I am spending part of the fall down at Duke University visiting the well-known group of innovation folks at Fuqua and co-teaching a PhD innovation course with Wes Cohen, who you may know via his work on Absorptive Capacity (EJ, 1989), the “Carnegie Mellon” survey of inventors with Dick Nelson and John Walsh, and his cost sharing R&D argument (article gated) with Steven Klepper. Last week, the class went over a number of papers on the diffusion of technology over space and time, a topic of supreme importance in the economics of innovation.
There are some canonical ideas in diffusion. First, cumulative adoption on the extensive margin – are you or your firm using technology X – follows an S-curve, rising slowly, then rapidly, then slowly again until peak adoption is reached. This fact is known to economists thanks to Griliches 1957 but the idea was initially developed by social psychologists and sociologists. Second, there are massive gaps in the ability of firms and nations to adopt and quickly diffuse new technologies – Diego Comin and Burt Hobijn have written a great deal on this problem. Third, the reason why technologies are slow to adopt depends on many factors, including social learning (e.g., Conley and Udry on pineapple growing in Ghana), pure epidemic-style network spread (the “Bass model”), capital replacement, “appropriate technologies” arriving once conditions are appropriate, and many more.
One that is very much underrated, however, is that technologies diffuse because they and their complements change over time. Dan Gross from HBS, another innovation scholar who likes delving into history, has a great example: the early tractor. The tractor was, in theory, invented in the 1800s, but was uneconomical and not terribly useful. With an invention by Ford in the 1910s, tractors began to spread, particularly among the US wheat belt. The tractor eventually spreads to the rest of the Midwest in the late 1920s and 1930s. A back-of-the-envelope calculation by Gross suggests the latter diffusion saved something like 10% of agricultural labor in the areas where it spread. Why, then, was there such a lag in many states?
There are many hypotheses in the literature: binding financial constraints, differences in farm sizes that make tractors feasible in one area and not another, geographic spread via social learning, and so on. Gross’ explanation is much more natural: early tractors could not work with crops like corn, and it wasn’t until after a general purpose tractor was invented in the 1920s that complementary technologies were created allowing the tractor to be used on a wide variety of farms. The charts are wholly convincing on this point: tractor diffusion time is very much linked to dominant crop, the early tractor “skipped” geographies where were inappropriate, and farms in areas where tractors diffused late nonetheless had substantial diffusion of automobiles, suggesting capital constraints were not the binding factor.
But this leaves one more question: why didn’t someone modify the tractor to make it general purpose in the first place? Gross gives a toy model that elucidates the reason quite well. Assume there is a large firm that can innovate on a technology, and can either develop a general purpose or applied versions of the technology. Assume that there is a fringe of firms that can develop complementary technology to the general purpose one (a corn harvester, for instance). If the large firm is constrained in how much innovation it can perform at any one time, it will first work on the project with highest return. If the large firm could appropriate the rents earned by complements – say, via a licensing fee – it would like to do so, but that licensing fee would decrease the incentive to develop the complements in the first place. Hence the large firm may first work on direct applications where it can capture a larger share of rents. This will imply that technology diffuses slowly first because applications are very specialized, then only as the high-return specialties have all been developed will it become worthwhile to shift researchers over to the general purpose technology. The general purpose technology will induce complements and hence rapid diffusion. As adoption becomes widespread, the rate of adoption slows down again. That is, the S-curve is merely an artifact of differing incentives to change the scope of an invention. Much more convincing that reliance on behavioral biases!
2016 Working Paper (RePEc IDEAS version). I have a paper with Jorge Lemus at Illinois on the problem of incentivizing firms to work on the right type of project, and the implications thereof. We didn’t think in terms of product diffusion, but the incentive to create general purpose technologies can absolutely be added straight into a model of that type.
A Fine Theorem 
Wonderful! But did you mean to write “farms in areas where tractors diffused late nonetheless had substantial diffusion of automobiles, suggesting capital constraints were NOT the binding factor.”
Indeed – thanks!