Adaptive local parametric estimation of crop yields: implications for crop insurance rate making

Abstract

A rigorous estimation model of crop yields which ensures accurate and actuarially sound insurance premiums is of utmost importance to maintain sustainable and viable risk management solutions for producers, insurers, and governments. A major challenge in estimating crop yield models arises from non-stationarity of the data generating process due to technological change and climate change. In this paper, we introduce a local adaptive parametric approach to deal with the non-stationarity of crop yields and to estimate the time-varying parameters of crop yield models. Results from an empirical application to major crops in the U.S. indicate that the proposed model precisely captures the evolution of crop yield risks: yield risks for corn and cotton are decreasing, but are increasing for winter wheat. In terms of forecasting performance, the adaptive local parametric model, in general, outperforms the linear spline model that is commonly used in the current rating methodology. A rating analysis suggests that the proposed model has the potential to obtain more accurate rates and that most current insurance premium rates are overestimated for corn and cotton, but are underestimated for winter wheat.

Simultaneous borrowing of information across space and time for pricing insurance contracts: An application to rating crop insurance policies

“…Consider we have counties each with adjusted yields where represents the adjusted yield realization in time from county . We follow the literature (Shen et al, 2018) and partition the yield data into sets of 20 years. Given that we have yield data from 1951 to 2017, we have three sets of historical yield data: 1998–2017; 1978–1997; and 1958–1977.…”

“…To evaluate whether the proposed estimators are more efficient than the current RMA methodology, we conduct an out‐of‐sample retain‐cede rating game, where two players using different methodologies estimate premium rates and adverse select against one another. The game was first proposed by Ker and McGowan (2000) and has since been employed by Ker and Coble (2003), Racine and Ker (2006), Harri et al (2011), Annan et al (2014), Tack and Ubilava (2015), Tolhurst and Ker (2015), Zhang (2017), Shen et al (2018), Park et al (2018), and Ramsey (2019) to justify alternative rating methodologies. The game was modified with an additional test of rating efficiency in Ker et al (2016).…”

“…With respect to crop insurance, it does not seem likely that yield losses from the 1950s and 1960s can inform, to the same degree as yield losses from the 2000s, about possible losses in 2019. Shen, Odening, and Okhrin (2018), using adaptive smoothing, found that yields should be trimmed after approximately 20 years. Liu and Ker (2019), using nonparametric hypothesis tests, found that yields should be trimmed after 25–30 years.…”

“…The Bayesian methodology is the most flexible, in that the weight varies not only between space and time but within space and time as well. Note, all three proposed methods allow historical trimming (as per Liu & Ker, 2019; Shen et al, 2018) without completely discarding the trimmed yield data. Moreover, the proposed methods capture possible efficiency gains from smoothing across space (as found by Ker et al, 2016; Park et al, 2018; Ramsey, 2019).…”

When Less Is More: On the Use of Historical Yield Data with Application to Rating Area Crop Insurance Contracts

“…Specifically, the game allows two players using different methodologies to estimate premium rates and adversely select against one another. The game was first proposed by Ker and McGowan (2000) and has since been employed by Racine and Ker (2006), Harri et al (2011), Annan et al (2013), Tack and Ubilava (2015), Zhang (2017), and Shen, Odening, and Okhrin (2018) to justify alternative rating methodologies. The game was modified with an additional test of rating efficiency by Ker, Tolhurst, and Liu (2016).…”