1、技术创新的元胞自动机模型 祝树金 赖明勇 (湖南大学经济与贸易学院，长沙，410079) Cellular Automata Model of Technology Innovation Based on Dual Role of R&D and Technology Spillovers Zhu Shujin Lai Mingyong (College of Economics and Trade, Hunan University, Changsha, 410079, China) * 本文得到国家自然科学基金资助项目（70273010 ）资助 作者简介 ： 祝树金 （1974） ，男，汉
2、族，湖南省隆回县人，湖南大学经济与贸易学院博士生 主要研究领域：经济管理系统复杂性、国际贸易系统工程 通讯地址：湖南大学经济与贸易学院 邮政编码: 410079 E-mail: 赖明勇 （1965） ，男，汉族，江西省吉安市人 湖南大学经济与贸易学院院长，教授、博士生导师 主要研究领域：系统工程理论与应用、国际贸易与经济增长 通讯地址：湖南大学经济与贸易学院 邮政编码: 410079 E-mail: _http:Cellular Automata Model of Technology Innovation Based on Dual Role of R&D and Technology
3、Spillovers#Zhu Shujin Lai Mingyong (College of Economics and Trade, Hunan University, Changsha, 410079, China) Abstract： New growth theory and empirical study have shown that in-house R&D has the dual role, which not only generates new information, but also enhances the firms ability to assimilate a
4、nd exploit technology spillovers. Based on two faces of R&D we put forward a cellular automata model to investigate the complexity of the innovation diffusion of economic system in the long run. The simulation results show that the roles of in-house R&D and network externality on the average rate of
5、 innovators in the economic system own the characteristics of S-shaped curve. Increasing the level of in-house research may shorten the take-off phase of the economy and improve the stability of the long run level of innovation rate. Key words: complexity； R&D； technology innovation； cellular automa
6、ta 1 Introduction In the open economy the innovation of a country mainly steps from in-house R&D and technology spillovers. Many empirical studies have shown the existence of spillovers1-2. However researches on the developing countries have denied this effect of technology3-4. Some economists advoc
7、ate that a key factor is absorptive capacity of host country, which is firstly proposed in 5. 5 argues that the effects of R&D on the technology progress in a country involve two sides, i.e. not only directly generating new information, but also enhancing the firms ability to assimilate and exploit
8、existing technology. Based on this idea， Kinoshita (2000) also parts effects of R&D in host country into two faces: the innovation effect and the learning effect of R&D. The international technology diffusion is a complex, nonlinear system. 6 provides a cellular automata (CA) model to study technolo
9、gy spillovers. The results demonstrate that the strength of spillovers gives rise to a nonlinear effect on the average innovativeness and increasing the level of in-house research has only a linear effect on the innovativeness of the economy. In fact they neglect the effect of in-house R&D on spillo
10、ver. Based on the dual role of R&D on innovation shown by the growth theory and empirical study, this paper formulates a stochastic CA model on the diffusion of technology innovation. With a large number of simulations, it is hold that in-house R&D plays a pivotal role on the technology innovation a
11、nd diffusion of the economy system in the long term. Simulation results show that the roles of in-house R&D and network externality on the average rate of innovators in the long run own the characteristics of S-shaped curve. Increasing the level of in-house research may shorten the take-off phase of
12、 the economy and improve the speed of catch-up of economy. 2 The CA model of technology innovation All firms in the economy system compose a network, which is represented by a cellular space with dimensions. Each firm in the network is defined as an agent or a cell of space. The Von-Neumann neighbor
13、hood is assumed in the model and the edges of the space are joined to each other to allow a continuous neighborhood effect. Thus the model can be conveniently represented in matrix form. The location of a firm on the network is represented by an ordered pair（ ） （ ） with particular firm denoted . An
14、example of such a firm and its neighborhood in the network system nnji, nji ,1,L=jiF,#This subject is supported by National Natural Sciences Foundation of China (70273010). *E-mail address: *E-mail address: 1中国科技论文在线_http:are given in Figure 1, where the black grid is this particular firm and the
15、grey cell is the immediate neighbors of . jiF,jiFigure 1 The firm and its neighborhoods in the cellular space The state set of cellular space is 1 ,0=C， 0=c means that the firm dont generates the innovation and denotes the firm with innovation. Assuming that there exists a threshold value during the
16、 process of firms innovation, which is normalized to one. A firm makes a new innovation only when total knowledge accumulated by the firm in a period exceeds 1. 1=cBased on the growth theory and empirical studies, the total new knowledge denoted by of a firm in period depends on in-house R&D and kno
17、wledge received by the firm from spillovers in period (denoted by ), that is )(,tKjijiF,t )(,tKRjit )(,tKSji)()(,tKtKKSjiRjiji+= （ 1） In the equation (1), if , the firm will make a new innovation in period and it state value equals 1. If , the state value for the firm in period t is zero. We postula
18、te that is uniformly distributed on and thus the average new knowledge generated internally in a period is , although the actual amount will vary randomly across firms and over time. It should be noted that is referred to in-house R&D level of a firm and 1)(,tKji jiF,t1)(,rRI，022（ 4） 0sRI，022Finally
19、, simulations show that the take-off of economy can occur as in-house research spendings increase and the larger is R&D investment, the shorter is take-off phase. Table 1 and Figure 4 illustrate this property. Utilizing the industrial data between 1974 to 1990 from 12 OECD countries, 7 finds that in
20、 industrial countries with lower productivity, if there are remarkable R&D spendings, their catch-up will accelerate. In addition Table 1 also presents that internal R&D play an important role on the stability of perpetual innovation. As the domestic researches rise, the volatility of technology inn
21、ovation is weakened. Therefore it can be concluded from simulation that in-house R&D provides an inner dynamic of persistent growth for the rapid, stationary development of economy. 4 Conclusions Based on dual role of firms in-house research: the innovation effect and the learning effect, the modeli
22、ng theory and method using cellular automata are applied to study the complexity of spillovers of technology innovations. An evolving model based on stochastic cellular automata for innovation spillovers is formulated. By a large number of simulation experiments we argue that the effect of internal
23、R&D on the long-term innovation can be described by S-shaped (logistic) curve, and that raising domestic research level can accelerate technology innovation, improve the stability of innovation in equilibrium and shorten take-off time span of economy. Results and analyses confirm that sustainable de
24、velopment of the economy and technology innovation must base on the domestic R&D, which not only propels directly technology advance, but also can determine their capabilities to assimilate and exploit externally available technology spillovers. Consequently our country should invest more in R&D and
25、 education when broadening reform and opening, especially increase R&D spending on the technology-intensive industries. References 1. Coe D.T., E.Helpman. International R&D spilloversJ. European Economic Review, 1995, 39: 859-887. 2. Keller W., Knowledge spillovers at the worlds technology frontier.
26、 CEPR Working Paper, 2001， No.2815. 3. Aitken B., A.Harrison, Do domestic firms benefit from direct foreign investment, Evidence from VenezuelaJ. American Economic Review, 1999, 89(3): 605-618. 4. Lai mingyong, Bao qun, Survey on technology spillovers and absorptive capacityJ. Economic Perspectives,
27、 2003, 8(in Chinese). 5. Cohen W., D. Levinthal. Innovation and learning: The two faces of R&DJ Economic Journal, 1989, 99: 569-596. 6. Meagher, K., M. Rogers, Networks, spillovers and models of economics growth, mimeo, The Australian Econometric Society Meetings, 1997. 7. Grittith, R., S.Redding, J. Van Reenen., R&D and absorptive capacity: from theory to data, mimeo, London School of Economics, 2000, November. 5中国科技论文在线_http:
