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The effect of education subsidies on regional economic growth and disparities in China
Economic Modelling 27 (2010) 1061–1068
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Economic Modelling j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e c m o d
The effect of education subsidies on regional economic growth and disparities in China Yuko Shindo Graduate School of Economics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8601, Japan
a r t i c l e
i n f o
Article history: Accepted 26 April 2010 JEL classification: C68 D63 D91 I22 R11 Keywords: Overlapping generations Regional inequity Human capital Education subsidies Economic growth
a b s t r a c t This paper examines the impact of education subsidies on regional economic growth and the disparities between two Chinese regions, Jiangsu and Liaoning, by simulating their economies in a six-period overlapping generations model in which individuals decide their length of education. This study estimates the long-run growth rates, that is, the steady growth paths of the regional economies based on current education subsidies, and explores their effect on human capital accumulation, namely in terms of economic growth while considering the increase in education subsidies. Because greater government subsidies in education induce individuals to invest in human capital, both regions achieve higher economic growth. Moreover, because of the large differences in productivity between the regions, the growth gap widens with evenly raised education subsidy rates. © 2010 Elsevier B.V. All rights reserved.
1. Introduction This paper conducts a macroeconomic simulation in two Chinese regions, Jiangsu and Liaoning, using a six-period overlapping generations model (OLG) and examines the different effects of education subsidies on human capital accumulation, namely economic growth. Since 1978, China has moved from a centrally planned economy to a market-based economy and has achieved a GDP growth rate of nearly 10%. With this open economy, foreign direct investment (FDI) has increased, and education in science and technology has been promoted. Fig. 1 shows three indices: GDP, FDI in fixed assets, and enrollment in senior secondary and higher education since 1985 (taking the 1985 figures as a baseline). It is clear that the GDP has increased significantly during this timeframe. Although the FDI declined during the Asian financial crisis, it has increased more sharply than the GDP over this period. Unlike GDP and FDI, school enrollment cannot increase, due to the nature of population growth, and is still restrained, considering the school-life expectancy from primary to tertiary education of 11.2 years in 2006 (according to UNESCO). In addition, enrollment has only increased since 1995. Because FDI inflow can advance economic growth along with a well-educated workforce that can use high technology, it is natural to consider that FDI and human capital are the major factors in accelerating economic growth and disparities in China. Figs. 2 and 3 are scatter diagrams between the regional GDP per capita and the share of FDI in total investment in fixed assets and between the regional GDP per capita and enrollment in senior secondary and higher
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education students per 100,000 people in 2007 for 31 Chinese regions. The dots indicate the 22 provinces, 4 municipalities, and 5 autonomous regions.1 The scatter plot on each figure shows positive trends, but a wide range of differences exist along the lines. The figures highlight the following two features. First, the positive trends indicate that FDI and education are important determinants of economic growth. More specifically, the correlation coefficient in the latter is even larger: 0.495 in the former and 0.691 in the latter. Second, the differences among the regions reveal that regional inequality exists. For this reason, instead of examining the national average, we selected two regions, Jiangsu and Liaoning, as a contrasting example to assess the differences in economic development. Despite the similar GDP growth rates, 14.9% in Jiangsu and 14.5% in Liaoning, Jiangsu shows superior performance to Liaoning in all three indices. The regional GDP per capita in 2007 is 33,928 yuan in the former and 25,729 yuan in the latter. The share of FDI in total investment in fixed assets is 9.1% in the former and 3.0% in the latter, and the number of senior secondary and higher education students per 100,000 persons is 6571 in the former and 5588 in the latter. This analysis considers the following educational and technological effects on economic growth. With the advance of information and communication technology (ICT) in recent decades, the sources of FDI have dramatically changed from traditional natural resource-oriented production to knowledge-based production. Like many other emerging economies, China requires more knowledge and skills in the workforce to
1 The special administrative regions of Hong Kong and Macao along with Taiwan are excluded.
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Fig. 1. China's macroeconomy since 1985. Source: China Statistical Yearbook 2008.
Fig. 3. Regional GDP/cap vs. education in 2007. Source: China Statistical Yearbook 2008.
raise its economic competitiveness in the world market. Consequently, the government could consider increasing education subsidies, especially for upper secondary students, to improve the quality and level of education and to strengthen their absorptive capacity for advanced technology. There are many theories that address the importance of human capital accumulation for economic growth and inequality. Romer (1986) and Lucas (1988) are pioneers who first established this foundation of this line of theory. Many others have since studied economic growth theories that focus on the role of education for human capital accumulation. For example, Azariadis and Drazen (1990) and Glomm and Ravikumar (1992) use an OLG model with an endogenous growth framework to analyze the impact of education on long-run economic growth rates. In parallel with these theoretical analyses, Auerback and Kotlikoff (1987) develop a dynamic simulation model based on the OLG model created by Diamond (1965) and analyze the impact of public policies on the economy by focusing on the tradeoff effects between generations. Following Auerback and Kotlikoff (1987), many studies have discussed various public policies, including education. For instance, Docquier and Michel (1999) examine the tradeoff between education subsidies for the younger generation and old age pensions in aging societies in Europe with a simple three-period OLG model. Fougère and Mérette (1999) also conduct a simulation in seven OECD countries using a 15-period OLG model in their study of the impact of human capital investment on economic growth. Although these studies are credited with contributing to the establishment of simulation models, there are some drawbacks. One of the inadequacies in Docquier and Michel's study (1999) is that they may not have sufficiently considered the impact of education on individual lifecycles by dividing the lifecycle into only three periods. It is more appropriate to consider longer lifecycles to examine the education effect. Another concern is that although Fougère and Mérette (1999) analyze the effect of an aging population on investment in education and on human capital accumulation, they did not analyze the influence of public policy.
We should not exclude the substantial role of the government in financing education, which significantly affects individual incentives to accumulate human capital. Bouzahzah et al. (2002) extended their model to a more realistic sixperiod OLG model and specified the growth rate as a function of the time invested in education. They showed the effect of changing policies in debt repayment, retirement, social security, and education in a European economy and proved that an endogenous growth model only plays an important role when the effect of education policy is considered. Applying Bouzahzah et al.'s (2002) framework, this paper conducts simulations in two Chinese regions to explore the relationship between education subsidies and growth rates based on the individual choice of educational investment. However, this study differs from that of Bouzahzah et al. (2002) in the following manner. First, we examine different growth paths in two regions to investigate the long-run regional disparities between the two areas. The importance of education and technology policies is emphasized because the differences in productivity are the crucial development factor. Second, we do not include an intratemporal externality, where average human capital increases productivity, as in Lucas (1988), because our aim is to ensure a situation where a constant economic growth rate is achieved in the long run. Third, we incorporate technology transfer as a share of FDI in total investment, applying the output elasticity estimated for China by Yao (2006) in the production function because FDI characterizes China's economic growth. Findlay (1978) and Das (1987) have theoretically examined the relationship between FDI and technology transfer for economic growth, while Yao (2006) and other various empirical studies support the notion that not only better infrastructure and human capital but also more FDI inflow spur economic growth through technology transfer in developing countries. Finally, we do not analyze the transition path between the two steady growth paths, instead focusing on comparing the paths before and after the policy changes. Two main findings are obtained in this paper. First, the increase in government subsidies for education promotes individual investment in human capital, and economic growth is accelerated. Second, differences in productivity exist between the regions; over time, the growth gap widens with the even increase in the subsidy rate. This paper is organized as follows. Section 2 describes the framework of the model. Section 3 explains the parameter settings and constructs the steady growth paths of the two regional economies. Section 4 simulates the regional economies by increasing educational subsidies and examines its impact on economic growth for the new steady growth paths. Section 5 concludes the paper. 2. The model
Fig. 2. Regional GDP/cap vs. FDI in 2007. Source: China Statistical Yearbook 2008.
There are two regions in the economy. Each region has closed goods and labor markets. Regarding a capital market, FDI or capital from other countries is allowed to flow into the market in each region. Because in
Y. Shindo / Economic Modelling 27 (2010) 1061–1068
China labor mobility is restricted and capital inflow and outflow are controlled, these assumptions are not too strong. Three economic agents, a firm, individuals, and a regional government exist in a perfectly competitive environment in each region. Economic activities are conducted in discrete time, 1, 2,…, ∞, with 10 years considered as one period. The firm and individuals have perfect foresight regarding government policy. The individuals are homogeneous, conduct economic activities from 15 to 74 years of age for six periods, and are raised by their parents until they are 14 years old.2 There is no uncertainty in their life span. For analytical simplicity, the population is unchanged; the population in each age group is normalized to one.3
A representative firm produces goods that can be either consumed or used as capital, employing labor and capital to maximize its profit. The labor market is perfectly competitive in each region. The aggregate labor supply in region i in period t is thus given by j
2.2. Individual behavior The individuals derive their utility from consumption. We define individuals who begin economic activities from period t to period t + 5 as generation t. The instantaneous utility function in each period is given in CES form, while the lifetime utility function consists of the sum of the instantaneous utilities (i.e., additively separable in time) with the time preference rate. The expression is 6
j−1
Ui;t ≡ ∑ γ j=1
1 j 1−1 = σ c −1 ; 1−1 = σ i;t + j−1
j
Li;t ≡ ∑ li;t hi;t ;
ð1Þ
j=1
where ci,t + j − 1 is the per capita consumption level in age group j in period t in region i and γ(0 b γ b 1) and σ ∈ R are the time preference rate and an intertemporal elasticity of substitution, respectively. The lifetime expenditure of the individuals of generation t is the sum of expenditures that consist of the consumption and the consumption tax rate in each age group. The present value of their lifetime expenditure is given as 6 j t+j Ei;t ≡ ∑ ci;t + j−1 1 + τc;i;t + j−1 Ri;t ; j=1
where j denotes an age group (for example, j=1 is from 15 to 24 years old, j j etc.), and li,t and hi,t are, respectively, the labor supply and human capital level (or effective labor) of individuals in age group j in region i in period t. The aggregate production function is given by a Cobb–Douglas form that is homogeneous of degree one: α β ε AKi;t Li;t Kˆ i;t ;
ð2Þ
̂ are, respectively, aggregate output, capital and where Yi,t, Ki,t, and Ki,t technology transfer through FDI inflow in region i in period t. A (N0) is an exogenously given technology parameter that explains growth not accounted for in the factors of production. α, β, and ε are the output elasticities of capital, labor, and technology transfer, respectively, and are assumed to be in the relationships 0 b α, β, ε b 1, and α + β + ε = 1. For analytical convenience, we assume K̂ ≡ χi,tKi,t, where χi,t represents the ratio of FDI to total investment in each region (0 b χi,t b 1) and is given exogenously.4 Thus, the firm can identify the amount of technology transfer that occurs through FDI in each period. Defining the capital stock per effective labor unit as ki,t ≡ Ki,t/Li,t, we have a ε α+ε production function per effective labor unit as yi,t = Aχi,t ki,t . Given the firm's profit maximization, we obtain conditions where the prices of the factors of production equal the marginal productivity for each region: α + ε−1 δ + rdi;t = Aαχεi;t ki;t ;
ε−1 α + ε−1 δ + rfi;t = Aðα + εÞχi;t ki;t ;
ð3Þ
and ε
α + ε
wi;t = Að1−α−εÞχi;t ki;t
;
ð4Þ
where δ(0 b δ b 1) is the capital depreciation rate, and rdi,t, rfi,t and wi,t are the rates of return to domestic capital, foreign capital, and labor per effective labor unit, respectively. 2 The assumption of this lifespan corresponds to the fact that the CIA estimates life expectancy in China in 2008 to be 73.18 years according to The 2008 World Factbook. 3 Although China is an aging society, we will not consider a negative growth rate to avoid zero population along the long-run steady growth paths. 4 The characteristics of FDI remain very controversial. Here, we assume that FDI and domestic capital are complementary rather than substitutes based on the statistical data in China. FDI peaked in the 1990s before the Asian crisis and has remained around 3–5% on average. This assumption is employed by Yao's (2006) empirical study as well as Findlay's (1978) theoretical study.
ð6Þ
where τc,i,t(0 b τc,i,t b 1) is a consumption tax rate in period t and t+j
Rti,t+ j ≡ ∏ (1 + rdi,s)− 1. The present value of the individual's lifetime s=t+1
income is defined by 6
Yi;t =
ð5Þ
j
2.1. Firm behavior
5
1063
Wi;t ≡ ∑
j=1
j j j t+j 1−τw;i;t + j−1 wi;t + j−1 li;t + j−1 hi;t + j−1 + Ti;t + j−1 Ri;t ; ð7Þ
where τw,i,t(0 b τw,i,t b 1) is the wage income tax rate in region i in j period t. Ti,t denotes a public transfer that individuals in age group j receive in period t. The individuals of generation t inherit the human capital of the previous generation in the second age group, h2i,t, without depreciation.5 Based on this, individuals choose their education time, ei,t, and formulate their human capital as: 2 ψ 1 hi;t + 1 = 1 + ξei;t hi;t ;
ð8Þ
where ξ (N0) and ψ(0 b ψ b 1) are parameters for human capital productivity and education investment, respectively. Based on the above assumptions, maximizing their utility, individuals spend a positive amount of time in human capital formulation. After formulating human capital for the first age group, individuals continue to accumulate the capital through their lifetime with the influence of on-the-job training exogenously given as θj(j = 2, 3, 4, 5, 6). Thus, the human capital level in each age group is defined by 1 2 3 4 5 6 6 hi;t ; hi;t + 1 ; hi;t + 2 ; hi;t + 3 ; hi;t + 4 ; hi;t + 5 2 ψ 3 ψ 4 ψ 5 ψ 6 ψ 1 ≡ 1; θ 1 + ξei;t ; θ 1 + ξei;t ; θ 1 + ξei;t ; θ 1 + ξei;t ; θ 1 + ξei;t × hi;t :
ð9Þ By normalizing one period as one time unit, the time not spent on education, 1 − ei,t, is allocated to labor. The second, third, and fourth age groups inelastically supply one unit of their time. The fifth age group supplies the time unit of labor, 1 − ζi,t + 4(0 b ζi,t + 4 b 1), which is
5
The effect of on-the-job training is factored out. Note that Bouzahzah et al. (2002) assume that the human capital stock in the sixth age group is defined as 0. We assume that the sixth age group can hold the same level of human capital as the fifth age group which is more relevant to the real world. 6
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exogenously given, and then retires. In sum, the individual labor supply is 1 2 3 4 5 6 li;t ; li;t + 1 ; li;t + 2 ; li;t + 3 ; li;t + 4 ; li;t + 5 ≡ 1−ei;t ; 1; 1; 1; 1−ζi;t + 4 ; 0 : ð10Þ The government provides individuals with two types of public j transfer, Ti,t (j = 1, 2, 3, 4, 5, 6), namely, education subsidies in the first age group and public pension payments in the fifth and six age groups: 1 2 3 4 5 6 Ti;t ; Ti;t + 1 ; Ti;t + 2 ; Ti;t + 3 ; Ti;t + 4 ; Ti;t + 5 1 5 6 = νi;t ei;t 1−τw;i;t wi;t hi;t ; 0; 0; 0; ζi;t + 4 pi;t + 4 hi;t + 4 ; pi;t + 5 hi;t + 5 ;
changes in debt issues in each period because our interest lies in the changes in the debt level that influence capital accumulation.8 Therefore, the government budget constraint in region i in period t is τc;i;t Ci;t + τw;i;t wi;t Li;t + Di;t + 1 1 = νi;t ei;t 1−τw;i;t wi;t hi;t + Pi;t + Gi;t + 1 + rdi;t Di;t ;
where Ci,t, Pi,t, Gi,t, and Di,t are, respectively, aggregate consumption, the pension payment, the other government expenditures, and debt issues in region i in period t. Defining gi,t and di,t as exogenous given other government expenditures per effective labor unit and debt issues per effective labor unit, respectively, we have aggregate variables as follows:
ð11Þ where νi,t(0 b νi,t b 1) is an education subsidy rate against an opportunity cost and pi,t is the exogenously given public pension payment rate per effective labor unit. Therefore, individuals maximize their lifetime utility in Eq. (5) subject to their lifetime budget constraint Ei,t = Wi,t in Eqs. (6) and (7) j by choosing their education time, ei,t, and consumption, ci,t + j − 1. First of all, we determine the level of ei,t. The optimal education time, ei,t⁎, is directly obtained by maximizing lifetime income: 1 1 j j ð1−ψÞ 1−τw;i;t + j−1 wi;t + j−1 li;t + j−1 θ t + jA @ * = ξψ ∑ : Ri;t ei;t j=2 1−τw;i;t wi;t 1−νi;t 6
j ci;t + j−1
=
j = 2; 3; 4; 5; 6: ð13Þ
On the other hand, per capita assets for each age group are defined
j
j j + 1−τw;i;t + j−1 wi;t + j−1 li;t + j−1 hi;t + j1 j j j = 2; 3; 4; 5; 6: + Ti;t + j1 −ci;t + j1 1 + τc;i;t + j1 ; ð14Þ j1 t + j−1 + j−1 ≡ ai;t + j−2 Ri;t + j−2
Thus, the optimal asset level in each period in per capita terms is obtained by substituting c⁎i in Eq. (14). 2.3. Government behavior In each period, the government equates the tax revenues from consumption and wage incomes and the revenue from debt issues with the expenditures for education subsidies, pension payments, other government expenditures and interest payments for the debt issues.7 The government keeps the budget balanced through the 7
6 j Pi;t ≡ ∑ ζi;t + 1 pi;t hi;t ;
ð17Þ
j=5 6
j
ð18Þ
j
ð19Þ
Gi;t ≡ ∑ gi;t hi;t ; and j=1
j=1
j j j Because pi,thi,t , gi,thi,t , and di,thi,t represent expenditures per capita, pi,t, gi,t, and di,t become constant in the steady growth paths.
2.4. Intertemporal equilibrium Economic growth in this model is achieved by both physical capital and human capital accumulation per effective labor unit. The physical capital level per effective labor unit takes a constant value, while the human capital level achieves a constant growth rate in the steady growth path. First, aggregate assets less aggregate debt issues in the next period equals aggregate capital less FDI inflow in the next period for a capital market equilibrium in region i in period t as(1 − χi,t + 1)Ki,t + 1 = ∑ 5j= 1aji,t − Di,t + 1. From Eqs. (1) and (19), this can be rewritten as
by: ai;t
ð16Þ
ð12Þ
!σ j−1 ci;t + j−2 ;
j
j=1
Di;t ≡ ∑ di;t hi;t :
The following three aspects are worth noting. To start with, ei,t⁎ has a positive correlation with the wage income rate for the second to fifth age groups; however, the first age group shows a positive correlation between ei,t⁎ and the education subsidy rate and a negative correlation between ei,t⁎and the wage income rate. This is because the marginal benefit of education time results in an increase of income from the second age group onward, while marginal cost is decreasing in the income of the first group (i.e., the opportunity cost). Another feature is that ei,t⁎ does not depend on the human capital level; individuals determine their education time regardless of their level of human capital. Last, it is a decreasing function of the interest rate. Next, when individuals choose the consumption level for each age group, the following five Euler equations hold: 1 + τc;i;t + j−2 t + j−1 γR 1 + τc;i;t + j−1 i;t + j−2
6
Ci;t ≡ ∑ ci;t ;
5
0
ð15Þ
We assume that China has no capital gains or corporate taxes because there is no reliable information.
1−χi;t + 1 ki;t + 1 =
5
5
j=1
j=1
j j j ∑ aˆi;t hi;t + 1 − ∑ di;t + 1 hi;t + 1
!
=
5
j
j
∑ li;t + 1 hi;t + 1
j=1
ð20Þ j is the asset per effective labor unit. Further, modifying the where âi,t dynamics of human capital accumulation in Eq. (8) using Eqs. (3), (4), (10), and (12), we can obtain the human capital or the economic growth rate, which depends only on ki,t as
ψ hi;t + 1 = 1 + ξe ki;t : hi;t
ð21Þ
Therefore, we know that k⁎i , â⁎i , d⁎i , and l⁎i in Eq. (20) become constant in the steady growth path. Moreover, substituting k⁎i into Eq. (21), we have the constant growth of hi in the steady growth path. To summarize, the equilibrium of the economy is defined as follows. Definitions. When the initial individual assets, aggregate total capital stock, initial individual human capital, and policy variables (χi,t, τc,i,t, 8 It is also possible to assume that the debt level is exogenously given, whereas tax levels are endogenously determined. Bouzahzah et al. (2002) set the wage income tax, which directly influences the selection of education time, as an endogenous variable.
Y. Shindo / Economic Modelling 27 (2010) 1061–1068
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Table 1 Effect of raising education subsidy rates in the new steady growth paths (h1i = 1). Education subsidy rate (%)
Lifetime consumption per person in present value (10,000 yuan/60 years) Lifetime assets per person in present value (10,000 yuan/60 years) Lifetime utility per person (10,000 yuan/60 years) Interest rate (%/10 years) Human capital/economic growth rate (%/10 years) Education time per persons in t in age group 1 (years) Education subsidies per person (10,000 yuan/10 years) Capital stock per effective labor unit (10,000 yuan/10 years) Assets per effective labor unit (10,000 yuan/10 years) Debt level per effective labor unit (10,000 yuan/10 years)
Jiangsu
Liaoning
23.5
33.5
43.5
30.2
40.2
50.2
25.625
25.586
25.601
22.558
22.713
23.030
32.715
32.713
32.706
23.413
23.384
23.304
16.942
17.003
17.076
14.250
14.292
14.345
68.0
68.6
69.0
57.2
57.0
56.5
27.0
28.4
30.2
26.8
27.9
29.3
1.42
1.71
2.12
1.32
1.61
2.05
0.328
0.562
0.906
0.310
0.504
0.801
7.906
7.840
7.782
6.447
6.462
6.520
11.874
11.725
11.535
7.350
7.231
7.053
4.593
4.505
4.368
1.148
1.015
0.781
τw,i,t, νi,t, pi,t, ζi,t + 4, and gi,t) are given, the intertemporal equilibrium of the economy is defined as: (1) under given prices (wi,t, rdi,t, and rfi,t), the firm's behavior is determined; (2) under given prices (wi,t, rdi,t, and rfi,t), the individual choices (ci,tj, j j j j ai,t , li,t , ei,t, hi,t , and Ti,t ) are determined; (3) the capital market clears; and (4) di,t is determined as the government budget is balanced. 3. Calibration 3.1. Parameter settings In this section, we calibrate the parameters using regional data for Jiangsu and Liaoning and obtain a growth rate in each steady growth path to conduct simulations with the model explained in the previous section. Considering one period as 10 years in this model, we use the available and most up-to-date data for the past 10 years, from 1998 to 2007, and input the annual average values into the model to determine the parameter values. The values that we calibrate as well as the data source are summarized in Annex 1. Using the parameter values, we perform a calibration to obtain equilibrium values in the steady growth paths as the base cases. To start with, normalizing h1i as one, we obtain the initial capital stock per effective labor unit, k0⁎ as 7.906 for Jiangsu and 6.447 for Liaoning.9 We then obtain the equilibrium values of the other endogenous variables and the human capital/economic growth rates. These values are listed in boldface in Table 1 in the next section.10 We define these equilibrium values as the base cases; that is, the education subsidy rates are 23.5% for Jiangsu and 30.2% for Liaoning in each steady growth path, as shown in Annex 1.
9 Because h1i grows at a constant rate in the steady growth path, we only calibrate the relative values of the capital stock per person when h1i is set to one. We can obtain the absolute value by multiplying the relative value by the h1i level in a specific period in each region. 10 By changing the exogenously given parameter of education investment, ψ, we examine values of k⁎ 0 to check the robustness of the model. When the parameter value changes from 0.280 to 0.279 and 0.281 for Jiangsu and from 0.208 to 0.207 and 0.209 for Liaoning, the value of k⁎0 becomes 7.903 and 7.909 for the former and 6.444 and 6.450 for the latter. Therefore, we conclude that robustness is satisfied.
3.2. Individual lifecycles in the steady growth paths Figs. 4 and 5 display the relative levels of consumption and assets per person in each age group in the steady growth paths when h1i is set to one. First, Fig. 4 shows that consumption increases with advancing age in both regions. However, consumption in Jiangsu is increasing in greater amounts than that in Liaoning. Because consumption is smoothed after individuals maximize their utility, the effect depends strongly on interest rates. In fact, interest rates are shown to be higher in Jiangsu than in Liaoning (Table 1). The higher interest rates lead to low intertemporal prices. That is why consumption in Jiangsu is much higher than in Liaoning relative to age. Assets are increasing in Fig. 5 until individuals reach the fourth age group. Because the individuals accumulate human capital with age, their wage income increases and so do their assets. In addition, they need to save assets to cover their consumption after their retirement in the middle of the fifth age group. Because the pension payments per effective labor unit are lower in Jiangsu than in Liaoning, as shown in Annex 1, the individuals in Jiangsu have to save more to prepare for retirement. Like consumption, assets in Jiangsu are much higher than in Liaoning with age, owing to the lower intertemporal price. Furthermore, we can see that the gap between the regions exist in the steady growth paths when h1i is one. Even if we take the differences in interest rates into account, the consumption is still larger in Jiangsu than in Liaoning, that is, the lifetime consumption in
Fig. 4. Relative level of consumption per person.
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Y. Shindo / Economic Modelling 27 (2010) 1061–1068
Fig. 5. Relative level of assets per person.
the present value is 256,250 yuan in Jiangsu and 225,580 yuan in Liaoning, as listed in Table 1. 4. Simulation results In this section, we conduct simulations by raising the education subsidy rates, νt from 23.5% to 33.5% and 43.5% in Jiangsu and from 30.2% to 40.2% and 50.2% in Liaoning. Table 1 summarizes the effects of raising the education subsidy rates on the equilibrium values of variables in the new steady growth paths when h1i is set to one. Four results are obtained from these equilibrium values. First, the contrasting effects on lifetime consumption are observed in the two regions. The different results are attributed to the interest rates, as the substitution effect dominates the income effect in this model. On the other hand, the lifetime assets in yuan per person decrease in both regions. The reason for the decrease is that the education subsidies encourage individuals to invest more in education or in human capital and to invest less in physical capital. Despite the opposite effects of interest rates, we can see that lifetime utility per person increases in both regions. It suggests that the reform is feasible in terms of the effect on individual welfare in both regions. Second, we should note that the higher education subsidy rates lead to higher rates of human capital/economic growth. When we increase education subsidies by 10% and 20% in each region, the net growth rates increase from 27.0% to 28.4% and 30.2% in Jiangsu and from 26.8% to 27.9% and 29.3% in Liaoning during the 10 years in the steady growth paths. (The growth rate per year is equivalent to increases from 2.4% to 2.5% and 2.7% in the former and from 2.4% to 2.5% and 2.6% in the latter.) The major reason for the increase in the growth rates is the longer education time. By boosting the education subsidy rates by 10% and 20%, the education time additionally increases by 0.29 years and 0.70 years in Jiangsu and by 0.29 years and 0.73 years in Liaoning over the 10 years. Conversely, the education subsidies per person swiftly increase by 2340 yuan and 5780 yuan in Jiangsu and by 1940 yuan and 4910 yuan in Liaoning. Because the education subsidy rates are defined by the opportunity cost, large amounts of resources are needed to invest in education with higher education subsidy rates. Third, the capital stock level per effective labor unit decreases in Jiangsu, whereas increases in Liaoning when the education subsidy rates increase by 10% and 20%.11 The changes in the capital stock are determined by four factors shown in Eq. (20). The first factor, the asset
11 This value is different from the value in Fig. 5, the former value being the assets per person in an individual's lifecycle, while the latter value is the assets per effective labor unit of aggregate assets in the steady growth path.
level per effective labor unit, decreases in both Jiangsu and Liaoning by boosting the education subsidy rates. The second factor, the debt level per effective labor unit, decreases in both regions. In Jiangsu, because the decrease in debt level is smaller than the decrease in assets, the capital stock per effective labor unit decreases. On the contrary, in Liaoning, because the decrease in debt level is larger than the decrease in assets, the capital stock per effective labor unit increases. Undoubtedly, a decrease in the third factor, labor supply, (that is, the increase in education time) causes an increase in the capital stock per effective labor unit if the assets and debt per effective labor unit and the human capital level are constant. Lastly, the transfer of technology has a limited effect on economic growth due to the small value of ε but contributes to an increase in total productivity. Nevertheless, as the economic growth rate is higher in Jiangsu than in Liaoning, we can confirm that the capital stock level per person in Jiangsu will exceed that in Liaoning in any period. Finally, we compare the differences in the human capital/ economic growth rates. Fig. 6 shows the relationship between the subsidy rates and human capital/economic growth rates in both regions. When the subsidy rates are increased by the same 10% and 20% in both regions, the growth rate in Jiangsu becomes higher than that in Liaoning in every case. When the subsidy rates are increased by 20%, the differences are even larger. More concretely, the net growth rates increase 1.4% and 3.2% with the rise in subsidies in Jiangsu, while the rates only increase 1.1% and 2.5% in Liaoning. Based on the results, we can draw the following two findings. First, the productivity of Jiangsu is potentially higher than that of Liaoning because both parameters for human capital productivity, ξ, and education investment, ψ, are higher in Jiangsu despite the lower subsidy rate. Hence, more subsidies for Jiangsu are preferable with regard to efficiency. Second, due to the different level of productivity, the differences in growth rates are expanded when the subsidy rates are evenly raised. Regarding equity, the subsidy rates need to be determined based on the economic circumstances of educational matters in each region. 5. Conclusion Two main results are found in the relationship between economic development and human capital accumulation in the long run in a sixperiod OLG model. In the simulation of the Jiangsu and Liaoning economies, we can first conclude that due to greater government subsidies in education, both regions achieve greater economic growth. Second, because of the large differences in productivity between the
Fig. 6. Relative level of human capital/economic growth rate with increase in subsidy rates (h1i = 1).
Y. Shindo / Economic Modelling 27 (2010) 1061–1068
regions, the growth gap expands with policy reform. We recognize the importance of education subsidies in the long run because any reform that results in an increase in education subsidies will contribute to a correspondingly higher economic growth while at the same time improving overall welfare. However, any policy change may ameliorate the regional disparities due to different levels of productivity. If China adopts a policy of pursuing a uniform growth rate, the differences in productivity in each region should be taken into account to set the subsidy rate. We could provide several long-run implications of the public policy in the area of education and technology based on existing Chinese data. However, we ignore several important issues. One of the concerns is that we do not analyze the burdens among generations during the transitional period. Because intergenerational conflicts arise, especially when a wide gap exists, further research should consider whether the government should retain a relatively low level of education subsidies. Another concern is that we only compare regions that attract FDI in the relatively developed eastern coastal areas. Further studies should expand the outlook to other regions in order to better capture the differences across the entire country. In spite of these limitations, the importance of education, especially government policy concerning education subsidies, has plausible and meaningful interpretations regarding economic growth rates and regional disparities. As part of its development strategy, China needs to implement education policies carefully in order not only to prioritize economic growth but also to reduce existing regional disparities.
Acknowledgements This research was supported by a Grant-in-Aid from the Asian CORE Program of Japan Society for the Promotion of Science (JSPS). I am grateful to Profs. Hideya Kato, Tsuyoshi Shinozaki, Nobuhito Takeuchi and Mitsuyoshi Yanagihara for their useful comments. I also appreciated the suggestions that I received from Profs. Takamune Fujii, Yuichi Furukawa and Akihiko Yanase at a workshop of the Nagoya International Economic Study Group, and from Profs. Tatsuyoshi Miyakoshi and Koichiro Morikawa at a conference held by the Japan Society of Household Economics. Finally, I thank two anonymous referees for their valuable comments.
Appendix A
Annex 1 Notation. General symbols i Region j Age group Endogenous variables L Aggregate labor K Aggregate capital Y Aggregate output K Aggregate technology transfer via FDI inflow rd Rate of return to domestic capital w Rate of return to labor per effective labor unit c Consumption per capita W Lifetime income e Education time C Aggregate consumption G Aggregate government expenditure d Debt issues per effective labor unit
t
Period/generation
l k y h
Labor per effective labor unit Capital per effective labor unit Output per effective labor unit Human capital
rf U
Rate of return to foreign capital Lifetime utility
E T a P D â
Lifetime expenditure Public transfer Asset per capita Aggregate pension Aggregate debt issues Asset per effective labor unit (continued on next page)
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Annex 1 (continued) Exogenous variables
Jiangsu
Liaoning
Source
α
Output elasticity of capital
0.383
0.363
β ε
Output elasticity of labora Output elasticity of technology transfer via FDIb FDI share in total investment Technology parameter Capital depreciation rate Time preference ratec
0.611 0.006
0.631 0.006
China Statistical Yearbook (1999–2008) ″ Yao (2006)
0.079
0.038
9.605 0.344 0.840
8.382 0.349 0.840
Intertemporal elasticity of Substitutionc OJT in age group 2 OJT in age group 3 OJT in age group 4 OJT in age group 5 OJT in age group 6d Human capital productivitye Parameter for education investmente Consumption tax rate
1.500
1.500
1.061 1.201 1.325 1.429 1.429 0.466
1.061 1.201 1.325 1.429 1.429 0.408
China Statistical Yearbook (1999–2008) ″ ″ Bouzahzah et al. (2002) Bouzahzah et al. (2002) Ma (2005) ″ ″ ″ ″ UNESCO
0.280
0.208
UNESCO
0.045
0.036
Wage income tax rate Education subsidy ratef Pension payment per effective labor unitg Retirement ratioh Other government expenditures per effective labor uniti
0.236 0.235 0.448
0.247 0.302 1.081
China statistical yearbook (1999–2008) ″ ″ ″
0.500 1.291
0.500 1.784
″ ″
χ A δ γ σ 2
θ θ3 θ4 θ5 θ6 ξ ψ τc τw ν p ζ g
a β is calculated from the compensation of employees by region divided by the net regional product at factor cost. b Technology transfer had a limited effect on economic growth as a result of the small value of ε, but it had a positive effect on growth. Yao (2006) concluded that FDI with combination of export had a strong effect on economic growth. In our model, the effect of export is excluded because our interest is not to examine the effect of trade but that of human capital. c There is no empirical study that estimates the parameters for China. Controversy exists even for developed countries because the values vary depending on the study. Obtaining realistic interest rates and saving rates later when we calibrate the model, we choose γ and σ employed by Bouzahzah et al. (2002) who simulated the European case. d The wage profile is not the inverted U-shape we often see in the case of developed countries but increasing in China. e We set ξ and ψ to match the long-run economic growth rate of 2.5% (as in many developed countries) and the national average school-life expectancy during the past 10 years of 10.63 years from UNESCO. f ν is calculated from the education expenditure per student divided by per capita net compensation of employees from 15 to 24 years of age. Although the cost of upper secondary education is usually higher than primary and lower secondary education, the education expenditure is set as an average of primary and secondary education owing to limited sources. g p is obtained from the total pension payment divided by the population over 65 years of age. The pension payments include only retirees of government agencies and institutions covered by the government budget. h ζ is set as 0.5 because the average retirement age for male workers is 60 years of age. i g is derived from total government expenditure minus total education expenditure, pension payments, and debt issues divided by the population.
References Auerback, A., Kotlikoff, L., 1987. Dynamic fiscal policy. The MIT Press, Cambridge. Azariadis, C., Drazen, A., 1990. Threshold externalities in economic development. The Quarterly Journal of Economics 105, 501–526. Bouzahzah, M., De la Croix, D., Docquier, F., 2002. Policy reform and growth in computable OLG economies. Journal of Economic Dynamics & Control 26, 2093–2113. Central Intelligence Agency, 2008. The 2008 World Factbook. Diamond, P., 1965. National debt in a neoclassical growth model. The American Economic Review 55, 1126–1150. Das, S., 1987. Externalities, and technology transfer through multinational corporations: a theoretical analysis. Journal of International Economics 22, 171–182. Docquier, F., Michel, P., 1999. Education subsidies, social security and growth: the implications of a demographic shock. The Scandinavian Journal of Economics 101, 425–440.
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Findlay, R., 1978. Relative backwardness, direct foreign investment, and the transfer of technology: a simple dynamic model. The Quarterly Journal of Economics 92, 1–16. Fougère, M., Mérette, M., 1999. Population ageing and economic growth in seven OECD countries. Economic Modelling 16, 411–427. Glomm, G., Ravikumar, B., 1992. Public versus private investment in human capital: endogenous growth and income inequality. The Journal of Political Economy 100, 818–834. Lucas, R., 1988. On the mechanics of economic development. Journal of Monetary Economics 22, 3–42. Ma, X., 2005. Chugoku toshibu niokeru danjokan chingin kakusa no youin bunkai. KUMQRP Discussion Paper Series, pp. 1–22.
National Bureau of Statistics of China, 1999–2008. China Statistical Yearbook. China Statistics Press. Romer, P., 1986. Increasing returns and long-run growth. The Journal of Political Economy 94, 1002–1037. UNESCO Website, (http://stats.uis.unesco.org/unesco/ReportFolders/ReportFolders. aspx), Retrieved June 21, 2009. Yao, S., 2006. On economic growth, FDI and exports in China. Applied Economics 38, 339–351.
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Economic Modelling j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e c m o d
The effect of education subsidies on regional economic growth and disparities in China Yuko Shindo Graduate School of Economics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8601, Japan
a r t i c l e
i n f o
Article history: Accepted 26 April 2010 JEL classification: C68 D63 D91 I22 R11 Keywords: Overlapping generations Regional inequity Human capital Education subsidies Economic growth
a b s t r a c t This paper examines the impact of education subsidies on regional economic growth and the disparities between two Chinese regions, Jiangsu and Liaoning, by simulating their economies in a six-period overlapping generations model in which individuals decide their length of education. This study estimates the long-run growth rates, that is, the steady growth paths of the regional economies based on current education subsidies, and explores their effect on human capital accumulation, namely in terms of economic growth while considering the increase in education subsidies. Because greater government subsidies in education induce individuals to invest in human capital, both regions achieve higher economic growth. Moreover, because of the large differences in productivity between the regions, the growth gap widens with evenly raised education subsidy rates. © 2010 Elsevier B.V. All rights reserved.
1. Introduction This paper conducts a macroeconomic simulation in two Chinese regions, Jiangsu and Liaoning, using a six-period overlapping generations model (OLG) and examines the different effects of education subsidies on human capital accumulation, namely economic growth. Since 1978, China has moved from a centrally planned economy to a market-based economy and has achieved a GDP growth rate of nearly 10%. With this open economy, foreign direct investment (FDI) has increased, and education in science and technology has been promoted. Fig. 1 shows three indices: GDP, FDI in fixed assets, and enrollment in senior secondary and higher education since 1985 (taking the 1985 figures as a baseline). It is clear that the GDP has increased significantly during this timeframe. Although the FDI declined during the Asian financial crisis, it has increased more sharply than the GDP over this period. Unlike GDP and FDI, school enrollment cannot increase, due to the nature of population growth, and is still restrained, considering the school-life expectancy from primary to tertiary education of 11.2 years in 2006 (according to UNESCO). In addition, enrollment has only increased since 1995. Because FDI inflow can advance economic growth along with a well-educated workforce that can use high technology, it is natural to consider that FDI and human capital are the major factors in accelerating economic growth and disparities in China. Figs. 2 and 3 are scatter diagrams between the regional GDP per capita and the share of FDI in total investment in fixed assets and between the regional GDP per capita and enrollment in senior secondary and higher
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education students per 100,000 people in 2007 for 31 Chinese regions. The dots indicate the 22 provinces, 4 municipalities, and 5 autonomous regions.1 The scatter plot on each figure shows positive trends, but a wide range of differences exist along the lines. The figures highlight the following two features. First, the positive trends indicate that FDI and education are important determinants of economic growth. More specifically, the correlation coefficient in the latter is even larger: 0.495 in the former and 0.691 in the latter. Second, the differences among the regions reveal that regional inequality exists. For this reason, instead of examining the national average, we selected two regions, Jiangsu and Liaoning, as a contrasting example to assess the differences in economic development. Despite the similar GDP growth rates, 14.9% in Jiangsu and 14.5% in Liaoning, Jiangsu shows superior performance to Liaoning in all three indices. The regional GDP per capita in 2007 is 33,928 yuan in the former and 25,729 yuan in the latter. The share of FDI in total investment in fixed assets is 9.1% in the former and 3.0% in the latter, and the number of senior secondary and higher education students per 100,000 persons is 6571 in the former and 5588 in the latter. This analysis considers the following educational and technological effects on economic growth. With the advance of information and communication technology (ICT) in recent decades, the sources of FDI have dramatically changed from traditional natural resource-oriented production to knowledge-based production. Like many other emerging economies, China requires more knowledge and skills in the workforce to
1 The special administrative regions of Hong Kong and Macao along with Taiwan are excluded.
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Fig. 1. China's macroeconomy since 1985. Source: China Statistical Yearbook 2008.
Fig. 3. Regional GDP/cap vs. education in 2007. Source: China Statistical Yearbook 2008.
raise its economic competitiveness in the world market. Consequently, the government could consider increasing education subsidies, especially for upper secondary students, to improve the quality and level of education and to strengthen their absorptive capacity for advanced technology. There are many theories that address the importance of human capital accumulation for economic growth and inequality. Romer (1986) and Lucas (1988) are pioneers who first established this foundation of this line of theory. Many others have since studied economic growth theories that focus on the role of education for human capital accumulation. For example, Azariadis and Drazen (1990) and Glomm and Ravikumar (1992) use an OLG model with an endogenous growth framework to analyze the impact of education on long-run economic growth rates. In parallel with these theoretical analyses, Auerback and Kotlikoff (1987) develop a dynamic simulation model based on the OLG model created by Diamond (1965) and analyze the impact of public policies on the economy by focusing on the tradeoff effects between generations. Following Auerback and Kotlikoff (1987), many studies have discussed various public policies, including education. For instance, Docquier and Michel (1999) examine the tradeoff between education subsidies for the younger generation and old age pensions in aging societies in Europe with a simple three-period OLG model. Fougère and Mérette (1999) also conduct a simulation in seven OECD countries using a 15-period OLG model in their study of the impact of human capital investment on economic growth. Although these studies are credited with contributing to the establishment of simulation models, there are some drawbacks. One of the inadequacies in Docquier and Michel's study (1999) is that they may not have sufficiently considered the impact of education on individual lifecycles by dividing the lifecycle into only three periods. It is more appropriate to consider longer lifecycles to examine the education effect. Another concern is that although Fougère and Mérette (1999) analyze the effect of an aging population on investment in education and on human capital accumulation, they did not analyze the influence of public policy.
We should not exclude the substantial role of the government in financing education, which significantly affects individual incentives to accumulate human capital. Bouzahzah et al. (2002) extended their model to a more realistic sixperiod OLG model and specified the growth rate as a function of the time invested in education. They showed the effect of changing policies in debt repayment, retirement, social security, and education in a European economy and proved that an endogenous growth model only plays an important role when the effect of education policy is considered. Applying Bouzahzah et al.'s (2002) framework, this paper conducts simulations in two Chinese regions to explore the relationship between education subsidies and growth rates based on the individual choice of educational investment. However, this study differs from that of Bouzahzah et al. (2002) in the following manner. First, we examine different growth paths in two regions to investigate the long-run regional disparities between the two areas. The importance of education and technology policies is emphasized because the differences in productivity are the crucial development factor. Second, we do not include an intratemporal externality, where average human capital increases productivity, as in Lucas (1988), because our aim is to ensure a situation where a constant economic growth rate is achieved in the long run. Third, we incorporate technology transfer as a share of FDI in total investment, applying the output elasticity estimated for China by Yao (2006) in the production function because FDI characterizes China's economic growth. Findlay (1978) and Das (1987) have theoretically examined the relationship between FDI and technology transfer for economic growth, while Yao (2006) and other various empirical studies support the notion that not only better infrastructure and human capital but also more FDI inflow spur economic growth through technology transfer in developing countries. Finally, we do not analyze the transition path between the two steady growth paths, instead focusing on comparing the paths before and after the policy changes. Two main findings are obtained in this paper. First, the increase in government subsidies for education promotes individual investment in human capital, and economic growth is accelerated. Second, differences in productivity exist between the regions; over time, the growth gap widens with the even increase in the subsidy rate. This paper is organized as follows. Section 2 describes the framework of the model. Section 3 explains the parameter settings and constructs the steady growth paths of the two regional economies. Section 4 simulates the regional economies by increasing educational subsidies and examines its impact on economic growth for the new steady growth paths. Section 5 concludes the paper. 2. The model
Fig. 2. Regional GDP/cap vs. FDI in 2007. Source: China Statistical Yearbook 2008.
There are two regions in the economy. Each region has closed goods and labor markets. Regarding a capital market, FDI or capital from other countries is allowed to flow into the market in each region. Because in
Y. Shindo / Economic Modelling 27 (2010) 1061–1068
China labor mobility is restricted and capital inflow and outflow are controlled, these assumptions are not too strong. Three economic agents, a firm, individuals, and a regional government exist in a perfectly competitive environment in each region. Economic activities are conducted in discrete time, 1, 2,…, ∞, with 10 years considered as one period. The firm and individuals have perfect foresight regarding government policy. The individuals are homogeneous, conduct economic activities from 15 to 74 years of age for six periods, and are raised by their parents until they are 14 years old.2 There is no uncertainty in their life span. For analytical simplicity, the population is unchanged; the population in each age group is normalized to one.3
A representative firm produces goods that can be either consumed or used as capital, employing labor and capital to maximize its profit. The labor market is perfectly competitive in each region. The aggregate labor supply in region i in period t is thus given by j
2.2. Individual behavior The individuals derive their utility from consumption. We define individuals who begin economic activities from period t to period t + 5 as generation t. The instantaneous utility function in each period is given in CES form, while the lifetime utility function consists of the sum of the instantaneous utilities (i.e., additively separable in time) with the time preference rate. The expression is 6
j−1
Ui;t ≡ ∑ γ j=1
1 j 1−1 = σ c −1 ; 1−1 = σ i;t + j−1
j
Li;t ≡ ∑ li;t hi;t ;
ð1Þ
j=1
where ci,t + j − 1 is the per capita consumption level in age group j in period t in region i and γ(0 b γ b 1) and σ ∈ R are the time preference rate and an intertemporal elasticity of substitution, respectively. The lifetime expenditure of the individuals of generation t is the sum of expenditures that consist of the consumption and the consumption tax rate in each age group. The present value of their lifetime expenditure is given as 6 j t+j Ei;t ≡ ∑ ci;t + j−1 1 + τc;i;t + j−1 Ri;t ; j=1
where j denotes an age group (for example, j=1 is from 15 to 24 years old, j j etc.), and li,t and hi,t are, respectively, the labor supply and human capital level (or effective labor) of individuals in age group j in region i in period t. The aggregate production function is given by a Cobb–Douglas form that is homogeneous of degree one: α β ε AKi;t Li;t Kˆ i;t ;
ð2Þ
̂ are, respectively, aggregate output, capital and where Yi,t, Ki,t, and Ki,t technology transfer through FDI inflow in region i in period t. A (N0) is an exogenously given technology parameter that explains growth not accounted for in the factors of production. α, β, and ε are the output elasticities of capital, labor, and technology transfer, respectively, and are assumed to be in the relationships 0 b α, β, ε b 1, and α + β + ε = 1. For analytical convenience, we assume K̂ ≡ χi,tKi,t, where χi,t represents the ratio of FDI to total investment in each region (0 b χi,t b 1) and is given exogenously.4 Thus, the firm can identify the amount of technology transfer that occurs through FDI in each period. Defining the capital stock per effective labor unit as ki,t ≡ Ki,t/Li,t, we have a ε α+ε production function per effective labor unit as yi,t = Aχi,t ki,t . Given the firm's profit maximization, we obtain conditions where the prices of the factors of production equal the marginal productivity for each region: α + ε−1 δ + rdi;t = Aαχεi;t ki;t ;
ε−1 α + ε−1 δ + rfi;t = Aðα + εÞχi;t ki;t ;
ð3Þ
and ε
α + ε
wi;t = Að1−α−εÞχi;t ki;t
;
ð4Þ
where δ(0 b δ b 1) is the capital depreciation rate, and rdi,t, rfi,t and wi,t are the rates of return to domestic capital, foreign capital, and labor per effective labor unit, respectively. 2 The assumption of this lifespan corresponds to the fact that the CIA estimates life expectancy in China in 2008 to be 73.18 years according to The 2008 World Factbook. 3 Although China is an aging society, we will not consider a negative growth rate to avoid zero population along the long-run steady growth paths. 4 The characteristics of FDI remain very controversial. Here, we assume that FDI and domestic capital are complementary rather than substitutes based on the statistical data in China. FDI peaked in the 1990s before the Asian crisis and has remained around 3–5% on average. This assumption is employed by Yao's (2006) empirical study as well as Findlay's (1978) theoretical study.
ð6Þ
where τc,i,t(0 b τc,i,t b 1) is a consumption tax rate in period t and t+j
Rti,t+ j ≡ ∏ (1 + rdi,s)− 1. The present value of the individual's lifetime s=t+1
income is defined by 6
Yi;t =
ð5Þ
j
2.1. Firm behavior
5
1063
Wi;t ≡ ∑
j=1
j j j t+j 1−τw;i;t + j−1 wi;t + j−1 li;t + j−1 hi;t + j−1 + Ti;t + j−1 Ri;t ; ð7Þ
where τw,i,t(0 b τw,i,t b 1) is the wage income tax rate in region i in j period t. Ti,t denotes a public transfer that individuals in age group j receive in period t. The individuals of generation t inherit the human capital of the previous generation in the second age group, h2i,t, without depreciation.5 Based on this, individuals choose their education time, ei,t, and formulate their human capital as: 2 ψ 1 hi;t + 1 = 1 + ξei;t hi;t ;
ð8Þ
where ξ (N0) and ψ(0 b ψ b 1) are parameters for human capital productivity and education investment, respectively. Based on the above assumptions, maximizing their utility, individuals spend a positive amount of time in human capital formulation. After formulating human capital for the first age group, individuals continue to accumulate the capital through their lifetime with the influence of on-the-job training exogenously given as θj(j = 2, 3, 4, 5, 6). Thus, the human capital level in each age group is defined by 1 2 3 4 5 6 6 hi;t ; hi;t + 1 ; hi;t + 2 ; hi;t + 3 ; hi;t + 4 ; hi;t + 5 2 ψ 3 ψ 4 ψ 5 ψ 6 ψ 1 ≡ 1; θ 1 + ξei;t ; θ 1 + ξei;t ; θ 1 + ξei;t ; θ 1 + ξei;t ; θ 1 + ξei;t × hi;t :
ð9Þ By normalizing one period as one time unit, the time not spent on education, 1 − ei,t, is allocated to labor. The second, third, and fourth age groups inelastically supply one unit of their time. The fifth age group supplies the time unit of labor, 1 − ζi,t + 4(0 b ζi,t + 4 b 1), which is
5
The effect of on-the-job training is factored out. Note that Bouzahzah et al. (2002) assume that the human capital stock in the sixth age group is defined as 0. We assume that the sixth age group can hold the same level of human capital as the fifth age group which is more relevant to the real world. 6
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exogenously given, and then retires. In sum, the individual labor supply is 1 2 3 4 5 6 li;t ; li;t + 1 ; li;t + 2 ; li;t + 3 ; li;t + 4 ; li;t + 5 ≡ 1−ei;t ; 1; 1; 1; 1−ζi;t + 4 ; 0 : ð10Þ The government provides individuals with two types of public j transfer, Ti,t (j = 1, 2, 3, 4, 5, 6), namely, education subsidies in the first age group and public pension payments in the fifth and six age groups: 1 2 3 4 5 6 Ti;t ; Ti;t + 1 ; Ti;t + 2 ; Ti;t + 3 ; Ti;t + 4 ; Ti;t + 5 1 5 6 = νi;t ei;t 1−τw;i;t wi;t hi;t ; 0; 0; 0; ζi;t + 4 pi;t + 4 hi;t + 4 ; pi;t + 5 hi;t + 5 ;
changes in debt issues in each period because our interest lies in the changes in the debt level that influence capital accumulation.8 Therefore, the government budget constraint in region i in period t is τc;i;t Ci;t + τw;i;t wi;t Li;t + Di;t + 1 1 = νi;t ei;t 1−τw;i;t wi;t hi;t + Pi;t + Gi;t + 1 + rdi;t Di;t ;
where Ci,t, Pi,t, Gi,t, and Di,t are, respectively, aggregate consumption, the pension payment, the other government expenditures, and debt issues in region i in period t. Defining gi,t and di,t as exogenous given other government expenditures per effective labor unit and debt issues per effective labor unit, respectively, we have aggregate variables as follows:
ð11Þ where νi,t(0 b νi,t b 1) is an education subsidy rate against an opportunity cost and pi,t is the exogenously given public pension payment rate per effective labor unit. Therefore, individuals maximize their lifetime utility in Eq. (5) subject to their lifetime budget constraint Ei,t = Wi,t in Eqs. (6) and (7) j by choosing their education time, ei,t, and consumption, ci,t + j − 1. First of all, we determine the level of ei,t. The optimal education time, ei,t⁎, is directly obtained by maximizing lifetime income: 1 1 j j ð1−ψÞ 1−τw;i;t + j−1 wi;t + j−1 li;t + j−1 θ t + jA @ * = ξψ ∑ : Ri;t ei;t j=2 1−τw;i;t wi;t 1−νi;t 6
j ci;t + j−1
=
j = 2; 3; 4; 5; 6: ð13Þ
On the other hand, per capita assets for each age group are defined
j
j j + 1−τw;i;t + j−1 wi;t + j−1 li;t + j−1 hi;t + j1 j j j = 2; 3; 4; 5; 6: + Ti;t + j1 −ci;t + j1 1 + τc;i;t + j1 ; ð14Þ j1 t + j−1 + j−1 ≡ ai;t + j−2 Ri;t + j−2
Thus, the optimal asset level in each period in per capita terms is obtained by substituting c⁎i in Eq. (14). 2.3. Government behavior In each period, the government equates the tax revenues from consumption and wage incomes and the revenue from debt issues with the expenditures for education subsidies, pension payments, other government expenditures and interest payments for the debt issues.7 The government keeps the budget balanced through the 7
6 j Pi;t ≡ ∑ ζi;t + 1 pi;t hi;t ;
ð17Þ
j=5 6
j
ð18Þ
j
ð19Þ
Gi;t ≡ ∑ gi;t hi;t ; and j=1
j=1
j j j Because pi,thi,t , gi,thi,t , and di,thi,t represent expenditures per capita, pi,t, gi,t, and di,t become constant in the steady growth paths.
2.4. Intertemporal equilibrium Economic growth in this model is achieved by both physical capital and human capital accumulation per effective labor unit. The physical capital level per effective labor unit takes a constant value, while the human capital level achieves a constant growth rate in the steady growth path. First, aggregate assets less aggregate debt issues in the next period equals aggregate capital less FDI inflow in the next period for a capital market equilibrium in region i in period t as(1 − χi,t + 1)Ki,t + 1 = ∑ 5j= 1aji,t − Di,t + 1. From Eqs. (1) and (19), this can be rewritten as
by: ai;t
ð16Þ
ð12Þ
!σ j−1 ci;t + j−2 ;
j
j=1
Di;t ≡ ∑ di;t hi;t :
The following three aspects are worth noting. To start with, ei,t⁎ has a positive correlation with the wage income rate for the second to fifth age groups; however, the first age group shows a positive correlation between ei,t⁎ and the education subsidy rate and a negative correlation between ei,t⁎and the wage income rate. This is because the marginal benefit of education time results in an increase of income from the second age group onward, while marginal cost is decreasing in the income of the first group (i.e., the opportunity cost). Another feature is that ei,t⁎ does not depend on the human capital level; individuals determine their education time regardless of their level of human capital. Last, it is a decreasing function of the interest rate. Next, when individuals choose the consumption level for each age group, the following five Euler equations hold: 1 + τc;i;t + j−2 t + j−1 γR 1 + τc;i;t + j−1 i;t + j−2
6
Ci;t ≡ ∑ ci;t ;
5
0
ð15Þ
We assume that China has no capital gains or corporate taxes because there is no reliable information.
1−χi;t + 1 ki;t + 1 =
5
5
j=1
j=1
j j j ∑ aˆi;t hi;t + 1 − ∑ di;t + 1 hi;t + 1
!
=
5
j
j
∑ li;t + 1 hi;t + 1
j=1
ð20Þ j is the asset per effective labor unit. Further, modifying the where âi,t dynamics of human capital accumulation in Eq. (8) using Eqs. (3), (4), (10), and (12), we can obtain the human capital or the economic growth rate, which depends only on ki,t as
ψ hi;t + 1 = 1 + ξe ki;t : hi;t
ð21Þ
Therefore, we know that k⁎i , â⁎i , d⁎i , and l⁎i in Eq. (20) become constant in the steady growth path. Moreover, substituting k⁎i into Eq. (21), we have the constant growth of hi in the steady growth path. To summarize, the equilibrium of the economy is defined as follows. Definitions. When the initial individual assets, aggregate total capital stock, initial individual human capital, and policy variables (χi,t, τc,i,t, 8 It is also possible to assume that the debt level is exogenously given, whereas tax levels are endogenously determined. Bouzahzah et al. (2002) set the wage income tax, which directly influences the selection of education time, as an endogenous variable.
Y. Shindo / Economic Modelling 27 (2010) 1061–1068
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Table 1 Effect of raising education subsidy rates in the new steady growth paths (h1i = 1). Education subsidy rate (%)
Lifetime consumption per person in present value (10,000 yuan/60 years) Lifetime assets per person in present value (10,000 yuan/60 years) Lifetime utility per person (10,000 yuan/60 years) Interest rate (%/10 years) Human capital/economic growth rate (%/10 years) Education time per persons in t in age group 1 (years) Education subsidies per person (10,000 yuan/10 years) Capital stock per effective labor unit (10,000 yuan/10 years) Assets per effective labor unit (10,000 yuan/10 years) Debt level per effective labor unit (10,000 yuan/10 years)
Jiangsu
Liaoning
23.5
33.5
43.5
30.2
40.2
50.2
25.625
25.586
25.601
22.558
22.713
23.030
32.715
32.713
32.706
23.413
23.384
23.304
16.942
17.003
17.076
14.250
14.292
14.345
68.0
68.6
69.0
57.2
57.0
56.5
27.0
28.4
30.2
26.8
27.9
29.3
1.42
1.71
2.12
1.32
1.61
2.05
0.328
0.562
0.906
0.310
0.504
0.801
7.906
7.840
7.782
6.447
6.462
6.520
11.874
11.725
11.535
7.350
7.231
7.053
4.593
4.505
4.368
1.148
1.015
0.781
τw,i,t, νi,t, pi,t, ζi,t + 4, and gi,t) are given, the intertemporal equilibrium of the economy is defined as: (1) under given prices (wi,t, rdi,t, and rfi,t), the firm's behavior is determined; (2) under given prices (wi,t, rdi,t, and rfi,t), the individual choices (ci,tj, j j j j ai,t , li,t , ei,t, hi,t , and Ti,t ) are determined; (3) the capital market clears; and (4) di,t is determined as the government budget is balanced. 3. Calibration 3.1. Parameter settings In this section, we calibrate the parameters using regional data for Jiangsu and Liaoning and obtain a growth rate in each steady growth path to conduct simulations with the model explained in the previous section. Considering one period as 10 years in this model, we use the available and most up-to-date data for the past 10 years, from 1998 to 2007, and input the annual average values into the model to determine the parameter values. The values that we calibrate as well as the data source are summarized in Annex 1. Using the parameter values, we perform a calibration to obtain equilibrium values in the steady growth paths as the base cases. To start with, normalizing h1i as one, we obtain the initial capital stock per effective labor unit, k0⁎ as 7.906 for Jiangsu and 6.447 for Liaoning.9 We then obtain the equilibrium values of the other endogenous variables and the human capital/economic growth rates. These values are listed in boldface in Table 1 in the next section.10 We define these equilibrium values as the base cases; that is, the education subsidy rates are 23.5% for Jiangsu and 30.2% for Liaoning in each steady growth path, as shown in Annex 1.
9 Because h1i grows at a constant rate in the steady growth path, we only calibrate the relative values of the capital stock per person when h1i is set to one. We can obtain the absolute value by multiplying the relative value by the h1i level in a specific period in each region. 10 By changing the exogenously given parameter of education investment, ψ, we examine values of k⁎ 0 to check the robustness of the model. When the parameter value changes from 0.280 to 0.279 and 0.281 for Jiangsu and from 0.208 to 0.207 and 0.209 for Liaoning, the value of k⁎0 becomes 7.903 and 7.909 for the former and 6.444 and 6.450 for the latter. Therefore, we conclude that robustness is satisfied.
3.2. Individual lifecycles in the steady growth paths Figs. 4 and 5 display the relative levels of consumption and assets per person in each age group in the steady growth paths when h1i is set to one. First, Fig. 4 shows that consumption increases with advancing age in both regions. However, consumption in Jiangsu is increasing in greater amounts than that in Liaoning. Because consumption is smoothed after individuals maximize their utility, the effect depends strongly on interest rates. In fact, interest rates are shown to be higher in Jiangsu than in Liaoning (Table 1). The higher interest rates lead to low intertemporal prices. That is why consumption in Jiangsu is much higher than in Liaoning relative to age. Assets are increasing in Fig. 5 until individuals reach the fourth age group. Because the individuals accumulate human capital with age, their wage income increases and so do their assets. In addition, they need to save assets to cover their consumption after their retirement in the middle of the fifth age group. Because the pension payments per effective labor unit are lower in Jiangsu than in Liaoning, as shown in Annex 1, the individuals in Jiangsu have to save more to prepare for retirement. Like consumption, assets in Jiangsu are much higher than in Liaoning with age, owing to the lower intertemporal price. Furthermore, we can see that the gap between the regions exist in the steady growth paths when h1i is one. Even if we take the differences in interest rates into account, the consumption is still larger in Jiangsu than in Liaoning, that is, the lifetime consumption in
Fig. 4. Relative level of consumption per person.
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Y. Shindo / Economic Modelling 27 (2010) 1061–1068
Fig. 5. Relative level of assets per person.
the present value is 256,250 yuan in Jiangsu and 225,580 yuan in Liaoning, as listed in Table 1. 4. Simulation results In this section, we conduct simulations by raising the education subsidy rates, νt from 23.5% to 33.5% and 43.5% in Jiangsu and from 30.2% to 40.2% and 50.2% in Liaoning. Table 1 summarizes the effects of raising the education subsidy rates on the equilibrium values of variables in the new steady growth paths when h1i is set to one. Four results are obtained from these equilibrium values. First, the contrasting effects on lifetime consumption are observed in the two regions. The different results are attributed to the interest rates, as the substitution effect dominates the income effect in this model. On the other hand, the lifetime assets in yuan per person decrease in both regions. The reason for the decrease is that the education subsidies encourage individuals to invest more in education or in human capital and to invest less in physical capital. Despite the opposite effects of interest rates, we can see that lifetime utility per person increases in both regions. It suggests that the reform is feasible in terms of the effect on individual welfare in both regions. Second, we should note that the higher education subsidy rates lead to higher rates of human capital/economic growth. When we increase education subsidies by 10% and 20% in each region, the net growth rates increase from 27.0% to 28.4% and 30.2% in Jiangsu and from 26.8% to 27.9% and 29.3% in Liaoning during the 10 years in the steady growth paths. (The growth rate per year is equivalent to increases from 2.4% to 2.5% and 2.7% in the former and from 2.4% to 2.5% and 2.6% in the latter.) The major reason for the increase in the growth rates is the longer education time. By boosting the education subsidy rates by 10% and 20%, the education time additionally increases by 0.29 years and 0.70 years in Jiangsu and by 0.29 years and 0.73 years in Liaoning over the 10 years. Conversely, the education subsidies per person swiftly increase by 2340 yuan and 5780 yuan in Jiangsu and by 1940 yuan and 4910 yuan in Liaoning. Because the education subsidy rates are defined by the opportunity cost, large amounts of resources are needed to invest in education with higher education subsidy rates. Third, the capital stock level per effective labor unit decreases in Jiangsu, whereas increases in Liaoning when the education subsidy rates increase by 10% and 20%.11 The changes in the capital stock are determined by four factors shown in Eq. (20). The first factor, the asset
11 This value is different from the value in Fig. 5, the former value being the assets per person in an individual's lifecycle, while the latter value is the assets per effective labor unit of aggregate assets in the steady growth path.
level per effective labor unit, decreases in both Jiangsu and Liaoning by boosting the education subsidy rates. The second factor, the debt level per effective labor unit, decreases in both regions. In Jiangsu, because the decrease in debt level is smaller than the decrease in assets, the capital stock per effective labor unit decreases. On the contrary, in Liaoning, because the decrease in debt level is larger than the decrease in assets, the capital stock per effective labor unit increases. Undoubtedly, a decrease in the third factor, labor supply, (that is, the increase in education time) causes an increase in the capital stock per effective labor unit if the assets and debt per effective labor unit and the human capital level are constant. Lastly, the transfer of technology has a limited effect on economic growth due to the small value of ε but contributes to an increase in total productivity. Nevertheless, as the economic growth rate is higher in Jiangsu than in Liaoning, we can confirm that the capital stock level per person in Jiangsu will exceed that in Liaoning in any period. Finally, we compare the differences in the human capital/ economic growth rates. Fig. 6 shows the relationship between the subsidy rates and human capital/economic growth rates in both regions. When the subsidy rates are increased by the same 10% and 20% in both regions, the growth rate in Jiangsu becomes higher than that in Liaoning in every case. When the subsidy rates are increased by 20%, the differences are even larger. More concretely, the net growth rates increase 1.4% and 3.2% with the rise in subsidies in Jiangsu, while the rates only increase 1.1% and 2.5% in Liaoning. Based on the results, we can draw the following two findings. First, the productivity of Jiangsu is potentially higher than that of Liaoning because both parameters for human capital productivity, ξ, and education investment, ψ, are higher in Jiangsu despite the lower subsidy rate. Hence, more subsidies for Jiangsu are preferable with regard to efficiency. Second, due to the different level of productivity, the differences in growth rates are expanded when the subsidy rates are evenly raised. Regarding equity, the subsidy rates need to be determined based on the economic circumstances of educational matters in each region. 5. Conclusion Two main results are found in the relationship between economic development and human capital accumulation in the long run in a sixperiod OLG model. In the simulation of the Jiangsu and Liaoning economies, we can first conclude that due to greater government subsidies in education, both regions achieve greater economic growth. Second, because of the large differences in productivity between the
Fig. 6. Relative level of human capital/economic growth rate with increase in subsidy rates (h1i = 1).
Y. Shindo / Economic Modelling 27 (2010) 1061–1068
regions, the growth gap expands with policy reform. We recognize the importance of education subsidies in the long run because any reform that results in an increase in education subsidies will contribute to a correspondingly higher economic growth while at the same time improving overall welfare. However, any policy change may ameliorate the regional disparities due to different levels of productivity. If China adopts a policy of pursuing a uniform growth rate, the differences in productivity in each region should be taken into account to set the subsidy rate. We could provide several long-run implications of the public policy in the area of education and technology based on existing Chinese data. However, we ignore several important issues. One of the concerns is that we do not analyze the burdens among generations during the transitional period. Because intergenerational conflicts arise, especially when a wide gap exists, further research should consider whether the government should retain a relatively low level of education subsidies. Another concern is that we only compare regions that attract FDI in the relatively developed eastern coastal areas. Further studies should expand the outlook to other regions in order to better capture the differences across the entire country. In spite of these limitations, the importance of education, especially government policy concerning education subsidies, has plausible and meaningful interpretations regarding economic growth rates and regional disparities. As part of its development strategy, China needs to implement education policies carefully in order not only to prioritize economic growth but also to reduce existing regional disparities.
Acknowledgements This research was supported by a Grant-in-Aid from the Asian CORE Program of Japan Society for the Promotion of Science (JSPS). I am grateful to Profs. Hideya Kato, Tsuyoshi Shinozaki, Nobuhito Takeuchi and Mitsuyoshi Yanagihara for their useful comments. I also appreciated the suggestions that I received from Profs. Takamune Fujii, Yuichi Furukawa and Akihiko Yanase at a workshop of the Nagoya International Economic Study Group, and from Profs. Tatsuyoshi Miyakoshi and Koichiro Morikawa at a conference held by the Japan Society of Household Economics. Finally, I thank two anonymous referees for their valuable comments.
Appendix A
Annex 1 Notation. General symbols i Region j Age group Endogenous variables L Aggregate labor K Aggregate capital Y Aggregate output K Aggregate technology transfer via FDI inflow rd Rate of return to domestic capital w Rate of return to labor per effective labor unit c Consumption per capita W Lifetime income e Education time C Aggregate consumption G Aggregate government expenditure d Debt issues per effective labor unit
t
Period/generation
l k y h
Labor per effective labor unit Capital per effective labor unit Output per effective labor unit Human capital
rf U
Rate of return to foreign capital Lifetime utility
E T a P D â
Lifetime expenditure Public transfer Asset per capita Aggregate pension Aggregate debt issues Asset per effective labor unit (continued on next page)
1067
Annex 1 (continued) Exogenous variables
Jiangsu
Liaoning
Source
α
Output elasticity of capital
0.383
0.363
β ε
Output elasticity of labora Output elasticity of technology transfer via FDIb FDI share in total investment Technology parameter Capital depreciation rate Time preference ratec
0.611 0.006
0.631 0.006
China Statistical Yearbook (1999–2008) ″ Yao (2006)
0.079
0.038
9.605 0.344 0.840
8.382 0.349 0.840
Intertemporal elasticity of Substitutionc OJT in age group 2 OJT in age group 3 OJT in age group 4 OJT in age group 5 OJT in age group 6d Human capital productivitye Parameter for education investmente Consumption tax rate
1.500
1.500
1.061 1.201 1.325 1.429 1.429 0.466
1.061 1.201 1.325 1.429 1.429 0.408
China Statistical Yearbook (1999–2008) ″ ″ Bouzahzah et al. (2002) Bouzahzah et al. (2002) Ma (2005) ″ ″ ″ ″ UNESCO
0.280
0.208
UNESCO
0.045
0.036
Wage income tax rate Education subsidy ratef Pension payment per effective labor unitg Retirement ratioh Other government expenditures per effective labor uniti
0.236 0.235 0.448
0.247 0.302 1.081
China statistical yearbook (1999–2008) ″ ″ ″
0.500 1.291
0.500 1.784
″ ″
χ A δ γ σ 2
θ θ3 θ4 θ5 θ6 ξ ψ τc τw ν p ζ g
a β is calculated from the compensation of employees by region divided by the net regional product at factor cost. b Technology transfer had a limited effect on economic growth as a result of the small value of ε, but it had a positive effect on growth. Yao (2006) concluded that FDI with combination of export had a strong effect on economic growth. In our model, the effect of export is excluded because our interest is not to examine the effect of trade but that of human capital. c There is no empirical study that estimates the parameters for China. Controversy exists even for developed countries because the values vary depending on the study. Obtaining realistic interest rates and saving rates later when we calibrate the model, we choose γ and σ employed by Bouzahzah et al. (2002) who simulated the European case. d The wage profile is not the inverted U-shape we often see in the case of developed countries but increasing in China. e We set ξ and ψ to match the long-run economic growth rate of 2.5% (as in many developed countries) and the national average school-life expectancy during the past 10 years of 10.63 years from UNESCO. f ν is calculated from the education expenditure per student divided by per capita net compensation of employees from 15 to 24 years of age. Although the cost of upper secondary education is usually higher than primary and lower secondary education, the education expenditure is set as an average of primary and secondary education owing to limited sources. g p is obtained from the total pension payment divided by the population over 65 years of age. The pension payments include only retirees of government agencies and institutions covered by the government budget. h ζ is set as 0.5 because the average retirement age for male workers is 60 years of age. i g is derived from total government expenditure minus total education expenditure, pension payments, and debt issues divided by the population.
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