Whither Broad or Spatially Specific Fertilizer Recommendations?

Are spatially specific agricultural input use recommendations more profitable to smallholder farmers than broad recommendations? This paper provides a theoretical and empirical modeling procedure for determining the optimal spatial scale at which agricultural researchers can make soil fertility recommendations. Theoretically, the use of Bayesian decision theory in the spatial economic optimization model allows the complete characterization of the posterior distribution functions of profits thereby taking into account spatial heterogeneity and uncertainty in the decision making process. By applying first order spatial scale stochastic dominance and Jensen’s inequality; theoretically and empirically, this paper makes the case that spatially specific agricultural input use recommendations will always stochastically dominate broad recommendations for all non-decreasing profit functions ignoring the quasi-fixed cost differentials in the decision itself. These findings are consistent with many economic studies that find precision agriculture technologies to be more profitable than conventional fertilizer (regional or national recommendations based) application approaches. The modeling approach used in this study however provides an elegant theoretical justification for such results. In addition, seasonal heterogeneity in maize responses was evident in our results. This demonstrates that broad recommendations may not only be wrong spatially but also seasonally. Further research on the empirical aspects of spatio-temporal instability of crop responses to fertilizer application using multi-location and multi-season data is needed to fully address the question posed initially. The decision making theory developed here can however be extended to incorporate spatio-temporal heterogeneity and alternative risk preferences.