THE REGIONAL ALLOCATION OF PUBLIC INVESTMENT: EFFICIENCY OR EQUITY?*

THE REGIONAL ALLOCATION OF PUBLIC INVESTMENT:EFFICIENCY OR EQUITY?*

Norihiko YamanoSocio-economic Research Center, Central Research Institute of Electric Power Industry,Ohtemachi 1-6-1 7F, Chiyoda, Tokyo 100-8126, Japan. E-mail: [email protected]

Toru OhkawaraSocio-economic Research Center, Central Research Institute of Electric Power Industry,Ohtemachi 1-6-1 7F, Chiyoda, Tokyo 100-8126, Japan. E-mail: [email protected]

ABSTRACT. In this paper we examine the effect of public investment on the regionaleconomies of Japan. The efficient policy for regional allocation of public capital is to investin highly productive regions, whereas the actual policy pursues equity goals by allocatingmore public investment to depressed regions. We determine the effects of this equity-oriented allocation by estimating the aggregate regional production function and calcu-lating the productivity of public capital stock for each region, using a cross-sectionaltime-series data set. Our results show that the marginal productivity of public capital hasrecently declined in most depressed regions, whereas the productivity in developed regions(e.g., Tokyo, Osaka) has increased slightly. We compare alternative policies of allocatingpublic investment and their effects on the regional and national economies using numeri-cal simulations. We then quantitatively describe the trade-off between the efficient andthe equitable allocation of public investment.

1. INTRODUCTION

Public investment affects the regional economy in two ways. The first is theshort-run effect. Because public investment is one of the largest expenditurecomponents of the economy, an increase in public investment directly andindirectly stimulates economic activity. In a period of recession, the governmentincreases the amount of public investment or advances the schedule of invest-ment to supplement the deflationary gap. The second is the long-run effect.Public investment inherently creates public capital such as highways, airports,railroads, and sewage and water systems, and yields from public capital have astrong influence on the productivity of the private sector over time.

Public investment plays an important role in the economy; however, thelong-run effect, which impacts regional as well as national development, has notbeen fully analyzed in many countries due to the lack of regional public capital

JOURNAL OF REGIONAL SCIENCE, VOL. 40, NO. 2, 2000, pp. 205–229

*We thank D. McCarthy, D. Merriman, T. Ohmori, N. Sakashita, and N. Yoshino for theircomments on the earlier versions of this paper. We also acknowledge anonymous referees andK. Hitomi for their helpful comments and suggestions.

© Blackwell Publishers 2000.Blackwell Publishers, 350 Main Street, Malden, MA 02148, USA and 108 Cowley Road, Oxford, OX4 1JF, UK.

205

data. The urbanized regions are usually characterized as having higher produc-tivity and per capita income, while the other regions are characterized as lowerproductivity and income. The lower income regions are given priority to con-struct industrial infrastructure. On the other hand, if the government were toallocate investment to highly productive regions the national economy wouldgrow faster but regional income disparities would increase. In other words,regional allocation of public investment faces a trade-off between efficiency andequity. Thus, the question arises as to what is the best policy for the governmentto allocate its investment? Before making this decision policy makers needuseful information about the regional allocation of public investment, and inparticular its long-term effects. We will analyze those effects by studying theregional production structure.

There are many studies that identify the effects of public capital on thenational economy, but little attention goes to the effects of public capital onthe regional economy. Over the past decade several studies have examined theprovision of public capital and the resulting productivity in the United Statesusing state-level data. Da Silva Costa, Ellson, and Martin (1987) produced theoriginal estimates of public capital and estimated a translog production function.Their result shows that public capital and labor have a complementary relation-ship. Aschauer (1989) empirically demonstrated the effect of public capital onproductivity in the U.S. economy and provided evidence that the decline inproductivity since the 1970s is due to the decline in public investment. Munnell(1990) also found that a decline in public capital investment decreased produc-tivity in the United States. Garcia-Mila and McGuire (1992) empirically showedthe positive contribution of highway and education expenditures in 48 states.However, Holtz-Eakin (1994) presented contradictory empirical evidence usingstate-level and region-level estimations. Garcia-Mila, McGuire, and Porter (1996)examined the effect of public capital on regional economies in detail by testingthe specifications of the production function. Holtz-Eakin and Lovely (1996) alsoexamined that effect using a two-sector model.

In Japan, boosting the regional economy by providing public capital hasbeen an important policy tool since the 1950s because regional development wasa key factor in the process of the postwar reconstruction of the economy. Theequitable policy called “harmonized regional development” has been used sincethe mid-1960s. In the mid-1960s, Fukuchi et al. (1967) developed a multiregionaleconometric model and analyzed the effect of regional public investment andpublic capital for the Economic Planning Agency (EPA) of Japan covering theyears between 1954 and 1963. They developed a comprehensive set of regionaleconomic data, which became a standard data set for Japanese regional economyduring the reconstruction era. Mera (1973) used Fukuchi’s data set and esti-mated a prefectural production function using employment, private capital, andpublic capital. Mera tested various combinations of explanatory variables inproduction functions and derived the marginal productivity of public capital.His study is one of the pioneering works in the field of productivity of publiccapital in Japan and elsewhere. Merriman (1990) also estimated the translog

© Blackwell Publishers 2000.

206 JOURNAL OF REGIONAL SCIENCE, VOL. 40, NO. 2, 2000

production function by using the data set and compared the role of public capitalin Japan’s regions and the U.S.’s states.

Until recently, regional data estimation, especially for public investmentand public capital, had not been executed since the mid-1960s. Ohkawara,Matsukawa, and Onojima (1990) presented the effect of reallocation of publicinvestment in 1970 through 1984 by using a nine-region econometric model.Asako et al. (1994), Ohkawara and Yamano (1995), and EPA (1997) each usedtheir own data sets for Japanese 47 prefectures and estimated the prefecturalproduction function and derived the contribution of public capital.1 Each con-cluded that public capital has a positive effect on the regional economy, althoughthe marginal productivity of public capital has recently declined in manyprefectures, especially depressed prefectures. Mitsui and Ohta (1995) alsoestimated the prefectural production functions, taking into account the spillovereffect of public capital. Japanese prefectures are relatively small in area so theexistence of spillover effects is undeniable. Asako et al. (1994) and Mitsui andOhta (1995) estimated the production function by ordinary least square (OLS)and instrumental variable (IV) methods, and found that there were essentialdifferences in estimated results.

The above studies with the U.S. state and Japanese prefectural data allestimated only the production function and derived the contribution of publiccapital to regional production. On the other hand, Mera (1986) and Merriman(1990) investigated the regional allocation of public capital using data from nineregions in Japan. Mera (1986) found that an egalitarian allocation policy wasfollowed until 1976, but an efficiency-oriented allocation policy was taken after1976. Merriman (1990) simulated the cost of income-equalizing allocations ofgovernment capital using the estimates of production function. His analysissuggested there was an allocation that simultaneously increased aggregate GDPand equalized per capita GDP in the chaotic period after World War II in Japan.However, in his analysis he focused on reallocation of public capital and not onpublic investment. Thus the different levels of public capital for every regionwere achieved instantaneously. In addition, the total amount of public capitalwas not kept constant in his simulation cases. This may be one reason why heinduced an efficient, equity-improving reallocation.

The purpose of this paper is to examine the productivity of public capital in47 prefectures of Japan and to study the effect of allocation of public investmentamong the prefectures through numerical simulations. We not only estimate theaggregate production function at the prefectural level and show the contributionof public capital, but we also analyze the trade-off relationship between effi-ciency and equity by comparing the per employment income and the nationalGDP. In our simulation analysis the prefectural capital is reallocated throughthe change of public investment. The total amount of public investment is keptconstant among different simulation cases. Therefore, the total public capital isindifferent across simulation cases.

1The 47 prefectures are aggregated to 9 regions. See Table A1 for the names of prefectures.


YAMANO & OHKAWARA: REGIONAL ALLOCATION OF PUBLIC INVESTMENT 207

The organization of this paper is as follows. In Section 2 we discuss themethod of data estimation and the economic situation in Japanese prefectures.We estimate the prefectural production function and calculate the marginalproductivity of each production factor in Section 3. In Section 4 we present anempirical test of the relationship between productivity and the allocation ofproduction factors. The simulation results of different regional allocations ofpublic investment (efficient, Rawlsian, equal) are presented in Section 5. InSection 6 we discuss our findings and options for extended analysis.

2. DATA

Before the analysis we briefly explain the characteristics of the data thatwe use in this paper. In Japan, not all regional economic data are officiallyestimated. Although there are plenty of related regional statistics, it is necessaryto compile data from various sources for an appropriate set of estimates. Weconstructed the prefectural production, private capital, and public capital our-selves—first for each of the 47 prefectures from 1970 to 1994, and then aggre-gated into one sector in the following estimation of the regional productionfunction. All data are constant prices expressed at 1990 levels. The totalemployment data for each prefecture is available in the Annual Report onPrefecture Accounts (ARPA).

Production

The annual nominal production (value-added) data of 16 industries arereported in the ARPA; however, real production is not presented and themanufacturing sector is aggregated. Previous studies such as Asako et al. (1994)and Mitsui and Ohta (1995) were obliged to use real expenditures to estimatethe production function instead of using real production. Considering the indus-trial mixture in each prefecture, real production and real expenditures havedistinctly different values. Therefore, we estimated real production using thefollowing procedure. The nominal aggregated manufacturing production wasdivided into 13 industries using the Census of Manufactures. The real produc-tion for each of 13 manufacturing and 12 nonmanufacturing sectors was thenestimated using the value-added deflators for the above 25 sectors reportedin the System of National Accounts (SNA). The agriculture, forestry, andfishery industries are aggregated into one sector in our data set because oftheir small share of GDP (less than 2 percent in the latest national average).Thus, the aggregated production data reflects the prefectural industrialmixture.

Private Capital Stock

Data for private capital stock at the national level by type for 15 manufac-turing and 14 nonmanufacturing sectors are reported in the Gross Capital StockStatistics of Private Enterprises (GSPE), which we set as the control totals forthe regional capital stock. The estimate of capital stock data heavily depends on



the 1970 National Wealth Survey of Japan (NWS), which offers the latestinformation available for both national and regional wealth.2 The capital stocksby industry at the end of 1970 are reported for the nine regions in the NWS.

To obtain the prefectural benchmark stock in each region, we dividedthe 1970 regional capital stock into prefectures using the average share ofprefectural cumulative investment from 1960 to 1970. The prefectural capitalstock by industry was then estimated by adding investment into the previousstock and subtracting the capital consumption. We divide the national invest-ment by industry reported in GSPE into prefectures using the investmentshare information derived from the ARPA, the Census of Manufactures, andthe Statistical Yearbook of Ministry of Agriculture Forestry and Fisheries. Atthe prefectural level, capital stock and investment of the private sector couldbe estimated for 15 manufacturing industries and the aggregated nonmanu-facturing industries. The national rate of capital consumption in GSPE wasapplied to all prefectures for each industry to maintain the aggregationcondition of capital stock.3

Public Capital Stock

To estimate the prefectural public capital we applied the modified per-petual inventory method. In this method public capital is constructed byaccumulating each year’s public capital formation and subtracting the capitalconsumption of previous investment. Again the 1970 NWS was used as thebenchmark for 12 types of public capital.4 The 1970 regional public capitalwas divided by the accumulated public investment share from 1963 to 1970for each region for each type of public capital. The 1970 NWS reported that70 percent of the public capital stock in 1970 was composed of capital that isless than 10 years old; thus using 1963–1970 investment share data isappropriate. The prefectural annual public investment of ARPA is dividedinto 12 types of investment by the share of the Statistics of Public Construc-tion Started and the Annual Statistics on Roads. We assumed the scheduleof capital consumption belongs to the gamma distribution with a mean of 30years and 90 percent of the investment would diminish after 40 years. Weexclude the capital stock of privatized public corporations (Nippon Telegraphand Telephone Corporation and Japan Railway Company, privatized in 1985and 1987, respectively) from our empirical study because our sample periodis from 1975 to 1994.

2Research on the national wealth is one of the major tasks of the EPA; however, the wealthcensus has not been executed for more than 25 years.

3See Ohkawara, Matsuura, and Chuma (1985) for an estimation of both private and publiccapital stock data.

4The 12 types are (1) agricultural, (2) road (national and prefectural), (3) road (toll), (4) portand airport, (5) transportation and telecommunication (former public corporation), (6) transportationand telecommunication (other), (7) road (municipality), (8) park and sewerage, (9) water, (10) socialwelfare, school and hospital, (11) general administration, and (12) landslide and flood prevention.



Prefectural Production and Public Investment

Now, let us briefly review the data for Tokyo, the prefecture with the largesteconomy, and Shimane, part of the Chugoku region, a typical prefecture with asmall economy.5 In 1994 Tokyo had a 17.1 percent share in production, 13.5percent in employment, 15.5 percent in private capital investment, and 9.3 per-cent in public capital investment. In the same year, Shimane had a 0.5 percentshare in production, 0.6 percent in employment, 0.5 percent in private invest-ment, and 0.9 percent in public investment.

Although the share of production and private capital stock increased inTokyo, it is noteworthy that Tokyo’s share of public investment fell from 11.7 per-cent in 1975 to 9.3 percent in 1994. On the other hand, Shimane increased itsshare of public capital investment from 0.8 percent in 1975 to 0.9 percent in1994. The other low-income prefectures tended to receive more public invest-ment relative to developed prefectures. This type of allocation may be one of thefactors contributing to the decrease of the prefectural income disparity.

In Figure 1 we show the distribution of per capita income in 1994. Japaneseprefectures are divided into five classes. In 1994, the lower two classes contained27 prefectures, more than half of the total number of prefectures. On the otherhand, the upper two classes only contained 5 prefectures. The prefectures inKanto and Kansai regions tend to have higher income prefectures (e.g., Tokyoand Osaka).

We can describe the share of production and public investment for twogroups of prefectures: high-income and low-income. In Figure 2 we show thehigh-income prefectures, which consist of prefectures whose per capita incomeis greater than the national average.6 Only in 11 prefectures is the incomegreater than the average income in 1994. The share of public investment in thehigh-income prefectures has been consistently lower than the share of produc-tion by about 10 percent since the mid 1970s.

3. THE PREFECTURAL PRODUCTION FUNCTION WITH PUBLICCAPITAL

We now proceed to the estimation of the aggregate production function. Wedemonstrate the prefectural production structure in Japan by introducing publiccapital into the aggregate production function and deriving the marginal pro-ductivity of public capital. Prefectural production Y is assumed to be a functionof private capital K, labor E, and public capital G. Considering the individualfirm’s production behavior in the agglomeration economy, public capital isassumed to be the surrounding environment.7 Aggregating the production

5See Tables A1 and A2 in Appendix for the other prefectures.6In 1975, 1985, and 1994, 10, 10, and 11 prefectures, respectively, belonged to the high-income

prefecture group.7See Kanemoto, Ohkawara, and Suzuki (1996) for discussions of aggregating individual firm’s

production function with the agglomeration economy.



function across the individual firms the production function can be written ingeneral form as

Yi = F(Ki,Ei,Gi)

Although a variety of functional forms is possible for the regional aggregateproduction function we chose the Cobb-Douglas because of its simplicity andcomparability

(1)

The main scope of this paper is to analyze several allocation policies of publicinvestment so the production functions with flexible form are not introduced.Furthermore, estimates of the Cobb-Douglas production function can be com-pared with the results of many studies using Japanese data.8

Y AK E Gi i i i= α β γ

FIGURE 1: The Income Distribution (1994).

8The elasticities of public capital are estimated at between 0.10 and 0.19 in the recent Japaneseprefectural studies (Asako et al., 1994; Mitsui and Ohta, 1995; Ohkawara and Yamano, 1995).



In Table 1 we show estimates of the production function under variousassumptions about individual prefectural effects. In Model 1 we estimate theCobb-Douglas function using the ordinary least squares method. The parame-ters of the production factors are significant and positive and the coefficient ofdetermination, R2, is sufficiently high. However, the F-statistic under thehypothesis of the different constant term (A) and parameters (B) suggeststhat the individual effects on the constant term or the parameters of theproduction factors should be considered. The fixed-effects model of the Cobb-Douglas function is estimated as Model 2. Again the parameters are signifi-cantly high and positive, but the null hypothesis that the parameters ofproduction factors take the same values across prefectures is rejected at ahigh level of confidence.

Thus, the prefectural individual effects on the parameters of productionfactors should be considered in the private capital, labor, or public capital term.Introducing the prefectural individual effects into all production factors isequivalent to estimating the 47 prefectural production functions separately.Dividing the panel data into prefectures, the desirable sign of parameters forthe public capital term is not generally obtained in low-income prefectures.9

Public capital is not allocated through the profit-maximization behavior of firmsso we assume that the parameters are different among prefectures with respect

9Sometimes the public capital parameter is estimated negatively because some of the de-pressed prefectures receive relatively more allocation of public investment.

FIGURE 2: Production and Public Investment Share in High-IncomePrefectures.



to public capital. The production function with dummy parameters on publiccapital is estimated as Model 3.10

The parameter ratio of private capital to employment in Model 3 is about1:3. This implies that the distribution share of employment is about 75 percent,which is a plausible share often observed in Japanese empirical studies. All ofthe dummy variables are significant at the 0.01 level except for Tottori (γ31)which is significant at the 0.21 level. The elasticities of public capital in Table 2range from 0.156 to 0.190. Because of the different parameter values for publiccapital, the degree of scale economy ranges from 1.245 and 1.279 amongprefectures. Model 3 is the production function that we will use throughout thispaper.

4. REGIONAL ALLOCATION OF THE FACTORS OF PRODUCTION

The parameters of private capital, public capital, and employment acrossprefectures were obtained in the previous panel estimation of the productionfunction, but the productivity of each factor also depends on the endowments offactors. In this section we examine the marginal productivity of each productionfactor.

Marginal Productivity

This subsection calculates the marginal productivity of private capital MPK,employment MPE, and public capital MPG using the estimated parameters ofthe production function obtained in the previous section. In the Cobb-Douglasfunction, the marginal productivity of each factor is defined as the product ofthe coefficient for the production factor and the ratio of production to that factor.In the calculation of productivity, we use the predicted value of production

10Significant and positive coefficients and high R2 values are obtained in the estimates withdummies on private capital and employment. However, the degree of homogeneity is higher thanthat of Model 3.

TABLE 1: Estimates of the Production Functions

Constant Ln K Ln E Ln G Adj-R2 F-statistic

Model 1: No Individual Effects 0.588* 0.402* 0.662* 0.034* 0.988 Fc = 58.94*(8.31) (36.8) (67.4) (2.83)

Model 2: Fixed Effects a 0.300* 0.877* 0.148* 0.998 Fd = 10.81*(20.0) (24.7) (9.17)

Model 3: Dummy on Public Capital –2.775* 0.287* 0.802* b 0.997(–5.65) (19.3) (19.5)

t-ratios in parentheses*: denotes significance at the 0.01 level.a: differ by prefecture. Range from –4.08 to –3.32.b: differ by prefecture. See Table 2.c: null hypotheses (A, B = Ai, Bi)d: null hypotheses (Ai, B = Ai, Bi)Number of observations: 940 (47 prefectures × 1975–1994)



instead of the actual value. Therefore, not only MPG but also MPK and MPE areaffected by our estimation of the prefectural individual effects. The difference inmarginal products among prefectures depends on the level of factors of produc-tion and the prefecture-specific parameter on public capital.

The MPK, MPE, and MPG for some prefectures are shown in Figure 3. Theseindicate that developed prefectures such as Tokyo and Aichi tend to have a higherMPE and MPG. The results of the calculation of the marginal productivity for allprefectures are listed in Table A3.

The variation in MPK is mainly due to differences in the ratio of productionto private capital because the coefficient for private capital is constant acrossprefectures. The MPK has been declining in all prefectures because the accumu-lation of private capital exceeded the growth rate of output. The rate of declinein Tokyo is greater than for other prefectures, implying that the values of MPK

are converging across prefectures. This is because private capital is invested topursue efficiency.

In most prefectures the MPEs have almost doubled since 1975, while theprefectural order of MPE in Figure 3 has not changed. The increasing trend of

TABLE 2: Coefficient for Public Capital Stock in Model 3

Region Prefecture Region Prefecture

Hokkaido Hokkaido 0.148 Kansai Shiga 0.190Kyoto 0.174

Tohoku Aomori 0.166 Osaka 0.156Iwate 0.158 Hyogo 0.163Miyagi 0.166 Nara 0.187Akita 0.165 Wakayama 0.170Yamagata 0.167Fukushima 0.161 Chugoku Tottori 0.184Niigata 0.157 Shimane 0.172

Okayama 0.167Kanto Ibaraki 0.165 Hiroshima 0.167

Tochigi 0.176 Yamaguchi 0.168Gunma 0.171Saitama 0.164 Shikoku Tokushima 0.175Chiba 0.163 Kagawa 0.175Tokyo 0.161 Ehime 0.164Kanagawa 0.163 Kochi 0.171Yamanashi 0.179

Kyushu Fukuoka 0.160Chubu Nagano 0.161 Saga 0.173

Gifu 0.167 Nagasaki 0.169Shizuoka 0.161 Kumamoto 0.165Aichi 0.156 Oita 0.170Mie 0.170 Miyazaki 0.162

Kagoshima 0.162Hokuriku Toyama 0.173 Okinawa 0.183

Ishikawa 0.167Fukui 0.169



MPE implies that the employment growth rate is less than the output growthrate, and labor has become a more scarce resource of production.

The MPG is constantly decreasing in most prefectures, except Tokyo andOsaka. Although most previous studies of public investment at the national levelconclude that the productivity of public capital has continuously decreased, wefound that there is a different trend in MPGs across prefectures. The prefecturaldifference in MPGs is noteworthy because such a difference is not found in MPK

or MPE. The relatively large amount of public investment in less-developedprefectures induces a constantly decreasing trend in MPG. On the other hand,MPGs of the developed prefectures (high-income prefectures) did not decreasein 1980s because they received a relatively small amount of public investmentrelative to their levels of production.

The estimated MPKs and MPGs are examined using a concept from Arrowand Kurz (1970). The necessary condition of maximizing consumer’s utility,which is a function of income and public capital, is violated if the marginalproductivity of public capital is larger than the marginal productivity of privatecapital.11 Comparing the marginal products of private capital and public capitalfor Tokyo, MPG exceeds MPK from the mid-1980s. The shortage of public capital

FIGURE 3: Marginal Productivity.

11Although the proposition of Arrow and Kurz (1970) requires that the production function behomogenous of degree 1, this proposition remains valid when the public capital yields externalities.

(a) MPK (b) MPE (c) MPG



in developed prefectures and the abundant capital in less-developed prefecturesare confirmed by the estimated marginal products.

Marginal Productivity and Factor Augmentation

If the private and public sector pursue efficiency in production, capital andemployment will increase more rapidly in the regions with an inherently highermarginal product. In this subsection we examine whether each factor of produc-tion (Fi,t; i = prefecture, t = year) has been allocated proportionally with respectto the prefectural productivity. We assume that the regional growth rate of afactor is decomposed into the national and regional environments. The nationalenvironment may be written as the average growth rate in the sample period(αF), and the regional environment is represented by the discrepancy in themarginal productivity from the national average productivity ( ). If marginal

productivity across prefectures is the same, the factor of production increasesat the speed of αF

(2)

where is the prefectural discrepancy in MPF. The discrepancy is defined by12

The parameters of above relationship is obtained by the linear least squaresmethod under the parameter restriction of (2). We report the estimates for thethree factors ( K,E, and G ) in Table 3.

The parameters of the constant term, αK, αE, and αG, are positive andsignificant. The estimates of αF demonstrate that the rate of employmentincrease was smaller than the increase in private and public capital for the yearsbetween 1975 and 1994 in Japan. A positive value for βF shows that theprefectures with high marginal productivity obtain more investment and em-ployment. A larger βF implies that a factor is more sensitive to a discrepancy inmarginal productivity. A negative parameter implies that the growth of thefactor of production is independently determined by the marginal productivity.Therefore, the results of estimate show that private capital and employment areallocated according to marginal productivity, whereas public capital is not.

σFi

F F F K E Gi t F F F i ti t, ,,, ,= + =−α β σe j 1 and

σFi

σF

Fj

Fj

jF

j

i t

i t j t

j t

MPF

FMP

F

FMP

,

, ,

,

.

.

≡

−F

HGG

I

KJJ∑∑

∑∑=

=

1

47

1

47

12For discussion of the prefectural discrepancies in factors of production, see Fukuchi andNobukuni (1970), and Sakashita and Kamoike (1973). The discrepancy in this study followsSakashita-Kamoike’s definition where the size effect of prefectures is taken into account bymultiplying the share of factor.



5. SIMULATIONS

In the previous section, we found that public investment is used as a policytool for diminishing prefectural income disparity. Allocating more public invest-ment to one prefecture increases the demand in a specific industry, such as theconstruction industry. In reality, relatively more public investment is allocatedto less-developed prefectures; thus, the government tries to reduce the prefec-tural income disparity.

Alternative Allocation of Public Investment

Using numerical simulations that change the prefectural allocation ofpublic capital we investigate the effect on the prefectural and national economy.The positive effect of public capital on prefectural production is revealed in theproduction function so if more public investment is allocated to a prefecture theproduction increases.

We examine alternative allocations of public investment in the followingnumerical simulations. In all simulation cases, the sum of the prefectural publicinvestment is equal to the actual amount of national public investment AIG

(3)

where IGi is the prefectural public investment and superscripts BA, EF, EQ, andRA are notations that correspond to the base case, the efficient case, the equalcase, and the Rawlsian case in the following simulation analysis, respectively.Adding the new public investment to the previous capital stock, the simulatedpublic capital in prefecture i is calculated.13 We calculate the prefectural pro-duction under the new allocation by substituting the new public capital stockinto Equation (1). The example for the efficient case is written as

AIG IGiB E E R

i

A F Q A==∑ , , ,d i

1

47

TABLE 3: Factor Growth and Marginal Productivitya

Factor αF βF Adj-R2

Private capital 1.0640* 0.0653* 0.99(76.7) (15.0)

Employment 1.0107* 0.0065* 0.99(26.4) (3.5)

Public capital 1.0541* –0.0072* 0.99(116.0) (–7.7)

*: denotes significance at the 0.01 level, t-statistics are in parentheses.a1976–1994, 47-prefecture pooled data

13It is possible to calculate the depreciation of capital under different allocations; however, thecalculated national level of government capital stock would have a different value from the actual.This problem makes the comparison of production between simulation cases difficult, so we keep theexisting public capital stock constant by using the actual capital consumption for every region.



The allocation is repeated from 1976 to 1994 for each simulation case. Inthese simulations the levels of national production and the prefectural incomedisparities are compared over the sample period. The behavior of the publicsector affects that of the private sector and causes the external economy.However, in the following simulations we assume the private capital investmentand labor allocations are not affected by the changes in public capital.

Efficient Allocation

If an efficient allocation of public investment had been achieved, themaximum level of national production may have been obtained. The main ideais that public investment should be allocated among prefectures according tothe magnitude of marginal productivity in each year. The first unit of investmentis given to the prefecture that has the highest MPG.14 Because the productionfunction is well-behaved, the marginal products of public capital decrease withadditional public capital. Initially, only the prefecture with the highest MPGgains investment. When the marginal productivity of the first prefecture dropsto the level of the prefecture with the second highest MPG, the second highestprefecture begins to receive the allocation. The first and second prefectures arethe only ones receiving allocations until the MPG decreases to the level of theprefecture with the third highest MPG. The other prefectures are also allocatedaccording to this rule until the sum of the investment ( ) equals the totalactual national investment (AIG). With this rule, it may happen that someprefectures do not obtain any public investment at the beginning of the simula-tion period because there is a MPG gap across prefectures in 1976.

The example of efficient allocation of public investment is shown in Figure4. In this example, Prefecture 1 gains public investment, then Prefecture 2follows. Prefecture 3 also gains some units of distribution. Before Prefecture 4obtains a share, the total amount of investment is completely allocated to thefirst three prefectures. The prefectures with less marginal productivity do notreceive any distribution of public investment. Consequently, all prefectures thatreceive an allocation of public investment have the same marginal productivity,ρ in Figure 4.

The efficient allocation procedure is repeated for each year from 1976 to1994. Tokyo and Osaka, the two most developed prefectures, are allocated morethan double the base case in 1976 (Figure 5), while no distribution is assignedto 32 prefectures. More (less) investment is allocated to the high (low) produc-tivity prefectures so the productivity decreases (increases) in the high (low)productivity prefectures. Repeating this process, all prefectures begin to obtain

Y AK E GiE

i i iEF F

i= α β γe j

∑ IGEF

14The unit is a sufficiently small amount; it equals one million yen in the following numericalexample where AIG in 1976 is 19 trillion yen.



FIGURE 4: Example of Efficient Allocation.

FIGURE 5: Allocation of Public Investment.



an investment allocation starting in 1983, but the allocation is smaller than thebase case in Iwate and Miyazaki.

Equal Allocation

Next we define another allocation rule: equal allocation per capita. In thissimulation case each prefecture receives a public capital investment allocationexactly proportional to its share of employment. This type of allocation givesmore investment than the base case to the developed prefectures, but less thanthe efficient case, Figure 5. The distribution to prefecture i is given by

Rawlsian Allocation

The actual allocation followed an income redistribution policy; however,there was room to reduce the resulting regional disparities. This allocation rulefollows the Rawlsian distribution criterion, requiring only that the poor receivemore resources than the rich when changing resource allocation.15 The followinginequality relationships satisfy the Rawlsian allocation of public investment

where n is the number of prefectures in the reverse order of per capita income.The Rawlsian criterion only claims an ordinal relationship, not a cardinal

relationship, between investment and income; we thus add another assumptionto obtain the exact amount of investment for the practical numerical simulation.The allocation for each prefecture is inversely proportional to per capita incomeso the highest income prefecture receives the minimum distribution. To derivethe allocation we first define the income deviation index

where (Y/E)Max is the maximum prefectural income among all prefectures.λi is zero in the highest income prefecture whereas the other prefectures

have negative values. We assume that the allocation for a prefecture with incomedeviation index λi is determined by the relation

(4)

IGE

EAIGi

E iQ =∑

IG IG IG

Y E Y E Y E

R RnR

n

A A A1 2

1 2

> > >

< < <

. . .

. . .b g b g b g

λ iiY E Y E

Y E≡

−LNMM

OQPP

b g b gb g

Max

Max

λ iiRIG IG

IG

A

=−Max

Max

15In practice there are many possible allocations that can follow the Rawlsian criterion.



This may be rewritten as

where IGMax is an unknown variable at this stage. From condition (3), AIG isgiven by

(5)

Solving Equation (5) for IGMax and substituting IGMax into Equation (4), weobtain

Figure 6 shows the comparison of accumulated public capital stock underactual, Rawlsian, and efficient allocation for the highest five and the lowest fiveprefectures according to the actual public capital. In the case of efficientallocation, the prefectures that contain large metropolitan areas, such as Tokyo,Osaka, Kanagawa, and Aichi, accumulate more public capital than the actual in1994. Both in the Rawlsian and efficient cases, Hokkaido receives less than halfof the actual allocation, although it has the second highest level of public capital,because it has the greatest area of all prefectures. The prefectures with smallpublic capital tend to receive more public investment in the Rawlsian case, thusthese prefectures except Shiga obtain more than double the actual public capital.The marginal productivity of public capital and income in Shiga is greater thanthe national average primarily because it is a part of Kansai Metropolitan Area.

IG IGiR

iA = −1 λb g Max

AIG IGjj

RA= −=∑ 1

1

47

λd i Max

IG AIGiR i

jj

A =−

−=∑

1

11

47

λ

λ

b g

d i

FIGURE 6: Public Capital of Top 5 and Bottom 5 Prefectures (1994).



Simulation Results

The results of the simulation cases are compared on two different standards:efficiency and equity. Efficiency is described by the national GDP and peremployment income. The other criterion, equity, is represented by the Ginicoefficient (GN) and the coefficient of variation of per capita income (CV). Theequity indices, GN and CV, are weighted by the regional difference index of theconsumer price index (the average of 47 prefectures is normalized to 100).Table 4 shows the GDP, the average per capita income, the GN, the CV, and theprefectural income ratio of maximum to minimum for each simulation case in1985 and 1994.

In the base case, the national GDP in 1994 is 480.2 trillion yen, and theaverage per capita income is 7.40 million yen. The GDP in the equal and efficientcases is greater than the base case by 4.9 and 7.7 trillion yen, respectively.Average per capita income also increases to 7.48 and 7.52 million yen, respec-tively. In the Rawlsian case the national GDP and the average per capita incomedecrease by decreasing the output in developed regions. In the efficient case, 11developed prefectures gain more output than in the base case, with the largestgain going to Tokyo with an increase of 11.6 trillion yen, 13.2 percent over thebase case. However, the simulated outputs in 10 prefectures decrease more than10 percent. Thus, the majority of the prefectures are not able to accomplish theiractual output under the efficient allocation policy.

The simulations have different effects in terms of equity, which can be seenin the coefficient of variation and the Gini coefficient. The income disparityacross prefectures enlarges in the efficient case whereas the Rawlsian caseyields the least disparity. Figure 7 shows the CVs of the actual and simulationcases. There is an improvement in the actual income equality in the beginningof the 1970s. The CV in the base case gradually decrease from the mid-1970s tothe mid-1980s, possibly due to the fact that relatively more public capital isallocated to low-income prefectures than to high-income prefectures. Then, thebase case CV keeps the 0.12 level until the mid-1990s. At the end of simulationperiod, both the CV and the GN reveal that prefectural income disparity isapproximately 50 percent higher in the efficient case than in the base case.

TABLE 4: Simulation Results of Prefectural Allocation of Public Investment

Base Rawlsian Equal Efficient

Year 1976 1985 1994 1985 1994 1985 1994 1985 1994

GDP (Trillion yen) 248.3 351.4 480.2 344.9 461.1 353.6 485.1 355.6 487.9

Average per EmploymentIncome (1000 yen) 4419 5920 7402 5811 7107 5957 7476 5990 7521

Gini-Coefficient 0.089 0.072 0.067 0.057 0.054 0.078 0.076 0.102 0.101Coefficient of Variation(Y/E) 0.157 0.128 0.122 0.104 0.101 0.140 0.140 0.183 0.185

Max/Min (Y/E) 1.77 1.69 1.76 1.69 1.73 1.78 1.89 2.08 2.23



The deviation of national average per capita income from the base case foreach simulation case is described in Figure 8. Compared to the base case, theefficient case has the highest and the Rawlsian case has the lowest income. By1994, the income difference between the efficient and the Rawlsian cases is aboutsix percent.

FIGURE 7: Coefficient of Variation.

FIGURE 8: Per Capita Income Differences.



The prefectural income distributions for the efficient, Rawlsian, and basecases are described in Figure 9. The histogram of the efficient case is the mostdispersed and has a higher degree of positive skewedness than the base case.This implies that a few prefectures gain more output than the base case whereasmost of the prefectures produce less output. The line of the Rawlsian case hasa higher degree of kurtosis so the Rawlsian allocation produces less incomedisparity than the base case.

From the above simulations we conclude that the actual allocation of publiccapital has placed more emphasis on equity than on efficiency and that highernational economic growth could have been achieved by changing the regionalallocation scheme.

6. CONCLUDING REMARKS

We investigate the productivity of public capital and the effect of changingthe allocation of public investment on national economic growth and disparityamong prefectures. Our major findings are summarized in this section. Theprefectural income disparity across the Japanese prefectures has been keptconstant since the mid-1970s under the policy called “harmonized regionaldevelopment.” The output share has increased in the developed prefectures inJapan but the share of public investment has decreased. Our empirical estimateindicates that public investment has not been allocated in accordance withmarginal productivity and that public capital investment is used as a policy toolfor adjusting income inequality. If the central government adopted a policy thatpursued efficiency, the level of national production would be greater than thecurrent level.

FIGURE 9: Income Distribution (1994).



In the numerical simulations, the trade-off relationship between economicefficiency and prefectural equity is quantitatively analyzed. Rawlsian allocationimproves the income disparity but the GDP in 1994 is almost 20 trillion yen(4 percent) less than the actual GDP. The simulation result for the efficient caseallows national production to increase more than 7 trillion yen in 1994. However,the efficient allocation increases prefectural income disparity by more than50 percent in both disparity indices, the coefficient of variation, and the Ginicoefficient. At the same time, the prefectural income ratio of maximum tominimum is also increased.

Although the prefectural allocation of public investment is one of the mostimportant political issues in the budget reform of the central and municipalgovernments, few quantitative economic analyses have been presented. As weinvestigate in our study, the regional allocation of public investment has a stronginfluence on regional economy and income equality, suggesting that this is animportant topic for further study.

The analysis of this paper could be extended in the following ways. The firstextension is to include the behavior of the private sector. Private investment andlabor employment in this paper are treated independently from the prefecturalpublic investment allocation. The allocation of public capital should affect theinvestment of the private sector and employment. The second importantextension is to decompose the aggregate production and build a multisectoralmodel. For example, the effects of the prefectural public capital on manufac-turing and nonmanufacturing industries are very different; this informationwould be useful to policy makers. Another possible extension is to introduce thedifferent types of public capital which we estimated in Ohkawara, Matsuura,and Chuma (1985). Although these extensions would be useful we believe thisstudy alone will contribute to further discussion of the regional allocation ofpublic investment.

REFERENCESArrow, Kenneth J. and Mordecai Kurz. 1970. Public Investment, the Rate of Return, and Optimal

Fiscal Policy. Baltimore: Johns Hopkins University Press.Asako, Kazumi, Jun Tsuneki, Shinichi Fukuda, Hiroshi Teruyama, Takashi Tsukamoto, and

Masanori Sugiura. 1994. “Shakaishihon no Seisanryoku Kouka to Koukyou Toushi Seisaku noKeizai Kousei Hyouka (Productivity of Government Capital and the Welfare Evaluation ofGovernment Investment Policy),” Keizaibunseki, 135, 1–9.

Aschauer, David. 1989. “Is Public Expenditure Productive?” Journal of Monetary Economics, 23,177–200.

Da Silva Costa, Jose, Richard W. Ellson, and Randolph C. Martin. 1987. “Public Capital, RegionalOutput, and Development: Some Empirical Evidence,” Journal of Regional Science, 27, 419–436.

The Economic Planning Agency. 1997. Keizai Hakusho (Economic Survey of Japan). Tokyo: PrintingBureau, Ministry of Finance.

Fukuchi, Takeo and Makoto Nobukuni. 1970. “An Econometric Analysis of National Growth andRegional Income Inequality,” International Economic Review, 11, 84–100.

Fukuchi, Takeo, Masami Yasui, Hiromi Muramatsu, Osamu Takenaka, Masakuni Yasutomi, Hi-royasu Yamakawa, and Yoshie Oka. 1967. “Zenkoku Chiiki Keiryo Moderu no Kenkyu (A Studyon Japan’s Nation-wide Regional Econometric Model),” Keizaibunseki, 18, 1–569.



Holtz-Eakin, Douglas. 1994. “Public Sector Capital and the Productivity Puzzle,” The Review ofEconomics and Statistics, 12–21.

Holtz-Eakin, Douglas and Mary E. Lovely. 1996. “Scale Economies, Returns to Variety, and theProductivity of Public Infrastructure,” Regional Science and Urban Economics, 26, 105–123.

Kanemoto, Yoshitsugu, Toru Ohkawara, and Tsutomu Suzuki. 1996. “Agglomeration Economies anda Test for Optimal City Sizes in Japan,” Journal of the Japanese and International Economies, 10,297–398.

Garcia-Mila, Teresa and Therese J. McGuire. 1992. “The Contribution of Publicly Provided Inputsto States’ Economies,” Regional Science and Urban Economics, 22, 229–241.

Garcia-Mila, Teresa, Therese J. McGuire, and Robert H. Porter. 1996. “The Effect of Public Capitalin State-Level Production Functions Reconsidered,” The Review of Economics and Statistics, 78,177–180.

Mera, Koichi. 1973. “Regional Production Functions and Social Overhead Capital: An Analysis ofthe Japanese Case,” Regional and Urban Economics, 3, 157–186.

———. 1986. “Population Stabilization and National Spatial Policy of Public Investment: TheJapanese Experience,” International Regional Science Review, 10, 47–65.

Merriman, David. 1990. “Public Capital and Regional Output: Another Look at Some Japanese andAmerican Data,” Regional Science and Urban Economics, 20, 437–458.

Mitsui, Kiyoshi and Kiyoshi Ohta. 1995. Shakai Shihon no Seisansei to Kouteki Kinyu (Productivityof Public Capital and Public Finance). Tokyo: Nihon Hyoronsha.

Munnell, Alicia H. 1990. “How Does Public Infrastructure Affect Regional Economic Performance?”New England Economics Review, 11–32.

Ohkawara, Toru, Isamu Matsukawa, and Tomoko Onojima. 1990. “Changes in Regional Economy:Policy Simulations Using CRIEPI Japanese Nine-region Econometric Model (Chiiki Keizai NoKouzou Henka: Dennchuuken Zennkoku Kyuchiiki Moderu Niyoru Yosoku),” Regional ScienceStudies in Japan Section of Regional Science Association International (Chi-iki Gaku Kenkyuu),20, 1–15.

Ohkawara, Toru, Yoshinori Matsuura, and Masahiro Chuma. 1985. “Chiiki Keizai Data no KaihatsuSono 1—Seizougyou Shihon Sutokku to Shakai Shihon Sutokku no Suikei (The Estimation ofRegional Economic Data No.1—Manufacturing Capital and Social Overhead Capital),” CRIEPIReport, no. 585005.

Ohkawara, Toru and Norihiko Yamano. 1995. “Shakai Shihon no Seisanryoku Kouka: Chiki KeizaiHeno Eikyou Bunseki (The Productivity of Public Capital: Effects on the Regional Economy),”Denryoku keizai kenkyuu, 34, 45–58.

Sakashita, Noboru and Osamu Kamoike. 1973. “National Growth and Regional Income Inequality:A Consistent Model,” International Economic Review, 14, 372–382.



APPENDIX

TABLE A1: Production and Employment

Production* (billion yen) Employment (thousand)

Region Prefecture 1975 1994 1975 1994

Hokkaido Hokkaido 10245 (4.3) 17874 (3.9) 2537 (4.7) 2866 (4.4)Tohoku Aomori 2385 (1.0) 4112 (0.9) 701 (1.3) 718 (1.1)

Iwate 2272 (1.0) 4249 (0.9) 730 (1.4) 812 (1.3)Miyagi 3768 (1.6) 7842 (1.7) 943 (1.7) 1184 (1.8)Akita 2072 (0.9) 3559 (0.8) 630 (1.2) 629 (1.0)Yamagata 2111 (0.9) 3773 (0.8) 636 (1.2) 666 (1.0)Fukushima 3528 (1.5) 7186 (1.6) 1034 (1.9) 1157 (1.8)Niigata 4582 (1.9) 8562 (1.9) 1274 (2.4) 1351 (2.1)

Kanto Ibaraki 4323 (1.8) 10274 (2.2) 1105 (2.0) 1464 (2.3)Tochigi 3400 (1.4) 7232 (1.6) 835 (1.5) 1003 (1.5)Gunma 3099 (1.3) 7311 (1.6) 901 (1.7) 1065 (1.6)Saitama 7490 (3.2) 18478 (4.0) 1655 (3.1) 2626 (4.0)Chiba 7363 (3.1) 16859 (3.7) 1476 (2.7) 2192 (3.4)Tokyo 39794 (16.9) 78612 (17.1) 7065 (13.1) 8788 (13.5)Kanagawa 3196 (5.6) 27392 (5.9) 2503 (4.6) 3621 (5.6)Yamanashi 1277 (0.5) 2791 (0.6) 382 (0.7) 448 (0.7)

Hokuriku Toyama 2306 (1.0) 4074 (0.9) 558 (1.0) 604 (0.9)Ishikawa 2187 (0.9) 4088 (0.9) 552 (1.0) 622 (1.0)Fukui 1516 (0.6) 2838 (0.6) 408 (0.8) 458 (0.7)

Chubu Nagano 3722 (1.6) 7334 (1.6) 1073 (2.0) 1229 (1.9)Gifu 3395 (1.4) 6573 (1.4) 915 (1.7) 1055 (1.6)Shizuoka 6844 (2.9) 14445 (3.1) 1754 (3.3) 2143 (3.3)Aichi 14183 (6.0) 30060 (6.5) 3008 (5.6) 4070 (6.3)Mie 3201 (1.4) 5942 (1.3) 773 (1.4) 903 (1.4)

Kansai Shiga 2061 (0.9) 5206 (1.1) 464 (0.9) 594 (0.9)Kyoto 4700 (2.0) 9221 (2.0) 1163 (2.2) 1264 (1.9)Osaka 20481 (8.7) 36720 (8.0) 4076 (7.6) 5078 (7.8)Hyogo 10048 (4.3) 18700 (4.1) 2060 (3.8) 2278 (3.5)Nara 1542 (0.7) 3222 (0.7) 358 (0.7) 498 (0.8)Wakayama 2061 (0.9) 3046 (0.7) 488 (0.9) 506 (0.8)

Chugoku Tottori 1050 (0.4) 1929 (0.4) 316 (0.6) 329 (0.5)Shimane 1267 (0.5) 2165 (0.5) 412 (0.8) 403 (0.6)Okayama 3764 (1.6) 7088 (1.5) 900 (1.7) 970 (1.5)Hiroshima 6097 (2.6) 10223 (2.2) 1325 (2.5) 1485 (2.3)Yamaguchi 3272 (1.4) 5292 (1.1) 773 (1.4) 782 (1.2)

Shikoku Tokushima 1355 (0.6) 2326 (0.5) 391 (0.7) 397 (0.6)Kagawa 1924 (0.8) 3430 (0.7) 490 (0.9) 534 (0.8)Ehime 2692 (1.1) 4584 (1.0) 718 (1.3) 752 (1.2)Kochi 1337 (0.6) 2225 (0.5) 409 (0.8) 406 (0.6)

Kyushu Fukuoka 9213 (3.9) 16901 (3.7) 1987 (3.7) 2364 (3.6)Saga 1379 (0.6) 2568 (0.6) 396 (0.7) 436 (0.7)Nagasaki 2461 (1.0) 4412 (1.0) 685 (1.3) 719 (1.1)Kumamoto 2865 (1.2) 5194 (1.1) 818 (1.5) 910 (1.4)Oita 2044 (0.9) 4034 (0.9) 561 (1.0) 588 (0.9)Miyazaki 1662 (0.7) 2947 (0.6) 526 (1.0) 576 (0.9)Kagoshima 2545 (1.1) 4635 (1.0) 824 (1.5) 830 (1.3)Okinawa 1530 (0.6) 2960 (0.6) 368 (0.7) 504 (0.8)

Total 235609 (100) 460488 (100) 53957 (100) 64877 (100)

(share)*: constant price from 1990



TABLE A2: Private and Public Capital

Private Capital* (billion yen) Public Capital* (billion yen)

Region Prefecture 1975 1994 1975 1994

Hokkaido Hokkaido 10957 (4.3) 30382 (3.5) 13453 (7.5) 43675 (7.7)Tohoku Aomori 1831 (0.7) 7333 (0.8) 2331 (1.3) 7997 (1.4)

Iwate 2178 (0.8) 7734 (0.9) 2530 (1.4) 8412 (1.5)Miyagi 3846 (1.5) 15802 (1.8) 3122 (1.7) 11105 (2.0)Akita 1911 (0.7) 6488 (0.7) 2225 (1.2) 7681 (1.4)Yamagata 1912 (0.7) 6816 (0.8) 2011 (1.1) 7126 (1.3)Fukushima 4000 (1.6) 14804 (1.7) 2853 (1.6) 9718 (1.7)Niigata 5184 (2.0) 16591 (1.9) 4554 (2.5) 14764 (2.6)

Kanto Ibaraki 6437 (2.5) 17706 (2.0) 3448 (1.9) 13242 (2.3)Tochigi 4133 (1.6) 13792 (1.6) 1873 (1.0) 7243 (1.3)Gunma 3750 (1.5) 13461 (1.5) 2247 (1.3) 7293 (1.3)Saitama 8776 (3.4) 29564 (3.4) 5209 (2.9) 18594 (3.3)Chiba 11213 (4.4) 32996 (3.8) 6016 (3.4) 20548 (3.6)Tokyo 26626 (10.3) 135204 (15.5) 21037 (11.7) 52903 (9.3)Kanagawa 17423 (6.8) 49786 (5.7) 7665 (4.3) 27189 (4.8)Yamanashi 1133 (0.4) 5217 (0.6) 1510 (0.8) 4890 (0.9)

Hokuriku Toyama 3611 (1.4) 9926 (1.1) 2130 (1.2) 6153 (1.1)Ishikawa 2148 (0.8) 7619 (0.9) 2175 (1.2) 6299 (1.1)Fukui 2518 (1.0) 7552 (0.9) 1878 (1.0) 5862 (1.0)

Chubu Nagano 3325 (1.3) 14464 (1.7) 3698 (2.1) 13172 (2.3)Gifu 3490 (1.4) 13057 (1.5) 3085 (1.7) 9286 (1.6)Shizuoka 7497 (2.9) 25806 (3.0) 5142 (2.9) 13167 (2.3)Aichi 18885 (7.3) 66219 (7.6) 9960 (5.6) 25726 (4.5)Mie 4517 (1.8) 10893 (1.3) 2861 (1.6) 8356 (1.5)

Kansai Shiga 2980 (1.2) 9228 (1.1) 1287 (0.7) 4517 (0.8)Kyoto 4407 (1.7) 15533 (1.8) 2624 (1.5) 9258 (1.6)Osaka 21572 (8.4) 68536 (7.9) 12701 (7.1) 34736 (6.1)Hyogo 13404 (5.2) 38401 (4.4) 7878 (4.4) 25118 (4.4)Nara 1345 (0.5) 5193 (0.6) 1423 (0.8) 5342 (0.9)Wakayama 3033 (1.2) 7757 (0.9) 1859 (1.0) 5383 (0.9)

Chugoku Tottori 621 (0.2) 2928 (0.3) 1233 (0.7) 4002 (0.7)Shimane 896 (0.3) 4138 (0.5) 1460 (0.8) 5169 (0.9)Okayama 6422 (2.5) 15000 (1.7) 2817 (1.6) 10366 (1.8)Hiroshima 7067 (2.7) 19875 (2.3) 4168 (2.3) 13980 (2.5)Yamaguchi 4841 (1.9) 12240 (1.4) 2353 (1.3) 7747 (1.4)

Shikoku Tokushima 1451 (0.6) 4265 (0.5) 1677 (0.9) 4703 (0.8)Kagawa 2497 (1.0) 7152 (0.8) 1385 (0.8) 5009 (0.9)Ehime 3858 (1.5) 9619 (1.1) 2063 (1.2) 7157 (1.3)Kochi 1257 (0.5) 4128 (0.5) 1618 (0.9) 5299 (0.9)

Kyushu Fukuoka 10636 (4.1) 33686 (3.9) 5818 (3.2) 18898 (3.3)Saga 1364 (0.5) 4920 (0.6) 1614 (0.9) 5354 (0.9)Nagasaki 2084 (0.8) 7972 (0.9) 2264 (1.3) 7758 (1.4)Kumamoto 2621 (1.0) 10058 (1.2) 2398 (1.3) 8527 (1.5)Oita 3087 (1.2) 8880 (1.0) 2132 (1.2) 6662 (1.2)Miyazaki 1766 (0.7) 6429 (0.7) 1980 (1.1) 6585 (1.2)Kagoshima 1943 (0.8) 9326 (1.1) 2762 (1.5) 9946 (1.7)Okinawa 953 (0.4) 5048 (0.6) 751 (0.4) 7061 (1.2)

Total 257404 (100) 869523 (100) 179279 (100) 568980 (100)

(share)*: constant price from 1990



TABLE A3: Marginal Productivity

MPK MPE(million yen) MPG

Region Prefecture 1975 1985 1994 1975 1985 1994 1975 1985 1994

Hokkaido Hokkaido 0.27 0.20 0.17 3.25 4.33 5.07 0.11 0.08 0.06Tohoku Aomori 0.35 0.23 0.16 2.52 3.63 4.58 0.16 0.10 0.09

Iwate 0.28 0.20 0.15 2.36 3.27 4.02 0.13 0.09 0.08Miyagi 0.27 0.19 0.15 3.10 4.37 5.49 0.19 0.14 0.12Akita 0.30 0.20 0.15 2.55 3.58 4.45 0.15 0.10 0.08Yamagata 0.31 0.21 0.16 2.58 3.62 4.55 0.17 0.11 0.09Fukushima 0.26 0.18 0.14 2.81 3.90 4.88 0.20 0.14 0.12Niigata 0.26 0.19 0.14 2.95 3.97 4.91 0.16 0.10 0.09

Kanto Ibaraki 0.21 0.19 0.16 3.46 4.56 5.47 0.23 0.14 0.12Tochigi 0.25 0.20 0.15 3.43 4.75 5.95 0.34 0.21 0.18Gunma 0.27 0.19 0.15 3.12 4.31 5.33 0.27 0.19 0.17Saitama 0.25 0.23 0.19 3.69 4.74 5.88 0.24 0.18 0.17Chiba 0.19 0.18 0.15 4.06 5.11 6.25 0.20 0.15 0.14Tokyo 0.43 0.28 0.19 4.52 6.15 8.02 0.30 0.27 0.27Kanagawa 0.22 0.20 0.18 4.36 5.54 6.73 0.29 0.21 0.18Yamanashi 0.33 0.21 0.16 2.75 3.99 5.10 0.16 0.12 0.10

Hokuriku Toyama 0.19 0.15 0.12 3.46 4.49 5.47 0.19 0.14 0.12Ishikawa 0.29 0.21 0.16 3.14 4.27 5.31 0.17 0.13 0.11Fukui 0.18 0.13 0.11 3.09 4.12 5.02 0.14 0.10 0.08

Chubu Nagano 0.32 0.20 0.15 2.75 3.92 5.01 0.16 0.12 0.09Gifu 0.29 0.21 0.15 3.06 4.10 5.23 0.19 0.14 0.12Shizuoka 0.28 0.21 0.16 3.34 4.34 5.32 0.23 0.19 0.17Aichi 0.23 0.17 0.14 3.98 5.14 6.23 0.23 0.19 0.19Mie 0.22 0.18 0.16 3.51 4.40 5.26 0.20 0.15 0.12

Kansai Shiga 0.22 0.19 0.15 4.00 5.34 6.70 0.34 0.24 0.21Kyoto 0.32 0.23 0.17 3.34 4.64 5.88 0.32 0.22 0.17Osaka 0.27 0.21 0.17 4.04 5.17 6.31 0.25 0.20 0.18Hyogo 0.23 0.19 0.14 4.23 5.38 6.78 0.23 0.15 0.13Nara 0.31 0.24 0.20 3.24 4.56 5.73 0.19 0.14 0.12Wakayama 0.18 0.14 0.12 3.17 4.12 4.94 0.18 0.12 0.10

Chugoku Tottori 0.46 0.28 0.19 2.50 3.75 4.81 0.15 0.11 0.09Shimane 0.38 0.23 0.16 2.30 3.46 4.46 0.14 0.10 0.07Okayama 0.18 0.16 0.13 3.61 4.64 5.65 0.24 0.14 0.11Hiroshima 0.24 0.20 0.16 3.63 4.70 5.85 0.24 0.16 0.13Yamaguchi 0.19 0.15 0.12 3.36 4.40 5.34 0.23 0.14 0.11

Shikoku Tokushima 0.27 0.20 0.15 2.83 3.78 4.61 0.14 0.10 0.08Kagawa 0.22 0.17 0.14 3.06 4.18 5.09 0.24 0.14 0.12Ehime 0.20 0.16 0.13 2.95 3.82 4.66 0.21 0.13 0.10Kochi 0.30 0.21 0.16 2.55 3.55 4.41 0.14 0.09 0.07

Kyushu Fukuoka 0.24 0.18 0.15 3.58 4.86 5.82 0.24 0.16 0.15Saga 0.28 0.19 0.15 2.69 3.77 4.70 0.14 0.10 0.08Nagasaki 0.32 0.22 0.16 2.73 3.84 4.90 0.17 0.12 0.10Kumamoto 0.30 0.20 0.15 2.67 3.83 4.74 0.19 0.13 0.10Oita 0.21 0.15 0.12 3.18 4.23 5.19 0.18 0.12 0.10Miyazaki 0.26 0.17 0.13 2.40 3.37 4.15 0.13 0.09 0.07Kagoshima 0.36 0.21 0.15 2.39 3.62 4.60 0.14 0.10 0.08Okinawa 0.34 0.28 0.20 2.45 4.14 5.60 0.27 0.12 0.09



Documents

THE REGIONAL ALLOCATION OF PUBLIC INVESTMENT: EFFICIENCY OR EQUITY?*