'_|\l ‘w TH! 05! OF COBBDOUGLAS ANALYSIS IN EVALUATING THE MICHIGAN VOW}? EXTENSION PROGRAM Thai: for {he Dam or? M. S. MiGflGAN STATE UNIVERSITY Carl Eichar 1956 MSU LIBRARIES “ RETURNING MATERIALS: PIace in book drop to remove this checkout from your record. FINES wiII be charged if book is returned after the date stamped below. TIE USE OF COBB-DWGLAS ANAHSIS 1N EVAIUATING THE MICHIGAN TWIBHIP REGION madam Carl Echer AN ABSTRACT Suhnitted to the College of Agriculmre of Iflchigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agrimltural Economics Year 1956 Approved .4_#‘ c c <3 / — ABSTRACT The purpose of this study is to appraise the‘use of Cobb—Douglas analysis as a measure of economic efficiency for extension evaluation. In 1953, the Michigan Township Extension prog'am was instituted in five townships. Each township has a full time township extension agent. Forty farms were selected in each of the five experimental townships and surveyed in 1953 for benchmark information. Control townships were selected to match the experimental townships. Control township rams were paired with the experimental township farms and on the basis of benchmark, intermediate, and teminal surveys, the changes in the experimental township will be compared to the control township changes. The changes occurring in the experimental township will be credited to the township agent while control township changes will be attributed to the county extension organization. One of the major changes being measured in the experiment is economic efficiency. Economic efficiency is an instrumental value concerned with profit maximization of the firm. There are many avail- able methods for measuring economic efficiency. lhe traditional ram management technique and Cobb-Douglas analysis are being used in the township eaneriment. Since Cobb-Douglas analysis has not been used in extension evaluation it will serve a dual purpose in the township program evaluation by providing estimates of the changes of efficiency in the program and also by providing information to extension adminis- trators and evaluators on the cost, reliability, and value of using this method in extension evaluation. 11 The data for this stucnr were taken from one of the five experimental townships and its matched control township. flirty-three dairy farms in the experimental township and thirty-two dairy farms in the control township were used to fit Cobb-Douglas functions to establish the bench- mark level of efficiency in these two townships for 1953. Mm'glnal value product estimates for land, labor, expenses, live- stock-forage investment and machinery investment were derived for the two townships. Several statistical tests were used to determine if the level of efficiency for the two townships was the same for the bench- mark year. on the basis of these tests, it was found that there was not a significantly different level of efficiency between the experi- mental and control township for 1953 . Cobb-Douglas analysis has several advantages which may be of interest to extension evaluators. It is a valid measure of efficiency. It measures the net returns to categories of inputs and investments in margnal terms. also, it is a complete efficiency concept as it measures both input and output. 'Lhe reliability of this method cannot be fully appraised until the completion of the five year experiment. 0n the basis of this stucw, three functions had to be fitted in the control township; thus the resulting control estimates are not clearly defined. althougi more detailed information on the use of this method in extension evaluation will be available in 1958, it appears on the basis of using this method in measuring economic efficiency in two townships that is is one of the best measures of efficiency presently available. It is felt that an extension evaluation program can be strengthened if both Cobb-Douglas and traditional farm management analyses are used to measure econanic efficiency changes. iv THE USE OF COBB-DOUGLAS ANAHSIS IN WANATING THE MICHIGAN WI? HMICN FEW By Carl Bic-her A'IHEIS Submitted to the College of agriculture of Michigan State University in partial fulfillment of the requirements for the degree of MASTHI CF some: Department of Agricultural Economics August, 1956 acmcwmmrs 'lhe writer wishes to express his sincere appreciation to his major professor, Dr. James Nielsen, for rendering help during all stages of the developnent of this thesis . the empirical part of the analysis could not have been carried out without the use of data collected by the project evaluator of the Michigan Township Extension rrogram for the benchmark stucbv in the experimental and control townships. ,opecial assistance was given by members of the statistical pool in the Depu'tment of agricultural Economics. me financial assistance in the fan of a research assistantanip which was provided by the Deporhnent of ayicultural Economics, successively headed by ur. llamas K. Cowden and ur. Lawrence L. Roger is deeply appreciated. The writer also wishes to acknowledge his debt to Dr. Glenn 1.. Johnson who provided much insiQIt into the theoretical nature of the study. In addition gratitude is expressed to Christoph Beringer, Harold Cater, Burt cundquist, and albert Halter who contributed much to the content of this study. Finally, the writer thanks his wife, Joanne Bibolz Richer, for her help . W TABIBWCONMI‘S m I WMONOOOOOOOOOOOOOOOOOOOOOOCOOOOOOOOOOOOOOOOOOOOO. m3 Cooperative MOMS-on Smice..no....uunno.... me Midlim mem10n Serviceman""unnuun. The Michigan Township Extension Progran.............. Econmc EfficienCYOOOO0.0.00.0000...OIOOOOOOOOOOODOOOO Measuring Economic Bfficiency........................ II MIG”. 3&0“.me or com-DOUGLAS ANAIISB.......... Wed Dm1°ment...................0............. Ellperical Studies in Ammtmesssssssesssseseesees PrmCtion Fm‘lctions..nu.....uu.u.o............... Value ”motiflty WiOmeseesseessesssesseeseesee CObb-Douglaa Hometion Mimeeeesssseeseeseeseseeee Steps to Fellow in Fitting A Cobb-Douglas Function to Ammtural Data"...Hanan-o...u.............. Framework of Production Function Stva............... III COLIETION OF DATA AND FITTING THE FUNCTION.............. The Sample Townshipsessssssssszseesesesessesseeseseeess me MPSessssssesesseeessssassesssesseeessessese Market Outlets....u.uu.uu."0....nonuuuu. SOfl Typeeseeeeeeseseeeeeeeeeessseseeeeeeeeeseeesees. Climatic Factomeeesssesssseeseeeesseesesseeeeesseees Present Lam USOessseeesseeeseseeeeseeseseeeesessesee Data Emerationesseseesssseesssssesssesseeesseeeesee n16 SW18 Farms...”.nonun..."u.......u...o.... Fitting n10 Functionsassessseeeesssssssseseeeeesssseeas Appraisal of the Second Function for the Control TOWnShipessessssssesssesseessaeesseseseseseeseeseso Fitting the Third Function to the Control Township. . . Reorganization of the Ebnperimental and Control Township Moeeeseseeseeseeeeeeeesesssssessseeseseseseeeesse mmntal Tmpeesesseeessseesssassessesssseeeo Contra]. Tmpessesseeeseeeeeesseessesesseseeeseeoe IV STATISTICAL REULTS AND 30mm STATISTICAL TETS TO USE IN EVALUATING THE CHAN® IN ROMEO EFFICMCY‘AT THE CWION OF TIE Wesssssseeeessseesssssss vii 97 TABIECFCCNI‘ENTS-Contimed mm Page Interpretation of Cobb-Douglas Results in the Two TMipaeeeeesseseseesassessesosseesssseeesseeeeeeee 97 Camparisan Of Marginal Value PPOdnCtBesesssssesesssse 98 Statistical Tests Used to Compare Production Emotions and Regression Coefficients for the Experimental GDd ContPOI wanShipsesseessesseeesese 106 m Of Statinical Tests..o...u............o.... 113 Evaluating the Ganges in Economic Efficiency on the Basis of Cobb-Douglas Analysis at the Completion of the Township Extension Experiment.................... 11h Changes in Terminal survey schedule.................. 115 COlleCting‘the Data.................................. 115 Fitting the Functions................................ 116 Comparing the Terminal Estimates with the Benchmark Estimates......ooo.o................o.............. 116 mer SuggBStGd StatisticaJ. Tests.................... 120 Detemining my Efficiency Changes Occurred.......... 121 Appraisal of Cobb-Douglas Analysis as a Measure of Ilconomic:Ifficienqy.....o...o...oo.......o........... 122 Advantages of Cobb-Douglas Analysis.................. 122 mutiom Of CObbDOuglds maeeeesseessesseseo 123 Comparison of Cobb-Douglas Analysis with the mean- tial alaracteristics of a Good ”Measure of Economic mfldMeeeeeeseeesecessssseseseeseeeeesseeeeseee 126 V APPRAISAL (F 0083-wa ANAIlSJB AS A TOOL OF MION mmnmo...OOOOOOODOOOOOOOOOOO0.0.0....00.00.0000... 129 Econanic Efflczlelwy Redefmdesssessesseesssseseessee 129 MbthOdOIOgical PTOCOdnrOSeesssseeesseesseseeeeseeseee 130 Sampling..........o...o..................oooo...... 130 coateeeeeseesseeesseesesseseeesesesseeseseeeeseseee 131 Accounting..o..oogoo.......oo...................... 132 Fitting fihO Function...o.....o..................... 133 Price Ghangfi Adjustments..o........o.............o. 133 Interpretatian.............................o.o..... 133 Application...................o................o... 13h bWOO...........C0.......O.....................O. 13h W0...OOOOOOOOOOOOOOOOOOOO00.00....OOOOOOOOOOOOOOOOOOIO 136 APPmImOOOOOOO0.0.0.000...O0.00.00.00.000.0.0.0000...00...... 1&0 viii LIST OF TABIB mm 1. 2. 3. 7. 9s 10. W30!) of the Geometric Mean Organization of the Experimental Township With the Control Township, 1953...... Canparison of the Range in Inputs, Investments, and Gross Income in the Emerimental and Control Township, 1953...... Usual Organization and Estimated Marginal and Gross Value Products, Thirty-Three mcperinental Township Fams, 1953... Comparison Between the Estimated Reg‘ession Coefficients and the Regression Coefficients Required to Yield the Market Price of Resources for Thirty-Three Emerimental TWP Fm, 1530.00.00.0000000000000000000000000000000 Usual Organization and Estimated Marginal and Gross Value Products Minty-Two Control Township Farm, 1953, First WimOO00.0.0.0...000000000OOOOOOOOOOOOOOOOOOOOOO0.00.... Compm'ison of the Geometric Mean Averages of Input Cate- gories for the First and second Control Township Functions with the Experimental Township Function,-l953.............. Usual Organization and Estimated Margnal and Gross Value Products,‘niirty Control'TOwnship'Fanns', 1953,‘Second ’. ' MtimOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOCOOOOOOOOO0.0.0000... Conpuison of Cemetric Means, Regression Coefficients, Standard more and Marginal Value Products for Two Motions to Thirty-Two and Thirty Control Township Farms, 1953esseeeeesseeesseseeeeeesssesseseeeeeeeeeeessesseseeeeee me Geanetric Mean Organization, Regression Coefficients, standard Errors and Margnal Value Products for Thirty Control Township Fams, 1953, Third Fm1ction............... Comparison Between the Estimated Regression Coefficients and the Regression Coefficients Required to Yield the Page 67 68 72 75 78 81 8h 86 89 Market Price of Resources for Thirty Control Township Farms, 1953, mm Wineseeesessssseesssssssesesassessessessee Comparison of Number of Farms , Gross Incane , Multiple Coy-elation Coefficient (R), Coefficient of Detemination (R , Standardm'rorofEstimate (3) amtheb‘mnofRe- greasion Coefficients for mree thctions for 32 and 30 Fm in 15110 ContrOl Township, 1953sseseseseesseeessssesese ix 91 LIST OF TABLES - Continued TABIB Page 12. Comparison of quantity of Inputs and Marginal Value rroducts in the Ehcperimental and Control Townships, 1953. . . 98 13. Comparison of Geometric Means and Marginal Value Products for Land, Labor, and Livestock-Forage in the Experimental am m0]. TmahipS, 1953000eassessessessseeseesseeeesese 10h 1h. Canparison of Individual Regression Coefficients for the Experimental Township Function with the Control Township meta-on, 19530OOOOOOOOOOOOOOOOOOOCOCOOOOOOOOOOOOOOOOOOO000 109 15. Estimated Gross Income For a Farm in the rhcperimental TWP, 1953.00.00.00000000000000..0....OOOOOOOOCOCOOOOO. no LIST OF FIGURES FIGURE Page I Outline Map of Michigan Showing almont merimental and Burnside Control Township From Which the samples Were m for ma SWOOOOOOOOOOO0.000000000000000000000.0.0 3 II Total Physical Product, All Inputs Variable and Increased in com mortiomOOOOOOO0.0.00.0.0...IOOOOOOOOIOOOOO 31 III Diagrmn Slowing the law of Diminishing Returns............ 33 IV Diagram Showing the Relationship Betwaen the Value of Marginal rroduct, Total mysical Product, Average Ihysical Wt m .1116 Price Of the Variable Input............... 35 V Change in Economic Efficiency Resulting fran a Technolog Change mg 1953-1958esssssssessassessesssssssssssassess 118 VI Change in Econanic Efficiency by a shift in Fem Organi- zation. Increasing 16 from n in 1953 to B in 1958........ 120 01mm I IM'RGJUOTION The Cooperative Extension service has made important contribu- tiom in the development of American agriculture during the past forty-two years of its operation. One of the areas of extension work that has been receiving increased emphasis during the past decade is that of extension research. Research in extension is designed to measure the effectiveness of on-going extension programs, to experi- ment with new programs, and to point the way toward improved procedures for meeting the demands of modern agriculture. One of the important factors facing extension evaluators is to determine what to measure, how to meamre it, and to analyze the esti- mated cost and value of a specific type of measurement in order that a research program will yield the maxim useful information for extension administrators, specialists, and field workers. One of the factors to measure that confronts many extension evaluators is economic efficiency. Economic efficiency is an instrumental value that is concerned with profit maximization for the fam firm. Although economic efficiency is not an end in itself, it does provide an important avenue that farm funilies miglt use to improve their standards of living or to achieve broader goals and objectives in life. ‘ Many extension evaluators have successfully used traditional farm management methods to measure the changes in economic efficiency which have occurred as a result of extension education. his thesis is designed to appraise and present the preliminary results of experi- menting with a new method of measuring economic efficiency in extension evaluation by using a specific type of regression equation commonly known as Cobb-Douglas analysis. Cobb-Douglas analysis is based on static economic principles which measure returns to categories of inputs and investments in marfinal tems. This type of analysis is being used along with traditional farm management methods to measure the changes in economic efficiency that occur as a result of the five- year township extension experiment that was established in five townships in Michigan during 1953. Various proven economic and socio- logical indices are being used to measure the changes resulting from the intensive township experiment . In addition, new approaches such as Cobb-Douglas analysis are being experimented with in order to detemine their usefulness in extension evaluation. at the completion of the emeriment in 1958, a complete report on the use of Gobb- Douglaa analysis and other evaluation methods in the Michigan township prom will be presented. 'lhis thesis will report the preliminary findings in using the Cobb-Douglas method to establish a benchmark level. of economic efficiency for 1953 in one of the experimental and control townships in the Michigan township extension progam. This study uses the 1953 benchmark data for 33 dairy fauna in one of the five experimental townships named Almont and BO dairy farms in its matched control township of Burnside in order to fit Cobb- Douglas functions and outline the procedure followed in adapting this type of analysis for extension evaluation. Both the experimental and control townships used for this stuw are located in Lapeer County, Hichigan, as shown in Figure I. In order that the reader will understand some of the underlying factors about the nature of the Extension Service, extension evalu- ation, the mchigan township extension progrm, and the frmework of this story, the reminder of this chapter will include developments of the Extemion Service that led to the establishment of the township extemion program, the objectives, operation, and evaluation of the Michigan township extension program, and the need for studying economic efficiency by extension evaluators. The first objective of this stucv is to trace the historical and theoretical background of steaming econcmic efficiency. It will focus on empirical studies in agriculture and will discuss the pro- cedure for extension evaluators to follow when using Cobb-Douglas type of analysis in measuring the changes in economic efficiency resulting frat some phase of extension education. This objective will be presented in Chapter II . be second objective is to measure marginal returns to categories of inputs and investments in Almont experimental. township and its matched control township of Rn'nside for 1953, in order to compare the level of econmic efficiency in the areas before the township prom was started in late 1953. This will be covered in Chapter III. The third objective is to use the benchmark data in the experi- mental and control townships to develop statistical tests which compare eh w RAND M‘? NALI-Y LOOSE LEAF OUTLINE MAP MICHIGAN m / It“ a > f oucmol , I , L, P! / 'I iv I J wucowsm ".41.‘ IT ' "move" we: I ' I I ‘ g I 1 _ -.I__- 1 --— ' 7%” “‘I IALcea I TI ICHIPPEWA ‘ C A N A D A I I ' Im—cfiusoul _I.-__-_I:°"°°L°m IfiéxTfiE-JTI__,_ _ 1".“ e ~I. I . I ELTA I I '— - 1—-—' £3 ,1... r- L - ,- o I ' / . w newomwezi I '3 1 ""‘cwzsovoA mscowsm e \ \ I ,A: “I I IIIIIEEsou: wAnmmc i9 \ “I mammal: now‘r- TITLPTENA T on AN‘IT’RI—M ctssco I”°“"'°' iI __ I (Mn-.MIcn‘nani'm—‘vInna:— ’ ‘IocraAvqu 1 . ' I I I | -._.-.I_ ' -_ _-_.'._-_I.-__._ D “IwExrono I'ATIssAuxesIco nos- "IocmAw IIosco mum i i I .1 713—0 TILAK TAKE—T IOWEEILT I'cTAFIeT-IéLA-Evfiui T “Tm I I I I 'TTL. Huaow -.-—I— l ._-|_- BAY a ocaATwA I muooI MEOOST_1A TITmeuA IMIDLANDI I ' I I waif—I éfiiTuTc ~ I I _I—1—' I I , T—l WET—c— T oTAro't— ‘isAchAw . I "MEG“ PEA—.7” « I BURNSIDE I ' I“ -J—I I_,_.—_-—.'cswssm-_- orva , IIowIA _TITcuw'row Isuumsgg'f I IST.0LAIR I . I I _I_. _I. I _I. I STAKLATD ABBEII AIL—16m Tuner TuF-ow' TTITMHMTJIVINOSTODTI 1 .I I I . ALMONT I - - .1 . _ . _I- __ . I ..._'_ II wa— eunsw AuAIAzocI cALHouw .IAcx—sow ijsfinwAw—I—wmwe I I I I I I omens —. __ -L_ - __ . I -.._P—. IcAss ImosemITgfiu—c...’ “It; “italimwu I Mowsos BERRIEN' ' I I l ”stir—'1'. JOSE$H fum+ rumuuctl 'FfigfiJIML _ WAG Wee-15;; a d INDIANA I . ° I FIGTUTIT’T" 1. OUT]. IINE 111‘? CIFL ICFIGAH £311. 11.1 u .MLILONT EXI’LPLENTAL ALIT) . lmeSIL)... CUIJTIi-OL fL."-.‘-.-‘L LSHIPS 13101? 11'HIC. This 3151: TELLS I . . I 1. .. .1 .. .. .1 .11.. 11111111 911111111 FOR THIS STUDY I "05 1w u.s.A. L This Map is also availabIe in size 17x22 [56 03 021 the levels of efficiency in the experimental and control areas for the base year of 1953. In addition, statistical tests and a procedure will be presented for evaluating the Cobb-Douglas results that will beobtainedintheteminalsurveyin1958inordertocupareand evaluate the changes in economic efficiency that occur as a result of the five-year intensive extension emeriment. ‘Ihe fourth objective is to recommend procedures to follow in collecting and processing the tenninal survey chta in 1958 so that accurate results can be obtained and compared to the original bench- mark data. The third and fourth objectives will be discussed in Chapter IV . 'me fifth and final objective of this stw is to appraise the use of the Cobb-Douglas analysis for extension evaluators on the basis of collecting the data, analyzing the benchmark results, and computing various statistical tests in the two townships used in this study. althougi final recomnendations on the use of Cobb-mums analysis cannot be made until the completion of the experiment in 1958, sane of the basic questions as to the cost, interpretation, and other factors to consider about the use of this method will be presented. This objective will be covered in Chapter V. _‘1113 Cooperative Extension Service 'me Land Grant College system and the United states Deputment of agiculture were both authorized in 1862 to render educational and research aid to American agiculture. Various measures were used by both organizations to relay the results of agicultural research to famers . 'me Department of agriculture used demonstrations, such as the control of plant diseases, to reach famers, while the land-want colleges participated in the educational programs of established agricultural societies and of farmers' institutes. In l9u6 Smith County, Texas, provided county funds to contribute toward the salary or a “demonstrator" who conducted demonstrations on the standard ram crops, gardens, and pastures.1 'Ihis idea spread to counties in Louisiana in 1907. County funds were contributed toward the salaries of demonstrators of the United States Department of agriculture. Those demonstrators pioneered the county agent system. In 1911 the United States Department of agriculture made cooperative arrangements with the state agricultural colle gas for the initiation and management or the county demonstration projects. In 1912 a total of 639 county agents were at work in the South.2 'Ihe desirability of coordinating the efforts of the United states Deparhnent of spiculture and the land-grant colleges led to the passage of the with-Lever £615 in 1911; which provided for the Cooperative Extension Service. me act provided for a cooperative agricultural extension program between the agricultural colleges and the United States Department of agriculture. ‘Iho major purpose of lorville Kile, The Fan! hireau 'Ihroug mree Decades, (Baltimore: me Waverly 9:335, I958), p. 2 . 2 n1d.’ p. 28. cooperative extension work as stated in the Smith-Lever Act is : . . . to aid in diffusing among people of the United States useful and practical information on subjects relating to agriculture and hen: economics, and to encourage the appli- cation of the acne. From a pioneering handful of extension agents in 1912; the Cooperative Extemion Service has expanded to almost every county of the United states. The magnitude of the present day Extension Service is’ revealed in the following statement by Luke Schruben: 'lhe extension program today is a $100,000,000 operation with a staff of over 13,000 agents. Ten years ago the total budget was $36,003,000 and there were slidrtly less than 10,00) employees. no primary function of the Cooperative Extension Service is to provide educational information to rural and urban families so that they may identify and better solve their own problems. It is well recognized that one of the major roadblocks in providing more on-the- farm assistance by extension agents is that the heavy work load of the agents does not permit close attention to the problems of the indi- vidual. Currently there are over 1,100 farm families and 1,700 rural families per county agricultural agent; 3Ibid. , p. 35. "mke M. Schruben, 'Implanenting State Extension Research,” Research in Extension, National Workshop Report, Federal Extension Service , mm United States Department of agriculture, 1955) , p. 161. 5 Duke M. Sdmtben, “New Developments in Extension Work," (Paper read at the New mm Research Council Meeting, Burlington, Vemont, Jm 2h'25, 1951‘)’ po 2o In a recent survey conducted by the Prairie Farmer mam county agents reported an extremely heavy load of chores that prevented them from making on-the-fam visits. One agent in Indiana stated: With all the niyxt meetings there is not time to plan your work. ‘lho only time I have to pregare nw speeches is driving in the on. to my meetings. r— __ _I_..g—A To meet the challenge of providing more on-the-fam assistance, Congress appropriated funds in 19514 that made possible the employment of 1,000 new extension agents under the farm and haue developnent progrmn. 1311s prom, as viewed by Charles M. Ferguson, administrator of the Federal Extension Service, would provide one new extension agent for every three counties on a national basis.7 his increase was designed to render more individual on-the-fam assistance in order for farm families to make full and efficient use of their resources. In 1951; fifteen extension agents were employed as farm and home develop- ment agents in Michigan. To meet the challenge of providing scientific analysis of how the Extension Service can best maximize the returns for its 100 million dollar yearly investment, special funds have been made available to measure the effectiveness of on-going programs and to experiment with new programs. State extemion services interested in extension research have an opportunity to request funds for special research projects by suqutting a research proposal to the Federal Extension Service. 6 Paul C. Johnson, “Iour County agent,” rrairie Famer, CXIIII, (October 6, 1951), p. 2. 7Charles M. Ferguson, "me Unit a «mat Does It Expect of County agents," Better Farming Methods, m1, (December, 1951», p. 12. In addition, state cooperative extension services have received marked budget increases during the past decade. lhis increase in total available funds permits more money to be channeled into exten- sion research. it the present time each state extension service can use part of its budget for extension evaluation projects. In addition to federal and state funds that are available for extension research several states have received grants from foundations for research projects. During 1955 the Extension Services of Iowa, North Carolina, Washington and New York each received a grant from the Kellogg Foundation of httle Creek, Michigan, for a five-year evaluation of their farm and home developnent pregam. an example of the urgent request for extension evaluation is reported in a recent report of the Cooperative Extension Service in New York State : The extension agent had and still’has, more demands on his time than he can meet in carrying on this program. The best he has been able to do , then, has been a somewhat superficial. kind of evaluation in which there has been more concern about t has been done rather than the effects of what has been done. The Michigan Extension Service The Extension Service in Michigan has also moved ahead in offer- ing more assistance to farm fanilies and to urban people throng: urban 11-3, home demonstration agents, and commnity development specialists 8"The Evaluation of the Intensive County Extension rrograms in New York State ," (prepared by the Cooperative nxtension Service of Cornell University, Ithaca, New York, 1955), p. 2. during the past few years. 'Ihere are now over 1:20 extension agents employed in 78 of the 83 counties of Michigan. While the number of extension agents in Michigan has increased, the increase has not kept pace with the increased demands for assistance made upon the staff. To be more specific, the Michigan situation is pinpointed in the following statement: For example in the southern half of Michigan today one county agent attempts to serve as mam as 1:300 famers--obvious1y an impossible task. It is well recogfized that the major limiting factor in the effectiveness of the Cooperative ktension Service is the work load assigned to our county agents.9 The Michigan Township Extension Program In order to scientifically determine how a more intensive extension program could be carried out in Michigan a grant from the Kellog Foundation in 1953 made funds available to the Cooperative Extension Service of Michigan State University in order to set up, operate, and evaluate an intensive extension experiment in five townships distributed geographically about the state for a five-year period, 1953-1958. Since the inception of the mtension Service forty- two years ago, the smallest area for servicing farmers has usually been the county while this new experiment focused on the township. The progmn is supported on a cooperative basis with Michigan State University, the township involved, and the Kellogg Foundation 9"rroposel to the Kellogg Foundation for an Experimental Intensive Extension rrogram in Five Townships in Michigan," (prepared by the Cooperative Extension Service, Michigan State College, East Lansing, Mimi-gens 1953): P0 2- 10 participating. ‘Ihe contribution of Michigan State University is in the fom of 75 subject matter specialists in agriculture and social sciences who are available to focus attention on the special problems of the townships. The contribution of the township varies depending upon the financial resources available in each case. The average town- ship participation was estimated to not exceed $2500 per year. During the first two years of the experiment, most farmers have given voluntary contributions ranging from five to one hundred dollars per individual. a few farmers have participated in the township program but have not donated aw money. 'lhe contribution of the Kellogg Foundation is in the form of a grant to the Cooperative Extension Service of Michigan State University, to cover the difference between the total budget for each township and the amount which the township could contribute. The grant also covers the budget for a progmn coordinator and progam evaluation. The gent provides funds to cover the total cost of evaluating the experiment. m objective . an important objective of the township experiment is to detennine if the extension Service could make productive use of more resources and secondly, to determine if farmers would support an intensified approach of rendering more on-the-fam assistance to farm families. he basic objectives of the experiment as stated in the Preposal to the Kellogg Foundation were to: 1. Increase fam eamings 2 . Speed up the rate of adoption of improved farm practices 3. Raise standards of living for farm families 34. Inprove rural cammmities S . Increase agricultural output 6. Gain information on a. Effective extension methods b. Organizational patterns and techniques c. Cammmication skills 10 d. Community recreation. Ihe objectives of the township program as viewed by the present Michigan Extension Director, Raul a. Miller, are: 1. To determine how far the Extension Service can go quickly by applying the best in agricultural research and technolog to local fans problems. 2. To detemine how extension work can be carried on differently and more effectively. 3. To determine what new methods of cooperative financing can be developed between all concerned using local, state, federal and foundation funds.11 For this experiment an experienced extension agent was assigned in each of the five townships to work closely with individual farm families in an attanpt to bring all available local, state, and federal resources to play in solving on-the-fam problems both in the home and in the total farm business. The five experimental townships are located in the following types of farming areas: 1) dairy, 2) dairy and general farming, 3) general farming, h) cash crops, and 5) dairy, potatoes, and general farming. 1herearefrom160 to 200 famineach township comparedtohOOto 800 farms per county in the northern part of the lower peninsula of Hichim and from 2,000 to h,500 farms per county in southern Michigan. ‘ lone, pp. 2-5. 11Statement by raul a. Miller, Director of the Michigan Cooperative Extension Service, at a meetin of the state fam editors, Michigan State University, april 15, 19 6. 12 One township program was started in July, 1953, while the remaining four were added during the period of august, 1953, througl J armory, 195k. W the lingeriment. a project coordinator was selected to organize and direct the township proyam in the five localities and to coordinate the activities of the extension specialist staff who advise and assist the township agents. The township coordinator makes periodic visits to the five townships and arranges regular meetings for the agents to discuss administrative and operational procedures of the program. The project coordinator is a part of and is located with the rest of the state administrative staff of the Extension Service at Michigan State University. he township agents were selected from the ranks of county agents and assistant county agents. Four of the original five township agents are still located in their same townships, while one agent has tak'en up full-time farming. The agents spent about their first six months getting acquainted in their respective areas and offered assistance on a voluntary basis to all interested farm families. he mnnber of fem families actively participating in the township program ranges from hu to 9U depending upon the area, the type of fanning, and the intensity of assistance rendered by the agent. The township farmers participating in this experiment have elected a board of directors in each of the five townships. lhe board of directors is responsible for guiding the township agent and advising the agent as to the best method of operating the prom. Althoug1 13 the agents are not administratively responsible to their board of directors, they work closely with them and attempt to move forward on a sound platform of offering an intensive educational program so that farm families migzt better help themselves. In addition, the members of the board of directors solicit voluntary oontributiom from partici- pating fanners in an attempt to raise the needed township share of the mnds without involving the township agent. The boards of directors of the five towmhips hold an annual meet- ing at Michigan State University to discuss the promos of the progam during the past year and methods for doing a more effective Job. Subject matter support at the request of the township agent is received frau all departments at Michigan state University in the form of specialists who visit the townships, discuss new methods with the township agent, and make farm calls with the township agent. In addition, special, detailed soil surveys have been completed in three townships and soil booklets have been distributed to each famer. a farm management extension specialist on a half-time basis provides detailed econauc infonnation on budgeting, record keeping, and renders general assistance to each agent by making personal visits and also by making farm visits and analyzing farm business records. Brogan Evaluation. h project evaluator was assigned in 1953 to measure the degree to which the objectives of the operating program Were not during the five-year experimental period. 'Ihe objectives of the evaluation research project are l) to measure the extent to which the objectives of the operating township program are met, and 2) to provide interpretative or explanatory information}2 The research is attempting to measure what has happened as a result of the program and why these changes were made. In order to isolate the changes attributed to the township pro- yam, five control townships were selected to match the five experi- mental townships and thereby provide a basis of comparison of the intensive extension approach with the traditional county extension organization. lhe control townships were chosen by matching an area with an experimental township on' the basis of: . Markets . types of farming . soil association . Ethnic background of the farm people . County extension programs a. History of cooperation with extension in the area b. Current extension prom c. Distance from the county extension office d. availability of meeting places 6. Proadmity to large cities. Control fans were selected within each control township and paired with fans in the experimental township on the basis of age of operator, labor force, total acres, tillable acres, number of cows, Ult‘UMi-J and machinery investment. 'Ihe principal difference between the farmers in the experimental townships and those in the control townships is Participation in the pro gram. It is the effects of this participation that will be measured by various economic and sociological indices. ‘ 12 J ames Nielson, "Notes on the Research Design and rrocedure for Evalu- ating the Township mtension trogram, “ (Depm'tment of agricultural Economics, Michigan state University, East Lansing, Michigan, 1956), p0 o J mes Nielson, "Fan: Planning-Township Style,“I (Paper read at the ggghMglmg Research Council Meeting, Burlington, Vermont, June 21:45, ) ’ pa 0 15 an important element of the evaluation of the experiment was that measuranents designed to ascertain changes were set up to be used before, during, and after the completion of the experiment. lhe "before‘ moasvnements provided benchmark data which can be compared to the data recorded in the experimental and control townships during and at the completion of the experiment in order that any changes as a result of the township program can be isolated and interpreted. Forty fans in each of the five experimental townships and forty matching farms in each of the five control townships were surveyed by personal interview in 19511 to obtain basic information on the 1953 farm operation. A total of 1400 farms were surveyed for the benclunark survey; 200 in the five experimental townships paired with 200 in the five control townships. Each sample was homogeneous by farm type within the tmmship areas. The individual farm surveys pro- vided benchmark data for the measurement of changes that might occur as a result of the progam. 'Ihe survey schedule included all the information for Cobb-Douglas analysis and all the information commonly collected in the farm account project plus a net worth statement.114 In order to determine the extent to which the objectives of the Program are met, the following measurements are being used in the evaluation process : “lbs- .. “we! Objective 16 Measurement to Be Used and Methods of Getting Infomation 2. 3. Financial progress of the fam families adoption of farm practices Volume and efficiency of production Shifts in patterns of land use Farmer participation in the Township program Formal and informal partici- pation of farm families Decision-Mdng processes used by farm families Extension techniques and commmication methods 1. Farm earnings-deflated 2. Fanily earrdngs-—deflated 3. Family net worth his information will be gathered by bencl'nnark and terminal surveys. Extent to which farmers have adopted selected practices as reported by a benchmark, terminal and two inter- mediate farm surveys. a 1. Gross incane deflated by price 2. Traditional farm business analysis measures 3. Marginal returns to investments and other inputs (Cobb-Douglas analysis) This infomation will be gathered by benchmark and terminal surveys. Changes in acreage of land used for various purposes and implications of these shifts as determined by soil survey, and intermediate and terminal surveys. How many families participated in the progam, extent of their involvement, as determined by ncnthly and annual reports, case studies and ammo Kind and quality of participation of farm families in a limited number of activities as reported by case studies and surveys. Factors considered by farmers in mak- ing decisions and involvement of various family members in the decision- making process as reported by case studies and surveys. study of approaches and methods used in the township prog'am as determined by township agents' reports and administrative agents ' remarks . 17 9. Attitudes toward the pro- attitudes of the following people to yam and related matters be studied: 1. Farmers in the experimental areas 2. Famers outside the experimental areas 3. Township agents 1; . Administrative and supervisory personnel 5. County agents 6. Specialists Factor one will be studied by an intermediate and terminal survey. Factor two will be checked by a terminal survey of farmers in the control area. Factors three to six will be analyzed by consulting with all extension agents connected with the program.]5 Economic Efficim The efficiency of production or objective number three in the above chart is an important concept that farm management extension workers have attempted to define, measure, and interpret for many Years. Economic efficiency is defined as the best use of resources which will produce the mudmmn profit for a fim. Mam subjective factors such as a fanner's decision to substitute leisure time for work on oundsy or mmdmizing family welfare instead of profit maadmizimg, make it difficult to develop a useful efficiency concept that will in- clude all the subjective factors as well as maadmizimg profit. The intangible factors such as "living in the country” or ”being my own boss" are factors that have been ignored in previous efficiency ‘ 15 James Nielson, "Notes on the Research Desigl and rrocedure for Evaluating the Township utension rrogram," g. 93.3., pp. 11-6. 18 studies because of the lack of knowledge in defining and measuring these factors. ‘Ihis study will proceed as previous studies did and use dollar income or the profit motive as the index of measuring efficiency in order that a suitable efficiency measure can be devised to measure the changes in efficiency as a result of an extension progam. Measm'ing Economic Efficiency Measuring efficiency is of great importance to farmers, extension agents, researchers, and agricultural policy workers. Information on resource efficiency can be useful in guiding individual farmers into a more profitable allocation of their resources. a farmer wishing to maximize profits can find the optimum combination of resources to use by comparing the returns to the input categories to the cost of using these inputs. Economic efficiency studies can point the direction and the method of reaching an optimum efficiency pattern and hence a maddmum profit position. Use of input-output information draws to- gether all the resources into a single framework of the nature that farmers must consider when making decisions. Efficiency studies com- bined with budgeting can be used effectively by farm planners in adVising fumers ’how to make necessary farm adjustments. The importance of measuring economic efficiency from the stand- POint of extension workers can be discussed under 1) use in extension education, and 2) evaluation of extension programs . Extension agents l'1'34ed refined efficiency data in order to advise farmers how to make the necessary farming adjustment in order that they might nmdmize l9 profits. Efficiency studies for specific types of farming and for specific areas of the state are essential in budgeting and farm planning. Extension evaluators are faced with the important assignment of evaluating the changes that farmers make as a result of extension education and to determine why these changes were made. (he of the methods of scientifically determining the itrpact of a new extension approach or a more intensive extensicn program is to measure the changes in economic efficiency that occur as a result of the extension education. Since extension agents attempt to help farmers increase their efficiency in order to maximize profits it is important to evaluate the changes in efficiency that are brought about by extension agents. One of the goals of our society is that of securing the maximum If efficiency studies in agriculture indi- welfare for all members. cate low returns in agriculture relative to manufacturing, this suggests that too may resources are being used in agriculture and too few in Wacturing. Since society as a whole benefits in economic progress and increasing efficiency is one of the methods of reaching that goal, it is inportant to consider efficiency fran a policy standpoint. A180 econanic efficiency studies in agriculture indicating differences in resource productivity in different areas of the country provide S‘31’Lentific methods of suggesting shifts to be made in resources in 20 order to achieve maximum production in a period of needed increase in agricultural. output. he need for measuring the changes in economic efficiency in the Michigan township extension program is important not only to extension agents but to researchers and to the farmers in these five township areas. It is the belief that reliable economic efficiency information on the farm in the experimental townships will measure the results of township agricultural agents attenuating to speed up the educational assistance to a small you}: of farmers over a five year time period. The benchmark survey in 1953 established the basic efficiency condi- tions on the fams in the five experimental and five control townships. The teminal survey will report the changes in economic efficiency that have been brougit about by the township agents in the five experi- mental townships and the regular county extension organizations in the five control townships . Since one of the goals of extension education is to bring about Changes in technologr on merican fame, and, thereby, increase the el-f’l‘ioiency of production, one of the logical measures of an extension evaluation progam should be in the area of measuring economic - efficiency. It is the belief of the writer that farm families are interested 11-; profit maadmization as an avenue for improved standards of living. the fanners goal for profit Wing is successfully achieved if the farm fin: is able to make efficient use of its resources. Althougl M farmers do not openly admit that they are participating in 21 extension pregame in order to become more efficient operators, their basic reasons for participating often hides this important area. In a survey of 28 farmers in one of the five experimental townships after the program had been in operation for two years the farmers answered the lquestion "Why did you decide to participate in the prog‘am?" in the following manner-~(mltiple response): am . amen To obtain information 7 To get help 7 General feeling that it would be worth-while; had confidence in the Extension Service 5 Thougxt it would benefit the township or someone else in the township 5 other reasons _l_._2__ Total 36 '16 While the farmers in this experimental township did not openly mention that they were interested in increasing their efficiency of Operation, their request for more information is one of the first steps in the chain of decision making that leads to mater economic efficiency. It is necessary to outline the essentials of a good measure of efficiency before a specific method or methods can be recommended. It must be remembered that agriculture like other areas of production is a higfly complex process and that no measure of efficiency can ‘ 6 guesh Nielsen, How 7rHave FarmersA ted the Townshi Ebctension 0min 0"”!me Economics Wheaties: EH University, East Lansing, Michigan, April, 1956, pp. 21-22. 22 accurately predict all of the factors involved in the production process. The essential characteristics of a good measure of efficiency are: 1. To provide valid results by revealing the efficiency of the firm, provide an cptimum scale of efficiency, and provide a basis of cauparing efficiency over a time period. Two con- ditions necessary to provide valid results are that both input and output are measured and the results are stated in marginal terms. 2. To provide reliable results if the measure is repeated in the same parent population or in different sections of the country by the same or different researchers. The two methods of measuring economic efficiency in the township extension program are the traditional farm management approach and Cobb-Douglas analysis. These methods tend to canplement each other and provide a good over-all measure of the changes in economic efficiency. The results of using Cobb-Douglas analysis in this study will provide informatics: as to the advantages and shortcomings of this method in order that Cobb-Douglas analysis can be compared with the essential characteristics of a good measure. of efficiency. This comparison will be made in Chapter IV. A brief review of background of these two methods of measuring economic efficiency will be discussed in the following section. Traditicnal farm wagement M. The traditional farm management approach of measuring econanic efficiency has been developed. during the past three decades. Various plwsical ratios developed to measure efficiency in average toms are man work units accanplished 23 per man, crop yield index, and milk produced per cow. Financial ratios such as returns per $100 feed fed to various kinds of livestock, and gross income per man have been developed under this method. mile these efficiency measures like mamr other "rules of thumb" all provide useful infomation they fail to provide a canplete input—output con- cept. lhe traditional farm management approach for may years has centered around selecting samples of farms in specific types of farming areas and after the business record of these few are analyzed the low, average, and high incmne farms are compared in order to arrive at recmndations for reorganizing these fans. Economic efficiency under this system was computed byseveral cannon measures of output such as comparing gross income per $100 expense. This is a good over- all measure of efficiency but it does not reveal whether or not specific categories of inputs such as the livestock or machinery in- Ves‘huent were efficiently utilized during the year. althougx gross income per $100 omense does not measure returns to specific categories or inputs it is still a valuable index to use in extension evaluation. This index is a good over-all indicator of efficiency that can be easily and accurately computed for a m of fame before and after an extension educational program. The traditional methods also attempt to measure the efficiency of individual inputs such as labor, machinery, and feed expense. an ”ample of measuring labor efficiency is reported in the Area 6 and 7 report for 148 dairy farmers in Michigan for 1953: 21: Labor efficiency as measured by days of work per man was 15 percent higcer on the large farms. If measured by gross income per man there was little difference. The days per man measures the labor efficiency, thus showing the relation between the amount of business on the farm and the labor supply-17 A productive man work unit represents the amount of productive work that will be done by a man working at average labor efficiency in a ten-hour dw. The productive man work unit concept is an average rather than a marginal measure. Ellie weakness of this approach is the difficulty in comparing individual fame with the average farms, because there are mam variations in the amount of assets that each farm uses with its labor force. 'mis type of analysis does not indi- cate how much the last month of labor earns, for it takes the total of all inputs used in the production process and tells whether the days of work accanplished per man is higxer or lower than the different income W of farms. m M. The principles of marginality are also used to measure economic efficiency. Since the madman profits to a firm Canbe explainedonlyinterms ofmargnal analysis it is important to outline the teminologr and definitions of marginality. then a unit or input such as an acre of land is added to the production process, the resultant increase in total product is called marginal or additional returns. Marginal returns is the ratio of change in total product as related to the change in input. Madman profit and hence economic ‘ _- '17John Doneth, Farmin T , areas 6 and 7, Department of agricultural Econugfis, Mi gen :5 versity, East Lansing, Michigan, 1951:, ppo 9" o 25 efficiency is achieved when the marginal productivity of inputs and investments is such that it is impossible to shift the resources to different alternatives without causing the total product to decrease. For example, if the returns for one acre of land planted to corn yielded more profit than if the same acre were planted to wheat, then economic efficiency has not been met because it is still possible to cause the total product to increase by planting the acre to corn. The condition of ecmomic efficiency is not met until all resources have been shifted fran cne alternative to another, so that further reshuffling of resources will cause the total product to decrease. Marginal analysis measures labor efficiency by providing an esti— mate of what effect the last unit of input (1' investment had on gross income for the year. For example, if the last month of labor used on a dairy farm returns $80 the farmer could match the cost of a month 01' labor with the return and be able to determine how efficient his labor was for the year. This method also allows canparison of labor efficiency on dairy farms in different sections of the state or in different sections of the country. One of the more refined methods of deriving input-output data by using marginal analysis is an algebraic method lmown as Cobb- DOuglas axiallysis}8 Other algebraic functions capable of measuring ‘ 18 Paul H. Douglas, They 21; 31,333, (New York: The Hamillan Convener, 19314). 26 19 efficiency are the SpilJman function and the quadratic20 inaction. When measuring the effects of a large number (four to six; of variables such as land, labor, or machinery on gross income the Cobb-Douglas function has several important advantages over the other algebraic methods. some of these advantages were reported by Tintner: 'Ihe Cobb-Douglas function gives ilmnediately elasticities of the product with respect to the factors of production; this form of the production function permits the phenomenon of decreasing marginal returns to come into evidence without using too many degrees of freedom; and finally, if the errors in the data are small and normally distributed a logarithmic transformation of the variables will preserve the normality to a substantial ‘ degree.21 Cobb-Douglas analysis was selected for this stuchr in order that basic questions facing extension evaluators such as the cost, reli- ability, canputations and statistical tests employed can be analyzed in one of the experimental townships and its matching control town- ship. The results of using this analysis on the two townships will Provide insigit into the use of Cobb-Douglas as a possible measure of economic efficiency by extension evaluators. l 9 William J. opiJJnan, onential Yield Curves in Fertilizer eri- ments , United states gepment of ag‘iWe'TeHEcal allegin- 318, (Washington: Government Printing office, 191:3). 2 OMordecai Ezekiel, Methods 2;: Correlation M32: (New York: John Wiley and sons, 1930). 21 Gerhard Tintner, "A Note on the Derivation of the Broduction Func- tionséFrfim Farm Records," Econometrica, XII, No. 1, (January, 19M), pp. 2 "3 o CHAPI'HI II THEORETICAL BACKGRWND OF COBB-DOUGLAS M1513 Historical. Development Professor raul H. Douglas ,1 'of the University of Chicago pioneered production function analysis in 1928 by computing indices of labor and capital for smerican manufacturing firms . 2 Charles w. Cobb, a mathematician at worst College, co-mlthored the studs- and helped Douglas develop a function P - bLk 01'”k that measured the relative effect of labor and capital upon productivity duringthe period 1899 to 1922.3 The dependent variable (1*) expresses the total production value of industry, (C) is the total fixed capital available for production, (L) is the labor supply available to the entire industry and b is a constant. lhe exponents k and l-k are co- efficients of elasticity for P with respect to the independent vari- ables labor and capital.h Cobb and Douglas forced the exponents equal to one which indicated constant returns to scale. 'lhe production 1Now U. S. Senator Douglas from Illinois. 2 ‘ A Douglas, 3. gig. 3 Pull H. Douglas and Charles N. Cobb, "A Theory of Production,“- American Econaaic Review, XVIII, Supplement, (March, 1928), pp. 335-735: ll An elasticity of a particular independent variable is the percentage change in total product when the variable is increased by one percent. A. ..v w ~,‘.a., \ .LL _‘ ‘ 1i. ‘— 2!. .upu— 28 function devised by Cobb and Douglas is linear in logarithmic form. The values of elasticities can be estimated by a modified5 least squares type of regression analysis. A modification of the original Cobb—Douglas equation was made by Durand in 1937.6 Durand presented a broader function where P - bchj so that the sun of the exponents need not equal one. This allows increasing or decreasing returns to scale to be reflected in the total product. 'nle exponents k and 3 are the coefficients of elasticity of t’ with respect to labor (L) and capital (C) while b is a constant. The broader function is linear in logarithmic form and the values of 'b, k, and :1 can be estimated by the method of least squares. anirical studies in Agiculture Tintner pioneered production ftmctions in agriculture by using Durand' s modified regression equation to derive productivity estimates Of various input categories for 609 Iowa fans for 191:2.7 Tintner and Brownlee used detailed farm account records of 168 Iowa farms to derive estimates of earning power for categories of inputs and investments for the year 1939.8 \- s 6T1ntner, 33. g_i_t_._., p. 31. David mrand, "some 'nlouglts on Marmal troductivity with special erence to t’rofessor Douglas' is," Journal of rolitical Econ , m, (December 1937), pp. 7 0-758. 7 smith”, £0 E20, ppo 26'3’40 Gerhard Tintner and u. H. Brownlee, "Motion Functions Derived fI‘mFarnRecords'Jurnal IF Bonded. uVI 1M4 Pp. 566-571. ’ ----° 9—---"‘."‘---------° cs: ’ (““w’ 9 ” grhnmnfldklr r... . . . ... ...»... I. , . 29 Heady followed Tintner and Brownlee and fitted the function to data from a random sample of 738 Iowa fams for the calendar year 1939.9 Fienup, at Montana state College, used a random sample of wheat farms to study resource productivity on Montana dry land crop farms for the year of 1950.10 Drake at Michigan used farm account records for they ear of 1950 to gain estimates of the marginal productivity of inputs.u In 1952, Johnson at the University of Kentuclq, used a non- representative or “purposive sampling“ technique to select 23h Western Kentucky farms for Cobb-Douglas analysis.12 mrposive sampling is a refinement of Tintner's random sampling method and Drake's fam account sampling technique. It is a method of selecting sample fame that are not in scale line adjustment, thus reducing the intercom- lation among input categories and thereby increasing the reliability of the estimated regression coefficients. —‘ 9531.1 0. Heady, "rroduction Functions From a Random bamfile of Farms," 19 {canal 2; Fan: economics, XXVIII, No. h (November, 6), pp. 989- 10 Darrell F. F'ienup, Resource rroductivi on Montana Land Crfi Farms, l‘flmeog'aph W zanan: Ham e College, hauntural Experiment station, 1952). 11Louis Schneider Drake, "Problems and Results in the Use of Farm account Records to Derive Cobb-Douglas Value rroductivity Functions ," (Unpublished Ph. D. Dissertation, Department of Ag‘icultural Econmnics, Michigan b‘tate College, 1952). Glenn L. Johnson, sources of Income 9__n Upland Marshall Conny E3133, Progress Report No. I, and sources of Income 35 Elena McCracken County Farms, Progress Report No. 2, (Lexington: Kentucky Ia- c'ultural mcperiment station, 1952. 30 Similar studies employing purposive sampling techniques have been completed by Toon13 at Kentuclqr and Wagleyu‘ at Michigan. Since then several modifications and additions to Cobb-Douglas 15 production functions have been made at Michigan by Trant and 6 Cartel-.1 Production Functions The production function or input-output relationship is expressed in the following generalized form17 I - F (X1, X2, X3, Ah, ..., Xn) where Y refers to the value of the output and Ms refer to the inputs or quantities of the various resources used. If all inputs are variable and can be increased in constant preportions, then the output increases in constant proportions as illustrated geometrically in Figure II. I3 Thomas G. Toon, The Earnin Power 9! m Investment and ggendi- tune on land F on Bagnmz Durigg’EH, Progesyfiep No. 7,79%35»: §entucq Ail-alums]. Expefixnent Station, 1953) . 1"‘Robert Vance Wagley, “Marginal Productivity of Investments and Expendi- tures, Selected Inglan County Fans, 1952," (Unpublished M. S. Thesis, Department of Agricultural Economics, Michigan State College, 1953). 1 5Gerald Ion Trant, "A Technique of Adjusting Marginal Value Productivity Estimates for Changing Prices ," (Unpublished M. S. Thesis, Department or Agicultural Economics, Michigan State College, 1951;). 16 Harold 0. Carter, "Modifications of the Cobb-Douglas Function to Destroy Constant Plasticity and Symtry,” (Unpublished M. S. Thesis, Deparhnent of Agricultural Economics , Michigan State University, 1955). Richard G. D. Allen, Mathematical is for Economists, (London: as 00., 19W- 9 . 1 31 egg? (L1, XZ, L3,.ooooooooo, An) Figure II. Total Physical Product, All Inputs Variable and Increased in Constant Proportions. men some inputs are held constant and others variable, the "law of diminishing returns"18 or the "law of variable proportions" helds true. his relationship is stated as follows 2 as more units of variable inputs starting from zero are added to fixed inputs, the tetal physical product” increases at an increasing rate, then 2LIncreases at a decreasing rate and then decreases. \ 18 . Gear e J. Stigler The Then of Price, (New York: MW Co. 191955, pp. 1161'. ’ """' “ ’ This relatimship also holds true for the marginal and average Diwsical product. See Sidney Weintrsnb, Price They, (New York: Pitman Publishing Co., 19149), pp. 781‘. _" 32 The influence of fixed inputs is responsible for the occurrence of diminishing returns. For example the subfunction I - r(xlx2[x3 ...,xn) as illustrated geuuetrically in Figure III shows the effect of fixing X3 ...xn while x1 and x2 are variable. v The production function is divided into three stages. The second stage as illustrated in Figure III is the only rational one to produce in if it pays to produce at 1:11.20 'Ihe Cobb-Douglas function is capable of showing only one of the three stages of production at a time; therefore, since most farms are assumed to be operating in Stage II, purposive sampling is used to select farms that are operating in this stage.21 Value Productivity Functions In order to locate the optimum amount of inputs to use in produc- ing a product and also in order to determine the anount of a product to produce, the price of inputs and outputs as well as the physical relationships must be considered. The physical production relationships Outlined in Figure III are multiplied by the price of the product in Order to convert them into value productivity relationships . A value Productivity function expresses the relationship between the value of the products produced and the inputs and investments used in producing ‘ O fitigler, 92o Eli-:20, Pp: 1214-1250 1 Lawrence A. Bradford and Glenn L. Johnson Farm Managgent was, (New York: John Wiley and sons, Inc., 19%3), p. . 2 33 stage I stage II Stage III ' I i I . I 3 m l , i i i ' l I I . l m, l I ’ l APP l l. __ (X1, x2,| X3, oooooooooooo , Kn) Figure III. Diagram Showing the Law of Diminishing Returns. 3h those products.22 In Figure III the marginal plwsical product and the average plursdcal product are multiplied by the price of the product (I) and are thus converted into value productivity relationships. In Figure IV they are labeled, MVP, meaning marginal value product and AVP, meaning average value product. Since the total physical product is expressed in physical terms it is labeled TPP in Figure IV. The optimum amount of an input to use in producing a product is demmstrated by the intersection of the price line labeled PIC:L with the MVP curve or at point C in Figure IV. At this point the MVP ; ml which means that the value of the marginal product is equal to the cost of the last unit of input. Beyond C, the dollar returns derived by using another unit of input is less than the cost of the input. Use of less than C amount of X1 would permit additional profits to be made by using the additional units of X1 which would yield a dollar return in excess of their cost.23 In Figure IV the law of diminishing returns is reflected in the marginal and average value product and the total physical product as they start from zero and increase at an increasing rate, increase at & decreasing rate and then finally decrease. This phenanenon is caused by the fixed inputs, X2 --- Kn. The law of diminishing returns 3-130 holds true when more than one variable input is used in the pro- duction process. This means that marginal returns to 8111810 variable Iputs or to groups of inputs first increase, then decrease, an 31 1m 1" Jdmsm: "The Cobb-Douglas Production Functim with Special referm“ ‘50 Fitting Value Productivity Motions for Farm Businesses," 9111: ative draft of a technical bulletin, Department of Agricultural 23B On 1 increasing returns, if 2 bi's < l decreasing returns and if 2 bi's .- l constant returns to scale exist on the function. The marginal value productivity of an 1L1, which is the increase in gross income resulting from an increase in the use of xi with other resources held constant ,zgan be computed frnn the following equation: MVPx1 - iggIz where 30?) is the expected gross income of the set of ii's under con-- sideration. 22; 26?” p. SI b1 b2 bn b-lmbz b ' Phi III—E- d(ax1 12 ”.151 )ibiaxll ...)Lnn 7 - b1 allb .X2b2 in *1 - b1.e(r) 11 39 (6) Estimated MVPX1.8 are useful in locating least cost combi- nations of inputs and investments and highest profit levels of operation; hence, they have great practical significance in indicating profitable reorganization of farms as a basis for both public and private policy. Rules for Selecting Fame on the Same Production Function Toon outlined five conditions that should be met before a group of farms can be assumed to be operating on the same production func- tion: 1. All fame should be operating at the same level of technology. 2. All farms should be producing similar products. 3. Inputs within each category should be in optimum combination. 1:. All farms should be using the same inputs. 27 5. All farms should be on the same inherent soil productivity. (3293325 9; m. Accurate grouping of inputs and investments into meaningful categories of expenses and investments is a prequisite for obtaining reliable survey results. Therefore, in designing the schedule, the following rules of thumb for grouping inputs are sug- gested by Glenn L. Johnson: 1. That the inputs within a category be as nearly perfect sub- stitutes or perfect canplements as possible. 2. That categories, made up of substitutes (a) be measured according to the least cannon denminator (often physical) causing them to be good substitutes and (b) be priced on the basis of the dollar value of the least-camon-denomi- nator unit. 3. That categories made up of canplements (a) be measured in terms of units canbined in the proper proportions (which are relatively unaffected by price relationships) and (b) be k 27 Tom. a- 333., p. 20. ho priced on an index basis with constant weights assigmed to each complementary input. ’4. That the categories of inputs be neither perfect complements nor substitutes relative to each other. 5. That investments and expenses be kept in separate categories. 6. That maintenance expenditures and depreciation be eliminated from the expense cate gories because of the difficulty en- countered in preventing duplication. (This means that the earnings of the investment categories must 89 large enougn to cover maintenance and/ or depreciation. )2 steps to Follow in Fittfingga Cobb-Douglas Function to afi tural Data a detailed account of the general procedure to follow in setting up an hunt-output study, selecting the sample area, selecting the sample farms, designing the survey schedule, collecting the data, grouping the inputs, analyzing the data, fitting the function, statisti- cal tests, and interpreting the results of the data will be presented in the following section. Framework of Production Function study rroduction function studies or input-output studies as they are Conunonly called by farm management extension workers are used in agri- culture to provide estimates of the earning power of categories of inputs and investments that are used to generate gross income. The general production function or input-output relationship illustrates how goes income of Y depends upon the inputs and investments. In the ‘_‘ 28 Bradford and Johnson, a. 33.2., p. 11111. following general function I .- f(xl...xg*xg+1....xn) + U the output Y is dependent upon three classifications of inputs and investments. The variable inputs (x1 ....xg) are studied while fixed inputs designated (xgfl ...xn) are held fixed by the research design and the unmeasurable and unstudied variables designated U are assumed to be randomly and normally distributed. Examples of studied variables are: 1. land 2. labor 3. livestock-forage investment 14. machinery investment 5. cash expenses The fixed variables in an input-output study include some of the following factors: 1. type of farming 2. soil type 3. altitude h. rainfall 5. technology employed 6. geographic location as it is associated with the growing season ’ 7. all fame employing the same inputs 8. data are selected for only one year of Operation The unmeasured and unstudied variables that are assumed to be randomly and normally distributed in an input-output study include sane of the following: 1. managerial ability 2. geographic variations in price, weather and technologr 3. variation of productivity within soil types h. institutional factors 5. asset control The general framework of an input-output stuck is found in the function described above where the output depends upon studied vari- ables, fixed variables, plus certain unmeasured and unstudied factors h2 that are assumed to be randomly distributed in the sample area. In order to measure accurately the units of inputs that are used to create output during the fam year, a general sample design must be set up. First of all, it is important to know the theoretical nature of the function. This step is followed by analyzing the resources available for the study so that the intensity of the survey, the method of surveying, and number of farms surveyed can be determined. After selecting the sample area, the sample farms must be selected and surveyed. The data must be converted into logarithms and least squares regression analysis used to fit the function. The final step is to compute statistical tests for the fitted functions and to interpret the results of the study. Research M. The first step that researchers may follow in setting up an input-output study is to state the problem, available funds, and outline the alternative methods available to solve the Problem. In Michigan the cost of using Cobb-Douglas analysis to gather information on efficiency of production for an area has ranged from 3 900-1200 for a sample of 30-110 farms. This is approximately $30 per processed schedule, including the field interview and the statistical cmuputations. The cost of Cobb-Douglas studies will be further explored in Chapter V. The studied variables usually include land, labor, cash expenses, livestock-forage investment, and machinery intrestment. The fixed variables will depend upon the area under Study and the physical characteristics of the area that can be fixed m1d isolated by the researcher. For example, the ideal set-up for Ml]!!! mini! ... ... 1:3 handling fixed factors would be to obtain an area that has fixed patterns of soil, rainfall, type of farming, and so forth. It is realized that this is impossible; therefore, a researcher must in- clude tolerance for the factors that he is attempting to fix. The unmeasured and unstudied factors must be carefully examined, because one of two major variations in these factors on a particular farm or on several farms can bias the results so that they are unusable. another unstudied variable assumed to be randomly distributed is managerial ability. since it is impossible to classify or to measure managerial ability, it is one of the variables that must be given subjective consideration by every interviewer. Determining the singling technige _tg m. The three main sampling techniques used to collect data for input-output studies are: random sampling, farm account records, and the purposive sampling technique. Before amr one of the three can be recommended the character- iS‘tics of each must be carefully examined. The random sampling technique was used in the early Cobb-Douglas studies in agriculture whereby a number of farms (100-700) were selected to represent the universe or the complete data for the area. his method involves selecting a certain percentage of farms in an area without such regard for the range in the quantities of inputs u88d in the production process. For example, Tintner29 used random sampling to select 609 farms and Heady30 followed by using the same k 2 9T1ntner, gp. _c__i_t_. 30 Heady, 92. 333., pp. 989-1001;. procedure to select 738 farms. Minor restrictions such as limiting the fans to more than thirty acres in size can be used in a random sampling technique. The main limitation of this method is the cost of collecting the data. ht $30 a schedule ,a TOO-schedule survey would cost approximately 821,000. The farm account record system involves analyzing the data from a selected number of farm account records to derive productivity esti- mates. J ohnson3l discovered the lack of data on the livestock-forage and machinery investments was a major limitation of using farm account records. In addition, farm account record farms are usually well adjusted finns that are on a higher production function than the average farms in the area. The well adjusted factor causes higl inter- correlations between the input categories and thereby causes hid: standard errors of the bi's. The purposive sampling technique used by Johnson32 in Kentucky is a method whereby fame are selected with a wide range in the quantities and proportions of inputs. The wide Iflange in the input categories reduces the intercorrelation between the input categories; thereby, reducing the standard errors of the I"SEI‘Iassion coefficients. The equation33 used to compute the standard eITOI' is: ‘ 31 statement by Glenn L. Johnson, personal interview. 32 Johnson, sources 93 Income 93 gpland Marshall County Fame, g. _c_i_.t. 331!.ze1cie1, pp. 333., p. 502. LS b 13.23 - ['s'z 1.2: 11 0'72 (1-122 3.2M where n - the size of the sample, 03—2 - the variance in X3, R2 3.2h - the percent of variance in x3 explained by 1L2 and xh combined. The three factors that affect the size of the standard errors are: the size of the sample or n, the intercorrelations existing among independent variables or R2 and the range in independent vari- ables as measured by 02:2 or 573—2 in the above example. as the size of the sample or 032:2 increases or R2 decreases the denominator increases and the standard error of the bi decreases. In order to reduce the ”E, the researcher can either increase the n which involves an additional expenditure of mnds for extra smnpling, select farms that have a wide variation in the quantities of inputs and investments so that the R2 or correlation between the inputs is decreased and thus the standard error of the bi will be reduced, or increase the range in the observation of the independent variables. suppose the following inform- ation were available to a researcher: n I 140, R2 - .9 and 12 is 10. A purposive sampling plan which decreases R from .9 to .8 would decrease the standard error of hi as much as doubling the sample size n from 110 to 80.3h at $30 a schedule, the saving for ho records would be 81200. In addition to saving money by using purposive sampling to reduce the standard error of the bi's, this method also allows control 3hJohnson, "'Ihe Cobb-Douglas troduction Function with Special Reference to Fitting Value Productivity Emotions," fi. 933., p. 20. 116 to be maintained over the variables which the researcher wishes to hold fixed. This means that instead of selecting farms from several counties and running the chance of having wide variations in factors such as soil type, rainfall, the researcher is able to maintain con- trol over these factors when the sample area is restricted to a county size and purposive sanpling is used. Selecting the m _a_r_e_a. since the Cobb-Douglas function can accurately predict returns for one type of farming, it is necessary to analyze the area picked for the study and to determine if a sanple of 30 to to farms of a specific type of fanning can be selected. 'me usual area for accurate results in the mid-west section of the country is fran one to three counties with most cases falling in the one county limit. If a larger area than several counties is used for the sample area, it is difficult to maintain control over factors such as the type of soil, rainfall, and type of farming. It was found in one study in Michigan that increasing the size of the sample area from one to three counties caused sizable unexplained errors in the results so that the sample size was reduced to the original one-county area. several suggested methods for selecting the sample area are to consult with the soil science department, county agricultural agents, visit fans in the area under consideration and to compare the crop yields and characteristics of the fanns in the area by examining the census data and individual fann account records. accurate sanple areas cannot be mapped out in the office as it takes a thorougz knowledge of the local situation before a balanced area can be selected. 1L7 Selecting _t1_1e m g; _fegne. If purposive sampling is used to select farms for fitting a Cobb-Douglas function, the minimum number of farms to be selected on the basis of this study for a township or county area would be 35, while the masdmmn would be around 16. This allows five to ten schedules that do not meet the requirements for soil type, percentage of gross income from one type of fanning, or other accounting errors to be deleted from the sample. The minimum usuable schedules necessary to obtain a reliable Cobb-Douglas fit ranges from 25 to 35. The ideal method for selecting the farms is to plot the range of input data on a simple chart before each interview is taken. This method consists of asking a fanner the number of acres, and the months of labor, without getting involved in taking several hours time to take the interview and then being forced to delete it. For exanple, after finding a fam which produces more goes income from fruit than from its dairy enterprise, the farm could be by-passed. selecting the eagle m. The general criteria used to select farms for the type of farming requirement is to require that at least 50-60 percent of their pass income be derived from the type of farming under study. Minor deviations from the arbitrary standard can be made, but the more precisely the data are taken from a specific type of fanning area, the more reliable the results will be. In addition, the farms should be on the same type of soil and should be using the same inputs in producing the products. Desigeieg _t_he my schedule. The schedule should provide an account of all factors used in production during the year and the 118 resulting breakdown of the sources of income for the year. The de- tailed breakdown for the items to include in the survey schedule are discussed in Chapter III. 9312. enumeration. several helpful guides for collecting the data in the field include the following: record all data that is available from reliable record books or farm plans; back up several years with a famer and draw a map of his farm so that he can recall the age of the forage stand or the amount of fertilizer that was applied during the year; include the entire share of the farm operation, as many tenant famers keep records for their share of the business only; and finally carry a portable adding machine to check the totals of the schedules taken during the day so that any questionable point can be checked while the survey team is in the local area. about two hours per farm are required to collect the basic data for Cobb-Douglas analysis. w the data. The first step in processing the schedules is to set up a set of instructions to follow so that all schedules will be handled in the same manner. This is especially helpful if clerical staff workers are analyzing the data. The values of forage stands, prices of products, yards of~lime to tons and other such items should be clearly spelled out. It took about two to three weeks for a clerical worker to analyze the schedules and make the necessary cmlqmtations for Cobb-Douglas analysis on thirty to forty schedules in each township of this study. 149 After each schedule is analyzed, it is suggested that the totals for each farm by input and investment category and gross income be recorded on a large table. This permits a quick comparison of one farm with another to detect axw errors that were missed in the compu- tations. The schedules are then re-examined and the ones that are incomplete or fail to meet certain sampling specifications are deleted from the sample. About 15 per cent of the schedules were deleted in this study. Fitting technig . The general technique for fitting the function was taken from nzekiel.35 The first step in fitting the function is to convert all the inputs and investments for each farm into logarithms and then set the logarithms up into a table. The linear multiple intercorrelation procedure is used to fit the function. Cross multi- plications or extensions are computed for each variable for each farm, the sums of which are the cross products. Check sums are used to check the accuracy of the extensions. The Doolittle36 method is used to solve the normal equations for the b's and the c's. The c's are used to compute the standard errors of the regression coefficients (b's). The b's are then fitted into the estimating equation with the logarithm 01‘ the geometric means of the inputs and the equation is solved for the constant (log a). The antilog of (log a) is "a." The general Steps to follow in carrying out a Cobb-Douglas function after the values or the regression coefficients (bi's) have been computed are shown in x Ezekiel, 32. gi_.‘_t_., appendix I. 36 Ibid., p. 161. So the following case: Input quantity Category of Igmuts bi's 112 Land lh2.1 .2897’40 13 Labor 18.11. .160090 in Cash expenses 63,271 .28h260 1L5 Livestock-forage $7,227 .322018 X6 Machinery $6,073 .139h22 Value of a - .h2hh9h n - 30 farms The general equation for fitting a Cobb-Douglas function that has one dependent and five independent variables is: 11 . sausages? The meaning of each of the symbols in the equation will. be explained. The a is a constant; b2..... 6 are referred to as regression coefficients, for theymeasure the amountof change inalwithaunit change in 12....16. For example, the value or b2 of .2897ho indicates that a one Percent increase in the smotmt of land used in the production process Mld cause a .2897h0 percentage increase in the gross incane. The regression coefficients are also called elasticities. The 12 ....X6 are the gemetric mean proportions of the inputs used in the production Process. For emnple, the value of 12 was 11:2.1 acres. This is the geometricmeansverageoftheamotmtoflsndthstwssusedontheBO fem inthis case. Gross incune is designated 1:1 in the above eqclation. 51 Thenext step is to convert themeanvalues of the input and investment categories, 12...X6, into logarithms. The logarithms of 12 ...16, value of a, and b2..b6 are substituted in the equation in order to solve for X1. Log 11 - .lIZhh9h 4' .2897’40 (2.152576) '0' .160090 (1.263663) t .28’4250 (3511;655) t .322013 (3.853956) * .139h22 (3.7331125) Log 11 - 1t.Ol9703, the antilog of which is $10,1t6h. This illustrates how the geometric mean proportions of lh2.1 acres of land, 18.1; months of labor, 33,271 of cash expenses, $7,227 of livestock-forage investment and 86,073 of machinery investment produced a gross insane of 810,161: on the 30 fem in this case. be general statistical data for the function are expressed in the following section. The xmxltiple correlation coefficient (R) measures the relation of gross income with the independent variables such as 12 . . .16 in this case stucb'. It does not tell anything about the relative importance of each independent variable, but it does give an indication of the over-all effect of the variable upon the gross income. If no errors were made and all variables were included in the multiple correlation, the multiple correlation would approach 1.0. a h1g1 coefficient of multiple detennination such as .91 in this case study connotes a ma: degree of association behaen 12 ...X6 and X1. In many cases this hig1 coefficient might be caused by only one or two variables; so it is important to compute simple correlations of the independent variables. These will. be presented in a later section in this chapter. 52 The coefficient of determination or 122 indicates the percentage of variance in gross income that can be explained by the independent variables. In this case the value of R2 was .81; which meant that 8!; percent of the gross income is accounted for by the five independent variables. The retaining 16 percent is uneiqalained, as it might come frat factors such as management, soil variation, weather variation and other factors that were not studied but were assumed to be rsndanly and normally distributed. It is inportant for a ample to be able to have a 70-90 percent of its gross incane be explainable by the inde- pendent variables, as predictions for farm reorganization are of limited value if they are based on inputs that only partially explain gross income. The standard error of estimate 'S of gross insane indicates the closeness with which values of the dependent variable may be estimated from the independent variables. finall standard errors indicate low degrees of variability, whereas large standard errors reflect a large degree of variability within gross income. The standard error of .08793h for the logarithm of gross incano of h.Ol9703, the antilog of which is $10,1t6h, means that two-thirds of the time the gross incane for the sample farms would fall within the range of 38,5116 and 312,813. If the standard error were much higher in this study, the range of gross income for two-thirds of the farms might be fron $5,000 to $15,000; thereby, causing the predicticn of gross incane on farms to be of limited value. 0-“ ..V 53 Inc standard error of estimate of the regression coefficients was discussed in this section on page 1:5. _Majflnil value product . After the bi's, a, and 11 are computed, these factors can be substituted into the general equation Mai - bi E Y in order to detemine the marginal value products of the five innit and investment categories. The marginal value product refers to the net returns to the categories of inputs or investments. In the above equation the EU) is the expected gross income or moist that will be produced by the set of X2 .. X6. ‘Ihe bi in the equation refers to the regression coefficient or elasticity that is a constant for the 11.1'he x1 refers to the geometric mean of the in- Plrt or investment category. Both 8(I) and x1 are measured in natm‘al numbers. For oxmple the MVP of 12 in this case will be canputed. Thevalue of 12 - 1h2.l3 the value of bi - .289700 and the BC!) '- 310, 246,4. Substituting these values in the above equation gives MVP :12 - .289130 gloyyz or an m x, of $21.33. This means that the mmvunefaroduct ofthe lastacreoflandappliedtathe PPOduction process would return 321.33 above the cost of planting, ha-'I'-'V'esting that acre of land. Mnginal value product estimates are of value to farm managers, tea-chars, extension agents, eactemion researchers and- credit agencies, ‘15“)? they provide estimates of the earning power of inputs like cash eJCE’etnses and land for a specific area and a specific type of farming. ”19 Problems of budgeting are peatly sinplified if information is aVaIIable on marginal returns of the major categories of inputs and Sh investments. For example the basic principles of expanding output until the marginal value product equals the margnal factor cost can easily be derived by comparing the estimated marginal value products with the costs (sometimes subjectively determined such as the minimum costs of depreciation, repairs and maintenance of farm machinery ) of using that input or investment. If a manager requires a 20. per cent return on his machinery investment and finds the marginal value product of machinery investment yields a five to ten per cent return, the logical move is to decrease the amount of machinery for the present combination of inputs. If he finds that land and other inputs need to be expanded relative to the machinery investment it is possible to canbine the present machinery investment with the expanded inputs so that a more profitable total reorganization will result. USing this method allows a farm operator to increase the returns to the machinery investment while at the same time the returns for the other inputs and investments are increased. A sound decision as to how to best reorganize the farm operation can be made only after owning the returns to all inputs individually but at the same time. For example, the returns to one input or in- vestment might indicate a reduction in the use of that input would inerease gross income while another input could be expanded to increase gross insane. It is therefore necessary to consider the over-all effect of expanding or contracting the use of all inputs or investments rather than trying to reorganize the farm on the basis of changing the use 01‘ me input at a time. 55 A detailed discussion of the factors to consider in inter- preting the results of Cobb-Douglas analysis as a measure of economic efficiency will be discussed. in Chapter IV. The interpreta- tion of the results for extension evaluation will be presented in Chapter V. CHAPTER III (DLIECTION OF DATA. 1ND FITTING THE FUNCTION The data for this study were taken from tlfirty-eiglt dairy farms in almont experimental township and forty dairy farms in Burnside control township in Lapeer County for the year of 1953. 'Jhese areas were selected for study because they represent one of the five experi- mental and control townships in the township extension program in which the writer interviewed some of the famers and is familiar with the dairy type of fanning operation being carried on in both townships. 2113 single Townships almont experimantal township is six miles square in size. It had 181 fame in 1953 of which 65 were dairy farms, twelve vegetable farms, six commercial orchard farms and the mnaining 98 were engaged in general farming.1 ‘Ihe township agent, located in the village of Almerit, assists only the nlnont township farmers interested in the 1"Gunship extension program. file Burnside control township is located twelve miles north of “111mm township and is six miles by nine miles in size. In 1953, there were 251 farms in Burnside township, the higler number of farms \ l ‘3 bert Hall, "Monthly Report of almont Township Extension agent," Cooperative Mansion Service, Michigan state College, East Lansing, Mic-idem, 1953) . 56 57 than in aJinont township being partly attributed to the larger size of Wide township.2 Dairying is also the major enterprise of most farms in Burnside township . me famers in Burnside control township receive assistance from the Lapeer County extension staff located in the village of Lapeer which is 2’4 miles southwut of the village of Burnside. Lapeer county extension agents serve about 3,000 farmers. Ethnic (h‘oups me farmers of Almont and Burnside townships are primarily of west Elmopean origin. Market Outlets The principal fluid milk outlet for both townships is located at Inlay City which is 13 miles north of the village of lenont and nine miles south of the village of Blrnside. ‘Ihe county seat of Lapeer, an excellent farm shopping center, is fifteen miles northwest of W and titenty-four miles southwest of Bumside. soil Type The soils for nJmont experimental township are level to rolling “1‘1: have been developed from glacial till. hey are primarily Miami an1d Conover soil type, relatively high in fertility and are suitable \ 2 Statement by James Nielsen, persons]. interview. 58 for row crops such as beans, and corn.3 The soils of Burnside control township are of two major classifi- cations: ‘lhe northern two-thirds of the township has a nearly level, fertile type of soil that is high in organic matter. The southern third of the township is canposed of hilly, well-drained soils that have a low fertility. For this reason the sample of farms surveyed in Burnside township was taken from the northern two-thirds of the township, for the soil association closely matched the soil of Almont township. Two fanns located in the sanctr section of Burnside township were included in the control console but were later removed from this stuck, as they were on a lower production hinction than the remaining farms in ailment experimental and Burnside control township. The soil types in almont and Burnside township have approximately the one inherent characteristics and the some level of productivity with the exception oi the sandy southern third of Burnside township.b' Climatic Factors Although a wide variation in the length of growing season exists in many areas of Michigan, the length or g'owing season for both the experimental and control townships is from 150 to 170 days. . since the townships are located 15 miles apart there also is little 3 Eugene Mliteside, Ivan Schneider and Roy Cook, Soils 3; Midli , Special Bulletin h02, Michigan state University, East lansEl-g, Michigan, 1956, pp. 39-146. hfitatoment by Eugene Whiteside, personal interview. 59 variation in the amount of rainfall per season and the date of freezing} Present Land Use Lapeer county, in which both townships under stun are located, is a major dairy and cash crop area. It is close enough to the large nearby markets to favor dairy production and general farming. Dairy- ing is the most important enterprise for the area and on mow rains it is the sole source of income. The number of dairy cows per farm is among the higlest areas in the state. Dry field beans, wheat, and corn are the major cash crops. The ten year, 19h2-l951, average crop yields for Lapeer and two surrounding counties were: corn 32 bushels, oats 38, wheat 2h, barley 27, field beans 1h bushels, and hay 1.11 tons per acre. The average size of fauna in 1950 in Lapeer county was 117 acres. Data Emmeration The sample of farms for this study is composed of dairy farms frat almont experimental township paired with dairy fame from the matching Burnside control township . 'Ihe fame for the eiqaerimental township sample were selected after checking the county agricultural Stabilization Connnittee records of —‘ 5 Elton Hill and missell Madly, es of _F_____gsmin in Mchi , special ninetin 206, Michigan state (3%", —East Lansing, Mi gan, 19%. p 9- 6 “bid. 3 Po Bho the 181 fame in the experimental township with the township agent, project evaluator, and the board of directors of the Almont Township Extension Association. A schedule (see Appendix A) was designed to furnish the total dollar value of output in 1953 including inventory changes, and the quantities of various resources employed during that year in producing that output. file 1953 data were enumerated in 1951: by a field survey team. The total interview for traditional farm account data, Cobb- Douglas data and a net worth statment took approximately two to three hours per farm. About one hour per farm was used to acquire the special data for Cobb-Douglas analysis. 'Ihe special information collected for Cobb-Douglas analysis included the following items : Forage investment (page 3, appendix A) a. Costofporennialseedoandplnntsusodinl953. b. Hay and pasture inventory on January 1, 1953. 1111: included the kind, acres, age and condition of all hay and pasture fields and the month that am field was plowed down during the year. c. 'Ihe cost of machinery hired for nonnal land reclamation was also recorded for this category. Livestock Investment (rages h-E, appendix A) Beginning inventory value of all breeding stock plus the mmber of cattle raised, or died, and the number, value, andmorrth inwhich anybreedingstockwerepurchased or sold during the year. 61 Machinery Investment (rages 5-6, Appendix A). . The January 1, 1953 auction value of all Machinery and equipment including the farm share of the auto. In addition the date and value of am machinery or equip- ment purchased or sold during the year were recorded. Cash Expenses (Bags 11, Appendix A) althoug: all. cash expenses were collected for traditional farm management analysis only a portion of some items were included and some entire items were deleted for Cobb- Douglas analysis . Building Capacity (Page 8, Appendix A) Data were collected on farm building capacity for all breeding livestock. The return to this category was not cooputed in this study. Gross Income (Pages )4, 8-10, Appendix A) In addition to the information on cash receipts and inventory changes in livestock, feed, and seeds, the value of family living firmished by the farm was collected for Cobb-Douglas analysis. All information collected was treated as confidential; some fmailers were reluctant to disclose financial information unless it "Md be used only for resoarch at Michigan b‘tate University. Ihe fame for the control township wore selected after checking the cvunty agricultural stabilization Committee's statistics m the 251 ram in that township with the project evaluator, county agent, 62 preceding county agent, and members of the survey team. On the basis of Trenhlay' s7 pairing of farms in the Vemont Pam rlanning study, 38 fauna in the control township were paired with the 38 farms in the experimental township. ‘nlese farms were paired as closely as possible on the basis of the following factors: labor force available, age of the operator, total acres, tilleble acres, number of cows, and the machinery investment. Two additional schedules were comleted in the control township making a total of ’40 schedules collected for the control township and 38 in the experimental township. 'me following empirical techniques were used in this study in order to satisi)r the condition that all fame are operating on the same production function as outlined by Toon and quoted in Chapter II of this study: 1. 'lhe sample was restricted to single enterprise dairy fans which derived the maj or portion of t heir gross farm income from the sale of dairy cattle and dairy products. 2. Data were secured for the year 1953. 3. all five input and investment categories were used on all farms in the samples. h. Prices of feed, seed, livestock were held constant for the beginning and ending inventories. 'Jhis allowed the maranal value productivity estimates to reflect the true earning 7Raymond Tremblay, "Vemont Farm Flaming Study, " (Department of Ag-icultural Economics, University of Vermont, Burlington, Vermont, 19531) P0 10 63 power of the input and investment categories rather than be biased by the effects of inflation or deflation of farm prices during the year of the study. 5. line two samples were restricted to soil associations having the same inherent productive capacity. rurpesive sampling was used to select a wide range of quantities and proportions of inputs used. lhis method allows a smaller number of farms that are not in couxpetitive adjustment to be used in a sample than randan sampling or farm record project samples permit. This procedure reduces the correlation between inputs which in turn reduces the standard errors of the regression coefficients. turpesive sampling also reduces the cost of collecting data as compared to random sampling because of the smaller number (30-10) of fame required for a sample. un the basis of these conditions information collected on the 38 farms in the experimental and 1:0 in the control township included: i1 - Gross income measured in dollars X2 - Land, measured in total tillable acres 113 - Labor, measured in total months used on the farm xh - Expenses, current operating, measured in dollars is - Livestock-forage investment, in dollars 1L6 - Machinery investment, in dollars Gross income (11). This includes sales of all crops, livestock and livestock products 3 plus or minus changes in inventory of feed , seeds, crops, livestock or other fans-produced products; and the value of family living fIn'nished by the fam. Government payments were 6h excluded as they were not considered income from farm-produced products. Changes in inventory value of buildings and machinery due to depreciation were excluded from goes income. Therefore, gross income should be large enougz in this study to cover the maintenance of the machinery and building investment. The value of farm buildings was not counted as an input in this study; so gross income does not include the rental value of the farm residence. _I-EIE (X2). This category includes the total number of acres of land owned, rented, or leased by the operator. It was measured in tillable acres. Both townships are higfly developed, so practically all productive land is being utilized. In order to obtain an accurate estimate of the productivity of land, all land in woods, nontillable pasture, roads and building sites were excluded from this input category. The dollar value of land is difficult to estimate, therefore, land was measured in physical terms. 2222 (X3). Labor was measured in total months of labor used on the farm during the year. This includes the operator's labor plus hired and family labor. If the operator worked off the farm part-time, the time he spent off the farm was deducted from the number of months (usually twelve months) he might have spent on the farm. Current w eggsnses (1h). Included are all current operating expenses expected to yield dollar for dollar returns in a given year. It includes the following items: feed purchased, manual seeds and plants purchased, custom work or machinery hired, gas and oil for farm use, livestock expense, fertilizer and lime expense, 65 fam share of electricity and telephone, farm share of the auto and truck gas and oil, feeders purchased, value of clover stands destroyed during the year, beginning inventory value of feeder live- stock, and the value of perennials plowed down during the year. The cost of line was included in the expense category because the fame in both townships that did apply line during 1953 all used the normal maintenance rate of application. The cost of fertilizer was also included in the expense category as no excessive rates of application during 1953 were encountered on the sample fame . Beginning inventory value of feeder livestock plus the value of feeders purchased during the year were treated as an expense item, as feeders are expected to return a dollar for each dollar invested during the year. Livestock and _f_o_r_gg_e_ investment (15). his includes the dollar value of the investment in forage crops and breeding livestock for the 1953 year. Because of the hig': complementarity existing between forage and forage-consuming livestock, the two were cmbined into one category. The investment figures were computed separately for forage and livestock. Then the two were combined into this category. The total forage investment was computed by taldng the beglming of the year inventory value of all hay and pasture stands, plus the cost of machinery hired for land reclamation and the cost of perennial seeds purchased during the year, minus a proportional credit for hay and pasture stands destmd during the year. Beginning inventory value of hay and pasture stands included the cost of labor, seed and 66 fertilizer of establishing stands plus the subjective value of the stand in future years. Wagley and members of the Soil Science Department of Michigan state University computed the series of prices which were used for hay and pasture stands ranging from $28.22 per acre for first-year alfalfa-brome stand in excellent condition to $7.07 for third-year alfalfa-broom stand in poor condition to $5 per acre for permanent June grass and second-year clover stands.8 The age, condition, nmne of each grass or legume, and the number of acres in each hay or pasture field was recorded on each surveyed fann schedule in order to detemine the beginning of the year inventory values. The livestock investment was computed by taking the beginning inventory of breeding stock plus proportional credit for breeding stock purchased during the year unims proportional credit for breeding stock sold during the year: Machinery investment (X6). Included in this category is the entire machinery investment for 1953. It is composed of the January 1, 1953, auction value of all machinery and equipment, plus a pro- portional credit for machinery purchased during the year, mime a proportional deduction for machinery sold during the year. The minimm return to the machinery investment must be h1g1 enougi to cover maintenance, depreciation, interest , plus whatever subjective returns deemed necessary by the manager. 8Based on unpublished data on estimated establishment costs for forage crops and small grains, compiled by Harry Wilt, Department of Agri- cultural Economics, Michigan State College. 67 E3 Smle Fanns The nature of the sample farms may be derived by showing the range in the data for the several categories of variables studied and the "usual"9 farm organization. The “usual" organization for the farms in the eocperimental town- ship and control township is shown in Table l. TABIB]. 0019mb OF ms MIC MEAN ORGANIZATION OF ms MENTAL Townsmr WITH ms CONTROL TOWNSHIP, 1953 _v Input Category Experimental Control TWEL¢ Township___ 12 Iand,'acros tillable 1h2.1 153.3 1: Labor, months 18.h 17.2 Xi Cash expenses 83,271 83,1;88 £5 Livestock-forage investment $7,227 87,078 6 Machinery investment $6,073 some a comparison of the "usual" organizations in the two townships points out the big: dome of similarity in the quantity of inputs used. little variation in cash expenses, or machinery investment was found in the two townships while a mall difference in the amount of land, labor inputs and machinery investment existed. The "usual" organization of the control farms had eleven acres more land with one month less. labor than the "usual" farm organization. 'lhe combination 9The usual organization is considered to be at the geometric means of the various input categories. 68 of resources in Burnside control farms yielded a goes income of $11,065 or $601 more than the almont goes income of $10,!46h. The range in goes incane, inputs, and investments in the two townships is shown in Table 2. TABIEZ mammarmmmnmrs,mnm,mmcssmoam IN nu: ma AND CONTROL MINSHIP, 1953 — Category Ebcperimental Control Township Township GI‘OBS income 314,576‘329, 951 $3,533-321,818 Land ' 33-361 75-328 Labor 8-142 6-38 Cash expenses $1,268-$7,116 $1,277-$9 ,08’4 Livestock-forage $3 ,610-323 ,096 315131-313 ,102 “3011111017 152,565-315,006 $2,101-$l3,393 The total of 78 schedules, (ho from the control township and 38 from the experimental township) were carefully analyzed. since the Cobb-Douglas function provides reliable estimates for only single enterprise fame, it was necessary to select a homogeneous sample of dairy farms that derived their major portion of goes fem income from the sale of dairy products and dairy cattle. Thirteen schedules which failed to satisfy the homogeneous dairy type-of-faming classifi- cation or other accounting requirements were deleted hum this study. Five of the 38 experimental township farms were deleted for the following reasons: two were fruit farms, two farms operated only nine months during 1953, and one was a cash crop fan. This left 33 usable schedules for the experimental township function. 69 Eigit schedules of the original ho were deleted from the control township sample for the following reasons: three were beef cattle fame, two had incomplete schedules, one was a poultry farm, one famer was a cattle dealer, and one farm had only one cow. This left 32 usable schedules for the control township function. Fitting the Function a total of 6S schedules, 33 for the emefimental township and 32 for the control township were used to fit the first Cobb-Douglas function. The totals of each input and investment category and goes incuae on the 65 schedules were converted into logarithms. The Doolittlelo method of multiple correlation analysis was used to fit two least squares regression equations to the logarithms of the data; one for the thirty-three farms in experimental township and one for the thirty-two farms in control township . The mcperimental Township Results The regression coefficients and associated standard errors that were obtained by fitting the function to the 33 experimental township fans were: land b2 - .2897ho I .126122 Labor b3 - .160090 I .1187h6 Mousse bu - .2814260 1' .12298h Livestock-forage b5 - .322018 f .128h56 Machinery b6 - .1391422 - .mszo 10 Ezekiel, Q. git” appendix I. 70 The constant (log a) was computed and found to be .h2hh9h. In natural numbers the fitted regression equation was:. - o .2 o .2 o o 11 .hzuhgz. 12 827h0x3 169090xh 81.26%; 32g018x6 139h22 The geometric mean combination of inputs for the experimental township yielded a goss income of $10,h6h. Least squares regression analysis provides three types of infom- ation about regression coefficients-~the amount of change, the pro- 11 The amount portionate mortance, and the accuracy of the estimate. of change is indicated by the value derived for the regression co- efficient, the proportionate importance by the correlation, and the accuracy of the estimate by the standard error. These three factors were used to appraise the regression coefficients for the experimental and control townships. The amount of change as reflected by the regression coefficients was believed to be accurate for all inputs and investments in the experimental township. The amount of change occurring in gross income with a one percent increase in the amount of land to the production process is equivalent to .2897h0 which is the reg-ession coefficient for the land. Since all regression coefficients are less than one decreasing returns to scale are being experienced for all inputs and investments. The usefulness of repession coefficients depends upon their accuracy. The standard error of a regression coefficient determines 11 T'rant, pp. git” p. 37. 71 the degree of accuracy and is dependent upon three main factors: size of the sample, range in the observation of the independent variable, and the intercorrelations between the independent variables for which the regression coefficients are estimated. The influence of each of these factors won the standard error was discussed in Chapter II on page as . The multiple correlation coefficient or (R) was .91. Under con- ditions of random sampling, with five independent variables and one dependent variable, a multiple correlation coefficient this hig'x would be expected in one sample out of 20 if the true multiple correlation coefficient were .80. Consequently, the degree of correlation is significant. The coefficient of determination (R2 ) of .81. indicated that 81:, percent of the variance in gross income (X1) is associated with variations in the input and investnent categories. The remaining 16 percent of the variation in X1 may be due to nonstudied variables. The standard error of estimate (8') of the dependent variable (gross income) was canputed to be .0879311. The logarithm of gross income at the geometric mean was 14.019703, the antilog of which is 3510,1161» Under conditions of random sampling, given the weather and Price conditions for 1953, 67 percent of the time the logarithms of a<3‘l‘o‘ual gross income would be expected to fall within the range of 14-019703 1 .08793h or, in natural numbers, between $8,5h6 and $12,813. “Geording to these results, on the average, one farm out of three of 72 the usual organization would be expected to have a gross income greater than $12,813 or less than $18,516. Estimated m value product . The marginal value product estimates are shown in Table 3: TABIE 3 USUAL mum 11m ESTIMATE) menu AM) moss mum mowers, THIRTY-THREE mm TCMNSHIP was, 1953 Input Quantity (Log Category of Inputs Log X1 bi's liabi) WP _ Land 1112.1 2.152576 .2897h0 .623687 $21.33 Labor 18.11 1.263661; .160090 .202278 $91.21; menses $3,271 3.5111656 2811260 .9990'16 .91 Livestock-forage $7,227 3.858956 .322018 1.2142653 .h? Machinery $6,013 3.783h26 .139h22 .527515 .21: Log com (a) " o o o o o o 01121114914 Log 11 (Gross Income) - Log a + (b1.Xi) - 11.019703 The marginal value products represent the net return to the last unit of each input or investment category. For example the last acre 01‘ land was earning $21.33, the last month of labor was earning $91.21;, the last dollar of cash expenses was returning 91 cents while the 11Vestock-ferage investment was earning a 147 percent return and the maflhinery investment a 2h percent return. The accuracy of the regression coefficients and hence the marginal Value products depends on their standard errors. as discussed pa:‘e'v'iously the intercorrelation between independent variables is an 73 important factor in determining the size of the standard errors. The simple correlations that existed between independent variables were as follows: r23 .61 r21; . S 7 r25 .62 r26 .60 1'31: .29 r35 .16 r36 .32 r15 .61 r146 .70 r56 .72 Two hid) correlations were observed between cash expenses and machinery investment of .70 (14:6) and between livestock-forage invest- ment and machinery investment of .72 (r56). 'niese correlations must be taken into consideration when the marginal product estimates for expemes , machinery and livestock-forage are interpreted. The significance of the marginal value product estimates is closely related to the significance of the regression coefficient estinates. One method of detemining the significance of the regression coefficients is to test them against zero as a null hypothesis.12 lhis is the simple studenflo t test that is conputed by dividing a regression coefficient by its standard error. The coefficients b2 (land), bl; (cash expenses) and b5 (livestock-forage investment) were sigiificantly different from zero at the five percent level, while b3 (labor) was not significantly different frail zero at the five percent level, ad the standard error 01' b6 (machinery investment) was larger than the reg'ession coefficient of Machinery. ‘Ihe t values for land, expenses, and livestock-forage in‘restment were larger than 1.96 and less than 2.56 which means that in 95 out of 100 cases if functions were fitted to different samples \_ 12 Assumes that the difference between the estimated coefficient and the actual coefficient is null or zero. 7h from the same pepulation the regression coefficients would be as large or larger than the estimated coefficients for this function. a. set of minimum expected returns for the input and investment categories were used to test the actual regression coefficients of the sample against the minimum regression coefficients necessary to give marginal productivities equal to the market price or marginal factor cost of the resources. In other words, does the marginal return of $91.21; per month of labor differ significantly from $150, the market wage rate13 (plus room and board ) for labor in the dairy farming section of eastern Michigan or do the 33.91 returns differ significantly from the $1.00 cost of cash expenses? As a test of these possibilities, the regression coefficients of production necessary to give marginal products equal to the market cost of the resources were computed. The following set of minim expected returns were considered to be reasonable minima to expect: Labor $150.00 per mon 11‘ Land $10.00 per acre Cash expenses $1.00 per dollar expended Livestock-forage investment 10% of investment Machinery investment 20% of investment The regression coefficients or bi's of each input or investment are compared with a "standard" bi capable of yielding a marginal V‘lue product equal to the nxargnal factor cost for each input or \ 13 Karl Vary, "Wage Rates Reported by Farmers ," Michi Fans Economics, Cooperative Extension service, Michigan State allege, august, 1933. 1h an. 15 Based on 5% interest rate with land valued at $00 per acre. 75 investment. The "standard" b1 is detemined after solving the equa- tion MVr' - 324332111 for the bi after the minimum marginal value product has been detentined and substituted in the equation. The estimated bi is subtracted from the standard bi and the difference is divided by the standard error of the b1. 'me results of the test are shown in Table h. TABIEh OOIPARJBCB N THE BTIMATH) WSION CM’FICIENTS AND THE MICK CMFICM REQUIRE) TO YIBID TEE MARKET PRICE (F RBGJRCES Fat flaunt-mm EXPERIMENTAL T040511]? FAME, 1953 Input Estimated bi to yield bi-bi* (SI bid); bi's mm Return 553: Land .2897ho ..135798 .1539h2 .126123 1.220570 Labor .160090 .263761 .103671 .1187h6 .8730h8 Barriers“ .28h260 .312882 .028622 .12298h .232729 Livestock-forage .322018 .278172 .0h38h6 .128h56 .3h1330 Machinery .139h22 .116081 .0233h1 .1h152o .16h93o ‘ {- absolute value. Only the land regression coefficient is significantly different from the “standard" bi required to equate marginal factor cost and Wm value product of land. Thus it appears that the fame are "91—1 adjusted when analyzed at their geometric means. W305 of Egorimental Township Estth with Haglez' s W. 'Ihe most recent Cobb-Douglas stucw of dairy farms in fag: 76 Michigan was conducted by Wagley in 1952. He selected 33 dairy farms in Indian County (central Michigan, about 90 miles from the experimental township) and derived the following marginal value products: land, $16; labor, $30; expenses, 76 percent; livestock-forage, 6h percent; and machinery, 19 percent. By «sparing the experinental township returns with Wagley's estimates it is seen that the returns are within a close range of each other. Acceptance of: _thg Function £93: _t-1_1_e_ Emerinental Township. The first function for the eaqaerinental township was accepted as being an accurate measure of the earning power of the inputs and investments used on dairy fauna in the experimental township. lhe estimated re- turns to the input categories have low standard errors and are within a narrow range of the Mailman expected returns that are considered necessary for the dairy area in which the experimental township is located. Appraisal of the First Motion for the Control Township A total of 32 farms were used to fit the first function for the control township. 'Ihe regression coefficients and associated standard errors for the control township were: Land b2 - -.089608 1' .151361 Labor b3 - .23603h I .135821 nxpenses bh - .331296 3 .13h8h7 Livestock-forage b5 - .h39135 if .12h759 Machinery b6 - .259361 - .1168ho Ihe mount of change for the input and investment categories that "‘8 reflected in the control township's regression coefficients was 77 believed to be accurate for all inputs except land and labor. a negative elasticity of -.089608 was obtained for land. This means that increased quantities of land might possibly decrease gross in- come but it was not believed probable that it would do so. Tintner and Brownies pointed out that: "negative elasticities, within the range of inputs on most farms are meaningless."16 The simple correlations between the independent variables were foundtobe: r23 - .714 r2h - .32 r25 - .52 r26 - .62 1‘31; "’ .29 r35 " out 1‘36 " ohg r115 - .50 rh6 - .61 r56 - .51 Relatively hid: correlations between land and labor of .711 (r23), land and machinery of .62 (r26), and expensesoand machinery of .61 (r146), were partly responsible for the h1g1 standard error and reduced reliability of the regression coefficient for land. Thus, with a given amount of variance in the dependent variable that can be explained in the "best least squares fit" by the independent variables, over— estimation of one regession coefficient tends to necessitate some underestimation of one or more of the other regression coefficients.” This could be interpreted to mean that sane of the underestimation in land coefficient might be due to an overestimation of either the labor, °r machinery coefficients since both of these had high intercom- latione with the land input. \ 6 Tintner and Brownlee, 32. cit” p. 37. 1? Tan, @o 9-1;." PP. M‘UO 78 another factor responsible for the large standard error Of land can be traced to the failure in the sampling procedure to select a wide range of data from imperfectly adjusted fams. It was found that a large percentage Of the fame in the sample were well adjusted competitive firm. For instance, a cluster of farms with 12 to 1b months of labor and 130 to 150 tillable acres of land were discovered when data for the 32 farms in the sample were plotted on a simple graph. Therefore, the lack of range in the control data reduced the reli- ability of the regression coefficients by causing high standard errors for the coefficients. Estimated M Elli Products. The marginal value products computed for the first control township function are shown in Table 5. 1113125 113m ORGANIZATION AND sodium panama. m) (moss VAIIIE mamcrs imam-NO comm. IMISHIP PARIS, 1953, FIRST FUNCTION Input Quantity of (he __ Category Inputs Log X1 bi's X1.bi) WP Land 153.3 2.185565 -.O89608 -.19§8hh 8 -6.h6 I-l-bor 17.2 1.23h260 .23603h .291327 $152.26 Ebcpennee $3,168 3.5h2559 .331296 1.173635 1.05 L1'Vesimck-forage $7,078 3.818925 .h39135 1.690636 .68 inery $6,1h8 3.78870h .259361 .9826142 .ho L°8 constant (a) - .101568 L°g x1 (Gs'oss Income) - Log a . (hing) - h.oh396t \ MI.“- Lfl.5 t .. -..". ..wV Jr! 61"”. . . Jive.) e the.” 2r... [1 79 It is seen that the negative regression coefficient for land creates a negative marginal value product for land. It is believed that the returns to labor are partly reflecting the returns to land and hence in reality the actual marginal value product of land is positive while the return to labor is smaller than the estimated $152.26. The unexplained residuals in gross incane for each farm were com- puted in order to locate unusual discrepancies in data fran sample farms or unusual circumstances in the method of grouping the input categories and handling the data. This was done by substituting the log of each input category for each farm into the logarithmic form of the Cobb-Douglas function and solving for log 11. The antilog of log 11 was then determined and subtracted fran the actual gross income to determine the residual. Sizeable residual gross incomes of $3,698 and 86,517 were found on two farms while smaller residuals of $1,000 to $1,500 were discovered on several other farms. The two farms with actual gross incomes of $3,698 and $6,517 less than their expected gross incanes were re-interviewed during the fall of 1955. A gravel bed cutting across these two farms was found to be the major factor responsible for their actual incomes to be considerably lower than their expected gross incomes. Hence, these two farms were (:1 a dif- ferent production function than the other 30 farms in the sample and should be deleted for more accurate results. 80 The coefficient of determination for the control sample was com- puted to be .82 which may be interpreted as meaning that 82 percent of the variation in gross income (11) was associated with variations in the input and investment categories. The remaining 18 percent of the variation in X1 may be due to non-studied variables that were assmued to be randomly and normally distributed. After cmparing the residual gross iaccnes on each fem with the data on the survey schedule it was hypothesized that the wide variation in soil types on two farms was mainly responsible for the unemlained variance of 18 percent. ReJection of _t_h_e M Motion for _t_h_g Control Township. Since the negative coefficient for land was thought to be biased downward and the coefficient for labor was biased upward, due to a high inter- comlation between land and labor, the regression coefficients for the first control function were considered unreliable. The first function for the control township was rejected for the following reasons: 1) negative marginal value product estimate for land, 2) h1g2 my for labor, 3) large residuals of 353,698 and 156,517 on two farms , and 14) high degree of intercorrelation between several input cate gnries. appraisal of the second Function for the Control Township A new function was fitted for the control township after deleting “"5 farms that were located on a different soil type than the remaining 8al'lple fame, The "usual" organization of the thirty farms used to 81 fit the second control township function as compared to the organi- zation in the experimental township and to the organization of the farms used to fit the first control township function is shown in Table 6 . TABIB 6 OQIPARISW OF THE GECME'TRIC MEAN AWfi w INPUT GAME FCR THE FIRST AND SECOND CONTROL TCWNSHIP FUNCTIOBB WITH THE mama TORSHIP FUNCTION, 1953 Control Township Control Township Experimental Input First Function Second Function Township Catemies 32 Farms 30 Fggas 33 Fame Land 153.3 1119.8 1&2.1 Labor 17.2 16.8 18.1; Cash expenses 33,1188 $53,195 $3,271 Livestock-forage $7 , 078 $6 , 913 $7, 227 Machinery $6,1h8 36,0149 $6,073 F By examining Table 6 it is seen that the "usual" organization of all input and investment categories for the second control function is Smaller than the "usual" organization of the first control function Smnple. This occurred because the two famns that were deleted for the second function had a larger amount of inputs and investments than the "usual" organization for the sample fame in the first function. The combination of resources in the control township for the second function yielded a gross income of $11,1h8 which was $83 higier than that of $11,065 for the first function. Gross income ranged from a high or $21,818 to a low of $3,583. ‘15.}IIH' D... n- T. . I‘u ‘ mo .1 _ 82 The coefficients and associated standard errors that were obtained by fitting a Cobb-Douglas function to thirty farm were found to be: Land b2 - «015852 3 .noh72 Labor b - .255119 E .098623 Expenses bfi - .3563h2 - .075h20 livestock-forage b5 - .507209 1’ .0919142 Machinery b6 - .226173 I .08h955 The constant (log a) was computed and found to be -.228078. In natural mmbers the fitted regression equation was: “.228 8 “o0 8 2 o2 o 6 g r ‘ o _ 07 . X2 t; s . x3 ssns». It 35.3142. ,5 50;:sz ,6 22cm The multiple correlation coefficient (a) was .96. Under condi- x1 tions of random sampling, with five independent variables and one dependent variable, a multiple correlatim coefficient this high would be expected in one sample out of 20 on the average if the true multiple correlation coefficient were .89. Consequently, the degee of corre- lation is significant. Since extreme values were included in the sample, the value of the multiple correlation coefficient should be exPected to be higier than that existing in the universe, thougl not 18 I’d-glen: than for a similarly drawn sample for the same universe. The coefficient of detemination (R2) of . 91 indicates that. 91 Percent of the variance in gross income (11) is associated with vari- ttiona 1; the input, and investment categories. The remaining nine Percent of the variation in 11 may be due to nonstudied variables. ”‘6 unexplained variance of 18 percent in the first control function T\ ” BBzekiel, 32. 933., p. 320. 83 was reduced to nine percent in the second function after deleting two farms that were on different soil types. The standard error of estimate C§) of the dependent variable (gross income) was computed to be .059706. The logarithm of gross income at the geometric mean was b.0h7192, the antilog of which is 311,1h8. Under conditions of random.sampling, given the weather and price conditions for the year in which the sample was taken, 67 percent of the time, the logarithms of actual gross income would be expected to fall within the range of 11.011.71.92 I .059706 or, in natural numbers between $9,716 and $12,790. according to these results, on the average, one fans out of three of the usual organization would be expected to have a gross income greater than $12,790 or less than $9,716. Estimated W 11133 Products. The marginal value products inure conputed for the "usual" organization of the 30 farms in.the second control function. The marginal value estimates are shown in Table 7. By examining the MVr's it is seen.that land still.has a negative mgdnal value product while the marginal value products for labor, e-‘qbenses and livestock-forage investment increased, and the marginal Value product for machinery decreased. The simple correlations that existed between independent variables were : r23 .72 r21; .30 r25 .50 r26 .61 r314 .27 r35 .142 r36 .118 rhS .137 rh6 .60 r56 .h9 8b, TABIZ'I USUAL WTION AND BTIMATE) MARGINAL AND GR$S VAIJJB PRGXJCTS THIRTY CONTROL TWHI'P FAME, 1953, SECOND FUNCTION Input Quantity (L08 Category of Inputs Log x1 bi'a X1.bi) MVP Land 11:9.8 2.175579 -.oh5852 -.099755 8 -3.h1 Labor 16.8 1.225h6h .255119 .312633 $169.11 Expense $3,105 3.53h666 .3563h2 1.259550 1.16 mvesteck-rerage $6.913 3.839671; .507209 1.9h7529 .82 Machinery 86,0h9 3.781671: .226173 .855313 .1.2 Log constant (a) =- ... ... -.228078 Log 11 (Gross Income) - Log a -- (bi.X,-_) - b.0h7192 n small reduction in the correlations for each input category was noted for the second control township function as compared to the first control township function. Three of the ten correlations listed above dropped .03, while six dropped .02 and one dropped .01 after fitting the second function. Since the size of the sample for the second function was 30 as compared to 32 for the first function, it is seen that only a small reduction in each of the simple correlations occurred after fitting the second function. Three high correlations still exist after fitting the second function. These are: land and labor, r23 of .72 as compared to .71; in the first function; land and machinery, r26 of .61 as compared to .62 in the first function and expenses and machinery rh6 of .60 as compared to .61 in the first function. 85 Colmarison of the Two Functions for the Control Township. The purposes of fitting the second function to the control township were to attempt to: reduce the intercorrelation between independent in- puts, secure a more accurate estimate for the land input, reduce the standard error of the bi's, and obtain more accurate marginal value product estimates for all input and investment categories. The effect of fitting the second function to the control township is shown in Table 8. By examining Table 8 it is seen that all standard errors of the regression coefficients were reduced after fitting the second function; the marginal value product estimates were increased for all inputs except machinery; and the regession coefficients were increased for all inputs except machinery. Rejection 9}; _t_h_e_ 93% Function _fgr l‘hfi. Control Township. After examining the results of the second function, the livestock-forage investment was questioned as it yielded an 82 percent return cuapared t9 3 68 percent return in the first control township function and a 1*? percent return in the experimental township. since the level of milk production in the control and experimental townships and the value or dairy cows in the two areas was assmed to be about the same, the ("3" Values for each farm in the control township were plotted against the pounds of milk produced per cow on these farms. be same procedure “‘8 followed in the experimental township, and it was discovered that th° dairy herds in the control township were undervalued compared to 1° herds in the experimental township. The average pounds of milk 3%» H. ..‘rfi DIM! II haw/Pr _ JAE? . fig 86 6E...“ on op eons: HH defiefiai .efido am 3 teeth H seepage me. he. mmdgwo. camefla.u medpmm. Homdmm. ego.ee maa.e» auedfiheez mm. we. madame. emeemfl.n memeom. mmamme. mam.ea meo.~e ewepeo nxoopn obs ea.ee mo.He augmeo. panama.“ Namomm. mamamm. m~4.m« moh.m& reducers efl.deae em.mmae mwemmo. Hmmmme.n mHHmmm. hmoemm. w.efl «.5H pend; ea.m.¢ eh.e-e Neqofia. Hemama.u mmmmeo.- moemmo.- m.maa mrmma one: eraH em pew“, \mmw. humm, *H eewwuununnmruuuuu is: e.ap e.an poppet» we .85 2-843 ooefldueeo one: be» 38 03.; Hangman: nod-nonwom 038390 Rea .3: E932 nomazoo EB: 52 2.5.5 on g «28.5% 0% 8m EDGE as; $.52: 5:. mag gm .Eoflfioe 83% .5 as as GEES was 87 produced per cow on the 30 control township farms was approximately 9,000 pounds compared to 8,300 pounds on the experimental township rams. me average livestock investment was 35,822 for 20 cows and other brooding livestock in the control township compared to an average livestock investment of $7,067 for 21 cows and other breeding livestock in the experimental township. After analyzing the livestock investments in the two townships it was discovered that the experi- mental township survey team of three interviewers valued cows about 350 higher for all production levels than the other survey team of three interviewers did in the control township. Hence, the livestock investment of $5,822 in the control township compared to a $7,067 investment in the experimental township was due to undervaluing the control township herds. Un the basis of the undervalued livestock-forage investment in the control township the second function for the control township was rejected . Fitting the Third Function to the Control Township The livestock investment on 26 farms in the control township was adjusted upwards by checking each schedule and placing a value on the dairy herd corresponding to-the value of the cows with the same milk production in the experimental township. The geometric mean value of the livestock-forage investment increased from $6,913 to 37,6141: or $731 after revaluing the herds on 26 farms in the control township. One other minor discrepancy in the forage investment was noted in the 88 control township. It was discovered that on eight control township farms alfalfa-brome fields plowed down in June were counted as part of the forage investment rather than as a cash expense. The forage investment on these farms was adjusted for this factor and hence the forage investment for the third function decreased while cash expenses increased. The cash expense category increased from $3,h25 to $3,538 or $113 after the changes were made in the forage and cash expenses for the eight fams in the control township. The third function was fitted to the same 30 fans as the second function. Changes in the livestock-forage investment and cash expense were made so that the geometric mean average of the livestock-forage investment increased from $6,913 in the second function to $7,6Mi in the third function and cash expenses increased from 3%th to $3,533. Appraisal and acceptance _o_f_ t_h_e_ 3.1.19. Function £31; the Control Township. The results of fitting the third function to the control township data are presented in Table 9. The constant (log a) was -.151903. In natural numbers the fitted 1' egl‘ession equation was: -.025360 o186111 o 8 8 . x1 _ ”151903 . x2 . _ 13 . It 3h 5 x5 S56§h6x6.166067 This canbinatim of inputs and investments was expected to pro- duee a gross income of $11,1h8. The null hypothesis was used to test the probability that the “She asion coefficients obtained from a different sample of the same pomllattion would be as large or larger than the estimated regression coefficients. The regression coefficients , bl: (for expenses) and b5 89 TABIB9 ms mm m mGANIZATION, msmw cmcm, STANDARD mats um macnuL 1mm: manners Fan mm! CONTROL TWNSHIP rims, 1953, mm FUNCTION Standard Errors Regression of Regression M Categoq Mean Coefficients Coefficients _MVP Land 119.8 -.025360 .106929 $ -1.89 Labor 16.8 .186111 .09606h 35123.12 Expenses 33 ,538 . 3h8558 . 0721420 1 . 10 Livestock-forage $7 , 6M; . SS6Sh6 . 09hlh8 . 81 Machinery $6,010 .166067 .082293 .31 (for livestock-forage investment), were significantly different from zero at the one percent level of significance; b3 (for labor) and b6 (for machinery investment) were significantly different at the five Percent level aid the standard error of b2 (for land) was larger than b2. 'L'ne estimated bi's are compared with the bi's capable of yield- ing a marginal value product equal to the marginal factor cost in Table 10. It appears from this test that when the remssion coefficients are compared at their geometric means only the land and livestock- f°Page are significantly different from the "standard" bi required t° equal marginal factor cost and marginal value product. The multiple correlation coefficient or (R) was .96. The co- err 1911th of determination or (R2) was .92 compared to .91 in the secom function. This means that 92 percent of the gross income can TABIZ 10 COMPARIBCN mum: ms ESTIMATED melon cmcmms AND ms mam cmxcmfrs mum T0 mun ms mm mm or Resona- rm mm: comm. TWISHIP mars, 1953, 90 mm: FUNCTION Inn: Estimated bi to Yield 05' b t bi s runimmn bi-bio 1 b1- 1 Return B's—f '- Land -.02536o .13h373 .159733 .106929 1.103823 Labor .186111 .226oh9 .039938 .096061. .32h7oo Expenses .3h8558 .317366 .031192 .O72h20 .1430709 Livestock-forage .5565t6 .27h219 .282327 .09h1148 2.998757 Machinery .166067 .109139 .056928 .082293 .691772 as absolute value be explained by the five inwts and investments (:2—16). The standard error of estimate ('3) was .031912. time the actual gross income for the fams under study would fall This means that 67 percent of the Within the range of 11.0h7l92 I .031912 or, in natural numbers, between 310.359 and $11,997. The canpsrison of the statistical tests for the three functions f113th to the control township are shown in Table 11. By examining Table 11 it is observed that the following changes were recorded after fitting the third function to the control township: the multiple correlation coefficient increased from .91 .to .96; the coefficient of determination increased from .82 to .92 which means that 92 percent of the variation in gross income is explained by the 91 TABIEll comma! or m or was, (moss moms, HOLT cmnm cmcm (R), COEFFICIENT or manor: (R ), sum macs or ETIMATB (3') mom SUM OF march cmxcmn's rat Tim FUNCTIONS Fat 32 AND 30 FARIB 2m ms CONTROL mmsmr, 1953 Control Tomshi Item fiction I fiction fl him 31 32 Fans 30 Farm 30 Farms Number of fans 32 30 30 Gross income (11) 811,065 $11,1h8 811,211.18 (R) .91 .96 .96 R2 .82 .91 .92 § .08 .06 .03 Sum of regression coefficients 1.28 1.30 1.23 input categories, as compared to 82 percent in the first function and the standard error of estimate of goes income was reduced. The intercom-relations between input categories 'were as follows: r23 - .72 r221 - .211 r25 - .61 r26 - .61 r31; - .23 r35 - .55 r36 - .148 1445 " 050 1.1.6 " 056 1.56 " 062 The only sizeable change in the intercorrelations after fitting the third function was between livestock-forage investment and machinery, 1‘55 or .62 compared to .h9 in the second function. After plotting the livestock investment on each of the 30 farms against the machinery investment and likewise the forage investment against the machinery “We s'bment it was discovered that forage invesment “3 111511? 92 correlated with the machinery investment. The same machinery in- vestment had a marginal value product of .112 in the second function compared to .31 in the third function. It appears that the return for livestock-forage investment was overestimated while the machinery inves'hnent was underestimated . after the livestock-forage investment was increased $731 in the third function, the marmal value product dropped only one percent or from .82 to .81. In view of this small reduction of one percent it is believed that the hi @er correlation of .62 for livestock-forage investment with the machinery investment is responsible for the sharp reduction in the marginal value product of machinery while only a sliglt decline occurred in the livestock- forage investment . In spite of several limitations caused by h1g1 intercorrelation between land and labor and livestock-forage investment and machinery investment the third function was accepted as a good measurement of economic efficiency in the control township for the benchmark year of 1953 for the following reasons: 1) a further reduction in the size or the sample for fitting another function would only tend to increase the standard errors of the bi's as the smaller the sample size, the larger the standard errors; 2 ) no accurate schedules were available “1‘ substitution or for increasing the size of the sample for another fit; .3) five farm account records for the control township for 1953 "we analyzed and found unusuable because of accounting difficulties and. lack of sufficient data for all input categories, and 1:) no 81231316 I‘°d":'-"~>‘l=ion in any of the simple intercorrelations was experienced after 93 fitting the third function and further "fits" were not believed to cause any great reduction. Reorganization of the Qerimental and; Control —— Town—ship Fame The purpose of this section is to suggest reorganization patterns for the two townships on the basis of their estimated regression co- efficients, statistical tests, and judgnent. The purpose of reorgan- izing rams is to achieve a more efficient production pattern for profit madmization or nonmonetary reasons such as insurance, and flexibility that may enter the decision making process. For this section the profit maximizing goal of farm families is taken to be of primary importance. Expanding the use of assets until a more efficient level of operation is reached offers an avenue .of profit maximization. There are many limiting obstacles that slow down or prevent farm firms from making reorganization plans for achieving greater efficiency. Dome of these are institutional factors such as capital rationing, acreage controls, lack of available inputs (such as no land for sale W1thin ten or fifteen miles from the farm site) , and personal factors (Such as old age and religious beliefS). These factors will not be °°n81dered in this section. The reconmendations for the experimental and control township will be brief and based only on the general approaches that may apply to the mean average of theihrms but not 8P'~'39==:l..fically to am' one farm in the sample. g 15.....- . 91.: Experimental Township The 32 farms provided the following marginal value estimates: land, $21 per acre; labor, $91 per month; emses, 91 cents; liv- stock-forags, I17 percent; and machinery, 214 percent. (11 the basis of these estimates the following adjustments should be made: expand land and livestock-forage production for their return exceeds their marginal factor costs; reduce labor and cash expenses for their return is less than their marginal factor cost; and use the present amount of machinery. On the basis of the statistical tests and judgment these recamendaticns seem to be in line. The proposed expansion of land in this experimental township has been verified by a recent survey in early 1956. In this survey 28 experimental township farmers in- creased their tillable acres of land to 177 as canpared with 151 in the benchmark stucb'. This indicates a 15 percent expansion in tillable acres of land in two years. On the basis of the marginal value product estimates the eaqaected gross inccme for each farm in the sample can be cauputed. This in- Volves taking the actual quantities of inputs and investments used and the regression coefficients in order to derive the estimated gross inc me. For example, the first farm surveyed in the experimental 1"oh'tlszhip had an actual gross income of $6, 820 compared to an estimated gross income of $7,082. Hence the estimated regression coefficients f0? this study could be used to estimate the gross income for each farm and the individual farm operator could canpare his actual gross incane 95 with his expected pose income. One of the limitations of this type of analysis than the standpoint of the individual famer is that he can use the data only insofar as he approzdnates the average farmer. The marginal value products are calculated at the gemetric mean therefore the individual farmer cannot rely on his production function being exactly the same as the average of the farms surveyed. In addition Cobb-Douglas results do not provide famers with information as to the item of machinery or the age of breeding livestock to purchase, or what expense items to change if these categories should be contracted or expanded. It also does not indicate whether the forage investment should be emanded to include more alfalfa-brow or clover hay. This forces the extension agent or researcher using the results of these studies to bring other types of analysis such as budgeting or linear prog‘amming into play so that the alternative'costs and returns from expanding individual items can be computed before successful reorganization plans can be adopted. Control Township The 30 farms in the control township smple provided the following "urginal value product estimates: land, $1.89 per acre; labor, $123 per month; expenses, $1.10 return on the-dollar; livestock- fOI‘age, 81 percent; and machinery, 31 percent return for 1953. On the basis of these estimates the following adjustments will lead 150 more efficient production: expand expenses, livestock-forage, and machinery, for their return exceeds the marginal factor cost; IQWWUHW. .W;1..x .. firth}... 96 reduce land and labor, for their return is less than the marginal factor costs of using these items. on the basis of the returns, statistical tests, and judgnent, it appears that the recommendations should be altered so that land is expanded rather than contracted. This recamnendation is based on the h1g1 correlation betmen land and labor and the sum of the regession coefficients being greater than but not significantly greater than one. This indicates that the returns to land are undervalued while labor is overvalued. In reality it appears that land and labor should be appraised together, as their higi correlation has considerable influence on the estimated negative returns to land. The recommendation for expanding livestock- forage investment will perhaps require additional land to increase the forage investment. It is possible that the quality of the present forage stands could be increased without purchasing any more land, but a sizeable forage expansion would require additional land to be purchased. MN surmmummmsumrmmrs TOUSIIN EVAIDATING '1!!! cmmm IN ECONOMIC EFFICIENCY AT THE MICK OF ms mm In order to detemine what changes take place during an experiment, it is necessary to establish a benchmark or starting point. The purpose of the first part of this chapter is to establish a benchmark level of efficiency for the experimental and control township for 1953 on the basis of the Cobb-Douglas results. If the townships were closely matched there should be little difference in the earning power of the inputs and investment for the benchmark year of 1953. Thus the 1958 estimates in the emerimental and control townships can be compared to the 1958 cownon benchmark level of efficiency. If the Cobb-Douglas functions indicate that different benchmark levels of efficiency existed in the two townships then the terminal estimates for each township are compared to their benchmark levels . Therefore, if one exPerimental and its matching control township have the same or dif- ferent level of benchmark efficiency, it is possible to canpute the Chi-age in efficiency resulting from the five year experiment. Intelpretatioa of Cobb-Dou Results 1.32 3.11.212 0 8 The geometric mean organization and marginal value products of the accepted experimental and control township functions are compared 1‘ T‘ble 120 97 98 TABI! 12 CMARBWGFQUANTMGDMHSANDMARGINALVAIDBPRWCTS INTI-IE MINERAL AND CWTROL TWIPS, 1953 Quantit of ts Mar Value Hamlets Input Category mental %rol final m 12 Land 1h2.l 110.8 321.33 8-1.89 x3 Labor 18.1; 16.8 $91.21; 3123.h2 1h Cash expenses $3,271. 33,538. .91 1.10 XS Livestock-forage $7,227. $7,6hh. .h? .81 X6 Machinery $6,073 $6,016. .214 .31 Comparison of Marginal Value troducts Q. The marginal value product of $21 for land in the experi- mental township appears to be in line with the emectatiom for the area. With land valued at $200 per acre in the area it should return at least $10 per acre if a five percent capitalization value is used a8 recommended by farm management extension specialists. Since land has a blgb intercorrelation (.61) with the labor input, it is possible that the actual return for the last acre of land is slidltly less than the $21 per acre while the labor we is sligltly higler than the estimted 391. The MVr for land in the control township function was a negative 31-89 per acre. A somewhat low or negative return to the last acre °f land might be expected 1: the land were in a raw and unproductive 99 state, and hirther, if only a small amount of resources (livestock- forage) were combimd with land. However, since a $7,6hh livestock- forage investment was combined with the land input, it was concluded that land should earn from $5 to $10 per acre if the five percent capitalization rate is used on the 8200 per acre market value of land. It was mothesized that in reality, land was earning more at the margin than the reported negative $1.89 per acre. It appears that the experimental township is making more efficient use of the land than the control township. However, due to hiya correlations with land and labor in the control township it appears that land is underestimated and that actually there is little difference in the level of land efficiency in the two townships. M. be MVP of labor for the experimental township was $91. The M3) intercorrelation betwun land and labor may be partly responsible for a lower MVP for labor. On some farms it is believed that the months of labor used per farm during the. year were over- estimated thus causing the MVP to be eligitly lower than it is in reality. Un m rams an accurate record of the family labor was not kept and in some cases 12 months of labor were reported by the operators even thong: they were not fully productive during the winter months . The MVP of labor of $123 for the control township is believed to be sligitly overestimated since the hid) intercorrelation bettreen land and labor causes the labor input to partly acoountforsome of \. \. \J the returns for land. \ \ h llglnndn .nJ. .‘ than“?! 100 The MVP results indicate that the control township has slidztly greater labor efficiency than the experimental township. However, due to 11131 correlations betnen land and labor in the control township, it appears that there is little difference in the level of labor efficiency in the two townships. 9.9.5:.“ emnse . 'Ihe MVP of cash expenses for the emerinental township was 91 cents on the dollar or sligatly below the minimal: expected dollar for dollar return. Since cash expenus such as ferti- lizer, gas and oil, and feed, are expected to return at least one dollar for every dollar expended during the year it is believed that cash expenses were being quite efficiently utilized on the experimental township farms. The MVP of cash expenses for the control township of $1.10 for each dollar emended during the year reveals a higi rate of return on this hxput. ihe returns indicate that there is little difference in the level of efficiency for cash expenses in the two townships. Livestock-foriagg inve s‘tment . The MVP for live stock-forage in- vestment of h? percent for the experimental township fams reveals that this category is being used efficiently, as it approaches the marginal factor cost of ho percent. “me retm'ns for the experimental township appear to be high on the surface to many extension agents and famers, but after careful examination of the forage and livestock investments it is seen that a to percent return is necessary to cover depreciation, maintenance, and risk of the investment. Dairy cows 101 have an average productive lifetime of four years . Since the average cow is in its second year of production, it has two productive years remaining. This requires a 50 percent return on the livestock invest- ment, but the salvage value of the cows will retm'n a small sum thereby reducing the minimnn required return from 50 to approximately 110 percent. the forage investment also requires a to percent return for the average alfalfa-brace stand is in good condition for only two to three years. 'Iherefore, the forage investment must return enougimoneytopayforthe cost ofestablishingnewstandsandtobe able to absorb losses of new seedings or drougat. 'lhe livestock-forage investment of $7,227 is higfly productive on the experinental township farms and should be expanded for the marginal value product exceeds the margnal factor cost. The MVP for the livestock-forage investment in the control town- ship farms returned 81 percent which indicates that the investment was hidfly productive during the year. Since the investment had a h1g1 intercorrelation with machinery it my be overestimating the return to the livestock-forage investment and underestimating the re- tuiui for machinery. It appears profitable for the control township famers to expand their livestock-forage investment. It appears that the experimental township had a more efficient livestock-forage proyam than the control townships for its h? per- cant return is close to equating the marginal factor cost of to percent. However, due to hip: correlatiom between land, machinery, and livestock-forage , it appears that the return for livestock-forage 102 is overestimated in the control township and that in reality the actual retum is less than the estimated 81 percent. m investment. The MVP for machinery investment on the experimental farms was 21; percent. 'Ihe minimum expected returns for machineryare about 20percentastheymustbe large enoughto cover repairs, depreciation, and maintenance. The machinery investment of 36,059 for the control township area eamed 31 percent on the investment during the year. The machinery investment had a hid) correlation with land and livestock-forage thereby causing biases to enter into the estimates, hence, making it difficult to predict the actual return to the machinery investment. It appears that there is little difference in the level of efficiency for the machinery investment in the two townships . The experimental township return of éh percent compared to a 31 percent control township return indicates that they are both close to equating their machinery investment MVP with the marginal factor cost of 20 percent . _Iaiggg, _la_x_1_d, and; livestock-forage mt. me hid: intercorre- lations bettmen land and labor, betmen machinery investment and live stock-forage investment caused considerable bias to exist in the returns to the control township. As it was pointed out in Chapter II, 11191 intercorrelation between input categories can cause unreliable marginal value product estimates by overestimating one input while underestimating another input. It was believed that livestock-forage was overestimated while land was underestimted in the control township. 103 since additional observations were not available for the control town- ship to increase the n and thereby reduce biases between land, labor, and livestock-forage, the three inputs were combined into one input. 'lhe combined marginal value product of one month of labor plus the mean proportion of land and livestock-forage investment will make it possible to canpare the canbined earning power of the three inputs in the control township with the same combination of inputs in the experimental township. me process of canbining inputs is called taking a ”partial total“ derivative of gross income with respect to the combined inputs.1 The temn derivative is used to express alge- braically the relationship between output or Y and an irnmt x . Consider the total derivative of £11 . me equation shows how the out- put I changes when the input 12 chagges, the other inputs varying in sane degree. the algebraic expression for the partial derivative is B! . A partial derivative measures the small change in 1‘ resulting fréi a small change in 11 as that change goes to zero, all other inputs held constant. be following example illustrates how to take a “partial total" derivative . Suppose that the inputs L1 and 13. are so higfly correlated that at! and 033 reduce significantly the value of bi and b3 and that the 013T and 0‘53 cannot be reduced.‘ ‘Ihe ”partial total" derivative equation is as follows : €231.52ix1.-me.1 311575 Jada 13611 1 Johnson, ”The Cobb-Douglas Production Function with special Reference to Fitting Value Productivity Functions ,” 92. cit., p. 20. 1011 since a partial derivative asmnes that the remaining inputs other than the ones studied are constant, these asmnrxptiom also hold true in this case: 1) that the 1's which are not 11 and 13 are constant, and 2) that 13 varies with 11 in the proportions in which they are observed to vary among the fame sampled. me resulting MVP is one of aMVP of a unit of X1 plus that amount of X.j observed to be used with a unit of X1. In order to apply this equation to the control township function, it is first necessary to state the inputs that will be combined. The "partial total" equation will be used in the control and ezqaerimental townships to combine labor, land, and livestock-forage into a new input. The resulting canbined marginal value products for the two townships will be compmd to see if there is anv difference in the combined earning power of these inputs in the two townships .2 The ' mom and MVP's of the inputs appear in Table 13. TABIE 13 cxumunlsou or GEDMETRICIHIANS.ANDIMIRGINILHVALUE!PRODUCTS ran LAND, IABGI, um LIVESTOCK-mm IN ms WI. AND comer. TCWNSHIPS, 1953 Input oetegg Wfifinfi Imum-o1 vWél' Land x2 1h9.8 1h2.1 $1.89 $21.33 Labor 1:3 16.81 18.35 $123M $91.21: Livestock-forage X; $7,6hh. - 87 ,2 27. .81 .h'? ‘ k 211‘ these tln'ec inputs were used to refit a new function it is prob- able that the resulting combined MVP of the three inputs would not be the same as the value derived by taking a "partial total" derivative. 105 Substituting the geometric mean values of 12, X3, and X5 plus the MVP's of 12, X3, and 15 in the control township equation gives the MVP of labor plus land and livestock-forage as follows: dllgdll (ill-fl dXz + £2: (flfferen‘tiallé * 11 d1; (113 (312 d1; 12 33- 13 differential I3 I; 613 mx312x5- ‘4‘89 E’i‘éfii‘t $123.1t2 [I] + ,81 [€13.39 - 8-1.89 2: $8.91 + $123M + .81 1: 81:51:42 - $46.83 4» $123.12 + $368.32 ‘meHVPI3XzI3 represents the earningpower ofamouthoflabor plus the earning power of land and livestock forage investment combined in geometric mean proportions for the control township. Substituting the experimental township values into the. equation gives the following results: c111 +§2+dx1.xl dXZ ... X1 differentialxa ... 11 E a’x'gdxzmi'g'fi'j fgdifferentiXB i's'dx3 421.33 [11" + $91.22; [1] + .h? Egg] 421.33 at $7.71; + $91.21. + .h7x8393.8h -$165.09 + $91.21. + $185.10 MVP X3X2X5 - 311111.16 106 The combined earning power of labor, land, and livestock-forage of 31171;.91 in the control township compared to 311141.113 in the experi- mental township indicates that the taco townships have almost identical earning powers for these inputs. 'mis comparison and the individual marginal value product comparisons previously made in this section indicates that when the two townships marginal value products are compared on the basis of judgnent and three inputs with big: corre- lations are combined into one input there is little difference in the level of economic efficiency in the two townships for the benchmark year of 1953. Statistical Tests Used to Compare Production Functions and Reyession Coefficients for the Experimental and Control Townships The purpose of this section is to present the results of various statistical tests that were used to determine whether the experimental township had the same or a different level of econanic efficiency than the control township function for the benchmark year of 1953 . mggmgggproductionmnction. Asitwas previously discussed in Chapter II, the sum of the reyession co- efficients in Cobb-Douglas analysis indicates whether increasing, constant, or decreasing returns to sale exist depending upon whether the fbi's is greater than, equal to, or less than one. In order to detemdne whether the Zbi's are mater (smaller) than one, a test is required that will detemine whether the stun of the regression coefficients in a particular sample is significantly different from one. 107 Ulkin of Michigan State University, developed a test using the F- statistics which permits statistical testing of the 311m of the re- gression coefficients against any constant 0.3 This test as well as the computations adapted to the Doolittle method are presented in Appendix B. The test has been carried out for both the experimental township and control township functions, the sum of the regression coefficients being tested against one. For the experimental and control township functions the ébl was not simificently different fron one. Thus, it is concluded that comtent returns to scale prevail for the experi- mental and control township functions for the benchmark year of 1953 . In order to determine if the sum of the regression coefficients for the experimental township function was significantly different frm the control township function the 2131 of the experimental town- ship (1.195529) was tested against the f bi of the control township (1.231925) function. be results of the test revealed that the slope of the two functiom was not significantly different from each other for the benchmark year. Morison 2f the individual reg_essiou coefficients. Confidence limits cannot be attached to marginal value product estimates because of the lack of a measure of the vu-iation of the expected goss income in the MVP equation MVP 11 - W. Therefore, 1: each 1 3Ingram Olkin, "Unpublished report about a problem in testing sums of regression coefficients of linear multiple regression lines against a constant." This report has been made by the statistical gnup of the Mathematics Department to Professor Glenn L. Johnson, Department of Agricultural Economics, Michigan State University. 108 individual regression coefficient for the experimental township were compared with the corresponding regression coefficient for the con- trol township, it can be detemined if the regression coefficient for the township is the same or significantly different frm the re- gression coefficient for the experimental township . Hannan at Michigan State University, suggested a t test for this cozuparison.h The test as well as the mechanics for carrying it out are presented in Table 111. me test has been carried out for each of the five regression coefficients b2 - b6. When the individual regression coefficients were camared with the {(35) level - 2.00 none of them, as shown in Table 11; were found to be siglificantly different from each other. Thus, it can be concluded that for the benchmark year of 1953 the individual estimated regression coefficients in the emerimental township were not siglificantly different frcm the estimated reg‘ession coefficients in the control township function. W 21?. 3.11.2 assess}: .Lre ”ion coefficients £92: 3211.2 _egerimental £5 control township functions. we purpose of this section is to determine if the totality of the regression coefficients for the experimental township mnction were significantly different from the control township function for the benchmark year of 1953. The procedure followed was to estimate the expected goes income for each farm in the experimental and control townships by using their respective sets of regression coefficients and the quantities 1Statement by James F. Hamissistant Professor of Statistics, Michigan State University, personal interview. 109 m- «2 + H2 3&wa Annapmmmm > FEM! + nMDW|> I. } .3 .. ..B 1 u h a 938. 83:. 388. $82. “was". 553 338. oméfi. 83mm. Bmomm. 38%. guistetfi ass. gas. mass. sass. 83a. 8.83 688. 25$. S88. Hood. 883. .53 «38”. «~32. 85.... 3&8. - 35.... on: ..3. 3 can”? ..3 309“ [was m " hood” ._ r .. 2-3;“ H mummmimmfi anaemmawmluoeoou _ .. “ #3m New maimed... Q3. £8823 Emcee Basso n2. EH: BEBE amass agn— Ba Us page asng gfifian .8 8338 fig 110 of inputs actually employed on each surveyed farm for 1953. For example the expected goss income for farm lumber one in the experi- mental township is shown in Table 15. mm 15 Barnum caoss mean not 1 man IN ms mm mmsnn, 1953 Regression 00- Input Category amount Logarithm of Regression efficient 1 Used amount Used Coefficient logarithm of amount Used Land 117 2.06819 .2897h .59923 Labor 10 1.00000 .16009 .16009 Expenses 32,5117 3.110603 .281126 .96819 Livestock-forage $5,102 3.7077h .32202 1.21639 Machinery 3h,132 3.61616 .139h2 .50b16 Constant (y .hzhh9 __ Total 3.85015 Gross Incane $7,082 The antilog of 3.85015 is $7,082, the estimated gross income for the farm as compared to the actual gross income of $6,820 reported on the survey schedule. The next step is to determine the expected gross income for this farm by using the control township regression coefficients and the actual quantities of inputs used on the farm. Ihe expected gross income thus computed is $6,812. The difference betwoen the two expected goes incomes is taken and the procedure is repeated for each farm in.the experimental township. The'expected gross incomes are canpared for each farm in the control township. The experimental townShip bi's are substituted into the estimating equation for each control township farm and the gross incane for each farm is estimated. The means of the gross income are compared to determine if there is an difference in the estimated gross income for the experimental and control townships when their’regression co- efficients are substituted. The basic principle of this method is to see if the estimated gross income for the experimental township is as accurate by using the control township bi's as it would be by using the experimental township bi's. The mean gross income of the experimental township was $11,105 compared to a mean gross income of 811,885 when the control bi's were used to estimate the gross income. The mean difference in the two expected gross incumbe'was 8390. The equation'used to test the two meansis S t-‘iflflill b‘ X 'lhis test and the canputations for the two townships are outlined in Appendix C. The t values of the two means for the experimental town- Ship is .1198 canpared t0 t(.95) - 1.9976, so it is concluded that there is no significant difference in the reg‘ession coefficients for cstimating the gross incane in the experimental township. k 5 George w. bnedecor, Statistical Methods, (Ames, Iowa: The Iowa State College Hess, 1536), p. 77. 1.12 The same procethlre was followed for the control township with the control township bi's yielding an estimated mean goss income of 311,661; carpal-ed to the experimental township bi's yielding a mean gross income of $11,676 for the control township or a difference of only $1. The t value of the two mean gross incanes for the control township was .003629 caupared to t - (.95) - 2.0016. Therefore, it is concluded that there is no significant difference in the experi- mental or control township regression coefficients for estimating the gross incane in the control township. On the basis of this test, it is concluded that for the bench mark year of 1953, the regession coefficients derived from the ample of 30 control township farms were not siglificantly different fran the regression coefficients derived from the sample of 33 fans in the experimental township. mmnwcmmmmwmym townships. It was pointed out in the first section of this chapter that sane of the individual regession coefficients for the control tomshipwereunreliable, thusitwasnecessarytocanbine threein- puts of lani, labor, and livestock-forage investment into one input category. The MVPX 325 in the emerimemtal township was MLM and the control 141113325 was M7h.91. Thus it is concluded that there is little difference in the level of efficiency of these three inputs in the two townships. 113 Summary of the Statistical Tests The purpose of developing and using statistical tests to compare the two functions has been to determine if the level of econanic efficiency in the two functions were the same or different from each other for the benchmark year of 1953. The following tests have been used to compare the two functions. The sum of the regression coefficients for each township, although larger than one, were found to be not significantly different from one or different from each other by the use of 011d.n's equation. The individual regression coefficients in each function were tested against the coefficients in No significant difference the other hmction by the use of a t test. The was found in any of the coefficients for the two townships. aggregate effect of interchanging the regression coefficients for the two townships to estimate gross income was tested by a t test of the "Bans of the expected gross incane. The results of the t test reveal no Significant difference in the r egression coefficients for the “'0 functions in the benchmark year. Since sane difficulty in interpreting the marginal value products existed due to high inter- correlations existing in the control township, three of the inputs, land, labor, and livestock-forage were canbined into one input. The results indicate that the earning power for the last month of 135°“ plus the mean proportions of land and livestock-forage invest- ment was within a few dollars of each other in the two functions . Thus it is concluded that little difference in the earning Lil“ 1"! 1111 power and the level of efficiency of labor, land, and livestock-forage existed for the two functions. The MVP's of expenses and machinery for the two functions were within a close range of each other; it was concluded that the level of efficiency for these two inputs was about the same. 011 the basis of these statistical tests and Jldgnent, it is concluded that the level of efficiency in the two functions was not significantly different from each other for the benchmark year of 1953. Bvaluatin the Changes in Economic Efficien on _t_h__e_ ‘55—? nan—nee mi. “W O EJ¢WW The same method of using Cobb-Douglas analysis to establish a benchmark of efficiency in the experimental and control township in this study was used to establish benchmark levels of economic efficiency in the other four experimental and their matching control townships for 1953. Terminal surveys on the same 100 benchmark fame in the amend and control townships will be made in early 1959 in order to collect infomation on the 1958 fem business year. This data will. be used to fit Cobb-Douglas emotions in each of the five experimental and fire control townships . a terminal level of efficiency will be determined on the basis of the fitted emotions. The change in e‘15.:lga-ctlmency in each of the townships during the five-year experiment "111 then be computed. The purpose of this section is to discuss some of the possible me thoda that miglt be used to measure the changes in efficiency on th e basis of Cobb-Douglas estimates of 1953, and 1958. 115 Changes in Terminal Sin-vey Schedule mile these recommendations are not based on an appraisal of each of the other four emerimental and four control township results for the benchmark year, it will draw fran the experience of the writer in collecting sane of the data in the control township and fitting functions to one experimental and its matching control township. The first recommendation is to value the dairy portion of the livestock imestment on the average milk production of each herd, rather than having the farmer or interviewer value the herd. The need for this changeisbasedonthenecessityofrevalningthedairyherd inthe control township and fitting a new function in this study. he only other minor suggestion is to alphabetize the machinery. and equipment items to save time during the interview. he expense page could be altered slightly so that the expenses used in Cobb-Douglas analysis are listed in a separate column. Collecting the Data 'Dle mjor suggestion for collecting the data is to plot the quanti— ties of inputs and investment used on each new farm surveyed in order that a wide range in the quantities of inputs can be selected. 'lhis “Wharton will have to fit in with the pairing procedure followed in the benchmk stuw, for the same farms surveyed in 1953 will also be I“"38I-n'veyed in 1958. lhis procedure could be used to select replace- ments for fanners interviewed in 1953 but who have quit farming, 116 refused to be reinterviewed, or for those schedules that were unusable for benchmark analysis. malt of the 140 control township schedules and five of the experimental schedules were unusable in this study. as an example, several fruit fame surveyed in 1953 in the control township offered little information about dairying,hence these farms couldbereplacedbydairyfamsintheteminalsurvey. Fitting the Emotions 'Ihe only change involved in fitting functions to the teminal data is to adjust the 1958 prices to the 1953 level in order that the effects of inflation or deflation will not enter the estimates. Thus , the changes in efficiency will reflect the changes in the quantities and combinations of inputs used rather than the influence of price changes. Comparing the Terminal Estimates with the Benchmark Estimates lhe objective of this procedure is to detemine the changes in econmic efficiency that have occurred during the five-year experiment. The first step involves comparing the terminal experimental township functions with their base year functions am similarly for the control Mp3. The changes in efficiency that have occurred in the experi- mental townships will be attributed to the township agent, and the ”Ml township changes will be attributed to the regular county malaion program. If the efficiency changes are greater for the 117 experimental townships than their corresponding control townships, this increase will be attributed to the township extension agent. However, if the control township changes are water or not signifi- cantly different from the experimental township changes, than it will be concluded that the township extension program was of no greater value in changing the level of efficiency than the traditional county extension program. One of the hypotheses of the total township progran was to detemine if the township agents could speed up the technolog in the township areas faster than the county extension agents could do in their county areas. Technolog change is one of the factors responsible for a change in efficiency. Two major factors leading to efficiency changes are a change in technologr and a shift in farm organization. A technolog change occurs when the me quantity or fewer inputs cause an increase in gross income. For emlple, if farmers increase their gross income during the five-year experiment by using the same quantities of inputs as in 1953, but improved seeds, feeds, and breeding practices cause the gross incane to increase, then the increase in gross income is attributed ‘ to technoloy change. lhe second factor, a shift in fem organization, occurs when input substitution causes a change in was incane. For example a change in gross income fran the use of more machinery and less labor is attributed to a change in the farm organization. This section will discuss several proposals for measuring these two factors that malt be responsible for changes in efficiency on thefamsduringtheexperiment. lhefirsttestistodetermineif 118 there has been a change in the production hmctions by a technologr change. Technolog M° For example the 1953 fimction is derived from the mean orgnization of imuts and investments used in the production process during that year as follows: Y - a 11131....J6b6. The 1953 function yields an estimated regression curve labled 1953 as shown in Figure V. x2 .00 X6,| Xg eoe Xn FIGURE V. Change in Econanic Efficiency Resulting from a Technologr Change During 1953—1958. By substituting the 1953 mean organization into the 1958 equation (in 1953 dollars), it will be possible to determine the regression curve that will result fran using the 1958 rey'ession coefficients and the 1953 mean quantities of inputs. The resulting 1958 regression curve is shown in Figure V. If the 1958 production function is significantly different from the 1953 production function, then it may be concluded that there has been a shift in the production function orachangeinthetechnolog. MechangeislabelediinFing. The change in technolog' is credited to the township agent in the 1.19 experimental townships and to the county extension organization in the control townships. If the change in technolog in the emerimental township is significantly greater than the control township change, then it is concluded that the township agent increased the rate of technoloy faster in a township me. than the county extension organi- zation did in a county area during the five yem‘ period. mile the total changes in efficiency for each township are useful for evaluation much insigt can be gained by analyzing the changes in efficiency on the iniividual fem basis . a suggested method of computing the changes in economic efficiency on the individual farm basis are suggested by Glenn L. Johnson as follows: 1. Deflate or inflate 1958 input data to 1953 price levels for each farm. 2. Deflate 1958 goes income to 1953 levels for each fam. 3. Estimate income from 1953 function using 1958 deflated input data. 14. Find proportion of positive deviations of 195 8 goes incane fran 1953 goes income. 5. Test with binomial against p-SO. 6 6. If significantly750, a technological advance has occurred. Fam orflzation m. a shift in farm organization is also responsible for a change in economic efficiency. For example consider a situation when the base year MVP of labor is $91, machinery is ’41 percent and the tenninal year MVP of labor is $1.148 and the machinery investment is 26 percent. 0n the basis of these estimates it is con- cluded that the 1958 farms are more efficient because their Wr's are closer to their marginal factor costs of $150 for labor and 20 percent for machinery. Toe increase in the efficiency migrt have been caused byusingmoremachineryaniless labor. snexampleofsuchashift —__n 6 statement by Glenn 1... J ohmon, personal interview. 120 in fem organization is illustrated in Figure VI. The machinery investment for 1953 is shown as point e and the 1958 investment as point B. _1 1958 Function Y . ., ‘ g 2’ flight-3.953 “1116131011 _ o’ o" . /, h ; ," /' i / i "I A B Xéllg...Xn 1' u Change in economic efficiency by A FIGURE VI. shift in Farm Urgnization. Increasing X6 fran A in 1953 to B in 1958. Thus the researcher can isolate the technology and farm organi- zation changes and measure their impact on the efficiency changes at the canpletion of the experiment . Other Suggested Statistical Tests Several statistical tests used to compare the levels of efficiency in this study are also suggested for use in evaluating the terminal Pea“ll—ts. These are: Ulldn's test of the a bi's against one, the e’qberhnental township g bi's against the g bi's of the control t0":‘3311:Lp; Harman's t test of the individual bi's of the experimental twp against the control township, and use of the t test of the ”18% of goes income to see how close the estimated mean goes income is 1‘ Or each experimental and control township when their bi's are thl‘Qhanged . 121 While these tests are not all-inclusive, they perhaps will pro- vide a guide for the project evaluator to follow in evaluating the changes in econanic efficiency at the canpletion of the experiment in 1958. Detemining Why Efficiency Changes Occurred after the changes in economic efficiency have been computed and the experimental townshipe' changes are canpared with the control townships' , it will be of interest to detennine wiv sane of these changes migt have occurred other than the two maj or reasons of technology change and fan: organization change. a factor to consider is the effect of inefficient farmers surveyed in the benchmark year who shift enterprises or quit farming. If ten of the 38 dairy fame in the experimental township change from dairy to beef production these ten miglt be replaced by more efficient dairy farms for the terminal survey. that effect will this change have on the efficiency level for the sample? supposedly, the control and emerimental farmers changing enterprises during the five-year period will counterbalance each other, but in the experimental township, the township agent is working closely with a small number of farmers while in the control township, farmers compete with 3000 other farmers for assistance from the county extension service. If a larger percentage of the dairy farmers in the experimental township are still in the dairy business after the five-year experiment than the control township , then it might be concluded that the township agent was responsible for helping 122 the dairy farmers adopt more efficient production processes so they could aw in business. Appraisal of Cobb-Don? #?1s 33 3 Measure __ Econ c fic m It is felt that both traditional farm management techniques and production function analyses can make a contribution in the field of fan: management. Both old and new approaches are useful in measuring econanic efficiency; both require interpretation based on statistical tests and sound judgment. The purpose of this section is to appraise the use of one of the new approaches in production function analysis that of Cobb-Douglas analysis as a measure of econanic efficiency. Advantages of Cobb-Douglas Analysis Both the advantages and limitations of Cobb-Douglas analysis will be discussed under the framework of measuring economic efficiency. The special advantages and limitations of its use in extension evalu- ation will be covered in Chapter V. be case of estimating the regression coefficients by ordinary least-squares regession methods after transforming the data into logarithms is one of the main ad- vantages of using Cobb-Douglas analysis. In addition this technique yields estimates of marginal productivities for individual categories of inputs and investments. mother advantage of Cobb-Douglas analysis is that it yields estimates with geater degees of freedan for a small sample than other techniques permit. 123 Limitations of Cobb-Douglas Analysis The limitations ofthis typeofanalysis canbepreserrtedunder three categories: inherent characteristics of the function itself, accountingproblems ofbothinputsand gross insane, andunmeasured variables. Inherent characteristics of _t_h_g function. The irqaortant short- cmings of the function itself are : l ) the function is limited to handle relationships for firms in only one stage of production at a time because the coefficients of elasticity are constant over the entire range of the function, 2) the function always originates at Y - x1 - 0 andinadditionifamrii -0, thenI-O, and3) symetryofthe function implies that there is an unlimited range in which the proportion of am two inputs could be used to produce a fiver: level of output? accountgg problems. accounting problems in Cobb-Douglas analy- sis center around measuring inputs, and measuring gross income. One of the first problems involved in measuring input categories is thatofestablisningaprocedureofdefirflngorsettingupthe categories. In Cobb-Douglas analysis the Li usually refers to a group of inputs instead of a single input. For example labor inputs represent a cmbimtion of hired, fnily, and the operators labor while the land input includes rented and owned land. he collective land input also includes all land that is used in the farming operation regardless of whether it is being used in row crops, legume. 01‘ in 7 Carter, ma 22.3.0, Pp. 11.1110 12h sinner fallow. The basic question which arises when setting up input categories is, "is there an ideal method of grouping individual inputs into cate gories?" 'Ihe preferred method states that all. inputs med together should meet the least-cost oombination.8 'Ihere is no set procedure in measuring categories of inputs that has been established, but the general rules that are suggested by Glenn L. Johnson9 offer a good guide to follow. The important factors involved in measuring inputs are those of establishing a standardized system for handling may of the subjective factors and then maintain- ing a consistent pattern throughout the entire study. he accounting problem which arise when measuring pose income are those of canbining the products of one or more enterprises into the value product for the whole farm and reflecting changes in inventory resulting fran various inve stments and expenditures made during the year.10 Multiple enterprises within a farm business can be combined into a single measure of gross income for the farm by restricting the sample under stuchr to fanns having one major enterprise or by fitting a separate production function for each enterprise. 1. physical cost 8 a least-cost canbination refers to the best way to spend a given amount of money on all pairs of inputs in order to produce any given on pu . 9Bradford and Johnson, 32. 93.33., p. lldi. 10Johnson, ”'Ihe Cobb-Douglas Production Function with special Refer— ence to Fitting Value Productivity Function for Farm Businesses," Q. 933., p. 31. 125 accounting system for handling multiple enterprises has been recently developed by Beringer.ll The second major accounting problem encountered in measuring gross income is that of handling depreciation, maintenance, and repairs in inventory changes. The difficulty of adjusting gross in- come arises since these items do not help generate gross income but rather, they protect the value of the fixed assets. The most accurate method for hmdling all items that do not help generate goes income 2 For example, by is to eliminate them frm the input categories.1 eliminating these items from the machinery investment, the marginal return to the machinery investment must be large enougl to cover repairs, maintenance, and/ or depreciation as well as whatever return the manager considers necessary. . Unmeasm‘ed variables. Certain important factors in the pro- duction process are difficult to define, record, and measure. These measured variables include intangible and subjective factors such as management, weather, and technolog. There are two methods of handling these factors (1) design study to hold these factors constant or to a non-troublesome range or (2) measure unemlained residuals and incorporate them into the study.13 l:I'Cllrin'toph Beringer, "A Method of Estimting Margiml Value Produc- tivities of Input and Investment Categories on Multiple Enterprise Farms," (Unpublished "th. 1)., Dissertation, Department of egricultural Economics, Michigan state University, 1955) . 2 1 Johnson, "lhe Cobb-Douglas Production Function with Special Reference to Fitting Value Productivity Functions to agriculture ," a; 33.3. , p . 3 . 13Ibid p. 26. ”.’ 126 lhe most important of these factors, management, is usually unmasured in value productivity studies because of the difficulty in defining and measuring it. {me most practical method of handling management in view of this is to use personal judgnent based on exist- ing managerial concepts when selecting farm managers for the sample. 'Jhis procedure attempts to restrict the fame in a sample to a range with respect to managerial capacity so that all fanns will be operating on the same managerial production function. A further refinement can be made by examining surveys with large mlexplained residuals; if these can be attributed to superior or inferior managers quitting or replacing these surveys will then more closely satisfy the condition that all fans will be on the same managerial production function. Comparison of Cobb-Douglas analysis With the Essential Glaracteristics of a Good Measure of Econanic Efficiency In Chapter I the characteristic of reliability and validity were suggested as being necessary for a good measure of economic efficiency. The purpose of this section is to compu'e the chmcteristics of Cobb-Douglas analysis on the basis of this study with these essential characteristics. It must be realized that some of the details of using this method cannot be fully appraised until the completion of the experiment. Validity. The characteristic of validity stated that the measure must reveal the level of econcmic efficiency for the firm. In order to meet this condition the output must be measured in margnal terms 127 and both input and output must be measured. Cobb-Douglas analysis meets the validity condition by providing an estimate of the level of efficiency for a sample of fans by estimating mglnal value productivities of inputs uni investments. These estimates can be capared with the marginal factor costs for each input and the level of efficiency for the sample can be derived. me optimum level of efficiency is derived by the marginal factor costs for each measured input and investment. Both input and output are measured in Cobb- Douglas analysis. The output is measured in marginal terms. Reliability. 'Ihe condition of reliability is met when a measure can be used by the same or different researcher in the same sanple area or different sections of the county to derive approximately the same estimates of productivity. 'Dle reliability of Cobb-Douglas analysis is dependent upon many factors s uch as the sampling procedure employed , the accuracy of grouping of inputs, and the statistical tests used. 'L‘nis type of analysis is subject to many of the common problems of conducting arnr type of anpirical research in agriculture, hence many of its short- comings are cannon to other types of production function analysis. On the basis of fitting this type of function to two townships in this study it is felt that the ezperimental township results were higfly reliable while some of the shortcomings in the sampling tech- niques caused only fairly reliable control township estimates. In the control township the ma: intercorre lations caused several unreliable marginal value products. It is felt that under new sampling procedures 128 in which a wider range in inputs were selected, more reliable control township results could be obtained. Some of the important factors affecting the reliability of this type of analysis were discussed in Chapter II. On the basis of this study and similar studies conducted across the country such as the Northern Iowa, southern Iowa, Montana and alabama stucv of resource productivity it appears that Cobb- Douglas analysis can be used to measure econanic efficiency in different parts of the country and for different types of farming.1h smarizing the results of canparing Cobb-Douglas analysis on the basis of the experienced gained in this stucnr with the necessary prerequisites of a good measure of economic efficiency reveals the following: it satisfies the validity characteristic, measures both input and output, output is expressed in marginal tenns, while the reliability characteristic was not fulfilled in the control township hence this characteristic cannot be fully appraised until the com- pletion of the experiment. marl 0. Heady rmd missell 31w, Resource Returns and Productivity Coefficients _i__n Selected F Areas of Iowa, Wind alabama, Researmin 525, Iowa state-Mlege, mneszEwa, 11m , 1955 . WV APPRAISALOFCOBB-DOUGIABANAIISBASATCDL OF MICK EVAIIIATICN his chapter lpprdfies the use of Cobb-Douglas analysis in extension evaluation on the basis of using this method to establish benchmark levels of economic efficiency in one of the experimental and its matched control township for this thesis study. Egonomig Hfipiengz Redefined One of the major tasks of fanning is to organize linited resources into the most profitable operating unit. A farmer faces nary alterna- tive uses for his capital and labor. With limited funds the farmer mist invest these where they will yield the greatest return. If this condition is followed, the returns for the fam firm will be maximized. mile fanners use their own knowledge to solve nary of the managerial decisions leading towsrds profit maadnization, they have an opportunity to obtain advice from local county extension agents, township extension agents, college specialists, commercial management finns, and to obtain educational infomation from feed or seed dealers and other agencies . since fanners request information from the county extension agents and even more intensive assistance from the township extension agents in order to achieve mater economic efficiency, one of the methods used to evaluate the township program is a measure of economic efficiency. 129 130 Cobb-Douglas analysis is used along with traditional farm management analysis to measure the changes in economic efficiency which occur as a result of the township extension program. Using the strong points of both methods of analysis will enable an evaluation procedure to be developed to record, measure, and interpret the changes in economic efficiency resulting from the township program. Methodological Procedures While the general nature of setting up a Cobb-Douglas problem was outlined in (hapter II, this section will cover some observations gained from surveying sane of the fans in the control township and fitting functions to both townships . Sampling A major decision facing extension evaluators who are measuring economic efficiency is the type of sampling method to employ. A dis- cussion of the three types of sanqalingnfarm record-keeping projects, random, and purposive was presented in Chapter II. Purposive BImPJ-ing was selected for 1: his stw in order to reduce the intercorrelation between the input categories and thus increase the reliability of the bi's and the MVP estimates. It is realized that by using purposive sampling in this study to select a mall number of fams that only one type of farming is analyzed. Restricting the sample to one type of fanning has been questioned by some extension evaluators. Evaluators want to know what changes occur in all types of farming 131 as a result of extension education rather than to have specific infom- ation on one type of farming. This is a problem faced in this study which is important not only in Michigan but in other states with a diversified agriculture. Several alternatives are available for an evaluator who wishes to emloy purposive sampling and still gain information on all types of farming in the area. a large randan sample of 100-200 farms can be drawn (this was impossible in a six square mile township area in this study as there were only 100-160 fame per township) and several sub- samples of 25-30 schedules of dairy, beef, or fruit fame could be used to fit dairy, beef or fruit functions. another alternative is to select a small sample of 25-140 farms purposively and then use Beringer's multiple enterprise Cobb-Douglas function to fit both crop, hog, dairy, or beef functions. In view of the cost of collecting data it appears that purposive sampling does have an important contribution to make in sampling for extension evaluation as it permits small samples of 30-h0 schedules canpared to several hundred as cannonly collected by randaa sampling methods. Cost the cost and benefit of any method of collecting and analyzing intonation for mking estimates of resource productivity is of great importance to extension administrators and evaluators . Currently, extension administrators in several states are in the process of evalu- ating their farm and hane developnent prog'ams. several states we 132 examining the possibilities of using Cobb-Douglas analysis as a tool of evaluation. althoudi no detailed cost studies have been made on using Cobb- Douglas analysis, it is estimated that the benchmark stmw cost per processed schedule was $30 each. ‘Ihis is broken down into approxi- mately 820 field cost and $10 statistical processing cost. it a cost of 330 each, the total cost of the 78 schedules for this study would be approximately $2,310. his compares with approximately $25 per schedule in the Michigan fam account project of over 500 fame. Glenn 1... Johnson, while at the University of Ken‘hmlq, conducted several Cobb-Douglas studies and estimated a $25 cost per completed processed schedule in 1952. lhe$30costperscheduleforthisetudyincludednotonly intonation necessary for Cobb-Douglas analysis but also such items 88 changes in farm practices, net worth, extemion participation, and traditional farm account infonnation. Consequently the cost per schedule for Cobb-Douglas analysis is under 330 if proportional credit is allowed for the information collected other than for Cobb- Douglas analysis. Accounting Glenn L. Johnson has stated frequently that accurate Cobb-Douglas 333-13813 depends upon a sound knowledge of basic farm accounting. This mailtenant, is important became the accuracy of grouping inputs, “fleeting the data, and interpreting the results all center around a. 133 knowledge of farm accounting. The problem encountered in accounting for both inputs and gross income are discussed in Chapter IV. 'mese problem and developing statistical tests were the two most difficult aspects of this stucw. Fitting the Function lhree functions had to be fitted to the control data because of a failure in the sampling procedure to first select a wide range in the quantity of inputs and investments. another error in the control data was undervaluing the dairy herd which caused an overestimated MVP of the livestock-forage investment. Because of such errors, it m be necessary to refit functions to insure accurate results. rrice Change Adjustments Formerly Cobb-Douglas results held from year to year only if the prices of input and output increased (decreased) proportionately or remained the same. However this situation has been recently corrected by Trent's method of adjusting prices of input and output by Laspeyre's index. 'Ihus it is possible to adjust Cobb-Douglas estimates to price changes and extend the useful life of the estimates. It is concluded tentatively that this method can be adopted for the 195 8 terminal data. Interpretation 11me are involvedininterpretingthe resultsof Cobb-g Douglas analysis. The use of sound judgnent based on a thorough 13h knowledge of the area under stucbr, basic accounting procedures, and knowledge of marginal analyses are important to the success of this type of analysis . Application although the Cobb—Douglas method was used previously in agri- cultural studies, it still remains to be widely used for estimating econanic efficiency in agiculture. An obstacle is that the results of Cobb-Douglas studies are limited to the specific type of farming and geog'aphic ma studied. For example, the results of this simdy will provide a framework for budgeting and analyzing dairy farms only in the experimental and control townships and surrounding areas. Extension evaluators have hesitated to use the method for a variety of sound reasons. among these are the lack of information about the procedure involved in adapting this type of analysis to extension evaluation, and the questionable reliability of the method. M531 0n the basis of this prelimimry stucw, the following higlligits of the potential use of this method in extension evaluation are: 1) It satisfies the condition of validity. 2) Its reliability is sanewhat questionable on the basis of the control township' 2: results. 3) A sound knowledge of farm accounting is extremely important to the success of Cobb-Douglas analysis. 135 h) Purposive saupling permits 30-h0 schedules to be selected per county or township. 5) lhe cost of using this method is about $30 per processed schedule. 6) Several statistical tests outlined in Chapter IV offer possibilities for measuring the siglificance of the levels of efficiency in a sample area. 7) The preliminary results of estimating and comparing benchmark levels of efficiency in two townships suggest that Cobb-Douglas analysis is a good over-all measure of efficiency and is better adapted to measuring the changes in efficiency for a group offm'ms than onan individual farm basis. BIBLIOGRAPHY Allen, Richard G. D., Mathematical @1522 £03 Economists, (London: Macmillan and Co."'l', 9377‘“. Beringer, ChristOph, "a Method of Estimating Marginal Value Productivi- ties of Input and Investment Categories on Multiple Enterprise Fams," (Unpublished rh. D. Dissertation, Department of agricul- tural Economics, Michigan state University, 1955). Bradford, Lawrence a. and Glenn L. Johnson Farm Mamant w, (New York: John Wiley and Sons, Inc.,’l953) Carter, Harold U. , "Modifications of the Cobb-Douglas Function to Destroy Constant Elasticity and symmetry," (Unpublished M. s. 'Ihesis, Department of Agicultural Economics, Michigan State University, 1955). Doneth, John, Ea'figp‘f% Areas 6 and 7, Department of Agicultural Economics, ch gan 5 te University, East Lansing, Michigan, 1951;. Douglasahrsnl H., been 2; Wags, (New York: The Macmillan Cmipany, l9 . Douglas, Paul H. and Charles W. Cobb, "A theory of Broduction,” American Economic Review, XVIII, supplement, (March, 1928) . Drake, Louis schneider, "Problems and Results in the Use of Farm Account Records to Derive Cobb-Douglas Value Broductivity Functions , " (Unpublished m. D. Dissertation, Department of agricultural Economics, Mulligan state College, 1952). Durand, David, “sane Thougits on Marginal r'roductivity with special Reference to Professor Douglas' analysis," Journal _<_>_f_ Political Econ , LLV, (December 1937). "Ey’aluation of the Intensive County Extension Programs in New York state,” (prepared by the Cooperative Inctension service of Cornell University, Ithaca, New York, 1955) . Ezekiel, Mordecai, Methods of Correlation M, (New York: John Wiley and sons, T935).— Ferguson, Qiarles M. , "The Unit approach-what Does It Expect of County agents,” Better Fanning Methods, UNI, (December, 1951;). 136 137 Fiemip, Darrell F. , Resourc_______e_ t'roductivitz 93} Montana Dr}; Land 922 ,Fanns Mimeograph Circular Bozeman: Montana state College, ng-icultural mcperiment Station, 195 2 ) . Hall, Albert, "Monthly Report of almont Township Extension agent,“ (Cooperative Extension Service, Michigan State College, East Lansing, Michigan, 1953). Reach, Earl 0., “Production hmctions Fran a Random Sample of Fame,“ Journal of Fan: Econanics mm, No. 1: (November, 19%). Ready, Earl G. and Ihlssell Shaw, Resource Returns and Hodu’ctivitl Coefficients in Selected FW‘TM owa, mm,mtfismge,1&a TEE-1955. Hill, Elton and fhlssell Mawby, mes_ of Farmin inMichiga_n, Special Billetin 206, Michigan State College, East Lansing, Michigan, 1951:. L Johnson, Glenn L. , Sources of Income on land L___U_IarshallCo:m Lame, Progress Repm,— and“ Sources oi Inc come _o_n Bland ccCracken Fame, Browse Report No. 2, uraI'E‘fierilnent Station, 1952 Johnson, Glenn L. , "The Cobb-Douglas noduction Function with Special Reference to Fitting Value rroductivity Functions for Farm Risinesses," Tentative draft of a technical bulletin, Department of agricultural Econanics, Michigan state University, 1956). Johnson, rail 0., "Your County agent, " Prairie .F_____anner, (XXIII, (October 6,1951). Kile, Orville, The Farm Bureau ME 'Jhree Decades, (Baltimore: The Waverly trees, T9535. Nielson, James, 'Fann Planning-Township Style,“ (Paper read at the New England Research Council Meeting, erlington, Vemont, Jung Zh'zs, 195,4)0 Nielson, James, H__9__w Have Farmers ace ted the '7;ng Extension _;l'_l_'g- calm _i_._n__ almontr M,eer Ef agri- conomics ru ca ion chigan State University, East Lansing, Michigan, April, 1956). Nielson, James , "Notes on the Research Desigl and Procedure for Evaluating the Township Extension Program, " (Department of agricultural Economics, Michigan State University, East Lansing, Michigan, 1956). 138 Olldn, Ingram, ”Unpublished report about a problem in testing sums of regession coefficients of linear multiple regression lines against a constant." 'Ihis report has been made by the statistical youp of the Mathematics Department to Professor Glenn L. Johnson, Department of Agricultural Economics, Michigan State University. “Proposal to the Kellogg Foundation for an Mental Intensive ktension Program in Five Townships in Michigan," (prepared by the Cooperative Extension Service, Michigan State College, East Lansing, Michigan, 1953). Schruben, Inks M. , "Ingalementing State Extension Research ,” Research in Extension, National workshop Report, Federal Ebctension Sefice, Washington: United states Department of agimlture, 1955) . Schruben, Luke M. , "New Developnents in Extension Work," (Paper read at the New mgland Research Council Meeting, Darlington, Vermont, June 211-525, 195,4). Snedecor, George W, Statistical Methods, (Ames, Iowa: The Iowa State College Press, 1 . Spillnan William J. ial Yield Curves in Fertilizer - ’ United sagfiram “ad"; calm et meats FIB", (Washington: Govermnent Printing Office, 191:3). Stiglegé ()Eecrge J., 313 1131321 9; Price, (New York: Macmillan Co., 1 o . Tintner, Gerhard, we Note on the Derivation cf'the Production Functions Fran Farm Records," Econggetrica, 1:11, No. I, (Jamary, 19th). Tintner, Gerhard and O. H. Brawnlee, "Production Functions Derived from Farm Records," Jamaal _o_fFam Economics, XXVI, (August, 19th). Toon, Thorns G., The Earnin Power of , Investment, ’g % mm on m fieaamw' . ,‘T : gFIEI _ Station, 1953). Trent, Gerald Ion, "A Technique of Adjusting Marginal Value Productivity Estimates for Changing Prices," (Unpublished M. S. Thesis, Depart- ment of Agricultural Boonqnics, Michigan State College, 1951:). Tremblsy, Raymond, 'Vemont'Farm Flaming Study,“ (Department of Agicultural Economics , University of Vermont , DirJington, Vermont, 1953). Very, Karl, "Wage Rates Reported by Fame," mchi Fem Ecomnfics, Cooperative Extension Service, Michigan """ege, W?— 1953. 139 Wagley , Robert Vance , "Marginl Productivity of Investments and hcpenditures, Selected Ingmm County Farms, 1952,“ (Unpublished M. S. ‘Ihesis, Department of agricultural Economics, Michigan State College, 1953). Weintraub, Sidney, Price meg, (New York: Pihuan Publishing Co., 19 9). Hhiteside, Eugene, Ivan Schneider and Ray Cook, Soils 3g Michiga_n, Special Balletin 1102, Michigan State University, East Lansing, Michigan, 1956. APPENDICES APPENDIXA summscxmmusmrocoxmcr muonmmzooumsm mmwrmmsmzoommsmm FIVE comer. mm Fat THE mm (1“ 1953 C— ON I ~IcD~E-N -T- I-A-L ‘ wv 4-- .--—.. Information on the attached confidential ~ survey form is to be used only for research at Michigan State College. — I, m Farm No. Interviewer Date of Interview Name Address County TWP. seCt e Qtre Location of Farm (Miles from town) SIZE OF FARM Total Acres Owned Rented Tillable acres Owned Rented Type of Lease CROPS RAISED Acres 1 CROP Corn for sila e Corn for ain Beans Potatoes ar S 0 bus es Oats {wheat Grass sila e s Aaa her N b pasture: Alfalfa Other" gums .4—‘. ~-<-——- moo—e...“ Green manure cro Idle ...—_— rho—«#— a 0W TOTAL TILLFBLE ACRES Woods not stured Farmstead, roads, lanes TOTAL ACRES FERTILIZER Amman m i953 Crop TOLaI Lbs 0 Lbs. per Acres Kind acre Pi‘ice F§rtilizer (:2 Corn Planting Sidgvdress ..——. - ‘ S _b. ~’— .— _7 OatsL seeded Oats+ not seeded Wheat, '52-53 A t Planting Seeded Top dress Wheat, '52-53 .Wew-.. .....A-t' Planfbing. ...NQt Seeded Top dress ._ ‘ I. -~—— -— 0— ‘o-—- -— —- ub‘.’ _ —1 U c - - -‘ p ...- ..- b “' LA. h I _. .- Wheat, ' 53-51; At Planting Hay, Top dress TOTAL FER 'IILI ZER 17‘7 Lbs. of fertilizer per tillable acre Cost of fertilizer per tillable acre 35 Acres LEE APPLIED IN 1953 Indicate field on which major time and fertilizer investments were made \. Tons Per Total Acre Tons Price Cost _._ JL_.___._.. it SEEDS AND PLANTS Cost of Perennial Seeds and Plants Used in 1953 (Grasses, Legumes, Fruit) . AcreS‘ *Lbs. Cost or Kind Seeded Seeded Value 1/ TOTALS l/Include value of seed on hand at beginning of year or raised during year along with note to that affect. Hay and Pasture Inventory on Jan. 1, 1953, and Amount Plowed Under During the Year Age and Value Total Plowed. Under Prop. Kind Acres Condition Per A. Value Month . Green Credit Manure? A E V} :9 '1!) TOTALS XXX XX XX XX :3 Inventory of Small Fruit and Fruit Trees, Jan. 1, 1953 Kind No. of Acres Value per Unit Total Value TOTALS st of mac or 1 rec ama on ’ LIVESTOCK INVENTORY AND Jan. 1 195 Add Subtract Kind 0 N0 0 NO 0 301d & 83 COWS if s ifers under V8 8 er TOTAL DAIRY ttle: Feeders TOTAL HOGS : ns and Roosters Tur TOTAL POULTRY GRAND TOTALS Heifers Freshenedj 39, Mbnth LIVESTOCK BOUGHI‘AND SOLD Livestock Bought During Year Livestock Sold During_Iear . H‘Opo . T HOP. Kind No. Date ¥$Cost $flgfi£ Kind No. Date #Rectd ”Credit. 5.) s.’ “2 V ir—--- MACHINERY AND EQUIPMENT BOUGHT AND SOLD IN 1953 .1/ ___1 Purchases. to Item Total val . . ded. ‘l/ Carry over to inven on following page. MACHINERY AND EQUIPMENT lNVleUfiI U Book Value Jan. 1, 1953 are Auction Value Jan. 1, 1953 pre- Book Value Item ciation Jan. 1, 195b u Farm Sh§;§.—__.=,3 TruCK Trailer ”fiagons and rack§,__ p-“M. M, ..Traatgrr --. to cultivator ~——-q Beet lifter or been pull an cker rn Grain dril n CoMbine or er 8&8 er “Newer y r e ._ y 0 er IEEVIiflifi‘ LManure Spreader . Manure loader o ones or stove house Br H er _Electric motors Mi 1k "mac Cream separator ans 5 e o s Totals l/ NEW IMPROVEMENTS BUILT DURING 1953: Estimated Month Item Cost Life ~——— ?* .. O l/ Carry to improvement inventory below. VALUE OF LAND AND BUILDINGS Market Value Market Value January 1. 1953 l/ January 1, ljSLL .1] _gmed land and buildings :3 . $3 .. .... ..—.~. —~- Rented land and buildings l/ Use sane values at beginning and end of year unless acreage has changed. ILIPROVEI-ILI‘IT INVZ‘JNTORY Book Value Book Value “Residence _TenanLhonse.-- ......e - _Dairy barn ..ch Corn rib Ho house Poul house 68 BUILDING CAPACI TI If the best combination of livestock were kept for the present buildings and feed storage, how many of each kind of livestock could be housed? Dairy cows Dairy young stock Beef cows Feeder cattle Sous Feeder h0g8 (100#) Sheep Laying hens Chicks Other FEED AND CROP INVLNTCRY J Jan. 1 1 Quantity Price Value Quantity ice Value fi Seed: Annual 8 88868 w.— Growing Wheat TOTALS Inventory change :3 \\ Us! CASH RECEIPTS Source Quantity Pri Livestock and Li vestock Products Sold: 9 , 8 ee try TOTAL CROPS ce oodl oduc ts tom k or" . rented Agricultural am payments urer -‘ Total Other TOTAL CASH RECEIPTS Dairy cattle income 53__ Beef income _ ‘ Hog income Sheep income Poultry income Total livestock income f‘ $__ Crop income __ \\ x. lO VALUE OF FAl-iILY LIVING FURNISHED BY FARM Farm Product Amount Price Total Value $ $ Milk Butter _E_gg§ (51on Poultry (lbs. or number) _Beef _ML __ _I_.lgutton lFruit W Wood Other m TOTAL XX): XXX mam Operator months 3 Family months; Hired months 5 Total No. of men MEX OFF THE FARM “ Kind of Work By Whom Days Rate eggeed ...... 7‘: m K V a? TOTALS xxx 1 xxx Total income from other nonfarm sources (interest, dividends, rents, oil royalties.) ‘ CASH EXPENSES Item Quantity 11 Cost —hired labor Feed purchased Seeds and_plants_purchased - annual h“- a-fi—an-u". “.--; “Seeds and plants purchased - perennial (page 3) Custom work or machinery hired Supplies purchased Wflmaintenage 2 Farm Share Gas and oil for farm use (less ref1n1_cl)j only _‘Improvement repair and maintenance _ldsmmuImiajnqumuL Fertilizer and lime (page 2) ‘Iaxes Insurance on property Interests ....Elsatrichmel w}§lephone_(farm.share)4 Baby chicks purchased Other farm expenses TOThL CASH EXPENSE ...-..- a——..——--..—.. -A APPENDIIB THBFEBTFGImeTIBSUMOmeSIONGCEFFICmS IN A IMF. MICK NATION AGAIIGT A CQBTANT TIEFESTFCRTETDWGTHBSUMCFTIEMSION WIRES IN A m WEN EQUATION AGAINST A CGBTANT me followingis amethod of testingthe sumoi’the regeseion coefficients of a regression line against a constant. The test was developed by Dr. Ingram Olkin, associate Professor of statistics at Michigan state University. The test is applicable in all fitting procedures which use an (n-l) x (n—l) mtrix when :1 parameters are being estimated. 331g Test: Consider a regression equation of the form Y'lel *pzx2*°"*fipxp* 5’ where {is mallydistributed with meanO and standard deviation 0'. A sample at N independent observations . ° . taken and the hypothesis p H :ZFi-chaneconstanwistobetested- 1 0 Solution: 1\ x11 3! Let y , 1L - ln 0 51 0000 En V“ A - I X', then A is a symetric prxp matrix. The normal equation leads to the least squares estimates of the B's, namely, b-A Xy,uhereb-. . The test to be used is: P 2 (1) (N'P) (6'21 131) u 2 - 1 ’ N'P 2 a s where N - umber of observations in the sample p - mmber of regression coefficients (excluding a) which are estimated c - sane constant (c - 1 in cases of linear hypothesis) 2 hi - sum or the reg'ession coefficients (excluding a ) ij -1 13 a - elements of the a matrix. The a are the c 1:) values obtained in the back solution of the Doolittle method, . 2 s2 - Y1 - £(bizz x312) -2é( biobj .21, x3 ) the statistic (1) has an F distribution with 1 degree of freedom in the numerator and N—p degrees of freedom in the denaninator. Large values of F are critical. APPENDIXC xtmrrmmmmmmmam mommusmomm POOIED VARIANCE cs ms mass m was mrm cmcmus FOR mm mm AND comm mmsm ARE mammal) itmrmmrmmmwmmossmammusmm POOIHJVARIANCB (FTHEMEMBWTHBREGIESION C(EFFICENTS FCR THE KIWI. AND CONTROL TWLBHIPS ARE W mesimplettestofmeamwassdaptedfranSnedecor'sbook Statistical W on page 77. me test was used to discover whether the estimated goss income in the experimental and control townships differed fran the estimated gross income when the regression co- efficients were interchanged. Consider the experimental township problem. The goss incane for each farm was estimated by using the cmerimental township regession coefficients. The goss income for each experimental township fan was again estimated by using the control township regession coefficients. The sum of the goss incomes is 379.3131 and divided by 32 degrees of freedom (n-l) - a mean goss income of 5511,1195 .18 which is the mean of the estimated goss incane whenthe experimental regession coefficients are used. The sum of the goss incomes for the experimental township when the control regession coefficients are used is 392,221; divided by 32 - $11,885.57 which is the mean goss incane for the experimental township when the control township regession coefficients are used. The difference bettteen the mean goss incomes is $39.39. The results are listed as follows: Experimental Township Number Degrees of Mean Gross Sum of Squares _ of Farms Freedan Incane ‘ Experimental bi's 33 32 $11,105.18 5,382,032,599 Control bi's 33 32 $11,885.57 5,829,987,241: ...!!! _ - n .931“- ? a! Sum - 61; Difference - Y $390.39 31:2 - ll,212,ol9,8112 Pooled variance - 52 - ll,212,019,8113/ 6h - 17S,878,8lO.5 s; - 2 32 / n - 2 (175,878,810.5) /33 - 3258.141: t - 390.39/ 3258.hh - .1198 (.95) " ”976 t of .1198 < 1.9976 so it is concluded that the regession For 6).: degees of freedom t coefficients to:- the control township are not significantly different from the regession coefficient for the experimental township when they are both used to estimste goss income in the experimental townShip. The calculations used to estimate t in the above section are smuarized in the following equation: t .3; nSn-lg S The gross insane for the control township was estimated by using the control township regession coefficients and by using the experi- mental township regession coefficients. The results are as follows: Control Township Number De gees Mean Gross Sum of Squares w _ _ggFannsfif Freedan _I_ncome w Control bi's 30 29 $11,661:.80 h,666,6h3,308 Emmi-mental bi'a 30 29 $11,676.73 h,63h,915,59h ‘# fi_ 58 Difference 11.93 Sara-9,301,558,902 t I .0036 For 58 degees of freedan 1:095) a 2.0016 t of .0036