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Asian Business Research Journal 
Vol. 5,  13-18, 2020 
ISSN : 2576-6759 
DOI: 10.20448/journal.518.2020.5.13.18 
© 2020 by the authors; licensee Eastern Centre of Science and Education, USA 

 
 

 

 
Influence of Endogenous Human Capital on China’s Economic Growth 

 
Zhao Li   

 

 
Glorious Sun School of Business and Management (GSSBM), DongHua University, China. 

  
( Corresponding Author) 

 
 

 

 

 
Abstract 

Based on the framework of endogenous economic growth, this paper took the education sector as 
a separate human capital production sector, and then an economic growth model with endogenous 
human capital accumulation is constructed, and a combination of theoretical derivation and 
simulation is used for the education investment behavior of the Chinese household sector, as well 
as the analysis of the efficiency of human capital accumulation. Based on above theoretical 
analysis, then to study the impact of educational investment on economic growth. The study 
found that the more the elasticity of education investment, the higher the efficiency of human 
capital accumulation, and the greater willingness of families to increase investment on education. 
Human capital accumulation is a key factor in determining the economic growth potential of a 
country or region, and education is the most important way for the accumulation of human 
capital. The investment in education is necessary for China under the condition of the economic 
growth rate slowing down. 

 
Keywords: Investment, Time-lag effect, Human capital accumulation, Economic growth. 

JEL Classification: E21, E22, H52. 

 
 
1. Introduction 

“Why are some countries richer than others?” Solow’s seminal paper showed that capital accumulation could 
account for differences in output per capita. Further, Lucas (1988) found that human capital disparities were key 
factor for countries differences. The following researches (eg. (Aisen & Veiga, 2013; Benos & Zotou, 2014)) have 
estimated the impact of human capital on economic growth through cross-section analysis and concluded that 
differences in the average schooling of countries are related to different economic growth rates. The concept of 
human capital can be interpreted as the set of intangible resources embedded in the labor factor. Individuals with 
more education are more productive and innovative leading to the creation of new products and improving the 
productivity of factors (Goldin, 2016).  

Although, human capital is key factor that affect the economic growth, how to measure and how the human 
capital accumulated are still controversial. The standard approach largely inspired by the work of Mincer (1974) 
takes estimates of the rate of return to schooling as building blocks to directly measure a country’s stock of human 
capital. Implicitly, this method assumes that the marginal contribution to output of one additional year of schooling 
is equal to the Mincerian rate of return. One problem with this procedure is that it is not well suited to handle 
cross-country differences in the quality of human capital. The main ways of accumulating human capital are 
education and learn by doing (Becker, 2009) and in general there is a positive correlation between an individual’s 
ability and their level of education. As a result, scholars often use the average level of education of employees as 
substitutes for human capital stock or human capital accumulation (Schündeln & Playforth, 2014). Using the 
education output to directly measure the stock of human capital, it may ignore the process how human capital 
produce, namely it lacks an education sector. 

Based on the above considerations, this paper firstly establishes a theoretical model that includes education 
sectors. The education sector generates human capital, and human capital as a factor of production enters the 
production sector, affecting the production of the national economy. Taking the duality of production function and 
cost function, the educational input (cost) is used as the explanatory variable of educational output (human capital). 
The investment in education has the time lag effect in the formation of human capital. That is, the current 
investment in education cannot be fully reflected in the stock of human capital in the current production field and 
therefore will not directly affect the output of the national economy in the current period, which is often ignored by 
mostly researches. 

This paper consists of six parts. The first part is the introduction. The second part is literature review. The 
third part is the derivation of the theoretical model, including the education production function, cost function in 

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the education sector, and the national economic production function in the production sector. The fourth part is 
calibration. The fifth part is conclusion. 
 

2. Literature Review 
At present, the main methods of measurement of human capital include “cost method”, “income method” and 

“education index method”. Among these methods, the education indicator method is relatively simple and easy to 
implement. The common education indexes are adult literacy rate, enrollment rate and average years of schooling 
(Laroche & Merette, 2000). However, the education indicator method only focuses on the simple arithmetic mean, 
which is not enough to reflect the difference in the return rate of education among different groups of people. The 
essence of cost method is to calculate all the expenditures in the process of human capital formation (Kendrick, 
1976). It is assumed that the higher the cost paid, the higher the accumulated human capital. Moreover, different 
from physical capital, human capital accumulation is a relatively long-term and complicated process. The time span 
of human capital accumulation determines that the cost method measures human capital requires long-term data 
support. It is difficult for China’s current data to support detailed cost method research. Different from the cost 
method, the income method regards human capital accumulation as a long-term investment, and measures the 
current human capital stock with the present value of individual lifetime return (Jorgenson & Fraumeni, 1992). 
However, the income method also has its defects. It is necessary to assume some important parameters, especially 
the income growth rate and the discount rate. For example, Li, Li, Qiu, Guo, and Tang (2014) used labor 
productivity growth as an approximation of the actual income growth rate to forecast future personal income, and 
use the OECD’s human capital discount rate. Since the income method has assumed the economic growth rate 
advanced, using human capital to explain the economic growth of a country will fall into the logical trap of circular 
argumentation. However, at present the education indicator are most popular used in the researches because of its 
easily measurement. 

The above methods are only the ways to measure the human capital stock, but about the process of how the 
human capital production is still hard to classify. Human capital accumulation is essential of the process to acquire 
knowledge and skills through education, experience and health care. Acquiring skills and knowledge is a means of 
capital formation by delaying consumption with the aim of increasing future income. Human capital improves the 
quality of labor, increasing its productivity (Bodman & Le, 2013). However, in most of the literature on education-
human capital as the driving force of economic growth, the input-output relationship of the education sector is 
often simplified: The education department with linear production technology mechanically converts inputs into 
human capital. Some scholars have modified the hypothesis of linear human capital production technology in the 
education sector and verified it using micro-level data. However, using macro-level data to empirically analysis the 
education sector’s production process and its efficiency is rare. This paper introduces the education sector into the 
endogenous economic growth model to show the process of the human capital accumulation. Combined with the 
characteristics of China’s education system, it analyzes the effects of education investment on human capital 
accumulation and further economic growth. 
 

3. Methodology 
3.1. Household Sector 

The representative consumer maximizes his utility across time. 

 U(𝑐𝑡) = ∫ 𝑒−𝜌𝑡
∞

0

𝑐𝑡
1−𝜃

1 − 𝜃
 dt （1） 

Where, θ the inverse of the elasticity of substitution, θ > 1 and ρ the discount rate.  

In period 𝑡0, the initial endowment of the household is 𝑘0units of physical capital and ℎ0units of human capital. 

Then each period, the household leases physical capital to the firm at a rent rate 𝑟𝑡and provides the firm with 

ℎ𝑡units effective workforce at a wage rate of 𝑤𝑡 . The household allocates total income between consumption, 
physical capital investment, and human capital investment. The corresponding budget constraints are: 

 𝑐𝑡 + 𝑒𝑡 + 𝑖𝑡 = 𝑤𝑡 ∙ ℎ𝑡 + 𝑟𝑡 ∙ 𝑘𝑡 （2） 

The capital accumulation equation is set as follows: 

 𝑘ṫ = 𝑤𝑡 ∙ ℎ𝑡 + 𝑟𝑡 ∙ 𝑘𝑡 − 𝑐𝑡 − 𝑒𝑡 − 𝛿𝑘𝑘𝑡 （3） 

Here, 𝛿𝐾 is depreciation rate of physical capital. 
 

3.2. Production Function 
In this paper, begin with a basic model of economic growth in which aggregate output at date t is determined 

by the size of the physical capital, human capital and the state of technology, then the production function will be 
set as: 

 𝑦𝑡 = 𝐴 ∙ 𝑘𝑡
𝛼 ∙ ℎ𝑡

1−𝛼 （4） 

Here,  𝑌t is final output, 𝐴 is a measure of technology，𝑘𝑡 is total physical capital, ℎt is human capital, 0 < 𝛼 <
1 is output elasticity of physical capital. 

In the complete competitive market conditions, the first-order conditions for maximizing the profit of a 
representative firm are: 

 𝑟𝑡 = 𝛼 ∙ 𝑧𝑡
𝛼−1, 𝑤𝑡 = (1 − 𝛼) ∙ 𝑧𝑡

𝛼 （5） 

Where, 𝑧𝑡 = 𝑘𝑡 ℎ𝑡⁄ , is the ratio of physical capital to effective labor. 



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3.3. Endogenous Human Capital 
ASSUMPTION1: Education investment is an important means to improve the quality of human capital, and it 

is also an important process for the accumulation of human capital (Sehrawat & Giri, 2017). Education can be 
divided into elementary education and higher education. Elementary education is compulsory education in some 
countries. At this stage, people receive general basic education, while higher education fosters scientific and 
technological progress in a country by cultivating high-tech talents. This in turn promotes productivity growth. 
Educational investment does not always positively co-relate to economic growth (Ahsana & Haque, 2017). The 
misallocation of human capital structures caused by over-education will inhibit economic growth (Teixeira & 
Queirós, 2016). Although human capital is a key factor in promoting economic growth, the structural 
unemployment caused by higher education misallocation makes the basic labor supply insufficient, which in turn 
hinders economic growth. Thus, the accumulation of human capital does not directly promote economic growth. 
The role of human capital depends on certain industry structure and the economic institutions. Besides, economic 
development level of a country determines the type of the dominant export sector and the type of major export 
products, which in turn leads to the demand for related talents. It promotes the demand for education. Among 
them, the growth of non-technology-intensive exports has inhibited the average number of years of education in 
the country, while the growth of technology-intensive exports has long-term role in promoting the country’s 
education level (Blanchard & Olney, 2017). For simplicity, assume that human capital has no depreciation. Then, 
the human capital accumulation function is as follow: 
 ℎ̇𝑡 = B ∙ 𝑒𝑡

𝛾
∙ 𝐼𝜈 （6） 

Here, B is constant, 𝛾 is elasticity of education investment, ν is elasticity of industrial structure. 
 

3.4. General Equilibrium and the Growth Path 
Objective function: 
 

𝑚𝑎𝑥 ∫ 𝑒−𝜌𝑡
∞

0

U(𝑐𝑡)dt （7） 

The constraint is: 
 𝑘ṫ = 𝑤𝑡 ∙ ℎ𝑡 + 𝑟𝑡 ∙ 𝑘𝑡 − 𝑐𝑡 − 𝑒𝑡 − 𝛿𝑘𝑘𝑡 （8） 

The Hamiltonian function for this problem is： 
 

H =
𝑐𝑡

1−𝜃

1 − 𝜃
+ 𝜆𝑡(𝑤𝑡 ∙ ℎ𝑡 + 𝑟𝑡 ∙ 𝑘𝑡 − 𝑐𝑡 − 𝑒𝑡 − 𝛿𝑘𝑘𝑡) + 𝜇𝑡B ∙ 𝑒𝑡

𝛾
∙ 𝐼𝜈 （9） 

In the above formula, 𝜆𝑡 is the shadow price of 𝑘𝑡 , 𝜇𝑡 is the shadow price of 𝑒𝑡 . Where, 𝑘𝑡  and ℎ𝑡  are state 

variables, ct and 𝑒𝑡 are control variables.  
According to the first order condition, then, 
 𝑐𝑡

−𝜃 = 𝜆𝑡 （10） 

 −𝜆𝑡 + 𝜇𝑡𝛾B ∙ 𝑒𝑡
𝛾−1

∙ 𝐼𝜈 = 0 （11） 

Then the Euler equation is, 

 
�̇�

𝜆
= −𝑟𝑡 + 𝜌 + 𝛿𝑘 （12） 

 
�̇�

𝜇
= 𝜌 − 𝑤𝑡 ∙ 𝛾B ∙ 𝑒𝑡

𝛾−1
∙ 𝐼𝜈 （13） 

TVC 

 lim
𝑡→∞

𝑒−𝜌𝑡 ∙ 𝜆𝑡 ∙ 𝑘𝑡 = 0 （14） 

Log-differentiating equations 10,11 and combining it with equations 13,14 produces consumption growth rate, 

and divide equations 8 both sides kt produces physical capital growth rate： 

 
�̇�

𝑐
=

1

𝜃
(𝛼 ∙ 𝑧𝑡

𝛼−1−𝛿𝑘 − 𝜌) （15） 

 �̇�

𝑒
=

1

𝛾 − 1
((1 − 𝛼) ∙ 𝑧𝑡

𝛼 ∙ 𝛾B ∙ 𝑒𝑡
𝛾−1

∙ 𝐼𝜈 − 𝛼𝑧𝑡
𝛼−1+𝛿𝑘) 

（16） 

 �̇�

𝑘
= 𝑧𝑡

𝛼−1 −
𝑐𝑡

𝑘𝑡
−

𝑒𝑡

𝑘𝑡
− 𝛿𝑘 

（17） 

Here 𝑧𝑡 = 𝑘𝑡 ℎ𝑡⁄ , is the ratio of physical capital to effective labor, and define 𝜒𝑡 = 𝑐𝑡 𝑒𝑡⁄ . Equations. 15 16 and 

17, fully characterize the dynamics of the economy. This system can be solved for its steady state, �̇� 𝑐⁄ = 0 �̇� 𝑘⁄ =
0, �̇� 𝑒⁄ = 0, then we can get ratio of physical capital to effective labor, the per capital effective consumption and per 

capita effective education investment in equilibrium state:𝑧∗, 𝑒∗, and 𝜒∗: 

 𝑧∗ = (
𝛼

𝛿𝑘 + 𝜌
)

1

1−𝛼
 （18） 

 𝑒∗ = (
𝜌

1 − 𝛼
(

𝛿𝑘 + 𝜌

𝛼
)

𝛼

1−𝛼 1

𝛾𝐵𝐼𝜈
)

1

𝛾−1

 （19） 

 𝜒∗ =
𝜌

1 − 𝛼

1

𝛾
−

𝛼

𝛿𝑘 + 𝜌

𝜌

1 − 𝛼

𝛿𝑘

𝛾
− 1 (20） 



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PROPOSITION1: There exists a BGP along which the income shares of capital and labor are constant and strictly 

positive when factors are paid their marginal products, only when 𝜌 𝛾(1 − 𝛼)⁄ > 𝛼𝜌𝛿𝐾 𝛾(𝛿𝐾 + 𝜌)(1 − 𝛼)⁄ + 1. 

From the Equation 19 we can know that the per capita effective capital in equilibrium state: 𝑧∗ is affected by the 

parameters fixed capital depreciation rate  𝛿𝑘 and time preference 𝜌 changes. When  𝛿𝑘or 𝜌 increases, the per capita 

effective capital will decrease. The education investment 𝑒∗  is affected mainly by the elasticity of education 

investment 𝛾 . When 𝛾  increases, the education investment will increase. The more the elasticity of education 
investment, the higher the efficiency of human capital accumulation, and the greater willingness of families to 
increase investment on education. 
 

4. Calibration 
The previous section analyzed the effects of household education investment on human capital accumulation 

and economic growth by constructing a theoretical model. However, there are many exogenous parameters in the 
model. Therefore, taking the China’s data from 1997 to 2016 as a sample, the paper firstly obtained a reasonable 
value for the structural parameters of the model and then calibrated the model. Second, the calibration was used to 
analyze the impact of household education investment on human capital accumulation and economic growth. 
 

4.1. Parameters Sets 
4.1.1. Utility Function Parameter Setting 

About intertemporal substitution elasticity, the results of foreign and domestic studies were widely divergent. 

Empirical analysis using total consumption data usually finds that cross-substitution elasticity 1 𝜃⁄  was close to 
zero, and a calibration model to match growth and fluctuation facts usually needed to set the value close or equal to 
1 Gu, Yan, and Chen (2013) measured the inter-substitution elasticity of consumption of China’s household 
consumption from 2000 to 2008 and found that the elasticity of intertemporal substitution in most years was 
around 0.3. With reference to relevant research at home and abroad, the benchmark intertemporal substitution 

elasticity value is set to 0.5, namely the risk aversion coefficient 𝜃 is 2. 
 

4.1.2. Firm Production Function Parameter Setting 
Estimated that the output elasticity of China’s physical capital from 1952 to 2010 was 0.6576; Zhu and Feng 

(2014) calculated that the output elasticity of physical capital from 1997 to 2011 was 0.745. Based on the above 
domestic research, we set the output elasticity of physical capital in the production function to 0.7. In addition, the 
technical parameter A of the production function is normalized to 1. 
 

4.1.3. Physical Capital Depreciation Rate 
Most of the literature set the depreciation rate of physical capital 5% or 6%. This paper calculates the average 

depreciation rate of fixed assets from 1997 to 2016 according to the relevant data according to the “China 
Statistical Yearbook”, was 5.23%, which is basically consistent with the general capital depreciation rate of the 
literature. Therefore, this paper sets the annual depreciation rate of physical capital to 5%. 
 

4.1.4. Human Capital Output Elasticity 
About the output elasticity of human capital γ, many studies at home and abroad pointed out that there was an 

important relationship between the output elasticity of human capital and the return on education investment. 
Psacharopoulos and Patrinos (2004) found that every extra year of education leads to an increase in wages ranging 
from 8.4% to 13.2%, with an average of 10.2%. Feng, Zhu, and Yang (2012) found that for every one year increase 
in the average number of years of education for Chinese employed personnel from 1998 to 2010, the average wage 
level will increase by 11%. Therefore, the paper set the rate of return on education investment to 10%, so that the 
calculated output elasticity of human capital was 0.8. In order to test the robustness of the value, the sensitivity test 
will be performed later. All the parameters set are shown in the Table 1. 

 
Table-1. Model parameters and variable values. 

Parameter Symbol Value 

Intertemporal substitution elasticity 1 θ⁄  2 

Total factor productivity 𝐴 1 

Physical capital output elasticity 𝛼 0.7 

Physical capital depreciation rate 𝛿𝑘 0.05 

Human capital output elasticity 𝛾 0.8 

                          
 

4.2. Calibration Results and Analysis 

Based on the model parameters set, then using the number simulation method, the calibration results are as 

show in the Table 2. Time preference rate 𝜌 is 0.9905 and technical level of human capital production function are 
0.610. According to the parameters, this paper further studied the effect of household education expenditure on 
output growth rate through numerical simulation. As is show in Figure 1. 

 
 
 
 
 



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Table-2. Calibration Results. 

Parameter Symbol Value 

Time preference rate 𝜌 0.9905 

Technical level parameters of human capital production function B 0.610 

 
Figure 1 shows that the household education investment is positively related with economic growth. 

Household education investment belongs to productive public expenditure and helps to increase the marginal 
output of physical capital. Therefore, household are willing to save more and promote the accumulation of physical 
capital. The increase in household education investment has positive effects on both human capital accumulation 
and physical capital accumulation, and promotes economic growth. 
 

 
Figure-1. Impact of household education investment on economic growth. 

 

4.3. Sensitivity Test 
Examining whether the parameters preset changes will significantly affect the simulation results, we analyze 

the effect of the sensitivity of the structural parameters on each endogenous variable in the model to check if the 
simulation results are robust. As is shown in the Table 3, firstly, firm sector, the lower value, benchmark value, and 
upper value of the output elasticity of physical capital are taken as 0.6, 0.7, and 0.8, respectively. Secondly, human 
capital production, the output elasticity of the human capital, lower value, the benchmark value and the upper value 
are 0.6, 0.8 and 0.90 respectively. 

 
Table-3. Impact of model parameters sensitivity analysis on economic growth. 

Parameters 
Endogenous 

variables 

Output elasticity of physical capital 𝜶 
Output elasticity of education investment 

𝜸 
Lower Benchmark Upper 

Trend 
Lower Benchmark Upper 

Trend 
0.60 0.70 0.80 0.60 0.8 0.9 

e/y 0.021 0.019 0.017 
Monotonous 

decline 
0.021 0.019 0.018 

Monotonous 
decline 

k/y 1.813 2.100 2.437 Monotonous rise 2.246 2.100 1.898 
Monotonous 

decline 

h/y 0.250 0.177 0.125 
Monotonous 

decline 
0.224 0.177 0.151 

Monotonous 
decline 

Δy/y 0.082 0.075 0.069 
Monotonous 

decline 
0.081 0.075 0.072 

Monotonous 
decline 

 
From above sensitivity analysis, it can be found that: The Chinese economic growth numerical simulation 

solution based on the accumulation of human capital and physical capital is robust; When the model parameters 
change near the benchmark value, the Chinese economic growth path will not appear obvious change. 
 

5. Conclusion 
Accumulation of human capital is a key factor in determining the economic growth potential of a country or 

region, and education is the most important way to accumulate human capital. Empirical researches of the 
economic growth model driven by the accumulation of human capital mainly tends to verify the relationship 
between education and economic growth. However, the production process (input-output relationship) in the 
education sector is a black box. The impact of education on the accumulation of human capital and the efficiency of 
education have not been given due attention. Based on the framework of endogenous economic growth, this paper 
took the education sector as a separate human capital production sector, and then an economic growth model with 
endogenous human capital accumulation is constructed, and a combination of theoretical derivation and simulation 
is used for the education investment behavior of the Chinese household sector, as well as the analysis of the 
efficiency of human capital accumulation. Based on above theoretical analysis, then to study the impact of 



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educational investment on economic growth. The study found that the more the elasticity of education investment, 
the higher the efficiency of human capital accumulation, and the greater willingness of families to increase 
investment on education. Human capital accumulation is a key factor in determining the economic growth potential 
of a country or region, and education is the most important way for the accumulation of human capital. Under the 
new normal, in order to achieve a change in the mode of economic growth, education investment should be 
increased. 
 

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Citation | Zhao Li (2020). Influence of Endogenous Human Capital 
on China’s Economic Growth. Asian Business Research Journal, 5: 
13-18. 
History:  
Received: 26 June 2020 
Revised: 29 July 2020 
Accepted: 12 August 2020 
Published: 2 September 2020 
Licensed: This work is licensed under a Creative Commons 

Attribution 3.0 License  
Publisher:  Eastern Centre of Science and Education 
 

Acknowledgement: This study contributes in the existing literature that this 
paper tried to construct an Endogenous Human Capital on China’s Economic 
Growth. 
Funding: This study received no specific financial support.    
Competing Interests: The author declares that there are no conflicts of 
interests regarding the publication of this paper. 
Transparency: The author confirms that the manuscript is an honest, 
accurate, and transparent account of the study was reported; that no vital 
features of the study have been omitted; and that any discrepancies from the 
study as planned have been explained. 
Ethical: This study follows all ethical practices during writing.  
 

Eastern Centre of Science and Education is not responsible or answerable for any loss, damage or liability, etc. caused in relation to/arising out of the use 
of the content. Any queries should be directed to the corresponding author of the article. 

 

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