HIAS-E-131

Estimation of firms' inflation expectations
using the survey DI

Jouchi Nakajima
Hitotsubashi University

July 2023

Hitotsubashi Institute for Advanced Study, Hitotsubashi University
2-1, Naka, Kunitachi, Tokyo 186-8601, Japan
tel:+81 42 580 8668 http://hias.hit-u.ac.jp/
HIAS discussion papers can be downloaded without charge from:https://hdl.handle.net/10086/27202
https://ideas.repec.org/s/hit/hiasdp.html

Estimation of firms' inflation expectations using the survey DI
Jouchi Nakajima†
July 2023
Abstract
This study uses the Bank of Japan's Tankan (Short-Term Economic Survey ofEnterprises in Japan) results to estimate the long-run time series of Japanese firms'
inflation expectations since 1990. In the Tankan, the series for "consumer priceinflation expectations" and "output price inflation expectations" go back to 2014,
while that for "output price DI" features a longer time series. Using the relationshipbetween these series for 2014–2022, we estimate one-year ahead consumer priceinflation expectations for 1990–2013 based on the output price DI. The firms'
inflation expectations obtained are found to have information that improves forecast
accuracy when forecasting consumer price inflation, which is not included in the lag
in inflation or the output gap, and enhances forecast accuracy more than using
economists' inflation expectations.
JEL classification: C22, E31, E37
Keywords: Inflation expectations, Output price expectations, Tankan

The author is grateful to Ichiro Fukunaga, Kakuho Furukawa, Masahiro Higo, Yoshihiko Hogen,

Yoshiyuki Nakazono, Tatsushi Okuda, Mitsuhiro Osada, Takatoshi Sasaki, Toshitaka Sekine, andShigenori Shiratsuka, for their valuable comments and discussions. The views expressed in this paper are
those of the author and do not necessarily reflect those of the Bank of Japan. Financial support from the
Ministry of Education, Culture, Sports, Science and Technology of the Japanese Government throughGrant-in-Aid for Scientific Research (No. 22K20157, 23H00050) and the Hitotsubashi Institute forAdvanced Study is gratefully acknowledged.
†Institute of Economic Research, Hitotsubashi University (E-mail: nakajima-j@ier.hit-u.ac.jp)

11. Introduction
In macroeconomics, inflation expectations are closely linked to economic activity andessential for various empirical analyses. However, fewer candidate inflation expectations
data are available for empirical analysis than other economic variables. In particular, when
the analysis covers a long period, time series data on inflation expectations are often difficult
to trace long into the past, considerably limiting the candidate data used in the empiricalanalysis.
Inflation expectations data can be categorized according to the forecast entity (e.g.,
Adachi and Hiraki, 2021). In addition to survey research, another method used to generate
data for financial market participants' expectations is to extract inflation expectations fromthe prices of financial instruments traded in financial markets. 1 However, data for
expectations of economists, households, and firms rely on survey research. In Japan, the"ESP Forecast" for economists, the Bank of Japan's "Opinion Survey on the General Public's
Views and Behavior" for households, and the "Tankan" (Short-Term Economic Survey ofEnterprises in Japan) for firms include questions concerning inflation expectations, and eachis used in empirical analyses.
Inflation expectations can vary in changes and determining factors depending on theentity making the expectations. Coibion, Gorodnichenko, and Kamdar (2018) and Coibion,
Gorodnichenko, and Kumar (2018) show that firms' inflation expectations differ
significantly from those of other entities regarding time series dynamics and determining
factors. Furthermore, as firms are price setters, firms' inflation expectations can beconsidered particularly important in empirical analyses in macroeconomics.
Nevertheless, no long-run time series data exist on firms' inflation expectations inJapan. The Tankan can only be traced back to 2014, when the survey began asking questions
for inflation expectations. The inflation expectations data that can be traced back to the past
the most is contained in the Cabinet Office's "Annual Survey of Corporate Behavior," only
going back to 2003.2 Moreover, the survey is only conducted annually. This lack of longrun time series data on firms' inflation expectations is a problem faced by researchers not
only in Japan but also other countries, as pointed out by Coibion et al. (2020).
The output price diffusion index (DI) in the Tankan is often used as a proxy variable in1

Specifically, the inflation swap rate or the difference between the interest rate on nominal government
bonds and inflation-indexed government bonds are often used. See Hiraki and Hirata (2020) for further
details.
2
The survey does not directly ask about inflation expectations but asks about expectations for nominal
and real GDP growth rates: the difference between the two is interpreted as expected inflation and used
for analysis. See Appendix 2 of this study and Kaihatsu and Shiraki (2016) for details.

2the analysis of Japanese firms' inflation expectations. The output price DI includes queriesof "actual" (current) and "future." As the "future" figure is the response concerning changes
to the firm's output prices from the present to three months ahead, it can be regarded as anindicator of expected price changes up to three months ahead. Long-run time series sincethe 1970s are available for the average series for all industries and sizes. In addition, series
by industry and size are also maintained. Meanwhile, Nakajima et al. (2021) attempt to
extract firms' inflation expectations since the 2000s using the text data of survey
respondents' comments accompanying the Cabinet Office's "Economy Watchers Survey."
The results indicate that the extracted series can be interpreted as inflation expectations forseveral months ahead. While these data are useful as a long-run time series of inflation
expectations, they are inflation expectations for only several months ahead.
This study generates long-run time series data on Japanese firms' inflation expectations
for one year ahead. Specifically, we develop a framework for estimating one-year-ahead
inflation expectations using the Tankan output price DI, for which long-run time series data
exist. The firms' inflation forecasts here are based on "outlook for general price inflation
expectations (all industries and all sizes)" in the Tankan. They can be interpreted
conceptually as the average of all industries and sizes of each firm's inflation expectations.
The Tankan began surveying the outlook for consumer price inflation (hereafter, "CPI
inflation expectations") and the outlook for the expected changes in firm's own output prices("output price inflation expectations") as of the March 2014 survey. This study develops aframework for estimating one-year ahead CPI inflation expectations from output price DI
using data from March 2014–December 2022 surveys. As the output price DI has been
available for a long period, even before 2014, it is used to estimate CPI inflation
expectations before 2014. Unless otherwise noted, in this study, CPI inflation expectations
and output price inflation expectations refer to one year ahead.
An important and unique aspect of this analysis is using data per industry and size fromthe Tankan. The Tankan has about 30 industry categories. There are also three size
categories: large, medium-sized, and small enterprises. Uno et al. (2018) show that a series
averaging three consumer-related industries ("retailing," "services for individual," and"accommodations, eating & drinking services") for industry-specific output price inflation
expectations draws close to the CPI inflation expectations. As the Tankan includes various
manufacturing and non-manufacturing industries, the output price expectations for allindustries and sizes include the prices of goods and services sold to trading partners andconsumers. Therefore, if we aggregate only consumer-related industries corresponding to
the latter, we obtain a series close to the movement of CPI inflation expectations. The
analysis in this study focuses on this consumer-related industry.
3

We consider three ways to estimate CPI inflation expectations for all sizes andindustries based on the output price DI by industry and size. The first method prepares
various combinations from industry- and size-specific series of output price DIs andregresses CPI inflation expectations on those series sets to construct a relational expression.
In addition to the combination above using only consumer-related industries, we consider
the case where all industry and size series are included in the estimation equation.
The second method uses output price inflation expectations by industry and size andthe output price DI. First, we perform a simple regression of each series of output priceinflation expectations by industry and size on the output price DI for the same industry andsize. Next, we regress CPI inflation expectations for all sizes and industries on a set of output
price inflation expectations series. Using the two-step relational expression thus obtained,
we develop a framework for estimating CPI inflation expectations from the output price DI.
As the same firms respond to the output price DI and output price inflation expectations foreach industry and size, we assume a reasonable correlation between these aggregate values.
In this case, rather than regressing the CPI inflation expectations directly on the output priceDI, obtaining a robust estimation formula may be possible by using the output price inflation
expectations as a bridge and regressing it indirectly.
In the third method, instead of estimating an equation relating the CPI inflation
expectations to the output price inflation expectations using the second method, the weightof individual items and services in the CPI is used. The estimated CPI inflation expectations
are the weighted average of the estimated output price inflation expectations for eachindustry sector based on this weight. Fixing the weights will result in a robust, overall
estimation framework. We examine various series sets as explanatory variables for theabove three methods and find the best method based on in-sample and out-of-sample
prediction errors.
The estimation framework proposed in this paper uses the relatively short-term
relationship for 2014–2022 to estimate historical long-run inflation expectations. The
historical period assumes that the relationship between the series concerning inflation
expectations is the same and constant as the one during 2014–2022. However, firms' views
on prices may change over time. Moreover, as inflation dynamics may have changed fromthe 1990s to the 2020s, the resulting estimates of inflation expectations should be viewed
with a reasonable range.
Regarding whether the estimates of inflation expectations going back in time are"correct," it is impossible to rigorously verify whether they are an appropriate series because
the true figures for inflation expectations are not known. Further, as noted earlier, as there4are no other long-run time series of inflation expectations for Japanese firms, comparisons
are impossible. Instead, this study puts the long-run time series of estimated inflation
expectations into a forecasting model of CPI inflation rates to test whether it has information
on future inflation rates that cannot be explained by other macroeconomic variables such as
foreign exchange rates and the output gap.3
Additionally, we conduct a comparative analysis of the differences in the estimatedfirms' inflation expectations from economists' inflation expectations. Coibion et al. (2020)
show that firms' inflation expectations in the U.S. and New Zealand differ from those of
economists. To the best of our knowledge, no study has analyzed these for Japan over a
sufficient sample period, mainly because obtaining a long-run time series of firms' inflation
expectations is impossible. Therefore, this study uses the Consensus Forecast's one-yearahead inflation expectations, obtained from Consensus Economic Inc., as the economists'
inflation forecast and compares it to the estimated firms' inflation expectations.
This study's first contribution to the literature is to present long-run time series data on
firms' inflation expectations in Japan. This is a necessary variable for various empiricalanalyses, and the ability to use price-setter firms' inflation expectations in empirical analyses
is an important contribution. To some extent, the proposed estimation method is adapted tothe data structure specific to the Tankan. However, it contributes to presenting amethodology in the context of the lack of data on firms' inflation expectations in othercountries, as Coibion et al. (2020) highlight.
Studies on firms' inflation expectations in Japan include those of Uno et al. (2018),
Inatsugu et al. (2019), and Kitamura and Tanaka (2019). They have presented additional
empirical analysis results on the determinants of firms' inflation expectations and otherfactors. A further important contribution is to compare Japanese firms' inflation forecastswith economists' inflation expectations and examine the differences. As previous studies inthis context, Nishiguchi et al. (2014), Kamada et al. (2015), Hori and Kawagoe (2015),
Nakazono (2016), Hogen and Okuma (2018), Maruyama and Suganuma (2019), andKikuchi and Nakazono (2021) analyze the inflation expectations of firms and other entities
in Japan.
The remainder of this paper is structured as follows. Section 2 provides a detailed
description of the Tankan series used in the estimation. Section 3 describes the framework
for estimating firms' inflation expectations and presents the estimation results. Subsequently,

3

Hajdini et al. (2022) use a survey to estimate U.S. consumers' inflation expectations. As they do notknow the true value of expected inflation, they conduct a quantitative analysis of the estimates obtained,
such as their relationship to macroeconomic variables, including the actual inflation rate.

5Section 4 analyzes the time series property and predictive power of the estimated firms'
inflation expectations. Finally, Section 5 concludes this paper.

2. Tankan index of inflation expectations
2-1. Available series
The Tankan is a survey of the actual corporate activity in Japan and has a long history, with
its predecessor surveys dating back to the 1950s. The current "Short-Term Economic Surveyof Enterprises in Japan" was launched in 1974, and its data from that time are available fordownload on the Bank's website. The survey reviews the companies and items surveyed toreflect the economic structure and corporate-sector developments. Consequently, someitems have only been surveyed at certain times in the past or only relatively recently. The
survey is currently conducted four times a year (March, June, September, and December)and is generally used as quarterly data.
Regarding the series on inflation expectations, the items of "Outlook of Output Prices"and "Outlook of General Prices (i.e., CPI)" were launched in 2014. The former survey asks
about companies' outlook for the sales price of its main products or the price of its main
service offerings one, three, and five years from now, compared to the current level. The
latter CPI inflation outlook asks for a one-year, three-year, and five-year outlook concerning
the year-on-year change in the CPI. Responses are based on a multiple-choice format, withexpectations in 5% bands (e.g., "around +10%" means the range from +7.5% to +12.4%)
for the output price expectations and 1% bands ("around +2% means the range from +1.5%
to +2.4%) for the CPI inflation expectations (see Appendix A for details). The "Average ofEnterprises' Inflation Outlook" is included as a reference value, a weighted average of thevalues for each option (e.g., +2% for "+2% or so" and +6% for "+6% or more") weighted
by the percentage of the number of companies for each option. While still a reference value,
when we speak of the Tankan's inflation expectations, we are generally referring to thisaverage of outlook.
Meanwhile, one of Tankan's DI items is the "Changes in Output Prices," with the three
options being "rise," "unchanged," or "fall." The output price DI, calculated by subtracting
the "fall" percentage from the "rise" percentage, is used in various analyses as a series close
to the concept of inflation expectations.4 One advantage of using this DI is the availability

4

DI calculated from selective (categorical) responses to surveys are often used in macroeconomic
empirical analyses because they have a high correlation with a range of economic variables. Pinto et al.
(2020) show that the utility of DIs derived from this kind of survey research for analyzing economic
developments theoretically and empirically.

6

of long-run time series from 1974 for all firm sizes and industries.
This study estimates the long-run time series for the one-year-ahead CPI inflation
expectations. The output price DI, for which a long-run time series is available, is used forthis purpose. The DI includes "actual" (current) and "future," with the "future" item asking
about changes in the next three months. We include one-year ahead CPI inflation
expectations in our analysis because it is expected that changes up to three months aheadcontain information about changes up to one year ahead.
In principle, it is possible to consider an estimation framework for CPI inflation
expectations three or five years in the future. However, the greater the number of years'
expectations, the less affinity they have with output price decisions, and the less accurate
the estimation will be. For a one-year forecast, the DI movements generated from responses
on recent developments are likely to contain considerable information, given that shocks
related to recent price changes will have a proportional impact on the inflation rate one year
ahead through inertia. Nevertheless, when the forecast is more than three years ahead, thecorrelation with the DI is lower because recent shocks decay over time. Therefore, inflation
expectations three and five years ahead are outside the scope of the main analysis. In
Appendix B, we estimate medium- and long-term inflation expectations by additionallyusing the "Annual Survey of Corporate Behavior."
2-2. Overview of inflation expectations in Tankan
Figure 1 shows one-year ahead CPI inflation expectations and output price expectations for
all firm sizes and industries.5 The one-year ahead CPI inflation expectations declined fromapproximately 1.5% in 2014, when the survey began, to the low 0% range in 2015–2016,
remained at the same level, and declined further in late 2019. This began to rise in 2021 androse significantly, to over 2%, in 2022. The one-year ahead output price forecast moves
similarly to the one-year ahead CPI inflation expectations but at different levels and rangesof change. In 2014, the decline was lower than CPI inflation expectations at approximately
1% and was larger than the 2019 decline. The increase for 2021 and 2022 are greater thanthe CPI inflation expectations. During this period, the output price DI also moved similarly
to the expectations series.
Figure 2 plots one-year ahead CPI inflation expectations for all firm sizes andindustries versus one-year ahead output price expectations for consumer-related industries.
For consumer-related industries, the figures for the three industries are weighted and
5

The Tankan price outlook is answered, excluding the impact of consumption tax hikes and othersystemic changes.

7

averaged by their weight in the CPI. Specifically, for the retailing, services for individual,and "accommodations, eating & drinking services," we use the weighted average of theweights in the 2020-based CPI for goods (weight: 0.5046), services excluding
accommodation and food services (0.4414), and accommodation and food services (0.0540).
Uno et al. (2018) note that the average CPI inflation expectations for firms aggregated acrossall industries and all sizes is considerably close to this consumer-related industry output
price expectations. We focus on these consumer-related industries when selecting variables
for the following estimation.

3. Method of estimating inflation expectations
3-1. Estimation formula 1: One-step direct regression
First, consider the following regression equation to estimate CPI inflation expectations forall sizes and industries from the output price DI series by industry and size:
𝑦

𝑐

𝒙𝒃

𝑒,

𝑡

1, … , 𝑛,where 𝑦 is the CPI inflation expectations for all firm sizes and industries for survey 𝑡,𝒙𝑥 ,…,𝑥is a vector of the selected 𝑘 industry- and firm-size-specific output
price DIs, and 𝒃
𝑏 , … , 𝑏 ′ is their regression coefficient. Using 𝑐̂ and 𝒃, estimatedusing the least squares method, the CPI inflation expectations before 2013 is calculated asfollows:
𝑦

𝑐̂

𝒙 𝒃.

If the number of selected series (𝑘) included in 𝒙 is larger than that of observations (𝑛) in
the estimation period, the least squares method cannot be used for estimation. In this case,the Lasso regression method is used to estimate 𝑐 and 𝒃, which minimizes the following
equation:
𝐿

∑

𝑦

𝑐

𝜆 |𝑐|

𝒙𝒃

∑

|𝑏 | .

For parameter 𝜆, we use the optimal value based on cross-validation.
3-2. Estimation equation 2: Two-stage indirect regression
Next, we consider how to indirectly use the series of one-year-ahead output priceexpectations by firm industry and size for estimation. Specifically, we consider thefollowing two regression equations:(Stage 1) 𝑧

𝑐

𝑥 𝑏

𝜀 ,

8

𝑖

1, … , 𝑘; 𝑡

1, … , 𝑛,(Stage 2) 𝑦

𝑐

𝒛𝒃

𝑒,

𝑡

1, … , 𝑛,where 𝑧is the output price expectations by industry and size, the vector defined as 𝒛
𝑧 , … , 𝑧 . We estimate the two equations separately using the least squares method, andthese estimated values are 𝑐̂ , 𝑏 , 𝑐̂ , and 𝒃 . Subsequently, we calculate the CPI
inflation expectations before 2013 in the following equation:
𝑧̂

𝑐̂

𝑥 𝑏 ,

𝑦

𝑐̂

𝒛𝒃 ,

𝑖

1, … , 𝑘,𝑧̂ , … , 𝑧̂ . Similar to the above one-step direct regression, if the number ofwhere 𝒛selected series (𝑘) is large, we estimate 𝑐 and 𝒃 using the Lasso regression method in
the second stage of estimation.
As one-step direct regression has fewer parameter constraints than two-step indirect
regression, the average difference between theoretical ( 𝑦 ) and observed ( 𝑦 ) values
obtained from the estimation equation are smaller. However, the two-stage indirect
regression is based on the idea that the relationship between 𝑥 and 𝑧 , where the samefirms respond by industry and size, is correspondingly strong. If we apply this to the data,
the forecasting accuracy may be higher than that in the one-stage direct regression.
3-3. Estimation equation 3: Two-stage weighted regression
We consider a method where the second estimation equation in Estimation equation 2 ismodified as in the following equation:(Stage 2) 𝑦

𝑐

𝑍𝑏

𝑒,

𝑡

1, … , 𝑛,where 𝑍 is the weighted average of 𝑧 , … , 𝑧 :
𝑍

∑

𝑧 𝑤,

with 𝑤 denoting the weighted average weight and ∑ 𝑤
1. Specifically, we use theweights for individual prices in the CPI, summed for the individual prices corresponding toindustry 𝑖, as 𝑤 . For example, if we use two industries, retailing (𝑖 1) and services forindividual (𝑖 2 ), as explanatory variables, 𝑤 and 𝑤 are standardized so that theweights in the CPI of goods and services excluding accommodation and food services,
respectively, sum to one. We calculate the CPI inflation expectations before 2013 as follows:
𝑧̂

𝑐̂

𝑥 𝑏 ,

𝑍

∑

𝑧̂ 𝑤 ,

𝑦

𝑐̂

𝑍𝑏 .

9

𝑖

1, … , 𝑘,Using a single weighted average explanatory variable (𝑧 , … , 𝑧 ) instead of multiple
explanatory variables (𝑍 ) in the second stage may remove the effect of outliers in the shortsample period for the second stage estimation and may increase forecast accuracy comparedto the Estimation equation 2.
The weights (𝑤 ) are those of the 2020 base CPI relative to individual prices. Although
it is possible to use historical standards and vary the weights at different times, we apply themost recent standards uniformly throughout the sample period to create the CPI inflation
expectations that are consistent with the latest CPI inflation rates.

4. Empirical analysis
4-1. Candidate explanatory variables and selection criteria
We estimate each set of explanatory variables listed in Table 1, and explore the best variable
set. Sets of variables are classified into three categories. The first approach uses a single
series, an all-firm-size series for all industries (Set 1), for retailing only (Set 2), and theconsumer-related industry average (Set 3). The second approach combines three consumerrelated industry breakdowns using two or three series (Sets 4–6). The third approach uses
individual industry series, testing industries of all sizes (Set 7) and industries by size (Set8). As Sets 1–3 are single series sets, we apply two types of estimation equations: (1) Onestep direct regression and (2) Two-step indirect regression. For Sets 4–6, we apply a third
type of regression, (3) two-step weighted regression. For Sets 7 and 8, as it is difficult toevaluate CPI weights tied to each industry sector, we apply only two types of regression:(1) one-stage direct regression and (2) two-stage indirect regression. For these sets we use
the Lasso regression method due to many explanatory variables.
The output price DI for services for individual, and "accommodations, eating &drinking services" can be traced only to the June 2004 survey. Before this, there was anindustry classification series called "Services," which can be traced back to the December
1990 survey. Therefore, those two series are, respectively, connected by subtracting thedifference between June 2004 DI survey and the "Services" DI survey from the "Services"
DI before the March 2004 survey.
As a criterion for choosing the best set of variables and estimation equations, we firstexamine the in-sample root-mean-squared error (RMSE) within the estimation period forthe difference between 𝑦 , obtained from the estimation equations and observed values. The
estimation period spans 36 survey cycles, from the March 2014–December 2022 surveys.
We next compare out-of-sample predictability. First, we create estimates using the10

sample for the March 2014–December 2017 surveys. The resulting estimates forecast CPI
inflation expectations one period ahead—from the output price DI in the March 2018 survey
to the CPI inflation expectations in the same survey. Next, we add the March 2018 survey
data and again produce estimates, similarly projecting CPI inflation expectations one periodahead of the June 2018 survey. This is repeated up to the December 2022 survey forecast.
We examine the RMSE for the difference between the forecast and actual observed values
from the March 2018–December 2022 surveys. To confirm the robustness of the results, we
also examine the RMSE changing the starting period of forecast to 2019–2021.
4-2. Estimation results
Table 2 shows in-sample RMSEs for each candidate set of variables and estimation
equations. As mentioned above, the in-sample RMSEs are smaller for all approaches
because one-stage direct estimation is less parameter-constrained than two-stage indirect
estimation. However, as the difference is at most 0.01, there can be almost no difference.
The RMSE is smaller when using the consumer industries in Sets 2–6 as explanatory
variables than when variable Set 1, featuring the series of all firm sizes and industries, isused to provide explanatory variables. The RMSEs for Sets 5 and 6, including retailing and"accommodations, eating & drinking services" are small. Sets 7 and 8, including nonconsumer-related industries, have relatively large RMSEs, indicating that the simpler model
focusing on consumer industries in Sets 2–6 is superior. Although Sets 7 and 8 are estimatedby the Lasso regression method, and the series of several industries including consumptionrelated industries are statistically significant, the estimated coefficient for consumptionrelated industries are shrunk to some extent. Therefore, it is considered that the in-sample
fit deteriorates. In-sample fit is important when creating inflation forecasts, and we do not
use Sets 7 and 8. We use sets 1–6 as candidates for comparison for the following out-ofsample forecasts.
Table 3 presents the RMSE of out-of-sample predictability. As with the in-sample, theRMSE is smaller when taking the consumer-related industries in Sets 2–6 as explanatory
variables than when using variable Set 1. In Sets 2 and 3, featuring only one explanatory
variable, the one-stage direct estimation has a smaller RMSE than the two-stage indirect
estimation. Conversely, in Sets 4–6, featuring multiple explanatory variables, the two-stage
indirect estimation has a smaller RMSE. This indicates that the supplemental use of data on
output price expectations improves forecast accuracy more than using output price DI alone.
Moreover, the out-of-sample RMSE is smaller for the two-stage weighted estimation
than for the two-stage indirect estimation. This suggests that a stable forecast can be11

produced by fixing each industry's weights to values consistent with the CPI. Among all thevariable sets and estimation equations, the two-stage weighted estimation in Set 6 produces
the smallest RMSE. This result is robust even when changing the beginning of the forecast
period. Thus, we employ the long-run time series of inflation expectations estimated using
this method to conduct our analysis.
It is of interest that the best results are obtained when using only consumer-relatedindustries as a model for estimating inflation expectations for all industries and firm sizes.
This result is quite reasonable as these industries constitute the CPI. One may argue that
additional information on corporate prices upstream in the production process may better fit
inflation expectations. However, the model incorporating each industry has a larger insample RMSE as explained above. Even when the forecast accuracy is calculated by adding
one other industry to the consumer-related industries, we do not find any set where the outof-sample RMSE is smaller than for consumer-related industries alone. These results
indicate that the relationship between corporate and consumer prices may have changed
over time or is not linear.
The Tankan includes questions concerning actual and future changes in the company's
input prices, and the results are published as the "Change in Input Prices DI." We also
attempt estimation using the input price DI instead of the output price DI or accompanying
output price DI. Nonetheless, the RMSE is not reliably smaller than for variable Set 6. This
result suggests that information about input prices that can affect inflation expectations ismostly factored into the output price DI.
4-3. Connecting estimated and observed inflation expectations
The long-run time series of inflation expectations are from the December 1990 survey, fromwhich the Tankan "Services" sector output price DI is obtained, to the most recent survey.
Figure 3 shows the long-run time series of estimated inflation expectations. The shadowed
ranges denote 95% confidence intervals calculated using the Monte Carlo method. A
comparison with the (observed) CPI inflation expectation data presented in Figure 3 showsthat the estimates fit the observed values reasonably well but that there is a divergence withobservations outside the 95% confidence interval for the March–December 2014 survey.
Our long-run time series of inflation expectations presented are estimated values up to theDecember 2013 survey and observed values as of the March 2014 survey. Owing to thedivergence between the December 2013 and March 2014 survey observations, it isinappropriate to connect them as is.
We consider connecting estimated values up to the December 2013 survey with the12observed values from the March 2014 survey, minimizing damage to the time series
character of the estimates. Specifically, we estimate an Autoregressive Moving-Average(ARMA) model for the estimated values up to the December 2013 survey. After searchingfor the formulization that minimizes AIC for the order of the AR term (0–3 lags), the orderof the MA term (0–3 lags), and with and without a mean parameter, we select the ARMA(1,1) model with no mean parameter.
Despite being a somewhat ad-hoc approach, we discount the difference between theestimate and observed values in the March 2014 survey backward at a set rate from
December 2013 and add to the estimate creating a connection. We take 𝑟 as this discountrate and 𝑔 as the observed value less than the estimated value in the March 2014 survey.
Taking the estimated inflation expectation value as 𝑦 and 𝑦 as the value corrected forthis connection, we correct the estimate values before December 2013 using the following
equation:
𝑦

𝑦

𝑔𝑟

,

𝑡

1, … , 𝑇1,

where 𝑇 denotes the March 2014 survey—the range of correction decays moving
backward through the sample period, from 𝑔𝑟 for the December 2013 estimate value, 𝑔𝑟
for September 2014, to 𝑔𝑟 for June 2014.
Regarding discount rate 𝑟, inserting the values from the corrected time series into the
ARMA(1, 1) model estimated above yields the 𝑟 with the smallest in-sample RMSE forthe four quarters before and after the connection period, from September 2013 to June 2014.
Then, we obtain 𝑟 0.852 . We correct the estimate values based on this 𝑟 value toconnect them to the observed values from the March 2014 survey. This correction ispreferable as the connection using this discount rate increases the accuracy of the inflation
rate forecast.
4-4. Long-run inflation expectations series
Figure 4 shows the estimated firms' inflation expectation; inflation expectations of 1–2% in
the early 1990s have hovered approximately 0% since the late 1990s. This rose toapproximately 1% around 2006–2008 amid rising oil prices but receded to 0% amid thereactionary fall in oil prices and the global financial crisis. Inflation expectations increasedaround 2013 and have since hovered at approximately 1%. Notably, in 2013, the Bank ofJapan introduced the 2% price stability target alongside Quantitative and Qualitative
Monetary Easing; these policies may have raised inflation expectations. Inflation
expectations subsequently jumped 2–3% from 2022 due to surging commodity prices.
A comparison of the actual CPI inflation rate (the total excluding fresh food, energy,
13and special factors; year-on-year; the same holds below) 6 and the firms' inflation
expectations, shown in Figure 4, suggests that movements in inflation expectations yield
information useful for predicting the actual inflation rate. The dramatic decline in inflationin the early 1990s and the increases in inflation in the late 2000s and 2013–2015 show that
inflation expectations anticipate actual movements. Table 4 shows the time lag correlation
between the CPI inflation rate and the firms' inflation expectations, which is about 0.8 one
year ahead (four quarters), suggesting a considerably high correlation.
While the actual values are larger and more negative around 2000 and 2010, inflation
expectations are higher than these values, resulting in a divergence. In 2010, in particular,
in the aftermath of the global financial crisis, inflation expectations fell only to about -0.5%,
while the actual figure fell to nearly -1.5%. This may be due to downward rigidity ininflation expectations, as noted by Gorodnichenko and Sergeyev (2021), and this notsignificantly-negative characteristic may also manifest in the inflation expectations
estimated in this study.
Figure 4 compares the year-ahead inflation expectation in the Consensus, aneconomists' forecast, with the inflation expectations we estimate. While similar on average,
closer scrutiny reveals important differences in their relation to the actual inflation rate.
Economists' forecasts are characteristically higher in the first half of 1990, while corporate
inflation expectations are correspondingly higher in 2022. Turning to the actual figures, andas noted above, firms' inflation expectations are more preemptive of the significant decline
in inflation rates in the early 1990s and the sharp increase in inflation in 2022. These trends
suggest that firms' inflation expectations may yield greater information about future
inflation rates than economists' forecasts.
We use the Granger causality test to examine the relationship between firms' inflation
expectations and CPI inflation. We consider the no-causality null hypothesis—in theGranger sense—to be where the length of lag in the forecast is four quarters. Table 5 presents
the results of the causality test, in which the null hypothesis of no causality from firms'
inflation expectations to CPI inflation is rejected at the 1% level. However, we do not reject
the null hypothesis of no reverse causality. This suggests that, as discussed by Fuhrer (2012),
inflation expectations contain information predicting future CPI inflation rates. Applying
the same causality test to economists' inflation expectations yields the same result.
We next analyze the role of inflation expectations in the CPI inflation rate forecast

6

The CPI inflation rate series used here is the figure estimated by Bank of Japan staff, which excludes
mobile phone charges and the effects of the consumption tax hikes, policies concerning the provision offree education, and travel subsidy programs.

14

equation. Coibion et al. (2018) examine whether, in addition to standard macroeconomic
variables such as the output gap, inflation expectations hold information that complements
the explanatory power provided by those variables. We examine whether the firms' inflation
expectations contain information that complements the explanatory power of thoseeconomic variables. Estimating a regression equation in which the explained variable is the
CPI inflation rate and the explanatory variables are the CPI inflation rate one quarter before,
the output gap, and the nominal effective exchange rate, we also estimate a regression
equation in which the firms' inflation expectation is added. The estimation period is
December 1990 survey to December 2021 survey. The 2022 sample is a period close to theend of the output gap estimate, and since there is a possibility that it will be revised to someextent in the future, the end of estimation period is set to 2021.
Table 6 shows the results of the regression analysis. First, the coefficients of all
explanatory variables are statistically significant in the regression equation without thefirms' inflation expectation. Next, in the regression equation with the added firms' inflation
expectation, the coefficients of the previous explanatory variables remain statisticallysignificant. A key is that the coefficients of the firms' inflation expectations are alsosignificant. This shows that the firms' inflation expectations bear information not included
in conventional macroeconomic variables.
Finally, we verify whether the firms' inflation expectation improves the accuracy of thesimple inflation forecast model. Using the data for the period up to the December 2014
survey, we estimate a regression equation taking the above inflation rate as the explained
variable and using the explanatory variables from the December 2014 survey to predict the
inflation rate for the March 2015 survey. Subsequently, we add the March 2015 survey tothe data and use this to project the inflation rate for the June 2015 survey. We iteratively
calculate values to obtain predicted values up to the December 2021 survey. Changing thelag of the explanatory variable from one quarter to two quarters, we calculate expectedvalues two quarters forward. In other words, we use data for the period up to the December
2014 survey to forecast the inflation rate for the June 2015 survey. Moreover, by setting thislag to three or four quarters, we obtain forecast values three or four quarters ahead. We
repeat these forecasts, adding one-quarter of data at a time until forecast values are available
for the December 2019 survey, up to the point at which the COVID-19 pandemic manifests,
which produces 20 quarters forecasts. We validate this forecast analysis with and without
the inclusion of firms' inflation expectations.7

7

Note that the inflation expectations used here are estimated using samples for the entire period, so theanalysis is not based on strictly real-time forecast.

15

Table 7 presents the RMSE of the difference between the forecast and actual CPI
inflation values. For 1–4 quarters ahead, the RMSE is smaller, and the forecast accuracy ishigher when using the firms' inflation expectations. Testing whether the difference in RMSE
is statistically different from zero using the Model Confidence Set (MCS) method proposed
by Hansen et al. (2011), we find that using the firms' inflation forecast offers substantiallygreater accuracy at the 5% level for forecasts four quarters ahead. This result indicates thatthe inflation expectations presented in this analysis contain information that evidently
improves the accuracy of one-year-ahead forecasts.8
We also calculate forecast accuracy using economists' forecasts instead of firms'
inflation expectations. We find that the firms' inflation expectations improve forecast
accuracy more than the economists' forecasts for all 1–4 quarters ahead, as presented inTable 7. Applying the MCS test to the difference in their RMSE shows that at the 5% level,
the difference between the first and second quarters ahead is not statistically significant.
Conversely, the difference between the third and fourth quarters ahead is statisticallysignificant. The same results for the above forecast analysis are obtained even when
extending the measurement period beyond 2020. This indicates that the firms' inflation
expectations estimated in this study are statistically significantly more informative in
predicting inflation three or four quarters ahead of economists. As discussed above, thissuggests that as price setters of consumer goods and services, firms' inflation expectations
are important to determine the inflation rate.

5. Concluding remarks
This study uses the output price DI in the Tankan survey to create a long-run time series ofJapanese firms' inflation expectations from 1990. After testing various variables andestimation equations, we find that estimates with higher forecasting accuracy are obtainedusing the output price DI in combination with the inflation outlook for the company's output
prices. The estimated inflation expectations contain information not available in otherstandard macroeconomic variables able to improve the forecasting accuracy of a simple
inflation forecasting model.
It is challenging to discuss whether the presented inflation expectations is a good seriesof firms' inflation expectations because the true inflation forecast is unknown. In such ascase, using multiple measures of inflation expectations for comparison is advisable. Given
8

The same forecast accuracy calculations for the series of inflation expectations calculated from thecandidate variable sets and estimation equations in Section 4-1 reveal the RMSE to be smallest whenusing the selected estimated inflation expectation.

16

the extremely limited availability of such time series data, the series presented in this study
can increase the number of inflation expectations series available for reference, expand thebreadth of analysis, and confirm the robustness of such analysis.
One caveat concerning our framework is that all relational equations are assumed to belinear. Although a nonlinear relationship can exist between two variables that construct a
relational equation, only 32 quarterly counts exist for March 2014–December 2021.
Therefore, the sample is insufficiently large to determine a nonlinear relationship. The
framework posits a linear relationship between the DI, created by aggregating qualitative
responses, and inflation expectations. The (forecast) output price DI is the percentage offirms that answer that their output prices "rise" over the next three months minus thepercentage of firms that respond that their output prices "fall." Thus, it can only take values
from -100 to 100. While Pinto et al. (2020) show that a DI constructed in this manner can
precisely approximate the average of responses to inflation expectations, the theoretical
relationship between the distribution of respondents to the DI items behind the DI and theaverage of responses to inflation expectations is beyond the scope of this study.
This study estimates short-term, one-year-ahead inflation expectations, but mediumand long-term inflation expectations are necessary for various empirical analyses. Appendix
B addresses them using an additional time series model, and the "Annual Survey of
Corporate Behavior" results to forecast Japanese firms' medium- and long-term inflation
expectations. Interpreting the results requires some ranges when estimating inflation
expectations several years into the future based on the actual and forecast output price DI.
Another caveat is that series created using only short-term information do not adequately
capture inflation expectations specific to medium- to long-term durations due to, forexample, inflation targets. It is important to continue uninterrupted survey research, such as
the Tankan survey, for medium- to long-term firms' inflation expectations data.99The series of inflation expectations proposed in this paper is published and updated at the author's
website, https://sites.google.com/site/jnakajimaweb/einf.

17Appendix A. Tankan price outlook survey methodology
The following are the questions and options for the "inflation outlook" in the Tankan, as of
the December 2022 survey.
(1) Outlook for output prices
Relative to the current level, what is your enterprise's expectations for the rate of change inthe selling price of your main domestic products or services for one year ahead, three years
ahead, and five years ahead, respectively? Please select the range nearest to your own
expectation from the options below.
Rate of changes relative to the current level1.

around +20% or higher (+17.5% or higher)

2.

around +15% (+12.5% to +17.4%)

3.

around +10% (+7.5% to +12.4%)

4.

around +5% (+2.5% to +2.4%)

5.

around 0% (-2.5% to +2.4%)

6.

around -5% (-7.5% to -2.6%)

7.

around -10% (-12.5% to -7.6%)

8.

around -15% (-17.5% to -12.6%)

9.

around -20% or lower (-17.6% or lower)

10.

Don't know(2) Outlook for general prices
What is your enterprise's expectations of year-on-year rate of change in general prices (asmeasured by the Consumer Price Index) for one year ahead, three years ahead, and five
years ahead, respectively? Please select the range nearest to your own expectation from theoptions below.
In annual percent rate changes
11. around +6% or higher (+5.5% or higher)
12. around +5% increase year-on-year (+4.5% to +5.4%)
13. around +4% increase year-on-year (+3.5% to +4.4%)
14. around +3% increase year-on-year (+2.5% to +3.4%)
15. around +2% increase year-on-year (+2.5% to +3.4%)

18

16. around +1% increase year-on-year (+1.5% to +2.4%)
17. around 0% year-on-year (-0.5% to +0.4%)
18. around -1% year-on-year (-1.5% to -0.6%)
19. around -2% year-on-year (-2.5% to -1.6%)
20. around -3% or lower (-2.6% or lower)
If you have no clear views on general prices, please select one of the three following
reasons.
21. Uncertainty over the future outlook is high
22. Not really conscious of inflation fluctuations because they should not influence thestrategy of the enterprise
23. Other19

Appendix B. Estimation of firms' medium- and long-term inflation
expectations
As discussed in this study, estimating inflation expectations using the output price DI, aforecast up to three months ahead is limited to one year ahead, and it is challenging to use
the same framework to estimate medium- to long-term inflation expectations such as those
three or five years hence. However, medium- to long-term inflation expectations areimportant when empirically analyzing inflation dynamics and policy effects. As long-run
time series data candidates are limited for Japan, estimating firms' medium- to long-term
inflation expectations using the Tankan DI significantly contributes to the wider body ofliterature.
Therefore, this appendix exploits the DI and inflation expectations from the Tankan toestimate a long-run time series of firms' medium- and long-term inflation expectations.
Specifically, we use the time series model of inflation dynamics proposed by Kozicki andTinsley (2012) to estimate medium- and long-term inflation expectations before 2013 using
the output price DI (actual), the estimated one-year ahead inflation forecast, and the Tankan
three- and five-year ahead inflation expectations. As we only have the output price DI before
2013, supplementing it with information on the medium- and long-term inflation
expectations are necessary. For this purpose, we use three-year-ahead inflation expectations
calculated from the results of the Cabinet Office's "Annual Survey of Corporate Behavior."
Appendix 2-1. Annual Survey of Corporate Behavior
The Annual Survey of Corporate Behavior (ASCB), conducted annually by the Cabinet
Office, asks Japanese firms about their expectations on various macroeconomic variables.
Figures on nominal and real GDP growth forecasts are available from the 2003 survey
onward, making it possible to calculate the inflation expectations. The figures include "nextyear," "next three years," and "next five years" forecasts. Kaihatsu and Shiraki (2016)
analyze the forward rate for 1–5 years using the next year and next five years counts as themedium- to the long-term inflation expectations. This study uses this forward rate as the
inflation expectations for three years ahead, midway between 1–5 years.
As the 2003 survey of the ASCB was conducted in January 2004, it is considered at
almost the same time as the December 2003 survey of the Tankan for estimation purposes.
As it is an annual survey, we use linear interpolation to create quarterly series. Moreover, as
seen from the indirect method of calculating inflation expectations discussed earlier, thisseries of inflation expectations correspond to the GDP deflator forecast, which is expected
to diverge from the CPI inflation expectations. Therefore, we adjust the level such that the20difference between the average three-year-ahead inflation expectations in the Tankan fromthe first quarter of 2014 to the fourth quarter of 2021 and the average of the relevant inflation
forecast in the ASCB becomes zero. The adjustment range is 0.73 percentage points,
consistent with the difference between the GDP deflator and the (aggregate) CPI inflation
rate for 1995–2019, averaging 0.66 percentage points.
For the period before the fourth quarter of 2003, we extrapolate by regressing the series
from the same quarter to the fourth quarter of 2021 on the variables considered to be
determinants of inflation expectations three years ahead and calculating the theoretical value
before the fourth quarter of 2003. Specifically, actual inflation in the previous quarter (theyear-on-year CPI inflation rate), the trend in actual inflation (the average of the year-onyear CPI inflation rate over the past two years), and the nominal effective exchange rate
(year-on-year) are estimated as regression variables. All the variables are statisticallysignificant at the 5% level. Appendix Figure 1 presents inflation expectations three years
ahead based on the ASCB; following a gradual decline from 2% around 1992 toapproximately 0.5% in the early 2000s, it remained steady until 2012. It has turned upwards
afterwards.
Appendix 2-2. Time series model
For the time series model used in the estimation, we first define 𝜋 as the inflation rate inperiod 𝑡. Following Kozicki and Tinsley (2012), we assume that the inflation rate follows
the equation:
𝜋

𝜇

𝜙 𝜋

𝜀 , 𝜀 ∼ 𝑁 0, 𝜎 .

𝜇

(A1)

Suppose that 𝜇 is constant, 𝜋 follows a first-order autoregressive (AR) model. We
assume that the time series of 𝜋 is stationary, and |𝜙| 1. Calculating the conditional
future expectation of 𝜋(ℎ 1) based on the information up to period yields
E 𝜋

1

𝜙 𝜇

𝜙𝜋 ,

E 𝜋

1

𝜙 𝜇

𝜙 𝜋,

1

𝜙 𝜇

𝜙 𝜋.

⋯
E 𝜋

(A2)

Thus, we obtainlim E 𝜋𝜇.

→where 𝜇 represents the expected convergence point that the inflation rate will reach,conditional on the information up to period 𝑡 . Considering the discussion of inflation
21

expectations, 𝜇 is viewed as the point of convergence of the inflation expectations term
structure in period 𝑡 and sometimes referred to as the trend inflation rate (see, e.g.,
Kaihatsu and Nakajima, 2018). Kozicki and Tinsley (2012) propose a framework for
estimating the parameters of Equation (A1) by assuming that 𝜇 follows a random walkand fitting Equation (A1) to a series of past inflation values and Equation (A2) to periods
ahead of inflation expectations.
Instead of actual inflation, this study creates a series of perceived inflation rate thatreflects firms' perception of the inflation rate over the past year from the actual output price
DI in the Tankan and fit Equation (A1) to this series. The reason for not using actual inflation
is to avoid using it twice in the same model because it is already used in the extrapolationof the ASCB described above. It also considers the possibility of firms emphasizing theirperceptions of inflation rates rather than actual inflation when forecasting inflation.
We denote the perceived inflation rate in period 𝑡 as 𝜋 | and the inflation forecast
for ℎ periods ahead as 𝜋 | . As the Tankan inflation expectations and estimated inflation
expectations are on a year-on-year basis, all variables in the model are assumed to be on a
year-on-year basis, including the perceived inflation rate. We create estimates using thefollowing equation as a model incorporating medium- and long-term inflation expectations.
(𝑡 up to the fourth quarter of 2013)
𝜋
𝜋
𝜋

|
|
|

1 𝜙
1 𝜙
1 𝜙

𝜙
𝜙
𝜙

𝜋|

𝜖
𝜖
𝑒

,

(A3)

1 𝜙
⎡
⎤
1 𝜙
⎢
⎥𝜇
⎢1 𝜙 ⎥⎣1 𝜙 ⎦

𝜙
⎡
⎤
𝜙
⎢
⎥𝜋 |
⎢𝜙 ⎥
⎣𝜙 ⎦

𝜖
𝜖
𝜖
𝜖

,

(A4)

𝜇

𝑣,

𝜇

(𝑡 from the first quarter of 2014)
𝜋
𝜋
𝜋
𝜋

|
|
|
|

(All periods)
𝜇(A5)

where 𝜖 ∼ 𝑁 0, 𝜎 , 𝑒 ∼ 𝑁 0, 𝜎 , 𝑣 ∼ 𝑁 0, 𝑤
estimated inflation expectations one year ahead, 𝜋, for 𝑖 1, … ,4 ; 𝜋 | is the| and 𝜋| are the three- andfive-year inflation expectations from the Tankan, and 𝜋| is the three-year inflation
expectations from the ASCB. Because there is no Tankan inflation expectations series before
the fourth quarter of 2013, the equation comprises three observation equations: two forperceived inflation rate and the estimate inflation expectations one year ahead, plus thethree-year ahead inflation expectations from the ASCB. The Tankan inflation forecast22becomes available in the first quarter of 2014, resulting in a four-observation equation. The
variance of the error term 𝜖 in the Tankan inflation forecast is set to be common tominimize the number of parameters, given the limited number of samples in the data series.
Kozicki and Tinsley (2012) apply their model to data from the U.S., fitting an AR (13)model, which has long lags, to the inflation rate dynamics because the data series aremonthly and available over considerably long periods. However, as the Tankan data arequarterly, and the inflation expectations series cover only a short period, a simple AR(1)model is assumed to conserve parameters.
We calculate the perceived inflation rate using the fact that the actual consumer-relatedindustry output price DI series weighted by CPI displays a high correlation with the inflation
rate (total excluding fresh food, energy, and special factors, year-on-year). The correlation
coefficient between the consumer industry output price DI and the inflation rate
simultaneously is high, 0.753 for the period from the third quarter of 1991 to the fourth
quarter of 2022. Further, as the output price DI series is an evaluation for the most recent
three months, a correlation coefficient becomes higher, namely 0.851, when calculated witha series in which a backward four-period moving average is taken for the DI consistent with
the inflation rate on a year-on-year basis. Therefore, a linear relationship between the two
can be calculated by regressing the inflation rate on the output price DI. As including a linear
time trend would be statistically significant at the 1% level, we included time trends in the
regression, and the results are used to estimate the theoretical value of the inflation rate
based on the output price DI, that is, the perceived inflation rate in this analysis.
Appendix Figure 2 shows the estimated perceived inflation rate, which is similar topast inflation overall but features some differences in each phase. For example, actual
inflation fell sharply into negative territory in 2000, but perceived inflation rate remained at
approximately 0%. Moreover, while actual inflation rose to approximately 0% in 2003,
perceived inflation rate was been as low as -1%.
Models (A3)–(A5) are estimated using the maximum likelihood method with Kalmanfilter and grid search. The range and increments of the grid search are, respectively, 𝜙 in
the range [0.85, 0.99] with 0.01 increments, 𝜎in the range [0.01, 0.10] with 0.01

increments, 𝜎 in the range [0.1, 0.2] with 0.01 increments, and 𝑤 in the range [0.1, 0.2]
with 0.01 increments. The estimation period runs from the third quarter of 1991 to the fourth
quarter of 2022, for which the perceived inflation rate are available. For simplicity, the initial
distribution of 𝜇 is set from actual inflation immediately before the start of the estimation
period and is set based on actual inflation in the second quarter of 1991 (3.0%) and thevariance (0.15) for the two years immediately preceding (i.e., from the third quarter of 198923

to the second quarter of 1991), that is, 𝜇 ∼ 𝑁 3.0, 0.15 . For 𝜋|

in the fourth

quarter of 2022, which is the end of the sample period, we compute it as the observed valueof five-year ahead inflation expectations is inserted into 𝜋 | in the first row of equation(A3), with its error term assumed to be zero.
Appendix 2-3. Estimation result
We obtain parameter estimates 𝜙 0.86 , 𝜎
0.07 , 𝜎0.12 , and 𝑤 0.14 .
Appendix Figure 3 shows the estimated value of 𝜇 , labeled "Trend inflation," and the fiveyear ahead inflation expectations estimated based on the estimated parameters and the valueof 𝜇 . The trend inflation is consistently around the same level as the 5-year ahead inflation
expectations. This is because the term structure of the inflation expectations is shaped toreach the convergence point level comparatively quickly, as 𝜙 is not so close to one.
Related to this, the characteristics of the term structure of inflation expectations can be
exhibited in Appendix Figure 4, which shows an estimated 1–10 years ahead of inflation
expectations. This finding is consistent with the empirical study by Maruyama andSuganuma (2019); they estimate inflation expectation curves from data on various inflation
expectations in Japan.
Appendix Figure 5 shows estimated 5-year ahead inflation expectations and its 95%
confidence interval. The observed values (actual Tankan values) fall within this interval,
except for a small portion of the period in 2021, indicating the estimate to be a good fit.
From approximately 1.5% circa 1992, 5-year ahead inflation expectations continued
intermittently, declining to approximately 1% circa 1995 and approximately 0.5% circa
2000. Subsequently, they increased around 2012, slightly above 1.5% in 2014. Appendix
Figure 6 shows the estimated values for the trend inflation, and its 95% confidence intervalshows almost the same movements as the 5-year ahead inflation expectations. In priorstudies, the firms' inflation expectations estimated in this analysis were somewhat lower in1990 than the long-term inflation expectations estimated by Hogen and Okuma (2018) andMaruyama and Suganuma (2019). However, their movements are broadly similar
throughout the sample period.
The five-year ahead inflation expectations form a series that uses estimated five-year
ahead inflation expectations up to the fourth quarter of 2013 and observed Tankan data fromthe first quarter 2014. Inflation expectations two-year and four-year ahead are estimatedvalues obtained from the model estimated in this analysis for the entire period. However,from the first quarter of 2014 onwards, in order to maintain consistency with the observed
values for one, three, and five years ahead, we adjust the differences between the observed
values and the estimated values for these maturities, albeit slightly. Specifically, after
24

rounding up the estimated values for the one-year and three-year ahead to the first decimal
place, take the difference from the observed values, average them for the one-year ahead
and the three-year ahead, and obtain the estimate for the two-year ahead series (rounded up
to one decimal place). Similarly, the average difference is calculated from the three-year
and five-year future series and added to the four-year estimate. Looking at the estimatedterm structure for six years or more ahead, it is almost the same level as five years ahead.
Therefore, we set the inflation expectations six years and more ahead as the value of fiveyear ahead series.
Appendix Figure 7(1) shows estimated firms' five-year forward inflation expectations
and economists' five-year forward inflation expectations, which is from Consensus
Forecasts. During the 1990s and 2000s, firms' inflation expectations were lower thaneconomists' expectations—the difference between the two averages was approximately 0.5
percentage points. In the late 1990s and 2000s, economists' inflation expectations rose toapproximately 1.5%, but no such movement was seen in firms' inflation expectations.
Appendix Figure 7(2) shows estimated firms' trend inflation and economists' 6- to 10-year
inflation expectations; these show similar differences from the 5-year inflation expectations.
We test the estimated firms' five-year-ahead inflation expectations and economists'
inflation expectations by performing the same analysis as in the main analysis of this paper
to identify differences in forecast accuracy in the inflation forecasting models. Specifically,
RMSEs were calculated 1–8 quarters ahead of inflation expectations from the first quarterof 2015 to the fourth quarter of 2019. Note that the series estimated using the method abovefrom the all-period data was uniformly used for firms' inflation expectations. In other words,
the forecast is not based on counts created from data available in real-time, which is a caveat
in this forecast analysis.
Appendix Table 1 presents the results, showing little difference in forecast accuracy
for the first five quarters. Meanwhile, forecast accuracy for the 6th–8th quarters is higher
when firms' inflation expectations are used. As in the main study, statistical tests are
conducted on these differences in predictive accuracy, but they are insignificant even at the
10% level. Although this does not yield statistical significance, the estimated firms' inflation
expectations contain information about their expectations as price setters, suggesting thatthey may include at least as much information about a future path of the inflation rate as
economists' inflation expectations and may be useful when analyzing inflation rates andpolicy effects.

25

References
Adachi, K., and K. Hiraki (2021) "Recent developments in measuring inflation
expectations: With a focus on market-based inflation expectations and the term structureof inflation expectations," Bank of Japan Research Laboratory Series, No. 21-E-1.
Coibion, O., Y. Gorodnichenko, and R. Kamdar (2018) "The formation of expectations,inflation, and the Phillips curve," Journal of Economic Literature, 56(4), pp. 1447-1491.
Coibion, O., Y. Gorodnichenko, and S. Kumar (2018) "How do firms form their
expectations? New survey evidence. American Economic Review, 108(9), pp. 26712713.
Coibion, O., Y. Gorodnichenko, S. Kumar, and M. Pedemonte (2020) "Inflation
expectations as a policy tool?" Journal of International Economics, 124, 103297.
Fuhrer, J. (2012) "The role of expectations in inflation dynamics," International Journal ofCentral Banking, 8(S1), pp. 138-165.
Gorodnichenko, Y., and D. Sergeyev (2021) "Zero lower bound on inflation expectations,"
NBER Working Paper Series, No. w29496.
Hajdini, I., E. S. Knotek, J. Leer, M. Pedemonte, R. W. Rich, and R. Schoenle (2022)"Indirect consumer inflation expectations: Theory and evidence," Federal Reserve Bankof Cleveland Working Paper Series, No. 22-35.
Hansen, P. R., A. Lunde, and J. M. Nason (2011) "The model confidence set," Econometrica,
79, pp. 453-497.
Hiraki, K., and W. Hirata (2020) "Market-based long-term inflation expectations in Japan:
A refinement on breakeven inflation rates," Bank of Japan Working Paper Series, No.
20-J-5.
Hogen, Y., and R. Okuma (2018) "The anchoring of inflation expectations in Japan: Alearning-approach perspective," Bank of Japan Working Paper Series, No. 18-E-8.
Hori, M., and M. Kawagoe (2013) "Inflation expectations of Japanese households: Microevidence from a consumer confidence survey," Hitotsubashi Journal of Economics, 54,
pp. 17-38.
Inatsugu, H., T. Kitamura, and T. Matsuda (2019) "The formation of firms' inflation
expectations: A survey data analysis," Bank of Japan Working Paper Series, No. 19-E15.

26

Kaihatsu, S., and N. Shiraki (2016) "Firms' inflation expectations and wage-setting
behaviors," Bank of Japan Working Paper Series, No. 16-E-10.
Kaihatsu, S., and J. Nakajima (2018) "Has trend inflation shifted?: An empirical analysis
with an equally-spaced regime-switching model," Economic Analysis and Policy, 59,
pp. 69-83
Kamada, K., J. Nakajima, and S. Nishiguchi (2015) "Are household inflation expectations
anchored in Japan?" Bank of Japan Working Paper Series, No. 15-E-8.
Kikuchi, J., and Y. Nakazono (2021) "The formation of inflation expectations: Microdata
evidence from Japan," Journal of Money, Credit and Banking, in press.
Kitamura, T., and M. Tanaka (2019) "Firms' inflation expectations under rational inattention
and sticky information: An analysis with a small-scale macroeconomic model," Bank ofJapan Working Paper Series, No. 19-E-16.
Kozicki, S., and P. A. Tinsley (2012) "Effective use of survey information in estimating theevolution of expected inflation," Journal of Money, Credit and Banking, 44(1), pp. 145169.
Maruyama, T., and K. Suganuma (2019) "Inflation expectations curve in Japan," Bank ofJapan Working Paper Series, No. 19-E-6.
Nakajima, J., H. Yamagata, T. Okuda, S. Katsuki, and T. Shinohara (2021) "Extracting firms'
short-term inflation expectations from the Economy Watchers Survey using text
analysis," Bank of Japan Working Paper Series No. 21-E-12,
Nakazono, Y. (2016) "Inflation expectations and monetary policy under disagreements,"
Bank of Japan Working Paper Series, No. 16-E-1.
Nishiguchi, S., J. Nakajima, and K. Imakubo (2014) "Disagreement in households' inflation
expectations and its evolution," Bank of Japan Review, No. 2014-E-1.
Nishino, K., H. Yamamoto, J. Kitahara, and T. Nagahata (2016) "Developments in inflation
expectations over the three years since the introduction of Quantitative and Qualitative
Monetary Easing (QQE)," Bank of Japan Review, No. 2016-E-13.
Pinto, S., P. D. Sarte, and R. Sharp (2020) "The information content and statistical propertiesof diffusion indexes," International Journal of Central Banking, 16(4), pp. 47-99.
Uno, Y., S. Naganuma, and N. Hara (2017) New facts about firms' inflation expectations:
Simple tests for a sticky information model," Bank of Japan Working Paper Series, No.
18-E-14.

27

Figure 1. Tankan index of inflation expectations (all firm sizes and industries, one year
ahead)
3.5

%

DI

60

3.0

50

2.5

40

2.0

30

1.5

20

1.0

10

0.5

0

0.0

-10

-0.5
2014

-20
2015

2016

2017

2018

CPI inflation expectations

2019

2020

2021

2022

Output price expectations

Output price DI (right scale)28

Figure 2. Tankan consumer-related industry output price expectations (all firm sizes, one
year ahead)
4.5

%

4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
2014

2015

2016

2017

2018

2019

2020

2021

2022

(a) Retailing(b) Services for individual(c) Accommodations, eating & drinking services
Consumer-related industry average
CPI inflation expectations (all industry)
Note: Consumer-related industries are weighted averages of (a) through (c), weighted according to theirweight in the CPI (see the text for details).

29

Figure 3. Estimated and observed values of firms' inflation expectations (one year ahead)
3.5

%

3.0
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
1990

1995

2000

2005

Estimates

2010

2015

2020

Observation

Note: The shadowed ranges show the 95% confidence interval for the estimates.

Figure 4. Estimated firms' inflation expectations and economists' inflation expectations

3

3.5

%

3.0
2.5
2.0
1.5
1.0
0.5
0.0

-0.5
-1.0
-1.5
-2.0
1990

1995

2000

2005

Firms' inflation expectations

2010

2015

2020

Economists' inflation expectations

CPI inflation rate (year-on-year)
Note: The CPI inflation rate is the total, excluding fresh food, energy, and special factors (see the text for
details). The economists' inflation forecast is the one-year-ahead Consensus Forecasts.

30

Appendix Figure 1. Three-year ahead inflation expectations estimated from the Annual
Survey of Corporate Behavior
3.0

%

2.5
2.0
1.5
1.0
0.5
0.0
-0.5
1990

1995

2000

2005

2010

Inflation expectations(Annual Survey of Corporate Behavior)

2015

2020

Inflation expectations(Tankan, 3-year ahead)

Appendix Figure 2. Estimated perceived inflation rate
3.5

%

3.0
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
1990

1995

2000

2005

Perceived inflation rate

2010

2015

2020

CPI inflation rate (year-on-year)

Note: The CPI inflation rate is the total, excluding fresh food, energy, and special factors (see the text for
details).

31

Appendix Figure 3. Estimates of firms' inflation expectations
3.5

%

3.0
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
1990

1995

2000

2005

2010

2015

2020

Perceived inflation rate

One-year ahead inflation expectations

Five-year ahead inflation expectations

Trend inflation

Appendix Figure 4. Estimated term structure of firms' inflation expectations
3.0

%

2.5
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
1990

1995

2000

One-year ahead

2005

2010

2015

2020

Two-year ahead (longer years in lighter colors)32

Appendix Figure 5. Estimated and observed firms' inflation expectations (5 years ahead)
2.5

%

2.0
1.5
1.0
0.5
0.0
-0.5
1990

1995

2000

2005

Estimates

2010

2015

2020

Observation

Note: The shadowed ranges show the 95% confidence interval for the estimates.

Appendix Figure 6. Estimates of firms' trend inflation
2.5

%

2.0
1.5
1.0
0.5
0.0
-0.5
1990

1995

2000

2005

2010

2015

Estimates
Note: The shadowed ranges show the 95% confidence interval for the estimates.

33

2020

Appendix Figure 7. Firms' and economists' inflation expectations(1) Five years ahead
3.5

%

3.0
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
1990

1995

2000

2005

2010

Firms' inflation expectations

2015

2020

Economists' inflation expectations

CPI inflation rate (year-on-year)(2) Trend inflation
3.5

%

3.0
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
1990

1995

2000

2005

Firms' inflation expectations

2010

2015

2020

Economists' inflation expectations

CPI inflation rate (year-on-year)
Note: The CPI inflation rate is the total, excluding fresh food, energy, and special factors (see the text for
details). Economists' inflation forecasts are Consensus Forecasts (trend inflation is 6-10 years ahead).

34

Table 1. Explanatory variables in the estimation modelSet

The number ofvariables

Explanatory variables

1

All industry average (all sizes)

1

2

Retailing (all sizes)

13

Consumer-related industry average (all sizes)

1

4

Retailing,
Services for individual (all sizes)

25

Retailing,
Accommodations, eating & drinking services (all sizes)

2

6

Retailing,
Services for individual,
Accommodations, eating & drinking services (all sizes)

3

7

Individual industries (all sizes)

23

8

Individual industries, individual sizes

69

Table 2. In-sample RMSE (from March 2014 to December 2022 surveys)

Set

1. One-step direct
regression

2. Two-stage
3. Two-stage
indirect regression weighted regression

1

0.31940.3225―20.24120.2415―30.23880.2391―40.24080.24170.2476

5

0.22300.23320.2307

6

0.22290.23270.24147

0.96740.3646―80.83000.3318―35

Table 3. Out-of-sample predictive accuracy (RMSE)(1) From March 2018 to December 2022 surveys
Set

1. One-step direct
regression

2. Two-stage indirect
3. Two-stage
regression
weighted regression

10.4006

0.4128―20.3146

0.3262―3

0.32680.3339―40.35630.31990.299150.32480.31410.29306

0.35230.30920.2830(2) From March 2019 to December 2022 survey
Set

1. One-step direct
regression

2. Two-stage indirect
3. Two-stage
regression
weighted regression

1

0.37830.3594―2

0.34940.3624―

3

0.34930.3588―40.37510.35580.32335

0.34730.34740.324860.37150.34370.304036

(3) From March 2020 to December 2022 surveys
Set

1. One-step direct
regression

2. Two-stage indirect
3. Two-stage
regression
weighted regression

1

0.4226

0.3869―20.3824

0.3980―3

0.34100.3592―4

0.39190.39190.341850.39500.37430.3477

6

0.40990.37120.3145(4) From March 2021 to December 2022 surveys
Set

1. One-step direct
regression

2. Two-stage indirect
3. Two-stage
regression
weighted regression

1

0.41950.4231―

2

0.41960.4432―

3

0.38920.4113―40.44180.43480.343050.35070.41720.3896

60.37110.41450.316537

Table 4. Time lag correlation coefficient between firms' inflation expectations and CPI
inflation rate (year-on-year)
Inflation expectations
lead (quarter)

Correlation

0

0.726

1

0.789

2

0.830

3

0.830

4

0.800

5

0.758

6

0.686

7

0.609

8

0.534

Note: The sample period is from the fourth quarter of 1990 to the fourth quarter of 2021. The CPI inflation
rate is the total, excluding fresh food, energy, and special factors (see the text for details).

38

Table 5. Results of the Granger causality test
Null hypothesis

F-valuep-value

CPI inflation rate does not cause inflation expectations

9.086

0.000

Inflation expectations do not cause CPI inflation rate

0.479

0.751

CPI inflation rate does not cause inflation expectations

6.157

0.000

Inflation expectations do not cause CPI inflation rate

1.694

0.156

a. Estimated firms' inflation expectations (one year ahead)a. Economists' inflation expectations (one year ahead)

Note: The sample period is from the fourth quarter of 1990 to the fourth quarter of 2021. The lag length
is four quarters. The CPI inflation rate is the total, excluding fresh food, energy, and special factors (seethe text for details). The economists' inflation expectations are the one-year-ahead Consensus Forecasts.

39

Table 6. Determinants of the CPI inflation rate
Dependent variables: CPI inflation rate

Variables
Lagged CPI inflation rate

Output gap

0.852 ***

0.811 ***

0.890 ***

0.847 ***

(0.031)(0.021)(0.034)(0.028)0.071 ***

0.043 **

0.052 ***

0.036 **

(0.024)(0.024)(0.021)(0.022)-0.007 ***-0.005 **(0.003)(0.002)

Exchange rate

Inflation expectations

Constant

0.184 ***

0.143 ***

(0.052)(0.060)0.043 *

-0.0370.041 **

-0.020(0.026)(0.036)(0.025)(0.035)

Standard errors

0.207

0.195

0.197

0.191

Adjusted R-squared

0.946

0.952

0.951

0.954

Note: The sample period is from the fourth quarter of 1990 to the fourth quarter of 2021. The CPI inflation
rate is the total, excluding fresh food, energy, and special factors (see the text for details). The CPI
inflation and exchange rates (nominal effective) are year-on-year values. We take a one-quarter lag forthe output gap and the exchange rate. Figures in parentheses show Newey-West HAC standard error. ***,**, and * denote statistical significance at the 1%, 5%, and 10% levels, respectively.

40

Table 7. RMSE in forecasting CPI inflation (with one-year ahead inflation expectations)b. With firms' inflation
expectations

c. With economists'
inflation expectations

Horizon(quarter)a. Without inflation
expectations

1

0.138

0.132

0.135

2

0.156

0.143

0.155

3

0.208

0.178

0.205 **

40.260

0.213 *

0.252 ***

Note: The forecast period is from the first quarter of 2015 to the fourth quarter of 2019. * indicates thatthe difference from (1) for (2) and (2) for (3) is statistically significant at the 10% level.

41

Appendix Table 1. RMSE in forecasting CPI inflation (with five-year ahead inflation
expectations)
Horizon(quarter)With firms' inflation
expectations

With economists'
inflation expectations

1

0.138

0.136

2

0.162

0.152

3

0.226

0.212

4

0.284

0.300

5

0.329

0.380

6

0.373

0.478

7

0.413

0.572

8

0.432

0.639

Note: The forecast period is from the first quarter of 2015 to the fourth quarter of 2019.

42