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Structural Econometric Models: Past and Future (with Special Reference to Agricultural Economics Applications)
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William G. Tomek |
Year: 1998 |
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Abstract
This paper has three objectives: to review the historical contributions of the literature on structural models, to outline the problems of obtaining robust estimates of parameters, and to discuss how to improve the quality of results. The paper emphasizes applications in agricultural economics. The outline of the paper follows these objectives. I first discuss the nature of the contributions to the literature, but not the details of results. Then, I characterize the problems that have arisen in estimation. This naturally leads to a discussion of the consequences of the problems for empirical results and the impacts this has had on empirical econometrics. The final section looks to the future: how can we improve the quality of our work?
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Futures Spread Risk in Soybean Hedge-to-Arrive Contracts
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E. Neal Blue, Marvin Hayenga, Sergio Lence, and E. Dean Baldwin |
Year: 1998 |
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Abstract
In the 1995/96 crop year, record high corn futures prices and inverted spreads eroded the cash flows and financial capabilities of both farmer hedgers and elevators who implemented the rollover provisions in hedge-to-arrive (HTA) contracts. Participants in the 1995/96 corn market who used the exotic HTA multiple-year mechanism faced large unexpected margin calls and/or sharply lower "net" prices than expected, as the July-December old crop-new crop inverted corn spread widened to very large negative levels. We evaluate the soybean futures spreads in the 1948-1997 period, and the associated monetary risks inherent in the rollover provisions of the HTA contracts. In the 50 years in which current soybean May, July, and November contracts have been trading, the probability of old crop-new crop spreads being in the plus/minus 10 percent range of the old crop "normal" price was approximately 75 percent and the probability of having negative spreads exceeding 10 percent was only 20 to 25 percent. However, the high-price years (over 20 percent above normal old crop price) had a 100 percent probability of having a negative spread and a 50 to 60 percent probability of having a negative spread exceeding 10 percent. Merchandisers offering HTA contracts should be aware of these risks and communicate them to farmers considering their HTA contracts.
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Design and Evaluation of Long Term Commodity Pricing Contracts
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James Unterschultz, Frank Novak, and Stephen Koontz |
Year: 1998 |
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Abstract
Window contracts and cost plus contracts are being used for managing risk in long term producer-processor contracting relationships. Window contracts place a floor price and a ceiling price on the value of the commodity to the producer. Cost plus contracts base the minimum price on the cost of inputs. These contracts can be decomposed into portfolios of specialized put and call options. Monte Carlo option valuation techniques evaluated the impact of different price process assumptions on the values in these contracts. The conclusions are that knowledge of the price process is very important. Mean reverting processes, where the mean is correctly identified, lead to lower valued implied options in both window and spread contracts. Different strike prices are required for different times to maturity if the value of floor price (put option) is to equal the value of the ceiling price (call option) for window contracts. The floor and ceiling prices for window contracts and the cost plus portion of spread contracts need to change with the expected delivery date. A contract covering 10 years of production cannot have one single set of window prices or spread cost plus components.
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Forecasting Crop Basis: Practical Alternatives
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Kevin C. Dhuyvetter and Terry L. Kastens |
Year: 1998 |
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Abstract
Being able to predict basis is critical for making marketing and management decisions. Basis forecasts can be used along with futures prices to provide cash price projections. Additionally, basis forecasts are needed to evaluate hedging opportunities. Many studies have examined factors affecting basis but few have explicitly examined the ability to forecast basis. Studies have shown basis forecasts based on simple historical averages compare favorably with more complex forecasting models. However, these studies have typically considered only a 3-year historical average for forecasting basis. This research compares practical methods of forecasting basis for wheat, corn, milo (grain sorghum), and soybeans in Kansas. Absolute basis forecast errors vary seasonally for all crops and are highest at critical production time periods. Thus, producers need to realize that in addition to increased price variability during these time periods there is also significantly more basis forecasting risk. Using an historical 4-year average to forecast basis for wheat was the optimal number of years. For corn, milo, and soybeans a longer-term average (5-7 years) was optimal. Incorporating current market information, such as futures price spreads or current nearby basis, into a basis forecast improves the ability to forecast basis 4-12 weeks in advance but for longer time horizons simple historical averages are better.
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Post-harvest Grain Marketing with Efficient Futures
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Terry L. Kastens and Kevin C. Dhuyvetter |
Year: 1998 |
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Abstract
This study is a simulation that tests whether Kansas wheat, corn, milo (grain sorghum), and soybean producers could have used deferred-futures-plus-historical-basis cash price expectations to profitably guide post-harvest grain storage decisions from 1985 through 1997. The signaled storage decision is compared to a representative Kansas producer whose crop sales mimic average Kansas marketings. Twenty-three grain price locations are examined. The simulation resulted in a 15 cent per bushel annual increase in grain storage profits for wheat producers, 23 cents for soybeans, -6 cents for corn, and -8 cents for milo; but storage profit differences varied substantially across locations. Inferences for random Kansas cash price locations were robust to alternative basis expectations, marketing year starting dates, model starting dates, interest rates, and storage cost structures.
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Crop Insurance and Pre-harvest Pricing of Corn and Soybeans: Case Studies for Selected States and Farms
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Robert N. Wisner, E. Neal Blue, E. Dean Baldwin, G. Art Barnaby Jr., and Daniel O'Brien |
Year: 1998 |
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Abstract
To test the effectiveness in managing net income risk and profit levels, pre-harvest corn and soybean options-based pricing strategies and crop yield and revenue insurance products were modeled for case study farms in three states. These combinations reduced income variability while increasing net incomes relative to harvest cash marketings. Adding crop insurance to pre-harvest pricing strategies reduced net incomes from those with pre-harvest pricing alone, but produced larger incomes than uninsured harvest sales. The Ohio model farm was modified to reflect (1) a debt-free operation, (2) a cash renter, and (3) a buyer-renter operation. No strategy was able to cover opportunity costs on investments for types (1) and (3). Both crop insurance and pre-harvest strategies are effective tools especially for highly leveraged farms.
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The Effect of Crop or Revenue Insurance on Optimal Hedging
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Keith H. Coble and Richard Heifner |
Year: 1998 |
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Abstract
The emergence of new risk management tools such as revenue insurance has dramatically expanded the tools from which producers may choose to manage revenue risk. Little is known regarding how these products interact with market-based risk management tools such as futures and options. Our analysis addresses this issue by examining optimal futures and put ratios under increasing levels of insurance coverage. Four alternative insurance designs are examined. Two are yield triggered and two reflect currently available revenue insurance designs. The analysis is conducted by using a revenue simulation model which incorporates four random variables: futures price, basis, county yield, and farm-county yield differences. Optimal hedge and at-the-money put option ratios are derived for an expected utility maximizing corn producer in four distinct geographical regions. Revenue insurance tends to result in slightly lower hedging demand than would occur given the same level of yield insurance coverage. To the extent that producers would switch from yield insurance to revenue insurance there would be a decline in the demand for hedging. If a person were to go from being uninsured to the purchase of one of the insurance designs, we find that the revenue products result in a hedge ratio that is at least as high as the uninsured case when considering the permissible levels of coverage.
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Innovative Hedging and Financial Services: Using Price Protection to Enhance the Availability of Agricultural Credit
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Francesco Braga and Brian Gear |
Year: 1998 |
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Abstract
The use of currency translated average rate options is shown to be a cost effective way to hedge corn and soybean price risk in Ontario when the timing of the cash sales extends over several months. Standardized contracts incorporating the over-the-counter instrument may be developed, and could be offered as an add-on to an operating line of credit. Lower average commodity prices would result in a reduced principal repayment obligation. Overall this would also lead to improved credit risk and lower cost of capital.
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Heterogeneous Subjective Moments and Price Dynamics
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Darren L. Frechette and Robert D. Weaver |
Year: 1998 |
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Abstract
Differential expectations have long been presumed necessary for the existence of speculative markets. At an empirical level, considerable evidence further suggests that agents may not hold rational expectations. The representative agent hypothesis is disputable on theoretical grounds because it is not consistent with observed trading behavior and the existence of markets. It has been favored in the past due to intractability of aggregation associated with heterogeneity. Now, due to improved computing technology, explicitly aggregation problems are becoming tractable. Heterogeneous expectations must be considered seriously in price analysis because they bring our models one step closer to reality.
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Spectral Analysis of Asymmetric Price Transmission in the U.S. Pork Market
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Douglas J. Miller and Marvin L. Hayenga |
Year: 1998 |
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Abstract
Economists have proposed a number of plausible explanations for observed price transmission asymmetries in commodity markets. The reasons may be broadly classified as theories of cooperative oligopoly, search costs in locally imperfect markets, or asymmetric costs of inventory adjustment. Unfortunately, the econometric methods commonly used in such studies do not allow us to distinguish pricing behavior under the competing theories. In this paper, we argue that the alternatives may be distinguished by firm responses to high and low frequency (rapid or slow) price cycles. We use Engle's band spectrum regression to examine the symmetry of price transmission for price cycles of different frequencies. The spectral analysis results indicate that changes in wholesale pork prices are asymmetrically transmitted to retail prices in relatively low frequency cycles, which is not consistent with the search cost theory. Conversely, wholesale pork prices asymmetrically respond to changes in farm prices at all frequencies, which is not consistent with the search cost or inventory management theories.
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Income Taxes and Price Variability in Storable Commodity Markets
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Kevin McNew and Bruce Gardner |
Year: 1998 |
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Abstract
Progressive income taxes lead to distortions in economic decisions made across tax years. This is particularly important when income can be quite volatile, as in the case of agriculture. Progressive taxes, therefore, can fundamentally change economic behavior over time. This study explores how progressive income taxes influence storage decisions and the markets for storable commodities. Under a progressive tax system, commodity storage tends to be lower in the aggregate, and, as a consequence, price volatility increases. These distortions could be eliminated by introducing a flat-rate tax or by changing the tax reporting system for farmers.
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Evaluating Potential Changes in Price Reporting Accuracy
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Clement E. Ward and Seung-Churl Choi |
Year: 1998 |
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Abstract
Non-cash-market transactions for fed cattle have increased. Price discovery depends in part on the accuracy of reported cash market prices. Cattlemen and others have expressed concern that as non-cash-market transactions increase, reported cash market prices may no longer accurately reflect supply-demand conditions. Equations based on Chebyschev's inequality are used in conjunction with experimental market data from the Fed Cattle Market Simulator to explore relationships related to price reporting accuracy for several subpopulations of prices versus the known population. Price means and variances and distribution of prices were invariant to number of transaction prices. Mean prices and variance of prices also were invariant to number of observations. Only when the reduction in prices reached 80% was there a significant relationship between number of observations and two pairs of variables, i.e., reported price precision and confidence of a given level of precision. With the exception of the smallest reduction in transactions, no differences were found between the subpopulations and population for reported price precision versus probability of a given level of precision, for reported price precision versus estimated number of observations with a given degree of confidence, and for probability of a given level of precision versus estimated number of observations with a given level of precision. Results suggest the possibility that number of non-reported fed cattle transaction prices could increase significantly before the industry faces serious concerns regarding the accuracy of reported prices certis paribus.
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Impacts of Reduced Public Information on Price Discovery and Marketing Efficiency in the Fed Cattle Market
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John Anderson, Clement Ward, Stephen Koontz, Derrell Peel, and James Trapp |
Year: 1998 |
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Abstract
There has been reduced government support and funding for market news and other information services in agricultural markets. This research examines the effect on the level of variability of cash fed cattle prices from reducing public information on price reporting. This information is provided by USDA Agricultural Marketing Service. The research also examines the effect of less information on marketing efficiency. The impact of reduced market information is measured with an experimental economics tool: The Fed Cattle Market Simulator. Results suggest removal, or reduction, in USDA-AMS information will fundamentally change the price discovery process. Participants rely more on futures and less on boxed beef to help discover cash cattle prices. There was an inconclusive change in mean transaction price -- favoring neither meatpackers or feedlots -- but an increase in transaction price variability. There was also greater mean-level dispersion in transaction prices across firms. Price discovery is less efficient. There is also a reduction in marketing efficiency. Cattle are marketed at high-cost weights. The experiment suggests there is a net loss to society, not just market participants, from reduced public price reporting information.
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Trends in the Accuracy of USDA Production Forecasts for Beef and Pork
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DeeVon Bailey and B. Wade Brorsen |
Year: 1998 |
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Abstract
Trends in the accuracy of USDA forecasts of beef and pork production and supply are evaluated. The USDA forecasts underestimated production and supply in the 1980s, but this bias has now disappeared. The variance of forecasts has also declined. Thus, the accuracy of the forecasts has improved. The most recent forecasts meet the criteria of optimal forecasts while the forecasts of the 1980s were not optimal.
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Cattle Basis Risk and Grid Pricing
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Jennifer L. Graff and Ted C. Schroeder |
Year: 1998 |
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Abstract
The beef industry is increasingly moving towards a more value-based pricing system in an attempt to send appropriate signals to producers. Beef packers have responded by developing grid pricing systems which value each carcass separately based on its own merit, as opposed to one price for an entire pen of cattle. This study estimates how the level of variability in basis is affected when cattle are sold on a price grid compared to traditional live and dressed weight pricing. In addition, we determine how basis risk is affected by general spatial price variability, uncertainty regarding cattle quality, variation in dressing percentage, and movement in the Choice-to-Select price spread. Weekly basis is evaluated using six alternative pricing methods over an eight-year period. Live-weight pricing has the lowest basis variability of the six pricing methods examined. Cattle sold using grids have greater basis variability primarily because of uncertainty regarding cattle quality and to a lesser extent, changes in grid premiums and discounts over time.
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Economic Implications of Show List, Pen Level, and Individual Animal Pricing of Fed Cattle
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Dillon M. Feuz |
Year: 1998 |
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Abstract
Fed cattle are currently sold on a show list (several pens of market ready cattle), pen by pen, or individual head basis and may be priced using live weight, dressed weight, or grid or formula pricing. Analysis of 85 pens, 5520 head, of fed cattle revealed that marketing level, i.e., show list, pen, or individual, had only limited impact on the variability of revenue on a pen average basis. Moving from live weight to dressed weight pricing did slightly increase the variability of pen average revenue. Revenue variability on an individual head basis increased with grid pricing. In explaining revenue variability, weight explained the majority of the variation in revenue. Marbling difference may account for about 25 percent of the variation, depending upon time period and grid. Fat thickness and ribeye area accounted for less than three percent of the variation in revenue.
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Can the Grain Marketing System Provide Sufficient Quality Incentives to Producers?
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Wes Elliot, Brian D. Adam, Phil Kenkel, and Kim Anderson |
Year: 1998 |
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Abstract
Kenkel, Anderson, and Attaway found that Oklahoma country elevators tended to overestimate test weight and underestimate dockage and undesirable grade factors, such as damaged kernels, shrunken and broken kernels, and foreign material for hard red winter wheat in the 1995 and 1996 harvests. This reflects an apparent pricing inefficiency in the Oklahoma wheat market in that elevators paid more than they should have for low quality wheat and less than they should have for high quality wheat. Measuring quality characteristics more accurately will cost elevators more, but will help them to increase price received from next-in-line (NIL) buyers and facilitate supplying products that meet consumers' needs. However, an elevator that imposes discounts for lower quality wheat, even while paying a higher price for high quality wheat, risks losing business if farmers believe that a competing elevator is more likely to pay them a higher price net of discounts. To the extent that maintaining volume is important to an elevator's profits, elevators may lose money by grading correctly and passing on premiums and discounts. A simulation analysis is used to determine the extent to which spatial competition limits the incentive for elevators to grade correctly and pay producers quality-adjusted prices. Results show that because of spatial monopsony early adopters of grading and quality-based pricing practices pass on to producers 70% of price differentials received from NIL buyers, and receive above-normal profits at the expense of their competitors. However, if competing elevators adopt such practices, profits of all elevators return to near normal. Then all elevators pass on to producers the full amount of price differentials received from NIL buyers, rewarding producers of high quality wheat at the expense of producers of low quality wheat. Further research is needed to explain the apparent reluctance of elevators to be first adopters.
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Risk and Expected Returns in Cattle Feeding
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Frederick A. Hampel, Ted C. Schroeder, and Terry L. Kastens |
Year: 1998 |
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Abstract
Numerous studies have shown average return on investment in cattle feeding compares favorably with returns on alternative investments. However, the volatility in cattle feeding returns is extremely high. The high profit risk in cattle feeding and the infrequency of profitable hedging opportunities when cattle are placed on feed raise questions regarding the relationship between perceived risk and expected returns. Previous research has not sought to explain the variation in expected cattle feeding returns. Under the assumptions of portfolio theory, a risk averse investor requires higher expected returns for investments that increase portfolio risk. A model is presented to test for a risk-return tradeoff in expected cattle feeding returns. Hedgeable returns are used as a proxy for expected returns. Alternative proxies for the risk perceptions of cattle feeders are tested in the model. Only one proxy, implied live cattle option volatility, proved statistically significant. Historical measures of risk were not significant, implying that cattle feeders are forward looking. Cattle on feed inventories and recent profits in cattle feeding did not affect expected returns. Since expected returns are shown to vary with risk, it is conceivable that futures prices are at least partially used as expectations.
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Risk Measurement and Supply Response in the Soybean Complex
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Matthew A. Diersen and Philip Garcia |
Year: 1998 |
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Abstract
Output price risk has been found to affect firm behavior in the soybean complex. Here, we investigate the influence of price risk on the supply of soybean products, using futures prices and implied volatilities from options markets to generate the first and second moments of the crushers' returns distribution. Our findings suggest that implied volatilities can be a useful measure of price risk in a supply response context. This measure has the advantages of being forward-looking, market generated, and relatively easily implementable for those commodities with futures and options markets.
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Agricultural Applications of Value-at-Risk Analysis: A Perspective
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Mark R. Manfredo and Raymond M. Leuthold |
Year: 1998 |
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Abstract
Value-at-risk (VaR) determines the probability of a portfolio of assets losing a certain amount in a given time period due to adverse market conditions with a particular level of confidence. Value-at-Risk has received considerable attention from financial economists and financial practitioners for its use in risk reporting, in particular the risks of derivatives. This paper provides a "state-of-the-art" review of VaR estimation techniques and empirical findings found in the finance literature. The ability of VaR estimates to represent large losses associated with tail events varies among procedure, confidence level, and data used. To date, there is no consensus to the most appropriate estimation technique. Potential applications of Value-at-Risk are suggested in the context of agricultural risk management. In the wake of the Hedge-to-Arrive crisis, the lifting of agricultural trade options by the CFTC, and the decreased government participation, VaR seems to have a place in the agricultural risk manager's toolkit.
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A Preview of the Usefulness of Placement Weight Data
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Bailey Norwood and Ted C. Schroeder |
Year: 1998 |
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Abstract
Knowing the number, timing, and weights of cattle placed on feed should be useful in forecasting beef supply. In 1996, the USDA began reporting cattle-on-feed placements in various weight groups. Placement weight data may improve beef supply forecasts because knowledge of placement weight distributions will provide information regarding expected slaughter timings. Currently, monthly USDA placement weight data are not numerically sufficient to derive and test statistical relationships between placement weights and slaughter. However, private data were collected to estimate placement weight data back to 1985. Placement weight data were estimated and used in various models to determine if they improve beef supply forecasts, fed-cattle price forecasts, and economic returns from using this information for selectively hedging. Use of placement weights improved beef supply forecasts only at a one-month horizon; it contributed nothing to price forecast accuracy or returns from selectively hedging. The futures price was the best fed-cattle price forecast among several tested. This suggests a better measure of placement weight data value is it impact on live-cattle futures prices, rather than price forecasting.
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Forecast Evaluation: A Likelihood Scoring Method
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Matthew A. Diersen and Mark R. Manfredo |
Year: 1998 |
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Abstract
While many forecast evaluation techniques are available, most are designed for the end user of forecasts. Most statistical evaluation procedures rely on a particular loss function. Forecast evaluation procedures, such as mean squared error and mean absolute error, that have different underlying loss functions, may provide conflicting results. This paper develops a new approach of evaluating forecasts, a likelihood scoring method, that does not rely on a particular loss function. The method takes a Bayesian approach to forecast evaluation and uses information from forecast prediction intervals. This method is used to evaluate structural econometric and ARIMA forecasting models of quarterly hog price.
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Performance Persistence for Managed Futures
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B. Wade Broersen and John Townsend |
Year: 1998 |
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Abstract
Past literature on managed futures funds has found little evidence that the top performing funds can be predicted. But, the past literature has used small datasets and methods which had little power to reject the null hypothesis of no performance persistence. The objective of this research is to determine whether performance persists for managed futures advisors using large datasets and methods which have power to reject the null hypothesis. We use data from public funds, private funds, and commodity trading advisors (CTAs). The analysis proceeds in four steps. First, a regression approach is used to determine whether after adjusting for changes in overall returns and differences in leverage that funds all have the same mean returns. Second, we use Monte Carlo methods to demonstrate that Elton, Gruber, and Rentzler's methods have little power to reject false null hypotheses and will reject true null hypotheses too often. Third, we conduct an out-of-sample test of various methods of selecting the top funds. Fourth, since we do find some performance persistence, we seek to explain the sources of this performance persistence by using regressions of (a) returns against CTA characteristics, (b) return risk against CTA characteristics, (c) returns against lagged returns, and (d) changes in investment against lagged returns. The performance persistence could exist due to either differences in cost or differences in the skill of the manager. Our results favor skill as the explanation since returns were positively correlated with cost. The performance persistence is statistically significant, but is small relative to the variation in the data (only 2-4% of the total variation). But, the performance persistence is large relative to the mean. Monte Carlo methods showed that the methods used in past research could often not reject false null hypotheses and would reject true null hypotheses too often.
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Compatibility of Government Guarantees with Flexibility in Canadian Wheat Price Pooling
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James Unterschultz and Frank Novak |
Year: 1998 |
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Abstract
Financial option theory is used to evaluate Canadian Wheat Board (CWB) price pooling and associated government guarantees. Price guarantees and final payments on the pool can be viewed as special financial derivative products. Financial models are used to evaluate pricing flexibility alternatives within the constrains of the CWB price pooling system and at the same time to provide a measure of the CWB dollars at risk associated with offering these contracts. Flexible pricing alternatives may not be compatible with a government price guarantee. The CWB dollar risk of flexible pricing could be substantial.
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The Emerging Futures Market for Cheddar Cheese: A Mechanism for Stability or Increased Spot-Price Volatility?
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Cameron S. Thraen |
Year: 1998 |
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Abstract
In the early 1990's, after four decades of relying on government authorized minimum price supports and the required public stockholding necessary to achieve price risk management, the United States dairy industry began a journey toward a shift to a market clearing equilibrium system. In this new era the forces of supply and demand determine product prices and changes in those prices. With this market clearing system comes an increase in the volatility of product prices and the risk associated with this volatility. A potentially important component of this new structure is the development of an operational futures market for selected milk and dairy products. In June of 1993 the Coffee, Sugar, & Cocoa Exchange (CSCE) introduced a contract on cheddar cheese. The Chicago Mercantile Exchange began trading a cheese contract in October 1997. Today there are contracts covering cheese, butter, nonfat dry milk and raw milk. As the production of cheese represents over one-third of the use of raw milk in the United States, this contract has the potential of serving as an important price risk management tool. An important question to be addressed is whether or not the speculative trading activity on these contracts will increase or decrease spot price volatility. This study investigates this question for the CSCE cash cheese market. The results suggest that the trading on the futures market for cheddar cheese has not increased the cheese spot market price volatility and therefore provides additional support for the continued development of the futures market as a price risk management tool by the dairy industry.
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Producers' Marketing Practices and Decision Making Processes
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James Sartwelle III, Daniel O'Brien, William Tierney, Tim Eggers, Robert Wisner, John Lawrence, and Walter Barker |
Year: 1998 |
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Abstract
A survey of Kansas, Texas, and Iowa agricultural producers and agribusiness was taken to examine the factors affecting their grain and livestock marketing practices. Qualitative choice models (multinomial and binomial logit) were used to determine whether marketers' choices of cash market, forward contract, or futures and options oriented marketing practices were significantly affected by their individual characteristics. These individual characteristics include years of experience, enterprise specialization, attitudes toward risk, management decisions, local market conditions, and preferences for alternative types of market-related information. Results indicated that years of experience, risk attitude, on-farm storage practices, and preferences for alternative types of futures and cash market information had significant effects upon respondents' choice of grain marketing practices. However, few factors significantly affected respondents' choice of livestock marketing practices.
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Perceptions of Marketing Efficiency and Strategies: Research vs. Extension Marketing Economists
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Joe Parcell, Ted Schroeder, Terry Kastens, and Kevin Dhuyvetter |
Year: 1998 |
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Abstract
Extension and research marketing economists spend considerable time educating clientele and publishing marketing and risk management strategies. Therefore, perceptions of extension and research marketing economists regarding price forecasting, futures markets, market timing strategies, and price risk management should be consistent. Results from surveys conducted of extension and research marketing economists found that perceptions differed in 7 of 12 questions posed to both groups. Increased collaboration between extension and research marketing economist appears to have merit in determining methods to solve these inconsistencies.
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