Investigating the Implications of Multi-crop Revenue Insurance for Producer Risk Management

Transcription

1 Mississippi State University Department o Agricultural Economics roessional resentation April 2000 Investigating the Implications o Multi-crop Revenue Insurance or roducer Risk Management orey Miller orresponding Authors Keith H. oble Barry J. Barnett Department o Agricultural Economics Mississippi State University.O. Box 587 Mississippi State, MS jcm5@ra.msstate.edu hone: (662) Fax: (662) Abstract This study investigates the potential or alternative multi-crop revenue insurance designs in comparison to single crop yield and revenue insurance designs. A non-parametric multi-crop insurance model is developed which subsumes the single crop designs. The results compare alternative designs in terms o rate levels and risk reduction gains or representative Mississippi producers. Keywords: crop insurance, revenue insurance, risk Selected aper 2000 Southern Agricultural Economics Association Annual Meeting Lexington, Kentucky January 29-February 2, 2000 opyright April 2000 by orey Miller. All rights reserved. Readers may make verbatim copies o this document or non-commercial purposes by any means, provided that this copyright notice appears on all such copies.

2 Investigating the Implications o Multi-crop Revenue Insurance or roducer Risk Management orey Miller Keith H. oble Barry J. Barnett Selected aper 2000 Southern Agricultural Economics Association Annual Meeting Lexington, Kentucky January 29-February 2, 2000 Abstract This study investigates the potential or alternative multi-crop revenue insurance designs in comparison to single crop yield and revenue insurance designs. A non-parametric multi-crop insurance model is developed which subsumes the single crop designs. The results compare alternative designs in terms o rate levels and risk reduction gains or representative Mississippi producers. The authors are graduate research assistant and assistant proessors, respectively, in the Department o Agricultural Economics at Mississippi State University. The contact author is orey Miller,.O. Box 587, Mississippi State, MS 39762, Telephone (662) , miller@agecon.msstate.edu.

3 Background With the advent o the Federal Agricultural Improvement and Reorm Act o 996 (FAIR), interest in crop insurance instruments o all kinds has increased. While the ocus on some o the more widely used instruments that insure against losses in yields has grown since this legislation became law, more undamental has been the growth o revenue insurance, which provides protection against the combined risk o price and yield shortalls. In the last three years, the availability and number o dierent revenue insurance policies has grown on a national and regional basis. The oremost is rop Revenue overage (R), introduced in 996. R was available in 36 states in 999, paying or losses below the yield guarantee at the higher o pre-season and harvest price. Other insurance products developed during this time include Income rotection (I) and Revenue Assurance (RA). These instruments pay indemnities when the product o appraised yield and harvest price is less than the revenue guarantee. I has been piloted on a ew crops on a limited basis in several Southern states; RA pilot programs have generally been conined to the Midwest. The development o revenue insurance policies resulted rom the demand or greater insurance against price and yield shortalls. In the same ashion, existing insurance policies have been augmented and others developed that provide protection against these shortalls beyond a single enterprise. RA oers producers a multiple crop option that recognizes the diversiication eect o insuring more than one crop. Adjusted Gross Revenue insurance (AGR), which provides gross revenue protection to producers without Multiple eril rop Insurance policies, emphasizes multiple crops and provides discounts or diversiication. The success o these aorementioned insurance instruments suggests producers have an interest in insuring a portolio o crops across -3-

4 the arm. The objective o this paper is to develop a model o revenue insurance that provides an insurance guarantee against shortalls in aggregate gross revenue o multiple crops. Rates are generated by this model or multiple crops and contrasted with comparable rates or single crop designs. These designs are compared in terms o rate levels and risk reduction gains or representative Mississippi producers. These rates are ound to be lower than those o single crop designs because o the diversiication eect, and risk-reducing eiciency is also higher because o more directly insuring total arm revenue (oble, et al. 999). The Model The multi-crop revenue insurance rating model is a non-parametric bootstrap simulation model which uses resampling to deine the probability distribution unction. The revenue distribution o each crop is assumed to be composed o the three random components o price, county yield, and arm yield deviations rom the county yield. The arm yield deviations across multiple crops are important because those actors aecting one crop on a arm may also aect other crops on the same arm. The non-parametric approach was used because it does not require the parametric distributional assumptions regarding the underlying random components. The nonparametric approach is expected to be a more robust estimator capable o addressing a variety o empirical data. To our knowledge, obtaining long time series o yields can typically only be done at the aggregate level. NASS data rom were used, both or county yield and the historical price series. Farm yield deviations rom county yields, however, combine county yields with shorter crop insurance AH yield histories rom This avoids decreasing the arm yield variability by aggregating less than perectly correlated yields. -4-

5 Regional Yield Trend and Varability To estimate aggregate yield, yield trend must irst be estimated to create a mean stationary sample o aggregate yield variation. hanges in technology, which may vary across dierent crops, are incorporated by the time trend. The trend is estimated separately or each crop although it is assumed that residuals may not be independent. Equation () uses a spline trend estimator where g(t) is estimated county-by-county as a linear spline unction with the knots constrained rom the endpoints (Skees, Black, and Barnett). () R R t = g(t) + e t where R t = predicted county yield (or now we will drop the crop-speciic subscripts i and j) g(t) = a unction o time, which may vary be county e R t = residual deviations rom county yield trend in year t Equation () diers rom Atwood, Baquet, and Watts who estimated trend at a multi-county regional level and then made county-speciic adjustments. A predicted county yield, R t, is speciied in Equation (), where county yield is a unction o time represented by g(t). The residual in Equation (), e R t, is used to bootstrap county yield variability. The residual deviations are percentage deviations, which should avoid potential heteroskedasticity. Multi-rop Farm Yield Simulation The yield simulation may now be extended to the arm level while accounting or multiple crops. The approach to yield variability is a generalization o Miranda s approach to the multicrop case. The model o arm yield is written in Equations (2a) and (2b): -5-

6 (2a) y ti = y i + B ii (R ti R i ) + B ij (R tj R j ) + e ti (2b) y tj = y j + B ji (R ti R i ) + B jj (R tj R j ) + e tj where i and j are dierent individual crops. These two equations describe the arm yield variability or a crop i or j in year t as a unction o the mean yield o the arm or that crop, the deviation o the county yield rom the expected county yield or that crop, and the deviation o the county yield rom the expected county yield or the other crop. The B ij /B ji coeicient accounts or the interaction between the arm yield o i and the county trend-adjusted yield o j. This coeicient allows or interaction between the disaggregate yield o one crop and the aggregate yield o another crop. Empirically, however, this appears to be o no consequence or the location we are examining. Thus, in the analysis that ollows B ii is assumed to equal and B ij = B ji = 0. The residuals, e ti and e tj, are jointly selected in the bootstrapping model by a random draw t so that each crop has its residuals drawn rom the same period. This maintains the empirical covariance across crops. These residuals were also taken rom AH records o arms that insured more than one crop. Farm Yield Deviations Given the assumptions made in the preceding paragraph, deviations in arm yield rom the county yield are needed to complete the yield simulation. Because county yield is an aggregate measure that contains arm yields, a statistical relationship exists between the two. Equation (3) derives arm yield deviations: (3) d t = y c t R t where d t = the absolute dierence in yield o arm and county yield in year t and -6-

7 y t = yield o arm in year t The absolute dierence d t is calculated or the subset o data that includes AH records. These records have up to ten years o arm yield data. In selecting records or this analysis, a lower limit o six years o actual recorded yields was imposed. Equation (4) computes the mean arm yield deviation or each arm: (4) d = / T ( y R ) = y R T = t t t where d = mean dierence o yield o arm rom county yield (and R t is constrained to include only those years with a corresponding value or y t ) T = total number o years o yield records o arm Equation (4) allows arm-level residual variability to be decomposed as in Equation (5): (5) e t = d t = (y d t y ) (R t R ) This equation can be rewritten as (5a) y t = y + (R t R ) + e t Recall that d = y R so (5a) can be rewritten as (5b) y s = R s + d + e t where the subscript s represents simulated. It may be useul to represent (5b) in terms o vectors, as each bootstrap simulation is computed by the random selection o a value rom each vector used in (5b): -7-

8 (5c) [y s ] = [R s ] + d + [e t ] rice-yield Relationships To begin the price simulation, the price-yield relationships must irst be established. ABW modeled a historical relationship between changes in utures prices rom the pre-planting period to the harvest. This relationship is ound in Equation (6a): (6a) Rt Rt = a + a ( R $ + T R $ ) ε t 0 2 t where t = utures price at harvest t T t = t t 0 t = utures price at planting a, a 2 = coeicients or deviation o county yield rom expected county yield or a given year R t = county yield in year t $R t = predicted county yield in year t T = total number o years o regional yield data or county ε t = residual deviations o price in year t The key to this equation is shown in parentheses as the dierence between the ratio o the county yield to the predicted county yield and the mean o this ratio or the data set. Equation (6a) can be modiied to produce a price simulation at harvest: 0 R t (6b) s = ( + a 2 ( + t R $ ) ε ) t where s = simulated price at harvest and other variables as in (6a) -8-

9 Here the mean county yield to predicted county yield ratio is assumed to be, and the equation is multiplied through by the utures price at planting to reach a simulated price at harvest. In addition to price-yield relationships, the multi-crop case must also include as with yields interactions between crops. Equation (6a) can be extended to capture this correlation or multiple crops: (7a) T T R R R R it it jt j = ai + aii ( aij R $ + + T R $ ) ( R $ T R $ ) ε it 0 it it t= it jt t= jt it (7b) T T R R jt jt Rit Ri = a j + a jj ( a ji R $ + + T R $ ) ( R $ T R $ ) ε jt 0 jt jt t= jt it t= it jt where i and j = individual crops Note that Equations (7a) and (7b) are similar to (6a) except they include another crop. All three equations take the dierence o the ratio o the expected county yield or a crop in a given year and the mean o this ratio or the entire data set. The bootstrapping model will use the parameters and residuals rom these equations to determine prices. The price residuals or each crop will be jointly selected by a random draw t so that each crop has its residuals drawn rom the same period. To complete the price simulations, Equations (7a) and (7b) are modiied as was Equation (6a) to get a harvest price simulation or each crop: -9-

10 Rit Rit (8a) is = 0 is ( + a ii ( + aij + it R $ ) ) ε ) R it it R R jt jt (8b) js = 0 js ( + a jj ( + a ji + jt R $ ) ) ε ) R Multi-crop Revenue Simulation jt Using Equations (2) and (8), the complete revenue simulation model can now be generated. The bootstrapping procedure will generate a random price and yield that account or the earlier speciied interactions. Equation (9) is the revenue simulation: jt = (9) M Re v A y s i i is is where MRev s = sum o revenues rom multiple crops or a arm A i = acres planted o crop i is = simulated price o crop i at harvest y is = simulated yield o crop i or a arm Equation (0) demonstrates how indemnities would be calculated under this model: 0 (0) Indemnity = Max( 0, L Aiit yi M Re vs ) i where L = coverage level (e.g., 75 percent) Equation (0) calculates indemnities as the dierence between the revenue expected at planting -0-

11 time and the revenue simulated at harvest time. Actuarially air estimates o rates are ound by bootstrapping 6,000 iterations that produce a dierent indemnity or each draw. Since each draw is equally random, the expected indemnity is the simple average o the indemnities or all iterations. Results Figure charts the premium rates generated by the bootstrapping procedure using 6,000 iterations. These data are or a representative Sunlower ounty, Mississippi, multi-crop revenue product or a combined cotton/soybean/wheat policy, as well as traditional single crop policies or yield and revenue insurance and area yield and revenue insurance. The rates are or a 75 percent coverage level and are based on a arm size o,000 acres. These premium rates or each o these combinations are ound on the Y-axis. Along the X-axis are various acreage combinations or the three crops cotton, soybeans, and wheat, respectively. The irst three combinations assume 00 percent o the acreage is planted to one o the three crops; i.e.,,000 acres planted in cotton, ollowed by,000 acres in soybeans, and then all,000 acres in wheat. The remaining seven combinations assume dierent shares o the acreage or each crop, such combinations, , etc. Thus, these irst three combinations would essentially be the same as traditional single crop yield and revenue insurance products, and there are our bars or the policies or these three combinations. These bars represent the rates or the our insurance products mentioned above in order, single crop revenue insurance, yield insurance, county yield insurance, and county revenue insurance. As would be expected, the rates rom the area insurance products are lower than their arm-level counterparts. These irst three sets relect what rates would be or single crop policies. The bars or the other seven combinations are the rates or the multi-crop revenue --

12 policy. These are the rates or insuring the entire acreage according to dierent shares or each crop. The signiicance o the multi-crop insurance product becomes evident in comparing the rates rom single crops to the multi-crop combinations. The rates or the dierent acreage combinations are less than the rates rom the individual crops (i.e., the 00 percent acreage combinations) For example, the single crop rate or wheat, a riskier crop in this data set, has a rate considerably higher than soybeans or cotton. However, its introduction into the crop mix does not result in substantially higher rates, as might be expected. In act, premium rates or those acreage combinations in which wheat has the largest share are less than or approximately the same as those in which cotton has the largest share. The reason rates are reduced when crops are combined is primarily the correlation between the crops. Because wheat is a crop planted and harvested at a signiicantly dierent time than cotton and soybeans, it is likely that its yield would be much less correlated with these two crops than cotton and soybeans are with each other. This situation is relected in Table, which contains a matrix o correlation coeicients or the three crops in this data set. This matrix was calculated rom county yield deviations. The correlation between cotton and soybeans is.50. The correlations between wheat and the other crops are even less, as only a.5 correlation exists between wheat and soybeans. Notice that these correlations have a rate-reducing impact even though they are positive. The correlations are relected in the rates, as a combination has a lower rate than a combination despite the act that wheat is a considerably riskier crop as evidenced by its own higher rate relative to cotton and soybeans. The lower correlations between wheat and the other crops allow a combination o wheat and soybeans or wheat and cotton to have a rate comparable to -2-

13 that o a combination o cotton and soybeans. Thus, the multi-crop product captures the beneits o diversiication in these three crops. This diversiication eect in dierent acreage combinations is tempered, however, by the act that wheat rates are very high. Also notable is that the lower rates are generally ound with greater diversiication. The combination and the , , and combinations have lower rates than most o the less diversiied crop mixes. Diversiying the crop mix under this design generally allows a producer to achieve a lower premium rate. An interesting comparison is also made between the multi-crop rates and the rates o the area insurance products. The rates or county yield insurance are considerably lower than those o its arm-level counterpart, as would be expected. An even greater dierence exists between the rates o county revenue insurance and those o single crop revenue insurance. rotection can be oered at lower rates or area insurance because it indemniies against shortalls in expected county yields. Thus, these policies should be less risky because they insure against a systemic or more widespread loss. For most o the more diversiied acreage combinations, the multi-crop revenue rate is comparable to the county revenue rates or each crop. As can be seen in Figure, generally the more diversiied the crop mix the more comparable the multi-crop rates are to the area insurance products. The risk reduction gains or Mississippi producers are also addressed in this analysis. The examples computed assume a beginning wealth o $500,000 and a relative risk aversion coeicient o 2. Ending wealth is ound by subtracting costs (according to enterprise budgets or the Mississippi Delta) and premiums, and adding indemnities to market revenue. Ending wealth is used to ind expected utility using the constant relative risk aversion utility unction: -3-

14 (a) S r WS E( U ) r r r = S, ω S = or (b) E( U ) r = s ln( Ws ), r = S S = ω where r = risk aversion coeicient W s = ending wealth. ertainty equivalents likewise are calculated using the expected utility ound in () by the ollowing ormula: (2a) r E = ( r) E( U ), r sr sr or E e E( U sr r sr = ), = (2b) The use o multi-crop revenue insurance, single crop revenue insurance, and yield insurance was ound to increase certainty equivalents or selected acreage combinations as compared to production with no insurance. Table 2 illustrates the average percentage increase in certainty equivalents or these three instruments or seven selected acreage combinations. The results indicate that the average increase in certainty equivalents is greatest or multi-crop and single crop insurance, as would be expected. However, in many instances the increases are only marginal at best. One can also see rom Table 2 that the increases or multi-crop and single crop revenue insurance are approximately the same, as single crop revenue is slightly higher or most combinations. This is due to the act that single crop revenue insurance pays indemnities in some instances where multi-crop revenue insurance does not, resulting in the higher rate. One can also -4-

15 notice in Table 2 that the increases are smallest where cotton makes up the largest acreage combination. This dominance o cotton in the crop mix may indicate a starting point or urther investigation. Figure 2 illustrates the revenues (market revenue plus insurance indemnities) per acre ound or the three insurance designs discussed in the preceding paragraph. The three designs are compared to the distribution o revenue with no insurance. As expected, each insurance product decreases the probability o the lowest revenues per acre, eectively truncating the lower end o the revenue distribution with no insurance. In the upper tail o the revenue distributions, the revenue distributions o the insurance designs lie slightly to the let o the revenue distribution with no insurance due the cost o a premium while receiving no indemnity. The revenue insurance products do the best job o eliminating the lower end o the revenue distribution. Multi-crop revenue insurance provides a smooth cuto at 75 percent o expected revenue. The multi-crop revenue insurance distribution has the lowest probability o low revenues. The single crop revenue insurance pays out in some cases when the multi-crop does not because the trigger can be reached on an individual crop while not occurring over multiple crops. onclusion This objective o this analysis was to develop a model o revenue insurance that would provide an insurance guarantee against shortalls in the aggregate gross revenue o multiple crops. A non-parametric approach was used to combine the random variables or both price and yield or multiple crops. It is the authors belie that this approach is undamentally sound to maintain a rigorous relationship between random variables such that valid estimates o the joint revenue across commodities or a single arm can be made, and at the same time allowing the expansion to -5-

16 multiple crops to be easible. A limitation to this methodology, however, is the lack o needed data or dierent commodities or a single arm. This limitation applies particularly to the Mid- South and other regions where participation is much less dense. In addition to the previously mentioned need or urther investigation, the underwriting issues associated with the design o the multi-crop product must also be addressed. A producer who insured under the product beore planting wheat would have knowledge o what wheat revenue would be prior to even planting other crops, such as cotton and soybeans. Thus, including wheat in the combination policy could potentially induce moral hazard on a second set o crops. Low wheat revenue could lead to a disincentive to eectively manage crops planted in the spring. In addition, knowledge o the acres o each crop being planted are required or this rating approach. roducers in Mississippi and other states could or legitimate reasons alter their acreage allocations between their crops, such as a staggered planting scenario. This situation, however, would have an eect on the appropriate premium rate. Insuring staggered seasoned crops under the multi-crop design could become problematic. -6-

17 Figure Mississippi 75% overage Multi-rop and Other Insurance Rates remium Rates Acreage ombination (% otton/soybeans/wheat) Single rop Rev. Yield Rates ounty Rev. ounty Yield Multi-rop Rev. -7-

18 Figure 2 Revenue er Acre Under Alternative Insurance Designs robability Revenue er Acre Rev Only Rev + rop Rev Rev + Yield Rev + Multi-rop

19 Table orrelation o Sunlower ounty, Mississippi crop yields otton Soybeans Wheat otton Soybeans 0.50 Wheat

20 Table 2 Average ercentage Increase in ertainty Equivalents or Selected Acreage ombinations Acreage ombination Multi-rop Rev. Ins. -rop Revenue Ins. Yield Insurance % 3.98% 3.63% % 2.60% 20.40% % 4.78% 3.64% % 0.9% 0.09% % 7.66% 6.7% % 4.84% 4.00% % 4.96% 3.96% -20-

21 Reerences Atwood, Joseph A., Alan E. Baquet, and Myles J. Watts. Income rotection. Department o Agricultural Economics and Economics Sta aper Montana State University: Bozeman, Montana, August 997. oble, Keith H., James. Miller, Barry J. Barnett, Thomas O. Knight. A roposed Method to Rate a Multi-rop Revenue Insurance roduct, A Report to the USDA/Risk Management Agency, 29 Nov Delta 999 lanning Budgets. Agricultural Economics Report No. 00, Mississippi State University, December 998. Miranda, Mario J. Area-Yield Insurance Reconsidered. American Journal o Agricultural Economics, 73 (99): Skees, Jerry R., J. Roy Black, and Barry J. Barnett. Designing and Rating an Area Yield Insurance ontract. American Journal o Agricultural Economics, 79 (997):