Single Equation Models

According to Feder et al. (1985), a basic adoption-decision model often takes the form of a utility function assuming an optimal trajectory of income. The model reflects the farmers’ distinct choices from several opportunities, including technology application. The expected income is assumed to vary according to the availability of land or other

adoption determinants and, hence, the extent of these relationships also represents both subjective and objective uncertainties related to the farmers’ objectives.

Most adoption analyses perceive limitations in some of the adoption variables, such as land, labour, inputs and credit (Feder et al., 1985). The models, thus, vary according to different technologies (divisible or non-divisible), environments, time, locations and levels of risk. For example, the models may reflect changes in farmers’ attitudes toward technology adoption that result from changes in some of the adoption

variables. The focus of the analysis is farmers’ adoption propensity based on future expectations from applying a technology (Batz et al., 2003; Besley & Case, 1993; Marra et al., 2003).

In this regard, Feder et al. (1985) suggest three possible approaches. First, the model may apply learning rules, such as Bayesian modelling, to explain the effect of learning on farmers’ adoption attitudes. The variables highlighted include extension services, the quality of human capital and other variables reflecting farmers’ information seeking and processing behaviour. The second approach considers that farmers change their adoption attitudes because they become more experienced through daily trials and monitoring. This approach focuses on the effects of extension services, the quality of human capital, the length of time of learning and trying a technology, the availability of land and the practices of other farmers. The last approach considers the changes in farmers’ attitude as a result of the changes in the market such as output and input prices, initial costs for implementing a technology, and marketing networks.

All of these approaches can be plotted in one equation reflecting a dynamic

technology adoption process that at the end indicates the accumulative proportion of adopters. Most adoption studies, however, focus only on adoption behaviour at one point of time for a particular technology in a particular farm setting. These studies, thus, may only present a snapshot explanation of farmers’ adoption behaviour.

Analyses, such as logit, probit and tobit, are commonly used for calculating the relationships between the independent and dependent variables in single equation models. The descriptions are as follows (Garson, 1998a, see

http://www2.chass.ncsu.edu/garson/pa765/logit.htm):

“… logit, and probit models extend the principles of generalized linear models (ex., regression) to better treat the case of dichotomous and polytomous dependent variables. It focuses on association of grouped data, looking at all levels of possible interaction effects…These methods differ from standard regression in substituting maximum likelihood estimation of a link function of the dependent for regression's use of least squares estimation of the dependent itself… The function used in logit is the natural log of the odds ratio. The function used in probit is the inverse of the standard normal cumulative distribution function.”

That is, the logit and probit models are developed to deal with categorical (binary or ordinal) dependent variables that are common in behavioural or rational choice studies (Aldrich, 1984). Both models allow the normalization of the subjective responses and, with similar attributes, both produce similar estimations (Aldrich, 1984). Meanwhile, the tobit model deals with dependent variables with values within a certain and limited interval (Aldrich, 1984) that exists due to the “extreme” skewness of some variables (Garson, 1998a; Hintze et al., 2003). The tobit model is an

expansion of the probit model created by Tobin in the 1950s (Aldrich, 1984). In the case of agricultural technology adoption, logit, probit and tobit models are used for predicting the rate and intensity of adoption among farmers (e.g. Adesina & Zinnah, 1993; Herath & Takeya, 2003; Kaliba et al., 1997; Neill & Lee, 2001; Pomp & Burger, 1995, see Appendix A).

Most of the logit, probit and tobit adoption models are based on an individual farmer’s ex-post decision and use a combination of both primary and secondary data. The dependent variable is usually either binary (adopt or not adopt) or ordinal (based on the characteristics of a technology, e.g. in the study by Negatu & Parikh, 1999). The independent variables are selected based on previous studies, the analysts’ own

premises, field observations, and/or the type of technologies (see Appendix A). Within the models, farmers’ adoption behaviour is often assumed to reflect the goal of maximizing utility (e.g. Adesina & Zinnah, 1993; Hintze et al., 2003; Lapar & Ehui, 2004; Munshi, 2004; Negatu & Parikh, 1999; Neill & Lee, 2001).

The results from these models are not without problems. The use of binary variables is often criticized for concealing farmers’ dynamic decision making processes and adoption practices. The dualistic approach may only capture the initial stage, or a snapshot, of the adoption process (Besley & Case, 1993; Feder et al., 1985). The actual adoption-decision appears to be flexible as farmers often make seasonal decisions following the fluctuations of labour supply, land availability (Damianos & Skuras, 1996; Moser & Barrett, 2003), and income (Adesina, Abbott, & Sanders, 1988; Damianos & Skuras, 1996; Moser & Barrett, 2003; Shapiro, Sanders, Reddy, & Baker, 1993). These result in several types of adopter and non-adopters (see Jangu, 1997 and Rogers, 1993).

Another issue relates to the assumption in binomial logit, probit and tobit analyses that only aggregate adopters or non-adopters exist, despite the use of data on individual farmers. The results might be useful for policy planning, but they may have little impact at the micro level, such as in extension services where a bottom-up approach is more useful (Jangu, 1997; McGregor et al., 2001). To address this issue, multi-equation modelling is recommended; and this will be discussed next.