Investigating the performance of different estimation techniques for crop yield data analysis in crop insurance applications

Abstract

We investigate the performance of the OLS-, M-, MM-and the Theil-Sen-estimator for crop yield data analysis in crop insurance applications using Monte Carlo simulations. In particular, the performance is assessed with respect to trend estimation, prediction of future yield levels and the estimation of expected indemnity payments. In agreement with earlier findings, other estimators are found to be superior to OLS in simple regression problems if yield distributions are outlier contaminated and heteroscedastic. While this conclusion is also valid for subsequent applications such as yield prediction and the estimation of expected indemnity payments, the difference between the considered estimators becomes less distinct.For these applications, we find particularly the M-estimator to be a good compromise between high breakdown (very robust) estimators and the very efficient OLS-estimator.Because no regression technique dominates all others in all applications and scenarios for error term distributions, our results underline that the choice of the estimation technique should be dependent on the purpose of the crop yield data analysis. However, alternative estimators such as M-, MM-and Theil-Sen-estimator can reduce (and bound) the risk of unreliable or inefficient trend estimation and applications.3 1 Introduction and MotivationCrop yield insurances are of increasing importance in agriculture (Bielza et al., 2008, Ozaki andSilva, 2009). In order to reduce the potential of market failures, appropriate design and specification of insurance contracts is of outmost importance. In particular, the identification of crop yield distributions and its parameters is a crucial step for the estimation of insurance premiums and the specification of trigger yield levels. To quantify risk exposure in crop production, it is essential to identify and remove deterministic trends in time series of crop yield data because crop yield variability would be overestimated otherwise. Thus, the detrending of crop yield data is usually a central aspect in the analysis of crop yield data for insurance applications and the determination of crop yield distributions.However, several alternatives to this trend removal approach have been suggested in the literature. For instance, the use of time series components and the simultaneous estimation of time trends and yield distribution parameters have been suggested (e.g. Bessler, 1982, Zhu et al., 2008. The use of deterministic trend models has been also critically discussed in other economic applications (e.g. Nelson and Plosser, 1982 Finger, 2010b, Gallagher, 1987, Just and Weninger, 1999, Kaylen and Koroma, 1991, Swinton and King, 1991. Furthermore, the implications of employed methods in trend analysis on subsequent steps of data analysis such as yield prediction and estimation of expected insurance indemnities have not been investigated so far. These are, however, of particular importance because the detrending of crop yield data is usually only the first step in crop yield data analysis. ...

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