The Adoption of Agricultural Technology - Food Security Group

Yt and we can estimate K (the maximum adoption expected)independenlly. In this case, we note that the equation of the logistic curvecan be transformed to:Y tIn (--) =a + bt .K - Y tSimple ordinary least squares regression of the transformed variableIn [Y t/ (K - Y t)] on a constant and time wiII then yield estimates of a and b(Griliches 1957). This kind of calculation is easy to do with manyspreadsheet packages. One could also fit a curve without regression withonly two observations, although the information from only a fewobservations is likely to be limited (see below).There are several methods of estimating K. The first is simply to plot thedata and to choose the level that appears to be the upper bound ofadoption. A second method is to run the regression using different valuesof K and choose the one that maximizes R 2 • (This is also readilyaccomplished with most spreadsheets. It should be noted that in general, R 2and t-statistics from these regressions have no statistical meaning. Thistechnique only helps to choose K to get a fairly close fit to the data.) Toreduce the time spent selecting K, a combination of Simple plotting andexperimental regressions might be used.Although the logistic curve is the most common way of representingtechnology diffusion, it is well to remember that it is based on certainassumptions about diffusion, and that t~e fixed parameters estimated forthe curve imply that the relevant price ratios, infrastructure, and thetechnology itself have remained constant over the period when the curve isfitted. An example of a logistic curve is shown in Box 7.Time FrameIt is also important to remember that not only is the diffusion of a newpractice among farmers a gradual process, but that individual farmertesting of technology may follow the same type of curve. If possible, afarmer wiII test a new technology on a small part of the farm, and if theresults are positive wiII gradually increase the use of the technology. Box 8shows this process for a new variety.If an adoption study examines a number of different practices, whether ornot they have been presented to farmers as a technological package, it isimportant to consider the relationships among the adoption patterns. Insome cases, different elements may be adopted independently, while inother cases there may be a sequential adoption pattern, as shown in the13