Abstract:    With increasing of service-oriented industrial structures, the low efficiency growth of the service industry has always restricted the high-quality development of Chinese economy. Improving the productivity of the service industry is an important policy orientation to solve the "triple period" economic growth dilemma, optimize the industrial structure and improve the growth performance. However, due to the weak scale economy of the service industry, insufficient tendency of globalization and low degree of capital deepening, the problem of how to improve the productivity of the service industry has been puzzling academic and political circles. The quantitative of supply chain length has always been a difficult problem in industrial economics. The existing research on supply chain is mainly concentrated in the field of manufacturing industry, ignoring the service industry. With the development of information communication technology, the tradable degree of service is increasing, and the production fragmentation of service gradually prevailing. The completeness of supply chain is crucial to the development performance of the service industry. The Fifth Plenary Session of the 19th Central Committee of the Communist Party of China pointed out: we should improve the modernization level of industrial chain supply chain, develop strategic emerging industries, and accelerate the development of modern the service industry. This paper link supply chains with the service industry, and discusses the effect of extending the length of supply chain on the productivity of the service industry. The research of this paper broadens the research scope of global value chain, extends the research of global supply chain to the field of service, and finds new endogenous power for the increasingly service-oriented global economy.
   As a latecomer in the global value chain, China has two congenital defects: lack of supply chain and innovation ability. As a part of the supply chain of developed countries, China is embedded in the global value chain. The supply chain of the industry is too short and the input of advanced service elements is insufficient, which can′t effectively help the industrial upgrading and transformation. To improve the productivity of China′s the service industry, we must extend the length of the industrial supply chain. This paper estimates the length of the supply chain in the upstream and downstream link by 120 input-output tables in 1997, 2002, 2007 and 2012. Based on the result, it inspects impact of extension of service supply chain on total factor productivity, which is from the perspective of the global value chain and the national value chain. The overall study shows that: on the one hand,when service supply chain extends 1% towards upstream, the TFP in service will improve 0.148%, however, the extension towards downstream will inhibit TFP in service; and on the other hand, the promotion effect of service supply chain extension on TFP in the national value chain displays higher than it is in the global value chain. Therefore, strengthening the quality of the service elements in the supply chain, improving the management capacity of the value chain and extending the length of the supply chain will increase service productivity and have important policy implications for achieving long-term and stable economic growth.
   This paper shows that: firstly, in order to solve the problem of "cost disease", promote the long-term and stable growth of the service industry, and improve the development performance of the service industry, the key lies in extending the supply chain to the upstream service link of the value chain, that is, improving the degree of "specialization". Enterprises can be encouraged to build up a supply chain system in the upstream links of consumer services and business services. Secondly, we should pay attention to the governance mechanism of domestic value chain, further improve the professional division of labor of domestic the service industry, encourage enterprises to carry out service outsourcing, and build a long-term mechanism to strengthen service association. Put the service industry in the gradient space of domestic industrial circulation, optimize the service quality, dredge domestic circulation channels, use cross regional service supply chain to break the market segmentation, improve the distribution efficiency of factors, and promote the flow of means of production to the service industry. Thirdly, from the strategic perspective of "double circulation", we should graft the bridge between "external circulation" and "internal circulation". Actively expand the international space of service supply chain, actively seek high-quality service resources, establish a global service supply chain system, siphon global high-end service elements.

Key words:  total factor productivity, supply chain, global value chain, national value chain