A. Model Specification, Variables, and Data
Using panel data for 30 Chinese provinces in the period 1985–2004, we investigate the relationship between human capital and productivity growth in China. The econometric model is specified as follows:
where t and i denote the time period and province, respectively, and ε is the random error distributed identically and independently. The dependent variable is the growth rate of TFP. It is represented by the natural logarithm of the measured Malmquist TFP index. The explanatory variables are defined as follows:
- (a) H is a vector of human capital variables, which are our main variables of interest. It is represented either in the aggregate or by its composition. In addition, compatible measures of human capital quality are also included.
- (b) X is a vector of other control variables that may affect TFP growth. It includes foreign direct investment (FDI), the degree of openness (Openness), and a proxy for infrastructure (Transport). FDI is measured as the ratio of foreign direct investment to real GDP deflated at 1995 prices. It acts as an important factor in promoting technology diffusion in China (Liu 2000). FDI provides China with needed capital and helps alleviate unemployment pressure. It also brings forward advanced machines, equipment, and better managerial skills. Openness is measured as the ratio of the sum of exports and imports to real GDP deflated at 1995 constant prices. It promotes across-the-board learning in product design, facilitates technology diffusion and imitation, and helps generate technological innovations (Wei et al. 2001). Openness also increases international competition and spurs technical efficiency improvements. Infrastructure is represented in terms of transportation, measured by the length of railway, road and inland navigable water network per square kilometer. It can promote productivity growth by reducing the delivery costs of new equipment and machines and also by facilitating the rapid diffusion of advanced technology.10
- (c) θ is used to capture the unobserved province-specific effects.
We use one-period lagged values of human capital variables to control for the possible endogeneity running from TFP growth to human capital variables. We apply the same procedure to other control variables to deal with the possible reverse causality from productivity growth. FDI is argued to be strongly endogenous, since FDI tends to earn higher returns in locations with higher TFP (Li and Liu 2005). We thereby follow Fleisher, Li, and Zhao (2008) and use the two-period lagged values of FDI in estimations to mitigate this effect. This lagged procedure is to some degree an appropriate way to handle the endogeneity issue, as the lagged values of variables are measured before TFP growth has occurred.
We restrict our attention to estimations using the fixed-effects model. This is because the omitted individual effects, for example, province-specific geographic factors, are mostly likely to be correlated with other regressors such as FDI and openness in the case of China. Note that we do not include capital variables as in Fleisher, Li, and Zhao (2008) and Fleisher and Chen (1997). This is because the TFP growth rate we measured includes changes in the technical efficiency term, which has been assumed to be independently identically distributed and uncorrelated with explanatory variables. If capital variables had been included as determinants of TFP growth, the orthogonal assumption of the technical efficiency term would no longer have been valid.
The measurement of our main variables of interest, namely the human capital variables, deserves some detailed explanation. The aggregate measure of human capital is often represented by the average years of schooling per capita, denoted as “schooling.” To calculate years of schooling, we use the perpetual inventorymethod. This method, initially proposed by Barro and Lee (2001), has been widely applied to measure the average years of schooling in the Chinese case (e.g., Démurger 2001; Wang and Yao 2003; Liu and Li 2006). We follow Démurger (2001) and measure years of schooling accumulated at three broad levels of schooling, namely, the primary, secondary (comprising junior secondary, senior secondary, and specialized secondary), and university education. The calculation is carried out in two steps. First, we calculate the respective human capital stock accumulated at three schooling levels, using the perpetual inventory method specified as follows:
where Hj,i,t is the number of accumulated graduates who have completed at least level j of schooling in province i at time t; Gradj,i,t is the annual number of net graduates with schooling at level j in province i at time t; δi,t is the depreciation rate represented by the mortality rate of the population; j denotes the level of schooling: specifically j= 1 indicates primary education, j= 2 secondary education, and j= 3 university education.
To obtain the initial values of accumulated human capital stock, we use the data from the 1982 population census that was carried out by sampling 1‰ of the population in 28 provinces. The initial values of human capital stock at the three schooling levels (H0,i,t) are defined as:
in which Prii,0, Seci,0, and Unii,0 are the initial values of the number of graduates from the respective levels of schooling. They are derived through multiplying the 1‰ sampling number of people who have completed their primary, secondary, and university education in province i by the total population in that province in 1982, Popi,0.
The second step is to take the weighted average of the accumulated human capital stock at different levels of schooling. The weights are usually defined as the lengths of the respective schooling cycles. Following Démurger (2001), we assign the weights for primary, secondary and university schoolings at 5, 10, and 14.5 years, respectively. After dividing by the total population Popi,t, we obtain the aggregate stock of human capital per capita, specified as
To measure the composition of human capital, we employ the rates of enrollment to primary school, secondary school, and university, denoted as “pri_enrol,”“sec_enrol,” and “uni_enrol,” respectively. The enrollment rate at a specific level of education is often used to measure human capital in the literature (e.g., Barro 1991; Mankiw, Romer, and Weil 1992; Chen and Fleisher 1996). Note that the enrollment rates we have applied here are different from the standard enrollment ratios. The standard enrollment rate is usually defined as the total number of students enrolled in a given level of schooling divided by the number of children in the official age range for that level of schooling (Hannum et al. 2008). However, in China, the data for the number of people in the official age range for that level of schooling is not available for a continuous time period. To provide a consistent data series for school enrollment rates over a long time period, we opt to calculate the enrollment rate by dividing the total number of students enrolled in a given level of schooling by the total population. This way of calculating China's enrollment rates is often seen in the literature (e.g., Chen and Fleisher 1996; Wei et al. 2001).
Compared to the standard enrollment rate, our computed school enrollment rates may have underestimated the actual enrollment rates because of dividing by a large denominator. This is largely constrained by data availability. Nevertheless, the inclusion of enrollment rates at all three levels of schooling may help alleviate the underestimation problem to some extent. As pointed out by Wößmann (2003) and Hanushek and Kimko (2000), the standard enrollment rate may not be able to accurately reflect changes in human capital stock, particularly in periods of rapid demographic transition. In contrast, our computed enrollment rates may get away from this problem in that the denominator used, namely the total population, is relatively less affected by the demographic transition that is driven by declining fertility and thereby results in substantial falls, mainly in young dependents.
In addition to quantitative measures, we also introduce quality measures of human capital. The quality of aggregate human capital is measured by the share of education expenditure in local government fiscal expenditure, denoted as “ed_exp,” or by the share of expenditure on culture, education, science, and health in local government general budgetary expenditure, denoted as “culture_exp.” We measure the quality of human capital components by teacher–student ratios at different education levels, denoted as “pri_teas,”“sec_teas,” and “uni_teas,” respectively. Increases in teacher–student ratios indicate improvements in education quality which may promote TFP growth. Hence, the teacher–student ratio is expected to be positively related to TFP growth. Also note that the quality measures applied here are input-based. It would be interesting to also apply output-based measures of education quality, like national assessments of student achievement, to our estimations. Unfortunately, these data are not available across all provinces and over time.
Furthermore, we introduce an alternative measure of education quality at the three levels of schooling, that is, interaction terms between enrollment rates and teacher–student ratios. They are denoted as “pri_enroll*pri_teas,”“sec_enroll*sec_teas,” and “uni_enroll*uni_teas,” respectively. The use of interactions may help alleviate possible multicollinearities among enrollment rates and teacher–student ratios at the three levels of education. Thus, we can capture the effects on TFP growth made both by changes in education quantity, represented by enrollment rates, and changes in education quality, represented by interaction terms. The estimated coefficients for interaction terms are expected to be positive.
Our data are mainly sourced from the Comprehensive Statistical Data and Materials on 55 Years of New China (NBS 2005) and China Statistical Yearbook (NBS various years). The sample period, 1985–2004, is largely constrained by data availability of FDI, which only becomes available from 1985. The sample size differs with human capital variables applied in the estimations. When human capital is measured by years of schooling, the sample size covers only 28 provinces, excluding Tibet and Hainan Provinces. For estimations using enrollment rates, the sample includes 30 Chinese provinces. In either case, the data for Chongqing, which has become a municipal city since 1997, have been combined into those for the Sichuan Province. The data for the Hong Kong and Macao special administrative regions and the Taiwan Province are not included in our study. Definitions of variables and descriptive statistics are displayed in Appendix Table 2.
B. The Impact of Aggregate Human Capital on TFP Growth
We start by estimating the impact of aggregate human capital, represented by years of schooling, on China's TFP growth using panel data for 28 Chinese provinces in the period 1985–2004. The estimation results are reported in Table 3. The incremental F-test suggests the OLS estimates displayed in column (1) are biased due to neglect of province-specific effects. Instead, the fixed effects models are preferred, as shown in columns (2), (3), and (4). In column (2), the average years of schooling have a significant and positive impact on TFP growth, though the magnitudes are rather small. The results suggest that an extra year of schooling can increase TFP growth by 0.1% on average.
Table 3. The Impact of Aggregate Human Capital on TFP Growth
|Human capital variables:|| || || || |
| ed_expt−1|| || ||−0.0027|| |
| culture_expt−1|| || || ||−0.0024|
|Control variables:|| || || || |
|Incremental F-test|| ||78.82***||73.72***||74.60***|
|No. of provinces||28||28||28||28|
In columns (3) and (4), we further introduce quality measures of aggregate human capital into the regressions, represented by the share of education expenditure and the share of culture expenditure, respectively. However, both estimated coefficients for the quality of aggregate human capital are negative, though statistically insignificant. This may be due to two reasons. First, the negative estimated coefficients on education quality may relate to the declining role of government in education investment. As we have shown in Figure 4 and Table 1, the share of government expenditure on education has been declining over time, although the level has increased. Increased tuition fees and miscellaneous fees largely aggravate the individual's education expenses. This may lower school enrollment rates or raise dropout rates, especially in poor regions. It may also undermine the quality of education because of insufficient funding and quality control. In this sense, the negative estimates may indicate that TFP growth is adversely, albeit insignificantly, affected by the decline in human capital quality. Second, measuring human capital quality is difficult and controversial. As argued in many studies (e.g., Hanushek and Kimko 2000), education expenditure may not be an adequate proxy for the quality of human capital. Other controls including FDI, openness, and infrastructure are all found to have positive and significant effects on productivity growth. These results are in line with the theoretical reasoning provided earlier in the paper.
C. The Impact of Human Capital Composition on TFP Growth
We examine the respective impact of enrollment rates at different levels of schooling on TFP growth. The results are reported in Table 4. Again, the large F-statistics are in favor of the fixed-effects model. In column (2), the three levels of schooling are found to have significantly positive impacts on productivity growth. The magnitude of their contributions increases with the level of schooling. University education, the highest level of schooling, has the largest impact on TFP growth. All other control variables remain significant and positive.
Table 4. Respective Impact of Human Capital Composition on TFP Growth
|Human capital variables:|| || || || || || |
| pri_teast−1|| || ||0.0009**|| || || |
| sec_teast−1|| || ||0.0011**|| || || |
| uni_teast−1|| || ||−0.0026***|| || || |
| pri_enrolt−1*pri_teast−1|| || || ||0.0052***|| ||0.0067***|
| sec_enrolt−1*sec_teast−1|| || || ||0.0033|| ||0.0053|
| uni_enrolt−1*uni_teast−1|| || || ||−0.0240|| ||−0.0212|
|Other control variables:|| || || || || || |
|F-test for fixed effects|| ||54.85***||55.71***||47.27***||56.78***||48.47***|
|Sargan test|| || || || ||2.26||2.79*|
|Wu-Hausman test|| || || || ||3.01***||5.80***|
|No. of observations||611||611||611||611||578||578|
However, the inclusion of quantitative measures of education alone may generate misleading information (Behrman and Birdsall 1983). We further include education quality measures, represented by teacher–student ratios, in the estimations. The results are reported in column (3). The estimates of the three levels of school enrollment rates are still positive and significant at the 5% level. Nevertheless, the ranking of their contributions change. Specifically, the primary enrollment rate has a larger and more significant estimated coefficient, whereas the estimated coefficients for the secondary and university enrollments are smaller and less significant. Moreover, the estimated coefficients for teacher–student ratios are positive and significant for primary and secondary schools. This indicates that improvements in primary and secondary education quality have significantly enhanced China's TFP growth. Unexpectedly, the estimated coefficient for the university teacher–student ratio is found to be significantly negative. Similar results are observed in Barro (1991). He includes enrollment rates and student–teacher ratios at primary and secondary schools in convergence regressions. His estimation results show a negative and significant estimate for primary school student–teacher ratios while a positive albeit insignificant estimate for secondary school student–teacher ratios. We conjecture that the unexpected result is to a large extent attributable to multicollinearity that may occur to teacher–student ratios at the three levels of schooling. For example, the teacher–student ratio for universities is significantly correlated with that for primary and secondary schools, with correlation coefficients of 0.933 and 0.970 respectively. As a rule of thumb, multicollinearity is likely to occur when the correlation coefficient of explanatory variables is higher than 0.9 (Asteriou 2006, p. 96). As a consequence of multicollinearity, estimates may be biased, t-statistics may be wrong, and the signs of estimated coefficients may even be the opposite of those expected.
Alternatively, we can capture education quality by interaction terms, which appear to have lower correlations11 and thereby are less likely to result in multicollinearity. The estimation results are displayed in column (4) of Table 4. We find that the three levels of school enrollments are still positive and significant as in column (2); quality improvements in primary education have significantly enhancing effects on productivity growth, while the effects of quality changes in secondary and university education appear to be insignificant. These may relate to the decreasing number of teachers relative to the increasing number of students enrolled, particularly in universities, as shown in Figure 3.
Furthermore, to address the possible endogeneity of human capital, we employ the instrumental variable and fixed effects estimator (IV-FE).12 We use the lagged values of explanatory variables to instrument their levels. The results are displayed in columns (5) and (6). Results of the Sargan test suggest the validity of the instruments. The null hypothesis of variable exogeneity in the Wu-Hausman test can be rejected at the 1% level in both columns. This confirms our preceding presumption that human capital variables and other controls are likely to be endogenous. The estimation results are similar to those in columns (2) and (4), suggesting that our findings are robust to different estimation methods.
In short, the results we obtained from different estimation methods are consistent with each other. We find that China's TFP growth has been significantly promoted by increases in enrollment rates at all levels of schooling, among which university education has the largest role. However, when education quality is controlled for, TFP growth is still significantly driven by all levels of school enrollments but insignificantly affected by quality changes in secondary and university education.
D. The Regional Impact of Human Capital Composition on TFP Growth
As suggested by Vandenbussche, Aghion, and Meghir (2006), human capital composition may have different impacts on TFP growth in economies at different levels of development. It is generally recognized that the three regions of China are roughly distinguished as three levels of economic development. The eastern region has grown more rapidly and is better developed than the other two regions, while the western region has lagged far behind due largely to its disadvantaged geographic location. Human capital composition may have different effects on TFP growth in these three regions. We examine the regional impact of human capital composition by splitting the sample into the three regions. The results are reported in Table 5.
Table 5. Regional Impacts of Human Capital on TFP Growth
|Human capital variables:|| || || || || || || || || |
| pri_enrolt−1*pri_teast-1|| ||0.0079||0.011|| ||0.0040***||0.0045***|| ||0.0153**||0.0590**|
| sec_enrolt−1*sec_teast-1|| ||0.1336***||0.1667***|| ||−0.0166***||−0.0119**|| ||0.0602**||0.0606|
| uni_enrolt−1*uni_teast-1|| ||−0.0189||−0.0405|| ||0.0387||0.0296*|| ||0.8905***||0.3663|
|Other control variables:|| || || || || || || || || |
|F-test for fixed effects||45.69***||41.59***||35.00***||32.49***||15.88***||14.95***||31.28***||26.12***||19.67***|
|Sargan test|| || ||2.09|| || ||24.06|| || ||1.832|
|Wu-Hausman test|| || ||2.96***|| || ||2.35**|| || ||1.34|
|No. of provinces||12||12||12||9||9||9||9||9||9|
As shown in columns (1), (4), and (7), in which enrollment rates are included in estimations, TFP growth in the eastern region is largely driven by secondary and university education. In the central region, it is mainly driven by university education and marginally driven by secondary education. In the western region, TFP growth is promoted by primary and university education. Moreover, a cross-region comparison shows that secondary education has the largest and most significant role in promoting eastern regional productivity growth. University education has the largest and most significant role in the central region; whereas the estimated coefficient for primary education is the largest and most significant in the western region. For other controls, FDI enhances productivity growth mainly in the eastern and central regions. Exposure to international trade has a significant impact on eastern regional productivity growth. Infrastructure benefits TFP growth in all regions of China.
We then introduce education quality, represented by the interaction terms, in the estimation. The results are shown in columns (2), (3), (5), (6), (8), and (9). We find that when education quality is controlled for, productivity growth in the eastern region is only significantly affected by secondary education via both enrollment rates and quality. In contrast to column (1), university education loses its significance owing to decreasing teacher–student ratios. The results are robust to the alternative estimator, IV-FE. In the central region, primary and university education significantly contribute to TFP growth, both quantitatively and qualitatively. In the western region, the estimated coefficients, by the fixed-effects estimator, for all three levels of schooling enrollments and quality are significant and positive, as shown in column (8). Nonetheless, the magnitude of the estimated coefficient for university enrollments is surprisingly large. After correcting it by the instrumental variable estimator, we find that the abnormally large coefficient for university enrollments disappears and becomes insignificant. However, TFP growth in the western region turns to be significantly attributable to enrollment expansion and quality improvements of primary education only.
The aforementioned results about the regional effects of human capital on TFP growth are summarized in Table 6. In general, we find that human capital composition affects productivity growth differently with respect to the three regions of China. TFP growth of the eastern region benefits mostly from secondary education, while in the central region, productivity growth is significantly attributable to primary and university education. Primary education has significantly enhancing effects on the productivity growth of the western region. This finding appears to be roughly in line with those of Vandenbussche, Aghion, and Meghir (2006). They argue that TFP growth in developed economies is mainly attributable to skilled human capital, while in less developed economies, it is largely driven by unskilled human capital.
Table 6. Summary of Estimated Results of Table 5
|Eastern region||secondary (+)*|
|secondary (+)*||secondary (+)*|
|Central region||secondary (+)*|
|Western region||primary (+)*|
in IV-FE: primary (+)*
Note that despite the compelling results obtained, our interpretation is highly tentative in the sense that our human capital measures do not take into account vast amounts of internal labor migration which may substantially affect our investigated regional impacts of human capital on TFP growth. For instance, the rapid economic growth of the eastern region has attracted a large number of rural migrants who may only have secondary education. However, this concern is hard to address, due largely to the shortage of time-consistent data for inter-provincial labor migration.