2009 Oxford Business & Economics Conference Program
ISBN : 978-0-9742114-1-1
New Evidence About Regional Income
Divergence in China
Lau Chi-Keung, Marco**
Hong Kong Polytechnic Universitya
Hang Seng School of Commerceb
Abstract
There are many empirical studies trying to test if there is income convergence
across the provinces of China.
In this paper, we bring new information to the current
literature by applying linear unit root tests and non-linear unit root test of Exponential
Smooth Auto-Regressive Augmented Dickey-Fuller (ESTAR-ADF) unit root test to
the time series data for the period 1952-2003.
The number of converging provinces
increases in both pre and post reform period when using ESTAR ADF test.
Furthermore, our results find evidence of increasing regional disparity that has been
prevailing in China since the open door economic reforms of the late 1970s.
Keywords: China Regional Income Convergence, Nonlinear Unit Root Test, ESTAR
JEL codes: R, C1, C52
**
Corresponding author: Lau Chi Keung, ITC, Hong Kong Polytechnic University, Hung Hum,HKa
.School of Economics and Finance, Hang Seng School of Commerce, HK b
Email: tcmarkov.lau@polyu.edu.hk ; marcolau@hssc.edu.hk
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1 Introduction
The analysis about convergence is based on Solow’s (1956) model; this
neo-classical growth model predicts that a poor economy tends to grow faster than a
rich one. Based on Solow’s model there are vast amount of studies devoted to
economic growth and convergence, see Barro, 1991; Barro and Sala-i-Martin, 1991;
Baumol, 1986; Button and Pentecost, 1995; De Long, 1996; Jones, 1997; Mankiw,
Romer, and Well, 1992; Pritchett, 1997 among others. The assumption of diminishing
returns is crucial for convergence hypothesis to hold. It is because economic agents
will allocate resource (i.e. labor and capital) across different locations so as to
maximize their wealth. As a result, differences in returns to labor or capital among
different regions will diminish over time.
However, we argue in our paper that only
when all economies are able to access to the same technology it may eventually leads
to convergence in the long run.
One channel for technology spillover across borders is though inter-regional
trade of manufactured goods and production specialization. Fan (2004) incorporated
the role of product quality and international trade to explain the East Asian Miracle
and the empirical finding of conditional convergence. He assumed that quality is a
superior goods and the demand for it increases with income.
Following the
implications of his model, it suggests a conflict in the preferences for the ideal quality
of consumption between rich and poor region.
A poor region may choose an
“inferior” autarkic production technology so that more quantity of “low” quality
goods could be produced given resources availability. By making such a decision, the
poor region forgoes the opportunity of joining the “global” markets and catch up her
neighbors by division of labor, production specialization, and technology spillover.
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Nevertheless, the poor economies will grow eventually when its human capital
accumulates though time. When human capital of the poor region approaches the
average levels of other regions the chance of participating in “global” industrial
specialization may occur. We denote a threshold level, “c” of human capital
accumulation whereas when this threshold is reached the economy will experience a
“jump” in its per capita human capital and income.
Therefore, in our paper we
model the growth dynamic of metropolitan areas in such a way that the economy may
only experience high economic growth rate when it reaches the threshold level of
human capital accumulation and starts to engage in trade with other regions. We use
ESTAR model to estimate the growth dynamic across states so as to capture the
likelihood that the growth rate of different regions will converge provided that they
reaches the threshold level of human capital accumulation.
The rest of this paper is organized as follows. Section 2 provides a brief literature
review on regional disparity.
Section 3 describes the empirical methodologies that
we employed. Section 4 evaluates the empirical findings from different unit root test
in determining whether provincial real income per capita is indeed converging or
diverging among Chinese provinces in the pre and post-reform periods. Section 5
concludes.
2. Previous Studies
The conditions of free factor mobility and free trade are essential and contribute
to the acceleration of the convergence process through the equalization of prices of
goods and factors of production.
In this context, the tendency for income disparities
to decline over time is explained by the hypothesis that factor costs are lower and
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profit opportunities are higher in poor regions as compared to rich regions. Therefore,
low-income regions will tend to grow faster and will catch-up the leading ones. In the
long run, factor prices, income differences, and growth rates will be equalized across
regions.
The most common measures of convergence are beta (β) and sigma (σ)
convergence in its conditional and unconditional version. . Beta convergence
identifies a negative relationship between the growth of per capita incomes and the
initial level of income per across regions over a give time period. Some empirical
studies find evidence in support of unconditional beta convergence across states
(Barro and Sala-i-Martin, 1991) in the United States. However, we believe that
unconditional convergence may not be expected when heterogeneous factors
endowment across countries is obvious. Therefore, we expect conditional
convergence instead of its unconditional version as shown by Barro and Sala-i-Martin
(1995).
In order to control for differences in steady state growth path Barro (1991),
Barro and Sala-i-Martin (1991, 1992) and Mankiw et al. (1992) includes explanatory
variables that change across countries like population growth, rate of capital
depreciation and technological progress in their study. The universal consensus is
that while there is no evidence of unconditional convergence among countries with
very different initial endowments, evidence in support of the conditional convergence
is found for group of countries with homogenous endowment. Barro and
Sala-i-Martin (1991) find evidence in support of unconditional beta convergence as
well as conditional beta convergence for states by introducing regional and sectoral
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dummy variables to capture the origin of the heterogeneous characteristics across
states.
In the same notion, Mankiw et al. (1992) also find evidence of unconditional
as well as conditional beta convergence for different countries by introducing saving,
population growth, and human capital accumulation variables.
Apart from studies in the United States, Cheung & Pascual (2004) use output
differential series from Summers and Heston (1991) and Maddison (1995) on the G7
countries. The decision of output convergence hypothesis is made based on whether
an output differential series is stationary or has a unit root. They found that the
evidence is mixed which depends on the power of unit root test applied.
Pedroni.&Yao (2006) finds evidence in support of the view that inter-provincial
inequalities have been widening since 1978 by using the provincial income data set
from Hsueh and Li (1999) from 1952-1997. In this paper we use the same data set of
Pedroni.&Yao (2006) but using non-linear unit root test instead.
2.2 Sigma Convergence
Another measure of convergence is sigma convergence; its magnitude is
measured by the standard deviation of per capita income across states over time.
(Quah, 1993).
Continuous decline in annual standard deviations of income across
state over time implies sigma convergence. Moreover, the use of cross sectional
regression on testing beta convergence may commit Galton’s fallacy of regression to
the mean and it implies biased estimates and invalid test statistics.
In response to
this fallacy, Friedman (1992) and Quah (1993) argue that sigma convergence is the
only valid measure of convergence. Barro and Sala-i-Martin (1991) test for sigma
convergence using state per capita income data from 1880 to 1988. Their results
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support sigma convergence for all decades except the 1920s and the 1980s by using
standard deviation of the log of per capita income as series of interest in cross section
regression.
Another reason for using sigma convergence is that the validity of beta
convergence implies convergence of its variance to the steady-state level, but it does
not implies its variance is diminishing over time. In this paper, we test both
unconditional beta and sigma convergence so as to provide robust results and we
believe that the legal system, language, currency, financial markets, and culture are
likely to be homogeneous across states.
Starting from 1960s there are vast amount of studies concern income
convergence, the hypothesis is examined for states (Borts, 1960; Borts and Stein,
1964) and for regions (Perloff, 1963). In most cases, there is evidence in support of
income convergence.
In contrast, numerous of studies find evidence against
convergence hypothesis across states (e.g., Browne, 1989; Garnick, 1990; Barro and
Sala-i-Martin, 1991; Blanchard and Katz, 1992; Carlino, 1992; Mallick, 1993;
Crihfield and Panggabean, 1995; Glaeser et al., 1995; Drennan et al., 1996;
Sala-i-Martin, 1996; Vohra, 1996; and Drennan and Lobo, 1999).
Our research differs from others in regional income convergence and growth in
China by several major attributes. Firstly, the sample period is extended to the most
recent years so that the trend of China regional convergence is better understood.
Secondly, we allow the convergence process following a non-linear dynamics across
states because the convergence process is through the equalization of prices of goods
and factors of production and this law of one price is following a non-linear dynamics
as supported by empirical evidence recently. Thirdly, we use relative growth
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differential as a complement to the standard deviation across states so that the sigma
converging member can be identified.
3. Methodology
The data set used in this study is annual panel data of provincial GDP for thrty
provinces1 in China for the period 1952 to 2003, which are collected from China
Statistics Yearbook of various issues. Real per capita GDP in each province was
generated by using provincial GDP deflator, taking the year 1952 as the base year.
Table 1 provides information on China’s provinces and geographical locations.
Following Evan (1998), the term of income convergence may be defined as the
convergence of long-run output differences as the forecasting horizon increases. It
implies that per capita GDP in any pair of provinces tends to converge to the same
level in the long run. In Statistical terms, the convergence to the provincial per capita
income means that the income gap between any two provinces must be meanreverting
or stationary.
Some empirical methodologies are introduced in the following
sections.
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Beta Convergence
Traditionally, the most commonly used regressions in growth studies are cross
sectional, see Baumol (1986) for beta convergence. The basic idea is to estimate the
1
The provinces are
Beijing, Tianjing , Hebei, Shanxi, Inner Mongolia, Liaoning, Jilin, Heilongjiang,
Shanghai, Jiangsu, Zhejiang, Anhui, Fujian, Jiangxi, Shandong, Henan, Hubei, Hunan, Guangdong,
Guangxi, Sichuan, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Ningxia, Xinjiang.
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coefficients of the following equation and evaluate the null hypothesis of divergence
(that is, β= 0) against the alternative hypothesis convergence, when β∈(-1, 0):
Pooled data regression is represented in equation (1).
yi ,T  yi ,0
T
   y i , 0  u i , 0
i= 1,…,N
(1)
where α is a constant (which captures the regions’ steady state), β captures the rate
or speed of convergence, and u is a disturbance term. Note that we only consider the
growth rate of output in the whole period of analysis (between t =0 and T = 1). One
modification of equation (1) is the panel data regression as represented in equation
(2).
yi ,T  yi ,t 1
T
   yi ,t 1  u i ,t ………………………(2)
where, in this case, T denotes the number of periods or years between t and t – 1.
One of the advantages of this technique is that it lets us take advantage not only of the
cross-sectional dimension, but also of the time dimension, thus providing greater
degrees of freedom. However, A valid criticism of regressions between the per capita
GDP growth rate and initial per capita GDP is that the test does not have a standard
distribution under the null hypothesis (β = 0), so making a comparison using the
traditional statistics and related critical values can lead to erroneous conclusion.
Following Evan (1998), the term of income convergence may be defined as the
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convergence of long-run output differences as the forecasting horizon increases. It
implies that per capita GDP in any pair of provinces tends to converge to the same
level in the long run. In Statistical terms, the convergence to the provincial per capita
income means that the income gap between any two provinces must be
mean-reverting or stationary.
Therefore, one possibility, then, is to examine whether
each regional income series independently presents a unit root (Dickey and Fuller,
1976)). However, it is well known that such a procedure suffers from serious power
problems, see for example, Levin, Lee, and Chu (2002); Breitung (2004); the
Fisher-ADF and Fisher-Phillips-Perron tests proposed by Maddala and Wu (1999);
and Choi (2001).
3.1 Linear Panel Unit Root Test
The notion of income convergence can be formalized by applying the concept of
cointegration. If yi,t and yj,t the capita GDP for province i and j respectively at time t,
is level nonstationary , yi,t and yj,t are covering toward the same income level in the
long run once they are cointegrated.
A common approach in the bivariate set up is to
examine whether the income differential between city i and j is stationary.
In the
following the empirical framework was started by carrying the ADF test for
stationsarity for pair-wise relative income differential series [ y ij,t  ln( y j ,t / y i ,t ) ].
Where yij,t is the income differential between the benchmark city i and city j at time t.
Beijing was selected as the benchmark city. We also use other cities and the arithmetic
mean as benchmark and the results are robust.
The standard ADF regression takes
the form:
K
y ij ,t   j   j y ij ,t 1    j ,k y ij,t  k   ij ,t
t=1,…,T ; j=1,…,N --------------(3)
k 1
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Rearrange equation (3) becomes:
K
y ij,t   j   j y ij ,t 1    j ,k y ij ,t  k   ij ,t
t=1,…,T ; j=1,…,N -----------(4)
k 1
Where  the first difference operator, k is is the number of augmenting terms
and {u ij ,t } ( j  1,2.., N ) are white noise series independently distributed across N=50
provinces, i.e. uij,t ~ id (0,  ij2,t ) . The number of augmenting terms is determined by
using the Akaiki information criteria (AIC). We need to include a constant term, α for
each city in order to account for province-specific fixed effects such as initial
endowment, employees’ educational attainment, and the preferential policy
implemented by the central government for different states. The purpose of including
the constant term is to differentiate between the concept of conditional convergence
(α≠0) and unconditional convergence (α=0).
3.1.1 The Levin-Lin (LL) Tests
Levin and Lin (1992) developed their panel unit root test which assumed each
panel member share the same AR(1) coefficient while allowing for individual effects,
time effects and possibly a time trend. Lagged augmentation terms may be introduced
to correct for serial correlation in the errors. However {u ij ,t } must be i.i.d for all panel
members in order to enable LL test statistic to have proper asymptotic and finite
sample properties. It implies that no assumption of contemporaneous cross-correlation
among panel members being allowed in this setup. The LL test specifies the unit root
null hypothesis and the alternative as:
H 0, LL :  j    0 , H 1, LL :  i    0
for j
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The LL test provides little information to researchers because of two reasons.
First, it does not make sense to assume that all provincial income are converging at
the same rate under the alternative. In addition, assuming all provincial income
differential contains a unit root is inappropriate under Null. Second, the assumption of
cross sectional independence does not make sense because cross sectional dependence
can always be the case due to global shocks like open-door policies within for
instance. In practice, the variance-covariance matrix of errors is rarely of Zero
off-diagonal elements. Once the time series exhibit contemporaneous cross correlation
the LL test is invalid due to inappropriate critical values are used.
3.1.2 The Im, Pesaran and Shin (IPS) Tests
Im, Pesaran and Shin(1997) modified LL test and based on the mean of the
individual ADF t-statistics of each member in the panel, the IPS test assumes that all
series are non-stationary under the null hypothesis. In contrast to LL test, IPS test
assumes that under the alternative hypothesis there are at least one series is stationary.
That is:
H 0, IPS :  j    0
( j=1,2,…,N)
H 1, IPS :  j    0 for
j=1,2,…, N1
and
 j  0 for j= N1 +1,…,N
(6)
However, similar to LL test, IPS test fails to take contemporaneous cross
correlation among panel members into account as well as to specify which panel
members are stationary and which are not.
3.1.3 The Maddala Wu (M-W) Tests
Maddala and Wu (1999) combined fisher type tests and IPS test so that
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unbalanced panel can be used to test for unit root hypothesis. M-W test is a
non-parametric test and once the observed p-values are available, the M-W test
statistic can be calculated such that:
N
MW  2  ln p j
(7)
j 1
Where p i is the p-value from individual equations from model (3). The MW statistics
was proved to have a  2 distribution with 2N degrees of freedom under the
assumption of cross-sectional independence.
3.2 Non- Linear Panel Unit Root Test
We believe that the growth dynamics across states follows non-linear patterns.
Firstly, we anticipate the economy may only experience high growth rate when it
reaches the threshold level of human capital accumulation and starts to engage in
trade with other regions.
Secondly, the equalization of prices of goods and factors of
production follows a non-linear dynamics as shown by many researchers (e.g.
Michael, Nobay and Peel, 1997; Taylor, Peel and Sarno, 2001; Sarno, Taylor and
Chowdhury; 2004).
Therefore, we use ESTAR model to specify the growth dynamic
of across states so as to capture the likelihood that the growth of different regions will
converge only if the region reaches a threshold level of growth rate. Kapetanois et al.
(2003) developed a new non-linear ADF test, which is based on the following
Exponential Smooth Transition Autoregressive (ESTAR) specification applying to the
de-meaned series of interest:
In its general form, we have:
h 1
h 1
h 1
h 1
*
yij,t   ij   ij yij,t 1    ijh yij,t h  ( yij*   ij* yij,t 1    ijh
yij,t h ) * F ( yij,t d )   ij,t
(8)
where
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F ( yij,t d )  1  exp[  ( yij,t d  c ) 2 ]
(9)
where  is a positive coefficient an c is the equilibrium value of income difference
between region i and j due to heterogeneous human capital accumulation between
region i and j.
Notice that when y ij ,t  d  c , F ()  0 and equation (8) is equivalent to
a standard linear ADF model of equation (3). However, when the magnitude of
income divergence between y ij,t  d and c becomes large and hence F ()  1 will
generate a new linear ADF model with parameter  ij   ij   ij* . In contrast when
income divergence is negligible,  * ij affects the flow of income differential in this
case.
However, when income divergence becomes more serious,  ij* plays a more
important role in governing the adjustment process.
We should take note that the
 ij   ij*  0 is the necessary condition for “Global Stability” to hold. Once the
condition of  ij   ij*  0 is fulfilled it is legitimate to have  ij  0 , if this is occurred
the implication is that income divergence follows a nonstationary growth path (e.g.
random-walk or explosive innovation within the “band of inaction” of c), and
eventually it converge back to its equilibrium once the magnitude of income
divergence is outside the “band”.

In a very simple version with d=1 we have:

yij,t  yij,t 1 1  exp( yij2,t 1   ij,t
……………………(10)
The null hypothesis of nonstationarity is H0:  = 0 against the alternative of H1:  > 0.
Because  in (10) is not identified under the null, it is not feasible to directly test the
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null hypothesis.
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Thus, the Kapetanois et al. (2003) reparameterize (10) by using a
first-order Taylor series approximation and obtain the auxiliary regression
yij,t  y 3 ij,t 1   ij,t ------------------(11)
For a more general case where the errors in (11) are serially correlated, regression (9)
is extended to
h 1
yij,t  y 3 ij,t 1    ijh yij,t h   ij,t -------------------(12)
h 1
The null hypothesis of H0
becomes : δ = 0 (divergence) against the alternative of H1 :
δ < 0 (convergence) can be tested using the critical values simulated
by Kapetanois
et al. (2003).
3.3 Sigma Convergence
Barro and Sala-i-Martin (1991) test for sigma convergence using state per capita
income. Data from 1880 to 1988 and find evidence in support of sigma convergence
for all decades except the 1920s and the 1980s. However, Drennan et al (2004) find
evidence against sigma convergence using data for all metropolitan areas in the
continental United States for the period 1969–2001. The series of interest is the
standard deviation of the natural logarithm of metropolitan PCPI at time t, denoted as
yt. We apply unit root test to this series and once evidence is found in support of the
unit root hypothesis for the standard deviations of the natural logarithm of PCPI it
would provide evidence against the convergence hypothesis. However, the use of
standard deviation is not satisfactory due to limited observations and bias of outliers.
Therefore, we use relative income differential as a complement to the standard
deviation across states’ income level so that the sigma converging member can be
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identified.
4. Empirical Results
Beta Convergence
In the case of regional output, the period of analysis is from 1952 to 2003. Figure
1 shows provincial income differences relative to Beijing. No conclusion regarding
the degree of income convergence could be derived from the diagram.
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. Table 2 shows evidence of income convergence among provinces using
univariate ADF test.
In the pre reform period, there are 4 out of 25 provinces reject
the null hypothesis of a unit root, indicating about 16% of provinces are converging to
the benchmark income level of Beijing at the 10% significant level. In contrast, there
is 5 out of 28 provinces or 17% shows evidence of convergence in the pos-reform
period. The evidence implies little improvement about income convergence in the
post-reform period.
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Table 3. shows that all of the four panel unit tests reject the unit root hypothesis
of no convergence in both pre and post reform periods. However, these traditional
unit root tests do not indicate which province is converging to the benchmark income
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level because the null hypothesis is that all members has a unit root against its
alternative of at least one member is stationary.
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Furthermore, we examine the convergence hypothesis using non-linear unit root
test. Table 4 shows that when non-linearity is incorporated in the testing procedure,
the nonlinear tests support beta convergence more often than using a linear ADF test.
The findings confirm our hypothesis that the growth dynamics across states follow
non-linear patterns and a region may only experience high economic growth rate
when it reached the threshold level of human capital accumulation and started to
engage in trade with other regions.
The proportion of provinces that support the
convergence hypothesis increases from 16% to 56% in the pre-reform period when
using non-linear unit root test. In the post-reform period, there are 28% of provinces
that support the income convergence. The evidence is clearly shows that there is less
provinces support income convergence in the post –reform period as compared to the
re-reform period.
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Sigma Convergence
-Figure 2 plots the standard deviation of the natural logarithm of provincial
per capita GDP in China from 1952 to 2003. Over 52 years, if the theory of sigma
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convergence is correct, one would expect to see a persistent downward trend in the
variable. It shows very clearly that provincial income is converging before the
pre-reform period while diverging over time after the post-reform period.
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5. Conclusion
In this paper we examine the empirical validity of both beta and sigma
convergence across China using provincial per capita personal income during 1952 to
2005. Using both linear and nonlinear unit root test we identify converging and
diverging provinces in China.
We confirm the view of Pedroni.&Yao (2006) that
interprovincial inequalities have been widening since 1978.
Our result suggests future research on the question of why the income is not
converging for some provinces in the long run. There could be some possible
explanations for the above puzzle.
Firstly, as argued by Drennan.et.al (2004)
transportation technology may be one important factor affecting the convergence
process. After the mid-1970s transportation technology did not improve significantly.
In contrast, the transaction cost of exchanging services and manufactured goods
across states have been reduced dramatically during 1952-1977. For example,
railroads, trucks, and the inter-provinces highway system served to raise the mobility
of labor and capital and commodities, and hence to equalize returns and prices across
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states. However, we believe this convergence process follows non-linear dynamics as
supported by various empirical studies in the filed of the Law of One Price (LOP).
Secondly, the conclusion of unconditional convergence could be derived from
neoclassical growth model only if certain assumptions hold in the nature of input
factors and agent’s maximizing behavior Mankiw et al. (1992). . The model assumes
diminishing marginal return to labor and capital, which in turn implies income
convergence across states because labor and capital are moving around seeking for the
highest returns.
However, Acemoglu (2002) argued that skill-biased technical
change might favor rich region and lead to the violation of diminishing marginal
return to labor at the initial stage of technical progress. Therefore we would expect a
“sudden jump” in the growth rate when the income level of a region exceeds a
particular threshold level. Again, this suggests that we should model growth dynamic
in a nonlinear set up.
Lastly, product quality and intra-regional trade may play a role in explaining
conditional convergence. There may be a conflict in the preferences for the ideal
quality of consumption between rich and poor metropolitan areas across states. A
poor region may choose an “inferior” autarkic production technology so that more
quantity of “low” quality goods could be produced given resources availability. By
making such a decision, the poor region forgoes the opportunity of joining the
“global” markets and boosts its growth by division of labor, production specialization,
and technology spillover. Again, we would expect a “sudden jump” in the growth rate
when the income level of a region exceeds a particular threshold level.
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Figure 1: Provincial incomes relative to benchmark incomes of Beijing
2
1
GDPCR2
GDPCR5
GDPCR8
GDPCR11
GDPCR14
GDPCR17
GDPCR20
GDPCR23
GDPCR26
GDPCR29
0
-1
-2
GDPCR3
GDPCR6
GDPCR9
GDPCR12
GDPCR15
GDPCR18
GDPCR21
GDPCR24
GDPCR27
GDPCR30
GDPCR4
GDPCR7
GDPCR10
GDPCR13
GDPCR16
GDPCR19
GDPCR22
GDPCR25
GDPCR28
-3
55
60
65
70
75
80
85
90
95
00
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Figure 2. Variation in China Provincial Per Capita GDP
.40
.36
.32
.28
.24
.20
.16
55
60
65
70
75
80
85
90
95
00
Table 1: List of China's Mainland Provinces and Geographic Location
Code Province Location -Pref. Level
Code Province Location -Pref. Level
1 Beijing Interior-Central medium
16 Henan Interior-Central low
2 Tianjing Coastal-Central high
17 Hubei Interior-Central medium
3 Hebei Coastal-Central high
18 Hunan Interior-Central low
4 Shanxi Interior-Central low
19 Guangdong Coastal-Central high
5 Inner Mongolia Interior-NW medium
20 Guangxi Coastal-SW high
6 Liaoning Coastal-NE high
21 Hainan NA high
7 Jilin Interior-NE medium
22 Sichuan Interior-SW medium
8 Heilongjiang Interior-NE medium
23 Guizhou Interior-SW low
9 Shanghai Coastal-Central high
24 Yunnan Interior-SW medium
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10 Jiangsu Coastal-Central high
25 Tibet NA NA
11 Zhejiang Coastal-Central high
26 Shaanxi Interior-NW low
12 Anhui Interior-Central medium
27 Gansu Interior-NW low
13 Fujian Coastal-Central high
28 Qinghai Interior-NW low
14 Jiangxi Interior-Central low
29 Ningxia Interior-NW low
15 Shandong Coastal-Central high
30 Xinjiang Interior
Table 2. Test of Beta Convergence
-Univariate ADF test-Comparison of Pre and Post Reform Period
Pre-Reform Peiod
Provinces Prob.
GDPCR2
GDPCR3
GDPCR4
GDPCR5
GDPCR6
0.1065
0.1782
0.075
0.2944
0.386
Lag
1
0
0
0
0
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Post-Reform Period
Provinces Prob.
GDPCR2
GDPCR3
GDPCR4
GDPCR5
GDPCR6
0.0509
0.1366
0.0884
0.2469
0.2117
Lag
1
1
0
1
0
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GDPCR7
0.0853
0
GDPCR7
0.295
0
GDPCR8
GDPCR9
GDPCR10
GDPCR11
GDPCR12
GDPCR13
GDPCR14
GDPCR15
GDPCR16
GDPCR17
0.1342
0.1152
0.1746
0.0001
0.1715
0.1403
0.1175
0.1998
0.1333
0.0477
0
0
0
0
1
0
0
0
0
0
GDPCR8
GDPCR9
GDPCR10
GDPCR11
GDPCR12
GDPCR13
GDPCR14
GDPCR15
GDPCR16
GDPCR17
0.8716
0.0462
0.4039
0.1214
0.3889
0.1895
0.8995
0.1354
0.1499
0.3013
5
5
1
0
1
1
0
0
0
0
GDPCR18 0.1954
0
GDPCR18 0.3806
GDPCR19
Dropped from Test GDPCR19 0.5417
GDPCR20 0.1367
0
GDPCR20 0.3231
0
1
1
GDPCR21
Dropped from Test GDPCR21 0.9724
GDPCR22
Dropped from Test GDPCR22 0.8135
GDPCR23
Dropped from Test GDPCR23 0.7716
GDPCR24 0.3584
0
GDPCR24 0.2334
GDPCR25 0.1469
0
GDPCR25 0.2094
GDPCR26 0.1182
0
GDPCR26 0.0003
GDPCR27 0.212
0
GDPCR27 0.9901
2
0
0
3
3
0
1
GDPCR28 0.32
GDPCR29 0.5083
GDPCR30 0.8667
0
0
0
0
0
2
GDPCR28 0.4097
GDPCR29 0.6184
GDPCR30 0.0765
Table 3. Tests for β Convergence in Income: Panel Unit Root Tests
Pre-Reform Period
Post-Reform Period
Test
Test-Stat.
Test-Stat.
Levin and Lin (1992)
p-value
-12.49
0
-3.243
0.006
Im, Pesaran and Shin (2002)
p-value
-8.244
0
-2.113
0.0173
Fisher-ADF
p-value
102.135
0
87.475
0.0074
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Fisher-Philips-Perron
113.292
p-value
0
78.477
0.038
Notes:
a: The null hypothesis is a unit root process (no convergence). P values are in parentheses.
b: LLC test assumes common unit root
Table 4. Tests for β Convergence in Income: Non-Linear Unit Root Test
Pre-Reform
Period
Provinces
Post-Reform
Period
Provinces
Stat.
***
GDPCR2
-2.067
GDPCR3
-2.843*
GDPCR3
-2.853*
GDPCR4
-3.515***
GDPCR4
-3.541***
GDPCR5
-3.113**
GDPCR5
-4.817***
GDPCR6
-3.067**
GDPCR6
-2.033
GDPCR7
-3.531
***
GDPCR7
-2.857*
GDPCR8
-5.146***
GDPCR8
-1.465
GDPCR9
**
GDPCR9
-1.930
GDPCR2
Stat.
-3.881
-3.398
GDPCR10
-1.797
GDPCR10
-0.313
GDPCR11
-34.178***
GDPCR11
-4.175***
GDPCR12
-2.186
GDPCR12
-0.932
GDPCR13
-3.959***
GDPCR13
-1.919
GDPCR14
-2.392
GDPCR14
-0.524
GDPCR15
-2.113
GDPCR15
-2.445
GDPCR16
-2.210
GDPCR16
-2.600*
GDPCR17
-2.475
GDPCR17
-3.312**
GDPCR18
-1.893
GDPCR18
-2.873
GDPCR19
-1.704
GDPCR20
-2.263
GDPCR19
GDPCR20
-NA
-2.624
GDPCR21
-NA
GDPCR21
-0.577
GDPCR22
-NA
GDPCR22
-1.127
GDPCR23
-NA
GDPCR23
-0.904
GDPCR24
-1.386
GDPCR24
-2.503
GDPCR25
-2.752
*
GDPCR25
-2.101
GDPCR26
-2.862*
GDPCR26
-3.942***
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GDPCR27
-2.999**
GDPCR27
-0.272
GDPCR28
***
GDPCR28
-2.218
GDPCR29
-1.531
GDPCR29
-1.361
GDPCR30
-1.499
GDPCR30
-1.971
-4.231
Note : ***, **, & * denote 1%, 5%, & 10% critical values respectively.
The critical values for 1%, 5%, & 10% critical values are -3.48,-2.93,& -2.66
respectively. Sources: Kapetanois et al. (table 1, pp. 364, 2003)
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