Monthly Prefecture-Level GDP in Japan*
Daisuke Fujii†

Taisuke Nakata‡

Takeki Sunakawa§

RIETI

University of Tokyo

Hitotsubashi University

April 9th, 2024

Abstract
We propose a new measure of monthly prefecture-level GDP in Japan. Our measure
is derived in two steps. In the first step, we compute the production-side GDP and
expenditure-side GDP using a variety of official statistics. In the second step, we computethe simple average of the two levels and make an adjustment to it to ensure consistency
with the official national quarterly GDP. For more recent periods when official statistics are not available, we estimate monthly GDP using alternative data. Our monthly
prefecture-level GDP measures can be used to analyze various economic questions atregional levels

Keywords: prefecture-level GDP, monthly GDP, time series forecasting, alternative data,regional economy
JEL classification: E01, E17, E37, C53, R11* We thank Tsunenori Ashiya, Keisuke Matsushima, Nao Sudo, Nariyasu Yamasawa, and the seminar participants at the Japan Society of Monetary Economics Fall Meeting 2022 and the Japanese Economic Association
Spring Meeting 2023 for their valuable comments. We also acknowledge Japan Center for Economic Research(JCER) for providing their national monthly GDP data. Hiroyuki Asai, Dai Sasaki, Kazuma Takakura, andMizuki Tanaka provided excellent research assistance. Daisuke Fujii is supported by JSPS Grant-in-Aid for
Scientific Research (KAKENHI), Project Number 23H00812. Taisuke Nakata is supported by JSPS Grant-in-Aid
for Scientific Research (KAKENHI), Project Number 22H04927, the Research Institute of Science and Technology for Society at the Japan Science and Technology Agency, the Center for Advanced Research in Finance at
the University of Tokyo, and the Tokyo Center for Economic Research. All errors are our own.
† Email: fujii-daisuke@rieti.go.jp‡ Email: taisuke.nakata@e.u-tokyo.ac.jp§ Email: t.sunakawa@r.hit-u.ac.jp (corresponding author)1

1

Introduction

For some policy analyses—including the analysis of pandemic and natural disasters—it is
crucial to have access to high-frequency economic data at the regional level. In Japan, oneof the fundamental statistics concerning regional economies is the Prefectural Economic Accounts. However, they are only published annually with an approximate lag of about two
years until their release.1 Some regional statistics—such as the Indices of Industrial Production (IIP) and Monthly Labor Survey (MLS) —are published on a monthly basis with ashorter lag. Yet, these datasets can only capture certain aspects of regional economies, suchas production and employment. To capture the current economic conditions in a region, it
is often necessary to synthesize these limited indicators along with micro-level qualitative
information.2
This paper aims to contribute to the literature on regional economic statistics by proposing a novel measure of monthly prefecture-level GDP (Gross Domestic Product) in Japan. We
also present a method for estimating—“backcasting”—recent values of monthly prefecturelevel GDP.
Here is the overview of what we do in this paper. First, we construct monthly economic
activity indicators for both the production and expenditure sides for each prefecture. Second, we take the simple average of these two indicators for each prefecture and make adjustments to it to ensure that the aggregated monthly prefecture-level GDP matches the national
quarterly GDP. This is our monthly prefecture-level GDP. Third, for the most recent months
where actual values cannot be calculated yet, we estimate GDP values using a statisticalmodel based on the relationship with available data (alternative data) that have a relatively
1 Several prefectures, including Hyogo, Fukuoka, and Ibaraki, estimate and publish quarterly GDP. Addi-

tionally, other prefectures such as Shimane published their quarterly GDP in the past. For those interested in
the methodology of creating these quarterly preliminary Prefectural Accounts, references can be found in thework of Ashiya (2009) and Shimaneken (2020), where they explain the procedures involved in generating theseestimates.
2 There are indicators for regional economic sentiment based on surveys, such as the Bank of Japan’s Tankan
survey, the Cabinet Office’s Economy Watchers Survey, and the Teikoku Databank (TDB) Economic Trends
Survey.

2

shorter lag until data release. This process is referred to as “backcasting” in this paper.
The distinctive feature of our monthly prefecture-level GDP—compared to several previous studies (e.g., Yamasawa (2014, 2022) and Yamada (2014))—is that it is constructed usinga wide range of information from both the production and expenditure sides. We will discuss these previous studies in detail shortly.
The monthly prefecture-level GDP constructed in this manner can be used for various
regional economic analyses. As an example, this paper explores time-series correlations between GDP and factors such as population movement, the number of new COVID-19 cases,
and the inflation rate in each prefecture. We find that while there are significant correlations
between GDP and population movement or new COVID-19 cases in many prefectures, thecoefficients of correlation vary widely among prefectures. Additionally, a positive correlation resembling the Phillips curve between monthly GDP and inflation rates is observed inmany prefectures.

1.1

Literature review

This paper is related to two strands of literature: construction of high-frequency economic
indicators at the state level and nowcasting economic activity.

1.1.1

High-frequency economic indicators at the state level

In recent years, there has been a surge of high-frequency economic indicators. Most studies
focus on the national , several studies analyze high-frequency economic indicators at thestate level. Crone and Clayton-Matthews (2005) estimate monthly coincident indexes for the
50 U.S. states using the methodology developed by Stock and Watson (1989). Baumeister
et al. (2022) develop a dataset of weekly economic indicators for the 50 U.S. states basedon mixed-frequency dynamic factor models. Chinn and LeCloux (2018) review the data
sources and series that are useful for developing high-frequency economic indicators at thestate level.
3

Our paper is closely related to Yamasawa (2014), Yamada (2014), and Yamasawa (2022)
which construct monthly prefecture-level GDP in Japan. Below, we discuss their work andour difference from their work in some details.
Yamasawa (2014) constructs expenditure-side monthly GDP for three disaster-affected
prefectures (Iwate, Miyagi, and Fukushima). He does so by combining the Regional Domestic Expenditure Index (RDEI)—which covers consumption, private residential investment,
private non-residential investment, and public investment—and estimates of public consumption, net exports to other countries and net exports to other prefectures. He estimatespublic consumption, net exports to other countries and prefectures via panel data analysis
exploiting the historical relationship between these variables and their key predictors.
Yamada (2014) constructs expenditure-side monthly GDP for all 47 prefectures in a similar manner to Yamasawa (2014), but with a different approach to estimating net exports
to other countries and prefectures. He utilizes data from the Trade Statistics published by
the Ministry of Finance and estimates prefecture-level net exports to other countries using
information on industrial compositions. He also estimates prefecture-level net exports toother prefectures using inter-prefectural freight transportation data and imposing a constraint condition that the total net exports nationwide must be zero. Government expenditure is not estimated in the Yamada’s study, unlike in Yamasawa (2014).3
Yamasawa (2022) constructs production-side monthly GDP for all 47 prefectures in asimilar manner to Yamasawa (2014), but with supply-side variables. Yamasawa (2022) firstregresses annual output of various industries from prefectural economic accounts on theannual values of the IIP, Indices of Tertiary Industry Activity (ITA), and construction output
data from the Ministry of Land, Infrastructure, Transport and Tourism (MLIT). With theestimated equations, he predicts monthly prefecture-level output of each industry using
the monthly data of the covariates. Finally, he constructs monthly prefecture-level GDP bysumming the predicted monthly output across industries.
3 Regarding government expenditure, although it constitutes a significant share of each prefecture’s GDP,

its impact on GDP fluctuations is relatively limited.

4

Our monthly prefecture-level GDP is different from these measures because we combine
expenditure-side GDP with production-side GDP. We also take a different approach to constructing the production-side GDP compared to Yamasawa (2022). Moreover, we propose
a backcasting methodology to estimate recent values of GDP using alternative data, while
they do not.

1.1.2

Nowcasting GDP

This paper is also related to the literature of nowcasting GDP. Since Giannone et al. (2008)
and Evans (2005), many researchers have proposed various methodologies to nowcast GDP
in different countries. Banbula et al. (2011; 2013) and Carriero et al. (2015)construct nowcasts
for GDP in the U.S., while Giannone et al. (2009) and Mitchell (2009) constructs nowcasts for
GDP in the Euro Area and the U.K., respectively. See Bańbura et al. (2013) and Bok et al.
(2018) for surveys on nowcasting in macroeconomics.
Several papers have constructed the nowcast of Japan’s GDP (Hara and Yamane (2013),
Urasawa (2014), Bragoli (2017), Hayashi and Tachi (2023), Nakazawa (2022) and Chikamatsu
et al. (2021)).4 These papers typically focus on nowcasting quarterly GDP, with Hara andYamane (2013) being an exception—they nowcast monthly GDP. Most papers use variantsof the dynamic factor model by extracting a number of primary components of large-scaledata, while Chikamatsu et al. (2021) adapts an equation-by-equation approach. We propose
a backcasting methodology based on the latter approach and adopt it to monthly prefecturelevel GDP in Japan.
This paper is organized as follows. Section 2 details the methodology for constructing
monthly prefecture-level GDP. Section 3 explains the methodology for backcasting GDP.
Section 4 presents several examples of analyses using the monthly prefecture-level GDP,and Section 5 concludes.
4 Recently, the Bank of Japan (BOJ) has been leading an initiative to utilize alternative data to nowcast eco-nomic activities in Japan (see Furukawa et al. (2022); Furukawa and Hisano (2022); Matsumura et al. (2021);
Nakazawa (2022); Okubo et al. (2022)).

5

2Construction of monthly prefecture-level GDP

In this section, we discuss the methodology for constructing monthly prefecture-level GDP
in Japan.
The following is an overview of our procedure: First, for each prefecture, we constructproduction-side and expenditure-side GDP measures at monthly frequency. The productionside GDP (GDP ( P)) is calculated as a weighted average using industry-specific weights for
manufacturing, construction, and service activities on a monthly basis. The expenditureside GDP (GDP ( E)) is computed as a weighted average of four series: consumption, private
investment, residential investment, and public investment.
Second, we aggregate these two GDP measures. According to the national income accounting identity, these two measures should be equal theoretically. However, due to measurement errors and the lack of information on certain components (for example, agricultural and forestry activities for production-side GDP, and public consumption and net exports for expenditure-side GDP), the production-side GDP and expenditure-side GDP typically do not coincide. To aggregate GDP ( P) and GDP ( E), we take their simple average(“unadjusted GDP”) and scale it so that, when prefecture-level GDP values are aggregatedto form the national GDP, that value aligns with the national quarterly GDP.

2.1

Production-side GDP

We calculate the production-side GDP for each prefecture by taking a weighted averageof the following three indices: IIP (manufacturing sector), "Construction Comprehensive
Statistics" (construction sector), and ITA (service sector).5 These three indices are weighted
based on the value-added share of each sector from the Economic Census - Activity Survey
published by the Ministry of Internal Affairs and Communications (MIC). Below, we will
provide a detailed explanation of the procedure for computing the production-side GDP for
5 IIP and ITA are published by METI while CCS is published by MLIT.

6

each prefecture.
For the manufacturing sector, we use the monthly IIP data for the seasonally-adjusted
composite index. The IIP (Indices of Industrial Production) is published by METI and provides monthly prefecture-level indices of manufacturing activity.
For the construction sector, we use the prefecture-level monthly data on regional construction output (nominal values) from “Quick Estimate of Construction Investment” provided by MLIT.6 We employ the MLIT’s "Construction Project Cost Deflator" (Construction
Comprehensive, Nationwide) to convert these nominal values into real values. We seasonally adjust these real-valued data using the X12-ARIMA method for each prefecture.7
For the service sector, we use the ITA (Indices of Tertiary Industry Activity) data. The
ITA is published by METI and provides monthly indices of industrial activity within service
sector at the national level. Prefecture-level ITA is not available in almost all prefectures,with Tokyo being an exception. However, industry-specific weights for each prefecture areavailable.
We compute prefecture-level ITA by taking a weighted average using these industryspecific weights. Specifically, we calculate the index of tertiary activity in prefecture k attime t, denoted by ITAkt , as follows
ITAkt = ∑ wik ITAitN
iwhere ITAitN represents the level of economic activity for industry i at the national level (N),and wik represents the weight for industry i in prefecture k.8 For the weights wik , we use
industrial value-added shares from prefectural input-output (IO) tables or the Economic
6 Since the most recent publicly available data starts from April 2017, we extend and connect the dataset

from April 2011 to March 2017, which was published in January 2021.
7 Yamasawa (2022) has created prefecture-specific monthly production indices for the construction industry
using a comparable approach.
8 In Appendix D, we attempt to modify the ITA index based on the monthly data of six business types (department stores, supermarkets, convenience stores, electronics retailers, drugstores, and home improvement
stores) from the METI’s "Commercial Activity Statistics," collected by each prefecture.

7

Census. Most of the prefectures construct their own IO tables. Since industry classificationsin those prefectural IO tables and ITA are similar, we use the industrial share informationfrom the IO tables. For prefectures whose prefectural IO tables are not available, we use
industrial value added shares from the Economic Census. Though the industrial shares fromthe Census are available in all prefectures, we prefer the IO weights to the Census weights
because ITA industrial classifications are more similar to the IO classifications than to the
Census classifications. See Appendix A and B for more detailed description of the IO andEconomic Census weights respectively.
After computing the monthly prefecture-level indices for the manufacturing, construction, and service sectors, we construct the monthly prefecture-level production-side GDP
by taking the weighted average of those three indices. The sectoral weights are computed
based on the value added from the Economic Census for each prefecture9 ; these weights areconstant over time during the sample period. If we denote I IPtk , Constkt , and ITAkt as themonthly data (with a base year average of 100 for the year 2015) for each sector in prefecturek, and skm , sks , and skc as the respective sectoral weights for prefecture k (adjusted to ensurethat their sum equals 1), then the production-side GDP for prefecture k at time t, denoted by
GDP ( P)kt , is given by
GDP ( P)kt = skm I IPtk + skc Constkt + sks ITAks= skm I IPtk + skc Constkt + sks∑ wik ITAitN!

i

Figure 1 represents the sectoral weights for each prefecture. According to the figure, they
cover nearly the entire economy, encompassing both the secondary sector—including theconstruction industry—and the tertiary sector.
noFigure 2 displays GDP ( P)kt , I IPtk , Constkt , ITAkt for Tokyo and Aichi. In Tokyo, the
9 It is important to note that the production-side GDP created here does not include the production activitiesof the agriculture, forestry, and fisheries sector. These sectors’ contribution to the overall GDP is relatively
small, and furthermore, there is no monthly data available for their production activities.

8

Figure 1: Sectoral weights by prefectureservice sector accounts for over 80% of the total weight. As a result, the fluctuation of its
production-side GDP is largely explained by the dynamics of ITA. Both the manufacturing
and service sectors experienced a significant decline in production around the time of thedeclaration of the state of emergency (SOE) in April 2020. Conversely, the construction sector
did not experience a substantial decline during the same period, although it does exhibit adownward trend throughout the COVID-19 crisis.10
In Aichi, the service sector carries around 60% weight while the manufacturing sector
accounts for around 40%. As a result, the production-side GDP fluctuates approximately
midway between ITA and IIP. According to the figure, IIP experienced a more pronounced
decline during the SOEs than ITA in Aichi.
10 Furthermore, it should be noted that monthly data of ITA (with a base year of 2015) for Tokyo are available.

These data closely mirror the movements of ITA’s monthly data created using national monthly industry-level
data and industry-specific weights for Tokyo.

9

Figure 2: Production-side GDP: Aichi and Tokyo

2.2

Expenditure-side GDP

We calculate the expenditure-side GDP for each prefecture using the "Regional Domestic Expenditure Index" (RDEI) provided by the Cabinet Office.11 The RDEI comprises four indices:
the regional consumption index, the regional private residential index, the regional private
corporate investment index, and the regional public investment index. For each of these
indices, monthly data (real, seasonally adjusted) are publicly available for each prefecture,
starting from January 2005 for the regional consumption index and January 2012 for otherindices. We seasonally adjust each of these indices using X-12-ARIMA. We compute theexpenditure-side GDP by taking a weighted average of those data (normalized to be 100 in2015), where weights are the real expenditure values of the corresponding items in the Prefectural Economic Accounts (PEA).12 We denote the expenditure-side GDP for prefecture k
at time t by GDP ( E)kt .
Figure 3 presents the growth rate of the expenditure-side GDP and its decomposition
into the four components of RDEI for Tokyo and Aichi since 2020.
11 For detailed documentation of RDEI, see Tanabe et al. (2012) and Mitani et al. (2019).
12 In the original data, the base year for the consumption series is 2012, while that for other three series is

2005.

10

Figure 3: Expenditure-side GDP (contribution decomposition): Tokyo and Aichi

According to the figure, private consumption is the primary driver of fluctuations inboth prefectures. However, private investment is also a significant component explaining
the fluctuation of RDEI in Aichi, whereas it is not in Tokyo. This difference is consistent withthe difference observed in the production-side GDP between Tokyo and Aichi prefectures,
as discussed at the end of Section 2.1.

11

2.3

Aggregation to prefecture-level GDP

Thus far, we have explained how to construct monthly production-side and expenditureside GDP at a prefecture level. We now explain how to aggregate them to obtain the monthly
prefecture-level GDP.
We start by taking a simple average of production-side and expenditure-side GDP.
g kt = 0.5 × GDP ( E)k + 0.5 × GDP ( P)kGDPttThis simple average—”unadjusted GDP”— for each prefecture can be aggregated acrossprefectures to obtain the national GDP. However, this national GDP may not necessarilyalign with the quarterly estimates (QE) of the national GDP published by the Cabinet Office.
To make our aggregated national GDP consistent with the QE for each quarter, we make thefollowing adjustments to the unadjusted GDP of each prefecture.
First, we aggregate GDP across prefectures using the value-added weights from the Economic Census for each prefecture, denoted by ω k . This aggregation generates the monthly
data for the national GDP
g nt = ∑ ω k GDP
g kt
GDP
k

g nt “the unadjusted national GDP.” Next, we time-aggregate the monthly values
Let’s call GDP
for each quarter to calculate the quarterly data for national GDP. Let’s normalize the official
national GDP from the Cabinet Office so that its average value in 2015 is 100 and call it
QEτn(t) . Then, we multiply each prefecture’s unadjusted GDP by the ratio of official national
GDP to the unadjusted national GDP.

GDPtk =

QEτn(t)!

g ns∑s∈S(τ (t)) GDP

g kt = κτ (t) GDP
g kt
GDP

This is our monthly prefecture-level GDP. In this equation, we use a set of quarter-specificcoefficients κτ (t) for an adjustment. Here, τ (t) represents the quarter that includes a specific12month t and S (τ (t)) denotes the set of all months contained within that quarter τ (t). For
example, when t is January 2020, τ (t) is the first quarter of 2020 and S (τ (t)) consists of{January 2020, February 2020, March 2020}. By construction, if we aggregate our monthly
prefecture-level GDP, both across prefectures and across months, the resulting national GDP
coincides with the official national GDP.13
Figure 4 displays the production-side GDP, expenditure-side GDP, their simple average,
and monthly GDP for Aichi and Tokyo (2015 = 100).

Figure 4: Monthly GDP: Aichi and Tokyo

Figure 5 compares our monthly national GDP with the official national quarterly GDP
and the national monthly GDP constructed by the Japan Center for Economic Research(JCER). For comparison, all three GDP measures are standardized to have an average of
100 for the first quarter of 2020. According to the figure, our monthly national GDP aligns
with the official quarterly national GDP. Our monthly national GDP also moves closely with
JCER’s monthly national GDP.
13 We haveQEτn(t) =∑ ∑ ω k GDPsks∈S(τ (t)) k

13

Figure 5: Monthly GDP: Nation

2.4

The timing of the construction of monthly prefecture-level GDP

The timing of constructing production-side GDP, expenditure-side GDP, and overall GDP
depends on the release schedule of the underlying data.
For the production-side GDP, we use three datasets: (i) national ITA, (ii) prefecture-level
IIP, and (iii) prefecture-level construction statistics. Preliminary and final values of the national ITA are released with a two-month and five-month lag respectively. Preliminary andfinal values of the prefecture-level IIP are released with a two-month and three-month lag
respectively. Final values of the prefecture-level construction statistics are released with a
two-month lag.14 Hence, we can compute the production-side GDP with a two-month lag.
For the expenditure-side GDP, we use prefecture-level RDEI, which is the only input.
Prefecture-level RDEI is released quarterly in March, June, September, and December. At
each release timing, monthly data for the previous quarter are published at a time, whichmeans that there is a lag of three to five months in updating the expenditure-side GDP.
14 Note that retrospective revisions to deflators can occur at any time.

14

To construct the monthly prefecture-level GDP, we also need the Cabinet Office’s Quarterly Estimates (QE). The Cabinet Office releases the preliminary estimate of the previous
quarter in February, May, August, and November. For example, the first preliminary estimate for the July to September period is published in November.15 Consequently, there is alag of three to five months in updating our monthly GDP.

3

Backcasting the prefecture-level GDP

As explained in the preceding section, we can only compute monthly prefecture-level GDP
with a lag of 3 to 5 months.16 In this section, we describe the methodology of backcasting—estimating GDP for the most recent months when the actual GDP is not yet computable.
The estimation takes the advantage of the statistical relationship between historical values
of GDP and alternative data—a collection of private sector data and public statistics that are
not part of the GDP calculation.
Table 1 summarizes the alternative data used in our backcasting procedure. For example, the private sector data include human mobility and web search results and public statistics include National Family and Income Survey by Ministry of Internal Affairs and Communications (MIC) and Commercial Statistics by Ministry of Economy, Trade and Industry(METI).
15 The second interim report update will occur thereafter (in March, June, September, and December).
16 For any particular month, it requires a lag of two months for production-side GDP and three to five months

for expenditure-side GDP to construct actual GDP from official statistics such as IIP or ITA. It requires a lag of
two to four months for the QE adjustments implying that we can compute our monthly GDP as soon as official
data for expenditure-side GDP are released.

15

Name
Mobility
Restaurants

Description
Mean of the monthly medians of the four
data: retail stores, amusement facilities,
public transportation, and offices
N of views of restaurant information,compared to 2019

DI AllBusiness diffusion index, all types (YoY)

DI
Manufacturing

Business diffusion index, manufacturing(YoY)

Job vacancy

N of job offers, vs. same period in 2019

Event tickets
HouseholdExpenditure
Grocery
Convenience

N of event ticket sales, vs. same month in2019
Amount of expenditure of households of
two or more people (YoY)
Amount of sales in department stores /supermarkets (YoY)
Amount of sales in convenience stores(YoY)

Electronics

Amount of sales in electronics stores (YoY)

Drugs

Amount of sales in pharmacies (YoY)

Construction

Amount of expected construction cost
(YoY)

TracksCars

N of sales of new light four-wheel vehicles
by prefecture (freight cars; YoY)
N of sales of new light four-wheel vehicles
by prefecture (passenger cars; YoY)

SourceGoogle "COVID-19:
community mobility
report "Retty "Food Data
Platform" *TDB, "Business Trends
Survey"TDB, "Business Trends
Survey"HRog "HRog list for
academia" *Lag

Ticket PIA*

2

MIC "National Family andIncome Survey"
METI"Commercial
Statistics"
METI"Commercial
Statistics"
METI "Commercial
Statistics"
METI "Commercial
Statistics"
MLIT "Report on
Statistical Survey onConstruction Start"
Japan Mini Vehicles
Association
Japan Mini Vehicles
Association

0
0
1
1
2

2
2
2
2
2
2
3
4

Table 1: Description of the alternative data: * Data are retrieved from V-RESAS. TDB =Teikoku Databank, MIC = Ministry of Internal Affairs and Communications, METI = Ministry of Economy, Trade and Industry, MLIT = Ministry of Land, Infrastructure, Transport
and Tourism.

Some of these variables are available at a frequency higher than monthly (e.g., Mobility,
Restaurants, Job vacancy, Event tickets). In our backcasting procedure, we aggregate all data
to a monthly frequency. We make seasonal adjustments to these variables by computing
year-on-year changes. Figure 6 illustrates the evolution of the alternative data for Tokyo.
The data used for backcasting GDP can be categorized into five groups based on when
they become available: (i) data that become available in the month when the actual GDP becomes computable (Mobility, Restaurants), (ii) data that become available with a one-monthlag (Job vacancy, DI All, DI Manufacturing), (iii) data that become available with a two16

Figure 6: Alternative data: Tokyo
month lag (Event tickets, Household expenditure, Grocery, Convenience, Electronics, Drugs,
Construction, production-side GDP), (iv) data that become available with a three-month lag(Tracks), and (v) data available with a four-month lag (Cars). We use our production-side
GDP described in Section 2.1 as one of the data sources because production-side data become available before we compute GDP and it can help us better backcast GDP.
Note that some variables might be useful in backcasting actual GDP in some times but
not in other times. For example, there is a strong correlation between Mobility and GDP
during COVID-19 crisis due to repeated declarations of a state of emergency. However, suchcorrelation has became weaker over time.17 Also some of the data may be discontinued at
17 In Section 4, an analysis is conducted regarding the correlation between monthly GDP at the prefectural

17

some point in time.18

3.1

Backcasting methodology

Let Tnow be the current period and TGDP be the most recent month at which we can computeour monthly GDP. Let s = Tnow − TGDP , representing the length of the backcasting period.
The objective of backcasting is to estimate GDP for the period when we cannot yet compute
GDP, specifically for t = TGDP + 1, TGDP+2 , ..., TGDP + s = Tnow .
Backcasting involves two stages.19 In the first stage, we estimate an Autoregressive Distributed Lag (ADL) model for each alternative data source. In the second stage, we combine
the projected values obtained from each alternative data source using weighted averaging,with the weights determined by the variances of the error terms of each estimated model.
Below, we elaborate each stage.
In the first stage, we estimate the following ADL model for each alternative data x listed
in Table 1 in each prefecture k:kGDPtk = µkx + γxk GDPtk−1 + βkx,0 xtk + βkx,1 xtk−1 + ekx,t for t = TSTART,x+ 1, ..., TGDP

(1)kwhere TSTART,xis the first date where data x is available in prefecture k, ekx,t is an i.i.d error

term with mean zero and standard error σk . GDPtk represents the our monthly GDP (inlogarithmic form). We assume GDPtk follows an I (0) process.20 We use the least squaresmethod to obtain estimates for the parameters µkx , γxk , βk0,x , βk1,x , σxk .
With the estimated parameters, we can project GDP for t = TGDP + 1, ..., Tnow recursively.
level and variables such as human mobility and the number of new infections.
18 Note that the Google Community Mobility Reports ceased to be published in October 2022.
19 We follow the approach of Stock and Watson (2003).
20 Assuming I (0) process for the level of GDP is a bit unusual, but makes sense in Japan for our sample
period. Also, our backcasting accuracy analysis shows that the backcasting is more accurate under the I (0)than under the I (1) assumption. See Appendix E for more information.

18

Namely,k k
k k
d kT +1,x = µ̂k + γ̂k GDPk
GDP
TGDP + β̂ 0 x TGDP + β̂ 1 x TGDP −1,
GDPk k
d kT + j,x = µ̂k + γ̂k GDP
d kT + j−1,x + β̂k x kGDP
0 TGDP + j−1 + β̂ 1 x TGDP + j−2,
GDPGDP

d kT + j,x for j = 2, ..., s, the right-hand side of thefor j = 2, 3, ..., s. In the projection of GDP
GDP
d kT + j−1,xestimation equation involves the recursive substitution of GDP values, with GDP
GDPbeing used iteratively. This projection is possible because alternative data are available forthe period t = TGDP + 1, ..., Tnow .
In the second stage, we average the estimated GDP values obtained from each alternative
data source in the first stage for each prefecture k. In computing the average, we put moreweight for an alternative data source that has a higher explanatory power. Note that theset of available alternative data depends on the projection horizon j because, as discussed
earlier, the timing of the release varies across alternative data. Specifically, the weight for analternative data source x with projection horizon j for prefecture k is denoted by ŵkj,x and isgiven by the following:ŵkj,x =

skx

 −1

∑ x ∈ XTTêkx,t+1
START,xGDP + j

where

v
u
u
u
k
s =t
x

 −1 ,



0

sk 0

(2)

x

∑t=GDP
Tkk
TGDP − TSTART,x
−4

.

(3)

Xt represents a time-varying set of alternative data available at time t and x ∈ Xt is a
specific alternative data in that set. skx is the standard error, the numerator of the right-handside of (3) is the sum of squared residuals for the estimation equation (1) using a particularalternative data source x.
The numerator of (3) is the sum of squared residuals for the estimation equation (1) using
a particular alternative data source x, and skx is the standard error. In other words, when skx

19

Figure 7: Backcasting: Tokyois larger, the weight assigned to the projected GDP value associated with x becomes smaller.
Using these weights, the average GDP in a prefecture k can be calculated as follows:d kT + j =
GDP
GDP

∑
0

d kT + j,xŵkj,x GDP
GDP

(4)

x ∈ XTGDP + j

for j = 1, ..., s. We take this value as our GDP backcast.
Figure 7 depicts GDP backcasts obtained in this manner for specific periods in time.
In particular, it shows backcasts for four different values of Tnow : March, April, May, andJune 2022. When Tnow is March 2022, TGDP —the most recent period in which actual GDP isavailable— is December 2021. In this case, s = Tnow − TGDP = 3 and we backcast GDP for
January, February, and March 2022, as shown by the red dashed line. When Tnow is April
20

Figure 8: Weights in backcasting (dot, square, star) and correlation between GDP and alternative data (black solid line): Tokyo
2022, TGDP is still December 2021. In this case, s = 4 and we backcast GDP for January,
February, March, and April 2022. Similarly, when Tnow is May 2022, TGDP is still December
2021. In this case, s = 5 and we backcast GDP for January, February, March, April, and May
2022.
When Tnow is June 2022, TGDP becomes March 2022. Thus, s = 3 and we backcast GDP
for April, May, and June 2022.
Note that there are three different backcasts for March 2022 GDP, corresponding to Tnow
being March, April, and May 2022. The set of available alternative data is different acrossthese three cases, and thus, the weight assigned to each alternative data within each set isdifferent across three cases. You can see the time-varying nature of available alternative
datasets and associated weights in Figure 8, which displays the weights ŵkj,x for j = 0 (dot),
j = 1 (square), and j = 2 (star) used for calculating the GDP backcast for March 2022. Theselags correspond to Tnow being March 2022, April 2022, and May 2022 respectively.

21

As shown in the figure, the set of available alternative data expands over time. In March(j = 0), there are only two alternative data sources (dot). In April, there are five (square). In
May, there are 13 available alternative data sources (star). Reflecting the changing set, theweight changes over time. For example, the weight for human mobility is 0.50 in March, but
it becomes 0.24 in April and 0.09 in May.
When a certain alternative data source exhibits a higher correlation with GDP, the source
tends to receive a higher weight. The solid black line in Figure 8 shows the correlation
coefficients between the actual GDP and each alternative data source x over the sample
periods. The production-side GDP exhibits a stronger correlation with GDP and receives
a higher weight. Electronics and Construction exhibit weaker correlations with GDP andreceive lower weights.
To better understand the structure of our backcasting procedure, it is useful to point out
that any given point in time t can be counted from either TGDP or Tnow . For instance, if we let
i = s − j for j = 1, 2, ..., s noting that TGDP + j = Tnow − s + j, we have Tnow − i = TGDP + j,ord kT −i,x = GDP
d kT + j,x
GDP
now
GDP
d kT + j,x for future
for i = 0, 1, ..., s − 1. In essence, calculating projected GDP values GDP
GDPperiods j = 1, 2, . . . , s, with TGDP representing the most recent point at which past actual
d kT −i,x for pastvalues are known, is equivalent to calculating projected GDP values GDP
now
periods i = 0, 1, . . . , s − 1, taking Tnow as the current time point.
Table 2 illustrates the relationship between the month Tnow − i when GDP is backcasted
and the values of TGDP , Tnow , and i. Let’s focus on the case where TGDP is December 2021
and Tnow is March 2022 (the fourth row in the table). When i = 0, we backcast GDP for
March 2022; when i = 1, we backcast for February 2022; and when i = 2, we backcast for
January 2022, looking backward from Tnow . This is equivalent to backcasting GDP whenj = 3, 2, 1 looking forward from TGDP . Note that more alternative data are available when iis larger or when j is smaller.
22

s
3
4
5
3
4
5
3

TGDP
9
9
9
12
12
12
3

i

0

1

2

Tnow
12
1
2
3
4
5
6

12
1
2
3
4
5
6

11
12
1
2
3
4
5

10
11
12
1
2
3
4

3

4

10
11

10

1
2
1

Table 2: Structure of backcasting
Note: Except for the row of i and column of s, numbers indicate months such as 9 = September.

3.2

Backcasting accuracy

In this subsection, we examine the backcasting accuracy through out-of-sample validation
using past data. To deepen our understanding of backcasting accuracy, we present several
figures and develop arguments step by step.
We begin by investigating the differences between the actual GDP and the backcasted
GDP for January to March 2022 when Tnow is May 2022. If Tnow = May 2022, TGDP =Dec 2021, as can be seen in Table 2. Figure 9 illustrates this difference. In the figure, ourbackcasted values (red dotted line) lie below the actual GDP (blue solid line), which canbe computed only in June 2022. We correctly predict the downward trend of GDP fromJanuary to March 2022, though the magnitude of the decline does not exactly match theactual decline. For TGDP = Dec 2021, we can draw two additional backcasting lines eachcorresponding to Tnow = April 2022 and Tnow = March 2022. For any TGDP , we can draw
Since the actual GDP can be computed every three months as discussed in 2.4, it is possible to draw a backcasting line from various points in time such as March, June, September,and December. For instance, when drawing the backcasting line from December, actual GDP
is known up to December, but values from January onwards are not yet known. This situation arises when calculating GDP backcast values for January and beyond in the months ofMarch, April, and May (as actual GDP up to March is revealed in June). Similarly, we can23

Figure 9: Actual and backcast values (Tnow = May 2022): Tokyo
draw a backcasting line from September onwards in December, January, and February. In
this way, for each quarter (March, June, September, and December), we can draw three distinct lines corresponding to different backcast points, as depicted in Figure 10. In the figure,a solid black line represents the actual GDP and red dashed lines are backcasted GDP values from different points in time. We have three distinct backcasting lines for March, June,
September, and December of 2021. Our backcasting lines for March overestimate the actual
GDP whereas backcasting lines for September underestimate it. The backcasting lines forJune predict the actual GDP quite well.
Now, let’s focus on the backcasting from December 2021 onwards. The three backcastinglines correspond to the prediction of GDP as of March, April, and May 2022. For a particularpoint in time (e.g. March 2022), we have three vertically aligned backcast values denoted bycircle (March, i = 0), square (April, i = 1) and triangle (May, i = 2), as shown in Figure 10. It
is evident that the triangle (i = 2) is the closest while the circle (i = 0) is the furthest from theactual value. Figure 11 presents these backcasting errors for the GDP of March 2022. Initially(as of March), the GDP value was backcasted to be about 1.75% lower than the actual value.

24

Figure 10: Actual and backcast GDP: Tokyo
However, as more alternative data became available, the backcasts are revised with a higher
accuracy.
kd t−i be the backcasted GDP for prefecture k, at a past time point t with an i-period
Let GDPlag, and GDPtk−i be its actual value. The backcasting accuracy for each prefecture k can beevaluated by using the following two metrics:kd t−i − GDPk
1 T GDPt −i
kMAEi = ∑kT t =1GDPt−i
v

2
u
k
u T
k
d
GDPt−i − GDPt−iu1 ,RMSEik = t ∑ 
T t =1
GDPtk−iwhere MAEik represents the Mean Absolute Error, while RMSEik represents the Root Mean
Squared Error.
Figure 12 displays the values of MAEik and RMSEik for Tokyo and the average values for25

Figure 11: Backcasting error (Tnow − i = March, 2022): Tokyo
Note: i = 0 indicates the backcast error as of March 2022, i = 1 indicates that of April 2022,
and i = 2 indicates that of May 2022, respectively. The actual value is computed in June2022.
all prefectures (k = 1, ..., 47) across different values of i. Notably, backcast accuracy improves
significantly at i = 2. This improvement occurs because the production-side GDP, which isused in the calculation of actual GDP, becomes available at i = 2.

4

Analyses using the monthly prefecture-level GDP

4.1

Comparison of the monthly prefecture-level GDP

Figure 13 shows the monthly GDP (normalized to 2020 Q1 = 100) for all 47 prefectures—thin grey lines—and the national monthly GDP—thick blue line—from January 2020 onwards. According to the figure, there is a considerable heterogeneity across prefectures regarding the evolution of the monthly GDP. For instance, the size of the decline in GDP in
May 2020—which is associated with the declaration of the state of emergency—varies significantly among prefectures. The subsequent recovery also exhibits heterogeneity across26

Figure 12: Backcasting accuracy
prefectures.
Figure 14 presents the monthly GDP for Tokyo, Aichi, Gunma, and Tokushima. Gunma
experienced the most significant downturn in May 2020, while Tokushima experienced theleast severe downturn during the same period. Tokushima’s GDP exceeded the pre-Covid
level after the summer of 2020. While GDP for Tokyo, Aichi, and Gunma generally follow
a similar trajectory, the decline in GDP in May 2020 was larger in Aichi and Gunma than inTokyo, likely reflecting the fact that Aichi and Gunma have a higher share of manufacturingindustries.

4.2

Analyses using the monthly prefecture-level GDP

The prefecture-level GDP can also prove its utility when combined with other datasets forregional economic analysis.21 In this subsection, we examine three empirical relationships
using our monthly GDP: (i) the relationship between GDP and population mobility,22 (ii) the
21 Serizawa et al. (2022) utilized annual GDP for each prefecture in prefectural economic accounts and paired

it with flood data for each prefecture to estimate the impact of floods on annual GDP.
22 For instance, Fujii and Nakata (2021) estimated the relationship between our monthly GDP and the population mobility data since 2020 and incorporated this relationship into an epidemiological macroeconomic
model to analyze the trade-off between economic activity and infection control measures.

27

Figure 13: Monthly GDP by prefecture
relationship between GDP and COVID-19 infection, and (iii) the relationship between GDP
and inflation.
Figure 15 presents the scatterplots of monthly GDP and population mobility for Tokyo,
Hokkaido, Gunma, and Hyogo from January 2020 to March 2022. Tokyo—shown by the topleft panel—exhibits the correlation coefficient between monthly GDP and population mobility of 0.69, which is the highest among the 47 prefectures. Hyogo—shown by the bottomright panel—exhibits a similarly high correlation coefficient of 0.68, while Hokkaido—shownby the top-right panel—exhibits the lowest correlation at 0.02. Gunma—shown by the bottomleft panel—exhibits the correlation coefficient of 0.43, which is the median value across all
47 prefectures. During the COVID-19 pandemic, there is a positive correlation between
monthly GDP and population mobility in all prefectures.
The correlation coefficient is larger in the early phase of the COVID-19 crisis (from January 2020 to March 2021) during which the first and second declarations of a state of emergency led sharp declines in both population mobility and GDP. In Figure 15, we report corre28

Figure 14: Monthly GDP: Tokyo, Aichi, Gunma, and Tokushimalation coefficients for the early phase of COVID-19 crisis as well as the entire sample period.
For example, it is 0.78 in Tokyo in the early phase of the COVID-19 crisis, versus 0.69 in theentire sample period.
Figure 16 displays the scatterplots of weekly GDP and the week-on-week change in
new COVID-19 cases for Tokyo, Kagoshima, Fukuoka, and Tokushima from January 2020
to March 2022. In this exercise, weekly GDP was derived through linear interpolation of
the monthly GDP. Tokushima—shown by the bottom-right panel—exhibits the highest correlation coefficient at 0.243, while Kagoshima—shown by the top-right panel—exhibits thelowest at -0.094. Fukuoka—shown by the bottom-left panel—exhibits the correlation coefficient of 0.024, which is close to the median value across prefectures. Tokyo—shown by
the top-left panel—exhibits the correlation coefficient of -0.006, ranking 34th among the 47
prefectures. There is a positive correlation between weekly GDP and the growth rate of newcases in 29 prefectures, alluding to the presence of a trade-off between economic activity andinfection control.

29

Figure 15: Monthly GDP and mobility: Tokyo, Hokkaido, Gunma, and Hyogo
The analyses presented above focus on the balance between infection control and economic activity using data from the COVID-19 pandemic period. In our last exercise, we
conduct a more classical macroeconomic analysis, namely the relationship between GDP
and inflation, including data outside the pandemic period. Figure 17 presents scatterplotsof monthly GDP and year-on-year change in Consumer Price Index (excluding fresh food)by prefecture for Tokyo, Fukushima, Yamagata, and Yamaguchi from April 2015 to March
2022.23 We observe a positive correlation between monthly GDP and inflation—reminiscentof the Phillips curve—in most of the prefectures (43 out of 47 prefectures). Tokyo—shownby the top-left panel—exhibits the correlation coefficient of 0.53. Yamaguchi—shown by thebottom-right panel—exhibits the highest correlation coefficient at 0.738, while Fukushima—
shown by the top-right panel—exhibits the lowest at -0.184. Yamagata—shown by thebottom-left panel—exhibits the correlation coefficient of 0.346, which is close to the median
23 We use the CPI in prefectural capital as prefecture-level data because they are the only available inflation

data by prefecture. To exclude the impact of the consumption tax hike in April 2014, the sample period was
set to begin from April 2015.

30

Figure 16: Weekly GDP and the growth rate of new COVID-19 cases: Tokyo, Kagoshima,
Fukuoka, and Tokushimavalue across prefectures.
To investigate whether the relationship between GDP and inflation changed during the
COVID-19 pandemic, we employ panel estimation following the methodology outlined byHazell et al. (2022). The estimation equation is as follows:

πit = Di + β 1 GDPit + β 2 It GDPit

Here, πit represents the prefectural CPI (excluding fresh food) year-on-year change (%),
GDPit is the prefectural GDP, Di represents prefecture dummies, and It is a dummy variable that takes the value 1 after February 2020 (indicating the post-COVID period). The
sample period covers from April 2015 to March 2022, with a sample size of 3,948.
Table 3 shows the estimation results. The slope of the Phillips curve, β 1 , is estimated to be
0.049, and it is statistically significant at the 1% level. Additionally, the post-COVID dummy

31

Figure 17: Monthly GDP and CPI inflation: Tokyo, Fukushima, Yamagata, and Yamaguchi
variable is found to have a negative and statistically significant coefficient, suggesting thatthe relationship between GDP and inflation weakened during the COVID-19 pandemic period.24

5Conclusion

This paper has presented a new measure of monthly prefecture-level GDP. Our measure isbased on the combination of production-side GDP and expenditure-side GDP. For periods
where more recent official statistics were unavailable, we backcast our monthly GDP using
alternative data sources. Readers can use our monthly prefecture-level GDP for a wide rangeof regional economic analyses.
24 When controlling for time dummies to account for medium to long-term inflation expectations and othermacroeconomic factors, β 1 becomes negative (-0.009) and statistically significant. Additionally, when using
the prefectural CPI (excluding fresh food and energy) year-on-year change as the inflation rate, β 1 remains
negative (-0.050) and statistically significant.

32

β̂ 1
β̂ 2

dep. var = πit
0.049(13.35)0.005(25.66)

N
R̄2

3948
0.256

Table 3: Estimation of the Phillips curve (t-statistics in parentheses)
Our analysis can be extended in two dimensions. First, there are ways to improve our
GDP measure itself. For instance, if alternative data for a particular sub-sector by prefecture(e.g. POS cash register data for restaurants or electricity usage in commercial districts) areavailable, we can incorporate them in our GDP construction to reflect the actual regional
economic conditions more precisely (Appendix D discusses the effect of incorporating alternative data in a retail sector). Second, there are ways to improve our backcasting methodology. The availability of higher-frequency alternative data may improve the accuracy ofbackcasting. Alternative methodologies such as mixed-data sampling (MIDAS), dynamic
factor model (DFM) and machine learning may improve the accuracy of backcasting. We
leave these extensions for future research.

33

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37

A

Industry weights using Input-Output (IO) data

As discussed in the main text, we use the 2015 prefectural IO tables to compute the ITA
industrial weights wik for 43 prefectures. We calculate the ITA weights based on IO tables
by matching industries from the ITA classifications to IO classifications based on industry names. Our classification mapping is either one-to-one or many-to-one. For instance,
the ITA classification “Electricity” corresponds to the IO classification “Electricity” (one-toone). However, the ITA classifications “Wholesale Trade,” “Retail Trade,” and “Real Estateand Land Sales” correspond to a single IO classification “Commerce” (many-to-one). When
mapping is many-to-one, we use the national-level ITA weights for proportional allocation.
Table 4 illustrates the matching between the ITA classifications and IO classifications. Some
IO industry classifications do not have corresponding ITA industry classifications.
We compute ITA weights using IO tables since ITA weights are not available at the prefecture level. However, at the national level, both ITA and IO weights are available. To
check the validity of our industry matching, we can compare the national-level ITA and
IO weights. Figure 18 displays the IO weights and ITA weights at the national level. Our
matching procedure appears reasonable for the purpose of making the weights as equal as
possible.

B

Industry weights using the Economic Census

In four prefectures (Niigata, Ishikawa, Nara, Okinawa), we use the 2016 Economic Census,
instead of IO tables, to compute the ITA industrial weights wik . We do so because for thesefour prefectures, prefectural IO tables are not available. Since the Census classifications and
ITA classifications cannot be matched easily, we use the IO classifications as an intermediate
step. For the mapping between the Census and IO classifications, we use more disaggregated industry classifications (subcategory) to merge the two datasets and aggregate up to
the IO classifications. Specifically, we use the methodology outlined by Urayama (2021) to38

Figure 18: IO weights and ITA weights
proportionally allocate the value-added for each subcategory in the Economic Census tosubcategories within the IO classification using national weights. For the mapping between
the IO and ITA classifications, we follow the approach described in Appendix A.
We can check the validity of our matching procedure from the Census to IO classifications in a similar manner to Figure 18. Comparing the Census-based weights and IO-based
weights at the national level as shown in Figure 19, we can confirm the similarity of these
two weights.

C

Comparison between our monthly prefecture-level GDP
and Prefectural Economic Accounts

The Cabinet Office publishes the Prefectural Economic Accounts (PEA), which is the only
official statistics of prefecture-level GDP and is available at annual frequency. As an external
39

Figure 19: IO weights and Census weights
validation, we compare our GDP to the Prefectural Economic Accounts (PEA). Since the PEA
is at an annual frequency, we aggregate our monthly prefecture-level GDP to an annual
level. Figure 20 compares our GDP and the PEA for each prefecture for the years 2013 to2018. Overall, our GDP aligns with the PEA though the difference can be non-trivial insome prefectures in certain years.
Figure 21 quantifies the difference between our GDP and the PEA for each prefectureusing Root Mean Squared Errors (RMSE). The mean RMSE is 2.2%. There is some variability
among prefectures. Shiga exhibits the largest RMSE (4%). Hyogo exhibits the smallest RMSE
(0.6%).

40

D

Modifications of ITA using the Current Survey of Commerce (CSC)

One concern about our production-side GDP is that our service sector index (ITA) may
not fully capture prefecture-specific shocks. By construction, our ITA index cannot reflect
month-prefecture-specific shocks since we use time-invariant industry weights by prefecture. In fact, if we compare the IIP—available monthly for each prefecture— and the ITA
data as in Figure 22, the ITA trends are substantially less heterogeneous across prefectures
than the IIP trends. To address issue, we can modify our ITA index by incorporating monthly
prefecture-level retail sector data. For the retail sector, the METI publishes monthly data forsix specific types of retail businesses (department stores, supermarkets, convenience stores,
electronics retailers, drugstores, and home improvement centers) in the Current Surveyof Commerce (CSC). Figure 23 displays the CSC retail index for 44 prefectures excluding
Kagoshima, Okinawa, and Kumamoto.2526 Unlike the ITA, substantial heterogeneity is evident among prefectures in the CSC data.
Figure 24 presents the modified prefectural-level ITA data with the CSC retail index.
While there is some degree of heterogeneity among prefectures, it remains limited as in theoriginal series in the bottom panel of Figure 22. The impact of using the CSC data is limited
because the retail industry share (around 10%) is limited in the overall service sector. If wehave access to monthly prefecture-level alternative data of other industries in service sector,
our ITA index can be improved capturing more prefecture-specific shocks.
25 For these three prefectures, the CSC data are not available.
26 We observe a notable upward spike in September 2019 corresponding to the consumption tax increase anda downward spike in April 2020 corresponding to the first declaration of a state of emergency due to pandemic.

41

E

Accuracy of the backcasting

In this section, we examine the accuracy of backcasting using different specifications for the
GDP estimation equation. There are eight different backcasting specifications based on the
combination of three factors: 1) whether the dependent variable in the estimation equation
is in logs or differences, 2) whether the estimated values for alternative data sources areweighted averages or simple averages, and 3) whether the data used for estimation comprises the entire historical sample or only the past 12 months.27
Figure 25 presents the backcasting accuracy of those eight specifications based on both
MAE and RMSE. Each line indicates the mean MAE or RMSE across the backcasting timing
i for each specification. Tables 5 and 6 show the corresponding numbers with more information. When comparing these backcasting methods, it becomes apparent using logged levels as the dependent variable in the estimation equation yields better backcasting accuracy
compared to using differences.28 Furthermore, employing a weighted average of estimatedvalues using the residuals of the estimation equation for alternative data sources appears
to enhance backcasting accuracy compared to taking a simple average. Finally, using theentire sample period, compared to the 12-month rolling window sample, may improve thebackcasting accuracy overall although there are some exceptions depending on i.

27 Since we have two options for each of the three factors, there are 23 = 8 combinations.
28 The null hypothesis, which posits the presence of a unit root, was rejected based on the results of theAugmented Dickey-Fuller test for GDP stationarity. Specifically, among the 47 prefectures, the null hypothesis
was rejected at the 5% significance level for 17 prefectures and at the 10% significance level for 22 prefectures.

42

ITA type

IO type

ITA type

IO typeElectricity

Electricity

Internet
Picture, sound, text
information
Medicine
Public healthSocial welfare andcare businessLeasing business(including
rent-a-cars)
Advertisement
Car mechanic (forbusiness use)

Internet
Picture, sound, text
information
Medicine
Public healthGas

Gas and heating

Heating
Water supply

Water supply

Waste disposal

Waste disposal

WholesaleCommerce
RetailReal estate sales
Finance andinsurance
Real estate broker
Rental office lessor

Finance andinsurance

Other mechanic

Real estate broker
and lessor

Car mechanics (forpersonal use)
Professional
service

Parking spacelessorHousing rental
RailroadRoad passenger
transportation
Road freighttransportation
Watertransportation
Aerialtransportation

Compound service
Employment
referral / agency

Housing rental
Railroadtransportation
Road passenger
transportation(business only)
Road freighttransportation(business only)
Water
transportation
Aerialtransportation

Care

Leasing business
Advertisement
Garage and othermechanic

Other businessservices

Security
Academic /research instituteTechnical service

Accommodation

Accommodation

Restaurant

Restaurant
Laundry,
hairdressing,
beauty, andbathingEntertainment

Warehouse

Warehouse

Laundry,
hairdressing,
beauty, andbathingServices
accompanying
transportation

Services
accompanying
transportation

Entertainment

Postal business

Postal businessCommunication

Communication

Broadcasting

Broadcasting

Information

Information

Other
living-related
services
Learning support
Pet andveterinarian

Other private
services

Table 4: Concordance between ITA and IO classifications
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Figure 20: Comparison to the Prefectural Economic Accounts: time series

44

Figure 21: Comparison to the Prefectural Economic Accounts: RMSE

45

Figure 22: Monthly IIP and monthly ITA by prefecture46

Figure 23: CSC retail index (seasonally adjusted) by prefecture

Figure 24: Monthly ITA by prefecture (with a correction by CSC)

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Figure 25: Backcasting accuracy
Note: In the legend, “v” denote the log values whereas “d” denote the differences. Also“12” indicates that the sample period is only the past 12 months, and “SA” indicates that theestimated value for alternative data are simple averages.

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Table 5: Backcasting accuracy: MAE

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Table 6: Backcasting accuracy: RMSE

50