I A FAMIW WWAW OF THE W ‘YOWNSHW WEWN macaw IN DINMARK TOWW WW 7H? MEN) 1953 TO 1958, UM CW ARMY!“ M kw H» Door» an! M. S. MICHé-GAN STATE UNIVERSITY Wiliiam Ross Bolgor I959 .zV'YY- Y‘,“ I ------ “It“. LIBRARY Michigan Stan University A PARIIAL EVALUATION OF THE MICHIGAN TOWNSHIP EXTENSION PROGRAM IN DENMARK TOWNSHIP OVER m PERICD 1953‘ TO 1958, USING COBB-D OUGLAS ANALYSIS By William Ross Bolger AN ABSTRACT Submitted to the College of Agriculture of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Economics 1959 Approved by ’ g gage L 43;. can L— 1 Vi lliam Ross Bolger ABSTRACT The ultimate objective of this study was to ascertain whether the Michigan township extension program was more effective in increasing the efficiency with which resources were used on cash crop.farms in Denmark township than was the traditional county extension program, over the period 1953 to 1958. To achieve this objective, experimental farms (those serviced by the intensive township extension program) were matched with control farms (those serviced by the traditiona ' al county extension program) on the basis of certain criteria, calculated to insure that the only difference between the experimental and control farms was the greater amount of "on the farm“ assistance which the township agent provided in the case of the experimental farms. Cobb-Douglas analysis and certain traditional farm management efficiency indicators were used to indicate changes in the efficiency in the use of resources. CobbéDouglas analysis indicated that the following efficiency conditions, with respect to resource use, existed: Eput Category 1253 1253 - xperimental arms - land maladjustment in adjustment labor ’ maladjustment in adjustment productive expenses maladjustment mladjustment inve me t in ad ustme t n ad ustmen - Control Farms - land maladjustment in adjustment labor in adjustment maladjustment productive expenses in adjustment in adjustment machinery investment in adjustment maladjustment ad (in fa 1‘8 00 2 William Ross Bolger In.the case of the 1953 experimental farms, there was mal- adjustment with respect to the use of land, labor and pro- ductive expenses; whereas, in the case of the 1953 control farms, there was maladjustment only in the use of land, relative to the other inputs. So, it appears that the 1953 control farms were using resources more efficiently, in.the aggregate, than were the 1953 experimental farms. However, such was not the case at the termination of the study.¢- Notice that, in the case of the 1958 experimental farms, there was maladjustment only with respect to productive expenses; whereas, in.the case of the 1958 control farms, there was maladjustment in the use of labor and machinery. Thus, it appears that the 1958 experimental farms were using resources more efficiently, in.the aggregate, than were the 1958 control farms. It should be evident, from the foregoing statements, that there was, in the case of the experimental farms, a significantly greater increase in.the efficiency in the use of resources than there was in.the case of the control farms. The analysis bears out that, although‘both the ex- perimental and control farms, at the outset, were operating under conditions of increasing returns to scale and, thus, could have increased the over-all efficiency with which resources were used by increasing the scale of operations, the Thu 3 William Ross Bolger there were no appreciable changes in the scale of operations. Thus, it becomes apparent that the significant increase in the efficiency in.the use of resources, in.the case of the experimental farms over that of the control farms was due Iggt,to changes in the scale of operations but was due, inp stead, to the fact that resources came to be used more nearly in the proper proportions relative to each other. Hence, the Michigan.township extension program was instrus mental in increasing the efficiency with.which resources were used on the experimental farms over that of the control farms, by virtue of the fact that the township agent was effective in.advising farmers as to what changes in.farm organization.could be implemented which would result in resources being used more nearly in the proper proportions, relative to each other. Insights gained by studying certain traditional farm management efficiency indicators suggested that there was a greater increase in.the efficiency in the use of resources in.the case of the experimental farms than.there was in.the case of the control farms, which is clearly consistent with the conclusion based upon CdbbADouglas analysis. It was ultimately concluded that the Michigan.towne ship extension program was effectual in.increasing the efficiency with which resources were used on cash crop farms in Denmark Township over that of the traditional county extension program. A PARTIAL EVALUATION OF THE MICHIGAN TOWNSHIP EXTENSION PROGRAM IN DENMARK TowNSHIP OVER THE PERIOD 1953 TO 1958, USING COBB-DOUGLAS ANALYSIS BY William Ross Bolger A THESIS Submitted to the College of Agriculture of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCES Department of Agricultural Economics 1959 1" _ The to Dr. J amt throughout Nielsen was Spec generously iginal mam The Mae and C Spec mate Etude: servedly, fellow grad deed appre >6; f ‘ . ACKNOWIEDGEMENTS _ The author wishes to express his sincere appreciation to Dr. James M. Nielson for his guidance and inspiration throughout the duration of this study. Working with Dr. Nielson was indeed a rewarding experience. Special thanks are due Professor WA. Cromarty, who generously gave of his time in critically reading the or- 1ginal manuscript. The constructive suggestions of Professors D.E. McKee and C.R. Hoglund were also appreciated. Special thanks are due Bill Crosswhite, fellow grad- uate student, for the assistance which he rendered unre- servedly. Thanks are also due Bob Bevins and John Lu, fellow graduate students, whose willing assistance was in- deed appreciated. .. The financial and clerical assistance rendered by the Department of Agricultural Economics were greatly appreciated. Special thanks are due Hrs. Sandra Rogers who typed the initial draft of this thesis. Finally, thanks are due the many Americans who were instrumental in making the author's sojourn in America quite an enjoyable experience. {SILAPTER I II III IV TABLE OF CONTENTS INTRODUCTION 0 e e e o e o e o o e e o e o o The Michigan Township Extension Program . Objectives of the Township Extension Program . . . . . Research Design of the Township Extension Program . . . Delineation of this Study in,Relation.to. the Michigan Township Extension.Program . Objectives of this Study. . . . . . . . . Thesis Organization . . . . . .-. . . . . GATHERING AND CATEGORIZING THE DATA. . . . . Procedures to be Followed to Insure that Conditions for the Application of Cobb- Douglas be Met. . . . Procedures Followed in Categorizing the Data 0 O O O O O O O 0 0 O 0 O o O O O O O METHODOLOGY FOR DETERMINING EFFICIENCY CI-IANGES . O O O O O O O O O O O O O O O O O . Determining Changes in Efficiency as Indicated by Cobb-Douglas Analysis. . . . Determining Changes in.Farm Resource Organization as Indicated by Changes in the Geometric Mean.Amounts of Inputs Used Determining Changes in.Efficiency as Indicated by Traditional Farm Management Efficiency Indicators . . . . . . . . Determining Changes in.Land Use, Fertilizer Use and Crop Yields. . . . . . EFFICIENCY CHANGES AS INDICATED BY COBB- DOUGLAS ANALYSIS 0 o o e e e e e o e o o o 0 Analysis of the Experimental Function, 1953. O O O 0 0 Analysis of the Control Function, 1953. Anaéysis of the Experimental Function, 195 e e e e o e e o e o e e o e e e e o 111 10 12 IA 1h 23 29 .29 38 39 #1 #2 #6 48 CHAPTER V E? TR 1:: VI O VII cc APPEEEICES A Pr fc B 34 PM w} CILAPTER VI ‘VII Analysis of the Control Function, 1958 Regarding the Efficiency with which Resources were Used by Input Categories Experimental Farms, 1953 Control Farms, 1953. . . Experimental Farms, 1958 . . . Control Farms, 1958. . . Regarding the Efficiency with which Resources Were Used in the Aggregate . Regarding the Scale of Operations. . Regarding Changes in.Farm Organization EFFICIENCY CHANGES AS INDICATED BY TRADITIONAL FARM MANAGEMENT EFFICIENCY INDICATORS. . . . . . . . . . . CHANGES IN LAND USE, FERTILIZER CROP YIEI‘DS O O O O O O O O O 0 Changes in.Land Use. . . . . Changes in Fertilizer Use. . Changes in.Crop Yields . . CONCLUDING STATEMENTS . . . . . APENDICES O Q 0 O O O O O O O O O C O O A Procedures Followed in.Preparing the Data for CobbeDouglas Analysis . . . Summary Sheet for Cobb-Douglas Analysis USE AND Hay-Pasture Evaluation, 1958 . . . Calculating Proportional Credits for Perennials Destroyed . . . Calculating Proportional Costs and Credits for Breeding Stock . . . Calculating Proportional Additions and O O O O O O O Deductions for Machinery Bought and Sold Statistical Tests to be Used When Studying Regression Coefficients, Individually as Well as in.Aggregate. . . . . . O 0 Observations Used in Fitting the Functions, Summarized by Output and Input Categories . 68 73 73 75 77 80 82 82 82 85 86 87 87 92 BIBLIOGRAPK CHAPTER Page D PROCEDURES FOLLOWED IN COMPUTING CERTAIN TRADITIONAL FARM MANAGEMENT EFFICIENCY INDICATORS................. 96 BIBLIOGRAPHY.................... 98 IUtBLE 10 ll 12 LIST OF TABLES Reservation.Prices . . . . . . . . . . . . . . Regressio Coefficients (bl's), Their Standard Errors ( bi's); "t" Values, and Level of Significance, Experimental Functions; 1953 . . Usual Organization, Marginal and Gross Value Products, Experimental Function, 1953. . . . . Regression Coefficients (bi's), Their Standard Errors (681's), "t“ Values and Level of Significance, Control Function, 1953 . . . . . Usual Organization, Marginal and Gross Value Products, Control Function, 1953 . . . . . . . Regression Coefficients (bi's), Their Standard Errors (681's), "t” Values, and Level of Significance, Experimental Function, 1958. . . Usual Organization, Marginal and Gross Value Products, Experimental Function, 1958. . . . . Regressign Coefficients (bi's), Their Standard Errors ( b1's), "t” Values, and Level of Significance, Control Function, 1958 . . . . . Usual Organization, Marginal and Gross Value Products, Control Function, 1958 ... . . . . . Comparisons Between the Estimated Regression Coefficients ( 1's) and the Optimal Regresson Coefficients (bi's), Experimental Farms, 1953. Comparisons Between the Estimated Regression Coefficients (bl's)'and the Optimal Regress- ion Coefficients (bi's), Control Farms, 1953 . Comparisons Between the Estimated Regression., Coefficients (b 's) and the Optimal Regression Coefficients (bi's), Experimental Farms, 1958. vi Page 31 #3 45 46 48 #9 50 52 53 55 56 57 TABLE Com 13 009 ion 11+ Eff sou Rd 15 Eff sou by Wit (MP 195 16 Chg Cor In; Far 17 18 19 20 21 22 23 TLABLE 2L3 1J+ 3&5 115 15’ 1&3 319 20 21 22 23 vii Page Comparisons Between the Estimated Regression _ Coefficients (bi's) and the Optimal Regress- ion Coefficients (bi's), Control Farms, 1958 . 58 Efficiency Conditions With Respect to Re- source Use, by Input Categories, Experimental and Control Farms, 1953 and 1958 . . . . . . . 60 Efficiency Conditions With Respect to Re- source Use, by Input Categories, as Indicated by Comparing Marginal Value Products(MVP's) With Their Respective_Marginal Factor Costs (MFC's), Experimental and Control Farms, 1953 and 1958. . . . . . . . . . . . . . . . . 61 Changes in the Determinants of Efficiency Conditions With Respect to Resource Use, by Input Categories, Experimental and Control Farms, 1953 and 1958 . . . . . . . . . . . . . 63 Changes in the Nature of Returns to Scale, Experimental and Control Farms, 1953 and 1958. 64 Changes in.the Usual Organization, Experi- mental and Control Farms, 1953 and 1958. . . . 65 Changes in Traditional Farm Management Effic- iency Indicators, Experimental and Control Farms, 1953 and 1958 . . . . . . . . . . . . . 70 Changes in the Ownership Status of Farm Oper- ators, Experimental and Control Farms, 1953 and. 1958 O O O o e e o o e o o o e e e e e e 0 74 Changes in the Average Acreage of Various Crops Grown, by Acres and by Percent of Till- able Acres, Experimental and Control Farms, 1953 and 1958. . . . . . . . . . . . . . . . . 76 Changes in.the Application of Plant Food per Acre on Various Crops, Experimental and Control Farms, 1953 and 1958 . . . . . . . . . 78 Changes in Crop Yields per Acre, Experimental and Control Farms, 1953 and 1958 . . . . . . . 79 viii TABLE . _ Page 214 Hay-Pasture Evaluation, 1958 . . . . . . . . . 81F 25 Observations Used-in Fitting the Experimental FuDCtion, 1953 O O O O 0 e e 0 e e o e o o e o 92 26 Observations Used in Fitting the Control Function,l953................ 93 2? Observations Used in Fitting the Experimental Function,l958................ 9’4 28 Observations Used in Fitting the Control Function, 1958 O O O O O O O O O O O O O O O O 95 29 Chart Used in Determining the Number of Productive Man Work Units. . . . . . . . . . . 97 LIST OF FIGURES FIGURE Page 1 Outline Map of Michigan Showing the Area From Which the Samples Were Drawn . . . . . . . . . 10 CHAPTER I INTRGDUCTION The use of Cobb-Douglas analysis in extension research evaluation is of rather recent vintage.l Cobb-Douglas analysis will be used herein, in.order to determine the levels of efficiency in the use of resources at two different periods in time, from which changes in the efficiency in the use of resources can'be ascertained. Knowledge of such changes in the efficiency in.the use of resources will then be used in evaluating, at least in a partial manner, the Michigan.township extension program. The author recognizes that a complete evaluation of the Michigan.township extenp sicn program should be presented in terms of a more ultimate 1The author knows of no study which has used Cobb—Douglas ‘analysis in actual extension evaluation research. However, Jhe would hasten to indicate that Carl Eicher, a former grad- ‘uate student, working with Dr. J. Nielson, in the Department of Agricultural Economics at Michigan State University, has made an important contribution in this respect. In his M.S. ‘thesis entitled, The Use of CobbéDouglas Analysis in.Eva1u~ gting the Michigan Township Extension Program, Eicher dis- ‘cussed procedures to be followed by extension evaluators, ‘when.using CobbéDouglas analysis in.measuring changes in economic efficiency, resulting from some phase of extension education, In addition, Eicher developed statistical tests ‘to compare the levels of efficiency in the use of resources 'between.areas as well as over time. Generally, it can.be said that Eicher's contribution was conceptual. ‘While this thesis can also be said to deal with procedural prdblems, it is primarily concerned with the application.of Cobb-Douglas analysis for the purpose of evaluating an extension program. goal, namely, that of maximizing satisfaction. However, in view of the difficulties involved in.measuring satisfaction,2 the author is left with the more workable goal of optimum efficiency in the use of resources. Although there can.well be a conflict between the goals of maximizing profit and maximizing satisfaction, the author believes that increased profits resulting from increased efficiency in the use of resources, over the range of incomes involved, will be re- flected in increased satisfaction for the farmers, generally. The author also is convinced that any increase in.the efficiency in the use of resources in.agriculture can be regarded as a net gain to society as a whole. Since farmers and society as a whole are affected directly by changes in the efficiency in.the use of resources, it seems that the author would be Justified in basing his evaluation of the Michigan.tcwnship extension program primarily on.whether or not it was inp strumental in increasing the efficiency with which resources *were used in the farming area participating in.the experiment. The Michigan Township Extensiog Prograg The Michigan township extension.program, an experimental intensive program, was inaugurated in.1953, at which time the 2Although it is possible to obtain.an ordinal measure of satisfaction, it is impossible to obtain a cardinal measure of such. w. K. Kellogg Foundation provided the Cooperative Extension Service of Michigan.State University with funds necessary to organize, operate, and evaluate a more intensive ex- tension.program in.five townships throughout the state for the five-year period, 195#-l958. The experiment was a coop- erative project sponsored Jointly by the W.K. Kellogg Foundation, the Cooperative Extension Service and the farmers who participated in.the program. The contributions of the three cooperators in.the project were as follows: (1) The W.K. Kellogg Foundation made available a grant3 which was intended to cover about one-half of the total cost of the program. (2) Michigan.State University made available special- ists in agriculture and the social sciences, whose task it was to focus attention on prdblems peculiar to the areas studied. (3) The participating townships made dollar contri- butions, in keeping with their financial resources. To cite a mean figure, the townships' contributions 3The Kellogg grant was intended to cover the costs involved in.the coordination and evaluation of the experiment and to make up any discrepancy between the total cost of the program for each township and the amount which each township was able to contribute on a voluntary basis: other costs involved were met out of regular extension.funds. were in.the neighborhood of $2500 per township, per annum. Local funds!“ were generally procured by members of the local board of directorss whose task it was to solicit voluntary contributions from participating farmers and local business- men. The maJor distinguishing feature of the township ex- tension program was the greater amount of cg the fgrm assistance which the township agents provided. Each of the five township agents concentrated his efforts on an average of 150 farms which represented a 16 fold reduction.in.the area and number of farmers normally assigned to a county extension.agent in Michigan. On the average, the township extension agents spent more time 9g the fagg‘assisting the farmers in the planning and management of their farm ‘businesses than did the county agents. On the other hand, Jhowever, the township agents spent less time on such.work as: In.general, farmers were not pleased with the manner in. which local funds for the support of the program were raised. Many farmers, when asked if there was anything about the Mich- :1gan township extension program which should be changed, re- :plied that the manner in which local funds were raised was ‘unsatisfactory. As an alternative to raising funds by volun- ‘tary donations, they suggested that the funds be raised by including a charge for the services of the township agent on every participating farmer‘s tax bill. 5Each of the five townships elected a board of directors comprised of six or seven members all of whom.were farmers. In addition to the board's aforementioned task, it was respon- sible for guiding the township agent in program development and execution. extension.organization, program planning and community develop- ment than.did the county agents. Objectives of the Township Extengion.Progggm The all-embracing objective of the township extension program was to determine whether or not the more intensive township extension program was sufficiently effective to Justify the additional costs involved as compared with the regular county extension program. More specifically, the objectives of the program as stated in.the proposalé to the U.K. Kellogg Foundation.were to: 1. Increase farm earnings. 2. Speed up the rate of adoption of improved farm practices. 3. Raise standards of living for farm families. #. Improve rural communities. 5. Increase agricultural output. 6. Gain information on: a. effective extension methods b. organizational patterns and techniques 0. communication.skills d. community recreation One glance at these objectives should serve to indicate 6Proposal to the Kellogg Foundation for gg:Egpgrimentgl tensive Extension Pro ram in Five T wnshi in chi prepared by the Cooperative Extension Service, Michigan State College. 1953). p. 2. that an evaluation of any program.which has such an.all-inp elusive list of objectives as were involved in this program, would, cut of necessity, involve the analysis of numerous var- iables, in.arder to cast light on.the nature of change -- knowledge of which is the prime requisite in.the evaluation process. Research.Desigg of the TownshipiExtension.Progggm7 In.crder to ascertain the amount of change, if any, which might be attributed to the more intensive township ex- tension program, samples of farmers were interviewed in.aach of the experimental townships.8 Matched control areas were selected on the basis of:9 1. Markets 2. Soil associations 3. Types of farming 7See Nielson, J. "Notes on the Research.Design and Pro- cedures for Evaluating the Township Extension Program", (un- published document, Department cf Agricultural Economics, Michigan State University, January, 1956)., 8The townships and dominant farm types selected were: Newton - heterogeneous as to farm type Tri-Township - Northern Michigan.dairy and potato Denmark - Saginaw Valley cash crop Almcnt - Southern Michigan.dairy Odessa - Southern Michigan dairy and general 9Nielscn, J., “Farm Planning-Township’Style", (a paper presented at the annual meeting of the New E land Research Council, University of Vermont, June 24, 1954 , p. 5. #, Ethnic background of the farm people 5. County extension programs a. History Of cooperation.with extension in the area . b. Current extension programs c. Distance from the county extension office d. Availability of meeting places 6. Proximity to large cities From each experimental township, farms, characterized by a wide range in.size, were selected if they were found to be representative of the dominant farm type, provided that cer- tain other criteria10 were also met. From each control town, ship, farms were chosen to match farms in the experimental township on the basis ole1 age of operator, labor force, total acres, tillable acres, number of cows, and machinery investment. Following this procedure, the experimental townships were subjected to the more intensive township ex- tension program, whereas the control areas were serviced by, the traditional but less intensive county extension.program.~ *Other things being equal between.each of the experimental and 0 These I'cther criteria“ apply to conditions which farms had.to meet in.order to be included in a CobbéDcuglas analysis: these ”other criteria” will be discussed later when.dealing specifically with the Denmark samples. 1 _ 1Nielson, ”Farm Planning-Township Style“, op, ci§., p.6. ..w..-§ control areas, via the research design outlined above, the excess of change (if there were any) in the experimental over that of the control areas can.be attributed to the more inp tensive extension program. However, if these 'cther things" are not equal,12 then changes could not, with any degree of exactness, be attributed to the Michigan township extension program. To indicate the adequate nature of the research design involved, the author appeals to the authority vested in the following quotation from a publication by Nielson and Cross- white,13 ”While no claim of perfect matching is made, the authors believe that the control samples match the experi- mental samples well enough to serve as highly useful check groups.” Information to be used in evaluating the township 1extension program was obtained in several ways. Foremost among these ways of obtaining information relevant to the study was the farm survey method. The benchmark survey provided information (1953 data) to be used in establishing 'beginning levels of efficiency. The terminal survey pro- vided information (1958 data) to be used in establishing ler randomly and normally distributed around a mean of zero so as to cancel each other out. laNielscn, J. and Crosswhite, W}, ”The Michigan Township Extensiom.Experiment - What Happened During the First Two Years,“ (Technical Bulletin 266, Michigan State University, Agricultural Experiment Station, February, 1958), p. 9. ending levels of efficiency. By comparing the 1958 data with the 1953 data, changes which occurred can be determined. The intermediate survey provided information (1955 data) to be used in determining the sequence of change or, more gene erally, the manner of change, (i.e., how farmers got from where they were in 1953 to where they were in 1958). The farm survey schedules14 included all the information needed to run.a Cobb-Douglas analysis, all the information usually collected in a farm account project plus a net worth state- ment.15 To insure reliable and unbiased enumerating and thus uniformity in the data collected, the necessity (on the part of the enumerator) of being "an impartial observer and re- corder of what people say and do" was stressed. Interviewers were instructed:16 l) to be sure to ask questions precisely as they appeared on the survey schedule, 2) to ask secondary questions only if necessary and to record the secondary question AA. luAbout 40 farm survey schedules were taken.for each of the experimental and control areas in 1954; the number of farm survey schedules taken in 1959 was somewhat smaller than.in 195# because of attrition. 1 . 5 SNielson, J. "Farm Planning - Township Style”, pp, 9i§,, p. . l6See I'IlEnstructions for Interviewers - Michigan.Township ,' Evaluation.ResearchF, available without charge from the De- partment of Agricultural Economics, Michigan State University. 10 if one were used, and 3) to record all answers 'ad verbatum“, in the first person. In addition to the information obtained in the manner , outlined above, interpretive information was acquired from 17 case studies involving a small number of participating farmers. Other useful information.was obtained from townp ship boards of directors, township agents, county agents, specialists, and administrative personnel. Delineation of this Study in.Felation.to the Miphigan.Township Extension Progrgm Whereas an overall evaluation of the Michigan township extension program.would involve all five experimental and control areas, this study, being a partial evaluation, will involve only one of the five areas, namely Denmark Township located in Tusccla County, in.the thumb region of Michigan, as shown.in.Figure 1. Cash cropping predominates in this area, the major crops being, corn, beans, wheat and sugar beets. So it is that this study will be restricted in the sense that only farms in.Denmark Township which qualify as cash crop farms will be studied. This study, out of necessity, will be restricted in yet another sense. On page 5, there 7To attempt to do so for a large number would not be feasible nor economical. RAND M9NALLY LOOSE isAr OUTLINE MAP MICHIGAN [Mum | '4’“ I Q r-'—'-I i I '(CANADA CHIPPEWA .i J! WWII i - __ - Emma»: )‘w—AEIITII’AE _"| ..... '7'...“ ‘ . I , I can I I wu‘Irosts: I, ._..L__' ‘ A0 LOREN - I I C! .r , 7 ' /'/'\ \ l l . o . newcmwcsi I '0 Mefl'cwuoy WIscowst g \ \ . I“? “I i Ipassous MARINE": f9 ‘ WW}- wowr- .ALP‘EW - 00 u ANTBTM "Fresco Imam" iI - ... MA cfiwicfioi'os—cofl— ills—05A— "scrum! ! . U -_-.!_ - |_-_!._-__!-_-_ names) wsxroso Wmfiiq'co not“ “Icons“! I Iosco I _- I_ _!.__ _!__-._'- ' "‘30 I'M Iowfiou [cuss IOWWIH‘ WW i i i i {—1. wusow -_!_____ _ - I ____ _I_.- __. “V a casual AYOO inseam TI—muu IIAIoLAIIc i ' I i ! ' II c CA—_| SA-N-I-Lic ' _.' | - _ .L_- _— J—l " 'I... . ' , ' _| E to III—II'A AfIO't— 'IsAc'IIIAw b I wanna}. um “ i ' ! 'f'" '1 ....l I !_ _L_.—Eo_sw:sss.'m‘“ I_.-——- mAwA , IIowIA —|'cuwros lsfllAWASSE'f I | V 15" 0W" | I . . ' I I i I I -)._.__.)__- ...L oAx.LAIIc IIAcowq AuséAII Tum Tsirou ‘iTI'Io'TILAw pvmcstorI ! _____ i __ i ! i __-__ AzocI cALwcuII IIAcII—sow IWASHTEIAWTWAYNE _. f, C I i I |_ I i ‘ CANADA _..__-I_ ‘ —'. - —'—p-§ -—._-—cfi DEBBIE" ' ' ‘ I MRIEImi3II—ffxi$fdcmsi ' Weir? fluid“:- 91555:- - ' .153); 7 fl INDIANA. ‘ ° ° Figure 1 Outline lisp of lichigsn Showing the Area from which the Samples Were Drawn 9!“ so so so so semis: "m m um. this Map is «so usilsbls'ln size I7 :22 '59 03 021 11 is a formal statement of the objectives of the Michigan township extension program. Of these six objectives, the author will be concerned directly with only three, namely, 1, 2, and 5. Hence, this study, as the title serves to in, dicate, is, in fact, a “partial“ evaluation of the program. Objectives of this Study The ultimate objective of this study is to determine whether there has been a greater increase in the efficiency in.the use of resources in the experimental area over that - of the control area, which might be attributed to the Mich- igan.township extensionprogram.18 The realization of this objective is dependent upon.the realization.cf two inter— mediate objectives, namely: 1) to determine benchmark levels of efficiency for both the experimental and control areas and 2) to determine terminal levels of efficiency for both the experimental and control areas. Assuming that there have been changes in the efficiency in.the use of resources, the author would pursue the study further in order to as- certain.what changes have occurred which could be said to have 1) accompanied or 2) resulted in.ohanges in.officiency. This involves an analysis of the nature and extent of changes 18 This statement presumes that the analysis will bear out that there has been an.overall increase in.the efficiency in.the use of resources over the period studied. 12 in farm organization, in terms of changes in the input mix, for both the experimental and control areas. The final objective of this study, in.view of the importance of land and fertilizer as input factors in cash crop farming, is to determine the nature and extent of changes with respect to land use, fertilizer use, and crop yields. Thesis Orggpizggigp , Chapter II will deal with "the data', which discussion will involve the delineation of steps to be taken in order to insure that the data meet the necessary conditions for CobbADouglas analysis. Considerations bearing upon the validity of the results will be discussed therein, The second section of Chapter II will deal with processing the raw data from the initial procedures to the final categor- ization.of such. The final section of Chapter II will deal with factor pricing by input categories. Chapter III will deal with the methodology in two parts. The first section will deal with Cobb-Douglas methodology, unique to this study. The second section will deal with the methodology involved in determining changes in land use, fertilizer use and crop yields. . Chapter IV will deal with Cobquouglas Analysis, and the interpretation.of such. 13 Chapter V will deal with.efficiency changes as re- flected.by traditional farm management efficiency indicators. Chapter VI will deal with changes in.land use, fert- ilizer use, and crOp yields. Chapter VII will present summary statements and over- all concluding remarks. w- Haj-7...“. 1“ CHAPTER II GATHERING AND CATEGORIZING THE DATA Definite procedures were followed to insure that the data collected would meet the specifications of the study. Procedures to be Followed to Insure that Conditions foppthe Application of CobbéDopglas Be Met An.important prerequisite to the realization of accurate results, when applying Cobb-Douglas analysis to farm survey data, is the use of as wide a range of data as is possible with respect to the prOporticns and quantities of inputs used in production, For instance, it is important to select, on the one hand, farms, characterized by their use of much labor relative to other inputs, namely land, machinery, etc., and, on the other hand, farms characterized by their use of little labor relative to other inputs. By following this procedure for all of the inputs, it is possible to obtain a sample of farms, characterized by: l) a high degree of variance with respect to the inputs used in.production and 2) a low degree of intercorrelation.among input categories. Accuracy can'be further enhanced by inp creasing sample size and/or by minimizing the sum of the squared residuals. By following any or all of these pro- cedures, the standard errors of the regression coefficients, 15 Cbxl's, are reduced,1 as can be seen from the following formula:2 iitfiz (Pb, = 1 N 6‘xi (1 " R§1 (X, ecceXh. XJ ooooxn) where: €02 is_the sum of the squared residuals (to be min- imized). N is sample sizel/ 6;? is the variance in.the factor - factor dimension (to be maximized), and Rifix, .... xh’ x3 .... xn) is the inter-correlation among the independent variables (to be minimized). The necessary requirement for the validity of least squares regression analysis is that the sum of the squared IAlthough it is impossible to place statistical limits on the accuracy of the marginal value productivity estimates, as is done in.the case of regression.ccefficients, it would appear that the greater the degree of accuracy with which _ the regression coefficients are estimated the more precise would be the estimates of the marginal value productivities. 2 I . Ezekiel, u., Mpthods or Correlgtion.Ana;1§iE, (second edition, New York: John Wiley and Sons, Inc., 19 9), p. 502. 3Sample size should be increased to the limit at which the marginal cost of the last survey schedule is just equal to the marginal value of the information gained by taking the last survey schedule. l6 residuals be minimized. The sum of the squared residuals will, in all likelihood, be minimized if: 1) there is homo- geneity in both the studied (e.g. land) and the unstudied (e.g. weather conditions) variables, 2) the correct form of the equation is used, 3) an.adequate number of variables is used, and h) an adequate number of observations is used. Minimizing the sum of the unexplained residuals was accomplished in.Denmark Township by choosing a group of experimental farms which were homogeneous with respect to soil type, climatic conditions, etc., by virtue of limiting the study to a limited geographic area. Control farms, which were homogeneous with respect to the aforementioned factors, were selected to match the experimental farms. This procedure was followed to insure that all farms selected had about the same inherent product- ivity. N can be varied in accordance with the degree of accuracy desired and the cost which the researcher is willing to incur. Since survey samples are costly, strict economy as to sample size becomes very important, which precludes the possibility of reducing the Cb11's significantly by ine creasing sample size.“ 4The marginal utility of increased information, as a re- sult of increasing N, might well be less than the marginal cost of acquiring more information (in the case of random sampling) . 17 But what can be said regarding the two remaining means of reducing the Cbxi's? What technique can be employed which will minimize the inter-correlations among input categories, while at the same time maximize the variances of the independ- ent variables? It should be apparent that random sampling will not achieve this desired end, because, as a general rule, farms selected in such a manner tend to be clustered around the high profit point, which tendency results in.a high degree of inter-correlation among the input categories. Due to this lack of range in.the data, the estimates of the regression coefficients and, hence, the estimates of the marginal value productivities are likely to be significantly in.srrcr unless sample size is very large.5 Thus, it becomes evident that the sampling device employed must allow one to observe the farms in advance to insure that, in aggregate, the sample of farms chosen is characterized by a wide range6 of db- servaticns with respect to the independent variables. The ‘ 5The cost involvedin getting a very large random sample is usually prohibitive. ' 6A check on the range obtained in.the sample can.be acquired by 131015151118 pairs Of input categories between which a high degree (of inter-correlation is thought to exist. If a relatively high (sorrelation were found to exist between.land and labor, farms (sould be sought which were using both greater and lesser amounts of land relative to labor. 18 sampling technique designed to permit the achievement of.this end is called purposive sampling.7 At the outset, it was in- tended that purposive sampling be used in acquiring sample farms in Denmark Township. However, the sampling technique used was not "purposive“ in the stricter sense of the word in that'there simply were not enough potential cooperators avail- able frcmwhich to choose a truly purposive sample. Be that as it may, the sample farms obtained in Denmark Township were characterized by a wide range with respect to the proportions and quantities of inputs used in production -- a prerequisite to the realization of small standard errors (of the regression coefficients) and accurate results in general. Another condition which must be met to insure the val- idity of Cobb-Douglas analysis, is that-all farms must be op- erating on. the same production function.8 Implicit in this statement are the necessary requirements that all farms: 7Purposive sampling is more efficient than random sampling in that it allows one, with a sample comprised of fewer farms, to get just as good or better results as one could get using ran- dom sampling techniques involving invariably a larger sample size. This is so, because, by using purposive sampling techniques, one is able to choose‘a wide range of farms which are not in competitive adjustment, which allows a smaller sample size than the random sampling technique would permit. ’ 8All farms must be on the same production fImction, be- cause the production function, estimated using the Cobb- I><3ug1as technique, while it is derived from data secured from a group of farms, is regarded as the production function for each individual farm. 7 19 l) have about the same inherent productive capacity, 2) be using the same range of technology from the given bundle of technology which is available, 3) be using inputs within.each input or investment category in.least cost combination, h) be of the same type, 5) be using the same categories of inputs, and 6) be Operated by managers possessing a similar degree of managerial ability. Although one would not expect to find these six conditions fulfilled in any group of farms selected, these are the condi- tions which should be approached to insure the realization of valid results. It is not known.definitely hOw well the farms com- prising the Denmark Township experimental and control samples met these conditions. However, it is known that much effort was expended in attempting to insure that such conditions would be met. There were two instances in.which it is definitely known that the Denmark Township samples fell somewhat short of fulfilling these conditions. The first of these was that, while 'bhe vast majority of the farms included in the sample had no live- stock or very little, not all of the farms, in the stricter sense of the word, could be said to be single enterprise cash crop farms. Hence, in fitting the functions, only those 20 farms which realized the majority of their incomes from cash cropping could be used. To have included all farms in fitting the functions would have resulted in problems sim- ilar to those dealt with.by Beringer,9 namely, the diffi- culties involved in estimating marginal value productivities for multiple enterprise farms. The second instance involved the requirement that all farms must be using the same input categories. ‘While many of the farms did not have any live- stock, scme did. Hence, it was decided that, for the purpose of explaining as much of the variation in the dependent variable (gross income), as was possible, in terms of variation.in.the independent variables (input categories), the livestock-forage investment category would be included in.fitting the functions. Thus, in those cases in which farms did not have any livestock-forage investment, it was 10 So it is evident necessary to use a “dummy“ variable. that, inasmuch as this study fell somewhat short of fulfilling the aforementioned conditions, it was primarily due to the fact that some farms, which realized part of their incomes ¥ 9Beringer, 0., 'Prdblems in Finding a Method to Estimate Fharginal Value Productivities for Input and Investment Cat- egories on Multiple Enterprise Farms , Resource Productivipy, Iieturns tp Sop e ppd Fapm Size, (edited by Heady, Johnson stud Hardin, Ames, Iowa: Iowa State College Press, 1956). 1Dana dollar was used as the "dummy“ variable in.oases in which the livestock-forage investment was zero, since the 108 of zero is undefined. 21 from livestock, were included in fitting the functions. However, the author would assure the reader that, in fitting the functions, there were good reasons for including some farms which had some livestock, the income from which in.no case exceeded 40 percent of gross income. Initially, in the Denmark experimental and control samples, there were 39 farms each. Sample size was reduced somewhat by attrition, which in the case of Denmark, was not very significant.11 The potential number of farms to be used in.fitting the functions was further reduced by the necessity of meeting the condition (for the first fit) that no farm could be in- cluded in fitting the functions if it had #0 percent or more of its income accruing from livestock. In.addition, the number of farms to be used in fitting the functions was further reduced in.view of the necessity of meeting the condition (for the second fit) that a farm could not be used in.fitting the 1953 functions, unless itwas also used in fitting the 12 1958 functions and vice versa. This matter was intensified ‘ 11 "Drop-cuts“ numbered three in the experimental area and two in the control area over the period 1953 to 1958. 12It was decided that farms which met the criteria for use Jun fitting the functions in 1953 but did not in 19 8, and vice Vnersa, would not be used at all for the second fit . If this <>onditicn.were not adhered to, one would not get a true measure (If change on particular farms, but instead would get a compound Imeasure of change composed of: 1) changes which occurred on the same farms over the period 1953 to 1958 plus 2) changes which resulted from the fact that certain farms used in fitting the 31958 functions very well might not have been.used in fitting the 1953 functions and vice versa. It is the latter type of change, 1.6., change due to changes in sample composition, which must be eliminated, if one is to be rigorous. 'l 22 by the fact that shifts in farm organization occurred to the extent that some farmers, who in.l953, had lppp_than.h0 per- cent of their incomes accruing from livestock, had pppp_than 40 percent of their incomes accruing from livestock in 1958. There were also shifts in the other direction, in.that farmers, who in.l953, had pppg’than.h0 percent of their incomes accruing from livestock, had l2§§_than.h0 percent, or in.some cases none of their incomes accruing from livestock in.l958. To meet the ccndition.of using only those farms in fitting the functions which could be used in fitting both the 1953 and 1958 functions, sample size, N, was reduced to 27 in the case of the control sample and 2# in the case of the experimental sample. To have reduced N further to elim- inate all those farms with some income from livestock, would have resulted in increasing the standard errors of the re- gression coefficients to the point where one would place little confidence, if any, on the reliability of the marginal value productivity estimates. Having made these abating statements, the author would hasten to suggest that all the farms used in this study do quite satisfactorily meet the :necessary conditions for using every one of them in fitting 'the functions, since, in all cases, the major portion of 'their gross incomes was derived from cash cropping. 23 Procedures Followed in.Categorizipg the Datg, In.that much has already been.written.regarding the categorization of inputs,13 it will be discussed only briefly herein, Inputs are aggregated into input or investment categories in.order: 1) to reduce the number of variables to manageable proportions and 2) to focus more clearly on the complex economic problem of imperfect complementarity and imperfect substitutability. The reasons for categorizing inputs infer, implicitly, the procedures which should be followed. One rule, which follows logically, is to group good complements together and good substitutes together, measuring the complements in terms of sets (e.g., one tractor-~one plough) and the substitutes in.terms of the least ccmmon.denominator (e.g., 2-12-10 fertilizer substitutes for h-Zh-ZO in the ratio of 2: 1). These sets of complements and sets of substitutes should be grouped into input categories, putting those which are good complements to, or good substitutes for, each other in the same input category. By so doing, the complex economic problem, involving imp perfect complementarity and imperfect substitutability, is ¥ 13See for example Bradford, L. and Johnson.G., £a__ liaisiagement Analysis, New York: John Wiley and Sons, Inc., 3 I P0 {Iohnson, G., 'Classification.and Accounting Problems in liitting Production.Functions to Farm Record and Survey Data”, Resource Productivit Returns to S lo and Farm Size pp. £11.! PP. 90-910 2h brought to the fore, where it can be studied more readily. This, then, is the theory upcn.which the categorization of inputs is based. In fitting the functions, the following variables were involvedxlu a) the dependent variable: Xl gross income, in dollars b) the independent variables: X2 land, in tillable acres X3 labor, in months Xu productive expenses, in dollars X3 livestock-forage investment, in dollars X6 machinery investment, in dollars X7 fertilizer expense, in.dollars Gross Income (x1) includes total cash receipts from the sale of all produce, plus or minus inventory changes with respect to livestock, feed, seed, etc., and the value of family living furnished by the farm. Items not included in gross income were: 1) government payments, since they were not regarded as income from farm-produced products and 2) changes in the inventory values of buildings and machinery 1 due to depreciation; 5 hence gross income should be large u A Mg? “Summary Sheet for Cobb-Douglas Analysis', Appendix I P0 o l SSince depreciation charges were not included in pro- ductive expenditures, expected to yield a dollar return plus .interest on.a dollar spent, changes in.the inventory values of buildings and machinery were excluded from gross income. 25 enough to cover depreciation and upkeep on buildings and machinery. LQEQ,(X2) includes the total number of tillable acres owned, rented, and/or leased by the farm operator. So as to obtain.an accurate estimate of the productivity of land, woodlots and other waste land were excluded from this category. L522£,(X3) includes the total number of months of labor used on the farm during the year, which includes the operator's labor, family labor and hired labor.l6 Several farm operators worked off the farm part-time, which was taken into account in.determining the number of months of opera- tor's labor used. Producpive exppnses (Xh) includes all expenses expected to yield a dollar plus interest return per dollar spent in 16This figure had to be adjusted upwards in many cases to include Mexican labor employed to block and thin sugar beets, but not recorded as part of the hired labor figure. In.a few cases, in which physical quantities of Mexican labor were recorded, the adjustments were made by merely adding the reported figure to the hired labor figure. More typically than not, however, the amount of Mexican labor employed was recorded in dollar terms, in.which case the following steps were taken. The dollar figure was converted to hours by Inultiplying by four-thirds (Mexicans received 75¢ per hour). flBhe hourly figure was then reduced to a monthly figure by «lividing by 250 (Mexicans worked a 10 hour day and a 25 day Inonth), The final adjustment was made by adding the number (of months of Mexican labor to the number of months of hired ILabcr. Thus, the total labor input figure in months was a summation of the operator's labor, family labor, hired labor and Mexican labor employed on the farm. 26 any given year. This category thus includes the following items: feed purchased, annual seeds and plants purchased, custom work or machinery hired, supplies purchased, gas and oil for farm use (less tax refund, of course), livestock expense, farm share of electricity and telephone expenses, farm share of auto and truck expenses and upkeep, beginning inventory of feeders and/or broilers, feeders purchased, be- ginning value cf clover stands, and beginning value of perennials destroyed prior to June 1. Certain nonproductive expenses such as depreciation charges, insurance charges, taxes, repairs, maintenance on investments, etc., were excluded from this input category. As a result of excluding 17 to be these nonproductive expenses, reservation prices, used in.determining the economic optimum, must be high enough to cover such nonproductive expenses. Livestock-forage inveptment (X5), a ”hybrid“ invest- ment category,18 so to speak, includes the total dollar in, l vestment in.breeding livestock 9 and forage crops. The total 17See p.1Il, for reservation prices used in this study. Livestock and forage investments, although computed separately, are commonly combined to form a single input cate- gory because of the high degree of correlation and comple- mentarity between livestock and forage investments. 1 9For the purpose of this study only dairy cattle, namelY. dairy bulls, cows, heifers, and calves, were regarded as breeding stock. All other livestock was regarded as feeder stock and, thus, was included infhe productive expenses input category. 2? livestock investment was computed by taking the beginning inventory value of all breeding stock, plus a proportional cost for breeding stock purchased during the year, minus a proportional credit for breeding stock sold during the year.20 The total forage investment was computed by taking the beginning inventory value21 of all hay and pasture stands (1.6., all perennial and second year clover stands), minus a proportional credit22 for perennials destroyed, plus the cost of machinery hired for land reclamation}3 plus the value of perennial seeds purchased and used during the year. Machinepy_;pvestment (X5) includes the beginning of the year auction value of all machinery and equipment, plus a proportional addition for machinery purchased during the year, minus a proportional deduction for machinery sold during the year.2u 20See Appendix A, p. 86, for the procedures followed in calculating proportional costs and credits for breeding stock. 21See Appendix A, pp. au-ss, for the values used in the hay and pasture evaluation.' 228cc Appendix A, p. 85, for the procedures followed in calculating proportional credits for perennials destroyed. 23The cost of machinery hired for land reclamation was not often incurred; however, when the cost of such, if not in excess of 100 dollars, was incurred, it was counted as part of the forage investment. See_Appendix A, p. 87, for the method used in calculating proportional additions and proportional deductions for machinery. 28 Fertilizer exppnse (X7), includes the total expend- iture on fertilizer purchased and used during the year. In view of the importance of fertilizer as an input in cash crop farming, the author deemed it meritous of special consideration. Consequently, fertilizer expense was studied 25 as a separate input category. 25On the basis of information obtained from fitting the functions once the decision.was made_to combine fertilizer expenses and productive expenses, hence eliminating fertilizer expense as a separate input category. 29 CHAPTER III METHODOLOGY FOR DETERMINING EFFICIENCY CHANGES Determinipg Changes in Efficiency as Indicated by CobbADopglas Analysis 1 In.view of the fact that the literature abounds with discussions regarding the methodological procedures to be 1 See for example, Beringer, C., A Method of Estimatipg Marginal value Productivities of Input and Investment Categozies on Multiple Enterprise Farms,*(unpublished Ph,D. Dissertation, Eggggtment of Agricultural Economics, Michigan State University, Bradford, L.A., and Johnson, G.L., op,ci§. Brooke, D.M,, Marginal Valuelgrcductivities of Inppts on Cgsh Crop Farms in the Thumpzand Saginaw Valley Area of . Miphigan, 1252, (unpublished M.S. Thesis, Department of Agricultural.Economics, Michigan State University, 1958). Drake, L.S., Prdblems and Results in the Use of Farm Apcount Records to Derive Cobb-Dopglas Vplue Productivity Functions, (unpublished Ph,D. Dissertation, Department of Agricultural Economics, Michigan State College, 1952). Eicher, C., The pp; cpCobbéDouglgs Analysis in.Eva1u- atipg the Michigan Township Extensgon Program, unpublished M.S. Thesis, Department of Agricultural Economics, Michigan State University, 1956). Resource Productivity, Returns to Scale and Fgrm Size, op,cit., see especially Chapters 1, XI, and XVI. Tintner, G., 'A Note on.the Derivation of Production Functions from Farm Account Records“, Econometrics, Vo1. 12, No. 1, (January, 1944), pp. 26-34. Tintner, G. and Brownlee, 0., "Production Functions Derived from Farm Records,‘ Journal of Farm.Economic§, Vol. 26, (August, l9uh), pp. 566-571. Toon, T., Margina1 Value Productivities of In uts, Investments and Expendgpures on Upland Grayson.County Fgrms gggépg 1251, (unpublished M.S. Thesis, University of Kentucky, Wagley, R., The Mgrginal Productivities of Investment gnd.Exp§nditure LSelected Ingham CountprarmsL_1952, unp published M.S. Thesis, Department of Agricultural Economics, Michigan State College, 1953). 30 adhered to when the Cobb-Douglas function.is used for the purpose of estimating marginal value productivities of var- ious input and investment categories on farms, the author shall take the liberty of limiting this section to the task of outlining the methodological procedures which were unique to this study. The initial procedure was to fit the functions in order to determine the bl's (the regression coefficients) from which the estimates of the marginal value productivities of the various input and investment categories were derived. The next step was to compare the estimated bi's with the bi‘s necessary to hield, at the margin, returns equal to a set of minimum expected returns, for the various input categories. Minimum expected returns at the margin or alternatively reservation prices, in this case, were taken to be the expected returns to the various input categories Just sufficient to invoke the use of the inputs in.production. But what is this return, which at the margin.is Just sufficient to invoke the use of the input (or in this case the input category)? It is none other than the MFC (marginal factor cost) of the input (or input category). Hence, it becomes apparent that by comparing the estimated bi's with the bi's to yield minimum returns at the margin, one actually obtains a measure of the divergence of the MVP's of the various input 31 categories from their reapective MFC's which.in.turn, gives one a satisfactory measure of the efficiency with which re- sources were being used. Reservation prices,2 from which bi's to yield minimum expected returns at the margin were derived, are presented in Table 1. TABLE 1 Reservation.Prices Input Category Units I743 195? Land Dollars per tillable acre 18.00;/ 30.00%; Labor Dollars per month 150.001/ 158.005/ Productive expenses Dollars per dollar expended 1.065/ 1.06 Livestock-forage W investment Percent on.investment #0.00é/' 40.00 Machinery investment Percent on investment 21.00 24.008 Fertilizer expense Dollars per dollar expended 1.06§/ 1.06—/ 1This was based on a 6 percent charge for interest (5 percent) and taxes (1 percent), with land valued at $300 per acre. 2This was based on a 6 percent charge with land valued at $500 per acre. 3This was based primarily on.Eicher's figure (op.cit., p. 7h); the author deems it suitable for use in this study in as much as Eicher's was a similar study involving 1953 data for an adjacent county, namely Lapeer, wherein.approximate1y the same alternative opportunities for labor were prevalent. a This was derived from the 1953 value by adjusting it upwards in.accordance with.the increase (5.5 percent over the period 2Reservationprices were established as a result of diligent study of original sources and discussion.with.Dr. J. Nielsen, Department of Agricultural Economics, Michigan State University. 32 1953 to 1958) in the annual average farm wage rate index for Michigan, see Farm Labor, Agricultural Marketing Service, United States Department of Agriculture, (Washington, D.C.: Government Printing Office, January, 1959). Although the reservation price of $158 for the last month of labor for 1958 was derived by adjusting the 1953 reservation price for labor in accordance with the increase in the farm wage rate index for Michigan, the reader might question the validity of it, suggesting that a somewhat higher reservation price should have been used. Inasmuch as the author anticipated that such a question might arise, optimal b 's for labor were derived for 1958 using reservation prices 0 : 1) $200 per month and 2) $250 per month. When reservation prices of $200 per month and $250 per month were used, the resulting efficiency conditions were not statistically different from the efficiency conditions when.a reservation price $158 per month was used. Thus, the author decided to use a reservation price of $158 per month -- the price which is in accordance with the increase in the farm wage rate index for Michigan, over the period 1953 - 1958. 5This was based on the fact that productive expenses should return a dollar plus interest at 6 percent per dollar expended. , 6This was based on the following charges: 9 percent for depreciation, 5.5 percent for maintenance and repairs, .5 percent for taxes, and 6 percent for interest. zThis was based on the same charges as were used in 1953 plus an additional charge of 3 percent to take account of increasing costs of repairs and maintenance over the period 1953 to 1958. 8This was based on the fact that fertilizer expense should return a dollar plus interest at 6 percent per dollar ex- pended e I In.astablishingthese reservation prices no allow- ance was made for_risk. Since risk is a highly personal and subjective factor, which varies from farmer to farmer, to have allowed 2 percent, 5 percent, or 10 percent would have been unrealistic. Having said this, the author would hasten 33 to say that risk is an important factor which farmers do take into account. Hence, anyone using these results for the purpose of assisting a farmer with problems involving changes in farm organization must take risk into account as it applies in the particular case at hand. The optimal b1's (bl's to yield MVP's equal to mine imum expected returns at the margin) were derived by sub- stituting the respective reservation prices in.the appropri- ate MVP equations, the general form of which is given.by: ”a Pe— where I is predicted gross income and X1 is the geometric mean amount of the particular input category under consid- eration. These equations were in turn.solved for the op- timal bi's. The estimated bl's were compared with the optimal bi's to ascertain whether or not there was malad- Justment with respect to the proportions in which resources, by input category, were being used. To determine whether or not there was a significant difference between the re- spectivebi's, the following statistic3 which has a 't" distribution.with.N - 1 - p degrees of freedom, was used: 3Dixon W., and Massey, F., Introduction to St tistical .Anallgis, (second edition, New York: McGraw-Hill Book Co., Inc., 1957), p0 115. 34 where: b1 is the estimated regression.coefficient b'1 is the optimal b1 6B1 is the standard error of the b1 N is the sample size p is the number of independent variables. If, for instance, the estimated bland were signifi- cantly different from the optimal bland' one would conclude that the MVPland was significantly different from the "Filand' i.e., that there was maladjustment with respect to land. If, on the other hand, the estimated b were not signifi- land cantly different from the optimal bland, one would conclude that the MVPland was not significantly different from the MFCland' i.e., that there was no apparent maladjustment in the use of land. The same procedure was followed in.study- ing the bi's of the other input categories. In order to determine whether or not there were a significant difference between the experimental and control functions for 1953 and 1958, respectively, a special 't' test5 “If the estimated b were significantly different from the optimal b1, and since t e b value is reflected in.MVP value, one could justifiably oonoldde that the estimated MVP was significantly different from its respective MFC (from which the optimal b1 was derived) which would indicate that there was maladjustment with respect to land. 53cc Appendix B, pp. 88-90 35 was constructed by which the regression coefficients of the experimental function.were to have been tested for significance against the respective coefficients of the control function. However, this test was not used, because large variance in the dependent variables precluded the possibility of obtains ing significant 't' values, even though the test stands up under statistical scrutiny. For the same reason as was cited above, it was im- possible to obtain.aignificant 't' values for differences between 1953 bi's and their respective 1958 bl's. In order to determine whether or not the sum of the bl's for each function were significantly different from 1, a statistic6 which has an "F“ distribution was derived. However, since the data7 required for the test were not readily available, the test was not used. Thus, statistical evidence was not available to support or reject possible . contentions regarding returns to scale. Yet, it becomes apparent that this was not a serious handicap from the standpoint of this study, when one realizes that it was more 6See Appendix B, p. 90 7The augmented moment matrix was available but could not be used in this case. The inverse matrix, which was applicable in this case and, hence, could have been used, was not readily available. 36 meaningful to compare the differences between the sum of the bi's for 1953 and 1958 for the experimental and control functions, respectively, which was in fact done. By so doing, changes in the nature of returns to scale were de- termined. While it was generally decided that, if there turned out to be a significant increase in the efficiency in the use of resources in the experimental area over that of the con- trol area, such would be attributed to the intensive townr ship extension program, the author recognized the necessity of maintaining a watchful eye throughout the analysis, in order to ascertain.whether the increase in efficiency should have been attributed, in part at least, to certain factors other than the intensive township extensive program. An alternative to following the procedures outlined above would have been to have used Trent'38 method of ad- justing MVP estimates for changing prices. Following Trant's method, the 1953 MVPestimates would have been adjusted to the 1958 price level, thus eliminating the effects of in! flation.and deflation over the period studied. To have followed Trant's method would have allowed one to make ' 8Trent, 0.1., A Technique of Adjusting Marginal value Productivity Estimateggfor Changing_Price unpublished M.S. Thesis, Michigan State College, 195 . 37 direct comparisons, by input categories between the 1953 MVP‘s, adjusted to 1958 price conditions, and the 1958 MVP's. However, this method was not followed because, in.the author's opinion, while it no doubt is interesting to know that the MVP of machinery for 1953 was 20 percent on investment and that the MVP of machinery for 1958 was 25 percent on.ine vestment, it is more meaningful to compare MVP's with their respective MFC's, for both the base and terminal periods, to determine whether the MVP of machinery for 1958 came more nearly to equality with the MFC of machinery for 1958 than.was the case in 1953. So, it becomes apparent that in attempting to ascertain the nature of efficiency changes, that the really relevant consideration is ppp by what percent did the MVP of machinery increase over the period studied, but rather, how did the MVP of machinery change relative to the MFC of machinery. Determining Changes in Farm Resoupce Organization as Indicated hx_Qfl§ng§§_in the Geometric Mean.Amount§ of Inputs Used Changes in.farm organization.re1ate to shifts along the production function, i.e., changes in farm organization occur when input substitution causes a change in gross ine come.' Farm organization changes were determined by ascertain- ing what changes occurred with respect to the geometric mean amounts of inputs which were used in the experimental area 38 as opposed to the control area over the period studied. QgtermininggChanges in.Efficiency as Indicated by Traditional Fapm Mapagement Efficieppy Indicators Changes in.afficiency as indicated by certain trad- itional farm management indicators of efficiency were exam- ined in.order to determine whether or not they were consistent with changes in efficiency as indicated by Cobb-Douglas analysis. The analysis of such was carried out using a 't“ test9 which was employed to indicate whether or not there were significant changes with respect to certain traditional farm management efficiency indicators in the experimental and control areas, over the period studied. While it would have been desirable to have used a ”t” test to determine whether or not there were significantly greater changes with respect to traditional farm management efficiency indicators in the experimental area over that of the control area, or vice versa, such.was not possible; due to correlation, the ordinary "t“ test was invalidated in that 9The hypothesis involved was that there was no significant difference between population means. Thefollowing statistic was used to test the hypothesis: t= in t N in?" - (£D)2 _ N - l where D is the difference between observations and N is the sample size. ' 39 the calculated 't" value was biased downward, in accordance with the degree of correlation, (i.e., the greater the degree of correlation, the greater the downward bias in the 't' value). Thus, it should be apparent that ”t" values, calculated without taking the degree of correlation.into account, would have been too conservative, i.e., the calculated 't' values would have been smaller than.the actual (but unknown) 't' values. Since the degree of correlation between the ex- perimental and control data was unknown, the degree of downy ward bias in the calculated "t" value, for any particular item, was also unknown. Thus, inasmuch as accurate 't' values were not obtainable, the author chose to make state- ments, based solely upon his judgment, as to whether or not there were significantly greater changes in the experimental area over that of the control area, or vice versa. Depepminipg C'flges in Land Use, Peppilizer Use and Crop Yields The methodology used in studying changes in land use, fertilizer use, and crop yields was practically the same as that used in studying changes in traditional farm management efficiency indicators. The only difference between the two was in.the use of statistical evidence in support of state- ments regarding the significance of changes. That is, state- ments regarding the significance of changes with respect to traditional farm amnagement efficiency indicators were based 40 partly upon.statistical evidence and partly upon the author's judgment; whereas, statements regarding the significance of changes with respect to land use, fertilizer use, and crop yields were based solely upon the author's judgment. 41 CHAPTER IV EFFICIENCY CHANGES AS INDICATED BY COBBADOUGLAS ANALYSIS As indicated in Chapter II, seven variables were initially used in fitting the functions. However, high simple correlations were found to exist between fertilizer and land, fertilizer and labor, and fertilizer and machinery. It is generally recognized that such high intercorrelation jeopardizes the accuracy of the estimated bl‘s and hence the reliability of the MVP's. In.an attempt to reduce the high intercorrelation present, fertilizer expense was comp bined with productive expenses, thus eliminating fertilizer expense as a separate input category. By so doing, the simple intercorrelations were reduced substantially, thus, improving considerably the reliability of the bi's. There- : fore, the results Obtained using seven variables in fitting the functions were not used in.the evaluation process. _ Acting in the light of the information presented above, two sets of functions were fit, using six variables. For the first fit, involving six variables, unmatched farms were used; whereas for the second fit, involving six variables, matched farms were used.1 The reasons for fitting the 1In.the case of the first fit, farms were unmatched in the sense that farms were used in.fitting the 1953 functions whether or not they were used in fitting the 1958 functions. In the case of the second fit, farms were matched in the sense that only those farms, which met the criteria for use in both 1953 and 1958, were used in fitting the functions. 42 functions, first, for unmatched farms and secondly, for matched farms were: 1) to ascertain whether or not the dif- ferences between the estimates obtained were sizeable, and 2) to determine the effects of reducing sample size to elim- inate unmatched farms. The differences in the estimates ob- tained by using matched farms rather than unmatched farms were generally not important; yet, it was deemed discreet, for the purpose of this study, to use only matched farms in the evaluation process. By so doing, it was possible to as- certain actual changes in efficiency on.the same farms over the period 1953-1958. Had unmatched farms been used in.the evaluation process, the estimates of change obtained would have been.compound2 in the sense that the estimates of change would have included actual changes on matched farms plus changes due to differences in.sample composition. Thus, only the functions involving six variables and including only matched farms are reported herein. Analygis of the Exmrimepta; Function, 1253 The 24 farms3 which were used in fitting the function yielded bi's and 631's as shown.in Table 2. Notice that the 2 See p. 21, footnote 12 38cc Appendix C, p. 92 , where the observations, summarized by input categories, are presented. #3 bl's for land and productive expenses, when tested against 14. the null hypothesis, were found to be significant at the TABLE 2 Regression Coefficients (bl's), Their Standard.Errors 631's), 't' values, and Level of Significance, Experimental Function, 1953. Input Category b1 (81 t Significant1 at Level Indicated12) x2, land .548881 ,141894 3,86 5 X , labor -.l53513 ,151263 1.01 40 X3, expenses .521516 ,120951 4.31 5 £5, livestock-forage .021142 .019587 1.07 30 6, machinery .047448 .105597 .44 70 55?. gross income 251 ".981; HI For N-l-p = 18 degrees of freedom, where p: number of independent variables. five percent level of significance. Notice also that the b1 for labor was negative; however, it was not significantly different from zero at the five percent level of significance. Thus, the b1 for labor was assumed to be zero and theibi value was adjusted upwards by .153, which gave an adjusted £b1 3 1.137. _The multiple correlation coefficient (R) was found to be .94, indicating a high degree of association between “The hypothesis was that the regression coefficients, taken.individually, were not significantly different from zero. the dependent and independent variables. The coefficient of determination (R2) of .88 indicates that 88 percent of the variance in gross income was associated with the independent variables. R? was found to be significantly5 different from zero at the one percent level of significance . The standard error of estimate (3) was computed to be .086695 in logarithms, while the logarithm of gross in- come at the geometric mean was 4.123510. Thus, in 67 per- cent cf the cases, under 1953 conditions, the logarithms of gross income would be expected to fall within the range defined by 4.123510 1 .086695 or, in.natural numbers, between 810870. and $16230. The geometric mean amounts of inputs used and the MVP's which relate to these are presented in.Table 3. These MVP figures represent the gross return to the marginal unit of each input or investment category. Hence, the last tillable acre of land was returning $53.25, the last month of labor was returning a negative $141.48, the last dollar of pro- ductive expenses was returning $1.57, the last dollar invested 5The hypothesis was that the true R2 = 0. The statistic used was R2 . N-p:; 2 F for p and N-p-l degrees of .1~R2 p of freedom, where p = number of independent variables. 45 in forage-livestock was returning 28 percent or $.28 and TABLE 3 Usual Organization, Marginal and Gross Value Products, Experimental Function, 1953 Input Geometric Mean MVP Categpryp Amounts of Inputs (in dollars) X2. land 136.8 tillable acres 53.25 X3. labor 14.4 months -l4l.48 X4, productive expenses 34388. 1.57 £5, livestock-forage 9.5 .28 , machinery $73 9. .085 X], gross income —$l3272. 1.024891 log a 1,024891 the last dollar invested in machinery was returning 8.5% or $.085. When interpreting MVP's it is important to consider carefully the degree of intercorrelation between the various input categories, because it is well recognized that high intercorrelation between any two input categories can ine troduce bias in the estimation of the bi's,which, in turn, is reflected in unreliable MVP's estimates. The simple (intercorrelations, in this case, were as follows: r2r3 .62 ran“ .65 rzrs .53 r2r6 .65 #334 .62 r3r5 .75 r3r5 .48 r4r5 .47 r4r6 .63 r5r6 .30 It can be seen, by examining the intercorrelations, that 46 only in.the case of rgrs, labor and livestock-forage, was there a high degree of intercorrelation. In all other cases the degree of intercorrelation was relatively low. Analysis of the Control Function, 1253 The 27 farmsé which were used in fitting the function yielded bl's and GBi's as shown in Table 4. Notice that the bi's for land, productive expenses and machinery, when tested against the null hypothesis, were significant at the five percent level of significance. Notice also thattbl = 1.28, indicating increasing returns to scale. TABLE 4 Regression Coefficients (b1 's), Their Standard Errors GBiW 't' values, and Level of Significance, Control Function, 953. Input Category b1 631 t Significant1 at ' Level 1W x2, land .574956 .198569 2.89 5 X , labor .141152 .123829 1.13 30 X2, productive . expenses .314875 .129919 2 .42 5 X5, livestock-forage-.OO4804 .013573 .35 80 X6, machinery .255337 .121452 2.10 5 X], gross income I ..i.128 lFor N-l-p 8 21 degrees of freedom, where p I the number of independent variables. The multiple correlation coefficient (R) was found to be .95, indicating a high degree of association between the _— __ f 6See Appendix C, p. 93 where the observations, summarized by input categories, are presented. 47 dependent and independent variables. The coefficient of determination (R2) of .90 indicates that 90 percent of the variance in gross income was associated with the independent variables. R2 was found to be signifi- cantly different from zero at the one percent level of signifi- cance, using a statistic which followed the 'F' distribution for 5 and 21 degrees of freedom. The standard error of estimate (3) was found to be .089907 in logarithms, while the logarithm of gross income at the geometric mean was 4.079573. Thus, in 67 percent of the cases, under 1953 conditions, the logarithms of gross income would be expected to fall within the range defined by 4.079573 3 .089907 or, in.natural numbers, between $9764. and $14780. The geometric mean amounts of inputs used and the MVP's which relate to these are presented in.Table 5. By examining the MVP values, it becomes evident that the last tillable acre of land was'returning $51.26, the last month of labor was returning $106., the last dollar of productive expenses was returning $1.06, the last dollar invested in livestock- forage was returning a negative 32 percent, and the last dollar invested in machinery was returning 42.5 percent. The simple intercorrelations were as follows: r2r3 .58 rzru .78 r2r5 -.O9 r2r6 .71 48 13m, .52 r3r5 .02 r3r6 .64 1‘41'5 .25 r,,r6 .53 r5r6 -.16 TABLE 5 Usual Organization, Marginal and Gross Value Products, Control Function, 1953 Input Geometric Mean NV? Category Amounts of Inputs (in.dollars) X2. land 134.6 tillable acres 51.26 X , labor 16. months 106. X2, productive expenses $3568. 1.06 X , livestock—forage $18.2 -.32 X2, machinery $7205. .425 X3, gross income $12000. lasiaai. 5 .582980 It can be seen, by examining the intercorrelations, that the highest degree of intercorrelation existed between land and productive expenses, while the next highest degree of intercor- relation.existed between land and machinery. Otherwise, the degree of intercorrelation.was relatively low. Analysis of the Expergmental:Function, 1258 The 24 farms7 which were used in fitting the function yielded b,'s and 681's as shown in.Tab1e 6. Notice that the b1 for productive expenses, when tested against the null 7See Appendix C, p.94 ‘where the observations, summarized by input categories, are presented. 49 TABLE6 Regression Coefficients(b1's), Their Standard Errors(Gb 's), 't' values, and Level of Significance, Experimental Func ion, 1958. 1 Input Category b 6b t Significant at 1 1 Level Indicatedflg) x2, land .295832 .200760 1.47 20 , labor .313313 .228412 1.37 20 , productive ' expenses .534822 .126719 4.22 1 X5, livestock- . _ . forage. .009900 .018698 .52 70 X5, machinery .0473 72 .118422 .40 7O X], grosspincome ilar l .12 1For N-l-p = 18 degrees of freedom, where p 8 number of independent variables. hypothesis, was found to be significant at the one percent level of significance, while the bl's for land and labor were found to be significant at the 20 percent level of significance. Thezibi value in this case was 1.19. The multiple correlation coefficient (R) was found to be .94, indicating a high degree of association'between.the dependent and independent variables. The coefficient of determination (R2) of .88 indicates that 88 percent of the variance in gross income was associated ‘with the independent variables. R2 was found to be signifi- cantly different from zero at the one percent level of sig- nificance, using a statistic which followed the 'F‘ distri- bution.with 5 and 18 degrees of freedom. . 50 The standard error of estimate (5), was found to be .105425 in logarithms, while the logarithm of gross income at the geometric mean.was 4.183615.» Thus, in 67 percent of the cases, under 1958 conditions, the logarithms of gross income would be expected to fall within the range defined by 4.183615 1 .105425 or, in natural numbers, between 311970. and $19450. The geometric mean amounts of inputs used and the MVP's which relate to these are presented in.Table 7. By examining the MVP values, it becomes evident that the last tillable acre of land was returning $30.44, the last month of labor was returning $291.53, the last dollar of productive expenses was returning $1.73, the last dollar invested in livestock-forage was returning 76 percent, and the last dollar invested in machinery was returning 9.7 percent. TABLE 7 Usual Organization, Marginal and Gress value Products, Experimental Function, 1958 Input Geometric Mean MVP . Category Amounts of Inputs (in dollars) X2, land 148.3 tillable acres 30,44 X., labor 16.4 months 291.53 Xi, productive expenses $4718. 1.73 X., livestock-forage $19.71 .76 é, machine ry_ $7439 . .09? X] gross income $15260; .999756 ...: O t 51 The simple intercorrelations were as follows: r2r3 .81 rzrh .67 rgrs .19 r2r6 .59 P334 .73 r3r5 .04 r3r6 .56 rhr5 .25 r4r6 .49 r5r5 .30 It can be seen, by examining the intercorrelations, that the highest degree of intercorrelation.existed between land and labor and between labor and productive expenses. The degree of intercorrelation otherwise was relatively low. Analysis of the Control Function, 1258 The 27 farms8 which were used in.fitting the function yielded bi’s and 6131's as shown in Table 8. Notice that the _b1's for land, labor and machinery, when.tested against the null hypothesis, were found to be significant at the five percent level of significance. The ‘bi value, in this case, was 1.35, indicating increasing returns to scale. The multiple correlation coefficient (R) was found to be .93, indicating a high.degree of association between the dependent and independent variables. The coefficient of determination (HZ) of .87 indicates that 87 percent of the variance in gross income was associ- ated with the independent variables. R2 was found to be 88cc Appendix C, p. 95 where the observations, summa— rized by input categories, are presented. 52 TABLE 8 Regression.Coefficients (b '3), Their Standard Errors (651.8), I't" Values, and Level of Significance, Control Function, 958 Significantl at Inuit Category b1 681 t Level Indicated(2_5) X2, land .268980 .123255 2.18 5 X , labor .566922 ..129665 4.37 5 , productive expenses .254063 .125223 2.02 10 X5, livestock- forage -.010749 .012859 .83 50 X5, machinery .289199 .095935 3491 5 X], gross income £21. In: 1For N-l-p - 21 degrees of freedom, where p = number of independent variables. significantly different from zero at the one percent level of significance, using a statistic which followed the 'F' distribution with 5 and 21 degrees of freedom. The standard error of estimate (3) was found to be .081101 in logarithms, while the logarithm of gross income at the geometric mean was 4.121146 i .081101 or, in natural numbers, between.$1096l and $15931. The geometric mean amounts of inputs used and the MVP's which relate to these are presented in Table 9. By examining the MVP values, it becomes evident that the last tillable acre of land was returning $22.72, the last month of labor was returning $435.44, the last dollar of productive expenses was returning $.99, the last dollar invested in 53 TABLE 9 Usual Organization, Marginal and Gross value Products, Control Function, 1958 Input Geometric Mean. MVP Category .Amounts of Inputs .(in dq;;gppl_ X2, land 156.4 tillable acres 22.72 X , labor 17.2 months 435.44 &, productive expenses¢3405. .99 X,, livestock-forage $15.8 ~8.9 é, machinery $8302. ‘ 1&2. X], gposs income £13211, log g ‘ . 12505 livestock-forage was earning negative returns,9 and the last dollar invested in.machinery was returning 46 percent. The simple intercorrelations were as follows: rzr3 .56 rzrh 468 r2r5 -.07 r2r6 .26 r3ru .59 r3r5 .09 r3r6 .15 rhrs .06 rhrg .41 r5r6 -.29 ’ It can be seen, by examining the intercorrelations, that the highest degree of intercorrelation.existed between land 9The author did not expect to obtain reasonable results for the livestock-forage input, because many farmers had no livestock-forage investment, in which case a "dummy'I variable of #1. was used. The livestock-forage investment category was included for the purpose of explaining as much of the variation.in the dependent variable, as was possible, in terms of variation in the independent variables--ppp_to ob- tain reliable MVP estimates for it. Hence, no further analysis will be applied to the livestock-forage investment category. 54 and productive expenses. The degree of intercorrelation, in all cases, was relatively low. Regardinggthe Efficiency with Which Resources More Used by Input Categorie§_ As indicated in Chapter 111,10 the efficiency with which resources were used, by input categories, was determined by testing the estimated regression coefficient (by) for each input category against its respective optimal regression coefficient (bi), to ascertain whether or not there was a significant difference between the two. The results of these tests are presented forthwith. Eppgpimental Farms, 1253 Comparisons between the estimated bi's and the opti- mal bi's are presented in.Tab1e 10. Notice that the estimated b1 of land was significantly different from its optimal b1 at the five percent level of significance. Thus, one would conclude that the MVP of land was significantly different from the MFC of land, i.e., that there was maladjustment 11 in the use of land relative to other inputs. The estimated 10 1]-The purpose of this section.is to indicate, by input category, whether or not there were maladjustment in the use of resources. The nature of the maladjustment can be de- termined by comparing MVP's with their respective MFC's. See Table 15, p. 61 See PP o 3 1-31} 55 b1 of labor was significantly different from its optimal b1 at the ten percent level of significance. Hence, it was TABLE 10 Comparisons Between the Estimated Regression Coefficients (b 's) and the Optimal Regression Coefficients (b '8), Experimental Farms, 1953 l/Gb ' Significilntz Input b b ' b -b'- t=b -b at Leve Category. 1 i 1 1 :1 @fi_ Indicated(%) x2, landw 4 .548881 .185533.363348 .141894 2.56 5 x , labor .153513 .162748.31626l .151263 2.09 10 X3. prod. ex. .521516 .340539.180977 .120951 1.49 20 x6, machinery .047448 .117763.070315 .105597 .66 , 6o lAbsolute value. . For N-l-p - 18 degrees of freedom, where p = number of independent variables. ~ concluded that there was maladjustment in the use of labor relative to other inputs. The estimated b1 of productive expenses was significantly different from its optimal b1 12 The author thus at the 20 percent level of significance. concluded that there was maladjustment with respect to pro- ductive expenses, relative to other inputs. Since the bi of machinery was ppp significantly different from its optimal b1, at the 20 percent level of significance, or lower, it was concluded that there was not maladjustment in the use of machinery relative to other inputs. Control Farmsy_l252_ Comparisons between the estimated bi's and the optimal bl's are presented in Table 11. The estimated b1 of land was 'IZIt was decided that the 20 percent level of significance should be regarded as the critical level. 56 significantly different from its optimal b1 at the ten percent level of significance. Thus, it was concluded that there_was maladjustment in the use of land relative to other inputs. TABLE 11 Comparisons Between the Estimated Regression Coefficients (bi's and the Optimal Regression Coefficients (bl's), Control Farms, 1953 In . ' y 6‘ .. Significintz put b b b -b b1 t=b -b at Love Category 1 1 i 1 Shy Indicated(%) X2,land .574956 .201900 .373056 .198569 1.87 10 X ,1abor .141152 .199375 .058223 .123829 .47 70 Xz,prod.ex. .314875 .314875 —- -- —- -- X6,machinery.255337 .126105 .129232 .121452 1.06 50 IAbsolute value. For N-l-p = 21 degrees of freedom, where p = number of independent variables. . Since none of the other estimated bl's was found to be sig- nificantly different from their respective optimal bi's, it was concluded that there was not maladjustment in the use of labor, productive expenses or machinery, relative to one another. Expgrimental Farms, 1258 . Comparisons between the estimated bi's and the optimal bi's are presented in Table 12. The estimated b1 of productive expenses was significantly different from its optimal b1 at the 20 percent level of significance. Hence, it was con— cluded that there was maladjustment with respect to productive expenses, relative to other inputs. Since none of the other estimated b1's was found to be significantly different from I. - owl's- ...! 57 TABLE 12 Comparisons Between.the Estimated Regression Coefficients (bi's) and the Optimal Regression Coefficients (bi'8)a Experimental Farms,1958 I 11AB 1 §1gniglcintz Input b b b -b1- t=b -b at ve Category 1 1 1 1 (81 Indicated(Z) X2,1and .295832 .291546 .004286 .200760 .02 -- x ,1abor .313313 .169803 .143510 .228412 .62 6o 4,prod.ex. .534822 .327724 .207098 .126719 1.33 20 X6,machinery.047372 .116996 .069624 .118422 .58 6o 1Absolute value. p 1 2For N-l-p = 18 degrees of freedom, where p = the number of dependent variables. the respective optimal bi's, it was concluded that there was not maladjustment in the use of land, labor, or machinery, relative to one another. Control Farms, 1258 Comparisons between the estimated bi's and the optimal bi's are presented in Table 13. The estimated b1 of labor was significantly different from its optimal b1 at the five percent level of significance. Thus, it was concluded that there was maladjustment in the use of labor relative to other inputs. Since the estimated b1 of machinery was significantly different from its optimal b1 at the 20 percent level of significance, it was concluded that there was maladjustment in the use of machinery relative to other inputs. Since neither the estimated b1 of land nor the estimated b1 of 58 TABLE 13 Comparisons Between.the Estimated Regression . Coefficients (b%'s) and the Optimal Regression bi's Coefficients ), Control Farms, 1958 * 2 Input bi bi bi-bilflbi t=b -b' 8:111:121n1 Categpry (gi_figpdicated(z) X2,1and .268950 .355158 .086178 .123255 .69 50 x ,1abor .566922 .205707 .361211 .129665 2.78 5 x2,prod.ex. .254063 .273204 .019141 .125223 .15 9o TAbsolute values. , 2ForN-l-p I 18 degrees of freedom, where p = number of independent variables. productive expenses was significantly different from its respective optimal b1', it was concluded that there was not maladjustment with respect to land and productive expenses, relative to each other. RegapdingtheIEfficiency‘With Which Resource; Were Used:;p,the Aggregate Efficiency conditions with respect to resource use are summarized, by input categories in Tables 14 and 15. Con- sidering Table 14, initially, notice that, in the case of the 1953 experimental farms, there was maladjustment in the use of land, labor, and productive expenses; whereas, in the case of the 1953 control farms, there was maladjustment only in the use of land relative to other inputs. Hence, it would seem logical to conclude that, in the aggregate, the 1953 control farms were in better adjustment than.were the 1953 59 experimental farms. So it was that the 1953 control farms were at an advantage, relative to the 1953 experimental farms, at the outset, so far as efficiency in the use of re- sources was concerned. However, at the termination of the program, such was not the case. By referring to Table 14, it can.readily be seen that, in the case of the 1958 experi- mental farms, there was maladjustment only with respect to productive expenses, whereas, in the case of the 1958 control farms, there was maladjustment in the use of labor and machinery. Thus, it would seem reasonable to conclude that, in the aggregate, the 1958 experimental farms were in better adjustment than were the 1958 control farms. Further insights regarding efficiency conditions can be gained by studying;Table 15, which presents comparisions between MVP's and their respective MFC's, by input categories, and, thus, serves to indicate: 1) the nature of efficiency conditions and 2) the adjustments which.were necessary if optimum efficiency in the use of resources were to have been achieved. . In view of the evidence presented in.Tables l4 and 15, it would seem logical to conclude that there was a significant increase in the efficiency in the use of resources, by input categories as well as in the aggregate, in the case of the 6O .hsosasoms no one one a.“ pace Iemofiomams mmapmoaosa .oosmoamam Iwam mo Hosea row on» no an acne usospmohsd psomommao hapsmoamaswam.mms an unospmsqum aw haosdaoms .mx momsomwo psmspmsnomImm mumaumsndm an oeaposeoao .ex .mopma no one on» ma poms Ipmsqomams wmapmoaosa .oosmoamds Imam no Hosea an on» no an some amoaommae zapsmcamaawam.mmz an pnospmmddm ma momma .mx .oms mama op soocmoa and: uses Immmwwmlludos manganese .oosooflnd psospmsdem_sa Imam mo Hoboa mod one no me some nsosoenno sansooHEsmam was we soon .mx I I I I I I I I I I II magma Howpaoo I IIIII I I I I I I I I , psospmoesa mmmmmmmdmmlmm escapquom_m¢ bwosacoms .mx .mommoowo .omnomwo obaposoomo op somehow and: pace osaposeoau on woodman and: uses .3 meaningless .ooasoflda I? wsaacoaoaa .ooaocfles Iwam mo Hosea Mom one as do some Imam mo aoboa RON on» pm me some momsomwo pmohommao mapsmoamamwam.mm3 «a unencumae meGmOAMHsmHm ems an obaposoomm .ax .nopma no on: on» ad uses ....o.m.s_.wosama_. meanness: seasoned: psospmsfiem.sa Imam no Ho>oa mod on» pm we scam psomoemae thSmoaeaswam was an momma .mx .oms coma on pooomon and: uses Immsnemams wsapmoaosa .oommoHMHs .mmmmmmmfimmlmw Imam mo Hosea mm one pm me some economic Sassodwsmam as. an ass.“ .mx IIIIIIIIIIIEamhpsoadnonwmIIIIIIIIIIIII mwma Immma mwmu emu wwma .mswom Acheson use Hopsosanomwm .moawcwopmo psasH an em: oossomom on accomom new: msoaoaosoo mosodoammm ad mammfi whowopmo psmmw 61 zoosmmoms msoapmsnom cocoon once can. no 950 msoz am. we. psoammsnem oz aw. was. msoammoasa zmmsamoma .mx cocoon macs modems mongoose newness oz cmsoso oz oo.a ea. osoaomsfios oz oo.a oo.n osaooseose .ex momma mnoammsnem cocoon once one do sac one: oo.mnmee.mme aaosnmsnoo oz 00.6mm oc.eom dogma .mx cocoon macs msosmmsfi Incense oz use case case oo.om ma.m~ comm once one oo.mm o~.mm comm .mg I I I I I I I I I I match Homosoo I I IIIIII I cocoon moms in “I modems Immsqem oz owners oz am. moo. msmsmmsnem oz Hm. mmo. msosmmohsm zaosmmoms .wx encammsn momsoawo IemHms mo comm o>mmoseoao Ice came omm mongoose chap macs asosH haommsdwomaz< wo.a mm.a Iosoono ones moosH mo.H mm.m monsoowo obmmosooao .ex cocoon macs msoapmsn I Ismsnoo oz use coda osso oo.mmnmm.am~ scams mmom Mme 00.0mm an.aemI momma .mx mm: as cocoon macs msoammsfi , scope on asap Ismsnoo oz new case memo oo.om ee.on names some once one oo.mm mm.mm ease .mx IIIIIIIImsamszmsmanzwm HIIIIIII 1 Hosanna modnowommo oeodmo< mansH om cocooz msoamdosoo hosoaoaw savaw_suv assuage oboamom om Am savmw.sdv cocoaomsnes Iaenm_sa newsman on: as: nausea assessmseos one can nwmwli (In (Noam mmma I wwww.4msamm Hospaoo use Hmmsoamn Mm n.0zz memoo homomm Home ems obamcoomom amoma_modz Am.m>zv mmoseomm osmm> Hangman: wsammesoo hm commoaosH mm .momwowommo msosH hm .omb oossomom op moozmom mod: mooamdusoo hosodoammm ma mamas 62 experimental farms over that of the control farms.13 But what were the factors which can be said to have caused the efficiency conditions, which prevailed at the outset,.to have changed? Such changes in efficiency con- ditions, over time can be said to be the result of: 1) changes in regression, i.e. changes in the input mix, and/or 2) changes in factor prices, which are reflected in changes in the optimal bi's. It will be recalled (see Tables 14 and 15) that, in 1953, land was out of adjustment relative to other inputs, for both the experimental and control farms; however, in 1958, land was in adjustment. This adjustment in.land use was the result of changes in the aforementioned factors, namely, lower estimated regression coefficients and a higher factor price for land, as shown in Table 16, in which changes in the socalled determinants of efficiency conditions are presented. Table 16 serves to indicate that changes in the efficiency conditions were primarily due to changes in regression. Of the two determinants of changes in efficiency conditions, it can be seen that, even.in the case of land, changes in regression were more important than the change in the factor price of land. 13The control farms were astually in worse adjustment in 1958 than they were in 1953. 63 Thus, in the light of the evidence presented so far, the author would conclude that the increase in the efficiency in resource use on the experimental farms over that of the control farms is attributable to the Michigan township extension program. TABLE 16 Changes in the Determinants of Efficiency Conditions With Respect to Resource Use, by Input Categories, Experimental and Control Farms, 1953 - 1958 Changes in.Efficiency Input Category Changes in.l Changes in Conditions Primarily Regressionl/thimal b1a_/Due to Chapges in: ----- Experimental Farms - - - - X2, land —.253049 +.106013 regression.and factor price X , labor +.466826 +.007055 regression X2, productive expenses +.Ol3306 -.012815 X6 , machinery investment -.OOOO76 -.000767 11 ------- 153ntrol Farms ----- X2, land -.306006 v.153258 regression and factor pr ce X , labor +.42577O +,006332 regression X2, productive expenses -.O60812 -.O4167l X6 , machinery investment -.O33862 ¢.02484l regression and factor price IChanges in regression, i .e., differences between respective b1' 8, and changes in optimal b s, are presented in absolute terms: (4) or )signs indica1e the direction of change. Regarding the Scale of Operatiopp Since the nature of returns to scale has been indicated for each function, it will suffice at this stage to ascertain 64 what changes, if any, have occurred with respect to the scale Of operations. Figures regarding the returns to scale for each of the functions are presented in Table 17. While increases in the scale of operations would seem to be desirable14 from the standpoint of increasing the effi- ciency of the Operations, in the aggregate, it can readily be seen that there have not been any appreciable changes TABLE 17 Changes in.the Nature of Returns to Scale,” Experimental and Control Farms, 1953 - 1958. 1953 1958 change Experimental farms 1.14 1.19 .05 Control farms 1.28 1.35 .07 in the scale of operations on either experimental or control farms, over the period 1953-1958. 14 This assumes that the farms used in.fitting the functions were operating under conditions of increasing returns to scale. While Statistical evidence was not available to support this contention, the author was of the opinion that the sums of the bl's for the 1953 and 1958 control functions, taken individually, were significantly greater than one (indicating increasing re— turns to scale). The author was less certain as to whether or not the sums of the bl's for the 1953 and 1958 experimental functions, taken individually, were significantly greater than one. Be that as it may, however, it seems reasonably certain that the sums of the b 's for the 1953 and 1958 experimental ‘ functions, taken indiv dually, were not significantly different from the sums of the b1's for the 1953 and 1958 control ' functions, respectively. Hence, the author would conclude that the experimental and control farms were operating under con- ditions of increasing returns to scale. This leads to the further conclusion that increasing the scale of Operations would lead to greater efficiency in the use of resources, in the aggregate. 65 Regarding_Changes in.Farm Organization The author clearly believes that, from the standpoint of this study, relative changes in the use of inputs are of considerably greater relevance than are absolute changes in such. However, absolute changes in the use ofresources, by input categories, are presented in.Table 18, in order to provide the reader with whatever insights might be gleaned from them. Inasmuch as the table is readily understandable, supporting discourse, in great detail, is not necessary. TABLE 18 Changes in the Usual Organization, Experimental and Control Farms, 1953 - 1958 Input Categoyy Units 1953 _p;258 Change -------- Experimental Farms - - - - - - - - X2, land tillable acres 136.8 148.3 11.5 X , labor months 14.4 16.4 2' X2, productive . expenses dollars 4388. 4718. 330. X5, machinery dollars 7369. 7439. 70. X1, gross income dollars 13272. 15260. 1988. ------------ Control Farms - - - - - - - X2, land tillable acres 134.6 156.4 21.8 X , labor months l6_ 17.2 1.2 Xi, productive _ , ‘ expenses dollars 3568. 3405. -163. X6, machinery dollars 7206. 8309. 1103. X1, gross income dollars 12000. 13211. 1211. However, the author would draw attention to the fact that the geometric mean.amount of productive expenses for the control farms actually decreased over the period studied.' 66 At first glance, this seems almost to be a paradox in that here is a case wherein productive expenses have decreased over the period 1953-1958, during which time farmers were involved in the “price-cost squeeze". In order to under- stand why productive expenses for the control farms decreased, it was necessary to consider, individually, specific ex- pense items, which comprised the productive expenses input category. It soon.became evident that the decrease in productive expenses for the control farms was due, in large measure, to the decreasing importance of livestock as a source of income. For instance, several expenses, namely, feed purchased, livestock expense, beginning inventory value of feeders, feeders purchased, value of beginning clover stands and value of perennials destroyed prior to June 1, all of which are directly chargeable to the livestock enterprise,15 decreased in importance over the period studied. In addition, there was a marked decrease in custom work expense, which seems to have been related to the fact that machinery investment (geometric mean) increased by 31103. per farm. So it was that decreases in the afore- mentioned expense items outweighed increases in other ex- 15This holds true except for clover grown.and plowed down for soil building purposes. 67 pense items, which resulted in the overall decrease in productive expenses in the case of the control farms. The author would further point out that while produc- tive expenses, in the case of the control farms, decreased. by $163., in terms of the geometric mean amount, productive expenses, in the case Of the experimental farms, increased by $330. The author would relate these changes, in part at least, to changes in the capital investment in livestock in.view of the fact that capital investment in livestock decreased by $402. per farm, in the case of the control farms, and increased by $500. per farm in the case of the experimental farms. 68 CHAPTER V EFFICIENCY CHANGES AS INDICATED BY TRADITIONAL FARM MANAGEMENT EFFICIENCY INDICATORS Useful insights regarding the nature of efficiency changes were gained by studying changes in certain farm management efficiency indicators,1 which are presented in Table 19. ‘While elaborate supporting discourse was deemed unnecessary, in view of the fact that Table 19 is readily understandable, it was deemed important that attention.be directed to certain of the more noteworthy insights which it purveys. Evidence of the fact that the experimental and control farms were reasonably well matched, at the outset, is found in the fact that the 1953 efficiency indicators2 for the experimental and control farms, taken respectively, were of approximately the same magnitude.3 In support of the pre- vicus statement, notice how closely the net farm income of the 1953 experimental farms ($6486) matched the net farm lSee Appendix D, pp. 96-97 where the procedures followed in computing certain traditional farm management efficiency indicators are presented.. Efficiency indicators are presented in terms of arith— metic averages. 3 . This supports the contention held by Nielson and Cross- white, Op,cit., that "the control samples matched the experi— mentalusamples well enough to serve as highly useful check groups . 69 income of the 1953 control farms ($6450). By merely com- paring the other 1953 efficiency indicators for the ex- perimental and control farms, the reader will recognize that such.was the case with respect to them also. On the other hand, the 1958 efficiency indicators for the experimental and control farms were generally not of the same magnitude, indicating differences in the efficiency in the use of resources on the experimental farms relative to the control farms. Inasmuch as efficiency in the use of resources is reflected in net farm income, it would seem- that the 1958 experimental farms were Operating more efficiently than were the 1958 control farms. For instance, the net farm income of the 1958 experimental farms ($7467) was considerably in excess of the net farm income of the 1958 control farms ($6300). This increase in the efficiency in the use of resources, in the case of the experimental farms over that of the control farms, was exemplified by the fact that in the case of the experimental farms there were significant increases in net farm earnings ($905) and net farm income ($981), whereas, in the case Of the control farms, there were actual decreases in net farm earns ings (-$340) and in net farm income (-$150). With respect to such efficiency indicators as net farm earnings, net farm income, gross farm.income per tillable TABLE 19 70 Changes in Traditional Farm Management Efficiency Indicators, Experimental and Control Farms, 1953 - 1958 Indicator 1953 _:l958 1., Chgpgp__ -Experimenta1 Farms - Net farm earnings 3 6744 8 7649 3 905 (c)(e) Net farm income 6486 7467 981 (c)(e) Gross farm income per $100 expense 195 172 ~23 (a) Cross farm income per tillable acre 98 116 18 (a)(e) Gross farm income per man 10581 13172 2591 (b)(e) Productive man work units per man 208 225 17 Productive man work units per tillable acre 1 108 2.1 .3(G)(e) - Control Farms - Net farm earnings 3 6813 $ 6473 $-34O Net farm income 6450 6300 -150 Gross farm income per $100 expense 188 173 -15 (0) Gross farm income per tillable acre 87 87 0 Gross farm income _ per man. 9671 11204 1533 (b) Productive man.work units per man 212 247 35 (a)(f) Productive man.work , units per tillable acre 2.]. 109 " 02 (O) (8) indicates a significant change . of significance. (b) indicates a significant change of significance. (c) indicates a significant change of significance. (e) indicates a significant change at the 1 percent level at the 5 percent level at the 10 percent level at the level of significance indicated and significantly more change in the experimental area than in the control area, based upon the author‘s judgment. (f) indicates a significant change at the level of significance indicated and significantly more change in the control area than in the experimental area, based upon the author's judgment. 71 acre, gross farm income per man and productive man work units per tillable acre, there was significantly more change in the case Of the experimental farms than there was in the case of the control farms. Only in the case of PMWU‘s per man (productive man work units per man) was there significantly more change in the case of the control farms than there was in the case of the experimental farms]1 On the basis of the insights acquired by studying selected farm management efficiency indicators, it would seem reasonable to conclude that there was a greater increase in the efficiency in the use of resources in the case of the experimental farms than there was in the case of the control farms.5 Regarding the nature of efficiency changes over the period 1953-1958, the author would draw attention to the fact 1+While increases in the number of PMWU‘s per man would seem to be desirable, so far as efficiency in the use of labor is concerned, such is not invariably the case. For instance, the number of PMWU's per man can increase as a result of using too little labor relative to other inputs. By referring to Table 9, it becomes apparent that labor, in the case of the 1958 control farms, was earning high returns ($435.44 per month at the margin), which is evidence of the fact that too little labor was being used relative to other inputs. 5Inasmuch as average net farm income actually decreased, over the period 1953-1958, in the case of the control farms, it would appear that resources were being used less efficiently on control farms at the termination of the study than was the case at the outset. 72 that the conclusion.drawn, as a result of studying changes in selected farm management efficiency indicators, was consistent with the conclusion drawn, as a result of studying changes in efficiency as indicated by Cobb-Douglas analysis. 73 CHAPTER VI CHANGES IN LAND USE, FERTILIZER.AND CROP YIELDS Inasmuch as land and fertilizer, important factors of production in cash crop farming, are important determinants Of yields, which are, in turn, determinants of gross farm ins come and, more ultimately, net farm income, the author deemed it important that special analysis be undertaken for the purpose of ascertaining changes in land use, fertilizer use and crop yields. While this section generally does not provide insights into the nature of efficiency changes similar to those already acquired, using Cobb-Douglas analysis and selected traditional farm management efficiency indicators, it does provide information regarding changes in land use, fertilizer use, and crop yields, without which an input— output study involving cashpcrOp farms would be incomplete. Changes in.Land Use When considering changes in land use, in the aggregate, changes in farm size and ownership status become of interest. Such information is presented in Table 20. Inasmuch as Table 20 is readily understandable, there is no need for extensive supporting discourse: however, the author would draw attention to the fact that farm size, as reflected by the average number of tillable acres operated, increased by significantly more in the case of the control farms than in the case of the 74 experimental farms. In keeping with this increase in farm size, the average number of acres owned increased significantly in both the experimental and control areas. Foremost among the changes in land use, by various crops, were the highly significant increases in the average acreages of beans and sugar beets and the significant decreases in the average acreages of wheat and hay, as indicated in TABLE 20 Changes in the Ownership Status of Farm Operators, Experimental and Control Farms, 1953 - 1958 Ownership Status 1953 1958 Changes - Experimental Farms - Total acres operated 164.8 174.9 10.1 Total acres owned 127.6 141.4 13.8 (c) Total acres rented 37.2 33.5 -3.7 Tillable acres operated 145. 152.4 7.4 . - Control Farms - Total acres operated 185.67 202.2 17.2 (b) Total acres owned 140.7 155.6 14.9 (b) Total acres rented 44.3 46.6 2.3 Tillable acres operated 156.4 174.8 18.4 (b)(f) (b) indicates a significant change at the 5 percent level of significance. (c) indicates a significant change at the 10 percent level of significance. (f) indicates a significant change at the level of significance indicated and significantly more change in the control area than in the experimental area, based upon the author's judgment. Table 21. For instance, the average acreage of beans and sugar beets increased by 27.5 and 111.1 percent, respectively, 75 in the case of the experimental farms and by 35.5 and 100 percent, respectively, in the case of the control farms. On the other hand, however, the average acreages of wheat and hay decreased by 38 and 64 percent, respectively, in the case of the control farms. Notice that, while the changes in the average acreages of beans, sugar beets, and hay were significant for both the experimental and control farms, the changes in the case of the experimental farms were not significantly greater than those in the case of the control farms, and vice versa. However, the decrease in the average. acreage of wheat, in the case of the experimental farms, was significantly greater than the decrease in the average acre— age of wheat in the case of the control farms. Further insights regarding changes in land use, which were deemed to be of lesser import and, hence, were not included in the discourse, can be gained by studying Table 21. Changes in Fertilizer Use Changes in fertilizer use are presented in Table 22, in terms of changes in the number of pounds of plant food applied per acre -- a distinctly more meaningful term than changes in the number of pounds of fertilizer applied per acre. In.aggregate, the average amount of plant food applied per tillable acre for the whole farm increased by approxi- mately the same amount for both the experimental and control farms. Specifically, there were significant increases in 76 TABLE 21 Changes in the Average Acreage of Various Crops Grown, by Acres and by Percent of Tillable Acres, Experimental and Control Farms, 1953 - 1958 1253 1258 Cha e Crop Acres Acres Acres % - Experimental Farms - Beans 49.7 34.3 63.4 41.6 13.7 27.5 (d) Sugar beets 9. 6.2 19. 12.4 10. 111.1 (d) Wheat 46.6 32.1. 28.9 19.0 -17.7 -38. (d)(e) Corn(for grain) 12. 8.3 13. 8.5 1. 8.3 cats 11. 7.6 14. 9.2 3. 27.0 (d) Hay ‘ 9.9 6.8 3.6 2.4 -6.3 -64. (d) Other 6.8 4.7 10.5 6.9 3.7 54. (d) Total tillable acres 145. 100. 152.4 100. 7.4 5.1 - Controlifiarms - Beans 50.2 32.1 68. 38.9 17.8 35.5 (d) Sugar beets 11. 7.0 22. 12.6 11. 100. (d) Wheat 34.8 22.2 28.3 16.2 -6.5 -19. (d) Corn(for grain) 12. 7.7 9. 5.1 -3. -25. (a)(f) Oats 15. 9.6 16. 9.2 1. 6.7 Hay 17.2 11.0 6.2 3.5 -11.0 —64. (d) Other 16.2 10.4 25.3 14.5 9.1 56. (d) Total tillable acres 156.4 100. 174.8 100. 18.4 11.8 (b)(f) (b) indicates a significant change at the 5 percent level of significance. (d) indicates a significant change based upon the author's Judgment . (e) indicates significantly more change in the experimental area than in the control area, based upon the author's judgment. (f) indicates significantly more change in the control area than in the experimental area, based upon the author's ngment 0 the average amounts of plant food applied per tillable acre with respect to all crOps under consideration.except for beans, in the case of the experimental farms, and cats in the case 77 of the control farms. Notice that in the case of the ex- perimental farms there were significantly greater increases in the application of plant food per acre on.corn (for grain) and oats than there were in the case of the control farms. On the other hand, however, in the case of the control farms there were significantly greater increases in the applica- tion of plant food per acre on.beans and sugar beets than there were in the case of the experimental farms. Changes in Crop Yields Changes in crop yields are presented in.Table 23. Notice that for both the experimental and control farms, the average yields of sugar beets, wheat, and oats increased, whereas, the average yields of beans and corn (for grain) decreased over the period 1953—1958. Inasmuch as the average amount of plant food, applied per acre on various crops, increased in all cases, it seems reasonable to have expected that crop yields would also have increased in accordance with the increased plant food applications. But why was this ex- pectation not realized with respect to bean and corn (for grain) yields? While there is no obvious answer to this question, the author would postulate that the decreases in the average yields of beans and corn (for grain) might have been due to a combination of weather conditions, which in 1953 were favorable to bean and corn production, resulting 78 TABLE 22 Changes in the Application of Plant Food per.Acre on Various Crops, Experimental and Control Farms, 1953 - 1958 Pounds of Plant Food per Acre on: 1953 1958_ Changg___ - Experimental_Farms- Beans ' 79.9 93.8 13.9 Sugar beets 192.1 301.2 109.1 (d) wheat 109.8 193.1 84.0 (d) Corn (for grain) 88.1 161.8 73.7 (d)(e) Oats 84.9 126.0 41.3 (d) (e) Pounds of plant food per tillable acre, whole farm 93.0 144.5 51.5 (d) - Control Farms - _ Beans 36.1 60.9 24.8 (d)(f) Sugar beets 103.0 257.9 154.9 (d)(f) Wheat 88.0 148.2 60.2 (d) Corn (for grain) 67.0 116.0 49.0 (d) Oats 74.8 95.0 20.2 Pounds of plant food per tillable acre, whole farm 53.2 102.1 48.9 (d) (d) indicates a significant change, based upon the author's Judgment. (e) indicates significantly more change in the experimental area than.in the control area, based upon the author's Judgment. (f) indicates significantly more change in the control area than.in the experimental area, based upon the author's judgment. in high yields, but in 1958 were unfavorable to bean.and corn production, resulting in somewhat lower yields. Notice, that in the case of the experimental farms, there were significantly greater increases in the average yields of cats and hay than there were in the case of the control farms. However, it should be recognized that this 79 TABLE 23 Changes in Crop Yields per Acre, Experimental and Control Farms, 1953 - 1958 Crop Units 1953 1958 Change - Experimental Farms - ~ Beans bushels ~ 23. 19. ~4. Sugar beets tons 13.8 19.6 5.8 (d) Wheat bushels 36. 62. 26. (d) Corn (for grain) bushels 81. 66. -15. Oats bushels 56. 110. 54. (d)(e) , Hay (alfalfa) tons 1.9 3.0 1.1 (a)(e) “- Control Farms - . Beans bushels 22. 20. -2, Sugar beets tons 11.9 16.6 4.7 (d) Wheat bushels 38. 57. 19. (c1) Corn (for grain) bushels 72. 58. -l4. Oats bushels 56. 88. 32. (d) Hay (alfalfa) tons 3.0 2.0 -1.0 (d) (d) indicates a significant change based upon the author's judgment. (0) indicates significantly more change in the experimental area than in the control area, based upon the author's judgment. significantly greater increase in the average yield of hay, in.the case of the experimental farms over that of the control farms, was not very important in that the average acreage of hay grown, on both the experimental and control farms, de- creased very significantly over the period 1953 - 1958. 80 CHAPTER'VII CONCLUDING STATEMENTS Ample evidence is now available to support concluding statements as to whether or not there was a greater increase in the efficiency in the use of resources in the case of the experimental farms (attributable to the Michigan township extension program) than there was in the case of the control farms. Without reiterating, step by step, what has already been stated explicitly in Chapter IV (see especially Tables 14, 15, and 1? and the supporting discourse which applies in each case), the author would conclude, on the basis of , evidence provided by Cobb—Douglas analysis, that there was, in the case of the experimental farms, a significantly greater increase in the efficiency in the use of resources than there was in the case of the control farms. Inasmuch as both the experimental and control farms, at the outset, were operating under conditions of increasing returns to scale, increases in the efficiency in the use of resources could have been achieved by increasing the scale of operations (i.e., by increasing the use of resources in the very pr0portions in which they were being used). How- ever, since the analysis bears out that there were no apr preciable changes in the scale of operations of either the experimental or the control farms, over the period 1953-1958, 81 it becomes evident that the significant increase in the efficiency in the use of resources, in the case of the ex- perimental farms over that of the control farms was not due to changes in the scale of operation. Thus, the author would conclude that the Michigan township extension program was instrumental in increasing the efficiency with which resources were used, in.the case of the experimental farms over that of the control farms, by virtue of the fact that the town? ship extension agent was effectual in advising farmers as to what changes in farm organization could be effected in order to cause resources to be used more nearly in the proper proportions relative to each other. On the basis of insights gained by studying selected farm management efficiency indicators (see Table 19 and the supporting discourse which applies), the author would COD! clude that there was a greater increase in the efficiency in the use of resources in.the case of the experimental farms than there was in the case of the control farms. Notice that this conclusion is clearly consistent with the conclusion drawn.as a result of studying changes in efficiency as in, dicated by Cobb-Douglas analysis. Thus, all the evidence supports the conclusion.that the Michigan township ex- tension program was more effective in increasing the efficiency with which resources were used on cash crop farms in.Denmark township than was the traditional county extension program. APPENDICES APPENDIX.A PROCEDURES FOLLOWED IN PREPARING THE DATA FOR COBBéDOUGLAS ANALYSIS 82 Summary Sheet for Cobb-Douglas Analysis Farm no.“ Area (1) Tillable acres flay ggd.pasture inventory Total beginning value of perennials and 2nd year clover Minus prop. credit for perennials destroyed Sub total Plus machinery hired for land reclamation Plus value of perennial seed purchase and used Plus value of excessive lime or fertilizer investment Total forage investment ______. Beginning value of one year clover stands ) transfer to Beginning value of perennials destroyed before June 1 ) expenses Livestock inventg_1_and balance Beginning inventory of Ending inventory breeding stock Beginning invenp Plus breeding livestock tory plus purchased purchases Beginning inventory plus purchases (total) Increase or decrease (circle one) Feeders on hand ) transfer Feeders purchased ) to expenses page. Livestock investment Beginning inventory of breeding stock Plus total prop. cost of breeding stock Minus prop. credit of breeding livestock sold Total breeding livestock investment Total forage investment (2) Total livestock - forage investment Hachinery.investment Auction value Januaryl .1253 (or Januar1_l 1958) Plus prop. additions Minusprgp. deductions PIE) ¥(3) Total machinery investment 83 Gross income Total value of family livinggfupnished by farm Zptal cash receipts Livestockgpvestmentp;;ncrease_pr deggpase Feed and seed investment, increase or decrease (4) Total gross income (5) Total months of labor Labor Productive expenses gpedpurchased Seeds and plants purchased annual Custom work or machinery hired §ppplies purchased st and oil for farm_u§e'(less refgdeD Livestock expense VElectriciti CFarm share) Telephone (Farm share) Baby Chicks purchased égtomobile(Farm shareip Tpuck upkeep (Farm share) 0thgp productive expenses Beginning inventory of feeders ander broglers Fpederspurchased Beginnipg value of clover stands Beginning value of perennials destro ed begore June 1 (6) Totalproduppive expenses (2) Fertilizer expgnse Final gummarz 1) Tillable acres (X2) (2) Total livestock-forage investment (X5) (3) Total machinery investment (X5): (4) Total gross income (X1) (5) Total months of labor (X3) (6) Total productive expenses (X4) (7) Fertilizer expense (X7) Hay-Pagpure Evaluationpl958l The values used in computing the investment in perennial forage stands were based on the estimated per acre cost of establishing the stands. Adjustments were made to take into account the quality and age of the stand as shown below in Table 24. TABLE 24 Hay-Pasture Evaluation, 1958 1) For perennials: Condition of stand Year Excellent Good Faip Poor lst $33 $33 726 819 2nd 33 26 19 12 3rd 33 19 12 12 4th 26 19 12 5 5-6th 19 19 12 5 7-8th 19 12 12 5 2) For reed canary grass: _ . ' , Year Excgllent Gogd Fair Poor lst $17.50 $17.50 316750 $10.00 3; For annuals: ‘ p P , ro . Excellent Good Fggr oor Red clover $24.50 $24.50 $23.50 §10.00 Red cloverrsweet - clover mixture 24,00 24,00 23.00 10.00 June clover-sweet _ . _ clover mixture 24.00 24.00 23.00 10.00 Sweet clover 23.50 23.50 22.50 10.00 Mammoth clover 23.50 20.00 19.00 10.00 Sudan grass 36.00 36.00 35900 10.00 Rye 26.00 26.00 25.00 10.00 Oats 30.50 30.50 25.00 10.00 J-The values used in the 1958 hay-pasture evaluation.were worked out by the author with assistance from Professor C.R. Hoglund, Department of Agricultural Economics, Michigan.State University. Professor Hoglund suggested that, because of in- creasing costs, (namely, machine cost, gas, oil, etc.) the values used in the 1953 hay-pasture evaluation be adjusted downward by five dollars per acre, which recommendation was followed herein. 85 Ordinary rough pasture was valued at five dollars per acre. Other pasture was valued in accordance with the quality of the stand, using the chart for the 1958 hay-pasture evaluation. leculatingProportional Credits for Perennials Destroyed The following criteria were used in calculating prop- ortional credits for perennials destroyed: 1. Proportional credit was computed only if the stand of perennials was destroyed (plowed down) on June 1 or thereafter. The beginning inventory value of alfalfa-brome was counted as an.expense, if plowed down prior to June. Proportional credit was computed, if alfalfa-brome was plowed down after June.1. In addition, the beginning inventory value of the stand minus the proportional credit was counted as an expense. Proportional credit was computed for alfalfa-brome plowed down in.August or September for wheat, even if it was clipped or pastured during the summer. Proportional credit was computed for any good stand of pasture which was plowed down for corn or cats in the spring. If a worthless stand of hay or pasture was plowed down, preportional credit was not computed. 86 7. Proportional credit was not computed for clover destroyed. First year clover was counted as an expense. Second year clover was considered as an investment at five dollars per acre. 8. Biennial seeding such as June clover, sweet clover, etc., was considered as an expense, except if seeded in a perennial mixture . Calculating Proppppional Costs and Credits for Breeding Stock For the purpose of this study, only dairy cattle were regarded as breeding stock -- the rest were considered as feeders for which.pp proportional costs or credits were calculated. The procedures followed are outlined below. If breeding stock were purchased (proportional cost) or sold (proportional credit) in: January, multiply value paid or received by 1. February .92 March . .83 April 975 May ’ .67 June .58 July 95 August .42 September .33 October .25 November .17 December .08 87 in order to determine the proportional cost or proportional credit. Calculating Proportional Additions and Deductions for Machinery Bought and son; The very same method was used in this case as was used in calculating proportional costs and credits for breeding stock purchased and sold. APPENDIX B STATISTICAL TESTS TO BE USED WHEN STUDYING REGRESSION COEFFICIENTS, INDIVIDUALLY AS WELL AS IN AGGREGATE 88 A 't' Test Employed to Determine Whether or Not Significgnt Differences Were Existent Between the Regression Coefficients of the Experimental and Control Areag The statistic used, which has a "t' distribution, is given below: 1;. B‘l) SP aii ‘ a'ii where: 0" p I! the general expression for a regression coefficient of the experimental function. 0‘ p- II the general expression for the corresponding re— gression coefficient of the control function. Sp is the pooled variance, derived from the following equation: Sp = (N-l)s2 . (Nl-l)s'2 (N-l) e (NI-1) where: N 8 number of observations in the experimental sample. Nl- number of observations in the control sample. 8285(yi-1)2 = estimated variance in gross income for the N - 1 experimental sample where: y1 = actual gross income y a arithmetic mean of gross income 89 s'z-r 501-502 = estimated variance in gross income N' - l for the control sample. aii indicates the diagonal element of the inverse matrix of the experimental observations. a'11 indicates the diagonal element for the control observations. The only difference between a11 and a'ii is in the matrix Z (due to different observations). Hence, it will suffice to demonstrate the way in which either 311 or a'11 is Obtained. The author has chosen to obtain aii° Consider the Z matrix, defined below, whose element is an observation on an independent variable, zij, i.e., the ith observation on the jth row: Z ' 1 211 z12 213 214 215 O O O O O O 1 zN1 2N2 2N3 2N4 2N5 Notice that five independent variables are involved. Now, Z'Z is the sample moment matrix, the inverse of which is denoted by: (Z'Z)'1. In the inverse matrix, next consider the diagonal element, aii: for i = l ... 6. Pick out the 9O aii value which corresponds to the particular regression coefficient which is being tested. The final step is to substitute these derived values in equation.B (1) which has the "t" distribution with N + N‘ -2 degrees of freedom. Two necessary assumptions which must be met in.order to use the above form of the “t" test are: 1) the assumption of independence between experimental and control samples and 2) the assumption that the variance associated with the experimental variables is the same size as the variance associated with the control variables. An ”F“ Test Employed to Determine Whether Or Not the SEQ, of the Regression CoefficientgngpSignificantly Dgfferent From The statistic used which has an "F" distribution.is shown below: F = (c'b-l Ic'(Z'§)'1c](c'b-1 , with 1 and N-6 degrees of freedom. 1 WW N-6 where: (c'b-l) 8 [(b2 + b3 + b4 + b5 + b5) ~11 (Z'Z)'l = inverse , matrix o C. H0 0 PHI-‘0 c'(Z'Z)’1c = sum of Squares and sums of cross products of the independent variables. N = number of farms in the sample. 91 N-6 ' number of degrees of freedom for 5 independent variables. 6'6 - sum of squared residuals = éf(actual income- 2 predicted income) The hypothesis is stated as: c'B s 1. If "F" calculated were greater than “F” in the tables for 1 and N-6 degrees of freedom, at the particular level of significance chosen, the hypothesis would be rejected. APPENDIX C OBSERVATIONS USED IN FITTING THE FUNCTIONS, SUMMARIZED BY OUTPUT AND INPUT CATEGORIES 92 TABLE 25 Observations Used in.Fitting the Experimental Function, 1953 Variable Productive Livestock- Machinery Gross Land Labor Expenses Forage Investment Income Farm No. (X2) (X3) (X4) (X5) ($5) (X1) 401 95. 15.6 $4850 3 1 $10423 $12225 402 288. 27. 8157 754 9856 31285 404 114 . 18 . 4700 1 8037 9613. 405 76. 21. 1959 180 3402 6581 406 74. 6.7 4268 1 2267 11458 407 343. 33.9 17195 1120 20930 40984 410 256. 18. 6577 1 15753 20672 411 91. 16. 5391 1 5998 9020 415 170. 15. 3308 531 7460 12358 416 95. 13. 2348 l 1975 7458 417 120.5 10.6 4750 1 10951 17759 419 70.6 10. 3384 1 5999 9165 422 255. 24.4 10205 840 6322 29331 423 176. 13.3 2824 1 7733 18601 426 140. 28.8 5160 4565 10933 16047 427 90. 8. 2626 1 4548 7224 428 156. 18.4 4572 1 9433 11521 430 133. 9. 2776 1 6480 8461 432 203. 17. 3730 554 5596 13612 433 190. 9. 3284 1 11899 16344 435 101. 8. 2196 l 6455 6023 437 141. 11. 4963 1 7262 14157 438 184. 29. 9029 4054 18118 26126 439 80 . 6. 4057 l 6443 9484 TABLE 26 93 Observations Used in Fitting the Control Function, 1953 Variable Productive Livestock- Machinery Gross Land Labor Expenses Forage Investment Income Farm No . (X2) (XQL (X4) (X5) (X6) (X1) 501 105. 10. $3548 $1661 3 3486 $ 5801 504 106.6 12. 2309 1 2401 7514 506 70. 15.6 3141 434 3819 4739 509 142. 17.7 4624 1458 5478 13555 510 182. 14. 3467 1 9817 13464 511 233. 16.3 5232 4576 9118 26389 512 105. 14. 2655 2175 4262 8334 514 95. 5. 1680 1 3022 5347 516 167. 20. 3897 2447 11663 14096 517 87.5 17. 3794 2955 5141 7416 518 138. 10.8 8008 466 8791 19200 519 132. 25.6 2463 1 7539 12232 520 221. 15.7 8054 1 14494 23704 521 70. 13. 677 1 5108 3784 523 277, 36. 6942 1 15974 24850 524 150. 14.4 5295 812 5859 12697 525 101. 24.8 3593 1037 9233 13533 526 113. 8.3 2072 l 8766 8058 527 66.5 8. 1274 1 4446 5578 528 154. 13. 5250 1 4916 12532 530 150. 21. 2836 1 9625 15369 531 139. 26.3 448 336 10509 15687 532 184. 22.6 665 1 10550 22109 533 75. 15. 2015 1 5944 10903 534 166. 18.3 3532 1 19258 14520 537 186.5 21.5 5565 1- 7931 , 16188 538 367. 35. 8772 1 15164 43884 A 94 TABLE 27 Observations Used in.Fitting the Experimental Function, 1958 Variable Productive Livestock- Machinery Gross Land Labor Expenses Forage Investment Income Farm No. (X2) (X3)( (X4) (X5) (X6) (X1) 401 95. 7.5 $3514 8 740 t 6033 811869 402 405. 48.9 9853 1 9809 45372 404 122. 18. 3213 57 6920 14134 405 132. 19. 3527 88 3456 10770 406 150. 20.1 15988 1 5129 29464 407 251. 33.1 20663 878 11202 48770 410 238. 21.7 4961 46 17107 21423 411 93. 14.2 4103 1 6719 13717 415 184. 19.6 3702 1 9645 12480 416 117, 10. 2259 20 3563 8331 417 185. 20. 5256 1 14210 21256 419 75. 14.4 4043 65 6691 12297 422 298. 34. 8321 - 1 13040 36773 423 163. 15.1 3322 99 10811 15006 426 157. 22.9 5075 3304 24333 17499 427 136. 18. 6137 230 7437 14400 428 105. 14. 4415 1 5084 9271 430 192. 13.2 2960 132 3508 14271 “32 175. 12. 4872 752 7035 9479 433 73. 7.7 1847 l 4963 7319 435 101. 9.8 2490 1 7262 4729 437 146. 13. 3499 1 6021 10556 438 283. 20. 15551 8205 16081 52163 439 74. 10.7 2288 1 2425 7894 95 TABLE 28 Observations Used in Fitting the Control Function, 1958 Variable Productive Livestock- Machinery Gross Land Labor Expenses Forage Investment Income Farm NO. (X2) (X3) (Xh) (X5) (X5) (X1) 501 175. 16.4 $3425 $1929 3 3297 $ 8604 504 108. 7.7 2611 1 23109 8466 506 68. 15.7 2253 137 10722 8643 509 155. 26. 2171 1 5180 13436 510 150. 17. 3774 96 10125 11286 511 155. 19.6 2785 1973 5329 13823 512 106. 11.6 2986 1 10375 9794 514 94. 14. 1592 414 4902 5738 516 159. 27.7 6485 6220 12003 16638 517 144. 18.1 4486 ‘ 291 5330 11852 518 237. 12.5 2543 579 6426 9653 519 115. 14.3 2378 75 10482 12301 520 198. 18.6 7151 1 9068 19575 521 144. 13.3 1712 l 6629 7590 523 276. 27.3 5508 1 10359 20875 524 182. 15.4 5742 271 5396 12885: 525 112. 18.7 4491 403 10088 21869 526 150. 15. 3084 1 6352 10783 527 117. 8.5 2280 l 7341 7548 528 168. 10.9 2419 l 7283 11858 530 152. 27.7 2923 1 11471 18662 531 164. 19.8 2375 37 6686 15034 532 186. 22.9 5054 l 7403 14199 533 72. 14.6 1944 1 5262 8939 534 487. 29.0 7463 34 17470 40536 537 225. 19.0 5381 1 12808 23068 538 355. 33.2 7475 1 17508 38262 APPENDIXID PROCEDURES FOLLOWED IN COMPUTING CERTAIN TRADITIONAL FARM MANAGEMENT EFFICIENCY INDICATORS 9.- 10. ll. 1. 2. 3 4. 5. b) PER TILLABLE ACRE (l 96 COMPUTING MEASURES OF FARM EARNINGS Total cash farm receipts 3 ea Livestock purchases Inventory changes: Feed and crops $_____ Livestock Total inventory change _____ GROSS FARM INCOME (l-Ze or - 3 Value of farm products used at home TOTAL VALUE OF FARM PRODUCTION (4 . 5) Total cash farm expenses Depreciation: Machinery Buildings Total depreciation Total cash expenses and depreciation (7 + 8) NET FARM INCOME (4 - 9) NET FARM EAMIINGS (6 - 9) COMPUTING MEASURES OF GROSS FARM INCOME Gross farm income Expenses and depreciation s $100 . Tillable acres Number of men GROSS FARM INCOME: 2) 3) a) PER $100 EXPENSES (1 cl. 0) PER MAN (1 e 4) COMPUTING MAN WORK UNITS 97 TABLE 29 Chart Used in Determining the Number of Productive man Work Units PNWU Crops Acres. Factor Total Corn, silage 1.5 Corn, grain 1.0 Oats .6 Wheat .6 Sugar beets 5.0 Soybeans .8 Alfalfa hay .7 Other hay .7 Grass or legume silage .7 Total, crops --- Livestock Number Factor Total Dairy cows 10-0 Bulls 8 .0 Calves and heifers 2-0 Beef cows 2.0 Feeders 105 Litters 3.0 Hogs bought ‘ ~25 Ewes and rams 95 Hens 918 Chicks bought ~06 Turkeys .3 Total, livestock _* Total PMWU, crops and liveStock PMWU per man PMWU per tillable acre 98 BIBLIOGRAPHY Beringer, 0., A Method of’Estimatipg Marginal Value Produptr ivities of Input and Investment Categories on.Multiple Enter ise Farms, (unpublished PhtD. Dissertation, Department of Agricultural Economics, Michigan State University, 1955). . 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