3.2.1. Conditional Logit (CL) Estimates
Column 2 of Table 4
presents the results of the CL model. As indicated earlier in the section on methodology, the CL model imposes the assumption of IIA. However, if the IIA assumption does not hold, then the CL model would yield biased estimates [33
]. The Hausman and McFadden test for the IIA property was applied under the null hypothesis of no violation in order to test the IIA assumption [34
]. Violation of the IIA assumption is not evident from the test results. This, therefore, suggests that the CL modelling results are likely to yield unbiased estimates of the attributes. We equally used the likelihood ratio (LR) test under the null hypothesis that all the coefficients of the model are equal to zero in order to test for model robustness. Since the computed LR statistic of x2
(7) = 3114.1 is larger than the computed t
-value of 18.5 at seven degrees of freedom, we reject the null hypothesis and conclude that the model has a robust explanatory ability.
As shown (column 2, Table 4
), most of the coefficients of the attributes of the CL model are highly significant at 5% and below, except for the alternative specific constant (ASC). The significance of the attribute and the sign shows that, ceteris paribus
, deep-well, drilling, drip irrigation, wastewater and organic matter from human sludge increase the likelihood of selecting a given AWM and RRR intervention option; while higher costs of a choice option decreases the probability that it would be preferred, keeping all other attributes constant. The positive and insignificant coefficient of the ASC suggests that farmers have preference for the proposed AWM and RRR intervention options. However, the expected utility impact is bidirectional. That is, it can occur from the attributes or from the status quo scenario. This is consistent with the results of the descriptive statistics (Table 3
), which show that about 33.33% of farmers were willing to keep their status quo level.
Overall, the CL results therefore suggest that farmers would prefer an AWM and RRR intervention solution that will guarantee constant water supply and availability (deep-well), efficient water use and labour saving (drip irrigation), abundant crop nutrients (wastewater), and soil health improvement and fertility restoration (organic matter). We also found considerable consistency with economic theory. Specifically, that the cost of an AWM and RRR intervention option reduces demand for a given AWM and RRR intervention option. The empirical findings, therefore, suggest the existence of significant values and preferences for the stated AWM and RRR attributes.
However, despite the fact that the IIA assumption holds in the CL model, CL further assumes homogeneity across individual preferences. Since preferences are heterogeneous, we need to account for this heterogeneity in order to obtain unbiased estimates of individual preferences. In addition, for a prescription of policies that take into account equity concerns, accounting for preference heterogeneity is critical [22
3.2.2. Latent Class Logit (LCL) Estimates
In order to explore if heterogeneity in farmers’ preferences may reflect systematic variation and be ascribed to groupings among farmers, we therefore used the latent class logit (LCL) model. The LCL model postulates a discrete distribution of tastes in which individuals are intrinsically sorted into a number segments (or classes), with each class holding the same preferences (homogenous in preferences) and heterogeneous across segments.
], the age, sex of the farmer, experience in dry-season vegetable production, average income earned from vegetable production, frequency of production in the dry-season, and land size were used to differentiate farmers into groups. The Akaike information criterion (AIC) and Bayesian information criterion (BIC) were used to select the preferred model in terms of the number of classes. According to [37
], the preferred model is the one with the lowest AIC and BIC. As observed (Table 5
), the criteria increase slightly as the number of class increases, but the improvements of the predictive quality are much smaller from models of class 2 to that of class 3. This suggests that a two-class solution may be appropriate. Hence, the model with two classes is the preferred specification.
shows the effects of farmers’ characteristics on the probability of class membership. As shown (Table 7
), the average probability of being in class 1 is estimated at 82.6% and in class 2 at 17.4%. Equally, while 84% of the sample holds class 1 membership, about 16% are in class 2. Furthermore, the class-membership model parameters reveal that the sex of farmers (male), age (older), higher income and larger land size holdings increase the probability of belonging to class 1. Similarly, in class 2, the class membership coefficients show that farmers having more experience in vegetable production and farmers that produce vegetables more frequently in the dry season are more likely to belong to this class.
The LCL results suggest that there is substantial heterogeneity in preferences for AWM and RRR attributes across classes, as indicated by the differences in the magnitude, significance and signs of the parameters (column 3, Table 5
). As expected, the coefficients of the cost attribute are highly significant, at 1% in both models. However, while it is negative in the class 1 membership model, it is positive in the class 2 model. The latter is so perhaps because class 2 farmers produced more frequently in the dry-season and, as such, are more willing to incur higher costs for a given AWM and RRR intervention option to ensure dry-season production.
The results reveal, furthermore, that farmers belonging to class 1 exhibit a positive preference for drilling, drip irrigation, treated wastewater and treated organic matter from human sludge, as demonstrated by the positive sign of the coefficients of these attributes. Thus, it seems that when the farmer is an older male, has large land holdings, and earns more from dry-season vegetable production, he would prefer to invest in drilling, drip irrigation, wastewater and organic matter to produce more in the dry season. This is not surprising considering the fact that dry-season vegetable production is labour intensive, very strenuous, time- and water-consuming, as well as being highly dependent on soil nutrients and fertility. Thus, investing in drilling, drip irrigation technology, wastewater and organic matter would not only guarantee a constant water supply and availability, but would equally ensure that water is efficiently used, time and labour is saved, crops will receive abundant nutrients, and that there would be improved soil health and fertility.
Furthermore, the results show, by contrast, that class 2 farmers have a positive preference only for drip irrigation. This is expected, as drip irrigation is widely presented as the ideal option for the efficient use of water in agriculture in a water-scarce region like Burkina Faso. In fact, because class 2 farmers produced more frequently in the dry season, water efficiency is of paramount importance to them. Thus, it is therefore not surprising that they expressed a higher preference for drip irrigation than other AWM and RRR attributes. Similarly, their preference for deep-well is negative, which means that they express a greater dis-utility for this attribute as a SWI to ensure water availability in the dry season. Based on their experience, it seems that deep-wells cannot provide and ensure constant water availability for production, especially during the dry-season. Even if they do, experience has shown that farmers might need to put in extra effort to ensure water availability.
The results of the LCL model that assumes homogeneity among farmers and heterogeneity across farmers’ group reveal significant preferences for the proposed AWM and RRR intervention solutions. However, the model does not show the sources of heterogeneity among farmers [26
]. To address this issue in our analysis, we used the mixt logit model.
3.2.3. Mixt Logit Estimates
In order to estimate the mixt logit (ML) model, the cost attribute and the ASC variable were specified as fixed. Also, to ensure that the signs of the standard deviations can change throughout the full range of the estimated model, all other attributes of the AWM and RRR solutions were entered as random parameters assuming a normal distribution [38
]. To test for model robustness, we again used the likelihood ratio test statistics. The LR test result reveals a computed value of x2
(5) = 16.93 as shown in column 4 of Table 4
. However, since the computed LR value is greater than the t
-value of x2
(5) = 15.1, we conclude that the model has a higher level of parametric fit with very robust explanatory ability. These results are shown in column 4 of Table 4
Note that, as in the case of the CL and LCL models the coefficients of cost attribute and the ASC in the ML model remained unchanged in signs. According to [39
], the estimated means and standard deviations of the normally distributed coefficients reported in column 4 of Table 4
provide information about the proportion of farmers anticipating a positive value on a particular attribute, as well as those that that place a negative value on that attribute (i.e., the probability distribution). Thus, an attribute is considered to have no impact on a farmer’s choice decision when both the estimates of the mean and the standard deviation are not significantly different from zero [41
Based on the derived standard deviations of parameter distributions, the results indicate the existence of heterogeneity in preference among the farmers for all attributes except deep-well and wastewater. This is based on the fact that, while the coefficients of the means for deep-well and wastewater are significantly positive, this does not hold for their respective standard deviations. In other words, although deep-well and wastewater are necessary interventions for farmers, the results suggest no diversity of preferences among farmers for these two attributes. This may be related to cost constraints. By contrast, the coefficients for means and standard deviations for drilling (borehole), drip irrigation, and organic matter attributes, were all significant and positive. This, therefore, shows that on average, vegetable farmers preferred AWM and RRR intervention policies that featured drip irrigation, drilling, and organic matter from human sludge. This is not surprising, as these attributes would guarantee a constant water supply and availability, efficiency in water use, time and labour saving, as well as improvements in soil health and fertility essential for dry-season vegetable farming.
Overall, the results indicate that there is a significant heterogeneity in preferences among farmers for drilling, drip irrigation and organic matter. However, not all the farmers felt that these three attributes were necessary. For instance, while an estimated 79.8% (The value of 79.75% (probability distribution of preference) is calculated as φ [−(mean parameter estimate/parameter standard deviation)] where [𝑥] is the cumulative standard normal distribution) of the farmers prefer drilling as SWI to ensure water availability in the dry season, more than 99.8% indicated a positive preference for the drip irrigation technology to save and use water efficiently. In addition, the use of the treated organic matter from human sludge seems to influence the preferences of almost all of the farmers. Evidence from the estimates parameters indicates that about 99.9% of farmers prefer organic matter from human sludge to ensure crop nutrients.
Judging from the high positive probability distribution, we may conclude as in [42
] that, collectively, the attributes used in the CE design captured the range of preferences of the farmers with respect to sustainable agricultural productivity through AWM and RRR intervention solutions.