Measurement of health human capital and its economic effect in China
Models and data
A Three-sector economic growth model (Barro and Jason, 1996) and a public health investment model (Agénor, 2008) were used as references in order to create an economic growth model that incorporates health, education, material capital stock, and government public expenditure, as shown in Eq. (8).
$$Y=A{(\mu {K}_{P})}^{\alpha }{(v{H}_{e})}^{\beta }{(\omega {H}_{h })}^{\gamma }{({nG})}^{1-\alpha -\beta -\gamma }$$
(8)
Where A represents exogenous technical parameters, \(A\, > \,0\)and \(\alpha ,\beta ,\gamma\) representing the elastic coefficients of physical capital, educational human capital, and HHC to total output respectively, \(\alpha ,\beta ,\gamma \in \left(\mathrm{0,1}\right)\) and \(0 \,<\, \alpha +\beta +\gamma\, < \,1\). \(\mu ,v,\omega ,n\) represent the proportion of material capital, the human capital of workers’ education, human capital of workers’ health, and the proportion of government public expenditure used in production respectively. Government public sector expenditure \(G\) is characterized by the nature of public goods, which individuals can utilize for production or health purposes.
The equation was log-linearized on both sides to minimize sample heteroscedasticity, resulting in the conversion of each index variable coefficient into an elastic coefficient. Given that the ordinary labor force plays a crucial role in influencing economic growth, it is included in the model as a control variable. The production function model of China over the years can be represented by Eq. (9).
$${y}_{{it}}={a}_{{it}}+{\alpha k}_{{pit}}+{\beta h}_{{eit}}+{\gamma h}_{{hit}}+{\varPhi g}_{{it}}+{\varphi l}_{{it}}+{\varepsilon }_{{it}}$$
(9)
Where \(i={1,2}… {N}\)each represents a different province in China. \({y}_{{it}}\) denotes the logarithm of the real GDP per capita of region \(i\) in China for the year \(t\). \({a}_{{it}}\) is the reciprocal of the TFP level of region \(i\) in China in year \(t\). \({k}_{{pit}}\) is the logarithm of per capita physical capital stock in region \(i\) of China in year \(t\). \({h}_{{eit}}\) denotes the logarithm value of the average years of schooling in year \(t\) within region \(i\) of China. \({h}_{{hit}}\) is the logarithm value of the HHC index of region \(i\) in China in year t. git is the representation of the per capita general public budget expenditures for region \(i\) of China in year \(t\). \({l}_{{it}}\) signifies the proportion of the working-age population in region \(i\) of China in year \(t\). \({\varepsilon }_{{it}}\) symbolizes the stochastic error term.
Data from the China Statistical Yearbook has been collected over the years. The per capita GDP data of China’s provinces are primarily sourced from the Statistical Yearbook of China. In this paper, the per capita GDP deflator is utilized to adjust for inflation and calculate the real per capita GDP based on 2005. The HHC index will serve as the proxy variable for HHC, offering a more comprehensive reflection of China’s health level compared to single indices like life expectancy commonly used in existing literature. The physical capital stock is determined through the perpetual inventory method. The per capita physical capital stock is calculated by dividing the local physical capital stock by the permanent population in that area. The per capita physical capital stock is adjusted by the price deflator of fixed asset investment. Tibet did not release the fixed asset investment price deflator, so the retail price index was utilized instead to account for fluctuations in price levels. Educational human capital is determined by the average years of schooling. The CPI deflator for the current year is utilized in determining per capita general public budget expenditure.
The descriptive statistical results are shown in Table 5.
Estimation of the impact of health human capital on economic growth
Using mixed regression (OLS) as the reference frame, the impact of HHC on economic growth was estimated through random effects (TE), fixed effects (FE), and Two-way FE models, as shown in Table 6.
The coefficient symbols of variables lnHi, lnCap, and lnGov in the mixed OLS regression results (refer to Column 1) are opposite to those of the other three models due to the mixed OLS regression not accounting for the individual effects of the model, as shown in Table 6. In column (2), the LM test’s p-value is 0, suggesting that the random effects estimation is superior to the mixed regression estimation. The fixed effect estimators are deemed superior as all Hausman test estimators in column (3) reject the null hypothesis. When addressing the issue of missing variables that remain constant for individuals but fluctuate over time, utilizing bidirectional fixed effects allows for controlling both time and individuals in estimation (refer to column (4)). This makes the bidirectional fixed effect model the most suitable choice.
The positive regression coefficients for the HHC index (lnHi), working-age population ratio (lnLab), and per capita general public budget expenditure ratio (lnGov) suggest a significant positive correlation with economic growth. The per capita physical capital stock (lnCap) is characterized by a negative numerical coefficient. Improving health investment has a crowding-out effect on physical capital, leading to a reduction in the accumulation of physical capital, which is detrimental to economic growth (Wang et al., 2008). The regression coefficient values indicate that the coefficients of the HHC index (lnHi), working-age population ratio (lnLab), and per capita general public budget expenditure ratio (lnGov) are 0.4809, 0.9448, and 0.2663, respectively. If lnHi, lnLab, and lnGov increase by 1%, then the corresponding percentage of economic growth is 0.48%, 0.94%, and 0.27%, respectively. The largest driving force for economic growth is the ratio of working-age population, followed by the HHC, with the per capita general public budget expenditure having a small impact on economic growth.
Robustness test
The level of higher education in the population can be measured by the proportion of individuals with advanced degrees. In this paper, the proportion of individuals with higher education (lnEduper) is utilized as a replacement for the average years of education (lnEdu). Furthermore, there are numerous outliers present in per capita real GDP, and these outliers could significantly influence the regression outcomes. To re-estimate the impact of HHC on economic growth, winsorize 97.5% on the right side of the explained variables of the sample. The educational human capital was represented by the proportion of individuals in higher education and the effect of the HHC index on economic growth aligned with the baseline regression. Following the tail reduction treatment, the HHC coefficient decreases to 0.4429, aligning with the baseline regression findings and demonstrating the robustness of the results (refer to Table 7).
Endogenetic processing
Endogeneity issues in the baseline regression could potentially introduce bias into the results of the model regression. Endogeneity is primarily caused by missing variables that are related to other variables in the model, as well as the interaction between explanatory variables and dependent variables, where they influence each other as cause and effect. The main endogenous issue in this paper is the problem of mutual causality, where HHC both promotes economic growth and economic growth, in turn, accelerates the accumulation of HHC to a certain extent. To enhance the robustness of the results, this paper treats the HHC index as an endogenous variable and chooses the first-order lag term of the endogenous explanatory variable as its instrumental variable (Bai and Bian, 2016). The first-order lag term of endogenous explanatory variables is significantly correlated with the current or future endogenous explanatory variables, indicating that the HHC in the previous period will have a notable influence on the current or future HHC. As the first-order lag variable of HHC has already taken place, it can be considered a predetermined factor, meeting the requirement of being unrelated to the current random disturbance term.
Even with controlling all control variables and double fixed effects, utilizing the instrumental variable-two-stage least squares estimation method (IV-2SLS), the HHC continues to show a significant positive influence on economic growth, as demonstrated in Table 8. During the initial phase, the F test value was 888.70, which was significantly higher than 10, as per the rule of thumb (Lin and Tan, 2019). This suggests a strong correlation between instrumental variables and endogenous explanatory variables. The regression coefficient of HHC on economic growth is significant at the 1% significance level in the second stage regression. The empirical results remain consistent before and after the addition of instrumental variables, indicating that HHC has a significant positive impact on economic growth. Hence, upon careful consideration and addressing any potential endogeneity issues in the initial regression model, the original findings of this study remain sound.
Test of heterogeneity
Regression of quantiles
Further explores the consequences of HHC on economic growth. The panel quantile regression model method (Koenker, 2004) is utilized to examine the impact of HHC on economic growth by selecting five representative sub-loci of real GDP per capita—10%, 25%, 50%, 75%, and 90%. This approach considers both time and individual effects.
The coefficient of the main explanatory variable in the bidirectional fixed effect is consistent across all quantile regression results, being at the average level. The estimated coefficient of the bidirectional fixed effect model and the estimated coefficient of the HHC at each quantile level are both significantly positive, suggesting that the HHC has played a significant role in promoting economic growth in China from 2005 to 2019 (refer to Table 9). The coefficient of the HHC index is displaying a rising trend. With every 1% rise in the HHC index, the per capita real GDP growth rate is projected to increase by a margin ranging from 0.36% to 0.60%. In controlled provinces and years, the promotion effect of economic growth by HHC is greater in provinces with higher per capita real GDP levels when considering quantile levels of different conditions. Regions that possess greater economic strength tend to exhibit higher levels of public service and are more likely to experience economic growth in the future. Enhancing the HHC level leads to economic growth and increases the disparity in regional economic growth.
Regional heterogeneity
Due to the significant variances in natural conditions, geographical features, modes of production, and cultural customs between the north and the south of China, there are differing degrees of influence on the health concept and health level of each region. These differences may also contribute to the varying levels of economic development between the North and the South. Using the Qinling-Huaihe River line as the dividing line, the 31 provinces (autonomous regions, municipalities directly under the Central government) were split into northern and southern sections. The panel two-way fixed effect model was employed to explore the North-South (ns) heterogeneity of HHC (lnHi) on economic growth. The interaction coefficient between HHC and the north and the south is notably negative at a confidence level of 5% (refer to Table 10). There is a difference in the impact of HHC on economic growth between the North and South, with a greater impact in the South than in the North.