Bayesian Estimation of Possibly Similar Yield Densities: Implications for Rating Crop Insurance Contracts

Abstract

The Agricultural Act of 2014 solidified insurance as the cornerstone of U.S. agricultural policy. The Congressional Budget Office (2014) estimates that this act will increase spending on agricultural insurance programs by $5.7 billion to a total of $89.8 billion over the next decade. In light of the sizable resources directed toward these programs, accurate rating of insurance contracts is of the utmost importance to producers, private insurance companies, and the federal government. Unlike most forms of insurance, agricultural insurance is plagued by a paucity of spatially correlated data. A novel interpretation of Bayesian Model Averaging is used to estimate a set of possibly similar densities that offers greater efficiency if the set of densities are similar while seemingly not losing any if the set of densities are dissimilar. Simulations indicate that finite sample performance—in particular small sample performance—is quite promising. The proposed approach does not require knowledge of the form or extent of any possible similarities, is relatively easy to implement, admits correlated data, and can be used with either parametric or nonparametric estimators. We use the proposed approach to estimate U.S. crop insurance premium rates for area‐type programs and develop a test to evaluate its efficacy. An out‐of‐sample game between private insurance companies and the federal government highlights the policy implications for a variety of crop‐state combinations. Consistent with the simulation results, the performance of the proposed approach with respect to rating area‐type insurance—in particular small sample performance—remains quite promising.

Value of Incorporating ENSO Forecast in Crop Insurance Programs

“…In this study, we focus on α = 0.9, which is the most commonly selected coverage level. It accounts for 95% of the recent policies (Ker, Tolhurst, and Liu ). An actuarially fair premium rate is given by: …”

“…Because crop yield distributions from geographically proximate areas tend to resemble one another due to common environmental and climatic conditions, pooling data from adjacent areas can often improve yield estimation. The benefit of pooling information from multiple units has been well established in the literature (Goodwin and Ker 1998;Goodwin and Mahul 2004;Annan et al 2013;Ker, Tolhurst, and Liu 2015;Zhang 2017). In this study, we adopt the flexible semiparametric density ratio approach developed by Zhang (2017).…”

“…We follow Ker, Tolhurst, and Liu (2015) and Zhang (2017) to estimate actuarially fair premium rates using a simulation-based method. First, we apply the DR approach to estimate yield densities from the pooled data and individual ENSO phases.…”

Assessing effects of federal crop insurance supply on acreage and yield of specialty crops

“…Much research focuses on federal crop insurance, but mostly in the context of field crops. Some of the research analyzes the demand for crop insurance (e.g., Coble, Knight, Pope, & Williams, ; Goodwin, ; Hazell, Bassoco, & Arcia, ; Mishra & Goodwin, , ) or producer responses to crop insurance (e.g., Du, Feng, & Hennessy, ; Du, Hennessy, & Feng, ; Miao, Feng, Hennessy, & Du, ; Quiggin, Karagiannis, & Stanton, ), whereas others explore the feasibility and design of the FCIP (e.g., Annan, Tack, Harri, & Coble, 2013; Chalise, Coble, Barnett, & Miller, ; Chambers, ; Coble, Knight, Pope, & Williams, ; Gardner & Kramer, ; Goodwin, ; Goodwin & Ker, ; Ker & Goodwin, ; Ker, Tolhurst, & Liu, ; Nelson & Loehman, ; Quiggin et al., ; Skees & Reed, ; Woodard, Pavlista, Schnitkey, Burgener, & Ward, ; Woodard, Sherrick, & Schnitkey, ; Woodard & Verteramo‐Chiu, ).…”

Development of public-private partnership in agricultural insurance (on the example of the Saratov region)

“…Теоретическую и методологическую основу исследования соста-вили труды отечественных и зарубежных уче-ных по вопросам агрострахования, разработки системы сельскохозяйственного страхования с государственной поддержкой и интереса сель-скохозяйственных товаропроизводителей к аг-рострахованию в целом [2,4,5,7,8], а также нормативно-правовые документы, в том числе федеральные законы РФ.…”