Open Access

Efficient scale of prefectural government in China

China Finance and Economic Review20164:2

DOI: 10.1186/s40589-016-0026-y

Received: 21 May 2015

Accepted: 1 January 2016

Published: 21 January 2016

Abstract

Background

China has five layers of government including the central government. Recently, some prefectural governments meet fiscal distress.

Methods

We investigate the effects of urban and rural populations and area sizes on the expenditures of the prefecture-level local government by estimating quintile regression.

Results

At around 220,000 people, per capita local government expenditure for urban populations is minimized in our simulation. The expenditure for rural populations is proportional to the population size. The expenditure in accordance with the areas is also proportional to the area size.

Conclusions

The cost structure is the reason why China’s recent rapid urbanization increases prefectural government’s fiscal distress.

Keywords

Efficient scale Local government Quantile regression China

JEL Classification

H40 H72 R51

Background

China has five layers of government including the central government. Each level of government, except the central government, receives financial transfers from the higher ranks of government and distributes the financial transfers to the lower levels of government. 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 the extrabudgetary expenditures for each level of government. There are several studies and explanations of this complex system. Ahmad (1997) reviews this system including its history, Bahl and Martinez-Vazquez (2006) summarize recent reforms to the system, and Man (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 the effects of intergovernmental fiscal transfers on the equalization of fiscal expenditures across counties. To remove or reduce such financial distress, several researchers have suggested several kinds of reforms of local government fiscal systems or intergovernmental transfer systems; for example, the World Bank (2007) discussed the reforms to China’s tax system and intergovernmental fiscal system and transfer totally, and Bahl (2011) examined decentralization and revenue assignment.

However, most studies have proposed changes to the intergovernmental financial transfer system or tax revenue systems. Few of them mention the adequacy of the five-layer government system or optimal level or size of local government or local government’s roles in providing public goods or services. Prefecture populations vary from 7000 to 2,239,000, and prefecture areas vary from 86 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 that maintains 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 prefectures from a minimizing government expenditure 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 that the total amount of government expenditures is determined by a quartic function of each factor. 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 U-shaped 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 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 the estimated results, we analyze the efficient scales for urban and rural populations and area size.

Methods

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 and Spolare (2003), examined the optimal size of governments or nations. Other authors have discussed the optimal combination or layers of local governments, for example, Hochman et al. (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 and local governments’ total expenditure and expenditures on some specific items using 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 specific public 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 of expenditures, which suggest the existence of economies of scale. Bodkin and Conklin (1971) conducted a similar analysis on per capita local public expenditures. They found a 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 outputs of 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 et al. (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 and Ulfarsson (2003) investigated the effects of population growth and changes in population densities from the aspect of urban sprawl. Duncombe and Yinger (1993) extended this type 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 or other specific public services. When we estimate the total expenditure function, we can directly investigate the efficient scale of the local government. However, this type of analysis 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 obtain each 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.

Econometric model for aggregated data

The details of local government expenditures are not available. We only have budgetary expenditures and extrabudgetary expenditures in total. Therefore, we investigate the determinants of total of budgetary and extrabudgetary expenditures (G). We assume that this total expenditure consists of three components: expenditure for urban population (G U), expenditure for rural population (G A), and expenditure related to area size (G S):
$$ G={G}_{\mathrm{U}}+{G}_{\mathrm{A}}+{G}_{\mathrm{S}}. $$
Then, each of these three components is a quartic function of each factor:
$$ {G}_{\mathrm{U}}={\alpha}_0+{\alpha}_1\mathrm{UPop}+{\alpha}_2\mathrm{U}\mathrm{P}\mathrm{o}{\mathrm{p}}^2+{\alpha}_3\mathrm{U}\mathrm{P}\mathrm{o}{\mathrm{p}}^{.3}{\alpha}_4\mathrm{U}\mathrm{P}\mathrm{o}{\mathrm{p}}^{.4}, $$
$$ {G}_{\mathrm{A}}={\beta}_0+{\beta}_1\mathrm{RPop}+{\beta}_2\mathrm{R}\mathrm{P}\mathrm{o}{\mathrm{p}}^2+{\beta}_3\mathrm{R}\mathrm{P}\mathrm{o}{\mathrm{p}}^3+{\beta}_4\mathrm{R}\mathrm{P}\mathrm{o}{\mathrm{p}}^4, $$
$$ {G}_{\mathrm{S}}={\gamma}_0+{\gamma}_1\mathrm{Area}+{\gamma}_2\mathrm{Are}{\mathrm{a}}^2+{\gamma}_3\mathrm{Are}{\mathrm{a}}^3+{\gamma}_4\mathrm{Are}{\mathrm{a}}^4, $$
Where UPop, RPop, and Area are urban population, rural population, and area size, respectively.5 We can write the equation for per capita expenditures as follows:
$$ \begin{array}{ccc}\hfill \frac{G}{\mathrm{Pop}}\hfill & \hfill =\hfill & \hfill \frac{\alpha_0}{\mathrm{Pop}}+{\alpha}_1\frac{\mathrm{UPo}\mathrm{p}}{\mathrm{Pop}}+{\alpha}_2\frac{\mathrm{UPo}{\mathrm{p}}^2}{\mathrm{Pop}}+{\alpha}_3\frac{\mathrm{UPo}{\mathrm{p}}^3}{\mathrm{Pop}}+{\alpha}_4\frac{\mathrm{UPo}{\mathrm{p}}^4}{\mathrm{Pop}}\hfill \\ {}\hfill \hfill & \hfill \hfill & \hfill + \frac{\ {\beta}_1}{\mathrm{Pop}} + {\beta}_1\frac{\mathrm{RPo}\mathrm{p}}{\mathrm{Pop}}+{\beta}_2\frac{\mathrm{RPo}{\mathrm{p}}^2}{\mathrm{Pop}}+{\beta}_3\frac{\mathrm{RPo}{\mathrm{p}}^3}{\mathrm{Pop}}+{\beta}_4\frac{\mathrm{RPo}{\mathrm{p}}^4}{\mathrm{Pop}}\hfill \\ {}\hfill \hfill & \hfill \hfill & \hfill +\kern0.5em \frac{\gamma_0}{\mathrm{Pop}}+{\gamma}_1\frac{\mathrm{Are}\mathrm{a}}{\mathrm{Pop}}+{\gamma}_2\frac{\mathrm{Are}{\mathrm{a}}^2}{\mathrm{Pop}}+{\gamma}_3\frac{\mathrm{Are}{\mathrm{a}}^3}{\mathrm{Pop}}+{\gamma}_4\frac{\mathrm{Are}{\mathrm{a}}^4}{\mathrm{Pop}}\hfill \end{array}, $$
and this equation can be rewritten as
$$ \begin{array}{ccc}\hfill \frac{G}{\mathrm{Pop}}\hfill & \hfill =\hfill & \hfill \frac{\delta }{\mathrm{Pop}}+{\alpha}_1\frac{\mathrm{UPo}\mathrm{p}}{\mathrm{Pop}}+{\alpha}_2\frac{\mathrm{UPo}{\mathrm{p}}^2}{\mathrm{Pop}}+{\alpha}_3\frac{\mathrm{UPo}{\mathrm{p}}^3}{\mathrm{Pop}}+{\alpha}_4\frac{\mathrm{UPo}{\mathrm{p}}^4}{\mathrm{Pop}}\hfill \\ {}\hfill \hfill & \hfill \hfill & \hfill \kern2em + {\beta}_1\frac{\mathrm{RPo}\mathrm{p}}{\mathrm{Pop}}+{\beta}_2\frac{\mathrm{RPo}{\mathrm{p}}^2}{\mathrm{Pop}}+{\beta}_3\frac{\mathrm{RPo}{\mathrm{p}}^3}{\mathrm{Pop}}+{\beta}_4\frac{\mathrm{RPo}{\mathrm{p}}^4}{\mathrm{Pop}}\hfill \\ {}\hfill \hfill & \hfill \hfill & \hfill \kern3.25em + {\gamma}_1\frac{\mathrm{Are}\mathrm{a}}{\mathrm{Pop}}+{\gamma}_2\frac{\mathrm{Are}{\mathrm{a}}^2}{\mathrm{Pop}}+{\gamma}_3\frac{\mathrm{Are}{\mathrm{a}}^3}{\mathrm{Pop}}+{\gamma}_4\frac{\mathrm{Are}{\mathrm{a}}^4}{\mathrm{Pop}}\hfill \end{array} $$
using the following reparameterization:
$$ \delta ={\alpha}_0+{\beta}_0+{\gamma}_0. $$
The relation between total population (Pop) and urban and rural populations,
$$ \mathrm{Pop}=\mathrm{UPop}+\mathrm{RPop}, $$
leads to
$$ 1=\frac{\mathrm{UPop}}{\mathrm{Pop}}+\frac{\mathrm{RPop}}{\mathrm{Pop}} $$
and we can rewrite the equation and add the error term as
$$ \begin{array}{l}\frac{G}{\mathrm{Pop}}={\alpha}_1+\delta \frac{1}{\mathrm{Pop}}+{\alpha}_2\frac{\mathrm{UPo}{\mathrm{p}}^2}{\mathrm{Pop}}+{\alpha}_3\frac{\mathrm{UPo}{\mathrm{p}}^3}{\mathrm{Pop}}+{\alpha}_4\frac{\mathrm{UPo}{\mathrm{p}}^4}{\mathrm{Pop}}\\ {}\kern2.56em +\left({\beta}_1-{\alpha}_1\right)\frac{\mathrm{RPo}\mathrm{p}}{\mathrm{Pop}}+{\beta}_2\frac{\mathrm{RPo}{\mathrm{p}}^2}{\mathrm{Pop}}+{\beta}_3\frac{\mathrm{RPo}{\mathrm{p}}^3}{\mathrm{Pop}} + {\beta}_4\frac{\mathrm{RPo}{\mathrm{p}}^4}{\mathrm{Pop}}\kern1em \\ {}\kern10.5em +{\gamma}_1\frac{\mathrm{Are}\mathrm{a}}{\mathrm{Pop}}+{\gamma}_2\frac{\mathrm{Are}{\mathrm{a}}^2}{\mathrm{Pop}}+{\gamma}_3\frac{\mathrm{Are}{\mathrm{a}}^3}{\mathrm{Pop}}+{\gamma}_4\frac{\mathrm{Are}{\mathrm{a}}^4}{\mathrm{Pop}}+u.\end{array} $$
Furthermore, we introduce a reparameterization of
$$ \phi ={\beta}_1-{\alpha}_1 $$
and an additional factor to determine the expenditures: number of towns or villages in each prefecture (NTowns). Finally, we obtain the estimation equation:
$$ \begin{array}{l}\frac{G}{\mathrm{Pop}}={\alpha}_1+\uptheta \frac{\mathrm{NTowns}}{\mathrm{Pop}}+\delta \frac{1}{\mathrm{Pop}}+{\alpha}_2\frac{\mathrm{UPo}{\mathrm{p}}^2}{\mathrm{Pop}}+{\alpha}_3\frac{\mathrm{UPo}{\mathrm{p}}^3}{\mathrm{Pop}}+{\alpha}_4\frac{\mathrm{UPo}{\mathrm{p}}^4}{\mathrm{Pop}}\\ {}\kern5.75em +\upphi \frac{\mathrm{RPo}\mathrm{p}}{\mathrm{Pop}}+{\beta}_2\frac{\mathrm{RPo}{\mathrm{p}}^2}{\mathrm{Pop}}+{\beta}_3\frac{\mathrm{RPo}{\mathrm{p}}^3}{\mathrm{Pop}}+{\beta}_4\frac{\mathrm{RPo}{\mathrm{p}}^4}{\mathrm{Pop}}\ \\ {}\kern8em +{\gamma}_1\frac{\mathrm{Are}\mathrm{a}}{\mathrm{Pop}}+{\gamma}_2\frac{\mathrm{Are}{\mathrm{a}}^2}{\mathrm{Pop}}+{\gamma}_3\frac{\mathrm{Are}{\mathrm{a}}^3}{\mathrm{Pop}}+{\gamma}_4\frac{\mathrm{Are}{\mathrm{a}}^4}{\mathrm{Pop}}+u\ .\end{array} $$
(1)
The reason why we introduce NTowns as an additional explanatory variable is that each prefecture makes fiscal transfers to towns or villages within the prefectures and each town or village has fixed costs associated with the provision of their public services. Of course, we can consider other variables to explain the per capita expenditures, e.g., prefectural government’s export, human capital or per capita GDP.6 In the present paper, we focus on investigating the effects of rural and urban population and areas, so we do not include other variables as explanatory variables except NTowns. Also, we cannot obtain the export and human capital data of prefectures. In the following sections, we estimate this equation (1) by OLS or another estimation method.

Results and discussion

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 or municipality are shown in Table 1. The coverage of our sample is 71.3 % because we delete 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 expenditures7 from the 2009 National Prefecture, City, County Fiscal Statistical Book. Summary statistics of the data are shown in Table 2. The measurement units of the data are as follows: G is in 10,000 yuan; Pop, UPop, and RPop are in 10,000 people; Area is in square kilometers; and NTowns is in number of towns. Table 2 also shows the summary statistics for the transformed data.
Table 1

Coverage of sample for each province or municipality

Provinces and municipalities

Sample

Total

Coverage

Beijing Municipality

5

18

0.278

Tianjin Municipality

4

16

0.250

Hubei Province

138

172

0.802

Shanxi Province

97

119

0.815

Inner Mongolia Autonomous Region

81

101

0.802

Liaoning Province

43

100

0.430

Jilin Province

41

60

0.683

Heilongjiang Province

65

128

0.508

Shanghai Municipality

3

18

0.167

Jiangsu Province

57

106

0.538

Zhejiang Province

55

90

0.611

Anhui Province

61

105

0.581

Fijian Province

57

85

0.671

Jiangxi Province

80

99

0.808

Shandong Province

91

140

0.650

Henan Province

107

159

0.673

Hubei Province

66

103

0.641

Hunan Province

84

122

0.689

Guangdong Province

74

121

0.612

Guangxi Province

81

109

0.743

Hainan Province

16

20

0.800

Changing Municipality

26

40

0.650

Sichuan Province

139

181

0.768

Guizot Province

76

88

0.864

Yunnan Province

120

129

0.930

Tibet Autonomous Region

72

73

0.986

Shaanxi Province

86

107

0.804

Gansu Province

75

86

0.872

Qinghai Province

38

43

0.884

Ningxia Hui Autonomous Region

13

22

0.591

Xinjiang Uygur Autonomous Region

86

98

0.878

Total

2037

2858

0.713

“Total” is the total number of county-level jurisdictions in 2009 reported by the 2010 China Statistical Yearbook. “Sample” is the number of observations used in this paper. “Coverage” is the coverage ratio of the sample to the total

Table 2

Summary statistics

Variables

Mean

Standard deviation

Minimum

Maximum

Original data

G

118863.8

104488.1

300

1504195

Pop

47.31635

34.89929

0.7

223.9

RPop

38.76117

30.29445

0.1

193.6

Area

4294.808

9945.455

86

198318

NTowns

14.70201

7.995951

1

72

Transformed data

\( \frac{\mathbf{G}}{\mathbf{Pop}} \)

3363.36

2814.228

34.09091

34087.64

\( \frac{\mathbf{1}}{\mathbf{Pop}} \)

0.054245

0.10624

0.004466

1.42857

\( \frac{\mathbf{UPop}}{\mathbf{Pop}} \)

0.20093

0.14346

0

0.99342

\( \frac{\mathbf{RPop}}{\mathbf{Pop}} \)

0.79907

0.14346

0.006579

1

\( \frac{\mathbf{Area}}{\mathbf{Pop}} \)

644.5605

4058.228

2.56667

85662.23

\( \frac{\mathbf{NTowns}}{\mathbf{Pop}} \)

0.5652

0.76666

0.031646

8.57143

Table 3 shows the results of the OLS estimation. Some coefficients are estimated as being statistically significant, whereas others are insignificant. The coefficient of determination (R 2) 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 normal. Robust t values are estimated t values calculated by White’s heteroskedasticity-consistent standard errors. The calculated standard t values and robust t values are different, 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 Fig. 1 to check the distribution of the error terms. This figure implies that the error terms are asymmetric 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 with this type of problem by applying a piecewise linear regression model. In this paper, we apply a quantile regression in the next section.
Table 3

Estimation results by OLS

 

Coefficient

t value

Robust t value

Constant

19860.4

23.842

10.526

\( \frac{NTowns}{Pop} \)

1002.82

7.980

4.573

\( \frac{1}{Pop} \)

115.802

0.090

0.005

\( \frac{UPo{p}^2}{Pop} \)

−1621.85

−13.424

−6.543

\( \frac{UPo{p}^3}{Pop} \)

56.5807

10.917

5.849

\( \frac{UPo{p}^4}{Pop} \)

−0.57576

−9.4678

−5.485

\( \frac{RPop}{Pop} \)

−19200.8

−18.218

−8.712

\( \frac{RPo{p}^2}{Pop} \)

0.095896

0.006

0.003

\( \frac{RPo{p}^3}{Pop} \)

0.084069

0.387

0.273

\( \frac{RPo{p}^4}{Pop} \)

−0.00066

−0.710

−0.637

\( \frac{Area}{Pop} \)

0.178648

1.580

0.051

\( \frac{Are{a}^2}{Pop} \)

−2.5E−06

−0.777

−0.021

\( \frac{Are{a}^3}{Pop} \)

2.58E−11

0.810

0.021

\( \frac{Are{a}^4}{Pop} \)

−8.9E−17

−0.960

−0.024

Adj R 2

 

0.4987

 

LM-hetero

 

85.507

 

RESET

 

52.927

 

Jarque–Bera

 

75719.2

 

Adj R 2, LM-hetero, RESET, and Jarque–Bera are adjusted R 2, test for heteroskedasticity, RESET test with squared fitted values, and Jarque–Bera test for normality. Italicized values mean statistically significant at the 5 % level

Fig. 1

Fitted values and residuals

Quantile regression approach

A well-known text on quantile regression is Koenker (2005). This method is usually 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:
$$ {y}_i={\mathrm{X}}_i^{\hbox{'}}\upbeta +{\upvarepsilon}_{i,},\kern2.5em i=1,2,3,\dots, N. $$
When we estimate the OLS estimator, we minimize the following objective function:
$$ S\left(\beta \right)={\displaystyle \sum_{i=1}^N}{\left({y}_i-{X}_i^{\hbox{'}}\beta\ \right)}^2\ . $$
As for the quantile regression, we set a quantile μ q and q as follows:
$$ q= \Pr \left({y}_i\le {\mu}_q\right) = {F}_y\left({\mu}_q\right), $$
where F y (μ q ) is the distribution function of y i . Of course, the inverse function of F y (μ q ) means
$$ {\mu}_q = {F_y}^{-1}(q). $$
If we assume \( {y}_i={X}_i^{\hbox{'}}\beta +{\varepsilon}_{i,} \), this inverse function could be rewritten in terms of conditional probability as follows:
$$ {\mu}_q(X) = {F_{y\Big|X}}^{-1}(q). $$
To estimate β q in a quantile regression requires minimization of the following objective function with respect to β q :
$$ S\left({\beta}_q\right)={\displaystyle \sum_{i:\ {y}_i\ge {X}_i^{\hbox{'}}\beta}^N}q\left|{y}_i-{X}_i^{\hbox{'}}{\beta}_q\right|+{\displaystyle \sum_{i:\ {y}_i<{X}_i^{\hbox{'}}\beta}^N}\left(1-q\right)\left|{y}_i-{X}_i^{\hbox{'}}{\beta}_q\right|. $$
This 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.
The results of the quantile regression when we estimate eq. (1) with q = 0.1, 0.25, 0.5, 0.75, and 0.9 are shown in Table 4. The results show that some coefficients are not statistically significant at the 5 % level in all settings of q, so we remove the corresponding variables from the equation and re-estimate the model. The results are shown in Table 5 as the selected model. This table shows the OLS estimation results using the same list of explanatory variables. Before going into the simulation analysis, we should mention about the possible meanings of a variation according to the setting of q. In the present paper, we do not include the per capita GDP or other variables as explanatory variables in regression equation. The effects from these variables present in the error terms and are estimated as a variation according to the setting of q. In the next section, using these results, we simulate the effects of UPop, RPop, and Area on \( \raisebox{1ex}{$G$}\!\left/ \!\raisebox{-1ex}{$ Pop$}\right. \). This type of simulation makes the robustness of the existence of the efficient scales.
Table 4

Estimation results by quantile regression: full model

Quantiles

0.10

0.25

0.5

0.75

0.90

Constant

8437.364

10865.07

14691.87

18867.71

25474.17

\( \frac{NTowns}{Pop} \)

186.2419

200.8443

472.8929

1246.982

2323.414

\( \frac{1}{Pop} \)

2790.369

2072.114

1612.773

−256.541

−2870.05

\( \frac{UPo{p}^2}{Pop} \)

−582.815

−790.664

−1124.87

−1489.6

−2170.34

\( \frac{UPo{p}^3}{Pop} \)

17.69066

25.17713

37.11554

52.52024

88.6423

\( \frac{UPo{p}^4}{Pop} \)

−0.1602

−0.24401

−0.36007

−0.5324

−0.96903

\( \frac{RPop}{Pop} \)

−6867.2

−9253.76

−13284.8

−17565.5

−24829.6

\( \frac{RPo{p}^2}{Pop} \)

−25.0469

−22.1984

−14.4934

−13.016

7.5451

\( \frac{RPo{p}^3}{Pop} \)

0.27828

0.22899

0.12407

0.16248

0.016699

\( \frac{RPo{p}^4}{Pop} \)

−0.00109

−0.00086

−0.00042

−0.00069

−0.00042

\( \frac{Area}{Pop} \)

0.12069

0.29961

0.4339

0.43212

0.36434

\( \frac{Are{a}^2}{Pop} \)

−2.17E−06

−4.66E−06

−7.83E06

−8.46E06

−7.46E−06

\( \frac{Are{a}^3}{Pop} \)

8.35E−12

1.92E−11

4.93E11

9.98E11

8.28E−11

\( \frac{Are{a}^4}{Pop} \)

1.17E−17

−5.10E−18

−9.84E17

−3.44E16

−2.85E−16

Adj R2

0.46307

0.47224

0.48437

0.48294

0.47717

Adj R 2 is adjusted R 2. Italicized values mean statistically significant at the 5 % level

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

\( \frac{NTowns}{Pop} \)

372.7542

310.7989

594.6125

1329.612

2163.313

980.2919

\( \frac{1}{Pop} \)

2965.341

3612.943

1550.574

1299.058

−3512.63

5.34297

\( \frac{UPo{p}^2}{Pop} \)

−708.287

−1004.27

−1298.16

−1540.59

−1887.98

−1590.68

\( \frac{UPo{p}^3}{Pop} \)

20.67388

32.16626

42.61537

53.8526

76.49473

55.56158

\( \frac{UPo{p}^4}{Pop} \)

−0.18161

−0.31268

−0.41115

−0.54328

−0.83928

−0.56619

\( \frac{RPop}{Pop} \)

−9113.59

−12080.4

−15627.1

−18605.9

−22888.9

−18819.8

\( \frac{Area}{Pop} \)

0.12268

0.18421

0.39747

0.27226

0.44509

0.19418

\( \frac{Are{a}^2}{Pop} \)

−2.88E−06

−2.83E−06

−7.61E06

−4.83E−06

−7.99E−06

−2.9E−06

\( \frac{Are{a}^3}{Pop} \)

1.73E−11

9.67E−12

4.85E11

6.95E11

8.22E−11

2.84E−11

\( \frac{Are{a}^4}{Pop} \)

−1.77E−17

8.49E−18

−9.67E17

−2.65E16

−2.77E−16

−9.6E−17

R 2

0.46899

0.4791

0.48777

0.48514

0.47876

0.50135

Italicized values mean statistically significant at the 5 % level

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 variable of focus. In this section, we investigate the effects of UPop, RPop, and Area on \( \raisebox{1ex}{$G$}\!\left/ \!\raisebox{-1ex}{$ Pop$}\right. \). For the former two populations, we assume a situation in which all the people in the prefectures 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 and setting the area and number of towns or villages under each prefecture at their average values: \( \mathrm{Area}=\overline{Area} \) and \( \mathrm{NTowns}=\overline{NTowns} \). Then, we calculate the effect of urban population on the per capita government expenditures corresponding to the changes in population as follows:
$$ \begin{array}{l}\frac{\widehat{G}}{Pop}(Pop)=\widehat{\alpha_1}+\widehat{\theta}\overline{\frac{NTowns}{Pop}}+\widehat{\delta}\frac{1}{Pop}+\widehat{\alpha_2} Pop+\widehat{\alpha_3}Po{p}^2+\widehat{\alpha_4}Po{p}^3\\ {}\kern11.5em +\widehat{\gamma_1}\overline{\frac{Are a}{Pop}}+\widehat{\gamma_2}\overline{\frac{Are{a}^2}{Pop}}+\widehat{\gamma_3}\overline{\frac{Are{a}^3}{Pop}}+\widehat{\gamma_4}\overline{\frac{Are{a}^4}{Pop},}\end{array} $$
where the parameters with hats are estimates and the variables with upper bars are average values. While the distribution of total populations ranges between zero and 2,250,000 people (Fig. 2), urban populations are distributed between zero and 620,000 people (Fig. 3). Therefore, we figure the calculated per capita expenditures from 2550 to 400,000 people in Fig. 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 per capita expenditures are as follows:
Fig. 2

Histogram for “Pop”

Fig. 3

Histogram for “Upop”

Fig. 4

Urban population and local government expenditure

  • 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 located mainly 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. This variation according to the setting of q may be caused by the interaction effect between omitted variables and error term in the equation. If q goes to zero asymptotically, this method becomes similar to that of corrected least square (COLS) in econometrics for efficiency and productivity.8 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 = APop and setting the area and number of towns or villages in each prefecture at their average values: \( \mathrm{Area}=\overline{Area} \) and \( \mathrm{NTowns}=\overline{NTowns} \). Then, we calculate the effect of the rural population on per capita government expenditures when the population changes as follows:
$$ \begin{array}{l}\frac{\widehat{G}}{Pop}(Pop)=\widehat{\alpha_1}+\widehat{\theta}\overline{\frac{NTowns}{Pop}}+\widehat{\delta}\frac{1}{Pop}+\widehat{\phi}+\widehat{\beta_2} Pop+\widehat{\beta_3}Po{p}^2+\widehat{\beta_4}Po{p}^3\\ {}\kern12.5em +\widehat{\gamma_1}\overline{\frac{Are a}{Pop}}+\widehat{\gamma_2}\overline{\frac{Are{a}^2}{Pop}}+\widehat{\gamma_3}\overline{\frac{Are{a}^3}{Pop}}+\widehat{\gamma_4}\overline{\frac{Are{a}^4}{Pop}}.\end{array} $$
Rural population distributes between zero and 1,950,000 people (Fig. 5). Therefore, we figure the calculated per capita expenditures from 10,000 to 1,500,000 people in Fig. 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 villages under each prefecture at their average values, \( \mathrm{Area}=\overline{Area} \) and \( \mathrm{NTowns}=\overline{NTowns} \), with estimated coefficients for the higher-order quartic equation being statistically insignificant. 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 = 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 in proportion to population size. However, its effects are very small, so per capita government expenditures for rural population are almost constant. In other words, total government expenditures are proportional to rural population. Furthermore, we should pay attention to the simulated level of expenditures. Comparing the simulated expenditures for rural populations with those for 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.
Fig. 5

Histogram for “Apop”

Fig. 6

Rural population and local government expenditure

Third, we simulate the effects of area holding the ratios of urban population and rural population to total population at their average values: \( \raisebox{1ex}{$\mathrm{UPop}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{Pop}$}\right.=\overline{\raisebox{1ex}{$\mathrm{UPop}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{Pop}$}\right.} \) and \( \raisebox{1ex}{$\mathrm{APop}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{Pop}$}\right.=\overline{\raisebox{1ex}{$\mathrm{APop}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{Pop}$}\right.} \), and the number of towns or villages in each prefecture at their average values, \( \mathrm{NTowns}=\overline{NTowns} \). Then, we calculate the effect of area on per capita government expenditures corresponding to changes in area as follows:
$$ \begin{array}{l}\frac{\widehat{G}}{Pop}(Area)\\ {}\kern10em =\widehat{\alpha_1}+\widehat{\theta}\overline{\frac{NTowns}{Pop}}+\widehat{\delta}\overline{\frac{1}{Pop}}+\widehat{\alpha_2}\overline{\frac{UPo{p}^2}{Pop}}+\widehat{\alpha_3}\overline{\frac{UPo{p}^3}{Pop}}\\ {}\kern10em +\kern0.5em \widehat{\alpha_4}\overline{\frac{UPo{p}^4}{Pop}} + \widehat{\phi}\overline{\frac{RPop}{Pop}}+\widehat{\beta_2}\overline{\frac{RPo{p}^2}{Pop}}+\widehat{\beta_3}\overline{\frac{RPo{p}^3}{Pop}\kern0.5em }\\ {}\kern10em +\widehat{\beta_4}\overline{\frac{RPo{p}^4}{Pop}\kern0.5em }+\widehat{\gamma_1}\frac{Are a}{Pop}+\widehat{\gamma_2}\frac{Are{a}^2}{Pop}+\widehat{\gamma_3}\frac{Are{a}^3}{Pop}+\widehat{\gamma_4}\frac{Are{a}^4}{Pop}.\end{array} $$
Area is distributed between zero and over 20,000 km2 (Fig. 7). Therefore, we calculate per capita expenditures from 389 to 16,000 km2 in Fig. 8. The results indicate that per capita expenditures are increasing slightly in all cases but at a slow rate. These results suggest that government expenditures corresponding to area are almost constant.
Fig. 7

Histogram for “Area”

Fig. 8

Area and local government expenditure

Conclusions

We investigated the effects of urban and rural populations and area size on the expenditures of the prefectural-level local government. Throughout the empirical investigation, we found the following three results. First, at around 220,000 people, per capita 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, per capita expenditures corresponding to area are almost constant. The last two findings mean that the expenditures are proportional only to population when all the prefectural 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 from rural 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 examined by Ward (1992). To consider the level of economic development, it should be called “rural city.”9 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 more than half of Chinese cities are undersized from the viewpoint of agglomeration effects on workers’ productivity. If further migration from rural areas to cities continues to seek higher wages in urban area, 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, they should 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 police and 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 layers of government or the efficient structures of local government systems. We could also investigate economies of scale in public expenditures for each item and economies of scope 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 of similar size but in prefectures with differences in terms of urban or rural populations and area size. This means that some governments spend considerably more than others and some spend considerably less. If we obtain prefectural socioeconomic statistics, which were used by Gyimah-Brempong (1989) to examine the determinants of the cost of providing public safety, we could identify the sources of variation in prefectural expenditures and provide the comparable efficiency ranking within similar size prefectures. However, because we cannot obtain the prefectural governments’ expenditures in detail, it remains as an unidentified problem for which prefectural expenditures are inefficient, rural or urban population or area. As for the third remaining problem, because of the data availability, we do not investigate the determinants of the prefectural governments’ expenditures in other years. This means that we cannot estimate the historical or dynamic changes in the efficient scale of the prefectural governments. This is also a remaining problem. We should investigate them in the future research. The fourth problem arises from the roles of the prefectural governments in the economic development.10 In this paper, we confine all the effects from the performances of the prefectural governments in supporting economic development into the residuals of the regression equation. This problem is crucial for our empirical research, but, at the present stage, we do not have a proper tool to investigate the performances of the prefectural government in economic development. One of the difficulties is that we might not assume profit maximization or cost minimization behavior for the prefectural government. This difficulty prevents us from taking cost function approach to the prefectural government expenditure. We will also try to solve this problem in the future research.

Footnotes
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 the minimum point.

 
3

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

 
4

Additionally, Andrews et al. (2002) conducted a literature survey of economies of scale in public education provision.

 
5

We consider the total expenditures consisted by these three components, so we cannot identify the effects from rural or urban population size if we consider an interaction term between rural and urban population to capture the effects of economy of scope in public expenditures. In this paper, we do not adopt some interaction terms as explanatory variables.

 
6

One of the referees suggests Rodrik’s (1988) finding of a positive correlation between an economy’s exposure to international trade and the size of its government. In our paper, we cannot obtain the measure for exposure to international trade for each prefectures

 
7

This total expenditure includes budgetary and extrabudgetary expenditures and expenditures of governmental funds in each prefecture.

 
8

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.

 
9

Chen 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.”

 
10

One of the referees also pointed that the role of the prefectural government is not supposed only to provide public services, but also to promote local development through promoting local investment to meet financial needs or get political promotion.

 

Declarations

Acknowledgements

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 and 15 K12461) for their financial support. The authors are also very grateful for two anonymous referees’ comments to clarify the remaining problems of our paper.

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors’ Affiliations

(1)
Graduate School of Economics, Osaka University
(2)
Department of Economics and Management, Dalian Nationalities University

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Copyright

© Fukushige and Shi. 2016