ISSN (Print) 0473-453X

Discussion Paper No. 1065

ISSN (Online) 2435-0982

DECOMPOSINGLOCAL FISCAL MULTIPLIERS:EVIDENCE FROM JAPANTaisuke Kameda
Ryoichi Namba
Takayuki Tsuruga

October 2019

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Decomposing Local Fiscal Multipliers: Evidence from Japan∗
Taisuke Kameda†

Ryoichi Namba‡,

Takayuki Tsuruga§

First draft: July 2017
This draft: October 2019

Abstract
Recent studies on fiscal policy use cross-sectional data and estimate local fiscal multipliers
along with spillovers. This paper estimates local fiscal multipliers with spillovers using Japanese
prefectural data comparable with the national accounts. We estimate the local fiscal multiplieron output to be 1.7 at the regional level. The regional fiscal multiplier consists of the prefecturespecific components and a component common across prefectures within the same region, which
we interpret as the region-wide effect. Converting the latter component into the spillover, we findthat the spillover is positive and small in size. We decompose the regional fiscal multiplier on
output into multipliers on expenditure components. The regional fiscal multiplier on absorption
exceeds 2.0 because of the crowding-in effect on consumption and investment. Moreover, wefind that the spillover to absorption is considerable in contrast to the spillover to output.
JEL Classification: E62, H30, R50
Keywords: Fiscal stimulus, spillover, geographic cross-sectional fiscal multiplier∗

We thank Andrew Hallett, Hirokazu Ishise, Yasushi Iwamoto, Yi Lu, Jun Nagayasu, Etsuro Shioji, Justin Wolfers,
Lianming Zhu, and seminar and conference participants at Osaka University, Shanghai University of International
Business and Economics, the University of Tokyo, the 19th Macroeconomic Conference, the Economic and Social
Research Institute international conference, and the WEAI international conference for helpful discussions and comments. Takayuki Tsuruga gratefully acknowledges the financial support of Grants-in-aid for Scientific Research(15H05729 and 15H05728), the Murata Science Foundation, and the Zengin Foundation for Studies on Economics
and Finance. The views expressed in this paper are those of the authors and do not necessarily reflect the official
views of the Government of Japan.
†
Cabinet Office, the Government of Japan‡
Chubu Region Institute for Social and Economic Research§
Osaka University; Cabinet Office, the Government of Japan; Centre for Applied Macroeconomic Analysis

11Introduction

One of the cornerstone issues of macroeconomics is the interaction of economic activity and government spending. This interaction is often measured by the fiscal multiplier, the percentage increasein output when government spending increases by 1% of gross domestic product (GDP). Although
the literature traditionally measures the fiscal multiplier using time-series data, recent studies relyon geographic cross-sectional variations in government spending. The fiscal multiplier estimatedfrom the regional cross-sectional data is often called the local fiscal multiplier (LFM). 1 Although
the LFM can be interpreted as a fiscal multiplier that measures the effect of government spending in one region within a monetary union (Nakamura and Steinsson 2014), the LFM differs fromthe traditional national fiscal multiplier in an important dimension. In particular, because local
economies have strong interdependence without the border effect, government spending in a local
economy can easily spill over into other local economies. According to Auerbach et al. (2019),
understanding the spillover from government spending is “a fundamental and largely unresolved
task in macroeconomics.”
In this paper, we estimate and decompose the LFM to understand the spillover in local economies.
The objectives of this paper are threefold. First, we provide evidence of the LFM in Japan, which
we can compare with LFMs in other countries. Second, and more importantly, we measure thespillover within the region using prefectural data. We separate the country into regions consistingof prefectures and estimate the regional fiscal multiplier (RFM) as the sum of the prefectural fiscal multiplier (PFM) and the region-wide effect. The former is a component of the RFM that is
estimated from variations in prefectural government spending. The latter is also a component of
the RFM but is estimated from variations in regional government spending and, thus, it is related
to the spillover. To be consistent with the literature, we convert the estimated region-wide effectinto the spillover within the region and assess the contribution of the spillover to the RFM. Third,
exploiting an advantage of Japanese prefectural data, we estimate the RFM on the expenditurecomponents of GDP. The prefectural data are drawn from the “prefectural accounts,” which arehighly comparable with the national accounts, as data on consumption, investment, government
spending, and net exports are available at the prefectural level. The data availability contrasts
1

Chodorow-Reich (2019) comprehensively reviews numerous recent studies on the LFM. Ramey (2011) surveys
fiscal and tax multipliers including the time-series evidence.

2

with the U.S. state-level data published by the Bureau of Economic Analysis.2 Exploiting the datacompiled by the single government agency, we measure the contribution of the RFM on expenditurecomponents, such as private consumption and investment, to the RFM on output. Based on thisdecomposition, we study which expenditure components of GDP are crowded out or in by local
government spending.
As the previous studies on the fiscal multiplier emphasize, identifying fiscal multipliers requires
isolating changes in government spending that are uncorrelated with shocks to the local economy.
We construct instruments from the national treasury disbursements in the local public financedata.3 The expenditure by the local governments depends heavily on the transfers from the central
government because of the large vertical fiscal gap between the central and local governments (seeBessho 2016). The national treasury disbursements are the earmarked, program-based transfersfrom the central government to the local government. By definition, the national treasury disbursements are financed by the national tax revenues, which are less likely to be affected by shocks to
specific prefectures’ economic activity. Furthermore, the data set allows us to identify purposes
and programs supported by the disbursements (e.g., education, social welfare, and construction).
Using the detailed information on the local public finance data, we exclude the transfers that arestrongly correlated with shocks to local economies (e.g., subsidies for recovery from disasters) inconstructing our instruments.
The main findings are as follows. First, when government spending increases at the regional
level by 1% of GDP, the regional output increases by 1.7%. In other words, the RFM on output
is 1.7. Second, we find that the spillover to output is positive but small in size. Our benchmark
estimation suggests that the spillover converted from the region-wide effect is, on average, 0.26,
out of the estimated RFM of 1.7. Third, regional government spending substantially crowds inprivate consumption and private fixed investment. In particular, the sum of the contributions ofthese expenditure components accounts for 65% of the RFM on output. As a result, the multiplieron “domestic absorption” or the expenditure before the leakage to the other local economies is
2For example, the Bureau of Economic Analysis does not publish data on net exports and business investment at
the state level. In the literature on the LFM in the U.S., data for state-level government spending are often takenfrom the U.S. Census Bureau.
3
Our approach is similar to Kraay (2012) and Guo et al. (2016), who use variations in the funds loaned ortransferred from an organization other than the local government for identification. Kraay (2012) estimates the fiscal
multiplier in developing countries with the instrument of World Bank lending. Guo et al. (2016) estimate the LFM
in China. To identify the LFM, they use the local public finance fact that poor Chinese counties receive preferential
earmarked treatment in transfers.

3also large. We find that the RFM on absorption is 2.2 in the benchmark regression. We also findthat the region-wide effect on absorption is statistically and economically significant, in contrast tothat on output. Our estimation suggests that the spillover converted from the region-wide effectis, on average, 0.68, out of the estimated RFM on absorption of 2.2. By contrast, net exports
decrease with regional government spending, suggesting a leakage in aggregate demand to otherlocal economies.
The literature on the LFM is very active, with contributions from many previous studies.4 Somestudies focus on spillovers in the context of the LFM. Dupor and McCrory (2017) discover evidence
for positive spillovers in wage bills and employment within the regional market. Dupor and Guerrero(2017), using federal defense contracts at the U.S. state level, find a positive interstate spillover
in income and employment multipliers. Auerbach et al. (2019) also use the U.S. federal defense
data and find positive spillovers across industries, as well as across locations. Suárez-Serrato andWingender (2016) explore the income spillovers across neighboring counties but find no evidenceof sizable spillovers. Acconcia et al. (2014) use Italian provincial data and find a statisticallyinsignificant spillover to the provincial output. Our paper studies the spillover more closely thanthese previous studies by examining the expenditure components of GDP, as well as output. Guo
et al. (2016) investigate Chinese county-level data and estimate the LFM on investment at thecounty level as well as output. They find that there is a crowding-in effect on investment without
assuming spillovers. Cohen et al. (2011) also estimate the impact of state government spending on
investment by publicly traded U.S. firms. They find negative impacts of local government spending
on firms’ investment and payouts to the investors of firms.
Brückner and Tuladhar (2014) and Bessho (2018) provide evidence on the estimated LFM in
Japan. The former focuses on the financial distress of the 1990s and its impact on the LFM and thelatter examines whether the LFM is related to ageing that varies across prefectures. Other previous
studies on the Japanese fiscal multipliers provide time-series evidence.5 Among these time-seriesbased studies, recent works emphasize the state dependence of the national fiscal multipliers.6
4

Examples of earlier works include Clemens and Miran (2012), Nakamura and Steinsson (2014), Fishback andKachanovskaya (2015), Shoag (2016), and Suárez-Serrato and Wingender (2016). Regarding the impact of theAmerican Recovery and Reinvestment Act on employment at the state and county levels, see Chodorow-Reich et al.
(2012), Wilson (2012), and Conley and Dupor (2013) among others.
5
For example, Watanabe et al. (2010) estimate the national fiscal multipliers using a structural vector autoregression approach that is similar to Blanchard and Perotti (2002).
6
See Morita (2015), Auerbach and Gorodnichenko (2017), Kato et al. (2018), and Miyamoto et al. (2018).

4

This paper is organized as follows. Section 2 describes the empirical strategies. In Section 3,
we discuss the data and the construction of instruments. Section 4 presents the main results andsection 5 shows robustness. Section 6 concludes.

2

Local fiscal multipliers and the region-wide effect

In the existing literature, the LFM is typically estimated using the following equation:
Gr,t − Gr,t−2
Yr,t − Yr,t−2= βR+ αr + δt + εr,t ,Yr,t−2
Yr,t−2(1)

where Yr,t is the regional-level per capita output in period t and Gr,t is the regional-level per capita
government spending. We refer to βR as the regional fiscal multiplier (RFM) because we estimate
βR using the regional-level data. The index r represents regions in a country, r ∈ {r1 , r2 , ..., rM },where the country has M regions. Note that αr and δt include the entity and time fixed effects,
respectively. For now, we assume no covariates to simplify the discussion, but our empirical analysis
includes covariates. The error term is εr,t . The entity fixed effect αr controls for the region-specificvariations in per capita output and government spending. The time fixed effect δt captures theunobserved nationwide effects of aggregate shocks and macroeconomic policy on the regional output(e.g., aggregate productivity, monetary policy, national tax changes, and predictable changes in thenational output and government spending). As a result of the fixed effects, βR measures how muchoutput in a region increases relative to that in other regions when government spending in the region
increases relative to that in other regions. The time unit is one year. Following Nakamura andSteinsson (2014), we take the two-year growth rate of output for the dependent variable. Therefore,βR is the two-year cumulative fiscal multiplier.
In this paper, our estimation equation takes the following prefecture analog of (1), but with anadditional regressor:
yr,p,t − yr,p,t−2
gr,p,t − gr,p,t−2
Gr,t − Gr,t−2
= γP
+ γS
+ ηr,p + δt + εr,p,t ,
yr,p,t−2yr,p,t−2
Yr,t−2(2)where yr,p,t is per capita output and gr,p,t is per capita government spending in prefecture p, which
belongs to region r. Formally, each region ri has Ri prefectures and the index pi is defined by5pi ∈ ri = {1, 2, ..., Ri } for i = 1, ..., M . For notational simplicity, we drop the index i from ri andpi in (2). As before, ηr,p captures the entity fixed effect, defined similarly to αr in (1). Note that(2) includes changes in both prefectural and regional government spending. We interpret γP as theprefectural fiscal multiplier (PFM) because, if γS = 0, (2) has the same structure as (1), in which we
discussed the RFM. However, if γS 6= 0, this equation indicates that the prefectural output growth
responds to changes in the regional government spending (scaled by the regional output). Even
if government spending in the prefecture stays constant, the output of the same prefecture may
change with regional government spending. Therefore, we interpret γS as the region-wide effect.
The sign of the region-wide effect γS can be positive or negative as a result of the spillover, as
discussed in the literature.7 On the one hand, an increase in government spending in a prefecture
may increase the relative price of the prefecture’s output to the same goods in other prefectures.
Thus, expenditure switches from the prefecture’s output to output in other prefectures, perhaps
those in the same region. This expenditure switching implies a positive γS . In addition, theincrease in the prefecture’s government spending may boost the demand of liquidity-constrainedhouseholds.8 If the increase in demand leaks into other prefectures in the same region, again γS
is positive. On the other hand, when the increase in government spending stimulates productionin the prefecture, it may lead to the relocation of factor inputs (e.g., labor) from other prefectures
within the same region. Because this may reduce the output in the other prefectures, the spillover
may produce a negative γS .
We show that the sum of γP and γS can approximate βR in (1). Let ωr,p be the time-seriesmean of the prefecture’s GDP as a share of regional GDP. Taking the weighted average of bothsides of (2) with the GDP share ωr,p , we can approximate the equation by:
Yr,t − Yr,t−2
Gr,t − Gr,t−2' (γP + γS )+ αr + δt + εr,t ,Yr,t−2
Yr,t−2(3)

P
where we redefine αr as the weighted average of ηr,p : αr =p∈r ωr,p ηr,p and the error termPεr,t = p∈r ωr,p εr,p,t . Here, the derivation of the above equation requires that the distributions of
output and population are stable over the sample periods.
7

For example, see Acconcia et al. (2014), Suárez-Serrato and Wingender (2016), and Chodorow-Reich (2019).
See Galı́ et al. (2007) for the model with liquidity-constrained households. They consider households that haveno access to capital markets. An increase in government spending that leads to higher household income can directly
increase their consumption.
86

∗∗ , respectively.
More specifically, let the levels of prefectural and regional GDP be yr,p,t
and Yr,tHere, a superscript ∗ on a variable denotes a level variable rather than a per capita variable.
∗∗ = Y N ∗ , where n∗∗
The levels of output are given by yr,p,t= yr,p,t n∗r,p,t , and Yr,tr,t r,tr,p,t and Nr,t

are the populations in prefecture p and region r, respectively. Note that the regional output and
P
P
∗ =
∗
∗
∗
the regional population satisfy Yr,tp∈r yr,p,t and Nr,t =p∈r nr,p,t , respectively. By the∗ /Y ∗ and n∗ /N ∗assumption of stable distributions of output and population, we mean that yr,p,t
r,t
r,p,t
r,t

do not substantially fluctuate over the sample periods (e.g., around the time-series mean). Under
this approximation assumption, Appendix A.1 shows that:
X

ωr,p

p∈r

yr,p,t − yr,p,t−2(Yr,t − Yr,t−2 )'.
yr,p,t−2
Yr,t−2(4)gr,p,t − gr,p,t−2
Gr,t − Gr,t−2'.
yr,p,t−2
Yr,t−2

(5)

and
X
p∈r

ωr,p

Comparing (3) with (1) yields βR ' γP + γS . Therefore, the RFM can be decomposed into the
PFM and the region-wide effect.
We emphasize that the estimated region-wide effect is not the same as the spillovers estimatedin the literature. The previous studies on the spillover in the fiscal multiplier have measured thespillover to a location (i.e., a prefecture in our case) by the coefficient on the sum of government
spending in other prefectures, rather than the coefficient on regional government spending as awhole. For example, Auerbach et al. (2019) employ the weighted sum of government spending
in other locations. Acconcia et al. (2014) and Suárez-Serrato and Wingender (2016) employ
government spending aggregated across adjacent areas (provinces or counties). To allow for the
spillover in our regression analysis, we use (5) to rewrite (2) as:X
gr,p0 ,t − gr,p0 ,t−2
gr,p,t − gr,p,t−2
yr,p,t − yr,p,t−2= (γP + ωr,p γS )
+ γS
ωr,p0
+ ηr,p + δt + εr,p,t . (6)yr,p,t−2yr,p,t−2yr,p0 ,t−20
p 6=pNote that the second term on the right-hand side is:γSX
p0 6=pωr,p0

X
gr,p0 ,t − gr,p0 ,t−2
gr,p0 ,t − gr,p0 ,t−2= γS (1 − ωr,p )ω̃r,p0 ,p,yr,p0 ,t−2
yr,p0 ,t−2
0
p 6=p

7

(7)

where ω̃r,p0 ,p = ωr,p0 / (1 − ωr,p ) andP

We define Yr,−p,t and Gr,−p,t by Yr,−p,t ≡
P
∗
∗
∗
∗
∗
∗
Yr,−p,t/Nr,−p,t
and Gr,−p,t ≡ G∗r,−p,t /Nr,−p,t, respectively. Here, Yr,−p,t= p0 6=p yr,p
0 ,t , Gr,−p,t =
P
P
∗
∗
∗
p0 6=p gr,p0 ,t and Nr,−p,t =p0 6=p nr,p0 ,t . In these definitions, we exclude prefecture p from thep0 6=p ω̃r,p0 ,p = 1.

∗∗
weight ω̃r,p0 ,p and the aggregate variables Yr,−p,t, G∗r,−p,t , and Nr,−p,t. Under the stable distributionsof output and population, we combine (6), (7), and the above definitions to obtain:9
yr,p,t − yr,p,t−2
yr,p,t−2gr,p,t − gr,p,t−2
Gr,−p,t − Gr,−p,t−2+ γS (1 − ωr,p )
yr,p,t−2
Yr,−p,t−2+ηr,p + δt + εr,p,t .

= (γP + ωr,p γS )(8)Here, γS (1 − ωr,p ) is the coefficient on the sum of government spending in other prefectures, so weinterpret γS (1 − ωr,p ) as the measure of the spillover for prefecture p in region r. In our analysis,
we use the data on ωr,p and assess the size of the spillover.
Our measure of the spillover γS (1 − ωr,p ) takes into account the relative size of the local economy
in the region, whereas the previous studies assume that the degree of spillover is the same across all
local economies. More specifically, if a prefecture is large relative to the region (e.g., Tokyo in the
Kanto region), the spillover to the large local economy is low. On the other hand, if a prefectureis small and has a negligible share in regional GDP (i.e., ωr,p ' 0), then the spillover to the small
local economy is close to γS . Put differently, the region-wide effect γS is the upper bound of thespillover within the region.
In our empirical analysis, we estimate γP and γS from (2) and report γP + γS as an estimate ofβR . However, other factors may weaken the link between γP + γS and βR . First, we must define
P
P
∗ =
∗
∗
∗
the region as a group. In other words, we must have Yr,tp∈r yr,p,t and Nr,t =p∈r nr,p,t .
Second, if we include the vector of prefectural control variables xr,p,t in (2), (1) is also required toPhave the vector of the control variables Xr,t = p∈r ωr,p xr,p,t as additional regressors. Therefore,
to maintain the approximation results of βR ' γP + γS , the control variables in (1) are the weighted
average of the control variables across prefectures. Likewise, if (1) includes additional regressorsthat are not the weighted average of prefectural control variables, the inclusion may weaken thelink between βR and γP + γS .
Regarding the control variables introduced in (2), the benchmark regression includes the dummy
variable for the Great East Japan Earthquake on March 11, 2011, the last month of fiscal year
9

See Appendix A.2 for the derivation of (8).

82010.10 We consider that this natural disaster shock has a prefecture- and time-specific negative
impact on the output growth in some prefectures off the northeast coast of Japan (the locationof these prefectures is shown in Figure 1). To control for the negative impact of the earthquake,E
we introduce a dummy variable Dr,p,tthat takes a value of one if prefecture p experienced strong

effects from the earthquake and if year t = 2011, 2012:11

E
Dr,p,t= 1 if the prefecture is Fukushima, Ibaraki, Iwate, or Miyagi, and t = 2011, 2012

 0

(9)

otherwise.

Another factor that we should consider in (2) is information on the revenue of the prefectural
government. The information on the local tax rates may be useful because they may directly
affect the prefectural output. However, the local tax rates in a given year are very similar acrossprefectures, and changes in the time-series dimension take place in the same fiscal year across all
prefectures. Therefore, the effect of local tax rates could be captured by the time fixed effects.

3

Data and the instruments

3.1

Data

We use the data on prefectural output and government spending from the Annual Report on Prefectural Accounts published by the Economic and Social Research Institute in the Cabinet Officeof the Government of Japan. The report provides “prefectural accounts” that are highly comparable with the national accounts. The report includes output, government spending, consumption,
investment, and net exports. The sample period is 1990–2012. Government spending used forthe regressions includes the government final consumption expenditure and the gross fixed capitalformation for the public sectors in the report.
Japan has 47 prefectures and is traditionally divided into eight regions (Hokkaido, Tohoku,
Kanto, Chubu, Kinki, Chugoku, Shikoku, and Kyushu).12 Each region has multiple prefectures,
10

The fiscal year in Japan begins in April and ends in March.
We choose the prefectures for the earthquake dummy based on whether they received the special earmarked
transfers immediately provided by the central government (the grants for recovery from the Great East Japan Earthquake). In the fiscal year 2011, only four prefectures received these transfers. In the next year, the central government
provided transfers to other prefectures but they were not necessarily severely damaged by the earthquake (e.g., Osakaand Kagawa prefectures located in the western area of Japan).
12
These regions are not officially specified because regions do not have their own elected officials and local policy
119except for Hokkaido, located in the north of Japan. Following the Annual Report on Prefectural
Accounts, we combine Hokkaido/Tohoku into one region (see Figure 1).
As we will elaborate in the next subsections, we utilize the cross-sectional variations of transfersfrom the central government to the prefectural governments in instrumenting government spending.
We take the data on the transfers from the Annual Statistical Report on Local Government Financepublished by the Ministry of Internal Affairs and Communications. All data are reported as nominal
variables. When we transform the nominal variables into real variables, we deflate them by theprefecture-specific GDP deflator, with 2005 as the base year.

3.2

Instrumenting government spending

Government spending is endogenous. Indeed, the government spending variables gr,p,t and Gr,t are
affected by the state of the local economy, because they are a policy variable. In the estimation, thetime fixed effect can control for all aggregate shocks to the prefectural output. However, government
spending is still correlated with prefectural-specific shocks to prefectural output. For example, if
a disaster decreases output in a prefecture, the local government would increase the government
spending to recover from the disaster, relative to other prefectures that are not affected by thedisaster.
To address the endogeneity issues, we use cross-sectional variations in transfers from the central
government to the local governments. To instrument government spending with transfers, we use
the following institutional facts regarding local public finance: (i) local government spending inJapan is highly dependent on transfers from the central government; (ii) the transfers from thecentral government are financed by the national tax revenue, which is unlikely to be affected by
local business cycles; and (iii) depending on their type, the transfers are disbursed to achieve specificnational objectives and are not designed to assist the local government’s discretionary policy tostimulate the local economy. We will discuss each institutional fact in turn below.

3.2.1

Institutional facts(i) Local government spending depends on transfers from the central government
Government activity in Japan is highly centralized, and the local governments rely on transfers or
decisions within the same region are independent.

10the redistribution of national tax revenue from the central government to finance their expenditure.
This dependence stems from the vertical fiscal gap between the central and local governments. Although the local governments are assigned various functions by the central government, they do nothave sufficient sources of revenues to carry out their functions (see Bessho 2016). In particular, thelocal governments’ expenditure accounts for about 60% of total government expenditure, but theirrevenue is only 40% of the total government revenue. This large vertical fiscal gap between the central and local governments means that transfers from the central government to local governments
are essential. In the fiscal year 2012, for example, these transfers from the central government
accounted for 34% of the total revenue of all prefectural governments. The transfers are comparable in size to local tax revenues, which account for 32% of the total revenue of the prefectural
governments (Ministry of Internal Affairs and Communications 2014). These facts suggest that
there would be significant correlations between the local government spending and the transfersfrom the central government.
(ii) Transfers are financed by the national tax revenue

The national tax revenue finances

the transfers from the central government. By construction, the national tax revenue is unlikely
to be affected by the state of the local economies because it is pooled in the central government.
Business cycle fluctuations and the fiscal policy at the national level strongly affect the nationaltax revenue. However, the time fixed effect in the regressions controls for such macroeconomic
variations over time, unless the macroeconomic shocks have heterogeneous impacts on the local
economy.
(iii) Depending on their type, the transfers are disbursed to achieve specific national
objectives The local governments in Japan broadly receive two types of transfers from the central government: “the local allocation tax” and the “national treasury disbursements.” Although
the former accounts for a substantial fraction of the total revenue of the prefectural governments(e.g., 18.3% in the fiscal year 2012), it is not suitable as our instrument because it is allocated toreduce the horizontal fiscal gap across local governments. For example, when the local tax revenue
in a prefecture is lower (because of a negative shock to income in the prefecture) than in otherprefectures, the central government allocates more funds to that prefecture to reduce the imbalance in the tax revenue across local governments. Therefore, the local allocation tax is likely to11

be strongly correlated with shocks to the local economy. Likewise, if the output growth in two
prefectures within the same region is similar, transfers from the local allocation taxes are likely to
comove in these prefectures because of the similarity in changes in their tax revenue. Again, thelocal allocation taxes are strongly correlated with shocks to the local economy.
For the second type of transfer from the central to local governments, (the “treasury disbursements” for short), these problems are much less severe. While these transfers account for 15.6% of
the total revenue in the fiscal year 2012, the treasury disbursements are grants to promote projects
that aim to contribute to specific national objectives (e.g., education, social welfare, and social
capital constructions). To acquire the treasury disbursements, local governments prepare applications describing specific projects, with an emphasis on the necessity and earmarking of grants.
Ministries in the central government review their applications and decide whether to approve thegrants and/or subsidies. In general, it is difficult for the local government to use the grants toimplement countercyclical fiscal policy because a fiscal stimulus to specific prefectures is not necessarily consistent with the national objectives. Of course, some projects supported by treasury
disbursements have purposes that relate to specific local economies. For example, the central government assists disaster-hit prefectures to recover from disasters (e.g., special grants to recover fromthe Great East Japan Earthquake in the item of the treasury disbursement). However, the data ofthe treasury disbursements includes various categories based on the grant purposes and programs.
Using this detailed information, we can remove the grants relating to the specific local economies
in constructing the instruments for the regression analysis.

3.2.2

Constructing the instruments

The Annual Statistical Report on Local Government Finance provides detailed information on the
purposes and programs of the treasury disbursements transferred to prefectures. Table 1 shows
the purposes and programs that we can identify from the report in 2012. As indicated in Table 1,
the main components of the treasury disbursements are education (30.3% of the treasury disbursements), construction (21.3%), grants and subsidies that may be related to local business cycles andcountercyclical policies (12.3%), and grants for recovery from disasters (9.2%).
We look for purposes and programs of the treasury disbursements that we can keep track ofduring the sample period to construct instruments. We choose three categories that are considered12to be uncorrelated to shocks to the local economy, based on the purposes and programs shown in
Table 1.
The first category that we choose is the treasury disbursements for education. This category
mainly includes compulsory education. The total amount of this subsidy largely depends on thenumber of teachers and staff in public schools, which is prescribed by law, and on their salaries,
which are insensitive to local business cycles.13 We argue that other subsidies and grants used for
education would vary based on the prefecture’s distribution of children within the population.
The second category that we select for constructing instruments is construction, which includes”ordinary construction” and “grants for comprehensive infrastructure development.” For example,
grants for building public facilities and infrastructure (e.g., construction and maintenance of public
facilities, road and bridges, river improvements, and coastal defenses) are included in this category.
Regarding the grants for comprehensive infrastructure development, the Ministry of Land, Infrastructure, Transport, and Tourism exclusively approves the infrastructure-related grants. To apply
for these types of grants, the local governments need to prepare an application describing how theirspending contributes to the national objectives.
We do not choose purposes and programs in the treasury disbursements that are strongly related
to shocks to the local economy. In particular, we do not select subsidies for livelihood protection(i.e., supplemental social security income for low-income people) and child protection because thesesubsidies depend on the number of recipients, which comoves with business cycle fluctuations at
the prefectural level. For the same reason, we do not choose the subsidy for self-support of thedisabled, though it is a more statutory subsidy than subsidies for livelihood protection and childprotection. We exclude grants for regional autonomous strategies in constructing our instruments
because local governments are permitted to use these for discretionary purposes. We do not include
disaster restoration because they are designed to stimulate the local economies.
The third category selected for constructing instruments is earmarked transfers, although thesetransfers account for only 3.6% of the treasury disbursements. Among these, the subcategory of“money in trust” corresponds to transfers to conduct national projects (e.g., national elections
and the collection of statistical and census data) and is fully funded by the central government.
Grants for locating electric power stations and petroleum reserve facilities are given to prefectures,
13

The transfers from the central government for construction of school buildings and related facilities are included
within the construction category in the treasury disbursements.

13

depending on the extent to which such facilities exist in the prefecture. It can be assumed thatthese subcategories of grants are unrelated to shocks to the local economy.
The Annual Report does not provide detailed information on other small grants, which accountfor 23.3% of the treasury disbursements. The report treats these grants as ”others” and we cannot
identify their programs and purposes. Therefore, we exclude this category in constructing our
instruments.
We construct the instruments used for our analysis by taking the sum of the grants in theselected categories of the treasury disbursements. In what follows, we refer to the sum as the“selected treasury disbursements.” Figure 2 shows how the selection of categories in the treasury
disbursements influences the data fluctuations. The figure plots the total and selected treasury
disbursements at the national level. The trend in the total treasury disbursements (shown by
the black line) reflects two large-scale changes in government spending in 2009 and 2011: a fiscal
stimulus package in the aftermath of the 2008 global financial crisis, and expenditure to assist
recovery from the Great East Japan Earthquake in 2011. Most grants related to the fiscal stimulus
package after the 2008 global financial crisis were temporary and discretionary and categorizedunder “other” grants. The earthquake recovery grants are categorized under “disaster.” Theselected treasury disbursements (shown in red) do not increase significantly in these years, because
we excluded these grants from the instruments.

3.2.3

First-stage regressions

With the above discussion in mind, we instrument two endogenous regressors in the estimation
equation (2) with changes in the lagged selected treasury disbursements. We employ the instruments at both the prefectural and regional levels because (2) includes the prefectural government
spending (gr,p,t ) and the regional government spending (Gr,t ). More specifically, our instrumentsare ∆sr,p,t−1 /yr,p,t−2 , ∆sr,p,t−2 /yr,p,t−3 , ∆Sr,t−1 /Yr,t−2 , and ∆Sr,t−2 /Yr,t−3 , where sr,p,t and Sr,t are
the selected treasury disbursements at prefectural and regional levels, respectively.14 Therefore, theresulting number of excluded instruments (denoted by L) is four, while there are two endogenous
regressors in the regression.
Table 2 reports the results of the first-stage regressions. The first-stage regressions suggest that14

We confirmed that the estimation results are essentially unaltered when we use instruments that are not scaledby output.

14

our instruments to identify the fiscal multipliers are not weak. In the table, the first and second
columns report the first-stage regression results for (gr,p,t − gr,p,t−2 ) /yr,p,t−2 and (Gr,t − Gr,t−2 ) /Yr,t−2 ,respectively. The Angrist–Pischke F statistics exceed 10 in both regressions (39.3 and 540.5, respectively) and the adjusted R2 s are also high, 0.64 and 0.82, respectively. The signs of thecoefficients are consistent with our prediction that higher treasury disbursements lead to higher
government spending. In particular, the coefficients on ∆sr,p,t−1 /yr,p,t−2 and ∆sr,p,t−2 /yr,p,t−3
in the first-stage regression of (gr,p,t − gr,p,t−2 ) /yr,p,t−2 are both positive (2.03 and 0.82, respectively). Similarly, the coefficients on ∆Sr,t−1 /Yr,t−2 and ∆Sr,t−2 /Yr,t−3 in the first-stage regressionof (Gr,t − Gr,t−2 ) /Yr,t−2 are both positive. Therefore, the signs of coefficients are consistent withthe expected relationship between regional government spending and transfers from the central
government.15

4Main results

4.1

Estimates of fiscal multipliers

Table 3 reports our results of the output multipliers estimated from (2). In all specifications, we
include the time and entity fixed effects at the prefectural level in the regressions. The numbers inparentheses below the estimates are the standard errors clustered by regions to allow for possible
correlations of error terms within regions. Note that the number of clusters is only seven (i.e.,
M = 7), as suggested in Figure 1. Cameron and Miller (2015) note that it is not appropriate to use
critical values obtained from the normal distribution with a small number of clusters. Accordingly,p
we make a finite-sample correction by rescaling the regression residuals by M/ (M − 1).16 Given
this finite-sample correction, it is common to use the critical value obtained from the t distribution
with M − 1 degrees of freedom.
Panel (A) of Table 3 describes the ordinary least squares (OLS) estimates for comparison withthe two-stage least squares (2SLS) estimates. The estimated RFM is 1.07 in the second column
15

We compute the standard errors of the estimated coefficients from the cluster-robust estimate of the variancematrix by regions. We also make corrections to mitigate the finite-sample bias arising from the small number ofclusters (i.e., regions). We will elaborate on this issue in Section 4.
16
We also make the finite-sample correction
for the numberof parameters in the estimation results. In other words,pp
we rescale the regression residuals by M/ (M − 1) × N/ (N − K), where N is the number of observations usedin the regression and K is the number of parameters.

15when we assume the region-wide effect.17 The RFM of 1.07 is decomposed into the PFM of 0.45 andthe region-wide effect of 0.62. In the second column of the same panel, we assume no region-wide
effect (i.e., γS = 0 and, thus, βR = γP ). In this case, the output fiscal multiplier equals 0.60, which
is substantially smaller than one.
Panel (B) reports the 2SLS estimates. The RFM is 1.74 and is statistically different from zeroat the conventional significance level. The estimate is larger than the OLS estimate. This result
may be due to the endogenous countercyclical policies undertaken by the prefectural governments.
The RFM when we assume no region-wide effect (i.e., βR = γP ) is 1.59, as shown in the second
column of Panel (B). Again, the estimate suggests a much stronger impact on output than does
the OLS estimate of 0.60. In Panel (C), we estimate the multipliers using the limited information
maximum likelihood (LIML), in which the bias arising from possible weak instruments is less severe
than that in 2SLS. The LIML estimates are very similar to the 2SLS estimates. For both estimates,
the p-values of the overidentifying restrictions suggest that the null hypothesis of the validity of
the instruments cannot be rejected.
Our estimates are broadly consistent with multipliers estimated by previous studies. Nakamura
and Steinsson (2014) report that the LFM is 1.43 or 1.85 using U.S. state- and regional-level data,
respectively. Shoag (2010) also uses U.S. data and finds that the LFM on the U.S. state personal
income is 2.12. Acconcia et al. (2014) use Italian provincial data and estimate the LFM on output
to be 1.5 or 1.9. These estimates of the LFM, including ours, may appear large if they are compareddirectly with the national fiscal multipliers. However, the estimated LFMs are in line with those in
the literature. Chodorow-Reich (2019) concludes that the cross-study mean of the LFM is about
two and Ramey (2011) reports that the LFM on income takes a value between 1.5 and 1.8.18
Before closing this subsection, two remarks are in order. First, we modified the standard errorsof the regression coefficients by rescaling residuals and referred to the t-distribution. However, thestandard errors may still be underestimated with a small number of clusters (Cameron et al. 2008,
Cameron and Miller 2015). Therefore, following the suggestions by Cameron and Miller (2015),
we also use the wild cluster bootstrap to test the statistical significance of regression coefficients.19
17

When we estimate βR directly from (1) by OLS, we obtain similar estimates.
Clemens and Miran (2012) argue that the LFM tends to be large when the source of variations in government
spending is “windfall-financed.” This may be another reason that we obtain relatively large estimates of the RFM
because our instruments are the transfers from the central government.
19
More specifically, we use a six-point distribution by Webb (2013) for the weights in constructing pseudo-residuals
to ensure a sufficient number (3,999) of bootstrap samples. In computation, we used the Stata package boottest
18

16Based on the bootstrap, we can reject the null hypothesis that γP + γS = 0 with a p-value of0.010 and the null hypothesis that γP = 0 with a p-value of 0.040. That is, both the RFM βR
and the PFM γP are significantly different from zero, similarly to the tests based on the standard
errors with the finite-sample corrections. Therefore, even if we use improved tests for the statisticalsignificance of coefficients, our results are unaffected.
Second, our estimates are larger than those in the study by Brückner and Tuladhar (2014),
who use the same data as in our paper to estimate the LFM. Using a sample period of 1990–
2000, they estimate the impact multiplier, defined as one-year changes in output in response to
one-year changes in government spending. Their estimates range between 0.55 and 0.78. To
see whether we can reproduce estimates similar to Brückner and Tuladhar (2014), we replace(yr,p,t − yr,p,t−2 ) /yr,p,t−2 and (gr,p,t − gr,p,t−2 ) /yr,p,t−2 in (2) with the one-year output growth andthe one-year change in government spending divided by the lagged output, respectively. Then, we
estimate the impact multiplier without the region-wide effect, using the sample period over 1990–
2000. Our estimation yields an estimated PFM of 0.78 with a standard error of 0.18, which is very
close to the results of Brückner and Tuladhar (2014).20

4.2

Geographic decomposition

We next move on to the geographic decomposition. We find that the estimated PFM and the regionwide effect are 1.43 and 0.30, respectively. The region-wide effect accounts for 17% of the estimatedRFM, but it is estimated somewhat imprecisely. Again, the results from the LIML estimates arevery similar to those from the 2SLS estimates. When we use the wild cluster bootstrap discussed in
the previous subsection, we find that the p-value for the null hypothesis that γS = 0 is 0.521. Thatis, γS is not significantly different from zero. This result is again very similar to the test based on
the standard errors with the finite-sample corrections.
Using the estimated region-wide effect and the data on the GDP share in prefecture p in regionr, we calculate the size of the spillover based on (8). We use the GDP share averaged over the
sample period for ωr,p and calculate γS (1 − ωr,p ). The spillover averaged across prefectures is 0.26,
which is relatively small compared with the RFM of 1.74. The spillover ranges between 0.16 anddeveloped by Roodman et al. (2019).
20
We obtain this result using ∆sr,p,t /yr,p,t−1 and ∆Sr,t /Yr,t−1 as additional instruments because the instruments
used in the benchmark regressions are weak.

17

0.29, depending on the value of ωr,p . It is lowest in Tokyo because its share of GDP is the largest
in the sample. Conversely, the spillover is high in prefectures with a low GDP share relative to theregion in which the prefecture is located.
The weak evidence for spillovers is also consistent with previous studies. For example, Acconcia
et al. (2014) find positive spillovers, but the spillover is small in size and statistically insignificant
at a 5% significance level. Suárez-Serrato and Wingender (2016) use U.S. county-level data toestimate the LFM. They find negative spillovers in their regression, but, again, the effect is notstatistically different from zero. Brückner and Tuladhar (2014) introduce government expenditures
aggregated across neighboring prefectures and estimate its coefficient. They find that the effect ispositive but not significantly different from zero. However, in the next subsection, we argue thatthe spillover may not be weak when focusing on expenditure within the prefecture.

4.3

Expenditure decomposition

Next, we focus on the decomposition based on the expenditure components in the “prefecturalaccounts,” using data on private consumption, private fixed investment, and net exports. Recall
that the point estimates of the RFM exceed unity. The large RFM implies that there is a crowdingin effect in some expenditure components. The question is, which expenditure components are
crowded in by local government spending?
To answer this question, we estimate the following regression equation:
dr,p,t − dr,p,t−2
gr,p,t − gr,p,t−2
Gr,t − Gr,t−2
= γP
+ γS
+ ηr,p + δt + εr,p,t ,
yr,p,t−2yr,p,t−2
Yr,t−2(10)

where dr,p,t is the expenditure component per capita in prefecture p in region r. Here, we slightly
abuse the notations for γP and γS because the dependent variable in (10) is not the same as
those in (2). The dependent variable in (10) is scaled by the prefectural output. Therefore,
an increase in government spending by 1% of the prefectural output leads to an increase in thecorresponding expenditure component of γP % of the prefectural output. Likewise, an increase inregional government spending by 1% of the regional output leads to an increase in the corresponding
expenditure component by γS % of the prefectural output. As before, we interpret γP + γS as theRFM (βR ) on the corresponding expenditure component and γS (1 − ωr,p ) as the spillover to thecorresponding expenditure component.
18

In what follows, we present our estimates of the RFM on consumption, investment, and “domestic absorption” (i.e., the sum of private consumption, government consumption, and the grosscapital formation in a single prefecture). Because absorption consists of only within-prefecture
aggregate expenditure, we measure the RFM on expenditure before the aggregate demand leaks toeconomies outside the region. We also estimate fiscal multipliers on net exports. Here, we construct
net exports by subtracting the domestic absorption from the prefectural GDP compiled from theproduction side.
Panels (A) and (B) in Table 4 present the estimated multipliers on private consumption andprivate fixed investment. Importantly, these two expenditure components are crowded in by local
government spending. In particular, the RFMs on private consumption and private fixed investment are estimated to be positive and statistically significant. In addition, they are economicallysignificant if we compare them with the RFM on output. The RFM on private consumption is0.48, or 27% of the RFM on output. The RFM on private fixed investment is also large at 0.66,
or 38% of the RFM on output. The sum of the contribution to the RFM on output is substantial,
estimated at 65% of the RFM on output.
As shown in panel (C) of Table 4, the RFM on absorption is 2.18, which is larger by 25%
than the RFM on output. The sum of the RFM on consumption (0.48), investment (0.66), andgovernment spending (which is unity by definition) roughly equals the RFM on absorption (2.18).21
Furthermore, the sum of the RFM on absorption and the RFM on net exports equals the RFM on
output. Thus, we expect that local government spending reduces net exports because the estimatedRFM on absorption is larger than that on output. Panel (D) of the same table indicates that theestimated RFM on net exports is −0.44, although it is not statistically different from zero. The
negative RFM on net exports implies that, taking regional exports as given, an increase in regional
government spending may generate a leakage of regional aggregate demand to other regions ofJapan or foreign countries.
Figure 3 summarizes the results of our decomposition of the RFM. The far left bar of the figure
represents the RFM on output, which amounts to 1.74. The middle bar represents the results when
we decompose the RFM on output (1.74) into the RFMs on absorption (2.18) and net exports(−0.44). We can further decompose the RFM on absorption (2.18) into private consumption (0.48),
21

The sum of the RFM is not exactly equal to the RFM on absorption because of the RFM on changes in inventory.
If we estimate the RFM on changes in inventory, the sum of the RFM coincides with the RFM on absorption.

19

private fixed investment (0.66), and government spending (1.00), with the remainder (0.04) beingchanges in inventories.
We find that the region-wide effect on the expenditure components is statistically and economically significant, in contrast to that on output. Panels (A)–(D) of Table 4 show the estimates of
γS . For private consumption, the RFM is 0.48 and the region-wide effect is 0.50. The spilloverγS (1 − ωr,p ) takes a value between 0.26 and 0.48. For private fixed investment, the RFM is 0.66 andthe region-wide effect is 0.28. The spillover is between 0.14 and 0.27. The estimated region-wide
effect of private consumption and private fixed investment is statistically significant at least at the
10% significance level.22 .
The economically and statistically significant region-wide effect is more clearly present in absorption, as shown in Panel (C) of Table 4. The estimated region-wide effect on absorption is 0.80.
If it is converted into the spillover to absorption, it has a mean of 0.68 and ranges between 0.41 and
0.77. The region-wide effect is precisely estimated with a standard error of 0.19. The p-value forthe null hypothesis that γS = 0 is 0.018, even using the wild cluster bootstrap. This statisticallysignificant region-wide effect in absorption sharply contrasts with the spillover in output. In otherwords, the positive and statistically significant region-wide effect can be supported by the data
if we concentrate on expenditure before its leakage to economies outside the region to which theprefectures belong.
Finally, the estimation results without the region-wide effect are shown in the second columnof each panel of Table 4. The estimated multipliers on the expenditure components are positive
except for net exports. Recall that the output multiplier without the region-wide effect was 1.59
(see the second column of Panel (B) of Table 3). Using the estimates shown in the second column ofTable 4, we decompose the output multiplier of 1.59 into absorption (1.80) and net exports (−0.21).
The multiplier on absorption (1.80) is decomposed into private consumption (0.24), private fixed
investment (0.53), and government spending (1.00). The remainder is changes in inventory (0.03).
In the RFM without the region-wide effect, however, we do not observe strong evidence for thecrowding-in effect in private consumption.
22

We reconfirm that γS is statistically significant based on the wild cluster bootstrap estimates of the standard errors
in regressions of private consumption and the private investment. In particular, the p-value of the null hypothesisthat γS = 0 is 0.020 in the regression of private consumption and the corresponding p-value for the regression ofprivate fixed investment is 0.058.

20

5

Robustness

In this section, we discuss the robustness of our results. To conserve space, we will report only themultipliers on output and absorption.

5.1

Adding control variables

Table 5 reports the results of the robustness checks for the introduction of additional control variables. In Panel (A), we follow Acconcia et al. (2014) and introduce the lagged dependent variables(e.g., (yr,p,t−2 − yr,p,t−4 ) /yr,p,t−4 ) into the regression. In Panels (B)–(D), we add the two-year
growth rate of the prefectural population and/or the two-year growth rate of the regional population into the regressions. We include these additional control variables because the decompositionof the RFM into the PFM and the region-wide effect relies on the assumption that the distributionof the population within the region is stable.
Overall, the results are robust to adding control variables. The RFM on output takes a value
ranging between 1.83 and 1.99, so that the estimated RFM is slightly larger than those in thebenchmark regression. The region-wide effect is estimated to be positive. The estimated regionwide effect is statistically insignificant in output, but it is economically and statistically significant inabsorption. As in the previous section, the region-wide effect would be converted into economicallysignificant spillover if we focus on absorption.

5.2

Dropping possible outliers

Next, we explore whether possible outliers may influence the results in Table 6. Panels (A)–(C)drop possible outliers in the cross-sectional dimension. Panels (D) and (E) exclude the samples inthe time-series dimension.
In Panel (A), we first drop the northern prefecture of Hokkaido and the southern prefecture of
Okinawa from the 47 sample prefectures. We remove these prefectures because they are separated
geographically from the largest main island of Japan. The results remain robust when droppingthese prefectures. In Panel (B), we eliminate Tokyo, the most economically important prefecture,from the samples, because the tax revenue collected in Tokyo may have a strong influence on thenational tax revenue as a whole. Nevertheless, our robustness check reveals no substantial changes
in the estimated multipliers and the region-wide effect. In Panel (C), we drop the samples in which21

EDr,p,tin (9) equals unity. In other words, we drop the four prefectures strongly affected in the year

after the Great East Japan Earthquake (Iwate, Ibaraki, Fukushima, and Miyagi). Once again, ourresults are robust to dropping the samples.
Panel (D) removes the sample periods between 2009 and 2012 to allow for possible heterogeneous
impacts of the global financial crisis. In principle, the time fixed effect could control for the impactof the global financial crisis to some extent. However, the crisis may have different effects on
prefectural output because of prefecture-specific shocks from foreign countries. In this case, thetime fixed effect may not fully control for the impact of the global financial crisis. Under the shorter
sample periods, the estimated RFM on output is 1.87, which is slightly larger than the benchmark
estimate of 1.74 in Table 3. The region-wide effect on output is 0.88, which is somewhat larger
than the benchmark estimate of 0.30. As before, the RFM on absorption is larger than that on
output, and the spillover is statistically significant only in absorption. Finally, we limit the data to
the sample period after the fiscal year 1995 in Panel (E). Miyamoto et al. (2018) define the period
after 1995:Q4 as the period of the zero lower bound on nominal interest. We follow their definitionand estimate the RFM. The resulting estimate of the RFM is 1.53, with the small region-wide effecton output. However, the RFM on absorption remains larger than the RFM on output, and theregion-wide effect on absorption remains economically and statistically significant, reconfirming therobustness of our results.

5.3

Cumulative multipliers

In the benchmark regression, we followed Nakamura and Steinsson (2014) to estimate the twoyear cumulative multipliers, using the two-year growth rate of output and the two-year change ingovernment spending scaled by output. In this subsection, we discuss the results using different
time horizons for the cumulative multipliers.
First, let us consider a one-year (impact) multiplier. In the regressions, we replace the dependent
variables by the one-year growth rate of output or the one-year change in absorption. To beconsistent, we replace the regressors by the one-year changes in government spending. With thereplacement, the resulting coefficients correspond to the impact multiplier. Unfortunately, theregression results for impact multipliers are somewhat unstable, depending on the sample period.
In particular, when we use the whole sample period over 1990–2012 for the regression of output

22

growth, the regression coefficients are imprecisely estimated. This result may arise from the large
swings in output and net exports that followed the global financial crisis and the earthquake in 2011.
Such large swings in the data may affect the regression fit for the impact multiplier more strongly
than that for the two-year cumulative multiplier because changes in output (and net exports) arenot smoothed out in the one-year change relative to the two-year change. For this reason, we
drop the sample period after 2009, as we did in Panel (D) of Table 6. To take the large swings
into account, we also use slightly different instruments, consisting of ∆sr,p,t /yr,p,t−1 , ∆Sr,t /Yr,t−1 ,∆sr,p,t−1 /yr,p,t−2 , and ∆Sr,t−1 /Yr,t−2 .23 Similarly, we consider the cumulative multipliers for threeand five years. In these specifications, we use the whole sample period, including the periods during
the global financial crisis, and the instruments are the same as those in the benchmark regression.
Table 7 reports cumulative multipliers with different time horizons. In the table, we compare
the cumulative multipliers for one, three, and five years. Panel (A) of Table 7 shows the resultswith these modifications. The estimated RFM on output is 1.98. The magnitude is slightly larger
than the benchmark two-year cumulative RFM of 1.74 (shown in the first column of Panel (B) of
Table 3) but is close to the two-year cumulative RFM of 1.87 based on the sample periods before
2009 (shown in Panel (D) of Table 6). Turning to the one-year change in absorption, we observethat the estimated coefficients are similar to the estimated coefficients in the two-year changes inabsorption. That is, the RFM is estimated to be around two, and the region-wide effect is positiveand large in magnitude (0.74). However, in this specification of the one-year change in absorption,
the region-wide effect is not significantly different from zero.
Panel (B) reports the multipliers on output and absorption for the three-year change, and Panel(C) provides those for the five-year change. In the point estimates, the RFMs on output are slightly
larger than in the benchmark case of the two-year change. The region-wide effect on output tends
to be larger in the specification of the three-year and five-year changes, although they continue tobe statistically insignificant. The RFM on absorption and the region-wide effect on absorption arevery similar to each other, regardless of the specification of the time horizon.
23

Another reason for changing the instruments is the possibility of weak instruments when the regressors are the
one-year changes. Under the benchmark instruments, the Angrist–Pischke F statistics for the first-stage regressions of (gr,p,t − gr,p,t−1 ) /yr,p,t−1 and (Gr,t − Gr,t−1 ) /Yr,t−1 reduce to 3.74 and 28.9, respectively. Under the new
instruments, however, the corresponding Angrist–Pischke F statistics are 47.4 and 67.0, respectively.

23

6Conclusion

This paper investigated LFM using data on the “prefectural accounts” and local public financein Japan. We estimated the LFMs for regions and decomposed the RFM into the PFM and theregion-wide effect. We identified the former from the prefecture-specific variations of government
spending and the latter from the common variations of government spending across prefectures
within the same region.
The region-wide effect is converted into the spillover across prefectures. The RFM on output inthe benchmark regression is 1.7. The region-wide effect on output is estimated to be positive but
not very strong. Based on the estimated region-wide effect, the spillover is less than 0.3.
The “prefectural accounts” data allow us to decompose the RFM on output into the expenditurecomponents of aggregate demand. We find that crowding-in effects occur in private consumption
and private fixed investment. Our results show that the RFM on absorption is 2.2, implying asubstantial leakage of aggregate demand to other prefectures and regions through net exports.
Moreover, in contrast to the region-wide effect on output, the region-wide effect on absorption is
economically and statistically significant, suggesting a positive spillover in the aggregate expenditure within the region.

24

A

Appendix: Estimation equation and weighted average

This appendix derives (3) and (8) from (2) under the assumption that the distributions of prefectural
output and population are stable over time.

A.1

Derivation of (3)∗ , G∗ , and N ∗ be GDP, government spending, and the population in region r, respectively.
Let Yr,tr,tr,t∗ /N ∗ , G
Because we use per capita output and government spending, we have Yr,t = Yr,t
r,t =
r,t
∗ . Similarly, we define GDP, government spending, and the population in prefecture p byG∗r,t /Nr,t∗ , g ∗ , and n∗ , respectively. Similarly, we can write y∗∗∗∗yr,p,tr,p,t = yr,p,t /nr,p,t , gr,t = gr,p,t /nr,p,t .
r,p,t
r,p,t
P
∗ is the sum of the prefectural output y ∗ : Y ∗ =∗We note that the regional output Yr,t
r,p,t
r,t
p∈r yr,p,t .

Likewise, the regional government spending is the sum of the prefectural government spending:P∗ .
G∗r,t = r∈p gr,p,tLet:!

ωr,p = E∗
yr,p,t
∗
Yr,t

!

n
ωr,p
= E

n∗r,p,t
∗
Nr,t

,
.

n ) are the time-series mean of the GDP (population) share of prefecture p in region
Here, ωr,p (ωr,pr. We assume that the distributions of the prefectural GDP and population are stable over the∗ /Y ∗ ' ω∗∗nsample periods. By these assumptions, we mean that yr,p,t
r,p and nr,p,t /Nr,t ' ωr,p .
r,t

Let us consider the numerator and the denominator of (yr,p,t − yr,p,t−2 ) /yr,p,t−2 and (gr,p,t − gr,p,t−2 ) /yr,p,t−2 ,respectively. These terms appear in (2). First, the numerator is:

yr,p,t − yr,p,t−2 =='∗∗
yr,p,t−2yr,p,t−n∗r,p,t n∗r,p,t−2∗∗∗ y∗Nr,t−2yr,p,t−2
Nr,tr,p,t∗ − n∗∗
n∗r,p,t Nr,tr,p,t−2 Nr,t−2∗∗
1 yr,p,t
1 yr,p,t−2
−
.
n N∗
n N∗
ωr,p
ωr,p
r,t
r,t−2

25

(11)

The denominator is:

yr,p,t−2 =
'

∗
∗
∗
∗
Nr,t−2
Yr,t−2yr,p,t−2yr,p,t−2=∗∗n∗r,p,t−2
Yr,t−2n∗r,p,t−2 Nr,t−2
ωr,pYr,t−2 .
n
ωr,p

(12)

Then, the growth rate of yr,p,t is:
y∗

y∗

r,p,t
− Nr,p,t−2∗∗Nr,tyr,p,t − yr,p,t−2r,t−2'yr,p,t−2ωr,p Yr,t−2(13)

Taking the weighted average of output growth with the GDP share yields:
P

yr,p,t − yr,p,t−2ωr,pyr,p,t−2
p∈r

X

'
=

∗
p∈r yr,p,t
∗
Nr,t

P

−

∗
p∈r yr,p,t−2∗
Nr,t−2

Yr,t−2
Yr,t − Yr,t−2.
Yr,t−2(14)

We repeat this calculation on (gr,p,t − gr,p,t−2 ) /yr,p,t−2 . The numerator is:
gr,p,t − gr,p,t−2 '∗∗1 gr,p,t
1 gr,p,t−2
−
.
n N∗
n N∗
ωr,p
ωr,p
r,t
r,t−2

(15)

Therefore, the resulting equation is:P

gr,p,t − gr,p,t−2ωr,pyr,p,t−2
p∈r

X

'
=

∗
p∈r gr,p,t
∗
Nr,t

P

−

∗
p∈r gr,p,t−2∗
Nr,t−2

Yr,t−2
Gr,t − Gr,t−2.
Yr,t−2(16)

Finally, taking the weighted average of both sides of (2), we have:
X
p∈r

ωr,p

X
X
X
yr,p,t − yr,p,t−2
gr,p,t − gr,p,t−2
Gr,t − Gr,t−2 X
= γP
ωr,p
+γS
+
ωr,p ηr,p +δtωr,p +
ωr,p εr,p,t .
yr,p,t−2yYr,p,t−2
r,t−2
p∈r
p∈r
p∈r
p∈r

26

By simplifying this equation, we have:
Gr,t − Gr,t−2
Yr,t − Yr,t−2' (γP + γS )+ αr + δt + εr,t ,Yr,t−2
Yr,t−2
which is (3) in the main text.

A.2

Derivation of (8)To derive the (8), it suffices to show that:X
p0 6=pω̃r,p0 ,pgr,p0 ,t − gr,p0 ,t−2
Gr,−p,t − Gr,−p,t−2=,
yr,p0 ,t−2
Yr,−p,t−2(17)∗because we can easily derive (6) and (7) from (3). Using the definitions of Yr,−p,t , Gr,−p,t , Yr,−p,t,∗, we can derive an equation similar to (13):G∗r,−p,t , Nr,−p,tgr,p0 ,t − gr,p0 ,t−2=
yr,p0 ,t−2

∗
yr,p
0 ,t

∗
Nr,−p,ty∗ 0,t−2− Nr,p∗r,−p,t−2ω̃r,p0 ,p Yr,−p,t−2.

By taking the sum of both sides of the equation with the weight ω̃r,p0 ,p , we obtain (17).

27

(18)

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[12] Clemens, J. and S. Miran (2012). “Fiscal Policy Multipliers on Subnational Government Spending,” American Economic Journal: Economic Policy, 4 (2), pp. 46–68.
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251–282.

30

Table 1: Components of treasury disbursements used in the construction of instruments
Category

Fractions

Included in IV?

Compulsory education

23.2%

Y

Subsidies for private senior high schools

1.7%

Y

Grants for not collecting tuition at public senior high school

3.4%

Y

Grants for financial support for senior high school attendance

2.0%

Y

Ordinary construction

11.8%

Y

Grants for comprehensive infrastructure development

9.5%

Y

Education (30.3%)

Construction (21.3%)

Grants and subsidies related to local business cycles/countercyclical policy (12.3%)
Livelihood protection

2.2%

N

Child protection

2.0%

N

Subsidies for self-support of the disabled

1.1%

N

Grants for regional autonomous strategies

7.0%

N

Unemployment measures

0.0%

N

Disaster restoration

5.8%

N

Grants for recovery from the Great East Japan Earthquake

3.4%

N

Money in trust

2.0%

Y

Finance subsidy

0.1%

Y

Grants for locating electric power stations

1.4%

Y

Grants for locating petroleum reserve facilities

0.1%

Y

23.3%

N

Disaster (9.2%)

Other earmarked transfers (3.6%)

Transfers for which grant purposes are not reported (23.3%)
Others

Notes: With regard to the components of the treasury disbursements, the fraction of each component is based ondata as of fiscal year 2012. Categories with “Y” are included in the construction of the instruments, whereas thosewith “N” are not included in the instruments.

31

Table 2: First-stage regressions
Dependent variable(gr,p,t − gr,p,t−2 )/yr,p,t−2(Gr,t − Gr,t−2 )/Yr,t−2∆sr,p,t−1 /yr,p,t−2

2.033***-0.212(0.438)(0.197)0.820**

0.0671(0.332)(0.0555)

0.831

3.660***(0.446)(0.604)1.372

2.550**(1.032)(1.030)Angrist–Pischke F-value

39.311

540.510Observations

940

940

R-squared

0.639

0.824

∆sr,p,t−2 /yr,p,t−3∆Sr,t−1 /Yr,t−2∆Sr,t−2 /Yr,t−3

Notes: The table shows the estimated coefficients of the first-stage regressions. The first (second) column corresponds to the first-stage regression where the dependent variable is the two-year change in the prefectural (regional)
government spending divided by the prefectural (regional) output. The regions are defined in the main text. The
numbers in parentheses below the estimates are standard errors clustered by regions. The Angrist–Pischke F -values
are calculated from the cluster-robust estimate of the variance matrix clustered by regions. The symbols *, **, and*** indicate that the coefficients are statistically significant at the 10%, 5%, and 1% significance levels, respectively,
based on the t distribution with M − 1 degrees of freedom, where M is the number of regions.

32

Table 3: Benchmark estimates of the LFMs
(A) OLS(B) 2SLS(C) LIML

(1)

(2)

(1)

(2)

(1)

(2)

1.068***

0.595***

1.738***

1.593***

1.741***

1.604***(0.221)(0.110)(0.272)(0.359)(0.274)(0.363)0.449***

0.595***

1.434**

1.593***

1.441**

1.604***(0.120)(0.110)(0.567)(0.359)(0.570)(0.363)0.618*

–

0.304

–

0.299

–

(0.263)–(0.485)–(0.487)

–

–

–

0.479

0.319

0.479

0.318

Observations

987

987

940

940

940

940

Adj. R-squared

0.524

0.516

0.475

0.458

0.474

0.456

Regional fiscal multiplier (βR )Prefectural fiscal multiplier (γP )Region-wide effect (γS )P-value ofoveridentifying restrictions

Note: The table shows the regressions for the LFM. In each column, the dependent variable is a two-year changeof the per capita GDP divided by the initial value. All regressions include the time fixed effect and the entity fixed
effect at the prefectural level. The benchmark regressions are 2SLS shown in Panel (B), where we use the treasury
disbursements at prefectural and regional levels as instruments. The regions are defined in the main text. The numbers
in parentheses below the estimates are standard errors clustered by regions. In computing the standard errors, we
make finite-sample corrections to mitigate the possible downward bias arising from a small number of clusters. Panel(A) reports OLS results for comparison. In each panel, specification (2) assumes no region-wide effect, implying thatβR = γP , so that we present the same estimate in each row. Panel (C) reports the multipliers estimated by the limited
information maximum likelihood (LIML) with the instruments used in the benchmark estimations. The p-values ofoveridentifying restrictions are calculated from the cluster-robust estimate of the variance matrix by regions. The
symbols *, **, and *** indicate that the coefficients are statistically significant at the 10%, 5%, and 1% significancelevels, respectively, based on the t distribution with M − 1 degrees of freedom, where M is the number of regions.

33

Table 4: Regressions of expenditure components
Dependent variable(A) Private consumption(B) Private fixed investment

(1)

(2)

(1)

(2)

0.475**

0.239

0.663***

0.530***(0.169)(0.127)(0.0900)(0.119)-0.021

0.239

0.385**

0.530***(0.123)(0.127)(0.135)(0.119)0.496**–

0.278*–(0.136)–(0.129)

–

0.412

0.134

0.105

0.219

Observations

940

940

940

940

Adj. R-squared

0.206

0.181

0.572

0.557

Regional fiscal multiplier (βR )Prefectural fiscal multiplier (γP )Region-wide effect (γS )P-value ofoveridentifying restrictions

Dependent variable(C) Absorption(D) Net exports

(1)

(2)

(1)

(2)

2.178***

1.798***-0.440-0.205(0.142)(0.174)(0.230)(0.344)1.380***

1.798***

0.0535-0.205(0.196)(0.174)(0.481)(0.344)0.797***–-0.493–(0.193)–(0.362)

–

0.128

0.293

0.293

0.484

Observations

940

940

940

940

Adj. R-squared

0.581

0.558

0.118

0.142

Regional fiscal multiplier (βR )Prefectural fiscal multiplier (γP )Region-wide effect (γS )P-value ofoveridentifying restrictions

Note: The table presents the regressions of the aggregate demand components on government spending. In eachpanel, the dependent variable is the two-year change of the per capita aggregate demand component divided by percapita GDP. The absorption is defined as the sum of private consumption, government consumption, and the grosscapital formation (including the inventory investment). In each panel, specification (1) assumes the region-wide effect,
whereas specification (2) does not. All parameters are estimated by 2SLS. For other details, see the notes to Table 3.

34

Table 5: Robustness: Additional control variables
(A)

(B)

Dependent variable

OutputAbsorption

OutputAbsorption

Regional fiscal multiplier (βR )1.992***

2.387***

1.934***

2.304***(0.379)(0.182)(0.365)(0.198)1.621**

1.536***

1.595**

1.499***(0.633)(0.215)(0.620)(0.214)0.370

0.851***

0.340

0.805***(0.460)(0.152)(0.472)(0.143)Lagged dependent variable

Yes

Yes

Yes

Yes

Prefectural population growth

No

No

Yes

Yes

Regional population growth

No

No

No

No

P-value of

0.205

0.548

0.190

0.541

Observations

893

893

893

893

Adj. R-squared

0.474

0.606

0.480

0.614

Prefectural fiscal multiplier (γP )Region-wide effect (γS )overidentifying restrictions

(C)

(D)

Dependent variable

OutputAbsorption

OutputAbsorption

Regional fiscal multiplier (βR )1.829***

2.193***

1.838***

2.218***(0.463)(0.284)(0.466)(0.280)1.593**

1.490***

1.585**

1.478***(0.621)(0.217)(0.619)(0.218)0.236

0.703***

0.253

0.739***(0.419)(0.176)(0.420)(0.160)Lagged dependent variable

Yes

Yes

Yes

Yes

Prefectural population growth

No

No

Yes

Yes

Regional population growth

Yes

Yes

Yes

Yes

P-value of

0.221

0.532

0.201

0.533

Observations

893

893

893

893

Adj. R-squared

0.482

0.614

0.483

0.617

Prefectural fiscal multiplier (γP )Region-wide effect (γS )overidentifying restrictions

Note: The left (right) column of each panel shows the regression results when the dependent variable is output(absorption). In Panel (A), we add the lagged dependent variables into the regressions. In Panels (B)–(D), we
include population growth rates in addition to lagged dependent variables. All parameters are estimated by 2SLS.
For other details, see the notes to Table 3.

35

Table 6: Robustness: Dropping possible outliers

(A)

(B)

(C)

Dependent variable

OutputAbsorption

OutputAbsorption

OutputAbsorption

Regional fiscal multiplier (βR )1.803***

2.127***

1.804***

2.211***

1.691***

2.203***(0.311)(0.161)(0.257)(0.148)(0.206)(0.142)

1.494**

1.342***

1.460**

1.398***

1.415**

1.412***(0.549)(0.195)(0.572)(0.189)(0.410)(0.155)0.308

0.785**

0.344

0.812***

0.276

0.791***(0.480)(0.235)(0.494)(0.199)(0.436)(0.165)

0.492

0.138

0.635

0.729

0.796

0.476

Observations

900

900

920

920

932

932

Adj. R-squared

0.481

0.597

0.479

0.584

0.498

0.563

Prefectural fiscal multiplier (γP )Region-wide effect (γS )P-value ofoveridentifying restrictions

(D)

(E)

Dependent variable

OutputAbsorption

OutputAbsorption

Regional fiscal multiplier (βR )1.866***

2.095***

1.527***

1.881***(0.304)(0.154)(0.340)(0.277)0.984**

1.274***

1.544*

1.245***(0.355)(0.120)(0.656)(0.260)0.882

0.821**-0.0169

0.635***(0.540)(0.249)(0.490)(0.154)

0.941

0.201

0.365

0.839

Observations

752

752

846

846

Adj. R-squared

0.428

0.543

0.523

0.604

Prefectural fiscal multiplier (γP )Region-wide effect (γS )P-value ofoveridentifying restrictions

Note: The left (right) column of each panel shows the regression results when the dependent variable is output(absorption). Each specification estimates the multipliers after dropping possible outliers. Panel (A) drops Hokkaido
and Okinawa prefectures (i.e., the northern and southern prefectures) from the sample. Panel (B) drops Tokyo, theeconomically largest prefecture, from the sample. Panel (C) drops the post-2011 data of the four prefectures thatwere severely damaged by the Great East Japan Earthquake. Panel (D) reestimates the model using the sample
period before 2009. Panel (E) uses the sample period corresponding to the period of zero lower bound on the nominalinterest rate specified by Miyamoto et al. (2018). All parameters are estimated by 2SLS. For other details, see thenotes to Table 3.

36

Table 7: Robustness: Different time horizons in cumulative fiscal multipliers
Dependent variable(A) One-year changes in:(B) Three-year changes in:(C) Five-year changes in:

OutputAbsorption

OutputAbsorption

OutputAbsorption

1.977***

2.013***

2.191***

2.251***

2.074***

2.295***(0.453)(0.312)(0.475)(0.198)(0.503)(0.207)0.888**

1.270***

1.181**

1.336***

1.186**

1.298***(0.268)(0.261)(0.436)(0.175)(0.341)(0.179)

1.089

0.742

1.010

0.915**

0.889

0.996**(0.642)(0.426)(0.711)(0.266)(0.721)(0.286)

0.192

0.902

0.384

0.808

0.799

0.363

Observations

799

799

940

940

846

846

Adj. R-squared

0.438

0.452

0.440

0.584

0.297

0.602

Regional fiscal multiplier (βR )Prefectural fiscal multiplier (γP )Region-wide effect (γS )37P-value ofoveridentifying restrictions

Note: The table reports the cumulative fiscal multipliers with different time horizons. Panel (A) shows the estimated impact of the one-year multipliers
on output and absorption. In this panel, we use the sample period covering the period before 2009 and use the instruments ∆sr,p,t /yr,p,t−1 , ∆Sr,t /Yr,t−1 ,∆sr,p,t−1 /yr,p,t−2 , and ∆Sr,t−1 /Yr,t−2 . Panel (B) shows the estimates of the three-year cumulative multipliers on output and absorption. Panel (C)presents the estimates of the five-year cumulative multipliers on output and absorption. In the specifications shown in Panels (B) and (C), the instruments
are the same as those used for the benchmark estimation for the two-year cumulative multipliers. All parameters are estimated by 2SLS. For otherdetails, see the notes to Table 3.

Figure 1: Regions in Japan and the prefectures heavily damaged by the Great East Japan Earthquake

38

Figure 2: Treasury disbursements per capita (constant 2005 JPY)

Figure 3: Decomposition of the RFM into demand components

39