THREE ESSAYS ON CROP INSURANCE: RMA’S RULES AND ...
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THREE ESSAYS ON CROP INSURANCE: RMA’S RULES AND PARTICIPATION, AND PERCEPTIONS BY ALISHER UMAROV B.S., North Dakota State University, 2000 M.S., North Dakota State University, 2003 DISSERTATION Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Agricultural and Consumer Economics in the Graduate College of the University of Illinois at Urbana-Champaign, 2009 Urbana, Illinois Doctoral Committee: Professor Bruce Sherrick, Chair Professor Philip Garcia Professor Scott Irwin Professor Gary Schnitkey Assistant Professor Joshua Pollet, Emory University
Transcript of THREE ESSAYS ON CROP INSURANCE: RMA’S RULES AND ...
THREE ESSAYS ON CROP INSURANCE: RMA’S RULES AND PARTICIPATION, AND PERCEPTIONS
BY
ALISHER UMAROV
B.S., North Dakota State University, 2000 M.S., North Dakota State University, 2003
DISSERTATION
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Agricultural and Consumer Economics
in the Graduate College of the University of Illinois at Urbana-Champaign, 2009
Urbana, Illinois
Doctoral Committee:
Professor Bruce Sherrick, Chair Professor Philip Garcia Professor Scott Irwin Professor Gary Schnitkey Assistant Professor Joshua Pollet, Emory University
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TABLE OF CONTENTS
INTRODUCTION......................................................................................................... 1
CHAPTER 1: Effect of Rules for Calculating APH on the Performance of APH
Insurance ....................................................................................................................... 6
CHAPTER 2: Crop Insurance Usage in Lake Woebegone........................................ 45
CHAPTER 3: Farmers’ Subjective Yield Distributions and Elicitation Formats...... 81
CONCLUSION ......................................................................................................... 114
REFERENCES.......................................................................................................... 117
AUTHOR’S BIOGRAPHY ...................................................................................... 121
1
INTRODUCTION
Since its inception in 1930, crop insurance programs have grown from minor
government programs to a major instrument for delivering government assistance.
In 2008 there were 1.96 million crop insurance policies sold with a liability of $90
billion, covering 272 million acres. For context, the corresponding figures in 1998
were 1.2 million policies sold with a liability of $27.9 billion, covering 182 million
acres. While these numbers are impressive, current levels of participation and the
associated actuarial performance in the program have been achieved only after
significant producer subsidies were instituted, and the program has struggled with
low participation levels and the poor actuarial performance for the major part of its
existence.
Because a broad level of participation in crop insurance is necessary for sound
actuarial performance of the program, the factors determining participation have
received considerable research attention. Lack of participation is often cited as the
result of crop insurance interactions with other risk management tools (Mahul and
Wright, 2003), presence of government subsidies, and adverse selection. While the
moral hazard, adverse selection, or government assistance play an important role in
explaining participation, there are other issues that could be important as well. For
example, risk perceptions of the producers might be crucial in determining crop
insurance decisions. If a farmer perceives that his yield is above average (both in
terms of level and safety), he might conclude that the insurance is overpriced.
Another factor that could influence participation is the insurance rating process.
RMA has documented consistent complaints from farmers stating that the current
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method for calculating APH yields and the insurance indemnity does not provide
sufficient level of protection.
The purpose of this dissertation is to further examine the factors that influence
farmers’ decisions to participate in crop insurance programs. The factors considered
are RMA rules and farmers’ yield perceptions. In particular, the first paper examines
the role of Risk Management Agency’s (RMA) APH calculation rules on the
performance, participation, and risk protection level of actual producer history
(APH) insurance. The second and third papers examine the presence of behavioral
biases, such as miscalibration and better-than-average (BTA) effect in farmers’
perceptions, and relate these biases to the participation.
Current RMA rules use a simple average of recent yields with required
substitution of lower “plugged” yield in period absent data. Several problems are
likely to arise as a result of using this formula. Because APH is a simple average
that relies on a small number of outcomes, it is easily affected by extremes and small
sample issues. Also, the APH effective coverage can be misstated if small sample of
outcomes contains several years of poor yields, or one or more years of well-above
average yields. Another problem involves trending yields and the process used to
compute APH. RMA rules ignoring trend induce an easily identified bias in
“expected” yields. As a result, an average of past data will result in APH values that
are on average below the “true” expected yield. This in turn will lead to a lower
effective protection level than would be the case if the APH accurately depicted the
mean of the contemporaneous yield distribution. A related problem is induced by
small sample variability. Because the APH mean utilizes a relatively small number
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of outcomes, the mean is subject to high variability and is a low-efficiency estimate.
A simple simulation can show that even with 10 years of observation, the precision
of the mean is likely to be significantly compromised. The first chapter therefore
examines the impact of the trend and of the sample size variability on the
participation, performance, and risk protection of APH insurance. The simulation
model is developed with controllable “true” distributions constructed from NASS
data for each county in Illinois, but can be easily extended for any farm-level
situation of interest.
While the first paper examines the influence of RMA’s rules on the
participation and actuarial performance, the second and third papers analyze the role
that cognitive biases may play in insurance decisions. Since the first papers in
behavioral economics were published, the field of behavioral economics/finance has
experienced tremendous growth. Currently, there are several journals in economics
and finance that specialize in behavioral research, and some universities teach the
subject in advanced courses. The results from related behavioral research indicate
that cognitive biases influence individuals’ decision-making. Two of the more
commonly expressed biases are “miscalibration” (defined as systematically misstated
correspondence between subjective and objective distributions) and the “better than
average” (BTA) effect (defined as individuals’ tendency to maintain unrealistically
positive assessment of one’s skills and abilities, especially in relation to peer group).
These two possibilities are examined in this dissertation.
The second and third papers examine producers’ yield perceptions and relate
them to their behavior. Both papers use data from the crop yield risk survey (CYRS)
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developed under a cooperative agreement with RMA and the University of Illinois.
Conducted in 2002, this survey covers corn and soybean producers from Indiana,
Iowa, and Illinois. The survey underwent an extensive reviewing process by
University personnel and economists from the Economic Research Service of USDA.
It elicited information on demographics, risk management, risk attributes and
perceptions, and the conjoint ranking of insurance products and attributes.
The second chapter examines the relationship between risk perceptions and crop
insurance by linking the BTA effect and miscalibration to crop insurance purchases.
Following numerous publications that showed the BTA effect and miscalibration
influence decision making and arguing that farming is likely to promote the BTA
effect, this chapter investigates whether the BTA effect systematically biases
farmers’ participation decisions. If a farmer believes that his/her farming skills are
above average, he/she may conclude that he/she is likely to outperform others and
consequently “average” priced insurance will be relatively less attractive. This
hypothesis was tested by using crop participation as a dependent variable and
subjective yield perceptions as independent variables. The analysis was
implemented on an individual product level (yield, revenue and CAT insurance) and
across all products.
The third paper examines the role of different elicitation formats on the
subjective perception by analyzing correspondence between yield perceptions and
county yield distribution. The subjective yield perceptions were elicited under two
different formats, directly and indirectly. Both directly and indirectly-stated
subjective yields were compared to the county yields. If one of these formats
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displays systematic differences from county-level yields, the argument can be made
that the elicitation approach substantially influences the measures of risk recovered
from producers, therefore further confounding efforts to design attractive and effect
insurance products.
Overall, this dissertation presents interesting findings about the role of
perceptions and RMA’s rules on the participation. The findings from the papers
illustrate that the current RMA’s rules reduce protection level, participation, and
performance of the APH insurance. The dissertation also illustrates that, behavioral
biases, while present, do not reverse directional effects in insurance purchase
decisions, but only affect extent and intensity. Finally, it is know that the probability
conviction elicitation framework provides more accurate results than direct yield
elicitation.
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CHAPTER 1
Effect of Rules for Calculating APH on the Performance of APH
Insurance
Abstract
The Risk Management Agency’s rules for calculating a farmer’s Actual
Production History (APH) yield create several problems for crop
insurance users. APH calculations ignore trend, are severely affected by
extreme values, and do not vary with the length of the observed history.
This study investigates the impact of these rules on the risk protection,
participation incentives, and actuarial performance by using a simulation
model with controllable “true” yield distributions. Existing rating
methods lead to a bias which results in wide differences in implied
subsidy impacts, variations across production regions, and reduce
incentives for participation.
Crop insurance products have become increasingly popular among farmers. In 2008
approximately 1.96 million of crop insurance policies were sold with a liability of
$90 billion covering 272 million acres of land compared to 1.2 million policies were
sold with a liability of $27.9 billion covering 182 million acres. The most popular
crop insurance products (such as actual production history, crop revenue coverage,
and revenue assurance) have covered 81% of insured acres in 2006. Calculation of
product guarantees and premium rates for these products depended on producers’
actual production history (APH) yields (Carriquiry, Babcock, Hart, 2005). In general
terms, under individual yield guarantee crop contracts, a farmer is eligible for
indemnity if the actual farm yield is less than the yield guarantee specified in the
contract. A grower can select the guarantee as a percentage (coverage level) of
historical average yield (4 to 10 years) the actual production history, and the
coverage levels range from 50% to 85% in 5% increments. A before-subsidy
premium for the insurance is the product of the yield guarantee, a price set by RMA,
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and the RMA established premium rate, provided that actual yield is below the
guarantee. The indemnity is the difference between the yield guarantee and the actual
yield times the price set by RMA.
The rules for calculating a farmer’s Actual Production History (APH) are
straightforward, and are intended to provide a simple mechanism to predict a
farmer’s yield-risk exposure while limiting the incidence of adverse selection and
other rating problems. In essence, the current rule uses a simple average of recent
yields (4 to 10 years) with required substitution of lower “plugged” yields for
missing observations. No attempt is made to reflect yield trends, nor any attempt to
reflect systematic and observable differences from expected production evident in
area yields. Instead, APH relies exclusively on an individual’s own available yield
history and adjusted county yields to replace missing data.
The paper examines the impact of the RMA’s rules for calculating Actual
Production History (APH) yields on the implied degree of risk protection, on
participation, and on the actuarial performance of crop insurance across a set of
conditions that represent the experience of a wide set of farms in Illinois. The
analysis uses a simulation model with controllable “true” distributions constructed
from NASS data for each county in Illinois scaled to reflect farm-level conditions
based on information from a broad set of farms enrolled in the Farm Business Farm
Management record keeping association (FBFM). To assess the actuarial
implications, the iFARM crop insurance evaluation program is used1.
The paper identifies the directional impacts and implications for risk
protections afforded by yield insurance under the existing rules. It demonstrates that
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both sample size variability and trend omission can have serious consequences on
participation decisions and risk protection. In particular, ignoring trend reduces risk
protection afforded by crop insurance (by introducing a lag in yields), and sample
size variability compromises the APH mean precision. While these results are
consistent with findings by Skees and Reed (1986), Carriquiry et al. (2005), the
paper contributes to the literature by modeling trend and sample size variability
simultaneously and doing so to examine the impact under the RMA premium rating
structure. The paper finds significant differences between actuarial costs and RMA
premiums and identifies the reasons for the discrepancies. The study also provides a
simple approach to adjust for the trend that would clearly and easily improve the
individual performance of crop insurance, and contribute to newly emerging
suggestions for improving APH style insurance.
Background
Currently the APH insurable yields and rates are calculated using at least four and
up to ten years of farm-level yields. If less than 4 years of yield data are available,
adjusted transition yields (which are county yields times a certain percentage),
known as t-yields are used as “plug-in” values in the farmer’s history. If the farmer
has more than 10 years of data, the most distant observations are ignored.
Importantly, RMA develops all insurance rates by county regardless of the
differences in participation rates, production intensities, and existing payout
experiences. RMA examines loss cost ratios (LCR - the ratio of indemnity to
liability) adjusted to 65% coverage level using liability dollar values for the last 20
or more years starting in 1975. To reduce the impact of a single year, RMA caps its
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individual loss cost ratios at the 80th percentile of the historic LCR and distributes
the excess across all counties in a state (Josephson, Lord, and Mitchell, 2001). RMA
calculates a county insurance rate as a weighted average (weights are not disclosed)
of a given county LCR and circle LCR (an average of surrounding counties LCR).
The averaging is done to increase the predictive value of the loss ratio (Josephson,
Lord and Mitchell, 2001). The county insurance rate is known as the base county
unloaded rate. The base rate is then adjusted by APH, reference yields, and fixed rate
loading:
Exponentail
APH YieldBase Rate County Unloaded Rate Fixed Rate Loading
Reference Yield
= +
(1)
where
APH is the actual production history, or average of 4 to 10 individual farm-level
yields,
Reference Yield is the yield set by RMA intended to reflect an average yield index
for a given county,
Exponential is the an exponential factor to control for “yield variability
differences”.2 and
Fixed rate loading is the provision for catastrophic losses.
Two implicit assumptions become clear when examining the base rate
formula. First, RMA treats all APH yields the same, regardless of number of years
used to calculate the average. Yet, samples based on shorter time periods tend to be
more variable. Secondly, no adjustments for the trend are made despite increasing
yield levels across crops and regions.
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Since yields exhibit an upward trend, the calculated APH yield is likely to lag
the expected yield. Consider a farmer with 10-year APH of 109 bu/acre but with an
expected yield due to increasing technology of 120 bu/acre. At 75% coverage level,
the APH insurance would cover 82 bu/acre (109 x 75%) rather than 90 bu/acre.
Skees and Reed recognized this effect and argued that “either RMA must attempt to
adjust APH yields for trends or they must reduce their rates to reflect the actual level
of coverage provided when trends are not adjusted”. Depending on the nature of the
underlying yield generating process, a significant probability mass could occur
between 82 and 90 bu/acre.
To examine the simultaneous impact of trend and sample size variability on
APH yield, consider figure 1.1. The figure illustrates the relationship between APH
and the expected (“true”) yield distribution. The figure depicts 5,000 simulated 4-
and 10-year APH yields with mean on the x-axis and standard deviation on y axis.
The figure illustrates the role of sample variations due to sample size on a
representative farm’s APH estimate. The simulation was constructed for a
representative case farm from Christian County, Illinois by first detrending corn
yields, fitting the resulting data to a Weibull distribution, and then simulating sets of
yields of various sample lengths, re-applying the trend and then calculating the
resulting APH mean and standard deviations for 4- and 10-year periods.3 The figure
highlights the potential variability in the mean and provides a sense of the rate at
which variability decreases as more observation/years are added, and how the mean
bias is affected by the sample length. In general, the shorter samples provide better
estimates of mean and worse estimates of variability. For example, the true
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(expected) mean and standard deviation for the representative farm in this is example
is 174 bu/ac and 24 bu/ac (shown as red and black lines in color-printed versions,
light and dark otherwise). The ten year APH yield has a mean of 164 bu/ac and
standard deviation of 24 bu/ac, while 4 year APH yield has a mean of 167 bu/ac and
standard deviation of 22 bu/ac. Given additional incentives for farmers to self-select
based on their yield experience, either because of the trend, or because of the
abnormal yields, the precision of the APH estimate is likely to be further
compromised. The figure also illustrates another potential problem a possible
dependence between lower moments. Figure 1.1 displays this effect in the “clouds”
whose points move up and to the left relative to the “true” data generation process
used (i.e. there a possible inverse relationship between standard deviation and mean).
Farmers have repeatedly voiced concerns about the inability of the APH to
adequately represent their yield risk exposure. They argue that the insurance
provides inadequate protection when they experience several consecutive years of
low yields because the APH in this case does not accurately reflect farmers’ future
risk, leading to adverse selection incentives. The implication is that their yield
histories make insurance too expensive and provide inadequate levels of protection,
or simply transfer subsidies non-uniformly and inequitably. Because the APH can be
affected by extreme values, there is an incentive to report only higher values, or to
“switch” reporting units to take advantage of favorable, but random, yield variations.
Consistent with this observation, anecdotal evidence suggests that farmers tend to
switch insurance agents and “forget” somewhat distant bad years when applying for
crop insurance (Rejesus and Lovell 2003). RMA has defended its insurance rating
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and pricing practices by arguing that under constant yield trends, stable yield
distributions, uniform participation, the current practices would lead to coverage
level selections that would misstate true coverage by a constant amount and the rates
would likewise adjust themselves through time. RMA also has stated that even
though the insurance premiums are set and a final pricing algorithm is available, the
specific mechanisms are intentionally undisclosed to prevent or dissuade moral
hazard and adverse selection.
Concerns about the role of the APH calculation on the performance of crop
insurance have become so well-known that the Risk Management Agency (RMA)
noted it is “the most frequent and consistent concern heard from producers” (U.S.
Congress, Subcommittee on General Farm Commodities and Risk Management of
the Committee on Agriculture, 2004). In April 2004, RMA requested proposals for
alternative methods for mitigating declines in approved yields due to successive
years of low yields. RMA’s administrator noted that the goals of request for such a
proposal were to find “…approaches to establishing approved APH yields that are
less subject to decreases during successive years of low yields as compared to
current procedures…”(U.S. Congress. House of Representatives. Subcommittee on
General Farm Commodities and Risk Management of the Committee on Agriculture
2006). RMA’s implicit recognition of the problems with the rating methodologies
remains at odds with their defense and continued use of the existing approaches. A
need for research to clarify the impacts and to identify potential improvements is
evident. Also, figure 1.1 highlights the error in logic of the implicit in the rules idea
that longer sample period should be a better estimator of the central tendency.
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In addition, trend and sample size variability issues may be interrelated. It has
been postulated that advancements in seed technology and disease control have
altered the underlying yield generating process through time. These genetic
improvements might have increased the trend, reduced the yield variance, or simply
changed the relationship between mean and variability. In particular, recent
advances in genetic technology and “bio-traits” have resulted in what many call yield
acceleration or a quantum jump in trend. Cursory examination of NASS state level
average corn yields seems to confirm this, as the state linear trend is 0.9 bu./acre for
the time period from 1973 to 1983, 2.15 bu./acre for the time period from 1984 to
1994, and 3.94 bu./acre from 1995 to 2005. While additional time and data are
required to confirm this effect, the possibility would further exacerbate the problems
with existing ratings methodologies4 (i.e. farmers who use seeds with bio-traits and
pay “average” RMA premiums might be overcharged).
Literature Review
This section examines previous work on trend and sample variability issues, and the
relationship between RMA premiums and actuarial costs. The literature related to
the impact of trend and variability on the APH estimation is fairly direct in its
implications. While both trend and sample size variability issues have been
examined, the references remain limited. Skees and Reed (1986) were among the
first to point out that when the yield trend is present, the expected yield will be
higher than the APH yield. Using farm-level data from Illinois and Kentucky corn
and soybean producers, they regressed standard deviations and yield coefficient of
variations on mean yield. They calculated a theoretical (actuarially fair) insurance
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rate as a function of yield and showed that the rates calculated under trend-adjusted
yields are consistently higher than the rates calculated under APH yield. They
further argued that RMA needs to introduce the rate adjustments for the trend. They
concluded that the rules are likely to lead to adverse selections since farmers with
high yields are less likely to receive indemnity payments, and the trend omission is
likely to result in lower indemnity payments. However, the authors did not examine
the impact from different base period APH yields and did not consider how the trend
omission influences the rates calculated under the RMA’s premium structure.
Barnett, Black, Hu, and Skees (2005) provided a brief theoretical argument
concerning the magnitude of the sample size error. Using a statistical rule stating that
the standard error of the estimate is the ratio of standard deviation of the true
underlying distribution to the square root of the sample’s size, they showed that the
samples with more observations should have a better precision. However, this rule is
true for detrended yields, since the presence of trend is likely to comprise yield mean
precision. Carriquiry et al. (2005) argued that since farmers whose past yields were
above expected yields were more likely to participate in crop insurance (they called
this a sampling error), the current rules for APH calculation were likely to lead to
adverse selection. This results because the sampling error would lead to higher loss-
to-cost ratios, and as a result, to higher insurance premiums. They used detrended
farm- and county-level corn yields from Iowa farmers to model the impact of
sampling error and suggested an alternative estimator to minimize the error. The
results showed that estimated ratio of APH indemnities to actuarially fair insurance
premiums is greater than 1 with and without adverse selection. The results also
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showed that the return to crop insurance decreases as number of years in the APH
period increases. A limitation of their work is that they used detrended yields5,
implicitly ignoring the relationship between trends and sample size variability. In
addition, their comparison relied on actuarially fair premiums, while RMA employs
a complex rating structure that is likely to violate the assumption of actuarial fairness.
Zanini, Sherrick, Schnitkey, and Irwin (2001) examined yield probabilities,
actuarially-fair premiums, and RMA premiums under 5 different parametric
distributions. They used farm-level data from 26 corn and soybean producers in 12
Illinois counties. They detrended yields using linear trend, and fitted Weibull,
normal, lognormal, beta, and logistic distributions. They compared actuarially fair
payments under various distributions and found that beta and Weibull distributions
provide the most accurate measure of payments. They reported values for both
premiums, and the calculated simple (unweighted) average ratio of actuarially fair
payments, and found that on average RMA premiums exceed actuarially fair
premiums by 3.3 times6. They also compared the actuarially fair payments to RMA
premiums and found no correlations between the two. They concluded stating “the
results raise questions about the efficacy of crop insurance rating procedures. In
particular, if actual premiums are not closely correlated with expected payments, the
significant problems in controlling payout ratios would be expected.”
Some of the inconsistencies empirically observed by research in crop
insurance can be linked to the issues of trend and sample size variability. A report by
the integrated Financial Analytics and Research (iFAR) for the Illinois Corn
Marketing Board analyzed the loss ratios Illinois corn and soybean producers. The
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report noted that the loss ratios for corn and soybean have been well below RMA’s
benchmark target ratios and that distribution of loss ratios is clearly not uniform.
The primary corn producing regions have much lower loss ratios (average loss ratio
for all crops from 1995 to 2005 are 0.52 for Illinois), than the areas in the fringes of
the corn belt. Such loss ratios imply that the farmers in these areas pay higher
premiums per unit of risk when compared to farmers from other states and regions.
The report lists possible explanations for the observed loss ratios emphasizing the
presence of high relative yield trends in corn and soybeans. Further, the report
argues that “yield acceleration” can create a situation where ratings based on
historical yields will overstate the premiums through understated coverage, stating
that “cursory examination verify that crops with higher rates of trend increase have
had lower loss ratios” by tabulating similar loss performance data across major crops.
The existing literature illustrates following gap in existing research. While
Skees and Reed (1986) examined the role of trend on the participation and Carriquiry
et al. (2005) examined the impact of sample size error, neither investigated trend and
sample size variability jointly. Since both trend and sample size variability impact
yield estimates simultaneously, they need to be examined jointly. Further, most of
the literature examined the impact from trend omission and sample size variability
on actuarially fair rates. In reality, farmers are charged RMA premiums, and RMA
premiums are not actuarially fair. Therefore, the impact of trend and sample size
variability needs to be examined under RMA’s premium structure.
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Empirical Approach
The analysis presented is performed for a case farm in each county in Illinois to
illustrate how the results differ among regions that vary in average productivity,
variability, and under different insurance premium rate structures. The steps in used
in the empirical model are shown in figure 1.2. To create a representative farm in
each county, the county-level yield data for the period 1972 to 2005 (NASS) were
detrended to a base year of 2006 using a linear time trend7 (2006 was chosen to be
consistent with the premium calculation algorithms used)8 and the mean and standard
deviation for each county were calculated (step 1). Because the farm-level yields are
more variable than county yields, the standard deviations were scaled up to represent
the difference between county and farm level data using an empirical relationship to
actual farmer data from farms enrolled in the Illinois Farm Business Farm
Management record-keeping system. The county-level standard deviations were
multiplied by the average ratio of farm to county standard deviations,9 and a method
of moments’ estimator then used to fit Weibull distribution to recover the implied
farm-level yield distribution.10
The county trend was added back to the representative farm distributions for
each county to create the data generating process used in the simulations.
Specifically, these distributions were used to estimate probabilities of reaching
expected yields (true probabilities) (step 4) and to generate pseudo datasets of
varying lengths (from 4 to 10 years) (step 5). For convenience, @Risk11 was used to
generate the pseudodata and Monte Carlo simulations were run, with 10,00012
iterations, to generate the sets of samples for the insurance evaluation phase of the
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study. The data were generated for representative farms in each Illinois county, and
the probabilities of reaching target yields under various scenarios estimated. Because
the representative farms differ in trends, mean, and standard deviation by county, the
model allows examination of the impact of these variables on the probability of
reaching different indemnified yields. Also, the model allows examining
probabilities across the counties, and for various sample periods.
To facilitate the explanation of the information presented, consider figure 1.3.
The figure shows two corn yield distributions for the case farm in Adams County,
Illinois. The continuous line denotes true or expected yield distribution; the dashed
line shows the distribution for the 10-year APH mean at a 0.85 coverage level. The
difference in the means between the representative distribution and the APH mean
distribution illustrates the bias induced by ignoring the trend. The graph also shows
the probabilities of receiving indemnity under the 10-year APH yield and under true
or expected yield distributions. The probability is shown as area to the left of the
dashed line that separates the lower left tail of the distribution. Since the area under
the case farm is smaller than the area under the 10-year APH, the probability of
receiving the indemnity is smaller under the representative yield distribution. Higher
levels of coverage are needed under the APH-mean yield distribution to provide the
same level of protection as warranted by the true yield distribution.
In step 6 (figure 1.2), we calculate actuarial costs and examine the role of
existing rules on the actuarial cost and expected participation. In step 7, the actual
premiums (under RMA’s “black box” approach for determining the coefficients)
were recovered to examine the impact of trend, sample size variability, and number
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of years in the sample, on the RMA’s premiums. Figure 1.4 illustrates RMA’s
premium calculation for the hypothetical corn farm in Adams County with an APH
yield of 168 bu./acre, coverage level of 85%, and $4.50 /bu contract price. The
calculation starts with estimating guarantee per acre (product of APH yield and
coverage level), liability (premium guarantee times price election), yield ratio, and
preliminary base rate. The rate is then adjusted for coverage level and the subsidy.
The premiums calculated under RMA’s algorithm were compared to the
actuarial cost under the simulated data. Since RMA uses empirical crop losses to
derive the rates, it believes that there should be no difference between a large scale
simulation cost and the stated rates. Thus the differences imply unintended impacts
of the methods used to arrive at the APH or simply ratings mistakes. The approach
in this study allows an isolation of the role of the APH portion of the difference
between actual and actuarially fair rates.
Results
Table 1.1 presents results for six selected counties and the state by comparing the
impact on true and APH implied probabilities from counties’ representative farms13.
It also implicitly illustrates the relationship between sample moments and the
likelihood and frequency of APH payments relative to “true” (expected), given the
existing rules of the APH calculation. The results are presented in 5% coverage level
increments, for APH mean yields calculated from sets of 4, 7, and 10 years. The first
column shows county mean, standard deviation, and trend. The third labeled “True
Prob” column presents the probability of reaching a particular yield level under
farm-level representative “true distributions” for a given coverage level. For example,
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in Jefferson County, the probability of a yield outcome under the “true” distribution
is 3.05% for the 0.55 coverage level, and 24.76% for the 0.85 coverage level. The
column labeled “APH implied probability” presents the probability for reaching a
particular yield level at the associated coverage level given the sample period and
implied yield under the existing rules for calculating the APH. To gauge the relative
impact of the APH sample period, a column labeled “Prob Ratio” is provided,
containing a ratio of implied APH probability to the “True Prob” probability. This
ratio shows the fraction of the actual protection provided by APH mean given true
probability, coverage level, and time period. For example, for Jefferson County,
under 0.55 coverage level, the mean value is 91.97%, under a 4-year sample period.
In other words, the protection level provided by 4-year APH level is reduced by 8%
as a result of using the APH mean rather than the true mean. The actual protection
level decreases as the coverage level increases, but the magnitude is small (91.97%
for 0.55 coverage level, compared to 89.93% for the 0.85 coverage level).
The probability ratio, however, is influenced by the number of years in the
APH sample period. For Jefferson County, for example, the ratio decreases from
91.97% (0.55 coverage level, 4-year APH) to 71.31% (0.55 coverage level, 10-year
APH). In effect, the protection level is reduced by 20% as the years in the base
period increase from 4 to 10. The pattern of relative probabilities is also influenced
importantly by trend. For instance, in Lee County where the trend is higher, the
impact is more pronounced with the relative probability decreasing at 0.85 coverage
level from 81.15% with 4 year coverage to 55.92% with 10 year coverage. Shifting
to the state level, the protection level is reduced by 24%, (from 88.23% for 0.55
21
coverage level and 4 year APH to 64.82% for 10 year APH same coverage level).
To the extent that rational producers respond to these differences, the implications of
the findings are clear. Use of APH yields decreases the probability of participation,
and the longer the number of years in the base period the less likely is the
participation decision. The results on interaction between APH yields and trend are
similar to results in Skees and Reed (1986) who showed that theoretical insurance
rates for trend-adjusted yields are always greater than the rates for APH yields and
argued that an adjustment is needed to prevent an adverse participation incentive.
If a farmer has experienced several years of abnormally high (low) yields, his
APH yield is likely to be greater (less) than his expected yield. In this situation, a
farmer is more likely to purchase crop insurance. This is an example of adverse
selection, and to model this propensity, a measure “participation prob” was
developed. For every iteration, a value of 1 was given if the APH sample yield was
greater than the actual expected yield, and zero otherwise. Averaged across all
iterations, the measure provides a farmer’s “pure participation probability” that arises
from experiencing several abnormal yield years that favorably classifies his yields
relative to true. The value of the probability can be indicative of the extent and
severity of adverse selection. For example, in Jefferson County, for 4 year APH
yield, this value is 36.59% indicating that there is a 36.59% chance that a given APH
mean will actually be greater than the true (expected) yield. As the number of years
in the base period increases from 4 years to 10, the probability decreases to 14.75%.
This decrease is due to the lag introduced by trend, where APH yield lags expected
yield so significantly that even random positive changes in yields are not large
22
enough to compensate for the lag. The probability differs across the counties due to
the interaction between trend and dispersion in yield, with lower trends and shorter
sample variability; it ranges from 33.21% for Macon, and 28.74% for Lee (4 year
APH mean). At the state level, the participation probability is 33.55% for 4 year
APH versus 10.15% for 10 year APH. High participation probability further
illustrates low efficiency of the APH estimate, and illustrates the impact of extreme
yield values on the APH yield.
RMA Premium Calculations
To examine the impact from trend and yield variability in a economic context, the
actual premium algorithm used by RMA14 was implemented to construct actual
premiums for each case farm. The model simply inputs true and simulated APH
yields into RMA’s pricing algorithm and compares the resulting impacts. The
algorithm calculates the actual price quoted to a farmer who wants to buy crop
insurance for each county using RMA’s technical coefficients and simulated APH
and true means. Figure 1.4 replicates RMA’s insurance pricing algorithm for a
hypothetical corn producer in Adams County that has an APH yield of 168 bu/ac,
selects 85% coverage level, with $4.5/bu contract price. The subsidized premium is
equal to $33.24 per acre; the unsubsidized premium is equal to $53.62 per acre.
Table 1.2 shows average, before subsidy, premium values for 0.85 coverage level15
for selected counties across the same APH base periods of 4, 7, and 10 years as were
in table 1.1. The table shows trend, true probability, APH mean, RMA premiums for
4, 7, 10 years and true yield. The results indicate that as the number of years in the
base period increases, the premium values increase as well but the change in the
23
values is small. In Christian County, for example, the difference between true dollar
premium and estimated dollar premium (10-year APH base period) is only $0.25
($28.87 minus $29.63) for an APH difference of 12 bushels. At the state level, the
difference of 7 bushels translates into premium difference of $0.90.
The insensitivity of the RMA insurance premiums to the changes in APH
yields is somewhat alarming, since RMA uses APH yield as an indicator for farm
yield variability. Such low sensitivity to APH yield could also potentially lead to
adverse selection, since originally APH yield was used as a proxy for the yield
variability and the premium values for the low and high APH yield do not seem to
differ substantially. One possible reason for low yield sensitivity could be the
provision for catastrophic losses used in ratemaking process. This loading is fixed,
and given high spatial correlation in yields is likely to be significant. This claim is
examined later in the chapter.
Actuarial Implications of Trend and Small Sample Variability of APH
Actual premiums are relatively insensitive to changes in the APH, and may not be
suitable to summarize the actuarial performance differences that exist in practice. As
a consequence, true actuarial costs are also calculated. The indemnity function can
be specified as [ ]max 0,k y p− , where k is coverage level times APH yield, y is
realized yield; and p is the indemnity price per bushel in the insurance contract. The
actuarially fair (expected) value of the contract can be calculated by Monte Carlo
integration and written as:
0
( ) ( )k
V p k y f y dy= −∫ (2)
24
where f(y) is the yield probability density function.
This framework provides the mechanism for calculating the actuarial values
and examines how the changes in underlying yield exposure and sample size
variability affect the fair values. These values and their changes across underlying
yield distributions can then be compared to the premiums calculated by RMA to
identify the effect of trend, sample period, and other variables. To make results
easily interpreted, the indemnity price is fixed at $4.50 and all results are presented
relative to that price.
Table 1.3 contains a summary of the actuarial costs for yield insurance across
the same representative counties, for the 0.85 coverage level that was chosen to be
consistent with RMA premium estimations. As shown, the actuarial costs are more
responsive to the trend and base period changes than the actual premiums. For
example, in Christian County, the cost decreases by $1.87 (from $7.11 for 4 year
APH to $5.24 for 10 year APH) as the number of years in the base period increases
due to the reduction in coverage provided. The magnitude provides direct
implications for the cost of the insurance program relative to actual premiums for
different sample. For counties with lower trends, the impact, or decrease in actual
costs is smaller. For Jefferson County (trend =1.3 bu/acre/year) the actuarial cost
decreases by $2.84 (from $14.54 to $11.70) as the number of years in the base period
increases, again despite the fact that the actual premiums paid would be unchanged
for the farmer.
More interestingly, the actuarial costs are substantially smaller than
unsubsidized premiums calculated in table 1.2. To facilitate the discussion, the
25
RMA premiums from table 1.2 and actuarial costs from table 1.3 are combined in
table 1.4 with the ratio of RMA premiums to actuarial costs. The ratios for all APH
base periods and for true (expected) yield premiums are greater than 2, and the ratios
decrease as number of years in APH yield decrease, reflecting the lag introduced by
trend. For instance, the ratio for 10 year APH yield ranges from 3.8 for Macon
County to 7.2 for Ogle County, and is equal to 3.8 at the state level. The ratio for 4
year APH yield ranges from 2.8 for Macon County to 5.2 for Ogle County, and is
equal to 3 at the state level. Using true (expected) yields, the ratio is 2.0 for Macon
County, 3.5 for Ogle County, and 2.2 at the state level. The premiums shown are for
0.85 coverage level, which currently has a subsidy level of 35%. After adjusted for
the subsidy, the ratios will be 35% smaller, but still greater than one. The ratios
calculated are in line with ratios obtained by Sherrick et al. (2004a), which ranged
from 1.3 to 7.6, with an average, unweighted value being equal to 3.3.
The reason for discrepancy between the actuarial and RMA premiums could lie
in RMA’s approach towards premium calculation. The actuarial cost calculated in
table 1.3 does not have a loading for catastrophe events (catastrophe rate). Since
yields losses tend to be spatially correlated, catastrophic provisions are likely to play
a significant role in determining premium value. To examine the premiums and the
cost on more comparable basis, the RMA premium values are re-calculated by
setting catastrophic provision equal to zero. The results are shown in table 1.5,
which compares RMA premiums without catastrophic provision to actuarial costs
and also provides the ratios of RMA’s premiums to actuarial costs. The RMA
premiums without catastrophic loading are significantly smaller than the premiums
26
with loading. For example, the premium for 4 year APH yield in Christian County is
only $14.87 compared to $29.36 (the premium with catastrophic provision in table 4).
At the state level, the same premium is $22.28 compared to $37.96. The ratios are
significantly smaller as well, they are near 2 for 4 year APH yields (4 with
catastrophic loading in table 1.4), and near 3 for 10 year APH (6 with catastrophic
loading in table 1.4). At true (expected) yield levels, the ratio is close to 1. The
results from the table suggest that the major reason for higher RMA premiums lies in
the catastrophic provision which seems to explain the significant differences between
the premiums and actuarial costs. Nonetheless, even after controlling for the
catastrophic provision, the ratios of the premiums to actuarial costs are still
significantly greater than one, reflecting the significant effect of the trend-introduced
lag.
Results after Trend Adjustment
Assuming linear trend, the bias in the mean induced by ignoring trend can be
expressed as ( 1) / 2nβ− + , where n is number of years in APH base period, and β is
yield trend. Here, we adjust for the trend bias using 4-year APH yields, and
calculate APH implied probabilities, RMA premiums, and actuarial costs. The
results are shown in table 1.6. The table also shows 4-year APH yield, 4-year trend
adjusted APH yield, and true (expected) yield. For example, for Christian county 4-
year APH yield is 167 bu/ac, however, when adjusted for trend, the yield increases to
171 bu/ac, which is about 3 bu/ac smaller than the true (expected) yield of 174 bu/ac.
APH implied probability increases from approximately 12% for 4 year APH to 14%
for when adjusted for trend. This value is close to the APH implied probability of
27
14%. There is a small reduction in premiums due to the APH trend adjustment for
Christian county. The premium decreases from $29.36 to $29.12, which is greater
than the RMA’s insurance premium under expected yield of $28.87. Finally,
actuarial cost increase from $7.11 to $9.20 due to the trend adjustment, with the
actuarial cost under true (expected) yield equal to $9.99. The adjustment improves
the protection level provided by APH insurance. It should also limit incentives to
report only recent yields, thus improving the APH mean precision (by reducing lag
introduced by the trend), reducing the negative impacts from sample size variability,
and potentially improving actuarial performance by limiting adverse selection.
Finally, note that suggested adjustment is relatively straightforward to implement, as
it does not require changing RMA’s current rating structure.
Scaler Sensitivity
In constructing county representative farms, we adjusted county-level yield
variability by the scaler (1.245) to make the county yields as variable as farm-level
yields. This ratio, while unbiased, remains subject to sample variation. To provide a
sense of its importance, we assess the sensitivity of presented results to different
scaler values. Table 1.7 contains estimates of the ratio of APH implied probabilities
to the probabilities obtained under true yield presented in table 1.1. Table 1.7
replicates the ratio under for values of 1.15, 1.2, 1.245 (base), 1.3, and 1. The ratio
steadily increases as the scaler value increases from 1 (county average yield standard
deviation) to 1.35. For example, for Christian county, the ratio increases from 52%
to 63%; at the state level the ratio increases from 56% to 67%. Arbitrary assuming
that the true scaler value lies between 1.15 to 1.35, the absolute level of error is 6
28
points at county level (67% minus 61%) or relative error is within 9% (6 points
divided by 64%). Thus, despite the fact that the scaling approach is subject to error,
it provides a strong sense of the magnitude of the most likely effect.
Summary and Conclusions
The current rules used to calculate a farmer’s APH yield are likely to result in
substantial departures from actuarial values, providing unintended incentives for
participation. Since the rules utilize an average based on a limited number of actual
farm observations, the resulting estimate is heavily influenced by extreme yield
observations. This influence is likely to lead to non-uniform impacts on probabilities
in indemnified ranges of farmers’ yield distributions. Due to the fact that the APH
yield is used in the calculation of yield guarantees and rates for the most popular
crop insurance products, the impact of the discussed problems is likely to affect large
number of farmers. We examine the impact of current RMA rules on a degree of risk
protection afforded by crop insurance, on participation incentives, and on the
actuarial performance of APH crop insurance. The approach utilized a simulation
model with controllable “true” distributions for each county in Illinois. Unlike
previous research, the paper models trend and sample size variability impact jointly
and examines the impact on actuarial costs and RMA premiums.
The results show the degree to which trends and sample size variability affect
the probabilities of reaching yield levels indemnified from lagged yield samples,
affect premiums, and actuarial costs of the actual versus APH implied distribution.
At the state level, the protection level afforded by the insurance drops by 21% as the
base period increases from 4 years to 10 years, and the counties with the high trend
29
tend to experience larger drops. The results also show that RMA premiums are not
highly influenced by actual APH yield changes. The findings suggested the large
differences between RMA premiums and actuarial costs are mostly due to the
catastrophic loading and lag in yields introduced by the trend. All these findings
have negative implications for the participation and actuarial costs.
We introduce the trend adjustment to correct the lag in the APH yields using
county trend. The adjustment improves the protection level provided by APH
insurance and should limit incentives to report only recent yields. The adjustment
seems to improve the APH mean precision, reduce the negative impacts from sample
size variability, and possibly improve actuarial performance by limiting adverse
selection.
Future research should examine spatial methods for calculating trend since
trend and yield variability issues seem to have spatial implications, and spatial
methods might lead to a better way to aggregate yields geographically. Another
potentially fruitful direction for research would be to examine impact of technology
on the trend and variability. If trends have accelerated in the last decade and
variance decreased, the current premiums are likely to be mispriced, since the current
rating structure does not take into account these developments.
Endnotes
1 The iFARM Crop Insurance Evaluation provides an evaluation of alternative crop
insurance choices for the case farm in the county and for the crop selected. The case
farm is intended to reflect conditions of a typical farm in each county and is based on
data from NASS, farm recordkeeping associations, and research at the University of
30
Illinois relating farm to county yields. The iFARM calculator is available at
http://www.farmdoc.uiuc.edu/cropins/index.asp
2 The exponential factor is an adjustment to reflect the inverse relationship between
APH yield and yield variability. Skees and Reed (1986) pointed out that the averages
of farm-level yields can be used as an (observable, but inaccurate) indicator of farm-
level yield variability. The RMA has nine discrete values for exponential factors that
are calculated by spreading county rates over a range of average yields using
proportional spanning procedures (Goodwin 1994). This factor ensures
(theoretically) that farmers who have APH above reference yield pay less in
premiums.
3 Christian County has a true mean of 174 bu/ac and a standard deviation of 24 bu/ac.
While a wide range of mean and standard deviations can be observed, Christian
County was selected to show the impact in what can be viewed as a county with low
trend.
4 Nonetheless, RMA has accepted the notion that particular biotech traits reduce
insurance exposure by recent implementation of Biotech Yield Endorsement (BYE)
in corn. This crop insurance product lowers premiums and recognizes growers who
plant certain biotech seeds.
5 Carriquiry et al. (2005) stated in the paper that “analysis abstracts somewhat from
reality and is conducted on detrended yield data” (p. 53).
6 The ratio was calculated using premiums reported here.
7 Sherrick, et al. (2004) find no evidence of a unit root in the yields.
31
8 RMA uses the same NASS data (but somewhat longer time periods) for crop
insurance rating, but does not disclose details on any use of detrending procedures.
9 To estimate the scaler, the following steps were performed. First, a sample of farms
(1056 producers) with 15 years of continuous farm-level yields was selected from
FBFM (15 years provided an optimal balance between the length of the sample and
number of observations). Farm yields for each county were detrended using a linear
trend. Second, the county-level yields (from NASS) for the same time periods were
selected and detrended using a linear time trend. The farm-level and county-level
standard deviations were calculated from the detrended samples. The standard
deviations for individual farms (from FBFM sample) were divided by respective
county standard deviations (from NASS). Third, simple averages of resulting ratios
for each county were calculated, and the simple average for Illinois was estimated
(individual county ratios were available for approximately 80 counties). An overall
average is used (following iFARM calculator algorithm) with sensitivity tests
performed around that value to illustrate the sensitivity of the results to that estimate
of relative farm variability. For Illinois, the multiplier was equal to 1.245, suggesting
that farm yields are on average 1.245 times more variable than county yields (the
same value is used in iFARM).
10 The choice of distribution is based on Sherrick et al. (2004) who suggested several
useful properties of the Weibull distribution for modeling crop yields including its
flexible non-symmetry, zero limit, and wide range of skewness and kurtosis.
32
11 @Risk is an “add-in” to Microsoft Excel; it has capabilities to model simulations
in Excel using Monte Carlo and Latin Hypercube sampling methods for any
specified parametric/non-parametric distribution.
12 Carriquiry et al. (2005) and others used the same number of iterations.
13 These six counties represent conditions in the north, center, and the south parts of
the state. The state averages were derived by weighting county data by percentage of
acres planted in the county in relation to the state
14 RMA publishes technical coefficients by county, but does not make public any
other ratings information. This allows rate quoting, but does not allow the
identification of how the technical coefficients would be affected by different
histories, nor provides a direct analytic method for relating items such as “bias” to a
pricing effect.
15 A maximum level of coverage (0.85) was chosen to illustrate the differences, the
premiums across coverage levels increase almost linearly.
33
Figures and Tables
0
10
20
30
40
50
110 120 130 140 150 160 170 180 190 200 210
Mean (bu/acre)
4 Year APH
10 year APH
True St.Dev
True Mean
10 year APH Mean =164 bu/acre 4 year APH Mean =167 bu/acre
St.Dev 10 Year APH = 24 bu/acre
St.Dev 4 Year APH = 22 bu/acre
Figure 1.1. Simulated 4 and 10 year APH yields (Christian County, IL, corn yield distribution for 2006, true (expected) mean of 174 bu and standard deviation of 24 bu, 5,000 iterations)
34
Figure 1.2. Steps in empirical model
Step 1: NASS county yields detrended using linear trend. Standard deviation and mean are calculated for each county
Step 2: Scaler (ratio of farm level variability to county level variability) is calculated using FBFM yields and standard deviations from Step 1 are multiplied by the scaler.
Step 3: Weibull distribution is fitted using means from step 1 and standard deviations from step 2 and method of moments is used to estimate representative “ true” farm- level yield distribution
Step 4: Trend is reapplied to the representative yield distributions. True probabilities are calculated by using mean of representative yield distribution times coverage level.
Step 5: APH implied probabilities are calculated by simulating yields and calculating 4- 10 years APHmean times coverage level.
Step 7: RMA ’ spremiums are calculated by feeding true and APH means through RMA ’ s premium structure. Contract price of $4.50/bu is assumed.
Step 6: Actuarial costs are calculated by simulating yields and using APH and true means as strikes. Contract price of $4.50/bu is assumed.
35
Figure 1.3. Representative case farm and APH based corn yield distributions for 2006 (Adams County, corn)
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
1 51 101 151 201 Yield (bu/acre)
Probability
True Yield Distribution 10-Year APH Yield Distribution Indemnity under 10-Year APH - 0.85 Coverage
Bias
36
APH yield 168 bu/ac
coverage level 85 %
indemnity price 4.50$ /bu
basic/optional 0.9 (.9 = basic, 1 = optional)
1. Calculate guarantee per acre
aph yield x coverage level
168 0.85 142.8
2. Calculate premium guarantee
premium guarantee x acres =
142.8 100 14280
3. Calculate premium liability
premium guarantee x price election x share
14280 4.5 1 64260
4. Calculate current year's yield ratio (rounded to 2 decimal places)
approved APH yield / Reference yield
168 125 1.34
5. Calculate the current year's continuous rate
1. Current year yield ratio** current year exponent
1.34 -1.926 0.5691099
2. 1's answer x current year reference rate + fixed rate load
0.5691099 0.038 0.023 0.0446262
9. Determine the preliminary base rate
lower of 5, 6, or 8 0.0446262
10. Adjusted base rate
preliminary base rate x adjustments
0.0446262 1 0.0446262
11. Calculate the base premium rate
adjusted base rate x coverage level
0.0446262 1.703 1.22 0.092718
12. Calculate the total premium
premium liability x base rate x unit factor x optional coverage factor
64260 0.092718 0.9 1 5362
13. Calculate subsidy
total premium x subsidy factor
5362 0.38 2038
14. Calculate producer premium
total premium - subsidy
5362 2038 3324
premium per acre 33.24
Figure 1.4. Illustration of premium calculation using RMA’s pricing algorithm (RMA’s black box) for a hypothetical corn farm in Adams County, Illinois
37
Tab
le1.1
. D
iffe
rence
s in
pro
bab
ilitie
s under
tru
e an
d A
PH
rule
s an
d m
iscl
assi
fica
tion r
ates
for
sele
cted
counties
in I
llin
ois
(co
rn)
County
Coverage
Levels
True
Proba
APH
implied
probb
Prob
Ratioc
Participation Prob
APH
implied
prob
Prob
Ratio
Participation
Prob
APH
implied
prob
Prob
Ratio
Participation Prob
Base Period
4 Years
7 Years
10 Years
%
%
%
%
%
%
%
%
%
%
Chri
stia
n
0.5
5
0.3
5
0.3
0
85.1
8
31.6
3
0.2
4
69.7
5
16.3
1
0.2
1
59.2
0
6.0
3
Tre
nd =
1.7
7 b
u/a
cre
0.6
0.7
3
0.6
3
85.1
5
31.6
3
0.5
1
69.7
7
16.3
1
0.4
4
59.2
4
6.0
3
Mea
n=
174 b
u/a
cre
0.6
5
1.4
6
1.2
5
85.1
1
31.6
3
1.0
2
69.8
1
16.3
1
0.8
7
59.3
1
6.0
3
St.D
ev=
24 b
u/a
cre
0.7
2.7
6
2.3
5
85.0
4
31.6
3
1.9
3
69.8
8
16.3
1
1.6
4
59.4
3
6.0
3
0.7
5
4.9
6
4.2
1
84.9
1
31.6
3
3.4
7
70.0
1
16.3
1
2.9
6
59.6
4
6.0
3
0.8
8.5
2
7.2
1
84.7
2
31.6
3
5.9
8
70.2
2
16.3
1
5.1
1
60.0
0
6.0
3
0.8
5
13.9
7
11.7
9
84.4
3
31.6
3
9.8
6
70.5
7
16.3
1
8.4
6
60.5
7
6.0
3
Jeff
erso
n
0.5
5
3.0
5
2.8
1
91.9
7
36.5
9
2.4
4
80.0
8
25.4
3
2.1
8
71.3
1
14.7
5
Tre
nd =
1.3
0 b
u/a
cre
0.6
4.7
1
4.3
3
91.8
0
36.5
9
3.7
7
80.1
0
25.4
3
3.3
6
71.4
2
14.7
5
Mea
n=
111 b
u/a
cre
0.6
5
7.0
0
6.4
1
91.5
7
36.5
9
5.6
1
80.1
4
25.4
3
5.0
1
71.5
8
14.7
5
St.D
ev=
25 b
u/a
cre
0.7
10.0
4
9.1
6
91.2
7
36.5
9
8.0
5
80.2
0
25.4
3
7.2
1
71.8
0
14.7
5
0.7
5
13.9
6
12.6
9
90.9
0
36.5
9
11.2
1
80.2
8
25.4
3
10.0
6
72.0
9
14.7
5
0.8
18.8
5
17.0
5
90.4
4
36.5
9
15.1
6
80.3
9
25.4
3
13.6
6
72.4
8
14.7
5
0.8
5
24.7
6
22.2
6
89.9
3
36.5
9
19.9
5
80.5
6
25.4
3
18.0
7
72.9
8
14.7
5
La
Sal
le
0.5
5
0.4
3
0.3
7
87.2
9
31.8
2
0.3
1
71.9
8
17.8
5
0.2
6
61.5
3
6.8
8
Tre
nd =
1.5
5 b
u/a
cre
0.6
0.8
8
0.7
6
87.2
6
31.8
2
0.6
3
72.0
0
17.8
5
0.5
4
61.5
7
6.8
8
Mea
n=
156 b
u/a
cre
0.6
5
1.7
0
1.4
8
87.1
9
31.8
2
1.2
2
72.0
4
17.8
5
1.0
5
61.6
4
6.8
8
St.D
ev=
22 b
u/a
cre
0.7
3.1
2
2.7
2
87.0
7
31.8
2
2.2
5
72.1
1
17.8
5
1.9
3
61.7
7
6.8
8
0.7
5
5.4
7
4.7
5
86.8
9
31.8
2
3.9
5
72.2
2
17.8
5
3.3
9
61.9
9
6.8
8
0.8
9.1
8
7.9
5
86.6
0
31.8
2
6.6
5
72.4
1
17.8
5
5.7
2
62.3
4
6.8
8
0.8
5
14.7
4
12.7
0
86.1
9
31.8
2
10.7
2
72.7
1
17.8
5
9.2
7
62.9
0
6.8
8
Lee
0.5
5
0.3
5
0.2
9
81.6
4
28.7
4
0.2
3
65.5
2
12.5
3
0.1
9
54.4
4
3.6
8
Tre
nd =
1.8
9 b
u/a
cre
0.6
0.7
4
0.6
0
81.6
3
28.7
4
0.4
9
65.5
5
12.5
3
0.4
0
54.4
8
3.6
8
Mea
n=
163 b
u/a
cre
0.6
5
1.4
7
1.2
0
81.6
0
28.7
4
0.9
7
65.6
0
12.5
3
0.8
0
54.5
5
3.6
8
St.D
ev=
22 b
u/a
cre
0.7
2.7
8
2.2
6
81.5
4
28.7
4
1.8
2
65.6
9
12.5
3
1.5
2
54.6
9
3.6
8
0.7
5
4.9
8
4.0
6
81.4
6
28.7
4
3.2
8
65.8
4
12.5
3
2.7
4
54.9
2
3.6
8
0.8
8.5
4
6.9
5
81.3
3
28.7
4
5.6
5
66.1
0
12.5
3
4.7
3
55.3
0
3.6
8
0.8
5
14.0
0
11.3
6
81.1
5
28.7
4
9.3
1
66.5
2
12.5
3
7.8
3
55.9
2
3.6
8
a D
enote
s pro
bab
ility o
f re
achin
g a
par
ticu
lar
yie
ld lev
el o
bta
ined
under
far
m-l
evel
rep
rese
nta
tive
“tru
e dis
trib
ution.”
bD
enote
s pro
bab
ilit
y o
f re
achin
g a
par
ticu
lar
yie
ld lev
el o
bta
ined
under
giv
en A
PH
yie
ld.
c Den
ote
s pro
port
ion o
f ti
mes
in s
imula
tion the
true
yie
ld p
robab
ilit
y w
as s
mal
ler
than
the
corr
espondin
g A
PH
yie
ld p
robab
ilit
y.
37
38
Tab
le 1
.1. V
alues
for
the
dif
fere
nce
and r
atio
bet
wee
n e
stim
ated
and tru
e pro
bab
ilitie
s, a
nd p
osi
tive
mis
clas
sifi
cation (
corn
) (c
onti
nued
) County
Coverage Levels True Proba
APH
implied
probb
Prob
Ratioc Participation Prob
APH
implied
prob
Prob
Ratio Participation Prob
APH
implied
prob
Prob
Ratio Participation Prob
Base Period
4 Years
7 Years
10 Years
%
%
%
%
%
%
%
%
%
%
Mac
on
0.5
5
0.6
8
0.5
9
87.7
0
33.2
1
0.4
9
72.7
8
18.7
2
0.4
2
62.5
4
7.8
8
Tre
nd =
1.8
6 b
u/a
cre
0.6
1.3
0
1.1
4
87.6
5
33.2
1
0.9
5
72.8
1
18.7
2
0.8
1
62.6
0
7.8
8
Mea
n=
177 b
u/a
cre
0.6
5
2.3
7
2.0
7
87.5
7
33.2
1
1.7
2
72.8
6
18.7
2
1.4
8
62.6
9
7.8
8
St.D
ev=
28 b
u/a
cre
0.7
4.1
1
3.5
9
87.4
3
33.2
1
3.0
0
72.9
4
18.7
2
2.5
8
62.8
5
7.8
8
0.7
5
6.8
2
5.9
5
87.2
2
33.2
1
4.9
8
73.0
7
18.7
2
4.3
0
63.1
0
7.8
8
0.8
10.8
7
9.4
5
86.9
2
33.2
1
7.9
7
73.2
7
18.7
2
6.9
0
63.4
9
7.8
8
0.8
5
16.6
4
14.4
0
86.5
2
33.2
1
12.2
5
73.5
8
18.7
2
10.6
6
64.0
7
7.8
8
Ogle
0.5
5
0.3
8
0.3
1
83.0
1
30.1
1
0.2
5
67.1
1
13.8
5
0.2
1
56.0
4
4.1
2
Tre
nd =
1.8
1 b
u/a
cre
0.6
0.7
9
0.6
5
82.9
9
30.1
1
0.5
3
67.1
4
13.8
5
0.4
4
56.0
8
4.1
2
Mea
n=
160 b
u/a
cre
0.6
5
1.5
5
1.2
9
82.9
5
30.1
1
1.0
4
67.1
8
13.8
5
0.8
7
56.1
6
4.1
2
St.D
ev=
22 b
u/a
cre
0.7
2.9
0
2.4
0
82.8
9
30.1
1
1.9
5
67.2
7
13.8
5
1.6
3
56.2
9
4.1
2
0.7
5
5.1
6
4.2
7
82.7
8
30.1
1
3.4
8
67.4
1
13.8
5
2.9
2
56.5
2
4.1
2
0.8
8.7
7
7.2
5
82.6
2
30.1
1
5.9
4
67.6
6
13.8
5
4.9
9
56.9
0
4.1
2
0.8
5
14.2
7
11.7
6
82.3
9
30.1
1
9.7
1
68.0
5
13.8
5
8.2
1
57.5
2
4.1
2
Sta
ted
0.5
5
2.4
0
2.1
9
88.2
3
33.5
5
1.9
3
74.4
7
20.4
6
1.7
4
64.8
2
10.1
5
Tre
nd =
1.6
8 b
u/a
cre
0.6
3.5
5
3.1
9
88.1
2
33.5
5
2.8
0
74.5
0
20.4
6
2.5
1
64.9
1
10.1
5
Mea
n =
125 b
u/a
cre
0.6
5
5.1
9
4.6
0
87.9
8
33.5
5
4.0
3
74.5
5
20.4
6
3.6
1
65.0
3
10.1
5
St.D
ev =
24 b
u/a
cre
0.7
7.5
0
6.5
8
87.7
9
33.5
5
5.7
5
74.6
2
20.4
6
5.1
3
65.2
1
10.1
5
0.7
5
10.6
8
9.3
1
87.5
3
33.5
5
8.1
3
74.7
4
20.4
6
7.2
4
65.4
7
10.1
5
0.8
14.9
8
13.0
0
87.2
0
33.5
5
11.3
6
74.9
2
20.4
6
10.1
2
65.8
5
10.1
5
0.8
5
20.6
7
18.8
6
86.8
0
33.5
5
15.6
5
75.1
9
20.4
6
13.9
5
66.4
0
10.1
5
a D
enote
s pro
bab
ilit
y o
f re
achin
g a
par
ticu
lar
yie
ld lev
el o
bta
ined
under
far
m-l
evel
rep
rese
nta
tive
“tru
e dis
trib
ution.”
bD
enote
s pro
bab
ilit
y o
f re
achin
g a
par
ticu
lar
yie
ld lev
el o
bta
ined
under
giv
en A
PH
yie
ld).
c D
enote
s pro
port
ion o
f ti
mes
in s
imula
tion the
true
yie
ld p
robab
ilit
y w
as s
mal
ler
than
the
corr
espondin
g A
PH
yie
ld p
robab
ilit
y.
dSta
te a
ver
ages
wer
e der
ived
by w
eighti
ng c
ounty
dat
a by p
erce
nta
ge
of
acre
s pla
nte
d in the
county
to s
tate
.
38
39
T
able
1.2
. Sim
ula
ted R
MA
pre
miu
m v
alues
for
sele
cted
counti
es (
bef
ore
subsi
die
s)
County
Coverage
Levels
Trend
True
Prob
APH
(bu)
RMA
Prem
($)
APH
(bu)
RMA
Prem
($)
APH
(bu)
RMA
Prem
($)
True
APH
(bu)
True
RMA
Prem
($)
Base Period
4 Years
7 Years
10 Years
Chri
stia
n
0.8
5
1.7
7
14
167
29.3
6
165
29.4
8
162
29.6
3
174
28.8
7
Jeff
erso
n
0.8
5
1.3
25
107
53.9
3
105
54.0
5
103
54.3
6
111
52.4
3
La
Sal
le
0.8
5
1.5
5
15
150
34.2
0
148
34.2
5
146
34.3
6
156
33.8
0
Lee
0.8
5
1.8
9
14
156
30.8
5
153
30.9
4
150
31.1
0
163
30.5
3
Mac
on
0.8
5
1.8
6
17
170
28.6
7
167
28.7
3
164
28.8
7
177
27.9
9
Ogle
0.8
5
1.8
1
14
154
33.8
9
151
33.9
8
148
34.0
9
160
33.5
3
Sta
tea
0.8
5
1.6
8
21
141
37.9
6
139
38.0
0
136
38.1
6
147
37.2
6
a Sta
te a
ver
ages
wer
e der
ived
by w
eighting c
ounty
dat
a by p
erce
nta
ge
of
acre
s pla
nte
d in the
county
to
sta
te.
39
40
Tab
le 1
.3.S
imula
ted a
ctuar
ial in
sura
nce
cost
s fo
r se
lect
ed I
llin
ois
counties
County
Coverage
Levels
Trend
True
Prob
APH
(bu)
Actuarial
Cost ($)
APH
(bu)
Actuarial
Cost ($)
APH
(bu)
Actuarial
Cost ($)
True
APH
(bu)
True
Actuarial
Cost ($)
Base Period
4 Years
7 Years
10 Years
Chri
stia
n
0.8
5
1.7
7
14
167
7.1
1
165
6.1
2
163
5.2
4
174
9.9
9
Jeff
erso
n
0.8
5
1.3
25
107
14.5
4
105
13.0
5
103
11.7
0
111
18.4
7
La
Sal
le
0.8
5
1.5
5
15
150
7.1
3
148
6.2
1
146
5.3
8
156
9.8
1
Lee
0.8
5
1.8
9
14
156
6.3
7
154
5.3
6
150
4.5
0
163
9.4
1
Mac
on
0.8
5
1.8
6
17
170
10.0
8
167
8.7
8
165
7.6
3
177
13.7
5
Ogle
0.8
5
1.8
1
14
154
6.5
7
151
5.5
8
148
4.7
0
160
9.5
4
Sta
tea
0.8
5
1.6
8
21
141
12.6
7
139
11.2
3
136
9.9
2
147
16.6
7
a Sta
te a
ver
ages
wer
e der
ived
by w
eighting c
ounty
dat
a by p
erce
nta
ge
of
acre
s pla
nte
d in the
county
in r
elat
ion to s
tate
.
40
41
Tab
le 1
.4. Sim
ula
ted R
MA
pre
miu
ms
and a
ctuar
ial co
sts
for
sele
cted
counties
County
RMA
Prem
($)
Actuarial
Cost ($)
Ratio
RMA
Prem
($)
Actuarial
Cost ($)
Ratio
RMA
Prem
($)
Actuarial
Cost ($)
Ratio
RMA
Prem
($)
Actuarial
Cost ($)
Ratio
Base Period
4
7
10
True
Chri
stia
n
29.3
6
7.1
1
4.1
29.4
8
6.1
2
4.8
29.6
3
5.2
4
5.7
28.8
7
9.9
9
2.9
Jeff
erso
n
53.9
3
14.5
4
3.7
54.0
5
13.0
5
4.1
54.3
6
11.7
0
4.6
52.4
3
18.4
7
2.8
La
Sal
le
34.2
0
7.1
3
4.8
34.2
5
6.2
1
5.5
34.3
6
5.3
8
6.4
33.8
0
9.8
1
3.4
Lee
30.8
5
6.3
7
4.8
30.9
4
5.3
6
5.8
31.1
0
4.5
0
6.9
30.5
3
9.4
1
3.2
Mac
on
28.6
7
10.0
8
2.8
28.7
3
8.7
8
3.3
28.8
7
7.6
3
3.8
27.9
9
13.7
5
2.0
Ogle
33.8
9
6.5
7
5.2
33.9
8
5.5
8
6.1
34.0
9
4.7
0
7.2
33.5
3
9.5
4
3.5
Sta
tea
37.9
6
12.6
7
3.0
38.0
0
11.2
3
3.4
38.1
6
9.9
2
3.8
37.2
6
16.6
7
2.2
a S
tate
aver
ages
wer
e der
ived
by w
eighting c
ounty
dat
a by p
erce
nta
ge
of
acre
s pla
nte
d in the
county
to s
tate
.
41
42
Tab
le 1
.5. Sim
ula
ted R
MA
pre
miu
ms
wit
hout ca
tast
rophic
load
ing f
or
sele
cted
counties
County
RMA
Prem,
no Cat.
Load ($)
Actuarial
Cost ($)
Ratio
RMA
Prem,
no Cat.
Load
($)
Actuarial
Cost ($)
Ratio
RMA
Prem,
no Cat.
Load
($)
Actuarial
Cost ($)
Ratio
RMA
Prem,
no Cat.
Load
($)
Actuarial
Cost ($)
Ratio
Base
Period
4
7
10
True
Chri
stia
n
14.8
7
7.1
1
2.1
15.2
1
6.1
2
2.5
15.5
9
5.2
4
3.0
13.8
6
9.9
9
1.4
Jeff
erso
n
36.3
2
14.5
4
2.5
36.7
9
13.0
5
2.8
37.4
0
11.7
0
3.2
34.2
9
18.4
7
1.9
La
Sal
le
17.9
1
7.1
3
2.5
18.2
3
6.2
1
2.9
18.5
6
5.3
8
3.5
16.9
2
9.8
1
1.7
Lee
16.2
0
6.3
7
2.5
16.5
6
5.3
6
3.1
16.9
9
4.5
0
3.8
15.2
6
9.4
1
1.6
Mac
on
15.2
1
10.0
8
1.5
15.5
0
8.7
8
1.8
15.8
9
7.6
3
2.1
14.0
4
13.7
5
1.0
Ogle
17.2
6
6.5
7
2.6
17.6
2
5.5
8
3.2
18.0
5
4.7
0
3.8
16.2
0
9.5
4
1.7
Sta
tea
22.2
8
12.6
7
1.8
22.6
1
11.2
3
2.0
23.0
9
9.9
2
2.3
20.0
0
16.6
7
1.2
a S
tate
aver
ages
wer
e der
ived
by w
eighting c
ounty
dat
a by p
erce
nta
ge
of
acre
s pla
nte
d in the
county
to s
tate
.
42
43
T
able
1.6
. T
rend a
dju
sted
APH
im
pli
ed y
ield
, pro
bab
ility, pre
miu
ms,
and a
ctuar
ial co
sts
Trend
Yield (bu)
Yield Implied Prob (%)
RMA Premiums ($)
Actuarial Cost ($)
(bu)
APH 4
APH
Adj.
Yield
b
True
APH 4
APH
Adj.
Yield
True
APH
4
APH
Adj.
Yield
True
APH
4
APH
Adj.
Yield
True
Chri
stia
n
1.7
7
167
171
174
12
14
14
29.3
6
29.1
2
28.8
7
7.1
1
9.2
0
9.9
9
Jeff
erso
n
1.3
107
110
111
22
25
25
53.9
3
53.3
9
52.4
3
14.5
4
18.7
9
18.4
7
La
Sal
le
1.5
5
150
154
156
13
15
15
34.2
0
34.0
2
33.8
0
7.1
3
9.1
1
9.8
1
Lee
1.8
9
156
161
163
11
14
14
30.8
5
30.6
2
30.5
3
6.3
7
8.0
3
9.4
1
Mac
on
1.8
6
170
175
177
14
17
17
28.6
7
28.4
0
27.9
9
10.0
8
12.7
8
13.7
5
Ogle
1.8
1
154
159
160
12
15
14
33.8
9
33.7
1
33.5
3
6.5
7
8.8
4
9.5
4
Sta
te
1.6
8
141
145
147
19
20
21
37.9
6
37.4
4
37.2
6
12.6
7
15.2
3
16.6
7
a S
tate
aver
ages
wer
e der
ived
by w
eighting c
ounty
dat
a by p
erce
nta
ge
of
acre
s pla
nte
d in the
county
to s
tate
.
bA
dju
sted
for
tren
d u
sing
(1)
/2n
β−
+, w
her
e n
is
num
ber
of
yea
rs in A
PH
bas
e per
iod, an
d β
is
yie
ld tre
nd.
43
44
Table 1.7. True and APH implied probabilities for different scaler values for APH period of 10 years and 0.85 coverage level
Scaler
1 1.15 1.2 1.245 1.3 1.35
Christian 52% 57% 59% 66% 62% 63%
Jefferson 66% 71% 72% 73% 74% 75%
La Salle 54% 60% 62% 63% 64% 66%
Lee 47% 53% 55% 56% 58% 59%
Macon 56% 61% 63% 64% 66% 67%
Ogle 49% 54% 56% 58% 59% 61%
Statea 56% 61% 63% 64% 65% 67% aState averages were derived by weighting county data by percentage of acres planted in the county state.
45
CHAPTER 2
Crop Insurance Usage in Lake Woebegone
Abstract
This paper assesses the extent of expression of a “Better Than Average”
(BTA) effect and the relationship between stated beliefs and implied
economic decisions by examining yield expectations elicited under two
different conceptual constructs from a sample of soybean producers. Using
simple risk measures and constructed proxies for the BTA effect, we
examined these effects in crop insurance demand models. The results
indicate the presence of the BTA effect; however, the demand model results
suggest that these biases are not likely to strongly influence the demand for
the insurance.
U.S. farmers have demonstrated a reluctance to purchase crop insurance unless
substantial premium subsidies are provided. Some researchers have argued that the
relationship between insurance and other risk management tools could explain the
need to offer subsidies to induce participation (Mahul and Wright, 2003); others have
cited the presence of large ad-hoc disaster payments and other forms of implicit
insurance against low incomes offered by government programs as explanation for
low participation (Van Asseldonk, Miranda, and Ruud 2002). However, the
relationship between subjective perceptions and decision to buy crop insurance has
not been extensively studied (Sherrick 2002; Egelkraut, Sherrick, Garcia, and
Pennings 2006a). A careful analysis of the farmers’ subjective perceptions is very
important for several reasons. Crop insurance is largely rated using county-level
yield data and minimal individual experiences. If a farmer does not possess well-
calibrated beliefs, he might perceive such crop insurance as mispriced. Such biased
perceptions may influence farmers’ participation decisions and could explain some
farmers’ reluctance to participate in crop insurance program. The paper investigates
whether yield risk perceptions influence farmers’ participation in crop insurance
46
program on an individual producer level. The study examines alternate measures of
risk and tests for impacts of these perceptions on crop insurance decisions, in the
presence of risk management alternatives.
Researchers in psychology have identified a number of misperceptions
(departures from reality) and heuristics (simplifications of reality) that individuals
tend to display in complex or uncertain decision-making situations. One recently
formalized misperception is known as the “better than average” (BTA) effect. The
BTA effect refers to an individual’s propensity to “judge themselves as better than
others with regard to skills or positive personality attributes.” The BTA effect occurs
particularly in situations where the individual believes his actions directly affect
outcomes (Glaser and Weber, 2003). Another bias is miscalibration which defined
as “an individual’s tendency to overestimate the precision of personal information”
(Biais, Hilton, Pouget and Mazurier, 2003). Lichtenstein, Fischhoff, and Phillips
(1982) provide a detailed overview of miscalibration and cite numerous examples
across professions. For example, they indicate that one of the few well-calibrated
professions seemed to be meteorology, although information that is available is
sometimes altered in presentation to mitigate asymmetric penalties for better or
worse than forecasted weather. Lichtenstein, Fischhoff, and Phillips argue that two
reasons could explain good calibration displayed by meteorologists: 1) repetitive
judgments and 2) regular, fast, and clear feedback.
The environment in which a farmer operates and makes decisions is likely to
promote both miscalibration and a BTA effect. For example, the actual yield
(feedback) is likely to be distant in time and influenced by weather and other
47
variables, thus not being clear or fast. Also, it is not unusual for a farmer to think that
his farming skills can influence yields. Such attitudes are likely to promote the BTA
effect. Despite growing evidence in the behavioral finance literature about the role
and the influence these misperceptions play in decision-making, few studies in the
agricultural economics literature analyze interactions between the crop insurance
participation and the misperceptions. One study by Egelkraut, Sherrick, Garcia, and
Pennings (2006b), found a negative relationship between the BTA effect and
likelihood of crop insurance purchase. Also, Eales, Engle, Hauser, and Thompson
(1991) found that farmers tend to underestimate the volatility of the futures and
options prices, and Sherrick (2002) showed that farmers maintained systematically
miscalibrated beliefs concerning precipitation. However, none of these papers
considered the relationship between the participation decision and misperceptions in
the presence of other risk management tools, a situation that a farmer faces.
The specific objective of the paper is to provide an assessment of the extent of
the BTA effect and miscalibration for the sample of soybean producers in Indiana,
Illinois, and Iowa, and to evaluate the effect of risk perceptions and other risk
management options on insurance purchasing decisions. The participants of the
study are commercial-scale farms, who are also likely to be intimately informed
about crop insurance. The analysis is conducted using data from the Crop Yield Risk
Survey (CYRS), conducted in 2002 covering corn and soybean producers in Iowa,
Illinois, and Indiana.
Along with demographic, business, and other information, the survey elicited
two separate measures of subjective yields. Yield perceptions were elicited directly
48
(by asking farmers to indicate their average yield and yield variability in relation to
the average county yield) and indirectly (by asking farmers to attach probabilities to
a sequence of yield intervals). The survey also elicited a likelihood of getting a crop
insurance payment and had extensive documentation of actual crop insurance
purchases and preferences for other risk management tools. In the analysis, the
elicited subjective yield measures were related to the county yields (estimated using
NASS county-level data). A regression analysis was conducted to examine the effect
of risk perceptions on insurance purchasing decisions on the individual product level
(yield insurance, revenue insurance, and CAT) and across insurance products.
The paper’s contributions are as follows. First, the study complements a
growing body of literature that analyzes interactions between risk perceptions and
financial decision making (in the context of crop insurance). Second, the study’s
results help in understanding the role of subjective perceptions in farmer insurance
decisions, which in turn will help design better crop insurance products, more
efficient crop insurance program, and highlight the need for an accurate
understanding of actual risks faced.
Background and Literature Review
The farm characteristics that might affect demand for crop insurance have been
examined extensively in the literature. For example, Smith and Baquet (1996) have
examined factors that influence demand for crop insurance using farm-level dataset
from a sample of wheat producers in Montana. They modeled participation decision
as two-step process; in the first step a farmer decides whether to purchase insurance
and (assuming the farmer has decided to purchase crop insurance) in the second step
49
a farmer chooses a coverage level. The results indicated that education, presence of
debt, perceived importance of yield variability, increased the probability of
participation and coverage level, and premium rates. Coble, Knight, Pope, and
Williams (1996) analyzed participation decisions of Kansas wheat farmers, where
they used participation decision as the dependent variable and farm-level data to
identify the variables that contributed to the probability of purchase. Results
indicated that returns from crop insurance increase the probability of purchase and
the variance of the return decreases likelihood of use of crop insurance. The market
returns from operations decreased purchase probability while the variance of market
returns increased it. Both net worth and diversification were likely to decrease the
probability of purchase. Sherrick, Barry, Ellinger, and Schnitkey (2004b) used
survey data, and modeled farmers’ participation decisions as a two-step choice. In
the first stage a farmer decides whether to insure or not, and in the second the
farmers makes a choice between yield insurance, revenue insurance, and or hail
insurance. The results indicated that size, age, leverage, greater share of leased land,
higher level of perceived risk, higher subjective yields, and a greater perceived
importance of risk management tools were likely to contribute to the probability of
insurance purchase. Overall, the econometric results of the demand for crop
insurance studies indicate that size is likely to increase participation, diversification
is likely to decrease participation, and higher yield/income variability is likely to
increase participation as well.
The role of farmers’ perceptions in the crop insurance decision has limited
presence in the literature. Sherrick et al.(2004b) using survey data analyzed demand
50
for crop insurance products found a significant and positive relationship between
decision to participate and subjective mean, indicating that producers with higher
mean yields are more likely to purchase insurance. They also document the roles of
education, size, tenure, and subjective means (estimated from indirectly elicited
subjective yield distributions) as a proxy for differences in soil quality or
management skills. However, Sherrick et al. (2004b) did not consider the impact of
miscalibration and the BTA effect. Shaik, Coble, and Knight (2005) elicited
subjective estimates of mean and variability for yield and price and also proxies for
risk aversion. Unlike Sherrick, Barry, Ellinger, and Schnitkey (2004b), they found a
negative and significant relationship between the subjective mean yield and the
participation decision, and a positive relationship between the participation and
subjective yield variability. For revenue insurance, the results indicated a negative
and significant relationship for subjective mean and a positive significant
relationship for the subjective yield variability. Shaik, Coble and Knight (2005) did
not consider the impact of the BTA effect on the crop insurance. Egelkraut et al.
(2006) investigated the influence of subjective perceptions on the producers’ crop
insurance decision using a dataset from a similar survey with responses from 258
Illinois corn producers. They elicited subjective yield perceptions using the
conviction weights approach (indirectly), and directly, by asking respondents open-
ended questions about farms’ yield level and variability in relation to an average
county farm. They used directly elicited yield perceptions as independent variables
in the regression analysis to explain the demand for crop insurance. The results from
the regression analysis indicated that farmers’ perceptions affected crop insurance, as
51
coefficients for the direct estimates for the mean yield and variability were
significant with expected signs. Egelkraut et al. (2006) did not consider the impact of
miscalibration on the participation decisions. Also, they did not consider the
influence of the BTA effect on the participation decisions in the presence of risk
management alternatives.
This paper continues investigating the role of cognitive biases on crop
insurance decisions by including information on alternative risk management tools
usage and miscalibration, in addition to the variables that were used in the previous
research. The inclusion of information on alternative risk management tools in the
analysis is relevant because when a farmer makes a decision regarding participation
she considers alternatives as well, so these alternatives should be included. Similarly,
as indicated by some of the findings, miscalibration and the BTA effect might
influence decision making. By adding these variables into the analysis, this paper
further contributes to the growing body of research and improves our understanding
of the producers’ perceptions and the role these perceptions play in decision making.
Survey
The study uses data from the crop yield risk survey (CYRS) conducted at the
University of Illinois under a cooperative agreement with the Economic Research
Service USDA and supported by the Risk Management Agency of USDA.
The mailing list used in the survey consisted of 3,000 farms from Illinois,
Indiana, and Iowa, purchased from “Progressive Farmer”, a company specializing in
communication with agricultural producers. Because the sample selected for the
survey was meant to be representative of large-scale, commercial farms, farms with
52
at least 100 acres or greater were selected. During the survey-formulation stage, two
focus groups with farmers were held by an independent market research firm; the
survey was reviewed by University of Illinois staff and economist from ERS USDA;
it also was pretested with a set of farmers who participate in the FBFM record
keeping association; and it was evaluated and tested by the Survey Design Research
Lab at the University of Illinois. The survey was mailed on March 2001 with a cover
letter, that stated the purpose, confidentiality, completion instructions, contact
information for any questions, and an honor payment for $3.00 to be cashed
conditional upon successful completion and mailing of the survey. The survey
included sections on demographic and business information, risk management; risk
perceptions, the conjoint ranking of insurance products and attributes, and other
related information (see Barry, Ellinger, Schnitkey, Sherrick, and Wansink 2002 for
more details about the survey and overall projects).
Indirect Yield Elicitation
The survey elicited subjective yields under two conceptually very different
constructs. Indirectly, the survey asked individuals to assign probabilities into
predefined yield categories (for an example see figure 2.1). The sum of the intervals
was stated as 100%, requiring respondents’ stated probabilities to add up to 100%.
This probabilistic approach, known as the conviction weights approach (Norris and
Cramer 1994), was employed by Bessler (1980) and Eales et al. (1990) as a means of
eliciting probabilistic beliefs by producers.
53
Direct Yield Elicitation
Yields also were elicited directly by asking respondents to indicate whether their
average farm yields are greater/smaller/same as their county average and whether
their farm yields experience greater/smaller/same degree of variability.16 If a farmer
indicated that his yield is smaller/greater than the county average, the survey asked
farmers to state the difference (in bushels) between county average and farm average.
Methods
Indirectly Elicited Subjective Yields
The survey elicited a subjective yield distribution by asking respondents to assign
probabilities to the yield intervals. These discrete probabilities were used to
parameterize subjective yield distributions by fitting a distribution using equation
(1):
( ) [ ]( )7 2 22
1 1 1 8 8
2
min ( ( | )) ( | ) ( | ) 1 ( | )i
i i ij j i j i i i
j
p D U p D U D U p D Uθ
θ θ θ θ−=
− + − − + − −
∑
(1)
Where pij - producer i stated probability for interval j
Uij – upper bound of the interval
D(.) – cumulative distribution of farm-level yields
iθ - set of i two dimensional parameters for producer i’s subjective yield
distribution
The Weibull distribution as parametric form was chosen because Sherrick et al.
(2004a) suggested several of its useful properties for modeling crop yields including
54
its non-symmetry, zero limit, and wide range of skewness and kurtosis. The CDF of
the Weibull has the following functional form:
( ) 1 0 x< , , 0
i
i
x
i iF x e
− = − ≤ ∞ >
α
β α β (2)
Objective Yields
The respondent’s typical objective yield was set equal to average county yield (and
also to state differences where relevant). Because the average is subject to historic
yield data which had a strong upward trend, to calculate the average and standard
deviation, the soybean county yields were obtained from NASS for the years 1972-
2002 and detrended to the 2002 using a linear trend at a county level (following
Sherrick et al.(2004a)).
Correspondence between Subjective Yield Perceptions and Objective Yield
Distribution
To assess the correspondence between subjective and objective yield distributions,
this paper compares directly-stated yields, indirectly-stated yields, and county yields.
T-test and Wilcox tests were conducted to examine if objective yields were
statistically different from indirectly-elicited subjective yields. If a farmer’s stated
yield differs from the objective yield, a BTA effect could be a possible explanation.
Demand for Crop Insurance
The relationship between crop insurance and misperceptions is examined in two
related steps, at individual product level, across the products. The demand for each
insurance product (yield, revenue, and CAT insurance) is analyzed separately using a
logit model to assess the influence of miscalibration and the BTA effect. The
rationale behind conducting analysis on the individual basis is to examine whether
55
the BTA effect and miscalibration influence various insurance products differently,
(i.e., misperceptions affect demand for yield insurance differently than they affect
the demand for revenue insurance). For the analysis across insurance products, the
product choices are aggregated (effectively representing the crop insurance usage
index), and the Poisson regression used to examine the relationship between key
variables and the index that represents an individual overall propensity to use crop
insurance products17.
Individual products. The relationship between biases and crop insurance for
individual products are examined separately for each crop insurance product. For
using the specifications given below yield insurance, equation (3) is estimated, for
revenue insurance, equation (4) is estimated, and for CAT insurance equation (5) is
estimated. The variables for the equations were obtained from the past studies and
will be shown in the parentheses. Since crop insurance participation decisions are
discrete, a binomial logit model was employed to analyze the relationship:
0 1 2 3 4 4 5 6YI AGE LOAN MBTA VBTA MRATIO VRATIO SIZEβ β β β β β β β= + + + + + + + +
7 8 9 10 11 12 13LSTOC APROB FRMS MRMS PRMS OTT EDUβ β β β β β β+ + + + + + + +
14 15 16IL IA INβ β β ε+ + + + ,
where YI denotes choice for yield insurance (binary, equals 1 if a farmer bought yield
insurance, and zero otherwise), AGE denotes producer’s age (Sherrick et al. 2004b),
LOAN is a binary variable (equals 0 if farmer has no debt, 1 otherwise) (Sherrick et
al. 2004b, various proxies used by Barnett, Skees, and Hourigan, 1990) MBTA is
mean BTA effect (discrete choice variable, equals 1 if a farmer claims his yields are
above or equal to county average, 0 if he claims they are below), VTBA is variance
BTA effect (discrete choice variable, equals 1 if a farmer claims his yields are less
(3)
56
variable or as variable as county average yield, 0 if he claims they are more variable),
MRATIO denotes mean miscalibration (difference between indirectly-stated
subjective mean and corresponding objective mean), VRATIO denotes variance
miscalibration (ratio of indirectly-stated subjective standard deviation divided by
objective standard deviation), SIZE is variable for farm size (in acres) (used by
Sherrick et al. 2004b, Coble et al. 1996, and Barnett, Skees, and Hourigan, 1990
among others), LSTOC is the diversification variable for livestock sales as
percentage of gross farm sales (used by Sherrick et al. 2004, and Skees, and
Hourigan, 1990, among the others), APROB denotes farmers’ probability of
receiving indemnity payments under 85% APH coverage level (used Sherrick et al.
2004b), FRMS is a discrete count variable, which denotes a combination of financial
risk management tools such as credit line, savings, government disaster payments
used by farmers to manage the risks, and etc (various proxies for disaster payments
were used by Smith and Baquet, 1996 among others), MRMS is a discrete count
variable, which denotes a combination of marketing risk management tools such as
forward contracting, usage of futures and options, etc. used by farmers to manage the
risks, PRMS is discrete count denotes combination of production risk management
tools such as farming in multiple locations, usage of multicrop enterprises, etc. used
by farmers to manage the risks (Sherrick et al. (2004b) used FRMS, MRMS, and
PRMS as a combined index denoting farmer’s usage of risk management instruments
in the past), OTT is ratio of owned acres to total acres (various proxies for tenure
were used by Goodwin (1994) and Sherrick et al. (2004b)), EDU is a discrete count
variable, denotes farmers’ education level (equals 1 if farmer completed high school,
57
2 completed some college, 3 college graduate, and 4 if farmer has graduate degree)
(used by Sherrick et al.(2004b)), Smith and Baquet (1996), and IL, IA, and IN denote
binary variables for location (equals 1 if farm is located in corresponding state and 0
otherwise).
To examine the relationship between revenue insurance and the biases
equation (4) is estimated as:
0 1 2 3 4 4 5 6RI AGE LOAN MBTA VBTA MRATIO VRATIO SIZEβ β β β β β β β= + + + + + + + +
7 8 9 10 11 12 13LSTOC APROB FRMS MRMS PRMS OTT EDUβ β β β β β β+ + + + + + + +
14 15 16IL IA INβ β β ε+ + + + , (4)
where RI denotes choice for revenue insurance (binary, equals 1 if a farmer bought
revenue insurance, and zero otherwise).
Similarly, the relationship between CAT insurance and the biases is
examined by estimating equation (5)
0 1 2 3 4 4 5 6CAT AGE LOAN MBTA VBTA MDIFF VDIFF SIZEβ β β β β β β β= + + + + + + + +
7 8 9 10 11 12 13LSTOC APROB FRMS MRMS PRMS OTT EDUβ β β β β β β+ + + + + + + +
14 15 16IL IA INβ β β ε+ + + + , (5)
where the CAT denotes choice for catastrophic insurance (binary, equals 1 if a
farmer bought catastrophic insurance, and zero otherwise). Equations (3), (4), and
(5) are each estimated using binomial logit.
Aggregate Use. Finally to analyze aggregate use of crop insurance, the variable user
was created, which is the sum of all crop insurance products that a farmer used, and
equation (6) was estimated
58
0 1 2 3 4 4 5 6USER AGE LOAN MBTA VBTA MRATIO VRATIO SIZEβ β β β β β β β= + + + + + + + +
7 8 9 10 11 12 13LSTOC APROB FRMS MRMS PRMS OTT EDUβ β β β β β β+ + + + + + + +
14 15 16IL IA INβ β β ε+ + + + , (6)
where USER is the sum of all crop insurance products used by a farmer (count
variable, 0 if a farmer used no crop insurance product, 3 if a farmer used all
insurance products). Since “user” is a count variable, Poisson regression model was
used to estimate the relationship (Greene, 2004).
Expected Relationships
In this section, the expected relationship between insurance, the BTA effect,
miscalibration, and the control variables are presented and discussed. These
variables are grouped into categories corresponding to BTA characteristics,
miscalibration, personal characteristics, risk management characteristics, and farm-
level characteristics.
BTA Characteristics: It is expected that an overconfident farmer would view
premiums as being relatively expensive and, therefore, would be less likely to
purchase insurance.
Miscalibration Characteristics: The mean ratio (between implied mean of the
subjective Weibull distribution and implied mean of the objective Weibull
distributions) and standard deviation ratio (between implied standard deviation of the
subjective Weibull distribution and implied standard deviation of the objective
Weibull distribution) were included to allow the model to capture the incongruence
between subjective beliefs and empirical representations of the yields. The expected
relationship between the mean ratio and participation is negative -- if producer’s
subjective mean is smaller than the objective mean, he might think that there is a
59
good chance to receive an indemnity.18 Thus, such producer is thought to be more
likely to purchase crop insurance. Similarly, if a producer’s subjective yield
variability is greater than objective variability, then, he is more likely to participate
in insurance than a producer with lower subjective yield risk. Therefore, the
expected sign between standard deviation ratio and the participation is positive.
Personal Characteristics: Among the demographic characteristics included are age
and education. The expected relationship between insurance use and education is
positive; risk management has become significantly more complicated through time.
Furthermore, this paper postulates a positive relationship between insurance use and
age. As a farmer gets older, he is more likely to be risk averse and thus is more
likely to purchase insurance.
Risk Management Variables: Because farmers have other risk management tools
available that might act as complements or substitutes for insurance, the survey
asked subjects to indicate what risk management tools they have used in the past.
The survey listed several risk management alternatives and asked whether a
respondent used a particular risk management alternative. The alternatives were
grouped in three categories corresponding to: i) financial risk management tools
(such as government programs, financial savings/reserves, back-up credit lines); ii)
marketing risk management score (such as hedging/options, spreading sales over
time, production/marketing contracts, forward contracting); iii) and production risk
management score (such as multiple crop enterprises, crop share leases, multiple
seed varieties, farming in multiple locations). Thus, if a respondent used forward
contracting, credit lines and savings, his financial risk management score would be
60
equal to 2 (credit lines and savings), marketing risk management score would be
equal to 1 (forward contracting) and production risk management score would be
equal to 0. All farmers in the samples used at least one of the risk management
alternatives.
Farm-level Variables: Additional variables such as farm size, diversification, debt,
and wealth, were included in the analysis. Large farms tend to be better managed;
therefore, size is indicative of better management skills and possibly, economies of
scale. Large farms are likely to be more diversified. Both of factors are expected to
reduce demand for crop insurance.
Debt and insurance use might be positively correlated, as lenders often require
farmers to purchase insurance. Wealthier farmers tend to self-insure, therefore,
percentage of owned acres to total acres (a proxy for wealth) is likely to be
negatively related to insurance use. Livestock ownership is another method for a
farmer to diversify, therefore, livestock sales as a percentage of gross farm income is
likely to be negatively related to insurance. Finally, to measure the level of insurable
risk, the perceived probability of receiving an APH yield insurance payment was
included following Sherrick et al. (2004b). A positive relationship is expected,
because higher risk levels will increase the probability of insurance purchase.
Survey Data
The survey was mailed to 3000 farmers, 930 farmers responded, resulting in
approximately 29% survey response rate. After removing incomplete and/or
inconsistent responses, the final sample consisted of 382 farmers.19 Because soybean
distribution intervals in the survey’s subjective distribution section provided better
61
range for actual yield than the corn distribution intervals, the soybean subjective
distributions were used in the analysis (note that the majority of soybean producers
also likely to grow corn). Table 2.1 reports average farm values by insurance
products. Among insurance products, revenue insurance was used by the largest
farms (in acres, as suggested by size), youngest, and most leveraged users with fewer
years of experience. The revenue insurance users also utilize fewer financial risk
management tools, have the lowest tenure, and report the lowest subjective
probability of receiving an indemnity payment under 85% APH. CAT insurance is
the least popular insurance product, with the oldest, most experienced and tenured
users, who have the smallest farms and report the lowest probability of receiving
indemnity under 55% coverage level.
As with any survey, it is possible that selection bias could affect the results. If
for some reason, large farmers self selected this survey, the reported farmers’
tendency to indicate above average yields could be the consequence of having a
sample of larger than average farms, rather than the BTA effect. Therefore, if one
could compare the survey sample characteristics to the actual farm data, any
discrepancies could be indicative of the sample selection bias. This hypothesis is
examined in table 2.2, which compares actual farmer data from producers enrolled in
the Illinois Farm Business Farm Management (FBFM) record-keeping system to data
from the survey (since FBFM covers only Illinois farmers, the Illinois subset was
used). FBFM maintains detailed records of its members, very large, commercial-
scale farms in Illinois, the type of farms that were original target of the survey.
Results from the table suggest that in terms of age, the farms in the sample and the
62
FBFM are distributed similarly. However, in terms of size, FBFM farms are larger
across all categories. Because FBFM farms are larger across all categories, one can
conclude that the survey might not be subject to the size selection bias, assuming that
the sample selection bias could be manifested as size or age differences between the
sample and population.
Results
Yield Elicitation Results: Continuous parametric forms of subjective yield
distribution were derived by minimizing (1), and solving for the parameters of the
Weibull distribution. These parameters were used to estimate indirectly-stated mean
and standard deviation using (7) and (8) as:
1(1 )i i iµ β α −= Γ + (7)
1 2 1(1 2 ) (1 )i i i iσ β α α− − = Γ + −Γ + (8)
The mean for a county yield was calculated from detrended NASS county
yields and the standard deviation for a typical farm was derived as county-level
standard deviation.
Table 2.3 summarizes the respondents’ direct statements of their own mean
yield and yield risk relative to county’s average yield. The majority of respondents
(53% in Iowa, 57% in Indiana, 61% in Illinois), indicated that their yields are higher
than average (on average by 8.9 bu/ac in Iowa, 8.8 bu/ac in Indiana, and 8.4 bu/ac in
Illinois). Thirty eight percent of respondents in Iowa, 41% in Indiana, and 31% in
Illinois indicated that their yields are about the same as average yield, and 9% of
respondents in Iowa, 2% in Indiana, and 9% in Illinois indicated that their yields are
below average. Table 2.4 reports producers’ subjective assessment of their yield risk.
63
Forty one percent of respondents in Iowa, 48% in Indiana, and 47% in Illinois
perceived their yields to be less variable than the county yields, and 20% of
respondents in Iowa, 15% in Indiana, and 10% in Illinois reported their yields to be
more variable than the yields of a typical county. Combining results from the two
tables, 80% respondents in the sample indicated that their yields are better and/or
their yields are less variable or are of the same degree of variability than the county
yields. These results are consistent with the “Lake Woebegone Effect” where all
managers believe themselves to be “above average”.
Comparison of response weighted indirectly-stated yields and county average
yields reveal well-calibrated subjective beliefs. The average, indirectly-stated yield
for Iowa was 45.40 bu/ac (44.97 bu/ac for Indiana, 46.03 bu/ac for Illinois, and 45.56
bu/ac for total sample), and the subjective mean was not statistically different from
county average yield of 45.19 bu/ac for Iowa, (45.45 bu/ac for Indiana, 45.46 bu/ac
for Illinois, and 45.32 bu/ac for total sample) at p>0.00120. The differences in
directly-stated, county average, and indirectly-stated yields are consistent with the
results from previous literature. For example, Egelkraut et al. (2006a) reported that
directly-stated yields were above county average and indirectly-stated yields. They
further argued that “the results reveal a fundamental contrast between producer’s
beliefs when asked for a simple statement of average yield as opposed to assessing a
complete probabilities version of their yield distribution”.
Overall, the presented comparison raises a question. Why the same farmers
who reported reasonably calibrated yield distributions in one survey section, would
reveal distorted beliefs concerning yields in another? As argued in the third paper,
64
one possible explanation could be elicitation formats. Recent findings in contingent
valuation literature showed that donation amounts elicited using direct elicitation
method are almost always lower than actual donation amounts and the amounts
elicited through continuous type of questions (Champ and Bishop, 2001). The
proposed explanation in the literature is that direct elicitation results in an upward
bias as some respondents tend to be less sure about their answers. We argue that this
“unsureness” could be the function of complexity of the elicitation format.
Answering direct elicitation does not require significant efforts and as a result such
format might lead to the answers that respondents are not sure about or the answers
that have not been evaluated carefully. As task complexity of elicitation format
increases from direct elicitation to probabilistic assessment, respondents are forced to
carefully evaluate their responses and to provide more accurate yield assessments.
Also, while some farmers displayed the BTA effect, a particular farmer would make
careful assessment of yields before purchasing insurance. So the effect, while
present, might not be significant in determining insurance decisions. The next
section examines this question in greater detail.
Crop Insurance Use
In this section the results from the regressions are presented and discussed. While
coefficients for logit and the Poisson regression models are helpful in providing
direction and significance, to facilitate the discussion, the marginal fixed effects are
also reported for each model. These effects refer to df () dxt evaluated at x, where
f( ) is an endogenous variable, x is a vector of exogenous variables used to explain
f( ), and xt is one of the exogenous variables. The effects can be used to describe the
65
change in probability due to a change in independent variable of interest (holding
other exogenous variables at their averages).
Table 2.5 shows correlations for the variables used in the analysis. The results
indicate that insurance products are positively correlated with each other and the
correlation is statistically significant. Variable for age (AGE) is positively correlated
with CAT insurance, and debt (LOAN) is positively correlated with revenue
insurance. Risk management strategies (FRMS), (MRMS), (PRMS), are positively
correlated with insurance products. However, none of the variables for the
subjective perceptions (MBTA), (MRATIO), (VBTA), and (VRATIO) are correlated
with insurance products. Interestingly, BTA and miscalibration proxies are
correlated, mean BTA (MBTA) effect is positively and significantly correlated with
mean miscalibration (MRATIO) and variance BTA effect (VBTA). Similarly,
variance miscalibration (VRATIO) is negatively correlated with mean miscalibration
(MRATIO) and positively correlated with variance BTA effect (VBTA). Also, mean
BTA (MBTA) is correlated with usage of marketing risk management tools (MRMS).
The econometric results are reported in table 2.6. The table reports
coefficients, signs, marginal effects, and significance by product. It also reports
pseudo R square, the likelihood ratio, and the percentage of correctly predicted
observations. For the yield insurance model (model 1), the results in the table
indicate that age (AGE), size (SIZE), livestock sales as a percentage of total revenue
(LSTOCK), probability of receiving an indemnity (APROP), financial risk
management score (FRMS), market risk management score (MRMS), and production
risk management score (PRMS) contribute to the yield insurance use. Older farmers,
66
riskier farms, smaller farms, farms with larger percentage of livestock sales, and
farmers who are more likely to try other risk management tools, are also more likely
to purchase yield insurance. None of the proxies for the behavioral biases were
significant.
For the revenue insurance model (model 2), results show that age (AGE), debt
(LOAN), size (SIZE), livestock sales as a percentage of total revenue (LSTOCK),
probability of receiving indemnity (APROB), and production risk management
(PRMS) score contribute to revenue insurance usage. Thus, younger farmers with
smaller farms, more leveraged farmers, riskier farms, and farmers who are more
likely to try production risk management tools are more likely to purchase revenue
insurance. As with yield insurance, none of the proxies for the biases were
significant.
For the CAT insurance model (model 3), the results show that age (AGE),
leverage (LOAN), size (SIZE), livestock sales as a percentage of total revenue
(LSTOCK), probability of receiving indemnity (APROB), and the market risk
management score (MRMS) are likely to contribute to CAT insurance use. These
results indicate that older, less risky, more leveraged users, who use market risk
management tools, and have smaller farms are more likely to use crop insurance.
The negative relationship between probability of receiving APH insurance payment
and CAT purchase is especially interesting. The CAT insurance is provided for a
nominal fee and lender often require borrower to purchase some type of crop
insurance. It could be that farmers who purchase CAT insurance do so to satisfy
lending requirement and do not expect to benefit from it. Again, as with the previous
67
models, the proxies for the biases were not significant. Note that predictive ability is
much lower for CAT insurance.
Table 2.7 presents results for the Poisson regression model with dependent
variable user (model 4). The only significant variables are age (AGE), size (SIZE),
livestock sales as a percentage of total revenue (LSTOCK), perceived probability of
receiving APH payment (APROB), and risk management scores (FRMS), (MRMS),
and (PRMS). Older farmers with smaller, less diversified farms, higher perceived
probabilities of receiving insurance payments and higher usage of other risk
management tools are more likely to buy crop insurance products.
The pseudo R-squared is low across both individual and aggregate use models,
but the likelihood ratios are significant. Overall, the results suggest that age
increases probability of yield and CAT insurance purchase, and decreases the
probability of revenue insurance purchase, leverage increases probability of purchase
for revenue and CAT insurance and decreases the probability for yield insurance and
the size decreases likelihood of purchase. Also, the results suggest that farmers with
perceived higher probability of receiving APH payment are more likely to participate
in yield and revenue insurance program (both at individual product and aggregate
use level) and less likely to participate in CAT insurance. Livestock sales as a
percentage of total revenue increased probability of participation for yield insurance
and decreased participation for all other types of insurance. Also farmers who
actively used risk management tools are more likely to use insurance products.
Unlike Coble et al.(1996), Smith and Baquet (1996), and Sherrick et al.
(2004b), the results detect no relationship between participation and net worth and
68
education (Smith and Baquet, 1996). The results indicate a relationship between
crop insurance use and leverage (consistent with Smith and Baquet (1996), and
Sherrick et al (2004b)), size and diversification (consistent with Coble et al.(1996)).
Interestingly, the variables that were consistently significant in all models are
risk management scores. There could be two reasons explaining the significance.
One reason is past experience with risk management tools. If a farmer had a positive
experience using one risk management tool, he is more likely to continue using it,
and is more likely to use other risk management instruments as well. The positive
past experience with risk management tools would explain high significance, and
provide some further empirical support to the academic literature on experience
based crop insurance discounts (see for example Rejesus, Coble, Knight, Jin, 2006).
Another, possibly complimentary, explanation is risk aversion. If a farmer is a risk
averse, he is more likely to try any and all risk management instruments. Therefore,
simple risk aversion would explain high significance observed in the regression
models.
No significant relationship was detected between misperceptions (both the
BTA effect and miscalibration) and crop insurance purchase. Thus, the results
suggest that the effect does not seem to influence crop insurance decisions. The
results are not consistent with Egelkraut et al.(2006b) who reported a negative
significant relationship between insurance purchase and the BTA effect. One
possible explanation could be in different specifications of the model, for example,
presence of risk aversion variables in Egelkraut et al. model (which were not
available in this survey).
69
Conclusion
The purpose of this paper was to assess the extent of the BTA effect and
miscalibration and examine whether these biases influence insurance purchasing
decisions using data from a survey that covered soybeans producers from Illinois,
Iowa, and Indiana. The survey elicited subjective yield perceptions using two
different elicitation methods. While a majority of farmers indicated that their
average yield is greater than the county yield, and similarly, that their yields are less
variable than the county yields, the means of the subjective yield distribution
recovered from indirectly elicited yields, corresponded closely to the county yield
means. The results are consistent with Egelkraut et al. (2006b), Bessler (1980),
Pease (1993), and Eales et al. (1990). The results illustrated that age increases
probability of participation for revenue and CAT insurance and decrease the
probability for yield insurance. Therefore, encouraging older farmers to participate
in revenue insurance could be an effective strategy to increase participation.
Leverage increases probability of participation for revenue and CAT insurance
products, size decreases the probability for all insurance products. Diversification
(measured as sales of livestock) decreases the likelihood of purchase across all
insurance products, and probability of receiving insurance payments increases the
likelihood for yield and revenue insurance, and decreases it for CAT insurance. This
significance is consistent with the results from the first paper that showed presence
of adverse selection. The results also suggested that farmers who had used other risk
management tools before are more likely to participate in crop insurance program as
well; suggesting that RMA should consider providing discounts for a continuous use
70
of crop insurance and target farmers who actively use risk management tools.
Accounting for trend and bringing more farmers through effective targeting (both in
terms of risk management usage and age) could mitigate adverse selection. Both the
BTA effect and miscalibration do not seem to affect crop insurance purchasing
decisions. This finding contradicts results by Egelkraut et al. (2006b) who a found
negative relationship between the BTA effect and insurance participation using s
similar survey that covered only Illinois corn producers. While results suggested
little relationship between BTA effect and participation, further training and
education might benefit farmers by making farmers aware of the bias.
The results imply that the biases discussed are likely to be present in farmers’
decision making. However, these biases are not likely to substantially influence
actual producer insurance decisions, further supporting the argument that will be
made in the third paper that the BTA effect likely to be due to the elicitation format
that has been shown to result in upward bias, rather than fundamental miscalibration
of beliefs. A related implication is farmers are rational when crop insurance
participation is involved. These implications provide different view from previous
findings and suggest that the role these biases play in the decision making might not
be as significant as some economists have argued in the past. Of course the results
are generalizable only to the extent our sample is representative of the farmers’
population and to the extent that the specifics of the crop insurance underwriting and
purchasing process is similar to other insurance products underwriting and
purchasing process. For this reason, a goal of the future studies may be to test the
71
role of these biases using different insurance products, or using sample of crop
insurance users from different geographical region, growing different crops.
Endnotes
16 An example of the question: “Relative to your primary county’s average yield,
would you say you average yield is (check box, fill in blank) __higher,
by___bu/acres, _lower, by __by/acres, about the same”, “Relative to the same county,
would you say your yields are (check box) more stable, more variable, same degree
variability”
17 The survey asked respondents following question: “Which of the following risk
management tools have you used in the past?” Such wording allowed some
respondents to indicate that they have used several insurance products (for example,
yield insurance and revenue insurance or yield insurance and CAT insurance and so
on). Since the choice of insurance products in this case is not mutually exclusive and
simultaneous, Poisson regression was thought to be more relevant than the
multinomial logit/probit models.
18 Note that all farms in a county get same rated insurance so directional relative
effects should be fairly sensible
19 Surveys with less than 10% summing errors in distribution section were rescaled
(divided by total of the reported probabilities) and used. Also, because soybean
distribution intervals in the survey’s subjective distribution section provided a better
range for actual yield than the intervals for the corn distribution, only soybean
subjective distributions were used in the analysis. As a result of this selection
72
criterion, the sample could include soybean producers who might/might not be corn
producers. Producers, who indicated that they farmed in several primary counties,
were also eliminated. Furthermore, all observations that had missing entries for the
variables used in the analysis were eliminated as well
20 Statistical significance was assessed using paired t-test to account for a possible
dependence between subjective and county means. (Bluman, 2001)
73
Figures and Tables
Figure 2.1. Sample question for indirectly-elicited yields
Corn-Yield range Probability Soybeans- Yield Range Probability
Less than 40 bu/acre Less than 10 bu/acre
41 to 60 bu/acre 11 to 20 bu/acre
61 to 80 bu/acre 21 to 30 bu/acre
81 to 100 bu/acre 31 to 40 bu/acre
101 to 120 bu/acre 41 to 50 bu/acre
121 to 140 bu/acre 51 to 60 bu/acre
141 to 160 bu/acre 61 to 70 bu/acre
More than 160 bu/acre More than 70 bu/acre
Total (Should sum to 100%) 100% Total (Should sum to 100%) 100%
74
Tab
le 2.1
. R
esponden
ts’
char
acte
rist
ics
for
Illi
nois
, Io
wa,
and I
ndia
na
soybea
n p
roduce
rs b
y insu
rance
pro
duct
Yield
Revenue
CAT
Average
St.Dev
Average
St.Dev
Average
St.Dev
Use
r 40%
-
40%
-
19%
-
Siz
e 788
698
825
668
731
705
Age
52
12
50
11
54
11
Hig
h S
chool
43%
-
44%
-
43%
-
Som
e C
oll
ege
29%
-
27%
-
31%
-
Coll
ege
Gra
duat
e 26%
-
26%
-
22%
-
Gra
duat
e S
chool
3%
-
3%
-
5%
-
Per
centa
ge
wit
h D
ebta
72%
-
79%
-
75%
-
Fin
anci
al R
isk M
anag
emen
t S
core
(num
ber
of
tools
use
d)b
2.0
1.2
2.2
1.1
1.9
1.2
Mar
ket
Ris
k M
anag
emen
t S
core
(num
ber
of
tools
use
d)c
2.5
1.1
2.5
1.1
2.2
1.2
Pro
duct
ion R
isk M
anag
emen
t S
core
(num
ber
of
tools
use
d)d
2.5
1.1
2.5
1.1
2.2
1.2
Liv
esto
ck S
ales
As
Per
centa
ge
of
Gro
ss S
ales
15.8
24.1
15.3
23.6
15.3
23.8
O
wned
to T
ota
l A
cres
40%
36%
39%
34%
49%
36%
S
ubje
ctiv
e pro
bab
ilit
y o
f re
ceiv
ing a
n insu
rance
pay
men
t under
85%
AP
H c
ov.lev
el (%
) 27
24
26
22
21
17
a)
Den
ote
s a
dum
my v
aria
ble
, eq
ual
s 1 if
farm
er h
as d
ebt, z
ero o
ther
wis
e.
b)
Num
ber
of
finan
cial
ris
k m
anag
emen
t to
ols
far
mer
use
d (
gover
nm
ent pro
gra
ms,
bac
kup c
redit lin
e, f
inan
cial
sav
ings/
rese
rves
).
c)
Num
ber
of
mar
ket
ris
k m
anag
emen
t to
ols
far
er u
sed (
hed
gin
g/o
ptions,
spre
adin
g s
ales
over
tim
e, p
roduct
ion/m
arket
ing c
ontr
acts
, fo
rwar
d c
ontr
acting).
d)
Num
ber
of
pro
duct
ion r
isk m
anag
emen
t to
ols
far
mer
use
d (
multip
le c
rop e
nte
rpri
ses,
cro
p s
har
e le
ases
, m
ultip
le s
eed v
arie
ties
, fa
rmin
g in m
ultip
le loca
tions)
.
74
75
Table 2.2. Farm characteristics for survey sample (Illinois subset, soybean) and FBFM, by age
Age Category less than 30 30 – 39 40 - 49 50 - 59 60 & over
Farm Distribution 3% 9% 35% 31% 22% Survey Data Tillable Acres (acres) 880 728 893 734 601
Farm Distribution 3% 9% 29% 31% 28% FBFM Data for
2006 Tillable Acres (acres) 971 1034 1061 991 878
76
Table 2.3. Producers average subjective yields relative to average county yield
Higher About the Lower
Yield by… Same Yield By… Obs
% bu/ac % % bu/ac Count
IA 53 8.9 38 9 6.2 190
IN 57 8.8 41 2 3.2 55
IL 60 8.4 31 9 5 137
Total 56 8.7 36 8 5.6 382
77
Table 2.4. Producers subjective yield variability relative to county yield variability
Less About the Same More
Variable Variability Variable
% % %
IA 41 39 20
IN 48 37 15
IL 47 43 10
Total 44 40 16
78
T
able
2.5
. C
orr
elat
ions
Yield
Insura
nce
Reve
nue
Insura
nce
CAT
USER
ILIA
AGE
LOAN
MBTA
Size
LSTO
CKAP
ROP
FRMS
MRMS
PRMS
OTT
EDU
MRAT
IOVB
TAVR
ATIO
Yield
Insur
ance
1
Reve
nue I
nsuran
ce0.2
944*
**1
CAT
0.152
2***
0.100
7*1
USER
0.747
4***
0.727
7***
0.538
5***
1
IL-0.
0387
-0.07
36-0.
0253
-0.06
981
IA0.0
647
0.080
90.0
669
0.104
3**
-0.74
63**
*1
AGE
0.076
8-0.
0747
0.115
9**
0.047
80.0
83-0.
0444
1
LOAN
-0.01
180.1
437*
**0.0
310.0
826
-0.05
980.0
442
-0.23
19**
*1
MBTA
-0.04
55-0.
0202
-0.00
24-0.
0358
-0.01
16-0.
0517
-0.02
830.0
164
1
SIZE
0.005
0.066
6-0.
0585
0.014
40.0
938*
-0.15
42**
*-0.
1714
***
0.208
1***
0.126
8**
1
LSTO
CK0.0
153
-0.00
530.0
008
0.005
6-0.
1698
***
0.175
3***
-0.17
13**
*0.1
187*
*0.0
205
-0.09
31*
1
APRO
P0.1
879*
**0.1
313*
*-0.
0246
0.159
3***
0.017
10.0
087
-0.06
850.1
337*
**0.0
042
0.061
50.0
171
1
FRMS
0.303
6***
0.256
8***
0.182
8***
0.371
***
0.049
7-0.
0389
-0.02
04-0.
0252
0.042
60.0
966*
-0.00
69-0.
0154
1
MRMS
0.269
8***
0.345
8***
0.110
4**
0.371
1***
0.025
8-0.
0661
-0.08
93*
0.069
70.1
051*
*0.2
97**
*-0.
0295
-0.04
890.6
313*
**1
PRMS
0.323
9***
0.354
7***
0.070
50.3
884*
**0.0
111
-0.01
94-0.
0166
0.078
80.0
198
0.205
6***
-0.06
0.027
20.6
638*
**0.6
456*
**1
OTT
-0.02
96-0.
0624
0.098
*-0.
0092
-0.06
10.0
684
0.342
3***
-0.19
42**
*-0.
0039
-0.13
18**
0.104
5**
0.005
3-0.
0201
-0.06
69-0.
0867
*1
EDU
-0.04
27-0.
0413
-0.02
72-0.
0555
0.122
4**
-0.14
64**
*-0.
122*
*-0.
0046
0.021
10.2
375*
**-0.
0822
-0.11
3**
0.068
50.1
483*
**0.0
552
0.009
71
MRAT
IO-0.
0509
-0.03
3-0.
018
-0.05
170.0
62-0.
0125
-0.14
11**
*-0.
0096
0.261
1***
0.128
7**
0.017
5-0.
058
-0.03
520.0
520.0
011
0.017
90.11
18**
1
VBTA
-0.00
08-0.
0833
0.019
5-0.
0368
0.126
5**
-0.12
74**
0.034
7-0.
0295
0.367
8***
0.06
0.067
20.0
147
0.025
10.0
438
0.002
40.0
451
-0.02
680.2
564*
**1
VRAT
IO-0.
0163
0.029
1-0.
0259
-0.00
360.0
317
-0.03
72-0.
0524
0.003
70.0
023
0.075
40.09
73*
0.142
1-0.
0263
0.034
1-0.
0285
0.039
7-0.
0295
-0.11
42**
-0.09
56*
1 N
ote
: *,*
*,a
nd *
** d
enote
sta
tist
ical
sig
nif
ican
ce a
t 0.1
, 0.0
5, an
d 0
.01 lev
el.
78
79
Tab
le 2
.6. In
div
idual
pro
duct
use
res
ult
s
Note
: *,*
*,a
nd *
** d
enote
s st
atis
tica
l si
gnif
ican
ce a
t 0.1
, 0.0
5, an
d 0
.01 lev
el.
a) T
he
ratio f
ollow
s C
hi-
squar
e dis
trib
ution w
ith d
egre
e of
free
dom
s eq
ual
to the
num
ber
of
indep
enden
t var
iable
s in
the
regre
ssio
n. T
he
null h
ypoth
esis
is
that
the
coef
fici
ents
are
not
signif
ican
tly d
iffe
rent fr
om
zer
o.
Model 1 (Dependent Variable: Yield
Insurance)
Model 2 (Dependent Variable: Revenue
Insurance)
Model 3 (Dependent Variable: CAT
Insurance
Coefficients
Marginal Effects
Coefficients
Marginal Effects
Coefficients
Marginal Effects
IL
-0.0
244053
-0.0
092963
-0.0
426071
-0.0
16279
0.1
466636
0.0
344139
IA
0.2
041488
0.0
777348
0.1
975291
0.0
755054
0.3
378917
0.0
777174
AG
E
0.0
168969**
0.0
06443
-0.0
035567**
-0.0
013614
0.0
171388***
0.0
039364
LO
AN
-0
.1421098
-0.0
546205
0.3
231633**
0.1
204951
0.3
413364***
0.0
724738
MB
TA
-0
.3619703
-0.1
420759
-0.0
425053
-0.0
163498
-0.0
141176
-0.0
032628
SIZ
E
-0.0
001353***
-0.0
000516
-0.0
001531***
-0.0
000586
-0.0
001856***
-0.0
000426
LS
TO
CK
0.0
025734***
0.0
009813
-0.0
014998**
-0.0
00574
-0.0
004989**
-0.0
001146
AP
RO
B
0.0
146075**
0.0
055701
0.0
083329**
0.0
031895
-0.0
010342***
-0.0
002375
FR
MS
0.2
163897**
0.0
825124
-0.0
158211
-0.0
060557
0.3
520407
0.0
808565
MR
MS
0.1
625625**
0.0
619874
0.2
900972
0.1
11038
0.1
03286*
0.0
237227
PR
MS
0.1
805055**
0.0
688293
0.2
286728**
0.0
875271
-0.0
959031
-0.0
22027
OT
T
-0.3
251529
-0.1
239854
-0.0
285801
-0.0
109394
0.2
730707
0.0
627187
ED
U
-0.0
344841
-0.0
131493
-0.1
069324
-0.0
409296
-0.0
344643
-0.0
079157
MR
AT
IO
-0.0
694492
-0.0
26482
-0.0
15978
-0.0
061158
0.0
273877
0.0
062904
VB
TA
0.0
499754
0.0
189543
-0.3
149895
-0.1
231454
0.1
185324
0.0
260726
VR
AT
IO
-0.0
987317
-0.0
376478
0.0
138567
0.0
053038
-0.0
262012
-0.0
060179
IN
-1.6
52185
-0
.8393554
-2
.780922
Pse
udo R
2
0.1
57
0.1
65
0.0
85
L
ikel
ihood
Rat
ioa
78.9
83.4
28.5
C
orr
ectl
y
Pre
dic
ted (
%)
36
37
15
79
80
Table 2.7. Aggregate product use results
Model 4 (Dependent Variable: User)
Coefficients Marginal Effects
IL -0.0202067 -0.0174616 IA 0.2117762 0.1839693 AGE 0.0088856*** 0.0077001 LOAN 0.1515867 0.1272708 MBTA -0.109015 -0.0989674 SIZE -0.0001423*** -0.0001234 LSTOCK -0.0003079*** -0.0002668 APROB 0.0068083*** 0.0058999 FRMS 0.1585426** 0.1373902 MRMS 0.1931505* 0.1673807 PRMS 0.1325118** 0.1148324 OTT -0.0280902 -0.0243425 EDU -0.0606925 -0.052595 MRATIO -0.0432156 -0.0374498 VBTA -0.0482842 -0.0425418 VRATIO -0.0314923 -0.0272906 IN -1.272242 - Pseudo R2 0.1 Likelihood Ratioa 87.9 Note: *,**,and *** denotes statistical significance at 0.1, 0.05, and 0.01 level. a) The ratio follows Chi-square distribution with degree of freedoms equal to the number of independent variables in the regression. The null hypothesis is that the coefficients are not significantly different from zero.
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CHAPTER 3
Farmers’ Subjective Yield Distributions and Elicitation Formats
Abstract
Subjective yield perceptions were elicited in two different formats from
Illinois, Indiana, and Iowa farmers and compared to objective county-level
yields. The results indicate that subjective perceptions elicited in a
probabilistic framework provide a reasonably accurate representation of
yields, suggesting that as a group, farmers’ perceptions are well-calibrated.
Importantly, this elicitation method is shown to be more accurate than
direct yield elicitation. The findings have important implications for survey
design/use and for the analysis of subjective beliefs elicited through surveys
involving direct elicitation.
Farmers’ beliefs about probabilistic events directly influence their production and
risk management decisions. However, since these beliefs cannot be directly
observed or measured through simple means, subjective estimates are often elicited
from farmers themselves through variously designed surveys. A natural question
emerges as to the reliability of these estimates relative to objective or resulting
distributions of outcomes. While it is reasonable to expect farmers’ subjective
perceptions to correspond to reality, the existence of such biases as overconfidence,
and person’s reliance on certain heuristics in decision-making might distort farmers’
perceptions. While this question has been examined in the past, Nerlove and Bessler
(2001) examining current evidence of our understanding regarding how individuals
form expectations and respond to these expectations, noted that “When asked in a
survey what they expect with respect to such-and-such, and what and how do
respondents answer? On the whole we remain ignorant of respondents’ state of mind,
and really carefully designed surveys directed to elucidating these matters remain to
be carried out.” (pg 199). In a related question, it is important to consider
82
differences in encoding or response validity among alternative elicitation methods.
This is especially relevant given recently observed differences in elicitation formats
in contingent valuation literature (Ready, Navrud, and Dubourgh, 2001).
The study addresses these issues by analyzing yield risk perceptions of
soybean producers from Illinois, Indiana, and Iowa. The paper utilizes data from
comprehensive survey mailed to 3,000 corn and soybean producers in the three states
identified. In addition to demographic, business, and other basic informational items,
the survey elicited subjective yield perceptions from respondents under two different
formats, referred to as direct and indirect approaches. The purpose of this paper is to
compare responses between the formats, identify differences, and to provide
plausible explanations. The accuracy of each approach is assessed by comparing
elicited subjective yield values from set of farmers to the county-level yield data
from which the responses were generated. So, apart from chapter two which
examined the influence of cognitive biases on the individual’s decisions to purchase
crop insurance in the presence of alternative risk management options, this paper
investigates the role of different elicitation formats on the accuracy of yield
perceptions by comparing farmers’ perceptions (as a group) to their county yields.
The county-level data was used in this analysis because farm-level data for the
respondents’ were not available. While this complicates the investigation, note that
because farm-level data are often not available, the county-level data is used instead,
in a variety of applications that might influence farmer’s decision making (for
example, crop insurance is rated at the county level, using county-level yields).
Therefore, in some cases, the comparison to county-level yields is more relevant than
83
the comparison to the farm-level yields. In addition, the addendum develops an
approach that allows one to adjust county-level yields for the higher variability by
estimating an average ratio of standard deviations of county level and farm level
yields.
The paper contributes to understanding in two areas: accuracy of subjective
yield perceptions and the role of elicitation format on the accuracy of subjective
yield perceptions. The producer’s ability to accurately process yield information has
significant implications for many purposes – in particular, in cases that require
farmers to begin with accurate understanding of the probabilities associated with
some random variables. Producers routinely rely on their yield perceptions,
especially when decisions involve risk management, crop insurance,
marketing/hedging, and others. Yet, research assessing the accuracy of the
perceptions is relatively limited (Sherrick, 2002). Role of elicitation format on the
accuracy of perceptions is also important. If one elicitation method is consistently
more accurate than another, there are obvious implications for survey design and use.
To aggravate the problem further, the yield elicitation methods are commonly used
in isolation in surveys, making comparison of elicitation methods challenging. By
examining the subjective perceptions elicited under different formats from the same
respondent, the paper addresses an issue in existing research that has not been
extensively targeted in the past.
Literature Review
Most of the literature on risk perceptions in agricultural economics is related to yield
perceptions, and particularly, to the correspondence between subjective and objective
84
yields. Because underlying assumptions regarding the true data-generation process
for crop yields are very important for the comparison of subjective and objective
yields, crop yield distributions (parametric and non-parametric) have been
extensively analyzed. For example, Nelson and Preckel (1989) used beta distribution,
while Jung and Ramezani (1999) used lognormal distribution. Others, such as Ker
and Goodwin (2000) used non-parametric distributions. Sherrick, Zanini, Schnitkey,
and Irwin (2004a) analyzed implications of using different distributional forms to
model yields using farm-level data for corn and soybeans. They detrended yields
using a linear trend (unit root test showed that yields time series were not stochastic),
and fitted normal, logistic, Weibull, beta, and lognormal distributions, and assessed
the fit using the Anderson-Darling and likelihood tests. The results indicated that the
Weibull provided a suitable representation for the crop yields. Further, the flexibility
of the Weibull makes it attractive as a measure across a wide set of moments
conditions.
While the subjective beliefs are important in forming expectations and making
decision, the number of articles that analyzed the producers’ subjective beliefs in
agriculture is limited. The second chapter of this dissertation analyzed the role of the
misperception biases in insurance-purchasing decisions. Results showed that the
BTA effect is present in farmers’ decision making, since majority of farmers were
overstating their yields in relation to the county average. The results from the
regression analysis indicated that the variables for age, likelihood to receive an
indemnity, diversification, and usage of alternative risk management tools were
significant in determining the demand for crop insurance. However, none of proxies
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for the biases were significant, suggesting that farmers are rational in crop insurance
decisions, and that the biases could a product of elicitation format.
Sherrick (2002), using a conviction weights approach (probabilistic approach),
elicited subjective distribution for precipitation and compared the parameterized
subjective distribution to the parameterized actual rainfall distribution. Sherrick
found that farmers tend to overstate average precipitation levels for April rainfall and
understate average precipitation for July rainfall. Similarly, he found that farmers
tend to understate the precipitation variability for July rainfall, and overstate the
variability for April rainfall. Eales, Engel, Hauser, and Thompson (1990) elicited
subjective distribution for options and futures prices from various market
participants and, assuming lognormal distribution compared the prices to actual
market values. They found that while their reported subjective means agreed in most
cases with corresponding market values, the respondents’ reported subjective
variances were significantly smaller than their market estimates. Pease (1993)
elicited yield distributions from corn and soybean producers and compared them
with producers’ production history. Using subjective means as a forecast, he
compared the means with linearly detrended farm-level historical yields. He reports
that while subjective means were slightly higher for soybeans, they were lower for
corn. He also reports that producers significantly underestimated yield risk.
Similarly, Bessler (1980) elicited yield distribution from farmers using conviction
weights or probabilistic approach. Aggregating the subjective yield distributions and
comparing the resulting values with the ARIMA forecast (derived based on actual
yields), he reported no significant differences between the forecast and subjective
86
mean values. He also noted that subjective forecasts tend to display a greater
variability. Using a format similar survey to the one employed here, Egelkraut,
Sherrick, Garcia, and Pennings (2006a) elicited subjective crop distribution from
Illinois corn producers. They elicited subjective yields directly (by asking farmers to
state their average yield and yield variability in relation to the typical farm in the
county) and indirectly (by asking farmers to assign weights to yield intervals) and
compared these estimates to the county-level data. They found that the differences
between county averages and directly stated yields were statistically significant.
Also, the differences between indirectly elicited measures and directly elicited
measures were significant as well, while differences between county estimates and
indirect estimates for mean and variability were not statistically significant. Nerlove
and Bessler (2001) provide an overview of the studies that examined correspondence
between respondents’ expectations (elicited in surveys among other methods)
regarding economic variables to the objective representation of these variables.
Major findings of their overview were as follows. First, the result indicated that
aggregated individual expectations approximated objective data better than
individual expectations. Second, respondents displayed a significant heterogeneity
in their expectations. Third, respondents were capable of identifying underlying data
generation process (i.e. random walk versus autoregressive pattern) but did not
always optimally incorporated the process into the expectations and forecast.
Overall, the results from past literature suggest that farmers (as a group) possess
reasonably accurate subjective estimates of mean and less accurate estimates of yield
87
variability. In addition, the findings indicate that indirectly elicited yields provide a
more accurate representation then directly-elicited yields.
In addition to the publications in agricultural economics, the literature related
to contingent valuation might provide insights toward a better understanding of the
role that elicitation format plays in recovering subjective beliefs. In contingent
valuation studies, information on donations is usually elicited in two ways: through
dichotomous choice (“Would you pay X for Y?” type of questions) and traditional
payment card, where individuals are asked to choose among several choices of
payment amounts. It has been observed in the literature that the donations elicited
through dichotomous choice tend to exceed actual donations, resulting in an upward
bias, which has been referred to as a “hypothetical bias” (Champ and Bishop, 2001),
while donations elicited through more continuous elicitation methods such as the
payment card tended to be lower and more in line with actual donations. It also has
been noticed that respondents in dichotomous-choice type questions tended to be less
certain about their answers. For example, Champ and Bishop (2001) after eliciting
responses in dichotomous-choice, followed up with “How certain are you that you
would (would not) donate the requested amount?” with a response scale ranging
from 1 (very uncertain) to 10 (very certain). They compared the responses to the
second sample where respondents actually donated money. The results indicated
that the donation amount elicited through dichotomous-choice has exceeded actual
amount donated. Also the proportion of the respondents who stated that they would
donate certain amount and are very certain to donate (10 on the scale) was similar to
the proportion that actually donated money. Ready, Navrud, and Dubourgh (2001)
88
argued that the differences between two methods could be explained by “how unsure
respondents answer these two types of questions.” (pg 325). Under dichotomous-
choice, the respondents who are not completely sure of their answers would be
classified as “yes”, because the question usually asks “would you pay X amount for
Y?” This does not happen under continuous choice because respondents are given
choices and therefore, could be more specific in their answers. In other words,
dichotomous choice might classify some of the “may be” answers as “yes”, resulting
in an upward bias. Ready, Navrud, and Dubourgh (2001) reported that the
differences between two elicitation methods were reduced if the respondents under
dichotomous choice were elicited certainty level (i.e. “I am 95% certain that I would
pay X amount for Y.”), and the answers were controlled for it. The obvious question
that arises from these findings is whether the differences in elicitation formats play a
similar role in elicitations of other variables, such as yield perceptions.
Given the limited research, the need for further analysis of producers’
perceptions is evident. Various audiences can gain from more a detailed analysis of
subjective yield elicitation. Findings can be helpful for researchers and survey users
since, direct elicitation of mean yield and yield variability is used extensively in
research; see for example Shaik, Coble, and Knight (2005). If different elicitation
formats lead to different responses, the discrepancies need to be accounted for in
survey designs and use. To date, only Egelkraut et al.(2006b) is known to have
considered directly and indirectly elicited yields elicitation in the same survey. This
study represents improvement over Egelkraut et al. (2006b) work by examining the
89
yield differences from different elicitation formats as function of age, education, size
using a bigger sample and a different crop.
Survey Description
The study uses data from a crop yield risk survey, which was conducted under a
cooperative agreement with the Economic Research Service USDA and supported by
the Risk Management Agency of USDA. While the survey is described in detail in
the second paper, elicitation methods used in the survey need additional discussion.
Yield perceptions for soybeans were elicited directly and indirectly, in separate
sections of the survey. The partitioning of these two sections was done by design to
separate task and context. For the indirect section, the perceptions were elicited by
asking respondents to assign probabilities into the predefined yield categories (figure
3.1). This probabilistic approach, known as the conviction weights approach (Norris
and Kramer 1990), was employed by Bessler (1980) and Eales et al. (1990). The
sum of the intervals was identified as 100%, requiring respondents’ stated
probabilities to sum to 100%, and readjust interval weights until probability is fully
assigned.
Farmers’ yield perceptions were also elicited by directly asking respondents to
indicate whether their yields are above primary county average (if yes, by how many
bushels), below the county average (if yes, by how many bushels), or the same as the
county average (figure 3.2 shows that part of the survey). Besides eliciting average
yield, the survey elicited yield variability by asking a respondent to state whether
respondent’s subjective yields are more variable than county average, less variable
than county average, or have the same degree of variability.
90
Methods
The directly-stated subjective yield averages were estimated as follows. If a
respondent indicated that his farm-individual yield is not different from county
average, his directly-stated yield average was set equal to the county average (since
the survey asked a respondent to refer to his county average). If the respondent
indicated that his yield is below/above the average, the directly stated yield was
coded as the county average yield minus/plus the stated difference.
In the indirectly-stated yield section, discrete probabilities were used to both
calculate implied weighted averages and to convert each individual response set was
to a continuous subjective yield distribution using:
( ) [ ]( )7 2 22
1 1 1 8 8
2
min ( ( | )) ( | ) ( | ) 1 ( | )i
i i ij j i j i i i
j
p D U p D U D U p D Uθ
θ θ θ θ−=
− + − − + − −
∑
(1)
where pij - producer i stated probability for interval j
Uij – upper bound of the interval
D(.) – cumulative distribution of farm-level yields
iθ - set of parameters for producer i’s subjective yield21
Distribution functions for Weibull, normal, and lognormal distributions were
fitted. Results are presented for the Weibull distribution because 1) it provides the
best fit22 and 2) to take advantage of useful properties of the Weibull distribution for
modeling crop yields including its non-symmetry, zero limit, and wide range of
skewness and kurtosis. The CDF of the Weibull has the following functional form:
91
( ) 1 0 x< , , 0
i
i
x
i iF x e
α
β α β
− = − ≤ ∞ >
(2)
The CDF for normal distribution has following function form:
1 x - ( ) 1 + erf 0 x< , - , 0
2 2F x
µµ σ
σ
= ≤ ∞ ∞ < < ∞ >
(3)
And CDF for lognormal has following distributional form:
1 ln(x) - ( ) 1 + erf 0 x< , - , 0
2 2F x
µµ σ
σ
= ≤ ∞ ∞ < < ∞ >
(4)
Where erf is defined as:
2
0
2( )
z
terf z e dtπ
−= ∫
The implied mean and implied standard deviation are then calculated under the fitted
distributions for each farmer and used as proxies for the indirectly-stated average
yield and yield variability.
The county distribution was used as a representative objective yield distribution
from the location indicated in the response as the primary county. Soybean county
yields were obtained from NASS for the years 1972-2002 and detrended to 2002 (the
survey date) using a linear trend at county level (Sherrick et al. (2004a)) found that
yields series tend to be stationary with s strong upward trend due to improved seed
technology). To estimate parameters for continuous distributional form equation (5)
was minimized;
( )22
,min | , ( | , )fit fitα β
µ µ α β σ σ α β− + − (5)
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Where µ is equal to the county mean.
fitµ is the fitted county mean
σ is the county standard deviation
fitσ is the fitted county standard deviation
,α β are the Weibull parameters for fitted distribution
Solving (5) for ,α β provides Weibull parameters for a continuous county yield
distribution with objective mean and objective standard deviation.
Survey Data
Of the 930 surveys returned, 896 were sufficiently complete to be usable, producing
a usable response rate of approximately 29%. This response rate exceeded (as
indicated by Progressive Farmer) anticipated total response rate of 15% to 20%.
Because soybean distribution intervals in the survey’s subjective distribution section
provided a better range for actual yield than the intervals for the corn distribution,
only soybean subjective distributions were used in the analysis. As a result of this
selection criterion, the sample could include soybean producers who might/might not
be corn producers.
Table 3.1 shows summary statistics for various farm characteristics for a raw
data sample (containing 930 observations) and a cleaned data sample (containing 382
observations). Various criteria were applied to the raw data sample that resulted in
elimination of the observations. If an observation had sum of the yield distribution
intervals less than 90% or more than 110%, it was eliminated (the observations with
greater than 90% or above 100% were rescaled by norming to their own sum). This
restriction eliminated 212 observations, with the majority of the eliminated
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observations having all yield intervals fields blank. The observations with less then
3 yield intervals were eliminated as well, resulting in 85 eliminated observations.
Such observations led to unreasonably high/low distribution moments. The
observations with more than one primary county (i.e. the county where a producers
mainly operates) were eliminated as well, resulting in 97 eliminated observations.
This restriction was imposed because farm-level yields would need to be compared
to specific (primary) county yields. Seventy one observations were eliminated
because they did not contain information on state or primary county (i.e. the fields
were left blank). Finally, eliminating missing observations for the variables used in
the analysis (age, education, debt, and so on) led to the elimination of 83
observations. These eliminations resulted in a clean survey sample of 382
observations. Because the raw data sample contains observations with missing
state/county fields, the characteristics for the raw sample were not sorted by state.
Table 3.1 shows average and standard deviation for raw and cleaned sample.
The standard deviations were not available for the proportions (for example,
proportion of farmers who graduated from high school). The farm sizes are similar
in the both samples; however, size in a raw sample has higher standard deviation.
Percentage of farmers with debt is higher in the raw sample, there are more insurance
users and more farmers own land in the clean sample (as owned to total acres much
higher).
The state comparison of a clean sample leads to the following conclusions.
Indiana has the largest farms in the sample and the youngest users, while Iowa has
the smallest size farms, with highest percentage of livestock sales.
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Equation 1 is used to estimate parameters for each of the candidate
distributional forms. Figure 3.3 shows an example of the fitted subjective and
county soybean yield distributions for Fayette County, Iowa, (the county and farmers
from each county were selected for illustration purposes only). As the figure
suggests, producers in the county display various yield expectations. Respondent 1
has a lower subjective mean and smaller variance, while respondent 2 has higher
mean and smaller yield variability.
Results
Table 3.2 summarizes the direct assessments of individual-farm yields by respondent.
The majority of respondents indicated that their yields are greater than the county
average (53% in Iowa, 57% in Indiana, and 60% in Illinois), or equal to county
average (38% in Iowa, 41% in Indiana, and 31% in Illinois). Similarly, the majority
of the respondents viewed their yield variability to be smaller than the county
average (41% in Iowa, 48% in Indiana, and 47% in Illinois) or equal to the county
average (39% in Iowa, 37% in Indiana, and 43 in Illinois). Approximately 79% of
farmers reported both less than or equal yield variability and same or greater average
yields.
To contrast these results with the indirect method, table 3.3 contains a summary
of the directly-stated yields, indirectly-stated yields (Weibull implied), county
average yields, the differences between directly-stated yields and county averages,
and the differences between indirectly stated yields and county averages for each
state. The average directly-stated yield for Iowa is 49.09 bu/ac (50.02 bu/ac for
Indiana, 49.95 bu/ac for Illinois), which is 6.8 bu/ac greater than the weighted county
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average (8.38 bu/ac bu/ac for Indiana, 6.75 bu/ac for Illinois) and 3.69 bu/ac greater
than indirectly-stated for Iowa (5.06 bu/ac for Indiana, 3.91 bu/ac for Illinois). The
corresponding differences between indirectly-stated and the county average yields
are 0.21, -0.49, 0.57, and 0.24 bu/ac. The paired t-test23 for the differences between
the directly-stated and county average yields indicated that the differences are
statistically significant while no such significance was detected in yield differences
between indirectly stated and county average. 24 Figure 3.4 illustrates the frequency
count of the differences between indirectly-elicited subjective yields and county
average yields for the respondents in each state. Overall, the mean differences
appear reasonably distributed, with subjective means being slightly greater than
county average means
This significance suggests that the farmers, as a group, display the “better-
than-average” effect when yields are directly elicited. On the other hand, the
differences between indirectly-stated yields and county average yields were not
statistically significant suggesting that farmers as a group, display well-calibrated
mean yield perceptions when yields are elicited in a probabilistic framework.
Contrary to the earlier directly-stated yields analysis, the results from
indirectly-stated yields analysis suggest that systematic differences do not exist
between subjective yield distribution and its objective counterpart, and subjective
yields assessed in probabilistic framework provide more accurate estimates of yield.
The effect disappears when the yield distribution is elicited from the farmers
indirectly.
96
The observed discrepancies are an example is the “better than average” (BTA)
effect. The BTA effect refers to an individual propensity to “judge themselves as
better than others with regard to skills or positive attributes.” (Glaser and Weber,
2003). Since yields could be viewed as an assessment of producer’s farming skills, it
is natural to expect such yield exaggeration from a farmer (Taylor and Brown, 1998).
What is not clear, however, is why the BTA effect is not observed in the probabilistic
yield assessment. After all, it is possible for a farmer to assign weights to the higher
yield intervals, thus increasing the mean of the yield distribution.
Recall that findings from contingent valuation literature were cited earlier with
similar results reported. After all, the respondents who overstated their donations in
the dichotomous choice could have overstated their donations in the payment card as
well. The proposed explanation by the contingent valuation literature is
dichotomous-choice questions result in an upward bias as the respondents tend to be
less certain in answering discrete-choice type question than answering continuous
choice or open end questions (see for example Champ and Bishop, 2001). We make
related argument by hypothesizing that the “unsureness” in our case could be a
function of task complexity. Answering direct yield elicitation questions (i.e.“Is
your yield above/same/below county average”) is an easy task; it does not require a
significant mental effort. As a result, some respondents might provide answers they
are not sure about or have not evaluated carefully. However, as a task-complexity
increases, as in estimating yield intervals for example, these respondents might be
forced to consider entire distribution of the variable of interest and as a result
97
carefully assess their choices. Note that the yield discrepancy could also be driven
by other factors, such as age, farm size (examined later in the section)25.
These results are consistent with findings from the previous literature. In
particular, the results are in agreement with the second paper’s findings, where
Weibull implied yields were not statistically different from county average yields.
These conclusions are also in line with findings by Nerlove and Bessler (2001),
Bessler (1980) and Eales et al. (1990) who did not find significant differences
between objectives and aggregated subjective estimates, and Egelkraut et al.(2006a)
who did not find statistically significant differences between county mean and
individual implied means. Furthermore, Egelkraut et al.(2006a) argued that farmers
are likely to recall yields in more recent years rather then yields in more distant years.
If a farmer experienced several favorable years, he is more likely to overstate the
yield in his direct yield statements. This hypothesis is examined by constructing
averages using 5 years (from 2002 to 1998) and 10 years (from 2002 to1993) of
NASS county-level yields. While the average differences between directly-stated
and 5 and 10 year averages were smaller (5 year average: IA=5.6 bu/ac, IN=4.7
bu/ac, IL=4.3 bu/ac, 10 year average IA=2.7 bu/ac, IN=4.3 bu/ac, IL=3.9 bu/ac) than
the differences reported in table 3.3, these differences remained statistically
significant at p<0.0001. These findings are consistent with Egelkraut et al. (2006a),
who reported similar results for corn producers.
To examine the correspondence between subjective perception and objective
measures of yield risk, the implied and county average standard deviations were also
compared. If a farmer assesses the yield risk accurately, his measure of yield
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variability should be greater than county-level variability, because aggregated yields
tend to be less volatile than individual yields. Results from a paired t-test suggest
that implied standard deviations (IA = 8.03 bu/ac, IN = 7.63 bu/ac, IL = 7.33 bu/ac)
are statistically different (p<0.0001) from county-level standard deviations (IA =
4.87 bu/ac, IN = 4.81 bu/ac, IL = 4.70 bu/ac). As expected, the farm variability
measures were larger then their county counterparts. Figure 3.5 illustrates the
frequency count of the differences between indirectly-elicited subjective yields and
county average standard deviations for the respondents in each state. While the bin
containing zero has the greatest frequency, the subjective standard deviations tend to
be larger than county yield standard deviations
The findings differ somewhat from those presented by Eales, et al. and
Egelkraut, et al.(2006b), whose results suggested apparent overconfidence. In
particular, Egelkraut et al. (2006b)reported that corn producers’ subjective standard
deviations were not statistically different from county-level standard deviations. The
discrepancy in the findings might be attributed to the differences in crops (Egelkraut
et al. (2006b) used subjective perceptions of corn producers, while this paper uses
subjective perceptions of soybean farmers), as the ratio of farm-level to countywide
risk for soybean yields tend to be slightly greater than the same ratio for corn yields.
The reported discrepancy between directly-elicited yields and county-level
yields could also be a function of various characteristic such as farmer’s education
level, farm size, experience, and etc. For example, more experienced farmer could
possess more accurate yield perceptions. To investigate this claim, following
equation is estimated:
99
0 1 2 3 4 5 6 7YD SIZE AGE EDU IN IL IA SSDβ β β β β β β β= + + + + + + + (6)
Where YD is the difference between means of directly elicited yields and county
average yields, SIZE is size of the farm, AGE is respondent’s age, EDU is
respondent’s education level (discrete variable, 1 denoting high school graduate, and
4 denoting graduate school graduate), IN, IL, and IA are dummy variables for states,
and SSD is implied (subjective) standard deviation. Also, following variations of the
equations (6) were tested:
0 1 2 3 4 5 6 7YDD SIZE AGE EDU IN IL IA SSDβ β β β β β β β= + + + + + + + (7)
0 1 2 3 4 5 6 7YV SIZE AGE EDU IN IL IA SSDβ β β β β β β β= + + + + + + + (8)
Where YDD was decoded as 1 if directly elicited yields were greater than county
average yields 0 otherwise in equation 7, and YV was decoded as 1 if a farmer
indicated that the yields had the same/less variability then county yields and 0 if the
yields were more variable then county yields.
The results from this test are shown in table 3.4. Equation 6 is estimated as
model 1, equation 7 and 8, as models 2 and 3 respectively. None of the variables for
the regression is significant and an F-test for overall significance suggests that
coefficients jointly are not significantly different from zero. The results indicate that
none of the considered variables explain the discrepancies observed. It is of course,
still possible that other variables not captured in this survey (risk aversion for
example), could explain the relationship.
Conclusion
This paper uses subjective yield perceptions elicited in two different formats from
soybean producers in Illinois, Iowa, and Indiana, and compares them to county-level
100
data. The results suggest that subjective yield perceptions elicited in a probabilistic
framework can provide a more reliable yield assessment of county-level yield data,
in particular with regard to a central tendency, and farmers as a group possess well-
calibrated yield expectations. In addition, the findings indicate that the probabilistic
elicitation approach is more accurate than direct yield elicitation at representing
county-level yield data and that the BTA effect observed in directly-elicited
subjective yields could be due to the elicitation format. The results suggested that
the aggregated indirectly-elicited farm-level yields were not different from the
county average yields, which is consistent with the second paper, with Nerlove and
Bessler (2001), Bessler (1980), Eales et al. (1990), and Egelkraut et al. (2006b).
However, unlike Eales et al. and Egelkraut et al. (2006b) no evidence of the
overconfidence is found when subjective standard deviation is compared with
county-level standard deviations.
The results are consistent with the findings from contingent valuation literature
that indicated that the dichotomous-choice type questions have an upward bias that is
not present in the continuous or open-end type questions. We argue that the
observed BTA effect could be due to task-complexity. As task complexity of
elicitation format increases from direct elicitation to probabilistic assessment,
respondents are forced to carefully evaluate their responses and to provide more
accurate assessments. Future research could test this hypothesis through yield
elicitation under gradually increasing complexity of the elicitation formats. The
major implication of this paper for researchers is that care should be exercised in
interpreting and using directly-elicited yields as true measures of producers’ beliefs.
101
Addendum
The purpose of this addendum is to introduce an approach that allows for an
adjustment of county-level yields for the higher variability of farm-level yields. The
approach is implemented in Schnitkey Sherrick, and Irwin (2003), where the ratio of
farm-level variability to county-level variability (scaler) was estimated, the county
level standard deviations were multiplied by this scaler to account for the higher
level of variability. Schnitkey, Sherrick, and Irwin estimated the scaler using FBFM
data, by detrending farm-level yields, and estimating the average (at the state level)
ratio of county level to farm level yields.
We adopted a similar approach and calculated the scaler values using two
methods. Firstly, the scaler was calculated using actual farmer data from farms
enrolled in the Illinois Farm Business Farm Management (FBFM) record-keeping
system, by detrending farm level yields (soybean yields from 1987 to 2002), and
estimating the average (at the state level) ratio of county level yield standard
deviation to farm level yield standard deviation. Secondly, the scaler was estimated
by calculating the ratio of subjective standard deviation (as implied by subjective
yield distribution from survey respondents) to objective (county level) standard
deviation. Because the FBFM has records for Illinois farms only, the survey sample
was limited to Illinois producers as well. The purpose of calculating the scaler using
two different approaches is the comparison of the resulting values. If the survey’s
respondents possess well-calibrated beliefs, then the two scaler values should
correspond to each other.
102
Table 3.5 shows scaler statistics from both approaches. The second column
shows scaler statistics estimated using survey data and the third column shows scaler
statistics estimated using FBFM data. The average value for subjective scaler is 1.67,
for FBFM scaler the average is 1.52, the difference of 0.15. The subjective scaler
has larger dispersion as measured by standard deviation and minimum and maximum
values. Given the difference of 0.15 between the scalers, one can say that there is a
close correspondence between the scaler values.
Endnotes
21 The optimization was implemented in Excel, by minimizing differences between
farmer’s stated probabilities and specified fitted distribution for each interval by
changing fitted distribution parameters.
22 The results confirm that the Weibull distribution provides the best overall fit by
displaying smallest sum of squared errors (41,213) across all surveys, followed by
the normal (47,502) and lognormal (633,360) distributions.
23 Because farmers' subjective means are paired to the county means where
producers farm, such samples are likely to be dependent. To account for this, a
paired t-test was used (Bluman, 2001). Note that t-test assumes that underlying
observations are normally distributed. To account for the possible non-normality,
Wilcoxon test was used as well.
24 Paired t-test and Wilcoxon test were conducted on two levels. First, individual
farmer’s subjective means were paired to the respective county means and critical
test values were calculated. Second, county-average subjective means were
103
calculated (equally weighted) and paired with respective county means. In both
cases, the differences between subjective and objective means were statistically
significant at p>0.001.
25 The discrepancy could also be the result of sample selection bias. However, in this
case, one would expect the selection bias manifest itself in both elicitation formats.
104
Figures and Tables
Figure 3.1. Survey section that elicited indirectly-stated yield perceptions
Corn-Yield range Probability Soybeans- Yield Range Probability
Less than 40 bu/acre Less than 10 bu/acre
41 to 60 bu/acre 11 to 20 bu/acre
61 to 80 bu/acre 21 to 30 bu/acre
81 to 100 bu/acre 31 to 40 bu/acre
101 to 120 bu/acre 41 to 50 bu/acre
121 to 140 bu/acre 51 to 60 bu/acre
141 to 160 bu/acre 61 to 70 bu/acre
More than 160 bu/acre More than 70 bu/acre
Total (Should sum to 100%) 100% Total (Should sum to 100%) 100%
105
Figure 3.2. Survey section that elicited directly-stated yield perceptions
106
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
1 11 21 31 41 51 61 71 81 91 101
Yield (bu/ac)
Probability
Respondent 1 Respondent 2 Respondent 3 County-Level
Figure 3.3. Subjective and county PDFs for Fayette county Iowa soybean producers
107
F
igure
3.4
. Y
ield
dif
fere
nce
s bet
wee
n indir
ectl
y-s
tate
d a
nd c
ounty
aver
age
yie
lds
020406080
-20
-15
-10
-50
510
1520
Yield Difference (bu/ac)
Frequency
05101520
-20
-15
-10
-50
510
1520
Yield Difference (bu/ac)
Frequency
0102030405060
-20
-15
-10
-50
510
1520
Yield Difference (bu/ac)
Frequency
Iowa
Indiana
Illinois
107
108
Fig
ure
3.5
. Y
ield
dif
fere
nce
s bet
wee
n indir
ectly-s
tate
d a
nd c
ounty
aver
age
stan
dar
d d
evia
tions
01020304050
-10
-8-6
-4-2
02
46
810
Yield Difference (bu/ac)
Frequency
05101520
-10
-8-6
-4-2
02
46
810
Yield Differen
ce (b
u/ac)
Frequency
0102030405060
-10
-8-6
-4-2
02
46
810
Yield Differen
ce (b
u/ac
)
Frequency
108
Iowa
Indiana
Illinois
109
Tab
le 3
.1. R
esponden
ts’
char
acte
rist
ics
by p
roduct
type
and s
tate
(av
erag
e an
d s
tandar
d d
evia
tion w
her
e ap
plica
ble
)
Raw Sample
Cleaned Sample
IA
IN
IL
Average
St.Dev
Average
St.Dev
Average
St.Dev
Average
St.Dev
Average
St.Dev
Siz
e 772
1193
769
630
657
537
909
742
867
676
Age
(yea
rs)
54
13
51
11
51
11
50
12
53
12
Hig
h S
chool
45%
-
40%
-
46%
-
44%
-
31%
-
Som
e C
oll
ege
27%
-
30%
-
30%
-
16%
-
36%
-
Coll
ege
Gra
duat
e 24%
-
25%
-
22%
-
35%
-
27%
-
Gra
duat
e S
chool
5%
-
4%
-
2%
-
5%
-
6%
-
Per
centa
ge
wit
h D
ebt
60%
-
42%
-
44%
-
42%
-
39%
-
Insu
rance
U
ser
49%
-
63%
-
70%
-
55%
-
57%
-
Ow
ned
to
Tota
l A
cres
49%
38%
71%
45%
73%
45%
73%
45%
69%
47%
L
ives
tock
(%
of
Sal
es)
16
26
15
25
20
27
14
24
10
22
Num
ber
of
Obse
rvat
ions
930
382
This
tab
le c
ame
from
KS
for
Wei
bull
, L
ognorm
al, N
orm
al, w
ith o
bs
count.xls
fil
e
109
110
Tab
le 3
.2. R
esponden
ts’
per
ceiv
ed a
ver
age
yie
ld a
nd y
ield
var
iability r
elat
ive
to the
pri
mar
y c
ounty
Average Yield
Yield Variability
Higher
Same
Lower
Less
Variable
Same
Variability
More
Variable
%
%
%
%
%
%
IA
53
38
9
41
39
20
IN
57
41
2
48
37
15
IL
60
31
9
47
43
10
110
111
Tab
le 3
.3. R
esponden
ts’
per
ceiv
ed d
irec
tly-s
tate
d a
nd indir
ectly s
tate
d s
ubje
ctiv
e av
erag
e yie
ld a
nd v
aria
bility a
nd c
ounty
aver
age
State
Directly-stated
average yield
Indirectly-stated
yield (Weibull
implied mean
yield)
County
average
yield
Directly- stated
minus county
average yield
a
Indirectly-stated
minus county
average yield
a
Observations
Count
bu/ac
bu/ac
bu/ac
bu/ac
bu/ac
IA
49.0
9
45.4
0
45.1
9
6.8
0***
0.2
1
190
IN
50.0
2
44.9
7
45.4
5
8.3
8***
-0.4
9
55
IL
49.9
5
46.0
3
45.4
6
6.7
5***
0.5
7
137
Tota
l 49.5
3
45.5
6
45.3
2
6.9
9***
0.2
4
382
a Sig
nif
ican
tly g
reat
er than
zer
o a
t p<0.0
5(*
), p
<0.0
1(*
*)
and p
<0.0
01 (
***).
111
112
Table 3.4. Regression results
Model 1: Yield
Difference
(Subjective -
Objective Mean)
Model 2: Yield Mean
(1 if above county
average, 0 below)
Model 3: Yield
Variability (1 if less or
as variable then county
average, 0 below)
Coefficientsa Coefficients
a Coefficients
a
Intercept 5.61367* 0.97256* 0.94782* SIZE 0.00103 0.00003 0.00004 AGE -0.02706 -0.0009 -0.00064 EDU -0.49932 0.0048 -0.02849 IA -0.51656 -0.06089 -0.05044 IL 0.07491 -0.06266 0.06428 SSD 0.04937 0.00044 -0.00748 Ajd R2 0.00215 -0.00638 0.01314
F(7, 382) 1.30745 0.76533 2.02008* a Significantly greater than zero at p<0.05(*), p<0.01(**) and p<0.001 (***).
113
Table 3.5. Subjective and objective scalers calculated using survey (Illinois producers) and FBFM data (averages, at state level)
Scaler Scaler Difference
Subjective
(Survey) FBFM Survey - FBFM
Average 1.67 1.52 0.15 Min 0.74 0.62 -1.54 Max 4.03 3.03 2.42 St.Dev 0.62 0.54 0.83 Count 137 1054 -
114
CONCLUSION
The purpose of this dissertation was to examine factors that affect farmers’
participation in crop insurance programs. In particular, the dissertation examined the
impact from RMA rules on the participation and relationship between farmers’
perceptions and crop insurance purchasing decisions. The first chapter analyzed the
impact of RMA’s rules on the performance, participation, and risk protection level of
APH insurance, using NASS county-level yield data. The second chapter
investigated the role of the misperception biases in insurance-purchasing decisions in
presence of risk management tools. The third chapter considered correspondence
between subjective yield perceptions recovered under different elicitation formats
and county-level yields.
The findings revealed a series of insights explaining the relationship between
participation, RMA rules, and farmers’ perceptions. Examination of RMA rules that
omit trend and sample size variability revealed that the current rules create a
significant lag in yields (relatively to the expected yields) leading to the lower
protection levels under APH yields (reductions from 16% to 34% depending on the
length of the APH period). Results also suggested the presence of adverse selection
as probability of APH yield being greater than expected yields ranged from 10% to
33% depending on APH base period. The results also revealed that the current RMA
premiums exceed actuarial costs even after controlling for catastrophic loading by
factor of 1.8 to 2.3. The lag in yields along with the resulting declines in protection
levels and increases in the premiums relatively to the actuarial costs, explain the
farmers’ reluctance to participate in the crop insurance program and justify current
115
provision of subsidies. The approach toward adjusting yields for the trend is
suggested that has potential to improve the protection levels and reduce RMA
premiums in relation to the actuarial costs. Implementing this adjustment would not
require changes in the current rating structure and has potential improving
participation and actuarial performance of the crop insurance.
The examination of the econometric results from demand model provides
further insights into farmers’ behavior. The results illustrated that age increases
probability of participation for revenue and CAT insurance, and decrease the
probability for yield insurance. Leverage increases the probability of participation
for revenue and CAT insurance products, while farm size decreases the probability
for all insurance products. Diversification (measured as sales of livestock) decreases
the likelihood of purchase across all insurance products, and the probability of
receiving insurance payments increases the likelihood for the use of yield and
revenue insurance, and decreases it for CAT insurance. This significance is
consistent with the results from simulation model that showed presence of adverse
selection. Results also suggested that farmers who had used other risk management
tools before are more likely to participate in crop insurance program as well. An
implication could be that RMA should consider providing discounts for a continuous
use of crop insurance, and target farmers who actively use other risk management
tools. Accounting for trend and bringing more farmers through effective targeting
(both in terms of risk management usage and age) could mitigate adverse selection.
Results also showed presence of the BTA effect in directly elicited yields while
revealing no such relationship for yield elicited under probabilistic framework.
116
However, the econometric results showed no relationship between subjective yields
and crop insurance purchase, suggesting that the BTA effect could be due mainly to
the elicitation format. We argued that direct elicitation does not require significant
mental efforts and may be viewed as less serious by the subjects, and as a result
directly-elicited yields tend to be less reliable. While results suggested little
relationship between BTA effect and participation, further training and education
might benefit farmers by making farmers aware of the bias.
The findings presented here are as with all empirical studies, subject to the
data and methods limitations. Future examinations of RMA rules for trend and
sample size variability might benefit greatly from incorporating spatial analysis of
crop yields, since spatial element in yields is likely to play a significant role in
determining yield trend and variability. Furthermore, continuous improvement in
seed varieties is likely to impact trend and sample size variability further. In
particular, for the behavioral implications, future analysis will benefit from a more
detailed examination of the factors that determine the discrepancies between
objective and subjective yield elicited in the probabilistic framework and subjective
yields elicited using open-ended questions. The future analyses of risk perceptions
and crop insurance participation would benefit from inclusion of more psychological
variables (such as risk aversion for example) in econometric demand models and
extending the analyses to different crops and geographical regions.
117
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121
AUTHOR’S BIOGRAPHY Alisher Umarov was born in Parkent, Uzbekistan, on May 29, 1978. He graduated
from North Dakota State University in 2000 with a degree in economics. He
completed a Master of Science in Economics from North Dakota University in 2003.
He is currently employed as a senior consultant for J.D. Power and Associates.
