THE ROLE OF HUMAN CAPITAL IN CHINA'S TOTAL FACTOR PRODUCTIVITY GROWTH: A CROSS-PROVINCE ANALYSIS

Authors


Abstract

This paper studies the role of human capital in China's provincial total factor productivity (TFP) growth over 1985–2004. The stochastic frontier approach is employed to measure the productivity growth of Chinese provinces. Human capital is measured both qualitatively and quantitatively. In particular, enrolment rates at various levels of schooling are used to represent human capital composition. After controlling for endogeneity, we find that human capital has significant and positive effects on the TFP growth of Chinese provinces. However, when education quality is incorporated, productivity growth appears to be significantly enhanced by quality improvements in primary education only. Regional impacts of human capital are found to differ at various levels of schooling. In the eastern region of China, productivity growth is significantly associated with secondary education. TFP growth in the central region is mainly promoted by primary and university education. Yet in the western region, primary education plays the most prominent role.

I. INTRODUCTION

The role of human capital1 in promoting total factor productivity (TFP) growth has been strongly supported by many economic theories. Nelson and Phelps (1966) argued that human capital can promote TFP growth by facilitating technology spillover. Romer (1990a, 1990b) and Aghion and Howitt (1998) contended that human capital can enhance productivity growth through accelerating domestic technological innovations. In the empirical literature, however, the impact of human capital on TFP growth is rather mixed. Some studies report a significant and positive estimated impact of human capital on the growth of TFP (e.g., Fleisher and Chen 1997; Vandenbussche, Aghion, and Meghir 2006; Fleisher, Li, and Zhao 2008), while others find significant and negative effects of human capital (e.g., Pritchett 2001). The divergent results are attributable to many causes. Among them, the most widely addressed reasons include the endogeneity of human capital (Bils and Klenow 2000; Krueger and Lindahl 2001) as well as the inadequate measurement of human capital particularly through neglecting human capital quality (Hanushek and Kimko 2000; Bosworth and Collins 2003).

In addition, the ambiguity of the empirical evidence may also relate to variations in the measurement methods of TFP growth. Many methods can be used to measure TFP growth, such as the growth accounting, time trend, and frontier approaches.2 While each method has its advantages, none is perfect. For example, both traditional growth accounting and regression analysis derive productivity growth as a mechanical residual. The time trend approach hinges critically on the specification of the production function. The frontier approaches, data envelopment analysis (DEA) and stochastic frontier analysis (SFA), have an advantage in deriving technical efficiency and technical change and combining them into the Malmquist TFP index (Isaksson 2009). While the DEA does not require specific functional forms of the production function, it cannot take statistical noise into account and is highly sensitive to outliers. In contrast, the SFA can accommodate the measurement errors which often occur in statistical data of developing countries (Coelli, Rao, and Battese 1997). The disadvantage of the SFA, however, is the need to assume the distribution of the error term and the functional form of the production function. In this paper, we adopt the SFA to measure TFP growth. In particular, we conduct the hypothesis tests to select the appropriate distributional and functional forms to alleviate the weaknesses of the SFA.

In this paper, we assess the role of human capital in TFP growth in the Chinese economy. Since the 1978 economic reform, the Chinese economy has experienced unprecedented growth. Human capital in terms of education has experienced remarkable changes, both quantitatively and qualitatively. China's human capital has accumulated at a rapid pace. The illiteracy rate of the Chinese population has been ameliorated from 52% in 1964 to 9.31% in 2006. More Chinese people now tend to pursue higher education. According to the National Bureau of Statistics of China (NBS 2007), the number of students enrolled in secondary schools increased from 26.98 million to 27.94 million over 1978–2006, while that for universities rose from 0.4 million to 17.38 million. Meanwhile, TFP has substantially increased in post-reform China. According to the World Bank (1997), China's TFP growth was around 4.3% per annum, contributing 52.4% of GDP growth over 1978–95. Whether China's rapid TFP growth is correlated with its improved human capital is an important topic to study. In this paper, we adopt the SFA to measure TFP growth in China. We then empirically assess the relation between China's TFP growth and human capital by taking into account human capital quality and controlling for the possible endogeneity of human capital.

Compared with the existing studies (e.g., Fleisher and Chen 1997; Fleisher, Li, and Zhao 2008), our paper has four distinct features. First, inspired by production frontier analysis, we apply SFA to measure TFP growth in China. Change in technical efficiency and technical change are both accounted for in TFP growth and are represented in terms of the Malmquist TFP index. Second, in addition to the aggregate measure of human capital, namely average years of schooling, which is applied in most studies, we particularly focus on human capital composition and its effect on TFP growth. We measure human capital composition by enrollment rates at three levels of schooling, including primary school, secondary school, and university. Third, in addition to its quantity, we take into account human capital quality. The quality of aggregate human capital is measured by the share of government expenditure on education and the share of government expenditure on culture, education, science, and public health. Teacher–student ratios at the three levels of schooling are used to proxy for the quality of human capital composition. Fourth, we also explore the distinct impacts of human capital components on TFP growth in China's three geographic regions, namely the eastern, central, and western regions. This may help deliver important policy implications for promoting China's regional productivity growth in the future.

Our empirical study is based on panel data for 30 Chinese provinces in the years 1985–2004. We apply the fixed-effects model to account for unobserved province-specific effects and use the lagged values of explanatory variables to control for possible endogeneity. Using the aggregate measure of human capital in estimates, we find that human capital is positively and significantly related to China's TFP growth. This finding does not change when human capital is measured by its components, that is, enrollment rates at primary and secondary schools and universities. When education quality is taken into account, productivity growth is still significantly attributable to human capital quantity but unrelated to its quality. Especially, it is unrelated to the quality of secondary and university education. Only quality improvements in primary education appear to have significant effects on TFP growth. Moreover, when investigating the regional impact of human capital components, we find that TFP growth in the eastern region is mainly attributable to secondary education; productivity growth in the central region is significantly associated with primary and university education, whereas primary education has its most significant and largest contribution to productivity growth in China's western region.

This paper is organized as follows. Section II previews China's TFP growth and human capital changes in the post-reform period. Section III briefly reviews the relevant literature on the effect of human capital on China's TFP growth. Section IV discusses the measure of China's TFP growth rates, after providing some theoretical backgrounds for SFA and the Malmquist TFP index. Section V presents the empirical model specification and the data, and also discusses the estimation results in detail. Section VI concludes the paper.

II. CHINA'S TOTAL FACTOR PRODUCTIVITY GROWTH AND HUMAN CAPITAL

Since the 1978 economic reform, China's TFP growth has improved significantly. According to Chow (1993) and Chow and Li (2002), China's TFP growth has risen to 2.6% per year in the years 1978–98 in contrast to zero in the pre-reform period. This remarkable increase in TFP growth has greatly contributed to China's economic growth. Using traditional growth accounting, the World Bank (1997) reported that China's TFP grew at 4.3% per annum and contributed 52.4% of GDP growth during the period 1978–95. Wang and Yao (2003) measured TFP growth by traditional growth accounting, which includes human capital as represented by years of schooling. They found that TFP growth was 2.41% over the period 1978–99, accounting for 25.4% of GDP growth in China. Islam, Dai, and Sakamoto (2006) applied the dual approach to growth accounting. They reported that China's TFP growth rate was around 2.95% per annum during the period 1978–2002 and accounted for 31.5% of GDP growth. Studies using frontier analysis also report substantial improvements in China's TFP growth. For example, Wu (2008) estimated a translog production function using SFA. He found that 26.61% of Chinese GDP growth was due to TFP growth, which occurred at a rate of 2.94% per annum during the period 1993–2004. Henderson and Russell (2005) applied DEA to study the sources of China's economic growth in the years 1978–2000. They found that the spurt in China's labor productivity was attributable to technological change (5.5%) and efficiency improvement (19.7%), in addition to the main driving force of physical capital accumulation.

There are also pessimistic estimates of TFP growth in the literature. For example, Young (2003) reports 1.4% TFP growth in China, after making laborious adjustments to the data. Another skeptical voice is Woo (1998), who argues that the net TFP growth rate in 1979–93 ranges from 1.1% to 1.3% per annum. The World Productivity Database (Isaksson 2007) also shows low estimates for China's annual growth rates of TFP, averaged at 1.1% to 1.9% over 1978–2000. In sum, both the optimistic and pessimistic estimates show that TFP growth has increased in the post-reform period. Moreover, China's TFP growth has contributed a substantially larger share to its economic growth than that of other countries like South Korea and Japan in the years 1960–93 (Liu 2000).

During the process of rapid economic development, China's human capital accumulates at an increasing speed. This is particularly evident in higher educational attainment. Figure 1 plots the total number of students enrolled in primary school, secondary school, and at university. Obviously, the number of students enrolled in universities increases steadily and rises dramatically, particularly after 2000. This is due mainly to the implementation of education reform which called for a large expansion in student enrollments in universities. As a result, university enrollments increased from 1.14 million in 1980 to 5.56 million in 2000 and 17.38 million in 2006. Secondary school enrollments declined temporarily at the start of the economic transition. This might be related to the shutdown of some unqualified rural secondary schools (Hannum et al. 2008). Since 1997, the number of students enrolled in secondary schools has started to rise. Nevertheless, primary school enrollments are found to decline especially after 1997.

Figure 1.

The Number of Student Enrollments by Different Types of Schooling 1978–2006 #0013;Source: NBS (2007).#0013;Note: Unit is million persons.

Figure 2 shows the number of graduates at different levels of schooling. Similar patterns are observed. The number of students graduating from universities soared from 0.16 million in 1978 to 3.78 million in 2006. Secondary school graduates increased from 23.8 million to 27.9 million over 1978–2006. Primary school graduates decreased from 22.88 million in 1978 to 19.60 million in 1997 and 19.28 million in 2006.

Figure 2.

The Number of Graduates by Different Types of Schooling#0013;1978–2006 #0013;Source: NBS (2007).#0013;Note: Unit is million persons.

The quality of education is such an important aspect of human capital that it cannot be neglected. It can be represented by input-based measures such as the teacher–student3 ratio, the qualification of teachers, per-pupil expenditures, and government expenditure on education. Alternatively, it can be represented by output-based measures such as national assessment of student achievements. Measures of this type are generally regarded to be more effective and accurate (Hanushek and Kimko 2000) than input-based quality measures. Unfortunately, the data for these measures are not available. Thereby, we have to rely on input-based measures, including the teacher–student ratio and government expenditure on education, to display changes in China's education quality in the post-reform period.

The teacher–student ratio reflects the number of teachers per student. Its increase may indicate improvements in education quality. As Figure 3 shows, the teacher–student ratio of primary schools rose from 0.03 in 1978 to 0.05 in 2006. For secondary schools, it increased modestly from 0.05 to 0.06; whereas for universities, it decreased dramatically from 0.24 to 0.06 in the period 1978–2006.

Figure 3.

Teacher–Student Ratios by Different Types of Schooling#0013;1978–2006 #0013;Source: NBS (2007).

As shown in Figure 4, whether in nominal or real terms, government expenditure on culture, education, science and public health and government appropriation for education have increased rapidly and continuously since the reform in 1978. In 1995, the Chinese government spent about 141.2 billion RMB (yuan) on education, which accounts for 2.5% of GDP (Heckman 2005). In 2005, government appropriation for education amounted to 516.1 billion and government expenditure on culture, education, science and public health reached 610.4 billion.

Figure 4.

Government Expenditure and Appropriation on Education#0013;1978–2006 #0013;Source: NBS (2007).#0013;Note: Unit is billion RMB. Price deflator is consumer price index (base year = 1995).

Although the level of government investment in education has risen substantially, the share of government in total education expenditure has declined over time. As shown in Table 1, the total education expenditure increased dramatically, especially after 2000. Nonetheless, the share of government appropriation for education has significantly declined from 84% to 61% in the period 1992–2005. In contrast, the share of tuition and miscellaneous fees has increased dramatically. In 2005, it amounted to 18.4% of total education expenditure. The increased education expenditure increases the individual's responsibility for education and may give rise to inequality in access to education, especially for children in poor rural areas and descendants of rural–urban migrants.

Table 1.  Sources of Education Expenditure
YearTotal Education Expenditure (100 million RMB)Share of Total Education Expenditure in GDP (%)Government Appropriation for Education (%)Social Funds for Education (%)Tuition and Miscellaneous Fees (%)
  1. Source: Authors' calculation based on NBS (2007).

  2. Note: Social funds for education include funds from social organizations and citizens for running schools, donations, and fund-raising for running schools, and other educational funds.

1992867.03.2284.010.95.1
19931,059.93.0081.99.98.2
19941,488.83.0978.911.29.9
19951,878.03.0975.214.110.7
19962,262.33.1873.914.611.5
19972,531.73.2173.613.612.9
19982,949.13.4968.918.512.5
19993,349.03.7368.317.913.8
20003,849.13.8866.618.015.5
20014,637.74.2365.918.016.1
20025,480.04.5563.719.416.8
20036,208.34.5762.019.918.1
20047,242.64.5361.719.718.6
20058,418.84.5861.320.218.4

III. LITERATURE REVIEW

The theoretical literature suggests that human capital enhances TFP growth. Human capital affects TFP growth by facilitating the adoption and implementation of new technology developed exogenously (Nelson and Phelps 1966), and/or by promoting the domestic production of technological innovations (Romer 1990a, 1990b; Aghion and Howitt 1998). However, there is mixed evidence for the significantly positive relation between human capital and TFP growth from empirical studies. For example, Benhabib and Spiegel (1994) specify a model in which human capital determines a country's ability to innovate and catch up with advanced technologies. They empirically examine this model using cross-country growth accounting regressions and find a positive effect of human capital in promoting TFP growth. Vandenbussche, Aghion, and Meghir (2006) provide empirical evidence showing that the closer the country is to the technological frontier, the greater is the effect of human capital on economic growth. Miller and Upadhyay (2000) highlight the role of human capital in determining the level of TFP, particularly in outward-oriented countries. Nonetheless, the study by Pritchett (2001) strongly questions the role of human capital in productivity growth and economic growth. His estimation results show a large and significantly negative impact of human capital on TFP growth.

Many studies have examined the impact of human capital on China's TFP growth and again, mixed results are observed. For example, using China's provincial-level data in the years 1978–93, Fleisher and Chen (1997) estimate the effect of human capital on the level or growth rate of TFP, measured by growth accounting. After controlling for the possible endogeneity of human capital, they still find a positive and significant impact of human capital on the TFP level and growth rate. Fleisher, Li, and Zhao (2008) also report the evidence of positive effects of human capital on TFP growth. They apply the model of Benhabib and Spiegel (1994) to estimate the effect of human capital on China's TFP growth over 1988–2003. Their results show that human capital has positive and significant effects on technology spillover and positive, though not always significant, effects on technological innovation. Nevertheless, Wei et al. (2001) include FDI, trade, R&D, and human capital to represent technological progress in growth equations. They find that human capital has positive but insignificant effects on technological progress.

The mixed empirical evidence may be due to many possible causes. For example, it may be attributed to measurement errors in the international education dataset (Krueger and Lindahl 2001; Bosworth and Collins 2003) or the disturbance made by influential outliers in the dataset (Temple and Voth 1998; Temple 1999). Nevertheless, as strongly addressed in many studies (e.g., Bils and Klenow 2000), the endogeneity of human capital may seriously bias the estimation results. The quantitative measures of human capital alone also give rise to misleading results (Behrman and Birdsall 1983; Hanushek and Kimko 2000; Wößmann 2003).

The ambiguity of the empirical evidence may also relate to difficulties in measuring TFP growth. In existing studies of human capital, TFP growth has been measured by different methods. Traditional growth accounting is widely used for measuring TFP growth due to its unrestricting of the specification of production functions (e.g., Fleisher and Chen 1997; Pritchett 2001). However, it is criticized for employing constant income shares for computing TFP growth (Lau and Park 2003). More importantly, the measured TFP growth is neither distinguishable from estimation residuals nor subject to tests of statistical hypotheses (Easterly and Levine 2001). There are also studies (e.g., Collins and Bosworth 1996; Rodríguez-Clare 1996) using regression analysis to estimate income shares based on country-specific characters and compute TFP growth. Nonetheless, the measured productivity growth is still a mechanical residual, like in traditional growth accounting. Studies (e.g., Kim and Lau 1996; Felipe 1999) using the time trend method measure TFP growth as the shift of the production function over time. However, this method is limited to the specification of the production function. The above methods are all constrained by an important implicit assumption: that countries are technically efficient and TFP growth is driven by technical change (Nishimizu and Page 1982; Färe et al. 1994; Felipe 1999; Isaksson 2009). However, in reality, technical inefficiency often occurs to production, particularly in developing countries.

Recent productivity studies propose an alternative way of measuring TFP growth, that is, frontier analysis. TFP growth measured by this method accounts for both technical efficiency and technical change and is represented as the Malmquist TFP index. Two popular techniques are employed in the frontier analysis, namely DEA and SFA. The DEA is not subject to function specifications or error distributions, but is highly sensitive to outliers and not statistically testable. On the contrary, SFA is more preferred for studying productivity growth, especially in developing countries, since it is capable of dealing with measurement errors in data (Coelli, Rao, and Battese 1997, p. 219). Moreover, SFA is subject to tests of statistical hypotheses. SFA has often been adopted for measuring TFP growth (e.g., Färe et al. 1994; Felipe 1999; Fu, Huang, and Lovell 1999; Wu 2000, 2008; Hao 2007). However, it has rarely been applied to assessing the relationship between human capital and productivity growth in the literature. The SFA is also fraught with drawbacks. For example, it requires a specific functional form and distribution assumption on the error term. To deal with these caveats, we adopt a relatively flexible functional form and error distribution, and then implement hypothesis tests to select the model that gives the most adequate presentation of our data.

In short, the mixed empirical evidence on China's human capital and TFP growth may be due to many possible causes. Although the endogeneity of human capital has been controlled for to some extent in a few studies, no special attention has been paid to the quality of human capital. Nor has the measurement issue of TFP growth been addressed. To fill in the gaps, in this paper, we revisit the relationship between China's TFP growth and human capital by measuring TFP growth by SFA and the Malmquist index, taking into account the quality of human capital, and controlling for the possible endogeneity of human capital.

IV. MEASURING CHINA'S TOTAL FACTOR PRODUCTIVITY GROWTH

A. The Stochastic Frontier Approach and the Malmquist TFP Index

The most widely applied frontier analysis4 is the output-oriented stochastic frontier approach (SFA). It was independently proposed by Aigner, Lovell, and Schmidt (1977) and Meeusen and van den Broeck (1977). The basic idea of SFA is that there is an unobserved best-practice production frontier corresponding to the set of maximum attainable output levels for a given combination of inputs. Production often occurs below the best-practice production frontier due to the presence of technical inefficiency. Following this idea, the stochastic frontier production model with panel data (Aigner, Lovell, and Schmidt 1977) is written as:

image(1)

in which the yit are outputs; the xit are vectors of explanatory variables; the vit are independently and identically distributed normal random variables with zero mean and constant variance; and the uit are identically and independently distributed non-negative random variables used to capture technical inefficiency, following a certain distribution such as the half-normal, truncated-normal, or even exponential distributions.

Technical efficiency (TEit) is measured as the ratio of observed output to the corresponding stochastic frontier output. It measures the difference in the observed output of the firm relative to the output produced by a fully efficient firm using the same amount of inputs. It can be predicted by the following equation,

image(2)

The measured technical efficiency takes a value between zero and one. The closer the observed point is to the frontier, the higher is the technical efficiency of the firm.

To represent changes in TFP, we opt to use the Malmquist index. The Malmquist TFP index not only takes into account the technological change, represented by shifts of the frontier, but also the technical efficiency change, represented by shifts towards the frontier. Technically, it measures changes in TFP between two observed points as a ratio of the distance functions of each point relative to a common technology. When the distance functions are measured by the stochastic frontier production model, the efficiency change index for firm i is the ratio of the observed technical efficiency in time period t to that in time s, that is,

image(3)

The technical change index for firm i between period s and period t is computed as the geometric mean of two partial time derivatives of the production function, that is,

image(4)

The product of these two indices gives the Malmquist TFP index, showing the TFP change between period s and period t, that is,

image(5)

Note that a value of the Malmquist TFP index larger than one signifies improvements in TFP; a value equal to one implies the stagnation of TFP; while a value less than one indicates declines in TFP.

B. Specification of Estimation and Data

We start by estimating the stochastic frontier production model in a translog form and then choose the most appropriate specification of the frontier production function using the likelihood ratio (LR) test. The use of the translog form of the production function has many advantages. The translog production function is not subject to the assumptions restricting the Cobb-Douglas production function, such as fixed returns to scale and unity elasticity of substitution (Coelli, Rao, and Battese 1997, p. 35). It also allows the marginal rate of technical substitution to vary with time (Coelli et al. 2005, p. 213). In other words, it allows for the existence of the non-Hicks neutral technology.

The panel data version of the translog stochastic frontier production function is defined as:

image(6)

in which Y, K, L, and t are output, capital, labor, and time trend, respectively.

We impose constant returns to scale5 (CRS) upon the production technology by assuming

image(7)

Substituting equation (7) into equation (6), we have

image(8)

where y is output per unit of labor and k is capital per unit of labor.

Following Battese and Coelli (1992), we specify the inefficiency term uit to be time varying and take the form of

image(9)

where uit is assumed to be an identically and independently distributed generalized truncated-normal random variable, and η is an unknown scale of parameters to be estimated. If η= 0, the inefficiency effects model becomes time invariant.

The data used for estimation covers 30 Chinese provinces in the period 1978–2005. Output is measured by real GDP per worker deflated by the implicit deflator provided by the National Bureau of Statistics of China (NBS). The labor force is measured as the number of employed workers. The provincial stock of physical capital is calculated in two steps. First, following Young (2003), we divide the provincial real investment in 1952 by 10% as our initial capital stock. Since our initial capital stock is estimated far from our sample period, the importance of its starting value is diminished over time due to depreciation. Second, we use the perpetual inventory method based on the equation Ki,t=Ii,t+Ki,t−1 (1–δ), where Ki,t and Ki,t−1 denote the capital stock at time periods t and t–1, respectively, Ii,t is the real investment in fixed assets in time period t, and δ is the depreciation rate of capital. The real investment is calculated by deflating the gross fixed capital formation by the implicit investment deflators (1952–95) and the price index of investment (1996–2005). The depreciation rate is assumed to be 9.6% according to Zhang, Wu, and Zhang (2004). The maximum likelihood (ML) estimator6 is applied for estimation.

C. Analysis of Estimation Results

The estimation results are reported in Table 2. We run five regressions by the ML estimator. The column “Reg 1” shows the estimation results of the translog frontier production function as specified in equations (8) and (9). The columns “Reg 2” to “Reg 5” show the results when certain variables are excluded from the specification of regression 1.

Table 2.  Estimation Results of the Stochastic Frontier Production Function
Dependent variables: Log of Annual GDP per Worker (lny)
VariableCoefficientReg 1Reg 2Reg 3Reg 4Reg 5
  • Note: Figures in parentheses are t-statistics. Variable definitions are displayed in Appendix Table 2.

  • † 

    This tests for the existence of the technical inefficiency effect in the model.

  • ‡ 

    The LR test applied is the one-sided generalized likelihood-ratio test with its statistic asymptotically distributed as a mixture of chi-square distributions. The critical values can be found in Table 1 of Kodde and Palm (1986).

  • § 

    This test is used to select the suitable specification of the model. The LR statistic follows the standard chi-square distributions.

  • ***, **, and * 

    represent statistical significance at the 1%, 5%, and 10% levels, respectively.

Constantβ00.8381.292***0.677***1.02***1.191***
(1.19)(25.09)(15.51)(23.09)(23.31)
lnkβK0.3010.319***0.503***0.42***0.325***
(0.37)(16.99)(14.62)(24.27)(16.36)
tβt0.0360.022***0.025***0.040***0.029***
(0.46)(9.40)(3.34)(15.33)(7.81)
(lnk)2βKK0.054    
(0.19)
(lnk) tβKt−0.0090.007***0.002** 0.005***
(−0.18)(7.74)(2.41) (4.34)
t2βtt0.001−0.0002**  −0.000
(0.37)(−2.16)  (−0.71)
muµ0.0370.545***−0.405*0.586*** 
(0.04)(6.86)(−1.75)(9.05)
etaη0.0040.009***0.0090.0010.004
(0.09)(5.38)(1.01)(0.36)(1.30)
Parameters:      
 sigma-squared 0.1360.084***0.160***0.097***0.497***
(0.26)(7.09)(2.82)(9.95)(3.33)
 gamma (γ) 0.9200.882***0.925***0.888***0.979***
(1.29)(81.54)(17.26)(121.48)(155.33)
 log likelihood 608.87653.25582.20619.77648.21
 No. of observations840840840840840
Tests:      
Tests for technical inefficiency effects      
 H0: γ= 0 1.11−5.31−32.00−48.366−5.31
 H0: γ > 0 1215.511317.121228.411336.2791307.03
  No. of restrictions33332
  LR test statistics2428.78***2644.85***2520.83***2769.29***2624.67***
  Result of test Reject H0Reject H0Reject H0Reject H0Reject H0
Tests for model specification§      
 H0   Reg 3Reg 4Reg 5
 H1   Reg 2Reg 2Reg 2
  No. of restrictions  121
  LR test statistics  142.09***66.96***10.09***
  Result of test   Reject H0Reject H0Reject H0
  In support of   Reg 2Reg 2Reg 2

Firstly, we test for the existence of technical inefficiency effects by the LR test. The hypotheses of the test are specified as

image

If the null hypothesis cannot be rejected, the technical inefficiency effects do not exist and the traditional average response function is an adequate representation of the data. Otherwise, the rejection of the null hypothesis indicates the presence of technical inefficiency effects, which lead production to deviate from the production frontier. Our results show that the null hypothesis can be rejected at the 1% level in all regressions. This implies the presence of technical inefficiency effects.

Secondly, we select the appropriate model specification using the LR test. In regression 1, none of the estimated coefficients are significant. Once the variable of (lnk)2 is excluded,7 all estimates are very significant at the 5% level in regression 2. The LR test of regression 3 against regression 2 indicates that the technical change is non-monotonic, captured by a significant time-squared variable. The LR test of regression 4 shows that the technology is non-neutral, indicated by a significant product of the time trend and capital variable. It also implies that the Cobb-Douglas form is inappropriate for the estimated production function. In regression 5, we assume the inefficiency effect follows the half-normal distribution with a zero mean, namely, µ= 0. However, the LR test against regression 2 indicates that the truncated-normal distribution of uit in regression 2 is an adequate representation of the data. In sum, we find that regression 2 gives the most appropriate representation of the data.

The estimation results displayed in regression 2 show that GDP per worker is positively and significantly related to capital per worker, the time trend, and their product. The estimated coefficient of the time trend squared is negative and significant, implying that technological changes contribute to income at a diminishing rate. The estimated time differential is (0.022 + 0.007lnk–2 * 0.0002t). The estimated elasticity of capital per worker is (0.319 + 0.007 *t). The significant estimated coefficient for η indicates that technical inefficiency effects are time-varying.

D. China's TFP Growth in the Period 1979–2005

Based on the estimation results of the stochastic frontier function, we measure China's TFP growth rates in 1979–2005 by the Malmquist TFP index. The detailed cumulative indices of TFP growth, technical efficiency change and technological change at the national level are reported in Appendix Table 1.

Figure 5 presents the annual change in China's TFP and its components at the national level. Both the Malmquist TFP index and its two component indices are larger than one, indicating improvements in China's TFP, technological change, and technical efficiency change. In 1979–2005, the average annual growth rate of TFP is approximately 4% in China. This finding falls into the range reported in most of the literature and is much closer to the figure reported by the World Bank (1997). Technological progress grows at around 3.5% per annum, while technical efficiency change is only around 0.7% per annum. Moreover, technical efficiency change is improved at a diminishing rate over time, indicated by a slightly declining slope of the curve. The decline in technical efficiency improvement is trivial, in a range of −0.01% to −0.007% per annum, but it reflects that economic reform has to some extent overemphasized technological progress at the cost of achieving technical efficiency improvements.8

Figure 5.

The Malmquist Total Factor Productivity (TFP) Index for China#0013;1979–2005 #0013;Source: Authors' calculation.

Figure 6 illustrates the TFP index in the eastern, central and western regions of China. All values of the indices are always larger than one, implying that the three regions experience remarkable improvements in their TFP. The coastal region has experienced the most rapid and largest TFP growth, driven mainly by its significant technological progress. The TFP of the central region has a very similar pattern as that at the national level. In the western region, TFP grows at a decreasing rate and then starts increasing substantially at the end of the 1990s with the implementation of the West Development Strategy.9

Figure 6.

The Malmquist Total Factor Productivity (TFP) Index for China's Regions#0013;1979–2005 #0013;Source: Authors' calculation.

V. ESTIMATING THE ROLE OF HUMAN CAPITAL IN TOTAL FACTOR PRODUCTIVITY GROWTH

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:

image(10)

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:

image

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:

image
image
image

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

image

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
Dependent Variables: Annual Average Growth Rate of TFP
 (1) OLS(2) FE(3) FE(4) FE
  • Notes: 1. OLS = ordinary least-squares estimator; FE = fixed-effects estimator.

  • 2. Figures in parentheses are t-statistics. Figures in brackets are p-values. Variable definitions are displayed in Appendix Table 2.

  • *** 

    represents statistical significance at the 1% level.

Human capital variables:    
 schoolingt−10.0006***0.0009***0.0009***0.0009***
(8.05)(11.29)(11.32)(10.45)
 ed_expt−1  −0.0027 
(−1.04) 
 culture_expt−1   −0.0024
(−1.26)
Control variables:    
 FDIt−20.0154***0.0042***0.0043***0.0043***
(7.06)(2.97)(3.05)(3.02)
 Opennesst−10.00080.0014***0.0014***0.0014***
(1.61)(3.60)(3.42)(3.45)
 Transportt−1−0.00040.0078***0.0079***0.0078***
(−0.68)(10.18)(10.22)(10.19)
 constant0.0353***0.0307***0.0311***0.0315***
(69.00)(62.78)(49.40)(37.94)
Incremental F-test 78.82***73.72***74.60***
[0.00][0.00][0.00]
No. of provinces28282828

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
Dependent Variables: Annual Growth Rate of TFP
 (1) OLS(2) FE(3) FE(4) FE(5) IV-FE(6) IV-FE
  • Notes: 1. OLS = ordinary least-squares estimator; FE = fixed-effects estimator; IV-FE = instrumental variable and fixed-effects estimator.

  • 2. Figures in parentheses are t-statistics. Figures in brackets are p-values. Variable definitions are displayed in Appendix Table 2.

  • ***, **, and * 

    represent statistical significance at the 1%, 5%, and 10% level, respectively.

Human capital variables:      
 pri_enrolt−10.0481***0.0215***0.0357***0.0450***0.0245***0.0544***
(7.26)(5.02)(7.86)(5.46)(4.94)(5.56)
 sec_enrolt−10.0447***0.0589***0.0249***0.0678***0.0582***0.0731***
(6.64)(9.57)(2.98)(3.39)(8.59)(3.30)
 uni_enrolt−10.4479***0.1950***0.0789**0.1381*0.1688***0.1305*
(11.58)(6.24)(2.44)(1.91)(4.99)(1.69)
 pri_teast−1  0.0009**   
(2.28)
 sec_teast−1  0.0011**   
(2.31)
 uni_teast−1  −0.0026***   
(−9.67)
 pri_enrolt−1*pri_teast−1   0.0052*** 0.0067***
(3.21) (3.39)
 sec_enrolt−1*sec_teast−1   0.0033 0.0053
(0.59) (0.84)
 uni_enrolt−1*uni_teast−1   −0.0240 −0.0212
(−1.16) (−0.96)
Other control variables:      
 FDIt−20.0167***0.0054***0.0029**0.0054***0.0029**0.0029**
(7.18)(4.01)(2.22)(4.01)(1.94)(1.97)
 Opennesst−10.00040.0018***0.0016***0.0019***0.0022***0.0023***
(0.94)(4.76)(4.54)(5.06)(4.51)(4.58)
 Transportt−1−0.0015**0.0040***0.0032***0.0039***0.0043**0.0041***
(−2.28)(4.49)(3.85)(4.34)(3.75)(3.59)
 constant0.0306***0.0319***0.0335***0.0315***0.0315***0.0308***
(37.73)(55.35)(20.72)(52.75)(48.89)(46.18)
F-test for fixed effects 54.85***55.71***47.27***56.78***48.47***
[0.00][0.00][0.00][0.00][0.00]
Sargan test    2.262.79*
[0.13][0.09]
Wu-Hausman test    3.01***5.80***
[0.00][0.00]
No. of observations611611611611578578

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
Dependent Variables: Annual Growth Rate of TFP
 Eastern RegionCentral RegionWestern Region
 (1) FE(2) FE(3) IV-FE(4) FE(5) FE(6) IV-FE(7) FE(8) FE(9) IV-FE
  • Notes: 1. FE = fixed-effects estimator; IV-FE = instrumental variable and fixed-effects estimator.

  • 2. Figures in parentheses are t-statistics. Figures in brackets are p-values. Variable definitions are displayed in Appendix Table 2.

  • ***, **, and * 

    represent statistical significance at the 1%, 5%, and 10% level, respectively.

Human capital variables:         
 pri_enrolt−10.00150.0410.05950.00960.0484***0.0502***0.0709***0.1310***0.3006***
−0.16−0.79−0.93−1.41−4.45−4.24−10.53−4.5−2.8
 sec_enrolt−10.0669***0.4889***0.5910***0.0210*−0.0504**−0.03530.00470.1954**0.2064
−6.93−5.2−4.27−1.67(−2.03)(−1.50)−0.29−2.17−1.37
 uni_enrolt−10.1371***0.15380.0720.3518***0.6510***0.5563***0.2906***1.9425***0.3821
−2.51−0.4−0.14−4.83−5.39−5.29−3.3−3.16−0.65
 pri_enrolt−1*pri_teast-1 0.00790.011 0.0040***0.0045*** 0.0153**0.0590**
−0.57−0.64−3.11−3.05−2.01−2.06
 sec_enrolt−1*sec_teast-1 0.1336***0.1667*** −0.0166***−0.0119** 0.0602**0.0606
−4.67−3.93(−3.09)(−2.37)−2.25−1.38
 uni_enrolt−1*uni_teast-1 −0.0189−0.0405 0.03870.0296* 0.8905***0.3663
(−0.15)−0.23−1.61−1.68−2.84−0.52
Other control variables:         
 FDIt−20.0068***0.0059**0.0060**0.0204***0.0210***0.0163**0.00290.00250.0103*
−2.65−2.47−2.09−3.21−3.64−2.24−1.51−1.23−1.92
 Opennesst−10.0022***0.0017***0.00080.00310.0007−0.00520.00190.0012−0.0054
−4.52−3.49−1.23−1.14−0.28(−1.61)−1.43−0.97(−1.08)
 Transportt−10.0043***0.0064***0.0081***0.0040*0.00080.00060.0093***0.0077***0.0038
−3.35−4.93−4.22−1.81−0.4−0.25−3.88−3.23−1.19
 constant0.0328***0.0273***0.0252***0.0339***0.0356***0.0328***0.0308***0.0261***0.0024***
−25.77−17.5−13.74−34.48−80.96−31.64−35.17−19.55−11.86
F-test for fixed effects45.69***41.59***35.00***32.49***15.88***14.95***31.28***26.12***19.67***
[0.00][0.00][0.00][0.00][0.00][0.00][0.00][0.00][0.00]
Sargan test  2.09  24.06  1.832
[0.15][0.00][0.17]
Wu-Hausman test  2.96***  2.35**  1.34
[0.00][0.02][0.22]
No. of provinces121212999999

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
RegionWhen Enrollment Ratios Are Included in EstimationsWhen Education Quality Is Also
Included in Estimations
Columns (1), (4), (7)Columns (2), (3), (5), (6), (8), (9)
Enrollment RatesEnrollment RatesEducation Quality
  • Note: (+) indicates the estimated coefficient is positive, while (−) indicates the estimated coefficient is negative.

  • represents statistical significance at the 10% level.

Eastern regionsecondary (+)*
university (+)*
secondary (+)*secondary (+)*
Central regionsecondary (+)*
university (+)*
primary (+)*
university (+)*
secondary (−)*
in IV-FE:
secondary (−)*
primary (+)*
university (+)*
secondary (−)*
in IV-FE:
secondary (−)*
Western regionprimary (+)*
university (+)*
primary (+)*
university (+)*
secondary (+)*
in IV-FE: primary (+)*
primary (+)*
university (+)*
secondary (+)*
in IV-FE:
primary (+)*
National
(Table 4)
primary (+)*
university (+)*
secondary (+)*
primary (+)*
university (+)*
secondary (+)*
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.

VI. CONCLUSION AND RECOMMENDATIONS

In this paper, we empirically investigate the role of human capital, especially the role of human capital composition, in China's TFP growth over the period 1985–2004. We firstly generate measures of productivity growth for China using the Malmquist TFP index based on the production frontier estimation. We then assess the relationship between human capital and TFP growth by taking into account the quality of human capital and controlling for the possible endogeneity. Our results show that human capital has a significant and positive impact on China's TFP growth. Increases in student enrollments at all levels of schooling significantly contribute to the overall productivity growth. However, when education quality is controlled for, productivity growth is still attributable to the three levels of school enrollment rates, but is only significantly affected by quality improvements in primary education. The regional impact on TFP growth is different with various levels of schooling. Secondary education significantly enhances productivity growth in the eastern region. TFP growth in the central region is mainly promoted by primary and university education. Primary education plays a pivotal role in promoting TFP growth in the western region of China.

Our empirical study shows evidence from Chinese provinces on the prominent role of human capital in productivity growth. To continue enhancing productivity growth, China should further improve its educational attainment at all levels of schooling. Moreover, China should continue improving the quality of education particularly at the university level. The government should increase educational expenditure to ameliorate inequality in the access to education. Furthermore, investment in primary education should be largely increased, particularly in the western region. This would take advantage of the large contribution of primary education to productivity growth, and may also help alleviate China's regional income inequality.

Footnotes

  • 1

    In the literature, human capital is generally regarded to affect economic growth through three channels. Human capital can accumulate as an input factor (e.g., Mankiw, Romer, and Weil 1992), attract physical capital investment, or enhance TFP growth (e.g., Benhabib and Spiegel 1994). In this paper, however, we narrow our focus to the impact of human capital on TFP growth, which is one of the hotly debated topics in recent studies.

  • 2

    In the World Productivity Database (Isaksson 2007), the measurement methods of TFP growth are summarized into four categories: growth accounting, regression analysis, data envelopment analysis, and stochastic frontier analysis.

  • 3

    In most human capital studies, for example Barro (1991), the student–teacher ratio is used to proxy for education quality. It represents the average size of classes. It is negatively related to education quality and its increase indicates the possible decline in education quality. In this paper, however, we represent education quality by the teacher–student ratio, which has the same indication as the student–teacher ratio but is positively related to education quality. When including this ratio, the estimation results become more intuitive to interpret.

  • 4

    The content of this subsection is largely based on Coelli et al. (2005).

  • 5

    It should be noted that imposing CRS may neglect the contribution of the scale change to measured TFP growth. Recent studies suggest approaches of calculating the scale change. However, scale effects are found to be fairly small in TFP growth for China (Isaksson 2007). We therefore opt to focus on the results obtained with CRS in order to provide clear and concise analyses of the topic.

  • 6

    The ML estimator is applied due to its desirable properties. First, it is asymptotically efficient (Coelli et al. 2005). Moreover, rather than the ordinary least squares and all other corrected ordinary least squares methods, the ML estimator assumes that the most efficient firms have a greater influence on the shape of the estimated production frontier (Coelli et al. 2005, p. 203).

  • 7

    If we differentiate lny with respect to lnk and let it equal zero, we have 0.301 + 2 * 0.054 * lnk-−0.009 *t= 0. As t falls between [1, 28], lnk- lies between [−2.704, −0.454]. As the value of lnk exceeds that of lnk-, it appears to be reasonable to exclude (lnk)2.

  • 8

    Wu (2000) obtains similar results using SFA. He explains that China's economic reform has resulted in significant improvements in technical efficiency as discussed in many studies like Borensztein and Ostry (1996). Nevertheless, the potential in efficiency improvement was almost exhausted by the 1990s and then gave way to the development of new technology.

  • 9

    The West Development Strategy is a policy implemented by the Chinese government since 2000. It covers many fields, from infrastructure and FDI to education. The purpose of the strategy is to boost economic development in the less developed western regions of China.

  • 10

    We have also tried to include other variables that are often incorporated as determinants of productivity growth, such as market-oriented reform, fiscal decentralization, and inflation. However, none appears to be significant in regressions.

  • 11

    Multicollinearity does not seem to exist among interaction terms between enrollment rates and teacher–student ratios. The correlation coefficients for the three interactions are 0.880, 0.303, and 0.552, respectively.

  • 12

    We estimate the IV-FE model using Stata with the commands xtivreg and xtivreg2.

  • We would like to thank Professor John Fender, Dr. Marco Ercolani, Professor Shujie Yao, Professor Somnath Sen, and Professor Anindya Banerjee for their helpful comments.

Appendix

Table APPENDIXTABLE1.  Cumulative Indices of the Malmquist TFP Change, Technical Efficiency Change, and Technological Change
YearMalmquist TFP IndexTechnical Efficiency Change IndexTechnological Change Index
  1. Notes: 1. Indices in this table show the average total factor productivity (TFP) growth, technical efficiency change, and technical progress at China's national level over the period 1979–2005.

  2. 2. “Efficiency change” is calculated using equation (3) for each province and for each pair of adjacent years. “Technological change” is calculated using equation (4) by differentiating the estimated production function with respect to time t and computing the geometric average values in each pair of adjacent years. The subsequent indices are then converted into the cumulative (chain) indices reported in this table. The “Malmquist TFP index” is the product of technical efficiency change and technical progress.

19791.04001.00801.0318
19801.03981.00791.0317
19811.03961.00781.0315
19821.03931.00771.0313
19831.03921.00771.0313
19841.03931.00761.0315
19851.03951.00751.0318
19861.03981.00741.0321
19871.04001.00741.0324
19881.04011.00731.0326
19891.04011.00721.0326
19901.03991.00711.0326
19911.03981.00711.0325
19921.03981.00701.0326
19931.04001.00691.0328
19941.04031.00691.0332
19951.04071.00681.0336
19961.04101.00671.0340
19971.04131.00671.0344
19981.04161.00661.0348
19991.04211.00651.0353
20001.04251.00651.0358
20011.04281.00641.0361
20021.04301.00631.0365
20031.04331.00631.0368
20041.04371.00621.0372
20051.04411.00611.0377
Average1.04081.00701.0348
Table APPENDIXTABLE2.  Descriptive Statistics of Variables
VariableObs.MeanStd. Dev.Min.Max.Definition
y8409,898.5510,234.861,371.7384,990.59Real GDP per worker
k84019,395.3724,325.61914.08200,010.70Real provincial capital stock per worker
TFP index8101.040.001.031.05Malmquist TFP index
schooling6726.811.623.3611.06Average years of schooling
pri_enrol84011.512.733.0418.17Ratio of primary school enrollment to total population
sec_enrol8405.671.580.9712.99Ratio of secondary school enrollment to total population
uni_enrol8400.380.460.043.56Ratio of university enrollment to total population
ed_exp81015.503.245.4227.86Share of education expenditure in local government fiscal expenditure (%)
culture_exp81024.834.7011.7638.37Share of culture, education, science and public health in local government general budgetary expenditure (%)
pri_teas8100.258386.091650.000003173.4154Primary teacher-student ratio
sec_teas8100.062160.018510.0000040.147727Secondary teacher-student ratio
uni_teas8100.164620.075980.0000050.594669University teacher-student ratio
FDI6493.065.390.0052.58Foreign direct investment as a percentage of real GDP
Openness80319.6528.940.17224.88Sum of imports and exports as a percentage of real GDP
Transport8030.300.230.011.68Length of railway, road, and inland navigable water network per square kilometer

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