Probability Distributions of Crop Yields: A Bayesian Spatial Quantile Regression Approach

Probability distributions of crop yields are important for understanding technological change, the effects of weather on crop production, and production risk. It can be difficult to model these distributions because they are time‐varying and do not follow a particular parametric form. To overcome some of the empirical challenges inherent in yield modeling, we implement a Bayesian spatial quantile regression model for the conditional distribution of yields. The statistical model is semiparametric, borrows information across space and quantile level, and models the complete quantile process. We use the model in two empirical applications where flexible modeling of the yield distribution is essential. First, we evaluate the effects of weather across quantiles and conduct a Bayesian test of the difference in the rate of technological change at opposite ends of the yield distribution. We then derive crop insurance premium rates and compare the predictive performance of the Bayesian spatial quantile regression to other existing approaches for modeling time‐varying yield distributions.