Appendix 5: Percentage of Boarding Students Receiving Living
4.5 The Analysis of Horizontal Equity: Theil Coefficient
4.5.1 Theil Coef fi cients for Regular Expenditures and Physical Facilities
In Guangxi, the Theil coefficient for regular expenditures for primary and junior secondary schools increased gradually from 2001 to 2006. The Theil coefficients for budgetary regular expenditure, teacher’s salary, non-personnel expenditure, capital equipment, and books show irregular changes. However, we were glad to see that the Theil coefficients of 2006 were lower than those of 2005, except for books.
In Hubei, the Theil coefficient for regular expenditures for primary and junior secondary schools has an upward trend withfluctuations. The Theil coefficients of other resources are all changed irregularly. However, the Theil coefficients of 2006 are all higher than that of 2005, excluding that of capital equipment for junior secondary schools.
In Zhejiang, the Theil coefficient showed the steadiest changes. For regular expenditures, the Theil coefficient for junior secondary schools had a small and steady increase, but primary schools showed a decreasing trend. The Theil coeffi- cients of other resources changed irregularly. Only the Theil coefficients for capital equipment and books for junior secondary schools and non-personnel expenditures for primary schools were higher in 2006 than in 2005.
In Heilongjiang, the Theil coefficient for regular expenditures in junior sec- ondary schools is much higher than that for primary schools in each year. However, there is not a regular development trend. The Theil coefficients for other resources
have the same characteristics. The Theil coefficient for each primary school resource in 2006 was lower than for 2005. For junior secondary schools, the Theil coefficients for budgetary regular expenditure and non-personnel expenditure were higher than those for 2005.
Among the four provinces, the Theil coefficient for each resource has different characteristics. However, if we compare the Theil coefficient to the Gini coefficient we computed, we find they have similar characteristics. That is, both the Theil coefficient and Gini coefficient show the same inequity trend. However, the importance of the Theil coefficient is that it can be decomposed by inter-group and intra-group. This may be helpful to determine the source of the inequity. In the next section, we decompose the Theil coefficient by intra-county and inter-county at first. Secondly, we break up the Theil coefficient into inter-rural/urban inequity, as well as intra-rural inequity and intra-urban inequity. The decomposition may tell us how to reduce and even eliminate the inequity (Tables4.5,4.6,4.7and 4.8).
4.5.2 The Decomposition of the Theil Coef fi cient:
Intra-county and Inter-county
In this section, we present the contribution ratio of intra-county and inter-county inequity to total inequity. If the contribution ratio of intra-county inequity is higher than that of inter-county inequity, the government should reduce intra-county inequity in order to reduce or eliminate the total inequity. We only decomposed the Theil coefficients of Guangxi, Hubei, and Zhejiang from 2004 to 2006, because these three provinces use the school as the unit of the education revenue and expenditure statistic; Heilongjiang still takes the county as the unit.
Table 4.5 Theil coefficients for regular expenditures and physical facilities of Guangxi
Year RE BRE TS NPE CE BO
Junior secondary school 2001 0.032 0.046 0.015 0.079 0.195 0.050 2002 0.035 0.050 0.017 0.091 0.372 0.050 2003 0.048 0.048 0.019 0.122 0.130 0.060 2004 0.046 0.053 0.023 0.091 0.117 0.052 2005 0.052 0.075 0.036 0.076 0.406 0.045 2006 0.055 0.054 0.034 0.085 0.098 0.044
Primary school 2001 0.058 0.076 0.020 0.103 0.374 0.052
2002 0.064 0.089 0.017 0.125 0.223 0.049 2003 0.070 0.073 0.016 0.126 0.291 0.080 2004 0.074 0.084 0.020 0.118 0.286 0.056 2005 0.078 0.090 0.032 0.127 0.201 0.045 2006 0.088 0.081 0.031 0.096 0.152 0.051 RE regular expenditure; BRE budgetary regular expenditure; TS teacher’s salary; NPE non-personnel expenditure;CEcapital equipment;BObooks
In Guangxi, the contribution ratio of inter-county inequity to regular expenditure and budgetary regular expenditure inequity is higher than 50 %. The contribution ratio of inter-county inequity to teacher’s salary inequity is greater than 67.2 %.
However, the inequity of non-personnel expenditure from intra-county inequity is gradually becoming higher, at least higher than 50 %. As for capital equipment and books, the contribution ratio from inter-county inequity is much higher.
In Hubei, the contribution of inter-county inequity to budgetary regular expen- diture and teacher’s salary is much higher. The capital equipment and books Table 4.6 Theil coefficients for regular expenditures and physical facilities of Hubei
Year RE BRE TS NPE CE BO
Junior secondary School 2001 0.083 0.108 0.039 0.110 0.114 0.065 2002 0.073 0.068 0.021 0.167 0.151 0.068 2003 0.088 0.077 0.025 0.161 0.151 0.052 2004 0.087 0.080 0.024 0.146 0.192 0.049 2005 0.087 0.086 0.029 0.127 0.164 0.064 2006 0.100 0.114 0.031 0.151 0.182 0.066
Primary school 2001 0.087 0.156 0.035 0.119 0.136 0.063
2002 0.104 0.121 0.027 0.199 0.276 0.071 2003 0.108 0.104 0.026 0.181 0.230 0.067 2004 0.090 0.078 0.030 0.178 0.165 0.057 2005 0.092 0.082 0.029 0.152 0.203 0.059 2006 0.106 0.096 0.033 0.174 0.179 0.064 RE regular expenditure; BRE budgetary regular expenditure; TS teacher’s salary; NPE non-personnel expenditure;CEcapital equipment;BObooks
Table 4.7 Theil coefficients for regular expenditures and physical facilities of Zhejiang
Year RE BRE TS NPE CE BO
Junior secondary school 2001 0.032 0.037 0.020 0.060 0.157 0.068 2002 0.032 0.031 0.021 0.076 0.115 0.056 2003 0.040 0.034 0.025 0.095 0.105 0.056 2004 0.041 0.037 0.026 0.131 0.104 0.046 2005 0.041 0.036 0.028 0.128 0.101 0.038 2006 0.040 0.035 0.022 0.115 0.111 0.043
Primary school 2001 0.041 0.035 0.025 0.116 0.139 0.066
2002 0.042 0.041 0.020 0.126 0.126 0.068 2003 0.042 0.038 0.026 0.104 0.127 0.058 2004 0.038 0.036 0.025 0.107 0.115 0.055 2005 0.042 0.033 0.028 0.108 0.136 0.050 2006 0.036 0.027 0.025 0.116 0.135 0.046 RE regular expenditure; BRE budgetary regular expenditure; TS teacher’s salary; NPE non-personnel expenditure;CEcapital equipment;BObooks
inequity is mainly from intra-county inequity. The inequity of regular expenditure for primary schools mainly is derived from inter-county inequity. However, this inequity for junior secondary schools was from inter-county inequity in 2004, but was from intra-county inequity after 2004. The inequity of non-personnel expen- diture has the same characteristics.
In Zhejiang, inter-county inequity’s contribution to regular expenditure for pri- mary and junior secondary schools was going down. In 2006, intra-county inequity exceeded inter-county inequity. The inequity of budgetary regular expenditure, non-personnel expenditure, capital equipment, and books mainly derived from intra-county inequity. However, the teacher’s salary inequity is still mainly from inter-county inequity.
Based on the above analyses, the inequity of these three provinces may reflect the same two characteristics. Firstly, the teacher’s salary inequity is mainly caused by inter-county inequity. The Gini coefficient and Theil coefficient may be used to reflect the inequity of teacher’s salary, but not per student average teacher resources. Suppose that one teacher teaches a student all the time. If this teacher works in county A, he or she may be paid 2000 Yuan as the salary. However, if the teacher works in county B, he or she may be paid a higher or a lower salary.
Although the teacher receives a different salary, the students receive the same teacher resource. Secondly, the inequity of capital equipment and books is mainly derived from intra-county inequity.
In terms of policy intervention, if the intra-county inequity is playing an important role in a dominating inequity, the county government shall be responsible for reducing or eliminating inequity. If the inter-county inequity takes an important role, the central and provincial governments should take the main responsibility (Tables4.9,4.10 and4.11).
Table 4.8 Theil coefficients for regular expenditures and physical facilities of Heilongjiang
Year RE BRE TS NPE CE BO
Junior secondary School 2001 0.132 0.118 0.031 0.299 0.375 0.117 2002 0.121 0.117 0.037 0.203 0.195 0.113 2003 0.074 0.057 0.024 0.167 0.124 0.145 2004 0.135 0.118 0.046 0.306 0.292 0.101 2005 0.109 0.097 0.043 0.184 0.289 0.105 2006 0.139 0.127 0.040 0.273 0.240 0.103
Primary school 2001 0.048 0.052 0.026 0.164 0.364 0.087
2002 0.041 0.042 0.034 0.161 0.258 0.092 2003 0.049 0.046 0.034 0.177 0.295 0.102 2004 0.047 0.041 0.039 0.197 0.291 0.112 2005 0.054 0.047 0.037 0.143 0.299 0.131 2006 0.036 0.037 0.023 0.116 0.264 0.119 RE regular expenditure; BRE budgetary regular expenditure; TS teacher’s salary; NPE non-personnel expenditure;CEcapital equipment;BObooks
In Zhejiang, the inequity of every resource for both primary and junior sec- ondary schools shows the same characteristics. From 2001 to 2003, the intra-urban inequity contributed to total inequity at a very high ratio; however, after 2004, the inequity of every resource was mainly derived from intra-rural inequity. The inter-rural/urban inequity still contributes a small ratio.
Table 4.9 Theil coefficient decomposition of intra-county and inter-county differences in Guangxi
Difference Contribution ratio (%):
primary schools
Contribution ratio (%):
junior secondary schools
2004 2005 2006 2004 2005 2006
RE Intra-county 30.3 33.8 29.8 47.5 45.5 41.1
Inter-county 69.7 66.2 70.2 52.5 54.5 58.9
BRE Intra-county 28.6 32.9 32.1 45.8 42.4 44.8
Inter-county 71.4 67.1 67.9 54.2 57.6 55.2
NPE Intra-county 50.9 56.4 53.5 55.6 70.7 58.7
Inter-county 49.1 43.6 46.5 44.4 29.3 41.3
TS Intra-county 22.9 23.1 25.8 32.8 19.2 20.5
Inter-county 77.1 76.9 74.2 67.2 80.8 79.5
CE Intra-county 51.0 62.2 64.9 64.9 53.9 74.5
Inter-county 49.0 37.8 35.1 35.1 46.1 25.5
BO Intra-county 58.5 73.4 69.2 61.2 75.4 70.5
Inter-county 41.5 26.6 30.8 38.8 24.6 29.5
RE regular expenditure; BRE budgetary regular expenditure; TS teacher’s salary; NPE non-personnel expenditure;CEcapital equipment;BObooks
Table 4.10 Theil coefficient decomposition of intra-county and inter-county differences in Hubei Difference Contribution ratio (%):
primary schools
Contribution ratio (%):
junior secondary schools
2004 2005 2006 2004 2005 2006
RE Intra-county 33.8 40.5 38.3 33.8 65.1 65.1
Inter-county 66.2 59.5 61.7 66.2 34.9 34.9
BRE Intra-county 39 45.8 44.8 38.1 41.4 39.6
Inter-county 61 54.2 55.2 61.9 58.6 60.4
NPE Intra-county 49.4 54.6 55.1 45.8 51.1 46.3
Inter-county 50.6 45.4 44.9 54.2 48.9 53.7
TS Intra-county 29.3 36 36.1 37.9 40.7 38.1
Inter-county 70.7 64 63.9 62.1 59.3 61.9
CE Intra-county 63.4 64.3 65.9 56.9 65.5 61.0
Inter-county 36.6 35.7 34.1 43.1 34.5 39.0
BO Intra-county 59.8 69.0 71.8 65.6 64.5 67.2
Inter-county 40.2 31.0 28.2 34.4 35.5 32.8
RE regular expenditure; BRE budgetary regular expenditure; TS teacher’s salary; NPE non-personnel expenditure;CEcapital equipment;BObooks
In Heilongjiang, the inequity of each resource for primary schools is contributed mostly by intra-rural inequity. However, for junior secondary schools, the inequity of regular expenditure, non-personnel expenditure, teacher’s salary, and capital equipment is mainly caused by intra-urban inequity. However, budgetary regular expenditure and books inequity mostly comes from intra-rural inequity. The con- tribution ratio of inter-rural/urban inequity is very small.
In these four provinces, the inter-rural/urban inequity of Heilongjiang is the lowest, and that of Hubei is the highest. Compared with intra-inequity, inter-inequity is much lower. Although this seems like a positivefinding, it does not illustrate that the difference of education resources input into rural and urban areas is very small. We just know that intra-inequity contributed a higher ratio than inter-inequity. Therefore, it is necessary to compute the difference between rural and urban areas, as shown in Sect.4.7(Tables4.12,4.13,4.14and 4.15).