LES AN ECCVQM {C AHALYSES GE- E£2 [AEM MA CHEREEY VALUES -. Thesis {'09 {he Dogma of M. 5. MICEKGJLR STATE UNIVERSETY ngid L. Peacock £957 .. .—_ _—-_._ THESI: 'py b a?!“ ‘ “MHMHA‘ LIBRA R Y “7 Mulligan State University ‘ Mr: V! .J ‘3 ABSTRACT AN ECONOMIC ANALYSIS OF USED FARM MACHINERY VALUES by David L. Peacock It is quite well known that common depreciation methods are poor estimators of used machinery values. Yet they continue ‘u3be used for this purpose due to a shortage of better inform- ation. It was the lack of such information which prompted this study. The objectives of this study were to: (l) discover how used farm machinery values change over time, and (2) learn what factors affect these values. Various models were developed invblving variables which were hypothesized to have an effect on the market value of Lmed farm machinery. Each model was tested by least squares Hmltiple regression methods using the Official Tractor and EflmlEquipment Guide "as-is" values to represent market Values. Equations were computed for farm tractors, combines, forage harvesters, balers, and cornpickers. These machines were all studied over a ten year time span, 1953 through 1953, ”Sing 1953 models and a five year time span: 1958 through 1963 using 1958 model equipment. Every equation based on the "Current" dollar value of the used machine was duplicated by an equation using "real" dollar (deflatEd) values as the dependent variable- As might be anticipated, age of the machine was the most important variable. Alone, it was capable of eXplaining from 57% to 89% of the variation in used machinery values. Curvil- inear models demonstrated that the rate of "loss-in-value" associated with age declines as the machine becomes older. Realized net farm income, lagged one year, seemed to have little or no effect on the demand fOr used farm equipment. This was also true of farm prices, as measured by the USDA prices received by farmers index. It was somewhat surprising to find that it was impossible to obtain a consistent l-2-3-——n ranking of the different makes of machinery. Consequently the information provided by these variables is of little general use in predicting used values, even though it was extremely helpful in explaining them. A variable designed to measure the effect of the introduct- ion of new models on the used value of older models did not produce any consistent results. The acreage of crops harvested (combined acreage, and corn acreage)and livestock numbers seemed to have no significant effect on the used values of combines, cornpickers, forage harvesters, and balers. There was a significant difference in the rates of "loss- in-value" for gasoline and diesel tractors, and for pull type and self propelled combines. Less important technical diff- erences, such as wire as opposed to twine-tie balers and pull type as opposed to mounted cornpickers, had no recognizable effect on used values. A comparison of the equations based on "current" dollars with those using "real" dollars indicated that inflation had a considerable effect on used farm machinery values. The estimated used values obtained from the regression equations were, of course, quite different from those calculated using common depreciation schemes. (1) The initial (first year) drOp in machinery values tended toward or exceeded the maximum depreciaton allowed by the Internal Revenue Service. (2) The so-called "salvage" value (at ten years of age)in current dollars, was estimated to be considerably greater than the traditional assumption of 10%. (3) Yearly "loss—in-value" (with the exception of the first year) is usually less than assumed by depreciation schemes. AN ECONOMIC ANALYSIS OF USED FARM MACHINERY VALUES By David L. Peacock A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Agricultural Economics 1967 b“ <+ '7 .- ’ 1 xx.- 5 J I‘ “‘x " '; ‘4‘ / ‘ ACKNOWLEDGEMENTS I would like to express my appreciation to Dr. John R. Brake for his considerable guidance and direction in the devel- opment and completion of this thesis. His encouragement and many suggestions were invaluable. Thanks are also due Dr. Larry Connor and Dr. John Moroney (Economics Department) for their review of a later draft of the manuscript. The author expresses his appreciation to Dr. L.L. Boger, Head of the Department of Agricultural Economics, for his financial assistance by way of a graduate assistantship. A special thanks to my wife Carolyn, for her enduring patience and countless hours of help from beginning to completion of this endeavor. The author wishes to thank his wife's family for their hours of help in preparation of the data and proof—reading of the manuscript. I would also like to thank Mrs. Beverly McVannel for typing the several drafts of this project. The author assumes responsibility for any errors in the thesis. TABLE OF CONTENTS ACKNOWLEDGEMENTS ......................................... LIST OF TABLES ........................................... LIST OF FIGURES .......................................... CHAPTER I. II. III. IV. INTRODUCTION ....................................... The Problem ..................................... Contribution of the Study ....................... Objectives ....... ........... .................... DATA AND METHODS OF ANALYSIS ....................... ANALYSIS OF USED FARM TRACTOR VALUES ............... Introduction ....................................... Variables..... ....... . ..... . ......... . ............. Estimating Equations ............................... Interpretation ..................................... ANALYSIS OF USED COMBINE VALUES .................... Introduction ........... . ............... . ........... Variables .......................................... Estimating Equations ............................... Interpretation.. ........ . .......................... iii Page ii 23 23 23 31 50 81 81 81 8A 107 CHAPTER PAGE V. ANALYSIS OF USED FORAGE HARVESTER VALUES ........... 131 Introduction.. .................................. 131 Variables...... ..... ....... ..................... 131 Estimating Equations.. ...... ......... ........... 13A Interpretation .......................... . ....... 146 VI. ANALYSIS OF USED BALER VALUES ...................... 158 Introduction .................................... 158 Variables ....................................... 158 Estimating Equations ............................ 159 Interpretation .................................. 173 VII. ANALYSIS OF USED CORNPICKER VALUES ................. 189 Introduction ................ ' .................... 189 Variables ....................................... 189 Estimating Equations ............................ 190 Interpretation... ............... . ...... . ........ 200 VIII. APPLICATION OF THE RESEARCH RESULTS AND GENERAL CONCLUSIONS ............................. . .......... 21A Application of the Research Results ............. 21A General Conclusions ............................. 236 APPENDIX.... ............................................. 2A1 BIBLIOGRAPHY ............................................. 272 iv TABLE 10. LIST OF TABLES PAGE Differences betweeen the market value and values estimated by common depreciation methods for a used 1953 "Super M" Farmall Tractor ..... . ........ 5 1966 Market Values of selected used tractors taken from Official Guide and Blue Book .......... 8 Percentage figures, suggested by Blue Book, to determine the depreciated value of Optional equipment not included in the model specifications 10 Official Guide market values and Blue Book market values corrected to provide valuations for selected tractors with given model specifications---l966 editions .................. . .. ................... 11 Market values for 195“ Farmall "Super M" and 1954 John Deere "60" from 1957, 1958, 1959 editions of Official Guide and Blue Book, and the new value of Optional equipment necessary to equate used values from the two sources ............... . ...... 12 Linear Regression of the percentage values of sel- ected 195A tractors-—obtained from Blue Book-- on tractor age ................................... 17 Dollars value and percentage values for 1953 Farmall "Super M" and 1953 John Deere "60" tractors ........................... . ............. 21 Summary of the b values for the age variable from equations 1 through 24. ... .. ......... ...... 51 Estimates of the percentage value for 1953 diesel and gasoline tractors computed from equations 1 through A ...................................... 53 Percentage values for one year old gasoline and diesel tractors, 1953 and 1958 models, as estim- ated by equations # 1,3,5, and 7 ................ 5A TABLE PAGE 11. Average yearly residuals from the regression equations, Y = f (Age), for 1953 and 1958 gasoline and diesel tractors ........... . ......... 56 12. Percentage values of selected 1958 Allis Chalmers gasoline tractors----"B", "CA", "WD-A5" models introduced in 1953 and "D-17", "D-lA" models introduced in 1958 over the period 1958-1963 ..... 6A 13. Average values of 1958 Allis Chalmers "B", "CA", and "WD-A5"---with "CA" and "B" adjusted to compensate for lower value due to smaller horse- power---contrasted with 1958 Allis Chalmers "D-l7" and "D-lA" models ......................... 65 1A. Standard error of the regression estimates of 1953 gasoline tractor values for each year, 195A- 1963, calculated from the residuals of equations #1 and #9 ........................................ 67 15. The percentage value of five year old 1953 model tractors computed from the estinmting equations with and without the horsepower effects ........ 7O 16. Yearly "loss-in-value" for 1953 gasoline tractors, as a percent of their original cost, computed from equations #25 and 26 ........... . .......... 75 17. Average yearly residuals for equation #25 ......... 76 18. The b values for age from all the linear equations estimated for combines---1953 and 1958 ......... 108 19. Average residuals computed for eadi. year of age from combine equations #33,35,37, and 39 ....... 111 20. Standard error of estimates for each year for 1953 pull type combine equations Y1 = f (Age) ....... 11A 21. Percentage value estimates for one year old 1953 pull type combines as calculated by equations Y = f (Age, Make) and Y = f (Age, Make, Engine DAiven) equations numberS Al and A9 respectively 121 vi TABLE 22. 23. 2A. 25. 26. 27. 28. 29. 30. 31. 32. PAGE Differences between b values for the Y and Y formulations of the dependent variable from selected equations for 1953 and 1958 model combines..... .............. . .............. 12A Estimates of used value and yearly "loss-in-value" for 1953 pull type combines, computed from equa- tions 53 and 61 ................................. 126 Average yearly residuals for equation # 61--—a curvilinear model for 1953 pull type combines... 127 Multiple determination coefficients of the linear regresssion equations Y = f (Age) for tractors, combines, and forage harvesters... .............. 1A7 Average yearly residuals for forage harvester equation #73 .................................... 1A8 Yearly decline in value and estimated used value for forage harvesters, computed from equations #73, 75, 81, and 83 ............................. 15A Average yearly residuals for equation #81, cur- vilinear model for 1953 forage harvesters ....... 155 Average yearly residuals for 1953 and 1958 balers estimated from equations #85 and 87 ............. 175 Standard error of estimate related to each year of age computed from regression equations for Y = f (Age) and Y1 = f (Age, Make)...............;.... 178 Estimated percentage values for each make of 1953 balers at six years of age, as estimated by re- gression equations for Y = f (Age, Make) and Y = f (Age, Make, Engine Driven) ......... . ...... 180 Estimates of the percentage value, and yearly "loss- in-value" for 1953 and 1958 model balers, computed from equations #97, 99, 101 and 103 ............. 18“ vii TABLE 33. 3A. 35. 36. 37. 38. 39. A0. A1. A2. A3. Average yearly residuals for used baler value estimates computed from the regression equ- ation #101--—Curvilinear Model....... ........... Average yearly resiudals for 1953 and 1958 corn- pickers, computed from equations #105 and 107... The standard error of estimates calculated for each year from equations #105 and 109 ........... Estimated percentage values and yearly "loss-in+ value" as a percent of original value, computed from equations #109 and 117 ..................... Average yearly residuals from equation #117 --— curvilinear model ............................... The "standard difference" for different methods of estimating used values of randomly selected 1956 model farm machinery ....................... Estimated used values for a $2A15.00 forage har- vester, computed from various depreciation systems; and equations #69 and #81 of Chapter V. Estimated yearly ownership costs for a $2A15.00 forage harvester computed from various dep- reciation systems and equations #69 and 81 of Chapter V ...................................... Total ownership costs for selected machinery used a varying number of years, as computed from estimating equations and depreciation methods.. Average annual ownership costs for a $2A15 forage harvester, computed from various depreciation systems and equations #69 and 81 of Chapter V.. Average annual ownership costs for selected mach- ines and periods of use, computed from the est- imating equations and various depreciation schemes....... ............... .... ....... . ...... viii PAGE 185 202 20A 210 212 215 220 221 225 227 228 TABLE PAGE AA. Estimated 1965 values of selected combinations of farm machinery; computed from various dep— reciation schemes, estimating equations, and "as-is" figures from the Official Guide ......... 231 A5. Amount of taxable income if a 1956 Allis Chalmers "WD-AS" gasoline tractor was sold after a given a 2 number of years use........... ..... ............. ‘3 A6. Used baler values as contrasted to the unpaid bal— . ance for loans of selected terms ................ 23A ix FIGURE 1. LIST OF FIGURES The decline in percentage value of selected 1953 model tractors.. ............................ Linear regression line for 1953 gasoline tractors and regression line "adjusted" by adding the average residual for each year... ... ......... Linear regression line for 1958 gasoline tractors and regression line "adjusted" by adding the average residual for each year ................... Percentage values of 1953 John Deere "60" and 1953 Case "DC" from 1953 to 1963 ...................... PAGE 57 58 68 INTRODUCTION CHAPTER I THE PROBLEM Current agricultural production is increasingly dependent upon the services of farm machinery. In the past two decades we have witnessed considerable growth in the use of farm machinery, and a simultaneous decline in the size of the farm labor force. From 19A0 through 1960 the number of trucks and tractors used by farmers more than doubled, grain combines increased to more than five times their 19AO level, and corn pickers (including picker shellers) expanded to greater than seven times their earlier number.l/ In this same span of time the size of the farm labor force fell from nearly eleven mill- ion workers to slightly over seven million. (This trend 'toward fewer farm workers is continuing in the 1960's.)g/ Further the total number of farms dropped from 6,350,000 in 19A0 to 3,9A9,000 in 1960,;/ while total acreage devoted to farm use was slightly larger in 1960.5/ The unavoidable 1/ — U.S. Department of Agriculture, Farm Cost Situation, FCS-35 November 1963, p. 15. g/U.S. Department of Agriculture, Farm Cost Situation, PCS-36, November 196A, p. 11. i/Ibid., PCS-35. fl/Land in farms increased from 19A0 to 1950, 1,061 million acres to 1,159 million acres, and declined to 1,120 million acres by 1959; see U.S. Department of Agriculture, Agricultural Statistics 1963, p. A35. 1 -2- conclusion is that fewer farmers are Operating larger farms and depending upon increased use of farm machinery to accomplish the task. Although the trend toward greater numbers of farm machines has tended to level off since 1960 and in some cases show slight reductions, the concurrent trend toward larger capacity! and more complicated machinery continues. Another approach to indicating the importance of farm machinery in modern agriculture is to illustrate how it fits into the financial structure and operation of the individual farm businesses. In 1963 the depreciated value of farm machinery inventories averaged 12.7 percent of the total farm invest- ment for COOperators of the Michigan Mail-In Record Project. (The range by types of enterprises is from an 8.98 percent average for beef—hog Operations to a 17.82 percent average for dairy and potato combinations.)i/ This same group Of farmers averaged annual farm machinery ownership costs, as measured by the depreciation taken, of $2,682 or roughly nine percent Of their total farm expenses. When one adds the average cost of Operating the machinery (gas, oil and main- tenance) amounting to $2,611 to the ownership costs, (as 5/ — Computed from information presented by Leonard R. Kyle in Michigan Farm Business Report for 1953 ( Michigan State University Experiment Station; Research Report No. 30)p.3. -3- specified above——exc1uding any interest payments) their annual machinery expense turns out tO be $5,293, or nearly 17.5 percent of total farm eXpenses.§/ While the above figures are impressive, they undoubtedly do not represent an accurate statement of either the average value of the COOperators' farm machinery investment or their machinery ownership expenses. This is because the figures reported were computed using common depreciation methods. These methods tend to yield estimates of farm machinery values which differ considerably from their market values. Table 1 illustrates the divergence between market values and those computed by depreciation schemes. Despite the evident inadequacies of depreciation schemes for this purpose, little seems to have been done toward developing improved methods of estimating used farm machinery values. It was the lack of such information that prompted this study. The study explores how used farm machinery values change over time and considers certain variables that were expected to effect these values. é-/Ibid., p. 8. -14- CONTRIBUTION OF THE STUDY It would seem appropriate to establish the usefulness of this study before progressing very far. The following, there- fore, suggest some applications of improved information about used farm machinery values. Farm Planning. The farmer could use this type of information to improve his estimates Of the cost of owning and operating farm machinery. These improved cost estimates in- turn could be used in a number of planning and budgeting situations. Where machinery costs are important production expenses, more accurate comparisons Of alternative enterprises could be made. Applied directly to farm machinery; improved decisions could be made with respect to determining the profitability of owning a given machine, the prOper complement of machinery for a given farm situation, whether to buy new or used equipment, and when to trade. Tax Purposes. The income tax law has recently been changed to prevent farmers from considering the excess of the disposal value of farm machinery over their depreciated value as capital gains.l/ 7/ — For additional information see the Farmers Tax Guide, U.S. Internal Revenue Service. _ 5 _ A.mum .mmma-mmma ..osH .mcoHSSOHanm «mmmz mmfisoq .pmv .mefizu Osmaaaswm Epmm Ocm LOpompB HQHOAMMO .coapmfioomm< mLOHmOQ onEQHSUm hmzom pew 89mm HmQOHpmz IIIAOSpm wasp pom pom: mohsow map Eopm mosaw> pmxpmz .o Odam> poxmeIOSHm> coapmfiooumon Osam> .OHQmOHHQQm no: ma osam> me>HMm Ohms: mocmamp wcflcflaooo pom pQOoxOIIOSHm> Omm>amm pcoopOQ 0H m mcfiw: OOpSQEOO mm: coaumaomnaoa .O pmxsae .COprozamo mo wonpoe po gouge MGHUQSOL Op Odo mummAHOIIAOpompp map mo Ozaw> Oww>amm map mpcmmOLQOA hawk npoa .p n moocmpomwap mepcmopom .w mmmfi A05- com Amp- omm Aam- 5mm AAA- mLm amL- 0mm AOL- mom .EA ogpoa mo cam mHMH Ame- 3S: AHS- :Hm ANS- mm: Amm- 33m ammu mam A©m+ Hom .sm ch Lo cam Szma Awm- mwm Ana- omHH azmu mam Ram- NSOH Am+ pamfl Amm+ coma .e» as: L0 eem :mwaa Ron mmnaa AHN+ mmflma am- ommfla ASH+ zaoma Rm+ mmmaa Aam+ mmmma .s» pma go new wmam>.nmum .Lw mpdwwm ammo .pw mocmamm .QOO .Lm pma OSHA Awow smthz uma .ee< mo sum .pmH.ee< Aom+ mcfieflaomm .eea Aom + pmmHAAsm mmmmfim Ham wcflcfiaomm mafia pemfimspm mo 53m Immac mnu ucommpaop mmzam> OMMpcoopomv wA.m®5Hw> UGXQME mflp EOLM mmgdm> COHPMHomhflmfi ho mmoflmhm .LOpOth HHmEme =2 poasm= mmma own: m pom muonpoe COHpmHomhflmfi COEEOO %D Umudgfipmm m®3Hm> USN 63Hm> p®XQME mflp C®®3P®D m®OQGQGM%HQII.H Mdm<9 -6— Farmers may find improved estimates Of farm machinery values useful in planning the depreciation Of these assets. Farm Management Research Researchers could use improved information about machinery values where they are an important part of budgeting or programm- ing studies. Such information would, of course, be particularly applicable to studies Of the economics of farm machinery use. Agricultural Credit Agencies Agencies supplying credit for farm machinery purchases may well be interested in using this type of information to design repayment plans and maturities that would better serve their customers. OBJECTIVES The Objectives of this study are as follows: (1) discover how used farm machinery values change over time, (2) to learn what factors affect these changes in value. PROCEDURE Briefly the procedure used in this study was to: (1) locate a reliable source Of market values for used farm mach- inery, (2) Obtain values for selected machines over five and ten years time span, (1958-1963, 1953-1963 respectively,) (3) develop a model relating the hypothesized factors to the market values of the machines selected, (A) test the model (by least squares multiple regression methods), and (5) analyze the result. CHAPTER II DATA AND METHOD OF ANALYSIS Chapter I pointed out the inadequacy of current depreciation schemes as estimators of the market value of used farm machinery. In addition, the Objectives of this study were listed. This chapter discusses the source Of data and the method employed in analysis of this data. Data The objectives Of this study presuppose the need for a sizeable quantity Of reliable "market value" data for used farm machinery. The possibility of Obtaining these data from primary sources was quickly dismissed. The cost of surveying a sufficiently large number Of farmers and farm machinery dealers would have been prohibitive. It is also questionable that accurate data could have been secured for years other than the present. Thus, locating a secondary source of data was necessary. Two sources Of such data were available: National Farm Tractor and Implement Blue Book Valuation Guide published by National Market Reports, Inc., and Official Tractor and Farm Equipment Gelee compiled by Nationa1°Farm and Power Equipment Dealers Association (hereafter referred to as Blue Book and Official Guide). However, the estimates of market value given by the above sources are not comparable. The following table illustrates the disparity between the two. -7- —8- TABLE 2.---l966 Market Values of selected used tractors taken from Official Guide and Blue Book. (The "as—is" value is the market value of the stated tractor in average condition.) Official Guide Blue Book Year Model "as—is" "as-is" 19u7 Farmall "H" $ 333 $-—-a 1953 Farmall "Super M" 9A7 -—— 195A Ford PNAA" 700 --- 1955 John Deere "60" 1062 --- 1956 Allis Chalmers "WDAS" 100A 850 1957 Oliver "Super 77" 1036 875 1958 Case "300" 988 735 1959 Oliver "880" 193A 1500 1960 Massey-Ferguson "65" 1730 1650 1961 John Deere "3010" 2335 1615 1962 Massey-Ferguson "85" 236A 2A10 1963 Farmall "50A" 2156 2285 196A Ford "6000" 2621 2700 1965 Minneapolis Moline "M-60A" A520 A900 over 10 years of age. 8‘Blue Book does not give "as—is" values for Tractors -9- The publisher of Blue Book contends in the statement below, that any disparity between their figures and those of another reputable source is more apparent than real. VALUATION COMPARISONS--Va1uation figures appear- ing in the Blue Book are as a rule lower than the valuations given in one of the leading reference guides for dealers. This sometimes leads to the mis- taken belief that Blue Book figures do not represent a true picture of used tractor and farm equipment values. A careful comparison of the two sets of figures, however, reveals that the higher valuations given in the reference guide are due to the addition of various special equipment items not included in the regular Factory List Price. Such extras may, or may not, actually be wanted by the individual who is interested in the machine. They frequently result in an increase of several hundred dollars, and in the case Of larger tractors, well over a thousand dollars in the indicated list price with an attend- ant increase in the valuation figures. Blue Book valuations, on the other hand, are based wholly upon the manufacturer's Factory List Price which includes regular equipment only. This is a more accurate and logical base price to use, since the tractor component parts are always standard and uniform for all sections of the country. Where special equipment items are taken by the original purchaser, the price of such extras should be added to the Factory List Price and prOperly adjust— ed in the valuation tables.§/ It is the author's Observation that Blue Book normally does use the most basic model, while Official Guides valuations are for models including certain supplemental equipment. g/Nationa1 Market Reports, Inc., National Farm Tractor and Implement Blue Book Valuation Guide, (Chicago, 111., l966),p.3. -10- Official Guide states their case as follows: "Values published herein for tractors and other machines include factory Options and extras normally sold by dealers, nationwide, as part of original equipment."2/ Blue Book suggests that correction of their values to include Optional equipment can be made using the following table. TABLE 3.---Percentage figures, suggested by Blue Book, to determine the depreciated value of Optional equipment not included in the model specifications--l966 edition.19/ 1965 196A 1963 1962 1961 1960 Current 1 Year 2 Years 3 Years A Years 5 Years Year Old Old Old Old Old 80% 70% 55% A5% 35% 25% a'This table was reproduced exactly as it was found in the 1966 edition of Blue Book. The author finds this table somewhat confusing. For example, does "current year" under 1965 refer to 1965 or 1966? If, in fact, it refers to the depreciated value of 1965 optional equipment in 1966 it should be labeled 1 year Old (and "five years Old" then actually refers to equipment six years Old). However, if it refers to the value of the equipment in the "current year" it should be under 1966, not 1965. The author assumes that what is meant by "current year" is actually 1 year Old and similarly for the other labels. 9/ - National Farm Power and Equipment Dealers Association, Official Tractor and Farm Equipment Guide, (St. Louis, Missouri, Spring 1966) p.3. AL-gr/B1ue Book, p.3. -11- The method of correction is to multiply the original cost Of the "extra" equipment by the percentage of its value remaining, as given in Table 3, and adjust the "as-is" value by this amount. Although these corrections improve the comparability of the two sources, disparity still exists (See Table A.) Note that the largest differences seem to be in the earlier models. TABLE A.--Official Guide market values and Blue Book market values corrected to provide valuations for selected tractors with given model specifications----l966 editions. Official Guide Blue Book Year_ Mpdel "as-is" Corrected Value 1956 Allis Chalmers "WD-A5" $100A $ 850 1957 Oliver "Super 77" 1036 916 1958 Case "300" 988 776 1959 Oliver "880" 193A 1759 1960 Massey-Ferguson "65" 1730 1650 1961 John Deere "3010" 2335 1918 1962 Massey—Ferguson "85" 236A 2A10 1963 Farmall "50A" 2156 2285 196A Ford "6000" 2621 2700 1965 Minneapolis Moline'WL60A" A520 A900 are responsible for the differences in valuations given by the An alternative method of testing the assertion that "extras" ..Ch two sources is to necessary to make given by Official Guide. was to divide the -12- determine the new value of Optional equipment Blue Book "as-is" values equal to those The method used for this determination difference between "as-is" values for a given tractor by the apprOpriate percentage figure from Table 3. This was done for two popular 195A tractors and the results appear in Table 5. TABLE 5.--Market values for 195A Farmall "Super M" and 195A John Deere "60" from 1957, 1958, 1959 editions of Official Guide and Blue Book, and the new value Of Optional equipment necessary to equate used values from the two sources. Official Value of Required Year Guide Blue Book Extra quipment 195A Farmall "Super M" 1957 $1510 $13A5 $ 300 1958 1A75 1195 622 1959 1AA9 lOAO 1168 195A John Deere "60" 1957 $153A 1270 $ A80 1958 1A15 1160 566 1959 1368 965 1151 -13- Since the total possible value of optional equipment for the 195A Farmall "Super M" was $A86.00 and for the 195A John Deere "60" was $579.00ll/ as contrasted to necessary options valued in excess of $1100.00, differences in equipment does not seem to provide an adequate reconciliation of the two sources. Thus, the overall conclusion is that the data are differ- ent and the immediate job is to select between them. The choice for this study is the Official Guide. This is based mainly upon conclusions about how the valuations were compiled, while there are other minor considerations (to be discussed later). The most pressing concern is that the data must be reflective Of "market values". The conclusion here is that the valuations printed in the Official Guide are derived empirically, based on the reported experiences of farm machinery dealers, and therefore should be a fairly accurate portrayal of the "market values" desired. The Blue Book, however, is somewhat nebulous about how their valuations are derived and it appears that they may be based on a mathematical formula with adjust- ments for the judgement Of the publishers. The Official Guide receives reports from farm machinery dealers semiannually and processes them to be used by the industry in the following period. ll/Computed from information found in Spring 1965 Edition of National Farm Power and Equipment Dealers Association, Official Tractor and Farm quipment Guide, pp. 113, 163. _1u_ The values quoted herein...are based upon reports of thousands of sales....These reports come from representative dealers handling all makes Of agricultural tractors and allied equipment. Since the values quoted herein are based upon prevailing retail sales prices Of used equipment, they are assumed to be accurate and dependable. ig/ ”The method Of processing these reports into published "as-is" values is given below: 1) Retail prices for each make and model are averaged. 2) The average cost Of reconditioning the equipment is computed. 3) Average reconditioning cost is subtracted from the average retail price. A) Twenty percent is deducted from the remainder. (This is to cover dealer overhead and profit.) 5) The resulting "as-is" figure represents what a machine in average repair is worth to the dealer. Example: Average resale $800 Average cost of reconditioning —55 7A5 Minus 20 percent of 7A5 -1A9 Average as—is $595 If the farmer is able to perform the reselling services Of the dealer, the farm equipment in question may be worth more than the Official Guide as-is value. For this study, however, it is assumed that farmers as a whole do not make a practice of reselling their own equipment or if they do, the price Obtained is somewhere near the as-is value. This lg/drficiai Guide, 1966, p. l. -15- assumption may bias the results downward slightly, but such an error is believed to be more than Offset by the advantages Of using this rather easily available market value. Unquestion- ably the use Of average retail prices would be unrealistic (would assume that all machines on farms are in "good saleable condition") and the resultant upward bias would be considerably more damaging to the study. Blue Book makes no clear-cut explanation of how they arrive at their valuations. In reply to my inquiry, J.F. Heffinger, President Of National Market reports, Inc., which publishes Blue Book writes: The manner in which we arrive at the "as-is" value is generally defined in our "Introductory Section." As is true of all of our valuation guide books, the arrival at valuations is not a seience, but an art. There are, of course, basic criteria, such as production volume, general acceptance, bank and insurance company experiences. They of course, become a function of the ultimate values placed in our guide book. 13/ As suggested, one might look to the "Introductory Section" of Blue Book for clarification of their procedure. This is not particularly fruitful, however, as the following statements illustrate. 13/ Taken from a letter to the author from J. F. Heffinger, president of National Market Reports, dated January 19, 1965. -16- 1956 Edition--- Careful planning, analysis and research are employed in the preparation of the various guides we have published for years, among others, the Red Book and Blue Book Used Car Appraisal Guides. The same analytical approach and time tested methods, together with a thorough study of thousands Of sales reports from farm implement dealers, have been used in the preparation of the material for this edition.lA/ 1966 Edition--- Government figures show that the average life of a tractor is approximately 12 years. The rate of yearly depreci- ation used in computing Blue BOOk valuations corresponds to this figure. It follows the accepted sliding-scale pattern advocated in government publications and widely used in various state assessment Offices. Blue Book valuations are also checked against average prices prevailing at regional auction sales. 15/ The results of three simple linear regression equations leads the author to conjecture that Blue Book used a formula as the basis for some Of its valuations (and therefore would not provide useful data for this study). A regression of "as-is" tractor values (in percent of new cost) on tractor age was calculated for two pOpular 195A models for the years 1955 through 1959. Then a similar regression was calculated for the combination of the two models. The results are given in Table 6. lfl/Blue Book, 1956, p. 2. li/Biue Book, 1966, p. A. -17- TABLE 6.--Linear Regression of the percentage values Of select— ed 195A tractors-—Obtained from Blue BOOk--on tractor age. Model Equation R2 195A "Super M" Y = 69.97 - 5.81 X1 .9922 195A "60" Y = 69.58 — 5.9A X1 .9918 Combination Y = 69.77 - 5.87 X1 .9892 where Y = Estimate of percentage value x1 = Age, given by 1955=1, 1956=2,----1959-5 Note the very high R2's which mean that a straight line is nearly a perfect fit to the data. The uniformity of the equations suggest that the formula Y = 70.0 -6.0Xl could be used to compute values,-—-for the given tractors--nearly duplicating the "as-is" values from Blue Book. In addition to evidence that Official Guide is more representative of "market values," it has the advantages of (1) being more Often recommended by individuals concerned with the farm machinery business and (2) being more complete and easier to use than Blue Book. Method of Analysis The first step toward analyzing the data was to convert the "as-is" values to percentages Of the original value. The original value was designated as equivalent to the new cost to the farmers. -18- Discussions with branch offices of the farm machinery manufacturers and their local dealers revealed that the initial bargaining price to the farmer was the factory f.o.b. price (as reported in Official Guide) plus allowances for freight charges and excise taxes. NO effort was made to take into consideration freight charges and excise taxes as they vary from area to area. It was assumed that the resultant upward bias of the values does not warrant the effort necessary to attach average freight and excise taxes tO each f.o.b. prices. Secondly, it was assumed that local dealers normally sold machines below the f.o.b. price. The dealers interviewed agreed that a 5 percent discount from f.o.b. price would be typical in 1953, further than 5 percent to 7 percent would be reasonable for 1958 and figures from 5 percent to 10 percent were appropriate currently. The percentage values used in this study were computed by reducing the f.o.b. price by 5 percent and dividing the resultant "new cost" into the value given for each year. Example: 1953 "Super M" Farmall $2728 (f.o.b. 1953) x (5%) = $136 $2728 - $136 = $2592 (Assumed "New Cost" to the farmer) (195A $ value) $179A +$2592 69.2% (of "New Cost") (1958 $ value) $1386 +$2592 «II 53.5% (1963 $ value) $1226 +$2592 A7.3% -19- It was readily apparent that a graphical analysis was not sufficiently powerful to meet the Objectives of the study. From both the data and simple graphical presentation, one Observes differences between years, make of machinery and models. (See Table 7 and Figure 1 on the following pages.) It is evident that variables other than age should also be considered. The method of analysis employed must then accommodate multiple variables and have the capacity to test their significance. Again, it must give some measurable estimate Of the effect of individual variables on the percentage values. A model to which least squares multiple regression could be applied seemed to meet these require- ments.lé/ In addition, the results can be put in a form that is reasonably easy to understand by farmers and others who may wish to use them. Not all of the equations computed are reported in the text that follows. In general, the equations selected were required to meet the following criteria: (1) The variable in question (those unique to the specific equations) must make a significant contribution to the fit of one or more of the equations including it as part of the model. 16/ ———For an understanding of multiple regression, one can look to any Of a number of standard statistic textbooks, includ- ing: George W. Snedecor, Statistical Methods, (Ames, Iowa, 1957, Iowa State College Press.) -20- (2) And the overall statistical results, related to the given variable, must be explainable in theoretical terms. In other words, they must be indicative of a reasonable economic "cause and effect" relationship. The inclusion of several equations involving new model variables (explained in the Chapter III) is somewhat of an exception to the second criterion. These equations were included to indicate the likelihood of a relationship which the variable in the particular form used, did not adequately measure. The used farm machinery values in this study were for the periods 1953 through 1963 (1953 models) and 1958 through 1963 (involving 1958 models.) At the outset of the study, used values for the year 1963 were the most recent data available. The ten year span Of 1953 through 1963 was then chosen to con- form with length Of time usually associated with depreciation, (as used for income tax purposes) under the assumption that the most recent experience would be most relevant. The choice of the ten year span, as might be expected, was to make comparisons of the statistical results and common depreciation schemes as easy as possible. The shorter period of time, 1958 through 1963, was used to test the validity of the findings of longer period, and to identify any trends or changes in used ‘Values that might be associated with later model equipment. new» m we; pa swap whoa sumo: msaon nonempp m mo :ocwEocch mSOHQSO Oge .mmma ca pouommp on» pom pawn o>mn Oasoz manmpopd mLOEpmM pmszlllpcmopoa m mssae moapa .o.o.m on» ma pmoo 3oz O .Oaphp map Ga LOALO cm pom ma Loaahmo O .Ooana 3m: map An Ozam> Own: mnp wcawa>ap mp OOCHELOpOU mam mOSam> owmpcoogom m m.~: :.m: m.mz 0.0m m.am m.mm m.am m.mm m.wm m.mo IIIA =2 hmdsme mmma moma mama mama mmma mwma mama moma woma :mwa momma aamEAmm m.m: m.mm m.©m a.om m.mm ©.mm m.oe A.:h m.mm ©.AA uuua eooe moaa :mma mmma maza wmma moma mmza mmma mmza :mma ammma OLOOQ snow .II wbpmool%ocv mema mama amma omma mmma wmma amma emma mama :mma mmma aeeoz n.mhouomhp =om= OLOOQ snow mmma pad :2 poasm= aamEpmm mmma pom Onam> o®mu:oopma 02m OSam> mamaaomll.> mam<9 m -22- 100 90 80 70 60 . ~~~~~~ John Deere 50 \\ ‘~«\ \ “ H H A0 \\\\\\ 60 \\\\ Allis Chalmer —————-————\ 3O \\\\ "CA" \-..—-""\ 20 \“x 10 Case "SC" —_ 195A 1955 1956 1957 1958 1959 1960 1961 1962 1963 Figure l---The decline in percentage value (used value/new cost) of selected 1953 model tractors. Chapter III ANALYSIS OF USED FARM TRACTOR VALUES INTRODUCTION This chapter is concerned with presenting and evaluating selected variables which were expected to have an effect on used tractor values. The tractors chosen for the study were typical farm tractors, as Opposed to industrial and track- type tractors, and include mOdels from all the major manufactur- ers. The data consisted of two samples. One involved tractors manufactured for sale in 1953 and analyzed over the period 1953 to 1963. The other was comprised Of 1958 models, examined from 1958 through 1963. The tractors involved were subdivided into groups of gasoline and diesel powered units. The author hypothesized that they were regarded as somewhat different entities by farmers, and it would therefore be appropriate to examine them separately. .Further, the author chose to omit consideration Of liquified pertroleum (LPG) units, regarding them as a minor part Of the market. VARIABLES The variables selected reflect the "demand side" of the used farm machinery market. While demand conditions in the new machinery market (OligOpOlistic in structure) may not Play a very heroic part in new tractor price-setting, it would -23- -2u_ be unrealistic to discount the role of demand in establishing the value of used farm machinery (a competitive market). The "supply side" of the used farm machinery market was not considered. Estimating the supply of used machines would be a considerable undertaking; and it is doubtful that, given the Objectives of this study, such an.effort could be justified on the basis Of any new knowledge Obtained. The following variables were included in the analysis of used tractor values. Age It seems reasonable that age should have an important effect on the value of a used machine, as Obsolescence and deterioration are closely associated with it. Farmers and farm machinery dealers undoubtably associate increasing age with decreasing equipment values. This relationship could be formalized in the following way. Farm machinery has a certain useful life (before it becomes so Obsolete or so worn out that it is no longer serviceable), and the value of a used machine should reflect the value of services which can still be obtained from it. The depreciation schedules used for tax purposes embody these concepts, and, in fact, assume implicitly that age is the only variable affecting used values. In this study, age Was not expected to be the sole determinant of used values, -25- but it was expected to be a variable of primary importance. Realized Net Farm Income Farmers probably do little separating of farm income and family income. The net income realized from the farm, plus limits on the amount of available credit (Often self- imposed), then serves as a constraint on the amount Of product- ion and consumption goods purchased by the farm family. (Let us disregard the unnecessary complication of supplementary non-farm income.) There is really no problem of noncompar- ability Of production and consumption goods,,as investments in'prQchtion goods may be thought of as deferred consumption. In short, as realized net farm income increases, the budget constraint permits consideration of new consumption possibilities. Expansion of farm incomermnrallow consideration of remodeling the home, learning to play golf, a new hog waterer, an additional tractor or any number Of things not possible with the smaller budget constraint. In the usual economic terminology the farm family chooses the combination of consumption goods‘and deferred consumption, savings and investments in production goods, which maximize their utility. Aggregating consumption plans of farm families, if increased farm income means a greater number of farmers planning to purchase used machinery, it also -26- means a greater demand for used tractors (combines, plows, -—--, wagons) and higher used values given fixed supplies. Realized net farm income was lagged one year, because it was thought that the financial position the farmer found himself in at the years end was most relevant to the following year's machinery investments. It might also be hypothesized that the farmerisexpectation for this year's farm income is strongly influenced by last year's net farm income. Thus he might be expected to expand or contract his purchase of pro- ductive inputs, including used farm machinery, as a result of his past years experience. The outcome Of this situation is consistent with the rationale already hypothesized. Prices Received by Farmers Index In recognition of the importance Of product price in determining the level of input use, this index was included as a variable. If farmers operate on the basis Of marginal adjustments, an increase in the price of a farm product should motivate an increase in the inputs acquired for its production. Since farm machinery is one important input, a change in product prices could change the demand for used machinery and consequently their used values. This price index is a combination of prices for various groups Of commodities weighted by the average quantitites Of individual goods sold during 1953 to 1957. It therefore,need not be the same 55 farm income. -27- Make Each of several manufacturers are competing for the farmer's machinery dollar by offering a differentiated product. Although each company has several alternative models, there is a definite similarity within the "make". The hypothesis here is that buyers of used machines attach different values to the various makes. "Make" preferences are undoubtably deveIOped over time on the basis of the farmer's own experience and information Obtained from neighbors, dealers, and advertizing. The make variable differs from those already discussed, because it is qualitative, not quantitative in nature. As a result, it requires a different system Of including it in the regression equations. Thus a set of dummy variables is used to represent the makes. (This is also true of the horse- power variable to follow.) Each make is represented by a separate variable. When the observation in question is a given make, say Oliver, a one is entered under the appropriate makevariable (Oliver) and all other make variables are assigned a zero. One make must be omitted from the variables to serve as a comp- arison for the others. In this case it was Minneapolis Moline which, from examining the data,was expected to have the lowest uSed values. In essence, when a one is entered for a make, tile regression equation compares that particular make's used VEilues with those Of Minneapolis Moline. This brief explan- -28- ation of the functioning Of dummy variables can be applied to other variables using this system. Horsepower The sample Of tractors studied encompasses models with widely differing horsepower ratings. It is conceivable that models with certain horsepower ratings could be in greater or lesser demand than others. One might also reason that a given range would include the models with the most popular horsepower ratings. The existence of such a horsepower range would depend upon an associated range of tractor sizes suited to the greatest number of farming Operations. The author expected 30 to A0 horsepower and 30 to 50 horsepower to be the most popular ranges for 1953 and 1958 models respectively. Two dummy variables representing three horsepower ranges were used to test the above prOposition. In essence, tractors with less than 30 horsepower and more than either A0 horse- power (1953 models), or 50 horSepower (1958 models), were compared with those included in what was expected to be the mOst pOpular horsepower range. (The measure of the individual tractor's horsepower rating was maximum drawbar horsepower given by the Nebraska test dated nearest to the given model year.) -29- New Models The new models variable was included to study the effect of the introduction of a new model on the value of the model it replaces. This is a particular type of Obsolescence which is unrelated to the age of the machine. To be more specific, does the introduction the Allis Chalmers "D—lA" model in 1957 affect how "up—to—date" the farmer regards a 1953 Allis Chalmers "WD-uS"? Does the farmer consider the 1953 John Deere "70" now Obsolete even though it has many Of the same basic technical features Of the "3010" John Deere introduced in 1961? This type of Obsolescence is not cumulative over time, but occurs suddenly when a new model is introduced to which an Older one may be contrasted. liaise; Machinery can be labor-saving, and thus a substitute for farm labor. As the price of farm labor increases relative to substitutable machinery inputs, marginal analysis suggests that farmers would demand more machinery and less farm labor. Since there is no reason to believe that farmers do not respond to the "better buy" in farm inputs, increasing labor costs could be expected to retard the rate of decrease in used mach- inery values over time. -30- Inflation Inflation could also be eXpected to partially offset the decline Of used farm machinery values. For this study, the Bureau Of Labor Statistics wholesale price indices for farm machinery (tractors, balers, combines, forage harvesters, and cornpickers) were used to construct the variable. The logic Of this choiCe of indices rests on a concept of equilibrium between the new and used machinery markets. If new machinery prices rise relative to used machinery prices (a substitute for new machinery), used machinery becomes a "better buy" and prices are bid up in the competitive used equipment market. Consequently a 2% yearly increase in new farm machinery prices should result in a 2% increase in used farm machinery values. The variable inflation is examined in a somewhat indirect way. The Yl values (percentage of original value remaining) were deflated by the appropriate wholesale price index creat- ing a new dependent variable called Y This approach was 2. used because early experience indicated that the indexes, if used directly as a variable, would be highly intercorrelated with the variable eg_. High intercorrelations between var- iables makes it difficult for a meaningful analysis of the variable in question. -31- ESTIMATING EQUATIONS IE In order to assess the contribution of age to tractor value determination, four linear, least squares regression equations were computed with age as the only independent variable. Each of the subdivisions Of data, 1953 gasoline tractors, 1953 diesel tractors, 1958 gasoline traCtors and 1958 diesel tractors are represented by equations given below. 1953 Gasoline Tractors; Equation #1 Y = 6A.287 - 3.072Xl** 1 (0.955) (0.152) 2 R = 0.57A3 S.E. = 7.5833 Equation #2 Y2 = 65.6A8 - A.100Xl** (0.869) (0.139) R2 = 0.7A36 S.E. = 6.9027 1953 Diesel Tractors Equation #3 Y1 = 59.367 — 2.758Xl** (1.260) (0.192) R2 = 0.65A2 S.E. = 5.7302 Equation #A Y2 = 60.320 - 3.669xl** (1.12M) (0.171) R 0.8080 S.E. 5.1llA -32_ 1958 Gasoline Tractors Equation #5 Y1 = 7A.582 - A.33uxl** (0.8A9) (0.250) R2 = 0.5723 S.E. = 5.1693 Equation #6 Y2 = 72.662 - 5.07AX1** (0.788) (0.232) R2 = 0.6805 S.E. = 4.7965 1958 Diesel Tractors Equation #7 Y1 = 76.100 - 5.398Xl** (0.852) (0.253) R2 = 0.8193 S.E. = 3.5636 Equation #8 Y2 = 7A.103 - 6.052Xl** (0.783) (0.233) R2 = 0.8708 S.E. = 3.277u Where. is the estimated value of the machine-—in percent Of its origlnal cost--based on current dollars. is the estimated value of the machine—-in percent of its originaI cost--based on constant dollars (as adjusted by the Bureau of Labor Stat— istics wholesale indices). X is the age of the tractor in years. is the coefficient of multiple determination. S.E. is the stgndard error of estimate. *indicates the variable was significant at .05 level, and ** indicates significance at .01 level. Judging from the R25 given above, age makes a consider— able contribution tO describing the "loss-in—value" of used farm tractors. ("Loss-in-value" will be used rather than "depreciation" to avoid confusion with depreciation as it is used for income tax purposes.) Also noteworthy is the sign- -33- ificance of the variable. In all cases the b value for ege was significantly different from zero at the .01 level. It should be noted that the R2's and 0's for Y2 equations are larger than their Y counterparts. This is exactly the 1 relationship that should be expected if inflation is important to understanding "loss-in-value". The greater R2's indicate that the removal of inflation permits ege to explain a larger portion of the variation in used values. The larger b's support the proposition that without inflation the "loss-in- value" over time would be more rapid. Finally, b values for 1958 equations exceed those for comparable 1953 equations, and the diesel equations appear to be somewhat different than their gasoline counterparts. Consideration of the questions raised by these relationships will be deferred until later in the chapter. Maia. The following equations include, along with age, the make of the tractor. _3A- 1953 Gasoline Tractors Equation #9 Y1 59.229 - 3.0A7X1** + 8.69AX2** — 1.513X 3 (1.106) (0.108) (1.3A8) (1.23A) + 3°232XA* + 13.632X5** + 8.7A2X6** (1.336) (1.2u3) (1.925) * + 18.802k7** + 6.9A5X8** + 3.157X9 + 1.201Xlo (1.925) (1.336) (1.2A3) (1.250) R2 = 0.7931 S.E. = 5.3680 Equation #10 Y2 = 61.255 - A.078Xl** + 7.560X2** - 1.382X3 (1.0A5) (0.102) (1.27A) (1.175) + 2.619Xu* + 11.917X5** + 7.6A6X6** (1.263) (1.175) (1.819) + 16.A11X7** + 6.061X8** + 2.836X9* + 1.023XlO (1.819) (1.263) (1.175) (1.181) 32 = 0.8656 S.E. = 5.0729 X1 = Age XA = Cockshutt X7 = Ford X2 = Allis Chalmers X5 = John Deere X8 = International Harvester X3 = Case X6 = Ferguson X9 = Massey Harris X10 = Oliver (Minneapolis Moline is the base for make comparisons) -35- 1953 Diesel Tractors Equation #11 Y = 57.892 — 2.950Xl** + 1.9llX + 10.858X3** 1 2 (1.353) (0.153) (1.A97) (2.502) + 10.90AXu** + 1.625X5 + 0.586X6 (1.582) (l-3A3) (1.315) R2 = 0.7981 S.E. = u.u827 Equation #12 §2 = 58.955 - 3.833x1** + 1.612x2 + 9.382x3** (1.233) (0.1A0) (1.36A) (2.280) + 9'526XA** + 1.515X5 + 0.67OX6 (1.AA1) (1.223) (1.198) R2 = 0.8830 S.E. = A.0850 X1 = Age X“ = International Harvester X2 = Cockshutt X5 = Massey Harris X3 = John Deere X6 = Oliver (Minneapolis Moline is the base for make comparisons) 1958 Gasoline Tractors X = A Equation #13 Yl 2 R = 0.7535 Equation #1A Y2 R Age Allis Chalmers Case - Cockshutt John Deere 0.8138 —36- 71.217 - A.588Xl** + 1.696X2 + 10.028X3** (0.99M) (0.196) (1.133) (1.106) 5.A73xu** + u.780x5** + 5.736x6* + 6.898x7** (1.202) (1.085) (2.455) (1.286) A.585X8** + 6.A08X ** - 0.832Xl 9 (1.0A9) (1.202) (1.085) O S.E. = A.0052 69.529 - 5.306Xl** + 1.596X2 + 9.23AX3** (0.927) (0.183) (1.057) (1.032) 5'158XA** + A.A12X ** + 5.227xg + 6.316X7** 5 (1.121) (1.057) (2.291) (1.200) A.21Ax8** + 6.023x9** — 0.732xlO (0.979) (1.121) (1.012) S.E. = 3.7368 X6 = Ferguson >< II Ford X8 = International Harvester X = Massey Harris X = Oliver (Minneapolis Moline is the base for make comparisons) -37- 1958 Diesel Tractors Equation #15 Y1 = 7A.72O - 5°500X1** + 1.1470X2 + 5.0u7x ** 3 (1.29A) (0.187) (1.u29) (1.391) + 3'107Xu + 5.000x5** + 2.860X6 + 1.853x7 (l-3A7) (1.650) (1.650) (l-3A7) + 3.680x8 - 2.128x9 (1.u29) (1.278) R2 = 0.9110 S.E. = 2.6082 Equation #16 Y2 72.7AA - 6.1A1Xl** + 1.570X2 + A.575x3** (1.182) (0.171) (1.305) (1.271) + 2.987Xu + A.720X5** + 2.720X6 + 1.900X7 (1.230) (1.506) (1.506) (1.230) + 3.A30X8* - 1.956X9 (1.305) (1.167) R2 = 0.9372 S.E. = 2.3820 X1 = Age X5 = John Deere X2 = Allis Chalmers X6 = Ford X3 = Case X7 = International Harvester X“ = Cockshutt X8 = Massey Harris X9 = Oliver (Minneapolis Moline is the base for make comparisons) The following list summarizes for both model years the makes which were significantly different from zero, and can generally be thought of as significantly different in value from Minneapolis Moline. -38_ 1953 Gasoline Allis Chalmers** Cockshutt* John Deere** Ferguson** 1958 Gasoline Case** Cockshutt** John Deere** Ferguson* 1953 Diesel John Deere** International Harvester** Ford** International Harvester** Massey-Harris** 1958 Diesel Case** Cockshutt* John Deere** Massey Harris** International Harvester** Massey Harris*# Ford** (As in the equation * indicates significance at .05 level and ** indicates significance at .01 level.) Since several of the individual makes were not significant, doubt may exist as to the contribution of the make variables taken as a group. In order to determine if their overall contribution was significant the following F-test was made. . SSR with make variables—SSR without make variables F(r-k,n~r-l)= r-k 7” ’ SSE‘In-r-l) ,n-r-l Where: n is the number of Observations, k is the number of variables for the equation without make variables, r is the number of variables for the equation with make variables. -39- The contribution of the make variables in aggregate turns out to be significant at .01 level for 1953 gasoline, 1953 diesel, 1958 gasoline, and at the .05 level for 1958 diesel tractors. Horsepower With the following set of equations the effect of the selected horsepower ranges was studied in conjunction with age and make. Only the range of 0 to 30 horsepower (30-) and A0 or more horsepower (A0+) in 1953, or 50 or more horse- power (50+) in 1958, appear as variables in the equations. lfimemid-Pangficd'horsepower (30-A0 or 30-50) serves as a basis of comparison. -40- 1953 Gasoline Tractors A Equation #17 Yl (1.158) (0.097) 60.AA5 - 3.063Xl** + 11.008X2** - 0.28OX 3 (1.281) (1.1A1) + 5.A28Xu** + 1A.865X5** + 12.603X6** (1.270) (1.141) (1.800) + 22.663X7** + 7.3O2X8** + 3.1A1X ** 9 (1.800) (1.21A) (1.1A9) + 1.23OXlO - A.99AXll ** + 0.52AXl2 (1.159) (0.690) (0.810) R2 = 0.8342 S.E. = 4.8212 Equation #18 72 = 62.427 — 4.092xl** + 9.522x2** - 0.339123 (1.114) (0.093) (1.232) (1.097) + A.A77Xu** + 12.9605X (1.221) (1.097) + 19.7A7X7 5** + 10.982X6** (1.731) ** + 6.339x8** + 2.771x9** (1.731) (1.167) (1.105) + 0.993XlO - A.A3AXll ** + 0.30AXl2 (1.11A) (0.663) (0.779) R2 = 0.8885 S.E. = 4.6367 X1 = age X5 = John Deere X9 = Massey Harris X2 = Allis Chalmers X6 = Ferguson X10= Oliver X3 = Case X7 = Ford X11: 30-h.p. X = Cockshutt X = International X = AO+h.p. u 8 12 Harvester (Minneapolis Moline is the base for make comparison, 30-A0 h.p. is the base for horsepower comparisons.) -01_ 1953 Diesel Tractors EQuation #19 Y1 57.931 — 2.928Xl¥* + 3.629X2 + 10.797X3** (2.371) (0.1A7) (2.A28) (2.386) + 10.891Xu** + 1.578X5 + 1.954X6 - 4.586X7** (1.508) (1.370) (2.315) (1.303) - 0.166X8 (1.890) R2 = 0.8200 S.E. = A.27A2 Equation #20 Y; = 58.AA7 - 3.809X1** + 3.683X2 + 9.31AX3** (2.163) (0.13A) (2.215) (2.177) + 9°511XA** + 1.606X5 + 2.A21X6 - A.l35X7** (1.376) (1.250) (2.112) _(1.189) + 0.367X8 (1.72A) R2 = 0.8796 S.E. = A.1900 X1 = age X5 = Massey Harris X2 = Cockshutt X6 = Oliver X3 = John Deere X7 = 30-h.p. XA = International Harvester X8 = AO+h.p. (Minneapolis Moline is the base for comparison of makes, 30-A0 h.p. is the base for horsepower comparison) 1958 Gasoline Tractors Equation #21 Y1 R2 = 0.7718 A Equation #22 Y2 R2 = 0.8273 age Allis Chalmers Case Cockshutt X8 (Minneapolis Moline is h.p. -142- 71.119 - A.57AX1** + 2.821X ** + 10.8AOX ** 2 3 (0.973) (0.190) (1.129) (1.090) 6.127Xu** + 5.376X5** + 5.778X6* (1.177) (1.119) (2.377) '§« ** ** 6.9A7X7 + 5.28AX8 + 6.39AX9 (1.252) (1.056) (1.162) 0.067XlO — 2.671X11** + 0.280Xl2 (1.072) (0.696) (0.7A0) S.E. = 3.8713 69.A52 - 5.293Xl** + 2.627X2** + 9.975X3** (0.909) (0.177) (1.054) (1.018) 5.769Xu** + A.977X5** + 5.253X6* (1.099) (1.045) (2.220) 6.348x7** + 4.879x8** + 6.013x9** (1.169) (0.987) (1-085) 0.101X10 — 2.A82Xll** + 0.193Xl2 (1.002) (0.650) (0.691) S.E.= 3.6157 = John Deere X9 = Massey Harris = Ferguson X10: Oliver = Ford X11: 30—h.p. = International X12= 50+h.p. Harvester the base for comparison of makes, 30-50 is the base for horsepower comparisons) _u3_ 1958 Diesel Tractors Equation #23 Y1 = 73.978 - 5.500Xl** + 2.212X2 + 5.969X3** (1.478) (0.185) (1.595) (1.461) + 3.602Xu** + 5.000X5** + 3.602X6* + 2.348X7 (1.420) (1.630) (1.791) (1.420) + 4.422X8** - 1.021X9 - 1.282XlO + 0.742Xll (1.595) (1.395) (0.921) (0.7A2) R2 = 0.9149 S.E. = 2.5775 Equation #24 §2 = 71.934 — 6.141xl** + 2.380x2 + 5.490X3** (1.347) (0.168) (1.453) (1.331 + 3'527X4** + 4.720X5** + 3.530X6* +2.440X7 (1.294) (1.485) (1.632) (1.294) + 4.240X8** - 0.858X9 - 1.124X10 + 0.810Xll (1.453) (1.271) (0.839) (0.676) R2 = 0.9403 S.E. = 2.3481 age X6 = Ford Allis Chalmers X7 = International Harvester Case X8 = Massey Harris Cockshutt X9 = Oliver John Deere X10: 30-h.p. X11 = 50+h.p. (Minneapolis Moline is the base for comparison of makes, 30-50 h.p. is the base for horsepower comparisons) -00- The upper range of horsepower (40 + h.p.-—-l953 and 50+ h.p. —-- 1958) was not significantly different from zero in its effect on any of the models. The lower range (30-h.p.), however, had a significant effect on 1953 gasoline, 1953 diesels, and 1958 gasoline tractors, but not 1958 diesel units. Using an F-test equivalent to the one applied to megee, the combination of horsepower variables was found to be sign- ificant at the .01 level for 1953 gasoline, 1953 diesel, 1958 gasoline tractors; and at the .10 level for 1958 diesel tractors. All of the make variables which were significantly diff- erent from the base make at the .05 level before horsepower was included, were again significant with its inclusion. In addition, Allis Chalmers became significantly different from zero (.01)for 1958 gasoline tractors and Ford for 1958 diesel tractors (.05). Although the b values are different, as would be expected, for the Y=f (Age,Make, H.P.) and Y=f (Age,Make) equations, the relationships between the individual makes appear to be consistent. _05_ Curvilinear Function Analysis of the linear equations and their residuals indicated that a function which was curvilinear for age might more nearly fit the data. The following equations constitute an attempt to fit this type of curvilinear equation to the samples. These equations differ from the ones reported in the previous section only with respect to a e, which here consists of two variables X and X2. Thus, 1 l the equations in this section are of the form: - 2 A Y — a + lel + bl-axl + b2X2 + ----*ann -05- 1953 Gasoline Tractors Equation #25 § 65.293 - 5.426Xl** + 1 (1.362) (0.411) - 0.270X + 5.450X 3 4 (1.078) (1.200) + 12.636X6** + 22.696X7 (1.701) (1.701) + 3.144x9** + 1.301xlO (1.086) (1.095) R2 = 0.8525 S.E. Equation #26 i2 = 70.489 — 8.082X1** + (1.137) (0.344) — 0.322X3 (0.890) (1.002) + 11.036X6** + 19.802X7 (1.420) (1.420) ** + 2.775X9 + 1.112Xlo (0.907) (0.91A) R2 = 0.9252 S.E. X1 = age X5 = John Deere X2 = Allis Chalmers X6 = Ferguson X3 = Case X7 = Ford X“ = Cockshutt X8 = International Harvester 0.217Xi**+ 11.123X2** (0.036) (1.211) ** + 14.875X5** (1.078) ** + 7'305X8** (1.147) - 5.023Xll** + 0.551Xl2 (0.652) (0.766) = 4.5558 0.361x§** + 9.713x2** (0.030) (1.011) + 4.514xu** + 12.976x5** (0.890) ** + 6.344x8** (0.957) - 4.486Xll** + 0.349Xl2 (0.544) (0.639) = 3.8035 X9 = Massey Harris X10: Oliver X11= 30eh.p. X12: AO+h.p. (Minneapolis Moline is the base for make comparisons, 30-40 h.p. is the base for horsepower comparisons) 1953 Diesel Tractors A Equation #27 Y1 = R2 = 0.8201 Equation #28 Y; = R 0.9065 Age Cockshutt John Deere International Harvester IA7- 58.297 - 3.083Xl** + 0.014Xi + 3.585X2 (2.816) (0.655) (0.057) (2.445) 10.770X3** + 10.876Xu** + 1.569X5 ( 2.400 (1.516) (1.377) 1.912X6 — A.587X ** - 0.199X8 7 (2.332) (1.309) (1.904) S.E. = 4.2940 62.924 — 5.712xl** + 0.169xi** + 3.150x2 (2.430) (0.566) (0.0A8) (2.110) 8.988X3** + 9.334Xu** + 1.489X5 + 1.9O7X6 (2.071) (1.309) (1.188) (2.013) 4.154x7** - 0.036x8 (1.130) (1.643) S.E. = 3.7059 X5 = Massey Harris X6 = Oliver X = 0-h. . 7 3 9 X8 = AO+h.p. (Minneapolis Moline is the base for make comparisons, 30-40 h.p. is the base for horsepower comparisons.) 1958 Gasoline Tractors Equation #29 Yl -48— 75.088 - 7.862Xl** + 0.535xi** + 2.83AX2** (1.483) (0.962) (0.154) (1.101) + 11.156X3** + 6.131Xu**'+ 5.377X5** (1.066) (1.147) (1.091) + 6.037X6** + 7.258X7** + 5.285X8** (2.319) (1.224) (1.030) + 6.393X9** + 0.075XlO - 2.692Xll** + 0.305Xl2 (1.133) (1.046) (0.679) (0.721) R2 = 0.7841 S.E. = 3.7744 Equation #30 i2 = 73.863 - 8.947xl** + 0.595xi** + 2.642X2** (1.368) (0.888) (0.142) (1.016) + 10.326X3** + 5.773Xu** + 4.978X5** (0.98A) (1.059) (1.007) + 5.541X6** + 6.693X7** + 4.879X8** (2.1A0) (1.129) (0.950) + 6.012X9** + 0.110Xlo - 2.505Xl1** + 0.220Xl2 (1.045) (0.965) (0.627) (0.665) R2 = 0.8405 S.E. = 3.4832 X1 = age X5 = John Deere X9 = Massey Harris X2 = Allis Chalmers X6 = Ferguson X10: Oliver x3 = Case x7 = Ford x11: 30—h.p. X4 = Cockshut X8 = figfieggegional X12: 50+h.p. (Minneapolis Moline is 30-50 h.p. is the base the base for comparison of makes, for horsepower comparisons.) 1958 Diesel Tractors Equation #31 Y1 2 -49- 73.946 — 5.474Xl** — 0.004xi + 2.212x 2 (1.86A) (0.963) (0.155) (1.604) 5.967X3** + 3.602X4** + 5.000X5** (1.472) (1.428) (1.639) 3.602X6* + 2.3A8X7 + A.A22X8** - 1.021X9 (1.801) (1.A28) (1.60A) (1.403) 1.282XlO + 0.7A2Xll (0.926) (0.747) R = 0.9149 S.E. = 2.5919 Equation #32 22 = 72.930 - 6.978xl** + 0.138xi + 2.380x2 (1.689) (0.873) (0.141) (1.453) + 5.56AX3** + 3°527XA** + A.72OX5** (1.33“) (1.39A) (1.485) + 3.530X6* + 2.AA0X7 + A.2AOX8** - 0.858X9 (1.632) (1.294) (1.A53) (1.272) - 1.12AXlO + 0.810Xll (0.839) (0.677) R2_=.0.9409 S.E. = 2.3487 X1 = Age X4 = Cockshutt X7 = International Harvester X2 = Allis Chalmers 5 = John Deere X8 = Massey Harris X3 = Case X6 = Ford X9 = Oliver x10 = 30-h.p. xll = 50+h.p. (Minneapolis Moline is the base for comparison of makes, 30- 50 h.p. is the base for horsepower comparisons.) ...-I .F. v N -50- The b values for the variable age squared were sign- ificantly different from zero for 1953 gasoline Y1 and Y2 equations, 1958 gasoline Y1 and Y2 equations, and the 1953 diesel Y2 equation; It was not significant, however, for the 1953 diesel Y equation, or 1958 diesel Y and Y equations. 1 l 2 In general, the squared term was quite helpful in explaining "loss-in-value" for the gasoline tractOrs, but not very useful when applied to the diesel units. (This Observation will be examined later in the chapter.) In no instance did the addition of the age squared variable significantly change the b values for geAe and Aeeeeg power from those given by the simpler equation, Y = f (Age, Make, Horsepower) INTERPRETATION Analysis of the Equations To Obtain the maximum amount of information from the regression equations, it is necessary to go beyond examining individual equations. The analysis to follow is the product of comparisons of equations, and certain statistical tests. Age Age is a highly significant and important variable. The significance level for the variable indicates that there is less than one chance in a thousand that age could have had no effect on the value of used farm tractors. More importantly, -51- ege seems to be capable of explaining from 57 percent to 87 percent Of the variation in used value for the tractors sampled. In addition, the b values for the ege variable are very consistent throughout the linear equations. The table below lists the b values for ege with each model and equation. TABLE 8---Summary of the b values for the age variable from equations 1 through 24. MODEL Y=f (Age) Y=f (Age,Make) Y=f (Age,Make,H.P) 1953 Gasoline--Yl -3.072 -3.047 -3.063 1953 Gasoline--Y2 —A.1OO -A.O78 -A.O92 1953 Diesel-—Yl -2.684 —2.881 —2.858 1953 Diesel—-Y2 -3.669 -3.779 -3.753 1958 Gasoline—-Y1 -4.334 -4.588 -A.574 1958 Gasoline--Y2 -5.07A —5.306 -5.293 1958 Diesel--Yl -5.398 -5.500 -5.500 1958 Diesel-—Y2 -6.052 -6.1A1 -6.1Al There are no significant differences between the b values for the various equations Of each model and dependent variable formulation. This means that make and horsepower are comple- mentary to age, rather than substitutes for it. -52- The author's contention that diesel and gasoline tractors should be studied separately can be examined using the simple Y = f (Age) equations. It is a minor task to show that the equations for 1958 diesel and gasoline tractors are sign- ificantly different. Using the first step of covariance analysis, the slopes of the equations were found to be sign- ificantly different at the .005 1eve1.fl/ A statistical argument for separating 1953 diesel and gasoline models will not be attempted. The first step of covariance analysis failed to indicate a significant difference between the b values of their respective equations. And to test the significance of the difference between the constant terms would involve computation of a combined regression equa- tion. The calculation of separate equations did, however, bring out an interesting point that would have otherwise gone unnoticed. Comparison of these equations seems to indicate an increasing acceptance of used diesel tractors. 1 —Z/See George Snedecor, Statistical Methods. (Iowa State College Press, Ames, Iowa, 1956), pp. 394-398 for details on this method. -53- TABLE 9---Estimates of the percentage value(used value/ new cost) for 1953 diesel and gasoline tractors computed -*‘from equations 1 through A. -. h) '17 4 Years of Age MODEL 1 2 3 4 5 6 7 8 ' 9 10 (Percent) 1953-D-Yl 56.4 53.7 51.0 48.3 45.7 43.0 40.3 37.6 34.9 32.2 1953-G-Yl 61.2 58.1 55.1 52.0 48.9 45.9 42.8 39.7 36.6 33.6 1953-D-Y 56.7 53.0 49.3 45.6 42.0 38.3 34.6 31.0 27.3 23.6 2 1953-G-Y 61.5 57.4 53.3 49.2 45.1 41.0 36.9 32.8 28.7 24.6 2 Yl represents percentage value based on current dollars, Y2 is percentage value based on constant dollars. Note that the magnitude of the differences between 1953 gasoline and diesel tractor values, as estimated by Y=f (Age), lessens as the tractors grow Older. Based on this Observation, it could be hypothesized that farmer's attitudes toward used diesel tractors changed over the decade, 1953 to 1963. This would be consistent with the increasing number of diesels among farm tractors, as reported by the U.S.D.A.l§/ A com— parison Of first year values (as estimated by equations #1,3,5, and 7) for 1953 and 1958 diesel and gasoline tractors gives some support to the hypothesis. 18/ —— Diesel and LPG tractors were about one-half of tractor population in 1963, as Opposed to 5 percent in 1952. LPG numbers have remained almost unchanged since 1958. U.S. Dep- artment of Agriculture, Farm Cost Situation,FC-35, November 1963, P. 14. _50- TABLE lO.—--Percentage values (used value/new cost) for one year old gasoline and diesel tractors, 1953 and 1958 models, as estimated by equations # 1,3,5, and 7. Model Year Gasoline Diesel 1953 61.2 percent 56.4 percent 1958 70.3 percent 70.7 percent In 1954, the one year Old diesel tractor was not as well received as the gasoline models. By 1959 the one year Old diesel tractor seems to be as well accepted as its gasoline counterpart. This is probably due to farmers' increased experience with diesel tractors during the period studied. At this point the discussion is directed toward explaining the differences in constant terms and b values for comparable 1953 and 1958 equations. At first glance it would appear that 1958 models had a smaller initial drop in value than 1953 models (approximately 30 percent and 40 percent respectively) and a more rapid rate of decline thereafter (4.3 percent as Opposed to 3.0 percent for gasoline models.) A closer examination reveals that the difference is probably due to curvilinearity, rather than any important difference in data. -55- The average Of the residuals (actual value minus the value estimated by the regression equation) for each year of age was computed for several equations. This was done by group- ing all the residuals associated with a given year of age (l,2,3,--—, 10), and taking the arithmetic average of each group. In general, these residuals vary from the regression line in a systematic manner. Table 11 below illustrates the pattern Of variations. -56- mm.ol pm.o :a.o oa.OI No.0I aommam wmmallwm oa.a Ao.a| mm.on mm.o Am.o OsaaOmmu wmmallma mm.a| ma.OI ma.m oa.a om.m mm.MI :m.ml ww.OI w:.o mm.m aowoam mmmallmm aa.a 25.0 am.o wa.a mm.o mo.MI ma.mt a:.al ma.al m©.m OCHaOmmw mmmallam mpcflom Owensooeom oa m m A o m a m m a eoaeomom ow< mo memow oeaaomow mmma one mmma hoe .Aowav e one Eoem Aosam> UmmeameIosaw> adopomv mamsoamOL mahmom ommeo><|||.aa mamaw m eog coapm>aomno mo popes: one ma : .Laom co>aw a Canvas Ozaw> UmpoEaumo an: ouoaaaomddm on» ma w .amoa co>aw a mom modao> adopom aam ma auoaonz mammaaaa.a u .m.m aw.aa aw.aa am.:a am.aa am.aw ao.ma am.a~ am.oa a:.am aa.mm Aaa \ Am- am.m aa.a oa.a aa.a 0a.: oa.a mm.a aa.a am.m as.» aoxez.om monomap ocaaOmmw mmma mo momeapmo coammoawoa one mo aoeao ULMUCMlellaa mam own map Aaco mo>ao>ca coamehomca O>onm ones am.a am.a aa.m mm.m ma.a am.a am.a am.a am.a mm.am m am.aoeoomeoea w oQaaommu mmma mm.a m>.a mm.m am.m :o.m w:.m mm.m am.a ow.: mm.o: a Am-fi QCOLLSOV % Ozaaommw mmma ApsooaOQ- da 3 a H a as s m U H 92 Eda-(om Ow< mo mamom m.am pea mma meoapmsoo Eoem OOOBQEOO .Omoo amsawaao paozp mo pcooe09 a ma .mLOpomap Ozaaommw mmma pom zonam>ucalmmoas haemowlulaa mam emmeameIIOSam> amSPOmv mamzoamoa haemom owmao>aam meawsm awe mmam.mu ........ maam.a- mmom.au a ooaaoaoem maom aama ommm.au ........ meam.an omaa.mu a ooaaoooam eaom aama maom.au ........ amas.a- amma.s- a ooaaoooem maom mama aaam.m- ........ amaa.m- aomm.mu a ooaaoooem eaom mama mmmm.au amaa.au mmaa.m1 aaoa.mu mm tame aasm aama mmma.a1 sacs.au mamm.mu aamm.au aw tame aasm mama maao.a- mmmm.a- aaam.mu amaa.an mm tame aasm mama amam.a- msoa.s- mmaa.a- omma.a- as tame aasa mama A.z.24a.o.m4osozwmm<-mum A.o.m.ose24uw D. mflaH-llle magma-«H- -]_09- the variables indicated are clearly complimentary to age, rather than substitutes for it. One should expect some "trade-Off" between age and new models as both of them are related to only downward movements of used values. If part of the decline in used values is due to the introduction of new models, the b value for age,in conjunction with new model variables, may not need to be as large as when it was assigned all the downward trend. In chapter III it was found that the differences in b values between 1953 and 1958 equations are likely to be the result of a curvilinear "loss-in—value" function. In order to determine if this assumption is true for combines, certain expiOrations must be performed. Our first concern is to determine if the equations for 1953 and 1958 are in fact significantly different. If the b values for ege in the simplest equation-- Y = f (Age,)-- are significantly different from 1953 and 1958, there is ample reason to believe that the more involved equations will also be significantly different. The test applied to these b values is the first step in the analysis of covariance for regression 1 equations with one variable. The F statiStiCS computed indicated that comparable 1953 and 1958 equations were sign- 1See George W. Snedecor, Statistical Methods, (Iowa State College Press, Ames, Iowa, 1956) pp. 394 -399 for discussion of this method. —110- ificantly different at .005 level. Having concluded that the 1953 and 1958 equations were significantly different, the next step is to determine if this difference is due to dissimilar data during the first five years of use. In other words, did the value of 1958 combines fall faster in this length of time than 1953 models? To answer this question the average yearly value was calculated for the first five years for both 1953 and 1958 models, and a t-test was used to find out if these average yearly values were sign- ificantly different. 1953 self propelled model averages were compared with 1958 self propelled, 1953 PTO models with 1958 PTO models, and engine driven for 1953 with those in 1958. In no case were the average yearly values significantly diff- erent. The final step was to average the residuals consistent with each year Of age and determine if a pattern Of curvilinear- ity was present. (See Chapter III for explanation of this procedure) Average yearly residuals were calculated for 1953 1958 pull type Y and pull type Y 1953 self propelled Y 1’ 1958 self prOpelled Y 1’ equations. 1’ l -111- TABLE l9—--Average residuals (actual value—estimated value) computed for each year Of age from combine equations #33. 35, 37. & 39. Year of Age Combine 1 2 3 A 5 6 7 8 9 10 (Percentage Points) Equation #33- 1953 Pull Type 4.8 1.8 -1.6 -3.9 -3.1 -l.5 0.3 1.9 2.0 2.2 Equation #35 ------- 1953 Self Propelled 4.4 1.5 -1.9 -3.0 —2.8 -3.9 2.9 3.3 1.5 1.5 Equation #37-- 1958 Pull Type -1.7 1.3 2.0 -l.4 -.31 Equation #39 ------- 1958 Self PrOpelled—1.9 0.9 2.7 -1.1 -1.7 The pattern of the residuals for 1953 equations indicates that the linear equations underestimated the average value in years one and two, overestimated the average value for years three: through six, and underestimated them again for the last four years. This indicates that the first year value calculated is lower than the average first year value, and that the slope of the "loss-in-value" function is probably greater in the first few years and less in the later years than given by the linear regression equation. Although the 1958 equations do not exhibit a pattern consistent with the 1953 equations, it does not negate the hypothesis Of curvilinearity over the longer span of time. The conclusion is that an appropriateocurvilinear -112- model could be expected to fit the 1953 combine data somewhat better than the linear models used here. The simplest equations containing only age as a variable can also be used to support the author's early contention that pull type and self propelled combines should be examined separately. Using the covariance method of determining whether regression equations are significantly different (as was done previously in comparing 1953 and 1958 equations) the pull type and self prOpelled equations for both 1953 and 1958 were found to have significantly different b values-- at the .05 and .01 levels respectively. Realized Net Farm IncomevaNFI) This variable was significant at .05 for 1953 pull type, 1958 pull type, and 1958 self propelled combines in both the Y1 and Y2 formualtions, it was significant for 1953 self propelled combines in the Y2 form, but not with Y Even though it appears 1. to be rather significant, the RNFI variable was dropped from the equations recorded in this chapter. The reason for its omission is that the variable takes on a negative sign in all the 1958 equations. Theoretically the sign for RNFI should be positive as it is in 1953. A negative sign is unacceptable as it says that with more spendable income farmers pay less for used combines.Some sort of a rationalization might be developed to explain a negative RNFI variable if it were neg- ative in both 1953 and 1958. However, there is no reasonable -113- way to explain a positive sign in 1953 and a negative sign in 1958. Mags As noted earlier in this chapter the aggregate of EEEE variables was usually significant. Also noted were those makes which were significantly different from zero in their effect on used combine values. In this section EEKSE are examined in greater detail by using a t-test to determine which ones are significantly different from one another. The summary and conclusions of these comparisons are presented here. By way of a general comment, BEES seems to be a more important consideration in the second five years than in the first five years of machine life. This concept was first suggested by the fact that the aggregate of make variables is less significant for 1958 pull type combines than for 1953 pull type combines, as measured by an F—test. A comparison of the standard error of estimates for each year ( l, 2, 3, ---, 10) from 1953 pull type combine equations Y = f (Age) and Y1 = f (Age, Make) also seems to support this 1 suggestion. 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Home. moms. mesa Haze wmma ones. mmwm. ..... oooe. Hmoe. eeHHeeoem camm mmmfi mmmo. ammo. mwwe. meme. mmoe. - meme Haze mmma emmeeee -quz .om Amm.mxez+ww pcmocmmmo on» mo mCOHpmHSELow mw pom w on» now modam> n Comzpmo mmocohoMMfianllmm mqmeeo $2.: R:.: &:.: &:.z &:.z &:.: a:.: $3.: &:.: Rm.mm am * .cum. Ilamooz pmmcflq moam>chammoq mammow Rm.mm Rm.:m xm.mm &o.om &N.mm aa.wm &m.m: &o.m: R:.mm sm.m© mm * .cvm Ilamcoz Lmocfiafi>mso &H.mm &m.wm Rm.om em.mm fin.mm &H.:: em.m: &m.mm Rm.>m RN.H© Hm * .cam Ilamooz pmmcfiq mmzaw> mmmpcmopom OH m m 5 m‘ m a m m H coapmsvm mummw :H mw< ~126- m.Hm can mm mCOHpmsvm Song oopsosoo emocHoEoo camp HHSQ mmma pom Apmoo HmcHwfiho Mo pcoopoo m mm npoov :m:am>lcfilmmoa= mahwmm paw moam> pom: go mwpmaapmmlllmm mqmpzo Hoe .cem _ N. Amchom mwmpCmopmm QHV l. _ OH . i .m... m x w w m z m . m H COHpmem mummy .mocHnEoo comp HHSQ mmmH pom HmooE pmmcHHH>nzo m IIme COHpmsqo pom AmsHm> ommeHpmoluosHm> Hoopomv mesonmh mHnwom mwwhm> ome on» mo poommm one m.Hm m.mm p.02 3.3m H.mm ecccaq mmmH me .eam o.mm e.mm m.m: m.mm m.mm acacHHH>9so wmmH mm .cem c.0H 0.0m m.mm :.mm w.mm o.mm m.m: o.m: m.om m.mm accch mmmH me .cam e.mH w.Hm m.mm m.wm m.mm H.em m.H: m.c: m.Hm c.0m acccHHH>aao mmmH Hm .cem 03Hc> 600: ecemeHcmm e.e e.e a.» e.e m.em accceq mmmH me .cam o.m e.©. :.w H.0H H.0m ceccHHaeaso wmmH mm .cam m.: m.: m.: m.: m.: m.: m.: m.: m.: m.:: ammcHH mmmH mp .cwm HHm :.m s.m m.m m.z m.: w.: m.m m.m :.m: nmmcHHH>pso mmmH Hm .cam msHm> CH mcHHomQ anmmw OH m m e m m a m m H eczema cue H0602 mw< Qo mhmww 0.mw 6cm Hm.me.me a chHpcaac Eonm Umpsqeoo .mpmpmo>pm£ mwmpoe now Apmoo HmchHpo mo ucoopmn m mmv msHm> pom: empwEHpmm paw Humoo HmcHwHao mo pcmopmn m mmv msHm> CH mcHHomo thmmwlulwm mqm¢e -155- Even though the curvilinear model provided a considerable improvement in fit, there remains evidence of unexplained curvilinearity in the average residuals. This is no doubt due to the mathematical restrictions of the squared term. (Table 28) Note that along with the familiar pattern of variation, there is a slight overestimation of the values for the last two years. In general, the particular curvilinear model used here seems to be a closer approximation of the "loss—in-value" function, but does not completely eliminate the pattern of variation from the regression estimates found in the linear models. Summary Used forage harvester valuess are closely related to the age of the machine, even more closely than used tractor and combine values. In fact, age was capable of explaining 81% to 89% of the variation in used forage harvester values, as given in current dollars, and 84% to 91%, as given in constant dollars. The used values for forage harvesters were slightly effected by both realiaed net farm income and numbers of liver stock on farms. In both cases the relationship was significant -156- mw.ol H:.ot :m.o am.H oo.m sm.Hn mn.H| ow.o| ms.o m>.o Lopmm>hmm emancm mmmH OH m w a m m n m m H mnHaowz ow< mo mpmow .mhmpmm>nmc owmnom mmmH pom HoooE nwocHHH>hdo .Hwe COHpmsvo mom AmsHm> oopmsHpmwlmsHm> Hm5pomv mHmsonom anmoz mwmho> pom: oomeHpmoaosHm> pom: HmSpom- mHmsonoa mewom owmpm>¢nllmm mqm mm.w am.a HH.: am.a oe.HH oe.m Ha .com --Aomav one AH- AmchoQ owMucooLoQ CHV :omeHpmm eo sophma 0H m w m. a 1M) 7m mm m H COHpmSUm ow< momwmow . oxmz .mw< m u H% pom ow< m n H% mom mooHpmsvo COHmmmmmop A v A V Eonm oopSQEoo own mo pooh zoom on ompmHop opmermo mo Hogan onmocmpmlulom mqm<9 -179- This seems to occur in 1960, but would not occur at all if the differences in values for makes were really a constant over time. There seems to be a reasonable explanation for the effect of make varying as a function of time. Certainly time would be required for dissemination of information about the various makes. Engine Driven The 1953 equations indicated that there was a significant difference in value between engine driven and comparable PTO balers. The engine driven units appear to be worth about 6.0 points less in percentage value than their PTO counterparts. However,this does not seem to be the case with the 1958 models. The significant effect of engane driven for 1953 equations and lack of significance for 1958 seems to support the hypothesis advanced to explain this same condition for pull-type combines. The hypothesis was that engines either deteriorate more rapidly than the rest of the used machines, or are the object of greater ‘uncertainty to the potential buyer as the machine becomes older. Since the introduction of engine driven alters the b values for Inake as given in the equation without the variable, it may be clifficult to see the relationship between the two equations. m -180- The author found the following table useful in examining the relationship between engineidriven and_make variables. TABLE 3l—--Estimated percentage values (used value/new cost) for each make of 1953 balers at six years of age (1959), as estimated by regression equations for Y = f (Age, Make) and Y = f (Age, Make, Engine Driven.) Y=f (Age,Make,Engine Driven) Y=f (Age,Make) Make Engine Driven PTO Allis Chalmers 39.53% 45.69% - 43.21% Case 25.10 ----- 25.35 John Deere 29.11 35.27 32.28 International Harvester 31.31 37.45 34.63 Massey Harris 33.77 ----- 34.00 New Holland 34.81 ----- 35.04 Oliver 29.23 ----- 29.46 Minneapolis Moline 31.16 ----- 31.39 Livestock Numbers Since balers, like forage harvesters, are tied to the livestock industry; it seemed only reasonable to try live— stock numbers as a variable. It was not significant in 1953 model baler equations. With 1958 models it was significantly different from zero at .01 level, but its use caused the constant —l8l- (”a" value) to become a very large negative number. In addition, the b value for age is nearly doubled. This situation is undoubtedly the result of a very high intercorrelation between age and the 1959-1963 data for livestock numbers, 0.98608. There is probably good reason to believe that used baler (and forage harvester) values are little affected by marginal changes in livestock numbers. New Models The results of the new models variable for 1953 equations are believable---each succeeding model causes a greater decrease in value of the original model, until another new model is no longer important———but the outcome of the variable was unrealistic for the 1958 equations. For the 1958 Y2 equation the sum of b values for new models was positive (2.025) and only slightly negative (-0.089) for the Y equation. 1 (See Chapter III and IV for discussions of the possible problems involved with this variable.) Twine, Wire-Tie The variable pm;me, used to measure difference in value between wire and twine-tie balers, was not included in the final equations. The b values were significant and positive for all the 1958 equations. The b values for the 1953 equations were not significant unless new models was also a variable,' Then —l82- it was significant and negative. Apparently, some of the influence of this variable was associated with new models. In general, the variable seems to give no clear-cut answer regarding any difference between the values of twine-tie and wire—tie balers. Inflation Inflation of new baler prices (Bureau of Labor Statistics wholesale price indices) was approximately 1.7% per year from 1953 to 1963 and approximately 2.5% per year for 1958 to 1963. Quite logically, the effect of inflation on the b values for age was greater for 1958 equations than for 1953 equations—- an average numerical increase of 0.55 and 0.33 percentage points respectively. A yearly change in b value of 0.33 seems relatively small, but at ten years of age inflation accounted for about 25% of the machines's value. The only method of measuring the contribution of inflation —-—an F-test is not applicable as two separate equations are involved—-is to observe the amount of variance which is explained by the variables in the Y2 equations as compared to those same variables for Yl equations. As before, comparable R2'S indicate that a substantially better "fit" is obtained from enquations computed for the Y2---"constant dollar" —- formulation tharlfor the Yl-flcurrent dollar"-—formulation of the dependent ‘variables. On this basis, one can assume that inflation makes _183- a worthwhile contribution toward understanding used baler values. Curvilinear Model The curvilinear model was a significant improvement in fit over the linear model, at the .05 level, as measured by F—tests. A comparison of the used value estimates of the two models, Y = f (Age, Make, Engine Driven) and Y = f (Age + Age2, Make, Engine Driven)—-1inear and curvilinear respect- ively——is given in the table on the following page. As compared to the better estimates provided by the curvilinear model, the linear model is shown to have over- estimated the initial drop in value, underestimated the next few years "loss-in-value" and overestimated the later years. Even with improvement offered by the curvilinear model, a patt- ern of variance from the regression curve still seems to exist. 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OHHNO mpmoo mHCmCoCzo Hmpoe uuuochooz 302 HHO oncoHonHo0em0O HON + 0cHH HHOHOCOO —224— With this example, the equation estimated the difference in total ownership costs, between a new and a one—year-old machine (each used nine years), as $542 more than was cal- culated by the depreciation method. It was no doubt observed in Table 40 that total forage harvester ownership costs, for the ten year period, were small— er if the computations were based on the estimating equations, rather than depreciation schemes. Table 41 illustrates that accumulative ownership costs computed by this method were less than those given by depreciation schemes for even shorter periods of time. Note that total ownership costs for a 1956 tractor, baler, and self propelled combine as measured by the estimating equations---were less than those given by "sum of digits" and "declining balance" methods by the end of the fourth year, less than "straight line + 25%" by the sixth year, and smaller than"straight line" method by the eighth year. (Examples from pull-type combines and corn— pickers could have been used equally as well to illustrate this phenomenon.) This application of the research find- ings leads directly to the second conclusion. If one looks at the average yearly ownership costs for different periods of use, (Tables 42 and 43) it is discover- ed that estimates based on the research findings are higher mONH omHH HOOH OHH OOHOHO 0o eon OONH OOHH OOOH HNO 0000H0m OchHHotn OONH HOOH OOO NHO HON + 00HH oOmH000m OONH OOOH OOH HOO .000O ocHH OOOH00OO NOOHO HHm O OHH O HNO H coHpnaom 000cHH n-1OOHHH . 00Hcm OOO =OO= OanHoO :02 OOmH--- OOHH OOHH OOOO ONHN OOHOHO 0o aam HHOH OHOH OHOO OmON 0000Hnm wchHHoon OHHH HNHO OOOO NOON HON + 0OHH HOOH00HO OHHH ONOO OHON HOHH .000O ocHH occh0om omOOO HNOOH mOONO OmNNO coHucoom 0000HH ---OOmHO . 0OHOEoO O0HH00o0010H0m :OH: 0000O anoO OOmHuuu OmmN OOHN NHHN OOOH OHHOHO 0o Sam OHOO OHON OOHN OHmH 0000Hnm wchHHoon OHOO OHON HHON OOOH HON + 00HH HOOH00OO OHOO NHHN mOOH OONH .000O 00HH oan000m ONNNO 1- ONONO :HHOHO OOOHO coHpcaom 0000HH squOOOO . 0o0000e =OOH= HHOE000 OOmHau- OH O O H COHpmpsQEoo 000: m0: 0OHCocz 009 0000» HO ©0000: .mOonoE COprHomCQOO OCO mCoHpmsoo mCHmeHpmo EOCH OmnCQEoo mm .0000» Ho 009E5C mCHOLO> 0 Com: OCoCHComE OopooHom 00H mpmoo QHCmCoCzo HOHOBIIIHH mqm<9 —226— for short periods of use and lower for longer periods of use than those computed from depreciation schemes. This should be expected, considering the high initial "loss-in-value" and the lower long-run ownership costs previously observed. The third conclusion follwos directly from this analysis. Considering conclusions 1,2, and 3; there are three apparent economic adjustments that alert farm managers might find useful. (1) Other things being equal, used mach- inery could be purchased instead of new equipment, thereby reducing total ownership costs over a given period of time. (2) The use of additional or larger machinery may be just- ified by lower than previously expected long-run ownership costs. (3) Farm machinery may possibly be used for longer periods of time in order to take advantage of the lower average ownership costs. The farm manager who is examining the relative merits of diesel and gasoline tractors will be interested in what might be termed the "hidden cost" of owning a diesel. While deprec— iation schemes do not differentiate between gasoline and diesel tractors, the research findings indicate that "loss-in-value" was more rapid for diesel units. (This may cease to be the case in the furture, as an increased portion of the farm tractor population becomes diesel powered.) This faster rate of decline HHN HON HON mHN OmN OHO OOO OOO OHO OmO OOHOHO 0o Sam OHN NON HON NHN HmN HNO OOO OmO OOH OOH .Hnm OcHeHHo0O HHN HHN HHN HHN HHN HHN HHN HHN HHN HHN 0oH00H00000O .00HH HOOH00HO L. OmH OHN ONN OHN HHN OOO HOO OOH OOO OHOH HOH .comuuH0Ooz % 0moCHHH>0Co _ OmHO OONH mHNO OONH OONH ..mONH , OOOH OHHH OOOH OOOHO mOH .com IIHoCoz CmoCHH OH O m, H O m H m m .1H COHpmpdqeoo O0czo 0H 00Heotz 0:9 0000H HO 00neaz Ho Oo000z .> HomeCO HO HO OCm OOH mCOHpmon OCO mEomem COHpmHooCQmO OCOHHO> EOCH OOHCQEoo .00pmm>me owOCOH mHHmH m 00H wpwoo QHCmCoCzo HOCCCO oww00> OCO mCoHHOCOo wCHpOEHpmm OCH Eo0m OOOCQEoo .oms Ho mOOH0OQ OCO mOCHCOmE OOHOOHOO Com mpmoo QHCOCOCzo HOCCCO owm0o>¢nllmz mqm<9 —229— is, in effect, an additional cost to the diesel owner. The following example illustrates this "hidden cost". Suppose a 1958 "D-l7" Allis Chalmers tractor that could be purchased as gasoline unit for $3200 is compared with a diesel unit priced at $4000. According to equations #5 and 7, they would have been worth $1695 and $1970, gasoline and diesel respectively in 1963. The total ownership costs for five year's use would have been $1505 for the gasoline tractor and $525 more, or $2030, for diesel tractor. Had gasoline and diesel tractors "loss-in-value" been at the same rate (gasoline tractor rate); total ownership costs for the diesel would have been estimated at $1877, or $153 dollars less than they probably were. Since the additional costs of owning a diesel model should be covered by savings in fuel costs; the diesel tractor must operate at $105 a year less than comparable, gasoline models. The "hidden costs", de- scribed above,account for $30.60 of this needed fuel savings. The farmer is often concerned with developing some measure of his net worth. Accurate estimates of the current value of his assets are essential to calculating a net worth statement. Table 44 contrasts the use of depreciation methods and estimating equations for this purpose. One will immediately notice that the only difference between Statement -230- #1 and Statement #2 is the choice of combines. Yet, the depreciation methods giving the best "total value" estimates, compared to the Official Guide column, are not the same for both statements. A closer inspection reveals that even the best "total value" estimates obtained with depreciation methods result from errors of overestimation and underestim- ation cancelling each other out. In short, the use of a combination of the five year estimating equations (for machinery less than five years old) and ten years equations is a better technique for deriving the used farm machinery values for inclusion in net worth statements. Still another application of the research findings might be useful. The tax laws have recently been changed to prevent farmers from considering the excess of the sales value of farm machinery over its depreciated value (as shown on the tax forms) as capital gains. Since this excess is now taxable as regular income, the farmer may wish to know how the market value of his farm machinery compares to depreciated values over time. With this knowledge he would be in a better position to balance the gains from rapid "write-offs" against future tax liabilities, and choose a depreciation method that best fits his tax strategy. Table 45 contrasts estimated market values from linear equations with deprec— iated values computed by different methods. The negative -23]_- .Omm: mm: mCoHpOSOo LOOCHH 000% Coo OCO 000% O>HH Ho CoHpOCHoEoO a .m mHO.O ONO.O HOO.H HHO.O HOO.O HNH.O HHHOH HNO OHO OHO mOO OHO HOO 00o00>00m 0000o0 H000 =HH 000O OOHO0EH00O 0010o000z .0OHsO H0H0H00O 000 ao00 000OOH0 :mHlmO: OCO .OOCOHHOOOO wCHOOEHOmm .moEOCom COHpOHOOCOmO mOoH00> Eo0H OOOCQEOO HOCOCHCome ECOH mo mCOHOOCHnEoO OOHOOHOO Ho 005H0> OOOH OOOOEHpmmnIIH: mqm Umpmflompammlmzaw> umthzv mEoocH manwxmell111 OH O O , w., N O m z m m H coapmfiompgwm No Oonpmz mm: ho mummy .mms O0 mummx mo LOQESC cm>flm m memm UHom mm; pepompp mcHHOONm :mzlazz mLmEszo mflaa¢ omma O OH Amzfiw> Umpmflompgmw 1 mSHm> pmxpmev mEoocfi mapmxmp mo pcsoE<111ma mqm pmamo 0mm: no mumsflpmm poow >Lm> w mfi.owa wcflhocmfi .HmUOE mecfiafl>950 on» .mpmamp mo ommo on» CH -234- m 0.0 3.0 m.5H 0.0m m.mm .flifim m.mm m.H0 0.05 50m 0 0.0a 0.0a 0.0m 0.0m 0.0: 0.00 0.00 0.05 0.00 50m 0 m.HH 0.0a m.mm m.mm m.m: H.0m :.50 5.05 0.00 50H 0 m.mH m.ma 0.0m 0.5m 0.0m m.m0 bhm5 0.50 0.00H 50 m 5.HH m.HH m.mm 0.0m : m.mm 0.05 50m 0 m.ma m.ma mfl0w- H.0n :Jmm 5.00 0.00 50m 0 O.OH OHOH--OhOm,.OWOq o OO, OHON 0.00. 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OOH O 0.0m 0.0m 0.0m ©u00 0.0m110.00H 50 m O.5H O5501-d1Om- O.NO c.05 OOO : 0.0m omom- 0.00 0.00 0.00 50m : O.NN O NN.-Q.OO- OJ5O 0.00. _OOH : 0.0m 0.0m 0.0m 0.m5 0.00H 50 : m.mm 04mm mumm 0.05 50m m 0.0m m.mm m.mm 0.00 50m m 0.0m -0.0m 0.00 0.00, 50H m m.mm m.mm 0.0m 0.03 0.0 m 0.0m 0.0m 0.05 50m m 0.0: 0.00 0.00 00m m 0.0: 0.00 0.00 50H m 0.00 0.00 0.00H 50 m Apmoo mo 50 psoEOmm Amgmowv .mmm go .pE< c300 hpflhdpmz 111Apmoo chflmflpo mo p:mopomv mocmamm UHOQCD111 2.0H m.mm 0.0m 0.Hm 0.0m. 0.H: 0.0: m.mm 2.00 0.00 111%pmoo Hmcflwfipo mo pcmopmmv pmfimm mgp mo mzam>111 0H .. m w 5 0 m a m m H 11‘,».|o‘ ‘1 .Aswofl H0000 opp mo 0000900 0 mm 0008me mapmmz MQHUSHUCHV .mEpmp Umpomaom go mcmoa pom mommamp pflmgcs map Op ompmmgpcoo mm Amaoam cowpmsqmv mmsHm> Loamp pom01110: mqm<8 -235- Checking over the table we find the following: 1) No loan is "safely secured" the first year. 2) The year a loan is "safely secured" is not necessarily a function of its length of maturity. 3) The amount of the down payment has a large effect on when the loan is "safely secured". u) The larger the down payment and the longer the repay- ment period, the easier the loan payments should be to meet. Although not at all surprising individually, the inter- relation of these factors yields some interesting results. For example, a five—year—20% down payment loan is "safely secured" the same year as a three—year-lO% down payment loan, and the payments are nearly halved. A six-year-30% down payment loan is ”safely secured" at the same time as a two—year—30% down payment loan, and the payments are only one—third of those for the latter. In light of this information, lenders should re—examine their present practices for extending credit for farm machinery. Perhaps it would be possible for lending agencies to improve their agricultural credit services if better information about used machinery values were provided them. -236- GENERAL CONCLUSIONS This section is intended to cover only the more general conclusions of this study. More specific information on the effect of each variable is given in the summary section at the end of every analysis chapter. 552 Age, as had been anticipated, was the most important of the variables hypothesized to have an effect on used machinery values. It alone was capable of explaining from 57% to 89% of the variation in used value for the machines in this study. The consideration of additional variables, in general, does not seem to alter the effect of age. Most of these additional variables provide information which supplements that already obtained from age; The rate of "loss-in—value" associated with age tends to decline as the machine gets older. This point was illustrated quite conclusively, by the improved fit of the curvilinear models for all the machines studied over the ten year span, 1953 through 1963. Realized Net Farm Income The RNFI variable was expected to help explain the upward and downward shifts of used machinery values (as found in Table 6, Chapter II), but the results of its use ranged from a small effect to the completely unacceptable response of negative coefficients. —237- m It was somewhat of a surprise to find that it would be impossible to give a consistent l-2-3----n ranking of the different makes. Consequently the information provided by the meke variables is not very useful for predicting used values of machinery outside of the data. Nonetheless, the meke variables were very helpful for explaining used values within the data. This suggests that no one manufacturer consistently pro- duces what farmers consider the "best" machine. Instead diff- erent makes at different times seem to attract the farmer's fancy. It is interesting to note that the differences between makes increase as a function of time. This is, no doubt, consistent with the need for time to disseminate information about the various makes and models of machinery. New Models In only one case, cornpickers, did the effect of new models (as the variable was constructed for this study) appear to be reasonable for all the equations related to a given machine. In certain other cases the introduction of each new model depresses used value of the original model during one of the time spans (1953-1963 or 1958-1963), but not the other. -238- In one particular case, 1958 model balers, the introduction of several models was reported to slightly increase the value of the original model. All that may be concluded about eew models is that refinement of this variable is doubtless a necessity if consistent estimates of the effect of this type of obsolescence are ever to be obtained. Inflation The "real" values of farm machinery declined more rapidly, from 0.33% to 1.00% annually of the original value of the machine than their ”nominal" values. For example, the "nominal" value of a 1953 forage harvester in 1963 might equal 18.7% of its original cost. The "real" value of this same machine could well be only 11.8%, or 36.8% smaller than the "nominal" value. Other Variables Changes in the acreage of crops to be harvested by combines, the amount of corn that might be picked with cornpickers, and the number of livestock to consume chOpped or baled forage seemed to have little or no effect on the used values of these machines. (Combined acreage, livestock numbers, and corn acreage were all intercorrelated with age). There also seemed to be no recognizable effect on used values for such technical var- iations as different attachments for forage harvesters, one-row or two—row cornpickers, wire and tWine-tie balers, and pull type -239- as opposed to mounted cornpickers. There were, however, significant differences in "loss—in-value" between pull type and self prOpelled combines, and gasoline and diesel tractors. Used tractors of less than thirty horsepower were worth a smaller percentage of their original cost than larger models of the same age. And engine driven machines were often valued at less of their original cost than their PTO counterparts (measured over the ten year period of 1953—1963.) Estimated Values of Used Farm Machinery Our previous concepts of machinery "loss—in-value", based on depreciation methods, will need to be revised in line with the information provided by this study. (1) The initial (first year) drop in machinery value tended toward or exceeded the maximum first year depreciation allowed by the Internal Revenue Service. Loss-in-value the first year, depending upon make and machine is apt to be 30% and greater. One est- imate, for 1953 cornpicker models, was as high as “7%. (2) Yearly "loss-in—value" (with the exception of the first year) is usually less than assumed with depreciation schedules. (See Table 39, Chapter VIII). (3) The so-called "salvage" value (at ten years of age in "current dollars") was estimated to be roughly two and three times the traditional 10% for self ~2u0- propelled combines and tractors respectively. Estimates of the tenth year value for pull type machines also exceeded the 10% figure, by approximately 5% to 8%. In "constant dollars", a salvage value of 10% is still too small for tractors and self propelled combines, but is a reasonable estimate for pull type harvest machinery. 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coma ooma ooma coma mcce ammo: mcn< mamce xaozmccc -252- m.m: m.cm m.mw .©.om m.mc mm :om: m.m: m.cm m.mw m.ow m.mc o: :02: c.om m.cm m.:© o.oc m.cc II :mm: m.oc c.ao c.co o.co c.cc cm =cm= pcccmxcoc c.oo o.mo c.oo c.mo nu co =cacmEnoncmcc aac: m.mm m.H© m.mm m.mm II m: :HHN: c.co o.co c.co o.oc nu cmccachnonmmcc maao= m.co c.mo c.mo o.oc II H: :mHHm: c.co c.mo c.oo c.ac uh am =caccEnoncmcc ccc: c.oo c.ao m.oo c.cc nn am =mccmz c.mo c.co c.ac c.cc nu om =maam= mmcc m.mm H.OQ m.mm H.w© m.cw o: :m2I03: m.co m.:© w.mw :.m© ©.ww w: :NHIQ: H.mm O.Hm c.ao m.co m.mo mm zzauQ: m.oa m.m: m.mm 3.00 m.mm 2m : Ummbnnanm mamgcm accoacccpmpca c.co c.oo c.co c.oo nn ac =aom= a.ao a.mo o.co c.co nn cc =acc= c.oo c.mo m.co a.oo nn mm caccc c.mo m.co o.oo c.co nn ac cacoz cpom a.oo c.mo c.ao nn nn mm com: cowscpcm o.co o.co m.co o.mo c.cc co =cmc= a.mo a.co c.mo c.cc o.cc mc =cmo= a.oo c.co m.co c.co c.cc cm =cco= c.co o.co c.oo c.mo c.co om =cmc= a.oc c.co o.oo a.mo m.oo nn =cmm= mummc czoc coma moma aoma coma moma .c.m ammo: mac: a.o.psooc anm mamce caczmmmc -25u_ c.mo c.oo c.co c.co nn co =caccEnonmmmc acc= c.co c.mo c.co c.co nn cc =acc= o.co o.mo c.mo c.mo nn mc =cccc= cmcc a.cc c.oo a.co c.co o.oo cc ocnczc c.co o.mo o.ao c.co c.oo cc =canc= mamEaccc maaac qmcmac m.cc c.ao c.oo c.co o.co un =mm= c.co c.co c.co a.co c.co co =cc= amczc c.oc m.co m.co o.co c.co cc =cc= pmccc acco c.oc m.co c.co m.oo cc zoo: pmcsc m.ac o.cc c.co o.ao c.co mm =coo: m.cc m.oc m.ao m.co o.co am =oo= pmcsc c.ao c.cc c.co o.co c.co nn =cc= meSc cm>aac nn nn nn nn c.mo oc =cc omcc cc: o.co m.co c.mo c.co c.oo co =mc= c.ao c.oo a.co o.co c.co nn =coo= o.mc c.co o.oo o.mo o.cc ac =occ: c.co c.cc c.co m.co c.cc mc =2omm= o.cc m.oc o.mc c.co o.oo am =omc: mcaaoz maaocccccaz coma coma aoma coma moma qmccz mccz .m.m a.o.pcooc anm chcc caczmccc -255- II m.mm mofim II II NF zzwmmz m.oc c.mo c.co c.co a.co ao ..mm= m.m: m.Hm m.mm m.mm w.ww om =®®= c.cc m.co c.co a.mo o.co cc =cc= o.cc a.co c.co c.mo o.oo cc coo: mc>aac II II II II m.ow ll :mD= a.cc o.co c.mo c.oo a.oo co coonmcz ccaaoz maaoccmcsaz o.cc a.oo c.ao m.oo c.mc cc =ccc= a.oo o.oo a.ao c.oo c.cc mm =mmm= mammcm mcwmcz a.oc c.oo o.ao m.oo c.cc nn =coo= o.co o.ao m.co o.co a.cc oc =coc= c.mc a.ao m.oo m.oo o.cc cc ..com= mmcmc>mcm accoapccmmpca c.mc c.co c.co c.oo c.mc om =cauczm= cmom c.mo m.oo o.co c.co m.cc co =ccc= cmmmm cmoc c.mc o.co c.co c.co c.cc cc =co= c.co c.co m.co c.mo o.cc nn =caccm sccaocc $.33 m.om H.mw 3.50 3.MN O: :03: PUZCWXOOO coma coma aoma coma moma .m.m mmccz mmmz A.U.pcoov Him mamm 3.0m m.m0 m.:0 08m .0 :NN:: PpSQmXOOQ m.mm 2.0: m.mm m.mm H.00 mm .m :0HH: II II m.mm m.m0 5.50 mm .N. ..NN... m.mm m.om m.mm :.m0 0.30 08m .N :55: ll IW m.:m m.mm 5.00 mm .5 :m5: m.NN :.mm o.om O.mm ll 08m .5 :m5: ,m un nn c.cc c.oo o.co mm .o oo= x” a.mc c.cc c.mo o.co c.co cam .o =oo= _ c.ac c.cc o.ao m.oo m.oo cam .o coo: mmmc m.mm 0.0: 2.5m m.:0 N.N0 OHm .N\H b :00: II II o.mm m.m0 0.00 mm .0 Cam me =00: H.0m 0.0: H.mm m.m0 Hum0 OB&.0 Cflm me :00: mhmEHmflo mHHH< BmOO BMZ m0 mwfiBzmommm mmMB 443m m0mH N0mH H0mH O0mH mmmH mmwB AMQOE MM¢S m¢mw Ac on momma.n.o.mv mmoo 3m: mcmnm mo mcmomma CH mmcHnEoo HmUoE coma mo m®5am> Ummbquwm mqmcac II II :.:m 3.00 2.00 Um.w :mw: c.cc c.cc c.co c.co c.oo cec .c =cc= c.cc c.cc c.co c.co c.co cm.ca =ccanc= mcaaoz maaoccmcsaz nn nn c.co c.ao o.co mm .c cmcccaac co: c.cc c.cc m.co c.co m.co cam .c =mocmfiac co: nu nn c.co c.co c.oo mm.o cmmmmaac co= m.oc c.oc c.co c.co a.oo cmm.o zcmcmaac co: a.cc c.cc o.mc c.oo c.co 09m.c zemcoz nn nn c.cc m.mo o.co Qm.c =Bmoo= cowswmmm cmmmmz c.co m.cc c.co c.ao c.co oem_m =ccc= un un c.co a.co a.co cm.m =cca= c.cc c.cc c.co o.mo c.ao oem.c =oc: nn nn c.ao c.co c.mo cm.c =oc= pmpmm>mcm Hmcocumcmmch coma coma aoma coma moma mmce mmccz mac: Ac.ccocc HHnm mmmce xamzmmmc -258- .mmwmmn mnp mo nmwcz mgp om mmmmmm .wcnnnn.o.o vcm mmomxwp mmzoa mc 09m .cm>cmo mccwcm mc om "mLmQB c.o: m.cc m.co o.mo m.co .oc :om: mm>cco 2.2m m.mm 0.02 2.mm m.mm .MH :w0Hlmmm= m.mm N.M2 c.mo 2.H0 m.c0 .mH :w0almm: mccaoz mccoammCCHE 2.0m 0.0m m.mm 0.20 N.H0 .NH :mm: m.oo m.m: m.co o.co o.co .oc =mw= o.mm m.02 m.co c.mo 0.N0 .OH :00: Comswpmm hmmmmz 2.02 N.Om N.0m O.N0 ll .mH :HmH: m.mm m.cc m.co c.mo c.mo .oc :Hccz a.oo 2.mo 2.0m m.m0 H.m0 .OH :HOH: memm>hmm Hccocmmcmmch 0.mm w.Hm m.mm II II .le.2H :mm: .N.02 2.50 N.H0 2.m0 0.N0 .2HI.NH =mm: c.cc c.oc c.co c.ao c.co .can.c =oc= mpmcm cmoc c.oc c.co c.mo c.co c.co .ca =ccc= c.oc a.cc o.oc c.oo c.co .ca =ccc= upcnmxcoc 6.2m H.Hm N.00 m.m0 m.mw .OH :OmH: mmwo m0mH m0mH H0ma o0mH momc mmwB ammo: -.c_pcooo amnm mamce mamzmmmc -259- nn nn c.cc a.cc o.co ccncm =occ= nn nn c.cc c.cc c.co ocncm =occ= nn nn c.cc c.cc c.co cmncm =occ= a.cc m.mc c.oc c.mo o.co ccncec =ccc= c.cc c.ac o.cc c.ao o.co omncem =ccc= o.cc m.cc c.cc a.ao c.co cmncem =ccc: c.cc o.cc c.cc m.cc nn coacmm =cac= c.cc m.cc c.cc c.cc nn omcomm =cac= o.mm o.cm o.m2 m.cz II smIOBm zmcmz o.cc o.cc o.oc c.co nn ccncem =aac: c.cc c.ac c.cc o.co un omncem =aac= o.oc c.ac c.oc o.ao nn ccncem =aac= mmmc un nu m.oc a.co o.co omncm nn nn nn o.cc c.co a.co cmcccncm nu c.cc c.ac m.cc c.ao o.mo omncmm nn c.oc c.mc a.cc m.co c.cc smcccncem nn mmcEaccc maaa< cccc 3mz mc mccmzmcmmm coma aoma coma moma mmce mmccz mccz mcmc Aoo.un.o.mv mmoo 3mm pcmgm mo pcmomma Cc whommm>mmn mwmmom HmUoE womc mo mmdcm> UmmDIIHHHnm mqm2 c.co 0.00 omlom zom: II II 2.02 c.mo 0.20 nowdmlam :om: c.om m.o2 o.02 H.0o 2.20 omIOBm =om: m.mm 0.mm 0.02 N.0m O.H0 nowSmIOBm :om: Cowswhmm zmmmmz II II 0.m2 m.co m.m0 DOIQm :Olom: II II 2.02 m.mo m.m0 omlmm :Olomz II II c.oo 0.mo a.c0 zmnam :onomz m.mo m.o2 2.oo o.mo m.o0 nonoem =onom: 2.0m 2.o2 m.co 0.mo m.o0 omIOBm =OIom= H.O2 0.52 m.mo o.m0 m.m0 zmloem :OIom: hmpmm>hmm accocpmcmmch u ...H cc 2m ”3 E. .... 0 00 N0 no em II II 0.52 m.mo 0.00 omlmm II H.O2 m.m2 H.mm m.m0 m.m0 QUIOBm II H.mm m.c2 o.m2 m.mo o.o0 omIOEm II m.mm m.M2 m.m2 m.o0 5.00 SmIOBm II Hnmo m0mH m0mH H0mH o0mH mmma mmwB ammo: mmaao nn nu c.mc o.co un nonmm zcccz nn nn c.mc c.co nn omnmm =ccc: nn nn c.mc c.co nn :mnmm =ccc= c.ac c.oc c.mc o.co nn ncnoem =ccc= c.ac c.oc c.mc c.co nn omnomm =ccc= c.ac c.oc c.mc c.co nn smnoec =ccc= un nn o.mc c.co c.ac nonmm =aco= nn un o.mc c.co m.cc omnmm =aco= nn nn o.mc c.oo o.cc :mnmm =aco: m.oc c.cc c.mc m.co c.mo ccnoem =aao= a.oc c.cc c.mc c.co c.mo cmnoem =aao: c.oc m.cc c.mc m.co c.cc smnoem =aao= cacaaom 3m: coma coma aoma coma moma mcce ammo: mac: Ac.pcocc aaanm mamcm aamzmmmc .pcmesomppm.mmnmmpp50 mmmeaoca no new .pcmecompmm @090 30a mmmcoanca om .mcmenommmm azaoam mmpmoaUCa 5m .cmomxmp pmzoa ma 09m .cm>am© mCamcm ma mm .mLmSB nn nn a.o2 c.co 2.o0 ponom =cm: II II m.22 2.50 2.00 OEIQM :Nm: un nn o.mc c.oo m.mo smnmm =mm= 0.02 0.02 0.02 m.m0 2.00 DDIOBm =Nm= 0.N2 0.02 2.02 m.m0 2.00 omlOBm :NQ: c.ac c.cc c.oc c.mo c.oo smuomm =cm= cmmcm m0ma coma a0ma ooma moma mmwe ammo: macs ac.ccocc aaanm mamce aaczmcmc nn nn c.cc c.oo c.co gumm =3ncac= a.cc o.cc m.cc c.oo c.co znoem =3ncac= nu nn o.mc c.oo m.oo mnmm =encac= o.cc o.cc c.co c.co c.oo encem =mncac= nn nn c.mc c.oo m.co mncm =,anca= m.oc c.cc c.ao c.oo c.co mncmm cancac mpmmc acoc o.oc c.cc a.oc c.co nn zucem coca: nn nn c.oc a.oo nn 3nmm =oca: c.mc c.cc c.cc c.co nn zucem =3coa= nn nu c.cc c.co nn :ncm =3coa= o.mc m.ac c.cc o.oo nn mncmm =m.coa: nn nu m.ac c.oo nn encm =m.coa: c.oc c.cc a.cc c.ao nn zucem =3cca= . nn nn o.ac c.co nn :ncm =acca= m o.ac o.cc a.cc c.mo o.co ancmc ..cca= . nn nn o.cc o.mo m.oo mnmm cccac mmcc nn nu c.mc m.ao o.mo mncm =cecmc c.cc a.cc c.mc c.co o.co encem cceccz mmeaccc maaac eccc 3m: mo mccezmcmmc coma coma aoma coma moma mmae amcc: mac: Aco n mocha .p.o.mv mmoo 3m: mamgm mo unmommg Ca mamamp amUoE woma Mo mmSam> UmmDII>HIm mam<8 xHszmm< -266- c.cc c.cc c.co c.mo c.cc encec cmccp aacc= czaao: maaoccccca: o.cc o.ac c.cc c.ao a.mo encmc =c= II II 2.22 N.O0 m.m0 BIQM zm: c.cc c.cc c.oc o.co c.oo mnoem ca: nn nn c.oc m.co c.oo mnmm =a= mappcm :mmmc: nn nn m.cc c.co o.oo gumm =3noo= c.cc c.mc o.cc c.mc c.oo :ncem =3noo= nu nn c.oc c.co c.co enmm =mnoo= m.oc c.oc c.oc c.co c.co enoem =mnoo= II II 0.02 m.20 0.20 Elam :Bl02: m.M2 N.M2 m.m0 0.00 m.m0 BIOEm :Bl02: nn nn c.cc c.co c.co mnmm canoc= c.cc o.oc c.mc c.oo c.co encec canoc= pmpmm>pcm accoacmccmpca o.cc c.cc c.co m.co c.co enoem cccncac =coc= II II ©.Nm :.H© m.N© Elam :HNIJH: zomN: nn nn c.cc o.oo a.co cnmm =mcnca= ccom II II N.52 0.20 $.50 Elam :NHlm: m.ca c.oc c.cc c.co a.oo enoec =canm= comcmpcm coma aoma coma moma mmce ammo: AU.pcoov >Hlm mamamc mcawcm ma om .mmmnz m.mm 0.mm a.o2 a.co nn zloam =3uo0= II II m.o2 c.mo II Blam :3Io0: nn nn m.oc a.mo c.oo 3nmm =oca= nu nu a.22 c.mo c.20 atom :00: c.mm o.02 m.22 m.mo o.20 Enoem =00: cam>aao In In 0.o2 0.mo m.00 znmm :mm: o.om c.cm a.w2 0.2o m.c0 Buoem zcm: II In c.m2 o.0o m.ac zlom =cm: a.oc c.oc c.co c.co o.oo encmm =cc pmccc= nn nn c.mc c.oo c.co enmm ccc mmmzm= c.oo m.oo m.mc m.co 0.00 Enoem :00: II II 0.m2 2.00 m.00 Elam :00: nn nn o.co c.co m.oo encm =oo mmmscc m.m2 m.02 c.mc o.0o 0.c0 Enoem =00 mmmsm: unmaaom 3mz m0ma m0ma a0ma o0ma moma mmwe ammo: mac: Ac.csocc >anm mamce aamzmmcc -268— 0.0m 0.5m m.02 0.20 m.m0 ml.Up2 :222 w mmm: a.ca c.oc c.cc c.oc o.co a n cc =a= comccpmm :mmmc: 0.0m 0.m2 0.52 2.00 0.20 ml 092 :omlzm 2m: 0.2m 0.2m 0.22 II 0.20 HI Uuz :0HION: 0.02 m.m2 m.mm 0.N0 2.m0 N I pm :mmlm: m.mm m.22 2.02 2.H0 m.20 H I am :mmIHz hmpmm>hmm accoapmcmmmcH N..02 0.02 N..20 0.00 0.00 N l 092 =00|0H: 0.22 0.00 2.00 m.00 0.00 H I 692 =00I0H= c.cc c.cc o.co c.co c.co a n pm =cnoac cpom N.O3 H.mm Nowm m.mo m.mo N I UPS =NNN: 0.0m m.m2 0.H0 H.m0 o.m0 H I Up: :NNH: mhwmo CQOh N.H2 N.02 0.00 0.00 II N I 692 :0N2: O.Hm 0.0m 0.22 m.00 H.O0 m I Up: :om2: 0.22 m.00 0.02 0.00 0.00 H l pm :mm: m.m2 0.20 0.00 0.00 0.20 H I am :m: mmmo 2.0m 0.02 N.20 m.20 II N I 092 :NH: N.0m 0.02 H.02 0.00 0.00 H I um :0m: ®.H2 0.02 0.00 0.H0 2.20 m I .092 :mm: mhwsHmnv mHHH< E000 3mz m0 madezmommm m0mH m0mH H0mH o0mH mmmH mmwB ammo: mm UmeII>Im mqmde xamzmmm< -269- 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ponlmmmpmm>mwm mmmmom map mAaz mom cc 3 van map mcazp mom ma BIImmmamm smoaz mmvmmn om mmmcmm .2aIIII5IImm2anEoo ”mom 0cm chomxmp mm3oa mmmmoavca Gem "mmms3 nn o.cc o.cc o.ac o.ac c.cc m.oo o.co m.co c.oo cnpm =cmamsc= ccaao: maaommeCHZ nn o.cc m.cc c.cc c.oc o.oo c.co c.co c.mo a.co cncp: =oonoa= cuom nn a.cc m.cc c.cc o.cc c.co c.mc o.mc a.mc m.co anec =mm= mmcc cmmacac zmoc a.ac o.cc o.oc c.mc c.oc c.cc o.cc c.co c.oc c.oo cm zcnccz mmpmm>pcm ammoapmcmmmcH m.ac c.cc c.cc c.ac a.oc o.cc o.co m.oo nn nn cc =cconm= aom a.oc c.cc c.cc c.cc o.cc c.cc c.oo a.co nn c.oo cm nn anmc c.oc c.cc c.cc c.oc o.ac c.cc c.oo o.co c.co nn cc =cm= ccccm ccmecm>mcm mccmcm c.cc c.oc c.mc c.cc c.oc c.cc o.oc c.mc m.co c.co mncmm =co= pc>aac ooma ooma Icoma coma coma aoma comannmoma coma coma cmcac ammo: mac: ac.ccocc auc mamcm aaczmmmc [l] [2] [3] [A] [5] [6] [7] [8] [9] [10] BIBLIOGRAPHY Public Documents U.S. Department of Agriculture. ,Farm Cost Situation, PCS—35, November 1963. U.S. Department of Agriculture, ~Farm Cost Situation, _FCS—36, November 196“. "' U.S ~Department of Agriculture. Agricultural Statistics, 1963. W ; fl U.S. Department of Agriculture. Agricultural Statistics,L 1965. ' U.S. Internal Revenue Service. Farmers Tax Guide, 1965. Books Doane Farm Management Guide, (Doane Agricultural Service, Inc., St. Louis 8, Missouri). George W._Snedecor. Statistical Methods,(Ames, Iowa, State College Press). Periodicals and Articles Leonard R. Kyle. Michigan Farm Business Report, (Michigan State University Experiment Station; Research Report, No. 30, 1963). National Farm Power and Equipment Dealers Association. Official Tractor andgFarm Equipment Guide, (St. Louis, Missouri, Spring, Eds. 1953-1966). National Market Reports, Inc. National Farm Tractor and Implement Blue Book Valuation Guide, (St. Louis, Missouri, Spring, Eds. 1953-1966). -272- MICHIGAN STATE UNIVERSITY LIBRARIES I! III II uninmm 3 42 8 56 In“! 1293