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STS452 Yang C. et al.
                                                  = ( − )                                           (5)
                                                              −1
                                                  
                          Where, c is a row vector of row vector of CO2 emissions coefficients
                      representing  CO2  emissions  per  unit  of  economic  output  by  sector  of
                      different sized firms.

                      2.2 Data source
                          For  the convenience of the study and data availability, the original
                      China’s 2012 non-competitive input-output table was aggregated into 29
                      sectors, including 24 industrial sectors. The firm size division criteria of
                      different sectors is based on the ‘Statistical Dividing Method for Large,
                      Small and Medium-sized Micro-firms (2011)’ published by the National
                      Bureau of Statistics of China(NBS). The division criteria of industrial sector
                      are shown in Table 2, and the firms of industrial sector are divided into
                      three firm size types: large, medium, and small according to the indexes
                      of  employment  and  revenue.  Based  on  the  firm-level  data  and  the
                      economic census data, we can obtain the initial estimated value of LMS
                      model  including  intermediate  flow  matrix,  the  import  matrix,  the  total
                      matrix, and the final demand matrix, respectively. After obtained all the
                      initial data of LMS model, then RAS method was applied to get the new
                      extended input-output table. Specifically, because of the firm-level data
                      limitation of the other sectors, some assumptions of different sized firms
                      are applied. So in this study, we only analyse the results of the industrial
                      sectors considering the data accuracy.

                                     Table 2 The division criteria of firm size
                          Sector        Index     Unit   Large      Medium     Small
                                  Employment(X)   Person   X≥1000   300≤X<1000   X<300
                         Industrial   Revenue (Y)   10 RMB  Y≥40000  2000≤Y<40000   Y<2000
                                                  4

                  3.  Results
                      This section illustrates the different roles of large, medium, and small-sized
                  firms in China’s economy and environment. First, it shows the distribution of
                  the  value  added,  output,  export,  and  CO2  emissions  generated  by  different
                  sized firms in the industrial sector. Then, we present results of several input-
                  output  analysis  obtained  by  using  the  newly  constructed  extended  input
                  output table.

                      3.1 Firm-level contribution to China’s economy and CO2 emisisons
                          Using the estimation method described in the previous section, we
                      estimated an extended noncompetitive I/O table distinguishing the firm
                      size  types.  Table  3  shows  the  output,  value  added,  export  and  CO2
                      emissions share of different sized firms in the industrial sector.

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