3.1. Role of Agricultural Cooperatives
Ma et al. (
2018) report that agricultural cooperatives positively influence farms’ economic performance through several pathways. First, cooperatives enhance farmers’ access to advanced technologies, contributing to more efficient production input use. The technical efficiency of cooperative members is often higher than that of non-members (
Ma et al. 2018;
Neupane et al. 2022;
Olagunju et al. 2021), resulting in an increase in farm yields. Indeed, empirical study results indicate that cooperative membership increases members’ production yields (
Hoken and Su 2018;
Michalek et al. 2018;
Mishra et al. 2018). Cooperative membership improves the technical efficiency of farmers, thus enabling members to achieve higher productivity than non-members (
Neupane et al. 2022;
Olagunju et al. 2021). Agricultural cooperatives encourage farmers to adopt advanced technology, which thus increases farm productivity and income (
Zhang et al. 2020).
Second, cooperatives can purchase and deliver farm inputs and supplies to their farmer members (
Cropp and Ingalsbe 1989). Cooperatives can also facilitate better access to farm input, financial support, and linkage for the output market (
Abebaw and Haile 2013). Agricultural cooperatives, a crucial institution of the agricultural sector, are also considered a vital actor in supply chains with respect to encouraging farmers to adopt sustainable practices. (
Candemir et al. 2021). Consequently, farmer members may acquire better productive inputs at a reasonable cost.
Third, agricultural cooperatives, when used as an effective marketing channel, may help farmers gain significantly higher farm income per capita and household income per capita due to better selling prices (
Liu et al. 2019). Agricultural cooperatives also provide their members with information about outlet channels and market prices, which may support farmers’ ability to sell their output at a higher price (
Hao et al. 2018;
Hoken and Su 2018;
Ma and Abdulai 2017;
Wollni and Zeller 2007). Cooperatives may play an important role in marketing, e.g., with respect to handling, processing, selling farm produce, and bargaining for higher prices (
Cropp and Ingalsbe 1989).
In short, the three pathways for enhancing farm performance through cooperative membership are illustrated in
Figure 1.
3.2. Impact Estimation Strategies
The primary aim of this study is to investigate the impact of participation in agricultural cooperatives on return on cost (ROC). Thus, ROC is a linear function of a cooperative membership binary variable (
) and a vector of farm and household characteristics. The function can be specified as follows:
where
is defined as ROC;
is a binary variable, equaling 1 if household
i is a cooperative member, and 0 otherwise;
is a vector of farm and household characteristics;
and
are unknown parameters to be estimated; and
is a random error term.
The core objective is to estimate the
representing the marginal impact of cooperative membership on the outcome. However, many empirical studies have shown that agricultural households’ decision to join cooperatives depends on their farm and household characteristics or self-selection into cooperative membership rather than randomly assigned participation (e.g.,
Afolabi and Ganiyu 2021;
Wang et al. 2021;
Mojo et al. 2017;
Hoken and Su 2018). This possibly results in selection bias. Consequently, if the ordinary least squares (OLS) model is employed to estimate the ROC of cooperative membership, Equation (1) may yield biased results.
Following (
Ofori et al. 2019;
Chagwiza et al. 2016), and
Shumeta and D’Haeseb (
2016), this study employed the PSM method to estimate average treatment effects controlling for observable factors, but it cannot account for unobservable selection bias. Therefore, adopting the approaches used by
Attipoe et al. (
2021),
Ma and Abdulai (
2017),
Zheng et al. (
2011), and
Miyata et al. (
2009), a sample selection model developed by
Heckman (
1979), called the two-stage Heckman model, was further employed to examine the impact of cooperative membership on ROC while accounting for both observable and unobservable selection biases in our study.
Fortunately, both models proceed through a two-stage procedure. Within this framework, they model the determinants of households’ participation in cooperatives (first stage) and the impact of cooperative membership on households’ ROC (second stage).
Determinants of a household becoming a cooperative member (first stage): It should be based on a random utility framework in which farmers choose to participate in cooperatives. Contingently with this framework, a farmer may choose to become a cooperative member if the potential utility obtained from membership is larger than that gained from non-membership. Thus, we can express the utility gained from membership as a function of the observable attributes in a latent variable framework as follows:
where
is a latent variable defined as the utility difference between becoming a member and non-membership.
Zi is a vector of covariates that might influence farmers’ decisions to become a cooperative member, while
γ denotes a vector of unknown parameters to be estimated.
is random disturbance.
is already denoted above.
Hence, binary regression (a probit model in this study) was employed to estimate the probability of cooperative membership.
Treatment effects estimated by PSM technique: Since we sought to measure the average treatment effect on the treated (ATT), the expected outcomes were primarily compared with and without membership in the agricultural cooperatives for the same household simultaneously. Assuming that
is the ROC of the household as a member of the agricultural cooperative and
is the ROC of the same household not being a member of the cooperative, ATT can be written as follows:
where ATT is defined as a difference between the mean values of the expected ROC of the household when participating and the expected ROC if this household is not participating in the cooperative.
was defined earlier.
Estimating the ATT value in Equation (3) is impossible since the outcome created in the case of not participating in the cooperative for the same household that actually joined the cooperative cannot not be observed simultaneously. The counterfactual outcome—E[
|
= 1]—was missed or unmeasured; thus, a suitable substitute must be used to estimate the ATT. However, the value of the outcome for actual non-members—E[
|
= 0]—that is simply used to replace E[
|
= 1] is often not employed because variables affecting the decision to participate in the cooperatives might simultaneously influence the expected outcome, causing biased estimates (
Caliendo and Kopeinig 2008).
Fortunately, the PSM technique developed by (
Rosenbaum and Rubin 1983) can treat households that participate in the cooperatives as a treated group and other households that do not participate in the cooperatives but have similar propensity scores with households’ in the treated group as a control group. Consequently, the expected ROC of the control group is used as the counterfactual outcome: E[
|
= 1]. Thus, the ATT might be measured as the difference between the mean values of the treated and the control groups. In general, a PSM estimator can be written as follows:
where
P(
Zi) denotes the probability of participation in cooperatives for each household, which is known as the propensity score; this probability was computed by the probit regression model in the first stage.
The nearest neighbor-matching (NNM) and kernel-matching (KM) methods were used in the present study to match cooperative members with non-members regarding the propensity scores since these matching techniques were often seen as the most used (
Becerril and Abdulai 2010). NNM uses the individual households in the control group to match a treated individual household that had the closest propensity score, thus reducing bias. Meanwhile, KM uses the weighted averages of all individual households in the control group to construct the counterfactual outcome, thereby yielding low variance since it uses all the information from the controls (
Caliendo and Kopeinig 2008). As a consequence, these matching methods are primarily complementary.
It is necessary to thoroughly examine the matching procedure’s quality before discussing the causal impacts of cooperative membership. First, systematical differences should not remain among the covariates between the treated and untreated groups after matching based on the propensity score (
Caliendo and Kopeinig 2008). Second, the mean absolute standardized bias in the matched samples should be less than 25% (
Stuart and Rubin 2007), suggesting that the matching process is appropriate. Third, the pseudo-R
2 values show how well the regressors explain the likelihood of participation in the cooperative from the propensity score estimation before and after matching. These values should be fairly low after matching since systematic differences were eliminated among the covariates between the two groups (
Maertens and Vande Velde 2017).
Treatment effects estimated by the Heckman model: PSM is recognized as a non-parameter method, whereas the Heckman model is known as a parameter one. Indeed, the Heckman method (second stage) modified the OLS model by adding an inverse Mill’s ratio (IMR) generated in the first stage to correct possible selection bias stemming from self-selection in the simple OLS model. Thus, Equation (1) is rewritten as:
where
is defined as the inverse Mill’s ratio (IMR);
refers to the standard normal density function;
denotes the standard normal distribution fuction;
is a parameter to be estimated. The rest have already been described. Remarkably, the coefficients of
or
will display the status of the selectivity bias. If the coefficient of
is statistically significant, it indicates the presence of selection bias and vice versa.