Structural breaks, rural transformation and total factor productivity growth in China

Abstract

This paper carries out an empirical investigation into the contribution of rural transformation, which can produce efficiency gains over and above those associated with technical progress, to total factor productivity in China during the post-reform period 1980–2010. For the first time for China, the roles of rural transformation and technical progress are examined whilst structural breaks are taken into account. We employ Bai and Perron (Econometrica 66:47–68, 1998; J Appl Econom 18:1–22, 2003a; Econom J 6:72–78, 2003b) methods which allow for multiple structural breaks at unknown dates and can be applied for both pure and partial structural changes. We also evaluate the robustness of our results by employing alternative production functions and two capital series. Two structural breaks near the Tiananmen Square incident in 1989 and the implementation of further reforms and opening-up measures in 1995 were identified for both capital series. We found the contribution of rural transformation to total factor productivity to be significant and positive across all regimes. However, its importance to the growth of total factor productivity has been declining over time, while that of technical progress has been increasing.

Appendices

Appendix 1: CES and VES production functions with rural transformation

The CES production function assumes varied returns to scale and an elasticity of substitution different from unity. Following Brown and De Cani (1963), CES production function takes the form:

$$ Y = A[\delta K^{ - \rho } + (1 - \delta )L^{ - \rho } ]^{ - \varphi /\rho } ; $$

(9)

where ρ is the substitution parameter that determines the elasticity of substitution σ. δ is the distribution parameter; for any given value of σ (or ρ), δ determines the functional distribution of income. φ is the returns to scale parameter. The elasticity of substitution (σ) is given by σ = 1/(1 + ρ). When φ = 1 and ρ = 0, Eq. (9) collapses to the Cobb–Douglas production function.

In contrast to CES production function, the VES production function assumes that the elasticity of substitution is a linear function of capital over labor ratio (Revankar 1971). We consider the following VES production function:

$$ Y = AK^{\theta \varphi } [L + \eta \theta K]^{(1 - \theta )\varphi } ; $$

(10)

where φ is the returns to scale parameter. Both θ and η determine the capital share and the labor share of income. The elasticity of substitution is derived as σ = 1 + η(K/L). Hence σ varies linearly with the capital-labor ratio around unity. If φ = 1 and η = 0, Eq. (10) collapses to the Cobb–Douglas production function.

Similar to Eq. (2), we decompose total factor productivity into net factor productivity and rural transformation for Eqs. (9) and (10), and then by taking natural logarithms we obtain Eqs. (7) and (8) respectively:

$$ \ln Y = c + \beta t + \gamma \ln RT - (\varphi /\rho )\ln (\delta K^{ - \rho } + (1 - \delta )L^{ - \rho } ) $$

(7)

$$ \ln Y = c + \beta t + \gamma \ln RT + \varphi \theta \ln K + \varphi (1 - \theta )\ln (L + \eta \theta K) $$

(8)

Appendix 2: Data sources and variable measurement

The main data sources are China Statistical Yearbook (CSY) 2011 of China National Statistical Bureau, Chow and Li (2002) and Bai et al. (2006a). Sample period is 1980–2010.¹⁴

• 1. Real GDP of China (Y): it is constructed by adjusting nominal GDP using GDP deflator. Data of nominal GDP is collected from CSY 2011. The GDP Deflator is calculated using the same methodology as Jun (2003).¹⁵

• 2. Total Number of Employed Persons (L): data is collected from CSY 2011.

• 3. Rural Transformation (RT) (%): it is defined as the ratio of employed persons by non-agricultural sectors (which include industrial and services sectors) to total number of employed persons. A higher percentage implies a higher level of rural transformation, i.e. proportionally fewer farmers work in the field. Data of the employed persons by industrial and service sectors is collected from CSY 2011.

• 4. Real Capital Stock (K1): it is obtained by extending the real capital series of Chow and Li (2002) from 1952–1998 to 1952–2010 using same methods. Details of the methods can be found at Chow and Li (2002) and hence are not repeated here. Data needed for our extension include real GDP, GDP deflator, real consumption, real net export and depreciation. Data for nominal net exports and nominal consumption are from CSY 2011 and these are adjusted by the GDP deflator and Consumer Price Index (obtained from CSY 2011) respectively to obtain the real values. Total depreciation is the sum of provincial depreciation, data of which is from various issues of CSY.

• 5. Real Capital Stock (K2): it is obtained by extending the real capital series of Bai et al. (2006a) from 1952–2005 to 1952–2010 using same methods. For detailed explanation of these methods, please refer to Bai et al. (2006a). Data needed for our extension include investment in construction and installation, investment in equipment and instruments, price index of investment in construction and installation and price index of investment in equipment and instruments. All data are collected from CSY 2011.