China's regional convergence in panels with multiple structural breaks

Abstract

This study investigates the existence of regional convergence of per capita outputs in China from 1952 to 2004, particularly focusing on considering the presence of multiple structural breaks in the provincial-level panel data. First, the panel-based unit root test that allows for the occurrence of multiple breaks at various break dates across provinces is developed; this test is based on the p-value combination approach suggested by Fisher (1932). Next, the test is applied to China's provincial real per capita outputs to examine the regional convergence in China. To obtain the p-values of unit root tests for each province, which are combined to construct the panel unit root test, this study assumes three Data Generating Processes (DGPs): a driftless random walk process, an Autoregressive Moving Average (ARMA) process and an Autoregression (AR) process with cross-sectionally dependent errors in Monte Carlo simulation. The results obtained from this study reveal that the convergence of the provincial per capita outputs exists in each of the three geographically classified regions–the Eastern, Central and Western regions–of China.

Acknowledgements

We would like to thank Chen Kuang-hui, two anonymous referees and the seminar participants at Yokohama Symposia in 2007 for their helpful comments.

Notes

¹ Bernard and Durlauf (1995), Oxley and Greasley (1995), Hobijn and Franses (2000), Pesaran (2004), Lim and McAleer (2004), etc.

² The studies on regional growth in China which have not adopted the nonstationary time series or panel techniques are Chen and Fleisher (1996), Jian et al. (1996), Gundlach (1997), Raiser (1998) and Weeks and Yao (2003).

³ Carlino and Mills (1993), Greasley and Oxley (1997) and Li and Papell (1999) have examined convergence using unit root tests which can deal with a breaking time series.

⁴ This classification of provinces is nearly identical to that of Zhang et al. (2001), but the aggregation of provincial series is not conducted in this article. The details will be described in the subsection ‘Data’.

⁵ Studies on multi-country convergence often use the deviation from the cross-sectional mean and look into its nonstationarity (Evans and Karras, 1996; Lee et al., 1997; Evans, 1998), which will be described in the later sections.

⁶ In general, existing panel-based unit root tests which allow for breaks may be too restrictive for empirical applications based on the convergence hypothesis. Specifically, these tests are based on two major assumptions: the presence of a linear time trend in a series and the absence of cross-sectional dependence between error terms in the Data Generating Process (DGP). In the case of the former assumption, the tests defined under the DGP with a time trend are not directly applicable to investigations on convergence. In these investigations, the difference between two series or the deviation from the mean value of all cross-sectional units is usually used, and the difference or the mean deviation is often assumed to be zero mean stationary when absolute convergence exists, or level stationary when conditional convergence exists (Bernard and Durlauf, 1995; Evans and Karras, 1996). Thus, these analyses require tests which are defined under DGPs without a time trend, instead of DGPs with a time trend. In the case of the latter assumption, cross-sectional correlation between error terms is a major issue in dynamic panel estimation because neglecting this correlation may lead to a bias of an estimated parameter and increase its variance (O’Connell, 1998; Phillips and Sul, 2003).

⁷ Banerjee and Carrion-i-Silvestre (2006) have dealt with several issues on structural breaks and cross-sectional dependence in a nonstationary panel framework.

⁸ Evans and Karras (1996) have postulated that convergence is absolute if has a zero mean for all i, or conditional if has a nonzero mean for some i. According to Evans and Karras, when all the series of are stationary and have some structural breaks, convergence can be considered as being absolute if has a zero mean for all i after the last break date, or conditional if has a nonzero mean for some i after the last break date.

⁹ This proof is available on request.

¹⁰ Although Becker (1997) compared the performance of 16 p-value combination tests, including the Fisher test, he concluded that there was no test that was the most accurate or effective.

¹¹ To remove cross-sectional dependence in the panels with structural breaks, the common factor model is also applicable. See Banerjee and Carrion-i-Silvestre (2006).

¹² The chain index of the per capita GRP is computed as , where is the chain index of the per capita GRP. Further, Y _t is the index of the per capita GRP (preceding year = 100), and Y ₅₂ is set to 100.

¹³ The quality of official Chinese statistics has been argued by many researchers (e.g. Chow, 1986; Rawski, 2001; Holz, 2006). Currently, it is widely recognized that official Chinese data at the national and provincial levels have certain inconsistencies and miscalculations due to factors such as the lack of technical personnel for the collection of statistics and political pressure to exaggerate statistics at the lower levels. However, our results, which will be presented in the subsection ‘Test results and discussion’, remain valid as long as the stochastic properties of the series used in this article do not change even if there are certain inaccuracies in them.

¹⁴ The Eastern region has the following 10 provinces: Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Shandong, Fujian and Guangdong. The Central region includes the following nine provinces: Shanxi, Inner Mongolia, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei and Hunan. The Western region consists of the following 10 provinces: Guangxi, Chongqing, Guizhou, Yunnan, Tibet, Shaanxi, Gansu, Qinghai, Ningxia and Xinjiang.

¹⁵ For example, for the series (in logarithms) in 2004, the difference between the series of Guangxi and Hebei (the closest series among other Eastern provinces) is 0.87. In contrast, the difference between the series of Guangxi and Yunnan (the closest among the Western provinces) is 0.09. In addition, the series of some other provinces in the Western region (Guizhou, Qinghai and Xinjiang) are also close to that of Guangxi.

¹⁶ With regard to these issues, Perron (1989), Leybourne et al. (1998) and Im et al. (2005) have revealed that ignoring breaks in a single time series or panel data can lead to an erroneous inference in a test, while O’Connell (1998) and Phillips and Sul (2003) have argued that estimated parameters tend to be biased by the presence of cross-sectionally correlated errors.

¹⁷ We have also obtained test results for cases in which the mean deviations of log per capita outputs display a linear time trend for Liaoning in the Eastern region and Heilongjiang and Hubei in the Central region. Since these results are quite similar to those tabulated in Table 3, they have not been reported but are available on request.

¹⁸ All the test results discussed in this subsection have been omitted but are available on request.

¹⁹ In addition, the sample consisting of whole provinces has been tested; moreover, a significant rejection of the unit root null hypothesis has been obtained. However, we believe that further information (e.g. the homogeneity of provinces classified into different regions) is needed to arrive at a conclusion.