Discussion Paper No. 627

THE PRODUCTIVITY OF PUBLIC CAPITAL:EVIDENCE FROM
THE 1994 ELECTORAL REFORM OF JAPANDaiji Kawaguchi
Fumio Ohtake
Keiko Tamada

February 2005

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

The Productivity of Public Capital:
Evidence fromthe 1994 Electoral Reform of Japan1
Daiji Kawaguchi2
Fumio Ohtake3
Keiko Tamada4
January 2005

1 We thank Hisahiro Naito and Facundo Sepulveda for their stimulating discus-

sions.
2 Graduate School of Humanities and Social Sciences,
University ofTsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573 Japan; E-mail:kawaguch@sk.tsukuba.ac.jp
3 Institute of Social and Economic Research, Osaka University, 6-1 Mihogaoka,
Ibaraki 567-0047 Osaka, Japan; E-mail: ohtake@iser.osaka-u.ac.jp
4 Faculty of Economics, Fukuoka University, Nanakuma 8-19-1, Jonan, Fukuoka
814-0180 Japan; E-Mail: ktamada@econ.fukuoka-u.ac.jp

Abstract
This paper attempts to estimate the causal effect of public capital stock on
production using Japanese prefectural data. We first articulate the difficultyof consistently estimating the regional-level production function with public capital due to the endogeneity of the public capital stock amount. As
the central government allocates most of the public capital across regions inJapan, the stock amount of public capital could be endogenous because it
could be allocated to either booming regions to support private activity or to
stagnating regions to help them become more productive. The endogeneityof public capital is more serious when local governments make decisions regarding public capital investments, as in the US, because such decisions are
directly affected by local governments’ budgetary constraints.
We need an exogenous variation of public capital investment across regions in order to estimate the causal effect of public capital on production.
Japan’s electoral reform in 1996 offers an exogenous variation of this sort.
The reform drastically changed the distribution of political representation in
the Lower House across regions, and it accordingly changed the allocationof public capital across regions as well. The productivity of public capital
based on this natural experimental identification strategy indicates higher
productivity due to public capital than indicated by the OLS estimation.
JEL Classification: C25

Key Words: Public Capital, Productivity, Political Economy, Instrumental
Variable Estimation.

1

Introduction

Estimates of the productivity of public capital, such as highway, port, water,and sewer systems, are crucial in public policy debates. As of fiscal year 1996
in Japan, about 8 trillion yen has been spent on public investment annually,
while the total government budget has been about 82 trillion yen and the
GNP has been about 500 trillion. Whether this expenditure can be justified
heavily depends on the estimated productivity of public capital.
To facilitate public policy debates, economists have attempted to estimate
the productivity of public capital. For example, Aschauer (1989), Munnell(1990), Garcia-Mila and McGuire (1992), Holz-Eakin (1994), Evans and Karras (1994), and Garcia-Mila, McGuire, and Porter (1996) have attempted
to estimate the public capital productivity for the US. Mera (1973), Asako,
Tsuneki, Fukuda, Teruyama, Tsukamoto, and Sugiura (1994), The Economic
Planning Agency (1997), Iwamoto, Ouchi, Takeshita, and Bessho (1996), andYamano and Ohkawara (2000) did the same for Japan. Identifying the causal
effect of public capital on national or regional production is difficult, however, because the invested amount in public capital is not randomly decided
and is likely to be correlated with a nation’s or region’s economic condition.
Thus, the stock amount of public capital is most likely to be endogenous
in the production function. Previous studies have attempted to deal withthis endogeneity using panel data, but not much variation in public capitalstock remains after partialing out the regional and time fixed effects, and1this small, remaining variation makes a precise inference very difficult.
The purpose of this study is to identify the causal effect of public capitalstock on production, using a recent electoral reform in Japan as a natural experiment that created an exogenous variation of public capital across regions.
The drastic electoral reform of Japan in 1994 changed the regional allocation of both political influence and public capital drastically. We exploit
this exogenous change in public capital allocation to estimate the productivity of public capital. The estimation results indicate that public capitalis modestly productive and suggests a possible downward bias in the OLS
estimation that does not consider the endogeneity of the public capital allocation. A reliable instrumental variable fixed effects estimation is hamperedby possible measurement errors in input amounts.
The rest of this paper is organized as follows. Section 2 reviews theexisting literature and introduces the Japanese political economy of public
capital allocation and the 1994 electoral reform, and its effect on public
capital allocation. Section 3 discusses the empirical methodology, and section
4 describes the data. Section 5 reports the estimation results, and section 6
discusses the results’ robustness. The last section concludes.

2

Background

2.1

The Existing Literature

The estimation of the marginal productivity of public capital in the US was
spurred by Aschauer (1989)’s work, which pointed out that lower produc2

tivity growth in the US during the 1970s is mostly explained by reduced
investment in public capital during that period. Munnell (1990) also reported similar findings. Their studies both were based on macro time-series,and some economists criticized their findings, pointing to the possible endogeneity of public capital because the public capital investment could havebeen hampered by low tax revenue due in the stagnated economy during
the 1970s. Garcia-Mila and McGuire (1992) also found a significant effectof public capital on states’ output based on state-level panel data. However,Holz-Eakin (1994) and Evans and Karras (1994) cast doubt on the results
because such data do not allow for state fixed effects. After allowing forstate fixed effects, they did not find any significant effect of states’ public
capital on states’ output. Garcia-Mila, McGuire, and Porter (1996) also provided a skeptical view on the causal relationship between public capital stock
and production, applying a fixed effects estimation on the first-differenced
data using state panel data. Studies have indicated that allowing for state
fixed effects is important because those states with persistently high levels of
production are more likely to hold higher levels of public capital. This is anatural consequence of the fact that state-level public capital is likely to befinanced through states’ tax revenue in the US. Due to this local government
budget constraint, the OLS estimates are likely to suffer from an upward
bias. After a decade-long dispute, US economists seem to have reached anagreement that the state public capital does not positively affect state pro-3

duction.1 However, it should be noted that there is not much variation inlabor, private capital, and public capital input after state and year fixed
effects are partialed out (Ai and Cassou (1997)).2 .
The estimation of the production function with public capital has attracted economists’ interest for a longer time in Japan than in the US, probably because public capital is centrally allocated by the national government
and the allocation of public capital had been used as a crucial policy instrument to attain “balanced growth” across regions. Mera (1973) estimated theregional production function that includes labor, capital, as well as public
capital, as inputs. Since his classic work, numerous studies have attempted
to estimate the causal effect of public capital stock on production using prefectural data (Asako, Tsuneki, Fukuda, Teruyama, Tsukamoto, and Sugiura(1994), Mitsui and Ohta (1995), The Economic Planning Agency (1997)).
For example, Yamano and Ohkawara (2000) estimated the production function with prefecture fixed effects without year fixed effects, and the elasticityof public capital on production was estimated to be 0.15 with statistical significance. However, in our calculation with prefecture and year fixed effects
based on their data, the significantly positive effect disappears.3 The regres1

Some studies have paid attention to the fact that public capital could affect different
sectors in different ways. See Holtz-Eakin and Lovely (1996) for theory and evidence andChandra and Thompson (2000) for the effect of the interstate highway system on the
different sectors of a regional economy.
2
Ai and Cassou (1997) regressed public capital stock on state and year dummies andobtained R2 = 0.996 using Holz-Eakin (1994)’s data. They found similar results for thedata of Evans and Karras (1994).
3
We thank Norihiko Yamano and Toru Ohkawara for providing us with their data.

4

sion of public capital on time and prefecture dummies renders R2 = 0.994.
This fact by no means implies that Yamano and Ohkawara (2000)’s conclusion was wrong, but it is worth noting that once both year and prefecture
fixed effects are taken into account, empirical studies using Japanese dataalso suffer from the multicolinearity between public capital and state andyear dummies, as articulated by Ai and Cassou (1997).
The above literature review shows the typical robustness-efficiency trade
off that empirical economists face. Researchers can deal with the correlation
between state (prefecture) unobserved heterogeneity and the stock level of
public capital by using a fixed effects estimation; however, the variation of
public capital within a state over time is small. Accordingly, the fixed effects
estimation tends to render imprecise estimates. Thus, to execute a precise
estimation, it is necessary to exploit the variation of public capital acrossregions due to the exogenous shock by the instrumental variable estimation.

2.2

The Political Economy of Public Capital Allocation in Japan and the 1994 Electoral Reform

The electoral reform of Japan in 1994 offers an ideal ground to obtain acrossprefecture exogenous variations of public capital. The electoral reform caused
a drastic change in the distribution of each prefecture’s political representation in the House of Representatives (Lower House), and, accordingly, itchanged the allocation of public capital investment across prefectures due topork-barrel politics, as already pointed out by Horiuchi and Saito (2003) in5the form of the allocation of subsidies from the central government to local
governments. Because subsidies often are tied to public capital investment,
we can expect that the electoral reform created an exogeneous variation of
public capital amounts across prefectures. We use this exogeneous variation
as an instrumental variable to identify the causal effect of public capital on
prefecture production.
In Japan, the central government provides most of the funds for public
capital and allocates it across regions. Although government bureaucrats
draft the fiscal budget plan, politics are involved in the public capital allocation decision-making process.4 Okuno (1988), Okuno, Yakita, and Yagi
(1994) and Yoshino and Yoshida (1988) have shown that the central government mostly has allocated the public capital to rural, less developed areas
in order to attain the goal of “balanced growth” across regions after the mid
1960s. One major reason why rural areas have attracted more public capital
investment per capita than urban areas is the malapportionment of electoral
districts in Japan. Under the electoral system that was used before the 1994
reform, the number of the seats in the House of Representatives based on the
population had been higher in rural areas because the seat allocation had
been relatively fixed while Japan experienced urbanization after World War
II.5 Yoshino and Yoshida (1988) showed that the number of seats per popu4

For a description of the process of how the Japanese government drafts the fiscal budget plan, see Ishi (1996). For evidence of political intervention in the budget’s allocation,
see Meyer and Naka (1998).
5
See Horiuchi and Saito (2003) for evidence.

6

lation positively affected the amount of public capital intended for industrial
purposes that each region received. Meyer and Naka (1999) showed that the
per capita representation of each prefecture determines the amount of subsidy transfer from the central government to the local government. Horiuchi
and Saito (2003) used the more detailed municipal data to show the positiveand significant relationship between the seats per capita and the amount ofsubsidy transfer.
We used the 1994 electoral reform in Japan that conducted drastic reapportionment as a natural experiment.6 The reform applied to the election
system of the House of Representatives (Lower House), while the electoral
system for the House of Councilors (Upper House) stayed constant. Before
the reform, all 500 members of the House of Representatives were electedby a single, non-transferable vote system with multi-member districts. Afterthe reform, 300 members were elected by the single-member district (SMD)
plurality rule, and another 200 members were elected by the proportional
representation (PR) system. For the SMD part, a single seat is allocated toeach of the 47 prefecture and the rest are allocated according to the size ofthe prefecture population. For the PR part, seats are allocated to 11 blocks
proportional to the population of each bloc. The first Lower House election
after the reapportionment occurred in October 1996.
The change of seat allocations across prefectures is tabulated in Table 1.
6

For details of the electoral reform, see Christensen (1994), Christensen (1996), Christensen (1998) and Horiuchi and Saito (2003)

7

The first column tabulates the number of seats assigned for each prefecture
before the electoral reform. The second column tabulates the number ofseats assigned for the SMDs after the reform. The third column tabulates
the estimated number of seats elected by the PR system after the reform.
Seats for the PR system are allocated for 11 blocs, so we allocated the seatsassigned to each bloc using the weight that is proportional to the number ofvoters for each prefecture. The fourth column tabulates the total number ofseats allocated to each prefecture, which is the sum of the third and fourthcolumns. A striking finding is that the total number of seats allocated to eachprefecture did not change much due to the electoral reform, as indicatedby the first and fourth columns. However, the number of seats that are
directly elected by voters changed drastically, due to the electoral reform, as
evidenced by comparing the first and the second columns.
In our analysis, we focus on the change in the number of seats that are directly elected by politicians’ names. This is because those politicians who areelected by their names in their respective electoral districts presumably havea stronger incentive to do pork-barrel politics. In addition, it is widely believed that those Lower House members elected from the SMD have stronger
political influence than those who are elected by the PR system. Reflecting
this widely shared view, those Lower House members who are elected fromthe SMD are called Gold members, while those who are elected from thePR system are called Silver members (Asahi Shinbun (2000) and Yomiuri
Shinbun (2000)).
8

The large change in the number of Lower House members who are directly
elected by their names by prefectures presumably created a large variationin the public capital allocation.

3

Empirical Model

We estimated the standard prefecture-level Cobb-Douglas production function:ln yit = β0 + β1 ln lit + β2 ln kit + β3 ln git + yearβ4 + ci + uit ,(1)

where yit is the gross prefecture domestic product, lit is the total hours
worked defined by person-hour, kit is the service flow of private capital,
and git is the service flow from government capital stock, year is the setof year dummy variables, i is the subscript for prefecture, and t is the subscript for year. The error term consists of time-invariant prefecture effects
ci and idiosyncratic shock to production uit . If the prefecture effects are notcorrelated with explanatory variables, (i.e. E(ci |li , ki , gi , year) = 0, wherexi ≡ [xi1 , xi2 , ..., xiT ]), and the idiosyncratic error term is strictly exogenous(i.e. E(uit |li , ki , gi , year, ci ) = 0), then the OLS estimation renders a consistent estimator.
The first assumption, E(ci |li , ki , gi , year) = 0, is often refuted in empiricalstudies because those regions with high output levels tend to have high levelsof public capital stock through local government budgetary constraints in the
US. This assumption is also likely to be violated in Japan because the central
9government tends to allocate public capital to the permanently stagnating
regions in order to attain “balanced growth.” Reflecting the difference inthe source of the endogeneity of public capital, the OLS estimates are larger
than the fixed effects estimates in the US (Holz-Eakin (1994) and Evans
and Karras (1994)), but the OLS estimates are smaller than the fixed effects
estimates in Japan (Asako, Tsuneki, Fukuda, Teruyama, Tsukamoto, andSugiura (1994) and Yamano and Ohkawara (2000)).
The second assumption, E(uit |li , ki , gi , ci , year) = 0, may also be violated,
although this has not often been pointed out in previous studies. To articulate this point, we assume that the public capital of prefecture i in year t isdetermined as:
ln git = δ0 + δ1 ln lit + δ2 ln kit + δ3 ln yit + zit γ + yearβ4 + αci + vit ,(2)

where z is the vector of instrumental variables that determines the public capital stock, but does not directly determine the output level after conditioning
on ci (i.e. E(uit |li , ki , zi , ci , year) = 0). If α 6= 0 then E(ci |li , ki , gi , year) = 0
is violated because the unobserved heterogeneity that determines prefectures’ output also determines the level of public capital. If δ3 6= 0 thenE(uit |li , ki , gi , ci , year) = 0 is violated because the current shock to production affects the current level of public capital. The coefficient δ3 is expected
to be positive if the public capital investment in region i at year t is limitedby the tax revenue in the same region at the same time. However, if the central government heavily invests in the stagnating regions, δ3 is expected to10

be negative. Under the condition, δ3 6= 0, the productivity of public capital,
which is β3 in (1), is identified only if the instrumental variables exist for
public capital; i.e. γ 6= 0 in (2). The cross-sectional, instrumental variable
estimator is consistent if the instrumental variable is exogenous from prefecture heterogeneity, E(ci |li , ki , zi , year) = 0, and strictly exogenous fromidiosyncratic shock, E(uit |li , ki , zi , ci , year) = 0. The fixed effects instrumental variable estimator is consistent if E(uit |li , ki , zi , ci , year) = 0. Thisimplies that we can obtain a consistent estimator even when uit and git are
correlated, as far as uit and zit are not correlated conditional on li , ki , ci .
The number of Lower House members who are elected by their names
who represent prefecture i in year t is used as the instrumental variable forpublic capital stock in the corresponding prefecture and year. Because we
do not have theoretical guidance of functional form to relate the numberof directly elected members and the log of public capital, we tried several
specifications and decided to directly include the number of members whoare elected by their names as zit in (2).7 The reduction of the total numberof directly elected Lower House members in 1996 might have changed thetotal amount of public capital allocation, but this effect is captured by theyear dummies.
7

Note that this functional form issue is not very important because this is an auxiliary
regression function to attain an instrumental variable estimation of the equation (1).

11

4

Data

We used the aggregate data of 47 prefectures between 1994 and 1998. These
years were chosen in order to include data before and after the electoral
reform. The first Lower House election after the electoral reform took place in
October 1996, and the last election before the reform took place in June 1993.
The effect of reapportionment on public capital allocation presumably started
to appear in fiscal year 1997. Thus, we have three years of observations before
the reform and two years of observations after the reform. We used grossprefecture product (y) as the measure of prefectural value-added product.
These data were taken from Cabinet Office (Each Year). As for person-hourlabor input (l), we multiplied the average number of work hours and thenumber of regular workers taken from Ministry of Labor (Each Year).8 The
private and public capital stock amounts were taken from Doi (2002). These
stock data include the amounts at the end of fiscal year, and the effects ofthe privatization of the telephone, tobacco, and railway public companies(Dendenkosya, Senbaikosya, and Nihon Kokuyu Tetsudo) and the 1995 Kobe
earthquake are adjusted. The number of seats in the Lower House was takenfrom Ministry of Home Affairs (Each Year), which reported the number ofseats for each election year. This is the number of seats elected from themultiple- member districts before the reform and from the single-member
districts after the reform. Because Lower House members who occupied
8

Regular workers (Jōyō Rōdōsha) include all those who work without fixed-term contracts. This definition includes both part- and full-time workers.

12

seats in year t exercised their political influence on the budget plan for the
fiscal year of t + 1, the number of seats in year t − 1 is used to explain the
public capital amount if year t. As we discuss later, controlling for the capitalutilization rate is important, and we used the annual electric power boughtby large- scale buyers reported in Federation of Electric Power Companies ofJapan (Each Year). Table 2 reports the descriptive statistics of the data.
Figures 1 and 2 implement a “visual” IV estimation. Figure 1 plots therelationship between the log of stock amount of public capital and the lagged
number of directly elected members in the House of Representatives, after
adjusting for the log of total hours worked, log capital, and year effects.
This figure shows that the number of seats in the House of Representatives
positively affects the stock amount of public capital. Figure 2 plots therelationship between the regression-adjusted log output and the regressionadjusted lagged number of seats. This figure indicates that the number ofseats positively affects the prefectural output. If the number of seats allocatedto each prefecture affects production only through public capital provision,then the productivity of public capital is the ratio of the slope coefficient of
Figure 2 and the slope coefficient of Figure 1.

5

Results

Table 3 reports the regression results on the determination of public capital allocation across prefectures. In addition to the number of seats in theLower House, the specification includes all the other exogenous explanatory
13

variables in the second-stage regression. Column (1) reports the result of the
OLS regression, and it indicates that 10 seat increase in the directly electedseats in the Lower House results in about a 20 percent increase in public
capital allocation. Column (2) reports the fixed effects result. This result indicates that ten-seat increase in the Lower House increases the public capital
allocation by about 3 percent. This huge drop in the coefficient’s magnitude
implies that the unobserved prefectural heterogeneity that positively affects
public capital allocation is negatively correlated with the number of Lower
House seats. This is not surprising because a large prefecture, in terms ofeither area or population, attracts more public capital and has more seats in
the Lower House, even after controlling for labor and capital inputs. In both
the OLS and fixed effects, the number of seats explains the allocation of public capital across prefectures, and this evidence is consistent with the previous
finding by Horiuchi and Saito (2003). This finding assures that having seatsin the Lower House works as a good instrument for public capital allocation,in that it affects prefectural production only through this allocation.
Table 4 tabulates the estimation results of the prefectural production
function that includes public capital, private capital, and employee-hours as
inputs. Column (1) reports the OLS regression result. In this specification,
prefecture public capital does not significantly explain prefecture production,
but the coefficient for labor is 0.60 and the coefficient for capital is 0.42, which
are standard values in the estimation of the production function.9 The coeffi9

It should be noted that the estimated coefficient for inputs could be biased if the input

14

cient for public capital changes significantly once the possible endogeneity of
public capital is taken care of by an IV estimation, whose result is reported
in Column (2). The result of the IV estimation that uses the lagged number of directly elected seats in the Lower House indicates that a one percent
increase in public capital increases the output by 18 percent, but this effectis not precisely estimated, as indicated by the large standard error. The coefficient for labor input was reduced from the OLS estimate of 0.60 to 0.45
because the public capital amount and the labor input are positively correlated, and the downward bias for the public capital coefficient was canceledby the upward bias for the labor coefficient. If we take this change in thecoefficient seriously, it implies that the unobserved prefecture production heterogeneity and the stock amount of public capital are negatively correlated.
This result is consistent with those of previous studies that have pointed outthat public capital is strategically allocated to Japan’s poorer prefectures. If
only the variation in public capital that is explained by the variation in seat
allocation is used for the estimation, the estimate points to public capital’s
positive contribution to production.
Another strategy to deal with the possible endogeneity of public capital
is to use a fixed effects estimation that allows for the correlation of timeconstant prefecture heterogeneity and explanatory variables, including public
capital. The result of the estimation appears in Column (3). The estimatedamount responds to the regional-level, unobserved technological shock that is not capturedby the year dummies.

15

coefficient for public capital is 0.15 with a standard error of 0.15. Although
this estimate is not precise, this again suggests that the OLS estimate, which
was 0.01, was downward biased. This significant change in the estimatessuggests a negative correlation between the time-constant, unobserved prefecture heterogeneity and public capital. This finding is consistent with thefinding in the IV estimate, and this is probably because public capital investment is distributed toward the poorer prefectures. The coefficients for laborand private capital inputs are both insignificant; this is probably because ofmeasurement errors in these inputs, and thus the attenuation bias becomes
serious in the fixed effects estimation. The results of the fixed effects IV
estimation appears in Column (4). In this estimation, the change in public
capital allocation due to the change in the Lower House seat allocation isused to identify the productivity effect of public capital. In this estimation,
the coefficient for public capital jumps very significantly, but this estimate is
not reliable, as the large standard error indicates. The estimated coefficientfor public capital is not precise because the variation in the change in public
capital due to the change in the number of seats in the Lower House is notlarge.
Overall, we take the cross-sectional instrumental variable estimates as
our preferable estimate because this estimate resolves the endogeneity issue
and the size of coefficients for labor and private capital are sensible. The
fixed effects estimates seem to suffer from an attenuation bias due to possible
measurement errors in the input variables. Although the coefficient for public
16

capital was not precisely estimated in the IV estimation, the result suggeststhat the OLS estimates are downward biased.

6

Discussion

6.1

Productivity or Keynesian Effect?

The discussion so far has assumed that public capital contributes to theprefecture production as an input; however, the traditional Keynesian argument claims that public capital investment stimulates the effective demandand increases production through mobilizing the unemployed resources. The
pure productivity effect of public capital on production can be estimatedby accurately capturing the level of private inputs because the Keynesianeffect operates through a change in the utilization of private inputs. Thus,by controlling for the level of private inputs, we can rule out the Keynesianeffect. However, as is commonly discussed in macroeconomics, measuring theservice flow from capital is very difficult. If the utilization of capital is not
appropriately measured, and a high capital utilization is induced by public
capital investment, then the Keynesian effect is captured as the productivityof public capital. The above discussion is illustrated by using the following production function, which incorporates the utilization rate of private
capital:ln yit = β0 + β1 ln lit + β2 ln(ait kit ) + β3 ln git + yearβ4 + ci + uit ,

17

(3)

where ait is the utilization rate of capital that takes values between 0 and 1,
but this utilization rate is not observed by us. Treating the ait as a part ofthe error term, the estimation equation becomesln yit = β0 + β1 ln lit + β2 ln kit + β3 ln git + yearβ4 + β2 ln ait + ci + uit . (4)If the increase in git is positively correlated with ait through the Keynesianeffect, the OLS estimator of β3 , which attempts to capture the productivity
effect of public capital, is upward biased, given β2 > 0. To reduce thisbias, we use the variation in electricity usage to capture the varying capitalutilization rate, as in Burnside, Eichenbaum, and Rebelo (1996). We assume
that the utilization rate of capital stock is proportional to electricity usageas:ln(ait ) = γ ln(mit ) + vit ,(5)where ait is the utilization rate of capital stock, mit is electricity usage, andvit is an error term that is strictly exogenous from all explanatory variablesin (4) and mit . By substituting this relationship into (3), we obtain:ln yit = β0 +β1 ln lit +β2 ln kit +β3 ln git +β2 γ ln mit +yearβ4 +ci +vit +uit . (6)This model is estimated by OLS, IV, fixed effects, and IV fixed effects procedures, as in the previous model. The results of the first-stage estimation
appear in Columns (3) and (4) in Table 3. The results indicate that the
number of seats in the Lower House is the valid instrument, as it enters theregression significantly, even after controlling for electricity usage. The results of the second- stage regression appear in Columns (5) through (8) in
18

Table 4. The results of the second-stage estimation did not change significantly. The coefficients for private capital have changed slightly from theresults in Columns (1) through (4), but the coefficients for public capital
have not changed much at all. This implies that the utilization of electricity
is not correlated with public capital stock, and the estimated effect of public
capital on production is not through the stimulation of effective demand, as
Keynesians typically presume. Overall, the analysis that attempts to control
for the capital utilization rate by using electricity usage indicates that an increase in public capital increases production through enhancing productivity
rather than stimulating effective demand.

6.2

The Effect of a Large-scale Earthquake

The Kansai area was hit by a large-scale earthquake, called the HanshinAwaji earthquake, on January 17, 1995. The Hyogo prefecture suffered most
severely from the earthquake.10 Although the data used in this study adjust
for the damage on private and public capital, if this earthquake had a negative impact on production that was not captured by the reduced amount of
input reduction, then the productivity effect of public capital can be underestimated because the Hyogo prefecture received a relatively large amountof public capital investment for its infrastructure recovery. To address thispossibility, we implemented the same estimation with a sample that does notinclude the Hyogo prefecture.
10

See Doi (2002) for the extent of the damage.

19

The result of the first-stage regression appears in Columns (5) through(8) in Table 3. The result of the estimation does not change drastically fromthe results that used all of the prefectures as a sample, which are reported inColumns (1) through (4) in the same table. Even after excluding the Hyogo
prefecture, the number of directly elected seats in the Lower House did affectthe amount of public capital formation.
Given this valid instrument, the estimation of the production function
was implemented, treating the public capital amount as an endogenous variable without the Hyogo prefecture. The estimation results of the production
function appear in Table 5. The results of the estimation are virtually thesame as the results without the Hyogo prefecture that are reported in Table
4. The OLS estimates indicate that the productivity of public capital is nearzero. However, once the possible endogeneity of public capital is controlled
for by IV or FE methods, the elasticity of public capital on production isabout 0.2, although the effects are not very precisely estimated. The FEIV
results indicate the very high productivity of public capital, but the standard
errors are too large to make something out of these results. We consider the
cross-sectional IV estimates and panel FE estimates as preferable results andinfer the elasticity of public capital on production to be about 0.2.

7

Conclusion

This paper has estimated the productivity of public capital using the 1994
electoral reform in Japan as a source of exogenous variation of public capital
20

allocation across regions. The estimation of public capital productivity isvery difficult because the public capital amount is endogenous. The 1994
electoral reform in Japan drastically increased the political representation ofrural area and increased the allocation of public capital to rural area due topork-barrel politics. We exploited this exogenous variation of public capitalto estimate its productivity. The OLS estimates that neglect the endogeneity of public capital are downward biased because public capital is allocatedmore heavily to stagnating regions. The IV estimates using the number ofseats allocated to each prefecture as the instrument indicate that public capital is moderately productive. The estimated elasticity of public capital on
production is about 0.2, although the effects are not precisely estimated.
The fixed effects estimation that allows for the correlated heterogeneity withpublic capital turned out to be imprecise because the effect from the measurement errors in public and private capital was exacerbated in the fixed
effects estimation.
Contrary to the widely held belief among the general public and the media that public capital in Japan is not productive, our estimates indicate thatpublic capital is still moderately productive. Public opinion may be subject
to the same sort of bias associated with cross-sectional OLS estimators. Because public capital is more heavily allocated to rural areas where economies
are stagnant, people may misperceive that public capital is not productive.
However, our IV estimates indicated that rural economies might have beeneven more stagnant if they had not received public capital. Our results cau21

tion that future policy discussions on public capital provisions should bebased on the estimation results that pay extra attention to the endogeneityof public capital allocation.

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26

Table 1: Number of seats in the House of Representative before and after the 1994
Electoral Reform
The first election after the reform took place in October 1996.
PeriodBefore the Reform
1995

Electoral
SystemSinglenon-transferable votesystem withmulti-member district.
(Chusenkyo-ku)

Prefecture
Hokkaido
Aomori
Iwate
Miyagi
Akita
Yamagata
Fukushima
Ibaragi
Tochigi
Gunma
Saitama
Chiba
Tokyo
Kanagawa
NiigataToyamaIshikawa
Fukui
Yamanashi
NaganoGifu
Shizuoka
Aichi
Mie

After the Reform
1996
Single-member Proportionally
district (SMD) Representative
plurality rule
(PR) System(Shosenkyo-ku)(Estimates)(Hirei Daihyo)

23
7
7
8
7
7
12
12
10
10
20
19
43
22
13
6
5
4
5
12
9
14
22
8

13
4
4
6
3
4
5
7
5
5
14
12
25
17
6
3
3
3
3
5
5
9
15
5

27

8
2
2
3
2
2
3
3
6
6
6
5
17
7
5
2
2
2
2
6
3
5
10
3

Total

21
6
6
9
5
6
8
10
11
11
20
17
42
24
11
5
5
5
5
11
8
14
25
8

Shiga
Kyoto
Osaka
Hyogo
Nara
Wakayama
Tottori
Shimane
Okayama
Hiroshima
Yamaguchi
Tokushima
KagawaEhime
Kochi
Fukuoka
Saga
Nagasaki
Kumamoto
Oita
MiyazakiKagoshima
Okinawa

5
10
28
19
5
5
4
5
10
13
9
5
6
9
5
20
5
9
9
6
5
9
5

3
6
19
12
4
3
2
3
5
7
4
3
3
4
3
11
3
4
5
4
3
5
3

2
4
13
8
2
2
1
1
3
4
2
1
2
2
1
7
1
2
3
2
2
2
2

5
10
32
20
6
5
3
4
8
11
6
4
5
6
4
18
4
6
8
6
5
7
5

Note: After the electoral reform, 200 members of the Lower House were elected by the
proportionally representative system from 11 blocks. We allocated these seats toprefectures proportionally, to the number of voters in each prefecture that consists of a
block. Because of rounding, the total number of PR seats does not add up to 200.

28

Table 2: Descriptive Statistics
Sample: All 47 prefectures between 1994 and 1998.

Output (Million Yen)
Annual Employee Hours (Million
Hours)
Private Capital Stock (Million Yen)
Public Capital Stock (Million Yen)
Electric Power (Million KWh)
Seats in Lower House Directly Elected

MeanStandard
Deviation

Minimum

Maximum

10182.9

13011.7

1928.680600.9

1571.52

1962.32327.7

12219.9

19474.2
14353.2
5498.98.2

24243.5
12283.95287.96.5

3164.54221.7603.0
2.0

159204.0
68100.025876.0
43.0

Note: N=235. Output and public capital stock are denominated in the 1990 price.
Capital stock is denominated in the 1990 price. Employment indicates the number ofregular workers, including both full- and part-time workers.

29

(1)
OLS

(2)

(3)

Fixed
OLS
Effects
47 prefectures

Fixed
Effects

(4)

OLS

(5)

Table 3: The Determination of Public Capital Assignment across Prefectures
Sample: All 47 prefectures between 1994 and 1998.
Dependent Variable: log (Public Capital)
Model
Sample

(6)

(7)

(8)

Fixed
Effects

0.03

Fixed
OLS
Effects
Without Hyogo

0.20

0.20

0.03

0.03

0.20

0.20

Seats in Lower House Directly

0.03Elected (10 seats) (t-1)
Log (Employee Hours)
Log (Capital)(0.01)
0.08(0.08)
0.11(0.12)-(0.11)
0.78(0.27)-0.18(0.24)-(0.11)
0.74(0.27)-0.13(0.24)-(0.01)
0.09(0.08)
0.12(0.12)-Log (Electric Power)(0.01)
0.08(0.08)
0.11(0.12)
0.00(0.01)
230
-

230
-

(0.11)
0.78(0.27)-0.18(0.24)
0.00(0.03)
0.007
230
0.92
0.007
230
0.92

235
-

(0.01)
0.09(0.08)
0.12(0.12)
0.00(0.01)
235
0.006
235
0.92

(0.11)
0.73(0.27)-0.12(0.25)-0.01(0.03)
0.006
235
0.92

Partial R2 for Instrument
N
R2

Note: Standard errors are in parentheses. Standard errors for the OLS estimation are robust against panel clustering.

30

Log (Public Capital)

Model
Instrument
0.01(0.06)
0.60(0.10)
0.42(0.08)
-

OLS
-

(1)

235
0.99

IV
LaggedSeats
0.18(0.16)
0.45(0.17)
0.45(0.09)
-

(2)

235
-

0.15
(0.15)
0.04(0.10)-0.10(0.24)
-

FE
-

(3)

235
-

FEIV
LaggedSeats
0.64(0.51)
0.03(0.11)-0.16(0.26)-(4)

Table 4: The Prefecture-level Production Function
Sample: All 47 prefectures between 1994 and 1998
Dependent Variable: log (Output)

Log (Electric Power)
235
0.99

Log (Capital)

Log (Employee Hours)N
R2

Note: The same note applies as in Table 3.

31

OLS
-

(5)

IV
LaggedSeats
0.20(0.15)
0.45(0.17)
0.42(0.09)
0.03(0.02)
235
0.99

(6)

0.15
(0.15)
0.04(0.10)-0.11(0.24)
0.01(0.01)
235
-

FE
-

(7)

FEIV
LaggedSeats
0.63(0.52)
0.03(0.11)-0.16(0.26)
0.01(0.01)
235
-

(8)

0.01
(0.05)
0.61(0.10)
0.39(0.08)
0.03(0.02)
235
0.99

Log (Public Capital)

Model
Instrument-0.00(0.06)
0.62(0.11)
0.41(0.09)
-

OLS
-

(1)

230
0.99

IV
LaggedSeats
0.17(0.16)
0.45(0.17)
0.44(0.09)
-

(2)

230
0.68

0.22
(0.14)
0.05(0.10)-0.10(0.24)
-

FE
-

(3)

230
0.67

FEIV
LaggedSeats
0.51(0.40)
0.05(0.10)-0.13(0.25)-(4)

Table 5: The Prefecture-level Production Function
Sample: All Prefectures except for Hyogo between 1994 and 1998
Dependent Variable: log (Output)

Log (Electric Power)
230
0.99

Log (Capital)

Log (Employee Hours)N
R2

Note: The same note applies as in Table 3.

32

OLS
-

(5)

IV
LaggedSeats
0.19(0.15)
0.46(0.17)
0.41(0.09)
0.03(0.02)
230
0.99

(6)

0.22
(0.14)
0.05(0.10)-0.10(0.24)
0.01(0.01)
230
0.68

FE
-

(7)

FEIV
LaggedSeats
0.51(0.40)
0.05(0.10)-0.13(0.25)
0.01(0.01)
230
0.67

(8)

-0.00
(0.06)
0.64(0.11)
0.37(0.09)
0.03(0.02)
230
0.99

Figure 1: Log (Public Capital) and Lagged Number of Seats

Lagged Seats vs. Log(Pub Capital).6
Log(Pub Capital)=0.020 Seats(0.011)

.4
.2
0
-.2

-.4
-5

0
5
10
Regression Adjusted Number of Seats, 1994-1998
log(Pub Capital)

15

Fitted values

Regression adjusted for Log (total hours worked), Log (capital), and year effects

Figure 2: Log (Output) and Lagged Number of Seats

Lagged Seats vs. Log(Output).2

Log(Output)=0.003 Seats(0.003)

.1

0
-.1

-.2
-5

0
5
10
Regression Adjusted Number of Seats, 1994-1998
log(Output)

Fitted values

Regression adjusted for Log (total hours worked), Log (capital), and year effects

33

15