WINWHIIIWHHIHIMINI/NWWWW! NW! ”4523i 3 RSITY LIBRARIES WWWWWWHIHHWHIH Ni WI 3 1293 0090 7 This is to certify that the thesis entitled An Economic Comparison of Narrow Cropping Systems and Conventional Cropping Systems in Michigan's Thumb and Saginaw Valley presented by Eric Allen DeVuyst has been accepted towards fulfillment of the requirements for M- St degree in WCS j Enjor professor Datelm ,5; qul 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution LIBRARY Michigan State University 1 PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. DATE DUE DATE DUE DATE DUE L— ——i . "I ‘_=‘=’7! MSU Is An Affirmative Action/Equal Opportunity Inmttution cmma-m AN ECONOMIC COMPARISON OF NARROW ROW CROPPING SYSTEMS AND CONVENTIONAL ROW CROPPING SYSTEMS IN MICHIGAN’S THUMB AND SAGINAW VALLEY By Eric Allen DeVuyst A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Economics 1991 ABSTRACT AN ECONOMIC COMPARISON OF NARROW ROW CROPPING SYSTEMS AND CONVENTIONAL ROW CROPPING SYSTEMS IN MICHIGAN ’S THUMB AND SAGINAW VALLEY By Eric Allen DeVuyst Farmers in Michigan’s Thumb and Saginaw Valley are losing their comparative advantage in dry bean production. To regain or maintain their advantage Michigan farmers are evaluating alternative production methods. One production method that appears to have the potential to increase profitability is narrow row cropping. An approximate decision analysis framework utilizing subjective probability distributions is developed to compare narrow row cropping systems and conventional row cropping systems. This analysis generates a distribution of break even returns to conversion costs of switching from conventional row widths to narrow (22" inch) rows. The results indicate that narrow row cropping systems have a high probability of increasing profitability for dry bean and sugar beet producers in Michigan’s Thumb and Saginaw Valley. ACKNOWLEDGEMENTS I thank my committee members Steve Hanson and Karen Renner for all of their useful suggestions and patience. I also thank Don Christenson for all of his input. Without Dr. Christenson, I can truly state that this thesis would not have been possible. Special thanks goes to Jim Hilker and Gerry Schwab. Thank you Cheryl for forcing me to finally finish. Linda Boster, Nancy Creed, Roxie Damer and Nicole Alderman are also owed a debt of appreciation. Finally, I thank my mentor and friend J. Roy Black. TABLE OF CONTENTS LIST OF TABLES ................................................... LIST OF FIGURES ................................................. CHAPTER 1. INTRODUCTION ....................................... 1.1 Background ................................................ 1.2 Problem Statement .......................................... CHAPTER 2. METHODS OF ANALYSIS ................................ 2.1 Introduction ................................................ 2.2 Structure of Problem ......................................... 2.3 Economic Model of Firm Behavior .............................. 2.4 Decision Analysis, Risk Analysis and Other Evaluation Criteria ......... 2.5 Risk Analysis .............................................. 2.6 An Approximate Decision Criteria .............................. 2.7 Elicitation of Joint Probability Distributions ....................... 2.8 Triangular Probability Distributions ............................. 2.9 Budgets as Random Variables ................................. 2.10 Updating Probability Distributions of Expected (Mean) Returns to Transition Cost ......................................... 2.11 Projecting Commodity Prices, Input Prices, and the Discount Rate . . CHAPTER 3. INFORMATION NEEDED AND SOURCES ................. 3.1 Introduction ............................................... 3.2 Rotations ................................................. 3.3 Commodity Price ........................................... 3.3 Seed Costs ................................................ Corn 23; Navy beans 24; Sugar beets 24; Soybeans 24; 3.4 Fertilizer Costs ............................................. 3.5 Herbicide Costs ............................................ 3.7 Insecticides ................................................ 3.8 Machinery Budgets .......................................... 3.9 Whole Farm Budget ......................................... CHAPTER 4. ANALYSIS AND RESULTS ............................... 4.1 Introduction ............................................... 4.2 Results ................................................... iv 9 10 10 13 16 17 20 20 20 21 23 25 25 31 31 36 42 42 42 4.3 Updating Subjective Probability Distributions ...................... 44 CHAPTER 5. CONCLUSIONS AND FUTURE RESEARCH ................. 47 5.1 Introduction ............................................... 47 5.2 Conclusions and Future Research Requirements ................... 48 BIBLIOGRAPHY ................................................... 50 APPENDIX A .................................................... 53 LIST OF TABLES Table 3.1 Estimated Relative and Absolute Commodity Prices ................. 22 Table 3.2 Estimated Prices Net of Hauling Costs ........................... 23 Table 3.1 Fertilizer Use .............................................. 26 Table 3.2 Fertilizer Prices ............................................ 27 Table 3.3 Fertilizer Costs, $/acre ....................................... 28 Table 3.4 Herbicide rates/acre, prices, and costs/acre ....................... 30 Table 3.5 Annual tractor and equipment Costs for 4 year beet rotation and 3 year wheat rotation ............................................ 33 Table 3.6 Annual tractor and equipment costs for 3 year beet rotation and 3 year wheat rotation ................................................ 34 Table 3.7 Annual Ownership .......................................... 36 Table 3.8 Whole Farm Budget for 600 Acre Farm with 80 Acres Per Crop in C - C - NB - B Rotation and 93 Acres Per Crop in C - NB - W Rotation ..... 36 Table 3.9 Whole Farm Budget for 600 Acre Farmwith 80 Acres Per Crop in C - NB-Band120AcresPerCropinC-NB-W ....................... 38 Table 3.10 Whole Farm Budget for 600 Acre Farm with 80 Acres Per Crop in C - 0 SB - B and 120 Acres Per Crop in C - SB - W ..................... 39 Table 3.11 Whole Farm Budget for 600 Acre Farm with 80 Acres Per Crop in C - SB - B and 120 Acres Per Crop in C - SB - W ....................... 40 Table 3.12 Annualized Difference in Mean Returns to Unallocated Costs for the Tenth and Ninetieth Percentiles .................................. 41 Table 4.1 Triangular Probability Distributions of Mean Returns to Transition Costs ....................................................... 44 Table 4.2 Example of Expert Resolution for Two Intervals ................... 46 Table 4.3 Example of Expert Resolution for Five Intervals ................... 46 Table A.1 Forecasted Relative Commodity Prices .......................... 60 Table A2 Regression Data ........................................... 61 Table A3 Models Describing the Relationship Between the Crop Prices and Explanatory Variables .......................................... 62 Table A.4 Correlations Between Explanatory of Variables .................... 63 vi LIST OF FIGURES Figure 1.1 Michigan’s ”Thumb and Saginaw Valley” .......................... 1 Figure 1.2 Michigan’s Share of North American Navy Bean Production ........... 1 _ Figure 2.1 The Triangular Probability Density Function. ..................... 17 Figure A.1 Relative Soybean Price vs. Time ............................... 53 Figure A.2 Relative Wheat Price vs. Time ................................ 55 Figure A.3 Relative Sugar Beet Price vs. Time ............................. 56 Figure A.4 Relative Navy Bean Price vs. Time ............................. 57 vii CHAPTER 1. INTRODUCTION 1.1 Background The fine textured soils in Michigan’s Thumb and Saginaw Valley (Figure 1.1) are very productive. In 1987, Arenac, Bay, Huron, Gratiot, Saginaw, Sanilac, and Tuscola counties accounted for 22% of corn grain, 28% of wheat, 25% of soybean, 73% of dry bean, and 92% of sugar beet production in Michigan. Figure 1.1 Michigan’s "Thumb and Saginaw Valley" Historically, Michigan has had a major share of North American navy bean production. However, Michigan’s production dry beans has fallen from 5412 cwt. in 1985 to 2220 cm. in 1988 (see Figure 1.2). Minnesota, North Dakota, and Ontario increased 2 total dry bean production 170 percent between 1972 and 1987, while Michigan’s production fell 35 percent (NASS, 1988). This is an indication that Michigan farmers’ comparative economic advantage in growing dry beans has diminished. In contrast to dry bean acreage, Michigan’s sugar beet acreage increased by 46.4% between 1980 and 1987. In this same time period United States sugar beet acreage increased only 5.3%. This suggests Michigan has a comparative advantage in sugar beet production over other producers in the United States. Figure 1.2 Michigan’s Share of North American Navy Bean Production 100 BOVA\/\ 60 v/\/\ ii L 5840 V .20 0 IIIFIIIIIIINJIII 7274 767880828486 7375777981838587 Year In order to regain or maintain their economic advantages, Michigan farmers are re-evaluating alternative production practices - particularly practices followed by 3 competing farmers in the Red River Valley of Minnesota and North Dakota. One promising practice is narrow row cropping systems. The yield and economic advantages of growing soybeans in narrower rows in the eastern corn belt are well known to researchers and farmers. The recent development in Michigan of upright dry bean varieties that can be direct harvested has increased farmers’ interest in producing dry beans in narrow rows. Narrow row1 sugar beets may offer an opportunity to increase Michigan’s comparative advantage in sugar beet production. Many farmers in the Red River Valley raise dry beans and sugar beets in 22 inch rows in contrast to the 28 and 30 inch rows used in Michigan’. Western European sugar beet growers, on soils similar to the fine textured soils in Michigan’s thumb, use a 19- inch row Spacing. Agronomic researchers believe Michigan farmers would have higher dry bean and sugar beet yields if they were to switch to narrower rows. A conference, "The Resource Efficiency in Agricultural Production," was held at Michigan State University in December, 1987 (Christenson, et. al., 1987) to address the engineering, agronomic, and economics issues of narrow row cropping. Participants included agonomists, plant pathologists, agricultural engineers, and agricultural economists from Indiana, Minnesota, North Dakota, and Michigan. Conference participants concluded: (1) a common narrow row width (row widths less than 28 - 30 inches) is needed for all row crops gown on a farm to avoid duplication of machinery; 1 Standard row widths in Michigan are 28 and 30 inches for corn, dry beans, sugarbeets, and soybeans. Some soybeans are grown in 7 inch rows, but it’s much less common than in Southern Michigan, Ohio and Indiana. 2 Estimates are 39% of navy beans are gown in 20-22 inch rows versus 54% grown in 28-30 inch rows (Poindexter and Rouget, 1989). Estimates are 22% pinto beans are gown in 20-22 inch rows versus 78% gown in 28-30 inch rows. Comparable survey information is not available on sugarbeets, but narrow rows are common. 4 (2) agicultural equipment manufacturers need to provide narrow equipment; (3) narrow row cropping systems can be more profitable than 28 or 30 inch rows systems when dry beans, sugar beets, or soybeans are a significant component of the system; and (4) there is a need for more research to clarify the conditions under which narrow row dry bean yields are increased. A particular issue to be addressed is pest and plant disease control, with white mold and related diseases in dry beans being the primary concern. Conference participants suggested a row width of 22 inches for the following reasons. An earlier canopy develops for 22 inch rows than 28 or 30 inch rows. This leads to improved natural weed control. A 22 inch row spacing permits mechanical cultivation for weed control. In rows narrower than 22 inches it is difficult to cultivate with large equipment. Dry beans can be pulled or direct harvested. In narrower rows than 22 inches, the same difficulty encountered in mechanical cultivation prevents pulling dry beans. Finally, the 22 inch width is adequate for mechanical harvesting of sugar beets. Much of the information regarding narrow row cropping systems presented at the conference was the subjective opinion of the conference participants. Most of this subjective information was disorganized and not in a form which could be utilized in a formal decision framework. Information from controlled experiments running 3-5 years under Michigan conditions is insufficient in length and quality to generate probabilistic information needed in decision analysis. Additionally, there was conflicting evidence on the response of dry beans yields to narrow rows, and farmers remain very concerned about the potential for increased risk of white mold. Also, while experiments have been done for individual crops, few studies have been done on narrow row crops in rotations over extended periods of time. 1.2 Problem Statement To address the issues raised at this conference, this study will focus upon determination of the conditions under which the switch from 28 or 30 inch row spacings to 22 inch row spacings will result in an increase in the net returns to fixed resources of farmers in Michigan’s sugar beet/dry bean/com production area of the fine textured soils of the Saginaw Valley and Thumb. The primary consideration is upon whether the conversion is profitable, under the most likely values for systems parameters, and an estimate of the probability of the conversion being profitable. The study assumes relatively high managerial skills upon the part of farmers, which is typical for those gowing sugar beets under contract. A formal decision approach, gounded in economic theory and formal statistical analysis, is needed to organize subjective information and experimental data on the question of whether there is an economic incentive to change from 28 or 30 inch spacings to 22 inch row spacings. The decision framework must consider: (1) subjective information and experimental information on changes in yields and input requirements between 28-30 inch rows and 22 inch rows; (2) the pertinent economic parameters (e.g., commodity and inth prices, interest rates); (3) the break-even machinery conversion costs, from an economic perspective, to warrant converting from 28-30 inch to 22 inch rows; (4) and the subjective probability a conversion from 28-30 inch rows to 22 inch rows would be profitable; (5) a formal method to revise estimates of parameters as new experimental and farm data become available. CHAPTER 2. METHODS or ANALYSIS 2.1. Introduction This chapter discusses the nature of the decision problem to be addressed, reviews the basic producer problem and discusses basic capital budgeting techniques. Decision analysis is introduced and other decision criteria are discussed. Risk analysis is briefly reviewed. The subjective probability elicitation procedure employed in this thesis is presented and the triangular probability distribution is introduced. A time series model is formulated to predict relative commodity prices. 2.2 Structure of Problem A farmer currently planting in 28 or 30 inch rows must decide annually whether to continue planting on that row spacing or to switch to a narrow row cropping system. If the decision is made to switch, the farmer must also decide how to convert his machinery-retrofit or replace. The farmer must also decide on the timing of machinery conversion. It is unlikely that most farmers would switch an entire machinery compliment in any given year. This study addresses the strategic question of whether there is an incentive to switch. The question of how and when to switch (if a incentive to switch exists) is left to subsequent investigations. 2.3 Economic Model of Firm Behavior The Profit Function and Capital Budgeting In a deterministic framework profits are defined as the sum of revenues minus the sum of operating costs and fixed costs: II=2Pi=IYiarAi-Zw,*)§-FC I , (1) s.t. Fiyx) = 0; where Pi is the price for commodity i, Yi is the yield/acre of commodity i, Ai is the number acres of commodity i, Wj is the price of input j, X)- is the amount of variable or allowable input j, PC is the sum of fixed costs and F(y,x)=0 is the production function. Fixed costs include annual ownership costs of machinery, land rent and non-allocated costs. This model is typically maximized with respect to the variable inputs to generate profit maximizing production plans. In a multi-period, deterministic model, the objective is to maximize the sum of discounted profit (i.e., net present value of total profits). This differs from the Single period model in the machinery can be purchased and sold (i.e., there are no fixed costs). Therefore, machinery replacement age becomes a decision variable. To calculate the optimal replacement age of machinery, the net present value of total profits is expressed as a function of machinery age and maximized with respect to replacement age: T IIi“) M NPV = M 2 ; “’9 (t) we M (1 l), (2) where “i is profits in year i as a function of replace age (t), d is the annual real discount rate and T is the time horizon of the project. Typically, this function is evaluated by allowing T .. co and iteratively searching for the optimal replacement age (t’). After the optimal replacement age of machinery (t*) is found it is substitute back into equation (2). The annualized equivalent return (AR) of this stream of profits is calculated as: g dtNPV(t °) AR __ 1-(1+d)" (3) (Copeland and Weston, 1987, pp. 47-55). Alternatively, the optimal replacement age of machinery can be found by minimizing the sum of discounted costs: min, 2 9") (4) . (1+d)’ where c,(t) is the ownership of machinery cost in year i as a function of replacement age t (Perrin, 1972). This expression is also typically evaluated iteratively to find the optimal replacement age t’. Substituting t‘ back into equation (4) yields the net present cost of machinery ownership. This net present cost can be expressed on an annualized basis by equation (2). For this study it is assumed that farmers minimize ownership costs of machinery and these costs are known with certainty. Denote the annualized cost as a function of the optimal replacement age as AC(t°). The net present value of profits as T .. on is found as equation (5): npvtz') 12.31 N: :3?”] (5) In a deterministic model the decision maker or farmer would be assumed to maximize the net present value of profits. In a risky environment moments other than the expected value of profits may be of importance to the decision maker. Therefore, 9 alternative objectives to profit maximization are used to model the decision process in a risky environment. The following section addresses modeling the decision maker in such an environment. 2.4 Decision Analysis, Risk Analysis and Other Evaluation Criteria The profit functions introduced in equations (1) and (2) are deterministic. All prices and yield relationships were assumed to be known with certainty. However, few real world production decisions are made where all variables are known. Actual production decisions are made in a risky environment. Decision analysis provides a theoretically sound approach to making choices in a position of uncertainty (Keeney and Raiffa, 1976). Decision analysis mathematically models decision makers as maximizers of expected utility. It is a necessity that the decision maker’s preferences and subjective probability assessments of random events are known or can be elicited. However, frequently only partial information regarding preferences is available. This information may take the form of a risk aversion coefficient. In this case mean- variance analysis might be employed. Mean-variance analysis is based on the argument that risk averse decision makers gain utility from higher mean returns and lose utility from high variability of returns. It can be argued that mean-variance analysis an approximation to expected utility maximization (Robison and Barry, 1987). This approximation may not be without error (DeVuyst and Preckel, 1991). If moments higher than the variance are important to the decision maker, mean-variance analysis may yield in appropriate conclusions (Hanoch and Levy, 1969). 10 If all that is known of preferences is that the decision maker is risk averse, the second order stochastic dominance criterion may imply actions that are consistent with decision analysis (Hanoch and Levy, 1969). Stochastic dominance criteria require a fully Specified probability distribution of returns for each possible action or choice. If this information is available stochastic dominance criteria may narrow the set of feasible solutions to a stochastically efficient set. However, the set may contain multiple actions and thus, fail to choose the action(s) consistent with expected utility maximization. 2.5 Risk Analysis Similarly to stochastic dominance criteria, risk analysis does not require much knowledge of the decision marker’s preferences. Risk analysis merely presents the cumulative probability distribution of returns to a decision maker and allows the decision maker to choose. For an example see Slovic et al (1979). From both a research and a cooperative extension point view, this approach is not satisfying. A goal of these goups is to help improve farmers’ decision making processes and to make sound recommendations. Risk analysis does little to aid in making recommendations but does provide information to the decision maker which may improve the decision process. 2.6 An Approximate Decision Criteria For the problem addressed in this thesis, preferences of decision makers are assumed to not be available. Nor given the complexity of the problem and lack of experimental data is it assumed the decision makers (i.e., farmers) can form subjective probability distributions for yields of rotation crops gown in a narrow row system. Thus, the standard decision criteria are inapplicable to this problem at the time of this study. 11 Despite the inapplicability of these decision criteria in this strategic decision problem, a method which systematically organizes available information and generates a first approximation to the optimal planting width is presented in this study. In order to develop this approximate decision method the available information is organized and some Simplifying assumptions are made. It assumed throughout this study that real input prices are known and constant and the expected relative output prices are known and held with subjective certainty. Available Information The available information at the time of this study is in the form of expert opinion. There have been few long run agonomic experiments studying narrows rows and their effects on yields for rotation crops. It is unreasonable to have confidence in expert subjective joint probability distributions for yields crops under these assumptions. The availability and frequency heuristic (Hogarth, 1987) suggest that expert opinion for mean yields and mean yield distributions are more reliable and can be confidently employed in the decision process. An appropriate elicitation procedure can be used to elicit mean yield distributions for crops in gown in various rotations for both 28 or 30 inch rows and 22 inch rows. An Approximate Risk Analysis Framework Utilizing the subjective probability of mean yield distributions, the row width which maximizes expectation of mean returns to machinery costs can be calculated for a given rotation the cumulative probability distribution of mean returns to transition for a conversion from 28 or 30 inch rows to 22 can be found. 12 The cumulative distribution of mean returns to transition cost is computed by calculating the distributions of mean or expected profits for 28 or 30 inch rows for a given rotation as in equation (5). E[II|y,] =p-y'. - w'x -AR, vy, (6) where Elm») is the expected profits given the yield vector yi has occurred, p is the vector of output prices, w is the vector of input prices, x is the level of variable inputs and AR is the annual ownership costs of machinery. Note, the assumption that only yields are stochastic is implicit in this equation and therefore the distribution of expected profits is a linear combination of the random mean crop yields. The distribution of mean or expected returns to machinery costs are computed for 22 inch rows and the same rotation and the annual ownership costs of machinery for 28 or 30 inch rows is subtracting. The distribution found in equation (5) is subtracted from the distribution of 22 inch returns to machinery costs less the annual ownership costs of machinery for 28 or 30 inch rows. This generates the distribution of mean returns to transition costs for a conversion from 28 or 30 inch rows. This distribution can be viewed as a first approximation of a risk analysis. An Approximate Decision Analysis Framework To find the new width which maximizes the expectation of mean returns to machinery costs, the distribution of mean returns to machinery costs are calculated for both 28 or 30 inch rows and 22 in rows. This is computed by equation (6): max Em| 9,3], One [22,30] (7) 13 where Horde.) = w - (Y‘Ie') - W - (“e-)1; is the realization of yield vector Yi given a row spacing 9,, p is a vector of output prices, W is a vector of input prices, (Xlen) is a vector of variable input levels for row width an and E[-] is the expectations operator. Equation (6) is maximized by the row width which has the highest expected mean returns to machinery ownership costs. This can be viewed as a first approximation to profit maximization. Note, throughout this discussion land rental costs have been ignored. The focus of this study is on the economic differences in mean returns between wide rows and narrow rows. In a partial equilibrium analysis, land rental rates do not differ between the row widths under consideration. Thus, land rental rates do not effect the relative economic advantages or disadvantages of 22 inch rows over 28 or 30 inch rows. 2.7 Elicitation of Joint Probability Distributions The procedure utilized to elicit the joint probability distributions of mean yields was designed to capture important interactions. The first interaction is the rotation effect on mean crop yields for crops gown in rotation for a given row width. For example, soybeans gown in rotation and in 30 inch rows with corn might increase mean corn yields and vice versa. The elicitation procedure was designed to aid the expert explicitly encode this rotation effect. The next relative effect is the interaction of row widths on mean yields. For example, crops gown in 22 inch rows might have higher mean yields than crops gown in 30 inch rows. This interaction also is explicitly incorporated into the elicitation procedure. It should also be noted that rotation effects might differ across row widths. 14 To capture these interaction effects the availability and frequency heuristics were employed with the anchoring and adjustment process (Hogarth, 1987). AS previously mentioned the availability and frequency heuristics imply expert opinion regarding the distribution of mean yields is likely to be more accurate than expert opinion regarding the distribution of yields. These heuristics also imply that an expert yield is likely to accurately assess the mode of the mean yield distribution. The mode or most likely mean yield is a point an agonomic expert easily conceptualize. The anchoring and adjustment process is a method that is used (often subconsciously) to estimate the relative magnitude of uncertain outcomes. In using this method, a well established or relatively certain point is used as a point of reference and the magnitude all other points are judged relative to this point of relative certainty. The point of relative certainty is referred as the anchor point around which adjustments are made. This method can help improve judgements. In the present context, the mode of a mean yield distribution may be utilized as an anchor point and enable the expert to improve his judgements regarding other points on the mean distribution. In the elicitation procedure employed in this study, the expert was also given another anchor or reference point. Continuous corn rotation in 28 or 30 inch rows have been well studied by the agonomic community. The availability heuristic suggests that this rotation is a good anchor point. The distribution of mean continuous corn yields gown in 30 inch rows is elicited and used in this study to aid the expert in formulating distributions of mean corn yields for other rotations and other row spacings (i.e., 22 inch rows). The last set of anchors utilized was the distributions of mean yields for rotations in 30 inch rows. Rotations gown in thirty inch rows have been studied more extensively that rotations in narrow rows. The availability heuristics suggest that once elicited these 15 distributions serve as good reference points when formulating the distributions of mean yields for rotations gown in 22 inch row spacings. The steps of this elicitation procedure are outlined here: 1. Elicit the mode or mostly like mean yield of corn gown in a continuous corn rotation and thirty inch rows. 2. Elicit approximate tenth and ninetieth percentile mean yields for corn gown in continuous corn rotation and thirty inch rows. 3. Repeat steps 1 and 2 for corn gown in rotation(s) to be studied (e.g., com- soybeans-wheat) gown in thirty inch rows. 4. Elicit the approximate mode, tenth percentile and ninetieth percentile yields of the other crops of the rotation gown in 30 inch rows. 5. Repeat steps 1 through 4 for twenty inch rows. 6. Steps three through five are repeated for each rotations gown on the farm being evaluated. By imposing a probability distribution on the three points elicited for each crop mean yield, the subjective probability distributions needed for the approximate decision analysis (or decision aid) and approximate risk analysis are generated. The probability distribution chosen this study is the triangular distribution. 2.8 Triangular Probability Distributions The triangular probability distribution is often used to represent continuous distributions under sparse data conditions (Keefer and Bodily, 1983). While this is an 16 imperfect representation, it does provide a reasonable approximation of the mean and variance. Black (1990) demonstrated the triangular distribution reasonably approximates several unimodal distributions. Black generated small (10 to 20 observations) random samples for these distributions and statistically tested the hypothesis that the samples were generated by triangular probability distributions. These tests were unable to reject this hypothesis. It seems reasonable to expect that mean crop yields are unimodally distributed. It is, therefore, reasonable based on Black’s studies to approximate mean crop yields with triangular probability distributions. The triangular probability distribution is uniquely defined by its mode and endpoints of its support. The density function is in fact expressed as a function of these three points: 2*(x-a) ifanSc m“ (b-aM-a) (8, 2*(b-x) Ifcfl_ _——— 7—_ —_- _— . 120 H. P. Tractor ; 160 H. P. Tractor 3.9 Whole Farm Budget Whole farm budgets were developed by combining of budgets for: C—C-NB-BwithC-NB-W, C-NB -BwithC-NB -W, C-C-SB -BwithC-SB -Wand, C-SB -BwithC-SB -W when C:Corn; NB: navy beans; B: sugar beets; SB: soybeans; and W: wheat. Tables 3.8 through 3.11 summarize the whole farm budgets for the difference in twenty-two inch row spacing and thirty inch row spacing annualized mean returns. These detailed budgets are on an annualized basis and are reported for the elicited most likely mean yields. The annualized mean returns for the tenth and ninetieth percentiles are reported in table 3.12. The differences in annualized mean returns were divided by the discount rate to generate the net present value of mean returns to transition. These net present values are reported in table 3.13. Table 3.8 Whole Farm Budget for 600 Acre Farm with 80 Acres Per Crop in C - C - NB - B Rotation 36 and 93 Acres Per Crop in C - NB - W Rotation Gross Revenue S/year ll Crop Acres 30" Rows 22" Row ’ Corn, lst year 174 54,062 55,725 Corn, 2nd year 80 21,988 22,753 Navy beans 173 92,313 106,160 Sugarbeets 80 61,618 69,082 Wheat 93 21,288 m 25,269 275,008 Seed Herbicide Insecticide Fertilizer Interest on Operating Machinery, labor & fuel land, management, and other costs Allocated Costs, 3/ Year “ $11,982 11,046 205 15,194 2,346 M $91,699 l I Annual net return to $159,570 $178,669 $13,327 12,453 383 16,683 2,567 .2922!) $178,669 Increase in net return to land, management and other unallocated costs associated with changing from 28-30” rows to 22" rows $19,099 37 Table 3.9 Whole Farm Budget for 600 Acre Farm with 80 Acres Per Cmp in C - NB - B and 120 Acres Per Crop in C - NB - W I Gross Revenue 3 / year Revenue Cro 30" Rows 22" Rows Corn, lst year 200 62,140 64,052 Navy beans 200 106,720 122,728 Sugarbeets 80 61,618 69,082 Wheat 12g 27,468 27,468 600 257,946 283,330 Allocated Costs, 3/ Year Seed 1 1,414 12,634 Herbicide 10,382 11,822 Insecticide 0 0 Fertilizer 14,497 16,092 Interest on 2,246 2,459 Operating Machinery, labor & 51,176 51,176 fuel 89,715 94,183 Annual net return to 168,231 189,147 land, management, and other costs Increase in net 20,916 return to land, management and other unallocated costs associated with changing from 28-30' rows to 22" rows Table 3.10 Whole Farm Budget for 600 Acre Farm with 80 Acres Per Crop in C - C- SB - B and 120 Acres Per Crop in C - SB - W l Gross Revenue S/year Revenue Acres Cro 30" Rows 22" Rows Corn, lst year 174 54,062 55,725 Corn, 2nd year 80 21,988 22,753 Soybeans 173 49,962 56,208 Sugarbeets 80 61,618 69,082 Wheat .23 A2133. 11.2% 600 208,918 225,056 Allocated Costs 5/ Year Seed 11,030 11,626 Herbicide 12,015 13,888 Insecticide 205 383 Fertilizer 13,814 15,182 Interest on 2,278 2,453 Operating Machinery, labor & 511,926 59,226 fuel . 90,268 93,958 Annual net return to 118,650 131,098 land, management, and other costs Increase in net 12,448 return to land, management and other unallocated costs associated with changing from 28-30" rows to 22" rows 39 Table 3.11 Whole Farm Budget for 600 Acre Farm with 80 Acres Per Crop in C - SB - B and 120 Acres Per Crop in C - SB - W I Gross Revenue S/year Revenue Cro 30" Rows 22" Rows Corn, lst year 200 62,140 64,052 Soybeans 200 57,760 64,980 Sugarbeets 80 61,618 69,082 Wheat 120 27,468 27,468 208,986 225,582 Allocated Costs, S/Year Seed 10,014 11,835 Herbicide 11,502 12,874 Insecticide 0 0 Fertilizer 13,361 14,356 Interest on 2,175 2,384 Operating Machinery, labor & 51,176 51,176 fuel Total Allocated 88,228 92,625 Costs Annual net return to 120,758 132,957 land, management, and other costs Increase in net 12,199 return to land, management and other unancated costs associated with changing from 28-30" rows to 22" rows 40 Table 3.12 Annualized Difference in Mean Returns to Unallocated Costs for the Tenth and Ninetieth Percentiles 30" Rows 22" Rotation Rows Percentile Pair Percentile 10th 90th 10th 90th C-C-NB-B 130149 179661 127139 224783 C-NB-W C-NB-B 135382 190408 132543 239936 C-NB-W C-C-SB-B 101448 135852 99386 162008 C-SB-W C-SB-B 102053 139482 99265 166169 C-SB-B = E Table 3.13 Net Present Value of Differences in Mean Returns to Transition Costs Rotation Percentile Pair 10th 90th C-C-NB-B -30106 451219 C-NB-W C-NB-B -28388 495280 C-NB-B C-C-SB-B -20618 261558 C-SB-W C-SB-B -27882 266866 C-SB-W CHAPTER 4. ANALYSIS AND RESULTS 4.1 Introduction The net present value budgets developed in chapter III were assumed to be generated from a subjective triangular distribution. Three budgets were developed for each rotation pair. The budgets associated with the tenth and ninetieth percentile yields approximate the tenth and ninetieth percentiles of the underlying triangular distribution. The budget associated with the most likely yield approximates the subjective mode of the underlying distribution. A triangular density function was imposed on these three points. Adjustments were made to the tenth and ninetieth percentile budgets to insure the resulting function satisfied the definition of a probability density function. These resulting distributions are used in this study to compare the relative economic advantages and disadvantages of twenty-two inch row spacing to thirty inch spacing. 4.2 Results Risk analysis typically leaves the decision of what action to be taken up to a manager. The information presented to the manager often takes the form a cumulative probability distribution. A primary result of this study is a cumulative probability distribution of expected returns to transition. This is not as complete as a cumulative probability distribution of returns to transition. However, it does provide considerable information to a farmer manager or to cooperative extension staff. These distributions of break even mean returns to transition are reported in table 4.1. The expected value of 41 42 each distribution is also reported. By the definition of a triangular distribution, each of these distributions are uniquely determined by its lower and upper bounds and the mode. Each of these rotation pairs has considerable promise for increased profitability based the results reported in Tables 3.8 through 3.11 and Table 4.1. The expected values of mean returns to transition costs range from $119,748 to $229,666. However, for each rotation pair there is a positive probability of a negative mean return to transition costs. The probability of a negative mean return ranges from approximately twelve to fourteen percent. This implies on average a farmer could expect to loose money by converting to twenty-two inch rows twelve to fourteen percent of the time. Without the complete distribution of break even returns to transition, it is inappropriate to apply mean-variance analysis to this study. However, it is noteworthy that as the expected value increases across the distributions, the support of the distributions also increases. This does not necessarily imply that the variability of the break even returns to transition are similarly affected. However, the rotations with the highest mean returns on average are those rotation with dry beans. Dry beans are generally considered a risky crop (relative to the to the other field crops grown in the Saginaw Valley). Therefore, it follows that the variability of returns associated with dry bean returns is relatively high and the variance of the mean return is also expected to be high. The results reported in this study are consistent existing information regarding the relative riskiness of dry beans. In each of the rotations studied here, the expected mean return to unallocated cost is higher for 22 inch rows than the same rotation grown in 30 inch rows. This is a first approximation of expected profit maximization. While this is an incomplete 43 analysis, it does provide evidence to suggest that expected profits are higher for these rotation when grown in a 22 inch row width. Finally, it should be noted which crops in the rotation pairs support the cost of transition. From the budgets reported in chapter three, it is clear sugar beets, dry beans and soybeans are the crops which generate increased profitability when grown in narrow rows. This is due the expected increase in yields due to narrow rows. Corn has very little change in returns. Wheat is drilled in both systems and, therefore, does not generate added profitability. Table 4.1 Triangular Probability Distributions of Mean Returns to Transition Costs Rotation Pair Lower Mode Upper Expected Bound Bound Value C - C - NB - B -203106 190989 634831 207571 C - NB - B C - NB - B -215388 209156 695229 229666 C - NB - W C - C - SB - B -126618 124461 365506 121116 C - SB - W C - SB - B -137882 121982 375144 119748 , C - SB - W 4.3 Updating Subjective Probability Distributions As experimental evidence is collected, the prior estimates collected in this thesis need to be updated to include the new information. Expert resolution is a general approach to combine multiple probability distributions of an event into one posterior probability distribution. Genest and Zidek (1986) discuss at length the various methods 44 of expert resolution. In the present context the prior distribution is the distribution of average returns to transition costs. The posterior distribution is the combined subjective probability distribution of the prior and the experimental data. A simple combination of these two sources of probabilistic information can be computed as follow. Divide the support of the prior distributions into a fixed number of disjoint and exhaustive intervals and calculate the probability of falling within that interval for both distributions. The combined distribution is found by averaging the probability under the prior for a given interval with probability implied by the experimental data. This method is consistent with many of the axiomatic approaches described by Genest and Zidek. Examples of this procedure are displayed in Tables 4.2 and 4.3. In Table 4.2 the support of the distributions are divided into two intervals, the probability of falling below zero and the probability of exceeding zero. In Table 4.3 the distributions are divided into five intervals. An alternative to this simple averaging would be to weigh one distribution more heavily than the other. The would be necessary if there was reason to believe one distribution was more representative of the true probability distribution of mean returns to transition. The weights are chosen to represent the relative confidence of each distribution and should sum to one. In Table 4.2 and Table 4.3, Prob(S) denotes the subjective probability of falling with a given interval, P(E) denotes the probability implied by experimentation of falling within a given interval, and P(C) denotes the combined probability falling within a given interval. 45 Table 4.2 Example of Expert Resolution for Two Intervals Range Probability that mean returns new <0 >0 i PROB (S) 0.142604 0.857396 PROB (E) 0.14 0.86 1 PROB (C) 0.141302 0.858698 Range «10000. W low? 100000 20000 PROB(S) 0.010764 0.13184 0.281857 0.339354 0.236185 PROB(E) 0.015 0.125 0.332 0.348 0.18 PROB(C) 0.012882 0.12842 0.3069285 0.343677 0.2080925 CHAPTER 5. CONCLUSIONS AND FUTURE RESEARCH 5.1 Introduction This study has addressed the issue of the potential economic incentives for growing crops in narrow rows in Michigan’s Thumb and Saginaw Valley. Prior experience in soybean production has demonstrated yield and economic advantages of narrow row soybeans. The exists some evidence that dry beans and sugar beets also have increase profit potential when grown in narrow rows. The objectives of this study have been to organize the available information regarding narrow production and provide an estimate of the economic incentives of narrow row cropping systems for Thumb and Saginaw Valley dry bean and sugar beet farms. Due to a lack of experimental data, a complete probability distribution of crop yields under alternative sequences for narrow rows as contrasted to conventional row widths can not be accurately approximated. Decision analysis and methods consistent with decision analysis require complete probability distributions. Complete decision analysis tools are not appropriate to investigate this issue at the time of this study. Therefore, a decision aid was developed to organize the existing biological and engineering information and to provide a first approximation of the expected returns to transition for farm managers and cooperative extension staff. The framework developed can be used for subsequent assessments as new information becomes available. The decision aid utilized subjective probability distributions of mean rotation crop yields. The estimated probability distributions of mean crop yields were generated by an elicitation procedure. The elicitation procedure was designed to utilize commonly known heuristics about how people judge and prcess information. 46 47 The input requirements for crops gown in narrow rows differ from the input requirements of crops gown in conventional row widths. Input requirements also differ across crop rotations. The decision aid employed incorporated these differences. Estimates of the value of input prices and input requirements were taken from the referenced sources. Relative commodity prices were estimated using econometric models. Mean crop yields were treated as jointly distributed random variables. All other relevant economic variables were treated as deterministic or held by the decision maker with subjective certainty. Cumulative probability distributions of net returns to unallocated costs were constructed for both 22 and 30 inch rows using the distributions of mean crop yields, input requirements and prices, and the forecasts of relative commodity prices. The cumulative probability distribution of mean returns to transition costs was found by subtracting the probability distribution of returns to unallocated costs for 30 inch row crops from the probability distribution of returns for 22 inch row crops. The expected returns to transition costs are the amount on average a farmer could pay to retrofit his equipment from conventional row widths to narrow row widths. The primary focus of this was on these cumulative probability distribution of expected returns to transition and choosing the row width which generates the highest expected mean returns to unallocated costs. Using the cumulative probability distribution as a decision aid, the questions to be answered are: Is there sufficient evidence of economic gains to encourage further research? Is there sufficient evidence of a economic gains that cooperative extension staff should in encourage farm managers to retrofit their equipment sets and plant 48 narrow row crops? Based on the available information at the time of this study the answer to the first question is affirmative. The second question remains unanswered. However, there is sufficient evidence to suggest that farmers should consider narrow row cropping systems as an alternative production practice. 5.2 Conclusions and Future Research Requirements From the results present in chapter IV it can be concluded that crops gown in narrow rows have a large probability of increasing average farm profits. It also can be concluded that more research is needed to fully analyze this problem. Agonomic research regarding the joint distribution of yields of rotation crops gown in narrow rows is lacking. Experiments with the same rotations but different row spacings need to be conducted to produce the complete probability information required by decision analysis. These experiments need to investigate the effect narrow row spacings have on yield interactions due crop rotations, fertilizer requirements, diseases, weed infestations and other pests, and drought, flood, heat tolerance, and the tillage problems associated with narrow rows. This research needs to be incorporated via expert resolution into the results of this study on an annual basis. This will improve the estimates generated here. As this research is conducted, the relevant research issue is when is there enough experimental evidence to move from the decision aid method presented in this study to a complete decision analysis. Economic researchers do not have a rule which tells what method should be employed. The decision is generally left to the researcher and his/her audience is left to decide how confidence to have in the results. However, Cooperative Extension staff require a large degee of confidence in their own analysis before 49 recommending large scale changes to a farmer’s production methods. Thus, a large amount of consistent information needs to be available prior to such recommedations. In the case of narrow row cropping systems versus common row spacings, it is clear that until complete rotations can be gown and harvested in experiments the data for decision analysis needed will not exist. This will take from three to seven years depending the length of the rotation and the experiments will need to be conducted at several locations to increase confidence in the results. After completing at least one full rotation on the same plot and several locations, a decision can be made on the appropriateness of the various decision analysis tools outline in this study. The experimental data may be combined with expert opinion via expert resolution to increase confidence in the cumulative probability distributions and reduce the impact of outlying data points. The potential for improved farm profitable by utilizing narrow row cropping systems clearly exits for farms with rotations containing dry beans, soybeans and/ or sugar beets. This preliminary study indicates that there is a high probability the narrow row cropping will increase average farm profits for Michigan’s dry bean and sugar beet farms. However, the adoption of this system will vary with the risk aversion of farm operator/managers, their position in the life cycle, the financial health of the farm and numerous other factors. The questions of which farmers will adopt this technology, when it will be adopted and how (referring to the dynamics of the transition process) farmers will adopt it are beyond the scope of this study. BIBLIOGRAPHY Bibliography ASAE (1987), American Society of Agricultural Engineers Standards. American Society of Agicultural Engineers, St. Joseph, MI. Black, J. R. (1990), Unpublished working paper. Black, J. R., G. Schwab, T. Harrigon, and B. Dawson (1989), "What are the Costs of Owning and Operating Farm Machinery." Unpublished. Christenson, D. R. and M. W. Adams (Feb. 1983), "Practices for Production of Erect Dry Beans in Michigan." Michigan Cooperative Extension Service Bulletin E-1525, Michigan State University. Copeland, T. and J. Weston (1988), Financial Theory and Corporate Policy (Third Edition). Addison-Wesley Publishing Company, Reading, MA., pp. 47-55. DeVuyst, E. A. and P. V. Preckel (1991), "The Risk Premium and Skewness." Unpublished working paper. Erdman, M. H., E. C. Rossman, and L. S. Robertson (Sept. 1989), "Profitable Corn Production in Michigan." Michigan Cooperative Extension Service Bulletin E- 1429, Michigan State University. Fuller, E. I. and M. F. McGuire (1989), ”Minnesota Farm Machinery Economic Cost Estimates for 1988.” Minnesota Cooperative Extension Service AG-FO-2308, University of Minnesota. Genest, C. and J. V. Zidek (1986), ”Combining Probability Distributions: A Critique and Annoted Bibleogaphy.” Statistical Science (1), pp. 114-148. Hanoch, G. and H. Levy (1969), ”The Efficiency Analysis of Choices Involving Risk.” The Review of Economics and Statistics (36), pp. 335-346. Hesterman, O. B., J. J. Kells, and M. L. Vitosh (Aug. 1987), "Producing Soybeans in Narrow Rows.” Michigan Cooperative Extension Service Bulletin E—2080, Michigan State University. ' Hogarth, R. M. (1987), Judgement and Choice (Second Edition). John Wiley & Sons, New York, N. Y. 50 51 Hogg, R. V. and A. T. Craig (1970), Introduction to Mathematical Statistics (Third Edition). The Mac Millan Company, New York, N. Y. Hoskin, R. L. (1981), "Analysis of Alternative Saginaw Valley Crop Rotations - An Application of Stocastic Dominance Theory." Ph. D. Dissertation, Michigan State University. Keefer, D. and S. Bodily (1983), 'l‘hree Point Approximations for Continuous Random Variables." Management Science (29), pp. 595-609. Keeney, R. L. and H. Raiffa (1976), Decisions with Multiple Objectives: Prefences and Value Tradeojfs. John Wiley and Sons, New York, N. Y. Kells, J. J. and K. A. Renner (Nov. 1989), "1989 Weed Control Guide for Field Crops.“ Michigan Cooperative Extension Service Bulletin E-434, Michigan State University. Leep, R. H. and L. O. Copeland (Oct. 1981), "Small Grain Production in Michigan." Michigan Cooperative Extension Service Bulletin E- 1522, Michigan State University. Michigan Farmer (May 6, 1989), ”Narrow Row Navies; More Beans-Better Quality. (D. Peterson),” pp. 8-9. NASS (1988), Michigan Agricultural Statistics. United States Deptartment of Agiculture National Agicultural Statistics Service. Perrin, R. K.(1972), "Asset Replacement Principles." American Journal of Agricultural Economics (52), pp. 60-67. Pioneer Newsheet (Spring 1989), ”Improved Quality Progam Here for 1989." pp. 3. Resource Efficiency in Agicultural Production Conference (Dec. 1987), Michigan State University. Renner, K. A., J. R. Black, and E. A. DeVuyst (1989), ”SOYHERB.” Agiculture Economics Staff Paper 88- 141, Michigan State University. Robison, L. J. and P. J. Barry (1987), The Competitive Finn’s Response to Risk. Macmillan Publishing Company, New York, N. Y. Slovic, P., B. Fischoff and S. Lichtenstein (1979), ”Rating the Risks.” Environment (21), pp. 14-20, 36-39. TELFARM (1987, 1988). Michigan State University Computerized Farm Record Keeping System. 52 Warnke, D. D., D. R. Christenson, and M. L. Vitosh (Sept. 1985), "Fertilizer Recommendations: Vegetable and Field Crops in Michigan.” Michigan Cooperative Extension Service Bulletin E-550, Michigan State University. APPENDIX A APPENDIX A COMMODITY PRICE MODEL Introduction The prices used are based on 1960-1988 price relationships. Figures A1 - A4 depict the relationship of wheat, soybean, dry bean and sugarbeet prices to the corn price over time; that is: c Pt mp 110°”. Two models were built. The first model was formed by regessing the price of each crop on corn price and the fraction of corn acres diverted under the USDA acreage reduction progam. The fraction of corn acreage diverted is a proxy for two influences. First, is as an indicator of price distortions due to government influence. Second, it serves as a proxy for US. stocks; when stocks are large relative to utilization, the government diverts a higher percent of corn acreage. A second model was built to test for a change in the market structures over time due to changes in relative rates of change in technology, preferences, etc. With the exception of wheat, time was found to be statistically significant and, therefore used to measure the trend at relative price changes. Figures A1-A4 demonstrate gaphically the trend in relative prices over time. Table A1 contains the data used in the regessions. As a simple test for multicollinearity, correlations of the explanatory variables were computed. Table A3 summarizes those correlations. The highest correlation was between the price of corn and year (0.7537). From this, it was judged that multicollinearity is not a serious problem in these models. 53 Soybean/Com price 54 FunnelLl Rekuheikutemnlikr‘m.Thne 2 L...._..._.- . __ -_.. -...._- ._.-.... 1 5 Wu..-” -.........-......... .. O 0.5 —---~--—-~~ -- moms—u —.-.~--——o—v._ manna-c -—..~..—.—— ———.-_ . -o —.¢—- —- .- o-..-—--- .- -- .. .—. .-- .o- ...-.o ~ v-..--D - -. .--_--—-4 -- ——-- . ~—~-. —-o o—-—-- --. ~0--.o—-.o- -.. . -u. unu- m-cWH—uo Lap—.- 0....- —»~I—b.“¢- m~--a~v—n .0 1960 1965 T l— r r 1980 1975 1985 Tine Wneot/Com price 1.8 1.6 1.4 L2‘ (18 0.6 ‘ 0.4 0.2 55 Figure“ RehfiveWbentPricemTi-e A \ i “‘1 l l --.———v ——. a--‘ -—I- -—-——¢—- u..-.. ———-———a.- ——-—-—q w—-— —--.-———.—--—.o .._- -——- ~o--. on u— u.- -- I... u—I—.— —-- —-1 v 6*- a... —- .0- -_ -— —— ——-—.-—o--—» n”: .——_-———.—. -— —- —--—-— — - —— -————— u—n- _— ...——_..-.. --... -- -.....____.._-. ..-.. - .._...-..fi' l —— o—— —— ————-0-- an ——-- — —o—-—-—- — -— .0 v- — — - —-—.—- — --—— J —. .0. -~ —- u—lI-o mo*--— -u-d 1 965 1 970 r 1 975 Ttme l r £3 a ,0 ..lL---- __-_ o 1 985 Sugabeet/Com price '56 Figure” RehflveSuglnBeetPrbemTine 22 T. 20 ~--- .- .3 18 A ..f ,5 .-_..__-_._-.-..__.- __..__._...._-.._ ____-, / \ _ 14 ...-..._..._._.. .__.__._,, ,_ , T _; 12v —----- - -........ .......... ....: 8 --._..._-....,_,,.___,,,_,___,_m________,_____ ______: s-L---~--—----- - — - -——— —-~— -- ~————-~ -— -’- - ..._.__,j 4 -...-...._... -- - ,--- -..- -.__...._._-._.g 2~L—-—-—-—---—- — -- -- __ “,3 0 I V F F r d 1 975 Tme 57 thuelLA RmhnhePunylkanihmuanTh-e 4-1!fi I.aw-tlA.lil - c o . .. . _ m . o m . . . . a .4 L , _ a . u v n . fl 5 a . w . . o a . o . . n m . w - 0 . .. n . . p w W a . a m M _ u _ . . H . m . . q. S. :14 til... u—o-o- o'coo -— c.- ~-~.----o—. 0' or. Mini 1990 ri 1980 F’ 1970 16 14 b.-. -_.. . . 1960 1985 1965 1975 line 58 Corn The corn price based upon AGMOD6 developed by Ferris. The average corn price over the 1990’s predicted by the model is $2.59/bu (in 1989 dollars). The AGMOD model run assumed government progams are replaced in the mid-1990’s by the Conservation Reserve. This prediction is used as the basis for predicting the price of the other crops. Soybeans The soybean price model regesses the prices of soybeans on the corn price fraction of corn acres diverted, and year. Each of the explanatory variables was statistically discernably geater than zero. The resulting equation is: Pts°ybeams = 143.90 + 1.247 ... (Fraction of corn acres diverted) + 1.851 * P,C°“‘ + 0.07345 It Year To find the long-run average soybean price in 1989 dollars, the $2.59/bu corn price of fraction of corn acres diverted was assumed to be zero, (assumes federal government price and income support progams are decoupled from acreage diversion), and year was varied from 1989 to 2000. The resulting prices were then averaged to find the long-run average soybean price. Wheat The wheat price model regessed the price of corn, fraction of corn acres diverted, fraction of wheat acres diverted under government progams, and a binary variable as a proxy for the distortion to the long-term corn-wheat price relationship “Dr. John Ferris, Department of Agicultural Economics, Michigan State University. 59 during the "Johnson" administration (1960-1968), and year. Only two explanatory variablesucorn price and fraction of wheat acres diverted were significant. The nonsignificant variables were dropped resulting in the following equation: thmat = 0.2212 - 0.984 * (Fraction of wheat acres diverted)t + 1.252 :- Pf“ ”i“ The long-run average wheat price in 1989 dollars, was found using the same averaging method described in the soybean model. Sugarbeets The sugar beet model was developed using the same explanatory variables as the soybean model. All explanatory variables were significant. The resulting equation is: P,sugarbeet = -501.2589 - 14.7134 at (Fraction of corn acres diverted), + 11.905 * P,corn (Corn Price) + 0.355 * year Navy beans The navy beans model was developed using the same explanatory variables as the soybean model. The price of corn, fraction of corn acres diverted and year were statistically significant. the resulting equation is: Wm = 695.754 - 7.089 :- (Fraction of corn acres diverted), + 5.581 * P,C°’“ + (Corn Price) + 0.355 a: year 60 This model exhibited positive auto-correlation, with a Durbin-Watson of 2.713. Since this study focuses mainly on long-run differences, no attempt was made to explain or correct for this auto-correlation.Table A1 reports the prices used to forecast and used in the economic evaluation. Table A.1 Forecasted Relative Commodity Prices Crop Units Relatire Price Absolute ‘ Corn Bu. 1.00 2.59 Soybeans Bu. 2.86 7.42 Wheat Bu. 1.34 3.47 Sugar beets Ton 14.83 38.41 Navy beans th 10.43 27.02 61 Table A2 Regression Data Michigan farm prices for corn, soybeans, dry beans, wheat, and sugarbeets, fraction of corn and wheat acres diverted, and Johnson era dummy variable. YEAR ' ' D D 1 Li. M 11111. M 1'1- 0 1113' D ' 1113' 1 1411’ 3 l- 1960 0.99 0.0 0.0 0.0 2.08 5.9 1.75 11.7 1961 0.99 0.17 0.0 0.0 2.23 6.4 1.73 9.7 1962 1.05 0.17 1.0 0.11 2.33 6.3 1.95 12.1 1963 1.08 0.12 1.0 0.17 2.50 6.5 1.76 13.0 1964 1.15 0.14 1.0 0.04 2.64 6.7 1.30 10.5 1965 1.15 0.14 1.0 0.07 2.56 8.2 1.40 10.6 1966 1.22 0.13 1.0 0.11 2.72 6.4 1.65 13.4 1967 0.97 0.0 1.0 0.0 2.47 8.4 1.26 13.0 1968 1.03 0.11 1.0 0.0 2.39 8.0 1.07 10.7 1969 1.14 0.11 0.0 0.13 2.33 6.3 1.20 13.1 1970 1.32 0.1 0.0 0.13 2.84 9.7 1.40 12.2 1971 1.03 0.0 0.0 0.0 3.05 11.5 1.34 13.4 1972 1.49 0.32 0.0 0.34 4.60 9.7 1.67 12.4 1973 2.52 0.1 0.0 0.17 5.73 27.3 4.30 30.5 1974 2.91 0.0 0.0 0.0 6.28 14.8 3.64 47.5 1975 2.35 0.0 0.0 0.0 4.78 25.9 3.22 24.8 1976 2.04 0.0 0.0 0.0 7.22 16.1 2.53 22.4 1977 1.92 0.0 0.0 0.0 5.54 18.3 2.02 20.1 1978 2.22 0.09 0.0 0.0 6.81 14.8 3.30 23.5 1979 2.48 0.09 0.0 0.0 6.13 18.5 3.82 38.9 1980 3.07 0.0 0.0 0.0 7.49 26.4 3.60 40.7 1981 2.35 0.0 0.0 0.0 6.04 25.6 3.47 26.5 1982 2.48 0.0 0.0 0.0 5.46 13.7 3.31 35.8 1983 3.20 - 0.32 0.0 0.31 7.82 23.2 3.39 36.2 1984 2.56 0.0 0.0 0.2 5.79 19.6 3.18 34.4 1985 2.14 0.0 0.0 0.1 4.93 15.0 2.84 29.6 1986 1.50 0.03 0.0 0.03 4.78 23.6 2.42 30.0 1987 1.94 0.15 0.0 0.0 5.88 14.8 2.57 31.0 1988 2.60 0.1 0.0 0.0 7.70 34.6 3.70 35.0 PDDVR: Fraction of corn acres diverted, JNDM: Binary variable for years 1962-68, WHTDV: Fraction of wheat acres diverted, MFPSOY: Michigan farm price for soybeans, MFPDRY: Michigan farm price for dry beans, MFPWHT: Michigan farm price for wheat, MFPBTS: Michigan farm price for beets. Table A3 Models Describing the Relationship Between the Crop Prices and 62 Explanatory Variables" Explanatory Models Variables Soybeans Wheat Sugarbeets Navybeans Constant -143.90 0.22 -501.26 -695.76 (3.21) (0.091) (1.8) (-2.26) ll Year 0.073 NS 0.255 0.355 (3.21) --- (1.81) (2.26) Corn price 1.851 1.252 11.905 5.581 (6.96) (12.3) (7.28) (3.0) Corn acreage 1.247 NS (-14.74) -7.089 diverted (0.87) --- (-1.6) (-0.72) Binary variable NC N 8 NC NC 1960-1968 Wheat acreage NC -0.983 NC NC I -- (-1.28) -- --- l Statistics Adjusted R2 0.882 0.843 0.868 0.673 Standard Error 0.67 0.390 4.12 4.60 Durbin-Watson 1.54 1.90 1.94 2.71 M NC: Not considered NS: Not significant 7The parameter estimates depicted are the regression coefficient and the associated "t” statistics. 63 Table A.4 Correlations Between Explanatory of Variables Corn Acreage Wheat Acreage Year Corn Diverted Diverted 1.000 Corn Price 0.7577 1.000 Fraction of -0.1953 -0.1409 1.000 Corn Acreage Diverted Fraction of -0.0379 0.0482 0.6743 1.000 Wheat Acreage Diverted nICHIan STATE UNIV. 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