Methods to stimulate Distributions of Rainfed Crop Yields Based of farmer Interviews

Abstract

Methods to derive and simulate crop yield distributions for use in stochastic analysis of farming systems are explained with examples from a rainfed farming area of NW Syria. MBASIC code, for implementation of the methods on micro-computers, is documented in the Appendix. Farmers were asked about their yields per hectare in good, normal, and bad years, and the frequency of such years in the past ten years. These estimates are combined to form an array of ten yield values for each farmer. The results for individual farmers are aggregated in a linear hierarchical model which allows calculation of a grand mean, a rand sum of squares, and sums of squares due to variation within farms over time and between farms. The mean sum of squares due to within-farm variation can be regarded as a true estimator for the year-to-year variability of yields per hectare in the study area: variance fol. the average farmer. The approach, of course, assumes that farmers have reliable knowledge about their own crop yields, can express these in terms of good, normal, and bad yields, and that the past ten years are representative of a longer series of years. This approach also assumes, for the sake of simplicity, that crop yields follow statistically normal distributions, fully described by their means and variances. A random series of normally distributed yield values are simulated with the Box-Muller approximation, using empirical estimates of the mean and standard deviation. This model is extended to the multivariate case of simulating correlated random series of yield values for n crops, based on a vector of empiric mean yields and an empiric variance-covariance matrix. Derivation of the latter from farmer interviews requires the additional assumption that, for each farmer, a "good year" for one crop is a "good year" for the other crops, a "normal year" for one crop is a "normal year" for the other crops, and so on. It is shown that crop yield distributions can be reproduced in the sense that (in the parameters) the simulated distributions are not significantly different from the empiric distributions. Such simulated yields are appropriate for driving stochastic whole-farm models. Where long-time series of yield data are not available, empiric estimates of crop yield distributions may be derived from interviews of farmers with long experience in the area.