最近,被邀请参加研究生答辩评委,发现有很多的学生在使用集中指数来衡量公平性。
首先:衡量公平性的指标有基尼系数、集中指数和泰尔指数等。在我理解,基尼系数,仅仅是在收入分类下的支出的公平性的测量。集中指数是可以把面积、人口密度、筹资水平的分类作为标准进行衡量公平性 的指标。泰尔指数的好处在于能够精确的分解组内和组外的不公平性来源。泰尔指数需要通过Excel来计算,而集中指数可以通过Stata来完成。命令使用conindex来完成。
例如:有以下数据
in是表示收入,out2表示卫生服务费用,Ftype是家庭类型,1表示农村,2表示城市;age_type是通过age取余后取整得到
命令:replace age_type=int(age/10),目的是将年龄分成10岁一段,并设Ftype和age_type为INt类型字段。
命令:conindex out2, rankvar(in1) truezero graph compare(age_type) ytitle("医疗服务利用") xtitle("收入情况")
------------------------------------------------------------------------------+
Index: | No. of obs. | Index value | Std. error | p-value |
-------------------+-------------+-------------+-------------------+----------|
CI | 2749 | .12714691 |.02647253 | 0.0000 |
------------------------------------------------------------------------------+
根据年龄分组的集中指数的分解:
For groups:
CI for group 1: age_type = 0
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Index: | No. of obs. | Index value | Std. error | p-value |
-------------------+-------------+-------------+-------------------+----------|
CI | 431 | .0427213 |.04412536 | 0.3335 |
------------------------------------------------------------------------------+
CI for group 2: age_type = 1
------------------------------------------------------------------------------+
Index: | No. of obs. | Index value | Std. error | p-value |
-------------------+-------------+-------------+-------------------+----------|
CI | 342 | -.04334135 |.05530033 | 0.4337 |
------------------------------------------------------------------------------+
CI for group 3: age_type = 2
------------------------------------------------------------------------------+
Index: | No. of obs. | Index value | Std. error | p-value |
-------------------+-------------+-------------+-------------------+----------|
CI | 416 | -.02477496 |.04854327 | 0.6101 |
------------------------------------------------------------------------------+
CI for group 4: age_type = 3
------------------------------------------------------------------------------+
Index: | No. of obs. | Index value | Std. error | p-value |
-------------------+-------------+-------------+-------------------+----------|
CI | 206 | .05030345 |.06996243 | 0.4730 |
------------------------------------------------------------------------------+
CI for group 5: age_type = 4
------------------------------------------------------------------------------+
Index: | No. of obs. | Index value | Std. error | p-value |
-------------------+-------------+-------------+-------------------+----------|
CI | 234 | -.13829476 |.08520336 | 0.1059 |
------------------------------------------------------------------------------+
CI for group 6: age_type = 5
------------------------------------------------------------------------------+
Index: | No. of obs. | Index value | Std. error | p-value |
-------------------+-------------+-------------+-------------------+----------|
CI | 250 | .14290261 |.10757915 | 0.1853 |
------------------------------------------------------------------------------+
CI for group 7: age_type = 6
------------------------------------------------------------------------------+
Index: | No. of obs. | Index value | Std. error | p-value |
-------------------+-------------+-------------+-------------------+----------|
CI | 439 | .23560486 |.08076595 | 0.0037 |
------------------------------------------------------------------------------+
CI for group 8: age_type = 7
------------------------------------------------------------------------------+
Index: | No. of obs. | Index value | Std. error | p-value |
-------------------+-------------+-------------+-------------------+----------|
CI | 326 | .10150221 |.052046 | 0.0520 |
------------------------------------------------------------------------------+
CI for group 9: age_type = 8
------------------------------------------------------------------------------+
Index: | No. of obs. | Index value | Std. error | p-value |
-------------------+-------------+-------------+-------------------+----------|
CI | 99 | .22947318 |.08512807 | 0.0083 |
------------------------------------------------------------------------------+
CI for group 10: age_type = 9
------------------------------------------------------------------------------+
Index: | No. of obs. | Index value | Std. error | p-value |
-------------------+-------------+-------------+-------------------+----------|
CI | 6 | .56975585 |.29308716 | 0.1238 |
------------------------------------------------------------------------------+
Test for stat. significant differences with Ho: diff=0 (assuming equal variances)
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F-stat = 2.7088678 | p-value= 0.0038 |
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集中曲线: