i SUPPLY RESPONSE OF CROPS IN THE SOUTHEAST Except where reference is made to the work of others, the work described in this thesis is my own or was done in collaboration with my advisory committee. This thesis does not include proprietary or classified information. ___________________________ Rachel Danielle Kichler Certificate of Approval: _________________________ ________________________ Henry W. Kinnucan Patricia A. Duffy, Chair Professor Alumni Professor Agricultural Economics Agricultural Economics and Rural Sociology and Rural Sociology _________________________ ________________________ James L. Novak Norbert L. Wilson Extension Specialist Professor Assistant Professor Agricultural Economics Agricultural Economics and Rural Sociology and Rural Sociology __________________________ George T. Flowers Interim Dean Graduate School ii SUPPLY RESPONSE OF CROPS IN THE SOUTHEAST Rachel Danielle Kichler A Thesis Submitted to the Graduate Faculty of Auburn University in Partial Fulfillment of the Requirements for the Degree of Masters of Science Auburn, Alabama August 9, 2008 iii SUPPLY RESPONSE OF CROPS IN THE SOUTHEAST Rachel Danielle Kichler Permission is granted to Auburn University to make copies of this thesis at its discretion, upon request of individuals or institutions and at their expense. The author reserves all publication rights. ________________________ Signature of Author ________________________ Date of Graduation iv VITA Rachel Danielle Kichler, daughter of Leonard and Susan Kichler of Elberta, AL, was born on June 27, 1984. She graduated from Foley High School in May 2002. She attended Auburn University for her undergraduate career. She graduated with a degree in Agricultural Economics and Business in May 2006. She continued on at Auburn University for a Masters of Science in Agricultural Economics in the Fall of 2006. She was married to Martin Dunbar Smith, son of Wilburn A. Smith and Ellyn Smith, on May 31, 2008. v THESIS ABSTRACT SUPPLY RESPONSE OF CROPS IN THE SOUTHEAST Rachel Kichler Masters of Science, August 9, 2008 (B.S., Auburn University, 2006) 80 Typed Pages Directed by Patricia A. Duffy A model was used to estimate the supply response of corn, cotton, and soybeans in the Southeast United States. The analysis includes state-level data from 1991-2005 in Alabama, Florida, Georgia, North Carolina, South Carolina, Tennessee, and Virginia along with wealth, revenue risk, and policy variables. The results indicate that cross- commodity variables, wealth, truncated net returns, and farm policy affect acreage decisions made by producers. vi ACKNOWLEDGEMENTS The author would like to thank Dr. Patricia A. Duffy for her time and generosity with the thesis analysis and as her academic adviser. The author would also like to thank Dr. Henry W. Kinnucan, Dr. James L. Novak, and Dr. Norbert L. Wilson for their work as committee members. The author would like to thank the United States Department of Agriculture for their funding and for allowing the author to work on the grant named "Supply Response under Farm Programs for Southeast Row Crops" which was a Cooperative Agreement. Also, the author would like to thank the Alabama Agricultural Experiment Station for their funding. vii Style manual or journal used American Journal of Agricultural Economics Computer software used Microsoft Office, Microsoft Excel, and SAS 9.1 (English) viii TABLE OF CONTENTS I. INTRODUCTION .............................................................................................1 Research Objectives ...................................................................................2 II. COTTON, SOYBEANS, AND CORN ........................................................... 3 Farm Programs ...........................................................................................9 III. REVIEW OF LITERATURE .........................................................................12 Early Theoretical Models .........................................................................12 Policy Variables .......................................................................................14 Risk ...........................................................................................................15 Theoretical Research ................................................................................17 IV. DATA AND MODELS ...................................................................................25 Expected Yields? ....................................................................................27 Truncated Price Distributions ...................................................................27 Expected Revenue ....................................................................................27 Models ......................................................................................................28 V. RESULTS ........................................................................................................30 VI. CONCLUSIONS..............................................................................................36 BIBLIOGRAPHY ........................................................................................................39 APPENDIX A ..............................................................................................................42 APPENDIX B ..............................................................................................................52 ix LIST OF TABLES Table 2.1 Cotton: Acreage Planted by State ........................................................................4 Table 2.2 Cotton: Yield per acre by State ............................................................................4 Table 2.3 Soybeans: Acres Planted by State ........................................................................6 Table 2.4 Soybeans: Yield per acre by State .......................................................................6 Table 2.5 Corn: Acreage Planted by State ...........................................................................7 Table 2.6 Corn: Yield per acre by State ...............................................................................8 Table 2.7 Rates for ARP ....................................................................................................10 Table 2.8 Loan Rates .........................................................................................................11 Table 4.1 Variables and Definitions ..................................................................................29 Table 5.1 OLS Estimations or Cotton Acreage .................................................................31 Table 5.2 SUR Estimations without Restrictions ..............................................................33 Table 5.3 SUR Estimations with Restrictions....................................................................34 Table 5.4 Short- and Long-Run Own Profit Elasticities ....................................................35 x I. INTRODUCTION The supply response literature has a significant presence in economic analysis. The analysis of the supply response of row crop production began in 1956 with work by Marc Nerlove and has progressed over the years, with many economists making significant advancements in the field over the latter half of the twentieth century. Literature on the topic has expanded since its inception to include other variables that help estimate supply, such as prices, policy, risk, and wealth. Building on a study by Lin and Dismukes, one that estimated supply response of row crops in the North Central United States, this paper estimates the supply response of row crops in the Southeast United States. Because there have not been any recent publications on supply response in the Southeast, this paper will provide updated estimations for the supply response of corn, cotton, and soybeans. Supply response models take into account farmers? expected planting decisions, expected prices, expected yield, costs of inputs, farm programs, risk, and wealth. Government sponsored farm programs have historically given producers incentives to either increase or decrease production of certain commodities targeted by the legislation. These farm programs serve to reduce the risk that farmers face when making planting 2 decisions. The producers? initial wealth may also impact their planting decisions, by allowing them to bear more risk. RESEARCH OBJECTIVES This study has three objectives for the supply response analysis. The first objective of this paper is to identify a consistent theoretical model for supply response of row crops in the Southeast. The second objective is to econometrically use data from 1991 through 2005 to estimate results. The third objective is to take into account how various farm program provisions as well as changes in market prices affect row crop supply in the target region. 2 II. COTTON, SOYBEANS, AND CORN Supply response analysis in agriculture focuses on crop production. Some of the major row crops produced in the Southeast U.S. are cotton, soybeans, and corn. Production for each crop varies within each state, but growing seasons tend to be constant throughout the Southeast. Because the three crops? growing seasons overlap, a producer can choose between growing one of the three crops on each acre, but doesn?t have the option of growing one of the others at a later point in the year on the same piece of land. The region that this study specifically covers includes Alabama, Florida, Georgia, North Carolina, South Carolina, Tennessee, and Virginia. Cotton is a textile fiber that is grown in over 80 countries (USDA). The average cotton acreage planted in the Southeast region from 1991-2005 is found in Table 2.1. It is interesting to note that despite the fact that the total cotton acreage planted by the 7 states increased by 66.9% (from 2,198.9 thousand acres to 3,670 thousand acres) over the 15 year period, the various states? individual percentages of the total cotton planted in the region changed a significant amount as well. Initially, Virginia planted the smallest amount of cotton acreage at 0.8% of the total acreage planted, but increased its share to pass Florida by producing 2.53% of the total cotton acreage planted in 2005. North Carolina had the largest percentage of cotton acres planted in 1991 at 20.92%, but slipped to second in cotton acreage planted at 22.21% due to a steady increase in acreage planted by Georgia (from 430 thousand acres in 1991 to 1220 thousand acres in 2005). 3 Table 2.1 Cotton: Acreage Planted by State (in thousands) Year Alabama Florida Georgia North Carolina South Carolina Tennessee Virginia Total Region 1991 410 50 430 460 211 620 18 2199 1992 415 50 460 380 197 625 22 2149 1993 443 54 615 390 202 625 23 2352 1994 463 69 885 486 225 590 42 2760 1995 590 110 1500 805 348 700 107 4160 1996 520 99 1340 740 284 540 103 3626 1997 535 100 1440 690 290 490 101 3646 1998 495 89 1370 710 290 450 92 3496 1999 565 107 1470 880 330 570 110 4032 2000 590 130 1500 930 300 570 110 4130 2001 610 125 1490 970 300 620 105 4220 2002 590 120 1450 940 290 565 100 4055 2003 525 94 1300 810 220 560 89 3598 2004 550 89 1290 730 215 530 82 3486 2005 550 86 1220 815 266 640 93 3670 Table 2.2 displays the average cotton yield per acre by state: Table 2.2 Cotton: Yield by State (pounds per acre) Year Alabama Florida Georgia North Carolina South Carolina Tennessee Virginia 1991 655 719 812 672 552 786 765 1992 731 701 783 596 651 565 621 1993 524 696 586 535 425 495 634 1994 766 735 843 820 726 846 944 1995 409 472 625 479 527 528 620 1996 734 637 747 659 611 774 748 1997 597 577 646 652 662 688 659 1998 559 489 578 699 589 587 765 1999 535 516 579 475 505 428 635 2000 492 480 591 742 603 627 738 2001 730 612 720 832 763 686 929 2002 507 439 557 421 741 314 465 2003 772 610 785 646 806 718 674 2004 724 601 674 900 900 875 956 2005 747 762 849 852 848 743 955 4 While the fluctuations in the levels of acreage planted found in Table 2.1 will be potentially explained by the models estimated later in this paper, yield per acre is subject to very different factors. Factors such as advances in technology, natural disasters, farm programs, and changing weather patterns all affect crop yields. All 7 states shown in Table 2.2 indicate fluctuating yields over the period; however, the yields seem to trend upward over the time period. It also must be noted that several of the states have years in which their yield dropped to levels below their 1991 levels. It is possible to attribute these fluctuations in yield per acre to changing weather patterns. Certain years such as 2002 saw 6 of the 7 states produce at well below their 1991 yield levels due to a drought, with some such as Tennessee producing at less than half (from 786 pounds per acre in 1991 to 314 pounds per acre in 2002). Soybeans are the most widely produced oilseed in the U.S. (USDA). Data of acres planted in the Southeast region of the U.S. by state from 1991-2005 are listed below in Table 2.3. The first point that one will notice in Table 2.3 is the general downward trend in soybean acres planted by state for 4 of the 7 states. Specifically, the state of Florida?s acreage planted decreased from 45, 55, and 55 thousand acres of soybeans planted in 1991, 1992, and 1993, respectively, to 13, 19, and 9 thousand acres of soybeans planted in 2003, 2004, and 2005, respectively. However, North Carolina, Tennessee, and Virginia have all maintained or increased their soybean acreage planted from 1991 levels. 5 Table 2.3 Soybeans: Acres Planted by State (in thousands) Year Alabama Florida Georgia North Carolina South Carolina Tennessee Virginia Total Region 1991 360 45 600 1350 650 1100 530 4635 1992 290 55 650 1400 690 1000 520 4605 1993 310 55 600 1350 600 1050 520 4485 1994 310 45 520 1400 600 1050 540 4465 1995 240 30 320 1150 550 1050 490 3830 1996 320 35 400 1250 560 1150 500 4215 1997 350 47 400 1400 580 1240 510 4527 1998 340 35 300 1475 540 1250 500 4440 1999 240 20 220 1400 480 1250 470 4080 2000 190 20 170 1400 450 1180 490 3900 2001 140 10 165 1380 440 1070 500 3705 2002 170 10 160 1370 435 1160 490 3795 2003 170 13 190 1450 430 1150 500 3903 2004 210 19 280 1530 540 1210 540 4329 2005 150 9 180 1490 430 1130 530 3919 Table 2.4 found below displays the soybean yields per acre by state. Table 2.4 Soybeans: Yield per acre by State Year Alabama Florida Georgia North Carolina South Carolina Tennessee Virginia 1991 23 27 27 30 30 22 29 1992 29 30 29 27 35 22 31 1993 24 25 17 24 31 15 22 1994 31 31 31 31 37 27 32 1995 24 26 27 25 32 24 24 1996 34 32 26 29 35 25 34 1997 25 25 21 29 34 23 23 1998 22 23 21 27 29 21 23 1999 16 32 19 23 19 20 27 2000 18 19 24 33 25 25 39 2001 35 29 26 32 34 21 36 2002 24 33 23 24 31 17 23 2003 36 30 33 30 42 28 34 2004 35 34 31 34 41 27 39 2005 33 32 26 27 38 21 30 6 In almost every year of the 14 year period listed, Tennessee had the poorest yields in terms of bushels of soybeans per acre. Even in 2003, when every other state managed to produce over 30 bushels per acre, with South Carolina producing 42 bushels per acre, Tennessee only managed to average 28. Corn is the most widely produced feed grain in the United States. It is used for human consumption, livestock production, and industrial production (USDA). Acres of corn planted in the Southeast region of the U.S. from 1991-2005 are listed below in Table 2.5: Table 2.5 Corn: Acreage Planted by State (thousands) Year Alabama Florida Georgia North Carolina South Carolina Tennessee Virginia Total Region 1991 260 110 600 1050 280 620 500 3420 1992 330 150 750 1150 375 740 520 4015 1993 300 140 650 1000 330 660 490 3570 1994 290 120 600 1000 370 670 500 3550 1995 250 100 400 800 290 640 430 2910 1996 300 140 580 1000 400 740 450 3610 1997 280 120 500 960 350 700 490 3400 1998 300 160 500 860 350 700 500 3370 1999 220 90 350 750 300 630 500 2840 2000 230 85 360 730 310 650 470 2835 2001 180 65 265 700 260 680 470 2620 2002 200 75 340 780 320 690 500 2905 2003 220 75 340 740 240 710 470 2795 2004 220 70 335 820 315 680 500 2940 2005 220 65 270 750 300 650 490 2745 Though there is somewhat of a gradual decreasing trend in some of the states? acreage planted, it can be observed that North Carolina planted the most acreage every year of the 15 year period and that Florida planted the least acreage every year of the 15 year period. However, despite the fact that North Carolina planted the greatest corn acreage each year, 7 the states? percentages of the seven states total acreage planted decreased over the 15 year period. In 1991, North Carolina planted 30.7% of the 7 state total corn acreage with 1050 thousand acres. In 2005, it only planted 27.3% with 750 acres. This could be due to a variety of different factors, including the fact that the 7 states experienced a 19.7% decrease in total corn acreage planted and that Tennessee increased its percentage of the 7 state total corn acreage planted by 5.5% from 18.1% to 23.6%. Table 2.6 displays corn yields from 1991-2005 by state. Table 2.6 Corn: Yield per acre by State (bushels per acre) Year Alabama Florida Georgia North Carolina South Carolina Tennessee Virginia 1991 80 68 100 90 86 85 84 1992 94 75 100 95 124 88 116 1993 55 65 70 65 84 40 60 1994 96 85 106 91 116 85 98 1995 75 90 90 107 118 91 111 1996 82 88 95 95 116 79 126 1997 87 80 105 89 102 95 93 1998 63 62 85 70 96 40 84 1999 103 93 103 80 102 70 78 2000 65 75 107 116 114 65 146 2001 107 87 134 125 132 108 123 2002 88 96 110 83 107 47 68 2003 122 82 129 106 131 105 115 2004 123 90 130 117 140 100 145 2005 119 94 129 120 130 116 118 The corn yield per acre shows a general trend upward in all 7 states over the 14 year period, marked by some decreases across the board in certain years such as 1998 and 2002. 8 FARM PROGRAMS Farm programs have existed since the 1930?s to help farmers stabilize price and support income. Historically programs included acre reduction programs and loan programs. The following policy information was gathered from various United States Department of Agriculture (USDA) publications listed in the Bibliography. The Food, Agriculture, Conservation, and Trade Act of 1990 (FACTA) contained several benefits for agricultural producers. One benefit was the establishment of target prices at fixed rates. Additionally, FACTA allowed for more planting flexibility by permitting farmers to plant any eligible crop, excepting fruits and vegetables, on up to 25% of their base acreage. As long as this percentage is not exceeded, the farmer?s base history is preserved, and he or she will receive deficiency payments on 85% of the crop base. Also, FACTA extended the Acreage Reduction Program to be utilized when the USDA predicts excessive supply of certain commodities. In addition, FACTA extended the Secretary of Agriculture?s ability to offer and loan deficiency payments (USDA). The Agricultural Marketing Transition Act of 1996 redefined policy specifications for income support and commodity loan programs. As stated above, the 1996 Act discontinued acreage restriction programs and allowed more flexibility in farms? planting decisions. The loan programs had few changes and loan rates were kept as moving averages of past prices of cotton, corn, and soybeans (Hoffman 1996). The 1996 Act covered the time period of 1996-2001. Another significant policy that affected cotton, corn, and soybean acreage was the Farm Security and Rural Investment Act of 2002 (FSRIA). First, it altered the requirements for the direct payment program. Under the 1996 AMTA, a producer had to 9 have participated in one of the eligible programs for at least 1 year from 1991 to 1995. He or she was then eligible to enter into a 7 year production flexibility contract which guaranteed payments through 2002. The FSRIA expanded eligibility for direct payment programs by recalculating base acreage. Also, it expanded the direct payment programs to include soybeans. The new base acreage reflected a four year average of planted acre from 1998-2001. The loan program was continued and fixed rates are established. In addition, nonrecourse loans with marketing loan provisions were extended. With a nonrecourse loan, a farmer may choose to forfeit his crop instead of repaying the loan (USDA). The 2002 Act covered the time period from 2002-2005. Acreage reduction programs (ARP) required producers to retire a specific amount of their base acreage to gain eligibility for loan benefits. These programs affected corn and cotton, but not soybeans. The 1996 Farm Bill ended the acreage reduction program (USDA). The ARP percentages are listed below in Table 2.7. Table 2.7 Rates for ARP (in percents) Year Cotton Corn Soybeans 1991 5 7.5 0 1992 10 5 0 1993 7 10 0 1994 11 0 0 1995 7.5 7.5 0 Marketing loan programs contain a specific loan rate under which producers can use their crop as collateral to receive a loan from the government. The loan rate is a guaranteed price the producer receives, when the market price falls below the loan rate. Alternatively, a farmer may choose to sell his crop at the market price and receive a loan 10 deficiency payment, which is the difference between the market price and the loan rate (USDA). The loan rates for each row crop from 1991-2005 are displayed the Table 2.8. Table 2.8 Loan Rates (Deflated) Year Cotton ($/lb) Corn ($/bu) Soybeans ($/bu) 1991 0.686 2.189 6.782 1992 0.703 2.310 6.742 1993 0.693 2.277 6.645 1994 0.654 2.471 6.432 1995 0.655 2.386 6.210 1996 0.640 2.330 6.126 1997 0.640 2.331 6.488 1998 0.657 2.391 6.655 1999 0.651 2.370 6.597 2000 0.616 2.242 6.239 2001 0.609 2.217 6.169 2002 0.624 2.377 6.003 2003 0.593 2.257 5.699 2004 0.558 2.092 5.365 2005 0.520 1.950 5.000 11 III. REVIEW OF LITERATURE Supply response models originally included prices and little else. Through the years, the theoretical research has progressed to capture other variables. This chapter reviewed published research on supply response. EARLY THEORETICAL MODELS Nerlove (1956) developed a model for estimating elasticities for cotton, corn, and wheat from 1909-1932. His work focused on estimating expected prices utilized by farmers in making acreage decisions. He proposed that farmers predicate part of their decision on expected future prices when considering how many acres to plant. Nerlove modeled expected prices as a weighted moving average of past prices. Because the expected prices used by producers to make their planting decision cannot be observed, other more readily available data was used to establish their estimates. Nerlove surmised that acreage decisions take into account more variables than merely the price of the previous year?s crop. He proposed that farmers base their ideas on expected prices for next year. Using a weighted moving average system, Nerlove took into consideration prices from previous years. Equation (3.1) below is the model proposed by Nerlove in which producers modify their expected prices for this year in proportion to the amount of error they estimated from the previous year. The coefficient of expectations is ? and t is a time subscript. (3.1) PCt ? PC t-1 = ?[AP t-1 - PC t-1], 0 < ? ? 1 12 Where PCt = the crop price expected that year PC t-1 = the crop price expected lagged by one year AP t-1 = the actual crop price lagged by one year Equation (3.2) illustrates how the expectations model above can also be represented as the expected prices being a weighted moving average of the past prices where the weights are a function of the coefficient of expectation. (3.2) PCt = ?AP t-1 + (1-?)?AP t-2 + (1- ?)2 ?AP t-3 + ? ? has value between zero and one which indicates that weight decreases to zero as time passes. Producers have a greater tendency to use previous expectations when ? is closer to zero. Thus, past prices cannot be overlooked. Equation (3.3) shows a linear relationship in which the amount of acreage planted is a function based solely on the expected price for a crop. Nerlove used this model to find both the coefficient of expectation and the elasticity of acreage to expected price. (3.3) At = b0 + b1 PCt + ut Where At = the amount of acreage planted that year ut = the random residual The expected price, PC t, cannot be observed. Equation (3.1) includes the expected price and the actual crop price. Therefore, the actual lagged crop price and the lagged acreage planted received is used in the place of PC t and PC t-1, respectively. After making the substitutions, Equation (3.4) is derived below: (3.4) At = ?0 + ?1 APt-1 + ?At-1 + ?t Where At-1 = the amount of acreage planted lagged by one year ?t = the random residual (ut ? ?t). 13 Nerlove conjectured that if an expected price is used to make decisions then there should be a relationship between the current year?s acreage and the previous year?s price and acreage. Two methods were used in an attempt to estimate the equation. The first was called the special method in which Nerlove restricted the coefficient of expectation, ?, to equal one. The second method, referred to as the general method, allowed the coefficient of expectation to be unrestricted. Both estimates of the elasticities of acreage with respect to expected price and coefficient of expectation were significant at the five percent level or higher. The special method estimated the R2 as 0.59, 0.64, and 0.22 respectively for cotton, wheat, and corn. The general method estimated the R2 as 0.74, 0.77, and 0.35. The R2 from the general method were higher in all three crops. The elasticities of acreage to expected price in the special method were 0.20, 0.47, and 0.09 respectively for cotton, wheat, and corn. The general method estimated elasticities of 0.67, 0.93, and 0.18 respectively for cotton, wheat, and corn. Overall, the general method generated higher estimates for the elasticities of acreage to expected price and the coefficient of expectation. Tomek (1972) modified Nerlove?s model by adding a supply shifting variable into the model and changing the price deflator. A dummy variable was used to capture the supply shift and the Index of Prices Paid by Farmers price index. Significant results were estimated for both the variables. POLICY VARIABLES Houck and Ryan (1972) analyzed supply relationships for U.S. corn acreage and the U.S. feed grain policy. Their model concentrated on taking government programs into account. They estimated the effects of price support and acreage restricting programs on 14 acreage decisions. The policy variables included were loan rates, price support, and diversion payment rates. The results indicated that from 1948-1970, 95 percent of the variation of U.S. corn acreage was linked with the policy variables. Lee and Helmberger (1985) estimated supply response of corn and soybeans by including the following farm program variables: participation decisions, cross- commodity effects, and a model for farm programs and the free market. Price responsiveness was estimated under a system including both a ?farm program? equation and a ?free market? equation, using pooled time-series and cross-sectional data for both. The farm program equation incorporated direct payments which includes allotments and set asides. Corn was more own-price responsive in years of acreage control programs versus years without acreage controls. Soybeans were less own-price responsive during ?farm programs? versus the ?free market?. Duffy, Wolhgenant, and Richardson (1987) analyzed the supply response of cotton under farm programs in four regions of the U.S. A weighted combination of expected market price and government policy was used to as the own-price variable. Results indicated that prices of competing enterprises were significant in acreage supply in 2 regions, Southern Plains and Southeast. The own-price elasticities of cotton for the short- and long-run were 0.273 and 0.573, respectively. RISK Just (1974) developed variables to capture risk when including government programs in estimating acreage response. He used an adaptive expectation geometric lag model. The model was generalized by geometrically including the quadratic lag terms. 15 Just estimated wheat and grain sorghum acreage in the San Joaquin and Sacramento Valleys in California. In his analysis of the San Joaquin and Sacramento Valleys, three different hypotheses were tested in the paper described below: Hypothesis 1: Decisions are not significantly affected by subjective variances or covariances, Hypothesis 2: Decisions are not significantly affected by the subjective covariances, and Hypothesis 3: the temporal lag distributions for the subjective mean and variance are equal. The model is equation (3.5) below: (3.5) Yt = A0 + A1? ? (1-?)k Zt-k-i + ? Where Yt = p x 1 vector of dependent variables Zt = n x 1 vector of explanatory variables including prices A0 = p x 1 parameter vector A1 = p x n parameter matrix ? = scalar parameter ? = stochastic disturbance p x 1 vector In equation (3.6), Z*t represents the decision maker?s expectations for the mean of prices and yields. These decisions are reflected in Yt. Alternatively, equation (3.7) geometrically weights past observations to predict decision maker?s expectation when considering [Zi,t - Z*i,t]2 as an observation of risk. (3.6) Z*t = ? ? (1- ?) k Zt-k-1 (3.7) [Zi,t - Z*i,t]2 = [Z i,t - ? ? (1- ?)k Zt-k-1]2 (3.8) W*i,t = ? ? (1- ?) k [Zi, t-k-1 ? Z*i, t-k-1] 2 16 In equation (3.8), W*i,t is an n x 1 vector and ? is a scalar geometric parameter. Thus, the original equation (3.5) is modified to equation (3.9) which includes. (3.9) Yt = A0 + A1Z*t + A2W*t + ? A2 is a p x n parameter matrix. Equation (3.10) is an observation of the covariance of the prices or yields. The covariance is considered to be important in the decision maker?s expectations. So, equation (3.11) includes the covariance in W* t. (3.10) ? i,j,t = [Zi, t ? Z*i, t] [Zi, t ? Z*i, t] (3.11) W*t = ? ? (1- ?) k ? t-k-1 Equation (3.12) is the final model which contains all the modifications from the initial equation (3.5). (3.12) Yt = A0 + A1? ? (1-?)k Zt-k-i + A2?t ? (1-?)k? t-k-1 + ? The estimation of model (3.12) produced the rejection of hypothesis 1 because risk was significant in most equations. The exception to risk not being significant was found only in the case where the crops were strongly regulated by government programs. Pope (1981) explored different levels of price expectations for aggregated supply response. Concave, convex, and linear supply functions are analyzed at different dispersion levels. Results were comparable to those of Just (1974) on supply response under risk. THEORETICAL RESEARCH Gardner (1976) used futures prices in his supply analysis of soybeans and cotton. Specifically, he used the prices of futures contracts for next year?s crop instead of using the lagged price to represent farmers? expected price. He addressed three problems 17 created by using futures prices. First, the futures price represents nonfarm speculators along with farmers. Second, there is a question of which specific futures contact should be used. Third, there is a question at which point in time should the price be taken. In the end, the use of futures prices proved to be comparable to the lagged prices in the estimations. Shumway (1983) analyzed Texas field crop production and estimations of product supply and input demand equations. These analyses were based on competitive behavior in output and variable input markets along with a twice continuously differentiable input requirements function. Specifically, the model included a lag structure for the product price and unobserved market price. The estimations indicate inconsistencies in the model and do not support the symmetry restrictions. Chavas and Holt (1990) used expected utility maximization to develop a supply response model when estimating corn and soybeans on a national basis. Their model took risk (using revenue uncertainty), wealth effects, and government programs into account. The utility maximization function by von Neumann Morgensten is assumed for household preferences. The model maximizes expected utility subject to equation (3.13), a budget constraint, and equation (3.14), an acreage constraint. Equation (3.13) includes the variables I (the exogenous income/wealth variable), R (the revenue variable), C (the total cost of production), and qG (the household consumption expenditures deflated). Equation 3.13 can also be represented as the second equation that breaks down revenue and total cost of production. The revenue variable includes p (the market price of the 18 crop), and Y (the yield per acre). The total cost of production is estimated with c (the cost of production per acre) and A (the number of acres planted). (3.13) I + R ?C = qG or I + ? pYA ? ? cA = qG (3.14) f(A) = 0 The variables subject to risk are p and Y. Neither variable is known when planting decisions are being determined. After making substitutions with equation (3.13), the final model is present in equation (3.15). (3.15) max {EU(w + ? i=1 ?A)} s.t. (3.14) Substitutions were made with w (wealth) and ? (profits per acre of crop) that take price, yield, and cost in account. Chavas and Holt denote A*(w; ?; ?) as the optimal level of acreage per crop which is dependent on wealth, expected profit per acre, and higher moments of the profit distribution (?). The decision of A* made by famers under risk is homogenous of degree zero in initial wealth (w), output price (p), input cost (c), and consumer price (q). Equation (3.16) represents the symmetry restrictions needed for expected utility. AC is the wealth compensated acreage decision. (3.16) dAC/d? = dA*/d? - dA*/dw A*? The wealth effects above reflect the different types of risks that can be assumed for optimizing acreage decisions. Specifically, if zero wealth effect is assumed then dA*/dw becomes zero and symmetric, positive semi definite matrix. The variance for untruncated normalized prices was calculated as equation (3.17), below. 19 (3.17) VAR (Pit) = ? ? j [ Pi,t-j - E t-j-1 P i,t-j] 2 The variance is weighted by the variable ? j of .5, .33, and .17 for t-1, t-2, and t-3, respectively. Price support, such as loan rates, sets a floor under market prices. Price expectations and riskiness of revenue are affected by the price support rates; the truncated distributions of price take the price support affects into account. The truncated mean for the normal distribution is below in equation (3.18), (3.18) E [P | P > S] = ? = ? P f(P|P>S) dx = ? + ? ?(?) where ?= (S- ?)/? and ?(?) = ?(?)/[1 ? ?(?)]. P is the expected crop price, S is the loan rate, ? is the untruncated mean, ? is the standard deviation, ?(?) is the inverse mills ratio, ? is the standard normal density, and ? is the standard normal CDF (Greene). The truncated variance for the normal distribution is ?2 = ? (P ? ?)2 f(P|P>S) dx (Greene). The equations below were used to generate the truncated price distributions. Hi represents the level of price support. They define xi a normally distributed random variable, as Hi if Xi is less than Hi and Xi if Xi is greater than or equal to Hi where i= 1, 2, and so on. Equation (3.19) and Equation (3.20) define the random variables ei and hi, respectively. (3.19) ei = (xi ? Xi)/ ?ii1/2 (3.20) hi = (Hi ? Xi)/ ?ii1/2 Equation (3.20) is the mean of ei where ?(.) is the standard normal distribution function and ?(.) is the bivariate standard normal density function. (3.21) E (ei) = hi ? (hi) + ? (hi) Equation (3.22) and equation (3.23) are the second moments of ei which were derived in Chavas and Holt?s appendix. 20 (3.22) Mii = E(ei2) = hi2 ?(hi) + 1- ?(hi) + hi ?(hi) (3.23) Mij = E(ei, ej) = F(hi, hj)?jj + [(1- ?ij2)/2?] 1/2 ?(Zij) + hi ?(hi) ?(kji) + hihj?(hi, hj) All of equation (3.23) substitutions are listed below. (3.24) F (hi, hj) = ? (hi, hj) + 1 - ? (hi) - ? (hj) (3.25) Zij = {(hi2 + 2?ijhihj + hi2)/(1- ?ij2)}1/2 (3.26) kij = (hi ? ?ijhi)/(1- ?ij2 )1/2 (3.27) ?ij = ?ij/(?ii?jj)1/2 Equation (3.28), equation (3.29), and equation (3.30) are the mean, variance, and covariance of xi , respectively. (3.28) xi = E (xi) = Xi + ?ii1/2ei (3.29) V(x1) = E (xi ? xi)2 = ?ii (Mii ? ei2) (3.30) COV (xi, xj) = E (xi ?xi)(xj ? xj) = (?ii ?jj)1/2(Mij? eiej) The farm value of proprietor equity was used for the wealth variable. Chavas and Holt defined profit below in equation (3.31). (3.31) ?jt = Et-1[(pjt/qt)Yjt ? (cjt/qt)|pt ? pst} The model estimated by Chavas and Holt is listed below (3.32) Ait = ai + ?i (wt-1 + ?j Aj?jt) + ?j Bij?jt + ? k?j ?j ?ijk?jkt + ?it + ?iD83 + ?it Where Ait = Amount of acres planted wt-1 = wealth (farm value of proprietor equity) ?jt = Truncated mean return per acre ?i = dAi/dw ?ij= dAi/d?jk ?jkt = covariances t = Trend variable D83 = Dummy variable for discount effect of the 1983 payment-in-kind program ?it = error term 21 Estimations from the model above indicated that risk and wealth effects were important in the choosing acreage allocation of corn and soybeans. The own-revenue elasticites were 0.068 and .279 for the corn and cotton equations, respectively. The own- revenue elasticites were 0.158 and 0.441 for the corn and soybeans model, respectively. Cross commodity prices effects were also important. When price support for a crop was increased, the expected price also increased and the acreage planted for the substitute crop decreased. Using the model developed by Chavas and Holt, Duffy, Shalishali, and Kinnucan (1994) analyzed supply response for corn, cotton, and soybeans in the Southeast. The Southeast region included Alabama, Georgia, North Carolina, and South Carolina. Three sets of equations were estimated. They also included variables to capture the diversion payments for cotton and corn. The own-revenue corn elasticity was 0.0954 along with the soybeans own-revenue of 0.560. Thus, the Southeast region was found to be more responsive to changes in profitability than the U.S. as a whole. Duffy, Shalishali, and Kinnucan also estimated a set of time-varying parameter models. The models allowed for stochastic and systematic changes. The stochastic changes took place around stationary and non-stationary mean values. The systematic changes took place by varying nonrandom parameter values. Results of the model suggested that over time cotton acreage has become more inelastic. Using a similar framework to that of Chavas and Holt, Lin and Dismukes (2007) analyzed supply response in the North Central region of the United States for corn, soybeans, and wheat. The North Central region included Wisconsin, Illinois, Indiana, Iowa, Michigan, Minnesota, Missouri, and Ohio. They used futures prices for expected 22 crop prices. Instead of price, they used expected variance and covariances of revenues to reflect price and production risk. The household wealth variable was farm operator household net worth which included both farm and non-farm sources. The estimations included a lagged dependent variable as an explanatory variable to take into account the cost of making adjustments in production over time. Their expected yields were generated by regressing actual yields on a trend variable. In addition to the cross- equation symmetry restrictions, Lin and Dismukes restricted the parameter on expected net returns of soybeans to 0.0090 in the soybean equation due to a high collinearity between corn and soybeans net returns. Equation (3.33) below is the linear acreage model and equation (3.34) is the acreage share model estimated. (3.33) Ai =a1i + bij ?j=1 NRTj + cij ?j=1 VARi + dij ? i/j, 1 COVij + eiWi + fiZi + ?i (3.34) Si= a1i + bij ?j=1 NRTj + cij ? j=1 VARi + dij ? i/j,1 COVij + eiWi + fiZi + ?i Where ? Si = 1 Ai = acreage planted Si = share combined acreage of crops NRT j = expected net returns VARi = expected variance of revenues COVij = expected covariance of cross-commodity revenues Wi = farm operator household initial net worth Zi = APR, state dummies, lagged dependent variable (Ai, t-1 and Si, t-1), and the error term The own-revenue elasticites were 0.170 and 0.158 for the corn linear and share models, respectively. The own-revenue elasticites were 0.295 and 0.304 for the soybeans linear and share models, respectively. The own-revenue elasticites were 0.336 and 0.248 for the wheat linear and share models, respectively. In the estimations of the model above, 23 risk did not prove to have strong effect across commodities in the North Central region of the U.S. Also, increased initial wealth lead to increased acreage planted of crops. 24 IV. DATA AND THE MODELS This analysis used time-series and cross-sectional data from 1991-2005. Data for cotton, soybeans, and corn were collected from the Southeast states of Alabama, Florida, Georgia, North Carolina, South Carolina, Tennessee, and Virginia. Planted acreage and market prices for each row crop from 1987-2005 for each state were collected from the United States Department of Agriculture?s Quick Stats website and can be located in Appendix A. All prices were normalized to 2005 levels using Producer Price Indexes for Farm Products. The Producers Price Index for farm products was found at the Bureau of Labor Statistics website and can be located in Appendix A. An average of three days of futures prices was taken for each crop from a specific time period with relation to the specific time of year the producers made their planting decisions to generate the expected price. This average represents the futures price used in the estimation. The futures data were collected from the period of 1989-2005 from Price Data and can be located in Appendix A. December cotton futures prices were collected in January on the second Tuesday, Wednesday, and Thursday during the same year. September corn futures prices were collected in January on the second Tuesday, Wednesday, and Thursday for the month during the same year. November soybean futures prices were collected in January for the second Tuesday, Wednesday, and Thursday during the same year. 25 Expected prices were developed by subtracting the futures prices from the state average market price to estimate the basis for that crop in each state. The average basis was then subtracted from the average futures price to get the expected price. The equations (4.1) and (4.2) below illustrate the formulas for the basis and expected price. (4.1) ?t=1 (Average Market Price t ? Average Futures Price t)/N = Average Basis (4.2) Average Futures Price t ? Average Basis = Expected Price t N is the number of observations. Costs of production, on a regional basis, were collected for each crop for the period 1991 to 2005. Costs of production for 1991-1995 were collected from Southeast region. In 1996, this series ended and was replaced by a new series with different regional names. The costs of production for 1996-2005 were thus collected from the Southern Seaboard region. Since the USDA changed the format of the costs of production from the original 1991-1995 data, the data from 1996-2005 were standardized to 1991- 1995 data by adding hired labor and subtracting interest paid on capital to operating costs. The costs of productions for each crop were gathered from the USDA and can be located in Appendix A. From 1990 to 1995, the loan rates were found in Cotton: Background for 1995 Farm Legislation and Feed Grains: Background for 1995 Farm Legislation by the USDA. After 1995, they were found in Provisions for the Federal Agriculture Improvement and Reform Act of 1996 by the USDA for 1996-2001. The 2002-2005 loan rates were found in The 202 Farm Act: Provisions and Implications of Commodity Markets published by the USDA. The Acreage Reduction Programs rates were found in Cotton: Background for 1995 Farm Legislation, USDA?s Federal Register: Rules and 26 Regulations, and Feed Grains: Background for 1995 Farm Legislation by the USDA. The wealth variable used farm equity and was from the Agricultural Resource Management Survey of the USDA and can be located in Appendix A. EXPECTED YIELDS The yield data from 1971-2005 was used to generate expected yields by equation (4.3) below: (4.3) E (Yt) = ? + ?1Yt-1 + ?2 T where Yt is the yield, Yt-1 is the lagged yield, and T is the trend variable. The yield data were gathered from the USDA Quick Stats website and can be located in Appendix A. The trend variable takes the value of 1 in 1971, 2 in 1972, and so on. In each year of subsequent estimation, a new year of data was added to the model. TRUNCATED PRICE DISTRIBUTION Because the loan rate "cuts off" the lower tail of the price distribution, the mean and the variance of price will be affected. Using the same formula as Lin and Dismukes, the mean of the truncated price variable is defined by equation (4.4.) below: (4.4) E(TP) = sp + ? (?) + ?p2 * (1/ ?(2* ?)) (-.5* ?* ?) + ep* (1- ? (?)) where sp is the support price; ep is the expected market price; ?p is the untruncated variance of price, calculated as a moving weighted average of the deviations of expected market price from actual market price, using a three-year lag and the weights (0.5., 0.3., and 0.2); ? is defined as (sp ? ep) / ?p and ? is the standard normal distribution. The truncated variance and covariances were created following the formula found in Greene, as applied by Lin and Dismukes. Also, they can be found in the literature 27 review of Chavas and Holt. The SAS Programs that were used to generate the variables are available in Appendix B. EXPECTED REVENUE Equation (4.5) is the formula for expected net revenues, taking into account the truncation of prices by the loan rate. (4.5) NRT = E(Y) * E(TP) ? CP + (1- ? (?)) * (?/? ?y2* ?p2)* ?y* ??tp2 E(Y) is the expected yield, CP is the lagged costs, ? is the correlation between untruncated price and yields, ?p2 is the variance of untruncated yields, ?p is the standard deviation for untruncated prices, ?y is the standard deviation for untruncated yields, and ?tp2 is the truncated variance of price. MODELS This analysis used the framework from Chavas and Holt?s model and Lin and Dismukes. Equation (4.6) is the cotton model, equation (4.7) is the soybeans model, and equation (4.8) is the corn model. (4.6) Ai =ai + bi ctexpre + ci sbexpre + di cnexpre + ei ctrvar + fi sbrvar + gi cnrvar + hi ctidle + ii covrsbct + ji covrcnct + ki wealthadj + li lctpa + mi AL+ ni GA + oi FL + pi NC + qi SC + ri TN + si VA + ti Fpdum + ?i (4.7) Ai =ai + bi ctexpre + ci sbexpre + di cnexpre + ei ctrvar + fi sbrvar + gi cnrvar + hi covrsbct + ii covrcnct + ji wealthadj + ki lsbpa + li AL+ mi GA + ni FL + oi NC + pi SC + qi TN + ri VA + si Fpdum + ?i (4.8) Ai =ai + bi ctexpre + ci sbexpre + di cnexpre + ei ctrvar + fi sbrvar + gi cnrvar + hi cnidle + ii covrsbct + ji covrcnct + ki wealthadj + li lcnpa + mi AL+ ni GA + oi FL + pi NC + qi SC + ri TN + si VA + ti Fpdum + ?i 28 The variables from the models above are listed in Table 4.1 below which also contains their definition. Dummy variables were created for each state to allow for different intercepts, with Alabama as the "base state" without a dummy variable. For example, in the column for Georgia the variable was equal to one and the other states were equal to zero. This was repeated for each state. Also, a policy dummy was used for the years 1991-1995 which pertained to the old farm bill. The year before the 1996 Farm Bill took the value of one and after took the value of zero. Table 4.1 Independent Variables and Definitions Variable Definitions A Acreage Planted Ctexpre Cotton Truncated Expected Net Returns Sbexpre Soybeans Truncated Expected Net Returns Cnexpre Corn Truncated Expected Net Returns Ctrvar Cotton Truncated Expected Variance of Revenue Sbrvar Soybeans Truncated Expected Variance of Revenue Cnrvar Corn Truncated Expected Variance of Revenue Ctidle Cotton in Acreage Reduction Program in Percentages Cnidle Corn in Acreage Reduction Program in Percentages Covrsbct Truncated Expected Covariance of Corn and Cotton Revenues Covrcnct Truncated Expected Covariance of Soybeans and Cotton Revenues Wealthadj Lagged Net Worth for Farm Households Lctpa Lagged Cotton Acreage Planted Lsbpa Lagged Soybeans Acreage Planted Lcnpa Lagged Corn Acreage Planted FL Florida Dummy GA Georgia Dummy NC North Carolina Dummy SC South Carolina Dummy TN Tennessee Dummy VA Virginia Dummy Fpdum Policy Dummy 29 V. RESULTS In the analysis, the equations were first estimated in OLS and then estimated in SUR. The Seemingly Unrelated Regressions model first estimates the equation in OLS, then takes into account the residual of the variance and covariance matrix to estimate the generalized least squares model (Lin and Dismukes). Two different SUR models were estimated, one with cross equations restrictions on the truncated revenues and one without cross-equation restrictions. The OLS equations are displayed in Table 5.1. The cotton model estimated in OLS contained the largest number of significant variables. Cotton truncated net returns were significantly positive as expected. Cross price effects of the soybeans and corn truncated net returns were significant and negative indicating a competitive relationship. The cotton variance was significant and negative. The cotton-soybeans covariance was significant and positive. The corn-soybeans covariance was significant and negative. The OLS soybeans model estimated significant and positive truncated expected returns of soybeans as expected. The OLS corn model estimated significant and positive truncated expected returns of corn as expected. Truncated expected net returns of cotton was positive and significant. The cotton-corn covariance was significant and positive in both the OLS and SUR unrestricted estimations. The farm program dummy was significant in the cotton and corn equations, negative and positive, respectively. 30 Table 5.1 OLS Estimations of Planted Acreage Variable Cotton Soybeans Corn Intercept 157.320 34.451 41.630 (50.595)*** (34.957) (55.555) Ctexpre 0.279 -0.041 0.316 (0.143)* (0.124) (0.162)* Sbexpre -0.883 0.822 -0.550 (0.383)** (0.339)** (0.454) Cnexpre -0.524 --- 0.497 (0.199)** (0.231)** Ctrvar -4947.281 --- 802.060 (1890.188)** (2518.725) Sbrvar --- 8.913 28.558 (10.424) (17.321) Cnrvar --- --- 57.629 (74.873) Ctidle 0.033 --- --- (0.005)*** Cnidle --- --- 0.003 (0.007) Covrsbct 584.432 -30.380 --- (195.037)*** (163.335) Covcnsb --- --- -46.81 (63.551) Covrcnct -2185.483 --- 1640.836 (480.864)*** (469.914)*** Wealthadj 0.000 0.000 0.000 (0.000) (0.000) (0.000) Lctpa 0.867 --- --- (0.046)*** Lsbpa --- 0.746 --- (0.066)*** Lcnpa --- --- 0.582 (0.109)*** FL 15.364 -67.644 -40.03 (36.250) (31.447)** (37.723) GA 147.836 7.308 27.242 (43.324)*** (27.573) (43.536) NC 81.588 279.483 243.105 (29.879)*** (77.625)*** (68.550)*** SC -20.658 69.731 16.994 (25.560) (27.830)** (28.754) TN 111.908 177.252 188.319 (40.133)*** (68.730)** (56.751)*** VA 99.065 12.722 100.781 (43.908)** (41.050) (44.782)** Fpdum -137.990 --- 51.996 (26.509)*** (26.085)** Observations 98 98 98 R2 0.9832 0.9877 0.9586 Note: The standard deviations are listed below the coefficient estimates in parentheses. The asterisks indicate a 1%, 5%, and 10% significance different from zero by ***, **, and *, respectively. 31 In the SUR unrestricted regression displayed in Table 5.2, the cotton model estimated significant and positive truncated cotton net returns as expected. The truncated expected net returns of soybeans were negative and significant indicating a competitive relationship. Similar results were estimated in the OLS regression in Table 5.1. In the soybeans equation, the truncated net returns of soybeans were significantly positive as expected. In the corn equation, the truncated expected net returns for corn were significant and positive as expected. The variance for soybeans was significant and positive. The SUR restricted model used the symmetry restrictions across each of the following equations: soybeans and cotton, corn and cotton, and corn and soybeans. The estimations are displayed in Table 5.3. However, two of the three restrictions are rejected. The soybeans-cotton restriction and the corn-cotton restriction were rejected in the F-test. The corn-soybeans restriction was not rejected in the F-test. The F-test information is also in Table 5.3. In the SUR estimations with restriction, there are not any significant net returns. Table 5.4 contains the short-run and long-run own-profit elasticities for all three estimations. The long-run elasticites were calculated using the formula from Duffy, Richardson, and Wolhgenant where the coefficient of the own-profit is divided by one minus the coefficient of the lagged acreage. In Chavas and Holt, own-profit elasticites are referred to as own-revenue elastic. Lin reported own-profit elasticity for corn (0.170) and soybeans (.295). Chavas and Holt reported own-profit elasticity for corn (0.158) and 32 Table 5.2 SUR Unrestricted Estimations of Planted Acreage Variable Cotton Soybeans Corn Intercept 29.129 45.458 117.882 -48.613 (35.370) (46.994)** Ctexpre 0.335 0.036 0.179 (0.157)** (0.123) (0.156) Sbexpre -0.973 0.597 -0.443 (0.422)** (0.337)* (0.420) Cnexpre -0.328 --- 0.391 0.204 (0.209)* Ctrvar -483.942 --- -1639.16 (1983.118) (2245.068) Sbrvar --- 9.586 35.102 (10.392) (14.602)** Cnrvar --- --- 56.511 (66.087) Ctidle 0.017 --- --- (0.004)*** Cnidle --- --- 0.002 (0.005) Covrsbct 241.917 48.750 --- (203.67) (174.678) Covcnsb --- --- -33.696 (53.372) Covrcnct -482.498 --- 678.730 (454.903) (405.401)* Wealthadj 0.000 -0.000 -0.000 (0.000)* (-0.000) (0.000)* Lctpa 0.827 --- --- (0.047)*** Lsbpa --- 0.806 --- (0.062)*** Lcnpa --- --- 0.602 (0.101)*** FL -41.245 -35.933 -28.606 (39.451) (31.443) (36.648) GA 133.431 16.026 53.550 (46.105)*** (27.649) (41.382) NC 69.039 228.836 241.067 (33.598)** (73.164)*** (64.236)*** SC -38.14 52.053 15.311 (28.506) (27.251)* (27.658) TN 97.063 151.469 184.657 (45.302)** (65.415)** (54.424)*** VA 49.394 22.239 97.463 (48.525) (40.334) (43.949)** Fpdum --- -26.012 --- (16.384) Note: The standard deviations are listed below the coefficient estimates in parentheses. The asterisks indicate a 1%, 5%, and 10% significance different from zero by ***, **, and *, respectively. 33 Table 5.3 SUR Restricted Estimations of Planted Acreage Variable Cotton Soybeans Corn intercept 23.383 29.680 127.334 (53.026) (45.226) (47.257)*** ctexpre 0.181 -0.108 -0.149 (0.169) (0.130) (0.129) sbexpre -0.108 0.551 0.042 (0.130) (0.388) (0.163) cnexpre -0.149 0.042 0.317 (0.129) (0.163) (0.196) ctrvar -597.616 2144.278 -1053.060 (2704.510) (2374.216) (2434.157) sbrvar -9.069 3.201 21.676 (16.802) (16.427) (13.101) cnrvar -22.446 23.825 50.604 (51.030) (65.723) (65.157) ctidle 0.0169 --- --- (0.004)*** cnidle --- --- 0.002 (0.005) covrsbct 149.009 20.066 --- (225.651) (182.204) covcnsb --- 8.011 14.920 (54.507) (52.049) covrcnct -713.960 --- 152.408 (543.902) (373.820) wealthadj 0.000 -0.000 -0.000 (0.000)* (0.000) (0.000)* Lctpa 0.842 --- --- (0.050)*** Lsbpa --- 0.832 --- (0.065)*** Lcnpa --- --- 0.630 (0.099)*** FL -68.929 -45.399 -46.227 (45.084) (33.306) (35.693) GA 108.034 4.512 63.279 (45.982)** (36.582) (39.923) NC 28.963 193.307 208.501 (32.929) (79.602)** (63.654)*** SC -29.737 39.940 14.937 (31.929) (32.843) (27.297) TN 10.275 116.506 130.315 (37.684) (69.466)*** (51.889)** VA -31.636 4.891 49.194 (46.477) (41.333) (40.222) Fpdum --- -14.978 --- (20.528) Restrictions Parameter Standard Error P-value Soybeans-Cotton -8.465 2.325 0.000 Corn-Cotton -12.556 4.249 0.002 Corn-Soybeans 3.117 2.202 0.158 Note: The standard deviations are listed below the coefficient estimates in parentheses. The asterisks indicate a 1%, 5%, and 10% significance different from zero by ***, **, and *, respectively. 34 Table 5.4 Short- and Long-Run Own Profit Elasticities OLS SUR Unrestricted SUR Restricted Crop Short-Run Long-Run Short-Run Long-Run Short-Run Long-Run Cotton 0.068 0.511 0.077 0.093 .041 0.262 Soybeans 0.094 0.224 0.074 0.185 .072 0.427 Corn 0.107 0.421 0.078 0.401 .060 0.162 soybeans (.441). Duffy, Shalishali, and Kinnucan reported a corn own-revenue elasticity of 0.0954 and a soybeans own-revenue of 0.560. The soybeans own-profit elasticites from this study are lower than in Duffy, Shalishali, and Kinnucan and the corn own-profit elasticites are higher than the Duffy, Shalishali, and Kinnucan. The own-profit elasticites from this study are lower than the other elasticites reported by Lin and Dismukes and Chavas and Holt. The APR program affected cotton and corn from 1991-1995. The coefficient of the cotton the ARP variable was significant and positive in the OLS, SUR unrestricted, and restricted estimations. Thus, more idled acres of cotton lead to an increase in acres planted. This could be a result of farmers trying to build their base acreage for cotton. However, the magnitude of the coefficient was small, .033 for the OLS estimations and .017 for the SUR estimation. Wealth was significant in the SUR unrestricted estimations for cotton and corn. Similar results were found in Lin and Dismukes. The lagged planted acreage for each individual equation in the OLS, SUR unrestricted, and SUR restricted estimations were significant and positive. Similar results can also be found in Lin and Dismukes. 35 VI. CONCLUSION This paper identified a theoretical model for supply response of cotton, soybeans, and corn in seven Southeast states based primarily on work by Chavas and Holt. Modifications were made to the model from literature by Duffy, Shalishali, and Kinnucan and Lin and Dismukes, such as the use of futures prices, variances of revenues, and covariance of revenues in the expected truncated net returns and including the dependent variable as lagged explanatory variables. Also, changes to the farm program variable and the wealth variable were made from the original model by Chavas and Holt. A set of three models were estimated in OLS, SUR without restrictions, and SUR with cross- equation restrictions using data from 1991-2005. The data included futures prices of row crops, market prices of row crops, row crop yields, costs of production, loan rates, ARP rates, and farm equity to generate the variables need for the supply response model. From the econometric estimations, the analysis took into account how loan rates, ARP rates, wealth, and prices affect row crop acreage decisions in the Southeast region. Farm programs were taken into account through the truncation effects for each crop and also through the cotton and corn acreage reduction variables in to account. The empirical results from the OLS, SUR unrestricted, and SUR restricted varied across model specification. The OLS model for cotton estimated cotton expected 36 truncated net returns, soybeans expected truncated net returns, and corn expected truncated net returns as significant. Soybeans and corn expected truncated net returns were negative indicating as corn and soybeans revenues go up the acreage of planted cotton decreases. Thus, there exists a competitive enterprise between cotton and soybeans and also corn and cotton in the Southeast. In the SUR estimations with out restrictions, the cotton equation estimated significant effect of expected truncated net returns of soybeans again. The SUR estimation with restrictions only estimated five significant variables other than the states dummies and rejected two of the three cross-commodity restrictions. The corn-soybean restriction was the only restriction that was not rejected. The rejection of the restrictions could have been a result of modeling the equations or the model might have needed to include other crops as variables that are competitive in the south with cotton, corn, and soybeans. Three of the significant variables in the SUR estimations with restrictions were the lagged planted acreage for each crop. The lagged planted acres were significant in the OLS, SUR with out restrictions, and the SUR with restriction. This indicates that the producers are responsive to changes in the markets. These changes can include but are not limited to technological updates, futures and market prices, and biological diseases within the plants. In the cotton equation, the cotton under the ARP was significant and positive. In the corn equation for both SUR estimations, the wealth variable was negative and significant, but the magnitude was 0.000. Overall, the short-run elasticities for own-profit generated in this paper were lower than the elasticities by Chavas and Holt, Duffy, Shalishali, and Kinnucan, and Lin 37 and Dismukes. This indicates the Southeast crops are less responsive to profitability in the short-run. It is hard for producers to make changes in their decisions with all of the fixed inputs, especially if the crops have already been planted. However, the long-run elasticities for the OLS estimations are considerable higher in magnitude than the short- run elasticities. Thus, in the long-run cotton and corn are more responsive to profitability. Also, this paper found that there was an importance of initial wealth when producers make planting decisions. Wealth was significant; however, the magnitude of the coefficient was zero to at least the thousandths decimal place. An increase in initial wealth does prove to increase planted acreage. The Acreage Reduction Program had positive effects on producers? decisions for cotton and corn acreage. Thus, the more cotton and corn acres under ARP, the more cotton and corn acres planted. Further empirical work could include more row crops that are competitive with cotton, soybeans, and corn. For example, peanuts might be considered a competitive crop in the Southeast during the planting season of cotton, soybeans, and corn. Also, further empirical work could include varying the level of farm program support. This would allow analysis of the change in acreage decisions in the Southeast for different levels of support. Also, a similar model could be used in other regions of the United States. Then, supply elasticities could be generated for comparison. 38 BIBLIOGRAPHY Bureau of Labor Statistics.?Producer Price Index.? http://www.bls.gov/ppi/. Chavas, J.P., and M.T. Holt. ?Acreage Decisions under Risk: The Case of Corn and Soybeans.? Amer. J. Agr. Econ. 72(1990):529-38. Duffy, P. A.; K. Shalishali, H.W. Kinnucan. "Acreage Response under Farm Programs for Major Southeastern Field Crops." J. of Agr. and App. Econ. 26(1994): 367 78. Duffy, P., J.W. Richardson, and M.K. Wolhgenant. ?Regional Cotton Acreage Response,? Southern Journal of Agricultural Economics, 19 (1987): 99-108. Gardner, B. L. ?Future Prices in Supply Analysis.? Amer. J. Agr. Econ. 58(1976): 81-84. Greene, W.H. Econometric Analysis. New York: Macmillan Publishing Company. 1990. Hoffman, Lin. ?Provisions of the Federal Agriculture Improvement and Reform Act of 1996? U.S. Department of Agriculture, http://www.ers.usda.gov/publications/aib729/aib729b.pdf. Houck, J.P., and M.E. Ryan. ?Supply Analysis for Corn in the United States: The Impact of Changing Governement Programs.? Amer. J. Agr. Econ. 54 (1972): 184-91. Just, R.E. ?An Investigation of the Importance of Risk in Farmer?s Decisions.? Amer. J. Agr. Econ. 56(1974):14-25. Lee, D.R. and P.G. Helmberger. ?Estimating Supply Response in the Presence of Farm Programs.? Amer. J. Agr. Econ. 67,2(1985):193-202. Lin, W. and R. Dismukes. ?Supply Response under Risk: Implications for Counter-Cyclical Payments? Production Impact.? Review of Agricultural Economics 29(2007):64-86. Nerlove, Marc. ?Estimates of the Elasticities of Supply of Selected Agricultural Commodities.? Journal of Farm Economics 38(May, 1956):496-509. 39 Pope, R.D., ?Supply Response and the Dispersion of Price Expectations,? Amer. J. Agr. Econ. 63(1981);161-163. Price Data. www.pricedata.com Shumway, C.R. ?Supply, Demand, and Technology in a Multiproduct Industry: Texas Field Crops.? Amer. J. Agr. Econ. 65 (1983):748-60. Tomek, W.G. ?Distributed Lag Models of Cotton Acreage Response: A Further Result.? Amer. J. Agr. Econ. 54(1972): 108-110. U.S. Department of Agriculture. ?Commodity Costs and Returns: U.S. and Regional Cost and Return Data.? http://www.ers.usda.gov/Data/CostsAndReturns/TestPick.htm U.S. Department of Agriculture. ?Provisions of the Food, Agriculture, Conservation, and Trade Act of 1990.? http://www.ers.usda.gov/publications/aib624/aib624.pdf U.S. Department of Agriculture, Economic Research Service. Cotton: Background for 1995 Farm Legislation. Washington, D.C., April, 2005. U.S. Department of Agriculture, Economic Research Service. ?Farm Bill 2002.? http://www.ers.usda.gov/Features/Farmbill/titles/titleIcommodities.htm U.S. Department of Agriculture. Economic Research Service. Provisions for the Federal Agriculture Improvement and Reform Act of 1996 http://www.ers.usda.gov/publications/aib729/aib729a4.pdf U.S. Department of Agriculture, Economic Research Service. Feed Grains: Background for 1995 Farm Legislation. Washington, D.C., April, 2005. U.S. Department of Agriculture, Economic Research Service. Oilseeds: Background for 1995 Farm Legislation. Washington, D.C., April, 2005. U.S. Department of Agriculture, Economic Research Service. The 202 Farm Act: Provision and Implications of Commodity Markets. http://www.ers.usda.gov/publications/aib778/aib778appa.pdf U.S. Department of Agriculture, ?Rules and Regulations?, Federal Register. 60:116 (1995): 1. U.S. Department of Agriculture. ?Quick Stats: Agricultural Statistics Data Base.? http://www.nass.usda.gov/QuickStats/ 40 APPENDICES 41 APPENDIX A The Data Used in Thesis 42 Corn Yields 1971-2005 Year Alabama Florida Georgia North Carolina Tennessee South Carolina Virginia 1971 45 49 54 57 54 57 68 1972 48 46 52 80 65 70 83 1973 46 43 48 82 58 66 86 1974 43 48 56 75 65 61 80 1975 50 45 55 67 60 68 88 1976 60 60 62 80 82 78 78 1977 29 35 24 51 68 39 55 1978 50 52 50 76 69 57 83 1979 61 53 65 76 85 80 83 1980 36 49 42 60 46 48 55 1981 55 57 50 77 84 58 90 1982 66 66 85 99 90 88 101 1983 59 67 75 60 48 62 48 1984 65 65 82 90 95 78 104 1985 75 65 84 79 98 88 99 1986 57 62 58 69 74 46 54 1987 72 69 84 68 91 78 63 1988 44 58 62 84 73 58 79 1989 81 74 95 93 107 91 110 1990 58 71 68 68 86 48 100 1991 80 68 100 90 86 85 84 1992 94 75 100 95 124 88 116 1993 55 65 70 65 84 40 60 1994 96 85 106 91 116 85 98 1995 75 90 90 107 118 91 111 1996 82 88 95 95 116 79 126 1997 87 80 105 89 102 95 93 1998 63 62 85 70 96 40 84 1999 103 93 103 80 102 70 78 2000 65 75 107 116 114 65 146 2001 107 87 134 125 132 108 123 2002 88 96 110 83 107 47 68 2003 122 82 129 106 131 105 115 2004 123 90 130 117 140 100 145 2005 119 94 129 120 130 116 118 43 Soybean Yields 1971-2005 Year Alabama Florida Georgia North Carolina Tennessee South Carolina Virginia 1971 26 28 25.5 24 21.5 26 24 1972 20 21 15 25 18.5 22 23 1973 21 24 21 24 19 23.5 27 1974 23 26 24.5 22 20 21 24 1975 24.5 24 25.5 23.5 25 22 25 1976 24 26 23.5 22 22.5 18 20.5 1977 21 25 20 21.5 23.5 20.5 19 1978 21 25 17.5 24 23.5 22 28 1979 25 29 28 23.5 27 24 28.5 1980 15 22 12 18 18 13 15 1981 23 24 19 25 25 20 28 1982 25 26 27 25 26.5 22 29 1983 20 25 21 20 16 16.5 16 1984 21 24 20 26 26 20 29.5 1985 27 26 24 23 31 20 25 1986 23 23 19 24 25 16.5 24 1987 18 25 21 24.5 23 22 22 1988 25 29 25 27 26 23.5 28 1989 21 22 26 27 24 21 32 1990 17 19 14 24 27 18.5 32 1991 23 27 27 29.5 30 22 29 1992 29 30 29 27 35 22 31 1993 24 25 17 24 31 15 22 1994 31 31 31 31 36.5 27 32 1995 24 26 27 25 32 24 24 1996 34 32 26 29 35 25 34 1997 25 25 21 29 34 22.5 23 1998 22 23 21 27 29 21 23 1999 16 32 19 23 19 20 27 2000 18 19 24 32.5 25 25 38.5 2001 35 29 26 32 34 21 35.5 2002 24 33 23 24 31 17 23 2003 36 30 33 30 42 28 34 2004 35 34 31 34 41 27 39 2005 33 32 26 27 38 20.5 30 44 Cotton Yields 1971-2005 Year Alabama Florida Georgia North Carolina Tennessee South Carolina Virginia 1971 640 . 374 135 528 275 . 1972 470 395 572 337 435 543 265 1973 423 499 522 514 473 472 440 1974 429 503 490 440 483 290 384 1975 405 346 443 412 339 454 344 1976 399 514 398 489 295 438 480 1977 337 425 232 305 407 342 194 1978 443 506 463 515 490 562 480 1979 510 565 486 459 357 510 320 1980 411 610 258 381 349 309 320 1981 545 601 436 556 496 667 480 1982 775 627 714 699 638 783 640 1983 409 608 467 350 337 369 360 1984 699 847 784 600 498 785 528 1985 795 693 725 646 600 708 443 1986 506 707 455 646 567 370 554 1987 572 646 662 495 700 428 373 1988 486 566 564 515 529 473 510 1989 571 557 631 615 497 626 498 1990 476 640 555 631 461 452 562 1991 655 719 812 672 552 786 765 1992 731 701 783 596 651 565 621 1993 524 696 586 535 425 495 634 1994 766 735 843 820 726 846 944 1995 409 472 625 479 527 528 620 1996 734 637 747 659 611 774 748 1997 597 577 646 652 662 688 659 1998 559 489 578 699 589 587 765 1999 535 516 579 475 505 428 635 2000 492 480 591 742 603 627 738 2001 730 612 720 832 763 686 929 2002 507 439 557 421 741 314 465 2003 772 610 785 646 806 718 674 2004 724 601 674 900 900 875 956 2005 747 762 849 852 848 743 955 45 Costs of Production 1989-2005 Year Corn Cotton Soybeans 1989 143.83 299.16 87.94 1990 141.17 303.74 85.54 1991 150.59 271.78 89.77 1992 152.04 275.91 91.92 1993 148.65 283.76 89.78 1994 157.32 291.02 95.1 1995 169.26 307.91 94.53 1996 170.32 308.16 98.88 1997 170.80 295.25 92.43 1998 159.03 285.26 95.09 1999 160.00 270.66 90.87 2000 171.63 320.72 92.89 2001 172.77 355.04 106.71 2002 162.21 327.59 81.98 2003 173.02 332.67 80.23 2004 186.85 339.48 90.21 2005 187.10 376.89 96.96 Producers Price Index 1981-2005 Year PPI 1982=100 PPI 2005=100 1987 102.8 0.653113088 1988 106.9 0.679161372 1989 112.2 0.712833545 1990 116.3 0.73888183 1991 116.5 0.740152478 1992 117.2 0.744599746 1993 118.9 0.755400254 1994 120.4 0.764930114 1995 124.7 0.792249047 1996 127.7 0.811308767 1997 127.6 0.810673443 1998 124.4 0.790343075 1999 125.5 0.797331639 2000 132.7 0.843074968 2001 134.2 0.852604828 2002 131.1 0.832909784 2003 138.1 0.877382465 2004 146.7 0.93202033 2005 157.4 1 46 Wealth Data 1987-2003 Year Alabama Florida Georgia Kentucky North Carolina South Carolina Tennessee Virginia 1987 8,067,850 19,512,129 10,699,033 12,701,022 11,938,761 4,426,151 12,323,456 10,526,941 1988 8,537,416 19,842,369 11,648,363 12,939,378 12,443,122 5,089,356 12,420,361 11,884,615 1989 8,860,721 21,611,740 12,669,650 14,195,560 12,409,352 5,293,368 13,055,678 14,045,262 1990 8,836,141 21,445,994 12,857,393 14,258,516 12,781,751 5,837,737 13,532,906 12,826,478 1991 9,302,355 20,806,689 12,173,740 14,383,457 13,192,918 6,093,872 13,820,863 13,770,226 1992 10,017,665 21,294,936 12,948,454 15,323,962 14,582,063 6,041,829 15,052,280 13,877,695 1993 11,145,404 21,565,533 13,130,817 16,285,613 14,863,138 6,198,473 15,491,161 13,693,565 1994 11,962,833 21,563,682 13,845,770 17,239,956 15,923,372 6,655,280 16,232,541 14,798,455 1995 12,042,339 21,809,354 14,458,341 17,469,770 16,815,609 6,728,346 17,907,111 15,463,697 1996 12,236,904 21,877,306 14,865,674 17,751,287 17,876,107 6,861,700 18,893,898 16,026,216 1997 12,762,245 21,967,793 15,691,183 19,129,257 18,291,250 7,200,659 20,616,218 16,304,481 1998 13,063,029 21,453,964 16,848,438 19,381,064 18,483,204 7,487,770 21,752,216 16,931,020 1999 13,867,959 22,542,383 18,986,873 20,165,915 20,960,013 7,152,699 23,473,630 18,151,617 2000 14,467,262 24,188,781 20,934,168 22,271,398 23,191,933 7,195,202 24,384,222 19,550,322 2001 15,025,621 25,840,392 22,401,044 23,126,887 23,713,362 7,568,972 25,708,547 20,552,015 2002 15,631,199 27,495,711 24,197,038 24,768,168 24,902,239 7,934,130 26,838,592 21,339,309 2003 16,556,581 29,178,606 25,912,192 25,936,437 26,491,053 8,372,628 27,636,085 22,358,828 Cotton Futures Prices 1987-2005 Year Dates Closing Price Tuesday Wednesday Thursday 1987 1/13,14,15 56.250 56.070 55.520 1988 1/12,13,14 62.000 63.050 62.550 1989 1/10,11,12 57.850 57.700 57.500 1990 1/9,10,11 63.520 63.400 64.200 1991 1/15,16,17 64.020 64.020 64.560 1992 1/14,15,16 62.600 62.660 62.250 1993 1/12,13,14 60.250 60.200 60.730 1994 1/11,12,13 67.900 68.500 68.300 1995 1/10,11,12 74.750 74.630 74.600 1996 1/9,10,11 77.500 76.700 76.500 1997 1/14,15,16 76.610 77.000 76.960 1998 1/13,14,15 71.650 71.820 71.780 1999 1/12,13,14 63.660 63.340 63.450 2000 1/11,12,13 58.990 59.190 59.500 2001 1/9,10,11 61.600 61.650 62.000 2002 1/15,16,17 43.310 43.710 43.980 2003 1/14,15,16 58.430 58.300 58.380 2004 1/13,14,15 68.770 68.880 69.450 2005 1/11,12,13 51.530 51.500 51.150 47 Soybeans Future Prices 1987-2005 Year Dates Closing Price Tuesday Wednesday Thursday 1987 1/13,14,15 481.000 484.750 484.250 1988 1/12,13,14 617.500 626.250 627.750 1989 1/10,11,12 744.750 740.250 741.250 1990 1/9,10,11 618.250 614.250 614.250 1991 1/15,16,17 601.500 606.750 614.250 1992 1/14,15,16 585.750 597.750 599.000 1993 1/12,13,14 596.750 596.250 592.000 1994 1/11,12,13 646.500 646.500 663.250 1995 1/10,11,12 587.750 586.750 585.750 1996 1/9,10,11 706.500 704.250 696.000 1997 1/14,15,16 686.750 688.500 688.750 1998 1/13,14,15 660.500 655.500 657.250 1999 1/12,13,14 554.000 546.500 547.000 2000 1/11,12,13 499.750 505.500 515.000 2001 1/9,10,11 510.250 506.750 496.500 2002 1/15,16,17 457.750 464.000 461.750 2003 1/14,15,16 505.750 510.750 512.000 2004 1/13,14,15 669.750 668.500 671.750 2005 1/11,12,13 562.250 551.500 556.500 48 Corn Future Prices 1987-2005 Year Dates Closing Price Tuesday Wednesday Thursday 1987 1/13,14,15 171.750 174.000 172.250 1988 1/12,13,14 204.000 206.000 206.500 1989 1/10,11,12 284.000 283.000 282.750 1990 1/9,10,11 249.000 247.500 247.000 1991 1/15,16,17 250.250 254.000 256.000 1992 1/14,15,16 266.250 269.750 267.000 1993 1/12,13,14 239.250 237.250 237.250 1994 1/11,12,13 289.000 286.500 291.000 1995 1/10,11,12 248.750 248.750 250.000 1996 1/9,10,11 314.000 310.250 305.250 1997 1/14,15,16 267.250 270.250 269.750 1998 1/13,14,15 278.500 280.250 283.250 1999 1/12,13,14 235.500 233.500 233.000 2000 1/11,12,13 228.750 236.500 241.500 2001 1/9,10,11 250.000 252.250 246.250 2002 1/15,16,17 231.750 233.500 232.000 2003 1/14,15,16 237.750 238.000 237.250 2004 1/13,14,15 268.500 270.000 270.500 2005 1/11,12,13 228.250 222.750 222.000 49 Corn Market Prices ($/bu) Year Alabama Georgia Florida North Carolina South Carolina Tennessee Virginia 1990 2.69 2.77 2.70 2.53 2.72 2.43 2.51 1991 2.60 2.72 2.60 2.63 2.65 2.50 2.60 1992 2.35 2.31 2.30 2.26 2.30 2.10 2.25 1993 2.64 2.72 2.55 2.65 2.75 2.55 2.65 1994 2.50 2.47 2.40 2.48 2.40 2.25 2.40 1995 3.50 3.55 3.20 3.54 3.40 3.50 3.35 1996 3.45 3.58 3.80 3.43 3.55 2.90 3.20 1997 2.82 2.90 2.90 2.83 2.79 2.65 2.69 1998 2.31 2.46 2.30 2.33 2.40 2.13 2.24 1999 2.26 2.27 2.32 2.27 2.29 1.92 2.15 2000 2.16 2.06 2.24 2.01 2.10 1.96 2.02 2001 2.35 2.32 2.25 2.36 2.20 2.06 2.14 2002 2.72 2.70 2.60 2.89 2.70 2.58 2.73 2003 2.36 2.45 2.55 2.68 2.70 2.37 2.57 2004 2.48 2.20 2.30 2.44 2.30 2.17 2.17 2005 2.50 2.20 2.00 2.33 2.19 2.07 2.14 Cotton Market Prices ($/lb) Year Alabama Florida Georgia North Carolina South Carolina Tennessee Virginia 1990 0.690 0.680 0.694 0.690 0.682 0.658 0.690 1991 0.566 0.554 0.600 0.593 0.604 0.539 0.593 1992 0.562 0.561 0.557 0.574 0.563 0.531 0.553 1993 0.571 0.555 0.599 0.577 0.607 0.587 0.570 1994 0.691 0.722 0.733 0.727 0.723 0.696 0.722 1995 0.729 0.800 0.766 0.783 0.797 0.750 0.730 1996 0.709 0.686 0.705 0.719 0.738 0.671 0.710 1997 0.673 0.654 0.677 0.659 0.701 0.653 0.675 1998 0.606 0.542 0.614 0.649 0.659 0.619 0.692 1999 0.478 0.425 0.453 0.455 0.455 0.436 0.473 2000 0.528 0.565 0.556 0.530 0.550 0.455 0.607 2001 0.277 0.295 0.306 0.317 0.320 0.305 0.301 2002 0.435 0.440 0.443 0.422 0.410 0.453 0.415 2003 0.596 0.655 0.612 0.647 0.623 0.570 0.640 2004 0.406 0.464 0.428 0.437 0.430 0.405 0.380 2005 0.495 0.510 0.491 0.454 0.490 0.471 0.455 50 Soybeans Market Prices ($/bu) Year Alabama Florida Georgia North Carolina South Carolina Tennessee Virginia 1990 5.89 5.65 5.74 6.68 5.78 5.95 5.55 1991 5.60 5.40 5.53 5.56 5.68 5.73 5.50 1992 5.63 5.20 5.49 5.48 5.44 5.61 5.50 1993 6.40 6.35 6.52 6.41 6.52 6.60 6.45 1994 5.65 5.40 5.37 5.36 5.47 5.62 5.35 1995 7.10 6.50 6.71 6.95 6.93 6.88 6.85 1996 7.40 7.00 6.87 7.07 7.40 7.25 6.80 1997 6.65 7.00 6.68 6.68 6.55 6.89 6.20 1998 5.30 5.20 5.24 5.03 5.00 5.37 5.30 1999 4.80 4.65 4.79 4.61 4.70 4.69 4.50 2000 4.75 4.45 4.43 4.51 4.50 4.69 4.35 2001 4.60 4.20 4.35 4.29 4.45 4.46 4.30 2002 5.55 5.35 5.45 5.63 5.60 5.70 5.54 2003 7.25 6.90 7.47 7.29 7.60 7.05 7.67 2004 6.25 5.60 5.60 5.56 5.60 5.58 5.32 2005 5.95 5.40 5.50 5.64 5.55 5.73 5.53 51 APPENDIX B SAS Programs 52 *This SAS Program was used to Estimate Expected Yields for Alabama /*Alabama*/ data fake; set Yields.Cotton_Yields; *CHANGE ADD TREND1 VARIABLE TO MAKE ESTIMATES; *CHANGE START TREND WITH NUMBER 1 instead of 0 for neatness; trend = year - 1970; trend1 = year - 1969; *CHANGE MAKE A SECOND YEAR VARIABLE FOR OUTPUT; YR1 = year + 1; vctyld = Alabama; ctyld = int(vctyld); lctyld = lag(ctyld); one = 1; run; proc print; run; data fakesim; set fake; *start simulation with data from 1990 for 1991 estimate; *if need more lags in estimates, create as variables (expand XVAR matrix, not years); if year gt 1985; *stop simulation with data from 2004 for 2005 estimate; if year lt 2005; data fake86; set fake; if year lt 1987; data fake87; set fake; if year lt 1988; data fake88; set fake; if year lt 1989; data fake89; set fake; if year lt 1990; data fake90; set fake; if year lt 1991; data fake91; set fake; if year lt 1992; data fake92; set fake; if year lt 1993; data fake93; set fake; if year lt 1994; data fake94; set fake; if year lt 1995; data fake95; set fake; if year lt 1996; 53 data fake96; set fake; if year lt 1997; data fake97; set fake; if year lt 1998; data fake98; set fake; if year lt 1999; data fake99; set fake; if year lt 2000; data fake00; set fake; if year lt 2001; data fake01; set fake; if year lt 2002; data fake02; set fake; if year lt 2003; data fake03; set fake; if year lt 2004; data fake04; set fake; if year lt 2005; proc reg data = fake86 outest=est86; model ctyld = lctyld trend; run; proc reg data = fake87 outest=est87; model ctyld = lctyld trend; run; proc reg data = fake88 outest=est88; model ctyld = lctyld trend; run; proc reg data = fake89 outest=est89; model ctyld = lctyld trend; run; proc reg data = fake90 outest=est90; model ctyld = lctyld trend; run; proc reg data = fake91 outest=est91; model ctyld = lctyld trend; run; proc reg data = fake92 outest=est92; model ctyld = lctyld trend; run; proc reg data = fake93 outest=est93; model ctyld = lctyld trend; run; proc reg data = fake94 outest=est94; 54 model ctyld = lctyld trend; run; proc reg data = fake95 outest=est95; model ctyld = lctyld trend; run; proc reg data = fake96 outest=est96; model ctyld = lctyld trend; run; proc reg data = fake97 outest=est97; model ctyld = lctyld trend; run; proc reg data = fake98 outest=est98; model ctyld = lctyld trend; run; proc reg data = fake99 outest=est99; model ctyld = lctyld trend; run; proc reg data = fake00 outest=est00; model ctyld = lctyld trend; run; proc reg data = fake01 outest=est01; model ctyld = lctyld trend; run; proc reg data = fake02 outest=est02; model ctyld = lctyld trend; run; proc reg data = fake03 outest=est03; model ctyld = lctyld trend; run; proc reg data = fake04 outest=est04; model ctyld = lctyld trend; run; proc iml; *read the parameter estimates into separate row vectors, keeping only the paramater estimates from the outputed estimated data set; use est86; READ all var{intercept lctyld trend} into b_86; use est87; READ all var{intercept lctyld trend} into b_87; use est88; READ all var{intercept lctyld trend} into b_88; use est89; READ all var{intercept lctyld trend} into b_89; 55 use est90; READ all var{intercept lctyld trend} into b_90 ; *print b_90; use est91; READ all var{intercept lctyld trend} into b_91; use est92; READ all var{intercept lctyld trend} into b_92; use est93; READ all var{intercept lctyld trend} into b_93; use est94; READ all var{intercept lctyld trend} into b_94; use est95; READ all var{intercept lctyld trend} into b_95; use est96; READ all var{intercept lctyld trend} into b_96; use est97; READ all var{intercept lctyld trend} into b_97; use est98; READ all var{intercept lctyld trend} into b_98; use est99; READ all var{intercept lctyld trend} into b_99; use est00; READ all var{intercept lctyld trend} into b_00; use est01; READ all var{intercept lctyld trend} into b_01; use est02; READ all var{intercept lctyld trend} into b_02; use est03; READ all var{intercept lctyld trend} into b_03; use est04; READ all var{intercept lctyld trend} into b_04; *concatenate the parameter estimates; Bmat = b_86//b_87//b_88//b_89//b_90//b_91//b_92//b_93//b_94//b_95//b_96//b_97//b_98// b_99//b_00//b_01//b_02//b_03//b_04; print Bmat; * get the data needed to do the rolling estimates of predicted yield and to output the variables; *CHANGE BRING IN YR TO READ OUTPUT BETTER; *CHANGE BRING IN TREND1 TO GET ESTIMATE; 56 use fakesim; read all var{one ctyld trend year} into X; read all var{YR1} into YR; read all var{one ctyld trend1} into XVAR; print X XVAR; * use matrix multiplication to get the output; *note the transpose operator is the backwards quote at upper left of keyboard; XTRAN = Xvar` ; print XTRAN; estfull = Bmat*Xtran; *estimators are in the diagonal of this matrix; *use element multiplication and add; esparts = Bmat#Xvar; est1 = esparts[,1]; est2 = esparts[,2]; est3 = esparts[,3]; *CHANGE MAKE CtYDAL INCLUDE YEAR; ctydsAL = est1 + est2 + est3; ctydAL = ctydsAL||YR; print ctydAL; * check against diagonal elements of estfull ; print estfull; *output the predicted values to a SAS data set; *CHANGE NAME TO INCLUDE YEAR AND MAKE CLEAR THIS IS EXPECTED YD; cname = {"exctydAL" "year"}; *note, this is a temporary data set, a permanent data set could also be created with only a little modifiction; create cottonydAL from ctydAL [ colname=cname ]; append from ctydAL; quit; *This SAS Programs was used to estimate the Net Worth Calculations data equity; set Rachel.networth; if year ne .; proc sort; by year; data usequity; set Rachel.Usequity; if year ne . ; proc sort; by year; data alleq; merge equity usequity ; by year; run; 57 * normalize wealth with PPI and put it in terms of avreage farm wealth for usda data; data new; set alleq; usfarmr= (1000*usequity)/(farms*ppi); ****************** ; alusdaf = 1000*(uswal/alnumb); alusdaf2 = 1000*(uswal/alnumarm); alusdafr = alusdaf/PPI; alusdaf2r = alusdaf2/PPI; alarmsr = alarms/PPI; **** ; gausdaf = 1000*(uswga/ganumb); gausdaf2 = 1000*(uswga/ganumarms); gausdafr = gausdaf/PPI; gausdaf2r = gausdaf2/PPI; gaarmsr = gaarms/PPI; ****************; flusdaf = 1000*(uswfl/flnumb); flusdaf2 = 1000*(uswfl/flnumarms); flusdafr = flusdaf/PPI; flusdaf2r = flusdaf2/PPI; flarmsr = flarms/PPI; ************************* ; kyusdaf = 1000*(uswky/kynumb); kyusdaf2 = 1000*(uswky/kynumarms); kyusdafr = kyusdaf/PPI; kyusdaf2r = kyusdaf2/PPI; kyarmsr = kyarms/PPI; ************************* ; tnusdaf = 1000*(uswtn/tnnumb); tnusdaf2 = 1000*(uswtn/tnnumarms); tnusdafr = tnusdaf/PPI; tnusdaf2r = tnusdaf2/PPI; tnarmsr = tnarms/PPI; ************************* ; ncusdaf = 1000*(uswnc/ncnumb); ncusdaf2 = 1000*(uswnc/ncnumarms); ncusdafr = ncusdaf/PPI; ncusdaf2r = ncusdaf2/PPI; ncarmsr = ncarms/PPI; ************************* ; scusdaf = 1000*(uswsc/ncnumb); scusdaf2 = 1000*(uswsc/scnumarms); scusdafr = scusdaf/PPI; scusdaf2r = scusdaf2/PPI; scarmsr = scarms/PPI; ************************* ; vausdaf = 1000*(uswva/vanumb); vausdaf2 = 1000*(uswva/vanumarms); vausdafr = vausdaf/PPI; vausdaf2r = vausdaf2/PPI; vaarmsr = vaarms/PPI; * generate state level estimates of wealth using us level from usda data ; title ; proc reg ; 58 model alusdafr = usfarmr; output out= alpred p= alwhat; title "alabama to alabama"; run; proc reg; model gausdafr = usfarmr; output out= gapred p= gawhat; title "georgia to national"; proc reg; model flusdafr = usfarmr; output out= flpred p= flwhat; title "florida to national"; proc reg; model kyusdafr = usfarmr; output out= kypred p= kywhat; title "kentucky to national"; run; proc reg; model tnusdafr = usfarmr; output out= tnpred p= tnwhat; title "tennessee to national"; run; proc reg; model scusdafr = usfarmr; output out= scpred p= scwhat; title "s.c. to national"; run; proc reg; model ncusdafr = usfarmr; output out= ncpred p= ncwhat; title "nc to national"; run; proc reg; model vausdafr = usfarmr; output out= vapred p= vawhat; title "va to national"; run; 59 * arms regressions -- regress on predictions from above models; proc reg ; model alarmsr = alwhat; output out= alpreda p= alwhata; title "arms to usda alabama"; run; proc reg ; model gaarmsr = gawhat; output out= gapreda p= gawhata; title "arms to usda georgia"; run; proc reg ; model kyarmsr = kywhat; output out= kypreda p= kywhata; title "arms to usda kentucky"; run; proc reg ; model flarmsr = flwhat; output out= flpreda p= flwhata; title "arms to usda florida"; run; proc reg ; model tnarmsr = tnwhat; output out= tnpreda p= tnwhata; title "arms to usda tennessee"; run; proc reg ; model scarmsr = scwhat; output out= scpreda p= scwhata; title "arms to usda south carolina"; run; proc reg ; model ncarmsr = ncwhat; output out= ncpreda p= ncwhata; title "arms to usda north carolina"; run; proc reg ; 60 model vaarmsr = vawhat; output out= vapreda p= vawhata; title "arms to usda virginia"; run; * wealth1 uses predicted values from regressions on arms models ; data wealth1; set vapreda; keep year alwhata flwhata gawhata kywhata ncwhata scwhata tnwhata vawhata; * wealth2 uses predicted values from regressions on usda data; data wealth2; set vapreda; keep year alwhat flwhat gawhat kywhat ncwhat scwhat tnwhat vawhat; data makenw; set vapreda; alarms2 = alarmsr ; if alarmsr = "." alarms2 = alwhata; gaarms2 = gaarmsr ; if gaarmsr = "." gaarms2 = gawhata; flarms2 = flarmsr ; if flarmsr = "." flarms2 = flwhata; kyarms2 = kyarmsr ; if kyarmsr = "." kyarms2 = kywhata; ncarms2 = ncarmsr ; if ncarmsr = "." ncarms2 = ncwhata; scarms2 = alarmsr ; if scarmsr = "." scarms2 = scwhata; tnarms2 = tnarmsr ; if tnarmsr = "." tnarms2 = tnwhata; vaarms2 = vaarmsr ; if vaarmsr = "." vaarms2 = vawhata; * note wealth3 uses arms wealth when available, fills in with estimate when not ; data wealth3; set makenw; keep year alarms2 garms2 flarms2 kyarms2 ncarms2 scarms2 tnarms2 vaarms2; run; quit; *This SAS Program was used to Estimate the Expected Profits /* Program to run data*/ data actprice; set actprices; data actyield; set actyields; data exprice; set exprices; data expyield; set expyields; data supprice; set supprices; data vcost; set vcosts; data profits; merge actprice actyield exprice expyield supprice vcost; by year; 61 run; quit; data variances; set profits; *NOTE: Make sure all prices and costs have been set to 2005 value by use of a price index!!! ; *MP1 = actual market price crop1, EP1 = expected market price crop1, SP1 = support price crop 1; *AY1 = actual yield of crop 1, EY1 = expected yield of crop 2; *Repeat codes for second crop (2) and so on up to all 4 crops; *sort data so that most recent year is at the bottom to create lags; * CROP ORDER: CORN COTTON SOYBEANS WHEAT ; sp1 = cnsup; sp2 = ctsup; sp3 = sbsup; sp4 = wtsup; cost1 = cnvcost; cost2 = ctvcost; cost3=sbvcost; cost4=wtvcost; ecost1 = lag(cost1); ecost2 = lag(cost2); ecost3 = lag(cost3) ; ecost4=lag(cost4); proc sort data=variances; by year; run; * ALABAMA DATA ****************************************** *created the untruncated variances of the market prices; data Alabama; set variances; **** SET THE DATA TO THE STATE************************; mp1 = scpcn; mp2 = scpct; mp3 = scpsb; mp4 = scpwt; ep1 = scepcn; ep2 = scepct; ep3 = scepsb; ep4 = scepwt; ay1 = sccnyd; ay2 = scctyd; ay3 = scsbyd; ay4 = scwtyd; ey1 = scecnyd; ey2 = scectyd; ey3 = scesbyd; ey4 = scewtyd; ************************* created price variances *************************; l1p1 = lag(mp1); l2p1 = lag(l1p1); l3p1= lag(l2p1); l1ep1 = lag(ep1); l2ep1 = lag(l1ep1); l3ep1= lag(l2ep1); varp1 = (l1p1-l1ep1)*(l1p1-l1ep1)*.5 + (l2p1-l2ep1)*(l2p1-l2ep1)*.3 + (l3p1- l3ep1)*(l3p1-l3ep1)*.2; l1p2 = lag(mp2); l2p2 = lag(l1p2); l3p2= lag(l2p2); l1ep2 = lag(ep2); l2ep2 = lag(l1ep2); l3ep2= lag(l2ep2); 62 varp2 = (l1p2-l1ep2)*(l1p2-l1ep2)*.5 + (l2p2-l2ep2)*(l2p2-l2ep2)*.3 + (l3p2- l3ep2)*(l3p2-l3ep2)*.2; l1p3 = lag(mp3); l2p3 = lag(l1p3); l3p3= lag(l2p3); l1ep3 = lag(ep3); l2ep3 = lag(l1ep3); l3ep3= lag(l2ep3); varp3 = (l1p3-l1ep3)*(l1p3-l1ep3)*.5 + (l2p3-l2ep3)*(l2p3-l2ep3)*.3 + (l3p3- l3ep3)*(l3p3-l3ep3)*.2; l1p4 = lag(mp4); l2p4 = lag(l1p4); l3p4 = lag(l2p4); l1ep4 = lag(ep4); l2ep4 = lag(l1ep4); l3ep4= lag(l2ep4); varp4 = (l1p4-l1ep4)*(l1p4-l1ep4)*.5 + (l2p4-l2ep4)*(l2p4-l2ep4)*.3 + (l3p4- l3ep4)*(l3p4-l3ep4)*.2; sdp1 = sqrt(varp1); sdp2 = sqrt(varp2); sdp3 = sqrt(varp3); sdp4 = sqrt(varp4); * create the yield variances; l1y1 = lag(ay1); l2y1 = lag(l1y1); l3y1= lag(l2y1); l1ey1 = lag(ey1); l2ey1 = lag(l1ey1); l3ey1= lag(l2ey1); vary1 = (l1y1-l1ey1)*(l1y1-l1ey1)*.5 + (l2y1-l2ey1)*(l2y1-l2ey1)*.3 + (l3y1- l3ey1)*(l3y1-l3ey1)*.2; l1y2 = lag(ay2); l2y2 = lag(l1y2); l3y2= lag(l2y2); l1ey2 = lag(ey2); l2ey2 = lag(l1ey2); l3ey2= lag(l2ey2); vary2 = (l1y2-l1ey2)*(l1y2-l1ey2)*.5 + (l2y2-l2ey2)*(l2y2-l2ey2)*.3 + (l3y2- l3ey2)*(l3y2-l3ey2)*.2; l1y3 = lag(ay3); l2y3 = lag(l1y3); l3y3= lag(l2y3); l1ey3 = lag(ey3); l2ey3 = lag(l1ey3); l3ey3= lag(l2ey3); vary3 = (l1y3-l1ey3)*(l1y3-l1ey3)*.5 + (l2y3-l2ey3)*(l2y3-l2ey3)*.3 + (l3y3- l3ey3)*(l3y3-l3ey3)*.2; l1y4 = lag(ay4); l2y4 = lag(l1y4); l3y4= lag(l2y4); l1ey4 = lag(ey4); l2ey4 = lag(l1ey4); l3ey4 = lag(l2ey4); vary4 = (l1y4-l1ey4)*(l1y4-l1ey4)*.5 + (l2y4-l2ey4)*(l2y4-l2ey4)*.3 + (l3y4- l3ey4)*(l3y4-l3ey4)*.2; stdevy1 = sqrt(vary1); stdevy2 = sqrt(vary2); stdevy3 = sqrt(vary3); stdevy4 = sqrt(vary4); *calculate the correlation between untruncated price and yields; varp1y1 = (l1y1-l1ey1)*(l1p1-l1ep1)*.5 + (l2y1-l2ey1)*(l2p1-l2ep1)*.3 + (l3y1- l3ey1)*(l3p1-l3ep1)*.2; 63 varp2y2 = (l1y2-l1ey2)*(l1p2-l1ep2)*.5 + (l2y2-l2ey2)*(l2p2-l2ep2)*.3 + (l3y2- l3ey2)*(l3p2-l3ep2)*.2; varp3y3 = (l1y3-l1ey3)*(l1p3-l1ep3)*.5 + (l2y3-l2ey3)*(l2p3-l2ep3)*.3 + (l3y3- l3ey3)*(l3p3-l3ep3)*.2; varp4y4 = (l1y4-l1ey4)*(l1p4-l1ep4)*.5 + (l2y4-l2ey4)*(l2p4-l2ep4)*.3 + (l3y4- l3ey4)*(l3p4-l3ep4)*.2; rhoy1p1 = varp1y1/sqrt(varp1*vary1) ; rhoy2p2 = varp2y2/sqrt(varp2*vary2) ; rhoy3p3 = varp3y3/sqrt(varp3*vary3) ; rhoy4p4 = varp4y4/sqrt(varp4*vary4) ; *created the truncated means and variances of prices; *normalize; h1 = (sp1-ep1)/sdp1 ; h2 = (sp2-ep2)/sdp2; h3 = (sp3-ep3)/sdp3 ; h4 = (sp4-ep4)/sdp4; *caldulate pdf value using formula; fi1= (1/sqrt(2*3.141592654))*exp(-.5*h1*h1); FIC1=probnorm(h1); fi2= (1/sqrt(2*3.141592654))*exp(-.5*h2*h2); FIC2=probnorm(h2); fi3= (1/sqrt(2*3.141592654))*exp(-.5*h3*h3); FIC3=probnorm(h3); fi4= (1/sqrt(2*3.141592654))*exp(-.5*h4*h4); FIC4=probnorm(h4); *truncated expected prices -- note will be higher than expected prices; tp1=sp1*FIC1 + sdp1*fi1 + ep1*(1-FIC1); tp2=sp2*FIC2 + sdp2*fi2 + ep2*(1-FIC2); tp3=sp3*FIC3 + sdp3*fi3 + ep3*(1-FIC3); tp4=sp4*FIC4 + sdp4*fi4 + ep4*(1-FIC4); *truncated variances -- note they will be lower than untruncated variances; tvarp1 = (sp1*sp1*FIC1) + (varp1*h1*fi1) + (2*ep1*sdp1*fi1) + (ep1*ep1 + varp1)*(1-FIC1) - (tp1*tp1); tvarp2 = (sp2*sp2*FIC2) + (varp2*h2*fi2) + (2*ep2*sdp2*fi2) + (ep2*ep2 + varp2)*(1-FIC2) - (tp2*tp2); 64 tvarp3 = (sp3*sp3*FIC3) + (varp3*h3*fi3) + (2*ep3*sdp3*fi3) + (ep3*ep3 + varp3)*(1-FIC3) - (tp3*tp3); tvarp4 = (sp4*sp4*FIC4) + (varp4*h4*fi4) + (2*ep4*sdp4*fi4) + (ep4*ep4 + varp4)*(1-FIC4) - (tp4*tp4); *calculate the covariance between prices untruncated; *there will be 6 of these for four crops; varp12 = (l1p2-l1ep2)*(l1p1-l1ep1)*.5 + (l2p2-l2ep2)*(l2p1-l2ep1)*.3 + (l3p2- l3ep2)*(l3p1-l3ep1)*.2; varp13 = (l1p3-l1ep3)*(l1p1-l1ep1)*.5 + (l2p3-l2ep3)*(l2p1-l2ep1)*.3 + (l3p3- l3ep3)*(l3p1-l3ep1)*.2; varp14 = (l1p4-l1ep4)*(l1p1-l1ep1)*.5 + (l2p4-l2ep4)*(l2p1-l2ep1)*.3 + (l3p4- l3ep4)*(l3p1-l3ep1)*.2; varp23= (l1p2-l1ep2)*(l1p3-l1ep3)*.5 + (l2p2-l2ep2)*(l2p3-l2ep3)*.3 + (l3p2- l3ep2)*(l3p3-l3ep3)*.2; varp24 = (l1p2-l1ep2)*(l1p4-l1ep4)*.5 + (l2p2-l2ep2)*(l2p4-l2ep4)*.3 + (l3p2- l3ep2)*(l3p4-l3ep4)*.2; varp34 = (l1p3-l1ep3)*(l1p4-l1ep4)*.5 + (l2p3-l2ep3)*(l2p4-l2ep4)*.3 + (l3p3- l3ep3)*(l3p4-l3ep4)*.2; *calculate rho; rho12 = varp12/(sqrt(varp1*varp2)); rho12s = rho12*rho12; rho13 = varp13/(sqrt(varp1*varp3)); rho13s = rho13*rho13; rho14 = varp14/(sqrt(varp1*varp4)); rho14s = rho14*rho14; rho23 = varp23/(sqrt(varp2*varp3)); rho23s = rho23*rho23; rho24 = varp24/(sqrt(varp2*varp4)); rho24s = rho24*rho24; 65 rho34 = varp34/(sqrt(varp3*varp4)); rho34s = rho34*rho34; *calculate terms needed in truncated covariance formula; e1 = fi1 + h1*FIC1; e2 = fi2 + h2*FIC2; e3 = fi3 + h3*FIC3; e4 = fi4 + h4*FIC4; pi = 3.141592654; * delete years with missing variables or functions will return error codes; data new; set Alabama; if year ge 1990; data Alabama; set new; BIVAR12=probbnrm(h1,h2,rho12); BIVAR13=probbnrm(h1,h3,rho13); BIVAR14=probbnrm(h1,h4,rho14); BIVAR23=probbnrm(h2,h3,rho23); BIVAR24=probbnrm(h2,h4,rho24); BIVAR34=probbnrm(h3,h4,rho34); BIGF12 = 1 - BIVAR12; BIGF13 = 1 - BIVAR13; BIGF14 = 1 - BIVAR14; BIGF23 = 1 - BIVAR23; BIGF24 = 1 - BIVAR24; BIGF34 = 1 - BIVAR34; Z12s = (h1*h1 + h2*h2 - 2*rho12*h1*h2)/(1-(rho12*rho12)); Z13s =(h1*h1 + h3*h3 - 2*rho13*h1*h3)/(1-(rho13*rho13)); Z14s = (h1*h1 + h4*h4 - 2*rho14*h1*h4)/(1-(rho14*rho14)); Z23s = (h3*h3 + h2*h2 - 2*rho23*h3*h2)/(1-(rho23*rho23)); Z24s = (h4*h4 + h2*h2 - 2*rho24*h4*h2)/(1-(rho24*rho24)); Z34s = (h3*h3 + h4*h4 - 2*rho34*h3*h4)/(1-(rho34*rho34)); z12 = sqrt(z12s); z13 = sqrt(z13s); z14 = sqrt(z14s); z23 = sqrt(z23s); z24 = sqrt(z24s); z34 = sqrt(z34s); fiz12 = (1/sqrt(2*3.141592654))*exp(-.5*z12*z12); fiz13 = (1/sqrt(2*3.141592654))*exp(-.5*z13*z13); fiz14 = (1/sqrt(2*3.141592654))*exp(-.5*z14*z14); fiz23 = (1/sqrt(2*3.141592654))*exp(-.5*z23*z23); fiz24 = (1/sqrt(2*3.141592654))*exp(-.5*z24*z24); 66 fiz34 = (1/sqrt(2*3.141592654))*exp(-.5*z34*z34); k12 = (h1 - rho12*h2)/(sqrt(1 - rho12*rho12)); k13 = (h1 - rho13*h3)/(sqrt(1 - rho13*rho13)); k14 = (h1 - rho14*h4)/(sqrt(1 - rho14*rho14)); k23 = (h2 - rho23*h3)/(sqrt(1 - rho23*rho23)); k24 = (h2 - rho24*h4)/(sqrt(1 - rho24*rho24)); k34 = (h3 - rho34*h4)/(sqrt(1 - rho34*rho34)); FICK12= probnorm(k12); FICK13= probnorm(k13); FICK14= probnorm(k14);FICK23= probnorm(k23); FICK24= probnorm(k24); FICK34= probnorm(k34); k21 = (h2 - rho12*h1)/(sqrt(1 - rho12*rho12)); k31 = (h3 - rho13*h1)/(sqrt(1 - rho13*rho13)); k41 = (h4 - rho14*h1)/(sqrt(1 - rho14*rho14)); k32 = (h3 - rho23*h2)/(sqrt(1 - rho23*rho23)); k42 = (h4 - rho24*h2)/(sqrt(1 - rho24*rho24)); k43 = (h4 - rho34*h3)/(sqrt(1 - rho34*rho34)); FICK21=probnorm(k21); FICK31=probnorm(k31); FICK41=probnorm(k41); FICK32=probnorm(k32); FICK42=probnorm(k42); FICK43=probnorm(k43); *calculate MIJ; M12 = BIGF12*rho12 + sqrt((1-rho12s)/(2*pi))*fiz12 + h1*fi2*FICK12 + h2*fi1*FICK21 + h1*h2*BIVAR12; M13 = BIGF13*rho13 + sqrt((1-rho13s)/(2*pi))*fiz13 + h1*fi3*FICK13 + h3*fi1*FICK31 + h1*h3*BIVAR13; M14 = BIGF14*rho14 + sqrt((1-rho14s)/(2*pi))*fiz14 + h1*fi4*FICK14 + h4*fi1*FICK41 + h1*h4*BIVAR14; M23 = BIGF23*rho23 + sqrt((1-rho23s)/(2*pi))*fiz23 + h2*fi3*FICK23 + 67 h3*fi2*FICK32 + h2*h3*BIVAR23; M24 = BIGF24*rho24 + sqrt((1-rho24s)/(2*pi))*fiz24 + h2*fi4*FICK24 + h4*fi2*FICK42 + h2*h4*BIVAR24; M34 = BIGF34*rho34 + sqrt((1-rho34s)/(2*pi))*fiz34 + h3*fi4*FICK34 + h4*fi3*FICK43 + h3*h4*BIVAR34; *calculate the truncated covariance; cov12 = sqrt(varp1*varp2)*(M12 - e1*e2); cov13 = sqrt(varp1*varp3)*(M13 - e1*e3); cov14 = sqrt(varp1*varp4)*(M14 - e1*e4); cov23 = sqrt(varp2*varp3)*(M23 - e2*e3); cov24 = sqrt(varp2*varp4)*(M24 - e2*e4); cov34 = sqrt(varp3*varp4)*(M34 - e3*e4); *calculate the expected profit of crop 1 to 4; *expected cost is lagged cost; term1 = (1-probnorm(h1))*rhoy1p1*stdevy1*sqrt(tvarp1); part1 = 1-probnorm(h1); part2 = rhoy1p1*stdevy1*sqrt(tvarp1); part3 = part1*part2; term2 = (1-probnorm(h2))*rhoy2p2*stdevy2*sqrt(tvarp2); term3 = (1-probnorm(h3))*rhoy3p3*stdevy3*sqrt(tvarp3); term4 = (1-probnorm(h4))*rhoy4p4*stdevy4*sqrt(tvarp4); prof1 =tp1*ey1 - ecost1 + term1; prof2 =tp2*ey2 - ecost2 + term2; prof3 =tp3*ey3 - ecost3 + term3; prof4 =tp4*ey4 - ecost4 + term4; data ALprofit1; set Alabama; alcnprof = prof1; alctprof = prof2; alsbprof = prof3; alwtprof= prof4; alvarcn = varp1; altvarcn = tvarp1; alvarct = varp2; altvarct = tvarp2; alvarsb = varp3; altvarsb = tvarp3; alvarwt = varp4; altvarwt = tvarp4; alcvcnct = cov12; alcvcnsb = cov13; alcvcnwt = cov14; alcvctsb = cov23; alcvctwt = cov24; alcvsbwt = cov34; data alprofit; set alprofit1; keep year alcnprof alctprof alsbprof alwtprof altvarcn altvarct altvarsb altvarwt alcvcnct alcvcnsb alcvcnwt 68 alcvctsb alcvctwt alcvsbwt sp1 sp2 sp3 sp4 mp1 mp2 mp3 mp4 ep1 ep2 ep3 ep4 ay1 ay2 ay3 ay4 ey1 ey2 ey3 ey4; run; /*data check2; set alprofit1; if year = 2002; data check; set check2; keep year part1 part2 part3 term1; run; proc sort; by descending year; run;*/ quit; *This SAS Program was used for Estimating the Models data rachel1; set rachel.stackdata ; lwealth = lag(wealth); lcnpa = lag(cnpa); lwtpa = lag(wtpa); lctpa = lag(ctpa); lsbpa = lag(sbpa); wealthadj = lwealth + cnpa*cnexpre + sbpa*sbexpre + ctpa*ctexpre; lcnexpre = lag(cnexpre); cnidle = cnidled*cnpa; wtidle = wtidled*wtpa; ctidle = ctidled*ctpa; data rachel2; set rachel1; if state='Alabama' then d1=1; else d1=0; if state='Florida' then d2=1; else d2=0; if state='Georgia' then d3=1; else d3=0; if state='NorthCar' then d4=1; else d4=0; if state='SouthCar' then d5=1; else d5=0; if state='Tennessee' then d6=1; else d6=0; if state='Virginia' then d7=1; else d7=0; label d1='Alabama dummy' d2='Florida dummy' d3='Georgia dummy' d4='Northcar dummy' d5='Southcar dummy' d6='Tennessee dummy' d7='Virgina dummy' 69 ; fpdum = 0; if year lt 1996 then fpdum = 1; sumpa = cnpa + sbpa + ctpa; lsumpa + lag(sumpa); blexpre = cnexpre*lcnpa + ctexpre*lctpa + sbexpre*lsbpa; blrvar = cnrvar*lcnpa + ctrvar*lctpa + sbrvar*lsbpa; run; title ; title 'OLS regressions'; title 'wheat'; run; proc reg; model wtpa = wtexpre wtrvar wealthadj wtidle lwtpa d2 d3 d4 d5 d6 d7 fpdum ; run; title ; run; title 'cotton'; run; proc reg; model ctpa = ctexpre sbexpre cnexpre ctrvar ctidle covrsbct covrcnct wealthadj lctpa d2 d3 d4 d5 d6 d7 fpdum ; run; title ; run; title 'soybeans' ; run; proc reg; model sbpa = sbexpre ctexpre sbrvar covrsbct wealthadj lsbpa d2 d3 d4 d5 d6 d7 ; run; title ; run; title 'corn'; run; proc reg; model cnpa = cnexpre ctexpre sbexpre cnrvar ctrvar sbrvar covrcnsb covrcnct cnidle wealthadj lcnpa d2 d3 d4 d5 d6 d7 fpdum; run; title 'all summer crops'; proc reg; model sumpa = blexpre blrvar lsumpa wealthadj d2 d3 d4 d5 d6 d7 fpdum; proc reg; model sumpa = cnexpre ctexpre sbexpre cnrvar sbrvar ctrvar lsumpa wealthadj d2 d3 d4 d5 d6 d7 fpdum; run; quit; title run; title 'system sur no restrictions - order ct sb cn' ; run; proc syslin sur; eq1: model ctpa = ctexpre sbexpre cnexpre ctrvar covrsbct covrcnct 70 wealthadj lctpa d2 d3 d4 d5 d6 d7 ctidle ; eq2: model sbpa = sbexpre ctexpre sbrvar covrsbct wealthadj lsbpa d2 d3 d4 d5 d6 d7 fpdum; eq3: model cnpa = cnexpre ctexpre sbexpre cnrvar ctrvar sbrvar covrcnsb covrcnct wealthadj lcnpa d2 d3 d4 d5 d6 d7 cnidle; run; quit; title run; title 'system sur with restrictions - order ct sb cn' ; run; proc syslin sur; eq1: model ctpa = ctexpre sbexpre cnexpre ctrvar sbrvar cnrvar covrsbct covrcnct wealthadj lctpa d2 d3 d4 d5 d6 d7 ctidle ; eq2: model sbpa = sbexpre ctexpre cnexpre sbrvar cnrvar ctrvar covrsbct covrcnsb wealthadj lsbpa d2 d3 d4 d5 d6 d7 fpdum; eq3: model cnpa = cnexpre ctexpre sbexpre cnrvar ctrvar sbrvar covrcnsb covrcnct wealthadj lcnpa d2 d3 d4 d5 d6 d7 cnidle; srestrict eq1.sbexpre=eq2.ctexpre; srestrict eq1.cnexpre=eq3.ctexpre; srestrict eq2.cnexpre=eq3.sbexpre; run; quit;