Discussion Papers In Economics
And Business

Efficient Scale of Local Government in China:
Quantile Regression Approach to County-Level Data

Mototsugu FUKUSHIGE and Yingxin SHI

Discussion Paper 14-15

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANEfficient Scale of Local Government in China:
Quantile Regression Approach to County-Level Data

Mototsugu FUKUSHIGE and Yingxin SHI

Discussion Paper 14-15
April 2014

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANEfficient Scale of Local Government in China:
Quantile Regression Approach to County-Level Data*

Mototsugu FUKUSHIGE†

andYingxin SHI‡

Abstract
We investigate the effects of urban and rural populations and area sizes on the expendituresof the prefecture-level local government. We found the following three results. The first
relates to the expenditure for urban populations. At around 220,000 people, per capita local
government expenditure is minimized in our simulation. The second is that the expenditure
for rural populations is proportional to the population size. The third finding is that theexpenditure in accordance with the areas is also proportional to the area size. This cost
structure is the reason why China’s recent rapid urbanization increases prefectural
government’s fiscal distress.

JEL Classification: H40, H72, R51
Keywords: Efficient scale, Local government, Quantile regression, China*

Shi is grateful to SEAC (2013-GM-022) and DLNU (ZJ13RWYB002) for their financial
support of the joint research on this topic with Fukushige. Fukushige is grateful to the Japan
Society for the Promotion of Science (Grant-in-Aid for Scientific Research A 23243038) for
their financial support.
†

Graduate School of Economics, Osaka University
1-7, Machikaneyama-cho, Toyonaka, Osaka 560-0043, Japan
E-mail address: mfuku@econ.osaka-u.ac.jp
Phone & Fax: +81-6-6850-5248 (M. Fukushige).
‡ Department of Economics & Management, Dalian Nationalities University
18, Liaohe West Road, Jinzhou New Area, Dalian 116600, China
E-mail address: yxshi2002@163.com
11. Introduction
China has five layers of government including the central government. Eachlevel of government, except the central government, receives financial transfers from thehigher ranks of government and distributes the financial transfers to the lower levels ofgovernment. This system has operated since China’s national foundation. As for the tax
collection system, the tax contracting system changed to the tax sharing system in 1994.
In addition to these tax collecting and intergovernmental financial transfer systems, there
is another set of financial resources for each level of government, for example, several
kinds of charges or rental fees. These are extrabudgetary revenues and these finance theextrabudgetary expenditures for each level of government. There are several studies andexplanations of this complex system. Ahmad (1997) reviews this system including its
history, Bahl and Martinez-Vazquez (2006) summarize recent reforms to the system andMan (2011) focuses on the local financial system.
Recently, urbanization in China has been rapid and nationwide. This trend has
induced additional demand for public expenditure at each level of local government.
Most prefectural governments face financial problems. Tsui (2005) investigated theeffects of intergovernmental fiscal transfers on the equalization of fiscal expenditures
across counties. To remove or reduce such financial distress, several researchers havesuggested several kinds of reforms of local government fiscal systems orintergovernmental transfer systems; for example, the World Bank (2007) discussed thereforms to China’s tax system and intergovernmental fiscal system and transfer totallyand Bahl (2011) examined decentralization and revenue assignment.
However, most studies have proposed changes to the intergovernmental financialtransfer system or tax revenue systems. Few of them mention the adequacy of the five1

layer government system or optimal level or size of local government or local
government’s roles in providing public goods or services. Prefecture populations varyfrom 7,000 to 2,239,000 and prefecture areas vary from 86 km2 to 198,318 km2.1 Some
prefectures consist only of farmers and others have relatively large urban populations.
Additionally, there are some prefectural governments in metropolitan areas, including
Tianjin and Shanghai. In such cases, it might be impossible to develop a reform thatmaintains the sizes or systems of prefectures. In this paper, to evaluate the adequacy of
the five-layer local government system, we investigate the efficient scale of prefecturesfrom a minimizing government expenditures viewpoint, using data from 2037 prefectures,
which excludes some prefectures within metropolitan areas and missing observations.
Following several previous studies, we consider whether local government
expenditures are determined by local population and area size. Most prefectures, however,are composed of both urban and rural areas, so we assume that local government
expenditures depend on urban and rural populations and area size. We also assume thatthe total amount of government expenditures is determined by a quartic function of eachfactor. This assumption corresponds to the assumption that per capita expenditures is a
cubic function. The reason why we assume a cubic function for per capita expenditures
is that several previous studies assumed a U-shaped function for per capita expenditures
for several public services or costs. Additionally, by allowing a nonsymmetrical Ushaped function for per capita expenditures in levels to capture the asymmetric marginal
effects below and above the lowest (optimal) point, we assume a cubic function.2 In the
1

These population and area data are minimums and maximums in the sample used in this paper.

2

Some researchers overcome this problem by logarithmic transformation of per capita

expenditures and explanatory factors and a quadratic function, which is symmetric around theminimum point.

2

estimation process, we find too much variation in per capita expenditures even when we
control several factors, so we apply a quantile regression approach to the data. From theestimated results, we analyze the efficient scales for urban and rural populations and areasize.
The paper proceeds as follows. In Section 2, we conduct a short literature survey
on the efficient scale for local government or several kinds of public services or costs. In
Section 3, we introduce our econometric model to analyze aggregated prefectural
expenditures. In Section 4, we conduct OLS estimation and diagnostics on the residuals.
In Section 5, we present the results of a quantile regression. We simulate the efficientscales for urban and rural populations and areas in Section 6. Finally, we discuss someshortcomings of our paper and possibilities for future research in Section 7.
2. Literature Survey of Efficient Scale of Local Governments
Oates (1972) examined fiscal federalism and several subsequent studies
investigated systems of local public finance. Some of these studies, such as Alesina andSpolare (2003), examined the optimal size of governments or nations. Others authors
have discussed the optimal combination or layers of local governments, for example,
Hochman, Pines and Thisse (1995) and Baleiras (2001).3 To investigate the real size of
local governments, we must first examine the cost structures of local public services. The
empirical analysis of Shelton (2007), which investigated the determinants of central andlocal governments’ total expenditure and expenditures on some specific items using

3

King and Ma (2000) investigated theoretically the relationship between congestion and the sizeof local government.

3international data, focused on the optimal allocation of service provisions among central
and local governments.
Many papers have examined the cost structure or efficiency of providing local
public services. Most of these studies attempt to investigate the cost structures of specificpublic services such as the police or fire department, schools, sewage or water supply
services and so on. For example, Hirsch (1959) investigated total expenditure on police
services, refuse collection, fire protection and education services. He fitted a quadratic
function of population and found inverted U-shaped relationships with various kinds ofexpenditures, which suggests the existence of economies of scale. Bodkin and Conklin(1971) conducted a similar analysis on per capita local public expenditures. They founda U-shaped relationship between per capita total expenditure and population, but did not
find U-shaped relationships with some specific public expenditure items. Beaton (1974)
fitted linear regression equations to the cost of police services by population size of cities.
Borcherding and Deacon (1972) also fitted simple log-linear equations to several outputsof public services.

Craig (1987), Craig and Heikkila (1989) and Edwards (1990)

introduced congestion functions and estimated the degrees of congestion in providing
public safety and others. Ladd (1992) estimated a piecewise linear function and obtained
asymmetric U-shaped cost function. Solé-Ollé and Bosch (2005) took a similar approach.
Duncombe, Miner and Ruggiero (1995) also found asymmetric relationships between
school size and expenditures. Several studies have fitted quadratic functions to the cost
structure of local public services: Hirsch (1965) for refuse collections, Knapp (1982) for
crematoria and Tao and Yuan (2005) for public elementary schools. Furthermore, in
relation to other aspects of cost structures, Ladd (1994) and Nelson (1992) investigated
the relationship between population growth and counties’ expenditures. Carruthers and4

Ulfarsson (2003) investigated the effects of population growth and changes in population
densities from the aspect of urban sprawl. Duncombe and Yinger (1993) extended thistype of analysis to multiple types of public services and estimated the degree of
economies of scope. Au and Henderson (2006) focused on the agglomeration effect of
cities in China and estimated an inverted U-shaped function for productivity.4
When we estimate the cost structure of specific public services, we cannot
determine the optimal size of the local government. However, this type of research
provides evidence regarding which level or layer of government should supply police orother specific public services. When we estimate the total expenditure function, we candirectly investigate the efficient scale of the local government. However, this type ofanalysis is limited by the existing roles of local government within the current central–
local government system.
In this paper, we investigate the efficient scale of prefectural government; thus,
our paper adopts the latter type of analysis. According to Martinez-Vazquez and Qiao
(2011), prefectural government mainly provides services related to public security, social
security and health care within the current five-layer government system in China. As
for the prefectural government’s expenditure shares, the top four items are capital
investment, education, government administration and public security. We cannot obtaineach prefecture’s detailed fiscal expenditures. This is another reason why we cannot
apply the former type of studies to some specific public services. In this paper, we
assume that total prefectural expenditures also have U-shaped cost structures as do
specific expenditures, e.g., public security, education or government administration.

4

Additionally, Andrews, Duncombe and Yinger (2002) conducted a literature survey of
economies of scale in public education provision.
53. Econometric Model for Aggregated Data
The details of local government expenditures are not available. We only havebudgetary expenditures and extrabudgetary expenditures in total.

Therefore, weinvestigate the determinants of total budgetary and extrabudgetary expenditures (G). We
assume this total expenditure consists of three components: expenditure for urban
population (GU ), expenditure for rural population (GA ) and expenditure related to area size(GS ):

G=GU +GA +. GS .

Then, each of these three components is a quartic function of each factor:

GU =α0 +α1 UPop+α2 UPop2 +α3 UPop.3 α4 UPop.4 ,GA =β0 +β1 RPop+β2 RPop2 +β3 RPop3 +β4 RPop4 ,GS =γ0 +γ1 Area+γ2 Area2 +γ3 Area3 +γ4 Area4 ,where UPop , RPop and Area are urban population, rural population and area size,
respectively. We can write the equation for per capita expenditures as follows:

6

G
Pop

=

𝛼0
UPop
UPop2
UPop3
UPop4
+𝛼
+𝛼2
+𝛼3
+𝛼4
Pop 1 Pop
Pop
Pop
Pop
2
3
𝛽1
RPop
RPop
RPop
RPop4
,
+
+ 𝛽1
+𝛽2
+𝛽3
+𝛽4
Pop
Pop
Pop
Pop
Pop
𝛾0
Area
Area2
Area3
Area4
+
+𝛾
+𝛾2
+𝛾3
+𝛾4
Pop 1 Pop
Pop
Pop
Pop

and this equation can be rewritten as

G
Pop

=

𝛿
UPop
UPop2
UPop3
UPop4
+𝛼1
+𝛼2
+𝛼3
+𝛼4
Pop
Pop
Pop
Pop
Pop
2
3
RPop
RPop
RPop
RPop4
+ 𝛽1
+𝛽2
+𝛽3
+𝛽4
Pop
Pop
Pop
Pop
2
3
Area
Area
Area
Area4
+ 𝛾1
+𝛾2
+𝛾3
+𝛾4
Pop
Pop
Pop
Pop

using the following reparameterization:

𝛿 = 𝛼0 + 𝛽0 + 𝛾0 .

The relation between total population (Pop) and urban and rural populations,

Pop=UPop+RPop,leads to1=

UPop RPop
+
Pop
Pop

7

and we can rewrite the equation and add the error term as

G
1
UPop2
UPop3
UPop4
=𝛼1 +𝛿
+𝛼2
+𝛼3
+𝛼4
Pop
Pop
Pop
Pop
Pop
+(𝛽1 − 𝛼1 )

RPop
RPop2
RPop3
RPop4
+𝛽2
+𝛽3
+𝛽4
Pop
Pop
Pop
Pop
+𝛾1

Area
Area2
Area3
Area4
+𝛾2
+𝛾3
+𝛾4
+u.
Pop
Pop
Pop
Pop

Furthermore, we introduce a reparameterization ofϕ = 𝛽1 − 𝛼1and an additional factor to determine the expenditures: number of towns or villages ineach prefecture (NTowns). Finally, we obtain the estimation equation:

G
NTowns
1
UPop2
UPop3
UPop4
=𝛼1 +θ
+𝛿
+𝛼2
+𝛼3
+𝛼4
Pop
Pop
Pop
Pop
Pop
Pop
+ϕ

RPop
RPop2
RPop3
RPop4
+𝛽2
+𝛽3
+𝛽4
Pop
Pop
Pop
Pop
Area

Area2

(1)
Area3

Area4

+𝛾1 Pop +𝛾2 Pop +𝛾3 Pop +𝛾4 Pop +u .

The reason why we introduce NTowns as an additional explanatory variable is that eachprefecture makes fiscal transfers to towns or villages within the prefectures and eachtown or village has fixed costs associated with the provision of their public services. In

8the following sections, we estimate this equation (1) by OLS or another estimation
method.
4. Data and OLS Estimation
In this section, we report the estimation results of equation (1) by OLS. Before
exploring the results, we describe the data used in this paper. We use data for 2037
prefectures in the estimation.

The coverage and sample size in each province ormunicipality are shown in Table 1. The coverage of our sample is 71.3% because wedelete the data of prefectures within metropolitan areas and some missing data exist. We
collect data for urban and rural populations and area size from the 2009 China County
Statistical Yearbook and prefectures’ budgetary and extrabudgetary expenditures5 fromthe 2009 National Prefecture, City, County Fiscal Statistical Book. Summary statisticsof the data are shown in Table 2. The measurement units of the data are as follows: G isin 10,000 yuan, Pop, UPop and RPop are in 10,000 people, Area is in square kilometersand NTowns is in number of towns. Table 2 also shows the summary statistics for thetransformed data.
Table 3 shows the results of the OLS estimation. Some coefficients are estimatedas being statistically significant, whereas others are insignificant. The coefficient ofdetermination (R2) is 0.49. This is relatively high for this type of cross-sectional data
analysis.

However, tests for heteroskedasticity (LM-hetero) and misspecification(RESET) imply misspecification or crucial heteroskedasticity. Jarque–Bera’s test for
nonnormality of the error terms implies that the distribution of error terms cannot be

5This total expenditure includes budgetary and extrabudgetary expenditures and expenditures ofgovernmental funds in each prefecture.

9normal. Robust t-values are estimated t-values calculated as White’s heteroskedasticityconsistent standard errors. The calculated standard t-values and robust t-values aredifferent, so these results also suggest the existence of heteroskedasticity in the error
terms. Then, we plot the fitted values of the regression equation and residuals in Figure
1 to check the distribution of the error terms. This figure implies that the error terms areasymmetric and heteroskedastic. Some of the residuals imply the existence of outliers.
A similar result is found in Solé-Ollé and Bosch (2005, Figure 2, p. 354). They dealt withthis type of problem by applying a piecewise linear regression model. In this paper, weapply a quantile regression in the next section.
5. Quantile Regression Approach
A well-known text on quantile regression is Koenker (2005). This method isusually applied when the error term has heteroskedasticity with respect to the levels of
the dependent variables. In this paper, we apply this method to multiple regression
models with a quartic function. Details of this procedure are available in Koenker (2005);
however, to summarize this method we assume a linear regression model with an error
term as follows:

y𝑖 = X𝑖′ β + ε𝑖, ,𝑖 = 1,2,3, … , 𝑁.

When we estimate the OLS estimator, we minimize the following objective function:𝑁

S(β) = ∑(y𝑖 − X𝑖′ β )2 .
𝑖=1

10

As for the quantile regression, we set a quantile 𝜇𝑞 and q as follows:q = Pr(y𝑖 ≤ 𝜇𝑞 ) = 𝐹𝑦 (𝜇𝑞 ),where 𝐹𝑦 (𝜇𝑞 ) is the distribution function of y𝑖 . Of course, the inverse function of𝐹𝑦 (𝜇𝑞 ) means

𝜇𝑞 = 𝐹𝑦 −1 (q).

If we assume y𝑖 = X𝑖′ β + ε𝑖, this inverse function could be rewritten in terms ofconditional probability as follows:

𝜇𝑞 (𝑋) = 𝐹𝑦|𝑋 −1 (q).

To estimate β𝑞 in a quantile regression requires minimization of the following objectivefunction with respect to β𝑞 :𝑁

S(β𝑞 ) =∑𝑁

𝑞|y𝑖 − X𝑖′ β𝑞 | +𝑖: y𝑖 ≥X′𝑖 β∑ (1 − 𝑞)|y𝑖 − X𝑖′ β𝑞 |.
𝑖: y𝑖 <X′𝑖 βThis is a variation of least absolute deviation (LAD) estimation. There exist various
methods to estimate the standard errors of the estimated parameters. In this paper, we use
the LAD command in TSP version 5.0. This command estimates the standard errors of
the coefficient using a bootstrap method with 500 replications.

11

The results of the quantile regression when we estimate equation (1) with q =0.1, 0.25, 0.5, 0.75 and 0.9 are shown in Table 4. The results show that some coefficientsare not statistically significant at the 5% level in all settings of q, so we remove thecorresponding variables from the equation and reestimate the model. The results areshown in Table 5 as the selected model. This table shows the OLS estimation results
using the same list of explanatory variables. In the next section, using these results, we
simulate the effects of UPop, RPop and Area on 𝐺⁄𝑃𝑜𝑝. This type of simulation makes
the robustness of the existence of the efficient scales.
6. Simulation for Efficient Scales
To simulate the effects of changes in the explanatory variables in the multiple
regression equation, we should control all explanatory variables other than the variableof focus. In this section, we investigate the effects of UPop, RPop and Area on 𝐺⁄𝑃𝑜𝑝.
For the former two populations, we assume a situation in which all the people in theprefectures live either in the urban or in the rural area: Pop = UPop or Pop = RPop.
First, we simulate the effects of urban population assuming Pop = UPop andsetting the area and number of towns or villages under each prefecture at their average̅̅̅̅̅̅̅̅̅̅̅. Then, we calculate the effect of urban
values: Area = ̅̅̅̅̅̅̅
𝐴𝑟𝑒𝑎 and NTowns = 𝑁𝑇𝑜𝑤𝑛𝑠
population on the per capita government expenditures corresponding to the changes in
population as follows:̂𝐺
𝑁𝑇𝑜𝑤𝑛𝑠123(𝑃𝑜𝑝) = 𝛼̂1 + 𝜃̂
+ 𝛿̂
+𝛼
̂𝑃𝑜𝑝
+𝛼
̂𝑃𝑜𝑝
+𝛼
̂𝑃𝑜𝑝
2
3
4
𝑃𝑜𝑝
𝑃𝑜𝑝
𝑃𝑜𝑝
+𝛾̂1

𝐴𝑟𝑒𝑎
𝐴𝑟𝑒𝑎2
𝐴𝑟𝑒𝑎3
𝐴𝑟𝑒𝑎4
+ 𝛾̂2
+ 𝛾̂3
+ 𝛾̂4
,
𝑃𝑜𝑝
𝑃𝑜𝑝
𝑃𝑜𝑝
𝑃𝑜𝑝

12

where the parameters with hats are estimates and the variables with upper bars are averagevalues. While the distribution of total populations ranges between zero and 2,250,000
people (Figure 2), urban populations are distributed between zero and 620,000 people(Figure 3). Therefore, we figure the calculated per capita expenditures from 2,550 to
400,000 people in Figure 4. From this figure, we can observe that there exist the points
to minimize the per capita expenditures in all the regression results: OLS, quantile
regressions with q = 0.1, 0.25, 0.5, 0.75 and 0.9. The calculated points that minimize percapita expenditures are as follows:

OLS:

212,000

q = 0.1:

264,500

q = 0.25:

243,500

q = 0.5:

237,500

q = 0.75:

210,000

q = 0.9:

170,500.

There exists a variation according to the setting of q, but it is located between 170,000
and 270,000 people. In particular, for the q = 0.5 and OLS cases, the points are locatedmainly around 220,000 people. These results suggest that there is a most efficient scale
for the urban population and it is located around 220,000 people. If q goes to zero
asymptotically, this method becomes similar to that of corrected least square (COLS) in

13

econometrics for efficiency and productivity.6 Therefore, if we assume that the case of q
= 0.1 is the lower 10% efficient prefectures results, the most efficient prefectures
minimize their expenditures when their urban populations are equal to or greater than
264,500 people.
Second, we simulate the effects of the rural population assuming Pop = APopand setting the area and number of towns or villages in each prefecture at their average̅̅̅̅̅̅̅ and NTowns = 𝑁𝑇𝑜𝑤𝑛𝑠
̅̅̅̅̅̅̅̅̅̅̅ . Then, we calculate the effect of thevalues: Area = 𝐴𝑟𝑒𝑎rural population on per capita government expenditures when the population changes asfollows:̂𝐺
𝑁𝑇𝑜𝑤𝑛𝑠
1
̂2 𝑃𝑜𝑝 + 𝛽
̂3 𝑃𝑜𝑝2 + 𝛽
̂4 𝑃𝑜𝑝3(𝑃𝑜𝑝) = 𝛼̂1 + 𝜃̂+ 𝛿̂+ 𝜙̂ + 𝛽
𝑃𝑜𝑝
𝑃𝑜𝑝
𝑃𝑜𝑝
+𝛾̂1

𝐴𝑟𝑒𝑎
𝐴𝑟𝑒𝑎2
𝐴𝑟𝑒𝑎3
𝐴𝑟𝑒𝑎4
+ 𝛾̂2
+ 𝛾̂3
+ 𝛾̂4
.
𝑃𝑜𝑝
𝑃𝑜𝑝
𝑃𝑜𝑝
𝑃𝑜𝑝

Rural population distributes between zero and 1,950,000 people (Figure 5). Therefore,
we figure the calculated per capita expenditures from 10,000 to 1,500,000 people in
Figure 6. In this figure, some simulated lines cross in the range between 10,000 and
100,000 people; this phenomenon is caused by fixing the number of towns or villages̅̅̅̅̅̅̅̅̅̅̅ ,under each prefecture at their average values, Area = ̅̅̅̅̅̅̅
𝐴𝑟𝑒𝑎 and NTowns = 𝑁𝑇𝑜𝑤𝑛𝑠
with estimated coefficients for the higher-order quartic equation being statisticallyinsignificant. Therefore, we do not investigate small rural population cases. When the
population is 100,000 and over, per capita expenditures are slightly decreasing when q =6

Winsten (1957) first proposed this method. It is referred to as COLS in the econometrics
of efficiency and productivity literature; for example, Fried et al. (2008, p. 35) explains
this method.
14

0.1, 0.25, 0.5 and 0.75 and slightly increasing when q = 0.95, and flat in the OLS case.
These results suggest that government expenditures for rural populations vary inproportion to population size. Furthermore, we should pay attention to the simulated levelof expenditures. Comparing the simulated expenditures for rural populations with thosefor urban populations, we see the former are much smaller than the latter. For example,
the former are about 1300 yuan, whereas the latter do not fall below 5000 yuan in the q =0.5 case. This means that the prefectural government that governs a rural population
operates cost-effectively.
Third, we simulate the effects of area holding the ratios of urban population andrural population to total population at their average values:̅̅̅̅̅̅̅̅̅̅̅̅̅
APop
APop
⁄Pop =⁄Pop and̅̅̅̅̅̅̅̅̅̅̅̅̅
UPop
UPop
⁄Pop =⁄Pop, and the number of towns or villages in each prefecture at theiraverage values, NTowns = ̅̅̅̅̅̅̅̅̅̅̅
𝑁𝑇𝑜𝑤𝑛𝑠. Then, we calculate the effect of area on per capita
government expenditures corresponding to changes in area as follows:̂𝐺
𝑁𝑇𝑜𝑤𝑛𝑠
1
𝑈𝑃𝑜𝑝2
𝑈𝑃𝑜𝑝3
(𝐴𝑟𝑒𝑎) = 𝛼
̂1 + 𝜃̂
+ 𝛿̂
+𝛼
̂2
+𝛼
̂3
𝑃𝑜𝑝
𝑃𝑜𝑝
𝑃𝑜𝑝
𝑃𝑜𝑝
𝑃𝑜𝑝
+𝛼
̂4

𝑈𝑃𝑜𝑝4
𝑃𝑜𝑝
+𝜙̂

𝑅𝑃𝑜𝑝
𝑅𝑃𝑜𝑝2
𝑅𝑃𝑜𝑝3
𝑅𝑃𝑜𝑝4
̂2
̂3
̂4
+𝛽
+𝛽
+𝛽
𝑃𝑜𝑝
𝑃𝑜𝑝
𝑃𝑜𝑝
𝑃𝑜𝑝
𝐴𝑟𝑒𝑎
𝐴𝑟𝑒𝑎2
𝐴𝑟𝑒𝑎3
+𝛾̂1
+ 𝛾̂2
+ 𝛾̂3
𝑃𝑜𝑝
𝑃𝑜𝑝
𝑃𝑜𝑝
+ 𝛾̂4

𝐴𝑟𝑒𝑎4
.
𝑃𝑜𝑝

Area is distributed between zero and over 20,000 km2 (Figure 7). Therefore, we calculate
per capita expenditures from 389 km2 to 16,000 km2 in Figure 8. The results indicate that15per capita expenditures are increasing slightly in all cases but at a slow rate. These results
suggest that government expenditures corresponding to area are determined in proportion
to area size.
7. Conclusion
We investigated the effects of urban and rural populations and area size on the
expenditures of the prefectural-level local government.

Throughout the empiricalinvestigation, we found the following three results. First, at around 220,000 people, percapita local government expenditure for urban populations has a minimum value in our
simulation. This can also be seen in the simulation results from the quantile regression.
Second, expenditure for rural populations is proportional to population size. Additionally,
per capita expenditures are much lower than those for urban populations.

Third,

expenditure corresponding to area is also proportional to area size. The last two findings
mean that the expenditures are proportional to population and area size when all theprefectural populations are rural. If we consider these results from another viewpoint,
China’s recent rapid urbanization has increased prefectural government expenditures
substantially.

It has also caused fiscal distress among prefectural governments.

Lichtenberg and Ding (2009) also discussed the present trend of land conversion fromrural to urban use and the associated problems.
It is of course impossible to stop the current urbanization trend in China.
However, prefectures that are heavily urbanized should be divided into prefectures of
efficient size, each of which consists of around 220,000 people, and rural populations.
This is similar to the concept of the “garden city” in urban planning, which was examinedby Ward (1992). To consider the level of economic development, it should be called16

“rural city.”7 Apart from metropolitan areas, the construction of rural cities from coast to
coast should be the best way to control prefectural government expenditures. However,this may contradict the findings of Au and Henderson (2006), which showed that morethan half of Chinese cities are undersized from the viewpoint of agglomeration effects on
workers’ productivity. If further migration from rural areas to cities increases wages
further, it is difficult to maintain the urban population in each prefecture at around
220,000. If the Chinese central or local governments cannot control migration, theyshould increase tax revenues or find other revenue sources to finance prefectural
government expenditures. Recent measures to reform resource-related taxation in China
are an example of the search for new revenue sources.
Finally, our study has some limitations. First, as we explained in the introduction,
we cannot investigate the efficient scales of specific public expenditures such as policeand fire departments or water supply. If we were able to investigate each type of
expenditure, we could consider the assignment of public services among the five layersof government or the efficient structures of local government systems. We could also
investigate economies of scale in public expenditures for each item and economies ofscope among several types of public expenditure. For example, Drake and Simper (2002)
emphasize the existence of economies of scope in public service expenditures. The
second remaining problem is a result of the quantile regression approach. The results also
shed light on the existence of the large difference in expenditure between governments ofsimilar size but in prefectures with differences in terms of urban or rural populations andarea size. This means that some governments spend considerably more than others andChen et al. (2008) proposed the “compact city” for sustainable growth in China,
focusing on land saving; thus, it is different from the concept of our “rural city.”
7

17

some spend considerably less. Such differences should be investigated to identify the
specific reason or factor for this by prefecture. Additionally, if we obtain prefecturalsocioeconomic statistics, which were used by Gyimah-Brempong (1989) to examine thedeterminants of the cost of providing public safety, they could help identify the sourcesof variation in prefectural expenditures and provide the comparable efficiency ranking
within similar size prefectures.

18

References
Ahmad, E., 1997. China, in: Ter-Minassian, T. (Ed.), Fiscal federalism in theory andpractice, IMF, Washington, DC, pp. 634–659.
Alesina, A., Spolare, E., 2003. The size of nations. The MIT Press, Boston.
Andrews, M., Duncombe, W., Yinger, J., 2002. Revisiting economies of size in American
education: are we any closer to a consensus? Economics of Education Review.
21(3), 245–262.
Au, C.-C., Henderson, J.V., 2006. Are Chinese cities too small? Review of Economic
Studies. 73(3), 549–576.
Bahl, R.W., 2011. Intergovernmental fiscal relations and local public finance: what is next
on the reform agenda?, in: Man, J. Y and Hong, Y.-H. (Eds.), China’s local publicfinance in transition. Lincoln Institute of Land Policy, Cambridge, pp. 247–271.
Bahl, R., Martinez-Vazquez, J., 2006. Fiscal federalism and economic reform in China,
in: Wallack, J.S. and Srinivasan, T.N. (Eds.), Federalism and economic reform:
international perspectives. Cambridge University Press, Cambridge, pp. 249–300.
Baleiras, R.N., 2001. To fragment or to consolidate jurisdictions: the optimal architectureof government. FEUNL Working Paper No. 401, Faculdade de Economia,
Universidade Nova de Lisboa.
Beaton, W. P., 1974. The determinants of police protection expenditures. National Tax
Journal. 27(2), 335–349.
Bodkin, R.G., Conklin, D.W., 1971. Scale and other determinants of municipal
government expenditures in Ontario: a quantitative analysis. International
Economic Review. 12(3), 465–481.
Borcherding, T. E., Deacon, R. T., 1972. The demand for the services of non-federal
governments. American Economic Review. 62(5), 891–901.

19

Carruthers, J.I., Ulfarsson, G.F., 2003. Urban sprawl and the cost of public services.
Environment and Planning B. 30(4), 503–522.
Chen, H., Jia, B., Lau, S.S.Y., 2008. Sustainable urban form for Chinese compact cities:
challenges of a rapid urbanized economy. Habitat International. 32, 28–40.
Craig, S.G., 1987. The impact of congestion on local public good production. Journal of
Public Economics. 32, 331–353.
Craig, S.G., Heikkila, E.J., 1989. Urban safety in Vancouver: allocation and productionof a congestible public good. Canadian Journal of Economics. 22(4), 867–884.
Drake, L., Simper, R., 2002. X-efficiency and scale economies in policing: a comparative
study using the distribution free approach and DEA. Applied Economics. 34(15),1859–1870.
Duncombe, W., Yinger, J., 1993. An analysis of return to scale in public production, with
an application to fire protection. Journal of Public Economics. 52, 49–72.
Duncombe, W., Miner, J., Ruggiero, J. 1995. Potential cost savings from school district
consolidation: a case study of New York. Economics of Education Review. 14(3),265–284.
Edwards, J.H.Y., 1990. Congestion function specification and the “publicness” of local
public goods. Journal of Urban Economics. 27, 80–96.
Fried, H.O., Knox Lovell, C.A., Schmidt, S.S., 2008. Efficiency and productivity, in:Fried, H.O., Knox Lovell, C.A. and Schmidt, S.S. (Eds.), The measurement of
productive efficiency and productivity growth. Oxford University Press, Oxford,
pp. 3–91.
Gyimah-Brempong, K., 1989. Production of public safety: are socioeconomic
characteristics of local communities important factors? Journal of Applied
Econometrics. 4(1), 57–71.

20

Hirsch, W.Z., 1959. Expenditure implications of metropolitan growth and consolidation.
Review of Economics and Statistics. 41, 232–241.
Hirsch, W.Z., 1965. Cost function of an urban government service: refuse collection.
Review of Economics and Statistics. 47, 87–92.
Hochman, O., Pines, D., Thisse, J.F., 1995. On the optimal structure of local governments.
American Economic Review. 85(5), 1224–1240.
King, D.N. Ma, Y., 2000. Local authority size in theory and practice. Environment andPlanning C: Government and Policy Journal. 18, 255–270.
Knapp, M., 1982. Economies of scale in local public services: the case of British
crematoria. Applied Economics. 14, 447–453.
Koenker, R., 2005. Quantile regression. Cambridge University Press, Cambridge.
Ladd, H.F., 1992. Population growth, density and the costs of providing public services.
Urban Studies. 29, 273–295.
Ladd, H.F., 1994. Fiscal impact of local population growth: a conceptual and empiricalanalysis. Regional Science and Urban Economics. 62, 891–901.
Lichtenberg, E. Ding, C. 2009. Local officials as land developers: urban spatial expansion
in China. Journal Urban Economics. 66, 57–64.
Man, J. Y., 2011. Local public finance in China: an overview, in: Man, J. Y, and Hong, Y.H. (Eds.), China’s local public finance in transition. Lincoln Institute of Land
Policy, Cambridge, pp. 3–17.
Martinez-Vazquez, J., Qiao, B., 2011. Assessing the assignment of expenditure
responsibilities, in: Man, J. Y, and Hong, Y.-H. (Eds.), China’s local public financein transition. Lincoln Institute of Land Policy, Cambridge, pp. 21–40.
Nelson, M. A. 1992. Municipal amalgamation and the growth of the local public sector
in Sweden. Journal of Regional Science. 32(1), 39–53.

21

Oates, W. E., 1972, Fiscal federalism. Harcourt Brace Jovanovich, New York.
Shelton, C. A., 2007. The size and composition of government expenditure. Journal of
Public Economics. 91(11), 2230–2260.
Solé-Ollé, A., Bosch, N., 2005. On the relationship between authority size and the cost ofproviding local services: lessons for the design of intergovernmental transfers in
Spain. Public Finance Review. 33, 343–384.
Tao, H.L., Yuan, M.C., 2005. Optimal scale of a public elementary school with
commuting costs—a case study of Taipei county. Economics of Education Review.
24(4), 407–416.
Tsui, K., 2005, Local tax system, intergovernmental transfers and China’s local fiscal
disparities. Journal of Comparative Economics. 33, 173–196.
Ward, S. Ed., 1992. Garden city: past, present and future. London, Routledge.
Winsten, C.B., 1957, Discussion of Mr. Farrell’s paper. Journal of Royal StatisticalSociety Series A, General. 120(3), 282–284.
World Bank, 2007. China: improving rural public finance for the harmonious society,
Report No. 41579-CN, World Bank, Washington, DC.

22

Table 1. Coverage of sample for each province or municipality
Provinces and municipalities
Beijing Municipality
Tianjin Municipality
Hubei Province
Shanxi Province
Inner Mongolia Autonomous Region
Liaoning Province
Jilin Province
Heilongjiang Province
Shanghai Municipality
Jiangsu Province
Zhejiang Province
Anhui Province
Fijian Province
Jiangxi Province
Shandong ProvinceHenan Province
Hubei Province
Hunan Province
Guangdong Province
Guangxi Province
Hainan Province
Changing Municipality
Sichuan Province
Guizot Province
Yunnan Province
Tibet Autonomous Region
Shaanxi Province
Gansu Province
Qinghai Province
Ningxia Hui Autonomous Region
Xinjiang Uygur Autonomous Region
Total

Sample

Total
5
4
138
97
81
43
41
65
3
57
55
61
57
80
91
107
66
84
74
81
16
26
139
76
120
72
86
75
38
13
86
2037

18
16
172
119
101
100
60
128
18
106
90
105
85
99
140
159
103
122
121
109
20
40
181
88
129
73
107
86
43
22
98
2858

Coverage
0.278
0.250
0.802
0.815
0.802
0.430
0.683
0.508
0.167
0.538
0.611
0.581
0.671
0.808
0.650
0.673
0.641
0.689
0.612
0.743
0.800
0.650
0.768
0.864
0.930
0.986
0.804
0.872
0.884
0.591
0.878
0.713

Note 1: Total is the total number of county-level jurisdictions in 2009 reported by the 2010 China
Statistical Yearbook.
Note 2: Sample is the number of observations used in this paper and coverage is the coverage ratioof the “sample” to the “total.”

23

Table 2. Summary Statistics
Variables

MeanStandard

Minimum

Maximum

deviation
Original data𝐺

118863.8

104488.1

300

150419547.31635

34.89929

0.7

223.9

38.7611730.29445

0.1

193.6

4294.808

9945.455

86

19831814.70201

7.995951

1

72

𝐺
𝑃𝑜𝑝

3363.362814.22834.09091

34087.64

1𝑃𝑜𝑝

0.054245

0.106240.004466

1.42857

𝑈𝑃𝑜𝑝
𝑃𝑜𝑝

0.200930.14346

00.99342

𝑅𝑃𝑜𝑝
𝑃𝑜𝑝

0.799070.14346

0.006579

1

𝐴𝑟𝑒𝑎
𝑃𝑜𝑝

644.5605

4058.228

2.56667

85662.23

𝑁𝑇𝑜𝑤𝑛𝑠𝑃𝑜𝑝

0.56520.76666

0.031646

8.57143

𝑃𝑜𝑝
𝑅𝑃𝑜𝑝
𝐴𝑟𝑒𝑎
𝑁𝑇𝑜𝑤𝑛𝑠Transformed
data

24

Table 3. Estimation Results by OLS

Constant
𝑁𝑇𝑜𝑤𝑛𝑠
𝑃𝑜𝑝
1
𝑃𝑜𝑝
𝑈𝑃𝑜𝑝2
𝑃𝑜𝑝
𝑈𝑃𝑜𝑝3
𝑃𝑜𝑝
𝑈𝑃𝑜𝑝4
𝑃𝑜𝑝
𝑅𝑃𝑜𝑝
𝑃𝑜𝑝
𝑅𝑃𝑜𝑝2
𝑃𝑜𝑝
𝑅𝑃𝑜𝑝3
𝑃𝑜𝑝
𝑅𝑃𝑜𝑝4
𝑃𝑜𝑝
𝐴𝑟𝑒𝑎
𝑃𝑜𝑝
𝐴𝑟𝑒𝑎2
𝑃𝑜𝑝
𝐴𝑟𝑒𝑎3
𝑃𝑜𝑝
𝐴𝑟𝑒𝑎4
𝑃𝑜𝑝

Coefficientt-value

Robust t-value

19860.4

23.842

10.5261002.82

7.980

4.573

115.802

0.090

0.005

–1621.85–13.424–6.54356.5807

10.9175.849–0.57576–9.4678–5.485–19200.8–18.218–8.712

0.095896

0.006

0.003

0.084069

0.387

0.273

–0.00066–0.710–0.6370.178648

1.580

0.051

–2.5E-06–0.777–0.021

2.58E-11

0.810

0.021

–8.9E-17–0.960–0.024

Adj R2

0.4987

LM-hetero

85.507

RESET

52.927Jarque–Bera75719.2

Note 1: Adj R2, LM-hetero, RESET and Jarque–Bera are adjusted R-squared, test forheteroskedasticity, RESET test with squared fitted values and Jarque–Bera test for normality.
Note 2: Bold values mean statistically significant at the 5% level.

25

Table 4. Estimation Results by Quantile Regression: Full Model
0.10

0.25

0.5

0.75

0.90

8437.364

10865.07

14691.87

18867.71

25474.17

𝑁𝑇𝑜𝑤𝑛𝑠𝑃𝑜𝑝

186.2419

200.8443

472.8929

1246.982

2323.414

1𝑃𝑜𝑝

2790.369

2072.114

1612.773–256.541–2870.05

𝑈𝑃𝑜𝑝2
𝑃𝑜𝑝

–582.815–790.664–1124.87–1489.6–2170.34

𝑈𝑃𝑜𝑝3
𝑃𝑜𝑝

17.69066

25.17713

37.11554

52.52024

88.6423

𝑈𝑃𝑜𝑝4
𝑃𝑜𝑝–0.1602–0.24401–0.36007–0.5324–0.96903

𝑅𝑃𝑜𝑝
𝑃𝑜𝑝–6867.2–9253.76–13284.8–17565.5–24829.6

𝑅𝑃𝑜𝑝2
𝑃𝑜𝑝

–25.0469–22.1984–14.4934–13.016

7.5451

𝑅𝑃𝑜𝑝3
𝑃𝑜𝑝

0.278280.22899

0.12407

0.162480.016699

𝑅𝑃𝑜𝑝4
𝑃𝑜𝑝

–0.00109–0.00086–0.00042–0.00069–0.00042

𝐴𝑟𝑒𝑎𝑃𝑜𝑝

0.12069

0.29961

0.43390.432120.36434

𝐴𝑟𝑒𝑎2
𝑃𝑜𝑝–2.17E-06–4.66E-06–7.83E-06–8.46E-06–7.46E-06

𝐴𝑟𝑒𝑎3
𝑃𝑜𝑝

8.35E-12

1.92E-11

4.93E-11

9.98E-11

8.28E-11

𝐴𝑟𝑒𝑎4
𝑃𝑜𝑝

1.17E-17–5.10E-18–9.84E-17–3.44E-16–2.85E-16

Adj R2

0.463070.472240.48437

0.48294

0.47717

Quantiles
Constant

Note 1: Adj R2 is adjusted R-squared.
Note 2: Bold values mean statistically significant at the 5% level.

26

Table 5. Estimation Results by Quantile Regression: Selected Model
Quantiles

0.10

0.25

0.5

0.75

0.90

OLS

Constant

9865.556

12879.36

16433.2

19494.19

23919.46

19595.94

𝑁𝑇𝑜𝑤𝑛𝑠𝑃𝑜𝑝

372.7542

310.7989

594.61251329.612

2163.313

980.2919

1𝑃𝑜𝑝

2965.341

3612.943

1550.574

1299.058–3512.63

5.34297

𝑈𝑃𝑜𝑝2
𝑃𝑜𝑝–708.287–1004.27–1298.16–1540.59–1887.98–1590.68

𝑈𝑃𝑜𝑝3
𝑃𝑜𝑝

20.67388

32.16626

42.61537

53.8526

76.49473

55.56158

𝑈𝑃𝑜𝑝4
𝑃𝑜𝑝

–0.18161–0.31268–0.41115–0.54328–0.83928–0.56619

𝑅𝑃𝑜𝑝
𝑃𝑜𝑝–9113.59–12080.4–15627.1–18605.9–22888.9–18819.8

𝐴𝑟𝑒𝑎𝑃𝑜𝑝

0.12268

0.184210.39747

0.27226

0.44509

0.19418

𝐴𝑟𝑒𝑎2
𝑃𝑜𝑝–2.88E-06–2.83E-06–7.61E-06–4.83E-06–7.99E-06–2.9E-06

𝐴𝑟𝑒𝑎3
𝑃𝑜𝑝

1.73E-11

9.67E-12

4.85E-11

6.95E-11

8.22E-11

2.84E-11

𝐴𝑟𝑒𝑎4
𝑃𝑜𝑝

–1.77E-17

8.49E-18–9.67E-17–2.65E-16–2.77E-16–9.6E-17R2

0.46899

0.4791

0.487770.485140.478760.50135

Note 1: R2 is R-squared.
Note 2: Bold values mean statistically significant at the 5% level.

27

2500020000

Residuals

15000

10000

5000

0

-5000

-10000
0

5000

10000

15000

Fitted Values
Figure 1. Fitted values and residuals

28

20000

25000

5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
130
135
140
145
150
155
160
165
170
175
180
185
190
195
200
205
210
215
220
225

Frequency
180

160

140

120

100

80

60

40

20

0

Total Population (in 10 thousands)

Figure 2. Histogram for “Pop”
29

450
400
350

Frequency

300
250
200
150
100

50
0
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62

Urban Population (in 10 thousands)
Figure 3. Histogram for “Upop”
30

3000025000

Expenditure

20000

15000

10000

5000

Urban Population (in 10 thousands)
0.1

0.25

0.5

0.75

Figure 4. Urban population and local government expenditure
31

0.9

OLS

38.25

36.25

34.25

32.25

30.25

28.25

26.25

24.25

22.25

20.25

18.25

16.25

14.25

12.25

10.25

8.25

6.25

4.25

2.25

0.25

0

5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
130
135
140
145
150
155
160
165
170
175
180
185
190
195
200

Frequency
180

160

140

120

100

80

60

40

20

0

Rural Population (in 10 thousands)

Figure 5. Histogram for “Apop”
32

3000

2500

Expenditure

2000

1500

1000

500

Rural Population (in 10 thousands)

0.1

0.25

0.5

0.75

Figure 6. Rural population and local government expenditure
33

0.9

OLS

145

137

129

121

113

105

97

89

81

73

65

57

49

41

33

25

17

9

1

0

0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
6500
7000
7500
8000
8500
9000
9500
10000
10500
11000
11500
12000
12500
13000
13500
14000
14500
15000
15500
16000
16500
17000
17500
18000
18500
19000
19500
Over 20000

Frequency
200
180

160

140

120

100

80

60

40

20

0

Area (in km2)

Figure 7. Histogram for “Area”
34

5000
4500

Expenditure

4000
3500
3000
2500
2000

Area (in km2)

0.1

0.25

0.5

0.75

0.9

Figure 8. Area and local government expenditure

35

OLS

15949

15171

14393

13615

12837

12059

11281

10503

9725

8947

8169

7391

6613

5835

5057

4279

3501

2723

1945

1167

389

1500