.. «aw-q... ADJUSTING FARH ACCOUNT“ DATA FOR REPRESENTAT‘NE RESEARCH USE Thesis {or Hm Dawn of Ph. D. MECHIGAN STATE UNEVERSWY Ranald R. Rhoaéa E955 LIBR‘ Mifinv _ L 1 I This is to certify that the d I thesis entitled AC’Jusf’ltflj Fdlr'm flacoonT de'h‘g FEW Refresanfaflc’c Keseqrcé} USE, presented by Roma/J /€ /?LOC\CJC has been accepted towards fulfillment of the requirements for Mdegree inwum/ [comm/c5 1 Date 7/7415” 0-169 Y .r‘ ADJUSTING FARM ACCOUNT DATA FOR REPRESENTATIVE RESEARCH USE By A} Ronald R. Rhoade A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1965 ABSTRACT ADJUSTING FARM ACCOUNT DATA FOR REPRESENTATIVE RESEARCH USE by Ronald R. Rhoade The primary purpose of this study was to investigate stratification as a technique for adjusting farm account data to be more representative of Michigan farms. Strata were established on the basis of type of farm and class of farm categories as defined in the census. Because of the large number of dairy farms in the account project, it was possible to further stratify several dairy categories on the basis of cropland harvested. Weights were assigned to the various strata based on the census. In all, twenty-one characteristics were compared. Eighteen of these are available from both the farm account project and the census. However, three of the compared characteristics were not available from the census. For these three, a regression procedure was employed to estimate what the census values would be expected to be. The three regression estimates were then compared with stratified account estimates. Comparisons were made between account derived estimates and census values for 1) all farms of economic class IV or larger 2) type of farm, and 3) economic class of farm (for classes I—IV). The statistics used in comparisons were the mean and total value. Ronald R. Rhoade Account project dairy farms showed the most research potential. This is because of the large number of such farms as well as their relative representativeness for census dairy farms. Other farm types showing research promise from account data were cash grain and livestock other than dairy or poultry. All farms in economic classes I-IV could be useful for limited research, and in a few instances, individual economic classes might be utilized. Several type of farm categories showed little potential for research needs where representative data are important. These were other field crOp, poultry farms and general farms. The comparisons gave little insight into the usefulness of account project fruit farms for research uses. The characteristics which were compared could be ranked according to how representative they appeared to be after stratifica- tion. Those showing the most promise were total acres, crOpland harvested, total receipts, number of dairy cows, animal units, total of specified expenditures, and non real estate investment. Several estimates became more representative with stratification but did not appear sufficiently representative for most research uses. These were livestock receipts, productive manwork units, net farm income and labor income. Other characteristics either showed no improvement or became less representative with stratification. The account project is apparently a less reliable source of information for most data than is a simple random sample of the same size. Ronald R. Rhoade However, if instead of sample size, cost of data is held constant; then for about 80% of the data compared, the farm accounts would have been a more reliable source of data than simple random sampling. ACKNOWLEDGMENTS Thanks are expressed to Dr. John R. Brake, the Committee Chairman whose help, advice, and guidance contributed greatly to the completion of this thesis. Appreciation is also due to the other members of the committee: Drs. Boris Pesek, Kenneth Arnold, Dale Hathaway, and Jay Artis. Thanks are due to Drs. Jack Vernon and James Stapleton for serving on the oral committee. The Department of Agricultural Economics is acknowledged for support in conducting this project. Special thanks are due to Mrs. Arlene King, Miss Marguerite Miller and the other department personnel who helped process the data and make this writing possible. Also, Mrs. Barbara Dougherty and other members of the clerical staff are extended appreciation for their c00peration in typing the rough draft. Special thanks are due to Mrs. John Ferris who assisted in editing the final draft and Mrs. Beverly Oetzel for her cooperation and efficiency in typing the final draft. Finally, I wish to express appreciation to my parents, Mr. and Mrs. Clayton L. Rhoade, for their encouragement and support, so necessary to complete this work. ~ii- TABLE ACKNOWLEDGMENTS . . . . . p . LIST OF TABLES . . . . . . . LIST OF FIGURES . . . . . . . LIST OF APPENDIX TABLES . . . Chapter I. INTRODUCTION . . . . The Problem The Need The Objectives Organization of the OF CONTENTS Thesis II. CHARACTERISTICS USED AND STRATIFICATION PROCEDURE Types of Characteristics in the Account Project Data Available from the 1959 Census Characteristics Used for Comparisons Stratification Considerations III. EVALUATION OF STRATIFICATION COMPARING EIGHTEEN CHARACTERISTICS . . . . . . . . . . . The Comparisons Type of Characteristics Compared Research Interpretation of the Comparisons IV. ESTIMATION OF SELECTED POPULATION CHARACTERISTICS FROM ACCOUNT DATA . Perspective and Approach Problems Encountered Strata Categories Used for Prediction Notation Regression Results Limitations and Other Considerations V. USE OF FARM.ACCOUNT DATA FOR RESEARCH PURPOSES . Value of Farm Account Data Use of Account Data to Supplement Census -iii- Page ii vii viii 25 72 96 TABLE OF CONTENTS - Con’t. Page Account Data and Regression Analysis Costs of Farm Account and Sampled Data Other Uses of Account Data Other Suggested Future Studies VI SMARY O O O O O O O O 0 O O O O O O O O O O O O O O 1.15 BIBLIOGRAPIH O O O O O O O O O O O O O O O O O O I O O I O 123 APPENDIX I: CENSUS DEFINITIONS AND FARM.ACCOUNT-CENSUS NUMBER OF FARMS AND PERCENTAGES 1959 . . . 121+ APPENDIX II: STATISTICAL FORMULAS . . . . . . . . . . . . 129 — 1v.- LIST OF TABLES Table Page 1. Farm Account Estimates as Percentages of Census values for All Michigan Farms of Classes I-IV Less Vegetable and Miscellaneous Farms-1959, by Levels of Stratification, Prdbability'Ranges for Completely Stratified Estimates . . . . . . . . 28 2. Farm Account Estimates as Percentages of Census Values for Classes I, II, III and IVinchigan Farms (Excluding Vegetable and Miscellaneous Farms), 1959, by levels of Stratification . . . . . 3o 3. Probability Ranges for Completely Stratified Farm Account Estimates of Michigan Farms - Classes I, II, III and IV Excluding Vegetable and Mil-8081181180115 Fams 1959 o 0-0 6 0 o o 0 o o o o o 31, A. Farm Account Estimates as Percentages of Census Values for all Michigan Dairy Farms, Classes I-IV, 1959 by Levels of Stratificatioanrobability Range for Completely Stratified Estimates . . . . . . . . 36 5. Farm Account Estimates as Percentages of Census values for Michigan Class II-IV'Dairy Farms-~l9S9 by Levels OfStratificationeoooococoa-.0000. 38 6. Farm Account Estimates as Percentages of Census Values for Michigan Grain Farms Classes I-IV, 1959 by Levels of Stratification--Probability Ranges for Completely Stratified. Estimates 0 o o o o o o o o o 39 7. Farm Account Estimates as Percentages of Census values. for Michigan Livestock Other than Dairy and Poultry Farms Classes IRIV, 1959 by Levels of Stratification- Probability Ranges for Completely Stratified Estimates..................... “‘2 8. Farm.Account Means as Percentages of Census Means by Strata, Excluding Dairy Classes II, III, and Iv. 71 9. Comparison of Farm.Account, Farm.Account Census weighted and Census Regression Estimates of Non Real Estate Investment by Farm Categories - Michiganl959................... 87 a. v— LIST OF TABLES - Con't. Table Page lO._ Comparison of Farm Account, Farm.Account Census Weighted and Census Regression Estimates of Net Farm Income by Farm Categories - Michigan 1959 . . . . . . . . . . . . . . . . . . . . . 88 ll. Comparison of Farm Account, Farm.Account Census weighted and Census Regression Estimates of Labor Income by Farm Categories - Michigan 1959.00.00.000000000.0000 90 12. Sample Sizes from Simple Random Samples which Will Give a 50% Chance of Differing from Census Values by at Least as Much as the Farm Account Stratified Estimates Differed from the Comparable Census Value . . . . . . . . . . . 107 .rvi- LIST OF FIGURES Figure Page 1. Strata and Substrate Categories USed for Census weightings by Farm Numbers to Obtain StratifiEd EStimateS o o o o o o o o o o o o o o 23 -vii- LIST OF APPENDIX TABLES Table A Page I. Number of Census and Farm Account Farms by Census Classes I-Iv and Farm Types . . . . . . . . 127 -viii- CHAPTER I INTRODUCTION The Problem One of the biggest problems involved in conducting research in the areas of farm management, agricultural production economics, and farm policy is that of obtaining good, reliable, yet representative input-output, cost, income, and investment data. Although the Census Bureau collects and publishes a certain amount of agricultural informa- tion, there are severe limitations to the types of data that this source provides. The census excludes the enumeration of some major cost, income, and investment measures which are vital to important studies involving farm resource availability, allocation, and returns. In many cases, researchers are forced to use surveys. This provides a.means by which data can be obtained precisely in the form desired. However, this method also has its disadvantages. Collecting data through surveys is very time consuming, costly, and often subject to severe memory bias. Furthermore, the data are often "out-dated" before they are put to use. In addition, with survey data as with census data, there is no direct incentive for accuracy on the part of the respondents; and biases established this way are not always easy to detect. The Michigan Mail-In Account program provides a reservoir of data including certain inputs and outputs along with costs, receipts, -1- 7|) .1. If v-4 -2- investments, gross income, net income, and labor income. Since these records serve the farmer for business analysis, and are also reported fresh from.memory, there is strong reason to believe that data from this source are relatively accurate. The one big problem in utilizing farm.account data for research rests on the supposition that the cooperating farms do not comprise a representative sample of the overall population of commercial farms in Michigan. In fact, one study indicated that they were something less than representative of the economic classes and types of farms which they were purported to represent.1 With the exception of only nine farms, the entire account sample fell within Census Economic Classes I-Iv in 1959. These classes consisted of all commercial farms that obtained at least $5,000 gross income. In the census, only 37,000 of the 112,000 Michigan farms met this criterion. Yet, 54% of the total state farm real estate value and 61% of the acres of cropland harvested in the state were credited to farms of these classes. In addition, 72% of the total value of farm products sold also came from farms in these classes. A big problem.then is to provide data which are representative of these 37,000 farms which fell into economic classes I-Iv. If a means can be found for adjusting farm account data to be representative of various parts of this portion of Michigan agriculture, its use would be very valuable for research involving resource availability, allocation, and returns. 1Karl T. wright and William H. Henneberry, "A.Comparison of Some Characteristics of Farms in the 1959 Michigan.Mail-In.Account Pro- ject and the 1959 Census of Agriculture," Unpublished Paper Michigan State University, 1963. The term representative will mean values close to those of the census. Ki. v- —rv- II J r 0 JJ -2- investments, gross income, net income, and labor income. Since these records serve the farmer for business analysis, and are also reported fresh from.memory, there is strong reason to believe that data from this source are relatively accurate. The one big problem in utilizing farm account data for research rests on the supposition that the COOperating farms do not comprise a representative sample of the overall population of commercial farms in Michigan. In fact, one study indicated that they were something less than representative of the economic classes and types of farms which they were purported to represent.1 With the exception of only nine farms, the entire account sample fell within Censuleconomic Classes I-IV in 1959. These classes consisted of all commercial farms that obtained at least $5,000 gross income. In the census, only 37,000 of the 112,000 Michigan farms met this criterion. Yet, 5A% of the total state farm real estate value and 61% of the acres of crOpland harvested in the state were credited to farms of these classes. In addition, 72% of the total value of farm products sold also came from farms in these classes. .A big problem.then is to provide data which are representative of these 37,000 farms‘Which fell into economic classes I-IV. If a.means can be found for adjusting farm account data to be representative of various parts of this portion of Michigan agriculture, its use would be very valuable for research involving resource availability, allocation, and returns. lKarl T. wright and William H. Henneberry, "A Comparison of Some Characteristics of Farms in the 1959 Michigan Mail—In.Account Pro- ject and the 1959 Census of.Agriculture," Unpublished Paper Michigan State University, 1963. The term representative will mean values close to those of the census. -3- The Need If it is possible to adjust the farm account data so that they are more representative of the types and classes represented, the data could be used to describe the resources which are maintained and utilized by very important groups of commercial Michigan farms. Also, these data can establish a basis for determining efficient utilization of Michigan Agricultural resources or for studying the earnings of the various resources under alternative uses. For studies of the above types, the census lacks some important types of data. Two important items,fertilizer expenditure and dollar livestock investments, are presented only for the aggregate of all Michigan farms. For classes and types of farms, these figures are difficult to arrive at since fertilizer utilization is presented by tons of all commercial fertilizer and liming:material applied. Livestock are presented in number of head by classes of stock. Dollar values can vary considerably for these items. Certain other vital measures are completely lacking from the Michigan Census of Agriculture. Among those lacking are some of the important cost measures. Maintenance and depreciation of buildings and machinery are excluded. Also, machinery investments are a very important exclusion. Although numbers of various kinds of machinery are enumerated, these serve only as a rough indicator of the investment value. Currently, linear programming and functional analysis are popular tools for determining Optimum combinations of resource employment. In -h- the first case, a complete knowledge of investments, costs, and returns as well as farm resources is necessary for each enterprise considered. In the latter case, a similar knowledge is necessary for the entire farm Operation. Census information does not give complete information for using these tools. Farm Account information, on the other hand, does include much of the additional information needed for these kinds of studies. Resource employment and returns studies can be very useful to the Extension Service. If they are kept current, they can serve as a basis for recommendations. From a policy standpoint, studies concerning resource returns can be used as a basis for comparing returns to labor and management between various classes and types of farms or between portions of the farm sector and other sectors of the economy. If account data can be made representative, there are almost innumerable valuable possibilities for utilizing these data. A study aimed at adjusting farm account data so that they'become more representative of certain types and classes of Michigan farms is especially timely. Information from both the 1959 Census of Agriculture and the Nfichigan Mail-In Account project is readily available, with much of the latter currently stored on I.B.M. cards. In 1961+, the Michigan Mail-In.Account project underwent considerable revamping. A study using 1959 data would serve as an indicator of the feasibility of adjusting future account data for use in research studies such as those just described. The 1964 Farm.Account Program in Michigan, under the name of 1) r 2 -5... "Telfarm", expanded the types of records kept by c00perators. Not only were the conventional records involving receipts, expenses, inventory, and depreciation included; but special accounts were added also for labor (amounts paid in wages and social security on each worker), farm credit (including outstanding credit, interest payments, and sources of credit), family living (involving non—farm deductible and non-deductible income and expenses), and farm enterprise accounts (including both internal and external accounts, along with physical quantities of inputs and products for selected enterprises). Although participation is presently limited for some of these special accounts, the future appears very promising. After this new program becomes well established, there are reasons to believe that the composition of cooperators will become relatively stable, primarily due to a fee charge and the services pro- vided. This would accentuate the value of this program.for research if the data can be adjusted to be more representative. The Objectives The purpose of this study is to utilize the 1959 Farm.Account and Census data to evaluate certain stratification procedures for making farm account data.more representative of Commercial Michigan farms with a gross income of $5,000 or more. Also, several other procedures for estimating or adjusting data along with some specific uses of account data will be explored. The farm account estimates will be derived using various levels of stratification. Farm Account data which have not been strata weighted -6- and census data will serve as a basis for evaluating the improvement toward representativeness that comes about through strata weighting. It is then planned to find the levels of stratification which give the closest estimates to census values for the various characteristics. Regression analysis will be used to predict 1959 census values for several important characteristics which are excluded from the census; these are non—real estate investment, net farm income, and labor income. The main purpose of these regression estimates in this study will be as a basis to evaluate stratified estimates. Since values for these characteristics cannot be obtained from the census, selected regression relationships will be used to predict values for the farm account sample, farm account stratified estimates, and census values. The predicted values can be compared against the actual values in the first two cases. It will be necessary to assume that these regression relationships are valid for the pOpulation of Michigan farms which they represent. Then the results can be used to evaluate farm account stratified estimates of these characteristics. The regression relationships will be studied for possible adjust- ments which will compensate for differences between farm account cooperators and the population which they are purported to represent. Organization of the Thesis This thesis will be composed of six chapters. Chapter Two will discuss the classification and selection of characteristics which will be utilized in this study. Also, alternative stratification procedures will be discussed and a selection made. In Chapter Three, selected -7- characteristics which are available from both the farm account sample and the census will be compared. Percentages of the farm account values relative to census values will be compared using various levels of stratification, including the non-stratified or farm account weighted values. In addition, certain probability levels will be established based upon the chances that differences at least as large as those between stratified account estimates and census values would result through sampling. Chapter Four utilizes regression procedures for deriving census estimates of three variables excluded from the census. These estimates will be used as a basis for evaluating stratification procedures for these characteristics. Chapter Five will cover some suggested methods of utilizing account data for specified applications. Estimation of data for inter— census years, census excluded data, and use of account data where a large number of observations are needed will be discussed. Finally, Chapter Six will summarize all chapters. CHAPTER II CHARACTERISTICS USED AND STRATIFICATION PROCEDURE Types of Characteristics in the Account Project An extensive amount of information from the 1959 farm.account project has been stored on I.B.M. cards. The characteristics which are included in this set of stored data vary somewhat as to their nature. Part of the characteristics represent physical measures; others place a dollar value on inputs and outputs, or represent residuals after certain charges are deducted from receipts. In addition, some characteristics listed are input-input and input-output ratios that serve as indicators for farm business analysis in the Farm Management Extension program. These ratios incorporate both physical and dollar measures. The physical inputs include measures of land, labor, and numbers of livestock from various classes. Two aggregated measures, productive manwork units and animal units, are included in this category. The first of these measures, P.M.W.U's., is based upon the labor require- ments from all of the various farm enterprises assuming average efficiency. P.M}W{U's., measure farm inputs on the basis of the amount of work a man can accomplish in one ten hour day at average efficiency. Animal units measure the total livestock volume on the farm, based primarily on the feed consumption of the various livestock. -8- -9- Physical outputs include measures of farm production from the various enterprises. CrOp production in bushels, tons, pounds, or hundred weight by commodities is listed. Livestock and livestock products are listed in number of head or pounds sold. Dollar costs are listed by major categories to which the specific costs belong. In addition to these direct costs, investments can be categorized into real estate, including value of land and improvements, and non-real estate which includes value of machinery, livestock, crop inventory, feed, and supplies. Some investments incur a depreciation charge extended over the useful life of the investment. This cost is included as part of the inventory change in the farm account data. In addition, an arbitrary interest charge is made against the investment to arrive at labor income in the account program. Investments are separately listed for real estate, machinery, crOp supply, supplies, feed, and each class of livestock. Receipts are listed for the various farm products which include a cr0p category and separate categories for the various livestock and livestock products. Non-farm product receipts including: improvement receipts, machinery sales, custom work, off-farm labor, and other receipts are also available. The net or residual income measures avail- able are: 1. Net cash income--cash receipts minus cash expenses 2. Net income-~net cash income adjusted for inventory change 3. Net farm income-~net income adjusted for value of family labor h. Labor income--net farm income less 5% on the average investment -10- 5. Management income Also, net crOp and livestock incomes are available. Among the more important items listed in the form of ratios are yields of the various crOps and milk production per cow. These are actually outputs per unit of land or per unit of livestock, and are essentially input-output ratios. Other input-output ratios include additional livestock performance factors such as pigs weaned/litter or lambs/100 ewes. Also various measures of receipts per man, tillable acres,or particular livestock measure are included. Several of these ratios are given entirely in dollar terms including gross income/$100 of expense and gross income/$1,000 of machinery expense. Most of the input-input measures are ratios involving physical inputs or dollar costs with manpower or with tillable acres. These latter two variables comprise a relatively large share of the inputs on.most farms, and ratios of this type have been found very useful in farm business analysis in the extension program. In addition to those data which are available from the 1959 account project and for other years prior to 1964, "Telfarm" has added special accounts for certain specific enterprises. Also, other information available from these accounts is outstanding credit by sources, labor costs, and family living expenses. Although this latter information is beyond the scope of this study except for conjecture and discussion, some very valuable information should be available for research in future years. -11- Data Available from the 1959 Census Census information for various characteristics was obtained in part by complete enumeration and in part through a 20% random sampling scheme. Not all of the information which is available from the farm account project in 1959 was included in the census presentation. Indeed, some of the more valuable information including important costs, net incomes, and dollar investments are excluded, or in some cases presented only for the aggregate of all Michigan farms. This latter group includes farms with gross income as small as $50.00 a year. Excluded from census costs are improvement and machinery maintenance and depreciation, taxes, insurance, utilities, and supplies. Fertilizer expense is pre- sented only for all Michigan farms. Included by the census for important categories enumerated are: feed for livestock and poultry, purchase of livestock and poultry, machine hire, hired labor, purchase of seeds, bulbs and plants, and purchase of petroleum products. On many farms, these included items make-up less than half of the total farm costs. For non-real estate investments, dollar values of livestock are presented by all Michigan farms only. Machinery on hand is presented only by numbers of specific machines. From a dollar standpoint, considerable variation exists between makes, models, size, and age of machines. The census does present much useful information on outputs, both in physical terms and in terms of receipts. Many of the input categories are included in the census enumeration, and it is possible to calculate productive manwork units and animal units from.the .F‘ -12- information which is presented. Also, corn yields and production per cow can be obtained. The input-input ratios with tillable acreage can be calculated, but manpower figures from the census are not very meaningful since hours of family labor are not included; therefore, ratios per man are not possible from census data. Incidentally, the census includes information pertaining to characteristics of the Operator, including tenure, color, and age which are not readily available from farm account information.1 Characteristics Used for Comparisons Characteristics in Both the Farm Account and the Census It would be impractical to attempt to utilize all data available from the farm account sample, or even all which can be compared with the census. Instead of attempting this, eighteen characteristics were chosen for comparison with census data. These characteristics were estimated using three different criteria to determine strata weightings. A discussion of the selection of stratification criteria comes later. The characteristics which were chosen for study included measures of physical inputs and outputs, together with dollar costs, real estate investments, and receipts. Also, three input-output ratios were included. Input-input measures were excluded even though such lU.S. Bureau of the Census. ‘U. S. Census of Agriculture: 1959, V01. 1, Counties, Part 13,.Michigan, U. S. Government Printing Office, washington, D. C., 1961, pp. 1-253. -13- measures are very important for business analysis involving individual farms. However, for research where several variables can be simultaneously incorporated into equational form, input-input and output-output relationships generally have little to offer. Such relationships can be expressed between terms in the equations and thus expanded to handle more than two variable relationships. Input-output measures, on the other hand, are very Often important for research since they are indicators of performance or efficiency of individual enterprises or for the entire farm business. A large prOportion of the coefficients used in linear programming, input-output analysis, and budgeting are measures of this type. Three input-output measures were chosen for study. These included corn yield per acre, wheat yield per acre, and pounds of milk per cow. The first two represented the most important individual crOps in the state. An apparent exception tO‘thiS‘WaS the acreage of alfalfa and alfalfa mixtures cut for hay, which exceeded the acreage of wheat harvested. The dollar value, however, was higher for wheat; and in addition, quality and pricing are much more uniform for wheat, thus making the comparison of data more meaningful. Pounds of milk per cow represents performance or efficiency of the most important livestock enterprise for the state in 1959. Input measures which were retained included total acres, crop acres harvested, acres of corn, and acres of wheat. For livestock, number Of milk cows and litters Of pigs were included. Also, animal units were retained as an aggregate measure for livestock and -14- productive manwork units as an aggregate measure Of the overall farm business volume. Dollar inputs were represented by real estate investment and the total of specified expenses. The only additional dollar input information which was available included the individual components of expenditures specified by the census and mentioned earlier. For purposes of this study, the total of these expenditures was considered sufficient. Physical outputs for wheat in bushels and milk in hundredweight ‘were used. Total corn output was excluded because the census does not give information on tons of corn silage produced, and with yields and acreage included in the study further consideration of corn output was not considered essential. Dollar receipts were included for crOps, livestock, and the total of crOps and livestock. Characteristics Not in the Census Three characteristics were chosen for study which were unavailable from the 1959 Census of Agriculture. For this reason, estimates were derived using the multiple regression technique. In Chapter Five, sample sizes were computed for simple random samples from the pOpulation. These samples would have a 50-50 chance of deviating from the census values by at least as much as the account stratified esthmates deviated from the census values. The procedure is similar to that followed for census compared characteristics, except that regression estimates were used in place of data presented by the census directly. USing this -15... scheme, it was possible to compare the cost of information of a given reliability, from account estimates as opposed to sampled estimates (assuming that the regression estimates are valid). It would have been possible to utilize many Of the components of net farm income and non-real estate investment using the regression strata weighted estimate and comparison procedures. However, for evaluating the procedures, rather than the characteristics themselves as presented in 1959, these three measures were exclusively chosen to represent data unavailable from.the census. Stratification Considerations Definitions Stratified Sampling-~Cochran describes stratified sampling as follows: In stratified sampling, the pOpulation of N units is first divided into subpopulations of N1, N2,...., NL units, respectively. These suprpulations are noneoverlapping and together they comprise the whole of the pOpulation, so that N1 + N2 + ... + NL — N The suprpulations are called strata. To Obtain the full benefit from stratifications, the values Of the Nb must be known. When the strata have been determined, a sample is drawn from each stratum, the drawings being made independ- ently in different strata. The sample sizes within the strata are denoted by n1, n2,..., nL respectively. If a simple random sample is taken in each stratum, the whole procedure is described as stratified random sampling. 2William G. Cochran, Sampling Techniques, New York, N. Y., John Wiley and Sons, Inc., 1960, p. 651 -16_ Stratified Random Sampling-—Propgrtional Allocation--If the sample number Of observations is proportional to the pOpulation number of Observations in all strata, the stratification is described as proportional allocation of the nh Nh nh n _ _ _ 3 nh i.e. n - n or Nh - N - Constant. Stratified Random Sampling-—Optimum Allocations- "In stratified random sampling, the variance of the estimated mean Vst is smallest, for a fixed total size of sample, if the sample is allocated with nh prOportional to NhSh." When strata sample sizes are determined by the prOportion of NhSh to N S _ h h . . . the sum Of all NhSh’ or nh — n-Efi—g— , the stratification is described as h h Optimum allocation of the Nb. This allocation is designed to minimize variance. h = standard deviation of strata h derived from the Nb Observations. In this study the value of S S h was derived from the farm account Observations. Therefore Observations Of nh were used to derive S in place of Observations h from Nh. Simple Random Sampling-- "Simple random sampling is a method of selecting n units out of the N such that every one of the NCn samples has an equal chance of selection." N = pOpulation number n = sample number of Observations NCn = sample of n units drawn from N units5 Mbst of the estimates derived from the farm account data were stratified estimates, but not from stratified random samples since 3Ibido, P0 67. Ll-Ibido’ Po 71+. SIbido, p. 3.10 m -17- the choice of farms from the farm account sample, along with the strata proportion, were fixed by the farms COOperating in the project. Several further definitions are presented at this point to clarify the discussion which follows. These definitions are for pur- poses of convenience and may not be found in general use beyond this writing. Type Of Farm Stratification--This refers to stratification using the census type of farm categories, as defined in the Appendix I, for stratification criteria. In this study seven types of farm categories were utilized. Class of Farm Stratification--Class of farm categories, as defined by the census, are determined by the magnitude of farm product sales. Although the census utilizes six commercial classes, essentially only classes I—Iv are represented by the farm account sample in 1959. These classes are defined as follows: Class I $40,000 or more gross farm.product sales Class II 20,ooo--$39,999 gross farm product sales Class III l0,000--$l9,999 gross farm product sales Class IV 5,000--$ 9,999 gross farm product sales As should be expected, class stratification refers to stratifying on the basis of product sales criteria. Complete Stratificatione-Three criteria were chosen for stratification, as will be subsequently discussed. These included class of farm, type of farm, and crOpland harvested for dairy classes II, III and IV. When -18- all of these criteria which can be utilized are utilized for any particular set of Observations, the stratification will be termed complete. Class and Type Stratification--This will refer to the use Of both class of farm and type Of farm stratification criteria. Seven type Of farm categories and four class of farm categories would yield 28 strata. However, Class I poultry was void of account farms and this class-type strata was combined with Class II poultry into one strata. In some of the discussion, the term "cross stratification" will be used interb» changeably with "class and type" stratification. Sub-Stratification--This will refer to stratification beyond "type and class" or "type" or "class" depending on the category of farms strati- fied. In this writing, sub—stratification will ultimately refer to stratification by crOpland harvested. Mere generally, it is meant to apply to stratification criteria which are census tabulated but not enumerated--that is the census presents numbers of farms which fall 'within specific ranges of the stratifying characteristic, but the census does not present a.mean or total for any characteristic including the stratifying characteristic for the farms included in the specified ranges of the stratifying characteristic. Sub-stratification in this thesis was only applied to Dairy Classes II, III, IV and only represents the further weighting of the class-type strata on the basis of crOpland harvested. It could be considered a subcomponent of complete stratifica— tion which considers class Of farm, type of farm as well as the crOpland VJ -19- stratification for the particular dairy classes. Basis for Stratification In order to stratify the farm account sample in such a way that estimates can be compared with census values, it was necessary to utilize the enumeration and tabulation categories which were presented by the Census of Agriculture. This left two possibilities Open. Estimates could have been derived, strata weighted, and compared by areas using counties or groups of counties. If this were done, it would not have been possible also to stratify by both type of farm and class of farm due to lack of census information for this breakdown. It would, however, have been possible to substratify by one or the other of these characteris- tics, and make comparisons at the stratified level-~i.e. comparing the estimate Of the combined substrata for the counties or areas. .A number of other characteristics were also tabulated by the census for counties, but none of these appeared as important for stratification criteria as class of farm or type of farm. Since only one characteristic could have been used in addition to county or area, these additional possi- bilities didn’t seem too relevant. Included in this group of characteris- tics were total and crOpland acres, tenancy, three levels of each Of the specified expenditures, numbers of certain classes Of livestock, and number Of acres of certain crops. The second possibility for stratification involved the use of state estimates--that is, estimates derived for the entire state and not given further geographical consideration. ‘Using this procedure, it was -20- possible to cross stratify by both class of farm and type of farm. In addition, it was possible to further substratify using one of the following characteristics: 1. Total acres 2. Cropland harvested 3. Age of Operators A. Number of tractors 5. Number of hired workers 6. NBgritude Of each specified expenditure 7. Numbers of certain classes of livestock including dairy cows 8. Litters of pigs 9. Acres of certain crops including corn lO. Tenancy After evaluating the possibilities, it was believed that a cross stratification by class of farm and type of farm would add more homogeneity to the strata units than would an area stratification plus sub-stratification by either class of farm or type Of farm. It was further believed that this class-type sort would incorporate many inter— area differences as well. For these reasons, this latter possibility was chosen. After strata numbers in both the census and the farm account project for 1959 were determined for each Of the class-type strata, the possibility of further sub-stratification was taken into consideration. It was noted that the bulk of the strata were quite "thin" in number-- with all except three having thirty or less account Observations. The three exceptions, dairy classes II, III and IV contained 162, 337, and 121 observations respectively in 1959. Since these strata were -21- considerably larger than the other strata, further sub-stratification for these strata was considered feasible. The various possibilities were studied. At first it was thought that number of dairy cows would serve as the most beneficial criterimlfor substratification. As it turned out, the delineation by dairy cows had little to Offer since the bulk of the farms fell into one or two categories by cow numbers. Two other possibilities also appeared feasible. These were, sub-stratification by total acres and by crOp acres harvested. Since total acres included non-tillable land of low value, or land set aside for non-agricultural purposes, crOpland harvested was chosen as a better measure to substratify dairy classes II, III, and IV. It was hoped that this criterizlwould add homogenity relevant to crOp volume. The final selection for stratification was a class of farmetype Of farm stratification with further substratification by crOp acres harvested for dairy classes II, III, and IV. One substrata, class III dairy farmS'with 100-199 crop acres harvested, contained a very large number Of Observations--2A3. There was no known way to further delineate the group or to utilize an alternative which would incorporate feasible stratification criteria without the existence of at least one large substrata group. Figure 1 illustrates the arrangement of strata groupings as they 'were used for deriving estimates in Chapter 3. Stratified estimates were derived for all account farms, each of the classes and each of the types. In addition to deriving estimates using all available strata and -22- substrata, estimates were derived using dairy type-class strata without the additional sub-stratification. Also, class of farm only and type of farm only weightings were utilized as a basis for comparison. In the case of all account farms, estimates were made using all strata and substrata weightings, secondly the substrata weightings were drOpped in lieu of strata only weightings. Also class of farm weightings and type of farm weightings were utilized alone, and finally the entire farm account sample was compared to the census without census weightings. That is, the means for all account farms were used to derive means and total estimates for the census. For the various classes and types, these same possibilities (as far as was relevant for the particular class or type category) were applied for Obtaining estimates. Reason for Using Stratification Technique Although stratification of the account sample does not yield a stratified random sample, the procedure was expected to give values closer to the census than without stratification. The account farms were concentrated heavier in classes II and III while census farms were concentrated in class IV. Also, account farms concentrated heavier in dairy type of farms than the census. The stratification procedure weighted the account means such that more weight was given to class IV farms and less to dairy farms, thus yield- ing values closer to those of the census. The difference in the distribution of the farm account and census farms is shown in Appendix Table l. Class Of Farm I II III Iv Cash ” Grain l 2 3 1+ T Other Field .Y Crop 5 6 7 8 P E Fruit 9 10 ll 12 Poultry 1A 15 F i L__ 'T I Q I I I 'r .T I - I F Dairy 16 u 17. : #8 g 3 E9 I A liiB 1C A1 ICJD AJBJCJD Livestock Other Than R Dairy and Poultry 20 21 22 23 M General Farms 21+ 25 26 27 Figure l. Strata and substrata Categories USed for census weightings by farm numbers to Obtain stratified estimates. Strata Identification 1. Class I Cash Grain 17. Class II Dairy 2. Class II Cash Grain 18. Class III Dairy 3. Class III Cash Grain 19. Class IV Dairy A. Class Iv Cash Grain 20. Class I Other Livestock 5. Class I Other Field Crop 21. Class II Other Livestock 6. Class II Other Field Crop 22. Class III Other Livestock 7. Class III Other Field CrOp 23. Class IV Other Livestock 8. Class IV Other Field CrOp 2A. Class I General 9. Class I Fruit 25. Class II General 10. Class II Fruit 26. Class III General 11. Class III Fruit 27. Class IV General 12. Class IV' Fruit . , 13. Classes I & II Poultry Dairy Substrata - Con t. 14. Class III Poultry 15. Class Iv Poultry 16. Class I Dairy 1See Appendix Table I for Farm Account & Census number of farms and percentages. -23- C4 -‘ Figure l Con't. - Dairy substrata 17A - 17B - 17C - 18A - 183 - 18C - 18D 19A 19B 190 19D Dairy Dairy Dairy Dairy Dairy Dairy Dairy Dairy Dairy Dairy Dairy Class Class Class Class Class Class Class Class Class Class Class -2u. II 200-99 Crop Acres II 100-199 Crop Acres II 30-99 Crop III 200-999 Crop III 100-199 CrOp III 59-99 Crop III IV IV IV IV 1—49 50-99 l-h9 Crop 2OO-A99 Crop 100-199 CrOp Crop Crop Acres Acres Acres Acres .Acres Acres Acres Acres Acres CHAPTER III EVALUATION OF STRATIFICATION COMPARING EIGHTEEN CHARACTERISTICS The Comparisons Comparison Criteria Two types of comparisons are made in this chapter for the eighteen characteristics found in both the 1959 Farm Account data and the 1959 Census of Agriculture for Michigan. The selection of these eighteen characteristics was discussed in Chapter Two. Comparisons are made on the basis of percentages and percentage deviations from 100% of farm account and farm account stratified estimates relative to census values. The percentage comparisons repre- sent the farm account mean or total values as percentages Of the census mean or total values. For comparing groups of characteristics the percentage deviations from 100% are also listed. The purpose of this measure is to give an indication of the magnitude Of the individual deviations from 100%? after they are combined. The percentage comparisons in contrast do indicate the general direction of the combined deviations, but do not always indicate the magnitude of the deviations due to Offsets from both sides of 100%. -25- rh- r) I) -26- .A third type Of comparison found in this chapter is presented in terms of probability levels. These probability levels estimate the chances that absolute differences from the census values as large or larger than those which occurred from the completely stratified account estimates would occur from stratified random samples using the same sample size and strata prOportion as found in the farm account sample. In some cases it might appear that the probabilities are not entirely consistent with the percentage estimates. Low percentage deviations and high probabilities do not necessarily need to accompany each other. The percentage estimates represent relative differences of the account estimates to census values, whereas the probabilities are derived using absolute differences and standard errors. Standard deviations from the farm account sample served as estimates of pOpulation standard deviations in deriving these probabili- ties. Information pertaining to standard errors from.census data is limited. Since there is fairly strong indication that the farm account sample is composed of a more homogeneous group of farms than found in the population, these standard deviations may be somewhat low. If this is the case, the probabilities presented in this chapter will also be too low with the result Of penalizing the true worth of account data for Obtaining representative estimates. This should be borne in mind when reading this chapter. r) -27- Comparisons by Selected Groups Of Farms Combined Farm Account Comparisons All of the account farms, with the exception of one vegetable farm and nine farms with gross incomes of less than $5,000, served as the largest comparison category of farms. This category was compared to classes I-IV census farms excluding vegetable and miscellaneous farms. The comparisons of the various characteristics are shown in Table 1. Mean percentage was computed by taking the account value Of.§§§§ characteristic as a percent of the census value and then computing the simple average of all eighteen Of these percentages. Mean percentage deviation from 100% is derived by taking each characteristic percentage as a difference from 100% and computing the simple average of these values from all eighteen characteristics. For these farms, the mean percentage (farm account relative to the census) Of the eighteen characteristics prior to stratification was 138% and the mean percentage deviation from 100% was Al% i.e. the excess over 38% was brought about by account values which were less than 100% of the census value. With complete stratification these percentages became 105% and 13%L showing considerable improvement in the direction of census values for the eighteen characteristics taken together. Two characteristics, acres Of corn and acres of wheat, were not improved by stratification and did not appear unreasonable as they stood. Class Of farm stratification (utilizing class of farm census weights for the combined account farms) gave the best estimates for corn yields, crop acres harvested, litters Of pigs, specified expenditures and total receipts. These estimates varied from 2% to 13% Of the census values with only one greater than 5%. Type of farm stratification (combined Farm Account stratified by type Of farm only) gave a better estimate for value Of land and buildings mowoma one carves moaa osam> heaaapwnonm Hanson one mpwhpm one msan magnum onto one campooo oH503.OHmamm secede doamapmhpm map pone deflowmm nonpadw ma pH .Uopnomoam .oamswm pnsooom such on» ca canon we? pomp soapsomoam .OHQBMm sonata emanapmapm m Honk HSOOO oasos «ooapma>oc osHm> mSchOnopmfiapmo podooom one no owned we ended pm sodaw> momnmo one 809% soapma>oo m pone Aoo.H Mo soapomnm m mmv monmno one OP whence who: cocawoo mm hpaaapmnonm a ao. v. moa coa ama moa mma neoaooom aspoe ao. v. oaa oaa sea asa mma npaaooom soopnoeaa Ho. V. mm mm mmH Hm mm mpmaooom mono om.-om. woa maa awa oea 0mm eaom saaz no .pao om.-om. mm mm mma me aaa sees; no naosnsm ao. v. we mm mm mm mm nmsaeaasm a soda cease ao. v. oaa oaa mea moa ema nonsense .oomm aupoa ao. v. mma ema ama msa sea .euzez.m oa.-mo. maa saa sea mma mma erase ansase oa.-mo. mma mma eca moa mma swam no nsoepaa om.-os. moa moa oma ama era nsoo haas no soossz ow.u0m. mm mm sma we eoa posse sa noso< oa.-mo. mm mm maa ae moa snoo ca nosoa om.-oa. moa moa mma moa mma eepno>ssm essaooso Os.-om. soa moa maa eoa ama noao<.aopoe ao. v. maa saa mma maa mma soo\oa saaz Os.-om. moa moa woa em :oa osod\sm eaoae pooh; ao. v. maa caa ama .maa maa osos\sm caoae ssoo I. w a a . a a a asoasooanapsspm Neaaaaasaalsuaom son nwsaehwaoz megaphwaoz omsasswaoz soaosoam oapnahspoossso opoamaoo oopmo>9mm onmdmoso mmmao each Each napwnpm Hoboq «mmmao somhev a omha mo make mo mmnHo Oz esaaaosoosm soapooaeaessem soapooauaoospm no ao>oa .,mo omnsm opoamaoo o5ac> mquoo moxa mm opmaapmm pcsooo<.aamm H nooosasnm ooanasonpn eaosoaesoo not nomssm epaaaoanonm .soapooanassspm no naoeoa so somma umanwm nnoonwaaoomaz one mapmpowo> mmoH >HIH mommmao Ho heath unmanOfiz HH< sow mofiac> mumnoo MO mowopnooaom mm mopdfifipmm pesooom.sumh H Hag-H. -28- will ‘1‘] . t’l' s_‘ I, 'II II' ‘IIIII .lll i I, I "J I; -29- (92% of the census). For all other characteristics, either type and class or complete stratification gave the closest estimate; but in all cases except milk sales the utilization of crOp acres harvested as a substratification criterimflmade very little improvement in the estimates. For milk sales, the estimate was 108% Of the census with the addition Of crOp acres harvested as a sub-stratification in contrast to 112% for the class-type stratification. Turning to the probability levels of the estimates as previously defined, only a few characteristic estimates are noteworthy. For acres of wheat, the probability fell in the .50 to .60 range. From a large number of stratified random samples, about half would carry sampled totals which differed from the census total by an amount equal to or greater than the amount Of difference between the census value and this farm account stratified estimate. Bushels of wheat produced also fell into this .50 to .60 range. Five characteristics fell into a probability range varying from .10 to .50. All other characteristics maintained probabilities Of less than .10. These probabilities assumed that the census values were reliable parameters of the popula- tion and that farm account standard deviations of the various characteris- tics were reliable population estimates. Economic Class Of Farm Comparisons Estimates were derived by each class of farm for Classes I-IV. The farm account farms of these classes were used for making stratified and non-stratified estimates of their respective census classes. As 'with the all Account estimates, vegetable and miscellaneous farms were excluded. Results are presented in Tables 2 and 3. .IJ ..L.he ~<.1~. swam MO wasp op soapaecm ca heath enema son mmoapcwaoz copmo>pmm octagono op msowos doaeapwnpm haopoamEOo .nmsaesmaoz a aaa maa moa moa woa moa ooa oo no mo oo nsoaooom assoe mma ema osa eaa eaa msa moa moa mma soa ama npoaooom soosnoeaa mm or ms so so om eo mo on em ms npdaooom mono oaa aaa oca eoa woa msa ooa sma emm oma mam oaom saa: so ago oo ao so mo so or eoa eoa ooa maa maa sees: no naosnsm oe ae to or on so me an we we on nmsaeaasm a esoa cease sma oma maa maa maa moa oo oo or ooa mo nonsense coauaooom aepoe msa ssa 8a maa eda maa oaa oaa osa oaa eoa Sesam- cma ema mma eoa moa maa maa maa msa moa osa spas: assass msa esa em osa esa coa maa maa eaa or moa swam no nsopsaa ooa eoa eoa ooa ooa oma ooa oo mea saa sam nsoo saa: to sneeze oo ao to co ao ow ooa ooa eoa ooa oaa pesos sa noses mm mm mm om am me 0e 0e mm sw mm choc ca moao< oaa maa soa moa moa ooa so so soa oo oo ooenoesom ossaooso eaa oma maa eo oo ooa oo oo ooa oe mm moses assoe oaa maa saa saa saa oaa saa saa oaa oaa mma soo\oa sans mo eo mo moa moa ooa eoa eoa oo moa moa onoo\sp eaoae secs: ama oaa oaa maa oaa maa maa eaa maa aaa woa annexes eaoae ssoo a a a a a o o a a a a soanap mesa coanap soanap nwsa coauap ooanap mesa soanap nwsa soauas oapnanopoonoso .osem -sawaoz -sssm .osem -somaoz. .ospm .ospm -shmaoz sonar unaware [seem Ema sash coz aha Show :02 aha each eoz sham coz nopoam 00 no make topodmaoo go make nopodgsoo MO @959 MO @958 ea nnoao aaa ansao Ha onsao a omsao osam> msmooo MO & mm mopmaapmm posooo< such noameflHapmapm no mHo>oA hp «mmma «Amanda msooomdaoomaz can oflnmpmwo> qudSHoxmv manna cmwanonz >H and HHH «HH «H mommmdo mom mosam> mumsoo MO mommpnoonom no mopoaapnm pnzooo< each m MHMSH -3Q- W... u we, ‘, ..\ p \ a TABLE 3 Probability Ranges for Completely Stratified Farm Account Estimates of Nnchigan Farms - Classes I, II, III and Iv Excluding Vegetable and Miscellaneous Farms 1959 Range of Probability Level Class Class Class Class Characteristic I II III IV Corn Yield bu/acre < .01 '< .01 < .01 < .01 Wheat Yield bu/acre .20-.30 .h0-.50 .02-.05 .50—.60 Milk lb/cow .02-.05 1< .01 < .01 < .01 Total Acres < .01 < .01 .u0-.50 .05-.10 Cropland Harvested .h0-.50 .02-.05 .50-.60 .10-.20 Acres in Corn .02-.05 < .01 .05-.10 .h0-.50 Acres in Wheat .60-.70 > .90 .01-.02 .AO-.50 NUmber of Milk Cows .10-.20 > .90 .90 .30-.AO Litters of Pigs .70 .60-.70 .01-.02 .30-.h0 Animal Units .80-.9O .02-.05 .02 .10-.20 P;M.W;U. .02-.05 < .01 < .01 < .01 Total Specified Expenses .80-.9O .10-.20 < .01 .02-.05 value Land and Buildings < .01 < .01 < .01 < .01 Bushels of Wheat .30-.40 .30-.h0 .05-.10 .60-.70 th. ijMilk Sold .05-.10 .30-.40 .h0-.50 .50-.60 Crop Receipts < .01 .40-.50 .05-.10 .10-.20 livestock Receipts .40-.5O .20-.30 < .01 < .01 Total Receipts .50-.60 .80-.90 < .01 < .01 —. Probability as defined here refers to the chance (as a fraction of 1.00) that a deviation from the census value, at least as large as the account estimate-census value deviation, would occur from a stratified random sample. It is further assumed that the stratified random sample would contain the same sample size and strata proportion that was found in the Farm Account sample. The actual probability value lies within the ranges presented. -31- -32.. Class I Estimates--Class I farms were those which obtained a gross income of $40,000 or more. The mean farm account census percentage Of all eighteen Characteris- tics without a type of farm stratification was 118%. The mean percentage deviation from 100% was 3A%. Incorporating a type of farm stratification brought these percentages to 99% and 13%. Corn and wheat yields, along with total acres, crOpland harvested, and acres of corn averaged closer to the census without stratifying. Of these, wheat yields and crOpland harvested were relatively close to the census values--103% and 99% respec- tively. All other characteristics were improved by stratification. Seven characteristics carried differences from the census such that the probability was .50 or greater that differences at least this large would occur though stratified random sampling. Five more Obtained probabilities between .10 and .50 and all others were less than .10. Class II Estimates--Class II farms grossed $20,000 to $A0,000. Estimates for this class were made without stratification, with type of farm stratification, and with crOp acres sub-stratification for dairy farms in addition to a type stratification. This latter sub-stratification im- proved the estimates noticeably in two cases. Litters Of pigs shifted from.ll8% Of the census to 112% of the census with the crop acres sub- stratification. Also, hundredweight of milk sold shifted from 12A% to 105%. Seven Characteristics were not improved by this stratification. The nonstratified farm.account value of four Of these compared favorably AI -33- with the census. These were: wheat yield, total acres, cropland harvested, and.bushels of wheat. The remaining eleven, two of which were discussed, ‘were improved by stratification. Of these eleven, seven estimates were relatively close to the census. Acres of wheat, number of milk cows, and total receipts were almost identical with census values. The probability levels Of the estimates were relatively high in several cases. For acres of wheat and number of milk cows probabilities exceeded .90. Two other characteristics Obtained probabilities greater than .60 and five others between .10 and .50. The remaining were less than .10. Class III Estimates--Class III represented the largest farm account class in 1959. These farms grossed between $10,000 and $20,000. The crOpland sub-stratification did not improve any of the estimates to a noticeable degree. Also, the mean percentage of the account estimates relative to the census values for the eighteen characteristics was about the same with type stratification and without using any census weightings. In each case it was about 105%; however, the mean percentage deviation from 100% shifted from about 20% to about 12% using a type Of farm stratification. Six characteristics maintained better estimates without stratifying. Five of these served as very good census estimates. Total acres, crOp- land harvested, and wheat yields were all very close to 100% of the census. Litters Of pigs were 106% and total receipts 108%. Average corn yield was less satisfactory. 0f the remaining, only four showed relatively close estimates after stratification. These were: animal units, number of milk cows, bushels Of wheat and crOp receipts. All others deviated -314. more than 10% from the census. The stratified.estimate for numbers of milk cows carried a probability of .90. Three characteristics fell in the range of .40 to .60, but all others were less than .10. Class IV Estimates--This class was characterized by farms with a gross income of $5,000 to $10,000. Farm account estimates without stratification averaged 105% of the census for the eighteen characteristics compared. The mean percentage deviation from 105% was 33%. 'Utilizing a type of farm stratification shifted these to an average of 111% and a 19%:mean deviation. Adding the crOp acres harvested sub-stratification did not affect the average but did improve the mean percentage deviation by 1%. Total acres shifted three percentage points closer to the census when using a cropland harvested sub-stratification—-the percentage moved from 120% to 117%. The crOp acres sub-stratification did not noticeably improve any other characteristic. Five characteristics gave better estimates of the census without stratification. Of these, only cropland harvested appeared to give a reasonable estimate--10h% of the census. Utilizing type of farm strati— fication, only acres and yield of wheat and number of milk cows gave estimates that deviated less than 10% from the census values. Type of Farm Comparisons Farm account farms meeting the definitional criteria for the census type of farm categories were used to make estimates for their respective census type of farm categories. -35- Dairy Farms Classes I-IVF-As defined by the census-~dairy farms obtained at least 50% of their income from dairy products and the sale of dairy stock. The results of the comparisons are shown in Table h. The mean percentage of the account estimates of all eighteen characteristics relative to the census values without stratification was 125%, and the mean percentage deviation from.100% was about 28%. With both type of farm stratification and type of farm stratification with additional sub-stratification by crOpland harvested, the mean percentages and mean percentage deviations from 100%5 relative to the census, were about the same--about 9h% and 15% respectively in both cases. However, the improvement brought about by these different levels of stratification varied between characteristics. Six characteristics gave estimates closer to the census without stratifying. All of these deviated more than 10% from the census value. 0f the remaining characteristics, wheat yields, total acres, cropland harvested, number of milk cows, animal units, total of specified expendi- tures, and total receipts yielded estimates which deviated less than 10% from census values when class of farm stratification was incorporated. By also utilizing the crOpland sub-stratification, wheat yield, total acres, crOpland harvested, and animal units gained some improvement. One characteristic, hundredweight of milk sold, moved four percentage points closer to the census when crOpland sub-stratification was added. Although several probabilities appeared high, most were low. This was largely due to the homogenity of the category and the accompanying low standard errors. Two characteristics which had probability values above TABLE 4 Farm Account Estimates as Percentages of Census Values for all ‘Michigan Dairy Farms, Classes I-IV, 1959 by Levels of l Stratification-Probability Range for Completely Stratified Estimates Farm.Account Estimate as % Range of of Census Value Probability Level1 2 2 No Class of Complete Complete Strati- Farm Strati- Strati- Characteristic fication weightings fication fication % Corn Yield bu/acre 121 116 120 < .01 Wheat Yield bu/acre 105 99 100 >'.90 Milk 1b/cow 118 111 112 < .01 Total Acres 119 104 101 .70-.80 CrOpland Harvested 129 103 99 .40-.50 Acres in Corn 89 58 56 < .01 Acres in Wheat 112 76 73 '< .01 Number of Milk Cows 126 99 98 .05-.10 Litters of Pigs 121 74 70 .< .01 Animal Units 122 94 96 .< .01 P;M.W{U. 1h5 119 118 .01-.02 Total Specified Expenses 153 103 103 .20-.30 Value Land & Buildings 89 63 62 .< .01 Bushels of Wheat 118 76 7h .< .01 th. of Milk Sold 158 111 107 .< .01 Crop Receipts 117 71 73 1< .01 Livestock Receipts 158 112 112 ‘< .01 Total Receipts 151 105 105 ‘< .01 1 Probability as defined here refers to the chance (as a fraction of 1.00) that a deviation from the census value, at least as large as the account estimate—census value deviation, would occur from a stratified random sample. It is further assumed that the stratified random sample would contain the same sample size and strata prOportion that was found in the Farm.Account sample. The actual probability value lies within the ranges presented. Complete stratification refers to CrOpland Harvested weightings in addition to Class of Farm weightings for Dairy Classes II, III and IV. -36- -37- .50 were: wheat yields and total acres. Two ranged from .20 to .50, but all others were less than .10. Dairy Farms of Classes II and III-~The nonstratified and cropland numbers of farm weightings were utilized to make estimates relevant to the particular dairy classes which are now discussed. The results are shown in Table 5. The average farm account-census percentage of the eighteen characteristics was 9h% and the mean percentage deviation from 100% was 11% for Class II prior to crOpland sub—stratification. .After substratifyh ing by cropland harvested, these became 97% and 10%~-very little aggregate improvement. For Class III, these comparable percentages were 98% and 11% for both the stratified and nonstratified estimates. In the case of Class II, ten characteristics maintained estimates 'with less than 10% deviation from the census. Estimates improved by crOpland sub—stratification were animal units, hundredweight of milk, and crOp receipts. For Class III, nine characteristics yielded nonstratified estimates which deviated less than 10% from the census values. Those improved by crop— land sub-stratification included animal units and total receipts. Most of the estimates for both Classes II and III were within 20% of the census values. Cash Grain Farms--Cash grain farms were characterized as those which received 50% of the their total farm product receipts from cash grain crOps. Table 6 shows the results of the comparisons. The mean percentage of the eighteen characteristic estimates relative to the census was 161% and the mean percentage deviation from 100% was 61% prior to a class of farm TABLE 5 Farm.Account Estimates as Percentages of Census Values for Michigan Class II-IV Dairy Farms--l959 by Levels of Stratification Probability Ranges for Completely Stratified Estilmatesl Characteristic Corn Yield bu/acre Wheat Yield bu/acre Milk 1b/cow Total.Acres CrOpland Harvested Acres in Corn Acres in Wheat Number of Milk Cows Litters of Pigs Animal Units P.M.W.U. Tbtal Specified Expenditures Value Land and Buildings Bushels of Wheat th. of Milk Sold Crop Receipts Livestock Receipts Total Receipts Farm.Account Estimate as % of Census Value No Stratification by Stratification Crop Acres Harvested % % '5 $5 % %’ Class Class Class Class Class Class II III IV II III IV 115 115 117 116 ' 118 120 96 102 95 95 103 96 113 112 108 114 113 110 92 98 114 92 97 109 96 100 107 96 98 102 69 64 45 69 63 43 101 83 58 102 80 54 91t 98 103 94 97 102 117 63 66 79 68 62 91 92 97 92 98 95 105 108 138 106 108 136 97 106 102 96 106 100 63 67 57 64 66 55 98 85 55 98 82 51 127 108 109 105 107 108 84 76 55 103 74 52 105 114 114 106 113 113 101 107 105 102 106 104 Range of Probability Level Stratification by CrOpland Harvested W Class Class Class II III /\ /\ /\ /\ /\ IV .01 < .01 < .01 .01 .05-.10.30—.4 .01 < .01 < .0. .01 .10-.20.10-.2 .01 .02-.05.20—gy: < .01 < .01 < .0: .60-.70 < .01 < .0: .< .01 .02-.05.40-gx .20-.30 1< .01.02-£X < .01..40-.50.02-.05 < .01 < .01.05-.1< .ll-O-.50.0l-.O2 < .01 < .01 o®-O7O < 001 .05-.10 .< .01 .60 < .01 < .01 << .01 .10-.20 1< .01 ,> /\ /\ /\ /\ /\ /\ 4% In (H CH In In In Prdbability as defined here refers to the chance (as a fraction of 1.00) that a deviation from.the census value, at least as large as the account estimate—census value deviation, would occur from a sthatified random sample. that was found in the Farm Account sample. the ranges presented. ~38- It is further assumed that the stratified random sample would contain the same sample size and strata prOportion The actual probability value lies within —| 177-7— 0 "' 1 A . ~ . r I ,7 . ..- . .. o H. II "‘ o o ,7 . I . , - L .—~——— 5 -:‘ ~,. ‘4'» - H." «a... . log \I TABLE 6 Farm Account Estimates as Percentages of Census Values for Michigan Grain Farms Classes I-IV, 1959 by Levels of Stratification--Probability Ranges for Completely Stratified Estimatesl Farm Account Estimate as % of Range of Census Value Probability Level No Class of Farm Class of Farm Characteristic Stratification Weighted Estimates Weighted Estimates ‘75 % Corn Yield bu/acre 119 115 .05-.10 Wheat Yield bu/acre 110 101 .80-.9O Milk lb/cow 146 125 . 0-.20 Total Acres 121 109 .50—.60 Cropland Harvested 131+ 108 .Ll-O—.5O Acres in Corn 152 1110 .20-.30 Acres in Wheat 1211L 93 03—O"20 Number of Milk Cows 168 129 .50-'60 Litters of Pigs 132 159 ~60“?O Animal Units 183 198 .30“ ‘ .03— P.M.W.U. 211 172 < cl Total Specified Expenses 224 164 < 'ILO Value Land and Buildings 95 75 .05’ '0} Bushels of Wheat 151 1.15 ’ “,0 out. of Milk Sold 239 156 .30” “,0 Crop Receipts 158 106 ~30” '0 5 Livestock Receipts 250 187 ~02“ .03/ Total Receipts 173 119 / at a 1919’ 1.15 Probability as defined here refers to the chance (as a fraction of.l.00) 6r}? guinea deviation from the census value, at least as large as the account estimate—C value deviation, would occur from a stratified random sample- that the stratified random sample would contain the same samp Proportion that was found in the Farm Account sample. lies Within the ranges presented. -39- The actu 9’ It is further g, 136 at? Vflj’ 1e size and stra a1 probabilitY -40- stratification. After stratifying by class of farm, these respective percentages became 132% and 35%. Without stratifying, only value of land and buildings appeared within 10% of the census. This estimate was 95% of the census. After stratifying by class of farm, five characteristics maintained estimates within 10% of the census values. Many characteristics, especially livestock factors, deviated substantially from the census even after a class of farm stratification was utilized. Important examples were animal units 198% and livestock receipts 187%. The large value of livestock receipts raised the level of total receipts to 119% of the census. The probability levels varied between characteristics. One characteristic,'Wheat yield, obtained a probability between .80 awKi '90‘ Four more gave probabilities between .40 and .70. Six showed probalrthb— ties between .10 and .110 and all others were .10 or less. . cl 3518 Fruit Farms-«Fruit farms were characterized by those farms which rec over 50% of their gross from fruit products. Class stratdjiication 51;L53-£3 rut improve the aggregate of the estimates for the eighteeul characteajf The mean percentage was 140% both with and without a class stratificg’ The mean percentage deviation was increased from 38% to 1+2% using the class of farm stratification. Two important characteristics did, howg yield fairly good estimates when the class of farm stratification was utilized. These were, total of specified eXpenditures 109% and 1301333- receipts 98%. -41- Other Livestock Farms--These fanns were characterized by 50% or more of their farm product receipts from livestock and livestock products other than those specified for dairy and poultry. The results are compared in Table 7. The mean percentage of the eighteen characteristics relative to the census was 150%5 and the mean percentage deviation from 100% was 54% prior to stratification. After stratifying, these became 113% and 31%. Estimates which deviated less than 10% from the census included total acres and value of land and buildings (see discussion for cash grain farms). After stratifying by class of farm, about half of the characteristics yielded estimates within 10% of the census values. However, some of the very important characteristics for this category did not show up favorably. The estinmte for animal units was 126% of the census value and litters of pigs 137% after stratifying. General Farms--General farms were those which did not fit into other categories and thus obtained income from three or more major sources. Stratification did improve estimates in the aggregate for this category. The eighteen characteristic estimates averaged 161% relative to the census with a mean percentage deviation of 61%. After stratifying, these respective figures became 110% and 19%5 showing considerable improvement. Without a class of farm stratification, only one estimate deviated less than 10% from the census. After stratifying, nine estimates deviated less than 10% from the census. TABLE 7 Farm.Account Estimates as Percentages of Census Values for Michigan Livestock Other than Dairy and Poultry Farms Classes I—IV, 1959 by Levels of Stratification-Probability Ranges for Completely Stratified Estimatesl Characteristic Corn Yield bu/acre Wheat Yield bu/acre Nfilk lb/cow Total.Acres Cropland Harvested Acres in Corn Acres in Wheat Number of Milk Cows Litters of Pigs Animal Units P.M.W.U. Total Specified Expenses Value Land and Buildings Bushels of Wheat M. of Milk Sold Crop Receipts Livestock Receipts Total Receipts Farm Account Estimate as % of Census Value No Stratification % 124 110 350 106 136 l38 137 73 172 166 136 209 97 151 75 142 194 185 Class of Farm Weighted Estimates %5 121 110 372 101 102 82 95 45 137 126 100 Range of Probability Level Class of Farm weighted Estimates 1 .O5-.10 005“ 0.10 ‘< .01 > .90 .70-.80 .02-.05 .70-.80 .01-.02 020—030 .05-.10 ~90 .30-.40 002'- .05 .70-.80 005' 010 01‘0“ o 50 002- 005 .05 w—v Probability as defined here refers to the chance (as a fraction of 1.00) that a deviation from the census value, at least as large as the account estimate-census value deviation, would occur from a stratified random sample. It is further assumed that the stratified random sample would contain the same sample size and strata prOportion that was found in the Farm.Account sample. lies within the ranges presented. -42- The actual probability value -43- Poultry and Other Field CrOp Farms--A1though both of these categories were relatively homogeneous and do present research potential, there were too few such farms in the 1959 Farm Account for them to be useful. Other field crOp farms consisted of those which received 50% or more of their farm product receipts from crOps listed as other field crops in the type of farm definitions in the appendix. Likewise, poultry farms received 50% or more of their total farm receipts from poultry and poultry pro- ducts. Type of Characteristics Compared Efficiency or Performance Characteristics It was noted that account farms averaged larger crop yields and production per cow prior to stratifying. The simple average of the account yields versus the census yields averaged across all categories of comparison-~that is, the average of the percentage comparisons of all account farms, each class of farm, each type of farm, and separate dairy class II, III, and IV estimates were 116% for corn yield, 104% for wheat yield, and 145% for pounds of milk/cow. After complete stratification, these percentages became 118%, 103%, and 140%. The overall effect where stratification was complete moved the estimate slightly away from the census figure. The directional shifts in the estimates from each stratification were approximately the same for wheat, except with complete stratification the estimates moved about one percentage point closer to the census for the average of all categories. -44- For milk production per cow, type of farm stratification had very little effect on the combined farm category estimates. Class of farm stratification did move the estimates somewhat closer to the census. CrOpland harvested had negligible effect in the stratification. Complete stratification moved the estimate from.l23% to 115% for all account farms and from 155% to 150% for the simple average of estimates from all observation categories. The probabilities of the estimates were very low for corn yields and milk production per cow. For most categories of observations these fell at about the 1% to 5% levels. For wheat yields, on the other hand, about one-third of the probabilities from individual category estimates were greater than .50. That is, there would be better than a 50-50 chance for about one-third of the estimates that stratified sample estimates using the same sample size and strata proportion as the fann account sample would carry differences from the census as large or larger than the difference of the account stratified estimate from.the census value. However, the differences between account estimates and census values were quite narrow before census strata weights were incorporated. CrOp Input Characteristics Included among the characteristics which were compared to the census values were several which were important as inputs for crop production. Included were total acres, cropland harvested, acres of corn and acres of wheat. USing the average of the combined account farms, each class and each type along with dairy classes II, III and IV estimates for total acres and crop acres harvested were closer to the census values _45- using complete stratification. The crOp acres harvested sub-stratification for Dairy Classes II, III, and IV moved estimates of these two characteris— tics about one percentage point closer to the census values for the all account farm category. For dairy farms only this latter sub-stratification improved the estimate by about three percentage points. Class of farm estimates were improved by about one to three percentage points by utilizing crop acres harvested sub-stratification for dairy classes in addition to the type of farm stratification. The effect from type of farm census weights was somewhat erratic reducing both total and crOpland acreages in some cases and increasing them in others. Looking across all of the various estimates (combined farm account, each class, each type and Dairy Classes II, III and IV), the average farm account-census percentage of total acres moved from 114%'without stratification to 105% with complete stratification. For crOpland harvested, this movement was from 121% to 107%. For specific acreages of corn and wheat, stratification did not prove beneficial for adjusting the estimates. The acreages without stratification approximated census values very closelyh-within 1% to 2%. The type stratification increased these estimates somewhat, but the class stratification lowered the estimates substantially. The average across all categories of observations--all farm account, types, and class of farm categories estimated separatelyh-indicated a greater difference from the census using complete stratification than did the nonstratified estimates. For corn acres, this difference moved from an average of 101% without stratification to 89% with complete stratification. Likewise for wheat, the estimates moved from an average of 102% to 91%. -46- For corn acreage, only two group of farm categories obtained probabili- ties of .50 or greater that stratified random samples would obtain a deviation as large or larger than those obtained by the account sample. For wheat acreages, seven out of fifteen categories showed estimates with probabilities of .50 or greater. For wheat, however, nonstratified account estimates were also quite close to the census. CrOp Output and Receipt Characteristics Two characteristics, bushels of wheat and crop receipts, were included for study. Wheat outputs were directly related to wheat acreages and yields. Wheat production gave a reasonable estimate for several of the farm categories, but did not for many. For the average of combined account farms, each type, each class, and dairy II, III and IV, crOp receipts were reduced using a class of farm stratification and increased using a type of farm stratification. The overall effect of using both tended to raise the estimates. Class of farm category estimates tended to be low and type of farm stratification raised the estimates somewhat. Type of farm estimates were high, and class of farm stratification lowered the estimates. In very few cases did either the stratified or non stratified estimates appear within 10% of the census value. Livestock Input Characteristics Three measures characterizing livestock inputs were utilized in this study. These were: (1) Number of milk cows, (2) litters of pigs and -47- (3) animal units. A very decided improvement came about in the estimates for number of milk cows by utilizing complete stratification for the combined account farms, each of the classes, dairy, cash grain, and general farms. Stratification did not improve the estimates for the other four types. For litters of pigs, both stratified and nonstratified estimates appeared very erratic when compared with the census. Except for class of farm.stratification of all account observations, all estimates deviated substantially from the census. Animal units were heavily weighted by dairy cows in both the farm account and the census in 1959. The effects of stratification were not as extensive as for dairy cows, although the shifts followed the same directions. Also, the initial deviations from census values prior to stratification were not as great for animal units as they were for dairy cows. Looking across all categories of estimates, the farm account average percentage of the census was 146%'without stratification and 126% with stratification. Completely stratified estimates appeared reasonable for classes I and III as well as dairy farms, but deviated considerably for most other categories. Livestock Output and Receipt Characteristics Two measures of livestock outputs and returns included for study were hundredweight of milk sold and livestock receipts. Stratification improved the estimates of milk sales for the combined account farms, all classes, dairy and general farms. The results were very erratic for other ~48- types of farms not listed here and nether stratified nor nonstratified estimates appeared satisfactory. Livestock receipts were improved using both type of farm and class of farm stratification. Improvement was noticed in all major farm observation categories using these two criteria for strata weighting. Sub-stratification by crOp acres harvested did not have a noticeable effect on the estimates. The amount of improvement varied considerably between farm categories. PMWU, Specified Expenditures, Value of Land and Buildings, & Total Receipts Three input measures, productive man work units, total of specified expenditures, and the investment value of land and buildings were not attributable directly to either livestock or crOp enterprises and are discussed separately. Total receipts, likewise, receives separate dis- cussion. The pattern of improvement resulting from stratification for PMWU's was very similar to that for animal units. Both type of farm and class of farm stratification moved the estimates closer to the census values for the combined account farms as well as each type and class of farm group. The stratified estimates, however, did not closely approximate the census values. Specified expenditures were in general improved by stratification. The class of farm stratification appeared to have more effect toward the census than did the type of farm weightings. Reasonable estimates were obtained for all account farms, classes I and II, dairy, other livestock and general farms. For value of land and buildings, the average -49- percentage across all observation categories was 78% or 22% lower than the census. The effect of stratification was to reduce this to an even lower estimate. Research Interpretation of the Comparisons For purposes of this writing, comparisons of account estimates to census values which deviate 10% or less from the census value will be considered reasonable. It is recognized that this deviation may be too large for reasonable use in some specific research studies. Combined Farm.Account Farms The combined group of account farms consisted of 91a farms. There were 35,428 Michigan census farms of classes I—IV. According to the census, farms in this category maintained 55% of the value of land and buildings, 61% of the crOpland harvested, and sold 72% of the value of farm produce of all Michigan farms in 1959. Although this category is not comprehensive enough to use for measurements of total agricultural resources and production of the state, it does represent the major part of Michigan commercial agriculture and can be used for aggregate studies of resource combinations, organization, output, description of the major sectors of farms in Michigan agriculture and also for future projection and prediction. For studies of the above types, nearly all of the characteristics selected for comparison and related types of characteristics can be utilized for research pertaining to all or selected classes of Economic -50- Classes I-IV. Estimates were made without census weightings along with type of farm census weightings only, class of farm census weightings only, both type and class census weightings, and with class and type census weightings plus the crOpland harvested weightings for dairy classes II, III and IV. Three characteristics - acres of corn, acres of wheat and wheat yields - gave reasonable estimates without stratification. The class of farm census weightings (without type of farm or cropland harvested ‘weightings) gave close estimates to the census for crOpland harvested, litters of pigs, total of specified expenditures, and total receipts. With these characteristics, the nonstratified estimates for the category appeared high and the type of farm census weightings resulted in accentuating these values, therefore the class of farm weightings appear as a feasible criteria for Obtaining these estimates. USing type of farm census weightings only improved the estimate for value of land and build- ings. This characteristic will be discussed later in the chapter. Total acres, number of milk cows, and bushels of wheat produced yielded reasonable estimates by using both the class of farm and type of farm census weighting criteria. .Milk sales seemed reasonable after the cropland substratification weightings were applied. These input and output values were improved through the size of farm shifts brought about by census class of farm weightings and the type of farm shifts. Corn yield per acre, cow production, animal units, productive man work units, cr0p receipts and livestock receipts were all improved through the type-class stratification, but the strata delineation was not complete enough (even though expanded to the limit of census presented information) to move the estimates close enough to serve as good census -5l- estimates. This is unfortunate because these performance and aggregate input characteristics are very important for certain types of research. Economic Class of Farm Categories These categories could be useful for research involving resource organization and production by size of farm.categories. Since size of operation is dependent upon the source of income, it is possible to subdivide the classes into type of farm strata (at least for the larger strata) and the use of class of farms as a size measure would be en- hanced. For each of the classes, estimates were derived for the census values of the census classes represented. Besides making estimates for the classes without stratification, estimates were derived using type of farm stratification. Additional estimates for classes II, III and IV were derived using cropland harvested census weightings in addition to type of farm weightings. Class I Farms - Farms of Economic Class I comprised the largest category of farms compared in terms of gross income. There were 812 census farms and sixty account farms in this class in 1959. Over half of the census farms and about one—third of the account farms from this class fell into the fruit and other livestock type of farm categories. These types would be expected to be well represented in Class I since they maintain enterprises which obtain large gross incomes, but likewise also maintain high accompanying expenditures. -52- This class is of research interest, even though it was the smallest in terms of number of farms in both the account project and the census in 1959. In terms of the future, this group of farms could help establish trends in resource allocation on.Michigan farms. The class would, there- fore, be of interest for descriptive studies, projection, as well as allocation and returns studies. Without stratifying the class by type of farm, corn and wheat yields along with crOpland harvested appeared to give reasonable estimates. 'Using the type of farm stratification, acres of wheat, animal units, total of specified expenditure, livestock receipts and total receipts appeared to give reasonable estimates of the census. Cow production, total acres, acres in corn, number of milk cows, litters of pigs, productive man work units, value of land and buildings, bushels of wheat produced, milk output, and crop receipts did not give estimates reasonably close to the census. .All of these except total acres and acres in corn were improved by type of farm stratification. If a finer delineation by source of income were possible, these characteristics probably would have shown up more favorably. There appears to be no apparent reason that stratified estimates of these characteristics should appear more representative using future account data. The divergence in both live- stock and crop intensity as well as livestock efficiency between account farms and census farms appeared instrumental in bringing about these estimate differences. These divergences will likely continue in the future. -53- Class II Farms - Class II was considerably larger in terms of numbers of farms then was Class I; there were 3,658 census farms and 252 account farms in this class. This was only about 10% of the census farms, but almost one-third of the account farms. By type of farm, about one-third of the census farms and over half of the account farms were dairy farms in this class. Even though this class was not the largest in either the farm account or the census in 1959, it will likely become a very important class as farm size continues to increase in Michigan. With this consideration, this class might well serve as a model class to typify future Michigan agriculture. The possibilities of type of farm shifts, shifts in livestock and capital intensity, and shifts in technology over time must be given due consideration if such studies are conducted. Although all of the characteristics compared serve a research interest, the input, receipt, and expense characteristics would be of Special interest. Wheat yields, total acres, and cropland harvested gave close estimates to the census without type of farm stratification. Acres of wheat, number of milk cows, total of specified expenditures, wheat production, cr0p, livestock, and total receipts all gave reason- able estimates after the type of farm stratification was applied. With the cropland harvested criteria also applied, the estimate for milk sales appeared reasonable. The estimates for corn yields, cow production, acres in corn, litters of pigs, animal units, PMWU's and value of land and buildings did not yield estimatesclose to the census. Litters of pigs, animal units, V41 -54— and PMWU were improved by stratification, but not enough to give reason- ably close estimates. The high values of PMWU and animal units appeared to come about through the greater livestock intensity on the part of account farms relative to census farms in the non dairy type of farm Strata. Class III Farms - There were 12,322 census farms and #41 account farms (nearly half of all account farms and the largest number of account farms of all classes) in Class III in 1959. The class is an.important one from the standpoint of number of farms in both the census and farm account. Although presently not as large in census number of farms as Class IV, it should gain in importance in the future. About half of the census farms and three-fourths of the account farms were in this class in 1959. Wheat yields, total acres, cropland harvested, litters of pigs, total of specified expenditures and total receipts gave close estimates ‘without a type of farm stratification. Acres of corn and wheat, number of milk cows, animal units, bushels of wheat produced, milk production, crop and total receipts all gave reasonable estimates using type of farm stratification. Three of these were almost identical with census values. The cropland sub-stratification did not appreciably improve any of the estimates. The estimates for corn yields, cow production, PMWU, value of land and buildings, and livestock receipts did not appear reasonable with or without stratification. Class IV Farms - This class was composed of 18,636 census fanms and lEXL account farms in 1959. Over half of the census farms, but only'l8%0f -55- the account farms fell into this class. In spite of the large number of census farms, this does not appear to be a good category for most research purposes since the gross income requirements are likely too low to be representative of a commercial farm category in future years. Also the estimates for many characteristics did not show up favorably. Summary of Class of Farm Estimates - Classes I, II, and III indicated promise for the use of certain characteristics in future research. Characteristics varied in their representativeness between classes. This was true for both stratified and nonstratified estimates. In general, however, two performance characteristics, corn yields per acre, and milk production per cow were not adjusted to satisfactory estimates using stratification. 0f the input characteristics, total acres and crOpland harvested gave close estimates without stratification. Stratified estimates of acres of wheat appeared good.but acres of corn did not. Stratified estimates for number of cows appeared good but litters of pigs did not. Animal units gave good estimates for Classes I and III, but PMWU’s were quite divergent for the three classes. Specified expenditures gave reasonable estimates in two out of three of the classes. Wheat out- put, milk sales, and cr0p receipts gave reasonable stratified estimates for Classes II and III while livestock receipts appeared within range for Classes I and II. Total receipts appeared reasonable in all three classes. Value of land and buildings did not appear reasonable in any of the three cases. This characteristic will be discussed later. -56- Type of Farm Estimates For each of the type of farm categories, estimates were made for the census farms belonging to the particular type of farm categories discussed. Estimates were made using number of farm census weights by class of farm only, and for dairy estimates were also derived using the crOpland sub-stratification described earlier. This is in addition to the class of farm only weightings for dairy. As with class of farms, estimates were also taken directly from the account type of farm category to estimate the census value. In other words the farm account mean of all farms within the type of fann category were used as estimates of the census mean of the type of farm category. Census total estimates were derived by multiplying the account mean by the number of census farms in the type of farm category. Daipy Farms Classes I-IV - This was the largest type of farm category for both the census and the farm account sample in 1959. About half of the census farms of classes I-IV (15,804 farms) and two-thirds of all account farms (654 farms) belonged to this type of farm category. Indications are that this type of farm will continue to play an important role in Michigan agriculture. The 1959 comparisons should give some indication of the future research potential of the compared characteristics and related characteristics. In addition to research involving resource allocation and returns, this category of farms offers the possibilities of descriptive research pertaining to detailed costs and investments. All of the compared _ 5']. characteristics serve a research interest of one kind or another. However, the input investment and expenditure characteristics are of special interest for detailed descriptive studies. Without using a class of farm stratification, only wheat yield appeared to give a reasonable census estimate, but this too was improved by a class of farm stratification. Very little improvement was gained using the crOpland sub-stratification for dairy classes II, III and IV. Total acres, crOpland harvested, animal units and milk sales did gain some improvement using this sub-stratification. USing the class of farm stratification, reasonable estimates of the census were obtained for wheat yields, total acres, cropland harvested, number of milk cows, animal units, specified expenditures and total receipts. These characteristics show promise for future research involving detailed costs, receipts, and investments. Due to greater crop and livestock intensity on the part of c00perators, pro- ductive man work units did not appear to be improved enough for representa- tive use. Also, due to the greater livestock intensity, livestock receipts were higher than the census after stratification, but with a higher prOportion of the farm produce fed, cr0p receipts were lower, and therefore the stratified estimate of total receipts was rather closely comparable to the census. It should be pointed out that the greater livestock intensity was reflected through better performance (production per animal) on account farms since the stratified estimate of cow numbers and animal '- ‘7 v r _ n 9 , W O ‘l u. .- .. 58- units showed up quite comparable to the census. Also, twelve out of the eighteen characteristics were improved by using the class of farm stratification. Five of these were not improved sufficiently for representative estimates. Separate Dairy Classes - The farm account sample maintained twenty-four class I, 162 class II, 337 class III and 121 class IV dairy farms in 1959. These represented a 20% sample for class I, 14% for class II, 5.33% for class III and less than 1% for class IV. Classes I, II and III should be of special interest for research. The type of studies applicable to the separate classes of dairy farms might be similar to those suggested for the combined dairy classes. For class I dairy, no additional stratification was applied, that is the mean estimates were compared directly with dairy class I census estimates. Ten out of the eighteen characteristics showed up within 10% of the census. These included the performance characteristics; corn yields, wheat yields and cow production. Also, included were cropland harvested, acres of wheat, productive man work units, total of specified expenditure, bushels of wheat produced, crOp receipts, live- stock receipts, and total receipts. The remaining classes (II, III and IV) were compared using the direct estimates, class of farm weighted estimates, as well as estimates using crOpland sub-stratification. For class II, this sub—stratification gave considerable improvement and reasonably close estimates for milk sales, and crOp receipts. The direct estimates appeared reasonable for r\ -59- wheat yield, total acres, cropland harvested, acres of wheat, number of milk cows, animal units, PMWU‘s, total of specified expenditure, bushels of wheat, livestock receipts, and total receipts. For class III only animal units obtained substantial improvement through the crOpland sub-stratification and yielded a relatively close estimate. None of the other characteristics were substantially improved using this stratification criterion. However, direct estimates for wheat yield, total acres, crOpland harvested, number of milk cows, animal units, productive man work units, total of specified expenditures, milk sales and total receipts gave relatively close estimates. These show promise for use in descriptive research. About half of the class IV account estimates (both cropland substratified and nonstratified) did not show up favorably, and in addition the category does not serve a major research interest. Dairy farms in this class are too small for consideration as major commercial farms. Cash Grain Farms - There were 6,550 census farms and 38 account farms in this category in 1959. Although the number of account farms might be considered marginal for yielding meaningful estimates, the category is relatively homogeneous and of interest for specific research purposes. There is some indication that the number of farms of this type may increase under the "Telfarm" program. Cr0p performance, inputs and outputs along with associated costs would comprise the main characteristics of interest. The class of farm stratification improved all but three estimates. Two of these (litters -60- of pigs and animal units) were not close in either case. value of land and buildings was close without stratification due to the larger farms in the account project coupled with low account appraisals. All of the remaining were improved by the class of farm stratification, but unfortunately only wheat yields, total acres, crop- land harvested, acres of wheat, and cr0p receipts were improved enough to yield reasonable estimates. If the number of farms in this type of farm category increases in the future, better estimates would be likely. Fruit Farms — There were 2,779 census farms and thirtyhfive account farms in this type of farm category in 1959. The number of farms in the category is relatively small for obtaining meaningful estimates and represented only a 1.26 % sample of the census in 1959. Since the category is composed of a unique set of specialized farms, many of the characteristics utilized in this study would not be of direct interest for research. Nevertheless, two characteristics did show up well by using a class of farm stratification. These were total of specified expenditures and total receipts. For some research purposes, especially those involving costs and net incomes, these characteristics and related characteristics might find use. Other Livestock Farms - The other livestock category was composed of 5,645 census farms and eighty-five account farms. Although the category is relatively uniform from the standpoint of livestock intensity, there is considerable variation in the kinds and classes of livestock held. For the most part, these farms maintained livestock enterprises consisting 1,- -61- of beef breeding and feeding, pig raising, hog feeding, sheep produc- tion, and combinations of these. In some cases, dairy existed also but not to the extent of obtaining 50% of the gross products receipts from this enterprise. By types of characteristics, those pertaining to livestock and livestock facility inputs, costs and investments would be of special concern. Some of these characteristics did not compare favorably with census values even after stratification by class of farm. 0f the eighteen characteristics compared nine did compare favorably with the census figures. These were wheat yields, total acres, cropland harvested, acres in wheat, productive man work units, total of specified expenditures, bushels of wheat produced, livestock receipts and total receipts. Four of these would apply to the livestock enterprises. General Farms - Since this category of farms received product receipts from three or more sources, there is considerable lack of homogeneity among farms. In addition, the composition is difficult to define. For these reasons the usefulness of this type for a research category is somewhat limited. There were 3,556 census farms and seventyhseven account farms in this category in 1959. About half of the characteristics did yield good estimates utilizing class of farm stratification. Poultry and Other Field Crop Farms - There were only sixteen other field crop and nineteen poultry farms in the 1959 account sample representing 955 and 1,139 census farms respectively. Due to the very low number of . .s. f - . ’- -r- - v- t I ..L I J 1 I v ' I - \ ,. . 7 . - ._ > ‘ O . h— \l v . ’ r a p _w 1.__ J . ,3 H ‘ f 5 I r -‘ )j , I , 7 \ t ‘ 7 . . I 1 ,-. . \ r I - . A e- -t I , ~ L . -62- farms in these types and with little encouragement of an increased number of these farms in the future, there appears to be very little potential for using account data for these specific farm types. Summary of Type of Farm Estimates - The type of farm categories which appeared to show promise for future research were dairy, cash grain, and other livestock farms. Dairy farms of the specific classes I through IV also showed research potential. Fruit farms did not lend themselves to the characteristics chosen for this study. General farms lacked homogeneity, while other field crop and poultry farms contained too few observations to be meaningful. Summary by Characteristics The effectiveness of the stratifications for each of the characteristics varied according to the category of farms compared. Some general comments, however, can be made about certain characteristics and types of characteristics. For the efficiency or performance characteristics wheat yields compared favorably with census values, even without stratification. Corn yields, milk production per cow did not show up favorably either with or without census strata weightings. It is suggested that the farm account sample is not a representative source of performance or efficiency data since co0perators of all types and classes showed better performance than their counterparts who were not inthe project. F J -63- Total acres and acres of crOpland harvested yielded representative estimates for most characteristics when the stratification was complete. Without stratification the account values of cropland harvested deviated more percentagewise from the census than total acres. This indicated that the cooperators showed greater crop intensity than the non cooperators. Both estimates appeared reasonable for most farm categories after stratification. Although it might appear that the above comparisons would indicate that account estimates would provide a representative source for crop input estimates, the estimates for individual cr0p acreages did not show up as well. Acres of corn and wheat deviated more from the census values than did total or cropland acres. For the aggregate of crOp inputs, the account sample should provide a better source than it would for individual crOps. Since account farms tended to be more livestock intensive, they fed more of their crOp production and hence showed lower crOp receipts. Livestock receipts were higher for account farms for this reason. Total receipts, although higher for most categories of farms did come relatively close to the census values when stratification was employed. (For characteristics involving cr0p outputs and sales, the Statistical Reporting Service provides valuable data also.) -64- Three measures of livestock inputs were compared. These were: number of milk cows, litters of pigs and animal units. Number of milk cows indicated good estimates for all account farms and dairy farms when stratification was employed. For the categories where dairy was of lesser importance, the stratified estimates did not show up favorably. Dairy factors would not be as important for research for these categories, however. The farm account estimates for litters of pigs generally did not show up favorably. Pork production was not a major agricultural industry in Michigan in 1959 and the distribution of hogs among the various types and classes of farms was sporadic in the account sample. For research dealing with pork production, the farm account does not appear to provide a representative source of data. Animal units were heavily weighted by dairy cows for all account farms and dairy farms. The stratified estimates werembasrepresentative for animal units as they were for number of dairy cows in these categories, but the shifts in the estimates took on much the same pattern. For non dairy type of farm categories, the estimates for both number of dairy cows and animal units deviated considerably from census values even after stratification. Two measures of livestock output were hundredweight of milk sold and livestock receipts. For milk sales, both class of farm census weightings and type of farm weightings improved the estimates; for all account farms, all classes, dairy and general farms. The stratified estimates appeared reasonable. For the remaining type of farm categories, the account farms were more dairy intensive than non c00perators for all -65- types except other livestock, in which case they were considerably less dairy intensive. Of these, stratification improved only the estimate for cash grain farms, which was not reasonably close to the census. Livestock receipts, as previously discussed, were generally higher on account farms due to greater livestock intensity. In general, the account bases were too high for stratification to give enough improvement. In the cases of classes I and II the stratified estimates did appear reasonable. Productive man work units was improved by stratification but as with animal units, the base prior to stratification was high and stratification improvement was not sufficient. The high account base was due to both high crOp and livestock intensity. In the case of other livestock farms, the stratified estimate equaled the census value and this was the one exception for this characteristic. With specified expenditures, the class of farm weightings moved the estimates downward as expected. The type of farm weightings had an upward effect on the estimates. It appeared that non dairy account farms produced more feeder stock than did census farms. The heavier census weightings for these types of farms raised the estimates. In several instances the account base was low and census weightings did actually give estimates closer to the census. This was true for classes I and II. For all account farms, the class of farm stratification by itself gave the best estimate. For most type of farm categories, the estimates were improved with a class of farm stratification and the estimates appeared reasonable for several important type of farm categories. -66- Value of land and buildings will be discussed separately as a special case. The total receipts category was previously discussed, but did indicate reasonable estimates when type and class stratification was employed. Concluding Remarks Categories of Farms with Research Potential - Of all of the various farm categories, dairy farms appear to offer the greatest possibilities for research. These farms were well represented in both the account sample and in the census (about two-thirds of account farms and one-half of the classes I-IV census farms). In addition, the category is the most homogeneous from the standpoint of enterprise inputs, products, costs and returns. Other type of farm categories of research interest are cash grain and other livestock farms. These categories were less well represented and were less homogeneous than the dairy category. Research involving allocation, returns, future prediction, and resource description are of interest for these categories. The all account sample and each of the classes I-IV also serve as useful research categories for some purposes. For description of the more important aggregate of Michigan agriculture or for size of farm studies aimed at resource utilization and enterprise combinations, these categories can be useful. ~67— Categories of Farms with Little Research Potential - Several of the type of farm categories appeared to have little research potential. Included among these were: other field cr0p, poultry and general farms. Other field cr0p and poultry were too thin in number of farms to give good results in 1959. Unless the number of farms in these categories should substantially increase in the future, there appears to be little research possibility from these categories taken individually. General farms obtained major income from three or more census defined sources. There is a lack of homogenity for these farms and a problem of category definition exists. For these reasons, this category appears to have little research promise. It is difficult to draw conclusions concerning the research potential of fruit farms from this study. Since this category maintains specialized production the types of characteristics utilized in this study do not lend themselves particularly well for evaluating the category. A special study relating directly toward evaluating this category would be of interest. Account - Census Farm Differences - Considering all of the account farms as opposed to census farms of classes I-IV, account farms were larger, and moreeefficient as indicated by cr0p yields and milk production per cow. They were also more crop and livestock intensive. That is, they harvested crops from a higher prOportion of total farm acres and maintained more animal units per acre than indicated by the average of census farms. H -68- One major bias appeared among the farm account data. value of land and buildings is an arbitrary value by nature, since the sale of farm prOperties is quite limited. The extension personnel encourage c00pera- tors to use a conservative value in order to prevent undue fluctuations in investment values and the associated effect on labor income. As a result of this, all account category averaged 15% lower than the census value. The effect of using census strata weightings was to lower this value still further. This came about primarily through the class of farm weightings. It appears that the farm account is not a good source of real estate values that would be expected through an enumeration of land values. If for certain specific reasons conservative values are desired, the account sample might serve as a possible source. Alternatively, it may be that the extension people in charge of the fann accounts should re-evaluate their approach to real estate values. Validity of Census Data - There appears to be very little reason to question census data from the standpoint of sampling biases. Most characteristics are enumerated using all farms which meet the census criteria. Several characteristics are derived from a 20% sample of respondents. Included in this list are: sales of livestock and livestock products, use of fertilizer and lime, farm expenditures, land use practices, farm labor, equipment facilities, real estate values, and farm mortgage debt.1 The size of these samples are large enough that sampling bias lU’.S. Bureau of the Census. ‘U. S. Census of Agriculture: 1959, Vol. I, Counties, Part 13 Michigan U.S. Government Printing Office, Washington, 11.0., 1961 p. )CEI. -69- should not be a problem. The problem of enumeration bias in the census is more difficult to evaluate. The proficiency of enumerators along with the accuracy of information presented by respondents is of major concern. Problems of memory bias and doubts about the confidential use of census information might cause low estimates for income, output, and investment variables. Certain characteristics can be compared with E.R.S., S.R.S. and Michigan Department of Agriculture data. Using Michigan Agricultural Statistics, out of eighteen characteristics compared all except three were higher than the census. Of the three, number of hogs was 19% lower, average size of farm 3% lower and value of land and buildings 1% lower. Of those which were higher, four were at least 10% greater than the census values.2 Since these data are sampled it is difficult to conclude that they are more representative than census data, but the figures are indicative that data from.separate sources may not duplicate the census. ‘Use of Class of Farm - Type of Farm - Strata Data for Research - In contrast to nearly all other sources of Michigan farm data (except census data), farm account data can be disaggregated for application to the type of farm - class of farm level. If the data are accurate and representa- tive at these levels, their value for research should be of major importance. At these individual strata levels, research results can become more directly applicable to specific farm situations. 2Ibid., U. S. Census of.Agriculture, pp. 1—131 and Michigan Department of Agriculture, Michigan Agricultural Statisitcs, Lansing, Michigan 1963 pp. 1-48. -70- Unfortunately, the number of account farms in most of the class of farm.- type of farm strata are too low to present reliable results. Two very important exceptions exist, however, these are dairy classes II and III. Dairy class II which contained 162 account farms in 1959 appears to show considerable potential for future research. Not only should there be an increasing number of farms in the future, but about half of the characteristics in 1959 gave estimates which were reasonably close to the census figures. Table 5 compares account estimates to census values for dairy classes II, III, and IV. All other individual class — type strata estimates are compared in Table 8. .o ashes ooh ss ens sss sss momaeso asses nos s ses ees sss ses mm oss mes ses om mms mss em oes so ees so ems mss oms mo mms sss ses ess measooom sesoe ses oss ess mms ses sms mes oes so mms mms oo ssm ess ees . oso oo oes ssm osm ems mos esm .asoom soosaoess eo om se os oo ess mes so we es es em mo sm ees men so sms ees se ses mes ees ems neasooom done me se ees ems ees eo mm me oe mmos mes oommwosm ems s osm oem ees . sem ses me mms emmsesom assz.so.sse oes se oes oo oo oes ees ess oo oms se no mo mmm esm es es so sou oms mms mes mss sss sees: no nsosnam ee oe ms ee me so ss ms mo ms me es me om mo so ms em sm oo se es so mms .neesm e.es.sa> ees sss sss mes ee mos eo ses so om me so ems oo eo sss mmm mos mmm me ees mes ees smm .aam.ooam sesoa oo sms sss oss eos ses se ess mo sem moo osm . u r . ses mms oms sss esm ess sss emm .eua.zao mm oms sms sss sss sss ess mms ses ems ems sms - - - - msm oe osm mo mem mms mms sem asses sassas ses esm mos esm oes ems sss mss es . em no em mss . u 1 mos - . mom sss m . mesa so massess em ees mes oms ssm mm em se oe mmes sss eeem sem eeo es ses sem ss eom smm mos ss ess mmo aaoe sss2.so.oz oo em eo ees so mo so ses mo mss sss oo ms mom ees es mm so ms sms mms eo .eo mss sense as means se me mos sm mm oe ses sw ss so mos os ss ems mm 1 : ssm : msm sss ems om esm shoe as noses mo mo ees mo es mss so ses om omm sss so ess oos mo sss mms ses ees me oss mes se ses .>nem eassoose em oes mo om ee mms os om ee ess ees em sms oss om so oes sms oms ss mms mo es mes noses sasos oes mes mss ses sss sso mem esm ssm ses sss sme eos sss . sss mes oes : sem ems ems sss mms soo\ns sss: ees ses oes so ems mss ess sss so mss es mo oms so sem ees oe se ems mes mo mes oss ess s s some: oes mss mms ees mes mms ess oss mss mss so oo me sms sms . . se - mes ess ess sms sss oe\ap esoss anoe s ssssss ss sssss ss ssssssss H >s sss Hs s >s sss ss H >H sss sses ss sss ss s ss sss ss s ss sss ss H mmveaw , 3.3.0 1 .mmmsd i mmmav r .336 immoao it - www.mo L snsnm ssaoaoe soosaosss sense sapsoom asses mono esoss sense aseae ante ossmsnosoeaese each so mafia , s ess .sss .ss moanese sassm easessoxm assessm an memo: unmnoo mo newspnmosom no names Pnsooo¢ each m msmas -71— {.I‘l ‘11 Viniul’r. CHAPTER IV ESTIMATION OF SELECTED POPULATION CHARACTERISTICS FROM.ACCOUNT DATA Perspective and Approach The Need As previously pointed out, some very important characteristics for research were included in the 1959 farm account data, but were excluded from the census. In 1959 and other years prior to the "Telfarm” project, characteristics involving a portion of farm costs, along with net farm income and a large share of non real estate investments were part of the data available from the account project but were not included in the census. With the advent of "Telfarm“, additional characteristics derived from the special accounts, i.e.-—credit, labor, enterprise, and family living will yield additional information not presently available from the census. Some of this information may be very important for future research. Since it is not possible to directly compare non weighted or strata weighted account estimates with non existent census data, some procedure was needed for estimating values applicable to the census categories. In some cases, estimates derived by sampling have been used to obtain population estimates of costs and income. The accuracy of -72- -73- these estimates based upon relatively low sample proportions has been questioned. In this chapter, the use of regression procedures to estimate pOpulation values is explored. Once the regression estimates are established, it is possible to compare these with census strata weighted account regression estimates and non weighted account regression estimates. Since the procedure to be followed is exploratory, it was decided to apply it to a limited number of characteristics. In future studies, this same technique might be employed using new data and additional variables. Several suggestions toward improving the procedure are listed in this chapter. It is suggested that these be noted before applying this procedure to other data. Dependent variables The specific characteristics selected were non real estate investment, net farm income, and labor income. Non real estate invest- ment was obtained by deducting value of land, buildings, and improvements from total investment and consists primarily of the values of machinery and equipment, livestock, feed, grain, and supply inventories. Net farm income was obtained by deducting cash expenses from.cash receipts, and adjusting for inventory changes and value of family labor. Labor income was equal to net farm income less 5% on the average total invest- ment. These variables are important for certain types of studies, such as Optimal allocation studies employing functional analysis. Some other types of studies require more detailed factors, but the exploration into -74— the use of regression using these three important aggregative measures should be indicative of the validity of regression procedures for deriving certain other measures. Estimating Procedures The procedure employed predictive equations using least squares regression. The independent variables were restricted to data contained in the census. This was necessary in order to have census data for predicting the dependent variables. After the equations were determined, they were then used to predict three values. First the farm account mean value of the independent variable was plugged in to obtain a regression estimate of the mean value of the dependent variable. This was then checked against the actual mean value of the dependent variable of the farm account category used for the regression. Except for certain problems which will be explained later, these two measures (the regression predicted mean value and the actual farm account mean value) should have been equal in all cases where the regressions were derived using the same observations that were later plugged in for prediction. Secondly, mean farm account estimates adjusted by strata census weightings were plugged in as independent variables for the same regression equations that were used for farm account weighted estimates described above. The resulting values of the dependent variables served to check the adaptibility of the equations after some adjustments were made in the independent variables toward the direction of census values. As recalled from Chapter III, the stratification procedure was ' . J _ s __ L d L I . . p 1' r J 1 r V l s, i I} I r J I l s . . 7 7 f: .1, “‘1 \r-. -75.. designed to make two kinds of adjustment. Class of farm stratification had the effect of weighting account data.more heavily toward the values of farms in the lower classes. This essentially had the effect of scaling down farm size. Type of farm stratification had the effect of weighting more heavily toward cash grain and other non dairy types and less heavily toward dairy farm data. This moved the estimates away from livestock intensity and especially dairy intensity. These adjust— ments moved most of the estimates in the direction of pOpulation values as noted by the results of strata census weighted estimates in Chapter III. The comparison of the predicted dependent variables using strata weighted independent variables and the actual strata weighted value of dependent variables (computed directly from account data) indicated the degree of adaptibility of the regression equations for these adjust- ments. Certain other conjectural differences between account farms and census farms were not encompassed within the set of independent variables. These problems will be discussed near the end of this chapter. Finally, mean census values for the independent variables were plugged into the equations, and from these, pOpulation estimates were derived. The farm account, non weighted regression estimates, and the farm account census weighted regression estimates were then compared to the predicted census values in order to obtain notions as to the degree to which the stratification procedures adjusted account data in the direction of census values. -76- Strata Categories USed for Fitting Initially, fits were made using all account farms, all dairy farms, cash-grain farms, other field crOp farms, poultry farms, other livestock farms, and general farms. Also, runs were initiated for Classes I, II, III and IV separately. In the initial phases, runs were made by dairy classes separately, but later these were drOpped in lieu of using all dairy farms. These latter fits maintained more observations and covered a wider range in the independent variables. They were more adapted to making predictions where more than one dairy class was included. Fruit farms were excluded as a separate category because the variables selected for the regressions were more adapted to grain- livestock Operations than fruit Operations. Fruit farms comprised only a small prOportion of account c00perators. Independent Variables and Functional Form Initially, the equations were fitted using all of the characteris- tics which were compared in Chapter 3. All eighteen of these characteris- tics were used as independent variables, but only in linear form--that is, each variable was represented by one linear term in the predictive equation. After plotting residuals from a number of these runs, it appeared that improvement could be made by adding squared terms--thus fitting curvilinear relationships to the data. Also, the problem of singularity indicated that some variables were extraneous in explaining -77- the dependent variables. In View of the above considerations, a number of variables were drOpped, and the remaining were run incorporating X? and X3 terms for each variable. For deleting variables, a good deal of consideration was given to the simple correlation between each independent variable and the dependent variable as well as between each of the independent variables. Also the logical relationships between variables were given consideration. With the high degree of intercorrelation involved, the task of choosing variables was not easy. Also, the effect of combining certain variables into joint terms was unknown, but this consideration was believed to be too complex for this study. In all, ten characteristics were chosen as independent variables for non real estate investment, and eleven for net farm income and labor income. The variables chosen for non real estate investment were: .1. Corn yield. 2. Animal units 3. Total of specified expenditures #. Acres in corn 5. Acres in wheat 6. Productive man work units 7. Crop receipts 8. Livestock receipts 9. Crop acres harvested 10. Value of land and buildings For net farm income and labor income, value of land and build- ings was drOpped since it seemed logical that real estate value would be more highly associated with non real estate investments than with residual incomes. The simple correlations tended to bear this out. Also, number of milk cows and pounds of milk per cow were added as variables. This was done because it was thought that dairy cow numbers and milk production -78— per cow was influential on income beyond the effect brought about through animal units. For non real estate investment, on the other hand, animal units which is based primarily on livestock feed consumption were considered important enough in explaining investment attributable to dairy cow numbers and production that these latter variables were excluded. Although the new selection of variables did not answer all problems nor make all of the improvements which might be desired, they did improve the results over the linear runs. In all cases except labor income for all dairy farms, the R2 values appeared as high or higher with the additional x2 terms than with all eighteen variables in linear terms only. With X3 terms added, the R2 values were as high or higher than all runs where linear terms only were incorporated. In.most cases, however, the difference between R2 where X2 and X3 tenns were employed was small and was not considered large enough to compensate the additional complexity required for applying X3 values to the predictive equations. The comparison of runs using eighteen linear terms against the ten or eleven variables incorporating X2 and X3 terms was based on five categories of observations and three dependent variables or fifteen runs in total. In addition to the general improvement in R2 using selected variables and X2 terms, matrix singularity did not become a limiting factor in any of the runs using the X2 and X3 terms. This was true in spite of the high correlation between X, X2 and X3 terms. Also, the 3 addition of X2 and X terms resulted in more reasonable intercept values -79- in most cases. That is, non real estate investment was positive and net farm income and labor income negative for zero values of all included independent variables in many more cases where X2 and X3 terms were used. Problems Encountered Several problems were encountered in applying these equations that were not anticipated at the time that the regressions were run. Mention will now be made of some of these problems: 1. 2. Equations were fitted to observations of X2 using the values of (IE) as the means in the computations. In the case of census data, it is possible to obtain (22) for use in the predictive equation by squaring the mean of census X values, but (RE) which is usually a larger quantity is not directly available from census data. If precise values of the census variances (02) were known for each of the independent variables, then the value of (£5) could be obtained by adding the variance to the value of (i)2 i.e. (RE): 02 + (k)2. Since the true census variance was not known for most characteristics, this latter computation was not used and (it)2 served as an estimate of (IE) in the predictions. Census data for yields of corn and pound of milk per cow were obtained by dividing total production by the number of acres of corn or number of cows.' For stratification purposes, number of acres of corn and number of cows on -80- account farms were used to weight the average of each farm corn yield and milk production per cow into a weighted account average in the strata. The strata averages were weighted by census number of acres or cows to arrive at stratified estimates for the relevant categories. The regressions, on the other hand, were fitted using the average yield or average cow production of each farm as observations. For farms with no acres or cows this resulted in a zero average production per cow or corn yield and drastically lowered the estimate for the strata. The differential between these types of weightings resulted from two separate effects. First, farms without corn acres or cows registered zero for the value of these independent variables. In the future, improvement would likely result in the regression equations if variables were added to account for lack of dairy cows and/or corn production, then if corn yield and/or cow production values were entered as positive, the added variable or variables would be entered as zero. If corn yield or milk production were entered as zero, then a one would be entered for the values of these variables. The second effect comes about through a relationship between number of cows or acres and production.or sales per cow or acre. Farmers who kept only a few cows and were not -81- specialized dairymen showed lower milk sales per cow than commerical dairymen with larger herds. ‘A weighted average, based upon number of acres or cows, would be consistent with the census data and also be a more realistic indicator of per unit production. One possibility of solving this problem.would involve fitting a weighted regression. The weights would not, however, be consistent with those needed for the other independent variables. 3. Value of land and buildings was obtained as an arbitrary measure. This problem is somewhat unique for this variable as compared to other variables used in the regressions. As noted in Chapter 3, account farms tended to have lower real estate values assigned to them than did census farms. Since the equations were fitted using account values, the relatively higher census values did not impute prOper values to non real estate investments. This did not appear especially crucial in cases where the regressions were used, but is indicative that it might have been best to exclude this variable. In several instances, problems 1 and 2 listed above appeared troublesome. Additional computation followed using only linear values in two cases where problem 1 was apparent. In one case where problem 2 was apparent, the farm weighted values of corn yield and milk production per cow were plugged into the curvilinear equation, along with the (R? values. This was done in order to sort out the corn yield and milk -82- production weighting problem from the (X2) problem. Strata Categories Used for Prediction Regression estimates were made for five categories of observations: (1) all account farms representing classes I—IV'census farms excluding vegetable and miscellaneous farms, (2) dairy farms, (3) dairy farms of class II--using all dairy farm regressions, (4) cash-crop farms and (5) livestock other than dairy and poultry farms. Regressions were run for several other categories but estimates were not made. Other field crOp and poultry farms were not included primarily since they contained too few observations. General farms were excluded since the category lacks homogeneity of farm type and was not considered of research importance for this reason. Surprisingly, the regression results did appear relatively satisfactory for this category. Class of farm runs 'were made and are available in the Appendix, but regression estimates from these categories are not included in the discussion. Notation In order to shorten the discussion pertaining to estimates, the following notation will be incorporated. A familiarity with the defini- tions and discussion of these terms will be helpful for the discussion which follows: I\ - Y .A regression estimate of Y with Y as the dependent variable and 21' . . Rh serving as independent variables. In all ..83- cases the regression fits were made using non weighted farm account X values. Subscript notation - Two subscripts will accompany each I. Example "I _ _. Following“! the first subscript signifies the source of the 21‘ - - — in values applied to the fit. If these values were obtained from the farm account source, then F appears. If census 2 values were used, a C appears. The second subscript signifies the weighting of the data used in applying the predictive equations. If farm account weights were employed (non-stratified estimates), an F will appear. If census strata weights were used a C will appear. In all cases where a C appears, complete stratification as defined in Chapter 2 will define the strata groupings for which census strata weightings were applied. For? these weightings were applied to the X values to arrive at 21— ~ - - in. 0* F The following values will be used in the discussion.Ypr YFC ) 4h 4A A A . . and YCC' The comparison of YFF and £0 to YCC serves as an indicator of the use of stratification as a technique for obtaining representative account estimates of the three variables used in this section. Regression Results Non Real Estate Investment In general, the regression results for non real estate investment ~84- gave the least trouble and apparently the most satisfactory results of the three variables for which regression was applied. These results appear in Table 9. All Account Farms - By applying the census weighted account values to the independent variables, the regression estimate came within 10% of the census regression estimate. In contrast, the non weighted account values yielded a regression estimate 51% greater than the census regressing estimate. This indicates that stratification moves the account estimate considerably in the direction of representativeness and enough that it may be satisfactory for some research purposes. Dairy Farms Classes I—IV - The farm account regression estimate (non weighted) for dairy farms was 139 % of the census regression estimate. Using the census strata weightings for the independent variables, the regression estimate came to within 6% of the census regression estimate. Based upon 1959 data, census strata weightings applied to dairy'farms should give a reasonably representative estimate of non real estate investment for dairy farms. Dairy Farms of Class II - The stratification procedure for class II dairy was confined to weighting by cropland harvested. For many of the independent variables, the effect of this weighting was to increase the account estimates. For this particular strata, both crop receipts and livestock receipts increased when strata weightings were employed. Using the regression non real estate investment actually deviated more from the census employing strata weighted independent variables. This -85- result suggests that the non crOpland harvested weightings give a better estimate of non real estate investment than by using crOpland weightings. The regression estimate using the non weighted account estimates of the independent variables deviated only 6% from the regression estimated census value of non real estate investment. Based on 1959 data, this suggests that the class II dairy category is quite representative of the census and based on 1959 results should give a reasonable mean estimate of non real estate investment of census class II dairy farms. Cash Grain Farms - The regression estimate of non real estate investment using class of farm census weights to derive the independent variables gave a closer estimate to the census regression estimate than the account regression estimate without census weights. However, this difference was still too large to be considered for representative use (202% of the census). Based upon this 1959 observation, it appears questionable that account data from cash grain farms would give a reasonably representative estimate of the components of non real estate investment for all cash grain farms. Other Livestock Farms - Improvement toward representativeness came about using class of farm'weighted independent variables. using these weights, the regression value deviated from the census regression value by only 4%. Based on 1959 data, census class of farm weightings applied to other livestock account farms show promise for deriving estimates of the components of non real estate investment. s I a 1 1 x ’ \ .__).' J 7 n u I, 1 a; J 1 .l_.‘ 1 4 L l U .- i) -86- Net Farm Income In the case of each of the five categories of farms for which regressions were applied, stratification did not show as much promise for net farm income as it did for non real estate investments. The results appear in Table 10. All Account Farms - The regression estimate using census s rata weightings for the farm account values of the independent variables, was 16% greater than the census regression estimate. This is considerably closer to the census estimate than the regression estimate without strata weightings for the farm account values of the independent variables. The stratified estimate is, however, too large to be relied upon for most research purposes. Dairy Farms Classes I-IV - For dairy farms of classes I—IV, the strata weighted farm account values of the independent variables yielded a regression estimate 12% greater than the census regression estimate. This is considerably better than the non weighted account regressions estimate, but is marginal for use as a reliable estimate. Dairy Farms of Class II - The non crOpland harvested weighted regression estimate was about 5% closer to the census estimate than the strata weighted regression estimate. Based on 1959 data, there is indication that a non weighted estimate of net farm income derived from class II dairy farms should be relatively representative of class II dairy farms in the census. u - ‘7‘ . ; ... , t A J a— TABLE 9 Comparison of Farm Account, Farm.Account Census Weighted and Census Regression Estimates of Non Real Estate Investment by Farm.Categories - Michigan 19591 A 22 7A 3 A u Category of Farms ‘EEE .EEC .399 1. Classes I-IV Less A $23, 560 $17,181 $15,577 R2 = .83 Vegetable & Misc. % of YCC 151% 110% 2. Classes I-IV Dairy’ A $22,196 $16,890 $15,978 R2 = .82 % of YCC 139% 106% 3. Class II Dairy5 A $31,358 $32,018 $29,707 (Same Eq. as #2) % of YCC 106% 108% u. Cash Grain Classes IRIV $20,208 $16,024 $ 7,93u R2 = .87 % of YCC 255% 202% 5. Other Livestock Clas es I—IV$3O,43u $20,654 $19,950 R2 = .93 % of cc 153% 104% Regression using selected X and X2 terms. Regression estimate of farm account mean value of non real estate investment, using farm account mean value of independent variables. 3 Regression estimate of farm account strata weighted mean value of non real estate investment using the farm account census strata weighted mean values of independent variables. Regression estimate of census mean value of non real estate invest- ment using census mean values of independent variables. 5 Classes I-IV dairy regression equation used with class II dairy values of independent variables. Census strata weights by cropland harvested. -87- TABLE 10 Comparison of Farm Account, Farm.Account Census Weighted and Census Regression Estimates of Net Farm Income by Farm Categories - Michigan 19591 A A A 2 3 A Category of Farms YFF YFC YCC 1. Classes I-IV Less A $ 5,559 $ 3,593 $ 3,147 R2 = 055 Vegetable and Misc. % of YCC 175% 116% 2. Classes I-IV Dairy ,‘ $ 6,314 $ h,61u $ u,129 32 = .62 % of ICC 153% 112% 3. Class II Dairy5 A $ 9,146 $ 9,569 $ 8,520 (Same Eq. as #2) % of YCC 107% 112% h. Cash Grain Classes I-IV $ 3:701 $ 2,504 $ 1,552 R2 = .87 5. Other Livestock Classes $ 1,512 $ 42.00 $ 240 R2 = .hl I-IV Regression using selected X and X2 terms. Regression estimate of farm account mean value of net farm income, using farm account mean values of independent variables. 3 Regression estimate of farm account strata weighted.mean value of net farm income, using the farm account census strata weighted mean values of independent variables. Regression estimate of census mean value of net farm income using census mean values of independent variables. 5 Classes I-IV dairy regression equation used with class II dairy values of independent variables. Census strata weights by crOpland harvested. -88- -89- Cash Grain and Other Livestock Farms - Percentages relative to census regression estimates are not listed for these categories. Some difficul- ties were encountered with the regression equations. Also with the low base values of the census estimates, the percentage differences could give a distorted picture of the absolute differences. In ab- solute terms, the difference in the strata weighted account regression estimate and the census estimate appears sizeable for cash grain farms, but within reasonable limits for other livestock farms.Due to the difficulties with these regressions, the results are less conclusive than the above three categories. Labor Income Due to low R2 values in all except one case, and difficulties encountered in applying the regressions, the discussion for labor income will be very brief. For reasonssdmilar to those described under net farm income, percentages were not listed for cash grain and other livestock farms. In all five cases, the weighted account regression estimates deviated too far from the census regression estimates to appear reasonably representative. These estimates appear in Table ll. Limitations and Other Considerations Regressions Not USable for Other Years It must be recognized that when one years observations are used in fitting a regression equation to data, the regression equation will TABLE ll Comparison of Farm Account, Farm.Account Census Weighted and Census Regression Estimates of Labor Income by Farm Categories - Michigan 19591 As 23 A 3 A. 4 Category of Farms ‘EEE .EEQ 'Egg 1. Classes I-IV Less A $2,195 $1,256 $1,017 R2 = .39 Vegetable & Misc. % of YCC 216% 124% 2. Classes I-Iv Dairy ,\ $2,252 $1,52h $1,163 R2 = .3u % of YCC 194% 131% 3. Class II Dairy5 A $3,457 $3,761t 2:987 (Same Eq. as #2) % of YCC 115% 126% u. Cash Grain Classes I-IV $—1,938 $-2,716 $—3,463 R2 = .85 5. Other Livestock Classes $—2,65O $—3,118 $~2,524 R2 .35 I-IV Regression using selected X and X2 terms. Regression estimate of farm account mean value of labor income, using farm account mean values of independent variables. 3 Regression estimate of farm account strata weighted.mean value of labor income using the farm account census strata.mean values of inde- pendent variables. Regression estimate of census mean value of labor income using census mean values of independent variables. 5 Classes I-IV dairy regression equation used with class II dairy values of independent variables. Census strata weights by cropland harvested. -91- only be useful for that years data or perhaps at best for years in which prices, technology, and weather conditions are quite similar. Even if variables of this type were included in the fit using only 1959 data, the lack of dispersion of these time variables would likely prevent the equations from being good predictors in years when prices, weather, and technology are quite different. It is thus emphasized that the initial purpose of using regression in this chapter was to set a predicted estimated base from which stratified estimates and nonstratified estimates could be compared. 1959 was somewhat unique from the standpoint of farm prices and weather conditions. Relative prices between agricultural commodities varied considerably from years on either side of 1959.1 Weather condi- tions varied throughout the state. Many of the farms in southern tier counties obtained low cr0p yields due to lack of rainfall.2 These counties contained a large share of the dairy and other livestock cooperators in the account project in 1959. The purpose of mentioning these conditions in 1959 is for the reader to appreciate the effect of these interyear conditions on the regression equations. The effect on the b values for the various independent variables is not difficult to speculate when net farm income or labor income are dependent variables and certain commodity prices make large shifts relative to input prices. lMichigan Dept. of Agriculture and Crop Reporting Service, ZMichigan Agricultural Statistics, Lansing, Michigan, July 1963, p. 4%. gFarijanagement Ektension, Farming Today,.Areas 1-17,,AEC 777-786, Michigan State University, Cooperative Extension Service, E. Lansing, Michigan, 1960. -92- Variables Restricted to Census Availability When independent variables are chosen for a regression fit, the use of economic logic is of uppermost importance in the selection. Often, this consideration is not given enough importance. In this study, the consideration was not overlooked, but the methodology required that the independent variables be restricted to those contained in census. This selection was not always consistent with a selection that would be the most directly pertinent from the standpoint of economic theory or of logical relationships. Problems of Census - Farm.Account Parameter Differences Another problem.is involved in using the regression equations to predict pOpulation estimates. Certain differences likely existed between account farms and census farms which were not expressed in the variables. It appears that these differences are not well encompassed within census characteristics and cannot easily be incorporated into predictive equations relevant for the pOpulation. In the case of non real estate investment, the included variables appeared to explain differences within the account sample relatively well as noted by the R2 values. These variables account for overall volume, and relative volume of individual enterprises. They do not, however, account for differences in capital intensity within given enterprises. Differences may exist in capital-labor substitution, such as the -93- use of more machinery and automated operations. Differences could exist in the value of livestock-~especially breeding and dairy stock. Also, considerations of excess capacity, well-planned facilities, and the ability of the Operators to obtain good buys when purchasing inputs should not be forgotten. From an accounting standpoint, the rate of depreciation will have a definite bearing on the value of the capital items. For net farm income, and labor income, many of these same considerations apply, but in addition, cost efficiency above and beyond that involved with the capital inputs must be considered. Although two of the variables used, corn yields and pounds of milk per cow, were associated to a degree with cost efficiency, they do not cover all facets of cost efficiency even for the enterprises directly involved. Empirically, it has usually been established that cost per unit of output of corn and milk is lower as yield per acre or production per cow is increased. The theoretical basis for this rests in lower fixed costs per output unit (for example cow maintenance) in the case of high production operations. Nevertheless, beyond this cost consideration, variability can exist in cost of production. Sharp, well-planned buys ing, or substitution of lower cost inputs, such as feeds, can often reduce production costs without an accompanying increase in yields or output per head of livestock. Product marketing must be especially considered in the case of livestock. Large differences can come about in income due to timing and execution of sales. -9h— Problems of Weighting and Use of (i)2 The use of (X)2 values as estimates of (X5) and the use of per farm observations of corn yield and milk production per cow in some instances caused problems which were discussed at the beginning of this chapter. For most of the predictions found in the chapter, these problems did not appear troublesome. In the cases of net farm income and labor income estimates for both cash grain farms and other livestock categories, problems appeared. These problems were detected through the comparison of the non weighted account regression estimates with the actual mean values computed for the categories. In all four of these cases considerable variation existed. When (XE) values and farm observation values of corn yields and milk production per cow were used, the equation did check out. In the future, estimates could be improved if these considerations are accounted for. Future Use of Regression Approach The regression approach offers several important uses for future research using farm account and census data. In addition to estimating census values of census excluded variables in census years, it should also be possible to estimate census values in non census and projected years. In addition, regressions using account data should find use for allocation work. It is suggested that additional work is necessary in order to make predictions for years after 1959. The problems discussed involving —i -95.. weighting of variables and use of curvilinear forms should be considered. In addition, an effort should be made to utilize independent variables which will account for some of the major account census parameter differences previously described. Although this would not be an easy task, a study of simple corrElations and use of joint variables in the regressions might lead to possible improvement in the regressions. For regressions which are applicable to years other than the one for which the equations were fit, variables relevant to weather and prices, and possibly technology should be included. Even though the census does not present this information, data from other representative sources can be used in the fits and the predictions. Also, at least several years account data should be used in the fit in order to provide dispersion in these time variables. CHAPTER V USE OF FARM ACCOUNT DATA FOR RESEARCH PURPOSES Value of Farm Account Data The value of farm account data for research is dependent upon the specific requirements of any given research project. The needed data as well as the degree of accuracy and representativeness of this data may vary depending on the specific research project. Since this study does not outline or prOpose specific projects utilizing account data, it is only possible to make some generalizations concerning the use of account data. In the final analysis, the individual user must decide whether certain account data will fit his particular needs. Problems of Representativeness The major problem in using account data is not one of accuracy. Since the accounts are used directly by the farmer cooperators for business purposes, there is relatively strong incentive for accuracy. The problem of representativeness is a separate problem. .As indicated by the findings of this study, the account sample is neither a simple random sample, nor a stratified random sample of the greater population of farms. A few individual strata do approach representativeness. -96- -97- Not all studies require representative data. Studies of a nommiive nature, involving allocation of resources, need not be inhibited by data representing a better than average group of farmers. Likewise, descriptive studies which purport to describe better than average farm Operations, do not hinder the use of account data. Studies, on the other hand, which are aimed toward prediction or description of situations involving average farm Operations have an inherent need for representative data. Representativeness of Account Data The question could then be asked, just how representative is farm account data? Based upon 1959 data, farm account farms of classes I—IV averaged 121% of census farms in these classes in total acres per farm. Cooperators averaged 128% of the census in acres of crOpland harvested, 155% of the census in terms of animal units per farm, 118% of the census for corn yield per acre, and 123% of the census in milk production per cow. These figures indicate that in 1959, account c00perators had larger farms, more crOp and livestock intensive farms and in addition displayed higher production per crOp acre and per animal than census farms of economic classes I-IV. Account Data Permits Observation Selectiveness Although several sources provide census type data plus additional cost, investment, and income data excluded from the census, the farm account provides about the only other source of data that can be derived -98- by specific type of farm and class of farm categories. In addition, the account sample can be sorted into as fine a delineation as desired on the basis of a large number of criteria. For this reason, account data are particularly applicable to studies which require a specific relatively homogeneous population. A problem may arise, however, in Obtaining enough account Observations to provide a reasonable size sample for a specified criterion. Use of Account Data to Supplement Census Farm account data can be used to supplement census data in several ways. It can be used to provide estimates for census excluded data. Another use is found in providing data for non census years or to supplement census data in making future projections. Supplementing Census Excluded Data Chapter 3 dealt primarily with the comparison of account values to census values for eighteen characteristics. The usefulness of such an analysis might be questioned on the grounds that the data are already available from the census. The real value of such an analysis should lie in the inference which can be made toward related variables which are not in the census. For the various categories of farms the feasibility of using either stratified or non stratified estimates of census excluded variables can be considered. Although space does not permit an exhaustive application Of this scheme to all variables pertinent for research, one example will -99- be cited. For a large group of farms, dairy cow investment per dairy farm is largely a function of number of cows and productive capacity per cow. For the aggregate, problems such as cow age, and registration value would likely not be significant. It is possible to use account values to fit a simple regression relating production per cow to value per cow. Census average production per cow could then be used to adjust the mean farm account dairy investment to be consistent with the average production per cow in the census. Secondly, the differential between the number of cows per farm in the account and this same estimate in the census could be used to adjust the total milk cow investment per farm.in the account to be consistent with number of milk cows per farm in the census. These two adjustments should yield a representative estimate of milk cow investment per farm for a particular category of farms and a particular year. Other characteristics excluded from the census including certain non specified expenditures and other livestock ins vestments, could be treated similarily to this with some modifications. It is suggested that stratified account estimates will form a better basis for adjusting these data than non stratified estimates. Account Data for Intercensus Years Farm account data can be used to derive estimates for the census in years when the census is not taken. For many characteristics the relative differences in the farm account mean values could be used to adjust data from census base years to inter census years. In general, a stratified account estimate will more nearly reflect census changes than a non stratified estimate. When a scheme Of this type is employed, ~100- caution must'be taken to see that the inter year shift in account values would be reflective of census shifts. There are several kinds Of shifts and trends which could lead to a distorted adjustment. Included are: l. A shift in account c00perators in various strata without an accompanying shift in the population. 2. A shift in the number of farmers in the various strata in the pOpulation without a similar shift within the account sample. 3. A shift or trend in the differential between the account and the census over time for certain characteristics. If a non stratified estimate is used for adjustment then inter year shifts which strongly influence particular types of farm categories will tend to distort the adjustment more than if stratified estimates were employed. Stratified Account Data, Census Data and Projections Agricultural economists are Often called upon to make future projections and predictions. Both census and account data provide information which can be used for this purpose. In addition to providing more characteristics than the census, the accounts also have the advant- age of more Observations for a given trend projection. Account data are available annually whereas census data are available only every fifth year. By using both census and account data, projection work should -101- have added potential. Though such a scheme adds complexity, the supplementary effect of the additional considerations brought to light when two sources Of data are utilized should enhance projection work. Account Data and Regression Analysis A very good prospective use of farm account data in research is for situations which call for a relatively large number of individual observations. This is very much the situation where regression analysis and functional analysis are employed. In Chapter A, regression analysis was used primarily as a basis to evaluate stratification as a tool for adjusting certain census excluded characteristics. Another approach for Obtaining representative estimates from the account sample would be the direct use Of regressions using account observations for fitting and then plugging census values plus representative values from other sources (such as price and weather information) into the predictive equations. This would be similar to the procedure followed in Chapter 8, except that certain additional considerations are suggested for using the regression estimates directly. Regressions of the type found in Chapter 4 were Of a one year cross sectional nature. Such regressions would only be usable in the years that the regressions were run or very similar years. It would be possible to fit the regression using several years account data. If both investment and income variables are derived, . Itru n.‘ [in 'r -102- the possibility of a two-stage model such as one including the lagged effect Of income on investment might also be considered. Certain time variables such as input and output prices along with weather indices would undoubtedly reduce the residual where several years data are applied. Where the independent variable concerns income, these price and weather variables might best be included jointly with the respective crop input variables since income is jointly affected by these variables. Such data, though not in the census, are available from several sources. It is more difficult to incorporate technology, especially that which is cost reducing rather than output increasing. SuCh relationships would likely show up as a function of time. It is further suggested that a weighted regression (using census strata numbers for weights) should yield a regression more applicable to the pOpulation situation than a non weighted account regression. The weighted data would be applied to fitting the equation. This is in constrast to the technique in Chapter 4 where weighted data 'were applied in the predictive equation, but the equations were fitted using non weighted data. To illustrate, if ten account Observations represent lOO census farms, then eadh observation would be weighted to represent 10 farms in the fit. Such weights placed on all observations would have an effect comparable to deriving a stratified estimate of the dependent variable directly. Certain technical problems Of weighting and use of squared coefficients which were encountered in the regressions in this study, Aft.‘ _lO3_ should be given careful consideration. These problems were discussed in Chapter 4. There are other problems which also add difficulty to the scheme. Census data, which are presented at five year intervals, place a limit on years in which the predictive equations can be applied using direct census values. In other years, interpolated or projected values would be required. Another problem which requires additional consideration for the regressions is the need to express elements Of enterprise, cost efficiency and enterprise capital intensity within the set Of independent variables. Variation in cost efficiency between various farmers can come about through substitution Of more economical inputs (factor- factor substitution) or through better bargaining in the purchase of inputs. Differences in capital intensity can come about primarily through the substitution of capital for labor. Examples Of this latter includes larger field machinery or automated feeding Operations. The fact that account farms are larger, show better yields and livestock performance, and also c00perate with the Extension Service suggests that COOperators on the average would employ up to date technology and utilize cost efficient techniques in production. The problem is that considerations Of these types are not easily taken into account when using census data. Costs of Farm.Account and Sampled Data Sampling as a.method of obtaining data has received little mention up to this point. Although this method of obtaining data yields ~104— a great deal of flexibility, it is Often very costly. The purpose of this section is to compare costs of using certain data with costs of comparable data from sampling. Costs of Obtaining Sampled Data Many factors affect the cost per questionnaire from sampling. Such factors as sample size; questionnaire deveIOpment; data tabulation and processing; nature Of the sample i.e., random, block random, group selection, replacement techniques - and presampling costs are all important considerations. For purposes Of this writing, however, a total cost of $30.00 per questionnaire will be assumed to cover all considerations. Costs of Obtaining.Account Data According to data processing personnel at Michigan State University, the cost of retrieving, sorting, listing and totaling fifty items of stored account data from_all account farms as the sample stood in l964, should be less than $100.00.1 If it is also assumed that strata weightings can be loaded and stratified account estimates also derived from all account farms for this cost and that approximately fifty informational items (or characteristics) would be obtained from a questionnaire, then three to four sampled questionnaires would be approximately equated with the cost of Obtaining stratified account informa- tion from all account COOperators. lInformation courtesy of Mrs. Arlene King. . :Alré -105- Presampling Considerations One of the big problems involved in sampling is the identification Of farms belonging to a given population or given stratum. Various means have been devised for doing this. In some cases, where all farms above a certain size in acres or gross income are desired, it is possible to utilize an area survey and use random dots on maps or random numbers for picking counties, townships, sections, and quarter sections. All farms which do not meet specified criteria can be dropped, but such techniques must be conducted carefully to avoid biases. If the pOpulation of farms to be utilized is more specific, other means must be used to locate farms. Often, livestock and dairy associa- tions, county extension personnel, banks, dealers, and AJS.C.S. Offices are utilized to locate farms which will meet the qualifications of a given population. When no other means are available, it is possible to use a mail survey to pre—identify farms and then use a personal interview to sample a portion of the pre—identified farms. The costs of pre-identification could vary to a great extent. A closely related problem is that of strata identification where stratified sampling is employed. In some studies using sampled farm data, farms are placed into strata ex post to the survey and the possibility of utilizing the technique of Optimum allocation is excluded. Where Optimum allocation is employed, the variance is minimized and the sample size necessary to Obtain a given reliability is reduced.2 2Cochran, William.C.,_§§mpli g Techniques, John Wiley and Sons, New York, N. Y., 1960, pp. 65-107. M —-.‘ -106- For many purposes utilizing farm data, the necessary information for identifying farms for specific strata is not available. The cost of pre-identifying these farms by strata might exceed the gain Obtained by employing Optimum allocation. Other Considerations Time Consideration - Another aspect involved with sampling is the time consideration. It is not uncommon for studies which call for large samples in the field Of agricultural economics to require more than one year for obtaining and processing the data. For some purpose, this delay will mean "stale" results which could have been far more useful if published earlier. This is a consideration which in some instances might favor the use of farm account stratified data. The account data can be quickly Obtained and processed once the year end summary data are available. Other Cost and Benefit Considerations - Looking at the cost Of research from a broad point of View, there are costs and benefits which result from accuracy, or inaccuracy of data that are attributable to the application of the results. Such costs and benefits are unique for each individual study and the application which is an outgrowth of the Study. Sample Sizes and Costs Table 12 lists sample sizes which will give a probability of .50 that simple random estimates will deviate from census values by as TABLE 12 Sample Sizes from Simple Random Samples which Will Give a 50% Chance of Differing from Census Values by at Least as Much as the Farm.Account Stratified Estimates Differed from the Comparable Census valuel’ Other Livest c All Account Dairy Farms Dairy Fa s Cash Grain Classgs Characteristic Classes I- Classes I—I Class II Classes I-IV3 I-IV yfi Corn Yield/Acre 3 A 2 6 2 Wheat Yield/Acre 352 5300* 24 271 10 Mhlk/Cow 8 u 2 3 l Tbtal Acres 126 1200* 9 33 600* Cropland Harvested 155 2500* 24 33 400* .Acres of Corn 2O 4 l 6 11 Acres of Wheat 80 9 250* 16 270* Number Of Milk Cows 1600* 32A 10 82 7 Litters of Pigs 54 4 69 14 24 Animal Units 19 129 5 2 6 P.M.W.U. 8 16 7 2 2700* Total Specified Expenditures 137 9 100* u 170 Value Land and Buildings 2 l l l 2 Bushels of Wheat Produced 327 16 325* 24 325* th. of Milk Sold 187 6A 25 57 9 Crop Receipts 4h 9 225* 108 135 Livestock Receipts 35 2 7 6 215 Total Receipts 116 16 43 15 325* Census Excluded Variables - Regression Estimated2 Non Real Estate Investment 32 75 14 2 263* Net Farm Income 233 29 16 19 2916* Labor Income 998 35 3O 22 18 See Appendix II for formula. Farm account estimates derived using type of farm and class of farm weightings. Also, cropland harvested for dairy classes II, III and IV.‘ All relevant weightings applied to each category. Census estimates derived through regression using farm account strata weighted values of the independent variables. 3 All sample sizes between one and thirty would require upward adjustments to compensate for t value differences. Downward finite population correction included. -107- -108- much or more than the stratified account values deviated from census values in 1959. This analysis assumes that census values are correct population values and also assumes that farm account standard deviap tions represent pOpulation standard deviations. Since Table 12 is self explanatory, it is not necessary to specifically discuss each Of the various sample sizes. It should be pointed out, however, that sample sizes which exceed three or four would involve a higher cost (based upon the previous assumptions) than stratified account information from all account c00perators or from.a group of account farms based upon type or class. From this standpoint, account data appears to be an economical source for acquiring research data. In several instances where large sample sizes were calculated, additional computations for sample sizes utilizing Optimum allocation followed. In most cases these involved only a fraction of the sample number for simple random sampling. Problems of preidentification and low number of Observations in many strata almost eliminates the use of this technique for many research problems in agricultural economics. For some isolated problems, the use of the technique might warrant pursuit. Other USes of Account Data Studies of Farm Organization Utilizing one or several of the major categories suggested, studies in resource organization could be one of the better uses for A“ ..., -109- account data. Two types of studies of this nature will be discussed. Even with possible biases from account data, organization studies which tend to be normative rather than descriptive or predictive might in some cases utilize account data to good advantage. FUnctional Analysis - One method of studying resource organization involves fitting of a regression to a set of empirical data. Once the predictive equation is established, the equation can be used to detere mine Optimum combinations of resource employment. Also, values can be placed on marginal additions of the various factors. Such information can be useful for farm.management and policy work. This kind of study would work best if type of farm categories were utilized because Optimum resource employment varies between enterprises. Needed variables include net income, costs, investments, land and manpower inputs. With all evidence indicating that account farms make more money thannon c00perators, an account sample might cluster closer to the Optimum employment of resources than the average farm or a group of non c00perating farms. This does not necessarily make the regression less useful for application to a greater pOpulation of farms. If the account farms do better primarily because of size and combination of factors - the results are useful for inference to other farms. The problem arises if account farms are more efficient in the use Of resources (gain more output and/or income from a given set of inputs) than non account farms. Even then the problem.may not be exceptionally crucial unless account farms are relatively more efficient in utilizing -110- some resources than non account farms. For example, account farms might be relatively more efficient in utilizing labor, and capital than non COOperators. If this consideration can be ruled out, account data could be valuable in advocating resource combinations which will more nearly maximize returns. Such information might also be an indication of the expected employment of resources by non cooperators in some future period of time. In fact, it might be interesting to utilize account samples in regressions which are census weighted by class of farm to see to what extent the different weighting affects the estimated coefficients. If this type of work incorporated successive year’s data in such a way as to take account of price and weather effects, the consistency of the results between the weighted and the unweighted regressions might have a direct bearing on the application to other farms. Linear Programming — With linear programming empirical farm income data per se are not utilized. However, information is needed on returns per enterprise unit, costs, input-output data, resources and other restric- tions. Details of the assumptions and application of the technique will not be explained here. With the new "Telfarm" information, a good deal of input-output information such as livestock feed conversion, crop input-yield data, along with yield information already available, should be Obtainable for use in programming. The solutions and subsequent incomes can be checked against empirical account results. Resulting program solutions would be somewhat normative in nature, but it is possible that some -lll- predictive value could be made of them also. In future years it should be possible to study the lag in some of the more important input-output data, such as crop yields and livestock feed conversions, between account farmers and non c00perators. The Economic Research Service and Statistical Reporting Service provide publications on the type of information which can supplement census information. If an average lag in years, or a trend in the lag can be established, it might be possible to predict on the basis of these trends a time period when such technical coefficients would be applicable to the greater population of farmers. Then by making additional assumptions pertain- ing to demands, prices, technologies, and weather conditions for that future period, a mechanism might be set up to do a limited amount of prediction. Descriptive Studies The use Of account data for descriptive purposes is especially difficult when comparable data are not presented in the census. This is especially the case for non real estate investment and income characteristics of the type analyzed in Chapter 4. Such variables as livestock investment; machinery investment, purchases, maintenance, depreciation, and repair, as well as improvement repair comprise a few Of these important variables. Although Michigan Agricultural _§tatistics along with other USDA publications do present data for the aggregate of Michigan farms pertaining to livestock investment, net incomes, and some census excluded costs - the reliability Of these -112- data gained from.relatively small samples might be questioned. Further- more, such data are not available for portions of Michigan Agriculture such as commercial farms of specific types and classes. For some of these census excluded variables, such as certain investments, a description from c00perator farms might serve as an indicator of expected values from non cooperators in a future period, provided price level adjustments are made. For these variables, the future period applicable to the population would be much more in question than is the case with census included variables, inasmuch as base information would be lacking for establishing the lag between non c00perators and cooperating farmers. For the income variables, this lag prediction technique would be more precarious than for many other variables due to the many dynamic influences which affect income. FUiure Uses of Special Accounts The new "Telfarm" program includes special accounts for out- standing credit, family living costs, and labor costs, in addition to the special enterprise accounts. The degree of participation by cooperators in these special programs and the degree of representativeness of the c00perators is a subject for future study. However, some possi— bilities for research do bear mention. Credit studies could be conducted to determine the amounts and sources of outstanding farm credit. Type of loan information could be included. In addition, present and future capital needs based upon Optimum requirements could be consolidated into such studies in order -113- to establish predictions Of future credit needs in agriculture. Such studies would serve an interest to both farmers and lending agencies. Also while such information might not be representative, it would reveal the need for further types of credit information on the part of large numbers Of farmers. Labor information, if studied over the years, could be used to predict future needs of labor in agriculture along with problems Of outmigration. Such studies would serve an interest to both farmers and policymakers. Family living accounts could serve as a source of information which would be of interest to homemakers. Studies using this kind of information might even find use for nonfarm as well as farm families. Farm Account Paneling Another possibility Of farm account data involves the use Of account information, along with survey type information from cooperators which will be coordinated with the direct account information. This procedure has already been used to some degree for intentions studies. Account c00perators were asked their intentions to purchase certain equipment. Later, the account records were studied to determine the degree to which these intentions were fulfilled. This type Of work Opens up a new approach to prediction procedure. The use of supplemental panels might find use for other purposes as well. . ..rbrl. -\ ~11h- Other Suggested Future Studies Throughout this chapter, suggestions have been made for employing farm account data for future research work. This study was aimed toward the general use rather than any specific use of future account data. This study dealt entirely with mean and total account as well as census values. A study dealing with farm account and census distributions Of certain characteristics would also be of research interest. This information would give some guidelines for logical research Observation categories. Also, it would be Of interest for regression techniques applied to account data. Another possibility for study would be a comparison of account cooperators according to the time that they joined the program. For some purposes a sample Of recent joiners might yield relatively representative estimates. CHAPTER VI SUMMARY One of the big problems Of doing farm management, production economics, and farm policy research in the field of agricultural economics is obtaining good, reliable, yet representative, input-output, cost, income, and investment data. The Agricultural Census, taken every fifth year, excludes some of the very important cost, income, and investment measures. The Michigan Mail-In Account program fills in many of these measures which are missing from the census. The problems with account data are that the c00perating farmers show larger size, greater livestock intensity and better than average performance when compared to similar census economic classes. The possibility of adjusting account data to be representative of commercial Michigan farms of classes I—IV would Open up the use of these data for studies which explore the resources maintained and utilized by specific groups Of Michigan farms. Furthermore, these data could be used as a basis for determining efficient utilization of Michigan agricultural resources and returns from such uses. Data from both the 1959 census of agriculture and the 1959 Michigan Mail-In Account Project were available with the latter information on IBM cards. This study using 1959 data exposed problems and set a basis for using the more recent 196A census and farm account information. -3_15.. lllf. __\ -116- The Objectives of this study were to evaluate stratification procedures as a means of adjusting account data to be more representative of farms included in the census. .Also, other means of Obtaining representative estimates, including regression, were explored and discussed. Prior to evaluating stratification as an adjustment technique, it was necessary to classify and select characteristics to be used as a basis for study. Also, stratification criteria needed to be established for use in strata weightings. Selected characteristics included those which were in both the account sample and the census and several‘Which were in the account but not in the census. These latter required separate treatment. The characteristics selected which were in both the account and the census were: (1) performance measures (corn yields/acre, wheat yields/ acre, and milk production/cow), (2) input and investment measures (total acres, acres of crOpland harvested, acres of corn, acres Of wheat, number of milk cows, litters of pigs, animal units, productive manwork units, census specified expenditures, and value of land and buildings), (3) output and returns measures (bushels Ofwheat, hundred— weight of milk sold, crOp receipts, livestock receipts, and total receipts). Three measures which were not in the census were studied. These were non real estate investment, net farm income, and labor income. Several alternatives were available for stratification. The two basic alternatives involved an area sort, or a type of farm-economic .1 .o' u.. .F'flfljfifiz‘vdfiuuca ~117- class of farm sort. After study, the latter alternative was chosen. In addition, several larger dairy classes were additionally sub-stratified by crOpland harvested. This latter added little improvement to the estimates but did exploit the possibilities of stratification more fully using information which was available from the census. Of all the various farm categories compared, dairy farms appeared to offer the greatest possibilities for research. These farms were well represented in the account sample. In addition, the category was the most homogeneous from the standpoints of enterprise inputs, products, costs, and returns. Furthermore about half of the characteristics compared were within 10% of the census value when strata weights were utilized in deriving the estimates. Other type of farm categories showing promise were cash grain and livestock - other than dairy and poultry farms. In addition, the all farm account category showed promise for limited research. Categories showing little research potential included other field crop and poultry farms due to so few observations. General farms were too heterogeneous as a research category. The orientatknlof this study prevented con- clusive results pertaining to fruit farms as a research category. The improvement of characteristics toward representativeness brought about by stratification varied between Observation categories. In general, however, the performance characteristics were not improved sufficiently. Some crOp input characteristics did show promise. Total and cropland acres gave relatively good estimates after stratifica- tion, but acres in individual crops showed less promise. CrOp receipts -118- were low for the entire account sample and the classes, but were high for the individual type of farm categories. Stratification did not improve the estimates sufficiently in most cases. Livestock receipts were high and stratification did improve the estimates, but not sufficiently enough to make good representative estimates. Total receipts did show considerable promise when stratification was employed. For dairy categories, stratified estimates Of dairy cow numbers appeared quite representative. This was not true for other classes of livestock and hence animal units did not give as representative estimates as number of dairy cows. Productive manwork units as an aggregate measure of inputs was improved by stratification, but not enough to appear reasonably representative. The total of specified expenditures appeared reasonably representative for most categories when stratification was employed. Perhaps the least promising of all characteristics was value of land and buildings which is inherently low in the account sample. The effect of stratification was to make these estimates still lower. In order to gain additional insight as to the representativeness of account data relative to census data, probabilities that the deviations between account estimates and census values would occur from stratified random samples of the same sample size and strata prOportion as found in the account sample were determined. For the most part, these were of low magnitude (less than .50) or less than 50-50 chance that these differences would occur from stratified random samples in most cases. -119- Chapter 4 took up the problem.of evaluating stratification procedures for characteristics excluded from the census. In order to establish a census value from which account census weighted and non- census weighted account estimates could be evaluated, multiple regres- sions were used. Non real estate investment, net farm income, and labor income served as dependent variables and characteristics both in the census and farm account were used as independent variables. Relationships were estimated for all account farms, dairy, cash grain, and other livestock. The equations derived from these runs were used to predict census values. Other fits were made but not used for prediction. These were: each class of classes I-IV, other field crop, poultry and general farms. At first the equations were fitted using all eighteen characteristics which were compared between the account and the census. Later, only a selected number of these were chosen with some squared and cubed terms also incorporated as independent variables. These latter runs gave better R2 values, better intercepts, and less problem with singularity than did the linear runs using all eighteen independent variables. Several problems were encountered in applying the equations for prediction. Corn yields and milk production per cow were weighted differently in fitting the regression than they were in deriving estimates for comparison. For the comparison, corn yields were weighted on the basis of acres Of corn, and milk production per COW'WaS based -l20- On the number of cows. These weightings made estimates comparable to the census values from a weighting standpoint. In the regression, however, each account farm served as an Observation, hence these values were weighted by farms without consideration Of the number of acres or cows on the farm. A.further problem became evident in the use of squared terms. The equations were fitted using values of (X5) which is not directly available from the census. (X)2 value were easily computed from census data by squaring the mean characteristic values. Although the latter quantities were somewhat less then the former, they did serve as satisfaCtory substitutes in some Of the predictions. It is, however, suggested that these problems be given consideration in future studies. In addition to these problems, it seemed logical that differences ‘ in capital intensity and cost efficiency between farms were not expressed in the variables. Although the inclusion of these influences in the equations appears particularly difficult with the data which are available, it does seem to be a good area for future studies. Since account farms tend to be larger and more livestock intensive than average Michigan farms, and in addition cooperate with the University, there could be reason to believe that they would also show better enterprise cost efficiency and greater enterprise capital intensity. Using the regression values as they were directly derived from the regression equations, for estimates of the census, stratified estimates appeared reasonably representative for non real estate investment, but did not for net farm income and labor income. flux-37w fi':r~‘r'-‘I'.“' ““ ’ '1 ‘ -121- Account data can be sorted on the basis of a large number of criteria. For this reason, account data are particularly applicable to studies which require specific relatively homogeneous populations. Census data can be supplemented by account data. Account data can provide information excluded by the census. Also, account data can be used to help interpolate or extrapolate census data to non census years. In addition account data can be used to supplement the census in making future projections. .Account data are particularly applicable to regression analysis, since a large number of observations are provided from which functions can be fitted. In this study regressions were used to establish a basis for evaluating stratification procedures. Many studies utilize sampling techniques to Obtain necessary data. The account source can substitute for sampled data in many cases. Though large simple random samples will give more representative data for many characteristics, the account source can provide data Of a given reliability for less cost. In general, samples exceeding more than four respondents will exceed the cost Of Obtaining account data relative to the same type of information. Sample sizes which would give the same reliability as the account estimates were calculated for the characteristics which were studied and were found to exceed a sample size of four in about 80% of the cases. Another use of account data is for studies of farm organization. Both functional analysis and linear programming can be employed for studies pertaining to agricultural resource allocation. Account data -l22- can be useful for providing data for both of these research techniques. Account data can be used for a large number of descriptive studies. Since c00perators tend to lead average farms in many factors, a description of account farms might be indicative of the expected employment of resources of average farms at some future period. The 1965 account program initiated some special accounts which should find valuable use for future research. Included were studies concerning credit, labor costs, and family living costs. For addi- tional information, a farm panel Offers a possibilityifor supplementary account information. This study emphasized the comparison of mean and total farm account and census values. Stratification was studied as a possible tool for adjusting estimates. Another type Of study which would also provide important basic information on data use would involve comparison of farm account and census distributions of characteristic data. This would give insights on the distribution of account farms into relevant research categories and also give an indication Of the feasibility of using account fitted regressions for census predictions. A further area for study would involve a comparison of account coopera- tors with census farmers according to the time cooperators joined the account program. BIBLIOGRAPHY Cochran, William C., Sampling Techniques, New York, N. Y., John Wiley and Sons, Inc., 1960. Dixon, Wilfrid J., and Massey, Frank J., Introduction into Statistical Anal sis, McGraweHill, New York, N. Y., 1957. Farm Management Extension, Farming Today, Area l-l7, AEC 777-786 Michigan State University, Cooperative Extension Service East Lansing, Michigan 1960. Kiel, Donald F0, and Ruble, William Lo, Use Of CORE Routine. Michigan Agricultural Experiment Station Program, Description #12, 1963. Michigan Department Of Agriculture and Crop Reporting Service, Michigan Agricultural Statistics, Lansing, Michigan July 1963. U. S. Bureau Of the Census, U. S. Census Of Agriculture, 1959, Vol. 1, Counties, Part 13, Michigan, U. S. Government Printing Office, Washington, D.C., 1961. Wright, Karl T. and Henneberry, William H., WA Comparison of Some Characteristics of Farms in the 1959 Michigan Mail—In Project and the 1959 Census of Agriculture, Unpublished Paper,.Michigan State University, 1963. -123- null. .Jllfl till] 14‘ [ill-Ill.“ APPENDIX I CENSUS DEFINITIONS AND FARM ACCOUNT-CENSUS NUMBER OF FARMS AND PERCENTAGES 1959 -125- Definitions of Census Classes and Types of Farmsl I. Class of Farm.Definitions Value of Farm A. Commercial farms Products Sold Class of farm I $’+0,000 and over II 20:000 - $39;999 III 10,000 - 19,999 IV 5,000 "' 9) 999 v 2.500 - 1+. 999 VI 50 - 2,599 B. Non-commercial farms Class VII - Part-time. Farms with value Of sales Of farm products Of $50 to $2,499 were classified as "part-time" if the Operator was under 65 years of age and he either worked off the farm 100 or more days or the income he and members of his household received from nonfarm sources was greater than the total value of farm products sold. Class VIII - Part-retirement. Farms with a value of sales of farm products of $50 to $2,499 were classified as "part-retirement" if the farm Operator was 65 years Old or over. Many of these are farms on which the income from nonfarm sources was greater than the value of sales of agricultural products. Others are residential, subsistence, or marginal farms. In previous censuses, the age Of the farm Operator was not a criterion for grouping farms by economic class. Since the number of elderly peOple in our population has been steadily increasing during recent years, a separate classification for farms Operated on a part—retirement basis was considered important for an adequate analysis of the agricultural structure of a county or state. Class IX - Abnormal - All institutional farms and Indian reservations were classified as “abnormal", regardless of the value of sales. Institutional farms include those Operated by hospitals, penitentiaries, schools, grazing associations, government agencies, ect. II. Definitions of Census Types of Farms. (Types and products relevant for Michigan) -126- Type Of Farm Source of Cash Income (Products with sales value repre- senting 50% or more of total value of all farm products sold.) Cash - Grain --------------- Corn, Sorghums, small grains, soya beans for beans, cowpeas for peas,' dry field and seed beans and peas. Other Field Crop ------------- Potatoes, sorghum for sirup, pOpcorn, sugar beets, mint, and sugar beet seed. Vegetable - - - ~ ------------ vegetables. Fruit and Nut -------------- Berries, other small fruits, tree fruits, grapes and nuts. Poultry ----------------- Chickens, eggs, turkeys and other poultry products. Dairy ------------------ Milk and cream. The criterion Of 50% of total sales was modified in the case of dairy farms. .A farm having value of sales of dairy products amounting to less than 50% of the total value of farm products sold was classified as a dairy farm, if - (a) milk and cream sold accounted for more than 30% of the total value of products sold and - (b) milk cows represented 50% or more of total cows and - (c) the value of milk and cream sold plus the value Of cattle and calves sold amounted to 50% or more of the total value of all farm products sold. Livestock other than dairy and poultry - - Cattle, calves, hogs, sheep, goats, and wool. General ---------------- — Field seed crops, hay silage. Also if cash income from.three or'more type: didn’t meet the criteria for any other type. Miscellaneous -------------- Nursery'and greenhouse products, forest products, mules, horses, colts and ponies. All institutional farms and Indian reservations. lU'.S. Bureau of the Census. . . ens of riculture: l 1 Vol. I, Counties Part 13 Michigan. U.S. Government Printing Office, washington, D.C., 1961 p. XXIV. Appendix - Table 1. Number of Census and Farm Account Farms by Census Classes I-IV and Farm Types2 1. All Farms-Classes Class I Class II Class III Class IV I-IV Less Vegetable Class a 812 3,658 12,322 18,636 and Miscellaneous f b 60 252 441 161 * Census Farms-35,428 0 C) 2.29% 10.31% 34.78% 52.60% ** Farm.Account Farms-914 Farm d) 6.56% 27.65% 48.20% 17.60% % Farm Acct. of Census-2.6% e) 7.39% 6.89% 3.58% .86% TYPE OF FARM TYPE OF 1. Cash Grain FARM a) Census Farms 6,550 a) 52 487 2,100 3,911 b Farm account farms 38 b) 1 9 23 5 c) % census farms Of all census (1*) 18.48% c) .14% 1.37% 5.92% 11.03% d) % farm account of all farm acct. (1**) 4.15% d) .11% .98% 2.51% .55% e) % farm account (b) of census (a) .58% e) 1.92% 1.85% 1.10% .13% 2. Other Field CrOps a 955 a) 103 171 326 355 b 16 b) 3 5 6 2 C 2069% C; 029% 0lt8% 092% 3.000% d) 1.75% d .33% .55% .66% .22% e) 1.68% e) 2.91% 2.92% 1.84% .56% 3. Vegetable (Not included in aggregate count nor %.) a 729 a) 48 91 235 355 b l b O l O O 4. Fruit a 2.779 a) 215 678 831 1,055 b 35 b) 7 l4 7 7 C 708)+% C) 060% 1.091% 203)+% 2097% d 3.83% d) 977% 1.53% .77% .7716 e) 1.26% e) 3.26% 2.06% .84% .66% 5. Poultry 1 a) 1,139 a) 69 125 375 570 b 19 b) 0 6 10 3 Ci 3021% C) 019% 035% 1.005% 3.060% d 2.08% d) 0% .66% 1.09% .33% e3 1.67% e) 0% 4.80% 2.67% .53% 6. Dairy a 15,804 a) 120 1,157 6,324 8,203 b 644 b 24 162 337 121 c 44.60% c; .33% 3.26% 17.85% 23.15% d 70.38% d) 2.62% 17.70% 36.83% 13.22% 6 4.07% e)20.00% 14.00% 5.33% 1.48% -127... 1 [will-Ilsfl, Ir . 71‘. Appendix - Table 1. Continued 1. All Farms-Classes Class I Class II Class III Class IV I-IV Less Vegetable Class and Miscellaneous * Census Farms-35,428 Of ** Farm Account Farms-914 Farm % Farm Acct. of Census—2.6% TYPE OF FARM TYPE OF 7. Other Livestock (other than FARM Poultry or Dairy) a 4,645 a; 262 615 1,179 2,589 b 85 b 16 30 30 9 c 13.11% c .7316 1.73% 3.32% 7.30% d 9.29% d) 1.75% 3.28% 3.28% .98% e 1.83% e) 6.11% 4.88% 2.54% .35% 8. General Farms a) 3,556 a) 60 356 1,187 1,953 b) 77 b) 9 26 28 14 C lO0O3% C) 016% l0OO% 3035% 5051% d) 8.42% d; .98% 2.84% 3.06% 1.53% e 2.17% e 15.00% 7.30% 2.36% .72% 8. Miscellaneous Farms (not included in % or count) a) 851 a) 139 143 217 352 b) 0 b) 0 0 0 0 Combined with Class II for computational purposes. Farm.Account and Census Number of Farms by CrOpland Harvested Appendix - Table 2. for Dairy Classes II, III, and IV.2 Dairy Class II Dairy Class III Dairy Class IV Acres Census Farm Account Census Farm.Account Census Farm Account 500 - 999 7 Farms 0 Farms 1 Farms 0 Farms 0 Farms 0 Farms 200 - 499 708 97 1003 49 122 2 100 - 199 411 63 4148 243 2924 49 50 - 99 30 2 1097 44 4542 67 30 - 49 1 0 50 1 535 3 2O - 29 O O 20 0 5O 0 10 - l9 0 O O O 20 O l — 9 O O 5 O 10 O 2 Ibid. Bureau.of the Census and 1959 Farm Account Information. ~128- e\ APPENDIX II STATISTICAL FORMULAS FORMULAS FOR FARM ACCOUNT ESTIMATED MEANS AND TOTALS 1. Farm.account census weighted stratified estimates of census means for corn yields, wheat yields and #milk/cow. k - X N Estimated mean = h;l éth'hl ih: Farm account strata.mean per acre or cow. Census number of acres in corn or wheat, or number of milk cows. Census number of acres or cows of combined strata for category estimates. Number of strata in category 2. Farm account weighted (non stratified farm account value) means of corn yields, wheat yields, and #milk/cow. Farm account mean = k - 11:21 (thh) X11: “h n k ’— —. Farm account strata.mean per acre or cow. Farm account number of acres in corn or wheat, or number of milk cows Ferm.account number of acres or cows Of combined strata for category estimate. Number Of strata in category. 3. Farm account census weighted stratified estimate of census totals used for 15 characteristics. k _ Estimated total = hgl (XhNh) ll Farm account strata.mean per farm. Census number of farms in strata. Census number Of farms of combined strata for category estimated, k hglNh_N k = Number of strata in category. 4. Farm account weighted (non stratified fann account estimate) estimate of census totals used for 15 characteristics. in? k - N Estimated total = hz’l (thh) H ~130- “h n .— ll Farm account strata mean per farm. Farm account number of farms in strata. Number of farm account farms of combined strata for category estimate, 2 an = n Census number of farms of combined strata for category estimate. Number of strata. FORMULAS OF STANDARD ERRORS FOR STRATA AND ESTIMATED CATEGORIES Strata standard errors were used in computing standard errors of the stratified estimates which in turn were used to determine t values and probabilities that the deviations of account estimates from the census values or larger deviations would occur from stratified random samples Of the same sample size and strata prOportion as found in the census. The strata standard errors were used in computing sample sizes under optimum allocation. Standard deviations and standard errors Of the combined strata into estimate categories (unweighted) were used in determining sample sizes using simple random sampling. These sample sizes were computed on the basis Of p = .50 that the farm account - census deviations or larger deviations would result from sampling. - 2 Standard deviation = S = 1;]- T (Derived from Farm.Account Observations) Xi = Individual value of X X = Mean Of X n = Number of farms, acres or cows in computation. Standard error of mean2 = S- = EL- }( VG? Standard error of mean with 3: 0_ =‘§_ .322 finite population correction Y \ffi' N n = Sample number of acres or cows. N = Census number Of acres or cows. -n Standard error of estimated total3 = o“ = FE- L Y’ Vfi' N Number of account farms. NUmber of census farms. N ‘fflfifl = finite population correction factor (f.p.c.) n lDixon, Wilfrid J., and Massey, Frank J., Introduction into Statistical.Analysis, MCGraweflill, New YOrk, N.Y., 1957 p. 19. 2Ibid0, P0 620 3Cochran,‘William C., Sampling Techniques, John Wiley & Sons, New York, NOYO’ 1960, pp. 16-170 -l3l— v—o .,. ‘— FORMULAS FOR STANDARD ERRORS OF STRATIFIED MEANS AND 'I'OTAIS)+ The standard errors of stratified means and totals were used in determining the probabilities that the deviations of the farm account stratified estimates from the census or larger deviations would result from stratified samples of the same sample size and strata prOportion as found in the farm account sample. L S 2 a) VGST) = 37;; hg Nh (Nh - nh) —h— 3'811 = Strata weighted mean of N nh combined strata estimate 2 for characteristic y. L S b) Without f.p.c. =-i— N 2 -—E—— V— = Variance of y . 2 hgl h nh yST ST N c) Combined standard error of mean Nh = Census Number of Standard error of stratification acres Of cows. mean = L S 2 1 - 2 h nh = Farm account number 'fi SyST = hél Nh QJH=} of acres or cows. h S = Standard deviation h . of yield per acre or milk/cow. L = Number of strata. d) Combined standard error of total Nh = Census number of farms. Standard error of stratified total = nh = Farm account number of farms. - _ L Nh . Sh 2 N SyST " 113:1 ("\/r""_) Sh = Standard deviation of farm totals. L = Number Of Strata. e) Determination of degrees of freedom 2 2 (2 thh ) Effective number of degrees of freedom = N8 = 2 ‘4 Z fh sh nh--1 h ‘ Nh (Nh'nh) nh uIbid., Cochran, pp. 72-73. FPC was accounted for in calculation Of standard errors of strata means and totals in cases where the sample proportion was 10% or greater. H) I -l32- COMPUTATION OF T VALUES FOR DETERMINING THE PROBABILITY THAT THE FARM.ACCOUNT STRATIFIED ESTIMATE - CENSUS DEVIATIONS OR LARGER DEVIATIONS WOUED RESULT FROM STRATIFIED RANDOM SAMPLES OF THE SAME SAMPLE SIZE AND STRATA PROPORTION AS IN THE ACCOUNT SAMPLE For means _ For totals _ I _ u X = Farm account _ NI _ Nu T — stratified T — Standard error estimated mean Standard error of stratified ° of stratified census weighted u = Census mean. census weighted mean total NE = Farm account stratified estimated ISO—ta]. 0 Nu = Census Total. Probability determined from T table using prOper degrees of freedom. SAMPLE SIZES USING SIMPLE RANDOM SAMPLING Sample sizes which will yield p = .50 that the stratified account - census deviations or larger deviations would result from simple random sampling. 82 V : —_ ran n S S... :: _.._. X fl For means For totals T = X - u T : NX — Nu 6 87‘”; N 87%- For 1 df, p = .50 ST 2 NST 2 (2 tail) T = 1.00 n = (:f—- n = (——:——-9 For 30 df p = .50 X-u N(X—u) (2 tail) T = .67 STRATIFIED RANDOM SAMPLES UTILIZING OPTIMUM.ALLOCATION — SAMPLE SIZES5 2 V = (ZNh Sh) Strata numb r = = Nh Sh opt nN2 e “h DENh sh SIbid0, COChraIl’ D0 770 §See 2—tail T distribution. -l33- T ---= " (2 NhSh n N n = (T (2 NhSh) 2 (I - u) N MULTIPLE REGRESSION - SEE STANDARD "CORE" ROUTINE7 7Kiel, D. F. and Ruble, W. L., Use of CORE Routine. Michigan Agricultural Experiment Station Program, Description #12, 1963. ~134— 3:: y; .45"? “It. '5- '