IMES DISCUSSION PAPER SERIES

Individual Trend Inflation

Toshitaka Sekine, Frank Packer, and Shunichi Yoneyama
Discussion Paper No. 2022-E-14

INSTITUTE FOR MONETARY AND ECONOMIC STUDIESBANK OF JAPAN
2-1-1 NIHONBASHI-HONGOKUCHOCHUO-KU, TOKYO 103-8660
JAPAN

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Monetary and Economic Studies.

IMES Discussion Paper Series 2022-E-14
August 2022

Individual Trend Inflation

Toshitaka Sekine*, Frank Packer**, and Shunichi Yoneyama***
Abstract
This paper extends the recent approaches to estimate trend inflation from the survey
responses of individual forecasters. It relies on a noisy information model to estimate
the trend inflation of individual forecasters. Applying the model to the recent
Japanese data, it reveals that the added noise term plays a crucial role and there exists
considerable heterogeneity among individual trend inflation forecasts that drives the
dynamics of the mean trend inflation forecasts. Divergences in forecasts as well as
moves in estimates of trend inflation are largely driven by a identifiable group of
forecasters who see less noise in the inflationary process, expect the impact oftransitory inflationary shocks to wane more quickly, and are more flexible inadjusting their forecasts of trend inflation in response to new information.

Keywords: Inflation forecast; Disagreement; Unobserved components model;
Noisy information; Inflation target; Quantitative and qualitative monetaryeasing; Bank of JapanJEL classification: E31, E52, E58* Hitotsubashi University and CAMA (E-mail: toshitaka.sekine@r.hit-u.ac.jp)** Bank for International Settlements (E-mail: frank.packer@bis.org)*** Director and Senior Economist, Institute for Monetary and Economic Studies, Bank of Japan(E-mail: shunichi.yoneyama@boj.or.jp)
We are grateful to Toshiaki Watanabe, Mototsugu Shintani, Jouchi Nakajima and seminar
participants at the Bank of Japan and the CFE 15th International Conference for useful comments
and discussions. Sekine gratefully acknowledges financial support from the Japan Center for
Economic Research. The views expressed in this paper are those of the authors and do notnecessarily reflect the official views of the Bank of Japan or the Bank for International
Settlements.

1

Introduction

There is no doubt that trend inflation, embedded in actual data of consumer prices and in
inflation expectations of various economic players, is one of the most important variables forthe conduct of monetary policy. For this reason, huge effort has been made by a number of
researchers to extract trend inflation. In this paper, we try to contribute to this literature byextending the existing studies in the following two ways.
First, we incorporate a noisy information model more explicitly in an unobserved components
model. An unobserved components model such as Beveridge and Nelson (1981) is a useful tool
to decompose actual data into its trend and transitory components. Stock and Watson (2007,2016) apply the procedure to estimate trend inflation by incorporating stochastic volatility in themodel. Kozicki and Tinsley (2012) use an unobserved components model to analyze inflation
forecasts. Other research papers, many of them more recent, have extracted trend inflationfrom actual and forecast inflation rates (Chan et al. (2018), Nason and Smith (2021), Patton
and Timmermann (2010) and Yoneyama (2021)).
In doing so, we add one extra disturbance term, which can be interpreted to represent anoise signal of Woodford (2003). Thus, our research is also related with long literature of
information rigidity developed by Mankiw and Reis (2002), Mankiw et al. (2004) and Coibion
and Gorodnichenko (2012, 2015). Shintani and Ueda (2021) have broken down noisy information
models between Lucas and Woodfordian variants, whereby the former assumes that forecasters
can observe the true state of realised inflation (including its trend and transitory components)
at the end of each period, while the latter assumes that realisations are never revealed. Ourmodel can be seen as Woodfordian.
Second, we apply the model to individual forecasts to extract individual trend inflation. The
above-cited studies utilize the average of individual inflation forecasts to derive trend inflation.
However, one of the important lessons coming from the information rigidity literature is theimportance of heterogeneity in forming inflation expectations. For this reason, it can be valuable
for us to work with individual responses to the survey when incorporating information rigidity
into our model. In the Japanese context, assuming specific models of the term structures ofinflationary expectations, Hattori and Yetman (2017) and Shintani and Soma (2020) derive2

long-run inflation expectations of individual forecasters. However, they do not analyze theheterogeneity of individual responses, including the degree of disagreement of inflation forecasts
across forecasters discussed in this paper’s later sections.
In order to demonstrate the utility of our approach, we apply it to recent Japanese data toshed light on the impact of introducing an explicit inflation target policy and various unconventional measures of monetary easing. The Bank of Japan (BOJ) adopted a 2 percent inflation
target in January 2013, which was followed by a series of monetary easing measures. These
include the Quantitative and Qualitative Monetary Easing (QQE) program in April 2013, theNegative Interest Rates Policy (NIRP) in January 2016 and the Yield Curve Control (YCC) of
10 year Japanese Government Bonds (JGB) in September 2016.
Thus, our paper relates to numerous studies investigating the effects of inflation targeting
policy as well as unconventional monetary easing, such as Hayashi and Koeda (2019), Christensen
and Spiegel (2019), Miyao and Okimoto (2017), Ehrmann (2015), Honda et al. (2013), Ehrmann
et al. (2012), Ueda (2012), and Capistran and Ramos-Francia (2010). In addition, Hattori
et al. (2021), de Mendonca and de Deus (2019), Hubert (2015), and Pederson (2015) discuss theeffectiveness of central bank communications and own forecasts through their impact on private
inflation forecasts.
To briefly preview our results, we first work with the mean of inflation forecasts, and showthat the added noise term improves the fit of the model dramatically. Trend inflation obtained
from the average inflation forecasts surged after the introduction of the 2% inflation target and
the QQE in 2013 and again after the adoption of the YCC in 2016. We then estimate individual
trend inflation rates and document considerable heterogeneity among the forecasters. Based ona cluster analysis of estimated parameter variables, we divide forecasters in two groups and findthat forecasters who see smaller noise in actual inflation also tend to think the effects of cyclicalcomponents of inflation will wane more quickly and are more likely to raise their assessment oftrend inflation. In fact, such forecasters were mostly responsible for the surge in average trend
inflation observed earlier, and also for the wider disagreement in trend inflation observed intandem. The adoption of the inflation target and subsequent unconventional monetary policy
measures succeeded in raising the trend inflation estimates of some forecasters but not all.

3

The rest of the paper will proceed as follows. In the next section, we introduce our model ofnoisy information as an extension of an unobserved components model. In section 3, we describe
the survey data from which we extract trend inflation. In section 4, after explaining how to bridge
the survey observations to the earlier noisy information model, we present our main estimation
results. In section 5, we interpret our findings and discuss the policy implications of our resultsin the light of the aggressive monetary policy efforts made by the Bank of Japan starting in2013 to lift inflation. Section 6 concludes the paper.

2

Model

We use the following noisy information model in order to retrieve trend inflation of individual
forecasters.
2
πt = τi,t + ci,t + ϵi,t , ϵi,t ∼ N (0, σϵi,t
)

(1)

2
τi,t = τi,t−1 + νi,t , νi,t ∼ N (0, σνi
)

(2)

2
ci,t = ρi ci,t−1 + ωi,t , ωi,t ∼ N (0, σωi)(3)where πt is the latest actual inflation rate available when forecaster i makes her inflation forecasts
at time t. She decomposes observed inflation into permanent trend τi,t , transitory ci,t and noise
ϵi,t components according to her interpretation of observations (equation (1)). She assumes thattrend and transitory components follow stochastic processes specified by equations (2) and (3).
Our model can be seen as an extension of an unobserved components model in a noisy
information setup. Instead of equation (1), a conventional unobserved components model suchas Stock and Watson (2007, 2016) uses
πt ≡ τt + ct .
Analysing individual forecasts, we add ϵi,t , the presence of which can be justified by a noisy signalof Woodford (2003). We assume stochastic volatility for this term to allow serial correlation of4its variance — once forecasters perceive the data is noisy, the situation may continue for a while.

2σϵi,t= γi exp (λi,t )(4)2
λi,t = θi λi,t−1 + ηi,t , ηi,t ∼ N (0, σηi).

(5)Based on this setup, forecaster i formulates her k-period ahead projection π̂i,t,+k at the timeof t as2π̂i,t,+k = τi,t + ρki ci,t + ui,t,+k , ui,t,+k ∼ N (0, σui,+k)(6)

where ui,t,+k is a measurement error. Provided |ρi | < 1, inflation projection converges to thetrend inflation as π̂i,t,+∞ = τi,t .
Equations (1) – (3) and (6) can be compactly summarized in a state-space form where theobservation equation is






πt





1





1


ϵi,t


  





  




 π̂i,t,+1   1  ρi 
 ui,t,+1 

  





 =  .  τi,t +  .  ci,t + ,.
.
  . 
 . 


..
..

  . 
 . 



  




k
π̂i,t,+k1
ρiui,t,+k(7)

and the transition equation is














 τi,t   1 0   τi,t−1   νi,t 

=

+
.
ci,t
0 ρi
ci,t−1
ωi,t

3

Data

3.1

ESP Survey(8)

For inflation forecasts, we take those from the ESP Survey from 2004M4 to 2020M3. The
ESP Survey is a survey of professional forecasters in Japan conducted by the Japan Center
for Economic Research (JCER). Each month, the JCER collects predictions from around 40
forecasters regarding various macroeconomic indicators (such as GDP and its components) as
well as financial variables (such as 10-year JGB yields, exchange rates, money growth, etc.). In
5this study, we will focus on core Consumer Price Index (CPI) inflation (excluding fresh food).
These professional forecasters are identified with an institution code with which those forecasters are aﬀiliated. Hence, strictly speaking, different persons may have submitted theirforecasts with the same ID, if there is a change in personnel in these institutions. The JCER
does not disclose names of forecasters nor their characteristics (age, gender, job experience,etc.). The only information we have is the type of institutions such that these institutions areassociated with banks, insurance companies, securities firms and others.1
Each month, the JCER surveys quarterly and annual (fiscal year) forecasts.2

We useqqaπ̂t,+0, ..., π̂t,+4(nowcast to 4-quarter ahead inflation) and π̂t,+1(inflation in the next fiscal year),q
where π̂t,+k
is a forecast of quarterly average year-on-year core CPI inflation for k quarters aheadais its annual average for k years ahead. Depending on the survey timing, the JCERand π̂t,+kq
q
a , but we do not incorporate
asks for inflation in the longer horizon like π̂t,+5, ..., π̂t,+8and π̂t,+2them in our estimation because they are not available consistently through the sample period.
The JCER surveys core CPI inflation forecasts with and without the direct effects of consumption tax hikes.3 We use ones excluding consumption tax effects because we are primarily
interested in the impacts of monetary policy on ESP inflation forecasts. Before the JCER began
to survey without-consumption-tax-effect forecasts in 2013M10, we subtract 2% points from core
CPI inflation forecasts (including consumption tax effects) for FY2014 (for 2012M10-2013M9
surveys) and the corresponding quarters (for 2013M1-2013M9 surveys).4 In its October 2012
Outlook, the Bank of Japan disclosed that it expected core CPI inflation would increase by 2
percentage points for the 2014 consumption tax hike. That impact seemed to become common
knowledge across ESP forecasters, if we look at the difference between with- and withoutconsumption-tax-effect forecasts from 2013M10.
1

Japanese securities firms partly correspond to US broker dealers and partly US investment banks (Ito andHoshi (2020), p.114).
2
Japanese fiscal year is from April to March of the following calendar year.
3
During the sample period, consumption tax was raised from 5% to 8% on April 1, 2014 and 8% to 10% on
October 1, 2019. The second consumption tax was originally scheduled on October 1, 2015, but in November
2014, Prime Minister Abe announced to defer it to April 1, 2017. In June 2016, he decided again to defer it to
October 1, 2019.
4
One forecaster (ID206) failed to submit the without-consumption-tax-effect forecasts in 2014M4 and 2014M5.
We fill these missing observations by applying the same 2 percentage points correction to his/her withconsumption-tax-effect forecasts. We also made adjustments for responses of ID205 in 2013M10 and 2013M11 sothat quarterly and annual figures become consistent each other.

6On a few occasions (corresponding to about 2% of 7,425 sample records), some forecasters
fail to submit their forecasts for a month or so. In the following estimation, we assume thatthe forecasters maintained their latent variables τi,t , ci,t and λi,t at the same levels during theirabsence from the survey. As a robustness check, we restricted the samples to the forecasters
who reported for more than 36 months consecutively (the sample records are then reduced to
5,617) and treated the forecasters as different entities before and after the interruption. The
results did not change materially (they are available on request).

3.2

Actual CPI

For actual CPI, we use a month-to-month change in seasonally adjusted core CPI (excluding
fresh food).
πt =Pt− 1 ≈ pt − pt−1 = ∆pt ,Pt−1

where Pt is CPI at time t and the lower letter denotes its logarithm.
The actual CPI that we use for the analysis should be real time data so as to faithfully
mimic the information set available to the forecasters at the time. This implies that at thetime of the rebasing of the CPI, that takes place every five years, we should use then oﬀiciallypublished seasonally adjusted series before the release of new series and switch to the new one
thereafter.5 For instance, when the the Statistics Bureau of Japan changed the base year from2000 to 2005 in August 2006, we use the 2000 year based CPI series up to July 2006 and switch
to the 2005-index series from August 2006.
In order to exclude the direct effects of the consumption tax hikes, 2 percentage points are
subtracted from π2014M 4 , which is consistent with the adjustment made for the ESP forecasts
mentioned above. In addition, 0.2 percentage points are subtracted from π2019M 10 , the effect ofwhich was published by the Statistics Bureau of Japan and also is consistent with what ESP
forecasters embedded in their forecasts.
5

Every five years, the Statistics Bureau of Japan switches the base years for the CPI calculation. At that time,
it changes the weight and the coverage of CPI baskets as well as compilation details such as quality adjustments.
These changes have sometimes resulted in significant revisions.

7

4

Estimation

4.1 State-Space Representation
As we use the ESP forecasts of annual changes in the quarterly and the annual average CPI (πtq
and πta ), we need to modify the above introduced observation equation (7) accordingly.
These inflation rates can be expressed by the month-to-month inflation πt as:
Pt + Pt−1 + Pt−2
−1
Pt−12 + Pt−13 + Pt−14[]′
1q≈ (πt + 2πt−1 + 3πt−2 + · · · + 3πt−11 + 2πt−12 + πt−13 ) = S
πt−13 · · · πt ,3
Pt + . . . + Pt−11
πta =−1
Pt−12 + . . . + Pt−23[]′
1a≈ (πt + 2πt−1 + · · · + 12πt−11 + · · · + 2πt−21 + πt−22 ) = S
πt−22 · · · πt ,
12
πtq =

[
where S q =

]
1
3

2
3

3
3

···

3
3

2
3

1
3

[
and S a =

]
1
12

2
12

···

12
12

···

2
12

1
12

.

q
q
a
Then, π̂i,t,+0, . . . , π̂i,t,+4and π̂i,t,+1
can be expressed as




πt−12
..
.




πt−12
..
.

























π
π̂


..




 t−12  i,t,+1 


.
 πt

 πt

 . 


..


 = [S1 |S2 ]  = S1  ..  + S2 
,

=S
.








 q









π̂
π̂
 π̂i,t,+4 
i,t,+1i,t,+1










π
π̂
t
i,t,+23
..
..




a
π̂i,t,+1
.
.








π̂i,t,+23π̂i,t,+23




π̂ q
 i,t,+0 (9)where S is a 6 × 36 selection matrix, an element of which consists of S q and S a (the exact form
differs according to the survey month — see Appendix for more details). This can be usefully
divided into a 6 × 13 matrix S1 and a 6 × 23 matrix S2 , where the former corresponds to actual
CPI (πt−12 , . . . , πt ), and the latter corresponds to its projections (π̂i,t,+1 , . . . , π̂i,t,+23 ).
Substituting equation (6) into equation (9), we have the new observation equation mapped8

to the ESP forecasts as








 q

 
 π̂i,t,+0    0   1
..

=
+
.




B
Zτ
 q

 π̂i,t,+4 aπ̂i,t,+1
where


ϵi,t

πt




 q
 ui,t,+0 
1   τi,t  

..
,


+
.



Zc
ci,t

 q
 ui,t,+4 
aui,t,+1






 

ρ
1
π
 i 
 
 t−12 
 . 
 . 
 . 
 . 
 . 
. 
B = S1  .  , Zτ = S2  .  and Zc = S2  .  .


 


ρ23
1
πt
i


Transition equation does not change from equation (8).














 τi,t   1 0   τi,t−1   νi,t 
=

+
.

ci,t
0 ρi
ci,t−1
ωi,t

4.2

Estimation Results

We estimate the above state-space form by a Bayesian Markov chain Monte Carlo (MCMC),
which exploits an eﬀicient Gaussian smoother developed by De Jong and Shephard (1995). For
stochastic volatility, we follow Nakajima (2011) who uses the multi-move sampler of Shephard
and Pitt (1997) modified by Watanabe and Omori (2004).6 That is, for each individual forecasters (62 in total), we run the Gibbs sampler for 21,000 replications, with 1,000 burn-in replications
discarded and 20,000 replications retained. On top of that, we repeat the same exercise for the
∑ q
∑ a
q
a
average of ESP forecasts, π̂∗,t,+k= i π̂i,t,+k/Nt and π̂∗,t,+k= i π̂i,t,+k/Nt (Nt is the numberof forecasters), treating a mean forecaster (denoted by ∗) as an additional individual.

9Table 1: Log Marginal Likelihood Estimates
Baseline Model: equations (1) to (6)Alternative Models:Drop a noise term ϵi,t from equation (1)Use only π̂i,t,+1 in equation (6)Assume stochastic volatility of νi,t and ωi,t in equations (2) and (3)-28.491-66.506-33.165-33.971q
Note: π̂i,t,+1 in equation (6) corresponds to π̂i,t,+0
in equation (9).

4.2.1

Mean Forecasts

Before going to the analyses of individual trend inflation, we examine how our model behaves
with mean inflation forecasts. Table 1 provides marginal likelihood of our baseline model andits alternatives. Following Chan et al. (2018), we calculate the marginal likelihood based on
the predictive likelihood in terms of actual inflation over the last 36-month period (2017M42020M3). The smaller negative values indicate the better fit of the model. That is, the baselinemodel shows the best performance compared with the alternatives.
More specifically, comparison with each alternative is as follows. First, dropping a noise
term ϵi,t from equation (1) drastically deteriorates the fit. This clearly indicates how crucial
our assumption of noisy information is. The second alternative sees the role of longer-term
inflation forecasts. As stated above, we add nowcast to 4-quarter ahead inflation forecastsqqa(π̂i,t,+0, . . . , π̂i,t,+4) and that of the next fiscal year (π̂i,t,+1) in the observation equations correq
sponding to equation (6). Restricting information just to nowcast π̂i,t,+0
worsens the marginal

likelihood compared to the baseline. The third alternative mimics Stock and Watson (2007,2016) by assuming stochastic volatility of νi,t and ωi,t in the transition equations (2) and (3).
This also leads to deterioration in the marginal likelihood compared to the baseline.
Table 2 summarizes posterior mean and standard deviation of parameters obtained from theaverage of sample forecasters. AR coeﬀicients for the transitory component (c∗,t ) and stochastic
volatility (λ∗,t ) are 0.887 and 0.933 respectively and show high persistence of these components.
In terms of trend inflation, σν,∗ is a key parameter that determines how smoothness the series is.
0.015% is more or less equivalent to standard deviation of the Hodrick-Prescott (HP) filtered πt(0.030%), that is, the obtained trend inflation indicated below is as smooth as the HP-filtered6
All the codes are written in Ox (Doornik (2007)), otherwise noted. We leave details of the algorithm to theaccompanied online appendix [not attached].

10Table 2: Posteriors for Mean Forecaster
Mean Standard Geweke’s
DeviationCDρ∗ (AR of c∗,t )
0.887
0.039
0.37
q
0.011
σu∗,+0q (π̂∗,t,+0) 0.2050.43qσu∗,+1q (π̂∗,t,+1 ) 0.204
0.011
-0.03
q
σu∗,+2q (π̂∗,t,+2) 0.159
0.009
-0.55
q
σu∗,+3q (π̂∗,t,+3 ) 0.112
0.007
0.34
q
σu∗,+4q (π̂∗,t,+4) 0.116
0.008
-0.60
a
σu∗,+1a (π̂∗,t,+1) 0.1100.007
0.49
σν,∗ (τ∗,t )
0.015
0.001
-0.62
σω,∗ (c∗,t )
0.018
0.002
-0.32
θ∗ (AR of λ∗,t ) 0.933
0.046
0.48
ση∗ (SV)
0.274
0.108
0.12
γ∗ (SV)
0.018
0.008
-1.09
Note: Geweke’s CD is Geweke’s Convergence Diagnostic
which follows N (0, 1).

trend.7
Figure 1 shows thus obtained posterior medians of trend/transitory components as well as
stochastic volatility (red solid lines) together with their 80% ranges (gray dotted lines). There
are several interesting observations.
First, the trend component (τ∗,t ) increased markedly after the introduction of the 2% inflation
target in 2013M1 and the quantitative and qualitative monetary easing in 2013M4 (the firstpanel). It reached 1.3% in 2014M10 and after some easing in between, 1.7% in 2018M7. This
trend component also increased in 2008 before the Great Financial Crisis (GFC) hit Japan’s
economy. It is interesting to observe these three hikes in trend inflation do not reflect the orderof actual inflation: although the elevation of actual inflation is more distinctive in 2008 comparedwith 2018 (and somewhere in between in 2014), trend inflation is higher in 2018 than those in
the first two hikes.
Second, transitory component (c∗,t ) hoovered small negative during most of the sample period(the second panel). This can be interpreted that ESP forecasters tend to think actual inflation
was pushed down by a transitory effect and anticipate that effect would diminish gradually going
forward. This implies that, as long as trend inflation is positive, inflation forecasts become higher
7

We use a Gamma prior which assumes a prior for σν,∗ is 0.1%. This is slightly lower than the actual standard
deviation of πt during the sample period (0.14%).

11

Figure 1: Estimates Using Mean Forecasts
Trend Component
2

Median

1

0

2

2005
Transitory Component

2010

2015

2020

2010

2015

2020

2010

2015

2020

2010

2015

2020

Median102005
Stochastic Volatility
0.075

Median

0.050

0.025

2005
Actual CPI (Y/Y)
2

CPI

1
0
-1
-2
2005

Note: Posterior medians and 80% ranges (gray dotted lines) derived from mean forecasts. Trend
and transitory components are expressed in annualized percent (the same, hereafter). Actual
CPI is year-on-year real-time core CPI (excluding fresh food) released from the Statistical
Bureau of Japan. The direct effects of raising consumption tax are excluded.

12

Figure 2: Individual Trend Inflation
6

5

4

3

2

1

0

2005

2010

2015

2020

Note: Posterior mean of trend components of individual forecasts.

in the longer time horizon (and converge to the trend inflation level). In an analogy of a yield
curve, an inflation forecast curve, drawn on the plane with the forecast inflation rate on thevertical axis and forecast horizon on the horizontal axis, has a positive slope in most of time.
Third, the noise (ϵ∗,t in our noisy information model of equation (1)) plays an indispensable role as its stochastic volatility is significant thorough the sample. The volatility increases
during 2008-2009, when actual inflation showed a large up and down due to commodity prices
developments and the GFC (the third and the fourth panels). Since then, the volatility had
gradually declined even though actual inflation rose after 2013. It shot up toward the end ofsample period, but this may be subject to the end-of-period problem of smoothing.
4.2.2

Individual Forecasts

Figure 2 displays all posterior means of trend components of individual forecasters (τi,t ). In avery broad view, these individual trend inflation rates move together—a surge in 2008, a rise after
2013 and another rise from 2017, but a more closer look highlights considerable heterogeneity

13Figure 3: Histogram of Individual Trend Inflation
15

2012M8

15

10

10

5

5

-1
0
2014M10
15

1

2

3

4

-1
0
2018M7
15

10

10

5

5

-1

0

1

2

3

2013M5

4

-1

0

1

2

3

4

1

2

3

4

or divergence among them.
That heterogeneity becomes more visible in their cross-sectional distributions. In Figure
3, we plot histograms at four data points. The first one is 2012M8 well before the launch of
Abenomics (the upper left panel);8 the second one is 2013M5 just after the introduction of thequantitative and qualitative monetary easing (the upper right panel); and the third and thefourth ones are 2014M10 and 2018M7 (two bottom panels), which corresponds to the recent
peaks of trend inflation in Figure 1. There is an apparent shift in the distributions to the right:
the mode was below zero percent in 2012M8: it turned into the positive territory in 2013M5 toreach slightly below 1 percent in 2014M5 and close to 2 percent in 2018M7. At the same time,
the heights of these modes lowered and the tails became more widely spread.
The heterogeneity is also clear in estimated parameters. The upper-left and the uppercenter panels in Figure 4 are the histograms of estimated ρi and θi , which are AR coeﬀicients ofindividual transitory component ci,t and stochastic volatility of noise term λi,t . The upper-right8

Abenomics refers to the economic policies introduced by Shinzo Abe, who served his second term of Prime
Minister from 2012M12 to 2020M8.

14

Fi g ur e 4: Hist o gr a m of Esti m at e d P ar a m et ers
ρi

θi

20

15

τi

20
10

10

10

0. 5 0ρi

0. 7 5

1. 0 0

20

5

0. 8
θi

0. 9

1. 0

-1
τi
15

0

1

2

0

1

2

20
10

10

10

0. 5 0N ot e:0. 7 5

1. 0 0

5

0. 8

0. 9

1. 0

-1

T h e u p p e r p a n el s a r e hi st o g r a m of e sti ∑m at e d p a r a m et e r s ρ i , θ i a n d t h e hi st o ri c alTm e a n of i n di vi d u al t r e n d i n fl ati o n τ i = T1
t τ i, t . T h e bl a ck a n d t h e g r e y p a rt s of t h e
hi st o g r a m s i n t h e l o w e r p a n el s a r e t h at c o n st r u ct e d f r o m G r o u p A a n d B i d e nti fi e d b yt h e cl u st e r al g o rit h m.

15

Figure 5: Trend and Transitory Components
Trend Component
2Group AGroup B

1

0

2

2005
Transitory Component

2010

2015

2020

2010

2015

2020

Group AGroup B

1

0

2005

panel is the histogram of the historical means of individual trend inflation, τi = T1∑Tt τi,t . Theirbi-modal shapes seem to indicate that these histograms are sampled from the mixture of two
distributions, that is, there are two types of forecasters whose characteristics are captured byeach distribution.
We segment 62 sample forecasters into two groups, Groups A and B, by applying the Kmeans clustering algorithm to these three parameter variables.9 These two groups correspondto the black and the grey parts of the histograms in the lower panel of Figure 4. The algorithm
identifies 12 forecasters as Group A whose trend inflation τi is high. Indeed, Group A forecasters
have persistently higher trend inflation than Group B forecasters, which is not for the case withtransitory components (Figure 5). At the same time, the figures show that Group A forecasters
entered the survey during the sample period: this is the reason why the red solid lines of GroupA started in 2008.
The lower panels of Figure 4 also suggest that Group A tend to be the lower side of distributions of ρi and θi . Comparison of posterior means of parameters between Groups A and B in
9

We use the sklearn.cluster.KMeans class of Python.

16

Table 3: Posteriors for Groups A and B
Group A Group B t-value q-value
ρi
0.589
0.708 -2.821
0.003
σu,i,+0q
0.294
0.285
0.379
0.353
σu,i,+1q
0.289
0.283
0.252
0.401
σu,i,+2q
0.247
0.236
0.606
0.273
σu,i,+3q
0.217
0.187
1.371
0.088
σu,i,+4q
0.249
0.220
1.301
0.099
σu,i,+a
0.207
0.181
1.339
0.093
σν,i
0.025
0.023
0.668
0.253
σω,i
0.026
0.026 -0.114
0.455
θi
0.882
0.916 -3.182
0.001
ση,i
0.145
0.251 -5.429
0.000
0.010
0.015 -3.1800.001
γiNote: t-value and q-value are tests for the same sample
means between Groups A and B.

Table 3 indicates that the difference is significant at the 5% level for ρi , θi , ση,i and γi . GroupA forecasters, whose trend inflation is higher than that of Group B forecasters, tend to see lesspersistence in cyclical component (lower ρi ) as well as in stochastic volatility (lower θi ), andsmaller volatility in noise (lower ση,i and lower γi ).
Where the difference in these parameter values come from can be seen in the inflation forecast
curves in Figure 6 which plots the average survey responses of Groups A and B against thecorresponding quarters for the entire sample period (left-hand-side panel) and in 2017-2018
when the trend inflation hit the peak in Figure 1 (right-hand-side panel). In either case, theinflation forecast curve of Group A is located higher and its curvature is steeper than thatof Group B. As explained above, trend components pin down the level of long-term inflation
forecasts and transitory components determine the slope from the short-end to the long-end
of forecasts (equation (6)). The combination of the near-zero cyclical component ci,r and thepositive trend inflation τi,t implies that inflation forecasts π̂i,t,+k are higher the longer the forecast
period horizon (the larger k), thus the term structure of inflation forecasts is positively sloped.
The smaller ρi for Group A forecasters is reflected in the steeper curve in Figure 6, and theirlarger τi,t is reflected in the higher curve.
The above heterogeneity can also be seen in disagreement about trend inflation, as graphedin the upper panel of Figure 7, which calculates the degree of disagreement by a dispersion

17

q
Figure 6: Quarterly Inflation Forecasts (π̂i,t,+k)

2017-2018
Group AGroup Binflation forecasts (%)
0.4
0.6
0.2

0.2

inflation forecasts (%)
0.4
0.6

0.8

1.0

Group AGroup B

0.8

1.0

Whole Sample Period012quarters ahead

3

4

0

1

2
quarters ahead

3

4

Figure 7: Disagreement across Forecasters
1.5

Trend Component

1.0

0.5

1.5

2005
Transitory Component

2010

2015

2010

2015

2020

1.0

0.5

2005

Note: Disagreement is calculated by the following dispersion measure: dt = Nt1−1x∗,t )2 where xi,t = τi,t or ci,t and x∗,t = τ∗,t or c∗,t respectively.

18

2020

∑ Nt
i

(xi,t −

measures:t
1 ∑(τi,t − τ∗,t )2 .
Nt − 1N

dt =i

Estimated disagreement about trend inflation peaked three times, in 2008, 2014 and 2018. Thesetimings coincide with episodes when both stochastic volatility and trend inflation surged. By
contrast, there is a little increase in disagreement regarding the transitory components around2014, though there were local peaks in 2008 and more recontly in both 2019 and 2020 (bottom
panel).

5

Discussion

5.1

Source of Heterogeneous Responses

The above findings can be restated that heterogeneous responses of forecasters, in particular thedisagreement about trend inflation after 2013 (Figure 7), played a key role behind the surge intrend inflation observed in the mean inflation forecasts (Figure 1). Some forecasters, labelled
as Group A above and who might be called “shifting trend believers”, see less noise in the
inflationary process, expect the impact of transitory inflationary shocks to wane more quickly,
and are more flexible is adjusting their forecasts of trend inflation in response to new information.
Another group of forecasters, labelled as Group B and who might be called “shifting trend
skeptics”, see more noise in the inflationary process, expect the impact of transitory inflationary
shocks to wane more slowly, and are less flexible in adjusting their forecast of trend inflation in
response to new information.
The fact that group A forecasters entered the survey relatively recently may provide anothersource of heterogeneous responses. Malmendier and Nagel (2016) note that young individuals
with less history update their expectations more strongly than older individuals, particularin times of highly volatile inflation. More generally, Clements (2021) notes that forecasts ofinflation of recent joiners to the survey they examine are found to be less accurate.
Differences in forecasters can also reflect strategic behavior on the part of forecasters who
may have incentives to differentiate themselves well beyond the signals they observe (Laster et al.
(1999), Ottaviani and Sørensen (2006)). Goldstein and Zilberfarb (2021) note that the strategic
19

Table 4: Aﬀiliations of Forecasters
Group A
Banks and Insurance Companies
3 (0.25)
Security Firms
6 (0.50)
3 (0.25)
Others (non-financial)Total
12 (1.00)
Note: Number of forecasters.
shares.

Group B
15 (0.30)
23 (0.46)
12 (0.24)
50 (1.00)

Figures in the parentheses aretendency of forecasters to “anti-herd” in this fashion is greater in times of higher inflation.
These forecasters might also be influenced by their aﬀiliations. Table 4 indicates that “shifting trend believers” (Group A) are more aﬀiliated with security firms while “shifting trend
skeptics” (Group B) are more likely to be with banks and insurance companies. As these security firms deal with the volatile equity market, arguably, they might be more flexible to change
their house views compared with rather conservative institutions like banks and insurance companies.10 One caveat, however, is that given the limited number of institutions, we are unable toinfer that the differences between Group A and B in sector aﬀiliation are statistically significant
at standard levels of significance.

5.2

Effectiveness of the 2% Inflation Target and UMP

How would these analyses of individual trend inflation lend themselves to the assessment of
BOJ’s enormous efforts to lift inflation? As stated above, the BOJ introduced the 2 percent
inflation target in 2013M1 followed by a series of monetary easing measures. These include
the Quantitative and Qualitative Monetary Easing (QQE) program in 2013M4, the adoption of
Negative Interest Rates Policy (NIRP) in 2016M1 and Yield Curve Control (YCC) of 10 year
JGB in 2016M9.
If, accompanied by the series of new measures, the new inflation target had been viewed as
perfectly credible, we would not have observed an increase in disagreement on trend inflation(Figure 7). Rather, all individual trend inflation forecasts would have risen to 2 percent. Moregenerally, Crowe (2010) and Ehrmann et al. (2012) show that the introduction of inflation
targeting tends to reduce the dispersion of inflation forecasts, but the opposite happened in10

In the literature, Ito (1990) finds that forecasters in the yen/dollar exchange rate survey tend to be biased
towards outcomes that favor their employers.

20

2013 in Japan. This likely reflects the diﬀiculty in targeting inflation from below, where, as
documented by Ehrmann (2015), under persistently low inflation below the central bank target,
expectations tend to be unanchored, and forecasters disagree more.11
Indeed, our analysis shows that some forecasters (Group A) lifted their trend inflation to
2% (Figure 5) and this was a cause of rising disagreement. Though other forecasters (Group B)
also raised their assessment of trend inflation, it was by much less.
The situation in the wake of the Bank of Japan’s introduction of an inflationary targeting
regime accompanied by large-scale monetary easing was that the glass was half full and half
empty. The measures succeeded in raising the trend inflation of ESP forecasters, but not byenough to re-anchor inflationary expectations at the target. Many did not adjust their forecastsof trend inflation fully towards the 2 percent target. Our findings are consistent with Hattori
et al. (2021), who show that on average ESP forecasters discounted the inflation forecasts madeby the BOJ after the central bank raised its forecasts of the next fiscal year CPI inflation in linewith the new 2 percent inflation target.

6

Conclusion

In this paper, we propose a noisy information model to extract trend inflation of individual forecasters. We find that the added noise term plays a crucial role and that there exists considerable
heterogeneity among individual trend inflation forecasts that drives the dynamics of the mean
trend inflation forecasts. Forecasters who see less noise in realised inflation tend to expect the
impact of transitory inflationary shocks to wane more quickly, and are more flexible in adjusting
their forecasts of trend inflation in response to new information. Their changing forecasts drove
the increase in observed forecast differences during the recent introduction of inflation targetingand unprecedented monetary easing measures in Japan.
It is straightforward to apply our model to inflation forecasts made by professional forecasters
in other countries. In principle, our model can also be applied to extract individual trend
11
It is also possible that the announcement of regime change whereby qualitative new monetary policy measures
were implemented could have been responsible for the increased disagreement, much as more controversial central
bank communications can trigger a divergence in views among non-experts (Ehrmann and Wabitsch, 2022).

21

inflation of other agents such as households or corporations.12 It would be interesting to see
whether there is heterogeneity in individual trend inflation forecasts that follows similar patterns
across these other groups, to shed further light on the formation of inflation expectations.

12

Diamond et al. (2020) shows that there is heterogeneity in household inflation expectations across generationsin Japan.

22

Appendix

Selection Matrix

S is a 6 × 36 matrix and S q and S a are 1 × 14 and 1 × 23 vectors respectively.
[
]
[ 1
2
12
2
S q = 13 23 33 · · · 33 23 13 and S a = 12
12 · · · 12 · · · 12

1
12

]

.

S is defined for each month such that S q and S a are placed at the following elements of thematrix, otherwise zero.
M1
M2
M3
M4
M5
M6
M7
M8
M9
M10
M11
M12

(1,4)
(1,6)
(1,5)
(1,4)
(1,6)
(1,5)
(1,4)
(1,6)
(1,5)
(1,4)
(1,6)
(1,5)

(2,7)
(2,9)
(2,8)
(2,7)
(2,9)
(2,8)
(2,7)
(2,9)
(2,8)
(2,7)
(2,9)
(2,8)

Sq
(3,10)(3,12)(3,11)(3,10)(3,12)(3,11)(3,10)(3,12)(3,11)(3,10)(3,12)(3,11)

23(4,13)(4,15)(4,14)(4,13)(4,15)(4,14)(4,13)(4,15)(4,14)(4,13)(4,15)(4,14)(5,16)(5,18)(5,17)(5,16)(5,18)(5,17)(5,16)(5,18)(5,17)(5,16)(5,18)(5,17)

Sa
(6,7)
(6,6)
(6,5)
(6,4)
(6,3)
(6,14)(6,13)(6,12)(6,11)(6,10)(6,9)(6,8)

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