CHAPTER 6 THE EFFECTIVENESS OF INNOVATION PLATFORMS IN
6.2 Methodology
6.2.4 Analytical framework
In assessing the effectiveness of innovation platforms, the study was designed in such a way that the empirical model sought to estimate the impact of adopting smallholder dairy innovation platforms on productivity (as measured by selected variables) and viability (income, variable cost and gross margin). The objective was to approximate the Average Treatment Effect on the Treated (ATT). Given the option to adopt (participate in the smallholder dairy innovation platform) or not to adopt, one can randomly assign individuals to either treatment (adopters of innovation platforms) or control (non-adopters) groups to successfully estimate the ATT as is usually the case in observational studies. Nevertheless, because this study relies on cross- sectional survey data rather than experimental data, assignment into treatment is not randomly distributed. According to Smith and Todd (2005), this implies that the outcomes for adopters and non-adopters might be systematically different. The risk is that the observed differences between the two groups in the absence of randomization might be mistaken for the impacts of innovation platforms (Mapila et al., 2012; Akinola and Sofoluwe, 2012).
The Propensity Score Matching (PSM) method was chosen to estimate the Average Treatment Effect on the Treated (ATT) to deal with the potential self-selection bias highlighted above. Desk reviews show the ATT as a better indicator for measuring the appropriateness of intervention strategies on smaller groups of interest such as smallholder farmers than the population-wide average treatment effects calculated via probit models (Rosenbaum and Rubin, 1983, 1985;
Heckman, 1996; Rosenbaum, 2002). A number of researchers have used PSM to control for self- selection bias (Faltermeier and Abdulai, 2009; Akinola and Sofoluwe, 2012; Amare et al., 2012;
Mapila et al., 2012; Matchaya and Perotin, 2013). Fundamentally, the PSM technique assumes that each surveyed farmer/household belongs to either the group of innovation platform adopters (treatment) or group of non- adopters (control) but not both. Based on insights from Heckman et al. (1997), let Y1 denote productivity or viability outcome of a farmer i after adopting innovation platform (T = 1) and Y0 denoting the productivity or viability outcome of the same farmer when they do not adopt innovation platform (T = 0). The observed productivity or viability outcome Y can thus be calculated as follows:
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Y = TY1 + (1–T)Y0 (1)
where Y1 is the productivity or viability outcome of farmer i when they adopt innovation platform (T = 1); Y0 is farmer i’s productivity or viability outcome when they do not adopt innovation platform (T = 0). The average treatment effect on the treated (ATT) can be calculated as follows:
ATT = E(Y1 − Y0|T = 1) = E(Y1|T = 1) − E(Y0|T = 1) (2)
In equation (2) above, the only observable productivity or viability outcome is for those farmers who adopted innovation platform E(Y1 | T = 1) and not the productivity or viability outcome of non-adopting farmers E(Y0 | T = 1). The idea, as already highlighted earlier, is to match innovation platform adopting farmers to non-adopting farmers using PSM. It is also worthwhile to note that vital for PSM is the conditional independence assumption which assumes random participation conditional on observed covariates (Wooldridge, 2002). Assuming that the conditional independence assumption is satisfied, the ATT can then be specified as follows:
ATT = E(Y1 − Y0|X, T = 1) = E(Y1, |X, T = 1) − E(Y0|X, T = 1) (3)
However, the researchers also took note of latent challenges given that matching the innovation platform adopting farmers to non-adopting farmers based on the observed covariates X might potentially result in the nuisance of the dimensionality problem, particularly in cases of a large number of covariates (Rosenbaum and Rubin, 1983). The researchers, therefore, chose to match the treatment group participants to the control group based on the propensity score p(X) and not on the observed covariates. In this circumstance, the propensity score is defined as the conditional possibility that farmer i adopts innovation platforms and is expressed as follows:
p(X) ;prob(T = 1|X) = E(T|X) (4)
where T = {0, 1} is the binary indicator representing the treatment group. A significant condition that has to be adhered to in PSM is the balancing property, expressed as T X|p(X). According to Lee (2011), the conditional distribution of X, given the propensity score p(X ) is the same in the comparative groups, in this case the innovation platform adopting and non-adopting groups.
Page 142 of 231 Considering the propensity score and the conditional independence assumption, the ATT specified in equation (2) above can thus be rewritten as follows:
ATT = E(Y1 − Y0|p(X), T = 1) = E(Y1, |p(X), T = 1) − E(Y0|p(X), T = 1) (5) where E(Y1, |p(X), T = 1) measures the observable productivity or viability outcome of the treated farmers (innovation platform adopters) and the second term E(Y0 | p(X ), T = 1) measures the productivity or viability outcome of the same farmers had they failed to adopt the innovations i.e. the counterfactual.
The PSM method is a two-step process that involves estimating a probit or logit regression on the first step to calculate the probability p(X ) that farmer i is in the innovation platform adopting group conditional on observed covariates as given in equation (4) above. The covariates vector X includes all the variables associated with innovation platform adoption. Once the propensity score in equation (4) above has been calculated, the second step involves matching innovation platform and non-innovation platform farmers based on the similarities or closeness of the propensity scores. To achieve this, the nearest neighbour matching technique, an algorithm that matches each innovation platform farmer to a non-innovation platform farmer on the basis of closely similar propensity scores (Becker and Ichino, 2002) was used to estimate the effect of innovation platforms on the selected farmer productivity or viability outcomes.
To ensure a maximum covariate balance and a low conditional bias, a one-to-one matching with replacement was used based on insights from Abadie and Imbens (2006). The kernel matching algorithm was also used to calculate the ATT, as a robustness check of our results. This algorithm involves matching all the innovation platform farmers with a weighted average of all the non-innovation platform farmers using weights that are inversely proportional to the distance between the two groups’ propensity scores (Becker and Ichino, 2002).
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