_{1}

^{*}

This paper focuses on examining differential convergence patterns in productivity growth in China. Our empirical analysis shows that the Chinese provinces exhibit absolute divergence and then absolute convergence respectively during 1990-2000 and 2000-2010. In addition, absolute convergence is present during 1985-1995 and 2000-2010 in the primary sector and during 1995-2010 in the secondary sector. Our regressions also show that either for the overall regional economy, or for any individual sector, growth in labor productivity exhibits strong convergence. Besides the convergence trends, we also find that the secondary and tertiary sectors have grown significantly faster than the primary sector.

China’s post-1978 reform has been widely regarded as a colossal success. Since 1978, the Chinese economy has grown very rapidly, making China one of the world’s fastest growing countries. Extrapolations suggest that the absolute size of the Chinese economy may be larger than that of the United States in two or three decades to come. By 2025, China is likely to become the world’s largest economic power by almost any measure [

The substantial disparities in incomes and growth rates in China attract the attention of researchers. Some argue that per capita incomes have been diverging across different regions as China is opened up greater foreign trade and foreign investment. Others, however, maintain that many large differences across the regions have declined over time and that poor regions have grown faster than rich ones since the initiation of China’s reform. For example, [

This paper focuses on examining differential growth and convergence in per worker value added (labor productivity) across different regions and sectors in China. Existing literature tends to suffer from data shortage, poor data quality, limited sample period, and inappropriate methodology used, all of which may significantly bias the conclusions reached. Aiming to provide a more comprehensive and realistic picture of the growth and convergence patterns of the regions and sectors, this paper uses consistent regional and sectoral data to analyze the true tendency of growth and convergence in China over the period of 1985-2010.

The application of the Ramsey growth model as the theoretical framework in this study is motivated by one major fact, which is that the Solow growth model [

The rest of the paper is organized as follows. In Section 2, we present the theoretical framework as the foundation for our subsequent empirical analysis. In Section 3, we set up our econometric model and discuss related issues concerning the variables. In Section 4, we present and analyze our regression results. Finally, conclusions are made in Section 5.

To build the theoretical foundation for our subsequent empirical analysis in this study, in this section we follow the study of [

We assume that aggregate output is produced with three inputs, that is, two types of capital (say, physical capital and human capital), and a non-reproducible factor, which is raw labor. The production function is assumed to be a Cobb-Douglas form of

where

where we work in terms of per unit of effective labor and, accordingly, define

The households own the three production factors and rent them to firms at competitive rental prices. Firms pay a proportional tax at rate ^{1}

where

These conditions imply that

Infinitely lived households maximize their lifetime utility, which is given by

where

time ^{2}. The households own the physical and human capital and also have the net stock of debt,

where ^{3}. Inserting conditions in (4) into the budget constraint in

(6) gives us

Therefore, households maximize utility in (5), subject to (7), given

closed economy,

of a broad capital stock,

where

The Euler equation is

Following basically the same procedure as in a standard Ramsey model, we can derive the steady-state situation as

and

where

Linearizing around the steady state, the adjustment process from an initial position toward the steady state can be described by

where

closed Chinese provinces (no capital mobility across regional borders), the speed of convergence,

where

If otherwise we allow for partial capital mobility across provincial borders, that is, we assume that the amount of debt, ^{4}, it can be shown that with this setup, the model predicts a speed of convergence that can be expressed as

where

same value that would arise in a closed province if it had the broad capital share

broad capital share that is less than

of convergence than the corresponding closed province.

Equation (11) above can be rewritten in per capita (per unit of labor, or per worker) terms. Noting that

in which

We can rewrite Equation (14) in conventional notations of a panel data specification as

where

and

As

The technology shifter

provinces in the current study), so the term

province heterogeneity

across economies. As a result, the term

term

The main difficulty that confronts us in our econometric analysis is that parameters such as

In view of the tradeoff discussed above, we finally opt to assume that

stant value of it for any given province. In fact, the very reason to include the term

regions and over time. Therefore, we opt to subsume the term

idiosyncratic error

With the considerations above, Equation (15) reduces to a regression of (the log of) the current per capita output on (the log of) the initial per capita output, the time-constant province heterogeneity term and a time-va- riant intercept.

Our sample includes 31 provincial-level regions (provinces for short) in China over the period of 1985-2010^{5}. Relevant data for our regression analysis can be obtained from the various official publications of the National Bureau of Statistics of China^{6}. We run both cross sectional and panel data regressions based on the model in (15). In our panel data regressions to come, we partition the entire sample length into five equally spaced time spans, namely, 1985-1990, 1990-1995, 1995-2000, 2000-2005 and 2005-2010, and employ four time dummy variables (along with a common intercept) to take account of secular changes across different time spans (sub- periods).

We first run cross section regressions. Our baseline estimation results are summarized in

Next, we examine “club convergence” across the provinces by adding two dummy variables, “East” and “West”, to capture the geographical locations of the provinces. “East” equals one if the province belongs to the eastern zone and zero otherwise, and “West” equals one if the province belongs to the western zone and zero otherwise. China is located in the east of Asia. There are oceans to the east and southeast of China, but then there is a gigantic desert in its far north and west and a very high mountain range—the highest in the world—in its southwest. Historically, differences in degrees of regional openness to the outside world can be explained to a large extent by the distances of the regions to the southeast coast of the country. The whole mainland of China is thus divided into three zones—the eastern coastal zone, the central zone and the western zone. The three big zones exhibit systematic differences not only in aspects such as climate and resource endowment, but also in aspects such as culture, policy and exposure to foreign trade and FDI. If all or some of these aspects can be regarded as elements to be included in the technology shifter

We then rerun the relevant regressions by sector. That is, we run regressions that are parallel to those above, but based on data of each individual sector rather than the overall regional economy. We break up the regional economy into three sectors, i.e. the primary sector, the secondary sector and the tertiary sector. The primary sector (denoted “Sector 1”) refers to agriculture, forestry, animal husbandry and fishery and services in support of these industries. The secondary sector (denoted “Sector 2”) refers to mining and quarrying, manufacturing, production and supply of electricity, water and gas, and construction. The tertiary sector (denoted “Sector 3”) refers to all other economic activities not included in the primary or secondary industries. Results in

However, we should note that Equation (14) above is associated with the concept of conditional convergence, as the specification contains a region heterogeneity term that conditions the steady state. By definition, conditional convergence means each region convergences to its own steady state. In

Further, to compare differences in growth rates between different sectors, we now shift to another approach: we pool all the province-sector pairs together as the sample points and use a Least Squares with Dummy Variables (LSDV) method where dummy variables are used to represent each province and each sector. As we have 31 provinces and three sectors, we end up having 93 cross sectional sample points. The dependent variable

Single cross section regressions (OLS) | |||||
---|---|---|---|---|---|

Dependent variable: | |||||

1985-2010 | 1985-1995 | 1990-2000 | 1995-2005 | 2000-2010 | |

1.057 (0.101) | 1.044 (0.103) | 1.264^{*} (0.064) | 1.029 (0.057) | 0.839^{*} (0.071) | |

_cons | 3.004 (0.758) | 1.259 (0.768) | –0.661 (0.519) | 0.843 (0.520) | 2.883 (0.681) |

0.7898 | 0.7810 | 0.9305 | 0.9174 | 0.8275 | |

obs | 31 | 31 | 31 | 31 | 31 |

Notes: Standard errors are in parentheses. An asterisk ^{*} denotes that the estimated coefficient on

Single cross section regressions (OLS) | |||||
---|---|---|---|---|---|

Dependent variable: | |||||

1985-2010 | 1985-1995 | 1990-2000 | 1995-2005 | 2000-2010 | |

0.929 (0.124) | 0.783^{*} (0.102) | 1.076 (0.071) | 1.041 (0.094) | 0.901 (0.114) | |

East | 0.230 (0.120) | 0.390^{*} (0.098) | 0.230^{*} (0.068) | 0.015 (0.101) | –0.091 (0.135) |

West | 0.035 (0.111) | –0.018 (0.091) | –0.030 (0.058) | 0.041 (0.079) | 0.006 (0.106) |

_cons | 3.865 (0.924) | 3.078 (0.761) | 0.789 (0.571) | 0.714 (0.833) | 2.322 (1.067) |

0.8169 | 0.8741 | 0.9560 | 0.9182 | 0.8308 | |

obs | 31 | 31 | 31 | 31 | 31 |

Notes: Standard errors are in parentheses. An asterisk ^{*} denotes that the estimated coefficient on

Single cross section regressions (OLS) | |||||
---|---|---|---|---|---|

Dependent variable: | |||||

1985-2010 | 1985-1995 | 1990-2000 | 1995-2005 | 2000-2010 | |

(i) | 0.936 (0.144) | 1.262^{*} (0.103) | 0.914 (0.092) | 0.873 (0.071) | 0.793^{*} (0.096) |

(ii) | 0.808 (0.251) | 0.941 (0.187) | 1.362 (0.189) | 0.664^{*} (0.152) | 0.636^{*} (0.143) |

(iii) | 1.378 (0.229) | 1.072 (0.205) | 1.344 (0.187) | 0.973 (0.098) | 0.886 (0.117) |

obs | 31 | 31 | 31 | 31 | 31 |

Notes: Standard errors are in parentheses. An asterisk ^{*} denotes that the estimated coefficient on

Single cross section regressions (OLS) | |||||
---|---|---|---|---|---|

Dependent variable: | |||||

1985-2010 | 1985-1995 | 1990-2000 | 1995-2005 | 2000-2010 | |

(i) | 0.702 (0.174) | 1.093 (0.122) | 0.725 (0.099) | 0.783^{*} (0.097) | 0.694^{*} (0.141) |

(ii) | 0.774 (0.279) | 0.722 (0.171) | 1.257 (0.219) | 0.588 (0.201) | 0.713 (0.173) |

(iii) | 0.997 (0.240) | 0.569^{*} (0.187) | 1.074 (0.271) | 0.924 (0.169) | 0.696 (0.169) |

obs | 31 | 31 | 31 | 31 | 31 |

Notes: Standard errors are in parentheses. An asterisk ^{*} denotes that the estimated coefficient on

Panel data regressions (FE) | ||||
---|---|---|---|---|

Dependent variable: | ||||

Overall | Sector 1 | Sector 2 | Sector 3 | |

0.410^{*} (0.084) | 0.403^{*} (0.094) | 0.508^{*} (0.097) | 0.335^{*} (0.087) | |

0.9878 | 0.9668 | 0.9729 | 0.9694 | |

0.9917 | 0.9840 | 0.9492 | 0.9810 | |

0.9163 | 0.8836 | 0.9506 | 0.8921 | |

obs | 155 | 155 | 155 | 155 |

Notes: Standard errors are in parentheses. An asterisk ^{*} denotes that the estimated coefficient on

is then the log of per worker value added in sector

Next, in the regressions in

From all the regressions above, we see that there is very little evidence for overall region-wide absolute convergence across the Chinese provinces. However, our empirical results provide strong evidence for conditional convergence. This is not surprising as our model above pertains to the case of conditional convergence, in which each economy is expected to converge to its own balanced growth path (steady state). Since different economies

Cross section regressions (OLS) | |||||
---|---|---|---|---|---|

Dependent variable: | |||||

1985-2010 | 1985-1995 | 1990-2000 | 1995-2005 | 2000-2010 | |

0.588^{*} (0.161) | 0.892 (0.114) | 0.463^{*} (0.136) | 0.582^{*} (0.122) | 0.545^{*} (0.120) | |

Sector 2 | 1.145^{*} (0.239) | 0.184 (0.169) | 1.225^{*} (0.192) | 1.162^{*} (0.188) | 0.982^{*} (0.229) |

Sector 3 | 0.748^{*} (0.191) | 0.231 (0.135) | 0.963^{*} (0.179) | 0.764^{*} (0.161)) | 0.572^{*} (0.193) |

0.9606 | 0.9704 | 0.9626 | 0.9655 | 0.9642 | |

obs | 93 | 93 | 93 | 93 | 93 |

Notes: Standard errors are in parentheses. An asterisk ^{*} denotes that the estimated coefficient on

Cross section regressions (OLS) | |||||
---|---|---|---|---|---|

Dependent variable: | |||||

1985-2010 | 1985-1995 | 1990-2000 | 1995-2005 | 2000-2010 | |

1.012 (0.115) | 1.135 (0.090) | 1.078 (0.081) | 0.853^{*} (0.060) | 0.778^{*} (0.068) | |

Sector 2 | 0.535^{*} (0.185) | –0.166 (0.145) | 0.396^{*} (0.127) | 0.765^{*} (0.107) | 0.551^{*} (0.145) |

Sector 3 | 0.269 (0.154) | –0.044 (0.121) | 0.196 (0.120) | 0.430^{*} (0.096) | 0.213 (0.127) |

0.8852 | 0.8935 | 0.9257 | 0.9388 | 0.9132 | |

obs | 93 | 93 | 93 | 93 | 93 |

Notes: Standard errors are in parentheses. An asterisk * denotes that the estimated coefficient on

Cross section regressions (OLS) | |||||
---|---|---|---|---|---|

Dependent variable: | |||||

1985-2010 | 1985-1995 | 1990-2000 | 1995-2005 | 2000-2010 | |

1.286 (0.052) | 1.058 (0.039) | 1.262 (0.041) | 1.179 (0.041) | 0.970 (0.036) | |

0.8712 | 0.8899 | 0.9140 | 0.8999 | 0.8900 | |

obs | 93 | 93 | 93 | 93 | 93 |

Notes: Standard errors are in parentheses. An asterisk ^{*} denotes that the estimated coefficient on

(provinces) may have vastly different balanced growth paths, we cannot reasonably expect that all provinces are converging to the same, unified growth path.

As a byproduct, we estimate the individual province effects (the estimated coefficients on the province dummies) in our regressions in ^{7}. If we run regressions by substituting the estimated province effects for the zone dummies in

Another important result is that from

The substantial disparities in incomes and growth rates in China attract the attention of researchers. This paper focuses on examining differential growth and convergence in per worker value added (labor productivity) across different regions and sectors in China. Aiming to provide a more comprehensive and realistic picture of the growth and convergence patterns of the regions and sectors, this paper uses consistent regional and sectoral data to analyze the true tendency of growth and convergence in China over the period of 1985-2010. Our regression analysis shows that, in terms of overall regional growth of per worker output, the Chinese provinces exhibited absolute divergence and then absolute convergence respectively during the two consecutive decades 1990-2000 and 2000-2010. When we look closer and break up the overall regional growth into growth in the individual sectors, we find that during the periods 1985-1995 and 2000-2010 growth in the primary sector displayed a trend of absolute convergence across the Chinese provinces, and that during 1995-2010 growth in the secondary sector exhibited a trend of absolute convergence. In terms of conditional convergence, our regressions show that either for the overall regional economy, or for any individual sector, growth in labor productivity (value added per worker) exhibits strong convergence. In addition to the convergence trends, we also find that the secondary and tertiary sectors have grown significantly faster than the primary sector.

The author thanks the anonymous reviewers and the editors of the Journal for their helpful comments and suggestions.