Income Disparities across Chinese Provinces: Revisiting the Convergence-Divergence Debate

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1 Income Disparities across Chinese Provinces: Revisiting the Convergence-Divergence Debate Ran Sha*, Wim Naudé** and Wilma Viviers* *School of Economics, North-West University (Potchefstroom Campus), South Africa ** World Institute for Development Economics Research, United Nations University, Helsinki, Finland. Corresponding author : naude@wider.unu.edu Katajanokanlaituri 6B, FI-00160, Helsinki, Finland Abstract. The literature on income disparities across China s provinces suggests that there has been (absolute) divergence in per capita incomes since 1978, a trend which has accelerated since the early 1990s. We contribute to this literature by updating the convergence analyses to include the most recent period ( ). Four methods (beta and sigma convergence, Markov chain and kernel density analyses) are used to ask whether provincial income disparities have increased or decreased since the mid 1990s. We find that the income disparity among the Chinese provinces has become wider between 1994 and 2003, which suggests stratification of income disparities. We also investigate the link between income disparities and export growth over the period and find that export is an important determinant of provincial economic growth but contributes to the growing income disparity between coastal and inland provinces, given that there is little trickle-down effect from exportoriented (coastal) provinces to the poorer, interior provinces. Key words: China, inequality, provincial growth, convergence, exports JEL Classification numbers: O10, O15, O40, O53 We are grateful to Waldo Krugell, Leonard Santana and Guanghua Wan for constructive comments on earlier versions of this paper. The usual disclaimer applies.

2 Income Disparities across Chinese Provinces: Revisiting the Convergence- Divergence Debate 1. Introduction Over the past three decades China has been amongst the fastest growing economies in the world. It is also one of the countries with the most unequal distribution of income in the world (Chang, 2002:331). Disparities in incomes extend from the individual and household level to the regional (provincial) level. Although the country as a whole has experienced significant economic growth, the income disparity between the country s various provinces seems to have increased in recent years. Recent overviews of spatial inequality in China are contained in Kanbur and Zhang (2006) and Wan and Zhou (2006). Yang (2002) pointed out that that China s regional income disparities are due to a growing rural-urban and inland-coastal income gap. An extensive and growing literature of research exist which addresses China s provincial income disparities, in terms of understanding its significance, causes and impacts. As far as the significance of provincial income disparities is concerned, the focus in the literature has been on testing for whether there is either convergence or divergence amongst provincial income per capita levels over time. The current conclusion is that there was no convergence before , limited convergence after 1978, with conditional convergence generally found for the period , but an increasing divergence since the early 1990s (Jian, et al., 1996; Chen and Fleisher, 1996; Li, et al., 1998, Jones et al., 2003). The key studies on China s provincial convergence in per capita income are mostly now more than a decade old (for instance Jian et al., 1996; Chen and Fleisher, 1996). Most other more recent studies used data for periods before the end of 1990s (e.g. Knight and Song, 1993; Hussain, et al., 1994; Wan, 1998 and Li and Zhao, 1999). In this light, the contribution of this paper is threefold. Firstly, we provide an overview of the literature, including recent extensions and views, on disparities in income between 1 The year 1978 was a significant one in terms of policy reform in China, and the subsequent period is often described as the reform era. 2

3 China s provinces. Secondly, we add to the literature by updating the convergence analyses to include the most recent period ( ) that has so far been neglected in convergence studies. In particular, we use four methods (beta and sigma convergence, Markov Chain analysis and Kernel Density estimates) to ask whether provincial income disparities have increased or decreased since the mid 1990s. The use of these methods is to avoid the possibility that results may be contingent upon specific measures used for each (Hansen, 1995). The third contribution of this paper is to focus on income disparities and the link between income disparities and export growth over the period , which has been one of the most open periods in the country s history. Specifically, China acceded to the World Trade Organisation (WTO) during this period (at the end of 2001). It has been pointed out that reforms during this period could have worsened spatial inequalities (see e.g. Anderson et al., 2004). Given that a key tenet of China s economic development strategy since 1978 was export promotion (Lin, 2001; Lardy, 2003; Lai, 2006) it is instructive to ask whether the export-growth relationship was valid at a provincial level between 1994 and The paper is structured as follows. Section two contains a selective overview of the growing literature on China s provincial income disparities, including the results from existence convergence studies. Section three discusses and test for absolute and conditional convergence in China over the most recent period (using data from 1994 to 2003). In section four we test for sigma convergence. In section five we apply a Markov- Chain analysis and Kernel Density estimates of provincial disparities over the period. Section six concludes. 2. Provincial income disparities in China: a literature overview China s economic reform was initiated in Since then, China s economy has grown rapidly. However, although the whole country has experienced significant economic 3

4 growth, disparity in regional economic development is also well-recognised (Li and Zhao, 1999; Fujita and Hu, 2001; Kanbur and Zhang, 2006; and Wan and Zhou, 2006). Table 1 shows the Chinese provincial economic performance between 1994 and The output data used in table 1 are provincial per capita GDP in constant prices based on per capita GDP deflators (1978 year). It can be seen that the disparity between coastal provinces and interior areas has become more pronounced. In order to emphasize this point, table 2 ranks the provinces according to the real provincial per capita GDP which are provided in table 1. It shows that both initially rich and initially poor provinces have increased in living standards. However, the extent of improvement has differed substantially. In terms of average annual growth rate of real per capita GDP, as shown in table 1, during the period from 1994 to 2003, the best performers, except Tibet in western region, are all in coastal China: Tianjin, Beijing, Zhejiang and Shanghai (in descending order). However, Tibet is still one of the poorest provinces in China. Other top provinces all had high initial output levels in 1994 (see table 2) and they still manage to record the highest average annual growth rates among China s provinces. However, during the same period, most of the provinces in the inland areas, especially in West China, have experienced the slowest average growth in their real per capita GDP. The provincial average growth rates of real per capita GDP are below 3% in five out of the nine west provinces. 4

5 Table 1: Provincial average growth rates of real per capita GDP in China, Province Per capita GDP 1994 (Yuan) Per capita GDP 2003 (Yuan) (%) Eastern (coastal) zone Beijing Tianjin Hebei Liaoning Shanghai Jiangsu Zhejiang Fujian Shandong Guangdong Guangxi Hainan Central zone Shanxi InnerMongolia Jilin Heilongjiang Anhui Jiangxi Henan Hubei Hunan Western zone Sichuan Guizhou Yunnan Tibet Shannxi Gansu Qinghai Ningxia Xinjiang Source: Author s own calculations using raw data from the China Statistical Yearbooks ( ) published by China s State Statistics Bureau. Note: 1. The data for Taiwan Province are not included. 2. In 1997, Chongqing, which used to be part of Sichuan Province, was granted the status of municipality (provincial level city). In order to make the number of observations consistent before and after 1997, the information of Sichuan includes that of Chongqing during the whole research period. 5

6 Table 2: The rank of the best and worst performers in real per capita GDP,1994 and 2003 Rank Best (1994) Worst (1994) Best (2003) Worst (2003) 1 Shanghai (c) Guizhou (i) Shanghai (c) Guizhou (i) 2 Beijing (c) Gansu (i) Beijing (c) Gansu (i) 3 Tianjin (c) Tibet (i) Tianjin (c) Yunnan (i) 4 Guangdong (c) Shannxi (i) Zhejiang (c) Guangxi (c) 5 Zhejiang (c) Jiangxi (i) Guangdong (c) Anhui (i) Gap 3617 (Yuan) 6178 (Yuan) Note: 1. (c) means the province belongs to coastal areas and (i) means it is a inland province. 2. Gap is real per capita GDP gap between the best performer and its counterpart in 1994 and 2003, respectively. The apparent widening income disparity (lack of convergence 2) across China s provinces or groups of provinces has been the subject of extensive debate and research since For instance Li, et al. (1998) found evidence for the conditional convergence among Chinese provinces but they also pointed out that, although every province converges to its own steady state in China, the gap between the steady states of different provinces has widened. Chen and Fleisher (1996) suggested that their result of convergence is conditional on coastal location, which means that convergence happens within the coastal areas and inland provinces (including central and western areas) but not between the two regions. Other studies, including Knight and Song (1993), Rozelle (1994), Jian, et al. (1996); Yao (1999), Yao and Zhang (2001a; b) and Zhang et a.l (2001) also support that the divergence of the coastal and interior regions of China, particularly in the late 1980s and 1990s. More recently, Jones et al. (2003) added a further dimension to the spatial inequality debate by finding that if city-level data is used, differences in growth rates across space is much higher than when higher levels of aggregation (such as provinces) are used. An important result to emerge from the literature is that, until the end of the 1990s, Chinese regions had converged into three distinctive geo-economic clubs of economic 2 Convergence is defined here as the phenomenon of income levels in poorer regions catching up in relative terms with those in the rich regions (Aziz and Duenwald, 2003). 6

7 growth, coastal, central and west. Within each economic club, there was a tendency to convergence but, between the clubs, there was a tendency to divergence (Yao and Zhang, 2001b: 182). A further result is that income inequality is not only pronounced between coastal and inland areas, but between rural and urban areas (Hussain et al., 1994; Yao, et al. 2004). The main studies on income convergence in China and their results are summarised in table 3 below. It can be seen from table 3 that existing empirical studies have yielded inconsistent or even conflicting findings. This is due to the fact that earlier studies may have been constrained by data shortage and quality, and that different data periods have been used. Despite this, it can be concluded that most of the empirical literature tends to find an increase in cross-region income inequality during China s reform period. Methodologically, the empirical results of the existing studies are mostly based on two statistics, unconditional and conditional beta-convergence or sigma-convergence, which draw inferences about whether relative incomes in China s provinces are converging or not (Aziz and Duenwald, 2003; 31). These two methods will be discussed in more detail in sections 4 and 5. Echoing the growing concern about increasing regional disparity in China, the factors that can explain China s coastal-interior divergence have also become the focus of current debate in China. Various researchers have emphasised different particular factors. Among a broad range of determinants that have been put forward, a number of scholars have considered that the selective export-promotion development strategy at the beginning of economic reforms results in present coast-interior divergence and they also provided empirical evidence that convergence is conditional on export performance (Chen and Feng, 1999; Fujita and Hu, 2001; Yao and Zhang, 2001a; b; Lin and Li, 2003;). In the next section of the paper, we provide a more extensive discussion of the determinants of provincial income growth rates in China. Because the majority of the empirical work in this area uses data for the period before the end of the 1990s, one of 7

8 the objectives of this paper is to test whether exports are still the vital determinant of regional economic growth during the latest and the most open period in Chinese history. From the methodological perspective, cross-section (e.g. Chen and Feng, 1999) or panel data approaches (e.g. Zhou, 2004) are usually applied in this regard. The panel data approach has some advantages over the cross-section approach, which can control for the region-specific effects and which is less subject to serious biases caused by the selection of data periods (Yao and Zhang, 2001b: 168). Table 3: A selection of empirical studies on provincial income disparities in China Author (s) Periods Methods Main findings Chen and Fleisher (1996) β-convergence Conditional β-convergence Jian, et al, (1996) β-convergence δ-convergence Absolute and conditional convergence; δ-convergence δ-divergence Gundlach (1997) β-convergence Absolute β-convergence Chen and Feng (1999) β-convergence Conditional β-convergence Li, et al, (1998) β-convergence Unconditional and conditional β- convergence Fujita and Hu (2001) Weighted coefficient of variation; the Theil index; β-convergence Coastal-interior divergence; Absolute β-divergence Yao and Zhang (2001b) β-convergence δ-convergence Absolute β-divergence and conditional β-convergence; δ-divergence Zhang et al (2001) β-convergence β-convergence Démurger, et al, (2002a; b) β-convergence Absolute β-divergence and conditional β-convergence Cai et al, (2002) β-convergence Conditional β-convergence with labour market distortions. Zhou (2004) Smyth and Inder (2004) β-convergence δ-convergence Conditional β-convergence; mixed process of δ divergence and convergence Testing for Unit Roots Finds that majority of provinces exhibit non-stationarity in GDP per capita, i.e. suggesting possibility for convergence. 8

9 From the summary of the literature in Table 3, the conclusion is that, until the end of 1990s Chinese regions had converged into three clubs of growth: Coastal, Central and West. Have the poorer provinces in China caught up with the richer ones during the more recent period? The rest of this paper will provide insights into the convergence process from 1994 to 2003 in China. 3. Empirical estimation : absolute and conditional convergence 3.1 Modelling framework The neo-classical growth model, known as the augmented Solow model is used as a basis for tests of unconditional or conditional convergence (see Mankiw, et al., 1992). In this model, initial income is negatively related to subsequent growth, because poorer countries and regions will grow more quickly over a transitory period since they have lower stocks of human and physical capital so that the marginal product of extra capital is higher. This phenomenon is known as the convergence property of the augmented Solow model (Mankiw et al., 1992). Convergence can be tested by regressing average annual growth rates of GDP per capita (yi) on the log of initial GDP per capita (denoted by yi0). In other words by estimating: y = α + β (1) i y i0 If β <0, it suggests that there is β -convergence (absolute or unconditional convergence) and that poorer countries and regions will subsequently grow faster (Barro, 1997). In practice, equation (1) is implemented in an ad hoc fashion following the approach of Barro (1991), namely to estimate a conditional convergence equation, consisting of (1) extended by a number of variables, most notably investment, human capital, population growth, and a number of other conditioning variables. The resulting equation to be estimated can be expressed as follows: 9

10 ln y y + α X + ε (2) βτ i( t 2) ln yi( t1) = (1 e ) ln i( t1) i i i Where y = per capita GDP of province i X i = a vector of determinants of economic growth rates ε i= an error term with the usually assumed properties, including E ( X i ε i) = 0. The parameter β can be interpreted as the rate of convergence to the steady state (Barro, 1997). 3.2 Conditioning variables Based on basic economic growth theory and the various explanations of economic growth offered in the existing literature, several economic variables will be included as right hand side variables in the growth regressions to identify the determinants of provincial economic growth in China between 1994 and These are initial provincial GDP per capita (Barro, 1997), export performance 3 (Chen and Feng, 1999; Wei, et al., 2001; Lewer and Vandenberg, 2003; Wacziarg, 2001; Campenhout, 2002 and Lin, 2001), population growth (Campenhout, 2002; Zhou, 2004), and human capital 4 (Chen and Feng, 1999: 8). In China, foreign direct investment (FDI) and the coastal dummy have been often emphasised as preferential-policy effects and geographic effects on regional 3 Exports (openness) are in many studies considered as the basic driving force in China s macroeconomic performance (Lai, 2006). Export performance has varied widely across China s regions exports from the coastal area have grown at a faster rate (281.2%) than the export growth in both central regions (111.27%) and western provinces (158.14%) during the period 1994 to According to Jones et al. (2003) annual growth rates of coastal cities in China is on average 3% higher than that of non-coastal cities. Unfortunately, the faster growth in the coastal cities has not had substantial spillover effects on growth in the poorer, inland rural areas (Brun, et al., 2002). 4 Wan and Zhou (2006:129) concluded that in China the contribution of education to income growth and inequality is expected to increase, - due to amongst others rising gaps in education and the fact that in the past policies favoured physical capital investment over human capital investment (Heckman, 2005:50). 10

11 growth in many empirical studies (Chen and Fleisher, 1996; Jian, et al., 1996; Démurger, et al., 2002). However, the correlation between FDI and export and FDI and the coastal dummy are and , respectively. This shows that during the research period, a multicollinearity problem exists if the model simultaneously includes exports, FDI, and coastal dummy as independent variables. Because we are interested in investigating whether the export-growth relationship is valid for provincial economies in China over the most recent past, the levels of provincial exports are used in this paper instead of FDI and a coastal dummy. 3.3 Data and estimators The primary data source for this chapter is from the China Statistical Yearbook complied annually by the State Statistical Bureau (SSB) of China. Two provinces, Tibet and Qinghai, are omitted because of lack of reliable data. Chongqing and Sichuan Province were only separated in 1997 and have therefore been included as one combined province, in order to make the number of observations consistent before and after For political and economic reasons, Taiwan Province is excluded for this group of observations. We firstly use a standard OLS model to estimate equation (2) without the conditioning variables (testing for absolute convergence) and secondly use a randomeffects panel data model to estimate equation (2) with the conditioning variables as discussed in section 3.2 included (testing for conditional convergence). All of the provincial GDP per capita are in real values measured by 1978 constant prices. The initial level of real per capita GDP is that of 1994 in both cross-section and panel data regressions. In the cross-sectional approach, like GDP, the initial year of 1994 is adopted for education. That is, the initial ratio of higher education is defined as the number of provincial graduates from universities and colleges in 1994 relative to provincial total population of the year of Other variables, such as the levels of provincial exports and population growth rates are averaged over the period 1994 to

12 In the panel data regression, the data set is a panel of 28 regions covering the research period. The first-order lag structure of provincial exports is used to capture the relatively longer period, which may be required for the impacts of exports to be felt on economic growth. Ratios of higher education and population growth rates are provincial annual variables from 1995 to It should be noted that the initial provincial per capita GDP and exports are adopted in the logarithmic forms in both approaches. 3.4 Regression results Two growth specifications are estimated in this section. The first specification is a test for absolute convergence in growth rates amongst China s regions, which contains only initial GDP per capita as an independent variable. The second specification makes convergence conditional on the variables that were discussed in section 3.2 above. Table 4 reports the regression results for the first specification. As discussed above, absolute convergence is tested by regressing average annual growth rates of GDP per capita (yi) ( ) on the log of initial GDP per capita (yi0) in the year The first specification rejects absolute convergence according to the significant positive coefficient of initial per capita GDP. It is clear that, during the period 1994 to 2003, the regions in China have shown a strong tendency of divergence. Table 4: Test for absolute convergence: dependent variable real GDP growth rate per capita, annual average Variables Coefficient Standard error t-value Constant ln(initial per capita GDP) ** Adjusted R-squared = Number of observations = 28 Note: *** Significance at the 1%, ** at the 5% level and * at the 10% level. 12

13 The results of the GLS random-effects panel data regression for conditional convergence are contained in table 5. The results indicate conditional convergence. The coefficient of the first-order lag structure of exports indicates export performance in the previous year has a significant positive impact on regional economic growth rate in the next year. The coefficients on education and population growth both have the expected signs and are statistically significant. Table 5: The random-effects GLS panel data regression results, dependent variable real GDP growth rate per capita Variable Coefficient Standard error z-value Constant ln(initial GDP per capita) ratio of High Education * ln(export) (lag = 1) ** population growth rate *** Number of observations = 252 Note: *** Significance at the 1%, ** at the 5% level and * at the 10% level. 4. Empirical estimation : sigma convergence Sigma convergence is found if the variance of per capita GDP among economies tends to decline over time. The variance or dispersion can be measured by the standard deviation across countries or regions of the logarithm of real GDP per capita (Jian, et al., 1996; Aziz and Duenwald, 2003). Table 6 indicates sigma divergence across 28 provinces in China during the period from 1994 to 2003, given the rise in the dispersion of real per capita GDP. It is also clear from figure 1 that GDP dispersion in coastal China is much wider than that in central and west China during the same period. The standard deviation of log of real per capita GDP across coastal areas increases from 0.42 in 1994 to 0.55 in 2003, while the extent of dispersion in 1994 in central and western regions are both higher 13

14 than those in From the trends as suggested in Table 6, it can be concluded that in coastal China, the tendency is δ-divergence during the period 1994 to 2003 and it is a mixed process of convergence and divergence in central and western China. Table 6: The dispersion of real per capita GDP in China, Year Western Central Coastal National Note: the figures are standard deviations of lg(real per capita GDP) in different years. It can also be seen from Table 6 that GDP dispersion in coastal China is much wider than that in central and west China during the same period. The standard deviation of log of real per capita GDP across coastal areas increases from in 1994 to in 2003, while the extent of dispersion in 1994 in central and western regions are both higher than those in It may be concluded that in coastal China, the tendency is δ-divergence during the period 1994 to 2003 and it is a mixed process of convergence and divergence in central and western China. 5. Empirical estimation: the distributional approach In the literature, both beta-convergence and sigma-convergence are referred to as the regression approach for the analysis of income convergence (Magrini, 2003). They can only provide a partial view of the convergence process and cannot provide a complete picture of the evolution of regional income differences over time (Aziz and Duenwald, 2003: 31). To obtain such a picture, an alternative approach, the distributional approach to convergence, has been introduced, and consists of Markov chain analysis and (stochastic) kernel density estimation. 14

15 5.1 Background and literature Quah (1996a: 1365) pointed out that conclusions on beta-convergence depends on the coefficients obtain from a regression analysis based on cross-section data and is uninformative for a distribution dynamics as these contain only summary information about the distribution such as the mean and dispersion (Sakamoto and Islam, 2005: 1). They belong to the class of parametric estimators, which have a fixed functional form (structure) and the parameters of this function are the only information to be stored. In contrast to these parametric estimators, the distributional approach to convergence analysis uses non-parametric estimators, which have no fixed structure and depend on all the data points to reach an estimate (Aroca, et al., 2006; Duong, 2001). From the viewpoint of the number of existing studies, most of the literatures of Chinese convergence so far have used the regression approach, either beta- or sigmaconvergence. The empirical literature using the non-parametric estimators or distributional approach has been relatively limited. Table 7 summarizes this literature. Table 7: Literature on convergence-divergence in China using the distributional approach Authors Period Method Perspective Conclusion Aziz and Duenwald Bhalla, et al., (2003) Kernel density Markov chain Li (2003) Markov chain Kernel Provincial income distribution Provincial GDP distribution Provincial GDP distribution The provincial relative income distribution is stratifying into a bimodal distribution with economic stricture and policies playing important roles. There is no clear evidence of club formation in the pre-reform period, but there is strong evidence of club formation in the reform period. There is a strong tendency to convergence within regions but no evidence is found of convergence between regions There is no convergence at the city level 15

16 Ho and Li (2005) Aroca, et al., (2006) density; Markov chain Kernel density; Markov Chain City income distribution Spatial effect at the provincial level during the post-reform era and the dynamic spatial dependence between cities is strong at the provincial level. There is a dramatic increase of the Chinese per capita GDP s spatial dependence in the post-reform period. China distribution has gone from convergence to stratification and from stratification to polarization (p.19) As summarized in Table 7 all of the studies using Markov chain analysis and/or kernel density estimator find growing divergence between coastal and interior provinces and also on the city level. The table indicates that, with the exception of the study by Ho and Li (2005) (who studies convergence on a city level) the time periods of these studies ended in the late 1990s. 5.2 Methodology In this section we outline the methods within the distributional approach used to analyse income disparities amongst Chinese provinces using data on the more recent period, 1994 to Because the implementation of this approach is based on the use of Markov (probability) transition matrix, we firstly present the methodology of Markov chain analysis, following Quah (1993). We first let Yt denote the distribution of per capita GDP across provinces at time t. We further make the assumption that the distribution follows a homogenous, stationary, first-order Markov chain process, the evolution of this discrete 5 distribution can be written as follows: Y t+1 = M Y t (3) 5 The discrete process here is to discretize the space of income values in order to simply count the observed transitions out of and into distinct discrete cells and normalize those counts by the total number of observations. Using discrete cells that span the space of all possible realizations, we can then construct a transition probability matrix (Quah, 1997: 9). The remainder of this section will discuss in detail the process of discretization (dividing the Chinese provinces into four groups or states: each state represents an income internal) and transition probability matrix in the case of China. 16

17 Where M is the transition probability matrix which maps one distribution into another, and tracks where in Yt+1 points in Yt end up (Bhalla, et al., 2003: 33). Assuming that the transition probability matrix remains the same over time, the distribution after N periods can be obtained by iterating equation (3) N number of times: Y = M Y N t+ N t (4) As N, the distribution converges to the ergodic distribution or the steady state distribution, Y 14, which can be characterised as: N N Yt+ N = M Yt Y (5) The ergodic distribution 6 depicts the eventual long-run income distribution (Sakamoto and Islam, 2005: 9-10). The ergodic distribution is constant, allowing us to write: Y = MY (6) If Y shows a tendency to a point mass, it would suggest convergence in per capita incomes. On the other hand, if it displays a tendency towards a bimodal (twopoint) or multimodal measure, it would be evidence of income polarization or stratification (Magrini, 2003: 33). Although Markov chain analysis has the advantage over the regression approach in the term of the dynamics of the entire cross-sectional distribution, it also has a limitation due to the discretization process because the discretization of a continuous first-order Markov process may remove the Markov property 7 (Magrini, 2003: 34) and distort the dynamics (Quah, 1997: 9). To avoid this limitation, Quah (1997) proposed use of the related method of stochastic kernels, which consists of estimating the probability density function in a 6 For the transition matrix to result in an ergodic distribution one of its eigenvalues needs to equal 1 with the remaining eigenvalues below 1 in absolute value (Sakamoto and Islam, 2005: 9-10). 7 A stochastic process can be said to have the Markov property if the conditional probability distribution of future states of the process is conditionally independent of the past states (the path of the process) given the present state. 17

18 continuous framework (Magrini, 2003: 34, see also Aroca, et al., 2006; Rey and Janikas, 2005: 161). In a typical Markov chain analysis, the income distribution across space is firstly discretized into distinct discrete cells (or income intervals) I, II, III and these discrete cells are then used to construct a transition probability matrix by estimating the probability of a region (province) that was in one discrete cell in one time period (for instance, province A in cell II at t time) transits into another discrete cell in a future time period (for instance, province A transits out of cell II into cell III [or I] at t+s period)(quah, 1997: 9; see also Rey and Janikas, 2005: 161). In order not to remove the Markov property, the number of distinct cells {I; II; III } are allowed to tend to infinity with the corresponding transition probability matrix then becoming a stochastic kernel (Quah, 1997: 9). A kernel estimator f(x) at any point Xj is constructed as X N 1 x j f ( x) = K (7) Nh j= 1 h Where Xj = data point, N = number of data points, h = window width/smoothing parameter/bandwidth and K = kernel/weighting function. The Gaussian normal kernel is the most often used as K and it will be also used in this paper. However, the quality of a kernel estimate depends less on the shape of the K than on the value of its bandwidth h. An important step is the selection of appropriate bandwidth, which can lead to a consistent density estimate and provide the optimal degree of smoothness imposed on the density estimate (Desdoigts, 1996: 482). It is not useful if a value of the bandwidththat is too small or too large, because small values of h lead to very spiky estimates (not much smoothing) while larger h values produce oversmoothing estimate (Duong, 2001). In this paper, the values of h will follow the procedure and bandwidth choice provided by the R function software. With the help of a kernel density estimate, we can obtain information on the multimodality and skewness in the data (Silverman, 1986: 2). Convergence or the absence thereof can be discerned from the shape of the density distribution of incomes. 18

19 For instance, if we start with a bimodal density in a given time period, indicating the presence of two groups in a population of economies (say a group of poor and a group of rich economies), convergence implies a tendency in the distribution to progressively move towards unimodality over time (Bianchi, 1997: 395; see also Henderson, et al., 2002: 6). 5.3 Results We can now present the results from applying the Markov chain and kernel density estimators as described above to data on China s 28 out of 32 provinces (see section 3.4) taken from the website of State Statistical Bureau of China ( The analysis of this section still focuses on the period from 1994 to Results of Markov chain analysis Firstly, we calculated the real per capita GDP of each province relative to the Chinese average. Relative per capita GDP is divided or discretized into four groups (states): lowincome, lower-income, higher-income and high-income. Operator M (see equation 4) is described by a 4 by 4 Markov Chain transition matrix. In the Markov chain transition matrix, its elements (i, j) are the probabilities that an economy in group (state) i transits to group (state) j. Table 8 reports the transition matrix, estimated by averaging the annual transitions for China s provinces every year. In table 8, group 1 comprises provinces that have the lowest level of per capita GDP in China. That is, per capita GDP is no greater than 64.6% of the national average. Group 4 comprises the richest provinces with per capita GDP over 140% of the national average, and group 2 and 3 comprise provinces whose levels of per capita GDP are between the group 1 and group 4. The dividing line between group 2 and 3 is 87% of the national average. It should be mentioned here that 19

20 the dividing lines are chosen because they divide provinces into roughly equal sized groups during 1994 to 2003, following the suggestion by Quah (1993a). The panel in table 8 contains the yearly transition matrix from to The total numbers of transitions with starting points in group i are given in the first column. Columns 2 to 5 are the yearly transition probabilities. A noticeable feature of the results is the high persistence in these four income groups (the diagonal entries exceed 80%), especially in the low-income (group 1) and high-income groups (group 4), which means that if a province is in group i in year t, the possibility of it being in the same group in year t+1 is over 80% and the transition possibilities between different income groups are small. For instance, 97% of the highincome observations remain in the same group in the next year. As the complement of the persistence (Aroca, et al., 2006), high mobility is found in the two middle groups in table 8. Both in group 2 and 3, the possibility of a higher income province falling into the lower income province is larger than that of its moving into the higher income province. For instance, the province in group 2 (or 3) is more likely to fall into group 1 (or 2) than to move into group 3 (or 4). The entrance and exit probabilities for the rich group (group 4) are only 3.2% and 3%, respectively, which shows that there is a strong trend that the rich stays rich. As far as the low-income group (group 1) is concerned, the entrance probability of group 1 (14.8%) is much larger than the exit probability (7.9%), which means that there is a tendency that the poor still keeps poor but the low-income group tends to expand in the research period. It can be concluded from the above results that China s provinces tend to form different income clubs. This finding is consistent with the ergodic distribution reported in the bottom of table 8. Note for instance that the ergodic distribution has the largest value in group 1 (0.419), which implies that, based on the trend for the period 1994 to 2003, the low-income group will have the largest number of members in the long run. It also shows that Chinese provinces converge into different levels of relative to the country GDP per capita in the future. Quah (1996a; 1997) labelled this as stratification. 20

21 Table 8: Markov Chain transition matrix for provincial per capita GDP (relative to China average), first-order, time-stationary, states: 4 Period ( ) (Number) Group 1 (0, 0.646] Group 2 (0.646, 0.870] Group 3 (0.870, 1.400] Group 4 (1.400, ) Ergodic distribution Results of (stochastic) kernel densities As discussed in section 5.2, when we study the dynamics of the income distributions over time by means of a continuous framework instead of a discrete number of states, it becomes a kernel density. Figure 1 presents two single density profiles for China for the years 1994 and The vertical and horizontal axes report the estimated kernel densities and provincial real per capita GDP relative to the Chinese average, respectively. Thus we can get the idea of how the density function has been changed during the decade. It can be seen from figure 1 that the 1994 and 2003 distributions both show the multimodal mode, providing the further evidence in favour of stratification and the formation of convergence clubs (and against the convergence hypothesis). In addition, because both distributions are skewed to the right (positive skew), this indicates that there are more units in the group of poor or low-income provinces than there are in the group of rich or high-income provinces during the period 1994 to However, it can also be observed that the lowest-income mode centred about 0.7 in 1994 slightly shifts to the right to the value of around 0.9 in 2003 but other centres of other income levels shift much more to the right, especially the highest-income centre. This suggests that there is a widening gap between poor and rich provinces during the same period. Figure 1: Gaussian kernel densities of provincial relative per capita GDP,1994 and

22 Note: In this figure, the bandwidth was chosen following the R function dpik (direct plug-in bandwidth) estimation, suggested by Sheather and Jones (1991). Figure 1 used kernel density estimation in the univariate situation, which are simply cuts through the plot of figure 2 in multivariate situation. It is noted that all the multivariate methods are generalizations of univariate methods. Figure 2 is the Gaussian kernel of the joint distribution of provincial relative income, which shows the shape of three-dimensional plot for 10-year transitions ( ) with the applications of density estimation to multivariate data. According to Quah s (1997: 9), if most of the graph were concentrated along the 45-degree diagonal, then elements in the distribution remain where they began (persistence). If, by contrast, most of the mass in the graph were rotated 90 degrees counter-clockwise from the 45-degree diagonal, then substantial overtaking occurs. If most of the graph were concentrated around the 1-value of the axis of the terminal year and parralleling to the axis of the intial year, it indicates a tendency towards 22

23 convergence to equality in the cross-distributional of per capita GDP during the time period (Quah, 1997: 9; Magrini, 2003: 35). As is evident from figure 2, the fact that a large portion of the possibility mass remains clustered around the 45-degree diagonal highlights the persisitence property among Chinese provinces over the period 1994 to Figure 3 is the corresponding two-dimensioanl contour plot to make this point clearer. And both figures also show that there is no convergence during the same period and the multiplicity of peaks again manifests, which provides further evidence for the presence of the convergence clubs discussed by Quah (1996 a; b). Figure 2: Relative income dynamics across Chinese provinces Note: The bandwidth for this figure is not chosen in exactly the same way as in the univariate plots (figure 4). We use the R function Hpi (the plug-in bandwidth) suggested by Wand and Jones (1994) for the bivariate plots. Since the two bandwidths differ slightly, they produce the similar results. Figure 3: Relative income dynamics across Chinese provinces contour plot 23

24 6. Summary and Conclusions In this paper we focused on the literature and more recent data in the light of growing concerns that income disparities between China s provinces are increasing. We set out to make three contributions. Firstly, we provided an overview of the literature, including recent extensions and views, on disparities in income between China s provinces. We found that there is growing agreement that after the commencement of economic reforms in 1978, there has been (absolute) divergence in per capita incomes between China s provinces, a trend which has accelerated since the early 1990s. A number of dimensions to growing income disparities were identified, such as growing coastal-inland disparities, growing urbanrural disparities, which gave an indication as to the major causes of these income disparities. It was noted for instance that policies adopted after 1978, such as the declaration of special economic zones (SEZs) in coastal cities, limitations on labour 24

25 mobility (migration), and inequalities in education (human capital formation) have all contributed towards the growing disparity of income between provinces. Secondly, we attempted to add to the above literature by updating the convergence analyses to include the most recent period ( ) that has so far been generally neglected in convergence studies. Four methods (beta and sigma convergence, Markov chain and kernel density analyses) were used to ask whether provincial income disparities have increased or decreased since the mid 1990s in order to ensure robustness of the results against possible misspecification. We found that the income disparity among the Chinese provinces has become wider between 1994 and 2003, which suggests that the Chinese provinces are in the process of grouping into different economic clubs (i.e. stratification). In particular we found that the richer provinces remained in their high-income group, but that as far as the low-income group of provinces are concerned, the entrance probability according to the Markov chain analysis is much larger than the exit probability which means that there is a tendency that poorer provinces remains poor but tends to increase in membership size over the period 1994 to Thirdly, we emphasized the link between income disparities and export growth over the period This period has been one of the most open periods in the country s history. We established that during this period, export is an important determinant of provincial economic growth and contributes to the growing income disparity between coastal and inland provinces, given that there is little trickle-down effect from export-oriented (coastal) provinces to the poorer, interior provinces. References Anderson, K., Huang, J. and Ianchovichina, E Will China s WTO accession worsen farm household incomes? China Economic Review, 15 (4): Aroca, P., Guo D. and Hewings, G Spatial convergence in China: UNU-WIDER Research Paper # 89. Helsinki, Finland. 25

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