Closing the Gaps in Experimental-Observational Crop Responses Estimates: Bayesian Approach

A stylized fact of African agriculture is that experimentally derived crop responses to inorganic fertilizer application are substantially greater than those from observational studies e.g., farm surveys and administrative data. The continuing divergence between experimental and observational crop responses reported in the literature coupled with the recent debates on the costs and benefits of the re-surging farm input subsidy programs in Africa have ignited the old problem of reconciling these estimates. This paper argues that progress on closing the gaps has been impeded by the focus on the mean crop response differences while ignoring the enormous uncertainty and heterogeneity. I show in this paper that a convenient way of dealing with different crop response function estimates is to use a Bayesian approach to get combined estimates that are weighted by the uncertainty in each data source and can be adjusted for unobserved heterogeneity using a Bayesian hierarchical model. The plausible assumption that makes this approach optimal is that the experimental process overestimates the “true” crop response while observational methods overestimate failures. Using nationally representative experimental, survey, and administrative datasets from Malawi, I find that even after combining the estimates; crop responses are low, heterogenous across space and that ignoring the parameter uncertainty and heterogeneity in crop responses inevitably results in wrong policy prescriptions.