Estimating shadow price for symbiotic nitrogen and technical efficiency for legume‐based conservation agriculture in Malawi

Abstract

Determining the value of legumes as soil fertility amendments can be challenging, yet this information is required to guide public policy and to incentivise prescribed landmanagement practices such as conservation agriculture. We use a directional input distance function (DIDF) to estimate shadow prices for symbiotic nitrogen and the technical efficiency for mixed maize-legume production systems in Malawi. The shadow prices reflect the trade-off between fertiliser nitrogen and symbiotic nitrogen required to achieve a given quantity of output. Our results reveal considerable technical inefficiency in the production system. The estimated shadow prices vary across farms and are, on average, higher than the reference price for commercial nitrogen. The results suggest that it would be beneficial to redesign the current pricesupport programs that subsidise chemical fertilisers and indirectly crowd-out organic soil amendments such as legumes.

Examining the relationship between farm size and productive efficiency: a Bayesian directional distance function approach

“…The highest posterior density intervals for all first‐order coefficients are either on the left‐side of zero (for outputs) or on the right‐side of zero (for inputs). Since our data were mean‐scaled prior to model estimation, these coefficients can be interpreted as elasticities evaluated at the mean of the sample (Hajargasht et al., ; Khataza et al., ). For example, the mean elasticities with respect to land, fertilizer, and labor are 0.50, 0.24, and 0.29, respectively.…”

“…For example, Khataza et al. () used the DIDF approach and reported mean TI of 0.52 for a sample of the Malawian integrated maize‐legume production system. For a sample of vegetable growers in Benin, Singbo et al.…”

“…In addition, this approach provides coefficient estimates and elasticities, which can aid further economic interpretations and policy conclusions. For example, by examining the estimated elasticity measures, one can explore the possibility of resource substitution or complementarity for a given production system (Khataza et al., ). Within the statistical methods available, the Bayesian method of inference is preferred here because, with this method, it is easy to impose regularity conditions implied by economic theory.…”

“…Generally, estimating directional distance function which assigns unit weights is a common empirical practice (see Färe et al. ; Hailu and Chambers ; Khataza et al., ). Since the data are deflated by mean values, the use of the unitary directional vector makes interpretation clearer in the sense that efficiency measures can be directly interpreted as proportions of sample mean values (Färe and Grosskopf, ).…”

“…Since the data are deflated by mean values, the use of the unitary directional vector makes interpretation clearer in the sense that efficiency measures can be directly interpreted as proportions of sample mean values (Färe and Grosskopf, ). The use of when the data are mean‐scaled is equivalent to using average values of inputs and outputs as directions for the translation (Färe and Grosskopf, ; Hailu and Chambers ; Khataza et al., ). As a robustness check, we apply alternative directional vectors which include the following: (1) output‐orientation or directional output distance function, which assumes that input quantities remain fixed as the frontier is approached by expanding outputs; (2) input‐orientation or directional input distance function (DIDF), which assumes that output quantities are fixed as the frontier is approached by contracting inputs; and (3) ratio vectors indicating farmers’ heterogeneity in terms of opinions or preferences for certain farm goals (see Agee et al., ; Berkhout et al., ).…”