A spatial econometric analysis of loss experience in the U.S. crop insurance program.

ABSTRACT

Patterns in loss-ratio experience in the U.S. corn insurance market are investigated with a spatial econometric model. The results demonstrate systematic geographically related misratings and provide estimates of the impacts of several observable factors on the magnitude of misrating in the program. The model is used to estimate actuarial cross-subsidizations across the primary corn-producing states and counties. The impacts of the primary factors are substantial, resulting in net premium transfers of approximately 26 percent of total premiums annually. The misratings likely have important insurance demand, welfare, and land-use implications.

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Insurance markets are typically best suited for risks that are uncorrelated, occur with high frequency, and have a large number of like participants--among a handful of other standard conditions. Systemic risks (such as in crop production) induce correlation in losses, violating the standard insurability conditions and potentially leading to market failures (Glauber, 2004). Complementary causes of market failures in such systemic risk markets may include capital market imperfections, inadequate reinsurance capacities, capital and information shocks due to unexpected events, fat-tailed distributions that prevent diversification, and agency problems (see, e.g., Froot, 2001; Brown, Kroszner, and Jenn, 2002; Jaffee, 2006; Ibragimov, Jaffee, and Walden, 2008). Private insurance firms typically respond to these risks by restricting the supply of insurance or simply not offering insurance at all (Froot, 2001; Cummins, 2006). In cases of private market failures, government is often persuaded to intervene.

Historically, this has been observed to varying degrees in catastrophic and other systemic risk markets, including those for flood, multiperil crop, earthquake, hurricane, and terrorism insurance. Yet, governments tend to be ineffective in the dual roles of insurance provider and regulator (Priest, 1996; Cummins, 2006; Jaffee, 2006; Michel-Kerjan and Kousky, 2010). As a result, such markets often suffer from severe adverse selection problems (see, e.g., Makki and Somwaru, 2001) and, subsequently, low participation rates (see, e.g., Kriesel and Landry, 2004). Government intervention in insurance markets can also cause price distortions that interfere with the efficient allocation of resources and crowd out private market solutions (Brown, Kroszner, and Jenn, 2002).

Agricultural crop production is characterized by a high degree of systemic risk, as spatially correlated weather events tend to induce correlation in production losses. With the exception of hail insurance (the risks of which are not generally systemic), virtually no private markets for agricultural insurance have historically existed in the United States. Rather, a significant government-sponsored crop insurance program has been in force since the Federal Crop Insurance Act of 1980. The Federal Crop Insurance Program is a unique arrangement between the government and private insurers and has several notable features. First, premiums are heavily subsidized by the government to encourage broad participation. On the delivery side, all policies are serviced and underwritten by private insurers. To induce private insurers to participate in the program, operating expenses are subsidized and losses are reinsured by the federal government. Importantly, insurance rates are set noncompetitively by the U.S. Department of Agriculture's Risk Management Agency (RMA)--the agency charged with administering the program--and market competition through differentiated rates is expressly illegal. The program has experienced rapid growth in participation in recent years and is also sizable program with total premium in 2008 of approximately $9.85 billion and total liabilities of $89.91 billion.

Throughout much of its history the program has been plagued by the perception of problems including the failure of crop insurance to replace other forms of disaster assistance (Glauber, 2004), low perceived operating efficiency (Paulson and Babcock, 2008), concerns about market distorting effects of subsidization (Glauber and Collins, 2002), the perception that the insurance industry is overly rewarded for the risks in which they share (Glauber, 2004), and the need for high premium subsidization to induce participation. In addition, stark disparities in loss experience across crops, regions, and products have led to the perception that the program is not properly rated (see, e.g., Glauber, 2004; Babcock, 2008). This observation is supported by Makki and Somwaru (2001), who find evidence of adverse selection in U.S. crop insurance and conclude that higher risk farmers are undercharged relative to lower risk farmers for comparable insurance. The nonuniform loss performance patterns are important as they imply that premium rates do not reflect the underlying risks accurately and that program benefits are not being distributed equitably--in conflict with a stated objective of the Act. Furthermore, participation in insurance can also significantly impact the producer's underlying income distribution (Schnitkey, Sherrick, and Irwin, 2003) and subsequently the implicit costs of private risk bearing (Chavas and Holt, 1996). Rating deficiencies also impact insurance demand and likely have resource-use and associated welfare implications. In particular, distorted ratings would be expected to impact land-use and cropping decisions (Chavas and Holt, 1996; Young, Vandeveer, and Schnepf, 2001; Lubowski et al., 2006). Negative environmental implications have also been noted due to the fact that the land most likely to move into or out of production as a result of changes in insurance costs tends to be less productive, more vulnerable to erosion, and closer in proximity to imperiled species (Lubowski et al., 2006). Moreover, incentive distortions can arise in markets with systematically low rates, potentially leading to higher average insurance costs and claim frequency (see, e.g., Weiss, Tennyson, and Regan, 2010).

While some research has been conducted identifying empirical disparities in program loss experience (Glauber, 2004; Babcock, 2008; Woodard, Sherrick, and Schnitkey, 2008), limited statistical evidence exists to support conjectures of systematic misratings and to explain why disparities occur. Proponents of the existing rating methods generally maintain that the program is adequately rated and that geographic differentials in losses are simply due to "good weather" or "bad weather" experienced in recent decades in certain regions. In response, the primary purposes of this study are to investigate whether loss experience in the program is geographically inequitable and to quantify factors that are systematically related to relative loss experience. A spatial econometric model of loss ratios is developed using loss data from RMA for corn insurance, which constitutes approximately 47 percent of the Federal Crop Insurance total premium. Several factors are identified that contribute to misratings. One motivation for the analysis is the simple premise that if rates embody all relevant available information, then no set of factors should exist that explains variation in the average loss ratios generated by those rates; the existence of such factors would indicate that the information contained in those factors is not appropriately embodied in the underlying rates, which opens the door for adverse selection problems. The results are then cast in a meaningful policy context by estimating the degree of implied actuarial cross-subsidizations attributable to the identified rating factor deficiencies for the corn insurance program across regions.

ASYMMETRIC INFORMATION AND GOVERNMENT INTERVENTION IN INSURANCE MARKETS

Cohen and Siegelman (2010) point out that one might expect the degree of adverse selection in any particular market to depend intimately on the characteristics of the insurance and the buyers, as well as institutional and regulatory factors. This observation is particularly relevant in the context of understanding the performance of government insurance programs. Relative to government insurance rating, private firms tend to be more efficient at segregating risks and perhaps have more incentives to monitor the policies they underwrite, thereby reducing adverse selection and moral hazard problems (Priest, 1996). Private firms, however, often lack adequate capital capacity to underwrite risks in systemic risk markets (or demand very high-risk premiums). Governments often have capacity to take on such risks but typically invest less in efforts to control information asymmetries, which can lead to fraud, moral hazard, and adverse selection problems (Priest, 1996). Government-run programs also tend to be subject to rating problems, as they often lack the technical capacity and/or incentives to estimate actuarially appropriate rates. These rate-making errors induce inequities across the insurance pool, causing government insurance programs to function in a redistributive role.

As a result of perceived failures in both government insurance programs and private systemic risk insurance markets, researchers have called for investigation into alternative market innovations that would allow for the capitalization of catastrophic and systemic insurance risks (see, e.g., Glauber, 2004; Cummins, 2008). This is motivated by the fact that risks resulting from catastrophic exposures are systemic in nature and thus are naturally more suited for capital markets than insurance markets. Indeed, several markets have begun to develop to address these challenges, including markets for weather derivatives, CAT bonds, and other risk-linked securities. These date back to at least 1992 with the launch of CAT futures (Cummins, 2008). In the case of U.S. crop insurance, however, these innovations so far appear to have been crowded out by the highly subsidized Federal Crop Insurance program.

A BRIEF HISTORY OF LOSS EXPERIENCE IN THE U.S. CROP INSURANCE PROGRAM

The Federal Crop Insurance program is administered by the RMA, which also sets insurance rates for the program (noncompetitively). Private companies underwrite and service the actual policies, but reinsurance and subsidies are provided by the federal government via a specific risk-sharing agreement called the Standard Reinsurance Agreement (SRA). Under the SRA, companies designate individual policies to different reinsurance pools; the reinsurance pools differ in terms of the liability and premium that the company retains. Prior to the 2009 crop year the Federal Crop Insurance Program had a mandated target overall loss ratio of 1.075 as well as a directive to ensure equity across producers and maximize participation. Yet, in addition to the stark differentials in loss experience that have been recognized across both regions and crops (Glauber, 2004; Babcock, 2008), and evidence of significant producer-level adverse selection (Makki and Somwaru, 2001), Approved Insurance Providers' have also shown an ability to adverse select against government via their reinsurance fund designations (Vedenov et al., 2004; Coble, Dismukes, and Glauber, 2007; Ker and Ergun, 2007).

Table 1 shows loss ratios for each program crop for 1995-2007. Corn and soybeans represent the largest programs yet have the lowest average loss ratios for major program crops (0.61 and 0.62). Meanwhile, several other crops experienced high losses for the period, including sunflowers with a loss ratio of 1.51, grain sorghum with 1.16, and tobacco with 2.14. The implied over (under) payments at these loss ratios on an aggregate level are sizable. In 2007 the total premium for the program was approximately $6.56 billion; corn premiums totaled approximately $3.11 billion, or 47 percent of total program premium volume, followed by soybeans at $1.07 billion, or 16 percent (Table 2). These facts--coupled with the fact that corn and soybeans have experienced particularly low historical loss ratios--have led to questions about implicit subsidization for losses on other crops. Similar loss disparities across space have been observed within the corn insurance market itself. Figure 1 shows a map of average county loss ratios for the 12 main corn-producing states for the period 1980-2006 (data from more recent periods displayed similar patterns). Note, persistent nonuniform loss ratio experience suggests underlying rating problems. The map illustrates a strong geographic pattern of low loss experience throughout the central Corn Belt regions, including large areas in Illinois, Iowa, Indiana, and Minnesota. This region represents very high volume, with Illinois, Indiana, Iowa, and Minnesota constituting approximately 50 percent of corn premiums. The remainder of the volume is spread over a number of less intensive and riskier states. Figure 1 also indicates that the areas outside the central Corn Belt have persistently higher relative losses.

[FIGURE 1 OMITTED]

THE MODEL

While the broad-level loss ratio information is well known and informative, less work has been done in terms of investigating why these patterns occur and if they are significant or correctable. To address this issue, a spatial model of loss ratios at the county level is estimated to investigate the impact that systematic factors have on loss experience. Rates are established at the county level; thus, this approach seems appropriate. The expected loss ratio is modeled as

L = X[beta] + [epsilon], (1)

where the dependent variable, L, is an N x 1 vector of expected loss ratios, X is an N x M matrix of systematic factors, [beta] is an M x 1 vector of parameters, e is an N x 1 matrix of error terms, N is the number of observations/locations, and M is the number of systematic factors. If rates embody all information in X, [beta] will be insignificantly different from zero and the intercept will approximate the target loss ratio. If there are systematic misratings, [beta] will have at least one nonzero coefficient. A nonzero [[beta].sub.t] indicates that the respective factor is not accurately embodied in the underlying rates.

HYPOTHESES, POTENTIAL SOURCES OF MISRATINGS, AND CONTROL VARIABLES

There are several potential rating issues that could manifest in geographically inequitable loss experiences. These include: RMA's reliance on uncorrected historical loss cost ratio (LCR) rate making, methods used for determination of guarantees and actual production history (APH) yields, potential mistreatment of intracounty risk heterogeneity, and the application of state excess loads. Hypotheses are developed related to these issues, and systematic factors are identified that can be used to test these hypotheses. The systematic factors identified arguably induce adverse selection into the system (i.e., their omission in the rating structure is a source of adverse selection). While these factors are technically observable, we relate their interpretation to adverse selection in the spirit of Chiappori and Salanie (2000) who point out that "government regulation can introduce adverse selection when it forbids the insurer to condition the contract on some observables" (p. 76). We dichotomize and refer to these resulting effects as related to either local adverse selection effects or global adverse selection effects. Local adverse selection refers to phenomena caused by information asymmetries that affect participation within a region. For example, certain regions may have characteristics that render it more difficult (under a given set of rating and underwriting procedures) to separate high- and low-risk producers, thus increasing adverse selection within the region and contributing to higher insurance costs over time. Global adverse selection refers to phenomena caused by factors that impact the actuarial fairness of rates across regions directly. For example, certain regions may possess characteristics that (under a given rating method) may be expected to always have upwardly or downwardly biased rates relative to other regions. There are also a number of other factors that can impact loss experience, and thus we discuss applicable controls for product type, coverage level differences, and short-sample weather variability.

Loss Cost Ratio Ratemaking 

The RMA primarily uses an LCR approach in deriving rates related to yield risk (Josephson, Lord, and Mitchell, 2000). In its simplest form, it consists of estimating LCRs (which equal indemnities divided by liabilities) for all historical policies; individual LCRs are then averaged (on an unweighted across years basis) to derive base rates for a county. This approach will result in biased rates in the presence of trending guarantees (or liability inflation) unless specific conditions with respect to the yield variance evolution process through time are met (Woodard, Sherrick, and Schnitkey, 2008). Specifically, the LCR approach will result in upwardly biased rates if the liability generating the indemnity increases through time and if the underlying variability is constant through time. RMA does not account for yield trends in their rating, and for corn, yield trends are clearly positive. Woodard, Sherrick, and Schnitkey (2008) show that rating biases that result from the RMA's use of LCR are often well in excess of 100 percent. Over time, we would expect high trend regions to have a disincentive to participate relative to lower trend regions, thus inducing (global) adverse selection into the system. This relationship presents the following testable hypothesis:

[H.sub.1]: Expected loss ratios are not impacted by yield trends.

Determination of Guarantees

Another potential source of rating error in the RMA methodology is related to the determination of APH yields that are used to calculate yield guarantees/liabilities. APH yield is typically calculated using a minimum of 4 and up to 10 years of past producer data. Yields--and subsequently guarantees--trend through time due to changes in technology. Failure to account for trend in APH causes guarantees to be biased downward (Skees and Reed, 1986). Since the indemnity function is convex with respect to APH, rates would be expected to be biased upward in areas with high trend bias (Carriquiry, Babcock, and Hart, 2008). That is, APH bias due to ignoring trend is expected to cause upward rate biases under the RMA's rate making via the determination of guarantees. This trend bias implies that areas with high trend would have lower loss ratios (H1), but via a different mechanism than through the LCR calculation.

The APH measure also does not take into account whether the set of years for which any particular farm's yields are available represents a "typical" set of years, and thus the efficiency of the APH measure is low (Skees and Reed, 1986). The inefficiency of the APH measure has the potential to induce detrimental adverse selection effects. For example, two producers with identical underlying yield distributions could receive APHs that are higher or lower than their "true" expected yield simply based on the particular set of years in which production is reported. As a result, regions with higher yield risk (and higher APH inefficiency) may be expected to experience higher degrees of (local) adverse selection related to this effect, and thus have higher expected loss ratios over time, versus counties with less yield variability. Thus, to the extent that higher risk areas experience higher degrees of guarantee distortions, these areas may have higher degrees of adverse selection and rate biases, and thus higher relative expected losses, suggesting a testable hypothesis:

[H.sub.2]: Expected loss ratios are not affected by relative yield variability differences.

Intracounty Risk Heterogeneity

RMA makes explicit assumptions regarding risk heterogeneity across insureds based on APH. Specifically, they assume that farms with higher APHs have lower relative risk, and thus those producers receive a lower rate under RMA rating. Yet, Goodwin (1994) presents evidence that indicates only a modest relationship between APH and risk at a local level. This fact, coupled with the APH distortions identified above, suggests that RMA's attempted treatment of intracounty risk heterogeneity itself also lacks efficiency. Thus, as higher risk areas have higher degrees of APH distortions, higher adverse selection may be expected, suggesting that higher risk areas will have higher expected loss ratios (H2). Thus, yield risk serves as a proxy for a source of (local) adverse selection in this respect as well.

State Excess Load Provisions

RMA rates contain a "state excess" load, which is designed to homogenize LCRs among counties by evenly distributing LCRs greater than the 80th percentile back to each county (Josephson, Lord, and Mitchell, 2000). The justification is that observed LCRs above the 80th percentile "lack credibility." While some smoothing is advisable, this procedure may distribute losses of fundamentally riskier counties back to less risky counties. Even Josephson, Lord, and Mitchell (2000) question the state excess load procedure in their evaluation of the RMA's methodology, pointing out that the procedure "possibly [causes] an inequitable shift of catastrophe exposure to lower loss cost areas" (p. 28). This process suggests that regions that are truly higher risk may be expected to have higher expected loss ratios. This observation, coupled with the fact that spatial patterns in yield risk tend to be regional, may result in spatial dependence in misratings due to state excess loads. Note, "overspreading" of catastrophe risk exposure across risk heterogeneous regions can result in long-run persistent (global) adverse selection, as low risk regions will have a disincentive to participate relative to riskier regions. This relationship leads to H3:

[H.sub.3]: County expected loss ratios are not spatially dependent.

The above hypotheses are tested by estimating indexes for yield trends (H1), and yield risk (H2). Furthermore, a spatial econometric specification is employed to model and test for spatial effects (H3).

Control Variables for Product and Coverage Differences, and Short-Sample Weather Variability

The crop insurance program offers several revenue insurance products with yield risk components in addition to the APH yield insurance product, across alternative coverage levels. Average coverage level buy-ups differ substantially across regions and product, and these differences could have impacts on relative loss rates because of the potential interaction of coverage levels and trending APHs in RMA's rating (Woodard, Sherrick, and Schnitkey, 2008). Group risk products--which provide insurance at the county level (not the farm level) and which use a slightly different rate-making methodology--have also gained popularity. Last, small-sample weather variability can have an impact on loss experience in any given subsample. If the period to be analyzed is short, then a measure of short-term adverse growing conditions should be employed to account for this in the estimation. Thus, to control for product mix differences and short-sample weather-related variability across counties, we construct control variables for group product participation, revenue product participation, coverage level elections, and short-term adverse growing conditions.

DATA, EMPIRICAL MODELS, AND VARIABLES

Insurance-related data are obtained from RMA's Summary of Business database (SOB), and yield data from the National Agricultural Statistics Service. The SOB database contains summaries of policy-level information for all policies sold since program inception in 1980, approximately 1.5 million summary records for all crops (approximately 400,000 of which are for corn). Corn is used for all analysis, as it is by far the largest program crop and historically has had the lowest loss ratio of all major program crops. All data and variables are aggregated to the county level. The 12 primary corn production states are used in the analysis (Illinois, Iowa, Indiana, Michigan, Minnesota, Wisconsin, Kansas, Nebraska, North Dakota, South Dakota, Missouri, and Ohio), resulting in 1,024 counties. A summary of all variables is located in Table 3. Table 4 presents the four models to be estimated, as explained below. Table 5 presents summary statistics for all variables. Two proxies of the expected loss ratio are constructed: (1) an average loss ratio that computes the loss ratio for every year and then averages across years and (2) a cumulative loss ratio that computes the loss ratio as the sum of all indemnities across all years divided by the sum of all premiums. The first method gives equal weight to each year of experience, while the latter weights each dollar of policy premium in the database equally. The cumulative measure implicitly gives equal credibility to all historical policy data. Participation in the program has been higher in recent years, and thus the use of a cumulative loss ratio will be more representative of recent experience.

To evaluate consistency and robustness of the empirical analysis, we also construct the average loss ratio that weights the years equally and places more relative weight on policies in years in which less insurance was sold. It could be argued that the average measure embodies a more accurate representation of the relative probabilities of different weather events that could occur. In addition, the expected loss ratios are constructed using data from two different subperiods: a recent subperiod from 2003 to 2006, and the entire sample period from 1980 to 2006 to assess the consistency and robustness (additional motivation and explanation of the sample period choices are provided below). Thus, a total of four different measures of the expected loss ratio (i.e., the dependent variable) are constructed and used in the estimation of Models 1-4, respectively: LR Avg '03-'06, LR Cum "03-'06, LR Avg '80-'06, and LR Cum '80-'06. Explicitly, the cumulative county loss ratio is obtained as [L.sub.c] = [[summation].sup.P,K.sub.p,k] [I.sub.p,c,k]/ [[summation].sup.P,K.sub.p,c,k], where [I.sub.p,c,k] is the indemnity and [[pi].sup.a.sub.p,c,k] is the premium on policy p in county c during time k. The average loss ratio is constructed similarly except the cumulative loss ratio is estimated for each year separately, and then averaged across years.

An average coverage level index (Cover), a group plan participation index (Group), and a revenue plan participation index (Rev) are also constructed using SOB data for the recent period 2003-2006. The coverage level index is calculated as the premium weighted average coverage level, Cove[r.sub.c] = [[summation].sup.P,K.sub.p,k]. [[pi].sup.a.sub.p,c,k] x [Cover.sub.p,c,k]/[[summation].sup.P,K.sub.p,k] [[pi].sup.a.sub.p,c,k,], where [Cover.sub.p,c,k] is the coverage level election on policy p in county c during time k. The Group index is calculated as the premium weighted percentage of policies in group policies calculated as [Group.sub.c] = [[summation].sup.G,K.sub.g,k] [[pi].sup.a.sub.g,c,k]/ [[summation].sup.P,K.sub.p,c,k], [[pi].sup.a.sub.p,c,k], where the subscript g denotes all policies in group policies. The Rev index is calculated as the premium weighted percentage of policies in revenue policies calculated as [Rev.sub.c] [[summation].sup.R,K.sub.r,k] [[pi].sup.a.sub.r,c,k]/ [[summation].sup.P,K.sub.p,k], [[pi].sup.a.sub.p,c,k], where r denotes all revenues policies.

County yield data from NASS are used to calculate trend and relative yield risk (Trend, CV). These variables are also estimated for the subperiods 1975-2002 and 1975-2006. Trend is calculated as the linear trend of yields on time. The coefficient of variation, CV, is a measure of risk obtained by dividing standard deviation by mean yield, r([CV.sub.C]) = [[sigma].sub.c]/[Y.sub.c]. A relative measure is desirable since the mean level of yields differs substantially across regions. SOB data for coverage levels, revenue participation, and group products are not as complete in the SOB database in earlier years, and thus those variables could not be constructed with the data available, and are not included in Models 3-4.

As noted, in addition to the full-sample loss ratio models (Models 3-4, constructed using loss data from 1980 to 2006), we also construct models using loss data from a more recent period, 2003-2006 (Models 1-2). In addition, we construct the control variables for the 2003-2006 subperiod and use a prior period (1975-2002) to construct the Trend and CV measures. There are several reasons for considering alternate sample periods. First, the more recent data are more representative of near-term future since the rating systems used by RMA to generate the rates evolve over time. Also, in some cases we would expect the loss ratio itself to trend downward over time, and thus the full-sample loss ratio would be a biased estimate of the current expected loss ratio (Woodard, Sherrick, and Schnitkey, 2008). In addition, this subperiod contains relatively good production years (e.g., 2004) as well as bad years (e.g., 2005), so overall is not unrepresentative necessarily. Perhaps a more important reason for adopting the sample period setups in Models 1-2 is that constructing a model with an expected loss ratio from a latter period--and Trend and CV variables from an earlier period--provides a stronger test of the impact of Trend and CV on the evolution of expected loss experience under RMA rating. That is, this framework essentially provides a test of the "predictive" power of Trend and CV on loss experience. There is also a good motivation for using nonoverlapping periods. In finite samples there will be a degree of estimation error when estimating the expected loss ratio as well as any systematic factors affected by yields. Because yield outcomes impact the loss ratio directly in a given year, any systematic factors that are calculated using yield data from the same time period used to estimate the expected loss ratio will induce bias in [beta] since their measurement errors will be correlated. This concern is ameliorated if a longer sample is used to construct the expected loss ratio measure. However, if the data used to estimate the expected loss ratio and the yield variables are from the same short period (e.g., 4 years), significant estimation problems remain. Thus, to alleviate this problem data are employed from a period prior to the period used to estimate expected loss ratios when estimating the potential misrating factors that are derived from yields (i.e., Trend and CV).

This framework is advantageous as it allows us to determine whether information embedded in past yields has any power in explaining forward-looking loss ratios. The presence of such effects provides strong evidence regarding whether the RMA rating system is systematically biased across regions due to those factors. A potential drawback is that if a significant relationship is found between Trend and CV from an earlier period and the expected loss ratio from a latter period, it does not rule out that the culprit of the loss experience patterns and an estimate of a relationship was due to abnormal short-sample weather variability during the latter period, which by chance was also highly correlated with the Trend and CV measured from the earlier period.

While it is unlikely that systematically unrelated variables (i.e., Trend and CV in one period, and stark deviations in weather or growing conditions from "normal" in another period) would happen to be correlated, it could create a problem akin to omitted variable bias if it were to occur. Thus, to address this we include a variable to control for any short-sample weather aberrations of this sort in Models 1-2, DownDevRatio, which is equal to average downside county yield deviations from trend in the latter period (2003-2006) divided by those in the former period (1975-2002). In Models 1-2, we expect that it will be positively related to the loss ratio, because areas that experienced worse than "normal" growing conditions during 2003-2006 will be expected to have higher insurance losses than normal, and vice versa.

ESTIMATION, MODEL SELECTION, AND SPATIAL ECONOMETRIC ISSUES

There are two main classes of spatial regression models outlined by Anselin (1988): lag, and error. Spatial lag models include a spatial lag term on the dependent variable. Spatial error models, on the other hand, model the spatial effect not via the dependent variable, but through the error term. The robust LM test indicates that the spatial lag is the preferred model for Models 1-4 (Table 6). Thus, the model estimated is

L = [rho]WL + X[beta] + u (2)

where W is an N x N spatial queen weights matrix, u is an N x 1 vector of errors, and [rho] is the spatial autoregressive coefficient. Under the queen contiguity criterion, two observations are considered neighbors if they share any point or boundary. A spatial lag is similar to a lagged dependent variable in a time-series context except the feedback process is multidirectional and multidimensional. When the data-generating process follows a spatial lag form, application of a simple linear specification that excludes the lag will result in biased and inconsistent estimates (Anselin, 1988). The intuition is that in the presence of multidimensional feedback effects, the spatial lag term [rho]W L will be endogenous (Anselin, 1988).

Diagnostics for heteroskedasticity and normality were also conducted (Table 6). The Jarque-Bera test strongly indicated nonnormal errors. While maximum likelihood and pseudomaximum likelihood approaches to estimating spatial lag models perform well under certain conditions without normality, GMM frameworks are robust to nonnormality and thus are adopted here. Specifically, a spatial two-stage least squares (S2SLS) estimator is employed, which is similar to a standard 2SLS procedure except the independent variables and spatial lags of the independent variables, Q = [x, W X], are used as instruments (Kelejian and Prucha, 1998). Letting Z = [WL, X] be the independent and spatial lag variables and [delta] = [[rho], [beta]] be the parameters, estimates of [delta] are obtained as [[??].sub.S2SLS]=[[Z'Q[(Q'Q).sup.-1]Q'Z].sup.-1]Z'Q[(Q'Q).sup.-1]Q'L.

The Breusch-Pagan and Koenker-Bassett tests indicated the presence of heteroskedasticity (Table 6). The S2SLS estimator is an asymptotic method, so is still consistent in the presence of heteroskedasticity, but the standard errors will be biased. Thus, spatial heteroskedasticity and autocorrelation consistent (SHAC) standard errors of Kelejian and Prucha (2007) are employed that are robust to spatial heteroskedasticity and autocorrelation of an unknown form. The SHAC standard errors use weighted cross-products of the residuals to estimate the covariance matrix, where the weights are determined using a kernel function of the distances between observations. We choose a variable bandwidth parameter that is determined by the distance from each point to its Kth nearest neighbor. Thus, the weight matrix employed by the SHAC estimator is a distance-based matrix; we use a 10 nearest neighbors (10 KNN) matrix, and a triangular kernel function. Following Kelejian and Prucha, we estimate [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is a kernel function, [d.sub.i,j] is the distance between i and j, and d is a bandwidth parameter. The bandwidth is the distance to the 10th nearest neighbor for each observation i. Classical goodness-of-fit measures such as [R.sup.2] are not appropriate in spatial models (Anselin, 1988). Thus, the pseudo-adjusted [R.sup.2] measure is reported to assess model fit.

MODEL RESULTS

Figure I displays a map of average county loss ratios during 2003-2006 and 1980-2006 for the 12-state sample. The cumulative loss ratio measures had very similar patterns (not presented). There are seemingly stark geographic pattern in loss experience across regions. In particular, large regions throughout central Indiana, Illinois, and Iowa appear to have persistently lower loss experience relative to some of the higher risk states. The loss experience patterns for the recent period (not presented) are quite similar to those in Figure 1, indicating that he pattern of loss experience is not likely simply due to subperiod effects or "abnormal" short-run weather.

Even in years when yield losses were relatively high in the low-risk regions, only modest insurance losses are observed. For example, by most accounts 2005 would have been considered a poor production year for Illinois. Illinois state corn yields in 2005 were almost 40 bu./acre below the previous year's yield in 2004. Furthermore, it was the driest year on record since 1994, and the hottest year since 1988 in Illinois (Woodard and Garcia, 2008). Still, the corn loss ratio in Illinois was only about 1.13 in 2005, only modestly above the target loss ratio of 1.075. A less obvious observation is that there are large regions in each state that have abnormally high or low loss ratios relative to the remainder of the state. For example, the lower risk areas throughout central Illinois appear to have lower loss experience relative to the southern- and northern-most sections of the state. Similar situations are evident for Wisconsin and Minnesota. This pattern could be due to the fact that RMA state excess loads redistribute losses from riskier to less risky regions. CV is highly correlated with the expected loss ratio variables, while Trend is strongly negatively correlated (Table 5). This is consistent with the anticipation that CV is positively related to loss experience and vice-a-versa for Trend. Maps of CV and Trend also exhibit a strong spatial correspondence to observed loss ratios (not presented).

Table 7 presents the regression results for the S2SLS loss ratio model. Table 8 presents the total effect sizes and the elasticities calculated at the mean. The total effect sizes are obtained as the estimated coefficient for each variable. The elasticities are calculated as the total effect times the mean of the independent variable, divided by the mean of the dependent variable. Two measures are reported for both the total effect and the elasticities in Table 8, direct and multiplier. Multiplier effects account for the proportion of the independent variable effect that impacts the dependent variable via the spatial lag term, and is calculated as the direct effect multiplied by 1/(1 - [rho]), a result derived from the reduced form (Kim, Phipps, and Anselin, 2003). The interpretation is that the direct effects are the (average) impacts that the independent variables have on the loss ratio taking into account only the own county's independent variable impacts. The multiplier effects are the (average) total impacts of the independent variables on the loss ratio including cross-border spillover effects. Because the independent variables tend to be highly spatially correlated and the spatial effect is positive (i.e., [rho]), the multiplier effect will be emphasized when discussing total effects as they represent total net effects of the independents on the dependent and most closely resemble the familiar interpretation of variable effects in standard nonspatial models (e.g., OLS). Turning attention to the regression results (Table 7), the pseudo-adjusted [R.sup.2] is quite high in all models, ranging from 0.374 to 0.588. The Anselin-Kelejian test (Anselin and Kelejian, 1997) indicates no residual spatial autocorrelation. The effects of the yield variables (Trend and CV), on loss ratios are statistically significant with the "expected signs" (given what is known about RMA rating methods). The magnitudes of the effects for Trend and CV are also large. The estimated elasticities for Trend range from -0.77 percent to -0.38 percent across Models 1-4, and for CV ranged from 0.53 percent to 0.80 percent (Table 8). The interquartile range (IQR) effect gives the implied effect of the independent variables on the expected dependent variable (L) over the interquartile range of the respective independent variable and provides a measure of the impact of the variables over their relevant ranges. The Trend IQR effect is consistently large, ranging in the -0.22 to -0.33 range. That is, a difference in the expected loss ratios for a county exhibiting a Trend in the 25th percentile of all counties versus a county in the 75th Trend percentile is -0.33. The CV IQR effect is large as well, ranging from 0.27 to 0.34. Combined, these results imply that a low-risk/high-trend county (25th percentile) would be expected to have a loss ratio that is about 0.60 lower than a higher risk/lower trend county (75th percentile).This result is striking since Trend and CV are calculated using data for a period prior to the period used to calculate the loss ratio (1975-2002 vs. 2003-2006) and thus that information would already be incorporated into the actual premiums generating relative losses in the latter period if the rating system were efficient and unbiased. This result indicates that past yield information is predictive of future loss ratios--again, a result that is not expected in the presence of accurate rating methods. Figure 2 presents a map of the estimated impact of Trend and CV on expected loss ratios for Model 3 (the map for other models exhibited similar patterns), and reveals again patterns of low expected loss experience throughout the central Corn Belt regions. These results provide novel and striking statistically significant evidence that the low-risk/high-trend regions within the interior Corn Belt are overrated relative to other areas and that the overrating stems from technical issues surrounding RMA rating procedures that appear to be possible to address but that may have been allowed to persist due to bureaucratic or political considerations.

[FIGURE 2 OMITTED]

The spatial lag coefficient, p, is significant and large (0.578-0.709) and indicates strong spatial dependence in loss experience across counties, perhaps due to the RMA's provision of state excess loads, other misrating spillovers, and spatially correlated unobserved variables. Cover is positive and significant in all cases. This result demonstrates that lower coverage level policies are overrated relative to higher coverage level policies, a finding consistent with Woodard, Sherrick, and Schnitkey (2008). The elasticities are quite large as well, ranging from 4.09 percent to 5.02 percent, as are the IQR effects (0.35-0.36). Group is significant and negative, indicating that group policy rates are overstated relative to other products and/or that there are benefits associated with reduced moral hazard and adverse selection that are reflected in lower loss ratios. The magnitude is not great, however, as the elasticity is only about -0.11 percent to -0.09 percent. Rev is positive and significant, but small in magnitude. The DownDevRatio growing condition correction in Models 1-2 is significant and positive as expected. The magnitude of this variable is not fundamentally important or interesting per se, but appropriately accounts for any small-sample weather or growing condition impacts in the 2003-2006 period and is simply interpreted as a sampling variability correction. This variable could also be interpreted as a proxy for changes in risk through time, though with admonition given the unknown relative impacts of sampling variability versus true risk changes in its measurement.

CROSS-SUBSIDIZATION ANALYSIS

Next, the models are used to measure the magnitude of implied actuarial cross-subsidizations due to the biased rating factors, Trend and CV. While we do not measure "welfare" explicitly, the cross-subsidizations convey a sense of the economic magnitude of the potential rating bias. To obtain the estimated cross-subsidizations, first the total multiplier effect coefficients for Trend and CV are multiplied by their respective variables and summed to obtain an estimate of the joint impact on the expected loss ratio for each model. Negative values imply that rates are overstated, and vice versa.

Next, to obtain an estimate of expected cross-subsidizations based on market premium levels, the estimated impact of Trend and CV on the expected loss ratio for each model above is multiplied by the annual average premium in the county during 2003-2006. This provides a measure of the dollar amount of additional premium that would be necessary to offset the expected bias in the loss outcome as implied by Trend and CV. Two methods of aggregating the over/underpayments are constructed to reflect cross-subsidizations: (1) total interstate transfers and (2) total absolute intercounty transfers. The first provides a measure of equality across states, while the latter is an absolute measure that equals the total difference (flow-for-flow distance) between over- and underpaying counties. The total implied cross-subsidizations are then aggregated by state to provide a measure of the magnitude of the implied actuarial cross-subsidizations (Table 9). Note, these measures are all relative to the Trend and CV variables only, and do not address additional cross-subsidization drivers such as those associated with group or revenue products, or those related to treatment of coverage levels. This is done so as to provide a conservative estimate of the impact of only the two primary factors impacting apparent biases in RMA rating. The true size of all including other potential misrating factors could of course be larger in total.

Cross-Subsidization Results

The left panel of Table 9 reports results for interstate transfers, while the right panel is absolute total intercounty transfers (aggregated by state). The interstate cross-subsidizations implied by the models in Table 9 are quite large, ranging from approximately $25 million annually for South Dakota (Model 3) to -$70 million for Iowa (Model 4). In total, the absolute intercounty transfers are quite large as well, with estimates ranging from approximately $177 million (Model 3) to $301 million (Model 1). As a percent of total premium, it is about 26.16 percent, or about $5.69/acre, meaning that on average, every dollar of premium paid into the program represents about a 26.16 percent or $5.69/acre over- or underpayment of premium relative to the expected loss cost. Note that Model 3 should be interpreted with caution since it uses the average loss ratio from 1980 to 2006 as the dependent variable, and we expect this measure to be an upward biased estimate of a forward-looking loss ratio under typical conditions in regions that are becoming relatively less risky and vice versa in regions becoming relatively more risky. Thus, this measure will dampen the size of the impacts and lead to lower than true estimates of the probable transfers. In addition, it is not as representative as the current rating environment. For these reasons, Models 1-2 are likely the best estimates of true expected forward-looking transfers. Notice, Models i and 2 do not vary substantially on any account, indicating that the analysis is not sensitive overall to the use of a cumulative versus an average loss ratio measure in the latter subperiod. Models 3 and 4, on the other hand, do differ significantly because the cumulative measure puts more weight on the latter years in the sample with most of the premium volume falling after 1995, which dwarfs the premiums early in the sample. A notable feature of crop insurance is that the level of premiums trend with prices, as insurance costs are tied to the market price of the insured crop. Recently, the prices of most major grains have risen substantially, causing significant increases in premium levels. Thus, the absolute transfers may be much higher at current prices. For example, at 2007 premium levels the implied cross-subsidizations due only to Trend and CV impacts are roughly $0.7 billion within this 12-state corn market alone.

These results indicate that there are significant disparities between states within the corn program. The results also suggest both global and local sources of adverse selection. What is striking about the systematic factors identified (which are the sources of these adverse selection effects) is that they are in fact observable, and their effects in many cases could be substantially mitigated quite easily; however, RMA seemingly ignores the information embedded in this information in making rates.

Furthermore, the model and results of the policy analysis do not appear to support the conjecture that differences in loss experience are negligible or due to "abnormally good weather" alone. Rather, it appears that the problem is a technical rating deficiency that is manifesting in the form of nonuniform loss experience across regions. The obvious question is "Why does this persist?" One possible reason is that that RMA is technically constrained. Babcock (2008, p. 1) articulates another viable explanation, hypothesizing that "... farmers in certain regions excessively benefit from the program and that members from these regions are protecting the interests of their farmers. Support for this hypothesis comes from Senator Roberts from Kansas and Senator Conrad from North Dakota who have argued that reform of the crop insurance program threatens the viability of the program in those regions that depend most heavily on insurance payments. Specifically, they worry that a drop in crop insurance participation by Corn Belt farmers might force farmers in higher risk areas to pay more for insurance." Thus, while the RMA may recognize the regional disparities, it may be constrained from acting on them (Ker and Ergun, 2007).

CONCLUSION

A spatial econometric loss ratio model is used to present evidence that loss experience is statistically related to observable systematic factors that do not appear to be captured in the RMA's rate making. The systematic effects identified are consistent with expectations regarding RMA's use of historical LCR rate making, determination of guarantees, treatment of risk heterogeneity, and applications of state excess loads. Most strikingly, even after controlling for product mix differences and potential short-sample growing condition effects, historical yield information from a prior period (1975-2002) was still predictive of subsequent loss ratios (2003-2006), suggesting that the geographic disparities are due to systematic and persistent rating biases. The results also indicate that the central Corn Belt regions--which tend to have higher yield trends and lower yield risk--have particularly low expected loss ratios relative to other regions. This finding implies that rates in these regions are overstated and that the federal program benefits are not being equitably distributed. The size of the implied cross-subsidizations is also large. At 2007 premium levels, a conservative estimate of the total cross-subsidization within the corn insurance program alone is approximately $0.7 billion annually. Overall, the results indicate a major ratings breakdown in the program, and past research collectively suggests that the presence of these apparent geographic misratings may be having important demand, land use, and environmental effects, and may also partially explain why such large degrees of premium subsidization have been necessary to induce participation in the program.

It is difficult to object the implications of the evidence developed here as a motivation for future rerating efforts, particularly with respect to issues of trend and RMA use of unadjusted loss cost ratio (LCR) ratemaking methods. Nevertheless, the RMA continues to rely on uncorrected LCR methods even in light of the fact that they may be causing large geographic inequities. This situation is not inconsistent, though, with the general observation of Priest (1996) and others, who observe that government insurance agencies tend to offer premiums to all insureds at prices that do not reflect their actual risk--thus inducing adverse selection problems--and often lack both the incentives and resources to refine their rating procedures.

These findings should be of interest to policymakers due to the fact that the program imposes large costs on taxpayers from an operational standpoint (Paulson and Babcock, 2008; GAO, 2007). Further, the presence of geographic misratings is inconsistent with what is typically considered to be good practice regarding government intervention in insurance markets, in that the government should seek to replicate how an unfettered market would perform in similar situations (Jaffee, 2006). To the extent RMA is constrained in implementing rerating efforts, future research could explore alternative policy structures for implementing a subsidized hybrid crop insurance program--perhaps along the lines implied by Miranda and Glauber (1997) and Woodard and Garcia (2008)--whereby the government could facilitate private insurers in bearing systemic risks by guaranteeing a secondary market for systemic risk hedging instruments (e.g., weather derivatives or state yield indexes) but would not interfere with the rating on products as it does currently.

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DOI: 10.1111/j.1539-6975.2010.01397.x

Joshua D. Woodard is Assistant Professor in the Department of Agricultural Economics at Texas A&M University. Gary D. Schnitkey and Bruce J. Sherrick are Professors, both in the Department of Agricultural & Consumer Economics at the University of Illinois at Urbana-Champaign. Nancy Lozano-Gracia is an Economist at the World Bank. Luc Anselin is Walter Isard Chair and Director, School of Geographical Sciences and Urban Planning, and Director GeoDa Center for Geospatial Analysis and Computation, Arizona State University. Joshua D. Woodard can be contacted via e-mail: [e-mail]. This manuscript is adapted from a chapter of Woodard's PhD dissertation. The authors would like to thank the editor, Georges Dionne, and two anonymous reviewers, as well as Jeffrey R. Brown, Philip Garcia, Nicholas D. Paulson, and seminar participants at Georgia State University, Iowa State University, University of Georgia, New Mexico State University, Purdue University, University of Illinois, and Texas A&M University for helpful comments and suggestions.

TABLE 1
U.S. Loss Ratios by Crop (1995-2007)

                                        Total           Average
Crop             Total Premium       Indemnities          LIZ

Corn             $3,042,192,318      $1,844,134,990      0.61
Cotton           $3,002,109,312      $3,332,465,580      1.00
Soybeans         $2,483,997,682      $1,630,598,368      0.62
Wheat            $2,090,489,798      $2,126,930,106      1.01
Grain sorghum      $439,803,618        $504,747,397      1.16
Sunflowers         $322,748,671        $485,917,308      1.51
Barley             $276,297,131        $323,772,812      1.22
Tobacco            $176,758,319        $415,473,168      2.14
Canola              $83,047,301        $111,142,570      1.41
Peaches             $41,532,888         $80,823,184      1.93
Millet              $26,575,412         $35,579,281      1.51
All other        $2,742,899,703      $2,190,207,003      0.85
Total program   $14,728,452,153     $13,081,791,767      0.88

                                             Yrs. Of
Crop             Total Premium    Cum. LIZ    Data

Corn             $3,042,192,318     0.61       13
Cotton           $3,002,109,312     1.11       13
Soybeans         $2,483,997,682     0.66       13
Wheat            $2,090,489,798     1.02       13
Grain sorghum      $439,803,618     1.15       13
Sunflowers         $322,748,671     1.51       13
Barley             $276,297,131     1.17       13
Tobacco            $176,758,319     2.35        8
Canola              $83,047,301     1.34       13
Peaches             $41,532,888     1.95        9
Millet              $26,575,412     1.34       12
All other        $2,742,899,703     0.80       13
Total program   $14,728,452,153     0.89       13

TABLE 2
Corn Premiums by State (2007)

                   Total Premium    % Share

Illinois             $487,150,800    15.66%
Indiana              $217,509,066     6.99%
Iowa                 $458,246,457    14.73%
Kansas               $150,746,381     4.85%
Michigan              $66,207,946     2.13%
Minnesota            $312,539,452    10.05%
Missouri             $108,736,733     3.50%
Nebraska             $320,828,665    10.32%
North Dakota         $140,314,708     4.51%
Ohio                 $121,500,201     3.91%
South Dakota         $235,507,345     7.57%
Wisconsin            $118,486,289     3.81%
All other states     $372,158,781    11.97%
Total              $3,109,932,824   100.00%

TABLE 3
Variable Definitions

Variable             Description             Definition

LR Avg '03'06    Average County Loss    Annual average of
                 Ratio                  total indemnities
                                        divided by total
                                        premiums for all
                                        policies, recent
                                        subperiod

LR Cum '03-06    Cumulative County      Total indemnities
                 Loss Ratio             divided by total
                                        premiums for all
                                        policies, recent
                                        subperiod

LR Avg '80-'06   Average County Loss    Annual average of
                 Ratio                  total indemnities
                                        divided by total
                                        premiums for all
                                        policies, entire
                                        sample

LR Cum '80-06    Cumulative County      Total indemnities
                 Loss Ratio             divided by total
                                        premiums for all
                                        policies, entire
                                        sample

Rev              Revenue Plan           Premium weighted
                 Participation Index    revenue plan (CRC,
                                        RA, IP)
                                        participation index
                                        (2003-2006)

Cover            Coverage Level         Premium weighted
                 Election Index         coverage level index
                                        for all policies
                                        (2003-2006)

Group            Group Plan             Premium weighted
                 Participation Index    group plan (GRIP,
                                        GRIP-HR or GRP)
                                        participation index
                                        (2003-2006)

Trend '75-'02    Trend (Yield           Linear regression
                 Productivity Gains)    coefficient of
                                        yields on time in
                                        bu.\acre covering
                                        early subsample
                                        (1975-2002)

CV '75-'02       Coefficient of         Standard deviation
                 Variation (Yield       divided by average
                 Risk)                  county yields in
                                        bu.\acre (1975-2002)

DownDevRatio     Ratio of Downside      Ratio of average
                 Yield Deviations       downside deviations
                 Across Sample          in county yield from
                 Periods                trend across sample
                                        periods (2003-2006)/
                                        (1975-2002)

Trend '75-'06    Trend (Yield           Linear regression
                 Productivity Gains)    coefficient of
                                        yields on time in
                                        bu.\acre (1975-2006)

CV '75-'06       Coefficient of         Standard deviation
                 Variation (Yield       divided by average
                 Risk)                  county yields in
                                        bu.\acre (1975-2006)

Variable                Source

LR Avg '03'06    Summary of Business

LR Cum '03-06    Summary of Business

LR Avg '80-'06   Summary of Business

LR Cum '80-06    Summary of Business

Rev              Summary of Business

Cover            Summary of Business

Group            Summary of Business

Trend '75-'02    National Agricultural
                 Statistics Service

CV '75-'02       National Agricultural
                 Statistics Service

DownDevRatio     National Agricultural
                 Statistics Service

Trend '75-'06    National Agricultural
                 Statistics Service

CV '75-'06       National Agricultural
                 Statistics Service

TABLE 4
Model Definitions

Model      Dependent Variables   Independent Variables

Model 1    LR Avg '03'06         Rev, Cover, Group, Trend '75-
                                  '02, CV '75-'02, DownDevRatio

Model 2    LR Cum '03-06         Rev, Cover, Group, Trend '75-
                                  '02, CV '75-'02, DownDevRatio

Model 3    LR Avg '80-'06        Trend '75-'06, CV '75-'06

Model 4    LR Cum '80-06         Trend '75-'06, CV '75-'06

TABLE 5
Summary Statistics

                     LR Avg    LR Cum    LR Avg    LR Cum
                     '03-'06   '03-'06   '80-'06   '80-'06   Cover

Mean                  0.723     0.711     1.125     0.867     0.717
Standard error        0.018     0.019     0.014     0.015     0.002
Median                0.537     0.517     1.085     0.736     0.722
Standard deviation    0.586     0.594     0.452     0.483     0.067
Variance              0.344     0.353     0.204     0.234     0.005
Kurtosis              1.888     2.240     0.677     1.694     0.836
Skewness              1.389     1.479     0.752     1.241    -0.530
Minimum               0.000     0.000     0.142     0.110     0.500
Maximum               3.616     4.089     3.003     3.678     0.892
Range                 3.616     4.089     2.861     3.569     0.392
Correlations
  LR Avg '03-'06      1.000
  LR Cum '03-'06      0.986     1.000
  LR Avg '80-'06      0.508     0.511     1.000
  LR Cum '80-'06      0.827     0.832     0.706     1.000
  Cover              -0.244    -0.272    -0.262    -0.358     1.000
  Group              -0.187    -0.214    -0.158    -0.295     0.655
  Rev                 0.013     0.029     0.072     0.054     0.045
  Trend '75-'02      -0.248    -0.224    -0.368    -0.400     0.102
  CV '75-'02          0.414     0.449     0.440     0.509    -0.522
  DownDevRatio        0.504     0.486     0.196     0.399    -0.317
  Trend '75-'06      -0.468    -0.439    -0.407    -0.547     0.233
  CV '75-'06          0.461     0.486     0.484     0.557    -0.533

                                         Trend      CV        Down
                     Group      Rev     '75-'02   '75-'02   DevRatio

Mean                  0.083     0.644    1.523     0.307      0.646
Standard error        0.005     0.016    0.024     0.006      0.024
Median                0.004     0.664    1.532     0.243      0.463
Standard deviation    0.156     0.525    0.761     0.180      0.772
Variance              0.024     0.275    0.580     0.033      0.596
Kurtosis              6.008   184.290    3.492    10.883     72.465
Skewness              2.442    10.071   -0.387     2.815      5.369
Minimum               0.000     0.000   -3.628     0.066      0.000
Maximum               0.934     0.935    5.432     1.721     13.339
Range                 0.934     0.935    9.060     1.656     13.339
Correlations
  LR Avg '03-'06
  LR Cum '03-'06
  LR Avg '80-'06
  LR Cum '80-'06
  Cover
  Group               1.000
  Rev                -0.177     1.000
  Trend '75-'02      -0.056     0.144    1.000
  CV '75-'02         -0.325    -0.020    0.056     1.000
  DownDevRatio       -0.216    -0.075   -0.041     0.231      1.000
  Trend '75-'06       0.046     0.202    0.909    -0.066     -0.341
  CV '75-'06         -0.398     0.100    0.026     0.871      0.365

                      Trend        CV
                     '75-'06     '75-'06

Mean                  1.645       0.215
Standard error        0.024       0.003
Median                1.688       0.186
Standard deviation    0.764       0.087
Variance              0.583       0.007
Kurtosis              3.332       2.685
Skewness             -0.695       1.464
Minimum              -3.628       0.043
Maximum               5.432       0.720
Range                 9.060       0.678
Correlations
  LR Avg '03-'06
  LR Cum '03-'06
  LR Avg '80-'06
  LR Cum '80-'06
  Cover
  Group
  Rev
  Trend '75-'02
  CV '75-'02
  DownDevRatio
  Trend '75-'06       1.000
  CV '75-'06         -0.117       1.000

Note: Table presents county/level summary statistics for the
dependent variables (LRs) and all independent variables. Cover,
Group, and Rev were calculated using data for 2003/2006 from the
Summary of Business Database. Trend and CV were calculated using
data from the National Agricultural Statistics Service for the
respective sample periods indicated. DownDevRatio was calculated as
the ratio of the average downside deviations in county yields from
trend for (2003-2006)/(1975-2002).

TABLE 6
OLS Diagnostics for Spatial Dependence, Normality, and
Heteroskedasticity

Test                                      Model 1     Model 2

Diagnostics for spatial dependence
  Lagrange multiplier (lag)                505.408     484.719
                                             0.000       0.000
  Robust LM (lag)                          115.021     104.812
                                             0.000       0.000
  Lagrange multiplier (error)              393.983     382.915
                                             0.000       0.000
  Robust LM (error)                          3.597       3.008
                                             0.057       0.082
Normality and heteroskedasticity tests
  Jarque-Bera                            3,221.011   2,254.209
                                             0.000       0.000
  Breusch-Pagan                          3,049.126     453.274
                                             0.000       0.000
  Koenker-Bassett test                     570.944     491.2906
                                             0.000       0.000

Test                                      Model 3      Model 4

Diagnostics for spatial dependence
  Lagrange multiplier (lag)              569.68902    569.689
                                           0.000        0.000
  Robust LM (lag)                         38.337452    38.33745
                                           0.000        0.000
  Lagrange multiplier (error)            565.59867    565.5987
                                           0.000        0.000
  Robust LM (error)                       34.247109    34.24711
                                           0.000        0.000
Normality and heteroskedasticity tests
  Jarque-Bera                            141.3792     348.7232
                                           0.000        0.000
  Breusch-Pagan                           89.99653    256.1454
                                           0.000        0.000
  Koenker-Bassett test                    50.87008    109.3427
                                           0.000        0.000

Note: This table reports OLS diagnostics. The p-value is below the
statistic value in italics. The selection process for choosing the
proper spatial model specification (lag or error) using the LM and
Robust LM tests are outlined in Anselin (1988). The selection
process is as follows: if the LM (lag) and LM (error) are both
insignificant, then do not use a spatial specification; if only one
of LM (lag) or LM (error) is significant, then use the use the
specification indicated, lag or error; if both LM (lag) and LM
(error) are significant, then select the specification that has a
higher value for the Robust LM statistic. Applying the selection
criteria indicates that a spatial lag model is appropriate.

TABLE 7
Spatial Two-Stage Least Squares Regression Results

Model                          Mode l          Model 2

Dependent variable          LR Avg 03-'06   LR Cum '03-'06
Independent variable
  Intercept                   -0.977 ***      -0.951 ***
                              (0.257)         (0.270)
  Cover                        1.499 ***       1.438 ***
                              (0.341)         (0.362)
  Group                       -0.228 **       -0.266 ***
                              (0.093)         (0.099)
  Rev                          0.053 ***       0.065 ***
                              (0.017)         (0.019)
  Trend                       -0.108 ***      -0.102 ***
                              (0.029)         (0.029)
  CV                           0.520 ***       0.538 ***
                              (0.143)         (0.167)
  DownDevRatio                 0.164 **        0.152 **
                              (0.064)         (0.061)
  [rho]                        0.704 ***       0.709 ***
                              (0.109)         (0.112)
Obs.                            1024            1024
df                              1017            1017
Sigma-sq.                      0.117           0.124
Psuedo adj. R-sq. (var.)       0.453           0.439
Psuedo adj. R-sq. (corr.)      0.476           0.464
A-K test for residual spatial autocorrelation
  Moran's I statistic         -0.137          -0.150
  LM statistic                11.298          12.633
  p-value                      0.001           0.000

Model                          Model 3          Model 4

Dependent variable          LR Avg '80-'06   LR Cum '80-'06
Independent variable
  Intercept                    0.395 ***        0.359 ***
                              (0.108)          (0.094)
  Cover

  Group

  Rev

  Trend                       -0.107 ***       -0.169 ***
                              (0.025)          (0.038)
  CV                           1.145 ***        1.335 ***
                              (0.243)          (0.292)
  DownDevRatio

  [rho]                        0.587 ***        0.578 ***
                              (0.096)          (0.097)
Obs.                            1024             1024
df                              1021             1021
Sigma-sq.                      0.078            0.064
Psuedo adj. R-sq. (var.)       0.374            0.569
Psuedo adj. R-sq. (corr.)      0.379            0.588
A-K test for residual spatial autocorrelation
  Moran's I statistic          0.061            0.010
  LM statistic                 1.015            0.056
  p-value                      0.314            0.813

Note: Table presents results for spatial two-stage least squares
(S2SLS) regression of spatial lag form for Models 1-4. Coefficient
values are in plain text, and the corresponding standard errors are
below in parentheses. Standard errors are spatial heteroskedastic
and autocorrelation consistent (SHAC) robust standard errors.
Significance: * = 10%, ** = 5%, *** = 1%.

TABLE 8
Estimated Variable Effects and Elasticities (at Mean) for S2SLS Loss
Ratio Model

                       Total Effect          Elasticity

                 Direct   Multiplier   Direct   Multiplier
Model l
  Cover           1.499        5.064     1.49         5.02
  Group          -0.228       -0.770    -0.03        -0.09
  Rev             0.053        0.179     0.05         0.16
  Trend          -0.108       -0.365    -0.23        -0.77
  CV              0.520        1.757     0.22         0.75
  DownDevRatio    0.164        0.554     0.15         0.49
Model 2
  Cover           1.438        4.942     1.45         4.98
  Group          -0.266       -0.914    -0.03        -0.11
  Rev             0.065        0.223     0.06         0.20
  Trend          -0.102       -0.351    -0.22        -0.75
  CV              0.538        1.849     0.23         0.80
  DownDevRatio    0.152        0.522     0.14         0.47
Model 3
  Trend          -0.107       -0.259    -0.16        -0.38
  CV              1.145        2.772     0.22         0.53
Model 4
  Trend          -0.169       -0.400    -0.32        -0.76
  CV              1.335        3.164     0.33         0.78

                       IQR Effect

                 Direct   Multiplier
Model l
  Cover            0.11         0.36
  Group           -0.02        -0.07
  Rev              0.02         0.08
  Trend           -0.09        -0.32
  CV               0.08         0.27
  DownDevRatio     0.15         0.49
Model 2
  Cover            0.10         0.35
  Group           -0.02        -0.08
  Rev              0.03         0.10
  Trend           -0.09        -0.31
  CV               0.08         0.29
  DownDevRatio     0.13         0.46
Model 3
  Trend           -0.09        -0.22
  CV               0.12         0.30
Model 4
  Trend           -0.14        -0.33
  CV               0.15         0.34

Note: Table presents estimated total effects and elasticities for
each variable in the S2SLS loss ratio models. Total direct effects
are equal to the coefficient estimates of the respective models.
The multiplier effect accounts for the proportion of the
variable's effect that impacts the dependent variable via spatial
spillovers in the spatial lag term, and is calculated as the direct
effects multiplied by 1/(1-p) (Kim, Phipps, and Anselin, 2003).
The elasticities are calculated as the products of the total effects
and the mean of the independent variables divided by the mean of the
dependent variable. The interquartile range (IQR) effect is the
implied effect of the independent variables on the expected
dependent variable (L) over the interquartile range of
the respective independent variable.

TABLE 9
Annual Estimated Actuarial Transfers Due to Systematic
Rating Biases Related to Trend and CV, by State

                      Interstate Transfers

State                Model 1         Model 2

Illinois           -$34,513,772    -$27,003,239
Indiana            -$15,302,127    -$11,871,941
Iowa               -$63,419,928    -$53,537,933
Kansas              -$5,807,697     -$2,636,278
Michigan            -$3,523,971     -$2,463,839
Minnesota          -$46,691,885    -$38,846,093
Missouri            -$8,442,852     -$5,475,830
Nebraska           -$37,829,449    -$31,366,866
North Dakota         $1,451,370      $5,126,564
Ohio                  -$866,612        $748,383
South Dakota       -$10,512,893     -$2,185,143
Wisconsin           -$6,703,714     -$4,335,554
Total             -$232,163,531   -$173,847,769
Percentage of        -20.16%         -15.09%
  total premium

                      Interstate Transfers

State               Model 3         Model 4

Illinois           -$3,060,975    -$38,768,705
Indiana            -$2,263,030    -$18,544,951
Iowa              -$19,997,512    -$70,749,138
Kansas             $17,932,008     $11,466,699
Michigan             -$164,598     -$4,830,044
Minnesota         -$11,195,878    -$47,699,431
Missouri            $8,061,395     -$1,614,141
Nebraska           -$8,573,985    -$38,995,315
North Dakota       $11,316,723      $1,516,487
Ohio                $3,942,117     -$2,844,405
South Dakota       $24,159,953      $1,523,093
Wisconsin           $5,368,559     -$1,751,280
Total              $25,524,777   -$211,291,129
Percentage of        2.22%          -18.35%
  total premium

                    Absolute Total Intercounty
                           Transfers

State               Model 1        Model 2

Illinois           $36,313,236    $30,165,122
Indiana            $16,001,045    $12,892,778
Iowa               $64,016,679    $54,944,238
Kansas             $20,523,100    $19,776,344
Michigan            $4,564,698     $3,812,098
Minnesota          $48,770,766    $41,733,144
Missouri            $9,143,102     $7,055,773
Nebraska           $42,626,573    $37,336,145
North Dakota       $16,583,651    $15,791,191
Ohio                $6,250,025     $5,702,166
South Dakota       $28,695,541    $25,783,738
Wisconsin           $7,789,694     $6,432,405
Total             $301,278,110   $261,425,143
Percentage of        26.16%         22.70%
  total premium

                    Absolute Total Intercounty
                           Transfers

State                Mode 3        Model 4

Illinois           $14,515,324    $40,721,399
Indiana             $6,389,990    $19,057,783
Iowa               $25,738,016    $70,923,503
Kansas             $23,900,937    $27,187,185
Michigan            $2,347,588     $6,118,018
Minnesota          $17,199,637    $50,650,082
Missouri            $9,664,831     $9,366,990
Nebraska           $25,567,708    $50,683,044
North Dakota       $11,776,506    $14,601,122
Ohio                $5,328,889     $7,578,323
South Dakota       $27,184,996    $33,105,699
Wisconsin           $7,117,437     $8,342,542
Total             $176,731,860   $338,335,689
Percentage of        15.35%         29.38%
  total premium

Note: This table presents estimated actuarial transfers both between
states and total among counties, presented by state. Transfer
estimates are based on the premium weighted impact of that Trend and
CV have on county-level expected loss rates from Models 1-4 of the
S2SLS regressions, and equal the total amount of annual over-
(under-) payments implied by rating biases due to Trend and CV.
Negative numbers reflect overpayment, while positive numbers reflect
underpayment. Premium weightings and levels are representative of
market average for 2003-2006.