Methodology Analysis for Weighting Historical Experience –

Implementation Report

1

Methodology Analysis for 

Weighting of Historical Experience

Implementation Report

September 5, 2011

By

Keith H. Coble

Mary Frances Miller

Roderick M. Rejesus

Ryan Boyles

Thomas O. Knight

Barry K. Goodwin

Contact:

George Duffield

Sumaria Systems

618-632-8450

gduffield@sumaria.net

Keith H. Coble

662-352-9491

khcoble11@aol.com
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Table of Contents

Executive Summary........................................................................................................................ 3

1. Study Background and Motivation.......................................................................................... 6

2. Background Summary of the Current RMA Loss Cost Rating System.................................. 9

3. Conceptual Explanation of Weighting and Loss Cost Adjustments .................................... 12

a. Weather Weighting ........................................................................................................ 12

b. Conceptual Assessment of Non-stationarity in Loss Cost Data .................................... 17

4. Proposed Weighting of Historical Experience ...................................................................... 23

a. Weather Weighting ........................................................................................................ 23

b. Proposed Non-Stationarity Loss Cost Adjustments....................................................... 45

c. Illustration of Combined Base Rating Procedures......................................................... 48

5. Implications of the Proposed Methods.................................................................................. 64

References..................................................................................................................................... 69

Appendix Research Team Credentials......................................................................................... 71
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Executive Summary

In March 2010, Sumaria Systems Inc. (Coble, et al. 2010) completed a comprehensive review of 

the methodology and procedures used to determine APH target rates and COMBO rates under 

the Federal Crop Insurance Program.1 The study provided several recommendations for 

modifying the current APH and Combo methodologies and suggested further evaluation of 

several other issues. One of those issues involved the current RMA practice of using equallyweighted, adjusted, historical, loss cost experience for a county/crop program as the cornerstone

of the current rating procedures. Sumaria Systems was subsequently contracted by the USDA/ 

Risk Management Agency (RMA) to conduct additional analysis of this issue. The statement of 

work for this project directs Sumaria to perform a detailed investigation and to develop an 

improved methodology for weighting, or otherwise adjusting, RMA’s historical loss cost data in 

order to maximize its statistical validity for developing premium rates. 

The project commenced in September 2010. A draft technical report examining various options 

and approaches to the issues was submitted to RMA in March 2011. The agency evaluated those 

options and determined which were preferred. The agency also commissioned further analysis 

and detailed explanation and documentation of the procedures selected for implementation. This 

report provides that additional analysis, explanation and documentation. 

Our team, including experienced crop insurance analysts, a leading professional actuary, and a 

professional climatologist, has reviewed the materials provided by RMA and additional materials 

that we collected independently. The credentials of our team are discussed in greater detail in 

the Appendix of this report. 

This report examines a number of conceptual considerations related to the issues we were tasked 

to address. Our team evaluated the alternative weather data available and issues associated with 

using those data to characterize weather probabilities. We have conducted analysis nationally for 

nine crops (apples, barley, corn, cotton, potatoes, rice, sorghum, soybeans, and wheat). Based on 

this analysis we make several recommendations.

Weather Probabilities

Recommendation 1. – We recommend that RMA use Climate Division Data for calculating cropspecific weather indexes. We believe the weather data collection that best meets the weatherdata criteria outlined in Section 4 of this report is the National Climatic Data Center’s Time Bias 

Corrected Divisional Temperature-Precipitation-Drought Index data, also called the climate 

division data. The climate division data provide several drought indexes and other weather 

variables that are time-aggregated to the monthly level and spatially-aggregated to the climate 

division level for the years back to 1895. Thus, the data allow RMA to compare the weather 

experience incurred by the modern program to weather extending 80 years prior to the 1975 cutoff of available loss-cost data. 

 1 This report is available at http://www.rma.usda.gov/pubs/2009/comprehensivereview.pdf.
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Recommendation 2. . – We recommend that RMA use fractional logit models estimated at the 

climate division level to relate loss cost experience to the Palmer Drought Severity Index (PDSI) 

and Cooling Degree Days (CDD). Time period variants of both weather indicators should be 

used for different crops and locations. An out-of-sample forecasting competition is suggested to 

select the time-period/variables for a crop/climate division, and if the models are not found 

statistically significant we recommend no weather weighting. This process creates a weather 

index from 1895-present which characterizes the growing conditions experienced in each year.

Recommendation 3. – Given recommendation 2 we propose that RMA categorize the loss cost 

experience observed over the period chosen into weather ‘probability bins’ or categories. These 

bins would be chosen according to an incremental procedure which would select a parsimonious 

number of bins for the crop/climate division. Once observed loss costs are categorized within 

bins, all historical loss costs within a bin are given equal weather probability. The bins 

recommended would have variable width but equal probability. The variable width binning 

process we propose ensures that at least one year during the rating period is classified in each 

bin, thereby providing proper weights that reflect all of the historical weather data.

Recommendation 4. – While not a directive in the statement of work, a conclusion reached 

during our analysis is that RMA should use all years available to calculate the catastrophic load 

and that extreme loss costs within the catastrophic load should be weighted using the weather 

index probabilities. Further, we recommend changing the catastrophic load cap to the 90th 

percentile and reducing the aggregation region for catastrophic load from the state level to a 

climate division, which is consistent with the weather weighting procedure. We also recommend 

dampening of the weight given to the most extreme weather years. Specifically, if the weather 

index for a particular year is above the 97th percentile, we recommend that the weight given to 

that year’s input to the catastrophe load be adjusted to reflect the percentile of the weather index. 

That is, if the data span 30 years of experience, a year with a weather index at the 98th percentile 

should be given 2% (1-in-50) weight rather than 3.33% (1-in-30) weight. The weight taken from 

the adjusted year should then be spread evenly among the remaining years. 

Changing Severity of Loss Costs

We were also directed to consider changing severity of loss costs over time due to technological 

advances and changing agronomic conditions. Finally we were asked to address how to

incorporate program participation changes over time in a way that represents the current 

program. In response to these tasks, we added an additional recommendation:

Recommendation 5. – A variety of factors suggests non-stationarity in some RMA loss cost data. 

Such factors include an expanding participant pool, evolving production systems, the advent of 

biotechnology, and changing program underwriting rules. In many cases it is difficult, if not 

impossible, to disentangle these effects. We recommend that RMA use adjustments to remove 
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non-stationarity from the loss cost history when statistical analysis supports the adjustment. We 

recommend estimating these adjustments at the national level for a crop and that weather should 

be taken into account when these models are estimated. Further, symmetric caps on the 

magnitude of the adjustments should be imposed to avoid excessive modification of the loss 

history in any particular location. 

We first recommend application of a discrete adjustment for data prior to 1995 to the adjusted 

loss cost data. Specifically, we recommend estimating the effect at the national level and 

calculating a percentage difference by state using the effect relative to the post-1995 average loss 

cost. However, we stress that where analysis indicates that non-stationarity in the loss cost 

history is not statistically significant, no adjustment should be made

Second, we recommend shortening the loss history for base rates to 20 years while using a longer 

series of years for catastrophic loading. This recommendation reflects the recognition that a 

longer time series is needed to capture extreme events than for measuring the risk quantified by 

the base rate. Finally, we recommend using net acreage weighting within probability categories 

or ‘bins’, which recognizes the additional credibility of experience that is based on more exposed 

acres. 

Report Organization

The primary focus of this report is to describe in detail the proposed method and illustrate how it 

would be made operational by RMA. First, a background of the issues investigated is provided 

and then the conceptual basis for the proposed method is discussed. In chapter 4 details of the 

components of the rating system are described and illustrated. In chapter 5 a summary of the 

aggregate effects for corn and soybean base rates is provided.

 
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1. Study Background and Motivation

The Federal Crop Insurance Program provides insurance products to agricultural producers in the 

U.S. In 2010, the program insured 256 million crop acres with a total liability of $78 billion. 

This public-private partnership involves private delivery of products designed and rated by the 

USDA. Private firms sell and service the products and are compensated for delivery and offered 

reinsurance. Producers are offered subsidized rates for the various insurance products. These 

rates are predicated upon RMA being able to quantify the actuarially fair insurance rate. 

Specifically, the Federal Crop Insurance Act was amended by the Agricultural Risk Protection 

Act of 2000 (PL106-224) to state the following regarding rate making: 

1) Sec. 508(i) (2) states “Review of rating methodologies. To maximize participation in the 

Federal crop insurance program and to ensure equity for producers, the Corporation shall 

periodically review the methodologies employed for rating plans of insurance under this subtitle 

consistent with section 507(c)(2).” 

2) Sec. 508(i) (3) states “Analysis of rating and loss history. The Corporation shall analyze the 

rating and loss history of approved policies and plans of insurance for agricultural commodities 

by area.” 

3) Sec. 508(d) (2) states “the amount of the premium shall be sufficient to cover anticipated 

losses and a reasonable reserve.” 

These three statements can be interpreted through standard actuarial definitions. The Statement 

of Principles Regarding Property and Casualty Insurance Ratemaking identifies a fundamental 

principle of insurance ratemaking as: “A rate is an estimate of the expected value of future 

costs.” Typically, the largest component of the rate is the provision for losses. While there are 

other important considerations in rate development, most of the actuarial foundations of 

ratemaking are intended to provide a framework for estimating the expected loss component of 

the rate. 

The current RMA COMBO programs are composed of a mix of individual-level revenue and 

yield insurance. The COMBO product rates are constructed on a foundation of yield insurance 

rates with revenue rates being overlaid on the APH yield rating system. In this analysis the focus 

is on proper weighting of historical experience to derive actuarially fair yield insurance rates. 

However, these results would then carry through to the related revenue insurance rates. Because 

different crops are subject to different perils and, therefore, varying loss costs, the APH 

procedure establishes rates for each crop separately. It is rare that a single insured, for any 

insurance coverage, will have a sufficiently large insurance history to allow expected losses to be 

derived solely from the insured’s own loss history. Thus, it is common and appropriate to 

consider the aggregate experience of a group of similar risks in developing rates. For APH, the 

aggregation is primarily done geographically. Rates are developed by geographic area, usually 
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the county. Thus, for each crop, the APH ratemaking process typically derives Loss Cost Ratios 

(LCRs), and consequently rates, by county. 

In March 2010, Sumaria Systems Inc. (Coble, et al. 2010) provided a comprehensive review of 

the methodology and procedures used to determine APH target rates and COMBO rating in the 

Federal Crop Insurance Program.2 The study provided several recommendations for modifying 

the current APH and Combo methodologies and suggested further evaluation of several other 

issues. One of those issues involved the current RMA practice of using equally-weighted,

adjusted, historical, loss cost experience for a county/crop program as the backbone of the 

current rating procedures. The current system uses a fairly lengthy data series of observed loss 

costs and gives each year’s experience equal weight. 

More specifically, RMA currently utilizes insurance experience back to 1975, where available. 

An earlier report by Josephson, et al. (2000) summarizes the history of how RMA has evaluated 

the length of experience period.3 According to this document, in a study in 1983 performed for 

FCIC, Milliman and Robertson (M&R) evaluated the length of the experience period. That study 

concluded “.... the FCIC should continue to use all available past history in the ratemaking 

process with possibly greater weight given to the more recent years.” (Josephson, et al. 2000, p. 

17). At the time of the 1983 study, each year was given equal weight in the determination of the 

county average. The suggestion to give greater weight to more recent years was made because of 

concerns about the impact of amendments to the FCIC Act of 1980, and the possibility that the 

pre-1980 experience might not be relevant. The issue was addressed again by M&R in 1995 and 

in 1996. In the latter report, M&R again recommended no changes to the practice of equal 

weighting of all years. 

The review of the APH Rating Methodology by Sumaria (Coble, et al. 2010) recommended that 

RMA continue to use loss experience as the foundation of the rating system. However, the study 

recommended that RMA evaluate alternative loss cost experience weighting procedures that 

incorporate additional information such as weather data, historical yields, or the amount of 

participation. The study recommended that RMA consider altering the weight given to its 

historical loss costs. The weights could potentially be based on a longer time series of weather 

variables. Another possibility, not necessarily mutually exclusive with the previous approach, is 

to adjust the weights according the level of participation (potentially measured by liability or the 

proportion of total acres insured). The study also suggested that changes in technology or in the

composition of the pool of insured producers over time may suggest that the loss costs observed 

from a particular historical event would be different had it occurred in today’s crop insurance 

program (see Section 6.11 of Coble, et al. 2010).

Sumaria Systems was subsequently contracted by the RMA to conduct additional analysis of this 

issue. The project commenced in September 2010. This implementation report describes a 

 2 This report is available at http://www.rma.usda.gov/pubs/2009/comprehensivereview.pdf.

3 This report is available at http://www.rma.usda.gov/pubs/2000/mpci_ratemaking.pdf .
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proposed procedure for weighting the historical experience used to develop rates for the APH 

product. Sumaria performed a detailed investigation to develop an optimal methodology for 

weighting, or otherwise adjusting, RMA’s historical loss cost data in order to maximize its 

statistical validity for developing premium rates. That report was provided to RMA which then 

selected the approach that best fit the needs of the program. This is a second report developed by 

the Sumaria team, which includes experienced crop insurance analysts, a leading professional 

actuary, and a professional climatologist (the credentials of our team are discussed in greater 

detail in the Appendix of this report.). In this report we present an implementation plan or model 

that RMA can incorporate into its current methodology.
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2. Background Summary of the Current RMA Loss Cost Rating System

The RMA rating procedures use historical loss cost experience for a crop in a county in 

developing county base rates. These county base rates are then adjusted for factors such as 

coverage level, unit format, crop type, and crop practice to obtain a rate for an insured unit. In 

this chapter we describe current procedures followed in developing county base rates. The 

summary provided here draws heavily from detailed descriptions contained in an RMA internal 

document entitled “Rate Methodology Handbook: Actual Production History” which is 

applicable for 2011 and subsequent years. We also draw upon the aforementioned 2010 Sumaria 

review (Coble et al. 2010). 

The Statplan database forms the foundation for the APH rating process. The result of these 

procedures is the construction of a set of data tables. Two of these tables, the production ratio 

table and the county summary table, contain the essential data that support the actual production 

history rating process. The production ratio table contains the data used in computing production 

ratios, which are discussed in detail in the 2010 Sumaria review (Coble et al. 2010),and the 

county summary table, which contains information summarized at the county level and is used in 

evaluating specific risks such as prevented planting. The following are several specific issues 

addressed in the development of the Statplan database.

• Adjusting for Winter Kill Experience in winter wheat and barley.

• High Risk Experience -- Because high-risk experience is not considered to be consistent 

with experience from other land in a county, this insurance experience is excluded from 

the production tables upon which base rates are determined.

• Whole Farm Units-- The Revenue Assurance product offered whole farm units which 

combine the coverage for two or more crops in a county. Experience for this combined 

coverage cannot be segregated by crop and is therefore excluded from all Statplan data 

tables.

• Prevented Planting-- Prevented planting is not considered to be a production loss and so 

prevented planting indemnities and associated liability are excluded from the production 

ratio tables. These indemnities and liabilities are captured in other Statplan databases for 

use in prevented planting reviews. 

• Written Agreements-- Insurance experience established under a written agreement is 

excluded from the standard Statplan rating data.

• Late Planted/Planting Adjustments-- Late planting insurance experience is first adjusted 

to reflect the correct liability/coverage (if it were not late planted) and is then included in 

the Statplan database. 

• Replants-- Indemnities paid to insured producers to cover the cost of replanting are not 

included in the base rate calculations and thus are not stored in the yield ratio or county 

summary tables. However, the liability and any indemnities paid on replanted acreage are 

included in the Statplan tables and in base rate development because the acreage is 

planted under conditions that are expected to produce at least the guaranteed yield.
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• Revenue Adjustments-- Three revenue insurance products were introduced by the RMA in 

the mid 1990s--Revenue Assurance (RA), Crop Revenue Coverage (CRC), and Income 

Protection (IP). All of these products insure producers against shortfalls of gross revenue 

below a guaranteed level and in all three the yield risk component of the coverage is 

based on APH procedures. RMA transforms indemnities for CRC and RA to be equal to 

what they would have been had the coverage been based on the fixed APH Price Election 

rather than the revenue plan base price and harvest price. The result is a calculated 

indemnity, for insured units that are indemnified, that is equal to what the indemnity 

would have been under APH yield insurance. This achieves consistency within the 

Statplan data across the APH yield insurance product, CRC and RA, with or without a 

harvest price feature or option4.

• Revenue Adjustments for Replanted Acreage-- The process described in the previous 

bullet is used to convert revenue product loss experience to equivalent yield losses. A

similar process is followed for replant losses.

• Coverage Level--The common coverage level used as the base for APH rating is the 65% 

coverage level. Therefore, loss experience for units insured at levels above 65% must be 

adjusted downward to reflect what it would have been at the 65% coverage level and loss 

experience for coverage levels below 65% must be adjusted upward to what it would 

have been at the 65% coverage level. 

• Once RMA has adjusted existing loss experience in the Statplan data development 

process, the actuarial branch begins a multi-step process to develop a target rate for each 

county/crop program. In effect, the target rate is the rate that should serve as the base 

upon which rates in a county are anchored. 

RMA uses a catastrophic loading procedure to reduce the influence of outliers in the experience 

of a county/crop program. Because crop losses are often characterized by infrequent but severe 

losses, even several decades of county loss experience may be subject to sampling error. 

Catastrophic loading is an actuarial technique used to mitigate the effect of sampling error when 

the true magnitude of the sampling error is not known. Catastrophic loading is intended to 

remove anomalous experience from the county/crop data while preserving normal loss 

experience. In general, losses deemed catastrophic are spread across all counties for a crop in a 

state. Thus, the capping of loss cost experience in a county/crop program is not a load in the 

sense that it is an additional factor added to rates, but rather it redistributes loss experience 

within a state/crop program. 

The current RMA procedure censors the county loss experience at the 80th percentile of the 

historical county experience. No distributional assumptions are required for the procedure. To 

illustrate this, assume 30 years of data are available for the county/crop program. Then the 80th 

percentile of the loss cost is the 24th highest observed loss cost ratio (note when the percentile 

does not fall on a discrete observation, a linear interpolation is used). All indemnities above the 

 4 IP experience is not included in APH base rate calculations because of differences in product design.
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truncation point are aggregated to the state/crop program level. For a county, the catastrophic 

(CAT) indemnity is calculated as follows:
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3. Conceptual Explanation of Weighting and Loss Cost Adjustments

a. Weather Weighting

One issue that should be considered in the weighting of historical loss experience is the 

representativeness of weather experience reflected in the Statplan data used for calculating 

county base rates. Statplan is a loss experience data set that utilizes information from 1975 

(where available) onward (i.e. 35 years of data in 2010). In many lines of insurance, 35 years of 

loss history would be considered a very “long” time series of data to use in rate making. 

However, 35 years may be a relatively short series for accurately reflecting probabilities of the 

weather events that are a dominant factor in crop losses.

For example, given the current use of simple averaging of loss cost data to calculate county base 

rates, the severe loss years of 1988 and 1993 are each given 1/35 weight but the long term 

frequency of the weather events that drove these losses may be greater or less than 1/35. It could 

be that the 1988 drought was a 1 in 20 year event rather than a 1 in 35 year event. If so, a larger 

weight than 1/35 would be appropriate for that year. Alternatively, it could be that drought 

events observed in 1988 only occur 1 in 50 years in a longer weather time series and should be 

given less weight than 1/35. The intent of weather weighting of loss cost data is to bring 

additional information from a longer series of weather variables to more properly weight the loss 

cost data used to calculate average county rates.

In developing a system to weight short loss experience data using longer weather/climate data, 

one has to consider the following issues: (1) the weather or climate data to use for weighting 

(e.g., the relevant weather data, the length of the data, the degree of coverage and/or level of 

aggregation, the relationship of such weather to losses, and the availability of weather variables), 

and (2) the development of a procedure to properly weight each year in the short loss data (e.g., 

categorizing each loss data year and creating weights for each year in a manner that is consistent 

with other parts of the rating process).

Weather/Climate Data

There is an abundance of weather data available in the U.S. that can be used for weather-based 

weighting of loss experience data. However, there are several issues to consider in choosing the 

weather data to be used. First, one has to consider the length of the different climate data series 

that are available. In the context of weighting insurance data, one would like to have the longest 

series of historical weather data available. This would help ensure that different weather 

outcomes, especially the rare extreme weather events that cause losses, would be adequately 

represented in the longer data series. Information about the probabilities of different weather 

events will be better captured if one has a very long climate data series.

However, the need for a long data series must be balanced with the second issue to consider – the 

degree of coverage and level of aggregation. For example, there may be weather data that are 
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available for 200 years, but these data sets may only contain data for a particular part of the 

country and/or aggregated at the national level. Crop insurance covers a large portion of the U.S.

and so weather data covering most or all states are needed. In addition, there is significant 

heterogeneity of the weather events that drive losses at the county level for a particular year. 

There is value in having data at a lower level of aggregation (i.e., county level or 5 x 5 mile 

grids) rather than at the national level only. However, in using weather/climate data at lower 

levels of aggregation, it may be the case that data interpolation methods were involved in the 

construction of the data, especially at the sub-county level where there frequently are no weather 

stations in a particular location.

Another factor to consider in choosing the weather or climate data to use in weighting loss 

experience is the availability of different weather variables that can be used. Longer series of 

climate data may be available for some basic variables like temperature or precipitation, but 

variables like drought indexes may not be available for this longer period of time. Climate data at 

lower levels of aggregation and with wider coverage may only be available for certain weather 

variables and may be absent for others. Hence, to have flexibility in determining the weather 

variables that can help to explain losses, the availability of different weather variables in a 

particular climate data set is also an important consideration.

Finally, in choosing climate data for weather weighting crop insurance loss cost data, the source 

of the data and the availability of the data in the future are also important considerations. The 

source of the climate data has to be reliable and must have a good reputation in terms of 

reporting weather/climate data. Moreover, there should be a reasonable expectation that the 

weather/climate data will continue to be routinely available in the future to support updating of 

weather weights and an official rapid assessment for each subsequent year’s weather influence.

Development of Weather Weighting Procedure

Once the weather data have been chosen, the next thing to consider is the development of a 

weather weighting procedure. The first important issue to evaluate is the choice of weather 

variables to use in classifying and weighting each loss experience year. A number of weather 

variables during a specific time period could be related to crop losses and one approach is to 

simply include all available weather variables (and all time periods) that exist in the chosen 

climate data. However, this straightforward approach would add complexity to the procedure and 

might generate a lot of noise, especially if there are a number of weather variables in specific 

time periods that do not have a statistically significant effect on losses. Further, there are often 

many different weather variables available such that the capacity to use everything that might 

exist is limited. Hence, there has to be a balance between simplicity/noise in the data and the 

number of weather variables (for different time periods) used in the weighting. Consulting the 

professional literature should provide some guidance as to which weather variables are relevant 

to yields and what time period to use (i.e., what weather variable at what time periods best 

explain crop losses). Procedures to evaluate the “best” combination of weather variables to use 

should also be considered. For example, regressions of losses on different weather variables at 
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different time periods could be conducted. In-sample or out-of-sample model fitting 

criteria.such as the adjusted r-square or a root mean squared error (MSE) can be used to evaluate 

the best combination of weather variables to be used in the weighting. Presumably, the weather 

variables and time periods chosen will be the ones that “best” explain crop losses over time. A 

weather index can then be created using the chosen weather variables and time periods. One 

issue to consider here is the level of aggregation to use in constructing the combinations of 

weather variables and time periods to be used. In other words, will the same weather variables 

and time periods be used for each county, state, and crop? Alternatively, is one combination 

appropriate for the entire nation? 

Based on the weather index developed, each year in the “shorter” loss experience data set has to 

be classified relative to the longer term weather index. This will allow for developing the proper 

weights to assign to each of the actual loss experience years in the shorter data series. There are a 

number of ways to classify a year and assign a weight. One approach is to generate a histogram 

with equal bin widths and variable probabilities (or frequencies) (see Coble et al., 2010, p. 85 

and Figure 3.1).5 The bins or groupings with equal widths can then be used to classify each year 

of the loss experience (i.e. which bin does the loss year belong to given the actual experience) 

and the probability associated with the bin assigned to the year will serve as the weather weight. 

An alternative that is recommended is to develop variable bin or grouping widths with equal 

probabilities associated with each bin (See Figure 3.2). The bins or groupings will again be used 

to classify each year, but since these are variable width bins with equal probability, there is no 

need to have differential weights for each actual year of experience. In both of these procedures, 

one has to evaluate the number of bins to be used and make sure that all bins are represented in 

the shorter loss data. If not, the weighted average may not fully reflect the available historical 

experience. In addition, the complexity of the procedure and the ease of implementation should 

also be a considered in choosing the approach to classify and assign weights to the actual loss 

years.

Another issue to consider in the development of the weather weighting procedure is its 

consistency with other rating procedures such as the catastrophic loading (i.e. state excess load). 

To the extent possible, the proposed weather weighting procedure should allow for the 

catastrophic loading currently used by RMA, which caps the adjusted loss cost ratio at a fixed 

percentile for all available years. There should also be some conceptual evaluation of the 

appropriateness of the catastrophic loading methods, given the introduction of weather weighting 

in the rating system.

 5 Alternative methods such as generating kernel densities or fitting parametric distributions can also be used instead 

of histograms. However, one should recognize that these more complex procedures may have implications for 

implementation. One has to weigh the relative benefits of more complex approaches against the efficiency and ease 

of more simple approaches (like using a histogram).
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Figure 3.1. Histogram with equal bin widths and variable probabilities for each bin.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

0

5

10

15

20

25

30

35

P

e

r

c

e

n

t

pl cr2
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Figure 3.2. Variable bin widths with equal probabilities for each bin.
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b. Conceptual Assessment of Non-stationarity in Loss Cost Data

The objective of ratemaking is to provide an estimate of the expected value of future costs. 

While historical exposure and loss experience provide the starting point for ratemaking, the 

relevance of the historical experience must always be considered. The Statement of Principles 

Regarding Property and Casualty Insurance Ratemaking6 (Casualty Actuary Society 1988) notes 

that ratemaking begins with historical experience, but then goes on to discuss necessary 

considerations in the ratemaking process that may affect the reliance the actuary can place on the 

data. Among other considerations, the Principles (Casualty Actuary Society 1988) call on the 

actuary to consider the following factors.

• Homogeneity of the data: including subdividing or combining data so as to minimize the 

distorting effects of operational or procedural changes.

• Trends: past and prospective changes in claim costs, frequencies, and exposures.

• Policy provisions: past and prospective changes in coinsurance, coverage limits, 

deductibles and other policy provisions.

• Mix of business: past and prospective changes in the distribution of policies among 

deductible, coverage selections or type of risk that may affect frequency or severity of 

claims.

• Operational changes: past and prospective changes in the marketing or underwriting 

process.

When the effect of such changes can be measured (historically) or projected (prospectively), the 

actuary adjusts the data accordingly. There is extensive actuarial literature on adjustments such 

as trending of loss and premium or exposure data, including a standard practice on trending 

procedures in ratemaking (Actuarial Standards Board 2009).

7

 

The property/casualty ratemaking process is a dynamic activity – insured characteristics, the mix 

of business and the economic environment are constantly shifting, making incorporation of 

appropriate adjustments for such changes extremely difficult even for relatively recent 

experience. Precedent and common usage within the actuarial profession steer the actuary to 

minimize the length of time spanned by the historical data used in the ratemaking process to just 

enough to be statistically reliable. In the absence of statistically reliable data beyond a relatively 

short historical time period, actuaries turn to credibility weighting against other contemporary 

estimates rather than expanding the history.

The reasoning behind using a relatively short time span for an insurer in a competitive market is 

clear: an insurer’s mix of business is bound to shift over time as its market position changes. 

 6 This document can be found at http://www.casact.org/standards/princip/sppcrate.pdf. 7 This document can be found at http://www.actuarialstandardsboard.org/pdf/asops/asop013_114.pdf.
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However, it is not only competitive pressures that affect the mix within an insurer’s experience. 

Characteristics of the same insureds change over time: policyholders age, their homes become 

older, they turn over older vehicles for new ones, etc. Commercial exposures also change over 

time: ownership changes, workplace safety improves, manufacturing processes are upgraded, etc. 

Insurer procedures also affect the underwriting results: policy provisions and settlement 

processes evolve over time. Capturing – and appropriately reflecting – all such changes (and 

their interactions) is virtually impossible. 

Thus, it is typical for the actuary to consider how short a time period is required for reliable 

ratemaking rather than how long is the period of available data. In general, the larger the size of 

the exposure, the smaller the time period utilized by the ratemaking actuary. While relatively 

small commercial carriers may use five to ten years of their own experience (weighted against 

rating bureau rates) and small personal lines carriers typically use five years of experience for 

property exposures and three to five years for automobile ratemaking, the National Council on 

Compensation Insurance (the rating bureau for workers compensation in most states) utilizes 

only two policy years in its standard ratemaking procedure. The NCCI’s database encompasses 

virtually all of the insured business within a state, so the mix of business itself is not an issue; 

however, changes within the insureds themselves are still assumed to be present, and the NCCI 

limits the historical data in its ratemaking process to the minimum needed to produce a stable 

indication. 

In cases where the data over a short time span are not considered to be fully credible, it is also 

common practice for the actuary to use a somewhat longer time period (such as five years of data 

rather than three), but then to judgmentally assign less credibility to the older periods through the 

use of decreasing weights. 

The exception to the common practice of using fewer rather than more years of data exists in 

procedures used to account for very infrequent extreme events. In that case, the actuary is forced 

to expand the time spanned by the ratemaking data in order to ensure that a reasonable estimate 

of the frequency and/or severity of large loss events are captured. In order to preserve the 

desired short-term nature of the historical data used for the non-catastrophic portion of the rate, 

extreme events are sometimes projected entirely separately from the rest of the rate. This 

method assumes that large events are independent of the smaller events, and also that the need to 

capture the extreme events in the rate outweighs shifts in the business that have not been 

captured by adjustments to the data. Alternatively and more typically, extreme event data over a 

longer time period are analyzed in terms of their ratio to losses excluding extreme events, and 

then the projected extreme event ratio is applied to the non-catastrophic portion of the rate

(Werner and Modlin 2010).

8

 This technique assumes that the extreme event ratio is relatively 

constant over time, and when it is applied to a non-catastrophic rate based on recent data, any 

changes in the mix of business will be captured. This assumption tends not to hold in the event 

of natural catastrophes because (a) the time period of available data is too short to capture the 

potential range of loss outcomes and (b) the mix of business has shifted dramatically toward 

 8 This publication is available at http://www.casact.org/pubs/Werner_Modlin_Ratemaking.pdf see pages 107-111.
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higher exposure areas, resulting in understated historical catastrophe to non-catastrophe ratios. 

The third method for catastrophe ratemaking involves direct modeling of the projected 

experience using a comprehensive tabulation of the exposures and an extreme event model 

derived from outside sources. The insurance industry typically relies on sophisticated natural 

catastrophe models for its hurricane and earthquake exposures and on scenario-based models for 

extreme events such as terrorism.

When applying these principles to RMA’s ratemaking process, we ask the following questions.

• How are current conditions and the mix of business different from those reflected in the 

historical experience, and can the data be adjusted appropriately?

o Are there identifiable significant shifts in the program that would be expected to 

affect all data prior to a particular date?

o Are there identifiable trends in the experience that can be captured?

• How many years of data are necessary for determination of the base rate?

• How many years of data are necessary for determination of the catastrophe provision?

Explicit Adjustments for Changes

We have observed that there is a significant discontinuity in the data for many crops that occurs 

around 1995. This corresponds to known changes in the way the program was administered and 

to a marked increase in program participation. Figure 3.3 provides evidence of the change in 

RMA’s book of business over the past three decades. This graph plots the net acres insured for 

the six major crops (corn, soybeans, wheat, cotton, rice, barley) from 1981-2009. One can see a 

distinct change in participation in 1995. Prior to 1995 there had been a strong upward trend in 

participation but legislative changes in 1994 resulted in an almost doubling of insured acres in 

1995. Further, after a slight drop off in 1996 and 1997 net acres have largely remained above 

170 million acres. While not shown in this graph, much of the 1995 participation was in 

catastrophic coverage policies, however much of that acreage has now migrated to buy-up 

coverage. 

This type of program dislocation is appropriately captured in the ratemaking process by 

measuring the average effect of the change at a macro level and then applying an adjustment to 

the data prior to the change. Comparable adjustments, for example, can be found in the NCCI’s 

process for accounting for benefit changes adopted by state legislatures. The expected effect of 

the benefit change is calculated, and all experience prior to the change is adjusted uniformly for 

the expected effect so long as it remains in the ratemaking data. Once the years prior to the 

change roll off, no adjustment is necessary. 

Selection of the Number of Years for Basic Ratemaking

RMA’s program differs from most property/casualty exposures in that the loss experience is 

highly correlated with weather patterns. Even after capping the experience at the 80th or 90th

percentile, it is still very important to capture a representative sample of weather outcomes 
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within the ratemaking process. The need to capture variation in the weather precludes the 

exclusive use of a very short time series of data as would be used in a more typical exposure. 

However, once we have identified how “typical” a year’s weather is via the weather index, we 

need only to ensure that we have captured sufficiently many observations within each range of 

weather outcomes. Although the range of modeled loss costs within the bins at the high end of 

the weather index will be very large, the loss costs within high end bins will generally be capped 

by the catastrophe procedure prior to their use in the basic ratemaking procedure. 

We examined the number of observations (years of data) necessary to ensure that there is a high 

probability that no one year will get too much weight in the calculation due to being the sole 

observation in a very large bin. With only 15 years of observations, there is about a 25% 

probability that the binning procedure will end up with five or fewer bins and that one of the bins 

will still only have one observation. That one observation would receive 20% weight in the 

calculation of the indicated base rate, which is more weight than we would like to place on a 

single year’s experience. With 20 years of data, the probability of a single year getting that much 

weight drops to about 8%, with 25 years it’s around 2.5%, and with 30 years of data it is about 

1%. 

The high probability of placing 20% weight on a single observation indicates that 15 years of 

data is probably insufficient. However, at some point actuarial judgment would lobby for 

dropping data years that are so far removed in time as to be unlikely to be representative of 

current experience: hence we recommend that RMA consider limiting the number of years of 

data for base ratemaking to 20 years.

Judgmental Credibility Weighting for More Recent Data

Given the long time span required to assure a reasonable weather distribution in the base rate 

calculation, generally accepted actuarial practice would consider judgmentally assigning less 

weight to older years in the data. The effect of the necessary adjustments for program changes 

and trend discussed above tend to be compounded over time, causing the loss cost estimates from 

older years to become more and more dependent on estimated adjustments over time. The 

proposed method for grouping the data by weather indexes would allow for a judgmental 

credibility weighting of observations based on time within the same weather index range.

Selection of the Time Period for the Catastrophe Load

When considering the catastrophe load, however, the maximum amount of relevant data should 

be used. RMA’s current procedure uses all available data, and we recommend that the full data 

series continue to be used, with the possible exclusion over time of early years if the covered 

acreage is very low relative to current acreage. On the other hand, if the weather index for a 

particular year is above the 97th percentile, one may want to adjust the weight given to that year’s 

input to the catastrophe load to reflect the frequency reflected by the percentile of the weather 

index. That is, if the data span 30 years of experience, a year with a weather index at the 98th
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percentile should be given 2% (1-in-50) weight rather than 3.33% (1-in-30) weight. The weight 

taken from the adjusted year should then be spread evenly among the remaining years. 
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Figure 3.3 Net acre insured change from 1981 to 2009.

 -

 50,000,000

 100,000,000

 150,000,000

 200,000,000

 250,000,000

19811982198319841985198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009

Net Acres Insured- 6 Major Crops
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4. Proposed Weighting of Historical Experience

a. Weather Weighting

In order to quantify the relative frequency of extreme weather events that may be associated with 

loss experience, a reference set of climate data is needed that meets the following idealized 

criteria.

(1) Provides climate information across all geographies where loss experience is 

observed.

(2) Provides climate information at sufficiently local scales to explain local loss 

experience.

(3) Provides the longest possible temporal record of climate events to ensure adequate 

analysis of the frequency of both normal and extreme climates.

(4) Provides specific climate variables that provide meaningful explanation of loss 

experience.

(5) Is operationally and routinely updated for use in future analysis and weighting.

There are several climate datasets that partially meet these 5 criteria. First, the National Oceanic 

and Atmospheric Administration (NOAA) Climate Prediction Center (CPC) Unified 

Precipitation Analysis is an interpolation of the available point-based precipitation gauge data 

collected by both NOAA and USGS. It meets the above criteria (1), (2), and (5), but provides 

only information on precipitation and has data only since 1948. Important information on 

temperature and drought are not provided, and these data do not allow for characterization of the 

relative frequency of known extreme drought events in the 1920s and 1930s nor hurricane or 

flooding events prior to 1948.

A national analysis of Palmer Drought Severity Index developed by Dai et al. (2004) meets 

criteria (1), (3), and possibly (4), but is not updated regularly and provides drought severity 

information only every 250 kilometers, which is insufficient to explain local loss experience.

Another group of data that partially meet the criteria involves atmospheric model simulations, 

including NCEP Re-analysis and the North American Regional Reanalysis (NARR). These 

products meet criteria (1), (2), (4), and (5), but NCEP re-analysis (and similar) only contain

information since 1948 and NARR only since 1979. Similarly, PRISM data from Oregon State 

University provide detailed model estimates of temperature and precipitation for a very long 

record and meet criteria (1), (2), and possibly (3), but PRISM does not provide drought estimates 

and is not considered operationally available.

The data collection that best meets all 5 criteria is the National Climatic Data Center’s Time Bias 

Corrected Divisional Temperature-Precipitation-Drought Index data, also called the Climate 

Division Data. Climate Division data provide monthly, serially complete information on 

temperature, precipitation, relative severity of dry and wet periods using drought indexes, and 
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degree day metrics of heat and cold accumulation since 1895 for the continental United States, 

grouped into 344 divisions. Updates are operationally provided each month by NOAA’s National 

Climatic Data Center. A useful description of the history and current status of climate division 

data is provided by Guttman and Quayle (1996). More technical details on the data and 

adjustment methods are given in NCDC (1994) and Karl et al. (1996).

Climate Division data are produced using more than 5,000 National Weather Service cooperative 

observer gauge reports. Climate Division boundaries group stations of similar climates into 

regions that adhere to state political borders. In most cases, the climate division boundaries also 

follow county boundaries. However, in regions with more complex geography (including some 

states with complex topography and/or shorelines), climate division boundaries follow river 

basins within each state. While climate divisions were originally designed in 1912, boundaries 

were adjusted in the 1940s to align with crop reporting districts or drainage basins. The Climate 

Division boundaries are shown in Figure 4.1a. In some instances climate divisions split counties. 

The assignment of counties used in our study is shown in Figure 4.1b. This allocation is based 

on relative area, geography and other factors.

There are limitations to using Climate Division data. Climate division boundaries are not always 

delineated for climate homogeneity. Especially in the mountainous terrain of the western US, the 

boundaries follow drainage basins and all locations within those boundaries are not likely to have 

very similar climate characteristics as climate changes quickly with elevation. Another weakness 

is that the station network used for each division calculations is not constant. Stations move, 

cease operation, and new ones are introduced throughout the history of the observing network. 

This introduces some error with any divisional calculations. Another weakness is the accuracy of 

division level data prior to 1931, when regression equations are used to estimate division-level 

data from statewide average data that were standard during that period.

Despite these weaknesses, Climate Division data provide the best operationally available climate 

information for crop loss analysis. They provide serially complete national coverage (with no 

missing data) at a geographic scale sufficient to characterize local climate extremes with a period 

of record sufficient to identify the relative frequency of climate events that may be associated 

with loss experience.

Data Preparation

The development of the weather weighting procedure starts by merging the climate data set (see 

previous sub-section) with RMA’s Statplan loss experience data (See Figure 4.1 for the different

climate divisions within states). Note that the climate data are observed at the climate division 

level as described above, while the RMA Statplan data are reported at the county level.9 This 

 9 The county loss data utilized in this study are typically aggregated for all types/practices (with the exception of 

wheat, where the data are separated to identify winter and spring wheat). This type of aggregation is consistent with 

the county level data used in calculating the base county rate (see Coble et al., 2010 p. 38). 
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difference necessitates the use of an additional data set that assigns counties to particular climate 

divisions. Most counties are entirely or nearly entirely contained by a climate division. Counties 

associated with each climate division are provided by NOAA NCDC. However, as some 

divisions (especially in the mountainous western US) are delineated to follow drainage basins, 

there are many counties (approximately 300) that are split by climate division boundaries. We 

developed a data set such that each county is assigned to a specific climate division10 based on 2 

criteria:

(1) Counties that are split by 1 or more climate divisions are assigned to the climate division 

that covers the greatest amount of area in the county.

(2) For counties that are not easily assigned according to (1), the county is assigned to the 

larger climate division as the larger climate division should have more weather stations in 

the aggregated value and therefore should have more confidence in the weather 

representation.

Based on this data set we are able to generate a merged climate-loss experience data set at the 

county and at the climate division levels.

All counties within a particular climate division have the same weather data. The loss data also 

must be aggregated to the climate division level. This is done by summing the adjusted 

indemnities and liabilities of all counties within a climate division level and then calculating loss 

cost ratios (LCR) based on these summed amounts. The climate division data are used to 

generate a weather index that is needed for classifying loss years, while the county data are used 

in averaging the loss cost data to calculate a base county rate.

Weather Index Development

A critical component in the development of a weather weighting approach is the choice of the 

weather variables that are used to determine the relative weights assigned to each year of loss 

data. One can use a single weather variable or a combination of different weather variables. 

Based on the literature (Wilhemy, Hubbard and Wilhite 2002) and the expert opinion of the 

climatologist in our team, we chose to examine a parsimonious set of weather variables – the 

Palmer Drought Severity Index (PDSI) and Cooling Degree Days (CDD). PDSI is a particularly 

good weather variable to examine because it subsumes effects of both precipitation and 

temperature and provides a locally relative scale ranging from very wet to very dry conditions. 

Wilhemy, Hubbard and Wilhite 2002 show that much loss experience is associated with drought 

 10 We build on the NOAA data set that assigns particular counties to climate divisions to develop this data set. This 

data set cannot be used ‘as is’ because there are a number of counties (approximately 300) that are assigned to 

multiple climate divisions. The starting point for the assignments is based on the listing provide by NOAA NCDC. 

The climatologist in our team (Dr. Ryan Boyles) set a criterion to decide which county is uniquely assigned to a 

particular climate division (see previous section). In addition, there are county codes created by RMA that are 

unique to the program (and FSA), such as having East (code=155) and West (code=156) Pottawatamie, IA while the 

NOAA data simply have Pottawatamie, IA (code =155). These occurrences were accommodated in the data set 

developed.
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conditions, but PDSI also allows for very wet (flood) conditions that may also be associated with 

loss. CDD allows for examining heat units for a particular time period that affects crop growth. 

CDD is equivalent to Growing Degree Days (GDD) at a base of 65F, and allows exploration of 

loss experience that may be associated with extended cold or heat that would not be captured in 

PDSI.

For the PDSI, we created two variables to represent positive PDSI and negative PDSI values. 

Positive PDSI values represent wet spells (i.e., larger positive numbers indicate more moisture) 

and negative PDSI values represent drought conditions (i.e., larger negative numbers represent 

more severe drought conditions). In addition, the positive and negative PDSIs we use are limited 

to the May-June and July-August periods (i.e., average May-June and average July-August 

PDSIs are utilized in the study). In summary, four PDSI measures are examined in the 

development of our weather index – May-June PDSI for positive values (mj_pdsi_p), May-June 

PDSI for negative values (mj_pdsi_n), July-August PDSI for positive values (ja_pdsi_p), and 

July-August PDSI for negative values (ja_pdsi_n). The CDD variables used in developing the 

weather index are total season CDD (from May to September) (total_cdd) and June-July total 

CDD (jaj_cdd). The June-July periods are periods in which crop growth is frequently adversely 

affected by heat units.11 

Based on these six weather variables, an index is created by estimating a fractional logit 

regression model (at the climate division level) where the dependent variable is the climate 

division adjusted loss cost ratio and the independent variables are the six weather variables 

discussed above (see Papke and Wooldridge 1994 for a discussion of fractional logit models).

Fractional logit regression is used to account for the proportional nature of the data and

censoring of loss costs at zero and one. This approach ensures that predicted values do not fall 

below zero or above one. 12 Based on our investigation of the degree of censoring of the data at 

zero, we believe that using the fractional logit is appropriate in this case. The degree of zero 

censoring in the data ranges from 6-11% for corn and soybeans, to about 30% for barley and 

potatoes. On the other hand, the degree of censoring at one is significantly lower in the data and 

it is below 1% for most crops (the exception is apples with censoring at one of about 1.1% ). 

 11 These six variables apply to all crops except winter and spring wheat. For winter wheat, the following variables 

are used: Sept./Oct average PDSI (positive and negative), April /May average PDSI (positive and negative), 

September to May total season CDD, and March to April total CDD. For spring wheat, the following variables are 

used: April/May average PDS (positive and negative), June/July PDSI (positive and negative), April to August total 

season CDD, and May to June total CDD. Further note that the durum wheat type has been aggregated with spring 

wheat.

12 Note that ordinary least squares (OLS) regression can also be used to estimate the index. The disadvantage of 

OLS is that predictions are not constrained to lie on the [0,1] interval. Nevertheless, one can argue that the predicted 

loss costs here are only used as a “tool” to rank the years in terms of having “good” vs. “bad” weather (i.e., one 

could interpret negative values as indicating good weather years). The magnitudes of the predictions are not used 

‘per se’. Using the OLS model to estimate the model did not result in significantly different classifications of the 

loss years (relative to the fractional logit model). However, we recommend using the fractional logit given the 

degree of censoring in the data and the intuitive concept of limiting predicted loss costs to lie between zero and one. 
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To have an even more parsimonious model specification, an out-of-sample competition for each 

state is conducted to determine which combination among the six initial weather variables best 

predicts losses (i.e., in this case which combination best predicts adjusted loss cost out-ofsample).13 A minimum mean square error (MSE) criterion is used to evaluate the model with 

best out-of-sample predictions:

2

1

1 n

i

i

MSE e

n =

  =     ∑ ,

where i e is the difference between the actual adjusted loss cost and a predicted adjusted loss cost 

(out of sample) based on the fractional logit regression model. A lower MSE means that there is 

a smaller discrepancy between the actual and predicted adjusted loss cost ratios and one would 

prefer the combinations of weather variables that produce the lowest MSE values. Note that we 

run independent regressions for each climate division within the state (i.e., climate divisions do 

not cross state lines), but undertake the out-of-sample competition to find the best combination 

of weather variables for the entire state. This implies that each regression model is estimated 

independently but a common specification, in terms of the weather variables included in the 

regression model, is applied for all climate divisions within a state for each individual crop. In 

other words, for a crop in a state, the same weather variables are used in the loss-cost regression 

though parameters on weather variables may differ across climate divisions.

To facilitate the out-of-sample competition for each state, we limit the number of weather 

variable combinations to be considered to seven: (1) May-June PDSI positive and May-June 

PDSI negative, (2) July-August PDSI positive and July-August PDSI negative, (3) total season 

CDD and June-July total CDD, (4) May-June PDSI positive, May-June PDSI negative, JulyAugust PDSI positive, and July-August PDSI negative, (5) May-June PDSI positive, May-June 

PDSI negative, total season CDD, and June-July total CDD, (6) July-August PDSI positive, JulyAugust PDSI negative, total season CDD, and June-July total CDD, and (7) May-June PDSI 

positive, May-June PDSI negative, July-August PDSI positive, July-August PDSI negative, total 

season CDD, and June-July total CDD. Limiting the combinations to these seven choices and 

estimating the model for each crop, covering all states allows for less of a computational burden 

(i.e., runs not to exceed six hours for each crop). A hypothetical example of how an out-ofsample competition works can be seen in Table 4.1. In this example, the lowest MSE is for 

combination 4. This means that, for this state, the best combination of weather variables to use in 

creating an index is the following: May-June PDSI positive, May-June PDSI negative, JulyAugust PDSI positive, and July-August PDSI negative. This combination best predicts loss costs 

out-of-sample.

 13 In-sample fit criteria (such as in a stepwise regression using an adjusted R-squared criterion) could also be used 

to determine the optimal combination of weather variables. However, there are a number of criticisms to this 

approach (i.e., bias in the tests to iteratively choose the best variables from the sample, as well as over fitting) that 

makes out-of-sample competition more attractive in this case (See, for example, Rencher and Pun 1980 and Copas 

1983). 
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Once the optimal combination of weather variables is chosen for a particular crop and state, this 

combination of weather variables is used to produce a weather index for all of the climate 

divisions within the state producing the crop. Essentially, the predicted values of the “best” 

regression model specification are used as the weather index for each year of weather data. Using

predicted values (i.e., predicted loss costs in this case), makes it possible to “backcast” a weather 

index for each year in which weather data are available (e.g., from 1895 onwards) even when 

there are no available loss experience data for the pre-crop insurance years (See Table 4.2). The 

relative probability of an extreme weather event can therefore be assessed over a 116 year time 

span (1895-2010) based on the predicted values. For example, the weather index for 1988 can be 

compared to other years from 1895 onward to determine the relative probability of this weather 

event occurring in the larger sample.

A concern with using the predicted values is that there may be cases when even the “best” 

combination of weather variables does not produce a statistically significant model that explains 

losses over time. For example, in some climate divisions, the Pearson chi-square test of overall 

model fit for the preferred model specification is not statistically significant and the correlation 

of the predicted values with the actual loss costs is actually negative. This means that the weather 

variables we considered do not have enough power to explain the pattern of losses observed over 

time and that there is no significant positive correlation between the model predictions and the 

actual loss costs. This situation occurs, for example, in some areas where extreme wet conditions 

are very rare and widespread irrigation makes drought conditions unimportant. In that case, we 

can fairly state that the weather has little effect on the crop insurance loss experience. We flag 

these cases, and the weighting methods based on the weather index developed are not applied 

(See a hypothetical example in Table 4.3).

Example Results

In Table 4.4, we show a hypothetical example of the estimation results from a fractional logit 

regression model based on data for corn in Illinois (climate division 5) and soybeans in Indiana 

(climate division 1). In these examples, the independent variables used are the “best” weather 

variables chosen based on the out-of-sample forecasting competition. For example, based on the 

out-of-sample competition results for corn (See Table 4.5) the “best” weather variables to 

explain losses in Illinois are the CDD variables (total_cdd and jaj_cdd), which are used in the 

fractional logit regression in Table 4 (top panel). 

Once the out-of-sample competitions and fractional logit regression estimations are undertaken, 

we flag climate divisions where the chosen models do not produce a statistically significant 

model fit. In Table 4.6, we show hypothetical examples for Indiana, Iowa, and Kansas where we 

flagged counties that have insignificant fractional logit regression models (in particular see the 

Iowa (19) climate divisions where Flag=1). Note that we also flag those climate divisions with 

less than 10 years of loss cost data (See State Proxy flag in Table 4.7). In these cases, we 

aggregate to the state level and use the fractional regression estimates at the state level to get the 
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predicted values for these “thin” data climate divisions. In rare cases where there is a climate 

division in a state without at least 10 observations, we do not apply the models and instead 

recommend that some form of subjective rating continue to be used to establish rates.

A hypothetical example of predicted loss costs for corn in Iowa (climate division 5) is presented 

in Table 4.2. The “backcasted” loss costs from 1975 to 1979 are presented in order to show that 

the predicted loss costs can be calculated for years in which there are no actual loss data. This 

facilitates the classification of years based on the weather index (predicted loss cost) for the 116 

years for which the weather variables are available. 

Loss Year Classification and Weight Assignment

Using the weather index values from the regression model, each year needs to be classified and 

assigned a weight that represents its likelihood as indicated by the longer weather series. As 

mentioned in section 3 above, one approach is to develop variable width bins (or groupings) with 

equal probabilities or weights. This approach is done by first determining the number of bins or 

percentiles and assigning the weather indexes to the appropriate bin or percentile cut-off. For 

example, assuming that we are interested in 10 bins we would like to find the weather indexes in 

the long history of weather data that correspond to the 10th, 20th, 30th, 40th, 50th, 60th, 70th, 80th, 

90th percentiles, in addition to the minimum and maximum values. In this case, we have variable 

width bins, since the ranges of the loss cost values used to delineate the bins are not equal across 

bins, but the probability of falling into each bin is always equal to 10% (See Figure 3.2 in 

previous section). If the predicted values are normally distributed, the tails (at both ends of the 

distribution) tend to have wider bin ranges since only a few observations fall in these areas, but 

the middle bins tend to have smaller widths because a lot of observations fall in these middle 

bins. 

Once the variable width bins are delineated, the weather index value for each year (from 1895 

onward) can be classified and assigned to the bin in which it falls. Using the above example, if 

the bin width for the 10th bin (from the 90th percentile to the maximum) is, say, from 0.09 to 0.15 

and the year 1988 weather index is 0.13 (i.e. one of the high loss years), then year 1988 is in the 

10th bin. Each year is similarly classified using predictions from the fractional logit regression 

models. Since the probability of each bin is equal in this approach, there is no need to assign a 

specific differential weight to each bin.

One issue that needs to be addressed is the number of bins needed to ensure that there is at least 

one year of loss cost data in each bin (to avoid empty bins). As discussed in further detail below, 

once the years from 1895 onward are classified based on the weather index, the RMA’s actual 

adjusted loss cost data from 1990 through 2009 are utilized to calculate the average loss cost for 

a county. Hence, it is possible that years from 1990 through 2009 do not contain a dispersion of 

data such that each bin has one or more loss costs (i.e., not all bins are represented in the 1990-

2009 period). For example, it may be that no year in the 1990 through 2009 period is classified 

as falling into bin 9. This will have adverse implications for the calculation of the average loss 
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costs if not all bins are represented in the 1990-2009 period (i.e., not all bin probabilities are 

represented). In particular, a range of observed weather history is not being captured in the 

weighting of loss costs. Therefore, to address the issue of empty bins and, at the same time, 

determine the appropriate number of bins, the approach we pursue is to first look at 15 bins and 

then move down one bin at a time (i.e., from 15 to 2 bins) to establish the largest number of bins 

for which there are no cases of empty bins in the years with loss data (1990-2009). A minimum 

bin number of 5 is applied so that no county will have less than five bins. If the “optimal” bin 

number without empty bins is less than five, then no weather weighting is applied (i.e. essentially 

just using one bin). This binning process is done for each climate division, and so the number of 

bins may vary for each climate division within a state.

The variable bin width with equal probability approach is a fairly straightforward method 

compared to the approach of using kernel densities or parametric distributions. This “simplicity” 

facilitates the practical implementation of this procedure for multiple crops and for nationwide 

coverage. Moreover, we believe this variable bin width approach may be better than a standard 

histogram approach (that has equal bin widths and variable probabilities for each bin) because 

this mitigates the “empty bin” issue described above. That is, the likelihood of having empty bins 

for the years with loss data (1990-2009) is smaller under this approach as compared to a 

histogram approach with equal bin widths and variable probabilities. The number of bins in the 

variable bin width with an equal probability approach tends to be greater than if we used the 

histogram approach. 

A hypothetical example of bin classification results for soybeans in Mississippi (climate division 

1) is presented in Table 4.7. In this example, the number of bins is 10 and this number assures 

that there are no “empty bins” from 1990-2009 at the climate division level. All bin 

classifications are represented in the 1990-2009 data (i.e., see Bin Classification column in Table 

4.7). We also show in this table that the model insignificance flag and state proxy flag are both 

equal to zero, which means that the model fit results for this climate division is significant and 

the number of observations used in the estimation is at least 10.

After each year is classified into a particular bin at the climate division level (for all 116 years), 

the classified data for each year and the insignificance flags (based on regression model) are then 

merged with the county level loss data. Since the regressions and year classifications based on 

the weather indexes are done at the climate division level, all counties within a particular climate 

division will initially have the same year classification and insignificance flags.

At the county level (where the climate division bin classification and actual county loss cost data 

are merged), it is possible that there are counties without actual loss cost data for the full period 

from 1990-2009. For example, there may be counties where no crop insurance was sold on a 

crop in, say, 1990-1995. This means that actual loss cost data from 1990-1995 are missing for 

this county. Hence, this again will mean that there may be empty bins when calculating the 

average loss costs. The binning process above is then re-applied to these counties with less than 

the full number of years of actual loss cost data. Only the years with actual data are considered in 
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the binning process. Although this is at the county level, the weather index values at the climate 

division level that have corresponding (i.e. existing) actual county loss cost data are still used as 

the basis for the second binning process. As with the climate division binning process, a 

minimum of five bins is the minimum threshold in this county level binning process. No weather 

weighting is applied if the “optimal” bin number is less than five.

Loss Cost Averaging Procedure

The average loss costs are next calculated at the county level using the 1990-2009 data. We first 

calculate the aggregate loss cost for each county, which is the current procedure used for 

computing the county base rate. Then we do a “weather weighting” average of loss costs for each 

county. This weather weighting is done by first taking the average loss cost within each of the 

defined bins and then taking the “average of the average loss costs” across the bins. For example, 

if there are 9 bins within a county, we first calculate a simple average of the loss costs within 

each of these 9 bins (i.e., one average loss cost for each bin that results in 9 “average” 

observations). Then, we take the average of the 9 average loss costs for the 9 bins (i.e., “average 

of the average loss costs”). Since the bins are constructed to have equal probabilities, there is no 

need for taking a “weighted average of the average loss costs”. However, given the approach 

described above, a recency weighting procedure can be applied when taking the average loss cost 

within a bin. That is, more recent years of data can be given more weight relative to older years 

within each bin. Net acreage weighting is the chosen recency weighting procedure applied within 

the bins. This means that a “net acre weighted average” of actual loss costs within bins is

calculated. This accounts for more recent years being more “informative” than older years (given 

that more recent years tend to have more acres insured than older years). The net acre weighting 

here also means that actual county loss cost calculated based on more acres insured tend to have 

more weight than county loss cost data computed from smaller acres insured.

To allow for consistency with the current catastrophic loading procedure, we also calculate the 

unweighted and weather weighted average loss costs where the adjusted loss cost data are 

censored at the 80th and 90th percentile. 

Example and National Summary Results

A hypothetical example where county level loss costs are merged with the bin classification data 

can be seen in Table 4.3 for corn in Dewitt County, IL. The unweighted and weather weighted 

average loss costs at the county level can be calculated using the data presented in Table 4.3. The 

bin classification column allows us to conduct the weather weighting procedure described above. 

If the insignificance flag for model fit is equal to one in any county, we do not recommend using 

weather weighting for the county. 

Hypothetical examples of unweighted and weather weighted average loss costs for several 

counties in Iowa are presented in Table 4.8. Note that we calculate six loss costs averages (i.e. 

six weighting types) per county where: Weighting type = 1 if the average loss cost is calculated 
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with no weather weighting; Weighting type =2 if the average loss cost is calculated with weather 

weighting; Weighting type = 3 if the average loss cost is calculated with censoring at the 80th

percentile and no weather weighting; Weighting type = 4 if the average loss cost is calculated 

with censoring at the 80th percentile and with weather weighting; Weighting type = 5 if the 

average loss cost is calculated with censoring at the 90th percentile and no weather weighting; 

Weighting type = 6 if the average loss cost is calculated with censoring at the 90th percentile and 

with weather weighting. In the example in Table 4.8, it can be seen that the weather weighted 

average loss cost tends to be smaller than the unweighted average loss cost. However, this is not 

a pattern observed in every county-crop combination. There are cases where the weather 

weighted average loss costs are higher than the unweighted average loss costs.

Table 4.9 presents the national average of the calculated unweighted and weather weighted loss 

costs for all crops we examined. This is the liability weighted average across counties (i.e., the 

liability weighted average (not simple average) of the average county level loss costs based on 

the 2009 liability of each county). For apples, barley, cotton, potatoes, rice, and spring/winter 

wheat, the weather weighted average loss costs (at the national level) tend to be smaller than the 

unweighted loss costs. However, for corn, cotton, sorghum, and soybeans the weather weighted 

average loss costs (at the national level) tend to be larger. A map showing the pattern of the 

difference between unweighted and weather weighted average loss costs for corn is presented in 

Figure 4.5. Around 51% of the counties have weather weighted average loss costs lower than the 

unweighted loss costs.
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Table 4.1. Example of a hypothetical out-of-sample competition for choosing the best weather 

variables to create a weather index for a state.

Combination 

No.

Weather Variable Combinations Mean squared 

error

1 ja_pdsi_n ja_pdsi_p 0.91210

2 ja_pdsi_n ja_pdsi_p total_cdd jaj_cdd 0.96825

3 mj_pdsi_n mj_pdsi_p 1.14213

4 mj_pdsi_n mj_pdsi_p ja_pdsi_n ja_pdsi_p 0.86039

5 mj_pdsi_n mj_pdsi_p ja_pdsi_n ja_pdsi_p total_cdd jaj_cdd 0.98366

6 mj_pdsi_n mj_pdsi_p total_cdd jaj_cdd 1.01876

7 total_cdd jaj_cdd 0.98623

Note: In the example above, Combination No. 4 is the best combination of weather variables based on 

a Mean Squared Error criteria. These will be the variables used in the fractional logit regression to create 

the weather index for a particular state and crop.
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Table 4.2. Hypothetical example of weather index values, net acres and actual adjusted loss costs 

for corn in Iowa (State=19), climate division 5 (1975-2009).

State

Climate 

Division Year Net Acres Actual Adjusted loss costs Weather indexes

19 5 1975 0.013088

19 5 1976 0.0066332

19 5 1977 0.01381172

19 5 1978 0.0155085

19 5 1979 0.00979918

19 5 1980 386569.9 0.00850007 0.01860698

19 5 1981 682904.5 0.00165572 0.0066969

19 5 1982 399409.3 0.00290903 0.00939713

19 5 1983 190959.8 0.03955581 0.02977137

19 5 1984 446252.2 0.00654651 0.00991062

19 5 1985 502489.2 0.00422874 0.00852455

19 5 1986 542506.4 0.00542233 0.0075103

19 5 1987 510334.5 0.00063739 0.01377865

19 5 1988 599368.5 0.1357396 0.05201126

19 5 1989 1392289.1 0.01159806 0.00765586

19 5 1990 1166061.1 0.00804332 0.0129854

19 5 1991 852311.4 0.00912895 0.01383259

19 5 1992 897023.9 0.00145545 0.00394455

19 5 1993 818194.7 0.1242836 0.00734594

19 5 1994 981496.4 0.00096833 0.00734679

19 5 1995 1035910.2 0.0045309 0.0170454

19 5 1996 599679.6 0.00172944 0.005732

19 5 1997 1033995.6 0.0015911 0.00671987

19 5 1998 1074943.8 0.0094961 0.04710033

19 5 1999 1150101.9 0.00057391 0.00677308

19 5 2000 1243181.5 0.00022049 0.01780193

19 5 2001 1237287.7 0.00437922 0.0106978

19 5 2002 1311398.1 0.00041306 0.00989905

19 5 2003 1334522.2 0.00168785 0.01217966

19 5 2004 1374407.5 0.00262745 0.00778709

19 5 2005 1332961.6 0.00067134 0.01534896

19 5 2006 1284211.9 0.00101743 0.01114424

19 5 2007 1469130.3 0.00063091 0.02610541

19 5 2008 1440665.6 0.0116602 0.00627608

19 5 2009 1567807.9 0.01434467 0.00631721

Note: The weather indexes are available from 1895-2010. In the interest of space, we only present data from 1975-

2009. However, this demonstrates that “backcasted” predicted values can be calculated in years without the actual 

loss cost data.
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Table 4.3. Hypothetical example of county-level data used for calculating weather weighted 

average loss costs for De Witt county (County=39), IL (State=17): corn.

State County

Climate 

Division Year

Actual Adjusted 

loss costs

Bin 

Classification No. of Bins

Flag =1 if 

insignificant

17 39 4 1980 0.1237103 10 11 0

17 39 4 1981 0.0083081 3 11 0

17 39 4 1982 0.0040853 2 11 0

17 39 4 1983 0.1285333 11 11 0

17 39 4 1984 0.0081736 5 11 0

17 39 4 1985 0 2 11 0

17 39 4 1986 0 5 11 0

17 39 4 1987 0 9 11 0

17 39 4 1988 0.1321881 10 11 0

17 39 4 1989 0.0007658 2 11 0

17 39 4 1990 0.0031037 3 11 0

17 39 4 1991 0.0008012 10 11 0

17 39 4 1992 0.0006445 1 11 0

17 39 4 1993 0.0004054 3 11 0

17 39 4 1994 0 3 11 0

17 39 4 1995 0.0185295 8 11 0

17 39 4 1996 0 2 11 0

17 39 4 1997 4.105E-05 2 11 0

17 39 4 1998 0.0009253 8 11 0

17 39 4 1999 0.0004244 6 11 0

17 39 4 2000 0 4 11 0

17 39 4 2001 0.0007537 4 11 0

17 39 4 2002 0.0125182 9 11 0

17 39 4 2003 9.802E-05 3 11 0

17 39 4 2004 0.0011999 1 11 0

17 39 4 2005 0.0031927 10 11 0

17 39 4 2006 0.0006764 7 11 0

17 39 4 2007 0.0020617 9 11 0

17 39 4 2008 0.0008186 3 11 0

17 39 4 2009 0.0026792 1 11 0
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Table 4.4. Hypothetical example of fractional logit regression results using selected “best” 

weather variables for the state: corn in climate division 5, Illinois (17) and soybeans in climate 

division 1, Indiana (18).

Corn: Climate Division 5, Illinois

 

 Analysis Of Maximum Likelihood Parameter Estimates 

 

 Standard Wald 95% Wald 

Parameter DF Estimate Error Confidence Limits Chi-Square Pr > ChiSq 

 

Intercept 1 -17.6357 15.7925 -48.5884 13.3171 1.25 0.2641 

total_cdd 1 0.0101 0.0181 -0.0254 0.0456 0.31 0.5774 

jaj_cdd 1 0.0055 0.0333 -0.0598 0.0707 0.03 0.8692

Criteria For Assessing Goodness Of Fit 

 

Criterion DF Value Value/DF 

Deviance 27 0.5804 0.0215 

Scaled Deviance 27 0.5804 0.0215 

Pearson Chi-Square 27 0.5873 0.0218 

Scaled Pearson X2 27 0.5873 0.0218 

Log Likelihood -2.7963 

Number of Observations Used 30

Soybeans: Climate Division 1, Indiana

 

 Standard Wald 95% Wald 

Parameter DF Estimate Error Confidence Limits Chi-Square Pr > ChiSq 

 

Intercept 1 -4.9453 3.2812 -11.3764 1.4857 2.27 0.1318 

ja_pdsi_n 1 -0.8383 1.4242 -3.6296 1.9531 0.35 0.5561 

ja_pdsi_p 1 0.2246 1.3966 -2.5127 2.9619 0.03 0.8722

Criteria For Assessing Goodness Of Fit 

 

Criterion DF Value Value/DF 

Deviance 27 0.4373 0.0162 

Scaled Deviance 27 0.4373 0.0162 

Pearson Chi-Square 27 0.5476 0.0203 

Scaled Pearson X2 27 0.5476 0.0203 

Log Likelihood -2.5996 

Number of Observations Used 30

Note: All fractional logit results for all “state-climate division-crop” combinations are available 

from the authors upon request.
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Table 4.5. Weather variables chosen for each state to calculate the weather index based on the 

out-of-sample competition: A hypothetical example for corn.

state Weather Variable Combinations

Mean squared

error

1 ja_pdsi_n ja_pdsi_p 5.1859665

4 ja_pdsi_n ja_pdsi_p 0.1061328

5 total_cdd jaj_cdd 9.7063898

6 total_cdd jaj_cdd 1.8864413

8 total_cdd jaj_cdd 0.5599298

9 ja_pdsi_n ja_pdsi_p 1.8823582

10 ja_pdsi_n ja_pdsi_p total_cdd jaj_cdd 0.3794463

12 total_cdd jaj_cdd 0.9065109

13 total_cdd jaj_cdd 7.304132

16 total_cdd jaj_cdd 1.4533495

17 total_cdd jaj_cdd 0.9245507

18 total_cdd jaj_cdd 0.9172543

19 total_cdd jaj_cdd 1.3256818

20 mj_pdsi_n mj_pdsi_p ja_pdsi_n ja_pdsi_p 3.0718882

21 ja_pdsi_n ja_pdsi_p 1.1527433

22 mj_pdsi_n mj_pdsi_p 7.3063892

23 ja_pdsi_n ja_pdsi_p 2.1138152

24 ja_pdsi_n ja_pdsi_p 3.0374947

25 total_cdd jaj_cdd 0.6621126

26 total_cdd jaj_cdd 6.7038752

27 total_cdd jaj_cdd 3.8878839

28 total_cdd jaj_cdd 10.240115

29 mj_pdsi_n mj_pdsi_p ja_pdsi_n ja_pdsi_p 2.141111

30 mj_pdsi_n mj_pdsi_p total_cdd jaj_cdd 2.4403504

31 ja_pdsi_n ja_pdsi_p 0.4422113

33 ja_pdsi_n ja_pdsi_p 0.1377493

34 ja_pdsi_n ja_pdsi_p 1.5424982

35 total_cdd jaj_cdd 4.1921117

36 total_cdd jaj_cdd 4.940591

37 mj_pdsi_n mj_pdsi_p ja_pdsi_n ja_pdsi_p total_cdd jaj_cdd 3.6997904

38 mj_pdsi_n mj_pdsi_p ja_pdsi_n ja_pdsi_p total_cdd jaj_cdd 9.0963143

39 mj_pdsi_n mj_pdsi_p ja_pdsi_n ja_pdsi_p 0.9783726

40 total_cdd jaj_cdd 8.4841414

41 ja_pdsi_n ja_pdsi_p 0.461521
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42 ja_pdsi_n ja_pdsi_p 4.7989437

44 mj_pdsi_n mj_pdsi_p ja_pdsi_n ja_pdsi_p 0.3507331

45 total_cdd jaj_cdd 5.3265052

46 mj_pdsi_n mj_pdsi_p 6.1671228

47 mj_pdsi_n mj_pdsi_p ja_pdsi_n ja_pdsi_p 0.9630748

48 mj_pdsi_n mj_pdsi_p 6.7365194

49 ja_pdsi_n ja_pdsi_p 0.4809822

50 ja_pdsi_n ja_pdsi_p 0.9504381

51 mj_pdsi_n mj_pdsi_p ja_pdsi_n ja_pdsi_p 1.8095605

53 ja_pdsi_n ja_pdsi_p 0.1583591

54 total_cdd jaj_cdd 6.3146905

55 total_cdd jaj_cdd 3.8595231

56 mj_pdsi_n mj_pdsi_p 2.7716175
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Table 4.6. Hypothetical example of climate divisions flagged as statistically insignificant in 

Indiana (State=18), Iowa (State=19), and Kansas (State=20) for corn.

State Climate division Correlation P value

Flag =1 if 

insignificant

18 1 0.697348 1.849E-05 0

18 2 0.8206735 2.804E-08 0

18 3 0.703589 1.442E-05 0

18 4 0.6154699 0.0002946 0

18 5 0.6592917 7.421E-05 0

18 6 0.7147064 9.123E-06 0

18 7 0.4857597 0.0065023 0

18 8 0.5676294 0.0010696 0

18 9 0.4039534 0.0268396 0

19 1 0.1176057 0.5359587 1

19 2 0.087774 0.6446394 1

19 3 0.4513596 0.0122938 0

19 4 0.2842945 0.1278601 1

19 5 0.4576954 0.0109846 0

19 6 0.8277632 1.67E-08 0

19 7 0.2724787 0.1451881 1

19 8 0.5400418 0.0020673 0

19 9 0.7837669 3.015E-07 0

20 1 0.8007809 1.072E-07 0

20 2 0.8111501 5.434E-08 0

20 3 0.7218704 6.715E-06 0

20 4 0.732416 4.203E-06 0

20 5 0.8057017 1.341E-07 0

20 6 0.8578067 1.388E-09 0

20 7 0.6950983 2.019E-05 0

20 8 0.4734226 0.0082312 0

20 9 0.9378357 2.15E-14 0

Note: If the Flag (last column) is equal to one then the fractional logit regression model is 

deemed to be insignificant (i.e. the correlation between actual and weather indexes has a p-value 

> 0.1) or the correlation is negative.
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Table 4.7. Hypothetical example of bin classification for soybeans in Mississippi (State=28) 

climate division 1 (1980-2009).

State

Climate 

Division Year

State proxy

flag=1 if used 

state predicted 

values Bin Classification

No of Bins for 

the Climate 

Division

Flag =1 if 

insignificant

28 1 1980 0 4 10 0

28 1 1981 0 8 10 0

28 1 1982 0 2 10 0

28 1 1983 0 5 10 0

28 1 1984 0 4 10 0

28 1 1985 0 8 10 0

28 1 1986 0 9 10 0

28 1 1987 0 1 10 0

28 1 1988 0 10 10 0

28 1 1989 0 8 10 0

28 1 1990 0 4 10 0

28 1 1991 0 6 10 0

28 1 1992 0 5 10 0

28 1 1993 0 2 10 0

28 1 1994 0 4 10 0

28 1 1995 0 1 10 0

28 1 1996 0 1 10 0

28 1 1997 0 5 10 0

28 1 1998 0 10 10 0

28 1 1999 0 5 10 0

28 1 2000 0 8 10 0

28 1 2001 0 5 10 0

28 1 2002 0 4 10 0

28 1 2003 0 5 10 0

28 1 2004 0 3 10 0

28 1 2005 0 7 10 0

28 1 2006 0 9 10 0

28 1 2007 0 8 10 0

28 1 2008 0 6 10 0

28 1 2009 0 4 10 0

28 1 2010 0 10 10 0

Note: The state proxy flag is equal to 1 if there are not enough observations (n>10) in the climate divisions to run a 

credible fractional regression model and calculate a weather index.
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Table 4.8. Hypothetical example of unweighted and weather weighted loss costs at the countylevel for Boone County (county=15), Dallas County (county=49), and Grundy County 

(county=75), IA (State=19).

State

Climate 

Division County

County Average loss 

costs

Flag =1 if 

insignificant

Weighting 

Type

19 5 15 0.0096378 0 1

19 5 15 0.0076921 0 2

19 5 15 0.0028386 0 3

19 5 15 0.0027737 0 4

19 5 15 0.0035587 0 5

19 5 15 0.0033862 0 6

19 5 49 0.0100697 0 1

19 5 49 0.0097928 0 2

19 5 49 0.0058953 0 3

19 5 49 0.0058029 0 4

19 5 49 0.007514 0 5

19 5 49 0.0075715 0 6

19 5 75 0.0091694 0 1

19 5 75 0.0051299 0 2

19 5 75 0.001323 0 3

19 5 75 0.0010593 0 4

19 5 75 0.0044935 0 5

19 5 75 0.0032308 0 6

Note: Weighting type = 1 if the average loss cost is calculated with no weather weighting and no 

censoring; Weighting type =2 if the average loss cost is calculated with weather weighting but no 

censoring; Weighting type = 3 if the average loss cost is calculated with censoring at the 80th

percentile and no weather weighting; Weighting type = 4 if the average loss cost is calculated 

with censoring at the 80th percentile and with weather weighting; Weighting type = 5 if the 

average loss cost is calculated with censoring at the 90th percentile and no weather weighting; 

Weighting type = 6 if the average loss cost is calculated with censoring at the 90th percentile and 

with weather weighting.
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Table 4.9. Liability weighted national average (across counties) of unweighted and weather 

weighted average loss costs for apples, barley, corn, cotton, potatoes, rice, sorghum, soybeans, 

spring wheat and winter wheat.

Crop

No. of 

Counties

Unweighted 

loss costs (no 

censoring)

Weather 

weighted loss 

costs (no 

censoring)

Unweighted 

loss costs 

(censoring at 

80th)

Weather 

weighted loss 

costs 

(censoring at 

80th)

Unweighted 

loss costs 

(censoring at 

90th)

Weather 

weighted loss 

costs 

(censoring at 

90th)

apples 140 0.1839529 0.1756118 0.1509251 0.1458255 0.1722479 0.1649113

barley 646 0.1033683 0.0952631 0.071994 0.0677116 0.088203 0.0820236

Corn 1930 0.0505333 0.0525652 0.028726 0.0293841 0.0394102 0.0409063

cotton 437 0.143511 0.1459077 0.1103868 0.1110684 0.1292813 0.1305584

potatoes 128 0.083174 0.0807186 0.0659818 0.0646853 0.0752233 0.0730846

Rice 84 0.0263574 0.0251909 0.015527 0.0148564 0.0203618 0.0193536

sorghum 750 0.1208383 0.1317581 0.0887164 0.09226 0.1079448 0.1140653

soybeans 1523 0.0542112 0.0538458 0.0384229 0.0379807 0.0467105 0.0460899

spring wheat 244 0.1218715 0.1171909 0.0887732 0.0872793 0.1094074 0.1063092

winter wheat 951 0.0982152 0.0852073 0.0719574 0.065563 0.0851164 0.0759965

Note: These are the liability-weighted, national average loss costs across all counties (i.e., 

liability weighted average) 
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Figure 4.1a. Map of U.S. climate divisions.

(Established by the National Climate Data Center of NOAA)
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Figure 4.1b. County assignment to climate divisions delineated within states.
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b. Proposed Non-Stationarity Loss Cost Adjustments 

Based on the discussion of non-stationarity of loss costs in section three, we conducted several 

empirical analyses to quantify these effects where possible. Ultimately, a combination of 

regression analysis and a credibility weighting scheme was selected. Based on regression 

analysis, the most consistent and robust difference in loss costs is represented by a fixed effect 

for the pre-1995 period. We also recommend an approach that gives more weight to 

observations with more insured acres. 

Regression Adjustment for the Change in Participation

Because we are attempting to measure broad effects such as technological change or significant 

program changes, our analysis is conducted by aggregating crop/climate division data to the 

crop/state level. Also note that because of the issues discussed in our analysis of weather effects 

we include the weather variables aggregated to the state level. This allows us to evaluate 

program non-stationarity while controlling for unique weather events that may drive the 

observed loss costs in the 1990-2009 data. The model applied is of the form: 

adj_yr_lcr = f(pre-1995, weather variables).

We suggest estimation with the fractional logit procedure used for developing the weather index. 

The Pre-1995 variable takes a value of 1 if crop year is prior to 1995. This variable is posited to 

capture differences in expected loss costs before and after the fundamental program changes that 

took place in 1995. No state/crop result is reported if there were not at least 15 years of loss cost 

data for the state. We also required at least 20,000 acres insured in the year except for apples 

where the limit was lowered to 5000 acres. Our previous analysis evaluated state, regional and 

national level estimates of the pre-1995 effect. In our opinion there is a trade-off between 

allowing regional variation of the pre-1995 effect and robustness of national estimates. 

Therefore we do not make a specific recommendation as to what level of aggregation should be 

used.

Weighting Approaches

In addition to the estimated pre-95 effect, we recognize program experience based on more data 

is more credible. Thus, we recommended net acre weighting. In this approach, we use the 

county level net acres insured as weights to account for credibility and recency. The county level 

net acre variable is a “proxy” for recency weights given that it has generally been increasing over 

time (from 1980 till the 2000s) (See Figure 3.3). 

Summary
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For the major commodity crops (e.g., corn, soybeans, spring wheat, and cotton), accounting for 

recency using all the weighting approaches above generally reduces the average loss costs 

compared to when recency is not accounted for. But for other crops like apples and sorghum, 

recency weighting generally increases the liability weighted average loss cost at the national 

level.

Liability average loss costs for corn, soybeans, spring wheat and cotton tend to be lowest under 

the linear weighting or net acre weighting procedure. It should be noted, however, that the 

resulting liability-weighted average loss costs for all the recency weighting schemes described 

above are similar to the approach of simply using 20 years of the most recent data in the 

calculation (See Table 4.11). Hence, there is appeal to using the “most recent 20 years” approach 

to account for recency because of its simplicity in implementation compared to the other 

approaches described above.

Using Shortened Loss Cost Series for Base Rates

Table 4.11 reports the national level averages from an analysis that reflects another alternative 

means to address non-stationarity in program loss cost expectations. These results largely follow 

the same approach as reported in Table 4.9. However, in this analysis data from earlier years are 

omitted from the base rate calculation if it more than 20 years old. The approach assumes that a 

longer time series would be used to quantify the catastrophic load. The results in Table 4.11 are 

derived by conducting the weather weighting procedure described earlier, but then any data older 

than 20 years is dropped from the binning step of the process. 

The table reflects three scenarios relative to the catastrophic load. First, we present the no 

censoring scenarios which use the full loss cost record and ignore catastrophic loading, then we 

report estimates assuming the loss cost is censored at the 80th or the 90th percentile. In each 

scenario we report both weather –weighted and unweighted results. All results are report as a 

percentage of the Table 4.9 results. Values greater than 100% indicate that the shorter series 

would increase rates relative to using 30 years of data, while values of less than 100% indicate 

that current rates would be lowered by shortening the base rate series. Within a crop the results 

are largely consistent across censoring scenarios. For example, all values for apples are above 

100% while all values for barley are less than 100%. 

The results for apples, cotton and winter wheat indicate that limiting loss cost histories to 20 

years would lead to substantially higher rates. Conversely, barley, corn, soybeans and spring 

wheat all are observed to have substantially lower rates. Note that significant variation is 

observed within a crop. 

 
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Table 4.11. Aggregate implications of shortening loss cost history to twenty years.

20 year loss cost as a percentage of 30 year loss cost 

Crop No. of 

Counties

Unweighted 

loss costs 

(no 

censoring)

Weather 

weighted 

loss costs 

(no 

censoring)

Unweighted 

loss costs 

(censoring 

at 80th)

Weather 

weighted 

loss costs 

(censoring 

at 80th)

Unweighted 

loss costs 

(censoring 

at 90th)

Weather 

weighted 

loss costs 

(censoring 

at 90th)

Apples 138 106% 106% 107% 107% 107% 107%

Barley 629 80% 85% 89% 92% 84% 88%

Corn 1914 82% 88% 88% 90% 86% 89%

Cotton 431 106% 97% 109% 103% 109% 101%

Potatoes 127 97% 98% 100% 100% 99% 100%

Rice 83 82% 90% 97% 98% 92% 96%

Sorghum 727 101% 102% 101% 102% 102% 104%

Soybeans 1512 84% 87% 84% 87% 84% 87%

Spring 

wheat

242 86% 96% 90% 95% 87% 94%

Winter

wheat

937 104% 105% 109% 107% 108% 107%
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c. Illustration of Combined Base Rating Procedures

The proposed procedure involves four primary changes to the current simple averaging of 

historical loss cost:

1. A pre-1995 adjustment, 

2. Weather weighting, 

3. Net acre weighting within probability bins, and

4. The use of a 20 year moving average of loss data.

To illustrate how these adjustments will be integrated with each other and into the RMA base 

rating system we provide a detailed illustration for corn in climate division 5 of Illinois. First a 

flow chart is provided in Figure 4.3 which provides an overview of the eight step process. 
Methodology Analysis for Weighting Historical Experience –

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Methodology Analysis for Weighting Historical Experience –

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50

Having given a general overview, a more detail explanation is provided next. We illustrate the 

process of calculating the expected loss cost when the following adjustments are accounted for: 

pre95 adjustment, weather weighting, net acre weighting, and use of 20 years of loss data. The 

example here utilizes data from the state of Illinois (17) and uses all the counties within climate 

division 5 (eastern climate division). Climate division 5 in Illinois is composed of the following 

counties: Champaign (19), Ford (53), Iroquois (75), Kankakee (91), Livingston (105), Piatt 

(147), and Vermillion (183).

The first step in the reweighting process is to combine the weather and loss data at the county 

level. In this case, all counties within a climate division have the same weather data. After this 

step, the pre-95 adjustment factors are applied to all data prior to 1995. Table 4.12 shows an 

example of how average loss costs are different with and without the pre95 adjustment factors 

applied to county level data (for corn).

After applying the pre95 adjustments, the data are aggregated up to the climate division level. 

These climate division data are then used in the fractional regression model to determine the 

“optimal” combinations of weather variables used in each state and to create predicted values 

that serve as the “weather index” to classify each year (from 1895- present) based on the longterm weather behavior in the climate division. An example of the weather indexes is seen in 

Table 4.13 for Illinois climate division 5.

The weather indexes at the climate division level are then used to classify each year into bins 

(i.e. years within the bins are years with similar weather). In this binning process, the number of 

bins is determined by looking at the 20-year period from 1991-2010 and making sure that there 

are no “empty bins” (i.e. each bin category is represented in this 20-year period). Fifteen (15) 

years is the initial number of bins investigated and if not all fifteen bins are represented in the 

latest 20-year period then 14 bins are examined (and so on). This process is continued until we 

find the largest number of bins where all bin categories are represented in the 20-year period (i.e. 

this process goes from 15 bins to as few as 5 bins). An example of the result of this binning 

process can be seen in Table 4.14 for Illinois climate division 5. In this case, there are 11 bins 

and all bins (from 1 to 11) are represented in the 1991-2010 period. Note that some bins have 

more years in them than others. As mentioned in p. 28-29 above, a county-level binning process 

is also implemented if there are counties with less than 20 years of data since these missing 

observations could also result in empty bins. But in this example, all counties have the full 20 

years of actual data and, therefore, the climate division level bin classification is the only one 

used here. In addition, the “optimal” number of bins is 11 and so the minimum threshold of five 

bins is not reached. 

The next step is merging the binning results (at the climate division level) to the county level 

actual loss cost data censored at the 90th percentile (See Table 4.15). This is the data set used for 

calculating the averages within bins and the overall average (average of the average within bins). 
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The average of the “average within bins” is the final result we are interested in (i.e., the final 

base premium estimate where all the adjustments in the first paragraph above are applied).

In Table 4.16, we show the average within bins for two counties in climate division 5 of Illinois. 

Note that the averages within bins are “net acre weighted” averages. This net acre weighting 

generally gives more weight to more recent years within bins (since more recent years typically 

have more insured acres).

After calculating the net-acre-weighted averages within bins, the average across all the bins (11 

bins in Table 4.16) is calculated. This is the base premium rate. The averages across bins for 

counties in Illinois climate division 5 is reported in Table 4.17.
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Table 4.12. Average loss cost ratios (LCR) for counties in Illinois climate division 5 (Corn; 

1980-2010): With and without pre95 fixed adjustment.

County Average LCRs

without pre95 adjustment

Average LCRs

with pre95 adjustment

Champaign (19) 0.0193 0.0124

Ford (53) 0.0374 0.0229

Iroquois (75) 0.0299 0.0191

Kankakee (91) 0.0307 0.0197

Livingston (105) 0.0355 0.0222

Piatt (147) 0.0132 0.0085

Vermillion (183) 0.0275 0.0176
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Table 4.13. Predicted LCRs from the fractional logit regression for Illinois climate division 5 

Corn; 1980-2010).

Crop Year Net Acres Actual Loss cost ratio Weather index

1980 46666 0.068 0.023

1981 99413 0.001 0.002

1982 72679 0.001 0.001

1983 35962 0.092 0.045

1984 147325 0.015 0.006

1985 171342 0.001 0.000

1986 196450 0.005 0.008

1987 189592 0.003 0.008

1988 203502 0.156 0.145

1989 890345 0.001 0.001

1990 667228 0.001 0.001

1991 590842 0.114 0.128

1992 865613 0.001 0.000

1993 798127 0.005 0.004

1994 858636 0.000 0.002

1995 888169 0.034 0.033

1996 834373 0.004 0.001

1997 838033 0.004 0.001

1998 832875 0.003 0.015

1999 890781 0.001 0.009

2000 964957 0.000 0.001

2001 946922 0.002 0.001

2002 970740 0.007 0.019

2003 1015135 0.001 0.001

2004 1049753 0.001 0.001

2005 1068085 0.004 0.025

2006 970250 0.004 0.004

2007 1214946 0.000 0.011

2008 1246866 0.001 0.002

2009 1357670 0.001 0.001

2010 1320642 0.007 0.040

Note: The predicted LCRs above serve as the “weather index” that allows for classification of all 

years based on the long-term weather pattern. Predicted values are available from 1895 to the 

present but the values reported above are only from 1980-2009.
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Table 4.14. Bin Classification for Illinois climate division 5 (Corn; 1991-2010). 

Crop Year Weather index Bin Classification Number of Bins in 

Climate Division

1991 0.128 11 11

1992 0.000 1 11

1993 0.004 6 11

1994 0.002 4 11

1995 0.033 10 11

1996 0.001 2 11

1997 0.001 1 11

1998 0.015 9 11

1999 0.009 7 11

2000 0.001 3 11

2001 0.001 3 11

2002 0.019 9 11

2003 0.001 2 11

2004 0.001 2 11

2005 0.025 10 11

2006 0.004 5 11

2007 0.011 8 11

2008 0.002 3 11

2009 0.001 2 11

2010 0.040 10 11
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Table 4.15. Bin classification data at the climate division 5 level merged with the county level 

actual loss cost data for Champaign (19), Illinois (Corn, 1991-2010).

Crop 

Year

Net 

Acres

County Actual 

Loss cost ratio

Climate division 

Weather index

Bin 

Classification

Number of Bins in 

Climate Division

1991 61179 0.086 0.128 11 11

1992 96491 0.000 0.000 1 11

1993 94245 0.001 0.004 6 11

1994 99534 0.000 0.002 4 11

1995 114330 0.049 0.033 10 11

1996 116142 0.000 0.001 2 11

1997 121611 0.001 0.001 1 11

1998 123625 0.002 0.015 9 11

1999 148622 0.000 0.009 7 11

2000 154932 0.000 0.001 3 11

2001 160025 0.001 0.001 3 11

2002 171460 0.005 0.019 9 11

2003 168850 0.000 0.001 2 11

2004 171604 0.001 0.001 2 11

2005 169562 0.000 0.025 10 11

2006 161666 0.001 0.004 5 11

2007 195712 0.000 0.011 8 11

2008 195980 0.001 0.002 3 11

2009 225837 0.000 0.001 2 11

2010 211735 0.003 0.040 10 11
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Table 4.16. Net Acre weighted Average loss costs within bins for Champaign and Ford counties, 

Illinois (Corn, 1991-2010).

County Bin Classification No. of years averaged Average loss costs 

within bins

Champaign (19) 1 2 0.00040

Champaign (19) 2 4 0.00032

Champaign (19) 3 3 0.00053

Champaign (19) 4 1 0.00009

Champaign (19) 5 1 0.00115

Champaign (19) 6 1 0.00089

Champaign (19) 7 1 0.00028

Champaign (19) 8 1 0.00004

Champaign (19) 9 2 0.00363

Champaign (19) 10 3 0.00741

Champaign (19) 11 1 0.02689

Ford (53) 1 2 0.00076

Ford (53) 2 4 0.00062

Ford (53) 3 3 0.00040

Ford (53) 4 1 0.00012

Ford (53) 5 1 0.00260

Ford (53) 6 1 0.00191

Ford (53) 7 1 0.00030

Ford (53) 8 1 0.00037

Ford (53) 9 2 0.00129

Ford (53) 10 3 0.00661

Ford (53) 11 1 0.01409
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Table 4.17. Average loss costs across the “average within bins” for Illinois counties in climate 

division 5 (Corn, 1991-2010).

County Average loss costs (across bins)

Champaign (19) 0.00378

Ford (53) 0.00264

Iroquois (75) 0.00700

Kankakee (91) 0.00612

Livingston (105) 0.00392

Piatt (147) 0.00183

Vermillion (183) 0.00491

Note: The average loss costs above are the base premium rate estimates for each county where 

the following adjustments/procedures are applied: pre95 adjustment, weather weighting

censoring at the 90th percentile, net acre weighting, and use of 20 years of loss data.
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d. Illustration of Proposed Catastrophic Loading Procedures

The first step in the recommended cat loading procedure is the same as in the current process: 

determine which years in the loss history are above the 90th percentile. (We note that the current 

procedure caps losses at the 80th percentile. Also note the change in catastrophic loading region 

from state to climate division.) We assume that the effect of changes in the program reflected in 

the pre-1995 adjustment apply uniformly to all losses; hence the catastrophe capping calculation 

is applied after the pre-1995 adjustment to the loss cost data. Table 4.18 continues our example 

by showing the determination of the 90th percentile for Champaign County, Illinois, with data 

from 1980 through 2010.

The next step is to determine whether any of the excess losses should be adjusted for highly 

unusual weather. We now rank each loss cost year’s weather index relative to full set of weather 

indexes and determine if any year in our data had weather above the 97th percentile. Figure 4.5 

illustrates this procedure. There are 116 years from 1895 through 2010, so the 4 years with the 

highest weather indexes make up the years above the 97th percentile. For corn in Illinois climate 

district 5, the 4 years with the highest indexes were 1936 (.5006), 1933 (.4408), 1988 (.1449) and 

1991 (.1284). The long term probability of weather as bad as that observed in 1988 is estimated 

at about 3/116 = 2.6%, and we would expect to see weather that bad only once in 39 years, not 

once in 31 years (the number of years in our data). We would expect to see weather as bad as 

1991 about once in 29 years, so its appearance once in the 31 year history is about as expected.

 

We now adjust the excess indemnity for 1988 to reflect the lower long-term probability of the 

weather for that year. Table 4.19 shows this calculation. Because we have 31 years of data 

(1980 through 2010), a simple average of the excess losses would give each year 1/31 (3.2%) 

weight, but we want to limit the weight given to 1988 to 2.6%. We therefore adjust the excess 

losses for 1988 by 2.6%/3.2% = .802 before adding them into the county’s contribution to the 

excess load.

The final step in the process combines the adjusted excess losses for all counties in the climate 

division to determine the cat load for the climate division. The cat load is the sum of the 

adjusted excess losses divided by the sum of the exposures (liability). An illustration is provided 

in Table 4.20.
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Table 4.18. Determination of excess loss costs after pre-1995 adjustment, actual loss cost data 

for Champaign (19), Illinois (Corn, 1980-2010).

Loss pre-1995 After Capped Excess

Year Cost Adjustment Pre95 Adj Loss Cost Loss Cost Liability

1980 0.08319 0.599730 0.04989 0.04989 0.00000 1,198,550

1981 0.00120 0.599730 0.00072 0.00072 0.00000 2,924,223

1982 0.00239 0.599730 0.00143 0.00143 0.00000 2,171,021

1983 0.15678 0.599730 0.09403 0.04989 0.04414 1,215,445

1984 0.01126 0.599730 0.00675 0.00675 0.00000 5,089,301

1985 0.00070 0.599730 0.00042 0.00042 0.00000 5,496,762

1986 0.00136 0.599730 0.00081 0.00081 0.00000 4,864,574

1987 0.00039 0.599730 0.00023 0.00023 0.00000 4,464,462

1988 0.13052 0.599730 0.07827 0.04989 0.02839 4,791,357

1989 0.00073 0.599730 0.00044 0.00044 0.00000 19,197,580

1990 0.00121 0.599730 0.00073 0.00073 0.00000 13,592,310

1991 0.14373 0.599730 0.08620 0.04989 0.03631 12,083,506

1992 0.00026 0.599730 0.00015 0.00015 0.00000 18,539,735

1993 0.00148 0.599730 0.00089 0.00089 0.00000 18,596,087

1994 0.00015 0.599730 0.00009 0.00009 0.00000 21,004,237

1995 0.04905 1.000000 0.04905 0.04905 0.00000 23,880,386

1996 0.00046 1.000000 0.00046 0.00046 0.00000 27,971,377

1997 0.00060 1.000000 0.00060 0.00060 0.00000 26,916,018

1998 0.00210 1.000000 0.00210 0.00210 0.00000 29,561,993

1999 0.00028 1.000000 0.00028 0.00028 0.00000 28,968,497

2000 0.00000 1.000000 0.00000 0.00000 0.00000 28,362,667

2001 0.00077 1.000000 0.00077 0.00077 0.00000 31,574,979

2002 0.00473 1.000000 0.00473 0.00473 0.00000 33,632,325

2003 0.00009 1.000000 0.00009 0.00009 0.00000 35,879,189

2004 0.00052 1.000000 0.00052 0.00052 0.00000 41,574,931

2005 0.00021 1.000000 0.00021 0.00021 0.00000 37,705,030

2006 0.00115 1.000000 0.00115 0.00115 0.00000 33,645,797

2007 0.00004 1.000000 0.00004 0.00004 0.00000 72,988,367

2008 0.00075 1.000000 0.00075 0.00075 0.00000 102,526,794

2009 0.00026 1.000000 0.00026 0.00026 0.00000 102,148,611

2010 0.00265 1.000000 0.00265 0.00265 0.00000 94,752,540

90th %ile 0.04989
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 Figure 4.5. Weather indexes for Illinois Corn, Climate Division 5 (1895-2010).

0

0.1

0.2

0.3

0.4

0.5

0.6

1895 1910 1925 1940 1955 1970 1985 2000

Weather Indexes
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Table 4.19. Weather adjusted excess losses, actual loss cost data for Champaign (19), Illinois 

(Corn, 1980-2010).

Excess Excess Weather Adjusted

Year Loss Cost Liability Losses Probability Adjustment Excess Losses

1980 0.00000 1,198,550 - 19.8% 1.000 - 

1981 0.00000 2,924,223 - 76.7% 1.000 - 

1982 0.00000 2,171,021 - 78.4% 1.000 - 

1983 0.04414 1,215,445 53,647 10.3% 1.000 53,647 

1984 0.00000 5,089,301 - 46.6% 1.000 - 

1985 0.00000 5,496,762 - 98.3% 1.000 - 

1986 0.00000 4,864,574 - 41.4% 1.000 - 

1987 0.00000 4,464,462 - 40.5% 1.000 - 

1988 0.02839 4,791,357 136,007 2.6% 0.802 109,040 

1989 0.00000 19,197,580 - 81.9% 1.000 - 

1990 0.00000 13,592,310 - 77.6% 1.000 - 

1991 0.03631 12,083,506 438,766 3.4% 1.000 438,766 

1992 0.00000 18,539,735 - 100.0% 1.000 - 

1993 0.00000 18,596,087 - 55.2% 1.000 - 

1994 0.00000 21,004,237 - 68.1% 1.000 - 

1995 0.00000 23,880,386 - 14.7% 1.000 - 

1996 0.00000 27,971,377 - 82.8% 1.000 - 

1997 0.00000 26,916,018 - 93.1% 1.000 - 

1998 0.00000 29,561,993 - 25.0% 1.000 - 

1999 0.00000 28,968,497 - 37.9% 1.000 - 

2000 0.00000 28,362,667 - 79.3% 1.000 - 

2001 0.00000 31,574,979 - 81.0% 1.000 - 

2002 0.00000 33,632,325 - 23.3% 1.000 - 

2003 0.00000 35,879,189 - 89.7% 1.000 - 

2004 0.00000 41,574,931 - 84.5% 1.000 - 

2005 0.00000 37,705,030 - 18.1% 1.000 - 

2006 0.00000 33,645,797 - 57.8% 1.000 - 

2007 0.00000 72,988,367 - 33.6% 1.000 - 

2008 0.00000 102,526,794 - 75.9% 1.000 - 

2009 0.00000 102,148,611 - 91.4% 1.000 - 

2010 0.00000 94,752,540 - 12.1% 1.000 - 

Sum 628,420 601,453 
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Table 4.20. Determination of climate division cat load, Illinois Corn Climate Division 5.

County Excess Losses Liability

Champaign 601,453 887,318,651

Ford 274,103 541,515,564

Iroquois 1,638,295 1,172,295,057 

Kankakee 1,072,824 666,762,452

Livingston 4,373,358 1,240,403,411 

Piatt 243,080 436,890,436

Vermilion 1,248,597 640,813,173

Climate Division 9,451,710 5,585,998,744 

Division Cat Load 0.001692
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5. Implications of the Proposed Methods 

As directed by the statement of work for this project, Sumaria has performed a detailed 

investigation of the proposed methodology for weighting, and otherwise adjusting, RMA’s 

historical loss cost data in order to maximize its statistical validity for developing premium rates. 

Our team has also provided analysis of the implications of the proposed approach. This section 

of the report summarizes the effect the proposed approach will have on RMA rates. Because 

corn and soybeans are a priority for implementation our results analysis focuses on those crops. 

Table 5.1 reports national average estimated changes in corn and soybeans base premium rates. 

These results are liability weighted averages of county level data. They are derived by assuming 

catastrophic loading will occur at the 90th percentile in the future rather than at the 80th as has 

been used in the past. The estimated base rate change is calculated by comparing the base rate 

derived using current procedures versus proposed procedures. Current procedures are modeled

using 30 years of adjusted loss cost data and using a simple average of the adjusted loss costs 

after the catastrophic loading procedure is applied. The proposed procedure includes four 

modifications of the current base rating procedure:

1. A pre-1995 adjustment, 

2. Weather weighting, 

3. Net acre weighting within probability bins, and

4. The use of a 20 year moving average of loss data.

The results in Table 5.1 reflect the combined effect of all four modifications. Note that these 

results do not impose restrictions on the annual magnitude of adjustment and do not include the 

catastrophic load portion of the rate. Further, these estimated changes impact only the yield 

portion of a rate and would not alter the price risk portion of a revenue insurance rate. 

The national average change in corn base premium rates is 19.1 percent and 25.2 percent for 

soybeans. However, while the percentage change for soybeans is larger than for corn, the 

national average soybean base rates are also higher. The table also reports a break out for four 

states (Illinois, Indiana, Iowa, and Minnesota). For corn, the percentage rate reduction in all four 

of these states is well above the national average. For soybeans, the rate reduction in Illinois is 

over 43.6 percent, but in the other three states the rate reduction is on par with the national 

average. 

Further disaggregation of the results can be seen in Figure 5.1 which shows county-by-county 

comparisons in a map. These results show even greater heterogeneity across locations. In 

general the greatest percentage rate reduction for corn occurs in major production regions and 

some outlying irrigated counties. While the national average base rate declines 19 percent, there 

are regions with substantial rate increases such as portions of western Kansas and portions of 

New England.
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Figure 5.2 reports the county-level results for soybeans. The variation across counties is 

somewhat less dramatic than for corn. In general, the Corn Belt is observed to have rate 

reductions which are largest in Illinois. Some other regions have similar reduction such as the 

Mid-South. Rate increases are suggested in some Western Plains states and portions of the 

Eastern Seaboard. 
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Table 5.1 Estimated effects on base rates. 

National 

Average

Illinois Indiana Iowa Minnesota

Corn Current Procedure 3.49% 1.66% 2.37% 1.45% 2.33%

Proposed Modification 2.83% 1.04% 1.60% 1.01% 1.31%

Percent change -19.1% -37.7% -32.6% -30.7% -43.8%

Soybeans Current Procedure 4.41% 1.82% 2.31% 1.38% 3.13%

Proposed Modification 3.29% 1.02% 1.77% 1.02% 2.32%

Percent change -25.2% -43.6% -23.3% -25.7% -25.7%
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Figure 5.1. County level changes in estimated base rate for corn.
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Figure 5.2. County level changes in estimated base rate for soybeans.
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Appendix . Research Team Credentials

Our research team includes: Dr. Keith H. Coble, Dr. Barry K. Goodwin, Dr. Rod Rejesus, Ms. 

Marry Frances Miller, Dr. Thomas O. Knight, and Dr. Ryan Boyles. Four of these team members 

(Coble, Goodwin, Rejesus, and Knight) are agricultural economists who have extensive 

experience in conducting risk management research. All of these individuals have active 

ongoing research programs focusing on crop insurance and risk management. In addition, Drs. 

Coble, Goodwin, Rejesus, and Knight have experience working with the RMA and other federal 

agencies on various research projects, as well as established records of successful project 

completion and timely performance. Mary Frances Miller has evaluated various crop insurance 

projects: Experience-based insurance discounts, biotechnology discounts, and aquaculture 

insurance. She also played a central role in our recent review of the APH and COMBO rating 

methodologies. Dr. Boyles is an applied climatologist with experience in using and evaluating 

climate observations and models for applications to crop models and decision systems. He is the 

North Carolina State Climatologist and is Director of the North Carolina State Climate Office at 

NC State University. 

Dr. Keith H. Coble

Dr. Keith H. Coble is a W.L. Giles Distinguished Professor at Mississippi State University. He 

earned his Ph.D. in Agricultural Economics at Texas A&M University in 1993. Dr. Coble came 

to Mississippi State in 1997 after serving as leader of the Crop Risk Management Team at the 

Economic Research Service of the U.S. Department of Agriculture. Dr. Coble has testified three 

times before the Congressional Agriculture Committees regarding government risk policy. His 

research has covered a broad range of risk, agricultural policy, and crop insurance issues, and has 

been frequently published in scientific research journals. He currently serves as the founding 

Chair of the Applied Risk Analysis Section of the Agricultural and Applied Economics 

Association. Dr. Coble has performed numerous analyses for the Federal Crop Insurance 

Corporation and Risk Management Agency including serving as an underwriting reviewer and 

technical expert for the Board of Directors of the Federal Crop Insurance Corporation. Among 

the other issues he has examined for the RMA are: (a) actuarially fair premium rate adjustments 

for optional versus basic units, (b) crop insurance demand, (c) analysis of rate relativities, (d) 

reviews of the Dollar Revenue Plans, (e) review of GRP, (f) review of AGR, (g) experiencedbased discounts, (h) reference yield updating, and (i) APH and Combo Rate Review.

Dr. Barry K. Goodwin

Dr. Barry Goodwin is William Neal Reynolds Professor in the Departments of Economics and 

Agricultural and Resource Economics at North Carolina State University. He holds a Ph.D. in 

economics with a minor in statistics from North Carolina State University. He has written over 

100 publications, including two books. He has held faculty positions at Kansas State University, 

Ohio State University, and North Carolina State University. He has worked on crop insurance 

issues for the past 18 years. He has authored a book on crop insurance that is widely cited. He 

has participated in many insurance plan reviews, including a recent comprehensive review of 

revenue insurance policies. He is a frequent consultant to the Risk Management Agency, and has 

also worked in consultation on actuarial matters with the insurance industry. 
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Dr. Roderick M. Rejesus

Dr. Roderick M. Rejesus is Associate Professor in the Department of Agricultural and Resource 

Economics at North Carolina State University. Prior to this position Dr. Rejesus was an Assistant 

Professor at Texas Tech University. Dr. Rejesus received his M.S. degree at Clemson University 

and his Ph.D. degree at the University of Illinois at Urbana-Champaign. He has an active 

research program that focuses on risk management and crop insurance issues, precision 

agriculture, and other issues related to agricultural economics. Dr. Rejesus has published 

research findings on ex-post moral hazard in crop insurance, determinants of anomalous 

prevented planting claims, the added land and new producer provisions in crop insurance, and 

many other crop insurance related issues. He has been involved in several RMA funded projects, 

namely: Unit Division Structure Review, Premium Rate Discount Project, the Reference Yield 

Update Methodology Project, the Climate Change Impacts on Crop Insurance, and (most 

recently) the Comprehensive Review of the APH Rating Methodology. 

Mary Frances Miller

FCAS, MAAA, FCA, Hon FIA, CPCU, ARe, AIM

Mrs. Miller is a founder and the senior consulting actuary with Select Actuarial Services. With 

more than 20 years of property and casualty actuarial experience, she provides actuarial 

consulting services on several major accounts and is additionally responsible for the professional 

development of the other members. Her expertise is frequently called upon to assist clients in 

making decisions regarding the maintenance and design of their risk management programs. 

Prior to the formation of Select Actuarial Services, Mrs. Miller was the Senior Vice President 

and Chief Actuary for five years at Sedgwick Actuarial Services. As Chief Actuary she 

performed a wide spectrum of actuarial studies and also managed the actuarial staff. Before 

joining Sedgwick in 1993, Mrs. Miller was reinsurance actuary with American States Insurance 

Companies, where her duties included pricing within the Reinsurance Division, as well as the 

design and development of specialized software targeting property catastrophe exposures, case 

reserving for automobile and workers' compensation long-term disability claims, and evaluating 

treaty commutation proposals.

Mrs. Miller graduated with highest honor from the Honors College at Michigan State University 

with Bachelor of Arts degrees in Mathematics and Linguistics. She is a Fellow of the Casualty 

Actuarial Society, a member of the American Academy of Actuaries, a Fellow of the Conference 

of Consulting Actuaries, and a Chartered Property and Casualty Underwriter. She was elected an 

Honorary Fellow of the Institute of Actuaries (UK) in 2005. She has been an active contributor 

to the actuarial profession since achieving fellowship in 1988, and has chaired the CAS 

Professionalism Education Committee, the Education Policy Committee, and task forces on 

mutual recognition and future education planning. She was Vice-President for Admissions of the 

Casualty Actuarial Society from 2000 to 2002, President-Elect in 2003, President in 2004, and 

she chaired the CAS Board in 2005. She has been a member of the Board of Directors of the 

American Academy of Actuaries and is a current member of the Board of Directors of the 

Conference of Consulting Actuaries. As a member of the Actuarial Standards Board 
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subcommittee on reserves, Mrs. Miller was a drafter of ASOP #36, the standard for reserve 

opinions in the United States. 

Career Experience

• Founding Member of Select Actuarial Services in 1999 

• Senior VP and Chief Actuary, Sedgwick Actuarial Services, 1993-1999 

• American States Insurance Company, 1984-1993 

Professional Activities

• Vice President of Admissions of the CAS, 1999-present 

• CAS Representative, International Actuarial Association Education Committee, 2001-

present 

• American Academy of Actuaries Committee on Qualifications, 1999-present 

• Actuarial Standards Board Subcommittee on Reserving Standard, 1997-1999 

• Frequent speaker at PRIMA, RIMS, CAS Loss Reserve Seminar and several statesponsored captive and self-insured organizations 

Education

• Bachelor of Arts Degrees in Mathematics and Linguistics, Michigan State University 

• Obtained FCAS designation in 1988, CPCU in 1995, Associate in Reinsurance in 1993, 

Associate in Management in 1994 

Dr. Thomas O. Knight

Thomas O. Knight is Emabeth Thompson Professor of Agricultural Risk Management in the 

Department of Agricultural and Applied Economics at Texas Tech University. He earned a 

Ph.D. in Agricultural Economics in 1984. Knight’s research program has focused on agricultural 

risk analysis. Since 1990, the primary focus of Knight’s research has been a wide range of issues 

relating to Federal crop insurance programs. Among the issues he has examined are: (a) crop 

insurance demand, (b) actuarial effects of moral hazard in crop insurance, (c) premium rate 

adjustments for optional versus basic units, (d) proper reference yields, and (e) experience-based 

premium rate discounts. Knight has (a) conducted a cost benefit analysis in support of the 

RMA’s implementation of prevented planting and double insurance provisions of the 

Agricultural Risk Protection Act of 2000 (ARPA), (b) completed a review of Dollar Revenue 

Plans of insurance applicable for 13 specialty crops, (c) collaborated in a team that examined the 

effects of crop insurance programs on cotton acreage changes, (d) collaborated in a team that 

examined premium rate relativities for alternative coverage levels, (e) and collaborated in a team 

that conducted a comprehensive review of rating methods used for the APH-based yield and 

revenue insurance programs. Knight also serves as an underwriting reviewer and technical 

expert for the Board of Directors of the Federal Crop Insurance Corporation.

Dr. Ryan Boyles

Dr. Boyles is the State Climatologist and Director, State Climate Office of North Carolina and 

Extension Assistant Professor, Department of Marine, Earth, and Atmospheric Sciences, North 

Carolina State University. 
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His educational background includes a M.S. and Ph.D. in Marine, Earth, and Atmospheric 

Sciences, from NC State University. He has served as the State Climatologist for North Carolina 

since 2006 and was Associate State Climatologist from 2001-2006. In that role his duties 

include oversight of climate services, outreach and extension, research, and systems 

development. He has served as a Member of the North Carolina Legislative Commission on 

Global Climate Change, has been a member of the American Meteorological Society since 1995 

and serves on the AMS Committee on Applied Climatology and Committee on Climate Services 

since 2009. Dr. Boyles has also served on the NC Drought Management Advisory Council for 

over 10 years and has received awards for his work on drought analysis and monitoring.

Dr. Boyles has a proven track record as a practicing climatologist who also conducts rigorous 

research. He has 11 refereed journal articles relating to climatology or meteorology. Several of 

these articles have direct application to agricultural applications. His work has appeared in 

Applied Engineering for Agriculture, Bulletin of the American Meteorological Society, Pure and 

Applied Geophysics, and Natural Hazards. He is quite familiar with the collection and uses of 

historical weather data, the limitations of such data and models derived from these data.