Estimating the spatial correlation and convergence of China’s healthcare resources allocation: evidence from the Yangtze River Delta Region – Archives of Public Health – Archives associated with Public Health
Methods
We first construct a healthcare resources supply index (HRS) using the entropy weight method, analyze regional differences, and then examine the sources of variations by using the Gini coefficient decomposition method given by Dagum [ 36 ]. Let G represent Gini coefficient, j plus h symbolize the number of regions, i and r stand for the quantity of cities in the particular region, k represent the total number of regions, n represent the total number of cities, plus n _{ j } ( and _{ h } ) represent the number of cities in region j ( h) . Further, y _{ ij } ( y _{ rh) } represents the HRS of city i ( r) within region m ( h) , and \(\overline y \) signifies the arithmetic mean of the HRS. The following equation can be obtained:
$$G = \frac 1 2n^2 \overline y (\sum\limits_ i=1 ^ n \sum\limits_r=1^ n ) = \sum\limits_ j=1 ^ k \sum\limits_h=1^ k \sum\limits_ i=1 ^n_j \sum\limits_r=1^n_h $$
(1)
After the overall Gini coefficient is calculated, nited kingdom regions are sorted according to the average HOURS in the particular YRD, namely y _{ 1 } ≤ … ≤ con _{ l } ≤ … y _{ k } , plus then the Gini coefficient G will be decomposed into three parts: (1) intraregional difference contribution ( G _{ w } ), (2) interregional difference factor ( G _{ nb } ), and (3) transvariation density contribution ( G _{ t } ), which meet the particular requirements associated with G = G _{ w } + Gary the gadget guy _{ nb } + G _{ t } .
Next, we use the KDE method to explore the spatial distribution dynamics of the HRS in the particular YRD. Specifically, we make use of Moran’s I to examine the spatial correlation from the YRD’s HRS. If Moran’s We is significant, the LISA cluster map will be used to determine whether the local correlation types and clusters in different regions are statistically significant. When Moran’s I actually value is usually [− 1, 0), 0, and (0, 1], it means negative correlation, irrelevance, and positive correlation, respectively. According to the MACK cluster map, four sorts of spatial agglomeration relationships can be identified: (1) highhigh agglomeration area (HH type), (2) highlow agglomeration area (HL type), (3) lowlow agglomeration area (LL type), and (4) low–high agglomeration area (LH type).
Both σ convergence estimation and β convergence estimation are commonly utilized in convergence analysis [ 58 ]. The former estimate does not rely on an econometric model plus uses the particular coefficient associated with variation in order to measure, which usually can confirm the previous Gini coefficient results. β convergence can be divided into absolute β convergence and conditional β convergence. The former is used to assess whether the supply of healthcare resources in various regions will converge in order to the same steadystate equilibrium point without considering the town heterogeneity factors. More importantly, we include spatial factors, heterogeneity, and health care policy as control variables in conditional β convergence for a more comprehensive evaluation.
The model for complete β convergence is set because follows:
$$\ln (\frac y_i,t+1 y_i,t ) = \alpha + \beta \ln (y_ i,t ) + \mu_ i + \eta_ t + \varepsilon_ it $$
(2)
where i symbolizes the city; t represents the time; y _{ i, t +1 } and y _{ i, to } signify the HOURS of town i in t + 1 period and capital t period, correspondingly; ln( y _{ i, big t +1 } /y _{ i, t } ) signifies the annual growth rate of HRS in city i during the time period from to to capital t + 1 ; plus β is the convergence parameter to become estimated, exactly where β < 0 means an absolute β convergence trend, and otherwise it indicates that there is a divergence pattern. α is definitely a constant term; μ _{ we } and η _{ t } represent regional and time effects, respectively; and ε _{ it } symbolizes the random interference term. The formula of convergence rate is \(v = — \frac 1 TS \ln (1 + \beta )\) , where TS represents the period span.
In case heterogeneous aspects such as economic development status, city size, and government fiscal capacity are included in the model, the particular model for conditional β convergence can be set as follows:
$$\ln (\frac y_i,t+1 y_i,t ) sama dengan \alpha + \beta \ln (y_ i,t ) + \gamma \ln (X_ i,t ) + \mu_ i + \eta_ t + \varepsilon_ it $$
(3)
where X _{ i actually, t } is the control variable; γ is certainly the unbekannte to end up being estimated with regard to the control variable; and the meaning of the other variables is the same as the formula ( 2 ).
Considering the possible impact of policies and external shocks on the conditional β convergence, we have:
$$\ln (\frac y_i,t+1 y_i,t ) = \alpha + \beta \ln (y_ i,t ) + \gamma \ln (X_ i,t ) + \delta P_ i,t + \tau [\ln (y_i,t ) \times P_i,t ] + \mu_ i + \eta_ t + \varepsilon_ it $$
(4)
exactly where P _{ i, big t } is a policy dummy variable, where if region i starts to implement the particular policy within period t , then P _{ i, to } is assigned the value of 1 throughout period capital t and after, plus P _{ i, big t } will be assigned a value of 0 before period t ; and δ signifies the effect of the policy upon the growth rate associated with HRS; τ represents the particular impact of policy around the convergence associated with HRS.

(3) Spatial panel model
Taking into account the spatial correlation, all of us construct a spatial econometric model of β convergence. In order to determine the exact form of the spatial effects entering the particular panel design, we first estimate the following three spatial models in the absolute β convergence estimation:
$$\ln (\frac y_i,t+1 y_i,t ) sama dengan \alpha + \beta \ln (y_ i,t ) + \rho \sum\limits_ j=1 ^ N W_ij \ln (\frac y_i,t+1 y_i,t ) + \mu_ i + \eta_ t + \varepsilon_ it $$
(5)
$$\ln (\frac y_i,t+1 y_i,t ) = \alpha + \beta \ln (y_ i,t ) + \mu_ i + \eta_ t + \varepsilon_ i,t, \varepsilon_ i,t = \lambda \sum\limits_ j=1 ^ N W_ij \varepsilon_j,t + \sigma_ i,t $$
(6)
$$\ln (\frac y_i,t+1 y_i,t ) = \alpha + \beta \ln (y_ i,t ) + \rho \sum\limits_ j=1 ^ N W_ij \ln (\frac y_i,t+1 y_i,t ) + \theta \sum\limits_ j=1 ^ N W_ij \ln (y_ i,t ) + \mu_ i + \eta_ t + \varepsilon_ it $$
(7)
Equation ( 5 ) may be the spatial autoregressive β convergence model (SAR), and Eqs. ( 6 ) and ( 7 ) are the spatial error β convergence model (SEM) as well as the spatial Dubin β convergence model (SDM), correspondingly. In these equations, ρ symbolizes the spatial effect coefficient of the explained variable, reflecting the influence from the described variable in the neighboring cities; λ represents the particular spatial effect coefficient of the error phrase, reflecting the random shock; θ represents the spatial effect coefficient of the particular explanatory adjustable, reflecting the influence associated with the explanatory variable of neighboring towns; and W _{ ij } signifies the spatial weight matrix. In this paper, we all use the inverse distance bodyweight matrix.
After estimating the particular three above spatial screen models, following Alhorst [ 59 ] and Han [ 60 ], we test and select appropriate spatial econometric models. First, the Lagrange multiplier (LM) test is performed based on the traditional panel design. If the LM test is substantial, the SDM model will certainly be used. Then, the likelihood ratio (LR) test plus Hausman test are used to figure out individual/time results and fixed/random effects. Subsequently, the Wald and LR tests are usually used to evaluate if the particular SDM model can be degraded to the SEM or SAR model. When the degraded result is usually inconsistent with the LM test result, the SDM design will be selected. In the conditional β convergence estimation, we also make use of the same strategy to determine the specific form associated with the spatial econometric model.
Data and variables
According to the particular State Council (2019) [ 26 ], the Yangtze Water Delta (YRD) region includes Shanghai (SH), Jiangsu (JS), Zhejiang (ZJ), and Anhui (AH), consisting of 41 cities at and over the prefectural level. The main variables plus data used in this study are reported below.
Because healthcare sources include human, material, and financial assets [ 11 ], two indicators are selected for each of the above three aspects according in order to the availability of data, and the entropy weight method is definitely used to create the HOURS index [ 22 , 61 ]. The data source and weight are documented in Table 1 . The HRS results associated with the 41 YRD metropolitan areas from 2007 to 2019 are reported in Desk 11 within Appendix . It can be seen that the HOURS from the YRD and subprovincial regions has shown a continuous upward tendency with certain differences among the provinces.
To be able to estimate conditional β convergence, it is necessary to control the particular heterogeneity elements across cities. Based on the availability of data, we include the following manage variables within the model: town size (SIZE), economic development level (GDP), urbanization level (UR), authorities financial capacity (GFC), plus government financial selfsufficiency price (GFS) [ 62 , 63 , 64 ]. The particular definitions and data sources of these variables are documented in Table 2 . Logarithm processing is utilized to eliminate the dimensional difference.
Due to the fact the existence of medical universities/colleges may affect the particular HRS of that specific city, all of us differentiate the city subsamples based on the existence associated with medical universities/schools and healthcare graduate programs in the starting year of the sample. The medical education information of different cities are reported in Table 12 in Appendix .
We also incorporated the particular main healthcare reforms into the empirical design. The policy variables are the descending health care resources reform (DHR) plus comprehensive healthcare reform (CMR). The descending healthcare resources reform is to encourage the balanced submission by building medical treatment combinations and increasing government investment [ 65 ]. Different towns usually experienced different timing of reforms. We take the time of 1st document issued by the nearby health departments (authorities) or the time of the very first medical therapy combination being organized since the change time point (see Desk 12 within Appendix ). All of us then define one plan dummy DHR, setting the particular afterreform period as 1 and the prereform time period as 0.
The comprehensive medical reform tries to reduce diagnosis and treatment costs and realize the goal of hierarchical diagnosis plus treatment. Within February 2015, Jiangsu and Anhui were identified as pilot provinces regarding comprehensive medical reform, followed by Zhejiang and Shanghai in May 2016. The date of publication by local health authorities or even the official launch date of the particular reform can be used as the time stage of change, so we all have the trick CMR. It should become noted that, if the over reform is certainly launched prior to July one of the current 12 months, the value of 1 is assigned for the current year, plus if the particular reform is launched after July 1 of the current yr, the value of 1 will end up being assigned from the next year.