Premium Estimation Inaccuracy and the
Actuarial Performance of the US Crop Insurance Program
Octavio A. Ramirez
1
and
Carlos A. Carpio
2
1
Contact Author: Professor and Head of the Department of Agricultural and Applied Economics,
University of Georgia, 301 Conner Hall, Athens, GA 30602, e-mail: oramirez@uga.edu, phone:
(706) 542-2481, fax: (706) 542-0739.
2
Assistant Professor, Department of Applied Economics and Statistics, Clemson University.
Selected Paper prepared for presentation at the Agricultural & Applied Economics
Association’s 2011 AAEA & NAREA Joint Annual Meeting, Pittsburgh, Pennsylvania, July
24-26, 2011.
Copyright 2011 by [authors]. All rights reserved. Readers may make verbatim copies of this
document for non-commercial purposes by any means, provided that this copyright notice
appears on all such copies.
Premium Estimation Inaccuracy and the
Actuarial Performance of the US Crop Insurance Program
Abstract
This article explores the impact of the likely levels of inaccuracy associated with two main types of
premium estimation methods, under different sample sizes, on the actuarial performance of the US
crop insurance program. The analyses are conducted under several plausible assumptions about the
insurer versus the producers’ estimates for their actuarially fair premiums. Significant differences
are found due to estimation method and sample size, with the currently used procedures resulting in
the worse actuarial performance. Several conclusions and recommendations are provided that could
markedly reduce the amount of public subsidies needed to keep this program solvent.
Key Words: Agricultural Subsidies, Crop Insurance Premium Estimation, Loss-Cost Procedures,
Risk Management Agency.
Crop insurance is the most popular risk management tool used by U.S. agricultural producers. In
2009, the U.S. crop insurance program covered close to 265 million acres, assuming nearly $80
billion in liabilities. The Risk Management Agency (RMA) (please refer to the glossary at the end
of the paper for a definition of all acronyms), a division within the US Department of Agriculture,
administers this program. The traditional and most popular product offered by the RMA, which is
the focus of this paper, is a farm level, multiple-peril, crop yield insurance policy (MPCI). This
policy protects against low yield and crop quality losses due to adverse weather and unavoidable
damage from insects and disease (Barnett, 2000). High participation has been achieved through
large subsidies, with farmers as a whole now paying less than 50% of the total amount of premiums
required to keep the program solvent (USDA/RMA 2010a). The need for substantial subsidies to
achieve high levels of participation has in part been attributed to “adverse selection,” which is said
to occur when the producers have more information about the risk of loss than the insurer and are
thus better able to determine the fairness of the premium rates (Harwood et al. 1999).
The perceived inability of the RMA to precisely estimate the actuarially fair premium that
should be charged to a particular producer is a matter of concern. Because of its obvious linkage
with crop insurance program performance, substantial research efforts have been conducted to
improve rating procedures at the farm level (Glauber 2004; Carriquiry, Babcock, and Hart 2008;
Anderson, Harri and Coble 2009; Rejesus et al 2010). Given the large disparities in program
indemnities versus premiums observed across crops and regions (Glauber 2004; Babcock 2008) it
appears that rating inaccuracy might be creating a problem at more aggregate levels as well. In
addition to their impact on the actuarial performance of the crop insurance program, incorrect rates
can affect the producers’ economic welfare and the incentives and returns to the private insurance
companies that sell Federal crop insurance at those rates.
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A critical issue affecting premium estimation accuracy is the choice of the method used to
model/approximate the underlying yield distribution. The three general procedures that have been
proposed for this purpose are non-parametric, semi-parametric and parametric in nature (Ramirez,
McDonald and Carpio 2010). The nonparametric approaches, such as those used by the RMA, are
free of a functional form assumption and thus generally more flexible. However, they can be
inefficient relative to parametric procedures under certain conditions. Specifically, according to Ker
and Coble (2003), “it is possible, perhaps likely, for very small samples such as those corresponding
to farm-level yield data, that an incorrect parametric form –say Normal– is more efficient than the
standard nonparametric kernel estimator.”
The parametric procedures assume that the data-generating process can be adequately
represented by a particular parametric probability distribution function. Therefore, the key to their
accuracy is that said distribution is flexible enough to closely approximate the stochastic behavior
of the underlying random variable of interest (Ramirez and McDonald 2006). The main advantage
of this method is that, if the assumed distribution can adequately represent the data-generating
process, it performs relatively well even in small sample applications. Semi-parametric methods
show significant potential because they encapsulate the advantages of the parametric and non-
parametric approaches while mitigating their disadvantages (Ker and Coble 2003; Norwood,
Roberts, and Lusk 2004).
Ramirez, Carpio, and Rejesus (2010) recently assessed the accuracy of select rating methods
under different field conditions encompassing sample size, the number of farms from which data is
available, and the level of yield correlation across farms. The rating methods evaluated by these
authors include non-parametric historical loss-cost procedures that rely on indemnity data (similar
to those currently used by the RMA) and flexible parametric methods which use simulations from
estimated yield distribution models to compute the premiums. While it is recognized that there are
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other worthy procedures that could be considered, this article builds on their work to explore the
impact of the likely levels of inaccuracy associated with these two particular premium estimation
methods under different sample sizes, on the actuarial performance of the U.S. crop insurance
program. The analyses are conducted under several plausible assumptions about the producers’
(versus the RMA) estimates for their true premiums, which is a critical issue that has not been
addressed in previous literature either. Several conclusions and recommendations are provided that
could substantially reduce the amount of public subsidies needed to keep this program solvent.
Theoretical Framework
A farmer participating in the Federal MPCI program selects one of several possible yield guarantees
( and some price guarantee level
. The expected value of indemnity for coverage at the
100% of the mean (M) level of coverage is given by
,
where
is the expectations operator and
the probability density function of yields. Knowledge of
is important for both the farmer and the insurer as they make their decisions to buy or sell a
yield insurance product. For example, as shown in Coble et al. (1996) a risk neutral producer will
only purchase yield insurance if
is higher than the premium charged.
From the insurer’s perspective,
is the actuarially fair premium, i.e. the one it needs to
charge to avoid an expected loss. Since
is unknown, it has to be estimated by both producers
and insurers and, therefore, is subject to sampling variability. Additionally, given that the type,
quality and quantity of information available these two parties are markedly different, the amounts
of variability in their estimated
are also likely to differ. For the remaining of the paper, since
the analysis is conducted from the insurer’s perspective, the actuarially fair premiums (
) are
also referred to as the true premiums (TP).
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