There are four common models of innovation diffusion: pure inertia (a constant percentage of those who haven’t adopted adopt in each period), social influence (common in sociology, where consumers adopt based on the percentage of other consumers who have adopted), contagion (common in marketing research, where consumers adopt after coming into contact with information about the good), and social learning (common in economics, where consumers adopt after Bayesian learning about the true utility of the innovation). Young notes that, even when agents are heterogeneous, these models imply rates of adoption that lead to different shapes of the adoption curve; for instance, pure inertia must be strictly concave. After deriving the implied shapes under each model, Young looks at the famous hybrid corn data from Ryan and Gross (1943) and sees evidence that that particular diffusion seems to have been driven by social learning. However, pure econometric tests are limited at this time by the lack of a high-frequency dataset on product adoption.
http://www.econ.jhu.edu/people/young/AERMS20071161R2FINAL.pdf (link is to the final working paper, but a polished version is in AER December 2009)
A Fine Theorem 