Appendix 5: Percentage of Boarding Students Receiving Living
4.4 The Analysis of Horizontal Equity: Gini Coefficient
In this chapter, we analyze the equity or inequity of education resource distribution in four sample provinces from 2001 to 2006. We grouped the students by county.
Although we should use the per student average education resources to measure horizontal equity, the unit of the statistics of educational revenue and expenditure is not consistent in this period. From 2002 to 2003, the unit is the township. After 2003, the unit becomes the school. To make the results of our analysis comparable, we need to use the same unit to compute the Gini coefficient and Theil coefficient for each year. Therefore, we selected the county as the analysis unit.
The perfect Gini or Theil coefficient should be computed with education resources received by each student. This is the true method to measure the equity or inequity of education resources among every student. However, we cannot know how many education resources a student receives. Therefore, we use the per-student average education resources of the analysis unit to compute the inequity.
There are two approaches to compute the equity, weighted with the number of students or not. What is the difference between the weighted and unweighted coefficients? Take the Gini coefficient as an example. We suppose there are two counties, A and B. There are 100 students in County A, and the per student average expenditure is 100 Yuan. There are 1000 students and 1000 Yuan per student average expenditure for County B. The unweighted Gini coefficient is 0.409 and the weighted one is 0.081. The former is the measurement of the difference between analysis units; the latter is the measurement of both the difference between analysis units and the difference between every student. However, the weighted coefficient truly ignores the changes of intra-analysis unit equity; we define that every student receives the same education resources in the intra-analysis unit. Although the
weighted Gini has some shortcomings, it is much closer to the perfect Gini than the unweighted one (Milanovic2007). So, we use the weighted Gini or Theil coeffi- cient to measure the equity in this study.
4.4.1 The Gini Coef fi cient for Education Revenue and Its Decomposition
4.4.1.1 Gini Coefficient for Education Revenue
The Gini coefficient of per primary student average education revenue shows that the inequity of Guangxi and Hubei was increasing, but the equity of Zhejiang and Heilongjiang fluctuated with a decreasing trend in the period of 2001–2006.
Contrastively, the Gini coefficient of Zhejiang and Heilongjiang is steadier than that of Guangxi and Hubei. In total, in each year of these 6 years, the Gini coefficient of Hubei was the highest, followed in order by Guangxi, Heilongjiang, and Zhejiang.
The inequity in junior secondary schools is different from that of primary schools. The Gini coefficient for a junior secondary school student in Heilongjiang is a steadier one. The inequity in Heilongjiang is the steadiest, although its inequity is always the highest. As for Hubei and Guangxi, the inequity was increasing from 2001 to 2006, which is the same as for primary school. In opposition, Zhejiang was making efforts to reduce the inequity. From 2001 to 2004, the Gini coefficient of Guangxi was the lowest, but Zhejiang’s has become the lowest since 2005.
If we compare Fig.4.1with Fig.4.2, there are some interestingfindings. Firstly, in Heilongjiang, the inequity in junior secondary school is much higher than that in primary school. Also, the difference between junior secondary school and primary school is expanding: in 2006, we can see that the inequity of the former increased and the latter decreased. Secondly, although the inequity of junior secondary school
Fig. 4.1 Gini coefficient for education revenue per primary school student
is lower than that of primary school in Guangxi, the difference of both keeps steady when they are increasing at a similar pace. Thirdly, in Zhejiang, the Gini coefficient of the education revenue per junior secondary school student is higher than that for a primary school student in 2001. As shown in Figs.4.1and4.2, the difference of both Gini coefficients was decreasing, and even became the same in 2006. Fourthly, as for the inequity of primary school and junior secondary schools in Hubei, the difference of both was decreasing in the period of 2001–2006, and it became the same in 2006. From 2001 to 2004, the pace of the former was faster than that of the latter; however, from 2004, the pace of the latter was faster.
Do thesefindings illustrate that the government’s decisions determine the trend of education revenue inequity? Theoretically, the government is the key provider of compulsory education. Therefore, we can use fiscal appropriation to reflect fund inputs from the government. Therefore, if we want to answer the question, we must decompose the Gini coefficient by fund input or education revenue sources.
4.4.1.2 The Decomposition of the Gini Coefficient by Revenue Source
We divided the sources of education revenue intofiscal appropriation and non-fiscal appropriation. To examine whether the government’s preference determines the equity of education revenue, we computed thefiscal appropriation contribution ratio to the Gini coefficient. The results are shown in Figs.4.3and4.4.
From these twofigures, we can see that the contribution ratio offiscal appro- priation became higher gradually in the period of 2001–2006. In 2006, the con- tribution ratio increased to 80 % at least. Therefore, we can say that the inequity of education revenue is determined by the preference choice of the government. If the government does not reform the formula offiscal appropriation, the inequity will Fig. 4.2 Gini coefficient for education revenue per junior secondary school student
increase with fiscal input increase, such as in the junior secondary schools of Guangxi and Hubei. If the formula offiscal appropriation results in more equity, the inequity will be reduced with fiscal input increases, as in the junior secondary school of Zhejiang. You also mayfind irregularfluctuation in Figs.4.1and4.2. The reason may be that the formula of fiscal appropriation is changed irregularly.
Therefore, we think that it is crucial for achieving the equity to design an equity formula to allocate or distributefiscal appropriations (Fig.4.5).
Fig. 4.3 The contribution ratio from thefiscal appropriation to the Gini coefficient of education revenue per primary school student
Fig. 4.4 The contribution ratio from fiscal appropriation to the Gini coefficient of education revenue per junior secondary school student
We have measured the equity of education revenue, but education revenue is not equal to education expenditure. If the education revenue reflects thefinancial ability to employ physical facilities and human resources for education, the education expenditure will be the true education provided for students. If we want to know how many education resources were received by each student and whether the distribution of education resources is equity, we must measure the Gini coefficient of per student education expenditures. In the next section, we compute the Gini coefficient of per student average regular expenditures, budgetary regular expen- ditures, non-personnel expenditures, and teachers’salaries.
4.4.2 The Gini Coef fi cient for Regular Expenditures
4.4.2.1 Gini Coefficient for Regular Expenditures and Budgetary Regular Expenditures
Figure4.6shows us the Gini coefficients of average regular expenditures per pri- mary school student for the four provinces, which are between 0.14 and 0.25. The Gini coefficient of Guangxi and Hubei is increasing, which indicates that the inequity of these two provinces was expanding. However, the inequities of Zhejiang and Heilongjiang do not have significant changes with small decreases.
Although the equity is improving, we dofind that the inequity expands at a slow pace or even does not expand with a small decrease. Zhejiang has the highest equity, followed by Heilongjiang, Guangxi, and Hubei in order.
From Fig.4.7, we can see that the Gini coefficient of average regular expenditure per junior secondary school student in the four provinces increased at a very slow Fig. 4.5 The difference between both contribution ratios (primary school and junior secondary school)
pace. In 2003, Heilongjiang had Gini coefficient singularity, which reached 0.458.
We hope to find out the reason in the next analysis. Zhejiang still has the best equity, followed by Guangxi, Hubei, and Heilongjiang. Perhaps we can conclude that the equity of education resource distribution is not only different between each province, but also between primary schools and junior secondary schools within a single province. Therefore, the equity or inequity is determined by the formula of fund input designed by the government (Figs.4.8and 4.9).
We also computed the Gini coefficient for average budgetary regular expenditure per student in order to compare it to the Gini coefficient of per student average regular expenditure. When the former is the same as or similar to the latter, the inequity of non-budgetary regular expenditures does not expand or reduce the total inequity. If the former is higher than the latter, the inequity of non-budgetary Fig. 4.6 Gini coefficient for average regular expenditures per primary school student
Fig. 4.7 Gini coefficient for average regular expenditures per junior secondary school student
regular expenditure eliminates the inequity of the former. This indicates that the groups who receive less budgetary regular expenditures will be provided with more non-budgetary regular expenditures. When the former is lower than the latter, we can say that the inequity of non-budgetary regular expenditures expands the total inequity.
At a primary school in Guangxi, the trends for budgetary regular expenditures and non-budgetary regular expenditures are opposite. The Gini coefficient trend for regular expenditures was going up from 2001 to 2006. However, the Gini coeffi- cient trend for budgetary regular expenditures was going down—greater than that of regular expenditure. Until 2006, the Gini coefficients of both were very close.
This illustrates that the inequity of non-budgetary regular expenditures reduces the inequity of budgetary regular expenditures during the period of 2001–2005.
Fig. 4.8 Gini coefficient for average budgetary regular expenditures per primary school student
Fig. 4.9 Gini coefficient for average budgetary regular expenditures per junior secondary school student
The primary school in Hubei and junior secondary school in Guangxi showed the same characteristic. However, for other provinces and education stages in most years, non-budgetary regular expenditures expanded the total inequity. Therefore, we can conclude that the equity method to distribute non-budgetary regular expenditures may improve the equity.
4.4.2.2 The Gini Coefficient for Teacher’s Salary
As a component of regular expenditures, the equity in personnel expenditures has always been an issue of public concern. If we compute the Gini coefficient of per student average teacher’s salary, the Gini coefficient will reflect the teacher resource received by every student. However, the central government has determined the ratio of teachers to students for primary and junior secondary schools since 2001.
Although teacher resources per student may be different in each school in a county, the ratio may be similar among counties. Therefore, for the Gini coefficient of per teacher average salary, we compute that the weight for the number of teachers not only reflects the teacher resources that students received, but also tells us the inequity of the per teacher average salary among counties.
Figures 4.10 and 4.11 present the changes in the Gini coefficient of average salary for primary schools and junior secondary schools in four provinces. For the primary schools, the inequity for teacher’s salary from 2001 to 2003 in Guangxi and Hubei decreased, and then presented an upward trend after 2003. The inequity of Zhejiang and Heilongjiang in 2005 was higher than that of 2001, while a con- spicuous decrease was shown in 2006. For the junior secondary schools, the inequity has been increasing at a very slow pace since 2001 in four provinces, while Heilongjiang and Zhejiang had a small decrease in 2006.
Fig. 4.10 Gini coefficient for average salary of a primary school teacher
The Gini coefficient for teacher’s salary has three remarkable characteristics (refer to Figs.4.10and4.11). First, the degree of inequity in teacher’s salary was rather low, with a small Gini coefficient ranging from 0.09 to 0.16 for primary school and 0.09–0.16 for junior secondary school. The possible reason for this result is that the teacher’s salary was given priority among all kinds of education expenditures. Also, many county governments take the teacher’s salary guarantee as the most crucial mission in education. In addition, all the local standards for the teachers’ basic salaries were highly consistent. Secondly, although the difference for average salary was smaller, the overall trend for the inequity was going up. Thirdly, the intra-provincial difference of teacher’s salary inequity narrowed gradually, which may have resulted from a county-centered system policy aiming to guarantee a teacher’s salary carried out from 2001.
After comparing the inequity of a teacher’s salary and budgetary teacher’s salary in four provinces, we found that the inequity trend of the budgetary teacher’s salary in Guangxi, Hubei, and Heilongjiang coincides with the teacher’s salary. This shows that the teacher’s salary in these three provinces was mainly dependent on budgetaryfiscal appropriation. In comparison, there was no remarkable similarity in Zhejiang. The inequity of the budgetary teacher’s salary was persistently lower than that of the teacher’s salary, which tells us that the teachers of some counties receive more non-budgetary salary than others (Table4.3).
4.4.2.3 The Gini Coefficient for Non-personnel Expenditures
Non-personnel expenditures are the main and important fund resources to ensure school operation and employ physical facilities. In the long term, the shortage of non-personnel expenditure is the biggest obstacle faced in education development;
Fig. 4.11 Gini coefficient for average salary of a junior secondary school teacher
this is mainly caused by inequity of education resource distribution. In recent years, one focus of education financing reform is to design a guarantee mechanism for non-personnel expenditures. After the implementation of a new mechanism, we hope to see the inequity of non-personnel expenditures reduced.
As shown in Fig. 4.12, the Gini coefficient of the average non-personnel expenditure per primary school student in four provinces ranged from 0.25 to 0.31, which was higher than that of regular expenditure and teacher’s salary. The trend of inequity went up in 2001 and 2002. After 2002, although there werefluctuations over the years, the overall trend of inequity was going down. However, in 2006, the inequity trend of Hubei increased.
As shown in Fig.4.13, the inequity of average non-personnel expenditure per junior secondary school student was lower than that for primary schools in Guangxi and Hubei in the period of 2001–2006. In Zhejiang, the inequity in junior secondary schools from 2001 to 2003 was lower than that of primary schools, but higher after 2004. Moreover, the inequity in Heilongjiang was persistently higher than that of Table 4.3 Gini coefficients for budgetary teacher’s salary
Province 2001 2002 2003 2004 2005 2006
Primary school Guangxi 0.113 0.108 0.105 0.118 0.134 0.133
Hubei 0.199 0.141 0.107 0.124 0.122 0.125
Zhejiang 0.111 0.103 0.101 0.097 0.103 0.110 Heilongjiang 0.128 0.142 0.131 0.136 0.140 0.111 Junior secondary
school
Guangxi 0.103 0.108 0.097 0.111 0.135 0.135
Hubei 0.191 0.121 0.105 0.109 0.122 0.127
Zhejiang 0.128 0.104 0.102 0.107 0.109 0.107 Heilongjiang 0.131 0.144 0.272 0.149 0.146 0.142
Fig. 4.12 Gini coefficient for average non-personnel expenditures per primary school student
primary schools from 2001 to 2006. Heilongjiang and Hubei were ranked at the top for inequity, and the inequity of these two provinces continued to increase from 2005 to 2006. The inequity in Guangxi displayed a downward trend in these 6 years, and it was the lowest among the four provinces as of 2004.
Although the inequity of non-personnel expenditures increased in some years, it decreased, kept a steady trend, or increased at a slow pace. This is the outcome we hope to achieve with compulsory educationfinancing reforms.
In these four provinces, wefind that the inequity for regular expenditures, tea- cher’s salary, and non-personnel expenditures decreased or kept steady based on the above analysis. This is a positive phenomenon, but what does it tell us? If the formula of appropriation does not change and this formula is not a fair one, the inequity will expand with the increase of per student average expenditure (see Sect. 4.6.2). When the inequity does not expand, we can conclude that the gov- ernment has revised the unfair formula of appropriation in order to improve the equity of education resource distribution.
4.4.3 The Gini Coef fi cient for Physical Facilities
Physical facilities can be represented by capital equipment value and books, which are the accumulative stock of education resources. If the government inputs more funds into schools with poor physical facilities to improve the per student average capital equipment and books, the Gini coefficient of these two resources may be reduced. We can say that the government has made efforts to improve the equity.
When the government provides the same fund input for the schools in poor and Fig. 4.13 Gini coefficient for average non-personnel expenditures per junior secondary school student
Table4.4Ginicoefficientofperstudentcapitalequipmentvalueandbooksperstudent PerstudentcapitalequipmentvaluePerstudentbooks Year200120022003200420052006200120022003200420052006 Primaryschool Guangxi0.4500.3500.3910.3880.3250.2890.1680.1690.2030.1800.1630.179 Hubei0.2840.3490.3580.3030.3240.3150.1980.2110.2020.1900.1950.203 Zhejiang0.2890.2820.2680.2630.2740.2790.1980.2060.1890.1860.1750.170 Heilongjiang0.4610.3820.4160.4040.4180.3900.2270.2310.2530.2660.2880.274 Juniorsecondaryschool Guangxi0.3390.3780.2700.2650.3460.2470.1720.1710.190.1770.1690.168 Hubei0.2560.2980.2950.3110.3080.3040.1940.2040.1820.1760.1990.206 Zhejiang0.3000.2680.2570.2560.2470.2560.2050.1860.1870.1690.1540.165 Heilongjiang0.4550.3440.6920.4060.4120.3740.2680.2610.5620.2520.2560.251
good facilities, or even more fund inputs for good schools, the inequity of these two resources may grow.
The inequity of per student average capital equipment for primary schools and junior secondary schools was generally decreasing with somefluctuation in the four provinces, excluding the junior secondary schools of Hubei. Although Hubei’s inequity of capital equipment value was going up until 2004, the inequity decreased to 0.304 from 0.311 since 2005. The inequity of Heilongjiang is the highest, and Zhejiang’s is the lowest.
The inequity of the average books per primary school student in Zhejiang, Heilongjiang, and Guangxi was generally decreasing with little fluctuation from 2001 to 2006. However, Hubei’s inequity from 2002 to 2006 is higher than that of 2001, although the inequity has been reduced gradually since 2002. For junior secondary schools, the inequity of Guangxi and Zhejiang shows regular changes, but Hubei and Heilongjiang do not. Another thing attracting our attention is that Heilongjiang’s inequity of per student average books is much higher than others, and Zhejiang’s is still the lowest (Table4.4).