Calculation results of EHRA index for each province
Table 2
Calculation results of EHRA Index in 22 provinces of China (2011–2020)
Province
|
Ranking
|
Mean
|
SD
|
Min
|
Max
|
Jiangsu
|
1
|
0.0186
|
0.0053
|
0.0147
|
0.0334
|
Shandong
|
2
|
0.0313
|
0.0053
|
0.0243
|
0.0415
|
Zhejiang
|
3
|
0.0344
|
0.0014
|
0.0311
|
0.0358
|
Hunan
|
4
|
0.0345
|
0.0062
|
0.0223
|
0.0413
|
Jiangxi
|
5
|
0.0361
|
0.0053
|
0.0262
|
0.0429
|
Anhui
|
6
|
0.0412
|
0.0125
|
0.0255
|
0.0624
|
Jilin
|
7
|
0.0505
|
0.0055
|
0.0450
|
0.0658
|
Guizhou
|
8
|
0.0520
|
0.0091
|
0.0434
|
0.0717
|
Shanxi
|
9
|
0.0545
|
0.0051
|
0.0411
|
0.0601
|
Liaoning
|
10
|
0.0548
|
0.0044
|
0.0475
|
0.0610
|
Henan
|
11
|
0.0574
|
0.0056
|
0.0497
|
0.0716
|
Guangxi
|
12
|
0.0685
|
0.0100
|
0.0528
|
0.0866
|
Ningxia
|
13
|
0.0729
|
0.0120
|
0.0527
|
0.0905
|
Hebei
|
14
|
0.0754
|
0.0104
|
0.0631
|
0.0937
|
Shaanxi
|
15
|
0.0848
|
0.0083
|
0.0770
|
0.1046
|
Hubei
|
16
|
0.0934
|
0.0040
|
0.0881
|
0.0998
|
Fujian
|
17
|
0.0944
|
0.0185
|
0.0706
|
0.1229
|
Heilongjiang
|
18
|
0.0948
|
0.0045
|
0.0893
|
0.1031
|
Guangdong
|
19
|
0.1253
|
0.0108
|
0.1103
|
0.1444
|
Sichuan
|
20
|
0.1442
|
0.0099
|
0.1347
|
0.1720
|
Gansu
|
21
|
0.1950
|
0.0156
|
0.1629
|
0.2158
|
Inner Mongolia
|
22
|
0.2376
|
0.0058
|
0.2301
|
0.2467
|
Note: SD Standard deviation. The ranking of each province is determined according to the annual average of the EHRA Index. |
Table 2 provides the results obtained from the preliminary calculation of the EHRA index for each province by comprehensively using the Theil index and entropy method. In general, affected by factors such as the level of economic and social development and differences in natural and geographical conditions, the cross-sectional values and interannual changes of the EHRA index in each province are different. On the one hand, from the perspective of interannual trend, Zhejiang, Hubei, and Liaoning have slight changes, with rangeability of only 0.0047, 0.0117, and 0.0135 respectively, while Gansu, Fujian, and Ningxia have sharp interannual fluctuations, with rangeability of 0.0529, 0.0523 and 0.0378 respectively. On the other hand, from the perspective of annual mean value, the EHRA index mean values of Jiangsu, Shandong and Zhejiang rank among the top three, while the EHRA index mean values of Inner Mongolia, Gansu, Sichuan and Guangdong all exceed 0.1, which shows that the healthcare resource allocation within the jurisdiction varies greatly.
Panel Unit Root Test
Table 3
Variables
|
Type(c,t,l)
|
LLC
|
IPS
|
Fisher-ADF
|
Fisher-PP
|
Smooth
|
THEIL
|
(1,0,1)
|
-3.0723 [0.0011]
|
1.5428 [0.9386]
|
2.6129 [0.0045]
|
2.1218 [0.0169]
|
YES
|
CV
|
(1,0,1)
|
-6.2910 [0.0000]
|
-0.7739 [0.2195]
|
4.3991 [0.0000]
|
6.2675 [0.0000]
|
YES
|
GINI
|
(1,0,1)
|
-6.5694 [0.0000]
|
-0.6769 [0.2492]
|
5.4675 [0.0000]
|
7.4709 [0.0000]
|
YES
|
IGHE
|
(1,1,1)
|
-12.7425 [0.0000]
|
-3.7924 [0.0001]
|
16.5861 [0.0000]
|
4.8814 [0.0000]
|
YES
|
AHRH
|
(1,1,1)
|
-16.5825 [0.0000]
|
-4.8315 [0.0000]
|
12.4263 [0.0000]
|
4.8800 [0.0000]
|
YES
|
FASG
|
(1,1,1)
|
-8.4136 [0.0000]
|
-1.6540 [0.0491]
|
0.8098 [0.2090]
|
6.4747 [0.0000]
|
YES
|
PGDP
|
(1,0,1)
|
-1.7818 [0.0374]
|
1.4939 [0.9324]
|
3.9335 [0.0000]
|
3.7478 [0.0001]
|
YES
|
PD
|
(1,0,1)
|
-3.2163 [0.0006]
|
2.2455 [0.9876]
|
3.9560 [0.0000]
|
19.5012 [0.0000]
|
YES
|
TA
|
(1,1,1)
|
-6.7772 [0.0000]
|
-1.6254 [0.0520]
|
6.1151 [0.0000]
|
0.7867 [0.2157]
|
YES
|
DR
|
(1,1,1)
|
-11.0506 [0.0000]
|
-3.2832 [0.0005]
|
4.8417 [0.0000]
|
5.4105 [0.0000]
|
YES
|
IR
|
(1,0,1)
|
-6.0050 [0.0000]
|
-3.1564 [0.0008]
|
10.0655 [0.0000]
|
2.7043 [0.0034]
|
YES
|
Note: In the test type, c the constant term, t the trend term, and l the lag order. Values outside square brackets are asymptotic statistics, and values inside square brackets are the corresponding p-values. In the Fisher-ADF test and Fisher-PP test, the statistics we report are the corrected inverse χ2 statistics and their p-values. |
To avoid the possible pseudo-regression phenomenon in the modeling process, we test each variable one by one to determine whether they have unit roots before econometric analysis. Referring to the practice of prior scholars [,], we choose to use four traditional unit root test techniques, LLC, IPS, Fisher ADF, and Fisher PP, to identify the stationarity of each variable. The null hypothesis of the four testing techniques is H0: The variable has a unit root. Nonetheless, due to the differences in the principle and premise of the unit root test, different test methods may draw different conclusions when testing the variable data. Hence, according to the principle of the minority obeying the majority, we comprehensively judge whether the data is stationary according to the four test results to improve the power and reliability of the test. As shown in Table 2, THEIL, CV, GINI, PGDP, and PD failed to reject the null hypothesis of the IPS test, and FASG failed to reject the null hypothesis of the Fisher-ADF test, and PHR failed to reject the null hypothesis of Fisher-PP test. But taken together, most panel unit root tests reject the null hypothesis at the 1% significance level (or 5% significance level). Based on the unit root test results, we believe that all the variables included in the model analysis have good stationarity and meet the requirements of subsequent econometric model analysis.
Baseline Regression Results
Table 4
Baseline regression results of the impact of FASG on EHRA
Variables
|
(1)
|
(2)
|
(3)
|
(4)
|
(5)
|
(6)
|
|
FE_1
|
FE_2
|
FE_3
|
FE_4
|
RE
|
OLS
|
FASG
|
-0.0795a
|
-0.0889a
|
-0.0849a
|
-0.0849b
|
-0.0652b
|
-0.0849a
|
|
(0.0197)
|
(0.0126)
|
(0.0156)
|
(0.0368)
|
(0.0313)
|
(0.0225)
|
PGDP
|
|
-0.0043
|
-0.0010
|
-0.0010
|
0.0050
|
-0.0010
|
|
|
(0.0036)
|
(0.0146)
|
(0.0392)
|
(0.0285)
|
(0.0236)
|
PD
|
|
0.0176
|
0.0123
|
0.0123
|
-0.0483a
|
0.0123
|
|
|
(0.0142)
|
(0.0119)
|
(0.0547)
|
(0.0138)
|
(0.0308)
|
TA
|
|
-0.0112a
|
-0.0129a
|
-0.0129b
|
-0.0151a
|
-0.0129a
|
|
|
(0.0013)
|
(0.0007)
|
(0.0051)
|
(0.0056)
|
(0.0029)
|
DR
|
|
-0.0470
|
-0.0980
|
-0.0980c
|
-0.1109b
|
-0.0980b
|
|
|
(0.0309)
|
(0.0568)
|
(0.0477)
|
(0.0559)
|
(0.0399)
|
IR
|
|
0.0841
|
0.1913
|
0.1913
|
0.2005
|
0.1913
|
|
|
(0.1518)
|
(0.1410)
|
(0.2435)
|
(0.2294)
|
(0.1890)
|
Constant
|
0.1257a
|
0.1265
|
0.1391
|
0.1391
|
0.4091
|
0.3671
|
|
(0.0099)
|
(0.0887)
|
(0.1805)
|
(0.5488)
|
(0.2817)
|
(0.2824)
|
Province FE
|
YES
|
YES
|
YES
|
YES
|
NO
|
YES
|
Time FE
|
YES
|
NO
|
YES
|
YES
|
YES
|
YES
|
R2
|
0.1253
|
0.2191
|
0.2443
|
0.4594
|
0.4484
|
0.9751
|
Observations
|
220
|
220
|
220
|
220
|
220
|
220
|
Note: Standard errors in parentheses, where Columns (1) to (3) report the Driscoll-Kraay standard errors, which are used to solve the three major problems of heteroskedasticity, autocorrelation, and cross-section correlation, Columns (4) to (6) report the cluster-robust standard errors, which are used to solve the two major problems of heteroskedasticity and autocorrelation. The R2 reported in Columns (1) to (4), (5), and (6) are Within R2, Overall R2, and Adj.R2, respectively. a P < 0.01, b P < 0.05, c P < 0.10. |
In our analysis, we also take into consideration whether there is multicollinearity between the independent variables included in the model, so we make a statistical test before estimating the baseline regression model. The test results show that the maximum variance inflation factor (VIF) is 7.70, the minimum VIF is 1.50, and the mean VIF is 4.10, which is less than the critical value 10. Hence, we believe there is no need to worry about the potential multicollinearity between variables.
When choosing a suitable model for regression, we first compare the pooled regression model and the fixed effects model (FE). In the case of considering the cross-sectional correlation of the data, the value of test F statistic of the province dummy variable is 6000.35 (P < 0.01), and the test result rejects the null hypothesis that there are no province fixed effects, which indicates that the fixed effects model should be selected for regression. We also compared the random effects model (RE) and FE, and the value of Hausman test statistics was 14.07 (P < 0.05), which still supported the acceptance of FE. In addition, this conclusion is still valid under the premise of considering and dealing with the three problems of heteroscedasticity, autocorrelation, and cross-sectional correlation, which shows that it is highly applicable to choose FE for regression.
Because the relevant tests in the model selection process show that εit has three major problems, including heteroscedasticity, autocorrelation, and cross-sectional correlation, we dealt with these problems in model regression and reported the estimated results of univariate two-way FE regression, one-way FE regression with control variables and complete two-way FE regression respectively in Columns (1) to (3) in Table 4. From the results of Columns (1) to (3), the estimated coefficients of FASG in different models are significantly negative at the 1% level. Columns (4), (5), and (6) respectively report the estimated results of two-way FE regression, RE regression, and pooled regression for comparison. It is interesting to note that in Columns (3), (4), and (6), the estimated coefficients of the core independent variable FASG and the control variable are all equal, and the estimated results of the core independent variable jointly show that FASG can significantly and negatively impact THEIL (β = -0.0849, P < 0.01). Although the estimated results of columns (3), (4), and (6) are very close, we prefer to believe the estimated results of Column (3), i.e., the results of two-way FE regression after dealing with the three major problems of εit. In the analysis based on baseline regression, we found that a more effective state of FASG is associated with a better EHRA, i.e., a more balanced and equal healthcare resource allocation. Meanwhile, the estimated coefficients of the control variables in Column (3) are all consistent with the theoretical expectations. Specifically, PGDP, DR, and TA all negatively impact THEIL, but only TA passed the significance test. PD and IR showed a positive effect on THEIL, but they were not statistically significant.
Endogenous Treatment
Table 5
2SLS regression based on instrumental variable
Variables
|
(1)
|
(2)
|
|
First stage
|
Second stage
|
FASGt−1
|
0.4694a
|
-0.2027a
|
|
(0.0736)
|
(0.0613)
|
Constant
|
-2.1434b
|
-0.6466
|
|
(0.8760)
|
(0.4217)
|
Control variables
|
YES
|
YES
|
Province FE
|
YES
|
YES
|
Time FE
|
YES
|
YES
|
Overall R2
|
0.7744
|
0.5254
|
F/Wald χ2
|
46.27
|
17107.82
|
Observations
|
198
|
198
|
Note: Standard errors in parentheses. a P < 0.01, b P < 0.05, c P < 0.10. The test statistics reported in Columns (1) and (2) are F and Wald, respectively. Cragg-Donald Wald F statistic is 40.682 (P < 0.01). |
Although the baseline regression model controls many potentially related provincial socioeconomic variables and unobservable provincial heterogeneity factors that do not change over time, it still may have endogeneity problems caused by the omission of variables, which may lead to the bias of regression results. Therefore, we take the lag phase of FASG as the instrumental variable (IV) of FASG to run two-stage least squares (2SLS) regression. In Table 5, we present the estimated results of 2SLS regression. Clearly, the test result in the first-stage regression shows that the correlation coefficient between IV and FASG is very statistically significant, and the F-statistic is much larger than the empirical value 10, indicating that IV has a strong correlation with the potential endogenous independent variable (FASG). Some observations similar to baseline regression can be made in the second-stage regression. Although the estimated coefficient of FASG has increased, the negative impact of FASG on Theil is still significant at the 1% level. After running 2SLS regression and dealing with possible endogenous problems, we found that the estimated results based on baseline regression were further confirmed, i.e., FASG showed a significant promotion effect on EHRA.
Robustness Test
Table 6 Robustness test
Variables
|
(1)
|
(2)
|
(3)
|
(4)
|
|
CV
|
GINI
|
TIME
|
CONTROL
|
FASG
|
-0.0478a
|
-0.0976a
|
-0.0924a
|
-0.0922a
|
|
(0.0115)
|
(0.0166)
|
(0.0204)
|
(0.0108)
|
Constant
|
0.6949c
|
1.1615b
|
0.1913
|
0.2162
|
|
(0.3364)
|
(0.4360)
|
(0.1489)
|
(0.3236)
|
Control variables
|
YES
|
YES
|
YES
|
YES
|
Province FE
|
YES
|
YES
|
YES
|
YES
|
Time FE
|
YES
|
YES
|
YES
|
YES
|
Overall R2
|
0.3218
|
0.4058
|
0.2933
|
0.2798
|
Observations
|
220
|
220
|
198
|
220
|
Note: The Driscoll-Kraay standard errors in parentheses. a P < 0.01, b P < 0.05, c P < 0.10.
To ensure the reliability of the conclusion, we will use three robustness test strategies to re-estimate the two-way FE regression model established above in this part. At first, replace the explained variable, i.e., use the new EHRA index constructed based on the coefficient of variation and Gini coefficient, both weighted by the entropy method as the dependent variables for regression.. Secondly, eliminate some samples, i.e., re-estimate the model after excluding the data of 2020, because there may be statistical fluctuations or even anomalies in some data on economic, social, medical, and health in 2020 due to the impact of COVID-19, which may have an impact on the estimated results. Finally, add additional control variables, i.e., add additional provincial control variables into the model, including the development level of the service industry (proportion of the added value of the tertiary industry in GDP), the level of subnational governments’ public service (proportion of general public service expenditure in total fiscal expenditure) and the intensity of educational investment (proportion of education expenditure in total fiscal expenditure), for re-estimating the baseline model. From the regression results, as shown in Table 6, the estimated coefficients of FASG in all columns are negative and statistically significant (P < 0.01), especially the estimated results in columns (3) and (4) are very close to the baseline regression results, which reconfirms the positive effect of FASG on EHRA and indicates the estimation results in this study are robust.
Mechanism Analysis
So far we have shown that FASG, to some extent, has shaped the EHRA. We now turn to test whether the impact of FASG upon EHRA work through some channels. Some studies have found that governments often make arrangements for fiscal expenditures in the medical and health field based on their fiscal capability [,] and the regional AHRH is a key factor affecting the equity and availability of medical resources under the leading role of government investment [,]. Therefore, to further explore how FASG affects EHRA, we will try to analyze the mechanism with the intensity of government health expenditure (IGHE) as one channel and the allocation of human resources for health (AHRH) as another channel. In this part, we will use Eq. (3) and Eq. (4) (IGHE and AHRH as dependent variables) for further analysis. Columns (1) and (2) in Table 7 report the estimated results of the above two equations, respectively. FASG has a significant positive impact on both IGHE and AHRH, which indicates that the stronger FASG is, the more favorable it is for the subnational government to increase fiscal expenditure in the health field and expand the supply of human resources for health, thus facilitating the EHRA.
Table 7
Mechanism analysis: IGHE and AHRH as two channels
Variables
|
(1)
|
(2)
|
|
IGHE
|
AHRH
|
FASG
|
0.0474b
|
0.1079a
|
|
(0.0189)
|
(0.0238)
|
Constant
|
2.3867a
|
-2.6754
|
|
(0.5694)
|
(1.6062)
|
Control variables
|
YES
|
YES
|
Province FE
|
YES
|
YES
|
Time FE
|
YES
|
YES
|
Overall R2
|
0.5937
|
0.9769
|
Observations
|
198
|
220
|
Note: The Driscoll-Kraay standard errors in parentheses. a P < 0.01, b P < 0.05, c P < 0.10. Due to the missing data on total social health expenditure in 2020, there are only 198 observations in Column (1). |
Heterogeneity Analysis
Table 8
Heterogeneity analysis: two-way FE threshold regression
Variables
|
(1)
|
(2)
|
(3)
|
|
PGDP
|
PD
|
DR
|
γ1
|
10.9019
|
5.7944
|
0.4640
|
γ2
|
11.1462
|
|
|
FASG·I(q ≤ γ1)
|
-0.0576a
|
-0.0750a
|
-0.0729a
|
|
(0.0212)
|
(0.0222)
|
(0.0244)
|
FASG·I(q > γ1)
|
|
-0.0286
|
-0.0981a
|
|
|
(0.0240)
|
(0.0246)
|
FASG·I(γ1 < q ≤ γ2)
|
-0.0369c
|
|
|
|
(0.0222)
|
|
|
FASG·I(q > γ2)
|
-0.0165
|
|
|
|
(0.0232)
|
|
|
F1 value of one threshold test
|
29.77b
|
38.39b
|
23.84c
|
|
[0.0333]
|
[0.0333]
|
[0.0733]
|
F2 value of two threshold tests
|
24.85b
|
|
|
|
[0.0267]
|
|
|
Control variables
|
YES
|
YES
|
YES
|
Province FE
|
YES
|
YES
|
YES
|
Time FE
|
YES
|
YES
|
YES
|
Overall R2
|
0.5071
|
0.2258
|
0.4961
|
Observations
|
220
|
220
|
220
|
Note: Values in parentheses are standard errors, and values in square brackets are p-values. a P < 0.01, b P < 0.05, c P < 0.10. |
In our view, the impact of FASG on EHRA may be restricted by different economic and social development conditions, which are likely to be heterogeneous. In this part, we will use Eq. (5) to conduct regression one by one with different control variables as threshold variables to verify whether the model has nonlinear characteristics. We first performed the threshold effect test to determine whether there was a threshold effect and how many threshold values were present and then used the bootstrap method provided by Hansen (2000) [] to obtain the statistic p-value for the test of the corresponding threshold. The estimated results shown in Table 5 and the graph of LR statistics estimated based on the bootstrap method shown in Fig. 1 indicate that PGDP, PD, and DR all passed the threshold test. According to the analysis of Column (1), there are two threshold values of PGDP, which are 10.9019 and 11.1462. When PGDP is lower than 10.9019, FASG has a strong and significant promotion effect on EHRA, with an estimated coefficient of -0.0576 (P < 0.01). When PGDP is between 10.9019 and 11.1462, the estimated coefficient of FASG on EHRA decreases to -0.0369 due to some economic constraints (P < 0.10). However, after PGDP exceeded 11.1462, the second threshold value, the effect mentioned above was further reduced and was not statistically significant, and the corresponding estimated coefficient was reduced to -0.0165 (P = 0.48). The results in Column (2) show that there is a single threshold value of PD. When PD is lower than 5.7944, FASG has a significant promotion effect on EHRA, with an estimated coefficient of -0.0750. When PD exceeded 11.1462, the estimated coefficient of FASG on EHRA decreased to -0.0286. The former is statistically significant (P < 0.01), while the latter is not (P = 0.23), which indicates that the over-concentration of the population will inhibit the promotion effect of FASG on EHRA. In addition, DR also has a single threshold value shown in Column (3). When DR is lower than 0.4640, FASG has a significant promotion effect on EHRA, with an estimated coefficient of -0.0729 (P < 0.01); and different from the threshold characteristics of PGDP and PD mentioned above, when DR exceeds 0.4640, the threshold value, the estimated coefficient increases to -0.0981 and remains statistically significant (P < 0.01), which indicates that the increase of DR will force subnational governments to pay more attention to the equal allocation of medical and health resources and amplify the promotion effect of FASG on EHRA.