Environmentally sensitive productivity growth and its decompositions in China: a metafrontier Malmquist–Luenberger productivity index approach

Abstract

The metafrontier Malmquist–Luenberger (MML) index was used to measure the environmentally sensitive productivity and analyze its decompositions on China’s regional productivity growth. Using the MML index, the environmental undesirable outputs and regional heterogeneities were analyzed simultaneously. The empirical results showed that although China had accomplished rapid growth rate of GDP over the last decade, environmentally sensitive productivity has been relatively constant with a low growth rate. The productivity growth is driven mainly by technology innovation. Regarding the regional differences, the eastern area showed the highest productivity growth, whereas the central and western areas showed productivity deterioration. Some implications and suggestions on the regional differences are proposed based on the empirical results.

Appendix: Estimating the trade-off factor

The trade-off factor is the slope of the environmental Kuznets curve (EKC). The estimation model is as follows:

$$\begin{aligned} \mathrm{per} {\mathrm{CO}_{2}}_{it} =\beta _0 +\beta _1 \mathrm{per}\mathrm{GDP}_{it} +\beta _2 \mathrm{per}\mathrm{GDP}_{it} ^{2}+\varepsilon _{it}, \end{aligned}$$

(10)

where per$\hbox {CO}_{2}$ is per capita $\hbox {CO}_{2}$ emission (unit: kg $\hbox {CO}_{2}$ per person); perGDP is per capita GDP (unit: RMB per person); $i$ and $t$ represent region and time, respectively. Since our sample is balanced panel data, the first step to estimation is to select a suitable estimation model for panel data regression. The Hausman test result signifies that the fixed effects model is superior to the random effects model (test statistics 218.9, degrees of freedom 2, critical value at the 1 % significance level 9.21). The fixed effects model estimation result is listed in Table 10, where the within estimator is used in estimating the fixed effects model.

Table 10 Estimation results of environmental Kuznets curve

The estimated parameter ${\hat{\beta }}_1$ and ${\hat{\beta }}_2$ is used for calculating trade-off factor of region $i$ at time $t$, $\beta _{it}$, as follows:

$$\begin{aligned} \beta _{it} =\frac{\partial \mathrm{per}{\mathrm{CO}_{2}}_{it}}{\partial \mathrm{perGDP}}=\hat{{\beta }}_1 +2\hat{{\beta }}_2 \mathrm{perGDP}_{it} \end{aligned}$$

(11)

Since $\mathrm{perGDP}_{it}$ in Eq. (11) is different across region and over time, the trade-off factor varies across region and over time.