Discussion Paper Series No. F-69
Empirics of the Median Voter Hypothesis
in Japan

Takero DOI*

May 1998*Research Associate, Institute of Social Science, University of Tokyo,
7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan. E-mail: tdoi@iss.u-tokyo.ac.jp

This is a revision of the paper presented at the 53rd Congress of International
Institute of Public Finance, August 1997. I'm grateful to Toshihiro Ihori and Isidoro
Mazza for their helpful comments. Also, it was presented at the meeting ofContemporary Economy Research Group (Gendai Keizai Kenkyukai), Institute ofSocial Science, University of Tokyo held on April 24, 1998. The comments received
from the participants are greatly appreciated. Any remaining errors are mine.

Empirics of the Median Voter Hypothesis in Japan
Takero DOI

Abstract
This paper offers a test of the median voter hypothesis in Japan. We havecomprehensively studied the hypothesis in Japanese local finance for first time.
Analyzing the hypothesis in Japan is important to investigate whether local
expenditures reflects voter’s preference or not. Unfortunately, we cannot obtain
official data on the median (voter’s) income in Japan. Therefore data by prefecture isconstructed in this paper. Using this, we estimate the demand functions of local
public goods in order to test the hypothesis. We obtain the result that the medianvoter hypothesis is supported by prefectural finance. This result is a reasonably
intuitive interpretation. In centralized local system such as Japan, the hypothesis
means that the central government manages local expenditures throughinterregional grants to reflect the preference of the median voter in its jurisdiction.

Key words: Median Voter Hypothesis, Local Public Goods, Japanese Local FinanceJEL classification: H72, D72

I . I nt r o d uc t i o n
The median voter hypothesis plays an important part in analyzing local
expenditures. There are many empirical studies of local government finance withthe hypothesis in the U.S. etc.. Examples of these are Borcherding and Deacon(1972) Bergstrom and Goodman (1973), Gramlich and Rubinfeld (1982), andTurnbull and Djoundourian (1994). In Japan, however, the hypothesis are notdirectly used for studies of local spending. This paper provides a direct test of the
hypothesis in Japanese local government finance.
Recently, this hypothesis is theoretically used for studies on not only local financebut endogenous growth theory like Perotti (1993), Alesina and Rodrik (1994),
Persson and Tabellini (1994), and so forth. In the endogenous growth theory, themedian voter theorem is employed to make policies (especially, income
redistribution policies) among heterogeneous individuals. Hence in order to examine
the relationship between fiscal policy and income distribution, the tests on the
median voter hypothesis are meaningful.
A significance of researching the median voter hypothesis in Japan is as follows.
Many Japanese consider that the Japanese central government is especiallysuffering from its unnecessary public expenditures and subsidies now. If the people
do not really want such expenditures and subsidies in this region, the central
government can reduce them. In this sense, it is very important in Japan that wetest the median voter hypothesis, by which we understand whether the Japanese
central government disburses expenditures and subsidies to answer the needs ofeach jurisdiction.
But we have never comprehensively researched it in the case of Japanese local
expenditure. Because the data used in testing the hypothesis, such as the medianincome by Japanese jurisdiction, is not available. So we try to construct the dataand check it in Japan, considering Japanese specific institutions.
In tests on the hypothesis, we have assumed that the median voter identifies the
person who earns the median income in the society. Several strong assumption
must be satisfied in order to prove this identification correct. Examples of this are a1

one-dimensional policy issue in majority voting, its level of which have a strong(positive) correlation with income, heterogeneity among voters and which aremainly represented by income.
Unfortunately, we cannot obtain official data on the median income in Japan.
Therefore data by prefecture needs to be constructed in this paper. In the present
circumstances, it is in prefectures that above suppositions may be satisfied. In
prefectures, income taxation accounts for more than 70% of the total prefectural tax
revenue, and each governor is directly elected under majority rule. In addition,
official data on income distribution by prefecture is available.
We conclude by estimations that the hypothesis is held in Japanese prefectures.
The interpretation of the median voter hypothesis is usually that local governments
determine their expenditure desired by the median voter. This interpretation in acentralized local system such as Japan is, however, different from that in a federal
system such as the U.S.. We insist that the hypothesis means the central
government decides their expenditure desired by the median voter in Japan. This
reason is as follows.
In the Japanese centralized system, each local government may formally decide
its expenditures, but the central government makes its decisions substantially andcontrols the discretion of local governments. The central government can manage
local finance without considering the results of local elections, that is, the medianvoter’s preference for expenditures in their prefectures. On the contrary, eachprefectural governor, needs to get support from the median voter in order to bereelected. There are many governors who are reelected in Japan. Therefore thecentral government reflect their preference for prefectural expenditures. The
hypothesis suggests this.
This paper is organized as follows: in section II, we introduce the Japanese local
finance system. Section III constructs models applied to the Japanese local financesystem. Section IV estimates the median and mean income by prefecture in Japan.
Section V reports the results of the test of the median voter hypothesis. Section VI
closely examines the superiority of the median income as the regressor on local

2

expenditures. Section VII concludes the paper.
II.
II. Jap
Japanese Local Finance System
We shall briefly explain the Japanese local finance system.1

There are threelevels of governments in Japan; the national government, prefectural government,
and municipal government. As we address prefectural expenditures in this paper,
we now focus on the subject of prefectural finance and politics.
First, we explain the prefectural revenues. The total revenue of all prefectures isabout 40 trillion yen (equals to about 4,000 billion dollars) as of the early 1990s.
They are divided into six categories; Local Taxes, Local Transfer Taxes, Local
Allocation Tax, National Government Disbursements, Local Public Bonds, andMiscellaneous Revenue. In Japan, the revenues can be nearly controlled by thecentral government. Rates and sources of Local Taxes are basically determined bynational laws, local governments rarely have discretion over them. Also issues ofLocal Public Bonds are controlled through the central government. Local Transfer
Taxes, Local Allocation Tax, and National Government Disbursements are
distributed to local governments by the central government.
Especially, the interregional distribution of National Government Disbursements
often affects political pressure, suggested by Doi and Ashiya (1997). Namely the
Dietmen and the prefectural governors appeal to the central government to
distribute more in their own jurisdictions. Getting more grants is important forthem to be reelected.
In the Japanese local election systems, the governor is elected not by indirectelection among assemblymen but direct election among the electorate. Hence theparty that the governor belongs to may be opposed to the party that shares the
majority in the assembly. However, these parties recently are the same in most
prefectures. So the gubernatorial election usually substantially reflects voters’
requests. Shown in Table 6, it indicates the number of times gubernatorial
candidates have been reelected. If the central government ignores the local elections,3the incumbent governor may not be reelected, and governors may change in every
election. There have been, however, many governors reelected several times.
According to Table 6, the share of governors who have not been reelected for somereason are only about 25% of all governors in Japan.
Analyzing the median voter hypothesis in Japan is important to investigate
whether local expenditures reflects voter’s preference or not. Because the Japanese
local system is centralized, hence the central government can control local
expenditures with ignoring voter’s preference. But if the central government does so,
the governor will be able to lose the next election. Therefore he appeals to thecentral government to reflect voter’s requests. Under a centralized local system, themedian voter hypothesis is held if the central government urged by the governor
controls local expenditures to be preferred by voters. The purpose of our paper is to
examine this.
III.
III. Models
In this section, models based on the previous studies on the median voter
hypothesis are modified to conform them to the local finance system in Japan.
III-1. Demand function for local public goods with supply side
Borcherding and Deacon (1972) are the pioneering test of the median voter
hypothesis that use demand function of local public goods on the assumption thatthe household maximizes the utility.2

The model based on Borcherding and

Deacon (1972) is as follows.
We presume that household i living in jurisdiction j obtains the utility throughconsumption of private good ( X ij ) and local public goods (Zj). Their utility function is
U ( X ij , Z j ) ,(1)

1 See Shibata (1993) for further details.
2 Borcherding and Deacon (1972) don’t explicitly show the utility function.

4

∂U
∂U
∂ 2U
>
0
,
>
0
,
< 0.
∂X ij
∂Z j
∂Z j 2

where

Assume that households maximize the utility without considering the effect of the
migration across jurisdictions. The local public goods allow for congestion. The
relation between consumption and provision (Gj) of local public goods is denotedγ

Z j = Gj N j ,(2)where Nj is population in jurisdiction j, and g is its congestion parameter (g = 0 when
it is purely public, and g = 1 when it is purely private). We usually assume 0 ≤ γ ≤ 1 .
Suppose private good is the numeraire. The budget constraint of the household is
X ij + Tji + τ ij = y ij

(3)where y ij is pre-tax income, Tji and τ ij are respectively local tax and national tax
paid by household i in jurisdiction j.
The central (national) government collects taxes from each household in eachjurisdiction, and distributes general lump-sum grants (Local Allocation Tax) andmatching grants (National Government Disbursements) to each local government(omitting national public goods provided by the central government). Each local
government collects (local) taxes, receives grants, and spends provision of local
public good. The budget constraint of the local government j is
Nj

(1 − m j ) E j = ∑ Tji + H j ,

(4)

i =1

where Ej is expenditure for the provision of local public goods, Hj is a general lumpsum grant (Local Allocation Tax) distributed to local government j, and mj is theratio of the matching grants (National Government Disbursements) that it getstotal expenditures. Expenditures for local public goods, Ej, are expressed:
Ej = qGj,
where q is the unit cost of local public goods.
The central government faces a budget constraint (there are J jurisdictions
around the country):

5

Nj

J

j =1 i =1

j =1

J∑∑ τ ij = ∑ (m j qG j + H j ) .

(5)

It decides Hj, mj, and the local tax system satisfying equation (5). The central
government requested by local governments or the households can Hj (Local
Allocation Tax) and local tax systems.3

In this paper, we focus on their demand for

local public goods or revenues.4
We shall define the tax share of the household i in jurisdiction j,
t ≡T
i
j

Nj

i
j

∑T .
i
j

i =1

Hence the budget constraint of the household i in jurisdiction j is rewritten by it
X ij = y ij − τ ij + t ij H j − t ij {(1 − m j )qG j }γ= y ij − τ ij + t ij H j − t ij {(1 − m j )qN j }Z j .

(6)γ

Define sij ≡ t ij {(1 − m j )qN j } in the last term of the right hand side in equation (6), sij
is the (local) tax price in terms of consumption of local public good. Now
Yji ≡ y ij − τ ij + t ij H j denotes after-tax income of household i in jurisdiction j.
The household wishes the quantity of local public goods by maximizing its utility.
Under appropriate conditions for utility function, we introduce the formulation thathousehold i’s demand function of local public good is

3 Under the present system, the distribution of Local Allocation Tax, and the rate and structureof local taxes are prescribed by national laws. Therefore each local government or household is
can hardly decide the revenue of Local Allocation Tax and local taxes directly. So local
governments or households require appropriate control of the revenue from the central
government.
4 Now, we do not explicitly consider the object function of the central government in this paper.

Because we want to focus whether or not the central government disburse subsidies to answer
the needs of each jurisdiction. In order to check it, we had better set the object function a priori.
But if pressed we would say that its object is that it disburse subsidies required by the medianvoter in every jurisdiction.

6

Z j = A( sij )η (Yji )δ ,(7)

where A is constant, h is its elasticity of tax price (supposing constant), and d is its
elasticity of income (supposing constant). Assume that each household is assessednational and local taxes, but chooses the level of mj as he desires. In assuming it, Zj
is a monotonic function of Yji (and y ij as well). Hence from the supposition of theutility function (1), the median voter hypothesis holds in majority voting on thequantity of local public goods with (7). Namely, the level of local government
expenditures in each jurisdiction is optimal for the median voter in its jurisdiction.
The hypothesis can be satisfied if the central government manages each local
expenditure to reflect the preference of voters in the jurisdiction (e.g. controlling the
distribution of National Government Disbursements, after all mj).5

This

explanation is valid for the suggestion of Doi and Ashiya (1997). Doi and Ashiya(1997) obtain the result that the interregional distribution of National Government
Disbursement is affected by the political power of the governing party (i.e., theLiberal Democratic Party).
On the supply side of local public goods, its production function is expressed,using the Cobb-Douglas assumption, by6β

G j = aL j K j1− β

0< β <1,(8)

where a is constant, Lj, and Kj are respectively labor and capital for its production.
Each local government decides the output to minimize cost for production of local
public goods,

5Each mj may be different. Though the rate of grant (the ratio of National Government

Disbursements to expenditure) for some specific purpose is almost the same across jurisdictions,the quantity of each expenditure varies in each local government. Hence each mj, the rate of
grant in the sense of aggregation, is not same.
6 This function must be linear homogenous in order to identify parameters in models when we

estimate them.

7

Lj =

βC j
(1 − β )C j
, Kj =,
wjr

where wj is wage in jurisdiction j (it varies from one jurisdiction and another), r isrental rate of capital (it equalizes across jurisdictions).7 From (8), the unit costfunction c j = C j G j isc j (w j ) =1 w j β r 1− ββ( ) () ≡ a ′w j ,
1− β
a β

where

a′ ≡

(9)

1 1 β r 1− β
( ) (
) .
a β 1− βHere cj = q (unit cost of local public good).8
From (2), (7), and (9), as the result of majority voting on local expenditures, total
expenditures in jurisdiction j Ej (= Cj), are chosen the following level preferred bymedian voter (superscript m denotes median voter).
E j = A′( w j ) β (η +1) {t mj (1 − m j )}η (Yjm )δ ( N j ) γ (η +1)
whereA′ ≡ A(a ′)η +1 .

In logarithmic form this becomes 9
ln E j = ln A′ + β (η + 1) ln w j + γ (η + 1) ln N j + η ln{t mj (1 − m j )} + δ ln Yjm(A)

III-2. Demand function without supply side
The model based on Bergstrom and Goodman (1973) deal with demand side only
and tax price explicitly. In addition to Borcherding and Deacon (1972), we posit themarginal rate of transformation of local public for private good is equal to 1 in eachjurisdiction.
7 The cost minimizing problem is

min C j = w j L j + rK js.t. (7) .

We posit that local governments supply public good efficiently. Moreover, we suppose labor isimperfectly mobile across jurisdictions, and capital perfectly mobile.
8 We allow that not only unit cost function, that is, wage w but q differ in each jurisdiction.
j
9 In Borcherding and Deacon (1972), the left hand side in the above equation or (A) is not total

expenditures but per capita expenditure.

8Equations (1), (2), (3), and (7) are the same in this section. Then total expenditure,
Ej (= qGj), is chosen under majority voting on local expenditure. The median voter’s
demand function for local public goods is represented:
Z j = A[t mj {(1 − m j )qN j γ }]η (Yjm )δ .
Therefore, from (2)ln E j = ln A′′ + γ (η + 1) ln N j + η ln{t mj (1 − m j )} + δ ln Yjm
where

(B)

A′′ ≡ Aq η +1 .

A, d, and h are as noted above.
III-3. Demand function with deferent benefit among individuals
The model based on Denzau and Mackay (1976) and used for empirical studies as
Gramlich and Rubinfeld (1982), Preston and Ridge (1995), and so on, differs from
Borcherding and Deacon (1972) in the relation between consumption and provisionof local public good (2). Substituting for (2), we postulate
Z ij = ρ ij

Gj
Nj

0≤γ ≤1γ

whereρ ij ≡ (Yji )αNj∑ {(Y )

i α
j

(2’)

N j}.

i =1

ρ ij is the benefit share of household i in jurisdiction j, parameter a “reflects in thesome sense the extent to which the distribution of the publicly provided good isbiased towards the more affluent groups relative to the situation of equal shares”(Denzau and Mackay (1976) p.72). a = 0 when benefits are distributed to all
households equally, i.e., as same as (2), a > 0 when more distributed to higher
income households, a < 0 when more distributed to lower income households. We
Njdefine Yj∗ ≡ ∑ {(Yji )α N j } .
i =1Budget constraint of household i can be rewritten:
X ij = Yji − {t ij (1 − m j )qYj∗ ( N j ) γ (Yji )α }Z j ,where the unit cost of local public goods, q (= cj), is represented by (9). Thus demand9

function for local public goods of the household i (maximizing the utility) isβη

Z j = A[t ij (1 − m j )qYj∗ ( N j ) γ (Yji )α ]η (Yji )δ = A(a ′)η w j {t ij (1 − m j )}η ( N j ) γη (Yj∗ )η (Yji )δ −αηA, d, and h are as mentioned above.
As for the local expenditures, Ej (= Cj = cjGj), chosen in majority voting, we have
E j = A′w jβ ( η +1)

[t mj (1 − m j )]η N jγ ( η +1)

(Yj∗ )η +1 (Yjm )δ −α (η +1)

A′ ≡ A(a ′)η +1 .

where
α

Now we can Yj∗ ≅ Yj ( Yj is mean income in jurisdiction j) from the definition of Yj∗ .
The above equation can be rewritten:
ln E j = ln A′ + β (η + 1) ln w j + γ (η + 1) ln N j+η ln{t mj (1 − m j )} + {δ − α (η + 1)}ln Yjm + α (η + 1) ln Yj .

(C)

After this, in order to test the median voter hypothesis, we estimate model (A),(B), and (C). The deference among them is shown in Figure 1. Before that, we must
estimate the median income as median voter, because we cannot get the data of
median income from existing statistics. In the next section, we begin to estimate
this.
IV. Estimating Annua
nnual Income and Tax Share ofo f M e d i an V o t e r
In Japan, the data concerning median income (as median voter) is not released
explicitly. So we need to estimate it from income distribution. Statistics of income
distribution by prefecture are obtained from “Employment Status Survey,”“Housing Survey of Japan,” and “National Survey of Family Income andExpenditure.”

These

are,

however,taken

quinquennially,

andsurveyed

independently. Hence we analyze them separately using cross-sectional data in thispaper.
We adopt lognormal distribution, a popular specification, as income distribution
in Japan.10

10Supposing annual (after-tax) income of a household, Y (omitting

Previous works on the hypothesis (ex. Romer and Rosenthal (1979)) and on the income

distribution Japan have already used this distribution.

10

indexes), has a lognormal distribution, ln Y is normally distributed with mean m andvariance s2 (ln Y ~ N(m,s2)). In standardizing z ≡ (ln Y − µ ) σ , z is standard normally
distributed (z ~ N(0, 1)). The cumulative distribution function of z iszz
ϕ = Φ( z ) ≡ −∞1
t2
exp( − )dt .
22π

We define the inverse function z = F-1(j) , and estimate
Φ −1 (ϕ ) =µ1
ln Y −σσ(10)using these surveys. We can estimate the parameters, m, s by prefecture.
µ$ , and σ$ respectively denote the OLS estimates of m, and s. Median and mean of Y
are as follows.
Median income:

Y m = exp( µ$ ) ,Mean income:

Y = exp( µ$ + σ$ 2 2) .

The values of these and the ratio of separation between them (＝ (Y − Y m ) Y ) byprefecture are reported in Table 1.
Table 1 implies that the ratio of separation differ from one prefecture to another,and the difference between maximum and minimum is 5% point and over. In testing
the median voter hypothesis, if median income (as median voter) is similarly
proportional to mean income in all prefectures, we can substitute the latter for theformer. However we can not substitute, because table 1 shows the former is notsimilarly proportional to the latter.
The income in Table 1 is levied national and municipal taxes and not levied
prefectural taxes. As Doi (1996) suggests, estimation using simple pre-tax income isincorrect. The tax burden is calculated on the condition that all income of thehousehold is earned income, and it consists of the householder earning, anunearning spouse, and dependents under 16 years old.11 In order to adapt it to above
models, a per capita (median or mean) income is derived by estimated income
divided by persons per household.

11 We refer to Ministry of Finance, “Ministry of Finance Statistics Monthly” (various years) for

tax rates and various deductions.

11V . E s t i m at i ng T he s e M o d e l s
In this section, we estimate models in section III using prefectural data. Except
for dependent and independent variables in models, we use the following data associo-economic characteristics; percentage of population aged 0 to 14 (PC14),
percentage of population aged 65 and over (PC65), rate of increase in population(INCPOP), rate of increase in gross prefectural domestic expenditure (at constantprices) (GROWTH), share of gross prefectural domestic expenditure of the primaryindustry (IND1), share of gross prefectural domestic expenditure of the secondary
industry (IND2), rate of change in land price at residential sites (LAND), ratio ofhigh school graduates who advanced to schools of higher grades (ADVANCE), area
(AREA), active job openings ratio, and financial capability index (in prefectural
finance). We don’t report estimates with insignificant coefficients.
Considering the budget process of the local government and the Japanese local
tax system, we use the data of the regressand (local expenditure) in the year, butthat of the regressors (median income, and so on) in the last year.12
Table 2 shows the results of estimation of model (A)~(C) using the data from the1984 National Survey of Family Income and Expenditure, the 1989 National Surveyof Family Income and Expenditure, the 1992 Employment Status Survey, and the1993 Housing Survey of Japan. There is no doubt that estimated coefficients differ
widely from each other, as median income is estimated using different surveys.
However the sets of estimates in Table 2 are close. Therefore it is robust.
First, from estimates of model (A) in Table 2, we obtain the result that eachcoefficient is significant in 1984 and 1989, but one of ln w is not significant in 1992
and 1993. Furthermore parameter b, denotes labor share in the production functionof local public good, is more than 1 in 1984, 1989, and 1993. In this sense, model (A)is not valid for the demand function of local public goods.

12 In Japan, every fiscal years start from March. The budget in the year begin to formulate inAutumn in the last year.

12Second, see the result of estimating the model (B). In each year, all coefficientsare significant and well-behaved, and the model has good fitness. Thus there is no
doubt that we can adopt the model as demand function of local public goods.
Finally, we find that in model (C), there is not a significant coefficient in every
year. Especially, the coefficient of lnY and ln w characterizing model (C) is not
significant. We reject model (C) as demand function of local public goods.
Let us consider the implication of the result obtained in model (A) and (C).
Minimizing the cost of production of local public goods is assumed in these models.
On the contrary, model (B) is not imposed on it. If provision of the local public goods
is not efficient (minimizing the cost), these models may be rejected. Considering the
known facts of local governments in Japan, this interpretation is plausible.
The result of model (B) leads to the conclusion that the median voter hypothesis
is supported in Japanese prefectural expenditure. Because parameters concerning
the median voter are significant and valid economically in model (B). Furthermore
this result is robust for it obtains estimation in 1984, 1989, 1992, and 1993, derived
from various statistics.
Additionally, we try to test whether the estimation of this model by OLS is correct.
we use Hausman (1978) test. The null hypothesis is that the independent variablesin the equation are exogenous variables, that is, the least square estimators are
BLUEs. From the result shown in Table 3, the null hypothesis cannot be rejected inevery year. Therefore it is necessary for us to use the instrumental variable
estimation, and so on when we estimate this model.
V I . S up e r i o r i t y o f M e d i an I nc o m eThus we explain the median voter hypothesis holds good in Japanese prefectures.
Until now, researchers on local expenditure in Japan have not used median income
but mean income (per capita income). We can not yet conclude that median income
is more powerful than mean income as an explanation of local spendings. As Mueller(1989) suggests, whether median income is better than mean income in order toexplain local expenditures depends on the differences between each other. The

13

separation is shown in Table 1. This implies that estimation using mean income is
not appropriate to the test on the hypothesis. To see it in Table 1, however, is notadequate to judge its superiority. Let us test it using the method introduced by
Pommerehne and Frey(1976).
Pommerehne and Frey(1976) estimate separately using median and mean income
from the same data set (in Switzerland). They appreciate the superiority for the
explanation by comparison of fitness and estimates between median and mean.
They conclude that the former is superior to the latter as the explanation of local
spending, because t-value of the coefficients and coefficient of determinants arealmost higher in the model using median income than using mean income.
In this paper, we adopt the method of their test, the estimation using mean
income is as follows: in model (B), we substitute mean income ( Y ) and its tax share( t ) into median income ( Y m ) and its tax share ( t m ) respectively. The result on
estimation of demand function of local public good is shown in Table 4. This mean
income is the one (levied national and municipal taxes) shown in Table 1. 13 From
the report in Table 4, the coefficient of lnY is not significant in 1984, 1989, and 1992,
and its t-value is lower than that of lnY m shown in Table 2 (p-value of lnY is 0.029
and that of lnY m is 0.0021) in 1993.
Furthermore, we directly test whether median income is better than mean
income in order to explain local expenditures. We use J test introduced by Davidson
and MacKinnon (1981). This specification test is as follows. We first set the
hypotheses;
H0:

ln E j = ln A0′′+ γ 0 (η 0 + 1) ln N j + η 0 ln{t mj (1 − m j )} + δ 0 ln Yjm ,H1:

ln E j = ln A1′′+ γ 1 (η1 + 1) ln N j + η1 ln{t j (1 − m j )} + δ 1 ln Yj ,where

A′′ ≡ Aq η +1 .

Suffix 0 or 1 denotes the parameter under the hypothesis 0 or 1. Next, we estimate

13

Many previous studies in Japan are often used per capita prefectural income as mean

(average) income. In our analysis, however, we use the mean income derived from the same
samples (statistics), in order to compare with the result using the median income in section V.

14

these models (hypotheses). Then we define
E 0 ≡ ln A$ 0′′+ γ$ 0 (η$ 0 + 1) ln N j + η$ 0 ln{t mj (1 − m j )} + δ$ 0 ln Yjm ,E1 ≡ ln A$1′′+ γ$ 1 (η$ 1 + 1) ln N j + η$ 1 ln{t j (1 − m j )} + δ$ 1 ln Yj .
Overscript ^ denotes the estimator of the parameter. Finally, we estimate for thistest
ln E j = ln A0′′+ γ 0 (η 0 + 1) ln N j + η 0 ln{t mj (1 − m j )} + δ 0 ln Yjm + λE1 + ε 0 j ,ln E j = ln A1′′+ γ 1 (η1 + 1) ln N j + η1 ln{t j (1 − m j )} + δ 1 ln Yj + ωE 0 + ε 1 j ,where e0 and e1 denote the error terms, and l and w denote the parameters. If the
hypothesis l= 0 is not statistically rejected in the upper equation, H1 is statisticallyrejected by H0. Similarly if the hypothesis w= 0 is not statistically rejected in thelower equation, H0 is statistically rejected by H1. In Table 5, we have t-value of l orw, and p-values (probabilities) that it is incorrect that the hypothesis l= 0 or w= 0 is
statistically rejected. From the p-values shown in Table 5, the probability ofrejecting the mean income‘s model is higher than the probability of rejecting themedian voter’s model in every year.
Therefore median income is better than mean income as the regressor of local
expenditures in Japan. Incidentally, the coefficient of lnY is negative in every year.
14VII.
II. Conclusion
We show, from what has been said above, that the median voter hypothesis is
supported in Japanese prefectures on the assumption that median income identifies
median voter. Its interpretation is, however, totally different from a decentralizedcountry like the U.S.. In a decentralized local finance system, the result supporting
the hypothesis is interpreted to choose the optimal level of local spending for the
median voter in their jurisdiction.

14 Income elasticity d becomes negative in this result. This implies that local public good isinferior good.

15

On the other hand, in a centralized system such as Japan, the result cannot begiven the same interpretation as above. In Japan, local governments cannot hardly
decide local taxes and expenditure for some purposes freely. It is the central
government that substantially controls them. Hence the following explanation isvalid under the present institution of politics and public finance. The central
government distributes interregional grants to each local government to reflect theresult of local elections (preference of median voter in the jurisdiction), even if local
governments impose financial constraints. If the central government ignores the
local election (and preference of median voter as well), the incumbent governor may
not be reelected, and governors (winners) may change every election. There havebeen, however, many reelected governors several times. Shown in Table 6, the shareof governors who have not been reelected for some reason are only about 25% of all
governors in Japan. This fact supports the median voter hypothesis.
In the conclusion, we should note the following. We posit in these models thateach household-voter is only interested in the quantity of local public good (Total
Expenditure). However we have no stylized evidence that this assumption is correct.
In order to test the median voter hypothesis, we can use the expenditure for specificpurposes(e.g.

Ordinary

Construction

Works

Expenditure,

Social

WelfareExpenditure, and so on). The spending which becomes an issue in an election is notalways the same in every jurisdiction. In a cross-section analysis, unless we verify it,a test using the specific spending may be incorrect. When the issue in voting is
Ordinary Construction Works Expenditure in one jurisdiction, or Social Welfare
Expenditure in another jurisdiction, the test across jurisdictions using Ordinary
Construction Works Expenditure is not meaningful. Therefore we can avoid thisproblem in testing the hypothesis of total expenditures.

Data Source
rces
Ej : Total Expenditures
Hj : Local Allocation Tax + Local Transfer Taxes16mj : National Government Disbursements / Total Expenditures
Ministry of Home Affairs, “Annual Statistical Report on Local Government
Finance”
Nj : Population
Ministry of Home Affairs, “Basic Resident Registers ”
wj : Average monthly salary of prefectural employees: All occupation
Ministry of Home Affairs, “Survey on Wage of Local Government Employees”
tmj : (prefectural taxes paid by median household / persons per median household) /Prefectural Taxes:
Ministry of Finance, “Ministry of Finance Statistics Monthly,” andMinistry of Home Affairs, “Annual Statistical Report on Local Government
Finance”
Percentage of population aged 0 to 14, and Percentage of population aged 65 andover:Statistics Bureau, Management and Coordination Agency, “Monthly Report on
Current Population Estimates ”
Rate of increase in gross prefectural domestic expenditure (at constant prices),
Share of gross prefectural domestic expenditure of the primary industry, andShare of gross prefectural domestic expenditure of the secondary industry:
Economic Planning Agency, “Annual Report on Prefectural Accounts”
Rate of change in land price at residential site:
National Land Agency, “Prefectural Land Price Survey”
Active job openings ratio:
Ministry of Labor, “Annual Report on Labor Market”
Ratio of high school graduates who advanced to schools of higher grade:
Ministry of Education, “School Basic Survey”
Area (in 1990):
Statistics Bureau, Management and Coordination Agency, “Population
Census”
Financial capability index (in prefectural finance):17

Ministry of Home Affairs, “Financial Index Table by Prefecture”

R e f e r e nc e s
Alesina, A. and D. Rodrik, 1994, Distributive politics and economic growth, Quarterly Journalof Economics 109, 465-490.
Bergstrom, T.C. and R.P. Goodman, 1973, Private demands for public goods, American
Economic Review 63, 280-296.
Borcherding, T.E. and R.T. Deacon, 1972, The demand for the services of non-federal
governments, American Economic Review 62, 891-901.
Davidson, R. and J.G. MacKinnon, 1981, Several tests for model specification in the presence ofalternative hypotheses, Econometrica 49, 781-793.
Denzau, A.T. and R.J. Mackay, 1976, Benefit shares and majority voting, American
Economic Review 66, 69-76.
Doi, T., 1996, Flypaper effect in Japanese urban expenditure, Financial Review (Ministry of
Finance) 40, 95-119 (in Japanese).
Doi, T. and M. Ashiya, 1997, Distribution of interregional grant and government party: National
Government Disbursement and LDP, Japan Center for Economic Research Economic
Journal 34, 180-195 (in Japanese).
Hausman, J.A., 1978, Specification tests in econometrics, Econometrica 46, 1251-1271.
Gramlich, E.M. and D.L. Rubinfeld, 1982, Micro estimates of public spending demand
functions and tests of the Tiebout and median-voter hypotheses, Journal of Political
Economy 90, 536-560.
Mueller, D.C., 1989, Public Choice II, Cambridge University Press.
Perotti, R., 1993, Political equilibrium, income distribution, and growth, Review of Economic
Studies 60, 755-776.
Persson, T. and G. Tabellini, 1994, Is inequality harmful for growth? American Economic
Review 84, 600-621.
Pommerehne, W.W. and B.S. Frey, 1976, Two approaches to estimating public expenditures,
Public Finance Quarterly 4, 395-407.
Preston, I. and M. Ridge, 1995, Demand for local public spending : Evidence from the British

18

Social Attitudes Survey, Economic Journal 105, 644-660.
Romer, T. and H. Rosenthal, 1979, The elusive median voter, Journal of Public Economics 12,
143-170.
Shibata, T. ed., 1993, Japan’s Public Sector: How the Government Is Financed, University ofTokyo Press.
Turnbull, G.K. and S.S. Djoundourian, 1994, The median voter hypothesis : Evidence fromgeneral purpose local governments, Public Choice 81, 223-240.

19

Figure 1
Models in this paper

Demand Side

Supply Side

Modelcongestion

benefit share

(A)

Yes

No

Yes

(B)

Yes

No

No

(C)

Yes

Yes

Yes

Table 1
Median and Mean Income by Prefectures
1984
1989
National Survey of Family Income and Expenditure
National Survey of Family Income and Expenditure(all household including one-person household)(all household including one-person household)Median Income Mean Income Separation(¥10 thousand) (¥10 thousand)(%)
Hokkaido
374.67417.66
10.29
Aomori372.56419.12
11.11
Iwate345.20395.32
12.68
Miyagi
400.62448.37
10.65
Akita
375.92423.92
11.32
Yamagata
396.75453.01
12.42
Fukushima
395.47449.34
11.99
Ibaraki
415.35472.48
12.09
Tochigi
456.35507.22
10.03
Gumma
425.36478.77
11.16
Saitama
449.99507.4411.32
Chiba
458.38522.6512.30
Tokyo
467.17527.67
11.46
Kanagawa
478.79542.89
11.81
Niigata
438.42496.4911.70
Toyama469.00532.57
11.94
Ishikawa
461.41522.6911.72
Fukui
476.54546.67
12.83
Yamanashi
438.09484.88
9.65
Nagano432.35482.5810.41
Gifu
438.76489.45
10.36
Shizuoka
433.34489.27
11.43
Aichi
467.84527.6911.34
Mie435.89489.52
10.96
Shiga
467.39535.8712.78
Kyoto
422.07488.0613.52
Osaka
407.38462.2711.87
Hyogo
436.35492.5811.42
Nara
447.08503.09
11.13
Wakayama
407.11460.57
11.61
Tottori
402.86462.23
12.84
Shimane414.32476.15
12.99
Okayama
406.77463.15
12.17
Hiroshima405.56462.48
12.31
Yamaguchi
388.14437.8011.34
Tokushima
414.42479.62
13.59
Kagawa400.99460.57
12.94
Ehime
364.10410.81
11.37
Kochi
349.35403.03
13.32
Fukuoka
384.08438.0112.31
Saga
380.71434.73
12.43
Nagasaki330.78375.93
12.01
Kumamoto
365.15408.1910.54
Oita
348.19390.27
10.78
Miyazaki312.30358.16
12.80
Kagoshima290.23324.67
10.61
Okinawa
278.85328.2515.05

R-square(Adj.)
0.98900.98550.99130.98020.98010.97680.9781
0.9817
0.99370.98750.96700.97320.9904
0.97680.97750.98550.97230.98150.99110.98950.9877
0.97390.97790.98150.96130.96750.9806
0.98710.98000.98460.98080.98250.98550.97690.98680.98640.98730.9906
0.9942
0.99350.98740.98340.98900.9914
0.99620.9914
0.9948Median Income Mean Income Separation(¥10 thousand) (¥10 thousand)(%)
387.92435.0810.84
395.67446.5011.39
392.71442.9811.35
442.51500.9511.67
422.84478.1911.58
488.94552.6311.53
443.91503.13
11.77
491.33560.6612.37
480.51545.5311.92
450.66511.5811.91
511.24578.5411.63
490.93568.5213.65
443.52536.6217.35
492.58571.95
13.88
462.59524.3311.78
510.01585.7712.93
485.43551.8912.04
510.06589.3013.45
469.49522.7310.18
455.89514.5211.39
475.12545.2612.86
496.92563.1911.77
475.49553.6114.11
479.90558.0914.01
530.45600.4911.66
434.29498.9812.96
439.33508.9813.68
447.34519.9213.96
501.25566.1511.46
382.00446.2414.40
476.88540.4911.77
445.72505.73
11.86
414.20483.0214.25
418.82477.5112.29
410.98466.31
11.87
421.38485.4013.19
444.25500.81
11.29
377.41430.01
12.23
369.37433.41
14.78
386.30441.0112.41
414.01469.5311.82
379.01423.12
10.43
396.28453.4612.61
382.24436.8812.51
350.44400.46
12.49
325.38370.8412.26
324.81
380.22
14.57

R-square(Adj.)
0.9886
0.9776
0.98980.9811
0.97880.9767
0.9766
0.9621
0.96180.98680.9836
0.96360.99090.97590.96920.94530.97200.97110.9871
0.97380.97020.9832
0.97190.95680.98650.95870.98530.97790.9816
0.96600.97700.98080.97520.97090.95880.9736
0.96990.98570.98200.98170.9781
0.9846
0.98420.98190.99190.99200.9939

Table 1 (continued)
Median and Mean Income by Prefectures
1992
1993
Employment Status Survey
Housing Survey of Japan(all household including one-person household)(ordinary household)Median Income Mean Income Separation(¥10 thousand) (¥10 thousand)(%)
Hokkaido343.26436.7921.41
Aomori
325.80417.3321.93
Iwate352.16446.7421.17
Miyagi394.40514.98
23.42
Akita
356.90452.42
21.11
Yamagata
418.98535.71
21.79
Fukushima
393.10505.51
22.24
Ibaraki451.64584.93
22.79
Tochigi
425.97563.0424.35
Gumma
411.76541.8324.01
Saitama
505.28663.0323.79
Chiba
493.08648.9824.02
Tokyo
461.78641.7728.05
Kanagawa
491.43635.04
22.61
Niigata
421.53547.21
22.97
Toyama473.17633.8825.35
Ishikawa
399.72549.9027.31
Fukui
451.11628.77
28.26
Yamanashi
408.26541.96
24.67
Nagano438.13573.9523.66
Gifu
446.58590.0924.32
Shizuoka
468.18617.7524.21
Aichi
465.78619.0924.76
Mie423.09571.8726.02
Shiga
462.25609.8924.21
Kyoto
381.95522.0626.84
Osaka
404.83536.8024.58
Hyogo429.58561.94
23.55
Nara
432.56607.7828.83
Wakayama
353.97471.55
24.94
Tottori
377.83502.8424.86
Shimane343.12454.58
24.52
Okayama
375.42505.7625.77
Hiroshima
390.34508.16
23.19
Yamaguchi
347.52455.4923.70
Tokushima
335.77457.67
26.64
Kagawa381.14511.9925.56
Ehime
308.00401.6223.31
Kochi
293.03389.97
24.86
Fukuoka
336.01447.4024.90
Saga
365.99470.86
22.27
Nagasaki307.23402.3523.64
Kumamoto
313.49421.0825.55
Oita
302.45400.2824.44
Miyazaki
301.08393.97
23.58
Kagoshima
257.39338.8924.05
Okinawa
259.67340.9623.84

R-square(Adj.)
0.95900.9562
0.94800.94510.92910.91960.94020.92750.91680.93320.91970.93430.96350.96310.91770.90770.91940.89620.93520.92700.93190.94030.94400.93480.91180.93680.94700.94890.9196
0.94770.92000.91730.9341
0.94940.93530.95200.93150.96070.95850.94900.9407
0.95340.94400.94880.95850.96380.9720Median Income Mean Income Separation(¥10 thousand) (¥10 thousand)(%)
333.58416.81
19.97
304.17378.9419.73
326.23403.2019.09
358.83453.1620.82
331.36407.01
18.59
372.26460.7319.20
352.74440.8919.99
403.93510.3620.85
398.09504.4421.08
373.56475.8821.50
452.04574.6321.33
456.81588.5422.38
417.85560.5725.46
469.13608.7622.94
383.02478.1519.89
411.66519.5020.76
375.85485.9022.65
402.60521.3922.78
356.45457.5722.10
377.49475.2820.58
397.37504.8721.29
421.38533.4321.00
421.18545.7622.83
381.20494.0622.84
429.55546.8321.45
360.70480.2524.89
375.94490.3023.32
397.91515.3022.78
426.39565.5724.61
316.63412.8023.30
343.04441.2822.26
333.35423.5021.29
351.84451.7722.12
361.88466.9622.50
327.95415.5221.07
297.95391.9723.99
344.57444.8422.54
292.94373.3521.54
269.21352.6623.66
323.75418.7622.69
339.01424.6120.16
306.01
384.1420.34
305.91
393.1622.19
296.51378.7421.71
275.52350.3821.37
242.65313.1322.51
229.94298.4922.97

R-square(Adj.)
0.96990.9721
0.96850.96200.96690.95640.9635
0.94300.9534
0.95430.93900.94400.96860.95000.95100.94180.94980.94870.9514
0.94770.9492
0.94990.9461
0.94420.92790.95010.96000.95390.94220.96370.95580.95750.94950.95180.9546
0.96370.95600.9661
0.96950.96230.96490.97030.96890.96200.9714
0.97320.9837

Table 2

Estimation of Models using OLS
Dependent Variable :

Year
Model
Intercept

ln w
ln N

ln{t m (1 − m)}
lnY m

(A)

1984
(B)

-12.752(-1.777)
1.492(2.636)0.363(3.097)-0.331(-2.960)
0.847(3.532)1.577(0.985)0.260(2.325)-0.500(-4.784)
1.200(4.432)

4.065(5.852)4.406(7.842)-0.012(-5.123)-0.033(-2.499)-0.013(-5.813)

lnY

AREA

ln E

1989
(B)

(C)

(A)

-13.787(-1.965)
1.567(2.886)0.361(3.253)-0.333(-3.102)
1.156(2.781)-0.293(-1.078)
4.000(6.104)-6.836(-2.292)
2.253(3.683)0.299(2.185)-0.408(-3.163)
1.233(3.741)0.248(2.032)-0.489(-4.374)
1.110(3.514)4.114(5.734)4.781(6.897)-7.026(-2.379)
2.017(3.251)
0.272(2.075)-0.433(-3.465)0.996(1.939)0.450(0.887)3.754(5.017)-0.012(-5.123)-0.030(-2.083)-0.010(5.224)-0.0092(-4.129)-0.010(-4.069)

0.045(-4.064)

0.037(4.324)0.049(5.595)-0.0053(-2.122)0.770(0.501)

(C)

IND1
IND2
PC14
PC65

0.041
(3.870)-0.0067(-2.925)

ADVANCE
LAND-0.0037(-2.485)

INCPOPGROWTH

0.013(2.180)

NOB
R2

47
0.976

0.013
(2.087)

47
0.972

47
0.976

47
0.973

47
0.969

47
0.975

-0.489(0.000)1.110(0.001)
0.486(0.001)-0.433(0.001)1.446(0.569)0.479(0.000)1.758(0.380)3.560(0.003)the above parentheses indicate the t-values using White's consistent covariance

η
δ
γ

α
β

-0.331(0.005)0.847(0.001)
0.543(0.000)2.231(0.003)-0.500(0.000)1.200(0.000)0.520(0.000)-0.333(0.003)0.862(0.028)0.542(0.000)1.734(0.301)
2.352(0.002)-0.408(0.003)1.233(0.001)
0.505(0.000)3.807(0.004)these parentheses indicate the p-values of the hypothesis: the parameter is equal to zero

Table 2 (continued) Estimation of Models using OLS
Dependent Variable :
Year
Model
Intercept

ln w
ln N

ln{t m (1 − m)}

lnY m

(A)

1992
(B)
1.968
(1.870)

1993
(B)

(C)

(A)
-2.108(-0.853)
1.042(1.156)0.413(3.634)-0.358(-3.020)0.720(2.405)-0.173(-0.085)

5.883(10.920)

4.657(6.822)

1.211(0.546)0.272(0.352)0.262(2.799)-0.443(-4.627)
0.918(4.087)0.258(3.016)-0.453(-5.677)
0.936(4.614)6.431(7.966)6.367(8.240)0.920(0.394)0.305(0.397)0.264(2.746)-0.440(-4.499)0.853(3.318)0.103(0.511)
6.459(7.885)-0.0056(-2.306)-0.0057(-2.390)-0.0058(-2.297)

0.033(6.670)0.033(6.871)

0.034(6.851)0.070(5.128)-0.014(-2.513)-0.128(-4.101)-0.013(-2.475)-0.132(-4.748)-0.014(-2.272)-0.131(-3.991)-0.037(-2.042)

47
0.977

47
0.977

47
0.976

47
0.967

lnY
AREA

ln E

0.382
(3.044)-0.407(-3.395)
1.096(3.294)

IND1
IND2

(C)
-4.452(-1.438)0.444(0.465)0.306(2.663)-0.486(-3.930)
1.074(3.704)0.464(2.049)4.530(7.424)0.043(3.796)-0.0057(-2.072)

PC14
PC65

0.056
(5.082)0.054(5.443)

47
0.967

47
0.971

-0.407(0.001)1.096(0.002)0.644(0.000)-0.486(0.000)1.538(0.057)0.595(0.000)2.089(0.117)0.863(0.622)ADVANCELAND
INCPOPGROWTHNOB

R

2the above parentheses indicate the t-values using White's consistent covariance

η
δ
γ

α
β

-0.443(0.000)0.918(0.000)0.470(0.000)0.488(0.716)-0.453(0.000)0.936(0.000)0.472(0.000)-0.440(0.000)0.956(0.055)0.472(0.000)1.523(0.607)0.545(0.681)-0.358(0.004)0.720(0.021)0.644(0.000)1.624(0.196)these parentheses indicate the p-values of the hypothesis: the parameter is equal to zero

Table 3

Specification Test
(Hausman Test)

Null Hypothesis:
independent variables are exogenous.
Year Statistics
1984
0.613

p-value
0.736

1989

1.290

0.525

1992

2.402

0.301

1993

0.014

0.907

Table 4
Demand Functions of Local Public Goods Using Mean Income(OLS)
Dependent Variable : ln E

Year

1984

1989

1992

1993

Intercept

5.457(4.387)0.314(2.257)-0.456(-3.250)
0.170(1.105)4.334(6.252)-0.014(-4.560)
0.052(4.071)-0.0087(-3.048)

8.320(7.271)
0.708(15.323)
0.442(3.891)-0.258(-1.076)
5.137(6.664)-0.012(-4.362)0.023(2.518)8.516(10.038)0.717(19.222)0.499(4.057)-0.335(-1.727)
5.198(7.322)-0.013(-4.257)
0.029(4.903)8.080(8.476)0.773(16.595)
0.430(3.333)-0.419(-2.265)
4.045(4.744)-0.011(-3.447)
0.035(3.504)ln Nln{t (1 − m )}

ln Y
AREA
IND2
PC65
ADVANCE
LAND

NOB

R

η
δ
γ

2

-0.0041(-2.785)

47
0.964

47
0.968

47
0.967

47
0.961

-0.456(-3.250)
0.170(1.105)
0.578

0.442
(3.891)-0.258(-1.076)
0.490

0.499
(4.057)-0.335(-1.727)
0.478

0.430
(3.333)-0.419(-2.265)
0.541

Figures in parentheses indicate the t-values using White's consistent covarianceTable 5Specification Test
(J Test)t-value
Hypothesis:
λ=0
ω=0

Year
1984

-0.032(0.975)3.240(0.003)

1989

0.988
(0.329)1.593(0.119)

1992

1.488
(0.145)4.909(0.000)

1993

2.752
(0.009)3.981(0.000)p-values are in parentheses.

Table 6
The Number of Times of Gubernatorial Reelection Until June, 1994
One
Hokkaido
Aomori
Iwate
Miyagi
Akita
Yamagata
Fukushima
IbarakiTochigi
Gumma
Saitama
Chiba
Tokyo
Kanagawa
NiigataToyamaIshikawa
Fukui
Yamanashi
NaganoGifu
Shizuoka
Aichi
Mie
Shiga
Kyoto
Osaka
Hyogo
Nara
Wakayama
Tottori
Shimane
Okayama
Hiroshima
Yamaguchi
Tokushima
KagawaEhime
Kochi
Fukuoka
Saga
Nagasaki
Kumamoto
Oita
MiyazakiKagoshima
Okinawa
Total
Share

Two

1
6
2
1
1
1
1
3
2
2

2
1
1
2

2
1
1
1
1
2
1
2
1
2
3
1
1
2
1
2
1
1

Three
1
2
2

Four
4
1

Six

1
3
1
1
1
1
1
1
4
1
2
3

2
2
1
1
3
1
1
4
1
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
61
27.23

Seven

Eight

Total

2
2
1
1

1
2

1
1
2

2
1

1

1
1
1
2
1
1
1
1
1
2

1

1

1

1
1
2
1
3
1
1

1
1

1

1
1

2
1
2

1
1
1

1
1
1

1
2
2
3
2
1

1
1
2
3

2
1
1
1
1
1

1
1
1

1
1
1

1
1
1

1
2
1

3
2
57
25.45

Five

3
1
48
21.43

34
15.18

Data Source: "Successive Governors in Japan"

1

14
6.25

7
3.13

1
0.45

2
0.89

4
4
5
9
4
4
6
4
5
6
5
6
3
3
7
5
3
5
5
3
5
6
4
3
6
4
5
5
4
3
5
6
4
7
4
6
4
4
5
5
5
5
5
4
5
5
4
224