Abstract:     Technological innovation is an important way to improve economic development and enhance the countries′ innovation competitiveness. The transformation efficiency of resource inputs to innovation outputs is a vital factor of national innovation development. It is worth noting that innovation is a value chain transfer process with multi-stages, from resource inputs to innovation outputs. But innovation value does not happen immediately when the organizations invest innovation resources, such as R&D funding, human resources, there is a lag period. This lag period leads to the time-lag effect at multi-stage innovation value chain. Therefore, it is meaningful to accurately evaluate the time-lag effect of value conversion in each stage. Calculating lag period is not only good at understanding the present situation of China′s innovation value transformation, but also providing parameters for the innovation efficiency measurement model. Additionally, the most important is that it can provide valuable decision-making basis for resource allocation of governments and innovation organizations.The time-lag effects express discriminating meanings during the different stages of innovation value transformation. This paper proposes a method to calculate the lag period based on the relationship between the similarity of time-series network and the time-lag effect of value conversion system. In this paper, we divide the transformation in innovation value chain into three stages: knowledge development, technical transformation and industrialization. Firstly, we prove the relationship between the time-lag effect of the innovation value conversion system and the time-series vector. Secondly, we build the inputs and outputs networks separately using the time series data and following the time series visualization approach. Thirdly, the network similarity between inputs and outputs is calculated by using the cosine similarity theorem. Then the optimal mapping solution indicate the lag period. Finally, an empirical study on time-lag effect in China′s provinces innovation value transformation is established to show the feasibility of our approach. We select data from 30 provinces (autonomous regions and municipalities) in China (excluding Hong Kong, Macao, Taiwan, and Tibet because of a lack of data). The time coverage of all research data is 1998 to 2016. In the start of the innovation stage, knowledge development stage, R&D investment and scientific research personnel full-time equivalent are considered the initial inputs. Considering the innovative outputs in the knowledge development stage include patents and research papers, this paper has produced two innovative value transformation chains. One is from inputs to the number of patent grants (K1), then vary to high-tech industry new product sales (T1), finally output the high-tech output value (I) (namely ‘patent-driven’). The other one from the same inputs, capitals and human resources, but transform into to research papers in the knowledge generation phase, then produce high-tech industry new product sales (T2) and the proportion of high-tech output (I) gradually (namely ‘paper-driven’).This research draws the following conclusions. (1) The time-lag effect of the innovation value conversion system is related to the time-series network structure of the input-output vector. The similarity between inputs and outputs time-series network can reflect the mapping relationship of the value conversion parameter. In addition, the maximum similarity reflects the time-lag effect, and years who have the maximum similarity reveal the lag period. (2) The average time-lag period of knowledge development stage, technical transformation stage and industrialization stage are 3-4 years, 2-3 years and 3-4 years respectively. The patent-driven and paper-driven value conversion period is about 8.66 years and 9.66 years separately. The lag period of value transformation with paper-driven chain is more stable, but the collaboration effect between scientific papers and new products sales is fluctuating. Because scientific papers are results which explore different principles of technological innovation, while the new product is the technical program finally realized. They are not always synchronized at the same stage. (3) Comparing the lag period of each province with the national average, we can divide the innovation path into four categories. Dual-path driven means the province′s conversion time in both innovative value chains is faster than the national average. If the province′s patent-driven innovation value conversion has a short time lag, it names a patent-driven innovation. Instead, it is called paper-driven innovation. The remaining provinces have longer conversion time. In 30 provinces, 11 provinces′ innovation are dual-path driven, 9 provinces are paper-driven innovation, and 2 provinces are patent-driven. (4) Further analyzing the stage differences of lag period, this paper finds the lag period in industrialization stage is longest at most provinces. This indicates that it takes a long time to materialize an industrial production project. Meanwhile, the lag period in knowledge development stage and industrialization stage are complementary. The provinces with longer lag period in knowledge development stage have shorter lag period in industrialization stage.Based on designing an approach to measure the lag period and time-lag effects on innovation value transformation, this paper also extends the suggestions on government policies in the following ways. Firstly, the governments can distribute their input resources to the distinct innovation stages according to the lag period of value transformation. Secondly, pay more attention to the regional innovation collaboration. Finally, the complementary phenomenon of the lag period between the knowledge development stage and the industrialization stage provides some recommendations for innovation management. Establishing a collaboration innovation network between universities, research institutions and enterprises can improve value conversion efficiency. This paper contributes to the existing literature in several ways. Theoretically, this paper establishes an analysis framework for time-lag effects of innovation value transformation systems. Then this paper demonstrates the mapping relationship between the parameter vector and the time-series network structure. Meanwhile, a method for calculation the time-lag effect and the lag period is also designed. It provides a direction and feasible way to study the multi-stage time-lag effect from the perspective of time-series network, and enriches the complex network application research system. Practically, we measure the lag period of each stage of the transformation of innovation value in China′s provinces. In addition, the results not only propose the path and direction for improving the innovation efficiency of value conversion, but also can be used to configure the lag period for the input-output analysis model.

Key words:  innovative value chain, multi-stage time-lag effect, lag period, time series network, cosine similarity