Diffusion And Adoption Modeling Overview

The study of adoption of agricultural innovations was spurred both by the failure of some very promising innovations, which in the lab seemed highly capable of being diffused among farmers, and the unexpected success of other innovations that did not seem as promising. Sociologists were the first to systematically study the spread of new innovations. They distinguished between two concepts—diffusion and adoption. Diffusion is the extent to which a given population utilizes a technology. One measure of diffusion of, say, tractors is the percentage of the farmers that utilize the tractor or percentage of land that is cultivated with the tractor. Adoption occurs when a particular individual utilizes a given technology or when a technology is utilized on a given field. Thus, one can use diffusion as a measure of aggregate adoption.

Statistical studies have found that diffusion is a dynamic process consisting of three stages: an early period of technology introduction where the diffusion rates are low, a second period of take-off, and a third period of saturation. Thus, diffusion curves are S-shaped functions of time. For almost every technology, there is also a final period of decline where the technology is replaced.

The survey by Sunding and Zilberman (2001) distinguishes between two major types of economic models of diffusion. The first assumed diffusion to be a process of imitation and technologies one modeled to spread in the same manner as infections (Mansfield, 1981). A key feature of the diffusion process is contact between individuals. In an early period, a small number of individuals are introduced to the technology and utilize it and, as more people are exposed, the diffusion process advances more rapidly until most of the population uses the new technology. Mansfield (1981) argues that the speed of imitation depends on factors, such as profitability, farm size, and industry structure. Econometric applications of these models were spawned by Griliches (1957); these studies have proven to be extremely useful in estimating diffusion patterns under many circumstances. They can be modified and applied extensively in marketing and economics. Although these models are useful statistically and provide evidence that economic considerations of profitability as well as farm size and other variables affect adoption rate, they lack an explicit microeconomic understanding of the working of the diffusion process.

An alternative approach, developed by Davis (1979), is the threshold model. This approach consists of three elements: (1) a microeconomic behavior, (2) a source of heterogeneity, and (3) a dynamic process affecting the microeconomics and driving adoption. Potential adopters consist of economic decision makers who are heterogeneous. The sources of heterogeneity may be such factors as the size of a farm, human capital and knowledge, time, risk preference, etc. These decision makers are assumed to pursue profit or to have objective functions that integrate profit as they choose between distinct technologies, for example, traditional and modern seed varieties. Since adoption decisions require investment, the decisionmaking criterion may aggregate economic benefits over several periods, for example, net present value of investment in new technology.

A key aspect of the threshold model is that constraints faced by producers are crucial in understanding and modeling adoption choices. Producers may be limited in their ability to finance new innovations. In addition, there may be comprehension and learning constraints such as individuals' difficulties comprehend with complex new systems. Because of heterogeneity, at each moment a subset of the population will choose the new technology, while another subset will stay with the traditional one.

Moreover, several dynamic forces drive the adoption process. One is learning by doing—the cost of the technology may decline as manufacturers improve their efficiency in producing it. Another is learning by using—the farmers adopting the technology become more adept in using it and, thus, the technology becomes more profitable over time, relative to the traditional technology. Changes in supply may affect the prices of output and, in some cases, enhance adoption, while in others, slow it. Most importantly, farmers adapt their perception and assessment of the technology as more information is accumulated, and if their perception of the technology improves relative to where it was initially, they will adopt it. The threshold model can generate S-shaped diffusion curves and the parameters of these curves depend on the distribution of the source of heterogeneity as well as the parameters of the dynamic processes driving the system. With the introduction of discrete choice estimation methods, the application and use of threshold models has proliferated.

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