreover, even if such policies were explicitly implemented, it would be difficult to disentangle their actual effects on the economy from other
past and concurrent policy. To circumvent the limitation in existing data, we design a series
of learning-to-forecast laboratory experiments to gain insight into the relative effectiveness of
state-dependent inflation targeting and expansionary fiscal policy in stimulating expectations
at the ZLB. The laboratory provides a convenient testbed to explore the robustness of policy
and central bank communication on real people’s expectations in an environment where we
can have precise control over the structure of the economy, information sets of individuals, and
the implementation and communication of policy. Such control enables a clear identification
of the effects of economic disturbances, policies, and communication strategies on individual
2
and aggregate expectations and the overall economy.
Our experimental macroeconomy follows a linearized New Keynesian data-generating process whereby output and inflation evolve in response to aggregate expectations and exogenous
observed disturbances. We impose large and persistent unanticipated negative demand shocks
to drive the economy down to the ZLB in order to study the expectation formation process
and experiment with alternative stabilization strategies. In our baseline treatment, the automated central bank follows a conventional Taylor rule with a constant inflation target. We
observe that expectations become pessimistic on impact of the large negative demand shock,
resulting in persistent recessions at the ZLB. In some cases, expectations continue to spiral
downward despite fundamentals returning to their steady state values.
In two additional treatments, we implement a state-dependent inflation target that rises
when past inflation levels are below target. The inflation target is communicated either
quantitatively as a numerical target or qualitatively in the form of a direction (e.g. ”positive”
vs. ”negative”). This distinction between quantitative versus qualitative forward guidance
is motivated by the fact that central bank forward guidance has been fluctuating between
qualitative and quantitative announcements since 2008, and has become progressively less
effective at influencing market expectations (Filardo and Hofmann, 2014). Compared to a
constant inflation target, we find that neither form of communication of state-dependent
inflation targets leads to a significant reduction in the severity or duration of liquidity traps.
Less is more when it comes to central bank communication of a state-dependent inflation
target. In the state-dependent inflation targeting treatments, we find that qualitative communication improves economic stability compared to explicit communication of a numerical
target. There are at least a couple of reasons why qualitative targets are more effective coordination devices. First, it may be easier for individuals and markets to coordinate on the
inflation guidance that is unchanging during the liquidity trap. Second, under a qualitative
target, the public simply observes an announcement that the central bank aims to achieve
positive inflation. By contrast, under an explicitly communicated target in an ever-worsening
recession, the public is continually reminded by the rising target that the economy is not
achieving the central bank’s goal of higher inflation. This additional information generates
increased pessimism and reduces the perceived credibility of the central bank, leading to a
more severe and prolonged recession.
Finally, our work contributes to the discussion of the role of fiscal policy at the zero lower
bound. We extend our baseline treatment with constant inflation targeting to study whether
announced expansionary fiscal policy can stabilize deflationary spirals. The expansionary
policy is implemented on impact of the negative demand shock and remains in place until
3
fundamentals return to the steady state. We find that expectations become highly focused
on the aggregate shock and recovery of fundamentals. Recessions are less severe and their
recoveries are significantly faster when the constant inflation target is supplemented with
fiscal stimulus. Announced fiscal policy works better than state-dependent inflation targets
to coordinate expectations because its actual effect on the economy occurs with certainty.
2
Policy and Communication: Theory and Evidence
This paper investigates whether monetary and fiscal policy can stabilize expectations at the
zero lower bound. Recent work has suggested that even when the zero lower bound on interest
rates binds, central banks are still able to influence the economy through the expectations
of future policy.1 Inflation targeting policies can reduce crises at the zero lower bound if
accompanied with a credible promise of future inflation. Eggertsson and Woodford (2003)
show that an optimal commitment policy would involve a moving price-level target that would
increase in response to historical inability to achieve its target. Because of the state-dependent
nature of the target, interest rates would remain at zero even as the economy improves. This
in turn should signal to agents that the central bank is willing to accept higher inflation in the
future, generating rational inflationary expectations. However, the authors acknowledge that
credibility might suffer if the private sector observes the central bank continually failing to
reach its target yet keeps raising it for the next period. Nakov (2008) applies global solution
methods to study a standard dynamic stochastic sticky-price model with an occasionally
binding zero lower bound on interest rates. He compares alternative non-optimal instrumental
rules to optimal policy under commitment and discretion and finds that price-level targeting
as in Eggertsson and Woodford’s framework performs better than other simple Taylor rules.2
An important contribution of our paper is to provide insight into how expectations respond
and evolve in response to moving inflation targets.
Much theoretical work has demonstrated that expansionary fiscal policy can stabilize expectations at the zero lower bound. When the monetary authority lacks credibility in generating inflation, Krugman (1998) and Eggertsson (2011) argue that fiscal expenditures are the
only way out of a liquidity trap. Fiscal stimulus does not suffer from commitment problems to
the same extent as expansionary monetary policy. Evans et al. (2008) demonstrate that learn1
See Walsh (2009) for a detailed discussion on the ability of inflation promises to stabilize expectations.
These state-dependent rules are also consistent with the policy advice given (though not taken) to Japan
when it faced its zero lower bound. e.g. Krugman (1998), McCallum (2000), Auerbach and Obstfeld (2005).
Price–level targeting policies achieve relatively greater economic stability than inflation targeting policies in
environments where central bank’s mistake private agents’ expectations as rational (e.g. Preston (2008)).
2
4
ing agents’ adaptive expectations can be stabilized with fiscally-generated aggregate demand.
In related work, Benhabib et al. (2014) show that with adaptive agents, a fiscal switching rule
that automatically triggers fiscal stimulus when inflation or expectation inflation falls below
a threshold can be effective in stabilizing expectations and aggregate activity.
The public’s understanding of the central bank’s objectives and policy rules in the future
is a critical component of the effectiveness of monetary policy (Woodford, 2005; Eusepi and
Preston, 2010). If agents form rational expectations, they should correctly infer the policy
rule that the central bank is following and adjust their spending and pricing decisions accordingly. However, if agents have to adapt or learn, or if they possess imperfect information or
understanding, a need for central bank communication arises.
But do central banks actually communicate effectively? The empirical evidence is mixed.
In some cases, central bank announcements about their policy objectives have created more
stability in financial markets and private sector forecasts in countries that pursue inflationtargeting policies (Connolly and Kohler, 2004; Fujiwara, 2005; Swanson, 2006). Other empirical work finds that announcements generate significant and undesirable volatility in U.S.
asset prices (Kohn and Sack, 2004; Ehrmann and Fratzscher, 2007). Importantly, communication may not be very effective once the central bank’s pre-existing policies are controlled for.
Gürkaynak et al. (2006) show that long-term inflation expectations derived from index-linked
bonds are significantly less responsive to central bank announcements in inflation-targeting
countries like Sweden and the U.K. than they are in the U.S., which has no explicit inflation
objective. Indeed, Siklos (2002), Johnson (2002) and Corbo et al. (2002) find in a series of
cross-country studies that the adoption of inflation targeting has led to lower forecast errors,
suggesting greater macroeconomic stability without the need for communication.
Central banks face risks when they communicate to the public. As Woodford (2005) points
out, communication of a central bank goal may be misperceived by the public as a promise.
If a central bank fails to live up to its stated goals or promises, it will lose credibility and the
public will stop conditioning their forecasts and behaviour on the announced goals. This is
why many central banks, including the Federal Reserve, have historically communicated very
little to the public.3
The success of central bank communication of monetary policy depends crucially on how
it is perceived and understood by the public, and the type of expectations the public forms.
3
For example, in December 2012, the Federal Reserve made an unusual announcement that it would keep
interest rates low at least as long as the unemployment rate remains below 6.5 percent, the outlook for
inflation one-to-two years ahead remains at or below 2.5%, and longer-term inflation expectations remain well
anchored. This forward guidance was intended to create long-run inflation expectations within an economy
that is perceived to be stuck in a liquidity trap.
5
Surveys of households and professional forecasters are widely used sources of direct evidence
on expectation formation. Mankiw et al. (2003) and Coibion and Gorodnichenko (2012) discuss recent studies of expectations from surveys of professional forecasters. While survey data
provides important insights into naturally-occurring expectations, they have limited ability
to identify agents’ information sets and the economy’s true underlying data generating process. This identification will certainly have an impact on the types of communication (e.g.
macroeconomic targets, forecasted paths of future interest rates, central bank outlooks) and
the formulation of monetary policies a central bank would find optimal to pursue. Laboratory
experiments serve as a useful complementary tool to understand expectation formation and
have the advantage of allowing for more precise control of conditions under which subjects
form their expectations. Moreover, experiments provide the opportunity to study policies for
which there is little data or may not have been previously implemented.4
Below we discuss three learning-to-forecast (LTF) experiments that are most closely related to ours. The experiment presented in this paper directly builds off of Kryvtsov and
Petersen (2015) who investigate the robustness of the expectations channel of monetary policy. The key difference in their setup is the absence of a zero lower bound on nominal interest
rates. They observe a significant but relatively weak expectations channel that is strengthened
with more aggressive monetary policy. Central bank forward guidance in the form of a multiperiod forecast of future nominal interest rates initially effective at coordinating expectations
and strengthens the expectations channel, but over time subjects stop conditioning on the
information and expectations become more volatile. Importantly, expectations are fundamentally stable and oscillate around the steady state. By contrast, our experiment shows that the
introduction of a zero lower bound and a large negative shock to the natural rate of interest
can generate significant deflationary spirals if fundamentals recover too slowly.
Using a similar LTF experimental design, Cornand and M’Baye (2014) observe that communicating an explicit inflation target is not essential for maintaining economic stability when
the central bank has a strict inflation target. However, if the central bank has a dual mandate to stabilize inflation and output, communicating to private agents the central bank’s
inflation target leads to significant improvements in stability and convergence to the target.
In our experiments, the central bank also faces a dual mandate that, in some treatments,
4
The use of laboratory experiments to study expectations and policy have been well established. e.g.
Arifovic and Sargent, 2003; Arifovic et al. 2013, b, Arifovic et al, 2014; Duffy, 2008, 2012; Adam, 2007;
Hommes et al, 2008; Pfajfar and Žakelj, 2014; Hommes, 2011, 2013 reviews the literature on the evidence
of heterogenous expectations hypothesis in the experimental economies; Chakravarty et al., 2011, review
the growing literature on experimental macroeconomics; Cornand and Heinemann (2014) for a survey of
experiments on monetary policy, and Amano et al. (2014) for a discussion of how the Bank of Canada is using
laboratory experiments to study expectations and monetary policy.)
6
involves a moving inflation target. In contrast to Cornand and M’Baye, we find that explicit
communication does not improve stability, and with learning, contributes to worse liquidity
traps.
Hommes et al. (2015) study behaviour in a non-linear New Keynesian experimental economy with a zero lower bound. They implement expectational shocks to study the dynamics at
the zero lower bound and compare the performance of an aggressive monetary policy versus a
combination of the aggressive monetary policy and fiscal stimulus. Their preliminary findings
indicate that monetary policy alone cannot take experimental economies out of the liquidity trap. Consistent with our results, they observe that additional fiscal stimulus alleviates
deflationary spirals and encourages convergence toward the high inflation steady state.
3
Experimental Design and Implementation
We designed a laboratory experiment to study expectation formation in the presence of the
zero lower bound under alternative monetary and fiscal policies. The experiments were conducted at the CRABE Lab at Simon Fraser University where the subject pool consisted of
undergraduate students recruited from a wide variety of disciplines. In each session, groups
of nine inexperienced subjects played the role of professional forecasters and were tasked with
submitting incentivized forecasts about the future state of the economy. The experimental economy that subjects interacted in followed a data-generating process derived from a
linearized version of the New Keynesian framework with optimizing households and firms.5
Specifically, the economy evolved according to the following system of equations:
xt = Et∗ xt+1 − σ −1 (it − i∗ − Et∗ πt+1 − rtn ) ,
(1)
πt = βEt∗ πt+1 + κxt ,
(2)
5
Specifically, the model assumes agents have identical information and initial starting wealth, and form
expectations rationally. The homogeneous rational expectations version of the New Keynesian model we implemented would not be correct if subjects’ expectations were not rational. Instead, heterogeneous expectations
versions of the model (see Preston (2008) and Woodford (2013) for examples) would be more appropriate.
However, versions of the model that employ heterogeneous expectations involve making an ex-ante decision
about the form of heterogeneity in expectations or require a much more complicated generalized reduced form
model that would be considerably more difficult for subjects to digest in a relatively short amount of time and
increase the likelihood that subjects’ behaviour is driven by confusion. In making our decision to implement
the homogeneous rational expectations version of the New Keynesian model, we opted to trade off model
precision for increased simplicity.
7

i∗ + φ (π − π ∗ ) + φ x
π
t
x t
t
it =
0,
if it ≥ 0
(3)
otherwise,
n
rtn = ρrt−1
+ t .
(4)
Equation 1 refers to the investment-saving equation and describes the dynamics of aggregate demand relative to its flexible-price level or the output gap.6 As aggregate expectations
of future demand (Et∗ xt+1 ) and inflation (Et∗ πt+1 ) increase, current demand and output also
increase. Exogenous increases in the natural rate of interest, rtn , has a positive effect on demand. Increases in the nominal interest rate, it , from its steady state value, i∗ will contract
demand and vice versa. We parameterize σ = 1 and i∗ = 75 basis points.
Equation 2 describes the evolution of aggregate supply or inflation. Inflation depends
primarily on aggregate expectations of future inflation (Et∗ πt+1 ) and, to a lesser extent, on
aggregate demand, xt . The parameters are assigned values of β = 0.995 and κ = 0.13.
Equation 3 is the central bank’s response function and describes how nominal interest
rates are set. The central bank aggressively responds to positive deviations of inflation from
its steady state, πt − πt∗ , and positive output gaps by adjusting nominal interest rates upward,
and vice versa. We parameterize the coefficients of the nominal interest rate rule as φπ = 1.5
and φx = 0.5. The monetary transmission operates by influencing the real interest rate
through movements in the nominal interest rate. Monetary policy would generally be able to
stabilize real output at its potential level for any fluctuation in rtn so long as it can adjust the
policy rate such that it − Et πt+1 − rtn can be stabilized to zero. However, in this environment,
the presence of a zero lower bound on nominal interest rates prevents the central bank from
lowering the nominal interest rate sufficiently in response to very low inflation and output.
Finally, Equation 4 describes the evolution of the natural rate of interest or, as we will refer
to it throughout the paper, the demand shock. The shock follows an AR(1) process where
ρ = 0.8, and t is drawn randomly from a normal distribution with mean zero and standard
deviation of 93 basis points. Equations 1-4 yield a steady state of x∗ = π ∗ = 0 and i∗ = 75.
Subjects were tasked with repeatedly submitting quarterly forecasts for future inflation
and output. At the beginning of each session, subjects participated in a 35 minute instruction
phase and a 10 minute practice phase. During the instructions we first explained the data
generating process qualitatively. We then provided subjects with a quantitative description
of the model and explained in careful detail the shock process and monetary policy rule. We
6
Throughout the paper, we refer to the output gap as simply “output” .
8
walked subjects through the software they would interact with in four practice periods to
familiarize them with the interface and provided them with an opportunity to ask questions.
The computer interface was highly visual. Subjects learned their forecast accuracy by observing changes in their points between rounds and by comparing visually (and by mousing over)
the distance between their forecast and the realized values. Instructions and screenshots of
the computer interface can be found in the Online Appendix. During the experiment subjects
were not allowed to communicate with one another and once play began were only allowed to
ask questions privately to the experimenter.
Subjects had access to the following information before submitting their forecast of next
period’s inflation and output. They observed all historical information up to and including
the previous period’s realized inflation, output, and nominal interest rate, as well as their
forecasts and their implied accuracy. Subjects also observed the current period’s shock and any
relevant policies or targets. After the instructions and practice phases were complete, subjects
submitted incentivized forecasts for an additional 75 minutes. Subjects had 80 seconds in the
first 10 rounds and 65 seconds thereafter to submit forecasts. Forecasts were submitted in
basis point measurements (i.e. 1% was inputed as 100 basis points) and could be positive or
negative. After all subjects submitted their forecasts or time ran out, the median submitted
forecasts for inflation and output were used as the aggregate forecast in the calculation of the
current period’s realized output, inflation and nominal interest rate.7
Subjects’ scores, and subsequently their earnings in the game, depended on the accuracy
of their forecasts each period:
Scorei,t = 0.3(e−0.01|Ei,t−1 πt −πt | + e−0.01|Et−1 xi,t −xt | ) ,
(5)
where Ei,t−1 πt − πt and Ei,t−1 xt − xt were subject i’s forecast errors associated with forecasts
submitted in period t − 1 for period t variables. The scoring rule incentivized subjects to
form accurate forecasts.8 This scoring rule was very similar to that used in the previous
7
Median, rather than average, forecasts were employed to minimize the ability a single subject could have
in manipulating aggregate expectations. This design decision is particularly useful when studying aggregate
behavior with a limited number of participants.
8
The underlying data-generating process assumes that households and firms form expectations in an effort
to maximize their expected discounted utility and profits, respectively. We deviated from this assumptions of
the New Keynesian model and instead incentivize subjects based on the accuracy of their forecasts. Consistent
with other learning-to-forecast experiments, our goal was to focus on how individuals form beliefs about the
economy. In order for subjects to take the task of forecasting seriously and for their decisions to be valuable
to us, it is important to reward subjects based on the appropriate task (see Smith (1974) for a discussion of
induced value theory). At the same time, we acknowledge the importance of studying expectation formation
when subjects’ forecasts play a critical role in influencing their consumption, labor and pricing decisions. We
leave that for future research.
9
experimental literature in that scores decrease monotonically with the forecast errors and the
minimum score a subject can earn in any period is zero.9 Subjects’ earnings, including a $7
show up fee, ranged from $20 to $38.50, and averaged $26 for two hours of participation.
Every session consisted of two repetitions of 40 periods each. To reinforce the steady
state values, we initialized each sequence at the steady state and showed five pre-sequence
periods where the economy was in the steady state. That is, output, inflation, and the shock
were initialized at zero while the nominal interest rate was initialized at 75 basis points. We
conducted two different repetitions on the same group of subjects to observe the effects of
additional learning on their forecasting behaviour.
The experiment focused on the ability of monetary and fiscal policy to alleviate the duration and magnitude of recessions at the ZLB. As such, we implemented economies that
would experience and remain at the ZLB for some number of periods. To generate such an
environment, we imposed a negative natural rate of interest shock of -400 basis points (±2
basis points) in periods 20 and 15 of the first and second repetitions, respectively. We chose
to shock the economies in different periods so that subjects would not anticipate the shock
in the second repetition. We selected approximately the same size shock (between -398 and
-402) in both repetitions to make consistent comparisons.10
In order to control for variability of draws across treatments, we preselected a set of six
shock sequences per repetition and implemented the same set in all treatments. We simulated
six hundred randomly generated shock sequences simulated using Equation 4, and we employed
social evolutionary learning, SEL (Arifovic et al., 2013a), to explore behavioural responses at
the ZLB and to select shock sequences that met the following criteria: 1) The economies did
not reach the zero lower bound prior to us imposing the liquidity trap shock, 2) the rtn shock
remained negative for 3-8 periods, and 3) the economies rebounded in the later periods with
few if any returns to the zero lower bound. 11 We explicitly communicated to subjects that
9
In the scoring rules used by Assenza et al. (2013) and Pfajfar and Žakelj (2014), forecasts are no longer
incentivized after a certain threshold. Under our rule, the per-period score reduces by 50% for every 100 basis
point forecast error for both inflation and output, continually incentivizing subjects to make the most accurate
forecasts possible.
10
Consistent with the theoretical literature, we study linear approximations to agents’ optimal decisions.
This implies that the only nonlinearity we consider is the one imposed by the zero lower bound. While
we may face poor approximations of inflation and output in response to large shocks, the simplicity of the
environment allows us to economize on the dimension of the state space, and avoid having to parametrize
higher order terms of the nonlinear model (for further discussion, see Adam and Billi, 2007). Moreover, the
linearized data generating process is considerably easier for subjects to understand. We chose the shock of
this magnitude in order to ensure that experimental economies reached and remained at the zero lower bound
for varied amounts of time.
11
For robustness, in one sequence per treatment (Sequence 1 - Repetition 2) we set the crisis shock to -600
basis points.
10
the randomly drawn shock sequences were preselected for experimental control.
Treatments and Predictions
We conducted a total of four treatments. Our baseline treatment, Constant Target (Constant),
involved the central bank responding to deviations of inflation from a constant inflation target.
Our second treatment, State-Dependent Target (SD), had the central bank respond to deviations from an explicitly communicated quantitative state-dependent inflation target. In the
third, Directional State Dependent Target (Dir. SD) treatment, we kept the state-dependent
inflation targeting rule, but communicated to the subjects only the direction of the movement
of the target. Finally, in our fourth,Fiscal Policy (FP) treatment, we added a pre-announced
expansionary fiscal policy to our baseline constant-inflation targeting environment. In all
treatments, the nominal interest rate generally took the form given in Equation 3.
Baseline Treatment
In our baseline treatment, an inflation target was set to a constant value, πt∗ = 0. In this Constant Target (Constant) treatment, we conveyed to subjects that the central bank’s objective
was to keep inflation and output as close to zero as possible.
Monetary Policy Treatments
In our state-dependent target treatments, the inflation target evolved based on past realized
inflation and output. The time-varying inflation non-optimal target is motivated in part by the
optimal history-dependent price-level target developed in Eggertsson and Woodford (2003).12
The inflation target we employed was computed as follows:
∗
πt+1
=
λ
1 ∗
λσ
(πt − πt ) −
(xt − xt−1 ) −
xt
β
κβ
β
(6)
The state-dependent inflation targeting rule consisted of an inflation component and an
output gap component. During a severe recession, the central bank may find it difficult to
meet higher inflation targets due to the zero lower bound on nominal interest rates. In such
cases, the first term of this rule implies that the central bank will increase its inflation target
for the subsequent period.
12
We chose to implement an inflation target rather than a price-level target to avoid introducing an additional
variable that subjects would have to consider when forming their forecasts. We rederived the optimal pricelevel target in Eggertsson and Woodford (2003) as an inflation target and implemented an approximation of
it in our ad-hoc Taylor rule. The derivation can be found in the Online Appendix.
11
When the economy exits the deflationary episode (either due to more optimistic expectations or improving fundamentals), the inflation target does not immediately return to zero.
Instead, the central bank gradually decreases the inflation target to allow for higher inflation
and output. The central bank accomplishes this by keeping nominal interest rates at zero
even after the economy has returned to the steady state. This feature can be observed in the
second term of the inflation targeting rule. The state dependent inflation target implies that
a credible central bank will accept higher future inflation, leading rational forecasters to form
inflationary expectations.
Simulations of the rational expectations equilibrium solution under constant and statedependent inflation targets are presented in Figures 1 and 2. These simulations were conducted using OccBin developed by Guerrieri and Iacoviello (2015). OccBin solves dynamics
models with occasionally binding constraints by solving for the piece-wise linear non-explosive
solution. The simulations presented show the linear solution that ignores the zero lower bound
as a red dashed line. The solid blue line is the piece-wise linear solution that accounts for the
zero lower bound that is present in our experiments. The simulated dynamics are the impulse
responses to a one-time negative natural rate of interest shock of 400 basis points that occurs
in period 5. Note that if the economies were to experience positive shocks, the piecewise linear
and the linear impulse responses would coincide.
The simulations indicate that economic recovery is considerably faster and the severity of
the crisis significantly lower under a state-dependent inflation target. When the central bank
implements a state dependent inflation target in the presence of a zero lower bound, output and
inflation are nearly three and five times less reactive, respectively, on impact of the negative
demand shock. Moreover, output and inflation return to and exceed their steady state levels
by periods 10 and 8 under a state dependent inflation target, while converge asymptotically
to the steady state under a constant inflation target. If our subjects behave in line with the
rational expectations equilibrium solution - that is, utilizing only fundamental shocks and
inflation targets to formulate their forecasts - we should expect to observe significantly faster
recoveries and less severe recessions in the State-Dependent Target treatment. We formulate
two hypotheses based on these treatments:
Hypothesis 1: Following a severe crisis shock, economies following a state-dependent inflation
target will return to the steady state in fewer periods than those following a constant inflation
target.
Hypothesis 2: Following a severe crisis shock, economies following a state-dependent inflation
12
target will exhibit lower standard deviations of inflation and output than those following a
constant inflation target.
The key assumption that underlines the success of state-dependent inflation targeting
rules is that agents form rational expectations. However, we know from previous learningto-forecast experiments that, initially, subjects do not form rational expectations forecasts.13
The question is whether they learn to form these expectations over time. If they do, and do
so fast enough, the inflation targeting policies can be successful in mitigating the impact of a
severe demand shocks. However, if subjects do not learn to coordinate their expectations on
fundamentals fast enough, these policies might prove ineffective in guiding economies out of
liquidity traps.
In our State-Dependent Target treatment, the central bank provided subjects a precise inflation target to coordinate their expectations on. Rational agents who use the central bank’s
inflation target will be able to respond to the explicitly communicated forward guidance. However, if agents fail to coordinate on the target and fundamentals, the target will continually
rise and subjects may come to perceive the quantitative target as irrelevant. By communicating the target qualitatively in the form of a direction, subjects may better understand the
central bank’s intentions and more easily coordinate in the central bank’s intended direction.
The possibility of perceived lack of central bank credibility provided the motivation to
conduct a third treatment in which the central bank communicates a qualitative inflation
target. In the Directional State Dependent Target (Dir. SD) treatment, the central bank set
monetary policy to stabilize inflation around a state-dependent inflation target (as in the SD
treatment), but only communicated to subjects the direction of the target. The direction was
presented as either “positive” or “negative.” As such, we removed the time-series graph of the
target.14 Ex-ante, we had no clear prior on how expectations would respond to a qualitativelycommunicated target. If subjects formed expectations according to fundamentals, vaguely
communicated targets would hinder coordination and economic recovery. If, on the other
hand, subjects were reluctant to employ the explicit target in their forecast or believed the
central bank to be non-credible, qualitative targeting may better coordinate expectations.
Thus, we form a set of conditional hypotheses:
13
Heuristics such as naive, trend-chasing, and constant gain learning have been observed by Pfajfar and
Žakelj (2014), Assenza et al. (2013), and Petersen (2014).
14
Our communication variation is similar to Cornand and M’Baye (2014) who vary whether the inflation
target is explicitly communicated in the form of constant numerical target or implicitly by communicating
the central bank’s objective to stabilize inflation. By contrast, our target fluctuates and we communicate the
direction of that fluctuation.
13
Hypothesis 3: Following a severe crisis shock, the communication of a state-dependent inflation
target does not influence the number of periods it takes for economies to return to the steady
state.
Hypothesis 4: Following a severe crisis shock, the communication of a state-dependent inflation target does not influence the standard deviation of output and inflation.
Fiscal Policy Treatment
We next consider whether economic crises can be effectively ameliorated by anticipated expansionary fiscal policy. As discussed in our review of the literature, much theoretical work has
demonstrated that anticipated effective government spending should create more optimistic
expectations about future demand and inflation. To determine whether this is the case, we
conducted a fourth treatment that introduces fiscal spending into our baseline constant inflation targeting environment.
In the Fiscal Policy (FP) treatment, subjects were informed each period of an automated
government’s certain policies in the following period. Subjects did not know the nature of
how fiscal spending was to be conducted other than the government could conduct positive or
negative stimulus that would have direct effects on aggregate demand and was not required
to balance its budget over the horizon of the game.15 Government expenditures or taxation,
denoted as gt , had a direct effect on aggregate demand, resulting in a modified I-S curve:
xt = Et∗ xt+1 − σ −1 (it − i∗ − Et∗ πt+1 − rtn ) + gt ,
(7)
The planned expenditures for the following period were displayed to subjects on their
screen in the form of a time series graph in the same panel as the nominal interest rate
and the natural rate of interest shock. During the practice phase, subjects encountered both
positive and negative government expenditures to ensure that they understood both were
possible.
During each of the two experimental repetitions, government spending was exogenously
set to zero until the crisis occurred. On impact of the crisis shock, the government announced
fiscal spending equal to 200 basis points, or 50% of the size of the aggregate demand shock for
15
We chose to have the government not balance its budget to give fiscal policy the best shot at stabilizing
expectations on impact of the crisis shock.
14
the following period.16 To capture the fact that fiscal authorities often takes time to enact new
expenditures, we introduced the fiscal spending in the period following the initial crisis shock
(periods 21 and 16 in the first and second repetition, respectively). The positive government
spending announcements remained for as long as the current natural rate of interest shock was
trending back up to the steady state. Thus, the last period of positive government spending
occurred in the period when the shock first became positive. The decision to keep government
stimulus positive until the shock returned to zero seemed to be a simple rule to follow and not
overly generous. Let tc denote the period in which the economy experiences the crisis shock
and tr=0 denote the first period thereafter when the nature rate of interest surpasses zero.
Thus, the government spending rule implemented in the experiment was given by:



0
if t < tc + 1


gt = 200 if tc + 1 ≤ t ≤ tr=0



0
if t > tr=0 .
(8)
We compute the rational expectations equilibrium solution for the fiscal policy environment
with constant inflation targeting and present the impulse responses associated with a -400
basis point natural rate of interest shock in Figure 3. On impact of the negative demand
shock in period 5, the government makes an announcement that it will increase government
stimulus to 200 basis points in period 6. The government continues to announce and deliver
in the following period 200 basis points of government stimulus for the rest of the 35 period
horizon as the shock never fully returns to zero. The impulse responses are simulated under
the assumption that agents fully anticipate next period’s government stimulus but form no
expectations of future spending thereafter.
Announced fiscal stimulus reduces the initial response to the shock in period 5. Under a
constant inflation target, the output gap decreases 26.3% and inflation decreases 9.3%. By
contrast, in the presence of announced fiscal stimulus to begin in period 6, output and inflation decrease 24% and 8.7%, respectively. Announced fiscal stimulus also reduces the amount
of time it takes for output and inflation. Output and inflation become positive by period 9
and period 12, respectively. These findings lead us to our key hypothesis for the fiscal policy
treatment:
Hypothesis 5: Supplementing a constant inflation target with expansionary fiscal policy re16
While our goal was to test whether fiscal policy would reduce the pessimistic reaction to the crisis, we did
not want to offset the shock entirely.
15
duces the duration and severity of recessions.
It is possible that subjects do not respond optimistically to the fiscal stimulus. The fiscal
spending may be insufficient to stabilize pessimistic expectations. In that case, we would
expect no significant differences in terms of macroeconomic dynamics between the Constant
Target and Fiscal Policy treatments.
Each treatment consisted of six independent sessions, where each session involved a different pair of shock sequences. Across treatments, the set of shock sequences were identical.
Thus, for any given pair of shock sequences, we can observe how behaviour may differ across
treatments. To avoid treatment contamination, we implemented a between-subject experimental design where subjects participated in only one treatment.
The different shock sequences implied that the number of periods it took for the fundamental shock to return to zero following a severe crisis shock varied across sessions within any
given treatment. If subjects utilize only fundamentals and the inflation target to formulate
their forecasts, then the number of periods that it takes for the fundamental shock to return
to the steady state should have no bearing on whether subjects’ forecasts are coordinated in
the direction of the target.
Hypothesis 6: Following a severe crisis shock, the coordination of expectations in the direction
of the target is not influenced by the number of periods that it takes for fundamentals to return
to the steady state.
If fundamentals recover slowly, then changes in inflation and the output gap will be primarily driven by changes in median expectations. Moreover, if expectations are formed adaptively
and subjects form initially pessimistic expectations following the crisis shock, slower recoveries
of fundamentals have the potential to reduce the perceived credibility of the central bank’s
inflation target and reduce its usage in subjects’ forecasts.
4
Aggregate Results
This section presents our findings for the aggregate economies. We begin the discussion with
results from the monetary policy treatments followed by the fiscal policy treatment. After 20
periods in Repetition 1 or 15 periods in Repetition 2, the experimental economies experienced
a crisis shock of -400 basis points. Thereafter, the shock trended back and surpassed zero.
Across different shock sequences we varied the number of periods it took for the shock to
16
reach zero. We define CrisisShockLength as the number of periods, including the period of
the initial shock, before the natural interest rate shock reaches zero.
On impact of the crisis shock, inflation and output expectations in all repetitions decreased
significantly, driving the economies down to the ZLB. However, some economies escaped the
ZLB and trended back up to the steady state, while others experienced persistent deflationary spirals. In all treatments, we observe liquidity traps where median expectations remain
pessimistic in the presence of expansionary monetary policy.
We present two examples of shock sequences where the economies, regardless of the treatment, either escaped or remained trapped at the ZLB.17 In Figures 4 and 5, times series of
output and inflation are presented in blue and green, respectively. The nominal interest rate
is presented in orange, while the shock is presented in bold red. Figure 4 presents the results
from sequence 3 where the CrisisShockLength is three periods in Repetition 1 and five periods
in Repetition 2. Across all treatments, expectations, and thus output and inflation, track the
shock well in the preshock phase. On the impact of the crisis shock, expectations drop and
even trend downwards one period after the crisis shock. However, median expectations are
quickly reversed and the economies all successfully return back to the steady state relatively
quickly in both repetitions. Sequence 4 presented in Figure 5 has a CrisisShockLength of 8
periods in both repetitions. Again, median expectations fall significantly on the impact of
the shock, but in all monetary policy treatments, they never return to the steady state, and
instead experience severe deflationary episodes with output and inflation reaching very large
negative levels. By contrast, in the Fiscal Policy treatment, we observe that expectations and
the aggregate economy remain relatively stable and follow fundamentals as the shock trends
back to the steady state.
We consider two measures of policy effectiveness. The first is related to the success of policy
in reducing the duration of a liquidity trap, while the second addresses the policy’s effectiveness
in reducing the severity (or standard deviation) of output gap and inflation following the crisis
shock. We begin with the duration of the liquidity trap. Because each shock sequence in a
given treatment has a different CrisisShockLength, we normalize the number of periods before
expectations are reversed by the CrisisShockLength. Specifically, we measure the duration of
the liquidity trap at the session-repetition level using Relative Trap Length:
Relative Trap Length =
Number of periods before expectations are reversed
Number of periods before shock becomes nonnegative
17
All time series graphs of inflation, output, interest rates, and forecast distributions can be found in the
Online Appendix.
17
The results are aggregated in box-and-whisker plots in Figure 6a.18 Among inexperienced
subjects (Repetition 1) in the monetary policy treatments, the relative traps are the lowest
in the Constant treatment where it takes an average of 9.5 periods for subjects to reverse
their expectations. By contrast, in treatments SD and Dir. SD, it takes an average of 15.2
and 13.8 periods, respectively. However, the differences across treatments are not statistically
significant (p-value> 0.126 for all pairwise two-sided Wilcoxon rank sum comparisons). For
experienced subjects (Repetition 2), the average relative trap length increases in the Constant
Target treatment with subjects taking an average of 12.9 periods to reverse their expectations.
The average relative trap length worsens in the SD treatments (with an average of 18 periods to
reverse the expectations) and decreases considerably in Dir. SD (with an average of 11 periods
to reverse the expectations). Again, none of these are differences in the second repetition are
statistically significant (with p-value> 0.469 in all cases).
Observation 1: The relative trap length does not differ significantly between the Constant
and SD inflation targets, irrespective of how the state-dependent target is communicated.
Figure 6b. presents standard deviations of inflation across treatments and repetitions (log
scale on the y-axis). During the first repetition, the standard deviation of inflation is significantly lower in the Constant treatment than in the SD treatment (p-value= 0.055). However,
because of the considerable variability of inflation across sessions of Dir. SD treatment, we
do not observe any statistically significant differences with respect to either the Constant or
SD treatments. For experienced subjects, the standard deviation of inflation worsens in the
Constant and SD treatments, and we fail to observe any statistically significant differences
between the two (p-value= 0.262). However, the qualitative communication in the Dir. SD
treatment is more effective at reducing inflation variability than quantitative communication
in the SD treatment (where the difference is statistically significant with p-value= 0.109). The
results for the output gap follow an identical pattern.
Observation 2: The severity of recessions, measured by the standard deviation of inflation and
output, is significantly lower under a constant inflation target than under an explicitly communicated inflation target when subjects are inexperienced. With experience, state-dependent
18
The following interpretation for box-and-whisker plots is given by Cox (2009). The eponymous box is
used to indicate the lower and upper quartiles of the variable or group being plotted against the magnitude
scale. The median is denoted by a line subdividing the box. The length of the box represents the interquartile
range (IQR). Whiskers are drawn to span all data points within 1.5 IQR of the nearer quartile. Any data
points beyond the whiskers are shown individually.
18
inflation targets communicated qualitatively result in significantly less severe recessions than
when communicated quantitatively. Neither form of state-dependent targets significantly reduces the standard deviation of inflation and output relative to a constant inflation target.
Does the CrisisShockLength influences the likelihood of over-reacting to the initial crisis
shock. We denote an economy as ‘stable’ if both output and inflation remain above -1000
basis points in the postshock phase, and ‘unstable’ otherwise. Figure 7 categorizes each repetition of each session as unstable or stable. Instability is strongly associated with increased
CrisisShockLengths in all inflation targeting treatments. With the exception of one session
in the first repetition of the Dir. SD treatment, we observe that CrisisShockLengths greater
than 5 periods result in unstable dynamics.
We further conduct a series of probit regressions to identify the effects of the CrisisShockLength on the likelihood of coordinating expectations in the direction of the inflation target.
We employ pooled data collected from both repetitions in the postshock phase. The results
for the monetary policy treatments are presented in the first three columns of Table 1, where
the data is pooled across repetitions and standard errors are clustered at the session level.
The results indicate that the longer the CrisisShockLength is, the lower the probability that
individuals will coordinate their expectation in the direction of the inflation target is. More
precisely, for every additional period it takes for fundamentals to return to zero, the likelihood
a subject forms expectations in the direction of the target decreases by 7.6%. The estimate is
large and statistically significant in the Constant treatment, but small and with large standard
errors in the two state-dependent treatments.
We also consider the possibility that larger adjustments in the aggregate shock in the period after the crisis shock may appear more focal and serve to effectively coordinate optimistic
expectations in line with the target. The results are presented in the second half of the table.
Indeed, in the Constant and Dir. SD treatments, a larger recovery of the shock immediately
after the crisis occurs significantly increases the probability that subjects’ expectations of
inflation increase relative to past inflation. However, in the SD treatment, a larger initial
recovery in fundamentals has no effect on the likelihood of forming more optimistic inflation
expectations.
Observation 3: A faster recovery of fundamentals increases the likelihood that subjects formulate forecasts in the direction of the central bank’s constant inflation target. The coordination
19
of expectations in line with the state-dependent inflation targets is not quantitatively or significantly affected by the speed of the recovery of fundamentals.
Observation 4: Larger initial adjustment in the fundamental shock immediately following the
initial crisis shock significantly increases the probability of forming optimistic expectations
under constant and directional state-dependent inflation targets.
Combining a constant inflation-targeting monetary policy with fiscal stimulus is effective
at stabilizing expectations during an economic crisis. The mean relative trap length under
the fiscal policy treatment is 0.937 (SD 1.053) in the first repetition and 0.441 (SD 0.049)
in the second repetition (see Figure 6a). This is considerably smaller than the relative trap
lengths observed in the Constant Target treatment, which have means of 1.652 (SD 0.977) and
2.536 (SD 1.903) in Repetitions 1 and 2, respectively. Two-sided Wilcoxon rank sum tests
reject the null hypothesis of equal distributions (p-value= 0.025) in the second repetition,
but fail to in the first repetition (p-value= 0.126). Only one economy in the fiscal policy
treatment experienced a severe liquidity trap (shock sequence 2, repetition 1). If we exclude
that repetition from our analysis, we find that the differences between the constant and fiscal
treatment are again highly significant (p-value= 0.028).
The standard deviations of inflation and output are also considerably reduced with the
introduction of fiscal policy. Figure 6b presents a comparison of standard deviations at the
session level in the Constant Target and Fiscal Policy treatments. The differences across treatments are visually dramatic. Two-sided Wilcoxon rank sum tests indicate that the differences
across treatments are stark. In the first repetition, we obtain p-value= 0.078 for inflation and
p-value= 0.109 for output, and when exclude the outlier session, the significance increases
considerably to p-value= 0.011 for inflation and p-value= 0.018 for output. With experience
in the second repetition, the differences are more significant: p-value= 0.010 for inflation and
p-value= 0.004 for output.
Observation 5: Supplementing a constant inflation target with expansionary fiscal policy reduces the duration and severity of recessions.
We report the results from a final series of probit regressions for the fiscal policy treatment
in Table 1. We find a small, positive effect of CrisisShockLength on the likelihood of expectations moving in the correct direction but the effect is not statistically significant. Figure 7
20
supports this finding in that all but one session remain stable regardless of the CrisisShockLength. Thus, fiscal policy is effective at reducing the pessimism generated by slow recovery of
fundamentals. Second, we observe that subjects in the Fiscal Policy treatment are also more
likely to adjust their expectations upward when fundamentals increase by a larger amount in
the period immediately following the crisis shock.
Observation 6: In the presence of a constant inflation target and expansionary fiscal policy,
increasing the speed of recovery of fundamentals has minimal effect on the likelihood subjects form expectations in the direction of the target. A larger initial upward adjustment in
fundamentals significantly increases the likelihood subjects form optimistic expectations.
5
Heterogeneity in Forecasting Heuristics
We next consider how expectations evolve under various forecasting heuristics: rational, where
forecasts condition solely on the fundamental shock, naive, where forecasts condition solely on
past realized output or inflation, and trend-chasing where forecasts condition on the change
in output or inflation over the past two periods. For each phase of each repetition, we run
the following OLS regressions for each individual i: Ei,t xt+1 = βrtn + t , Ei,t xt+1 = βxt−1 + t ,
and Ei,t xt+1 = β(xt−1 − xt−2 ) + t . For the state-dependent inflation targeting treatments,
we also estimate each individual’s responsiveness to the the central bank’s evolving inflation
target using the following regression equation: Ei,t xt+1 = βπt∗ +t . Finally, for the fiscal policy
treatments, we estimate subjects’ responsiveness to fiscal policy: Ei,t xt+1 = β1 rtn + β2 gt + t .19
These heuristics are motivated by extensive survey evidence of households and professional
forecasts, as well as laboratory experimental studies that demonstrate significant evidence
of backward-looking, rigid expectations (e.g. Pfajfar and Santoro (2010), Hommes (2011),
Coibion and Gorodnichenko, (2012), Assenza et al. (2013), Andrade and Le Bihan (2013)).
We consistently observe considerable heterogeneity in all treatments under all forecasting
heuristics. We compute a session-repetition-phase measure of the standard deviation of estimated coefficients from each forecasting model. On average, preshock heterogeneity is the
largest in the SD treatment, followed by the Dir. SD treatment, Constant treatment, and
finally the Fiscal Policy treatment. Two-sided Wilcoxon rank sum tests indicate that when it
comes to naive forecasting, subjects exhibit significantly more heterogeneity in their responses
to lagged output and inflation in the preshock phases (for both repetitions) of the SD and
Dir. SD treatments than in the Constant Target treatment (p < 0.025 in all cases).
19
All these variables are known to participants in period t when formulating their period t + 1 forecasts.
21
We attribute the increased lack of coordination on historical information to the increased
cognitive effort associated with the SD and Dir. SD treatments. In these treatments, subjects
are presented with an additional piece of information, namely the evolving inflation target, on
which they must decide how to condition their forecasts. Moreover, this information is only
effective at influencing the economy in the immediate future so long as a sufficient number of
subjects utilize it in their forecasts. This complicates the coordination process and contributes
to the lack of success of the state-dependent inflation target in the postshock phase.
Turning to the Constant and Fiscal Policy treatments, we find no significant differences
in preshock heterogeneity across any of the forecasting heuristics. However, in the postshock
phase we observe that, by the second repetition, Fiscal Policy subjects are significantly more
homogeneous in their responses to fundamentals and lagged outcomes for both their inflation
and output forecasts, as well as trend-chasing heuristics for output forecasts. In the Fiscal
Policy treatments, all the sessions converge relatively quickly back to the steady state, resulting in little confusion about the future state of the economy. By contrast, in the Constant
treatment, most of our sessions overreact on impact of the shock, creating more confusion and
heterogeneity in expectations, leading to slower recoveries.
Observation 7: In summary, subjects’ expectations are highly heterogeneous and responsive to
historical information. Introducing uncertain and evolving inflation targets in the SD and Dir.
SD treatments increases the set of information subjects utilize to formulate their expectations
and complicates their forecasting task. As a result, expectations formed in the SD and Dir. SD
treatment are significantly more heterogeneous than in the Constant treatment. By contrast,
expectations are more homogeneous when a constant inflation target is supplemented with
expansionary fiscal policy.
6
Discussion
We have demonstrated that severe, long-lasting expectations-driven liquidity traps can be
generated in the laboratory. With a large unanticipated demand shock, subjects can form
extremely pessimistic expectations, causing the economy to diverge into a deep recession.
Recent theoretical research suggests that state-dependent inflation targeting by central banks
can bring about greater economic stability and faster recoveries by committing to keep interest
rates low following a recession even after inflation has returned to its target. We conduct a
series of laboratory experiments to test whether such policies live up to these predictions, and
if not, to identify why this is so.
22
We find that state-dependent inflation targets do not lead to significantly greater stability.
In fact, in many instances, recession duration and severity are made considerably worse by
continually raising the central bank’s inflation target. This is particularly the case when fundamentals improve slowly. We attribute the relatively poorer performance of state-dependent
inflation targets to a loss of confidence in the central bank’s ability to stabilize the economy.
During a slower recovery, the central bank’s inflation target grows quite large as the economy
fails to live up to the state-dependent target. The disparity between the inflation target and
actual inflation - which is largely driven by non-rational expectations - grows rapidly. Such a
policy is unlikely to be successful if agents’ willingness to condition their expectations on the
central bank’s target is based on the central bank’s efficacy in achieving past targets. However, the faster fundamentals improve, the greater is the likelihood the central bank achieves
its inflation target and individuals coordinate their expectations in the direction of the target.
We emphasize that the central bank in our experimental economy is fully committed to
its state-dependent policy to keep interest rates low even after the economy begins recovering.
Unlike rational expectations’ frameworks where credibility and commitment are synonymous,
we have observed that agents may not perceive the central bank’s intentions as credible despite
the central bank’s commitment to its policies. In short, our subjects need to “see it to believe
it”.
Anticipated fiscal policy, by contrast, provides considerable support when fundamentals
improve slowly. Compared to our baseline of a constant inflation target, introducing fiscal
policy leads to significantly faster and more stable recoveries. Unlike state-dependent inflation
targeting monetary policies that provide a promise of future recovery in the uncertain future,
anticipated expansionary fiscal policy in our environment stimulates demand with certainty.
23
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Short-Term Interest Rates.” Journal of Money, Credit, and Banking, 38 (3): 791-819.
[50] Walsh, C. E. (2009). Using monetary policy to stabilize economic activity. Financial
Stability and Macroeconomic Policy, 245-296.
[51] Woodford, M. (2005). Central Bank Communication and Policy Effectiveness (No.
w11898). National Bureau of Economic Research.
[52] Woodford, M. (2013). “Macroeconomic analysis without the rational expectations hypothesis ” (No. w19368). National Bureau of Economic Research.
28
2494
7.67
N
χ2
2373
0.12
0.091
(0.48)
-0.019
(0.06)
2502
0.01
0.181
(0.38)
-0.006
(0.05)
2446
0.53
-0.065
(0.25)
0.035
(0.04)
107
10.62
0.000 0.007***
(0.00)
(0.00)
0.003
-0.482
(0.32)
(0.36)
108
106
4.873 0.0101
0.006**
(0.00)
0.029
(0.41)
106
14.07
0.008 ***
(0.00)
-0.131
(0.34)
Increase Forecast Relative to Past Inflation
Constant
SD
Dir. SD
Fiscal
I
parentheses and clustered at the session-level.
the constant in each specification. Significance levels:
∗
p < 0.10,
∗∗
p < 0.05,
∗∗∗
p < 0.01. Standard errors are presented in
number of periods it takes for the natural rate of interest shock rtn to return to zero following the onstart of the crisis. α denotes
(I) Specifications involve data from the pooled postshock data from Repetitions 1 and 2. CrisisShockLength refers to the
0.651***
(0.17)
-0.076***
(0.03)
Forecast in Target Direction
Constant
SD
Dir. SD Fiscal
α
n
rtn − rt−1
CrisisShockLength
Dep. Var
Treatment
Table 1: Probit Analysis of CrisisShockLength and Adjustment on Anchoring of Inflation Expectations
Figure 1: Simulation of parameterized environment with a constant inflation target
Figure 2: Simulation of parameterized environment with a state dependent inflation target
Figure 3: Simulation of parameterized environment with a constant inflation target and announced fiscal policy
Figure 4: Example of a stable shock sequence
Figure 5: Example of an unstable shock sequences
0
2
Relative Trap Length
4
6
8
(a) Relative Trap Length
Constant
SD
DSD
Fiscal
Constant
SD
Rep 1
DSD
Fiscal
Rep 2
Standard Deviation
(b) Standard Deviation of Inflation
1.0e+09
1.0e+07
1.0e+06
10,000
1,000
50
Constant
SD
DSD
Rep 1
Fiscal
Constant
SD
DSD
Fiscal
Rep 2
Figure 6: Duration and Severity of Crises in Constant Target, State-Dependent Target, and
Directional State-Dependent Target Treatments
3. Dir. SD Target, Rep 1
4. Fiscal Policy, Rep 1
1. Constant Target, Rep 2 2.State Dependent Target, Rep 2
3. Dir. SD Target, Rep 2
4. Fiscal Policy, Rep 2
0
1
0
Stable Economy = 0; Unstable Economy = 1
1
1. Constant Target, Rep 1 2.State Dependent Target, Rep 1
0
5
10
15
0
5
10
15
0
5
10
15
0
5
10
15
Crisis Shock Length
Figure 7: Stability of Economies by Length of Crisis Shock - By Treatment and Repetition
(a) Fundamentals-Driven Expectations - Output Forecasts
Repetition 2, preshock
0
.5
1
Repetition 1, preshock
CDF
-.5
0
.5
1
1.5
0
5
15
Repetition 2, postshock
0
.5
1
Repetition 1, postshock
10
-20
-10
0
10 -20
-10
0
10
20
Estimated coefficient on shock_{t} in output forecast
Constant
SD
Dir. SD
Fiscal Policy
(b) Fundamentals-Driven Expectations - Inflation Forecasts
Repetition 2, preshock
0
.5
1
Repetition 1, preshock
CDF
-.5
0
.5
1
0
4
6
8
Repetition 2, postshock
0
.5
1
Repetition 1, postshock
2
-10
0
10
-15
-10
-5
0
5
Estimated coefficient on shock_{t} in inflation forecast
Constant
SD
Dir. SD
Fiscal Policy
Figure 8: Distribution of Fundamental Types Across Treatments and Shock Phases - by
Repetition and Phase
(a) Naive Expectations - Output Forecasts
Repetition 2, preshock
0
.5
1
Repetition 1, preshock
CDF
-.5
0
.5
1
1.5
-2
0
4
Repetition 2, postshock
0
.5
1
Repetition 1, postshock
2
-4
-2
0
2
0
.5
1
1.5
Estimated coefficient on output_{t-1} in output forecast
Constant
SD
Dir. SD
Fiscal Policy
(b) Naive Expectations - Inflation Forecasts
Repetition 2, preshock
0
.5
1
Repetition 1, preshock
CDF
-5
0
5
-5
0
Repetition 2, postshock
0
.5
1
Repetition 1, postshock
5
0
10
20
0
10
20
30
40
Estimated coefficient on Inflation_{t-1} in inflation forecast
Constant
SD
Dir. SD
Fiscal Policy
Figure 9: Distribution of Naive Types Across Treatments and Shock Phases - by Repetition
and Phase
(a) Trend-chasing & Contrarian Expectations - Output Forecasts
Repetition 2, preshock
0
.5
1
Repetition 1, preshock
CDF
-1
0
1
2
-10
10
20
Repetition 2, preshock
0
.5
1
Repetition 1, postshock
0
-5
0
5
10
-2
0
2
4
6
Estimated coefficient on past output trend in output forecast
Constant
SD
Dir. SD
Fiscal Policy
(b) Trend-chasing & Contrarian - Inflation Forecasts
Repetition 2, preshock
0
.5
1
Repetition 1, preshock
CDF
-2
-1
0
1
2
0
4
6
8
Repetition 2, postshock
0
.5
1
Repetition 1, postshock
2
0
20
40
60 -20
0
20
40
Estimated coefficient on past inflation trend in inflation forecast
Constant
SD
Dir. SD
Fiscal Policy
Figure 10: Distribution of Naive Types Across Treatments and Shock Phases - by Repetition
and Phase
(a) Inflation Target - Output Forecasts
Repetition 2, preshock
0
.5
1
Repetition 1, preshock
CDF
-2
-1
0
1
-4
0
2
Repetition 2, postshock
0
.5
1
Repetition 1, postshock
-2
-.5
0
.5
-1
-.5
0
.5
Estimated coefficient on InflationTarget_{t} in output forecast
SD
Dir. SD
(b) Inflation Target - Inflation Forecasts
Repetition 2, preshock
0
.5
1
Repetition 1, preshock
CDF
-1
-.5
0
.5
1
-1.5
-.5
0
.5
Repetition 2, postshock
0
.5
1
Repetition 1, postshock
-1
-5
0
5
-10
-5
0
Estimated coefficient on InflationTarget_{t} in inflation forecast
SD
Dir. SD
Figure 11: Distribution of Responses to State Dependent Inflation Target Across Treatments
and Shock Phases - by Repetition and Phase
(a) Fiscal Policy - Output Forecasts
0
.5
1
Repetition 1, postshock
CDF
-.5
0
.5
1
1.5
0
.5
1
Repetition 2, postshock
-.5
0
.5
1
Estimated coefficient on g_{t} in output forecast after controlling for r_{t}
(b) Fiscal Policy - InflationForecasts
0
.5
1
Repetition 1, postshock
CDF
0
.5
1
1.5
0
.5
1
Repetition 2, postshock
0
.5
1
1.5
Estimated coefficient on g_{t} in inflation forecast after controlling for r_{t}
Figure 12: Distribution of Responses to Fiscal Policy Across Treatments and Shock Phases by Repetition and Phase
7
Online Appendix - Not for Publication
Derivation of State-Dependent Inflation Targeting rule20
Below we discuss how we develop our non-optimal state-dependent inflation targeting rule.
We are motivated by Eggertsson and Woodford’s optimal price setting rule:
p∗t+1 = p∗t +
1
1
(1 + κσ) ∆t − ∆t−1 (1)
β
β
where
∆t ≡ p∗t − p̃t (2)
Here p∗t denotes the price target and
λ
p̃ = pt + xt (3)
κ
refers to the output gap adjusted price level. Note that in the steady state, ∆t = 0.
We begin by defining the output gap adjusted inflation level as
π̃t = p̃t − p̃t−1 ⇔
π̃t = (pt − pt−1 ) +
π̃t = πt +
λ
(xt − xt−1 ) ⇔
κ
λ
(xt − xt−1 ) (4)
κ
Equation (1) can be rewritten as
p∗t+1 = p∗t +
p∗t+1 − p∗t =
∗
=
πt+1
∗
πt+1
=
20
1
1
(1 + κσ) ∆t − ∆t−1 ⇔
β
β
1
1 ∗
(1 + κσ) (p∗t − p̃t ) −
pt−1 − p̃t−1 ⇔
β
β
κσ ∗
1 ∗
pt − p∗t−1 − (p̃t − p̃t−1 ) +
(p − p̃t ) ⇔
β
β t
1
1 ∗
κσ ∗
pt − p∗t−1 − (p̃t − p̃t−1 ) +
(p − p̃t ) ⇔
β
β
β t
We credit Andriy Barynskyy for this derivation.
∗
πt+1
=
∗
πt+1
=
1 ∗ 1
κσ ∗
πt − π̃t +
(p − p̃t ) ⇔
β
β
β t
1 ∗
λ
κσ ∗
(πt − πt ) −
(xt − xt−1 ) +
(p − p̃t ) (5)
β
κβ
β t
Now, the first two terms are straightforward and can be easily calculated. What about
(p∗t − p̃t )?
the term κσ
β
P
Start with πt∗ = p∗t − p∗t−1 . After rearranging, note that p∗t = πt∗ + p∗t−1 = ti=1 πi∗ + p∗0 (6).
P
P
Similarly, p̃t = ti=1 π̃i + p̃0 = ti=1 π̃i + p0 + λκ x0 (7). If we assume that before period 1
po = p∗o , then these terms can be subtracted and we don’t care about price level:
κσ
κσ ∗
(pt − p̃t ) =
β
β
=
κσ
β
=
κσ
β
t
X
t
X
λ
π̃i − p0 − x0
κ
i=1
i=1
!
t
t
X
X
λ
∗
πi −
π̃i − x0
κ
i=1
i=1
!
t
t
X
X
∗
πi −
π̃i (8)
πi∗ + p∗0 −
i=1
!
i=1
Now substitute (8) into (5):
∗
πt+1
=
∗
πt+1
κσ
1 ∗ 1
πt − π̃t +
β
β
β
1
λ
κσ
1
(xt − xt−1 ) +
= πt∗ − πt −
β
β
κβ
β
∗
πt+1
t
X
πi∗ −
i=1
t
X
!
π̃i
⇔
i=1
πi∗ −
t
X
i=1
1
λ
κσ
= (πt∗ − πt ) −
(xt − xt−1 ) +
β
κβ
β
t
X
i=1
t
X
πi∗ −
i=1
t
λX
(xt − xt−1 )
πi −
κ i=1
t
X
i=1
!
πi
−
!
⇔
λσ
xt (9)
β
We then use equation (9) as the central bank’s inflation target when simulating the statedependent inflation targeting rule. The inflation target is implemented in a non-optimal Taylor
rule that has nominal interest rates responding to deviations of inflation from the target given
by equation (9) and output gap from zero:
it = r∗ + φπ (πt − πt∗ ) + φx xt
In designing our experiment and studying the space of parameters, we conducted simulations using social evolutionary learning agents to study dynamics in response to this statedependent inflation targeting rule. We found in numerous simulations that the economies
Pt
Pt
∗
−
π
due
π
were highly unstable when the inflation target included the term κσ
i
i
i=1
i=1
β
to the little weight agents placed on the target in early periods. In response to these initial
simulations, we opted remove the term from equation (9) and instead implement the following
which led to increased stability:
∗
πt+1
=
1 ∗
λ
λσ
(πt − πt ) −
(xt − xt−1 ) −
xt . (10)
β
κβ
β
Figure 13: Constant Target Treatment Screenshot
Figure 14: State Dependent Target Treatment Screenshot
Figure 15: Directional State Dependent Target Treatment Screenshot
Figure 16: Fiscal Policy Treatment Screenshot
Experimental Instructions for Constant Target Treatment
Welcome! You are participating in an economics experiment at CRABE Lab. In this experiment you will
participate in the experimental simulation of the economy. If you read these instructions carefully and make
appropriate decisions, you may earn a considerable amount of money that will be immediately paid out to
you in cash at the end of the experiment.
Each participant is paid CDN$7 for attending. Throughout this experiment you will also earn points based on
the decisions you make. Every point you earn is worth $0.50. We reserve the right to improve this in your
favour if average payoffs are lower than expected.
During the experiment you are not allowed to communicate with other participants. If you have any
questions, the experimenter will be glad to answer them privately. If you do not comply with these
instructions, you will be excluded from the experiment and deprived of all payments aside from the minimum
payment of CDN $7 for attending.
The experiment is based on a simple simulation that approximates fluctuations in the real economy. Your
task is to serve as private forecasters and provide real-time forecasts about future output and inflation in this
simulated economy. The instructions will explain what output, inflation, and the interest rate are and how
they move around in this economy, as well as how they depend on forecasts. You will also have a chance to
try it out in a practice demonstration.
In this simulation, households and firms (whose decisions are automated by the computer) will form
forecasts identically to yours. So to some degree, outcomes that you will see in the game will depend on the
way in which all of you form your forecasts. Your earnings in this experiment will depend on the accuracy of
your individual forecasts.
Below we will discuss what inflation and output are, and how to predict them. All values will be given in
basis points, a measurement often used in descriptions of the economy. All values can be positive, negative,
or zero at any point in time.
1
Score
Your score will depend on the accuracy of your inflation and output gap forecasts. The absolute difference
between your forecasts and the actual values for output and inflation are your absolute forecast errors.
Absolute Forecast Error = absolute (Your Forecast – Actual Value)
Total Score = 0.30(2^-0.01(Forecast Error for Output)) + 0.30(2^-0.01 (Forecast Error for Inflation))
The maximum score you can earn each period is 0.6 points.
Your score will decrease as your forecast error increases. Suppose your forecast errors for each of output and
inflation are:
0
-Your score will be 0.6
300
-Your score will be 0.075
50
-Your score will be 0.42
500
-Your score will be 0.02
100
-Your score will be 0.3
1000 -Your score will be 0
200
-Your score will be 0.15
2000 -Your score will be 0
Information about the Interface, Actions, and Payoffs
During the experiment, your main screen will display information that will help you make forecasts and earn
more points.
At the top left of the screen, you will see your subject number, the current period, time remaining, and the
total number of points earned. Below that you will see the interest rate for the current period. You will also
see three history plots. The top history plot displays past interest rates and shocks. The second plot displays
your past forecast of inflation and realized inflation levels. The final plot displays your past forecasts of
inflation and realized inflation levels. The difference between your forecasts and the actual realized levels
constitutes your forecast errors. Your forecasts will always be shown in blue while the realized value will be
shown in red. You can see the exact value for each point on a graph by placing your mouse at that point.
When the first period begins, you will have 65 seconds to submit new forecasts for the next period’s inflation
and output levels. You may submit both negative and positive forecasts. Please review your forecasts before
pressing the SUBMIT button. Once the SUBMIT button has been clicked, you will not be able to revise your
forecasts until the next period. You will earn zero points if you do not submit all three forecasts. After the
first 9 periods, the amount of time available to make a decision will drop to 50 seconds per period.
You will participate in two sequences of 40 periods, for a total of 80 periods of play. Your score, converted
into Canadian dollars, plus the show up fee will be paid to you in cash at the end of the experiment.
2
INFORMATION SHARED WITH ALL PARTICIPANTS
Each period, you will receive the following information to help you make forecasts.
Interest Rate
The interest rate is the rate at which consumers and firms borrow and save in this experimental economy.
The central bank’s objective is to keep the economy stable. It responds to changes in the current level of
output and inflation from the long run target of zero. The central bank aims to keep inflation at a level of 0
basis points per period by adjusting the interest rate. This will imply that, on average, the interest rate will be
75 basis points. The interest rate can be as low as zero and there is no limit on how high it can be.
Depends on: Inflation in the current period (+)
Example: If inflation increases today, the nominal interest rate will increase. If inflation decreases, the
interest rate will be decrease.
Depends on: Output in the current period (+)
Example: If output increases in the current period, the nominal interest rate will increase. If it decreases, the
interest rate will decrease.
Question: If inflation and output are -10 and -20, respectively, what sign will the interest rate be? _________.
What if inflation is -10 and output is 20?________
Current Shock
A shock is a random “event” that affects output. E.g. A natural disaster can suddenly destroy crops, or a
technological discovery immediately improves productivity.
Depends on: Random Draw
The central bank in the economy predicts that the shock will be relatively small most of the time. Two-thirds
of the time it will fall between -93 and 93 basis points, and 95% of the time it will fall between -186 and 186
basis points. On average, it will be 0.
Every shock takes some time to dissipate. Suppose the shock in the current period is 100. Next period, that
shock will now be 80% of 100, or 80 basis points. Assuming no new shocks were to occur, the value of the
shock next period is 80 points. Some shock is likely to occur.
Shock Forecast
The shock forecast is a prediction of what the shock will be next period. It assumes that, on average, next
period’s shock is zero.
Example: If the current shock is -200 points, the forecasted value of the shock tomorrow is -200(0.80) = -160
3
HOW INFLATION AND OUTPUT ARE DETERMINED
You will be making forecasts about what you believe inflation and output will be tomorrow, as well as
inflation four periods into the future.
1. Inflation
Inflation is the rate at which overall prices change between two periods.
Depends on: Forecasted inflation in the next period (+)
Example: If the median subject forecasts future inflation to be positive, current inflation will be positive, and
vice versa.
Question: Holding all else constant, will current inflation be positive or negative if the median forecast for
future inflation is -20? _________________.
Current output (+)
Example: If current output is positive, current inflation will be positive. If current output is negative, current
output will be negative.
Question: Holding all else constant, what sign is current inflation if current output is 50?______0?_________
2. Output
Output refers to a measure of the quantity of goods produced in a given period.
Depends on: Forecasted output in the next period (+)
Example: If the median subject forecasts future output to be positive, current output will also be positive.
Question: Holding all else constant, will output be positive or negative if the median subject forecasts output
to be -15 points next period?_____________
Forecasted inflation in the next period (+)
Example: If the median subject forecasts inflation to be positive next period, current output will likely be
positive.
Question: Holding all else constant, what sign will output be if the median subject forecasts inflation to be
250 points next period?_____________. What sign will inflation have? ___________.
Current interest rate (-)
Example: If the current interest rate is positive, current output will be negative.
Question: Holding all else constant, what sign will output be if interest rates are 10? ______________ What
sign will inflation have? _____________
Random Shocks (+)
Example: Positive shocks will have a positive effect on output. Negative shocks will have a negative effect
on output.
Question: Holding all else constant, what sign will output be if the shock is -50?_________ . What sign will
inflation have? ________________
4
How the economy evolves
You will submit forecasts for the next period’s inflation and output, measured in basis points:
1% = 100 basis points
3.25% = 325 basis points
-0.5% = -50 basis points
-4.8% = -480 basis points
The economy consists of four main variables:
• Inflation, Output, Interest Rate, Shocks
At any time, t, the values of these variables will be calculated as follows:
Shockt = 0.8(Shockt−1 ) + Random Componentt
• The random component is 0 on average.
• Roughly two out of three times the shock will be between -93 and 93 basis points.
• 95% of the time the shock will be between -186 and 186 basis points.
E.g.
Shock1 = 30
Shock2 = 30 × 0.8 + N ew Draw
= 24 + (30)
= 54
Shock2 = 24 + (−150)
= −126
1
How the economy evolves:
Inf lationt = 0.995(Median forecast of Inflationt+1 )+0.13( Outputt )
Outputt = Median forecast of Outputt+1 + Median forecast of Inflationt+1 − Interest Ratet + Shockt + 75
Interest Ratet = 75 + 1.5(Inf lationt − Inf lation T argett ) + 0.5(Outputt )
Inf lation T argett =0
• The interest rate can never go below 0. If inflation or output become sufficiently negative,
the interest rate will be zero.
• The Central Bank’s inflation target will always be 0. Its goal is to keep inflation and output
at 0.
• Expectations are self-fulfilling in this economy. If the median subject forecasts higher inflation
and output in the future, both inflation and output will grow higher in the current period.
Similarly, median forecasts of negative inflation and output will cause the economy to recede
in the current period.
2
How the economy evolves
You will submit forecasts for the next period’s inflation and output, measured in basis points:
1% = 100 basis points
3.25% = 325 basis points
-0.5% = -50 basis points
-4.8% = -480 basis points
The economy consists of four main variables:
• Inflation, Output, Interest Rate, Shocks
At any time, t, the values of these variables will be calculated as follows:
Shockt = 0.8(Shockt−1 ) + Random Componentt
• The random component is 0 on average.
• Roughly two out of three times the shock will be between -93 and 93 basis points.
• 95% of the time the shock will be between -186 and 186 basis points.
E.g.
Shock1 = 30
Shock2 = 30 × 0.8 + N ew Draw
= 24 + (30)
= 54
Shock2 = 24 + (−150)
= −126
1
How the economy evolves:
Inf lationt = 0.995(Median forecast of Inflationt+1 )+0.13( Outputt )
Outputt = Median forecast of Outputt+1 + Median forecast of Inflationt+1 − Interest Ratet + Shockt + 75
Interest Ratet = 75 + 3(Inf lationt − Inf lation T argett ) + (Outputt )
Inf lation T argett =(Inf lation T argett−1 − Inf lationt−1 )−0.33(Outputt−1 −Outputt−2 )−0.004Outputt−1
• The interest rate can never go below 0. If inflation or output become sufficiently negative,
the interest rate will be zero.
• The Central Bank’s inflation target will always be changing in response to the economy.
– If the economy is in a recession and past inflation is lower than the Bank’s target, the
target will be raised. The Bank will promise to allow for higher inflation for at least a
couple of periods after the economy comes out of a recession.
– If the economy has been growing above the Bank’s target and past inflation is higher
than the Bank’s target, the target will be lowered. The Bank will raise interest rates
more aggressively to reduce inflation. This will also persist for at least a couple of
periods after the economy returns to its steady state levels.
• Expectations are self-fulfilling in this economy. If the median subject forecasts higher inflation
and output in the future, both inflation and output will grow higher in the current period.
Similarly, median forecasts of negative inflation and output will cause the economy to recede
in the current period.
2
How the economy evolves
You will submit forecasts for the next period’s inflation and output, measured in basis points:
1% = 100 basis points
3.25% = 325 basis points
-0.5% = -50 basis points
-4.8% = -480 basis points
The economy consists of five main variables:
• Inflation, Output, Interest Rate, Government Spending, Shocks
At any time, t, the values of these variables will be calculated as follows:
Shockt = 0.8(Shockt−1 ) + Random Componentt
• The random component is 0 on average.
• Roughly two out of three times the shock will be between -93 and 93 basis points.
• 95% of the time the shock will be between -186 and 186 basis points.
E.g.
Shock1 = 30
Shock2 = 30 × 0.8 + N ew Draw
= 24 + (30)
= 54
Shock2 = 24 + (−150)
= −126
1
How the economy evolves:
Inf lationt = 0.995(M edian f orecast of Inf lationt+1 ) + 0.13(Outputt )
Outputt = M edian f orecast of Outputt+1 + M edian f orecast of Inf lationt+1 − Interest Ratet
+Government Spendingt + Shockt + 75
Interest Ratet =
75 + 1.5(Inf lationt − Inf lation T argett ) + 0.5(Outputt )
where,
Inf lation T argett =0
• The government will occasionally spend money to stimulate demand or tax to reduce demand.
At any point in time, you will see the government’s planned spending or taxation for the
next period. The government does not necessarily need to balance its budget. That is, if the
government spends in one period, they are not required to tax in the future, and vice versa.
• The interest rate can never go below 0. If inflation or output become sufficiently negative,
the interest rate will be zero.
• The Central Bank’s inflation target will always be 0. Its goal is to keep inflation and output
at 0.
• Expectations are self-fulfilling in this economy. If the median subject forecasts higher inflation
and output in the future, both inflation and output will grow higher in the current period.
Similarly, median forecasts of negative inflation and output will cause the economy to recede
in the current period.
2
(a) Sequence 1, Repetition 1
1. Constant Target, 0
1. Constant Target, 1
200
100
0
-100
-200
0
5
10
15
0
400
200
0
-200
-400
-20000
-40000
-60000
20
20
2.State Dependent Target, 0
5
10
15
20
15
20
15
40
25
30
35
40
4. Constant Target + Fiscal Policy, 1
200
100
0
-100
-200
10
35
400
200
0
-200
-400
4. Constant Target + Fiscal Policy, 0
5
30
20000
10000
0
-10000
20
200
100
0
-100
-200
0
25
3. Directional State Dependent Target, 1
200
100
0
-100
-200
10
40
400
200
0
-200
-400
3. Directional State Dependent Target, 0
5
35
1.0e+06
500000
0
-500000
-1.0e+06
20
200
100
0
-100
0
30
2.State Dependent Target, 1
200
100
0
-100
-200
200
0
-200
-400
0
25
Basis Points (Shock)
Basis Points (non Shock variables)
200
100
0
-100
-200
400
200
0
-200
-400
400
200
0
-200
-400
20
20
25
30
35
40
Subperiod
(b) Sequence 1, Repetition 2
1. Constant Target, 0
1. Constant Target, 1
200
100
0
-100
-200
200
0
-200
0
5
10
15
400
200
0
-200
-400
-600
10
2.State Dependent Target, 0
0
-5000
-10000
5
10
0
-1.0e+09
15
400
200
0
-200
-400
-600
0
-20000
10
20
30
40
4. Constant Target + Fiscal Policy, 1
200
100
0
-100
-200
10
30
20000
4. Constant Target + Fiscal Policy, 0
5
25
40000
15
200
100
0
-100
-200
0
20
3. Directional State Dependent Target, 1
200
100
0
-100
-200
10
200
0
-200
-400
-600
1.0e+09
3. Directional State Dependent Target, 0
5
40
2.0e+09
15
200
100
0
-100
0
30
2.State Dependent Target, 1
200
100
0
-100
-200
5000
0
20
Basis Points (Shock)
Basis Points (non Shock variables)
-400
0
-2.0e+07
-4.0e+07
-6.0e+07
-8.0e+07
500
400
200
0
-200
-400
-600
0
-500
-1000
15
10
20
30
40
Subperiod
Output
Inflation
Interest Rate
Inflation Target
Fiscal Exp.
Figure 17: Time series data, Pre and Post shock
Shock
(a) Sequence 2, Repetition 1
1. Constant Target, 0
1. Constant Target, 1
400
200
100
0
-100
-200
200
0
0
5
10
15
20
400
200
0
-200
-400
20
2.State Dependent Target, 0
200
0
-200
-400
5
10
15
200
0
-200
15
-2.0e+07
-4.0e+07
25
30
35
40
4. Constant Target + Fiscal Policy, 1
200
0
-200
15
40
400
200
0
-200
-400
20
200
100
0
-100
-200
10
35
0
4. Constant Target + Fiscal Policy, 0
5
30
2.0e+07
20
400
0
25
3. Directional State Dependent Target, 1
200
100
0
-100
-200
10
40
300
200
100
0
-100
-200
20
3. Directional State Dependent Target, 0
5
35
2.0e+08
1.0e+08
0
-1.0e+08
-2.0e+08
20
400
0
30
2.State Dependent Target, 1
5000
0
-5000
-10000
0
25
Basis Points (Shock)
Basis Points (non Shock variables)
-200
0
-10000
-20000
-30000
-40000
400
200
0
-200
-400
0
-5.0e+06
-1.0e+07
-1.5e+07
20
20
25
30
35
40
Subperiod
(b) Sequence 2, Repetition 2
1. Constant Target, 0
1. Constant Target, 1
300
200
100
0
-100
0
5
10
400
200
0
-200
-400
0
-200000
-400000
-600000
-800000
15
10
2.State Dependent Target, 0
200
150
100
50
0
5
10
0
-1.0e+07
10
400
200
0
-200
-400
0
-2.0e+07
10
20
30
40
4. Constant Target + Fiscal Policy, 1
300
200
100
0
-100
400
200
0
10
40
2.0e+07
4. Constant Target + Fiscal Policy, 0
5
30
4.0e+07
15
600
0
20
3. Directional State Dependent Target, 1
300
200
100
0
-100
10
400
200
0
-200
-400
1.0e+07
3. Directional State Dependent Target, 0
5
40
2.0e+07
15
600
400
200
0
-200
0
30
2.State Dependent Target, 1
300
200
100
0
-100
0
20
Basis Points (Shock)
Basis Points (non Shock variables)
600
400
200
0
1000
400
200
0
-200
-400
500
0
-500
15
10
20
30
40
Subperiod
Output
Inflation
Interest Rate
Inflation Target
Fiscal Exp.
Figure 18: Time series data, Pre and Post shock
Shock
(a) Sequence 3, Repetition 1
Output, Inflation, Interest Rate, Shock
i. Constant Target, 0
i. Constant Target, 1
400
200
0
-200
500
0
-500
-1000
0
5
10
15
20
20
25
ii. History Dependent Target, 0
30
35
40
ii. History Dependent Target, 1
200
0
-200
-400
200
100
0
-100
-200
0
5
10
15
20
20
iii. Directional History Dependent Target, 0
25
30
35
40
iii. Directional History Dependent Target, 1
300
200
100
0
-100
-200
500
0
-500
0
5
10
15
20
20
25
iv. Constant Target + Fiscal Policy, 0
30
35
40
iv. Constant Target + Fiscal Policy, 1
300
200
100
0
-100
400
200
0
-200
-400
0
5
10
15
20
20
25
30
35
40
Subperiod
Output Gap
Inflation
Interest Rate
Shock
Inflation Target
Gov't Spending
(b) Sequence 3, Repetition 2
Output, Inflation, Interest Rate, Shock
i. Constant Target, 0
i. Constant Target, 1
400
200
0
-200
500
0
-500
-1000
0
5
10
15
10
20
ii. History Dependent Target, 0
30
40
ii. History Dependent Target, 1
400
200
0
-200
-400
200
0
-200
-400
0
5
10
15
10
iii. Directional History Dependent Target, 0
20
30
40
iii. Directional History Dependent Target, 1
300
200
100
0
-100
-200
1000
500
0
-500
-1000
0
5
10
15
10
iv. Constant Target + Fiscal Policy, 0
20
30
40
iv. Constant Target + Fiscal Policy, 1
300
200
100
0
-100
400
200
0
-200
-400
-600
0
5
10
15
10
20
30
40
Subperiod
Output Gap
Output
Inflation
Inflation
Interest Rate
Interest Rate
Shock
Inflation Target
Inflation Target
Fiscal Exp.
Figure 19: Time series data, Pre and Post shock
Gov't Spending
Shock
(a) Sequence 4, Repetition 1
Output, Inflation, Interest Rate, Shock
i. Constant Target, 0
i. Constant Target, 1
400
300
200
100
0
-100
0
-200000
-400000
-600000
-800000
-1.0e+06
0
5
10
15
20
20
25
ii. History Dependent Target, 0
30
35
40
ii. History Dependent Target, 1
300
200
100
0
-100
2.0e+06
1.0e+06
0
-1.0e+06
-2.0e+06
0
5
10
15
20
20
iii. Directional History Dependent Target, 0
25
30
35
40
iii. Directional History Dependent Target, 1
300
200
100
0
-100
-200
3.0e+07
2.0e+07
1.0e+07
0
-1.0e+07
-2.0e+07
0
5
10
15
20
20
25
iv. Constant Target + Fiscal Policy, 0
30
35
40
iv. Constant Target + Fiscal Policy, 1
400
200
0
-200
-400
300
200
100
0
-100
0
5
10
15
20
20
25
30
35
40
Subperiod
Output Gap
Inflation
Interest Rate
Shock
Inflation Target
Gov't Spending
(b) Sequence 4, Repetition 2
Output, Inflation, Interest Rate, Shock
i. Constant Target, 0
i. Constant Target, 1
800
600
400
200
0
0
-5.0e+08
-1.0e+09
-1.5e+09
-2.0e+09
-2.5e+09
0
5
10
15
10
20
ii. History Dependent Target, 0
30
40
ii. History Dependent Target, 1
2.0e+08
1.0e+08
0
-1.0e+08
-2.0e+08
600
400
200
0
-200
-400
0
5
10
15
10
iii. Directional History Dependent Target, 0
20
30
40
iii. Directional History Dependent Target, 1
1000
2.0e+07
500
1.0e+07
0
0
-500
-1.0e+07
0
5
10
15
10
iv. Constant Target + Fiscal Policy, 0
20
30
40
iv. Constant Target + Fiscal Policy, 1
600
400
200
0
-200
-400
400
200
0
0
5
10
15
10
20
30
40
Subperiod
Output Gap
Output
Inflation
Inflation
Interest Rate
Interest Rate
Shock
Inflation Target
Inflation Target
Fiscal Exp.
Figure 20: Time series data, Pre and Post shock
Gov't Spending
Shock
(a) Sequence 5, Repetition 1
1. Constant Target, 0
1. Constant Target, 1
400
300
200
100
0
-100
0
5
10
15
500
200
0
0
-500
-200
-1000
20
-400
20
2.State Dependent Target, 0
0
-500
5
10
15
0
-500
15
0
-200
-400
200
0
-200
-2.0e+07
-400
25
30
35
40
4. Constant Target + Fiscal Policy, 1
400
200
0
15
40
0
20
400
300
200
100
0
-100
10
35
2.0e+07
4. Constant Target + Fiscal Policy, 0
5
30
4.0e+07
20
600
0
25
3. Directional State Dependent Target, 1
400
300
200
100
0
-100
10
40
200
20
3. Directional State Dependent Target, 0
5
35
1.0e+09
0
-1.0e+09
-2.0e+09
20
500
0
30
2.State Dependent Target, 1
400
300
200
100
0
-100
500
0
25
Basis Points (Shock)
Basis Points (non Shock variables)
600
400
200
0
400
200
0
-200
-400
20
200
0
-200
-400
20
25
30
35
40
Subperiod
(b) Sequence 5, Repetition 2
1. Constant Target, 0
1. Constant Target, 1
250
200
150
100
50
0
400
200
0
5
10
0
-500
15
10
2.State Dependent Target, 0
250
200
150
100
50
0
200
0
-200
5
10
0
-1.0e+13
10
400
200
0
-200
-400
-50000
10
20
30
40
4. Constant Target + Fiscal Policy, 1
250
200
150
100
50
0
400
200
0
10
40
0
4. Constant Target + Fiscal Policy, 0
5
30
50000
15
600
0
20
3. Directional State Dependent Target, 1
250
200
150
100
50
0
10
400
200
0
-200
-400
1.0e+13
3. Directional State Dependent Target, 0
5
40
2.0e+13
15
400
200
0
-200
0
30
2.State Dependent Target, 1
400
0
20
Basis Points (Shock)
Basis Points (non Shock variables)
0
400
200
0
-200
-400
500
600
400
200
0
-200
15
400
200
0
-200
-400
10
20
30
40
Subperiod
Output
Inflation
Interest Rate
Inflation Target
Fiscal Exp.
Figure 21: Time series data, Pre and Post shock
Shock
(a) Sequence 6, Repetition 1
1. Constant Target, 0
1. Constant Target, 1
200
150
100
50
0
-50
0
5
10
15
400
200
0
-200
-400
20
200
0
-200
-400
20
2.State Dependent Target, 0
200
150
100
50
0
-50
200
0
-200
5
10
15
15
200
0
-5.0e+07
-200
-1.0e+08
-400
20
0
-200
-500
-400
25
30
35
40
4. Constant Target + Fiscal Policy, 1
200
100
0
15
40
200
20
200
150
100
50
0
-50
10
35
0
4. Constant Target + Fiscal Policy, 0
5
30
500
20
300
0
25
3. Directional State Dependent Target, 1
200
150
100
50
0
-50
10
40
0
3. Directional State Dependent Target, 0
5
35
5.0e+07
20
300
200
100
0
-100
0
30
2.State Dependent Target, 1
400
0
25
Basis Points (Shock)
Basis Points (non Shock variables)
300
200
100
0
-100
400
200
0
-200
-400
20
200
0
-200
-400
20
25
30
35
Subperiod
(b) Sequence 6, Repetition 2
1. Constant Target, 0
1. Constant Target, 1
200
150
100
50
0
-50
0
5
10
0
-1.0e+06
-2.0e+06
-3.0e+06
-4.0e+06
15
400
200
0
-200
-400
10
2.State Dependent Target, 0
0
-500
5
10
0
-200
10
10
20
30
40
4. Constant Target + Fiscal Policy, 1
200
150
100
50
0
-50
10
40
400
200
0
-200
-400
4. Constant Target + Fiscal Policy, 0
5
30
1000
500
0
-500
-1000
15
300
200
100
0
0
20
3. Directional State Dependent Target, 1
200
150
100
50
0
-50
200
400
200
0
-200
-400
10
3. Directional State Dependent Target, 0
5
40
2.0e+08
1.0e+08
0
-1.0e+08
-2.0e+08
15
400
0
30
2.State Dependent Target, 1
200
150
100
50
0
-50
500
0
20
Basis Points (Shock)
Basis Points (non Shock variables)
300
200
100
0
500
400
200
0
-200
-400
0
-500
15
10
20
30
40
Subperiod
Output
Inflation
Interest Rate
Inflation Target
Fiscal Exp.
Figure 22: Time series data, Pre and Post shock
Shock
1, 0
1, 1
2, 1
0
150
-10000
60
-5000
100
40
-20000
20
5
10
15
20
-10000
50
-30000
0
Inflation Forecast
2, 0
200
0
80
0
20
25
3, 0
30
35
40
-15000
0
5
3, 1
200
15
20
15
20
25
5, 0
200
100
100
0
0
-100
-100
-200
0
5
10
30
35
40
15
20
40
35
40
-400000
0
5
5, 1
200
35
-300000
0
20
300
40
-200000
-200
10
35
-100000
50
5
30
0
100
0
0
25
4, 1
150
0
-100
20
4, 0
200
100
10
10
15
20
20
25
6, 0
30
6, 1
100
100
50
50
0
-50
0
20
25
30
35
40
-100
0
5
10
15
20
20
25
30
Period
Graphs by ShockSequence (1-6) and PrePostShock (0,1), Constant, Rep 1
1, 0
Standard Deviation of Inflation Forecasts
46.73626
1, 1
2, 0
17372.06
7.774602
63.6455
32.62284
0
5
10 15 20
3, 0
80.31189
13.33021
20 25 30 35 40
5
10 15 20
5
10 15 20
4, 1
3.33e+09
0
5
5, 1
10 15 20
20 25 30 35 40
6, 0
66.59392
8.343328
0
20 25 30 35 40
9.382312
114.5644
13.38843
10 15 20
4, 0
20 25 30 35 40
5, 0
63.24555
5
41.28996
25.3081
0
67.08038
0
3, 1
121.3752
18.5
2, 1
8559.83
5.276295
20 25 30 35 40
6, 1
116.8408
7.991315
0
5
10 15 20
20 25 30 35 40
Period
Graphs by ShockSequence (1-6) and PrePostShock (0,1), Constant, Rep 1
Figure 23: Distribution of Inflation Forecasts (25th, 50th, and 75th percentile and standard
deviation), Constant Rep 1
1, 0
1, 1
100
2, 0
0
50
-200000
100
-50
-1.0e+08
-100
0
Inflation Forecast
0
200
-5.0e+07
0
2, 1
300
5
10
15
10
20
3, 0
30
40
0
100
0
200
0
-200
100
-100
15
50
0
0
5
10
15
20
30
40
4, 1
0
-4.0e+09
-6.0e+09
-8.0e+09
0
10
20
30
40
0
5
5, 1
100
10
-2.0e+09
5, 0
150
15
300
-400
10
10
4, 0
200
5
5
3, 1
200
0
-400000
0
10
15
10
6, 0
150
100
100
-500000
0
50
-1.0e+06
-100
0
-1.5e+06
-200
-50
20
30
40
30
40
6, 1
200
10
20
0
-2.0e+06
0
5
10
15
10
20
30
40
Period
Graphs by ShockSequence (1-6) and PrePostShock (0,1), Constant, Rep 2
1, 0
1, 1
Standard Deviation of Inflation Forecasts
46.68244
2, 0
3.33e+16
2, 1
54.03188
9.565563
3317764
16.91236
0
5
10
15
10
3, 0
20
30
40
14.01884
15
20
30
40
10
0
5
15
10
15
40
10
20
30
40
6, 1
55.26778
10.92906
5
30
4, 1
6, 0
169.5214
0
20
1.41e+10
5, 1
8.700255
10
14.73469
10
5, 0
51.58919
15
182.1016
30.05597
10
10
4, 0
156.4049
5
5
3, 1
164.7695
0
103.8617
0
3.33e+18
11.75798
10
20
30
40
0
5
10
15
10
20
30
40
Period
Graphs by ShockSequence (1-6) and PrePostShock (0,1), Constant, Rep 2
0
Figure 24: Distribution of Inflation Forecasts (25th, 50th, and 75th percentile and standard
deviation), Constant Rep 2
0
0
1, 0
1, 1
2, 0
0
100
50
-1000
-200000
-5.0e+07
-2000
0
-400000
-50
0
Inflation Forecast
2, 1
0
0
5
10
15
20
-3000
20
25
3, 0
30
35
40
40
10
20
0
0
-10
-20
-20
10
15
20
30
35
40
10
15
20
35
40
35
40
35
40
-1.0e+06
-2.0e+06
0
5
10
15
20
0
-5.0e+07
0
30
35
40
30
6, 1
-50
25
25
0
50
0
20
20
6, 0
100
-1.0e+09
5
30
4, 1
-20
25
-50
0
25
1.0e+06
5, 1
-100
20
0
20
-5.0e+08
20
4, 0
0
0
15
0
5, 0
50
10
20
-40
5
5
3, 1
20
0
-1.0e+08
0
-1.0e+08
0
5
10
15
20
20
25
30
Period
Graphs by ShockSequence (1-6) and PrePostShock (0,1), SD, Rep 1
1, 0
Standard Deviation of Inflation Forecasts
50.95586
1, 1
2, 0
1001380
8.708575
334366.5
38.36991
0
5
10 15 20
2.773886
20 25 30 35 40
3, 0
67.70894
5
10 15 20
10 15 20
20 25 30 35 40
4, 0
4, 1
3771619
4.30439
20 25 30 35 40
5, 0
58.43396
5
36.75633
7.81025
0
0
3, 1
61.35756
5.019407
2, 1
3.33e+14
0
5
5, 1
10 15 20
16.74896
0 20 25 30 35 40
6, 0
3.33e+33
95.55757
8.61362
6, 1
2.87e+08
14.50862
0
5
10 15 20
20 25 30 35 40
0
5
10 15 20
20 25 30 35 40
Period
Graphs by ShockSequence (1-6) and PrePostShock (0,1), SD, Rep 1
Figure 25: Distribution of Inflation Forecasts (25th, 50th, and 75th percentile and standard
deviation), SD Rep 1
1, 0
1, 1
0
0
-1000
-2.0e+08
-2000
-4.0e+08
-3000
-6.0e+08
0
5
10
15
-2.0e+06
-4.0e+06
-20
15
3, 0
20
25
30
-6.0e+06
0
5
3, 1
40
10
15
-50 0
5
10
15
-2.0e+08
-3.0e+08
-200
10
5, 0
20
30
40
0
5
5, 1
100
0
50
-5.0e+12
0
-1.0e+13
-50
-1.5e+13
10
15
5
10
15
30
40
30
40
6, 1
0
-5.0e+07
-200
20
20
0
200
10
10
6, 0
0
0
40
-1.0e+08
-100
0
30
4, 1
0
0
20
0
100
0
-20
0
10
4, 0
50
20
2, 1
0
0
-8.0e+08
-4000
Inflation Forecast
2, 0
20
-1.0e+08
0
5
10
15
10
20
30
40
Period
Graphs by ShockSequence (1-6) and PrePostShock (0,1), SD, Rep 2
1, 0
1, 1
Standard Deviation of Inflation Forecasts
891.239
2, 0
7.79e+09
2, 1
52.55341
21.93171
7.41e+13
3.855011
0
5
10
15
15
3, 0
20
25
30
15.28889
15
15
10
20
30
40
4, 1
68.60211
8.917835
10
10
4, 0
74.91681
5
5
3, 1
49.23019
0
0
1.77e+37
2.666667
10
20
30
40
0
5
10
15
10
20
30
40
0
5, 0
5, 1
31.38073
6, 0
3.33e+37
6, 1
364.3316
3.586239
3.00e+14
28.44292
0
5
10
15
10
20
30
40
0
5
10
15
10
20
30
40
Period
Graphs by ShockSequence (1-6) and PrePostShock (0,1), SD, Rep 2
Figure 26: Distribution of Inflation Forecasts (25th, 50th, and 75th percentile and standard
deviation), SD Rep 2
1, 0
1, 1
2, 1
0
100
0
10
-2000
50
-1.0e+07
0
-4000
0
-2.0e+07
-10
-6000
0
Inflation Forecast
2, 0
20
5
10
15
20
-50
20
25
3, 0
30
35
40
-3.0e+07
0
5
3, 1
50
10
15
20
20
25
4, 0
35
40
35
40
35
40
4, 1
50
50
30
0
-5.0e+06
0
0
0
-1.0e+07
-50
-1.5e+07
-100
-50
0
5
10
15
20
-50
20
25
5, 0
30
35
40
-2.0e+07
0
5
5, 1
10
15
20
20
6, 0
3.0e+18
40
0
2.0e+18
20
0
-100
1.0e+18
0
-100
-200
0
-20
5
10
15
20
20
25
30
35
40
30
6, 1
100
0
25
100
-200
0
5
10
15
20
20
25
30
Period
Graphs by ShockSequence (1-6) and PrePostShock (0,1), Dir. SD, Rep 1
1, 0
Standard Deviation of Inflation Forecasts
22.76297
0
1, 1
2, 0
3159.453
3.965091
50.45773
7.440349
0
5
10 15 20
3, 0
47.01861
8.615941
20 25 30 35 40
5
10 15 20
10 15 20
0
5
5, 1
10 15 20
79.08979
20 25 30 35 40
6, 1
184.7674
7.361688
10 15 20
20 25 30 35 40
6, 0
14.77329
5
4, 1
3.28e+07
6.22718
4.30e+28
0
20 25 30 35 40
4, 0
20 25 30 35 40
5, 0
88.09717
5
43.83777
11.35537
0
50.5742
0
3, 1
95.05057
5.809475
2, 1
4.13e+07
20.99405
0
5
10 15 20
Period
20 25 30 35 40
0
Graphs by ShockSequence (1-6) and PrePostShock (0,1), Dir. SD, Rep 1
Figure 27: Distribution of Inflation Forecasts (25th, 50th, and 75th percentile and standard
deviation), Dir. SD Rep 1
1, 0
1, 1
30
2, 0
20
-2000
100
0
-4000
0
-10
-6000
-100
10
0
-2.0e+06
-4.0e+06
0
Inflation Forecast
2, 1
200
0
5
10
15
10
20
3, 0
30
40
-6.0e+06
-8.0e+06
0
5
3, 1
100
200
50
100
10
15
10
4, 0
0
0
-5.0e+06
-200
-200
5
10
15
-1.0e+07
-400
10
20
5, 0
30
40
-1.5e+07
0
5
5, 1
200
40
5.0e+06
0
-100
0
30
4, 1
200
0
-50
20
10
15
10
20
6, 0
40
6, 1
400
100
0
30
200
100
50
0
-20000
0
0
-100
-40000
0
5
10
15
-200
-50
10
20
30
40
-400
0
5
10
15
10
20
30
40
Period
Graphs by ShockSequence (1-6) and PrePostShock (0,1), Dir. SD, Rep 2
1, 0
1, 1
Standard Deviation of Inflation Forecasts
36.14938
2, 0
18949.81
4.737557
8.36826
0
5
10
15
20
30
40
6.763875
10
5
15
15
4, 0
20
30
40
0
5
10
15
15
71.1368
10
0
40
20
30
10
40
20
30
40
6, 1
202.0056
13.01068
10
30
4, 1
6, 0
12.25198
5
20
2.17e+18
5, 1
4.60e+20
0
10
5.525195
10
5, 0
95.46727
10
74.47446
24.69199
5
66.08475
0
3, 1
114.8749
0
1.48e+07
16.74067
10
3, 0
70.02995
2, 1
101.9792
43.05068
0
5
10
Period
Graphs by ShockSequence (1-6) and PrePostShock (0,1), Dir. SD, Rep 2
15
10
20
30
40
0
Figure 28: Distribution of Inflation Forecasts (25th, 50th, and 75th percentile and standard
deviation), Dir. SD Rep 1
1, 0
2, 0
100
50
50
150
0
0
100
-50
-50
50
-100
-100
0
Inflation Forecast
1, 1
100
5
10
15
20
-5.0e+07
0
20
25
3, 0
30
35
40
-1.0e+08
0
5
3, 1
150
100
2, 1
0
200
10
15
20
20
25
4, 0
400
100
200
50
0
0
30
35
40
35
40
4, 1
200
150
100
50
0
-50
-200
0
5
10
15
20
25
5, 0
30
35
40
200
100
0
5
-200
-100
15
20
10
15
20
25
30
25
35
200
100
100
50
0
0
-100
40
30
6, 1
150
-50
20
20
6, 0
0
10
0
5, 1
200
5
0
-50
20
400
0
50
-200
0
5
10
15
20
20
25
30
35
Period
Graphs by ShockSequence (1-6) and PrePostShock (0,1), Fiscal, Rep 1
1, 0
Standard Deviation of Inflation Forecasts
38.01645
1, 1
2, 0
35.17259
6.653409
80.74669
13.64225
0
5
10 15 20
8
20 25 30 35 40
3, 0
32.59218
5
10 15 20
5
10 15 20
5
10 15 20
6, 0
49.88181
4.428443
20 25 30 35 40
4, 1
5.238745
0
5, 1
12.36033
0
20 25 30 35 40
56.8348
6.385748
56.40036
24.62214
10 15 20
4, 0
20 25 30 35 40
5, 0
86.82783
5
22.88073
9.273619
0
0
3, 1
92.48033
6.482883
2, 1
2.91e+07
20 25 30 35 40
6, 1
0
74.22312
12.86576
0
5
10 15 20
20
25
30
35
Period
Graphs by ShockSequence (1-6) and PrePostShock (0,1), Fiscal, Rep 1
Figure 29: Distribution of Inflation Forecasts (25th, 50th, and 75th percentile and standard
deviation), Fiscal Rep 1
1, 0
1, 1
50
2, 0
300
400
100
200
200
0
100
0
-100
0
-200
0
-50
-100
-200
Inflation Forecast
0
5
10
15
-100
10
20
3, 0
30
40
50
0
0
-100
-50
10
15
5
10
15
40
30
40
30
40
4, 1
-100
0
10
20
30
40
-200
0
5
10
15
6, 1
100
100
50
0
0
500
0
-50
20
20
1000
150
10
10
6, 0
-100
0
30
0
200
-100
20
100
5, 1
0
10
200
100
300
100
15
200
5, 0
200
10
4, 0
-200
5
5
300
100
0
-400
0
3, 1
100
2, 1
200
30
40
-500
0
5
10
15
10
20
Period
Graphs by ShockSequence (1-6) and PrePostShock (0,1), Fiscal, Rep 2
1, 0
1, 1
Standard Deviation of Inflation Forecasts
31.15731
2, 0
65.84915
2.672612
17.5
0
5
10
15
20
30
40
3.789606
10
15
20
30
40
10
15
20
30
40
5.61496
0
40
30
4, 1
5
10
15
10
20
30
40
6, 1
397.0198
6.35304
10
20
120.5896
49.55664
16.52103
5
10
6, 0
429.2913
18.87459
15
4, 0
5, 1
54.61252
10
6.363961
10
5, 0
0
5
35.68964
8.268078
5
21.84319
0
3, 1
75.0424
0
194.715
3.767551
10
3, 0
647.2885
2, 1
94.89175
9.756764
0
5
10
15
10
20
30
40
Period
Graphs by ShockSequence (1-6) and PrePostShock (0,1), Fiscal, Rep 2
Figure 30: Distribution of Inflation Forecasts (25th, 50th, and 75th percentile and standard
deviation), Fiscal Rep 2