Expert Review

of

Methodology for Establishing Rates for 

Yield Exclusion

as presented in the report

“Review of Adjustment in Actual Production History to Establish

Insurable Yields: Determination of Actuarially Sound Premium Rates”

authored by

Thomas O. Knight

Mary Frances Miller

Keith H. Coble

and Barry J. Barnett

for Sumaria Systems, Inc.

Prepared for

FCIC Board of Directors

Prepared and Submitted by

Dmitry Vedenov, Ph.D.

Vedenov Consulting

1511 S. Texas Ave., Ste. 322

College Station, TX 77840-3303

vedenov@vedenov-consulting.com
Expert Review of Methodology for Establishing Rates for Yield Exclusion

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Executive Summary

The subject of the present review is the report entitled “Review of Adjustment in Actual 

Production History to Establish Insurable Yields: Determination of Actuarially Sound 

Premium Rates” prepared by Sumaria Systems, Inc. for USDA Risk Management Agency 

(hereafter referred to as “Sumaria Report”).

Sumaria Report provides feedback on the methodology proposed by the RMA to 

determine premium rates for the coverage based on APH yields with yield exclusion (YE) 

provision. Yield exclusion provision gives producers an option to exclude any recorded or 

appraised yield for any crop year in which the per planted acre yield in the county is at 

least 50 % below the simple average per planted acre yield during the previous ten 

consecutive crop years (Sumaria Report).

Exclusion of low yield experience results in an increase in the calculated APH average 

yields, with the net effect being the same as if the producer chose to insure at a higher 

coverage level, other things being equal. The Sumaria Report uses the term “effective 

coverage level”, i.e. the coverage level the producer would have to choose without yield 

exclusion to get the same production guarantee in absolute terms. The question then is 

how to adjust premium rates in order to reflect this increase in guarantee and thus 

associated risk of indemnities paid on the policy.

The proposed rate-making procedure can be reduced to three steps: (1) calculate the 

effective coverage level for the YE policy by dividing the implied production guarantee by 

the average APH yield without yield exclusion; (2) estimate corresponding coverage level 

differential (CLD) by either linearly interpolating between or linearly extrapolating beyond 

the CLDs established for the existing coverage levels; and (3) multiply the estimated CLD by 

the base premium rate for the 65% coverage.

Sumaria Report reviews the proposed methodology and finds it reasonable and 

appropriate. The report further recommends that

1. the RMA follows the approach they have proposed in computing effective coverage 

levels for policy units making use of Yield Exclusion in determining the yield 

guarantee;

2. the RMA adopts the proposed procedures for deriving effective coverage level 

differentials and premium rates for policy units making use of Yield Exclusion;

3. the RMA evaluates the feasibility of incorporating marginal premium rate caps such 

that the additional premium for any coverage interval cannot exceed the 

corresponding increase in liability;

4. the RMA re-evaluates the coverage level differentials and the behavioral component 

after two years of YE experience has been collected and continues capturing the 

data needed to refine current actuarial procedures;

5. the RMA adjust experience at the individual record level to the smaller of the 65% 

common coverage level or the effective coverage level prior to compilation in 

StatPlan, thus preserving the actual indemnity experience in the base ratemaking 

process as much as possible

6. the RMA continues its current methods for adjusting compiled data at the StatPlan 

level to the 65% common coverage level.
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Based on evaluation of the proposed methodology for establishing rates for APH 

policies with yield exclusion as presented in Sumaria Report, the reviewer concurs with 

Recommendations 1 (calculation of effective coverage rates) and 4 through 6 (data 

collection and analysis) of the Report.

However, the reviewer strongly disagrees with Recommendation 2 regarding the 

wholesale adoption of the proposed rate-making methodology. Based on the stochastic 

simulation analysis conducted by the reviewer, the assumption of linear dependence 

between the coverage levels and coverage level differentials is flawed. Since the 

proposed extrapolation method for determining premium rates for effective coverage 

levels above 85% is implicitly based on this flawed assumption, it leads to estimates of 

premiums that are substantially lower than they should be, thus undermining actuarial 

soundness of the program.

Instead, it is reviewer’s recommendation that the proposed rate-making approach is 

adopted only for the effective coverage levels below 85%. For the effective coverage levels 

above 85%, a two-prong approach is suggested.

First, it is recommended that either cubic or quadratic extrapolation procedure is used 

to estimate coverage level differentials. In simple terms, instead of drawing a straight line 

through two highest known CLDs at 80% and 85% coverage levels and then using it to 

project CLDs for coverage levels above 85%, either a quadratic function is drawn through 

three highest known CLDs (at 75%, 80%, and 85% coverage levels) or a cubic function is 

drawn through four highest known coverage level differentials (at 70%, 75%, 80%, and 

85% coverage levels). In the specific case analyzed by the reviewer, cubic extrapolation 

procedure resulted in reasonably accurate estimates of premiums (with less than 5% 

error) for the range of coverage levels up 110%.

Second, it is recommended that the RMA imposes a temporary cap on the effective 

coverage levels resulting from the yield exclusion provision in the APH policies so as to 

reduce the error in premium estimates based on extrapolation. The cap would be gradually 

increased as new data on actuarial experience for higher effective coverage levels becomes 

available (as per Recommendation 4 of Sumaria Report) and extrapolation procedure could

be adjusted. For example, if such a cap were initially set at 110% effective coverage level, a

cubic extrapolation procedure based on known CLDs at 70%, 75%, 80%, and 85% coverage 

levels could be used to provide a reasonably accurate approximation to the premiums for 

the range of effective coverage levels between 85% and 110%. Once sufficient data exists to 

re-estimate the coverage level differentials up to, say, 95% coverage level, the cap on 

effective coverage level could be increased to 120% with the now known CLDs for 80%, 

85%, 80%, and 95% coverage levels used for cubic extrapolation, and so on.

Lastly, it is the reviewer’s opinion that Recommendation 3 of Sumaria Report is moot at 

least in the context of the original proposal. Since the proposed linear extrapolation 

procedure results in premiums that are too low, capping them would only make the 

situation worse. For the actual premiums, marginal increases in premiums do not exceed 

corresponding increases in liability even for the coverage levels up to 300%. Therefore, 

even if an alternative extrapolation procedure is adopted, the proposed rate capping 

mechanism would not be triggered as long as the extrapolation is used only over the range 

where it produces estimates reasonably close to the actual rates. 
Expert Review of Methodology for Establishing Rates for Yield Exclusion

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Table of Contents

Executive Summary ......................................................................................................................................2

Table of Contents ...........................................................................................................................................4

Research Report.............................................................................................................................................5

Overview.......................................................................................................................................................5

Methodology ...............................................................................................................................................6

Items in Section C.4. Description of Work.......................................................................................7

Discussion and Recommendations ...................................................................................................... 11

References ..................................................................................................................................................... 11

Appendix ........................................................................................................................................................ 12

Qualifications of the Reviewer............................................................................................................... 18
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Research Report

The following abbreviations are used in the report:

APH policy/plan refers to Actual Production History policies

CLD refers to Coverage Level Differential

RMA refers to the Risk Management Agency

NASS refers to the National Agricultural Statistics Service

Overview

The subject of the present review is the report entitled “Review of Adjustment in Actual 

Production History to Establish Insurable Yields: Determination of Actuarially Sound 

Premium Rates” prepared by Sumaria Systems, Inc. for USDA Risk Management Agency 

(hereafter referred to as “Sumaria Report”).

Sumaria Report provides feedback on the methodology proposed by the RMA to 

determine premium rates for the coverage based on APH yields with yield exclusion (YE) 

provision. Yield exclusion provision is established in Section 11009 of the 2014 Farm Bill

and allows producers an option to exclude any recorded or appraised yield for any crop 

year in which the per planted acre yield in the county is at least 50 % below the simple 

average per planted acre yield during the previous ten consecutive crop years (Sumaria 

Report).

Exclusion of low yield experience results in an increase in the calculated APH average 

yields. However, excluded yields are still recorded in the StatPlan database and used to 

determine rate yields. Therefore, yield exclusion does not change the estimated 

distribution of yield, but rather increases the baseline yield level used to calculate 

production guarantee. Thus the net effect of yield exclusion is the same as if the producer 

chose to insure at a higher coverage level, other things being equal. The proposed RMA 

methodology and Sumaria Report refer to this as “effective coverage level”, i.e. the coverage 

level the producer would have to choose without yield exclusion to get the same production 

guarantee in absolute terms. The question then is how to adjust premium rates in order to 

reflect this increase in guarantee and thus associated risk of indemnities paid on the policy.

The RMA proposed a procedure that mimics the methodology currently in place to 

determine premium rates for the trend adjusted (TA) policies. Trend adjusted policies also 

result in effective increase of the production guarantee. Therefore, the associated premium 

setting methodology provides a reasonable basis for the rate adjustment procedures for 

the APH policies with yield exclusion.

Without repeating large sections of Sumaria Report and underlying RMA documents, 

the proposed procedure can be distilled to three steps: (1) calculate the effective coverage 

level for the YE policy by dividing the implied production guarantee by the average APH 

yield without yield exclusion; (2) estimate a corresponding coverage level differential 

(CLD) by either interpolating between or extrapolating beyond the CLDs established for the 

existing coverage levels (for effective coverage levels less than or more than 85%, 

respectively); and (3) multiply the estimated CLD by the base premium rate for the 65% 

coverage.
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Sumaria Report reviews the proposed methodology and finds it reasonable and 

appropriate. The report further recommends that

1. the RMA follows the approach they have proposed in computing effective coverage 

levels for policy units making use of Yield Exclusion in determining the yield 

guarantee;

2. the RMA adopts the proposed procedures for deriving effective coverage level 

differentials and premium rates for policy units making use of Yield Exclusion;

3. the RMA evaluates the feasibility of incorporating marginal premium rate caps such 

that the additional premium for any coverage interval cannot exceed the increase in 

liability;

4. the RMA re-evaluates the coverage level differentials and the behavioral component 

after two years of YE experience has been collected and continues capturing the 

data needed to refine current actuarial procedures;

5. the RMA adjust experience at the individual record level to the smaller of the 65% 

common coverage level or the effective coverage level prior to compilation in 

StatPlan, thus preserving the actual indemnity experience in the base ratemaking 

process as much as possible

6. the RMA continues its current methods for adjusting compiled data at the StatPlan 

level to the 65% common coverage level.

Methodology

The reviewer’s primary concern with the proposed methodology is the use of 

extrapolation of coverage level differentials for the effective coverage levels outside of the 

range of 85% coverage level, which is currently the highest available for the APH policies 

without YE. In order to evaluate the potential error in calculation of premiums, the 

reviewer conducted a stochastic simulation analysis using an empirical yield distribution 

based on historical yield data.

In particular, yield data for corn in Kossuth County, IA, for the period from 1968 to

2013 were obtained from NASS. This is the largest corn producing county in the largest 

corn producing state in terms of total harvest. Yield data were detrended using a simple 

linear trend and adjusted to their 2013 equivalents. The detrended yields were then used 

to construct the kernel-smoothed yield distribution (see, for example, Ker and Goodwin, 

2000). The mean of the distribution was used as a proxy for the APH yield.

Using the constructed distribution (Figure 1, Appendix), actuarially-fair premiums were 

calculated as expected indemnities for coverage levels ranging from 0% to 300% of the 

mean (in 5% increments) along with corresponding liabilities and premium rates (Figures 

2 and 3, Appendix). Without loss of generality, premiums and liabilities were expressed in 

units of yield. This does not affect the results of the analysis, since conversion to dollar 

amounts can be achieved by multiplying all relevant variables by a fixed nonrandom price. 

Furthermore, the main variables of interest are ratios and thus would not be affected by 

conversion from yield units to dollars.

In order to replicate the proposed rating procedure, coverage level differentials (CLDs)

were calculated as ratios of the actual premium rates to the premium rate at the base 

coverage level (65%). The CLDs for 80% and 85% were then used as a basis for linear 
Expert Review of Methodology for Establishing Rates for Yield Exclusion

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extrapolation beyond the 85% coverage level as per the methodology proposed by the RMA 

and reviewed in Sumaria Report. The extrapolated CLDs, as well as corresponding 

premium rates and premiums were then compared to the actual CLDs, premium rates, and

premiums implied by the original distribution (Figures 4 through 6). The results of the 

analysis are discussed below. Figures are included in the appendix.

Since the individual yields tend to be more variable than aggregated county yields, the 

analysis was repeated with yield data expanded around the mean in order to simulate 

higher variability of the distribution (up to 50% increase in standard deviation). In order to 

check the robustness of the results with respect to the choice of distribution, the analysis 

was also repeated using a normal distribution of yields with the same mean and standard 

deviation as the yield data sample. Lastly, in order to cross-validate the results, the same 

analysis steps were performed for Texas corn (same crop, higher variability of yields) and 

Texas cotton (different crop). In all cases, the results (not reported), while quantitatively 

different, led to the same qualitative conclusions as the baseline analysis.

Items in Section C.4. Description of Work

(1) Actuarial soundness

(A) Is adequate, credible, and reliable rate-making data available? Is it likely that the data 

will continue to be available? Is the data vulnerable to tampering if the proposed policy is 

approved?

The methodology proposed by the RMA and reviewed in Sumaria Report relies on 

existing RMA data and current data collection practices. Since the latter has been 

thoroughly reviewed and the collected data is used for all rating purposes by the RMA, 

it is the reviewer’s opinion that the rate-making data is adequate, credible, reliable, and 

not vulnerable to tampering. Furthermore, the data will continue to be available as long 

as the RMA maintains its current data collection practices. However, the reviewer 

concurs with Recommendation 5 made in Sumaria Report, which is to record the 

actuarial experience with APH YE policies at the effective rather than nominal coverage 

level in order to reduce the loss of information contained in data. Building up the 

database of such experience will help to improve the accuracy of rate making 

methodology particularly for the effective coverage levels in excess of the currently 

available 85%.

(B) Are the explicit and implicit assumptions used in the rating process reasonable?

The rating methodology presented in Sumaria Report relies on two implicit 

assumptions, namely (1) that the CLDs for coverage levels below 85% can be 

reasonably approximated by a linear function between the nearest available coverage 

levels (e.g. 65% to 70% or 75% to 80%) and (2) that the CLDs for coverage levels above 

85% can be reasonably approximate by a linear function based on CLDs for the two 

highest available coverage levels (i.e. 80% and 85%).

The results of the stochastic simulation analysis conducted by the reviewer indicate 

that, while the first assumption is reasonably justified and produces sufficiently 

accurate estimates of the CLDs, the second assumption is erroneous and results in 
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alarmingly high errors in calculation of CLDs and, consequently, premium rates and 

premiums for coverage levels exceeding 85%.

Figure 4 (Appendix) shows actual (calculated) coverage level differentials vs. those 

linearly extrapolated from the range between 80% and 85%. Corresponding premium 

rates and premiums are shown in Figures 5 and 6, respectively. Actual and extrapolated 

premiums are also reported in Table 2 in Appendix. 

All three graphs indicate a substantial difference between the actual and extrapolated 

values particularly as the coverage levels increase. The following table shows the error 

in the estimates of premiums based on extrapolated values of CLDs. The errors are 

calculated relative to the extrapolated values, i.e. as

(Actual Premium – Extrapolated Premium)/Extrapolated Premium.

Effective 

Coverage Level

% Error in Premium Estimates

Linear

Extrapolation

Quadratic

Extrapolation

Cubic

Extrapolation

80% 0.00% 0.00% 0.00%

85% 0.00% 0.00% 0.00%

90% 16.04% 5.28% 0.19%

95% 42.44% 14.18% -0.27%

100% 77.15% 25.20% -1.23%

105% 119.73% 37.74% -2.20%

110% 166.94% 49.66% -4.13%

115% 213.68% 58.61% -7.87%

120% 254.78% 63.09% -13.58%

125% 286.75% 62.77% -20.86%

130% 309.59% 58.82% -28.74%

135% 325.23% 52.78% -36.42%

140% 335.59% 45.72% -43.48%

145% 341.96% 38.29% -49.80%

150% 345.36% 30.85% -55.38%

Table 1. Errors in premium implied by extrapolated coverage level differentials for 

different extrapolation procedures.

For linear extrapolation (second column), the actual and extrapolated premiums 

coincide at 80% and 85% coverage levels by construction, but the extrapolated 

premiums severely underestimate actual premiums for higher coverage levels. The 

actual premium is nearly twice higher than the extrapolated at the 100% effective 

coverage level (the example used in Sumaria Report), while at the 150% effective 

coverage level, the actual premiums are almost 4.5 times higher than the premiums 

based on linear extrapolation of CLDs.
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As an alternative, quadratic and cubic extrapolation procedures were investigated. For 

the former, a quadratic function

β2Coverage

2 + β1Coverage + β0 = CLD

was constructed based on CLDs at coverage levels of 75%, 80%, and 85%. For the latter,

the cubic function

β3Coverage

3 + β2Coverage2 + β1Coverage + β0 = CLD

was constructed based on CLDs at coverage levels of 70%, 75%, 80%, and 85%. Since 

three points uniquely define a quadratic function, and four points uniquely define a 

cubic function, both procedures are exact and require solution of a system of three and 

four linear equations, respectively. The CLDs for the effective coverage levels beyond 

85% can be then calculated by substituting the corresponding coverage levels into the 

equations above.

The premiums based on quadratic and cubic extrapolation procedures are shown in 

Figures 7 and 8, respectively (Appendix). Corresponding errors in premiums are shown 

in the last two columns of Table 1 above.

The quadratic extrapolation procedure does much better job approximating actual 

premiums than the linear extrapolation. However, the premiums are still 

underestimated, and the relative error remains fairly high particularly as the coverage 

levels increase.

The cubic extrapolation procedure actually overestimates the premiums at higher 

effective coverage levels, but it appears to be much more accurate than the linear and 

quadratic extrapolation for a range of effective coverage levels close to 85% (up to 

110% in this particular case).

Clearly, the level of accuracy provided by each extrapolation procedure is conditional 

on the underlying distribution and cannot be predicted in advance if the distribution is 

not known. However, it seems that allowing for some form of nonlinear dependence 

between the coverage levels and coverage level differentials vastly improves the 

accuracy of premiums based on extrapolation beyond the currently available coverage 

levels.

(C) Are the technical analyses (e.g., stochastic and other simulations) correct? Do they provide 

credible, relevant results??

Sumaria Report does not provide any technical analysis beyond specific examples 

illustrating the application of the adjustment procedure proposed by RMA. There are no 

factual errors in these examples. However, they do not adequately address the validity 

of the proposed rate-making methodology.

(D)Is the data used for the analyses appropriate, reliable, and the best available?

The Sumaria Report does not appear to use any data other than a hypothetical example 

developed by the RMA. It is the reviewer’s opinion that this example does not provide 

adequate basis for evaluation of the proposed methodology.
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(F) Are the proposed premium rates likely to cover anticipated losses and a reasonable 

reserve?

No. Based on the reviewer’s analysis, the proposed adjustment procedure for 

establishing premium rates for effective coverage levels in excess of currently available 

85% would severely underestimate expected losses. Furthermore, the difference 

between the actuarially fair premium rates (i.e. expectation of anticipated losses) and 

the premium rates based on linear extrapolation of coverage level differential tend to 

increase with the higher effective coverage levels (see Figure 5 in Appendix and Table 1 

above). Over time, collecting premiums at the rates based on linear extrapolation 

procedure would result in loss ratios exceeding 1 and severe shortfalls of the reserves.

(G) Is the actuarial methodology appropriate for the insured risks?

With the exception of extrapolation of CLDs above 85% coverage level, the proposed 

actuarial methodology is appropriate for dealing with the APH YE policies. Treating 

APH YE policies as having higher effective coverage level is reasonable and reflects the 

increase in risk associated with the new policies. Furthermore, interpolation of CLDs 

between available coverage levels provides adequately accurate estimates of the 

premium rates. However, the linear extrapolation procedure designed to deal with the 

lack of data on actuarial experience at the effective coverage levels above 85% appears 

to be based on erroneous assumption and results in highly inaccurate premium 

estimates particularly as the effective coverage levels increase above 100%.

(2) Other considerations

Recommendation 3 in Sumaria Report suggests that the RMA incorporates marginal 

premium caps on premiums for APH YE policies based on the rule that the marginal 

increase in premiums does not exceed marginal increase in liability for any 5% interval in 

coverage level. Given the results of stochastic simulation analysis presented above, it is the 

reviewer’s opinion that establishing caps on premiums in any form is a moot point at least 

in the context of the original proposal. Since the premiums based on linear extrapolation of 

CLDs already underestimate actual premiums, establishing any caps on the (extrapolated) 

rates at any effective coverage level above 85% would only worsen the problem. The 

quadratic extrapolation procedure outlined above also results in premium estimates that 

are too low and thus does not call for rate caps either. Cubic extrapolation procedure does 

lead to premium estimates that are higher than the actual ones and thus may need to be 

capped at some coverage levels. 

Note, however, that for the actual premiums, the marginal increase in premiums over 

any 5% coverage level interval never exceeds the corresponding increase in liability 

(Figure 9, Appendix). Therefore, as long as premium determination is based on an 

extrapolation procedure that leads to premiums below or close to the actual premiums, the 

premium capping scheme recommended in Sumaria Report would never be triggered.
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Discussion and Recommendations

Based on evaluation of the proposed methodology for establishing rates for APH 

policies with yield exclusion as presented in Sumaria Report, the reviewer concurs with 

Recommendations 1 (calculation of effective coverage rates) and 4 through 6 (data 

collection and analysis) of the Report.

However, the reviewer strongly disagrees with Recommendation 2 regarding the 

wholesale adoption of the proposed methodology. Instead, it is the reviewer’s 

recommendation that the proposed rate-making approach is adopted only for the effective 

coverage levels below 85%. For the effective coverage levels above 85%, a two-prong 

approach is suggested.

First, it is recommended that either cubic or at least quadratic extrapolation procedure 

is used to estimate coverage level differentials. While the nonlinear extrapolation is not as 

intuitive as the linear procedure proposed by the RMA, implementation of either cubic or 

quadratic extrapolation procedure is computationally trivial and can be programmed in 

Excel or any statistical package in a straightforward way.

Second, it is recommended that the RMA imposes a temporary cap on the effective 

coverage levels resulting from the yield exclusion provision in the APH policies so as to 

reduce the error in premium estimates based on extrapolation. The cap would be gradually 

increased as new data on actuarial experience for higher effective coverage levels becomes 

available (as per Recommendation 4 of Sumaria Report) and extrapolation procedure could

be adjusted. For example, if such a cap were initially set at 110% effective coverage level, 

the cubic extrapolation procedure presented above (based on known CLDs for 70%, 75%, 

80%, and 85% coverage levels) could be used to provide a reasonable approximation to the 

premiums for the range of effective coverage levels between 85% and 110%. Once 

sufficient data exists to re-estimate the coverage level differentials up to, say, 95% 

coverage level, the cap on effective coverage level could be increased to 120% with the now 

known CLDs for 80%, 85%, 80%, and 95% coverage levels used for cubic extrapolation, 

and so on.

Lastly, it is the reviewer’s opinion that Recommendation 3 of Sumaria Report is moot at 

least in the context of the original proposal. Since the proposed linear extrapolation 

procedure results in premiums that are too low, capping them would only make the 

situation worse. For the actual premiums, marginal increases in premiums do not exceed 

corresponding increases in liability even for the coverage levels up to 300%. Therefore, 

even if an alternative extrapolation procedure is adopted, the proposed rate capping 

mechanism would not be triggered as long as the extrapolation is used only over the range 

where it produces estimates reasonably close to the actual rates.

References

Ker, A.P. and B.K. Goodwin. "Nonparametric Estimation of Crop Insurance Rates 

Revisited." American Journal of Agricultural Economics, 83(2000): 463–478.
Expert Review of Methodology for Establishing Rates for Yield Exclusion

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Appendix

Figure 1.

Figure 2.
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Figure 3.

Figure 4.
Expert Review of Methodology for Establishing Rates for Yield Exclusion

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Figure 5.

Figure 6.
Expert Review of Methodology for Establishing Rates for Yield Exclusion

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Figure 7.

Figure 8.
Expert Review of Methodology for Establishing Rates for Yield Exclusion

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Figure 9.
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Effective Coverage 

Level, %

Linear Extrapolation Quadratic Extrapolation Cubic Extrapolation

Premium, Actual Premium, 

Extrapolated

Premium, 

Actual

Premium, 

Extrapolated

Premium, 

Actual

Premium, 

Extrapolated

70 0.70869 0.10352 0.70869 0.84375 0.70869 0.70869

75 0.99392 0.72955 0.99392 0.99392 0.99392 0.99392

80 1.4381 1.4381 1.4381 1.4381 1.4381 1.4381

85 2.2291 2.2291 2.2291 2.2291 2.2291 2.2291

90 3.6003 3.1026 3.6003 3.4198 3.6003 3.5935

95 5.7808 4.0585 5.7808 5.0631 5.7808 5.7963

100 9.0293 5.097 9.0293 7.2119 9.0293 9.1413

105 13.663 6.218 13.663 9.9191 13.663 13.971

110 19.811 7.4214 19.811 13.237 19.811 20.665

115 27.313 8.7073 27.313 17.22 27.313 29.645

120 35.748 10.076 35.748 21.919 35.748 41.367

125 44.581 11.527 44.581 27.389 44.581 56.329

130 53.492 13.06 53.492 33.681 53.492 75.065

135 62.407 14.676 62.407 40.848 62.407 98.15

140 71.323 16.374 71.323 48.944 71.323 126.2

145 80.238 18.155 80.238 58.022 80.238 159.85

150 89.153 20.018 89.153 68.133 89.153 199.81

Table 2. Actual premiums vs. premiums based on extrapolation of coverage level differentials (CLDs). All premiums are 

expressed in units of yield. Linear extrapolation is based on actual CLDs at 80% and 85% coverage levels. Quadratic 

extrapolation is based on actual CLDs at 75%, 80%, and 85% coverage levels. Cubic extrapolation is based on actual CLDs at 

70%, 75%, 80%, and 85% coverage levels.
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Qualifications of the Reviewer

Dr. Dmitry Vedenov

Education

Ph.D. Agricultural, Environmental, and Development Economics, 2001

The Ohio State University, Columbus, OH

M.A. Economics, 1998

The Ohio State University, Columbus, OH

M.S. Applied Economics and Computers, 1993

Moscow Institute for Physics and Technology, Moscow, Russia

B.S. Applied Mathematics and Physics, 1991

Moscow Institute for Physics and Technology, Moscow, Russia

Employment

Associate Professor, Agricultural Economics, Texas A&M University, 2009–present

Assistant Professor, Agricultural Economics, Texas A&M University, 2007–2009

Assistant Professor, Agricultural and Applied Economics, Univ. of Georgia, 2001–2007

Fields of Expertise

Risk Management, Crop Insurance, Weather Derivatives, Stochastic Modeling, Dynamic 

Programming, Economic Modeling, Alternative Fuels

Selected Publications

Power, G.J., Vedenov, D.V., Anderson, D.P., and Klose, S. "Market Volatility and the 

Dynamic Hedging of Multi-Commodity Price Risk" Applied Economics, 45(27), 2013: 

3891–3903

Power G.J., Vedenov, D.V., and Hong, S.W. "The Impact of the Average Crop Revenue 

Election (ACRE) Program on the Effectiveness of Crop Insurance." Agricultural Finance 

Review (2009).

Vedenov, D.V. and Power, G.J. “Risk-Reducing Effectiveness of Revenue vs. Yield 

Insurance in the Presence of Government Payments.” Journal of Agricultural and Applied 

Economics, 40, 443–459 (August 2008).

Deng, X., Barnett, B.J., and Vedenov, D.V. “Evaluating the Viability of Area Yield 

Insurance for Cotton and Soybeans in the Southeast.” American Journal of Agricultural 

Economics, 89, 508-519 (May 2007).

Vedenov, D.V., Miranda, M.J., Dismukes, R., and Glauber, J.W. “Portfolio Allocation and 

Alternative Structures of the Standard Reinsurance Agreement.” Journal of Agricultural 

and Resource Economics, 31, 57–73 (April 2006).

Vedenov, D.V., Miranda, M.J., Dismukes, R., and Glauber, J.W. “Economic Analysis of 

Standard Reinsurance Agreement.” Agricultural Finance Review, 64, 119–134 (Fall 

2004).