Download Growth Convergence and Regional Disparity

Heterogeneous Production Functions，
Growth Convergence and Regional Disparity
①
Jia Nan
[email protected]
The Southwestern University of Finance and Economics
Gan Li
[email protected]
SWUFE and Texas A&M University
Jan 2009
Postal Address: No.55, Guang Hua Cun, The School Of Economics, The
Southwestern University Of Finance And Economics, Qingyang District,
Chengdu, China
email: [email protected]
Abstract: The literature about economic growth convergence and regional
disparity assumes the same gross production functions across countries or regions.
This paper allows the possibilities of different production functions for different
regions. Such differences come from the observed differences in the factor shares of
income. In steady states, a region with a higher capital share would have a higher per
capita output. Thus, the output differences among regions will be persistent if they
have different factor shares. Using the province-level data in China, I show that the
capital share in income indeed has a very significant and positive effect on the level
and the growth rate of per capita output.
Key words: factor share, production function, growth convergence, regional
disparity
JEL classification : O180 ,O470,R110
①
For helpful comments I thank Li Gan, Shihe Fu, Wenbin Zang, Zhen Lei, Liwei Shan, Xiaochen Cai, Xiaoling
Chen, Yi Li and seminar participants at South West University of Finance and Economics. For financial support I
thank the Leading Academic Discipline Program , 211 Project for SWUFE(the 3rd phase) and the Humanities and
Social Science project “Dynamic optimization and regulation for Monetary policy”（08JC790082）by the State
Education Commission. Any opinions expressed are those of the author.
1
1. Introduction
The neo-classic growth model suggests that economies with similar initial
conditions would achieve similar growth rate under the assumptions of decreasing
returns to factors, constant returns to scale, and similar aggregate production functions.
In this type of models, the poor economy would grow faster than the rich economy. In
the long-run, the growth rate of different economies would converge and the
differences among economies would be gradually reduced. This is the so-called
“convergence hypothesis”.
On the other hand, in the new growth models, the accumulation of physical
capital, human capital and knowledge capital would often have increasing returns to
scale. Economies with higher levels of capitals would have growth faster. As a
consequence, the growth of different economies would diverge and the disparities
among different economies would increase.
Empirically, a standard test of the two theories is to test the convergence of
various economies. In their classic paper, Mankiw, Romer and Weil (1992) (MRW
hereafter) introduce human capital into the standard Solow model to develop an
Augmented Solow Model. They find evidence that countries converge at about the
rate that the augmented Solow model predicts if holding population growth and
capital accumulation constant. This finding has been considered as the evidence of
“conditional convergence”. A large number of empirical studies has since used
alternative econometric methods and data samples, such as Barro and Sala-i-Martin
(1992), Bernard and Durlauf (1995), Islam (1995), Quah (1996, 1997), Dowrick and
Ngugen (1989), Bernard and Jones (1996), Andrade (2003), Mathur (2005) and D’uva
(2007). Most of them arrive at the same conclusion as MRW, i.e., economic growth
across countries has conditional convergence.
The topic of convergence across regions in China has also generated wide
interests in the literature. Most studies agree that the regional disparity in China was
reduced before 1990 and then was increased after 1990. Meanwhile there is
conditional convergence among regions and club convergence in the east region, the
middle region, and the west region. Those papers include Cai and Du (2000), Shen
and Ma (2002), Lin and P. Liu(2003), Wang (2004), Xu and Shu (2005),
Peng (2005,
2006), Wang and Zhang (2006), Zhang (2006), and Teng and Liang (2006). Figure 1
is the real per capita output of 30 provinces in China. From the figure, the difference
2
of real per capita output has been reduced before 1990 and then increased constantly
among different provinces. Within each of the east region, the middle region, and the
west region, the differences also increase. Comparing the three regions, the regional
disparity is the largest in the east region, and the smallest in the west region.
100000
50000
19
78
19
81
19
84
19
87
19
90
19
93
19
96
19
99
20
02
20
05
0
west
Figure 1：Real per capita output cross-provinces
The literature has provided several explanations on increasing regional disparity
since1990. One explanation is the scarcity of the human capital endowment, the
market distortion and the lack of openness (Cai and Du, 2000; Shen and Ma, 2002;
Wang and Fan, 2004; Wang and Zhang, 2006). Other people suggest that the
government development strategies are inconsistent to the regional comparative
advantage (Lin and P. Liu, 2003; Lin and M. Liu, 2003). A third alternative
explanation is that the labor force in the east region grows faster than the capital
accumulation. As a consequence, the marginal return to capital remains higher in the
east than in the west (Liu, 2001; Shen and Tang, 2006). A fourth one is that there are
technology spillover obstacles (Fu and Wu, 2006).
However, all empirical studies so far are built upon the assumption that all
countries or regions have identical aggregate production functions. This paper relaxes
the assumption, allowing the production function to be different across regions.
Therefore, it provides a new alternative interpretation about expanded regional
disparity cross-provinces in China. This paper argues that the differences in factor
3
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
120000
100000
80000
60000
40000
20000
0
1978
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
120000
100000
80000
60000
40000
20000
0
150000
1982
middle
east
1980
real per capita GDP
Real per capita GDP
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
120000
100000
80000
60000
40000
20000
0
1978
Real per capita GDP
Real per capita GDP
Whole country
shares in output in different regions lead differences in aggregate production functions,
which in turn would generates persistent differences in output. This hypothesis is
tested by using province-level data from 1990 to 2005 of China.
In this paper, I find that that the capital share in output affects real per capita
output significantly. The higher capital share, the higher the real per capita output. As
a result, regional disparity may increases. I also find that regions with larger
differences in factor shares have larger differences in their per capita output. For
example, provinces in the east region has the largest variation in their capital shares,
they also have the largest variation in the per capita output. Further, the growth rates
still satisfy the conditional convergence and the club convergence when controlling
factor shares. Yet the output elasticity of factors again has very significant impacts on
growth rate. The higher the output elasticity of capital, the higher the growth rates the
region. The effect leads to regional disparity become larger.
The rest of this paper is organized as follows: Section 2 provides the
interpretation about expanded regional disparity of this paper. Section 3 details the
empirical model as well as variables and data. Section 4 shows the empirical results.
Section 5 concludes.
2. A New Explanation
The current literature on economic growth across regions or countries imposes
very strong homogeneity assumptions on aggregate production function. The
assumption implies that the capital share in the national income (or the output
elasticity of the capital), and the labor share in the national income (or the output
elasticity of the labor) across countries or regions are identical. This assumption may
be true within a country since the capital share in national appears to be fairly
constant over a long period of time. Figure 2 show the time series for the United
States dating back to 1935 and Figure 3 shows the United Kingdom dating back to
1855 (Mitchell, 1988). These graphs suggest that the labor share moves very little
over time within a country.
4
Labor share
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1935
1945
1955
1965
1975
1985
Figure 2: labor share and GNP：United States 1935-1985
0.8
Labor share
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1855
1875
1895
1915
1935
1955
1975
Figure 3: labor share and GDP: United Kingdom 1855-1980
Across countries, however, there appear to be substantial differences in income
shares. Collin (2002) plots labor shares of 81 countries in most recent years available
(1987–92), against levels of real per capita output (Figure 4). Clearly there are wide
disparities in labor shares across countries, ranging from 0 to 0.7. It also appears a
positive relationship between labor shares and real per capita GDP.
There are several possible explanations on why factor shares might differ across
countries. One explanation is that countries do not operate the same aggregate
technology. The second explanation is that countries may share a common aggregate
technology but have different institutional arrangements. A third alternative is that
some countries might face imperfect factor markets, so that wages are not equated to
marginal products (Gollin, 2002).
5
Labor share/real per capita GDP
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
20,000
Real per capita GDP
Figure 4 labor share and real per capita GDP in 81 countries
1987-1992
Given the possible differences in factor shares, it is natural to allow that
aggregate production functions to be different across regions. Such differences in
aggregate production functions may contribute to the disparity in output. As a
consequence, economic disparity may continue to increase across countries or
regions.
3. Model and Data
3.1 Model
MRW (1992) demonstrate that the Solow model has impressive empirical
explanatory power. MRW approach the issue of non-steady-state behavior by
estimating rates of convergence and relating these to the parameters of the model. I
take a more direct approach: Based on the Solow model, the steady-state per capita
output depends on the capital share.
In addition, I find that the growth rates may
also depend on the capital share. Therefore, regions with different capital shares may
have increasing disparity.
Based on the Solow model, the motion equation per capita is
k  sy (t )  (n  g   )k (t ) ,
where y is the level of output per effective unit of labor, y 
capital per effective unit of labor, k 
Y
; k is the stock of
EL
K
, E is defined as the labor augmenting
EL
technological progress; s is the saving rate; n is the labor growth rate; δ is depreciate
6
rate; and finally, g is exogenous technological progress rate.
Output per capita is:
y (t )  k (t ) 
In the steady state:
sk (t )  (n  g   )k (t )
Or

s
k   
 n g 




1
y
(1)
In (1), since k is defined as the stock of capital per effective unit of labor, so,
capital stock per capita k l , is: k l  K / L . Rearrange (1):

s
k l  
 n g 

 1 
 E  y

(2)
From (2), output per capita is affected by the saving rate s, depreciate rate δ,
labor growth rate n, exogenous technological progress rate g, labor augmenting
technological progress E and capital share α. If these variables are the same in
different countries or regions, output per capita will ultimately converge. However,
if one of these variables is different, output per capita may not converge, and
regional disparity may persist. Current literature has studied the heterogeneity of
some of these variables. This paper focuses on the capital share parameter α, the
key parameter in the production function. If the capital shares are different in two
regions, the capital stock per capita may not be the same even though all the other
variables are the same. Figure 5 shows that any two economies with different
capital shares have different steady state, so their income disparity may not
disappear.
7
b
y”
a
y’
0

2
1
Figure 5：Output Elasticity of Capital and the Steady States
Taking logarithm of (2), we have:
s
   
ln y  
 ln 
1    n  g  

   ln E

(3)
For any two regions in a country, however, it is often plausible to assume they
have the same depreciation rate δ and exogenous technological progress rate g.
Because E denotes labor-augmented technological progress, it can be regarded as
the human capital. Two regions may have different levels of human capital,
different saving rates s, and different labor growth rates n. More importantly, they
are allowed to have the different capital share  .
Taking partial derivative with respect to  , s, n, E of (3):


 ln y
1
s
  ln E  0

ln 
2

1       n  g 
 ln y
 1

0
1    s
s
 ln y

1

0
1      n  g
n
 ln y
  0
 ln E
(4)
Accordingly, we can establish the following regression model:
ln y i  a 0  a1ˆ i  a 2 tˆi  a3 s i  a 4 ni  a5 E i  
8
(5)
Where ̂ is the average output elasticity of capital in the same region. In (5), we
also include the total factor productivity tˆ since it is obvious that this variable may
affect the output level. It is expected that a1>0, a2>0, a3>0, a4<0, and a5>0.
Further, to examine if the regional growth rate converges, I use the growth rate to
test if there is absolutely convergence under heterogeneous production function by
using the following model:
 ln y it  a 0  a1 ln y i 0 * ˆ it   i
(6)
Where ln y i 0 denotes real per capita output in the initial period,  ln y it denotes the
growth rate of per capita output in the end of the period. Equation (7) includes some
control variables:
 ln y it  a 0  a1 ln y i 0 * ˆ it  a 2ˆ it  a 3 tˆit  a 4 s it  a 5 nit  a 6 E it   i
(7)
It is easy to show that:
Where,
 ln y it
 a1 * ̂ it
ln y i 0
 ln y it
 a1 * ln y i 0  a 2
ˆ it
If
(8)
(9)
 ln y it
 0 , then there is conditional convergence in regional economic
ln y i 0
growth; If
 ln y it
 0 and is significant, then capital share has positive impacts
ˆ it
on economic growth, and the differences in α will result in different output in
different regions.
3.2 Data and measurement
The empirical analysis of this paper uses provincial level data in China. The sample
period is 1990-2005 because the purpose of this paper is to discuss why the economy
gap becomes larger among provinces in China after 1990, and because one of the key
variables, labor compensation, is available only after 1990. The city of Chongqing is
included in Sichuan because of missing data in early years.
The variables used in the analysis include real output, capital stock, labor force,
9
labor compensation, saving rate, labor growth rate, human capital and price index.
The official data of capital stock is not available in China. Following the literature, I
use the capital stock data of Zhang, Ying, Wu and Zhang (2004). Because their capital
stock data is deflated by constant price of 1952, all the nominal variables are deflated
using the constant price of 1952 to be consistent with the capital stock data of Zhang
et al (2004). Following MRW (1992), the percentage of the labor force with the
secondary school education is used as a proxy for the rate of human-capital
accumulation. All other data are come from various years of China Statistical
Yearbook.
To estimate the value of capital share α, we use the percentage of labor
compensation in GDP. Then we can calculate the implied capital share by assuming
constant return to scale:
̂  1 
labor compensation
GDP
(10)
To reduce measurement errors, we consider two types of labor shares: the average
labor shares between1990 and 2004, and the average labor shares 1990-2000. Figure 6
shows the ratio of labor compensation to GDP in thirty provinces. Labor share varies
from 0.3 to 0.8. Table 1 has the descriptive statistics by three regions within China for
labor shares and for per capita real output. The difference of the labor share within the
east China② area is the largest, and within the west China is the smallest. 1. The area
with the largest differences of labor share has the largest difference in per capita
output.
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Figure 6：Labor Share in Different Provinces
②
I partition the three areas conventionally. The east area includes Beijing, Tianjing, Hebei, Liaoning, Shanghai,
Jiangshu, Zhejiang, Fujian, Shandong, Guangdong, Guangxi and Hainan. The middle area includes Shanxi,
Neimeng gu, Jilin, Helong jiang, Anhui, Jiangxi, Henan, Hubei, Hunan. The west area includes Chongqing,
Sichuan, Guizhou, Yunan, Xizang, Shanxi, Gansu, Nixia, Qinghai, Xinjiang.
10
Variable
Real per capita
output
Labor share
Table 1：Descriptive Statistics of Variables
Obs
Mean
Std.Dev.
Area
③
Mix
Max
East
12
13269.7
7381.966
4651.364
32156.64
Middle
9
7136.358
2071.75
4782.829
10568.54
West
9
5595.108
1995.092
2902.795
10190.84
East
12
.4763484
.0695394
.3489196
.616737
Middle
9
.5543737
.0612278
.4527116
.611435
.4663748
.7369851
West
9
.5587092
④
.0764226
Finally, we can calculate the total factors productivity by estimating Solow
residual. Consider a Cobb-Douglas production function:
Y (t )  A(t ) K (t ) L(t )1
(11)
Where, Y is real output in period t, K is capital stock, L is labor force, A is total
factors productivity,  is output elasticity of capital.
Taking logs of both sides of (11), and then take a first difference, we have:
 ln Yt   ln At   ln K t  1    ln Lt
The Solow residual is basically  ln At , calculated by the difference:
 ln At   ln Yt    ln K t  1    ln Lt
Therefore,
tˆ   ln Y  ˆ ln K  (1  ˆ ) ln L
(12)
We can see from (11), the total factor productivity is also correlated to capital
share. Different output elasticity of capital will bring different TFP.
4. Empirical Results
4.1 The effect of heterogeneous production function on the level of the output
The regression equation in (5) is used to estimate the impacts of capital share on
the per capita output level. The key parameter of interest is the coefficient of the
③
In the east area, the differences of real per capita output among other regions and Beijing as well as Shanghai
are very large. If taking the two observations out, the variance of real per capita output in the east is 2867.94,
which is still bigger than middle and west.
④
Because of the special geography environment, the labor share in Xizang is remarkably higher than the average
level of the west, so as to its variance. If taking Xizang’s data out, the standard variance of labor share in the
west is smaller than the east and middle.
11
capital share variable. Further, to investigate whether the income gaps within each of
the east region, the middle region, and the west region areas are affected by different
production function, two dummy variables are introduced:
ln y i  a 0  a1ˆ i  a 2 tˆi  a3 s i  a 4 ni  a5 D1i *ˆ  a 6 D2 i *ˆ  
 1，west
D1 
 0，otherwise
Where,
 1，east
D2 
 0，otherwise
I consider two alternative measures in output levels. The dependent variable in
columns (1) and (3) use the per capita output in 2005, and the columns in (2) and (4)
use the average per capita output during the period of 2001 and 2005.
Further, when the dependent variable is the 2005 per capita output, the the
average saving rate, the average labor growth rate, the average human capital stock
and the average total factor productivity from 1990 to 2004. The regression results are
reported in columns (1) and (2).
Table 2： Output Elasticity of Capital and Real Per Capita Output
Dependent variable: real per capita GDP
(1)
(2)
(3)
(4)
3.312**
(1.44)
2.816**
(1.28)
3.626**
(1.49)
3.151**
(1.44)
Average total factor productivity
18.50**
(7.46)
14.93**
(5.72)
15.42**
(7.03)
11.61**
(5.57)
Average saving rate
2.158*
(1.16)
1.876*
(1.03)
0.0692
(1.39)
0.0229
(1.29)
Average labor growth rate
-0.714
(7.64)
-7.662
(5.50)
0.369
(7.22)
-5.413
(5.32)
Average human capital
-0.632
(3.71)
-0.672
(3.41)
3.538
(3.94)
2.614
(3.68)
west* 
-0.428
(0.41)
-0.412
(0.41)
east* 
0.611
(0.37)
0.586
(0.37)
Average output elasticity of capital
Constant

7.147***
(0.73)
7.547***
(0.58)
7.439***
(0.69)
7.838***
(0.56)
30
0.67
30
0.72
30
0.74
30
0.78
Observations
R-squared
Column (1) in table 2 is the regression of real per capita GDP in 2005 on the
12
average values of independent variables from 1990-2004. The results show that the
capital share has a strong and significant positive impact on real output. In particular,
if the capital share increase 1 percentage point, real per capita output increases about
3.312%。The results indicate that because the capital share is different among
provinces or because of the different production function, the provincial disparity of
the real per capita output becomes larger and larger.
As a robustness check, the second column in table 2 uses the 2001-2005 average
per capita output as the dependent variable, while independent variables are the
average values from 1990-2000. The result shows that the output elasticity of capital
still has a significant positive impact on real output..
Column (3) introduces regional dummy variables, using the 2005 per capita GDP
as the dependent variable. The regression result indicates that capital share still has a
very significant impact on the real output within the east region, the middle region,
and the west region. That is to say, the differences of output per capita may be larger
within three areas. For example, capital share increase per unit in the middle region of
China, real per capita output increases about 3.626%; capital share increase per unit in
the west part of China, real per capita output increases about 3.198% (t value is 2.35);
capital share increase per unit in the east China, real per capita output increases about
4.237% (t value is 2.95). The impacts that factors share act on real output are all
positive in three areas. Moreover, the impacts in the east are the biggest of three areas,
which is consistent with the biggest differences of labor share in the east China. And
also because of the biggest differences of labor share, the provincial gap is the biggest
in the east. Further, the disparity of labor share in the west China is the smallest, so
the provincial gap is the smallest in the west. The disparity of labor share in the
middle China is a little bigger than the west, its provincial gap is a little bigger than
the west. Therefore, the differences of output per capita among different regions have
very close correlation with the differences of factors share.
Column (4) is the robust test of result in column (3), which is introduced region
dummy variables based on model 2. Compared with model 3, the effect degree of
output elasticity of capital acting on real per capita output is lower. capital share
increase per unit in the middle China, real per capita output increases about 3.151%;
capital share increase per unit in the west China, real per capita output increases about
2.739% (t value is 2.16)；capital share increase per unit in the east China, real per
capita output increases about 3.737% (t value is 2.74). However, the output elasticity
13
of capital still has very significant positive impact on per capita output within three
areas. The larger the differences of factors share the region, the higher the impact of
capital share acting on real per capita output, and the larger the economic gap within a
area.
4.2 The impact of heterogeneous production function on the growth rate
To test whether the difference of production function affects the convergence of
growth rate, I use model (6) to examine the absolutely convergence and model (7) to
examine the conditional convergence. After introducing the area dummy variables, I
can examine the club convergence by using the following regression model:
 ln y it  a 0  a1 ln y i 0 * ˆ it  a 2ˆ it  a 3 tˆit  a 4 s it  a 5 nit  a 6 E it  a 7 D1i  a8 D2 i   i
The estimated results are displayed in table 3:
Table 3：The capital share and the economic growth rate
Dependent
variable: economic
growth rate
(1)
(2)
(3)
(4)
(5)
(6)
Initial output per
capita * 
0.00959
(0.0074)
-0.0632***
(0.019)
-0.0678***
(0.020)
0.0111
(0.0067)
-0.0455**
(0.017)
-0.0501***
(0.018)
Output Elasticity of
Capital 
0.570***
(0.18)
0.561***
(0.18)
0.409**
(0.16)
0.397**
(0.16)
Total factor
productivity
-0.117
(0.14)
-0.142
(0.14)
-0.222*
(0.13)
-0.247*
(0.13)
Saving rate
0.166***
(0.052)
0.148**
(0.056)
0.133***
(0.046)
0.119**
(0.050)
Labor growth rate
0.461**
(0.20)
0.414*
(0.21)
0.439**
(0.18)
0.390**
(0.19)
Human capital
0.00346
(0.0088)
-0.0602
(0.082)
0.00818
(0.0079)
-0.0577
(0.073)
west* 
-0.0213
(0.017)
-0.0190
(0.015)
east* 
0.107
(0.14)
0.111
(0.13)
Constant
0.213***
(0.035)
0.142***
(0.039)
0.183***
(0.057)
0.173***
(0.031)
0.139***
(0.035)
0.180***
(0.050)
Observation
R-squared
30
0.06
30
0.53
30
0.56
30
0.09
30
0.56
30
0.60
14
Column (1) is a test of absolute convergence. The initial real output is the real
per capita GDP in 1990. All other variables are at 2005 level. Based on the estimated
coefficients and equation (8), the initial per capita output has positive but
insignificant effect on the economic growth rate when the heterogeneity in
production functions are included. Since the absolute convergence requires a
negative coefficient, the result here clearly indicates no absolutely convergence
among provinces.
Column (2) is a test of conditional convergence. Since the coefficient of the
interaction term between the initial per capita output and the capital share is
significant and negative, there is conditional convergence among provincial growth
rates. Further, capita share has a very significant and positive impact on the growth
rate. Based on (9), the overall effect of capital share is positive, indicating that the
provinces with higher capital shares have higher growth rates. Therefore, the
difference in production functions in one of the important reasons causing regional
differences.
Column (3) is a test of the club convergence. It includes two regional dummy
variables. In this model, the initial per capita output still has a significant and negative
impact on the growth rate within the east region, the middle region, and the west
region. This result implies that there is club convergence among the three areas, which
is the same conclusion as current literature. Furthermore, capital share still has a very
significant and positive impact on the growth rate. Again, the overall effect of the
capital share is positive. That is, the higher the capital share, the higher the growth
rate within three regions. The difference in production functions may increase the
regional gaps.
In order to alleviate the effect of business cycle, I put up robust tests by using the
average growth rate covering 2001 to 2005 as dependent variables in Columns (4)-(6).
The signs of coefficients are the same with the columns (1) and (3), and magnitude is
slightly smaller.
5. Conclusion
This paper proposes a new explanation on the increasing disparity among
provinces in China after 1990. It argues that aggregate production functions may be
different from different countries or regions. The difference is reflected by the
capital share in total income. The higher the capital share, the higher the real per
capita output in the region. Real output per capita is divergent in different countries
15
or regions.
The empirical research using provincial level data in China indicates that the
impact of capital share on real per capita output is strong and very significant.
Provinces with higher capital shares have higher outputs. After controlling the
heterogeneous capital shares, there is still conditional convergence in the provincial
growth rate. And there is still club convergence within three areas. This conclusion is
consistent with current literatures.
Furthermore, capital shares also have very significant impacts on economic
growth rate. Provinces with higher the capital share would have higher growth rates.
Therefore, the difference in production functions is one of the key reasons to explain
the increasing economic disparity in China.
16
Reference:
1. Barro and Sala-i-Martin et al. “Convergence across States and Regions.” Brookings
Papers on Economic Activity, Vol. 1991, No. 1 (1991), pp. 107-182
2. Barro and Sala-i-Martin. “Convergence.” The Journal of Political Economy, Vol. 100,
No. 2 (Apr., 1992), pp. 223-251
3. Bernard and Durlauf. “Convergence inIinternational Output”. Journal of Applied
Econometrics, Vol. 10, No. 2 (Apr. - Jun., 1995), pp. 97-108
4.Bernard and Durlauf. “Interpreting tests of the convergence hypothesis.” Journal of
Econometrics, 71 (1996) 161-173
5.Danny T. Quah. “Twin Peaks: Growth and Convergence in Models of Distribution
Dynamics.” The Economic Journal, Vol. 106, No. 437 (Jul., 1996), pp. 1045-1055
6.Douglas Gollin. “Getting Income Shares Right.” Journal of Political Economy 110(2)
April 2002: 458-474.
7.Mankiw, Romer, Weil . “A Contribution to the Empirics of Economic Growth.” The
Quarterly Journal of Economics, Vol. 107, No. 2 (May, 1992), pp. 407-437
8.Nazrul Islam. “Growth Empirics: A Panel Data Approach .” The Quarterly Journal of
Economics, Vol. 110, No. 4 (Nov., 1995), pp. 1127-1170
9.William J. Baumol. “Productivity Growth, Convergence, and Welfare: What
the Long-Run Data Show”. The American Economic Review, Vol. 76, No. 5 (Dec., 1986),
pp. 1072-1085.
10. Fu Xiaoxia, Wu Lixue: “Technical Efficiency , Capital Deepening and Regional
Disparity.” Economic Research Journal, Oct, 2006 . pp 52-61
11. Liu Qiang: “The analysis about the convergence of economy growth in China.” Economic
Research Journal, Jun, 2001. pp 70-77
12. Lin Yifu, Liu Peilin: “Chinese Development Strategy and Economic Convergence.”
Economic Research Journal, Mar, 2003. pp 91-98
13. Lin Yifu, Pan Shiyuan: “Development Strategy , Absorptive Capability and Economic
Convergence.” The Journal of Quantitative & Technical Economics. Feb, 2006. pp3-13
14. Peng Guohua: “The Disparity of Income , TFP and the Convergence Hypothesis in
Chinese Provinces.” Economic Research Journal, Sep,2005. pp 19-29
15. Shen Kunrong, Ma Jun: “The Characteristics of Club Convergence of China’s Economic
Growth and Its Cause.” Economic Research Journal, Jan,2002. pp33-39
16. Shen Kunrong, Tang Wenjian: “An Analysis of Economic Convergence under Conditions
of Large2scale Labor Migration.” Social Science in China, May,2006. pp46-57
17. Dong Xianan: “Understanding the Regional Income Disparity in China , 1952-2002.”
Economic Research Journal, Sep,2004. pp48-59
18.Wang Xiaolu, Fan Gang: “Analysis on the Regional Disparity in China and the Influential
Factors.” Economic Research Journal, Jan,2004. pp33-44
17
19.Wang Zhigang: “Doubt on conditional convergence in China.” Management World,
Mar,2004. pp25-30
20. Wang feng, Zhang Zongyi, Kang Jijun: “Enterprise Reform, Openness and Conditional
Convergence in China.” World Economy, Jun, 2006. pp48-60
21.Xu Xianxiang, Shu Yuan: “Physical Capital, Human Capital and Twin-Peak Convergence
in China.” World Economy, Jan,2005. pp47-57
22.Xu Zhaoyuan, Li Shantong: “Analysis on the Trend of Regional Income Disparity in
China.” Economic Research Journal, Jul, 2006. pp 106-116
23.Zhang Ju, Wu Guiying, Zhang Jipeng: “The Estimation of China’s provincial capital
stock : 1952-2000.” Economic Research Journal, Oct,2004. pp35-44
18