An expected value of sample information (EVSI) approach for estimating the payoff from a variable rate technology.

Abstract

This paper examines the payoff to variable rate technology (VRT) using a Bayesian approach following literature on the expected value of sample information (EVSI). In each cell within a field, we compare the expected payoff from an optimal variable rate conditioned on a signal from that cell, with the expected payoff from a uniform rate technology (URT) that is optimal for all cells in the field. This comparison, when evaluated across the theoretical distribution of signals, provides an estimate of the expected gross benefit from VRT relative to URT. Under plausible assumptions, a closed-form algebraic solution relates this expected benefit to field and nitrogen response characteristics. We apply our approach to data from on-farm field-level experiments conducted by the Data-Intensive Farm Management Project (DIFM) (Bullock, et al. 2019), which examined nitrogen (N) response across cells for which soil electroconductivity (EC) served as the signal related to nitrogen response. We calculate the expected gross benefits to be about $1.81/ac, insufficient to support costs of VRT implementation. Our model provides quantitative estimates of the extent to which this poor outcome could be improved by a higher correlation between the EC signal and the state of nature of interest, by higher variability of the state of nature across cells, and by a sharper curvature of yield response to N