## 3 Methods and Data
### Data
Desirable output is measured by the industrial output of industrial enterprises above a designated size in the manufacturing industry. Since energy consumption is an obvious industrial intermediate input, industrial output is used as the desirable output. Since 2012, the industrial output data of China's manufacturing sub-sectors have not been released. In this study, the industrial added value rate (industrial added value/total industrial output value) is used to estimate the industrial output of China's manufacturing sub-sectors. First, we used the year-on-year growth rate of industrial added value to calculate the industrial added value of the manufacturing industry after 2007. Second, using the 2012 China Input-Output Table and 2017 China Input-Output Table to calculate the industrial added value rate of the manufacturing sub-sectors in 2012 and 2017, it is found that the average change in the value-added rate of the 26 manufacturing sub-sectors during the 5 years is 2.5%. It can be observed that the added value rate of the manufacturing industry is relatively stable in the short term, so it is reasonable to use the linear interpolation method to supplement the data from 2013 to 2016. Finally, the industrial output of the 26 manufacturing sub-sectors during this period are estimated by multiplying the industrial value added and the industrial added value rate. The price adopts the 2003 constant price. Relevant data come from the China Industrial Statistics Yearbook, 2012 China Input-Output Table and 2017 China Input-Output Table. Undesirable output is measured using the CO\({}_{2}\) emissions of the manufacturing sub-sectors. Relevant data come from China Emission Accounts and Datasets (CEADs). To sum up, there are 390 observations in total and the descriptive statistics of the original data are portrayed in Table 2.  
Table 3 shows the Pearson correlation coefficients. It can be observed that the correlation coefficients between the input and output variables are all \begin{table}
\begin{tabular}{c c c c c c} \hline
**Industry** & **Code** & \begin{tabular}{c} **Equipment** \\ **Manufacturing Industry** \\ \end{tabular} & \begin{tabular}{c} **High-Tech** \\ **Manufacturing Industry** \\ \end{tabular} & \
\begin{tabular}{c} **Consumer Goods** \\ **Manufacturing Industry** \\ \end{tabular} &
\begin{tabular}{c} **Energy-Intensive** \\ **Manufacturing Industry** \\ \end{tabular} \\ \hline Metal products & H20 & 1 & 0 & 0 & 0 \\ General machines & H21 & 1 & 0 & 0 & 0 \\ Special machines & H22 & 1 & 1 & 0 & 0 \\ Transport equipment & H23 & 1 & 1 & 0 & 0 \\ Electrical equipment & H24 & 1 & 1 & 0 & 0 \\ Electronic equipment & H25 & 1 & 1 & 0 & 0 \\ Measuring instruments & H26 & 1 & 1 & 0 & 0 \\ \hline \end{tabular}
\end{table} 
Table 1: \(Cont.\) \begin{table}
\begin{tabular}{c l l l l l l} \hline  & **Variable** & **Unit** & **Mean** & **Std** & **Min** & **Max** \\ \hline \multirow{3}{*}{Input} & Labor & Ten thousand persons & 277.63 & 194.16 & 18.61 & 911.69 \\  & Capital stock & 100 million RMB in 2005 prices & 9069.37 & 10.616.63 & 150.23 & 63,135.44 \\ \cline{1-1}  & Energy consumption & Ten thousand tc & 7133.23 & 129,87.89 & 110.94 & 694.20 \\ \cline{1-1}  & Industrial output & 100 million RMB in 2005 prices & 21,376.92 & 25,828.72 & 719.97 & 213,532.40 \\ \cline{1-1}  & Undesirable output & CO\({}_{2}\) emission & Ten thousand tons & 11,951.46 & 33,072.21 & 58.37 & 180,283.90 \\ \hline \end{tabular}
\end{table} 
Table 2: Descriptive statistics of the data. Pearson correlation analysis to test the correlation between the input and output variables. The test results show that there is a positive correlation between the input and output variables at the significance level of 1%. In other words, if input increases, output will increase accordingly. Therefore, the isotonicity property is satisfied.