Download The Comparison of the Solow Residual of Regional Economic Growth

The Comparison of the Solow Residual of Regional Economic Growth
in China
NIU Yongping1, XIAO Hong2
1. School of Economics, Shandong Institute of Business and Technology, Yantai, P.R.China, 264005
2. Library, Shandong Institute of Business and Technology, Yantai, P.R China, 264005
[email protected]
Abstract: Since the reform and opening up, China has experienced rapid economic growth. However,
the imbalance of regional economic development has been also growing. It can be found that the Solow
residual is not obvious in China's economic growth by calculating relevant data. However, by cluster
analysis we find that the Solow residual in economic growth of each provinces (or municipalities) vary
significantly. To improve this situation, we need to change the investment-based development model,
and gradually increase the rate of technical progress.
Keywords: Regional Economy, Solow Residual, Technical Progress
1 Introduction
Since the reform and opening up, China has experienced rapid economic growth .According to the data
of National Bureau of Statistics, the annual economic growth rate of China is 9.9% from 1978 to 2008.
At the same time, the imbalance of regional economic development has been growing. For example, the
per capita GDP of Beijing is 48193 and the per capita GDP of Tibet is 10246 in 2007.So, how
much the contribution of technological progress has been in our country's economic growth and regional
economic growth? If technical progress is difficult to be measured, how much the Solow residual has
been in our country's economic growth as well as regional economic growth? Some scholars have done
research about it, such as Xu Hui(2009) and Wu Qunli(2009) .The former analyzed the overall
contribution to China's economic growth of technological progress , the latter considered that there had
been obvious differences of total factor productivity (that is, Solow residual) in eastern, western and
central regions of China. Li Bin and Zhao Xinhua (2009) analyzed China's total factor productivity by
using trans-log production function .Some scholars such as Zhao Zhiyun et al. (2007) discussed that
technological progress could be implicated in capital accumulation. They consider that the integration of
capital accumulation and technological progress could conceal the technological progress of China, or
the Solow residual of Solow model could not be a true reflection of the technological progress of China.
We believe, despite that the Solow residual may not fully cover the technological progress, it would be
appropriate to be used for the comparison of the regional economy, and it would be meaningful.
￥
￥
2 The Logical Process of the Solow Residual
Assumptions are as following:
First, the production function is a homogeneous one, and there is constant-returns-to-scale in production.
Second, capital and labor can be completely replaced by each other, and that capital and labor follow the
law of diminishing-marginal-return.
（ ，）
We set up production function Q = TF K L , where T is a technical variable. T's role is reflected by
increasing amount of K and L simultaneously, so T can be presented as a coefficient. By differentiating
the production function, we can get:
（K，L）+T • MP
∆Q = ∆TF
K
T MP • ∆L
• ∆K + •
L
(1)
Where, MPK is the marginal product of capital and MPL is the marginal product of labor. Equation (1)
is divided by Q, we can get:
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∆Q ∆T MPK • ∆K MPL • ∆L
=
+
+
Q
T
Q
Q
(2)
Because of the constant- return-to -scale property of the production function and perfect competition of
market, MPL equals W/p(real wage is defined as the nominal wage divided by the output prices, under
the conditions of perfect competition, the real wage equals the marginal products). Thus,
MPK K / Q
MP L / Q
L
equals the share of labor
equals the share of capital cost in the total output, denoted by α,
cost in the total output, denoted by β. Similarly, we define α+β=1, that is the condition of constant
returns to scale. We can change Equation (2) into:
∆Q ∆T β • ∆L α • ∆K
=
+
+
Q
T
L
K
(3)
∆T ∆Q β • ∆L α • ∆K
=
−
+
T
Q
L
K
（）
4
In other words, the growth rate of output is equal to the sum of the following three: technical progress
β ∆L / L ;
rate ∆T / T ; the growth rate of labor input multiplied by the share of labor in production
and the capital growth rate multiplied by the share of capital in production α ∆K / K .
Further, we can change the output into per-capita output, capital into per-capita capital of equation (3):
Q
Q
∆Q
∆L L
∆Q ∆L
/
∆
=
−Q 2
=
−
L
L
L
L Q
Q
L so we can get:
As,
（ ） （
）
（QL ）/ QL = ∆TT + α（ ∆KK − ∆LL ）
∆
Then:
∆T
=∆
T
(5)
（QL ）/ QL − α（∆KK − ∆LL ）
∆K
∆L
−
∆
K
L equals the rate of change of per-capital capital
Also
（ ）
K
L
K
/
L
(6)
. We define
K / L = k and Q / L = q , where k is per-capital capital and q is per-capital output, we get:
∆T
T = ∆q / q − α • ∆k / k
(7)
That is, the rate of technological progress equals the difference of the rate of per-capita output growth
which can be observed and the product of the rate of change of per-capita capital and the capital share of
output (α). This is the Solow residual. For a long time, Solow residual has been the core of economic
growth and productivity analysis and has been the main theoretical framework. Of course, the Solow
residual is not only consisted of technological progress, but also system change and other factors which
are difficult to be measured.
3 The Solow Residual of Regional Economic Growth
3.1 The overall Solow residual of China's economy
Equation (4) or (6) can be used to calculate Solow residual. For simplicity, we use equation (4) to
estimate it. We use GDP to represent the output, the amount of employment to represent labor. All of the
data can be obtained at the National Bureau of Statistics web site. We use the capital stock to represent
K, according to method of Wu Qunli (2009).Because the data before 1995 is difficult to be obtained, our
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calculation is limited to 1995-2007. What need to be explained is that the labor share α and capital share
β. We define α equals to the quotient of total wages and GDP, so that the capital share equals to the
difference of 1 and α. And the actual results of α and β is basically consistent with results of other
scholars. As shown in table 1.
Table 1.The Overall Solow Residual of China’s Economy Between 1996 and 2007 (%)
Year
∆Q / Q
α
Residual
∆K / K
∆L / L β
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
mean
17.27
11.29
6.36
6.57
10.76
10.27
10.20
13.50
18.06
15.35
15.78
17.99
12.78
11.36
10.92
11.25
10.63
10.59
10.82
11.13
12.79
14.46
16.07
17.24
23.80
13.42
1.33
1.09
0.51
0.90
2.12
1.30
0.98
0.94
1.03
0.83
0.76
0.77
1.05
13.19
12.30
11.49
11.48
11.18
11.29
11.45
11.34
11.04
11.21
11.38
11.72
11.59
87.70
88.51
88.52
88.82
88.71
88.55
88.66
88.96
88.80
88.62
88.28
88.41
88.41
7.24
1.58
-3.66
-2.94
1.11
0.52
0.24
2.06
5.08
0.99
0.41
-3.11
0.79
According to Table1, we can find that the average residual is only 0.79%, less than 1% between 1996
and 2007. The maximum number of 1996 is 7.55% and the minimum one is -6.84% in 1998. Even if we
add technological progress embodied in capital to it, the average residual is less than 7%. However,
according to the calculation of Hu Lifa(2003), the average of Solow residual of foreign direct
investment(FDI) of China between 1993 and 2001 is about 19%. So we can conclude that the Solow
residual of China's economic growth has been very low .We believe that it is mainly due to the
following reasons:
The first is the mode of investment-dependent growth. We could find that the average growth rate of
investment has been more than the average growth rate of GDP growth beyond 3%, and since the labor
share (the rate of total wages in output) has been very low, and the capital share has been above 88%, so
the Solow residual is certain to be negative.
The second is that increasing-returns-to-scale has been not obvious. According to principal of Solow
model, if Solow residual is above zero, there probably is increasing-returns-to-scale in production
function. However, since 2000, the scale of real estate investment has been too large in China,,
simultaneously there has been excess capacity in the manufacturing industry, which led to constant
–returns- to- scale even diminishing –returns- to- scale.
The third is that technological change has been very slow. Under the premise of the economic system
will remain unchanged, Solow residual basically can be explained by technological progress. But as a
lot of papers shown, China's manufacturing industry is basically in the low-end of international
industrial chain, and the core technology in many industries has been controlled by abroad enterprises.
Further, the R&D investment of local enterprises has been less than abroad ones, and there has been
little original innovation, all of these lead to that the technological progress is not obvious in China.
3.2 The Solow residual comparison of each province (or municipality) of China
According to the above calculation method, we can find the Solow residual of each province (or
municipality) of economic growth. Due to data and space limitations, our calculation is limited to the
data from 2000 and 2007, not including Taiwan Province. We also sort the average value from 2000 and
2007. As shown in table 2.
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Rank
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Table 2.The Comparison of Solow Residual of Each Province (or Municipality) of China (%)
Region
00-01
01-02
02-03
03-04
04-05
05-06
06-07
Average
Beijing
1.95
-2.80
-8.46
-25.35
42.20
34.48
4.32
6.62
Guangdong
0.38
1.78
-8.08
-14.40
22.52
13.89
3.36
2.78
Shanghai
2.17
1.54
0.04
-18.28
7.02
19.47
4.63
2.37
Ningxia
-4.11
-4.37
-18.83
9.98
18.27
1.91
9.36
1.74
Qinghai
-9.39
-2.01
3.14
9.72
4.75
-3.75
6.39
1.26
Gansu
-4.22
-2.12
-4.46
5.67
7.20
3.12
-4.11
0.15
Hainan
-1.31
4.29
-11.31
-9.38
8.42
9.58
0.10
0.06
Xinjiang
-4.09
-2.98
-7.05
3.08
3.31
2.86
0.80
-0.58
Tianjin
-0.80
0.28
-9.53
-8.95
-0.58
18.11
-9.37
-1.55
Guizhou
-20.03
-6.09
-5.29
4.10
7.01
2.66
0.05
-2.51
Xizang
-4.61
-8.71
-7.79
-8.72
9.32
-2.77
4.19
-2.73
Zhejiang
-7.12
-8.23
-18.72
-9.79
7.34
8.10
8.61
-2.83
Shanxi
-8.93
-6.71
-15.05
-2.13
13.14
-2.63
-3.04
-3.62
Hubei
-0.62
2.17
-2.18
-7.45
-12.77
-4.66
-2.99
-4.07
Sichuan
-2.03
-4.83
-8.31
-0.39
-11.88
-1.02
-3.08
-4.51
Shanxi
-3.74
-5.06
-14.64
0.59
7.52
-6.52
-11.26
-4.73
Hebei
4.97
4.65
-9.11
-5.73
-9.89
-13.54
-6.05
-4.96
Heilongjiang -4.02
2.94
0.34
1.75
-14.69
-14.00
-8.51
-5.17
Hunan
-6.40
-4.19
-6.63
-7.80
-9.14
-0.47
-6.21
-5.83
Yunnan
-0.89
-0.87
-11.22
-9.16
-11.30
-6.54
-4.89
-6.41
Guangxi
-2.12
-2.21
-10.06
-15.62
-6.59
-4.56
-6.32
-6.78
Fujian
3.47
4.23
-6.18
-22.20
-12.43
4.60
-19.39
-6.84
jiangsu
1.83
-8.64
-33.88
-3.17
-6.46
1.72
-1.30
-7.13
Shandong
1.21
-11.11
-34.27
-3.79
-14.58
3.64
5.91
-7.57
Henna
-0.89
-0.91
-16.82
-10.96
-15.50
-11.37
-11.48
-9.70
Jilin
-1.88
-6.17
-4.65
-0.62
-29.71
2.61
-29.76
-10.03
chongqing
-8.89
-15.04
-14.17
-17.43
-8.50
2.36
-10.54
-10.32
Inner
-5.66
-22.34
-39.11
-14.04
1.42
-4.02
0.29
-11.92
Mongolia
Liaoning
-2.99
-1.37
-14.80
-28.81
-18.49
-12.53
-7.66
-12.38
Jiangxi
-11.27
-25.61
-28.82
-4.64
-12.35
-2.57
-2.98
-12.61
Anhui
-1.80
-9.40
-19.74
-13.90
-18.48
-15.98
-19.05
-14.05
Based on table 2, we find that Beijing’s Solow residual is the highest, an average of 6.62% and Anhui
lowest -14.05% in the past seven years. The average value of 31 provinces (or municipalities) is -4.5%
or so in the seven years, which seems inconsistent with the national average. But if we take into account
the investment impulse of local government which has been far greater than the central government
since 2000, this problem can be easy to be explained space limited, not to do in-depth discussion .The
Solow residual in 24 of 31 provinces (or municipalities) are negative, accounting for more than
80%.Even taking into account technological advances included in the capital (about 5-6%), Solow
residual of half of all provinces is almost zero .This is a thought-provoking questions.
We divide the data of table 2 into categories of eastern, western and central regions of China to discover
the differences among the three regions. The results show that the differences are not obvious, so we try
to use cluster- analysis method. We use SPSS statistical analysis software to make K-cluster analysis of
the data. After several attempts, we find that we can get good effect when the data are divided into four
groups, and it is relatively easy to give a reasonable explanation. Clustering results are as following:
The first class concludes only one region: Beijing and the central value of it is 6.62%;
The second class concludes 8 provinces (or municipalities): Guangdong, Shanghai, Ningxia, Qinghai,
Gansu, Hainan, Xinjiang and Tianjin, the central value of them is 0.78%;
The third class concludes 15 provinces: Guizhou, Tibet, Zhejiang, Shanxi, Hubei, Sichuan, Shanxi,
Hebei, Heilongjiang, Hunan, Yunnan, Guangxi, Fujian, Jiangsu and Shandong. The central value of
（
26
）
them is -5.05%;
The fourth class concludes seven provinces (or municipalities): Henan, Jilin, Chongqing, Inner
Mongolia, Liaoning, Jiangxi and Anhui, the center value of them is -11.57%.
In the first category, Beijing has experienced rapid economic growth and technological progress in the
past years, and its per-capita GDP has been the first in China. There are high population density,
high-quality labor force, high labor's share in the output, the highest proportion of the wages in
GDP( about 24%) and significant increasing-returns- to- scale.
In the second category, Guangdong, Shanghai, Hainan and Tianjin have experienced faster economic
growth and there are a certain degree of technological progress and increasing-returns-to-scale. The
Solow residual of Tianjin, for example, after adjusting, could reach 4%. What are worthy studying are
the following four provinces: Ningxia, Qinghai, Gansu and Xinjiang. Industries of these provinces have
been not developed very fast, why the Solow residual of these provinces are higher? We believe, it is
just because of the relative underdevelopment of industrial and lower investment that lead to a relatively
low increasing rate of capital, and a relatively high capital-output ratio, which lead to a higher Solow
residual.
The third category is typical, including the majority provinces of eastern, western and central regions.
The economic growth mode of this class can essentially represent the growth mode of China's economy.
The common features of these 15 provinces are, low technological progress, economic growth mainly
driven by investment, the increasing rate of investment often exceeding the economic growth rate,
constant-returns-to-scale and the rate of wages in output being low. In Jiangsu, for example, investment
accounted is for 55% (above a half) of GDP in 2007. The investment growth rate is 21%, while the GDP
growth rate is 18% in 2007. The rate of wages in output is only 13%.
In the fourth category, the central value of Solow residual is below -10% .The feature of economic
growth mode of this class is that the rate of economic growth has been far lower than the investment
growth rate, with relatively low per-capita wages, which leads to a higher share of capital in output, the
final result of these is that technological progress rate is negative and diminishing-returns-to-scale. In
Anhui Province, for example, the rate of wages in output is only 12%, and capital share is 88%.GDP
growth rate is 19% over the same period. However, the investment rate is above 40% in 2007.
4 Conclusion
We can draw the following conclusions through the above discussions:
First, the Solow residual of China's economic growth has been not significant. To change this situation,
we should quickly change the invest-independent growth mode, raise resident incomes and stimulate
consumption especially consumption of low-middle class. At the same time, we should accelerate
industrial upgrading and reduce excess industrial capacity.
Second, the gaps of Solow residual among regional economic growth in China are larger, and nearly half
of the provinces have no Solow residual or technological progress. This situation must be changed. We
believe that the regions where have no obvious technological progress are those where economic growth
rate has been very low. In order to narrow the regional disparities, it is not enough to simply depend on
the government's investment policies. We should play the local comparative advantages, increase R & D
input, and change the short-term growth into long-term growth.
References
[1]. Xu Hui, The Gray Econometric Model of Contribution Degree of Technological Progress to
Economic Growth and Application, Science and Technology Management Research,
2009(5),190-193(in Chinese)
[2]. Wu Qunli. The Calculation of Total Factor Productivity and Technical Options Based on
Provincial-level Data. Statistics and Decision, 2009(18):84-86(in Chinese)
[3]. Li Bin, Zhao Xinhua. An Estimate about China’s Total Factor Productivity: 1979~2006. Statistics
and Decision, 2009(14):103-105(in Chinese).
27
[4]. Zhao Zhiyun, Lu Bingyang, Guo Qiwang, Jia Junxue. On the Dynamic Integration of Capital
Accumulation and Technological Progress: A Stylized Fact in China' s Economic Growth.,
Economic Research Journa,2007(11):18-31(in Chinese)
[5]. Hu Lifa, Solow Residual and Empirical Analysis of Technological Contribution Rate of Foreign
Investment to Economic Growth, World Economy Study, 2003(10), 53-56(in Chinese)
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