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Modeling the behaviour of science and technology: self-propagating growth in the diffusion process

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Abstract

Through theoretical analysis and empirical demonstration, this paper attempts to model the behavior of science and technology by investigating the self-propagating behavior of their diffusion for South Korea, Malaysia and Japan. The dynamics of the self-propagating behavior were examined using the logistic growth function within a dynamic carrying capacity, while allowing for different effectiveness of potential influence of science and technology producers on potential adopters. Evidence suggests that the self-propagating growth function is particularly relevant for countries with advanced science and technology, like Japan. While self-propagating growth was also found for South Korea, the diffusion process remained fairly static for Malaysia.

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Notes

  1. National innovation system is the set of national institutions that contribute to the development and diffusion of new science and technology (Sharif 2006).

  2. We thank a referee for suggesting the alternative of Akamatsu’s flying geese model for explaining the development stages of science and technology. In competing for FDIs that have their source from the relocation of production from the developed countries (or the leaders in the flying geese model), the lagging economies will raise national investment to develop their infrastructure. As their production moves up the value chain, these economies will step up investment to improve their science and technological capability. The activities are mainly driven by science- and technology push factors at this stage (P1). As the production activities enter into maturity and when these initially lagging economies begin to catch up and expand the market for their products, market-pull factors will set in (P2).

  3. This argument applies for Malaysia. The expansion of the Malaysian economy relied heavily on its industrial development. Since the 1970s, the government invested heavily on basic infrastructure and modernization of the manufacturing sector to promote industrialization. Incentives were provided to attract FDIs, especially those with prospects of technology transfer, and to encourage R&Ds. In the 1980s, the science and technology policy of Malaysia focused on R&D incentives to support the innovation process. The increasing supply of engineers, scientists and R&D technicians through prioritization of science, technology and engineering-based fields in education, and increasing R&D investments, were some early signs of science- and technology push factors.

  4. The coefficients a and b were obtained through the data linearization technique proposed by Mathews (1992). See Appendix 1 for details.

  5. Malerba et al. (1997) suggested that the yearly production of papers (patents) is likely to propagate the potential of science (technology). Persistence in innovation is viewed as the conditional probability that innovators at time t will continue to innovate at time t + 1.

  6. According to Hu and Tseng (2006), the potential of diffusion is highly dependent on previous knowledge stock.

  7. According to Watanabe et al. (2009a, b), self-propagating behavior emerges in the early diffusion process. Therefore, the value of g is searched from the series of growth rate of production from the observed data.

  8. K k is estimated from the series values of K t through the data linearization method.

  9. Substituting p t from Eq. 4 into the right hand side of Eq. 2.

  10. Among these three countries, the lead goose in the region is Japan according to the flying geese model. As one of the newly industrialised economies, Korea falls in the second tier. Malaysia follows after the two countries.

  11. The ISI publications here refer to all fields of sciences, including natural, physical, health and social sciences. However, the share of papers in the field of social sciences and humanities of the total publications was low. The share for Japan, Korea and Malaysia is 1.7, 3.3 and 3.8%, respectively.

  12. Patents are recorded by grant year. The reasons for using these data are their availability and completeness for analysis, and comparability across different countries. We admit the shortcomings of the data, including the exclusion of the rejected applications that were also contributing to the innovation activities, and the time lag between application and approval that may misrepresent the actual year an innovation is made.

  13. An issue of contention is whether to deflate the total number by a normalizing factor, for instance, population or labour size. Kostoff (2004) argued that using normalized number of papers and patents [for example, the approach in the comparative study of King (2004)] may underestimate the emerging trend of developing countries in science and technology. Our approach is similar to Choung and Hwang (2000), Zhou and Leydesdorff (2006), and Leydesdorff and Zhou (2005) that employed the total number of papers and patents to study the growth behavior of science and technology. The reason for taking this approach is that we are not comparing the per capita ability to produce across countries, but the point of focus is the self-propagating behavior in the growth pattern. Further, for as long as the diffusion process is identical, a science or technology output produced by a country will impact its economy the same way as it would on another country that may have produced it, whether the population size of the two countries is comparable or not.

  14. The improvement of the fit is small due to small number of observations and limited fluctuations in the data series.

  15. Collective learning among the actors within the innovation system will improve the existing knowledge stock, and thus generate self-propagating behavior.

  16. To gain further insight into the results, we did some preliminary estimation using data on China and Thailand. The self-propagating behavior of China is stronger than Malaysia, but that of Thailand is comparable. Leydesdorff and Zhou (2005) argued that the strong human capital base in China has contributed to its advancement of science and technology. The details are not reported here but can be obtained from the authors.

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Acknowledgements

We are grateful to two anonymous referees for helpful comments and suggestions that led to improvement of the paper. We are solely responsible for any remaining errors. We would like to thank Kurunathan Ratnavelu and Behrooz Asgari for their generous input, in particular research materials for this paper. We would also like to express our appreciation to the participants of the 2009 IEEE International Conference on Advanced Management Science (Singapore) for feedback on an earlier draft of this paper. The funding from University of Malaya to support this research project is gratefully acknowledged.

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Correspondence to Chan-Yuan Wong.

Appendices

Appendix 1

The coefficients of a logistic function can be obtained through the least squares technique (Mathews 1992). The logistic growth function can be transformed into a log-linear model as follows:

$$ p_{t} = {\frac{K}{{1 + ae^{ - bt} }}} $$
(8)
$$ \begin{gathered} K = p_{t} \left( {1 + ae^{ - bt} } \right) \hfill \\ {\frac{K}{{p_{t} }}} - 1 = ae^{ - bt} \hfill \\ \log \left( {{\frac{K}{{p_{t} }}} - 1} \right) = \log \;a - bt \hfill \\ \end{gathered} $$
(9)

Equation 9 is of the linear form:

$$ M = A + Bt $$
(10)

The coefficients A and B in Eq. 10 were obtained from the least squares line that was fitted to the observed data. The coefficients a and b were then calculated as: \( a = e^{A} \) and \( b = - B. \)

Appendix 2

The Monte Carlo method proposed by Meyer and Ausubel (1999) was used to obtain parameter estimates that generate a growth function with the best fit. The following algorithm was applied in the estimation process:

  1. 1.

    A domain of possible values of g and K k is defined.

  2. 2.

    The initial knowledge stock value is estimated.

  3. 3.

    Deterministic computations are performed using the log-linear model to determine the coefficients a k and b k for the domain defined in Step 1.

  4. 4.

    The values that generate the growth function with the best fit are opted for estimating the parameters of the logistic function.

  5. 5.

    Go back to Step 2 to refine the initial knowledge stock value if the fit of the function is unsatisfactory.

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Wong, CY., Goh, KL. Modeling the behaviour of science and technology: self-propagating growth in the diffusion process. Scientometrics 84, 669–686 (2010). https://doi.org/10.1007/s11192-010-0220-x

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