Stochastic trends in crop yield density estimation

Abstract

The search for improved methods of estimating crop yield density functions has been a theme of recurrent research interest in agricultural economics. Crop yield density functions are the statistical instrument that generates probability estimates of yield risk, and risk is an important decision variable in production agriculture. Recent research in crop yield density estimation suggests that yield probability estimates can be sensitive to the way yield data are filtered, and if true, then the search for an “adequate filter” is warranted. Such a quest is pursued in this study. It is proposed that unit-root tests can be used to identify the time-series properties of yields and that the outcome of these tests makes the choice of an appropriate filter trivial. Once a filter has been chosen, then nonparametric methods can be used to more flexibly fit a crop yield density function. The study uses state and county level (aggregated) yield data for corn and soybeans in Arkansas and Louisiana for the period 1960-2008, comprising 121 yield series. The results identify three main types of yield processes (and filters), namely, a unit-root (first differences), a trend stationary process (detrending), and stationary (remove the mean). More specifically, the study finds that for Louisiana soybeans, for example, 73% of the county yields studied can be represented by a unit-root process, 12% followed a trend stationary process, and the remaining 15% were stationary. One important implication of this finding is that the use of a universal yield filter may generate inaccurate yield probability estimates, which translates into inaccurate estimates of crop insurance risk premia. To shed light into relevance of these findings, yield density functions were estimated under alternative filtering scenarios and pairwise probability estimates compared. In particular, the results suggest sizeable differences in the two estimates, which at times can reach -1,153.65%. In addition to providing a detailed analysis of the findings, the study assessed the relevance of the findings in the context of two current risk management programs, namely a group risk plan (GRP) and average crop revenue election (ACRE) program. Limitations of the study are also highlighted.