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Modelling the Emergence of New Technologies using S-Curve Diffusion Models


  • Miriam Steurer

    () (POLICIES, Joanneum Research Forschungsgesellschaft, Graz)

  • Robert J. Hill

    () ( Karl-Franzens University of Graz)

  • Markus Zahrnhofer

    (POLICIES, Joanneum Research Forschungsgesellschaft, Graz)

  • Christian Hartmann

    (POLICIES, Joanneum Research Forschungsgesellschaft, Graz)


Three theoretical benchmark models of diffusion of new technologies are the substitution, mortality and social-learning models. These models tend to generate symmetric, right-skewed and left-skewed S-curves respectively. The empirical literature has focused primarily on fitting either Logistic or Gompertz functions to real data. Given that Logistic is symmetric and Gompertz is right skewed, the former is typically matched with the substitution model and the latter with the mortality model. Neither function can be used to describe the left-skewed social-learning model. We show here how the Generalized- Extreme-Value (GEV) function – which includes Gompertz as a special case and can be either left or right skewed – is more flexible and can be matched with either the mortality or social-learning model. Using cumulative citations as a proxy for diffusion, we fit Logistic, Gompertz and GEV S-curves to 12 citations data sets. Logistic emerges as the best fit for 6 data sets and GEV for the other 6 (all of which are right skewed). It follows that the social-learning model does not fit with any of our data sets. Truncating our data sets in 1996 or 2001 in all but one case does not change the best fit function. This suggests that our fitted S-curves could be useful for modelling aspects (such as the asymptotic upper limit) of a new technology’s future path.

Suggested Citation

  • Miriam Steurer & Robert J. Hill & Markus Zahrnhofer & Christian Hartmann, 2012. "Modelling the Emergence of New Technologies using S-Curve Diffusion Models," Graz Economics Papers 2012-05, University of Graz, Department of Economics.
  • Handle: RePEc:grz:wpaper:2012-05

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    References listed on IDEAS

    1. Kevin Fox, 2000. "Information-rich expressions for model selection criteria," Applied Economics Letters, Taylor & Francis Journals, vol. 7(1), pages 59-62.
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    3. H. Peyton Young, 2009. "Innovation Diffusion in Heterogeneous Populations: Contagion, Social Influence, and Social Learning," American Economic Review, American Economic Association, vol. 99(5), pages 1899-1924, December.
    4. Markose, Sheri M & Alentorn, Amadeo, 2005. "The Generalized Extreme Value (GEV) Distribution, Implied Tail Index and Option Pricing," Economics Discussion Papers 3726, University of Essex, Department of Economics.
    5. King, Robert G. & Plosser, Charles I., 1994. "Real business cycles and the test of the Adelmans," Journal of Monetary Economics, Elsevier, vol. 33(2), pages 405-438, April.
    6. Harding, Don & Pagan, Adrian, 2002. "Dissecting the cycle: a methodological investigation," Journal of Monetary Economics, Elsevier, vol. 49(2), pages 365-381, March.
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    Diffusion of New Technologies; S-curve; Innovation; GEV function; Cumulative citations;

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