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Convergence of China's regional incomes
China Economic Review 12 (2001) 243 – 258
Convergence of China’s regional incomes 1952–1997 Zongyi ZHANGa,b, Aying LIUc,*, Shujie YAOc a
Department of Economics, University of Portsmouth, Hants PO4 8JF, UK b Chongqing University, Chongqing, China c Middlesex University Business School, The Burroughs, London NW4 4BT, UK
Abstract This paper employs time series techniques, with or without a structural break, to investigate the question of China’s regional per capita income convergence. Our results suggest that China’s regions, especially the eastern and the western regions, have converged to their own specific steady states over the past 40 years. The Gini coefficient, the ratio of per capita income between regions, and the coefficient of variation confirm our findings. We also identify the big shocks on the relative regional per capita income by allowing a time break. D 2001 Elsevier Science Inc. All rights reserved. JEL classification: C22; R12; R58 Keywords: Convergence; Regional per capita income; Time series; Gini coefficient; China
1. Introduction The 1980s experienced an explosion of research on economic growth. The papers by Lucas (1988) and Romer (1986) renewed interest in study in this area. A large amount of literature has been dedicated to applying cross-sectional and time series techniques to both cross-country and cross-regional data. Theories of economic growth attempt to explain the continuous growth in per capita income in the world economy over the last two centuries. An influential paper by Solow (1956) on the neoclassical growth model suggested that poor
* Corresponding author. Tel.: +44-20-8411-5209; fax: +44-20-8202-1593. E-mail address: [email protected] (A. Liu). 1043-951X/01/$ – see front matter D 2001 Elsevier Science Inc. All rights reserved. PII: S 1 0 4 3 - 9 5 1 X ( 0 1 ) 0 0 0 5 3 - 0
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countries would grow faster than rich ones. However, this prediction is not fully supported by evidence in modern history. Mankiw, Romer, and Weil (1992) revive the neoclassical growth model by extending Solow’s model to include human capital investment. According to the augmented model, an economy’s steady state for the logarithm of output per person follows a linear time trend. The slope of this linear trend is exogenously determined by the rate of technical progress, while the intercept reflects the rate of population growth and the shares of output devoted to investment in physical and human capital. If a poor economy tends to grow faster than a rich one, and the poor region tends to catch up to the rich one in terms of the level of per capita income or product, then it is called convergence across the regions. The cross-sectional regressions generally find no evidence of convergence across most countries as a whole (Barro, 1991; Baumol, 1986), but the convergence does hold among groups of countries with certain characteristics in common and among the regions within a country. That means that once the determinants of steadystate per capita income have been controlled for, economies exhibit convergence, and this is called conditional convergence. Some evidence of conditional convergence has been found for some countries with certain common characteristics.1 However, the cross-sectional technique for determining convergence has recently been under some criticism. Quah (1993a, 1993b) argues that regression to the mean problems would bias the results. Moreover, Evans and Karras (1996) show that the conventional cross-sectional technique produces invalid inferences unless the economies under study have identical first-order autoregressive dynamic structures and all permanent crosseconomy differences in their per capita GDP are perfectly controlled for, which may be highly implausible. In contrast to this cross-sectional notion of convergence, the existence of random but potentially permanent shocks to per capita income has led researchers to formulate a time series notion of convergence. By assuming that logged per capita income of an economy possesses a unit root, and by defining the stochastic convergence as cointegration between two (or more) such series, Bernard and Durlauf (1995) and Campbell and Mankiw (1989) show that there is little evidence of stochastic convergence among OECD economies in spite of the similar economic environment they share; their conclusion differs from the conditional convergence in the cross-sectional regressions. The same conclusion has been drawn for a large set of capitalist economies (US states economies), in which there exists nearly complete free trade and mobility of factors and nearly identical forms of government (Brown, Coulsou, & Engle, 1990; Quah, 1990). The inconsistency between the crosssectional and time series literatures on cross-country (region) convergence among similar economies is surprising. Alternatively, Carlino and Mills (1993) found that the stochastic convergence as the log of the per capita income of one region relative to the US economy as a whole is stationary. They addressed this inconsistency by investigating the convergence of relative per capita
1
Such as the OECD countries (Barro,1991; Mankiw et al., 1992) and across regions in Germany, France, the UK, the states of the US, and the prefectures of Japan (Barro & Sala-i-Martin, 1992, 1995).
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income and testing both stochastic and conditional convergence (what they refer to as bconvergence) for the eight US regions. Using conventional tests, they failed to reject the unit root hypothesis in the logged relative regional per capita income (to the US as a whole) for any region. By following Perron (1989) to allow for the existence of an exogenously imposed trend break, however, they obtained evidence supporting the stochastic convergence in three out of eight regions and supporting conditional convergence in all regions. Loewy and Papell’s (1996) study further strengthened the conclusion by rejecting the unit root in at least four regions. Thus, by allowing for a trend break, both studies were able to eliminate some of the inconsistency between the cross-sectional and time series evidence on US regional convergence. Convergence or divergence of China’s regional economic growth has become an important issue as the trend has been for the rapid economic growth to be concentrated along the coastal provinces. A number of studies have been carried out in the field.2 With some variation of the periods under study and the methods adopted, the previous empirical studies generally suggest that there was no convergence before 1978 but a mild convergence since the economic reforms. In this paper, we investigate the time series properties of per capita income in China’s regions. The results are used to make a comparison with the conclusions drawn by Carlino and Mills (1993) and Loewy and Papell (1996). The similarities and the differences in the convergence properties between the largest developed country and the largest developing country will help us to have a better understanding of the growth theories and will shed some light on the future development of developing countries. Our time series results are also used to compare with the cross-sectional results in the regional growth studies in China, and to check the consistency further between the time series techniques and the cross-sectional methods. The rest of this paper is organized as follows. Section 2 discusses the data of relative per capita income. Section 3 carries out Augmented Dickey–Fuller (ADF) tests on relative per capita income. We try to identify the most influential events on the history of China’s economy after 1949 in Section 4. Section 5 discusses the forming of regional clubs, and the paper concludes in Section 6. 2 For instance, Lardy (1980) concluded that regional inequality was reduced over time. Tsui (1991) reported the interprovincial income gaps did not narrow, but there was a mild decline in regional inequality since the economic reform using the 1952 – 1985 data. Chen and Fleisher (1996) reported that there was evidence of conditional convergence of per capita production across China’s 25 provinces from 1978 to 1993 after controlling for the variables of employment, physical capital, human capital, and the dummy for the coastal zone. Jian, Sache, and Warner (1996) found some evidence of convergence for 1952 – 1965 and 1978 – 1990 and strong evidence of divergence in 1965 – 1978. During 1990 – 1993, although convergence continued within the coastal provinces, regional incomes started to diverge once again. Using cross-sectional data, Gundlach (1997) found convergence of the regional output per worker across 29 Chinese provinces between 1979 and 1989 by applying the neoclassical growth model and predicted that the convergence rate would slow down after 1989 due to fiscal decentralization. Raiser (1998) found a reduction in interregional income inequality over the course of the economic reforms over the 1978 – 1992 period, but that the rate of convergence has declined since 1985 as a result of the reform shift from rural sectors to industrial sectors and the fiscal decentralization.
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2. Data Most previous studies use gross industrial output or national income data from the material product systems (Chen & Fleisher, 1996; Lardy, 1980; Tsui, 1991), since there was no provincial GDP data available for the period before the reform. In the present study, we are able to use the newly released provincial GDP series from 1952 to 1977. This makes it possible to compare our results with the results of the previous studies in an international context. Following the official definition, we combine China’s 30 provinces into three regions, the East (coastal), the Central, and the West. The constituents of each region are listed in Appendix A. Because of lack of data, Hainan in the East and Tibet in the West are omitted. This omission should not bias our results since they are the two smallest provinces by economic scale. The period of our data on current GDP, GDP indices, and population for China’s 30 provinces are from 1952 to 1997. These data come from Hsueh and Li (1999), Hsueh, Li, and Liu (1993), State Statistical Bureau (SSB) (1996), and China’s Statistical Yearbook 1997–1998 (SSB, various years). All the current values are calibrated by using the 1990 comparable prices and the provincial GDP deflators. The relative regional per capita GDP (to the national per capita GDP) is used as a proxy for the relative regional per capita income. Fig. 1 shows the log relative per capita income for each of the three regions. Not surprisingly, the East has per capita income above the national average, while the Central and West regions lie below the national average. From 1952 to the end of 1960s, the relative per capita incomes for the three regions are relatively steady. However, the gaps in income between the East and the other two regions has widened dramatically since the end of 1960s. Of interest here is whether those regions have been stochastically converging, in other words, whether any of them has a log relative per capita income that is stationary? To answer the question, we carry out the ADF tests in the following section.
Fig. 1. Changes of regional relative per capita income.
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3. ADF tests The existence of stochastic convergence is related to the unit root hypothesis (Carlino & Mills, 1993). If shocks to relative regional per capita income are temporary, then relative incomes will not have a unit root. We first perform standard unit root tests for the three regional log relative per capita income series in China. According to Dickey and Pantula (1987), two strategies, ‘‘testing downwards’’ and ‘‘testing upwards,’’ can be used in testing the unit root; if, however, a series has more than one unit root, the ‘‘testing upwards’’ strategy will possibly be invalid in the first few tests. Thus, we follow the ‘‘testing downwards’’ strategy in this paper and use the general ADF test with both a drift and a trend as the data illustrate a clear trend and there is no firm reason to prefer a particular equation form of ADF test (Eq. (1)). DRIt ¼ a þ bt þ rRIt1 þ
k X
qi DRIti þ et
ð1Þ
i¼1
where RIt is the log of relative per capita income at time t, DRIt is the first difference of RIt, k is the lag order of DRIt, and et is a serially uncorrelated error term with a zero mean and a finite variance. As indicated by Loewy and Papell (1996), there is considerable evidence that datadependent methods for selecting the value of k are superior to the approaches of choosing a fixed k a priori (Carlino and Mills, 1993). It was argued by Ng and Perron (1995) and Perron (1994) that the t-sig method is superior to various procedures based on information-based methods since the former produces tests with more robust size properties without much loss of power. We follow the ‘‘t-sig’’ method, suggested by Campbell and Perron (1991) and Perron (1994, 1997). Start with an upper bound, kmax, on k, which is determined a priori. If the last included lag is significant, choose k = kmax; if not, reduce k by 1 until the last lag becomes significant. If no lags are significant, set k = 0. Following Loewy and Papell (1996) and Perron (1989), we set kmax = 8 and use the two-sided 10% value of the asymptotic normal distribution to assess the significance of the lag. The results of ADF tests are reported in Table 1. Under the null hypothesis of a unit root, the statistics of r are not t-distributed, rather they are t-distributed, which can be derived from Monte Carlo simulations. The critical values of tr are widely available, and we list Table 1 ADF tests for China, kmax = 8 Region
a
b
r
k
East Central West
0.032 (3.00) 0.010 (0.82) 0.100 ( 3.65)
0.002 (3.60) 0.003 ( 2.43) 0.005 ( 4.41)
0.336 ( 3.71) ** 0.332 ( 2.72) 0.666 ( 4.25) **
5 5 6
The critical values for tr are 4.38 for 1%, 3.60 for 5%, and 3.24 for 10%. See Harris (1995). Values in parenthesis are asymptotic t statistics. ** Significant at the 5% level.
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them in the note of Table 1. The statistics for a and b are still conventionally t-distributed, given r = 0 rejecting. The null hypothesis of a unit root is rejected in both of the East and the West at the 5% significance level in Table 1. The significant b coefficients mean that the series of relative regional incomes in these two regions followed stationary processes from 1952 to 1997. Any shock to these two regions was temporary, but with a trend of stochastic convergence. The difference between those two regions was the rich (the East) became richer while the poor (the West) became poorer, as both the intercept and the slope for the East are positive, while they are both negative for the West. In contrast to the stochastic convergence of the East and the West, we cannot reject the null hypothesis of a unit root in the Central region; thus, a shock may be permanent or long and persistent in this region. A possible explanation of the phenomenon may be that both the significant upward trend in the East and a significant downward trend in the West influenced their common neighbour, the Central region, and this made the direction of change in the Central region more or less uncertain. The results of the present study suggest that the provinces were in a process of regrouping into different economic clubs as the East went up to its high steady state, the West down to its low equilibrium, and the Central swayed with the shocks between them. This point will be further explored in Section 5. The conclusive statements mentioned above, that the East and the West were stochastically convergent, seem contradictory with Fig. 1, which displays obvious trends of divergence of the relative per capita incomes in China’s three regions. The reason for that was the time trend. Only when the time trend is considered are the series of the relative per capita income in the East and in the West stationary. We carried out the ADF tests without the time trend as well, the results confirm that we cannot reject the unit root hypothesis without the time trend for all the regions.3
4. Identification of the influential events We have shown that both the East and the West were stochastically convergent. The issues we want to explore further are twofold: (1) whether the Central region was stochastically convergent with a break point; and (2) what the most influential shocks to the relative per capita income were. In short, we want to know if there was any structural change taking place in the trends. Although the unit root hypothesis has been rejected in the East and the West of China, there is no compelling reason to deny the existence of structural breaks. As stated above, Perron (1989) indicated the possibility that a break in the deterministic trend could be interpreted as the existence of a unit root and could lead to failures to reject the null hypothesis of a unit root. In the following, we intend to identify the most influential event in the evolution of the relative per capita income by allowing for a one-time break in the trend function. It would also be interesting to see if the unit root hypothesis will be rejected in the case of the Central with a one-time change in the trend.
3
The results are not presented here to save space, but are available from the authors on request.
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There are two types of models dealing with the one-time break: the additive outlier (AO) model and the innovation outlier (IO) model (Perron, 1989). The former allows for a change in the slope, but segments of the trend function are joined at the time of the break; the change is presumed to occur rapidly. The latter allows for a change in the intercept only or a change in both the intercept and the slope at the same time; the change is assumed to occur gradually and in a way that depends on the correlation structure of the noise function. Perron (1994) argued that whenever there exists a break in the intercept, the IO model has an advantage over the AO model. Therefore, we choose IO models to test the change in the intercept only (Eq. (2)) and the change in both the slope and the intercept (Eq. (3)). The IO models are DRIt ¼ a þ bt þ gDðTB Þt þ dDUt þ rRIt1 þ
k X
qi DRIti þ et
ð2Þ
i¼1
DRIt ¼ a þ bt þ gDðTB Þt þ dDUt þ hDTt þ rRIt1 þ
k X
qi DRIti þ et
ð3Þ
i¼1
where TB is the break year; D(TB)t = 1 if t = TB + 1, and equals 0, otherwise; DUt = 1 if t > TB, and equals 0, otherwise; and DTt = t TB if t>TB, and equals 0, otherwise. We again choose kmax = 8 and use the data-dependent ‘‘t-sig’’ method described above to decide the lag length k. The issue then here is how to find the most influential break point. When inspecting Fig. 1, one may find that it is difficult to choose the most influential break point exogenously for any series. Since our purpose is to select break points that are most influential to the path of relative per capita income, we cannot use the exogenous methods to test the years, as used by others (Carlino & Mills, 1993; Perron, 1989). The data-dependent methods, as suggested by some,4 however, can help us to solve the problem. Eqs. (2) and (3), which endogenise the break point by estimating it from the data, are estimated sequentially for any possible break year TB, TB = k + 2, . . ., T 1, where T is the observation number. The most influential break year is defined as the one that minimizes tr. The results with an endogenous break point are listed in Tables 2 and 3. Here, tr is still an indicator, showing whether a time series exhibits a unit root but with different critical values from Table 1. It has been used to select the most influential break year on the evolution of relative regional incomes. Both Models (2) and (3) in Tables 2 and 3 have identified the Cultural Revolution as the most influential event in the economic development in the Central region and the economic reform as the most marked event in the West over the sample period. However, the most notable event in the East varies depending on the models chosen, the Cultural Revolution has been identified as the key event by using Model (2) and the economic reform by choosing the more general Model (3). Although the break years are not the same in all the three regions in Tables 2 and 3, all of them are located at the beginning of either the Cultural Revolution or the economic reforms. They are the two most influential and well-known events in the social and economic development history of the People’s 4
See Banerjee, Lumsdaine, and Stock (1992), Christiano (1992), and Zivot and Andrews (1992).
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Table 2 ADF tests for three regions, with a break year, allowing changes in the intercept, kmax = 8 Break Region year a
b
d
g
r
k
East 1966 0.056 (5.39) 0.004 (5.06) 0.056 ( 3.81) 0.048 (5.41) 0.636 ( 6.36)*** 8 Central 1967 0.029 (2.38) 0.004 ( 3.45) 0.069 (2.95) 0.049 ( 4.13) 0.680 ( 4.49) 8 West 1984 0.101 ( 4.23) 0.009 ( 5.77) 0.038 ( 1.69) 0.053 (3.27) 0.918 ( 5.90)** 6 The critical values for tr are 5.92 for 1%, 5.23 for 5%, and 4.92 for 10%. See Perron (1997). Values in parenthesis are asymptotic statistics. ** Represents significance at the 5% level. *** Represents significance at the 1% level.
Republic of China. The former destroyed the national production bases and lowered productivity dramatically and the latter exploited the production potential unprecedentedly. The null hypothesis of a unit root for both the East and the West is rejected again in the tests presented in Tables 2 and 3, while we are still not able to reject the null hypothesis for the Central region in either Table 2 or 3. However, it is interesting to note the trends around the break points shown in Table 3. In the East region, the estimate of b is positive, and that of h is negative and smaller than that of b in absolute value. That is, the East increased its weight in relative per capita income over the whole study period, but the increasing pace slowed down from the inauguration of the economic reform. In contrast, the estimates of b and h are both negative in the western region. This implies that the weight of relative per capita income of the West declined over the period, but the speed has accelerated (although not significantly) since the beginning of the economic reform. The break year in the West lagged 4 years behind that in the East, coinciding with the fact that economic reforms began in the East and then extended to the West. The Central region was relatively stable with an insignificant time trend before 1967, but its relative per capita income kept declining, and the regional gaps between the East and the other two regions have widened since the Cultural Revolution (1967), which was much Table 3 ADF tests for three regions, with a break year, allowing change in both intercept and slope, kmax = 8 Region
Break year
East
1980
Central
1967
West
1984
a
b
g
d
h
r
k
0.009 (0.84) 0.072 ( 1.41) 0.105 ( 4.51)
0.007 (6.25) 0.003 (0.72) 0.008 ( 5.68)
0.011 (0.78) 0.073 (3.30) 0.028 ( 1.15)
0.023 ( 2.31) 0.076 ( 4.37) 0.068 (3.54)
0.004 ( 3.78) 0.008 ( 2.02) 0.003 ( 1.43)
0.591 ( 6.32)*** 0.855 ( 5.13) 0.908 ( 5.89)**
5 8 6
The critical values for tr are 6.32 for 1%, 5.59 for 5%, and 5.29 for 10%. See Perron (1997). Values in parenthesis are asymptotic t statistics. ** Represents significance at the 5% level. *** Represents significance at the 1% level.
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Table 4 ADF tests for the eight regions of United States, kmax = 8 No break year
With a break year
Region
r
tr
k
New England Mideast Great Lakes Plains Southeast Southwest Rocky Mountains Far West
0.07 0.07 0.27 0.17 0.17 0.13 0.19 0.30
2.30 1.49 3.12 1.80 2.98 2.22 2.52 3.29 *
1 6 2 1 8 5 0 0
1940 1948 1951 1949 1940 1940 1951 1942
r
tr
k
0.20 0.52 1.61 0.69 0.51 0.36 0.49 0.65
4.53 4.01 5.32* 5.78** 6.78*** 4.08 4.44 5.39*
1 8 8 0 3 8 0 7
Source: Loewy and Papell (1996). The critical values with a break year for tr are 6.32 for 1%, 5.59 for 5%, and 5.29 for 10%. We use the asymptotic critical values from Table 1 in Perron (1997), which are larger (in absolute value) than that used by Loewy and Papell (1996). * Represents significance at the 10% level. ** Represents significance at the 5% level. *** Represents significance at the 1% level.
earlier than the inauguration of economic reforms. Moreover, the economic reform slowed down the upward pace of the East. In the meantime, the economic reform widened the regional gap measured by relative per capita income. Based on the measurement of the relative per capita income, our results on the interregional convergence are inconsistent with the recent literature on China’s economic growth and inequality. The results suggest that China’s regions have different equilibrium and two out of three converge to their steady states with a time trend. The conclusion is similar to Chen and Fleisher (1996), using provincial per capita production and cross-section models which reported that there was evidence of conditional convergence with a significant regional dummy. In contrast to China’s regional economies, the regional economies of the US display a much different pattern over the period 1929–1990. In their paper, Loewy and Papell (1996) divided the US into eight BEA regions. Annual BEA data on personal income and population for the US regions during the period 1929–1990 were employed. Since regional price indices were not available, they did not deflate regional per capita income. Additionally, since all of their income measures are already in relative (to the nation) terms, the national CPI serves no purpose. Their results showed that none of the eight regions were stationary, which implies that no region in the US converged to its unique equilibrium or to the average income level of the whole nation; while two out of three regional economies of China are stationary. To lower the possibility of failures to reject the null hypothesis of a unit root, they followed Perron (1989) and others5 allowing for a one-time break in both the shift and the trend. Their results are listed in Table 4. Even with the one-time structural change, only four out of eight US regions can 5
Such as Campbell and Perron (1991), Carlino and Mills (1993), and Loewy and Papell (1996).
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reject the unit root hypothesis at the 10% significance level. However, stationary regions of China do not change with the one-time structural change. Compared with the US regions, it seems that the regions of China are prone to forming different regional economic clubs.
5. Any regional clubs? What we can draw from the ADF tests are that the rich region becomes richer and the poor poorer. However, we still cannot conclude that China’s provinces are forming different clubs since we know nothing about the income distribution within a region. We also know little about the inequality between regions. Does the inequality between the provinces within a region or between two regions decline or widen? To answer this question, we calculate the Gini coefficients for China and its three regions from 1952 to 1997. Table 5 presents the results. In general, the income disparity in China obviously increased over the sample period, especially after the economic reforms. However, China’s three regions display many different patterns of Gini coefficients. For the East, two peaks of the disparity occurred in 1960 and 1974, and its income gap has narrowed steadily since 1974 although with some slight fluctuations. The peak inequality year in the Central region was 1963 and then the income disparity declined down with only a mild echo in the second half of the 1970s. In sharp contrast to the above two richer regions, the West shows a low Gini coefficient over the period, the Gini coefficient only reached more than 0.1 for a short period (1960–1977). It is obvious that the income discrepancy within a region either declined dramatically or kept a very low level over the economic reform period, while the inequality throughout China, as a whole nation, rose pronouncedly. The opposite direction of income difference — increasing in China as a whole and declining (or staying steady) within each of China’s regions, is beyond our expectation. The only possibility for increases in inequality in China as a whole is due to the increase in the interregional inequality. However, what we want to know further is if all the interregional inequalities between any two regions rise at the same time. Only with the knowledge of the trends of Gini coefficients, both within a region and between regions, are we able to answer the question of whether China’s provinces are reforming into different clubs. The three regions are combined into three groups, the East and the West, the East and the Central, and the Central and the West. We know that the inequality within a region has declined or stayed a relatively stable at a low level over the period of the economic reforms, so the rising inequality within a group implies the widening of inequality between the related two regions, or the rising of interregional inequality. The series of Gini coefficients for the combined groups of two regions are listed in the last three columns in Table 5. The largest income gap at the provincial level appears in the group of the East and the West. There are three peak years for inequality in this group, they are 1960, 1976, and 1997. The Gini coefficient rose steadily following the beginning of the economic reforms except for a mild decline from 1978 to 1983. Similarly, the income gap at the provincial level in the group of the East and the Central rose dramatically over the period; the inequality reached its two peaks in 1960 and 1994. The income gap slightly narrowed in the group from 1978 to 1983, but has widened considerably
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Table 5 Gini coefficients in China and China’s regions
Year
China
East
Central
West
East and Central
1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995
0.153 0.166 0.155 0.153 0.159 0.166 0.184 0.217 0.248 0.206 0.191 0.201 0.190 0.182 0.178 0.170 0.203 0.202 0.201 0.196 0.189 0.198 0.221 0.217 0.234 0.215 0.201 0.194 0.198 0.198 0.195 0.191 0.195 0.196 0.200 0.204 0.212 0.210 0.209 0.218 0.227 0.236 0.245 0.249
0.137 0.191 0.172 0.163 0.184 0.200 0.212 0.241 0.278 0.205 0.187 0.199 0.192 0.191 0.189 0.168 0.183 0.197 0.211 0.208 0.194 0.205 0.235 0.226 0.226 0.212 0.199 0.199 0.200 0.193 0.183 0.185 0.191 0.194 0.198 0.197 0.196 0.193 0.193 0.188 0.183 0.177 0.177 0.174
0.119 0.112 0.132 0.122 0.129 0.119 0.155 0.181 0.176 0.161 0.155 0.183 0.159 0.149 0.141 0.124 0.133 0.135 0.136 0.132 0.116 0.125 0.135 0.137 0.140 0.137 0.144 0.137 0.132 0.121 0.127 0.117 0.121 0.111 0.111 0.109 0.111 0.110 0.112 0.116 0.107 0.095 0.089 0.082
0.079 0.061 0.070 0.080 0.070 0.065 0.053 0.088 0.135 0.153 0.137 0.127 0.121 0.100 0.116 0.114 0.118 0.129 0.106 0.102 0.112 0.116 0.134 0.128 0.154 0.113 0.079 0.073 0.078 0.079 0.078 0.073 0.069 0.076 0.081 0.078 0.087 0.086 0.088 0.088 0.088 0.085 0.085 0.087
0.130 0.160 0.158 0.147 0.163 0.170 0.194 0.221 0.244 0.192 0.179 0.196 0.182 0.178 0.172 0.152 0.164 0.177 0.185 0.181 0.168 0.179 0.204 0.201 0.208 0.199 0.198 0.192 0.198 0.188 0.185 0.181 0.187 0.189 0.193 0.198 0.207 0.205 0.206 0.215 0.221 0.226 0.231 0.231
East and West
Central and West
0.162 0.156 0.183 0.136 0.164 0.129 0.163 0.136 0.169 0.128 0.176 0.132 0.182 0.156 0.225 0.183 0.270 0.203 0.219 0.191 0.197 0.182 0.203 0.193 0.198 0.175 0.190 0.161 0.191 0.157 0.187 0.158 0.233 0.197 0.232 0.174 0.228 0.165 0.226 0.158 0.222 0.150 0.232 0.156 0.260 0.166 0.253 0.162 0.273 0.179 0.247 0.155 0.222 0.137 0.216 0.130 0.221 0.125 0.226 0.127 0.219 0.130 0.219 0.123 0.221 0.123 0.224 0.116 0.229 0.118 0.232 0.114 0.236 0.113 0.234 0.111 0.232 0.112 0.235 0.113 0.243 0.109 0.251 0.102 0.261 0.103 0.265 0.105 (continued on next page)
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Table 5 (continued)
Year
China
East
Central
West
East and Central
East and West
Central and West
1996 0.250 0.169 0.078 0.087 0.226 0.267 0.110 1997 0.252 0.168 0.079 0.088 0.226 0.269 0.112 The Gini coefficients for China are derived from per capita mean incomes at the provincial level. The Gini coefficients for the three regions are also derived from provincial level per capita incomes within each of the regions. Source: Authors’ calculation.
since then. A trivial but meaningful symbol is that the Gini coefficient has declined slightly since 1995. It may imply that the inequality in this group has reached its highest point and will be relatively stable in the near future. In striking contrast to our expectation, the inequality in the group of the Central and the West declined evidently over the period. The Gini coefficient climbed to its peak in 1960 and stayed relatively high over the period 1961–1977. It then declined steadily after the economic reforms. There are two possible explanations in the decrease of Gini coefficient in this group: It may be attributable either to declining inequality within the region, or to the narrowing gap between the two regions. For a robust and convincing conclusion, further study is needed. The analyses of the Gini coefficients within or between China’s three regions imply that, to a large extent, inequality relates to and is influenced by dramatic political events, severe natural disasters, and economic instability. In 1960, with the beginning of a serious natural disaster and the withdrawal of aids by the former Soviet Union, inequality reached its historic peak in all the groups, the Gini coefficient for the West nearly doubled from the previous year. Inequality increased significantly over the Cultural Revolution period (1966–1976) in the group of the East and the West, and the group of the Central and the West. Nevertheless, there is no evidence from that period to show that China’s provinces were re-forming into different income clubs. After the economic reforms, the evolution of Gini coefficients showed a much more stable picture with an obvious trend. The intraregional inequality dropped significantly in the East and the Central regions and stayed a low level in the West. However, inequality rose dramatically between the East and the Central and between the East and the West. Referring to the point made previously (Sections 3 and 4 of this paper) that the series of relative per capita income of the East and the West were stationary, it is safe to say that China’s provinces were re-forming into different income clubs over the reform period. That is, the eastern provinces were forming the rich club while the provinces from the West were forming the poor club. It is easy to reject the possibility that the provinces from the Central region were sliding into the rich one. However, there is no evidence that the Central region was joining the poor club or that it was forming its own income club. We also use another two indices to measure the income inequality within a region and between regions. They are (1) the ratio of per capita income between two regions, which measures the per capita income difference between two regions, (interregional inequality), and (2) the coefficient of variation, which measures the dispersion of per capita income across
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Fig. 2. Ratios of per capita income between regions.
provinces within a region. The results of those two indices, as presented in Figs. 2 and 3, clarify and enhance our discussion about the formation of income clubs. All the ratios were relatively steady (with some slight fluctuations) before the Cultural Revolution (the first half of 1960s). The ratios of per capita income between the East and the other two regions rose rapidly after the Cultural Revolution, showing that interregional inequality between the East and the Central or between the East and the West rose considerably. However, the ratio of per capita income between the Central and the West was relatively stable and close to 1, which suggests the interregional income difference between the Central and the West regions was small and stayed relatively steady over the whole study period, 1952–1997. On the other hand, the interregional coefficient of variation fluctuated increasingly in the prereform period, but declined significantly in all the three
Fig. 3. Dispersion of per capita income within a region.
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regions after the economic reforms, implying that interregional inequality indeed went down in the reform period. Both the ratios of per capita income between regions and the dispersion of per capita income within a region tell a similar story as illustrated by the Gini coefficient analysis. That is, the gaps within a region declined dramatically and the gaps between the East and the Central and between the East and the West widened pronouncedly during economic reforms. However, the gap between the Central and the West was small and relatively steady. This leads us to conclude that China’s provinces were forming distinct clubs after the economic reforms.
6. Conclusion This paper employs time series techniques to investigate the question of China’s regional per capita income convergence. Without consideration of the structural break, the unit root hypothesis is rejected in two of the three regions in China compared with none of the eight regions in the US. With a break point in the structure, the unit root hypothesis is rejected in four regions in the United States while no changes occurs in China’s case. We are able to identify the big shocks on the relative regional per capita income by allowing for a break in the structure. The economic reforms and the Cultural Revolution were the most important events that influence relative regional per capita income over the period of 1952–1997. The former slowed down the upward rate of the East but accelerated the downward rate of the West in terms of relative regional per capita income. The latter triggered the decline of the Central region. The regional gap between the East and the others widened much earlier than the beginning of economic reforms, however, economic reforms worsened the gap further. With the strong time trend (with or without a structural break), the series of relative per capita income of the East and the West are stationary. This implies that China’s regions, especially the East and the West, were converging to their own specific steady states. In other words, China’s provinces were re-forming into different income clubs. The decline in the Gini coefficient within a region and the increases in the Gini coefficient within a regional group (the East and the West or the East and the Central) support our arguments. Furthermore, the ratio of per capita income between regions is used to measure interregional income differences and the coefficient of variation of per capita income is used to measure the income dispersion within a region. Using those two indices has enhanced our conclusion from the previous analysis. However, further study is needed to answer the question that if the central provinces are joining the poor club or will struggle to form their own club.
Acknowledgments We thank the editor and an anonymous referee for several helpful comments and suggestions. The remaining errors and omissions are our responsibility alone.
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Appendix A The East (coastal) includes Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Shandong, Fujian, Guangdong, Guangxi, Hainan. The Central consists of Shanxi, Inner Mongolia, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, Hunan. The West includes Sichuan, Guizhou, Yunnan, Tibet, Shaaxi, Gansu, Qinghai, Ningxia, Xinjiang.
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Convergence of China’s regional incomes 1952–1997 Zongyi ZHANGa,b, Aying LIUc,*, Shujie YAOc a
Department of Economics, University of Portsmouth, Hants PO4 8JF, UK b Chongqing University, Chongqing, China c Middlesex University Business School, The Burroughs, London NW4 4BT, UK
Abstract This paper employs time series techniques, with or without a structural break, to investigate the question of China’s regional per capita income convergence. Our results suggest that China’s regions, especially the eastern and the western regions, have converged to their own specific steady states over the past 40 years. The Gini coefficient, the ratio of per capita income between regions, and the coefficient of variation confirm our findings. We also identify the big shocks on the relative regional per capita income by allowing a time break. D 2001 Elsevier Science Inc. All rights reserved. JEL classification: C22; R12; R58 Keywords: Convergence; Regional per capita income; Time series; Gini coefficient; China
1. Introduction The 1980s experienced an explosion of research on economic growth. The papers by Lucas (1988) and Romer (1986) renewed interest in study in this area. A large amount of literature has been dedicated to applying cross-sectional and time series techniques to both cross-country and cross-regional data. Theories of economic growth attempt to explain the continuous growth in per capita income in the world economy over the last two centuries. An influential paper by Solow (1956) on the neoclassical growth model suggested that poor
* Corresponding author. Tel.: +44-20-8411-5209; fax: +44-20-8202-1593. E-mail address: [email protected] (A. Liu). 1043-951X/01/$ – see front matter D 2001 Elsevier Science Inc. All rights reserved. PII: S 1 0 4 3 - 9 5 1 X ( 0 1 ) 0 0 0 5 3 - 0
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countries would grow faster than rich ones. However, this prediction is not fully supported by evidence in modern history. Mankiw, Romer, and Weil (1992) revive the neoclassical growth model by extending Solow’s model to include human capital investment. According to the augmented model, an economy’s steady state for the logarithm of output per person follows a linear time trend. The slope of this linear trend is exogenously determined by the rate of technical progress, while the intercept reflects the rate of population growth and the shares of output devoted to investment in physical and human capital. If a poor economy tends to grow faster than a rich one, and the poor region tends to catch up to the rich one in terms of the level of per capita income or product, then it is called convergence across the regions. The cross-sectional regressions generally find no evidence of convergence across most countries as a whole (Barro, 1991; Baumol, 1986), but the convergence does hold among groups of countries with certain characteristics in common and among the regions within a country. That means that once the determinants of steadystate per capita income have been controlled for, economies exhibit convergence, and this is called conditional convergence. Some evidence of conditional convergence has been found for some countries with certain common characteristics.1 However, the cross-sectional technique for determining convergence has recently been under some criticism. Quah (1993a, 1993b) argues that regression to the mean problems would bias the results. Moreover, Evans and Karras (1996) show that the conventional cross-sectional technique produces invalid inferences unless the economies under study have identical first-order autoregressive dynamic structures and all permanent crosseconomy differences in their per capita GDP are perfectly controlled for, which may be highly implausible. In contrast to this cross-sectional notion of convergence, the existence of random but potentially permanent shocks to per capita income has led researchers to formulate a time series notion of convergence. By assuming that logged per capita income of an economy possesses a unit root, and by defining the stochastic convergence as cointegration between two (or more) such series, Bernard and Durlauf (1995) and Campbell and Mankiw (1989) show that there is little evidence of stochastic convergence among OECD economies in spite of the similar economic environment they share; their conclusion differs from the conditional convergence in the cross-sectional regressions. The same conclusion has been drawn for a large set of capitalist economies (US states economies), in which there exists nearly complete free trade and mobility of factors and nearly identical forms of government (Brown, Coulsou, & Engle, 1990; Quah, 1990). The inconsistency between the crosssectional and time series literatures on cross-country (region) convergence among similar economies is surprising. Alternatively, Carlino and Mills (1993) found that the stochastic convergence as the log of the per capita income of one region relative to the US economy as a whole is stationary. They addressed this inconsistency by investigating the convergence of relative per capita
1
Such as the OECD countries (Barro,1991; Mankiw et al., 1992) and across regions in Germany, France, the UK, the states of the US, and the prefectures of Japan (Barro & Sala-i-Martin, 1992, 1995).
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income and testing both stochastic and conditional convergence (what they refer to as bconvergence) for the eight US regions. Using conventional tests, they failed to reject the unit root hypothesis in the logged relative regional per capita income (to the US as a whole) for any region. By following Perron (1989) to allow for the existence of an exogenously imposed trend break, however, they obtained evidence supporting the stochastic convergence in three out of eight regions and supporting conditional convergence in all regions. Loewy and Papell’s (1996) study further strengthened the conclusion by rejecting the unit root in at least four regions. Thus, by allowing for a trend break, both studies were able to eliminate some of the inconsistency between the cross-sectional and time series evidence on US regional convergence. Convergence or divergence of China’s regional economic growth has become an important issue as the trend has been for the rapid economic growth to be concentrated along the coastal provinces. A number of studies have been carried out in the field.2 With some variation of the periods under study and the methods adopted, the previous empirical studies generally suggest that there was no convergence before 1978 but a mild convergence since the economic reforms. In this paper, we investigate the time series properties of per capita income in China’s regions. The results are used to make a comparison with the conclusions drawn by Carlino and Mills (1993) and Loewy and Papell (1996). The similarities and the differences in the convergence properties between the largest developed country and the largest developing country will help us to have a better understanding of the growth theories and will shed some light on the future development of developing countries. Our time series results are also used to compare with the cross-sectional results in the regional growth studies in China, and to check the consistency further between the time series techniques and the cross-sectional methods. The rest of this paper is organized as follows. Section 2 discusses the data of relative per capita income. Section 3 carries out Augmented Dickey–Fuller (ADF) tests on relative per capita income. We try to identify the most influential events on the history of China’s economy after 1949 in Section 4. Section 5 discusses the forming of regional clubs, and the paper concludes in Section 6. 2 For instance, Lardy (1980) concluded that regional inequality was reduced over time. Tsui (1991) reported the interprovincial income gaps did not narrow, but there was a mild decline in regional inequality since the economic reform using the 1952 – 1985 data. Chen and Fleisher (1996) reported that there was evidence of conditional convergence of per capita production across China’s 25 provinces from 1978 to 1993 after controlling for the variables of employment, physical capital, human capital, and the dummy for the coastal zone. Jian, Sache, and Warner (1996) found some evidence of convergence for 1952 – 1965 and 1978 – 1990 and strong evidence of divergence in 1965 – 1978. During 1990 – 1993, although convergence continued within the coastal provinces, regional incomes started to diverge once again. Using cross-sectional data, Gundlach (1997) found convergence of the regional output per worker across 29 Chinese provinces between 1979 and 1989 by applying the neoclassical growth model and predicted that the convergence rate would slow down after 1989 due to fiscal decentralization. Raiser (1998) found a reduction in interregional income inequality over the course of the economic reforms over the 1978 – 1992 period, but that the rate of convergence has declined since 1985 as a result of the reform shift from rural sectors to industrial sectors and the fiscal decentralization.
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2. Data Most previous studies use gross industrial output or national income data from the material product systems (Chen & Fleisher, 1996; Lardy, 1980; Tsui, 1991), since there was no provincial GDP data available for the period before the reform. In the present study, we are able to use the newly released provincial GDP series from 1952 to 1977. This makes it possible to compare our results with the results of the previous studies in an international context. Following the official definition, we combine China’s 30 provinces into three regions, the East (coastal), the Central, and the West. The constituents of each region are listed in Appendix A. Because of lack of data, Hainan in the East and Tibet in the West are omitted. This omission should not bias our results since they are the two smallest provinces by economic scale. The period of our data on current GDP, GDP indices, and population for China’s 30 provinces are from 1952 to 1997. These data come from Hsueh and Li (1999), Hsueh, Li, and Liu (1993), State Statistical Bureau (SSB) (1996), and China’s Statistical Yearbook 1997–1998 (SSB, various years). All the current values are calibrated by using the 1990 comparable prices and the provincial GDP deflators. The relative regional per capita GDP (to the national per capita GDP) is used as a proxy for the relative regional per capita income. Fig. 1 shows the log relative per capita income for each of the three regions. Not surprisingly, the East has per capita income above the national average, while the Central and West regions lie below the national average. From 1952 to the end of 1960s, the relative per capita incomes for the three regions are relatively steady. However, the gaps in income between the East and the other two regions has widened dramatically since the end of 1960s. Of interest here is whether those regions have been stochastically converging, in other words, whether any of them has a log relative per capita income that is stationary? To answer the question, we carry out the ADF tests in the following section.
Fig. 1. Changes of regional relative per capita income.
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3. ADF tests The existence of stochastic convergence is related to the unit root hypothesis (Carlino & Mills, 1993). If shocks to relative regional per capita income are temporary, then relative incomes will not have a unit root. We first perform standard unit root tests for the three regional log relative per capita income series in China. According to Dickey and Pantula (1987), two strategies, ‘‘testing downwards’’ and ‘‘testing upwards,’’ can be used in testing the unit root; if, however, a series has more than one unit root, the ‘‘testing upwards’’ strategy will possibly be invalid in the first few tests. Thus, we follow the ‘‘testing downwards’’ strategy in this paper and use the general ADF test with both a drift and a trend as the data illustrate a clear trend and there is no firm reason to prefer a particular equation form of ADF test (Eq. (1)). DRIt ¼ a þ bt þ rRIt1 þ
k X
qi DRIti þ et
ð1Þ
i¼1
where RIt is the log of relative per capita income at time t, DRIt is the first difference of RIt, k is the lag order of DRIt, and et is a serially uncorrelated error term with a zero mean and a finite variance. As indicated by Loewy and Papell (1996), there is considerable evidence that datadependent methods for selecting the value of k are superior to the approaches of choosing a fixed k a priori (Carlino and Mills, 1993). It was argued by Ng and Perron (1995) and Perron (1994) that the t-sig method is superior to various procedures based on information-based methods since the former produces tests with more robust size properties without much loss of power. We follow the ‘‘t-sig’’ method, suggested by Campbell and Perron (1991) and Perron (1994, 1997). Start with an upper bound, kmax, on k, which is determined a priori. If the last included lag is significant, choose k = kmax; if not, reduce k by 1 until the last lag becomes significant. If no lags are significant, set k = 0. Following Loewy and Papell (1996) and Perron (1989), we set kmax = 8 and use the two-sided 10% value of the asymptotic normal distribution to assess the significance of the lag. The results of ADF tests are reported in Table 1. Under the null hypothesis of a unit root, the statistics of r are not t-distributed, rather they are t-distributed, which can be derived from Monte Carlo simulations. The critical values of tr are widely available, and we list Table 1 ADF tests for China, kmax = 8 Region
a
b
r
k
East Central West
0.032 (3.00) 0.010 (0.82) 0.100 ( 3.65)
0.002 (3.60) 0.003 ( 2.43) 0.005 ( 4.41)
0.336 ( 3.71) ** 0.332 ( 2.72) 0.666 ( 4.25) **
5 5 6
The critical values for tr are 4.38 for 1%, 3.60 for 5%, and 3.24 for 10%. See Harris (1995). Values in parenthesis are asymptotic t statistics. ** Significant at the 5% level.
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them in the note of Table 1. The statistics for a and b are still conventionally t-distributed, given r = 0 rejecting. The null hypothesis of a unit root is rejected in both of the East and the West at the 5% significance level in Table 1. The significant b coefficients mean that the series of relative regional incomes in these two regions followed stationary processes from 1952 to 1997. Any shock to these two regions was temporary, but with a trend of stochastic convergence. The difference between those two regions was the rich (the East) became richer while the poor (the West) became poorer, as both the intercept and the slope for the East are positive, while they are both negative for the West. In contrast to the stochastic convergence of the East and the West, we cannot reject the null hypothesis of a unit root in the Central region; thus, a shock may be permanent or long and persistent in this region. A possible explanation of the phenomenon may be that both the significant upward trend in the East and a significant downward trend in the West influenced their common neighbour, the Central region, and this made the direction of change in the Central region more or less uncertain. The results of the present study suggest that the provinces were in a process of regrouping into different economic clubs as the East went up to its high steady state, the West down to its low equilibrium, and the Central swayed with the shocks between them. This point will be further explored in Section 5. The conclusive statements mentioned above, that the East and the West were stochastically convergent, seem contradictory with Fig. 1, which displays obvious trends of divergence of the relative per capita incomes in China’s three regions. The reason for that was the time trend. Only when the time trend is considered are the series of the relative per capita income in the East and in the West stationary. We carried out the ADF tests without the time trend as well, the results confirm that we cannot reject the unit root hypothesis without the time trend for all the regions.3
4. Identification of the influential events We have shown that both the East and the West were stochastically convergent. The issues we want to explore further are twofold: (1) whether the Central region was stochastically convergent with a break point; and (2) what the most influential shocks to the relative per capita income were. In short, we want to know if there was any structural change taking place in the trends. Although the unit root hypothesis has been rejected in the East and the West of China, there is no compelling reason to deny the existence of structural breaks. As stated above, Perron (1989) indicated the possibility that a break in the deterministic trend could be interpreted as the existence of a unit root and could lead to failures to reject the null hypothesis of a unit root. In the following, we intend to identify the most influential event in the evolution of the relative per capita income by allowing for a one-time break in the trend function. It would also be interesting to see if the unit root hypothesis will be rejected in the case of the Central with a one-time change in the trend.
3
The results are not presented here to save space, but are available from the authors on request.
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There are two types of models dealing with the one-time break: the additive outlier (AO) model and the innovation outlier (IO) model (Perron, 1989). The former allows for a change in the slope, but segments of the trend function are joined at the time of the break; the change is presumed to occur rapidly. The latter allows for a change in the intercept only or a change in both the intercept and the slope at the same time; the change is assumed to occur gradually and in a way that depends on the correlation structure of the noise function. Perron (1994) argued that whenever there exists a break in the intercept, the IO model has an advantage over the AO model. Therefore, we choose IO models to test the change in the intercept only (Eq. (2)) and the change in both the slope and the intercept (Eq. (3)). The IO models are DRIt ¼ a þ bt þ gDðTB Þt þ dDUt þ rRIt1 þ
k X
qi DRIti þ et
ð2Þ
i¼1
DRIt ¼ a þ bt þ gDðTB Þt þ dDUt þ hDTt þ rRIt1 þ
k X
qi DRIti þ et
ð3Þ
i¼1
where TB is the break year; D(TB)t = 1 if t = TB + 1, and equals 0, otherwise; DUt = 1 if t > TB, and equals 0, otherwise; and DTt = t TB if t>TB, and equals 0, otherwise. We again choose kmax = 8 and use the data-dependent ‘‘t-sig’’ method described above to decide the lag length k. The issue then here is how to find the most influential break point. When inspecting Fig. 1, one may find that it is difficult to choose the most influential break point exogenously for any series. Since our purpose is to select break points that are most influential to the path of relative per capita income, we cannot use the exogenous methods to test the years, as used by others (Carlino & Mills, 1993; Perron, 1989). The data-dependent methods, as suggested by some,4 however, can help us to solve the problem. Eqs. (2) and (3), which endogenise the break point by estimating it from the data, are estimated sequentially for any possible break year TB, TB = k + 2, . . ., T 1, where T is the observation number. The most influential break year is defined as the one that minimizes tr. The results with an endogenous break point are listed in Tables 2 and 3. Here, tr is still an indicator, showing whether a time series exhibits a unit root but with different critical values from Table 1. It has been used to select the most influential break year on the evolution of relative regional incomes. Both Models (2) and (3) in Tables 2 and 3 have identified the Cultural Revolution as the most influential event in the economic development in the Central region and the economic reform as the most marked event in the West over the sample period. However, the most notable event in the East varies depending on the models chosen, the Cultural Revolution has been identified as the key event by using Model (2) and the economic reform by choosing the more general Model (3). Although the break years are not the same in all the three regions in Tables 2 and 3, all of them are located at the beginning of either the Cultural Revolution or the economic reforms. They are the two most influential and well-known events in the social and economic development history of the People’s 4
See Banerjee, Lumsdaine, and Stock (1992), Christiano (1992), and Zivot and Andrews (1992).
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Table 2 ADF tests for three regions, with a break year, allowing changes in the intercept, kmax = 8 Break Region year a
b
d
g
r
k
East 1966 0.056 (5.39) 0.004 (5.06) 0.056 ( 3.81) 0.048 (5.41) 0.636 ( 6.36)*** 8 Central 1967 0.029 (2.38) 0.004 ( 3.45) 0.069 (2.95) 0.049 ( 4.13) 0.680 ( 4.49) 8 West 1984 0.101 ( 4.23) 0.009 ( 5.77) 0.038 ( 1.69) 0.053 (3.27) 0.918 ( 5.90)** 6 The critical values for tr are 5.92 for 1%, 5.23 for 5%, and 4.92 for 10%. See Perron (1997). Values in parenthesis are asymptotic statistics. ** Represents significance at the 5% level. *** Represents significance at the 1% level.
Republic of China. The former destroyed the national production bases and lowered productivity dramatically and the latter exploited the production potential unprecedentedly. The null hypothesis of a unit root for both the East and the West is rejected again in the tests presented in Tables 2 and 3, while we are still not able to reject the null hypothesis for the Central region in either Table 2 or 3. However, it is interesting to note the trends around the break points shown in Table 3. In the East region, the estimate of b is positive, and that of h is negative and smaller than that of b in absolute value. That is, the East increased its weight in relative per capita income over the whole study period, but the increasing pace slowed down from the inauguration of the economic reform. In contrast, the estimates of b and h are both negative in the western region. This implies that the weight of relative per capita income of the West declined over the period, but the speed has accelerated (although not significantly) since the beginning of the economic reform. The break year in the West lagged 4 years behind that in the East, coinciding with the fact that economic reforms began in the East and then extended to the West. The Central region was relatively stable with an insignificant time trend before 1967, but its relative per capita income kept declining, and the regional gaps between the East and the other two regions have widened since the Cultural Revolution (1967), which was much Table 3 ADF tests for three regions, with a break year, allowing change in both intercept and slope, kmax = 8 Region
Break year
East
1980
Central
1967
West
1984
a
b
g
d
h
r
k
0.009 (0.84) 0.072 ( 1.41) 0.105 ( 4.51)
0.007 (6.25) 0.003 (0.72) 0.008 ( 5.68)
0.011 (0.78) 0.073 (3.30) 0.028 ( 1.15)
0.023 ( 2.31) 0.076 ( 4.37) 0.068 (3.54)
0.004 ( 3.78) 0.008 ( 2.02) 0.003 ( 1.43)
0.591 ( 6.32)*** 0.855 ( 5.13) 0.908 ( 5.89)**
5 8 6
The critical values for tr are 6.32 for 1%, 5.59 for 5%, and 5.29 for 10%. See Perron (1997). Values in parenthesis are asymptotic t statistics. ** Represents significance at the 5% level. *** Represents significance at the 1% level.
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Table 4 ADF tests for the eight regions of United States, kmax = 8 No break year
With a break year
Region
r
tr
k
New England Mideast Great Lakes Plains Southeast Southwest Rocky Mountains Far West
0.07 0.07 0.27 0.17 0.17 0.13 0.19 0.30
2.30 1.49 3.12 1.80 2.98 2.22 2.52 3.29 *
1 6 2 1 8 5 0 0
1940 1948 1951 1949 1940 1940 1951 1942
r
tr
k
0.20 0.52 1.61 0.69 0.51 0.36 0.49 0.65
4.53 4.01 5.32* 5.78** 6.78*** 4.08 4.44 5.39*
1 8 8 0 3 8 0 7
Source: Loewy and Papell (1996). The critical values with a break year for tr are 6.32 for 1%, 5.59 for 5%, and 5.29 for 10%. We use the asymptotic critical values from Table 1 in Perron (1997), which are larger (in absolute value) than that used by Loewy and Papell (1996). * Represents significance at the 10% level. ** Represents significance at the 5% level. *** Represents significance at the 1% level.
earlier than the inauguration of economic reforms. Moreover, the economic reform slowed down the upward pace of the East. In the meantime, the economic reform widened the regional gap measured by relative per capita income. Based on the measurement of the relative per capita income, our results on the interregional convergence are inconsistent with the recent literature on China’s economic growth and inequality. The results suggest that China’s regions have different equilibrium and two out of three converge to their steady states with a time trend. The conclusion is similar to Chen and Fleisher (1996), using provincial per capita production and cross-section models which reported that there was evidence of conditional convergence with a significant regional dummy. In contrast to China’s regional economies, the regional economies of the US display a much different pattern over the period 1929–1990. In their paper, Loewy and Papell (1996) divided the US into eight BEA regions. Annual BEA data on personal income and population for the US regions during the period 1929–1990 were employed. Since regional price indices were not available, they did not deflate regional per capita income. Additionally, since all of their income measures are already in relative (to the nation) terms, the national CPI serves no purpose. Their results showed that none of the eight regions were stationary, which implies that no region in the US converged to its unique equilibrium or to the average income level of the whole nation; while two out of three regional economies of China are stationary. To lower the possibility of failures to reject the null hypothesis of a unit root, they followed Perron (1989) and others5 allowing for a one-time break in both the shift and the trend. Their results are listed in Table 4. Even with the one-time structural change, only four out of eight US regions can 5
Such as Campbell and Perron (1991), Carlino and Mills (1993), and Loewy and Papell (1996).
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reject the unit root hypothesis at the 10% significance level. However, stationary regions of China do not change with the one-time structural change. Compared with the US regions, it seems that the regions of China are prone to forming different regional economic clubs.
5. Any regional clubs? What we can draw from the ADF tests are that the rich region becomes richer and the poor poorer. However, we still cannot conclude that China’s provinces are forming different clubs since we know nothing about the income distribution within a region. We also know little about the inequality between regions. Does the inequality between the provinces within a region or between two regions decline or widen? To answer this question, we calculate the Gini coefficients for China and its three regions from 1952 to 1997. Table 5 presents the results. In general, the income disparity in China obviously increased over the sample period, especially after the economic reforms. However, China’s three regions display many different patterns of Gini coefficients. For the East, two peaks of the disparity occurred in 1960 and 1974, and its income gap has narrowed steadily since 1974 although with some slight fluctuations. The peak inequality year in the Central region was 1963 and then the income disparity declined down with only a mild echo in the second half of the 1970s. In sharp contrast to the above two richer regions, the West shows a low Gini coefficient over the period, the Gini coefficient only reached more than 0.1 for a short period (1960–1977). It is obvious that the income discrepancy within a region either declined dramatically or kept a very low level over the economic reform period, while the inequality throughout China, as a whole nation, rose pronouncedly. The opposite direction of income difference — increasing in China as a whole and declining (or staying steady) within each of China’s regions, is beyond our expectation. The only possibility for increases in inequality in China as a whole is due to the increase in the interregional inequality. However, what we want to know further is if all the interregional inequalities between any two regions rise at the same time. Only with the knowledge of the trends of Gini coefficients, both within a region and between regions, are we able to answer the question of whether China’s provinces are reforming into different clubs. The three regions are combined into three groups, the East and the West, the East and the Central, and the Central and the West. We know that the inequality within a region has declined or stayed a relatively stable at a low level over the period of the economic reforms, so the rising inequality within a group implies the widening of inequality between the related two regions, or the rising of interregional inequality. The series of Gini coefficients for the combined groups of two regions are listed in the last three columns in Table 5. The largest income gap at the provincial level appears in the group of the East and the West. There are three peak years for inequality in this group, they are 1960, 1976, and 1997. The Gini coefficient rose steadily following the beginning of the economic reforms except for a mild decline from 1978 to 1983. Similarly, the income gap at the provincial level in the group of the East and the Central rose dramatically over the period; the inequality reached its two peaks in 1960 and 1994. The income gap slightly narrowed in the group from 1978 to 1983, but has widened considerably
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Table 5 Gini coefficients in China and China’s regions
Year
China
East
Central
West
East and Central
1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995
0.153 0.166 0.155 0.153 0.159 0.166 0.184 0.217 0.248 0.206 0.191 0.201 0.190 0.182 0.178 0.170 0.203 0.202 0.201 0.196 0.189 0.198 0.221 0.217 0.234 0.215 0.201 0.194 0.198 0.198 0.195 0.191 0.195 0.196 0.200 0.204 0.212 0.210 0.209 0.218 0.227 0.236 0.245 0.249
0.137 0.191 0.172 0.163 0.184 0.200 0.212 0.241 0.278 0.205 0.187 0.199 0.192 0.191 0.189 0.168 0.183 0.197 0.211 0.208 0.194 0.205 0.235 0.226 0.226 0.212 0.199 0.199 0.200 0.193 0.183 0.185 0.191 0.194 0.198 0.197 0.196 0.193 0.193 0.188 0.183 0.177 0.177 0.174
0.119 0.112 0.132 0.122 0.129 0.119 0.155 0.181 0.176 0.161 0.155 0.183 0.159 0.149 0.141 0.124 0.133 0.135 0.136 0.132 0.116 0.125 0.135 0.137 0.140 0.137 0.144 0.137 0.132 0.121 0.127 0.117 0.121 0.111 0.111 0.109 0.111 0.110 0.112 0.116 0.107 0.095 0.089 0.082
0.079 0.061 0.070 0.080 0.070 0.065 0.053 0.088 0.135 0.153 0.137 0.127 0.121 0.100 0.116 0.114 0.118 0.129 0.106 0.102 0.112 0.116 0.134 0.128 0.154 0.113 0.079 0.073 0.078 0.079 0.078 0.073 0.069 0.076 0.081 0.078 0.087 0.086 0.088 0.088 0.088 0.085 0.085 0.087
0.130 0.160 0.158 0.147 0.163 0.170 0.194 0.221 0.244 0.192 0.179 0.196 0.182 0.178 0.172 0.152 0.164 0.177 0.185 0.181 0.168 0.179 0.204 0.201 0.208 0.199 0.198 0.192 0.198 0.188 0.185 0.181 0.187 0.189 0.193 0.198 0.207 0.205 0.206 0.215 0.221 0.226 0.231 0.231
East and West
Central and West
0.162 0.156 0.183 0.136 0.164 0.129 0.163 0.136 0.169 0.128 0.176 0.132 0.182 0.156 0.225 0.183 0.270 0.203 0.219 0.191 0.197 0.182 0.203 0.193 0.198 0.175 0.190 0.161 0.191 0.157 0.187 0.158 0.233 0.197 0.232 0.174 0.228 0.165 0.226 0.158 0.222 0.150 0.232 0.156 0.260 0.166 0.253 0.162 0.273 0.179 0.247 0.155 0.222 0.137 0.216 0.130 0.221 0.125 0.226 0.127 0.219 0.130 0.219 0.123 0.221 0.123 0.224 0.116 0.229 0.118 0.232 0.114 0.236 0.113 0.234 0.111 0.232 0.112 0.235 0.113 0.243 0.109 0.251 0.102 0.261 0.103 0.265 0.105 (continued on next page)
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Table 5 (continued)
Year
China
East
Central
West
East and Central
East and West
Central and West
1996 0.250 0.169 0.078 0.087 0.226 0.267 0.110 1997 0.252 0.168 0.079 0.088 0.226 0.269 0.112 The Gini coefficients for China are derived from per capita mean incomes at the provincial level. The Gini coefficients for the three regions are also derived from provincial level per capita incomes within each of the regions. Source: Authors’ calculation.
since then. A trivial but meaningful symbol is that the Gini coefficient has declined slightly since 1995. It may imply that the inequality in this group has reached its highest point and will be relatively stable in the near future. In striking contrast to our expectation, the inequality in the group of the Central and the West declined evidently over the period. The Gini coefficient climbed to its peak in 1960 and stayed relatively high over the period 1961–1977. It then declined steadily after the economic reforms. There are two possible explanations in the decrease of Gini coefficient in this group: It may be attributable either to declining inequality within the region, or to the narrowing gap between the two regions. For a robust and convincing conclusion, further study is needed. The analyses of the Gini coefficients within or between China’s three regions imply that, to a large extent, inequality relates to and is influenced by dramatic political events, severe natural disasters, and economic instability. In 1960, with the beginning of a serious natural disaster and the withdrawal of aids by the former Soviet Union, inequality reached its historic peak in all the groups, the Gini coefficient for the West nearly doubled from the previous year. Inequality increased significantly over the Cultural Revolution period (1966–1976) in the group of the East and the West, and the group of the Central and the West. Nevertheless, there is no evidence from that period to show that China’s provinces were re-forming into different income clubs. After the economic reforms, the evolution of Gini coefficients showed a much more stable picture with an obvious trend. The intraregional inequality dropped significantly in the East and the Central regions and stayed a low level in the West. However, inequality rose dramatically between the East and the Central and between the East and the West. Referring to the point made previously (Sections 3 and 4 of this paper) that the series of relative per capita income of the East and the West were stationary, it is safe to say that China’s provinces were re-forming into different income clubs over the reform period. That is, the eastern provinces were forming the rich club while the provinces from the West were forming the poor club. It is easy to reject the possibility that the provinces from the Central region were sliding into the rich one. However, there is no evidence that the Central region was joining the poor club or that it was forming its own income club. We also use another two indices to measure the income inequality within a region and between regions. They are (1) the ratio of per capita income between two regions, which measures the per capita income difference between two regions, (interregional inequality), and (2) the coefficient of variation, which measures the dispersion of per capita income across
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Fig. 2. Ratios of per capita income between regions.
provinces within a region. The results of those two indices, as presented in Figs. 2 and 3, clarify and enhance our discussion about the formation of income clubs. All the ratios were relatively steady (with some slight fluctuations) before the Cultural Revolution (the first half of 1960s). The ratios of per capita income between the East and the other two regions rose rapidly after the Cultural Revolution, showing that interregional inequality between the East and the Central or between the East and the West rose considerably. However, the ratio of per capita income between the Central and the West was relatively stable and close to 1, which suggests the interregional income difference between the Central and the West regions was small and stayed relatively steady over the whole study period, 1952–1997. On the other hand, the interregional coefficient of variation fluctuated increasingly in the prereform period, but declined significantly in all the three
Fig. 3. Dispersion of per capita income within a region.
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regions after the economic reforms, implying that interregional inequality indeed went down in the reform period. Both the ratios of per capita income between regions and the dispersion of per capita income within a region tell a similar story as illustrated by the Gini coefficient analysis. That is, the gaps within a region declined dramatically and the gaps between the East and the Central and between the East and the West widened pronouncedly during economic reforms. However, the gap between the Central and the West was small and relatively steady. This leads us to conclude that China’s provinces were forming distinct clubs after the economic reforms.
6. Conclusion This paper employs time series techniques to investigate the question of China’s regional per capita income convergence. Without consideration of the structural break, the unit root hypothesis is rejected in two of the three regions in China compared with none of the eight regions in the US. With a break point in the structure, the unit root hypothesis is rejected in four regions in the United States while no changes occurs in China’s case. We are able to identify the big shocks on the relative regional per capita income by allowing for a break in the structure. The economic reforms and the Cultural Revolution were the most important events that influence relative regional per capita income over the period of 1952–1997. The former slowed down the upward rate of the East but accelerated the downward rate of the West in terms of relative regional per capita income. The latter triggered the decline of the Central region. The regional gap between the East and the others widened much earlier than the beginning of economic reforms, however, economic reforms worsened the gap further. With the strong time trend (with or without a structural break), the series of relative per capita income of the East and the West are stationary. This implies that China’s regions, especially the East and the West, were converging to their own specific steady states. In other words, China’s provinces were re-forming into different income clubs. The decline in the Gini coefficient within a region and the increases in the Gini coefficient within a regional group (the East and the West or the East and the Central) support our arguments. Furthermore, the ratio of per capita income between regions is used to measure interregional income differences and the coefficient of variation of per capita income is used to measure the income dispersion within a region. Using those two indices has enhanced our conclusion from the previous analysis. However, further study is needed to answer the question that if the central provinces are joining the poor club or will struggle to form their own club.
Acknowledgments We thank the editor and an anonymous referee for several helpful comments and suggestions. The remaining errors and omissions are our responsibility alone.
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Appendix A The East (coastal) includes Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Shandong, Fujian, Guangdong, Guangxi, Hainan. The Central consists of Shanxi, Inner Mongolia, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, Hunan. The West includes Sichuan, Guizhou, Yunnan, Tibet, Shaaxi, Gansu, Qinghai, Ningxia, Xinjiang.
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