The Elephant in the room, with diffusion research is the exceptions to the S-shaped curve rule, very few data series exist showing this divergent, nonconforming, behaviour, particularly in substitution pairs where data exists for both the new growing and the old declining technologies.
I am interested in all and any examples of such substitution pairs, particularly, but not exclusively any non-conforming data series.
Please visit the site at:
http://www-bcf.usc.edu/~tellis/Diffusion.pdf
Dear Murray,
This is an interesting question because one would expect that an S-shaped curve would explain the data well. I have in mind Kenneth Arrow’s work “The Economic Implications of Learning Doing,” Review of Economic Studies, 29 (1962), pp. 155-173
Arrow specified a relationship between output and experience, intending to capture the effect of education, besides standard neoclassical variables such as capital and labor. One could add substitutable inputs in this relationship such as between skilled male and female labor in addition to the new and old technologies you mentioned. One could do steady state analysis by taking the derivative of the function, and find its optimal state. Since knowledge is growing over time, the convex, inflection, and concave regions of the S-function should capture increasing, constant, and diminishing returns, respectively. Increasing returns to technology emphasized by modern growth models due to hi tech are therefore, accounted for as well.
Besides other developmental models such as creative destruction and flying geese models, it occurred to me that we can apply Cucker and Smale (2007a, 2007b) dynamic model of birds in flight to economic agents maximizing gains as individual in a group. Essentially when a member is displaced from the group, adjustment takes place to bring the group back into equilibrium. See the following two references:
Cucker, Felipe and Steve Smale, “Emergent Behavior in Flocks,” IEEE Transactions on Automatic Control, Vol. 52, No. 5, (May 2007a), pp. 852-862.
Cucker, Felipe and Steve Smale, “On the Mathematics of Emergence,” Japanese Journal of Mathematics, Vol. 2, pp. 197-227, (March, 2007b).
So, yours is an interesting question.
To Leonidas, Lall, and Hasret,
Thank you for your comments, it seems that your points bring us no closer to understanding if such examples of deviation from the S curve exist in the literature, or in peoples research files.
The rule is often proven by the level of exceptions to the rule.
What examples do we have of deviation? I ask that question yet one more time.
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