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 Econometric models are used by economists to find standard relationships among aspects of the macroeconomy and use those relationships to predict the effects of certain events (like government policies) on inflation, unemployment, growth, etc. . 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 ac·tu·ar·y
n. pl. ac·tu·ar·ies
A statistician who computes insurance risks and premiums.
[Latin 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.
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 Systemic Risk
Risk common to a particular sector or country. Often refers to a risk resulting from a particular "system" that is in place, such as the regulator framework for monitoring of financial_institutions. markets may include capital market imperfections, inadequate reinsurance The contract made between an insurance company and a third party to protect the insurance company from losses. The contract provides for the third party to pay for the loss sustained by the insurance company when the company makes a payment on the original contract. capacities, capital and information shocks due to unexpected events, fat-tailed distributions that prevent diversification Diversification
A risk management technique that mixes a wide variety of investments within a portfolio. It is designed to minimize the impact of any one security on overall portfolio performance.
Diversification is possibly the greatest way to reduce the risk. , 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 Terrorism insurance is insurance purchased by property owners to cover their potential losses and liabilities that might occur due to terrorist activities.
It is considered to be a difficult product for insurance companies, as the odds of terrorist attacks are very . Yet, governments tend to be ineffective in the dual roles of insurance provider and regulator regulator,
n the mechanical part of a gas delivery system that controls gas pressure that allows a manageable flow of drug vapor to escape.
see reducing valve. (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 allocation of resources
Apportionment of productive assets among different uses. The issue of resource allocation arises as societies seek to balance limited resources (capital, labour, land) against the various and often unlimited wants of their members. 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 cor·re·late
v. cor·re·lat·ed, cor·re·lat·ing, cor·re·lates
1. To put or bring into causal, complementary, parallel, or reciprocal relation.
2. 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 United States, officially United States of America, republic (2005 est. pop. 295,734,000), 3,539,227 sq mi (9,166,598 sq km), North America. The United States is the world's third largest country in population and the fourth largest country in area. . 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 sub·si·dize
tr.v. sub·si·dized, sub·si·diz·ing, sub·si·diz·es
1. To assist or support with a subsidy.
2. To secure the assistance of by granting a subsidy. 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 Operating expenses
The amount paid for asset maintenance or the cost of doing business, excluding depreciation. Earnings are distributed after operating expenses are deducted. 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 (RealMedia Architecture) See RealMedia. )--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 siz·a·ble also size·a·ble
Of considerable size; fairly large.
siza·ble·ness n. 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 sub·si·dize
tr.v. sub·si·dized, sub·si·diz·ing, sub·si·diz·es
1. To assist or support with a subsidy.
2. To secure the assistance of by granting a subsidy. (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 holt
A wood or grove; a copse.
[Middle English, from Old English.]
the lair of an otter [from , 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 This is an incomplete list of mathematical conjectures. They are divided into four sections, according to their status in 2007.
tr.v. em·bod·ied, em·bod·y·ing, em·bod·ies
1. To give a bodily form to; incarnate.
2. To represent in bodily or material form: 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 em·bod·y
tr.v. em·bod·ied, em·bod·y·ing, em·bod·ies
1. To give a bodily form to; incarnate.
2. To represent in bodily or material form: 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 Asymmetric Information
Information available to some people but not others.
In other words, the asymmetric information is held by only one side, meaning someone is keeping a secret. AND GOVERNMENT INTERVENTION IN INSURANCE MARKETS
(Hebrew: “priest”) Jewish priest descended from Zadok (a descendant of Aaron), priest at the First Temple of Jerusalem. The biblical priesthood was hereditary and male. 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 To insure; to sell an issue of stocks and bonds or to guarantee the purchase of unsold stocks and bonds after a public issue.
The word underwrite has two meanings. , thereby reducing adverse selection and moral hazard Moral Hazard
The risk that a party to a transaction has not entered into the contract in good faith, has provided misleading information about its assets, liabilities or credit capacity, or has an incentive to take unusual risks in a desperate attempt to earn a profit before the 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 capitalization n. 1) the act of counting anticipated earnings and expenses as capital assets (property, equipment, fixtures) for accounting purposes. 2) the amount of anticipated net earnings which hypothetically can be used for conversion into capital assets. 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 Weather derivatives are financial instruments that can be used by organizations or individuals as part of a risk management strategy to reduce risk associated with adverse or unexpected weather conditions. , 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 SrA
senior airman ). Under the SRA, companies designate des·ig·nate
tr.v. des·ig·nat·ed, des·ig·nat·ing, des·ig·nates
1. To indicate or specify; point out.
2. To give a name or title to; characterize.
3. 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 co·ble
1. Nautical A small flatbottom fishing boat with a lugsail on a raking mast.
2. Scots A kind of flatbottom rowboat. , 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 sorghum, tall, coarse annual (Sorghum vulgare) of the family Gramineae (grass family), somewhat similar in appearance to corn (but having the grain in a panicle rather than an ear) and used for much the same purposes. 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 geographic pattern A general descriptor for lesions in which large areas of one color, histologic pattern, or radiologic density with variably scalloped borders sharply interface with another color, pattern or density, fancifully likened to national boundaries of low loss experience throughout the central Corn Belt Corn Belt, major agricultural region of the U.S. Midwest where corn acreage once exceeded that of any other crop. It is now commonly called the Feed Grains and Livestock 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]
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 non·ze·ro
Not equal to zero.
Not equal to zero. coefficient coefficient /co·ef·fi·cient/ (ko?ah-fish´int)
1. an expression of the change or effect produced by variation in certain factors, or of the ratio between two different quantities.
2. . 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 See least cost routing. ) rate making, methods used for determination of guarantees and actual production history (APH APH American Printing House for the Blind, Inc.
APH Actual Production History
APH Association of Personal Historians
APH Antepartum Hemorrhage
APH A Pleasurable Headache (Matthew Good Band community) ) yields, potential mistreatment mis·treat
tr.v. mis·treat·ed, mis·treat·ing, mis·treats
To treat roughly or wrongly. See Synonyms at abuse.
mis·treat of intracounty risk heterogeneity het·er·o·ge·ne·i·ty
The quality or state of being heterogeneous.
the state of being heterogeneous. , 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 ar·gu·a·ble
1. Open to argument: an arguable question, still unresolved.
2. That can be argued plausibly; defensible in argument: three arguable points of law. induce adverse selection into the system (i.e., their omission omission n. 1) failure to perform an act agreed to, where there is a duty to an individual or the public to act (including omitting to take care) or is required by law. Such an omission may give rise to a lawsuit in the same way as a negligent or improper act. 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 di·chot·o·mize
v. di·chot·o·mized, di·chot·o·miz·ing, di·chot·o·miz·es
To separate into two parts or classifications.
To be or become divided into parts or branches; fork. 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 Underwriting
1. The process by which investment bankers raise investment capital from investors on behalf of corporations and governments that are issuing securities (both equity and debt).
2. The process of issuing insurance policies. 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 rate·mak·ing
The practice of establishing rates of payment, as for public transportation or utilities.
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 dis·in·cen·tive
Something that prevents or discourages action; a deterrent.
something that discourages someone from behaving or acting in a particular way
Noun 1. 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 Convex
Curved, as in the shape of the outside of a circle. Usually referring to the price/required yield relationship for option-free bonds. 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 det·ri·men·tal
Causing damage or harm; injurious.
detri·men 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 homogenize /ho·mog·e·nize/ (ho-moj´in-iz) to render homogeneous.
to convert into material that is of uniform quality or consistency throughout; to render homogeneous. 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 ad·vis·a·ble
Worthy of being recommended or suggested; prudent.
ad·visa·bil , 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 mathematical statistics, spatial dependence is a measure for the degree of associative dependence between independently measured values in a temporally or in situ 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 e·con·o·met·rics
n. (used with a sing. verb)
Application of mathematical and statistical techniques to economics in the study of problems, the analysis of data, and the development and testing of theories and models. 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 sub·sam·ple
A sample drawn from a larger sample.
tr.v. sub·sam·pled, sub·sam·pling, sub·sam·ples
To take a subsample from (a larger sample). . If the period to be analyzed an·a·lyze
tr.v. an·a·lyzed, an·a·lyz·ing, an·a·lyz·es
1. To examine methodically by separating into parts and studying their interrelations.
2. Chemistry To make a chemical analysis of.
3. 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 North Dakota, state in the N central United States. It is bordered by Minnesota, across the Red River of the North (E), South Dakota (S), Montana (W), and the Canadian provinces of Saskatchewan and Manitoba (N). , South Dakota South Dakota (dəkō`tə), state in the N central United States. It is bordered by North Dakota (N), Minnesota and Iowa (E), Nebraska (S), and Wyoming and Montana (W). , 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 summation n. the final argument of an attorney at the close of a trial in which he/she attempts to convince the judge and/or jury of the virtues of the client's case. (See: closing argument) ].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 (1) In word processing and scientific notation, a digit or symbol that appears below the line; for example, H2O, the symbol for water. Contrast with superscript.
(2) In programming, a method for referencing data in a table. 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 Nass (năs), river, 236 mi (380 km) long, rising in the Coast Mts., W British Columbia, Canada, and flowing SW to Portland Inlet of the Pacific Ocean. It is navigable for 25 mi (40 km) and has valuable salmon fisheries. 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 Coefficient of Variation
A measure of investment risk that defines risk as the standard deviation per unit of expected return. , 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 Adj. 1. unrepresentative - not exemplifying a class; "I soon tumbled to the fact that my weekends were atypical"; "behavior quite unrepresentative (or atypical) of the profession" 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 Inserted into. See embedded system. 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 DRAWBACK, com. law. An allowance made by the government to merchants on the reexportation of certain imported goods liable to duties, which, in some cases, consists of the whole; in others, of a part of the duties which had been paid upon the importation. 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 Downside
The dollar amount by which the market or a stock has the potential to fall.
You might hear someone say that the downside on stock XYZ is $10. What that means is that the stock could fall by this amount if things got bad. 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 VICE VERSA. On the contrary; on opposite sides. .
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 contiguity /con·ti·gu·i·ty/ (kon?ti-gu´i-te) contact or close proximity.
The state of being contiguous. 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 intuition, in philosophy, way of knowing directly; immediate apprehension. The Greeks understood intuition to be the grasp of universal principles by the intelligence (nous), as distinguished from the fleeting impressions of the senses. is that in the presence of multidimensional feedback effects, the spatial lag term [rho]W L will be endogenous endogenous /en·dog·e·nous/ (en-doj´e-nus) produced within or caused by factors within the organism.
1. Originating or produced within an organism, tissue, or cell. (Anselin, 1988).
Diagnostics for heteroskedasticity and normality normality, in chemistry: see concentration. were also conducted (Table 6). The Jarque-Bera test In statistics, the Jarque-Bera test is a goodness-of-fit measure of departure from normality, based on the sample kurtosis and skewness. The test statistic JB is defined as
GMM Gaussian Mixture Model
GMM General Membership Meeting
GMM Good Mobile Messaging
GMM GPRS Mobility Management
GMM Global Marijuana March
GMM Genetically Modified Microorganisms frameworks are robust to nonnormality and thus are adopted here. Specifically, a spatial two-stage least squares (S2SLS (Selective Laser Sintering) See laser sintering and 3D printing. ) 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 Autocorrelation
The correlation of a variable with itself over successive time intervals. Sometimes called serial correlation. consistent (SHAC SHAC Stop Huntingdon Animal Cruelty
SHAC Society for the History of Alchemy and Chemistry
SHAC Sydney Housing Action Collective (Australia)
SHAC Scenic Highway Advisory Committee (Florida) ) 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 In statistics and probability theory, the covariance matrix is a matrix of covariances between elements of a vector. It is the natural generalization to higher dimensions of the concept of the variance of a scalar-valued random variable. , where the weights are determined using a kernel The nucleus of an operating system. It is the closest part to the machine level and may activate the hardware directly or interface to another software layer that drives the hardware. 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 See point sampling. . Thus, the weight matrix employed by the SHAC estimator is a distance-based matrix; we use a 10 nearest neighbors (10 KNN KNN Kids News Network
KNN Kanda News Network (Japan)
KNN Kingdom News Network
KNN Kashmir News Network
KNN Kurdistan National Network
KNN K-Mart News Network
KNN K-Nearest Neighbor ) matrix, and a triangular kernel function. Following Kelejian and Prucha, we estimate [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII ASCII or American Standard Code for Information Interchange, a set of codes used to represent letters, numbers, a few symbols, and control characters. Originally designed for teletype operations, it has found wide application in computers. ] 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.
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 seem·ing
Outward appearance; semblance.
seeming·ly adv. 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 Central Illinois is a region of the U.S. state of Illinois that consists of the entire central section of the state, divided in thirds from north to south. It is an area of mostly flat prairie. 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 re·dis·trib·ute
tr.v. re·dis·trib·ut·ed, re·dis·trib·ut·ing, re·dis·trib·utes
To distribute again in a different way; reallocate. 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 In social science and statistics, particularlly econometrics, a reduced form equation is a method of dealing with endogeneity. A reduced form equation is defined by James Stock & Mark Watson (2007) in the following way: (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 spill·o·ver
1. The act or an instance of spilling over.
2. An amount or quantity spilled over.
3. A side effect arising from or as if from an unpredicted source: 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 OLS Ordinary Least Squares
OLS Online Library System
OLS Ottawa Linux Symposium
OLS Operation Lifeline Sudan
OLS Operational Linescan System
OLS Online Service
OLS Organizational Leadership and Supervision
OLS On Line Support
OLS Online System ). 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 In descriptive statistics, the interquartile range (IQR), also called the midspread, middle fifty and middle of the #s, is a measure of statistical dispersion, being equal to the difference between the third and first quartiles. (IQR IQR Interquartile Range (statistics)
IQR Internet Quick Reference
IQR Individual Qualification Record
IQR Internal Quality Review ) 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 Overrated was a Horde World of Warcraft guild, based on the US Black Dragonflight Realm. On November 2 2006, the majority of the guild members were indefinitely banned from the game for use of (or directly benefiting from) a third-party "wall-hack", used to bypass content relative to other areas and that the overrating o·ver·rate
tr.v. o·ver·rat·ed, o·ver·rat·ing, o·ver·rates
To overestimate the merits of; rate too highly.
Noun 1. 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 bu·reau·crat
1. An official of a bureaucracy.
2. An official who is rigidly devoted to the details of administrative procedure.
bu 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 o·ver·state
tr.v. o·ver·stat·ed, o·ver·stat·ing, o·ver·states
To state in exaggerated terms. See Synonyms at exaggerate.
o 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 Any formal verbal statement made during a trial by a judge to advise and caution the jury on their duty as jurors, on the admissibility or nonadmissibility of evidence, or on the purpose for which any evidence admitted may be considered by them. given the unknown relative impacts of sampling variability versus true risk changes in its measurement.
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 in·ter·state
Involving, existing between, or connecting two or more states.
One of a system of highways extending between the major cities of the 48 contiguous United States.
Noun 1. 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.
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 Dwarfs
Fannie Mae issued mortgage-backed securities pools that have an original maturity of 15 years. 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 CONJECTURE. Conjectures are ideas or notions founded on probabilities without any demonstration of their truth. Mascardus has defined conjecture: "rationable vestigium latentis veritatis, unde nascitur opinio sapientis;" or a slight degree of credence arising from evidence too weak or too 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 con·strain
tr.v. con·strained, con·strain·ing, con·strains
1. To compel by physical, moral, or circumstantial force; oblige: felt constrained to object. See Synonyms at force.
2. . 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).
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 rep·li·cate
1. To duplicate, copy, reproduce, or repeat.
2. To reproduce or make an exact copy or copies of genetic material, a cell, or an organism.
A repetition of an experiment or a procedure. 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.
Anselin, L., 1988, Spatial Econometrics econometrics, technique of economic analysis that expresses economic theory in terms of mathematical relationships and then tests it empirically through statistical research. : Methods and Models (Boston: Kluwer).
Anselin, L., and H. H. Kelejian, 1997, Testing for Spatial Error Autocorrelation in the Presence of Endogenous Regressors, International Regional Science Review, 20: 153-182.
Babcock, B. A., 2008, Corn Belt Contributions to the Crop Insurance Industry, Iowa Ag Review, 14(12): 1-3, 11.
Brown, J. R., R. S. Kroszner, and B. H. Jenn, 2002, Federal Terrorism Risk Insurance, National Tax Journal, 55(3): 647-657.
Carriquiry, M., B. A. Babcock, and C. E. Hart, 2008, Using a Farmer's Beta for Improved Estimation of Actual Production History (APH) Yields, Journal of Agricultural and Resource Economics, 33(1): 52-68.
Chavas, J. P., and M. T. Holt, 1996, Economic Behavior Under Uncertainty: A Joint Analysis of Risk Preferences and Technology, Review of Economics and Statistics, 78(2): 329-335.
Chiappori, P.-A., and B. Salanie, 2000, Testing for Asymmetric Information in Insurance Markets, Journal of Political Economy, 108(1): 556-578.
Coble, K. H., R. Dismukes, and J. W. Glauber, 2007, Private Crop Insurers and the Reinsurance Fund Allocation Decision, American Journal of Agricultural Economics Agricultural economics originally applied the principles of economics to the production of crops and livestock - a discipline known as agronomics. Agronomics was a branch of economics that specifically dealt with land usage. , 89(3): 582-595.
Cohen, A., and P. Siegelman, 2010, Testing for Adverse Selection in Insurance Markets, Journal of Risk and Insurance, 77(1): 39-84.
Cummins, J. D., 2006, Should the Government Provide Insurance for Catastrophes? Federal Reserve Bank of St. Louis Review, 88(4): 337-379.
Cummins, J. D., 2008, CAT Bonds and Other Risk-Linked Securities: State of the Market and Recent Developments, Risk Management and Insurance Review, 11(1): 23-47.
Froot, K. A., 2001, The Market for Catastrophe Risk: A Clinical Examination, Journal of Financial Economics, 60(2-3): 529-571.
Glauber, J. W., and K. J. Collins, 2002, Crop Insurance, Disaster Assistance, and the Role of the Federal Government in Providing Catastrophic Risk Protection, Agricultural Finance Review, 62(2): 80-101.
Glauber, J. W., 2004, Crop Insurance Reconsidered, American Journal of Agricultural Economics, 86(5): 1179-1195.
Goodwin, B. K., 1994, Premium Rate Determination in the Federal Crop Insurance Program: What Do Averages Have to Say About Risk? Journal of Agricultural and Resource Economics, 19: 382-395.
Government Accountability Office The Government Accountability Office (GAO) is the audit, evaluation, and investigative arm of the United States Congress, and thus an agency in the Legislative Branch of the United States Government. (GAO), 2007, Continuing Efforts Are Needed to Improve Program Integrity and Ensure Program Costs Are Reasonable, Testimony Before the Committee on Oversight and Government Reform, House of Representatives, Statement of Lisa Shames, Acting Director Natural Resources and Environment, May 3.
Ibragimov, R., D. Jaffee, and J. Walden, 2008, Nondiversification Traps in Catastrophe Insurance Markets, Review of Financial Studies, 22(3): 959-993.
Jaffee, D., 2006, Should the Government Provide Insurance for Catastrophes? Comments on a Paper by J. David Cummins, Federal Reserve Bank of St. Louis Review, 88(4): 337-379.
Josephson, G. R., R. B. Lord, and C. W. Mitchell, 2000, Actuarial Documentation of Multiple Peril The designated contingency, risk, or hazard against which an insured seeks to protect himself or herself when purchasing a policy of insurance.
Among the various types of perils for which insurance coverage is available are fire, theft, illness, and death.
PERIL. Crop Insurance Ratemaking Procedures, Prepared for USDA-Risk Management Agency by Milliman & Robertson, Inc.
Kelejian, H. H., and I. R. Prucha, 1998, A Generalized gen·er·al·ized
1. Involving an entire organ, as when an epileptic seizure involves all parts of the brain.
2. Not specifically adapted to a particular environment or function; not specialized.
3. Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model With Autoregressive Disturbances, Journal of Real Estate Finance and Economics, 17(1): 99-121.
Kelejian, H. H., and I. R. Prucha, 2007, HAC HAC Housing Assistance Council
HAC Hill-Start Assist Control (automobiles)
HAC Hearing Aid Compatible
HAC Havre Athletic Club (Le Havre, France)
HAc Acetic Acid
HAC Honourable Artillery Company Estimation in a Spatial Framework, Journal of Econometrics, 140: 131-154.
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1. Of, relating to, or marked by pleasure.
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The Morrill Act of 1862 granted each state in the United States a portion of land on which to establish a major public state university, one which could teach agriculture, mechanic arts, and military training, "without excluding other scientific .
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DOI (Digital Object Identifier) A method of applying a persistent name to documents, publications and other resources on the Internet rather than using a URL, which can change over time. : 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 Luc Anselin is one of the principal developers of the field of spatial econometrics. Life and contributions
Born in Belgium, he attended Vrije Universiteit in Brussels, receiving the Licenciate in Economics in 1975, and a Graduate Certificate in Statistics, Econometrics is Walter Isard Walter Isard is a prominent American economist, the principal founder of the discipline of Regional Science, as well as one of the main founders of the discipline of Peace Science. Chair and Director, School of Geographical Sciences and Urban Planning urban planning: see city planning.
Programs pursued as a means of improving the urban environment and achieving certain social and economic objectives. , and Director GeoDa Center for Geospatial Geospatial is a term widely used to describe the combination of spatial software and analytical methods with terrestrial or geographic datasets. The term is often used in conjunction with geographic information systems and geomatics. Analysis and Computation Computation is a general term for any type of information processing that can be represented mathematically. This includes phenomena ranging from simple calculations to human thinking. , Arizona State University Arizona State University, at Tempe; coeducational; opened 1886 as a normal school, became 1925 Tempe State Teachers College, renamed 1945 Arizona State College at Tempe. Its present name was adopted in 1958. . Joshua D. Woodard can be contacted via e-mail: email@example.com. This manuscript is adapted from a chapter of Woodard's PhD dissertation dis·ser·ta·tion
A lengthy, formal treatise, especially one written by a candidate for the doctoral degree at a university; a thesis.
1. . 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 History
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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.