PURCHASES OF NEW FARM TRACTORS AND MACHINERY IN RELATION TO THE NONFARM BUSINESS CYCLE, 1910:- 1956 Thesis for H19 Degree of M. S. MICHIGAN STATE UNIVERSITY Lyle P. F ettig 1958 ‘ mg \\l\\l1\\\;||[9\\|j\\\| w 1‘,“ w nix \m m m mu 7335 I. l } OVERDUE FINES: 25¢ per day per item RETURNING LIBRARY MATERIALS: :1; Yrfiii m 3 Place in book return to remove "' 102:, 1 «m 1w charge from circulation records PURCHASES OF NEW FARM‘TRACTORS AND MACHINERY IN RELATION TO THE NONFARM BUSINESS CYCIE, 1910-1956 BY Lyle P. Fettig A THESIS Submitted to the College of Agriculture of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Economics 1958 ACKNOWLEDGMENTS The author would like to express his sincere appreciation to all those who made the completion of this thesis possible. Foremost among those to whom the author is grateful is Professor Dale E. Hathaway, his major professor. His guidance and encouragement throughout the development of this thesis was invaluable. Professor Clifford Hildreth, now head of the Economics Department, and Professor Lester Manderscheid of the Agricultural Economics Depart- ment, made important contributions in working out the statistical aspects of the problem. Similarly, Professors Glenn L. Johnson andHWilliam Cromarty of the Agricultural Economics Department provided valuable insights into the analytical aspects of the problem. Thanks are also due Professor L. L. Boger for supplying financial aid in the form of an assistantship,making graduate study possible at this time. The cooperation of the statistical pool in carrying out the statistical computations and departmental secretaries in typing earlier drafts is sincerely appreciated. Typing of the final manuscript was done by my sister, Marilyn. The author is indebted to her for her patience in this task and aid in making the meeting of deadlines possible. Finally the author wishes to acknowledge the support of fellow graduate students, both material and moral, in the completion of a graduate program. The author bears full responsibility for the content of this thesis. 11 PURCHASES OF NEW FARM TRACI'ORS AND MACEDIERY IN MIC! TO THE NONFABM BUSINESS CYCIB, 1910-1955 By Lyle P. Fettig ARABSTRAQ‘ Submitted to the College of Agriculture of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of mm 01" SCIENCE Department of Agricultural Economics Year 1958 Approved 1:: -, J» .. T ABSTRACT Input flows into agriculture have been hypothesized as varying during different phases of the business cycle. This hypothesis has been investi- gated in this study for one of the groups of inputs from the nonfarm economy which flows into agriculture, farm.tractors and machinery. The primary purpose of the study was to determine if the relationships of factors associated with farm tractor and machinery purchases differed during different phases of the business cycle. The years included in the study, 1910 through 1956, were classified individually as being either a contraction year or an.expansion.year. This classification.was made on the basis of two criteria, (1) reference cycles for the general economy developed by the National Bureau of'Economic Research, and (2) gross national product estimates. Using these criteria, there were fifteen contraction years and thirty-two expansion years during this period. Synthetic variables were employed in the statistical models used in the analysis so that regression coefficients fer variables during contrac- tions could be compared with the regression coefficients for the corres- ponding variables during expansions. This method increased the computational efficiency and made it possible to use a common test in comparing regression coefficients. The single equation models were linear in the original vari- ables and fitted using ordinary least squares techniques. Twenty equations in all were included.in the four groups of equations that were examined in the analysis. The variables included in these equations were either machinery expenditures by farmers or shipments to iv dealers as the dependent variable, and independent variables consisting of: (1) net cash farm income, (2) capital gains and losses on livestock, crops, and real estate, (3) stocks of machinery on farms, (h) the price of machinery relative to prices received'by farmers, (5) the price of labor relative to machinery prices, and (6) a calendar time variable, assumed to represent a measure of the state of technolOg1cal advance. Variations in the form of the variables were made between equations and changes in the variables included.were made between groups of equations. The results indicated that different relationships between.variables have existed.during contractions and expansions in respect to net cash farm.income, capital gains and losses and "technological tre " as repre- sented.by the time variable. Changes in the rate of machinery purchase appear to have been more closely related to changes in farm income during contractions, and changes in the rate of machinery purchase appeared to be more closely related to capital gains and the presence of new technology during expansions. The relationship between the relative price of machinery and the rate of machinery purchase appeared.to be about the same in contractions and expansions. Changes in the rate of machinery purchase in relation to the stocks of machinery on farms appeared to be overpowered.by the develoPment of new technology. Evidence was not feund to support the hypothesis that the relative price of hired labor has been important in.the machinery - labor substitution that has taken place on the farms of America during this period. CHAPTER I. II. III. TABLE OF CONTENTS Page MODUCTIONOOOO0000000000000000 ..... 0.0000000000000000000000 Tm PrOblomoee ..... 0000000000 00000 0 00000000000000 00 Literature Leading to the Study.................. 00000 Scope and Objectives of the Study ............. . ..... ..... MHODOMY0000000000000000000000000000000000 The General Model Used in the Analysis... ....... .......... Classification of Years........................... The Dependent Variable.................................... 000000000 00000000 The Underlying Investment Theory. ....... .... ........ ... The Independent Variables........ ....... .......... Farm Income.............. ............. ............ . .. Capital Gains and Losses............................... The Stock of Machinery................................. The "Real" Price of Machinery.......................... The "Real" Price of Labor.............................. Time As a'Vsriable..................................... The U80 0f Legged variableeeeeooeoseeoeeoseeooeeooeeeeosee Prediction Versus Different Relationships Between the vuiabIOBOO00000.000000000000000000000000000000.0000000000 Criteria for Evaluation of Regression Coefficients........ Tm Ems OFTm ANALYSIS0000000000000000000000000000000000 The Results Presented............................. Group 100000000000 00000 00 000000000 0000000000000 Group 110000000000000000000000000000000000.0000 0000.000 000 Group 111000000000000000000000000000000000000000000 Group N0000000000000000000000000000000000 0000000000000 Recapitulation and Interpretation of’Results. ............. Fam Incm000000000000000.00000000000000000000 Capital Gains and Losses...................... The "Real" Price of Machinery.......................... Stocks of Machinery on Farms........ ........ ........... The ..Roa1"Price 0fIabor000000000000.0000000000000000. Tim A8avariab1°000000000000000...0000000000000000000 Expenditures Versus Shipments.......................... Variation in the unexplained Residual........... vi 1 1 2 5 6 7 9 11 13 18 20 21 22 22 2h 25 26 27 38 to as 53 53 55 5s 60 60 65 65 66 TABLE OF CONTENTS - Continued CHAPTER Page IV. SUIT-TRY AND CONCLUSIONS...................................... 7O BIBLIOGRAPHI......................................................... 76 APPENDIX I Statistical Test of Sigificant Difference Between Corresponding Regression Coefficients . . . . . . . . . . . . . . . . . . . . . APPEDEH'X II Times Series Used in the Analysis........................ vii LIST OF‘TABLES TABLE Page 1.0 Hypotheses Concerning Employment of Nonfarm Produced Dur- ables in Relation to the General Level of Business Activity. .. . 3 2.0 Classification of the Years Used in the Analysis . . .......... . . . 10 2.1 Expected Signs of Estimated Parameters.. .. .. . . . ..... . 28 3 .0 Variables Included and the Coefficient of Multiple Determina- tion, EaCthuation, Group 10000000000000000000000000000 0000000 30 3.1 Results From Using Farm Income As an Independent Variable, Group 10000000000000000000000...0.0000000000000000000000000000. 32 3.2 Results From Using Capital Gains and Losses as an Independent variable, GroupIo 0.000000000000000000000000000 00000000 0000 .00 33 3.3 Results From Using Stocks of Machinery as an Independent Variable, Group I ...... ...... 3h 3.14 Results From Using the Relative Price of Machinery as an Independent Variable, Group I 36 3.5 Results From Using the Relative Price of Labor as an Indepen- hnt variable, Gmllp 1.000000.0000000.00000000.000000000000000. 37 3.6 Variables Included and the Coefficient of Multiple Determina- tion, EaCthuation’ Gmup II0000000000000000000000000000000000 38 3.7 Results From Group II... ..... 39 3.8 Variables Included and the Coefficient of Multiple Determina- tion, Each Equation, Group III ’40 3.9 Results From Using Farm Income as an Independent Variable, Gro‘ulp III.00000000000000000000000000000000.00000000000000000000 1‘2 3.10 Results From Using Capital Gains and Losses as an Independent variablo’ Group III000000000000000000000000.0000000000000000000 1+3 3.11 Results From Using the Relative Price of Machinery as an Inapondantvariable’ Group III00000000000000000000000000000000 uh 3.12 Results From Using the Relative Price of Labor as" an Indepen- “nt variable, Group IIIOO00000000000000.0000.0.000000000000000 1‘5 viii LIST OF TABLES - Continued TABLE Page 3.13 Variables Included and the Coefficient of Multiple Determina- tion, Each Equation, Group IV ....... ............ .............. . 46 3.1% Results From Using Farm Income as an Independent Variable, Group N. ..... 00...... ..... ......OOOOOOOOOOOOOOOO ..... ......COOhB 3.15 Results From'Using Capital Gains and Losses as an Independent variable, Gmpm ..... 0.00.0.0 ....... ......OOOOOOOOOO0.0.0.... h9 3.16 Results From Using the Relative Price of Machinery as an napandont variable, Group NO.........O...‘...........0...... 50 3.17 Results From Using the Relative Price of Labor as an Inapondant variable, Group NOOOOI.........OCOOOOCOCCC0.00.... 51 3.18 Results From Using Time as an Independent‘Variable, Group IV... 52 FIGURE 2.0 3.0 3.1 3.2 3.3 3.1. 3.5 A 3.5 B 3.6 A 3.6 B LIST OF FIGURES Factors Considered to be Important in the Determination Ofmv03tmnt000000000000 ......... 00000000000000 000000 0000.00 18 Machinery Purchases by Farmers Related to Net Cash Farm Income, United States,l910~56................................ 5h Machinery Purchases by Farmers Related to Capital Gains and Losses in Holding Real Estate, Grape, and Livestock, United States, 1910-56....... ..... ............... ......... ... 57 Machinery Purchases by Farmers Related to Estimated Stocks of Machinery on Farms, United States, 1910-56. ........ ....... 59 Machinery Purchases by Farmers Related to the Relative Price of Machinery, United States, 1910-56 61 Machinery Purchases by Farmers Related to the Relative Price of Farm Labor, United States, 1910-56........................ 63 Unexplained Residuals, Equation 1, Group 1 67 Unexplained Residuals, Equation 5:, Group 3 67 Unexplained Residuals, Equation 6, Group hm... .. ..... . ..... 69 Unexplained Residuals, Equation 5, Group 1+. . . . . . . . . . . . . ...... 69 MI IMI'RODUOI’ION One of the more important gaps in the knowledge possessed by agricul- tural economists relating to the agricultural industry is a clear under- standing of the nature of the aggregate supply function for agriculture. Papers submitted to the Joint Economic comitteel suggest tmre is general agreement that the agricultural industry is out of adJustment at the pre- sent time. PrOposals for bringing the agricultural sector of the economy into adjustment are contingent upon asstnnptions concerning the nature of this aggregate supply function. Belief in a supply curve which is highly inelastic calls for programs involving stringent production controls and high price supports, while belief in an elastic supply function calls for reductions in price supports and relaxation of production controls. The Problem The task of this thesis is not to attempt to explain the aggregate supply function for agriculture. Much more must be lmovn before this can be done. The subJect matter of this thesis is closely related to the understanding of the aggregate supply function for agriculture, however. A responsive aggregate supply curve for agriculture may be explained in part by increases in resources used in agricultural production as a result of increases in the demand for agricultural products. This 1. Policy for Copercial Agflcultureg, ItsfiRelation to Economic Growth and Stability, Joint Economic Committee Print, November 22 , 1957. 2 was suggested in a paper by Hathawaye relating agriculture to the business cycle. Measuring the changes in these inputs which are used in agricul- ture involves many difficulties, so that rather than attenuating to work on all the inputs which go into agriculture, one of the maJor input categories, farm tractors and machinery, was examined. The findings of this study gives some indication as to the usefulness of looking at other inputs in a similar manner, and some of the problems involved if such investigations are to be made. The problem, simply stated, is that of examining farm tractor and machinery investments over the business cycle to determine if the variables which are associated with these investments are related differently during different demand conditions. These demand conditions are considered to be changing with changing conditions of well-being in the general economy, i.e., the business cycle. Literature Leading to the Study The development of the conceptual framework used in this study was done by Johnson and appears in the paper "Supply Function - Some Facts and Notions."3 Eypotheses are presented concerning resource employment in agriculture in relation to the general level of employment and business activity. The inputs used in agriculture have been classified into nine categories in Johnson's paper. The category "nonfarm produced durables" 2. Hathaway, Dale E., "Agriculture and the Business Cycle", in Polig' {gr Commercial Agriculturb Ibid, Table h, p. 58. 3. Johnson, Glenn L. , "Supply Function - Some Facts and Notions" in Agicultural Adjustment Problems in a G_;rewi__ng Rem, edited by Ready, et. al., Iowa State College Press, 195 , ch. 5. includes farm tractors and machinery. Table 1.0 presents hypotheses developed in Johnson's paper concerning nonfarm produced durables.“ TABLE 1.0 - HYPUI‘EESES CONCERNING mom OF NORFARM PRODUCED DURABLES IN RELATION TO THE GENERAL IEVEL OF BUSINESS ACTIVITY RECOVERY PROSPERITY RECESSION DEPRESSION Stable 4- Expanding 4» Stable «t Stab. or Contra.» The hypotheses in Table 1.0 were framed in reference to the fixed asset concept deve10ped by Johnson. An asset is considered fixed when its marginal value product is less than its acquisition cost and in turn, its salvage value is less than its marginal value product. In such a situation it doesn't pay to employ more of the input and the input will return more in its present use than through salvage. The fixed asset concept was offered as an explanation of Viv inputs do not leave agriculture during periods of low earnings and why more inputs do not enter into agriculture on the outset of a betterment of the terms of trade between agriculture and the non-agricultural sectors of the economy. In Table 1.0 we see that employment of nonfarm produced durables is hypothesized as being stable or contracting in three of the four stages of the business cycle. Employment of nonfarm produced durables is hypothe- sized as expanding only during periods of prosperity. The plus (+) signs indicate the influence of technological advance upon the employment of nonfarm produced durables. There is a plus sign for each phase of the h. Ibid, Table 5.1, p. 82. business cycle, suggesting that employment of nonfarm produced durables is increased in all phases of the business cycle due to this cause. How- ever, it does not suggest that the rate of increase from this cause will be the same in each phase of the business cycle, even though the effect is hypothesized to be positive. The interest in this study is in obtaining a more complete knowledge of the reasons for, or more correctly the factors associated with, variations in the rate of purchase of new tractors and machinery which become inputs in agriculture. Many valuable insights into demand factors of importance were obtained from Cromarty's recent investigation in this area.5 In his study he used conventional time series analysis. The approach in this study was differ- ent because the purposes of the study were different. This will be dis- cussed in more detail in Chapter II. Wilcox and Cochrane6 discussed the impact of business fluctuations on purchases of farm machinery and motor vehicles, pointing out the close association of these investments with changes in general business activity. They found that in "good times" , investment in this area was increased and in "bad times", investment was restricted. The other basic work involved, of which the present study is an out- growth, is Hathaway‘s paper "Agriculture and the Business Cys1e."7 Inpu- cit in this paper are the hypotheses that: (1) farm output is partially related to demand, and (2) part of the output increases which take place are a result of increased purchases of inputs from the nonfarm sector of 5. Cromarty, William A. , The Demand for Fem Machineq and TractorsJ Agricuiturei Experiment Station, 's'as't"'Len' sing, Techn- 'i'cei' suiie'tin (In Process). 6. Wilcox, w. W., and Cochrane, w. w., Economics of American Aflicul- ture, Prentice-Hall, 1951, p. h58-9. 7. Hathaway, Dale E., op. cit., p. 51-76. 5 the econony. It would be desirable to consider all inputs used by agricul- ture in relation to the business cycle to test these turpotheses. Such an inquiry is beyond the scope of the present study. Scope and Objectives of the Study Expenditures which farmers in the United States have made on tractors and machinery over the period 1910 to 1956 are investigated in the study. This input category was chosen because available data provide some measure of the magnitude of input in individual years. The primary objectives that are sought are: (1) the construction of a demand model for farm tractors and machinery that allows for, (2) deter- mination of the differences in the relationships of variables in this demand model, during periods of general business contraction and periods of general business expansion. The second objective, although necessarily related to the success of accomplishing the first, is the primary obJective of the study. In this light, the investigation might be considered as an attempt to deveIOp a demand model for new farm tractors and machinery over the business cycle. However, it should be pointed out that primary empha- sis is not on the deve10pment of a precise prediction equation, but rather upon possible differences in the relationships of variables with changes in general business activity. The methodology, involving the theory used in the analysis, is dis- cussed in Chapter II. Chapter III contains the analysis completed in the study along with its interpretation. Finally, in Chapter IV the findings of the study are sumarized and evaluated. CHAPTER II METHODOLOGY The present study deals with aggregates for the farm sector of the economy and as such lies in the realm of macroeconomics, which deals with mass economic behavior. The aggregates which are included in the malysis are considered to be derived from the many single units which constitute the whole. This approach to the deveIOpment of the theory which is used in the analysis is called the analog approach to the aggregate problem.1 Theory involved in the analysis of the macrovariables utilized in the study rests upon theory dealing with individual behaviors which are 'included in the composition of the aggregate. However, in dealing with the behavior of large groups of individuals, the "law of large numbers" tends to cancel out irregularities in the individual behaviors giving a resultant regular- ity in the aggregate behavior. The resulting aggregate is sufficiently stable to allow meaningful aggregative theories and measurement.2 Apart ‘ from this,’the objective of am study of this nature is to determine rele- vant and significant relationships and in this particular case the interest is in macroeconomic relationships.i y Macroeconomics looks at economic affairs from an overall viewpoint ,4 scanning the forest without looking at each of the trees individually. But, a forest is made up of individual trees, and it would follow that considerations pertinent to individual trees are important in molding the forest. It is here that microtheories aid in understanding the problem, in the deve10pment of a theoretical framework for the whole. This is the l. Theil, H., Linear e atio of Eco latio , North- Holland Publishing Company, Amsterdam, 1951;, p. 6. 2. Ackley, Gardner, An Introduction to Macroeconomic Theory, prelim- inary edition for student use, Gardner Ackley, University of Michigan, Sept. 1957, Ch. I, p. 15. t 7 approach of this study, in which demand for tractors and machinery by the farm sector of the econony is investigated. The General Model Used in the Analysis Variables associated with gross expenditures on tractors and machinery by farmers were examined. The selection of these variables, with the theory involved in their selection, is delayed to a later portion of the chapter. Before these variables are discussed, the development of a model which allows for differences in relations of the variables for years of contrac- tion and years of expansion is discussed. This is done so that the hypo- thesis that employment of tractors and machinery differs during different phases of general business activity may be evaluated. To test this hypothesis, it is necessary that theA demand model used provide for comparison of the relationships of variables during different phases of the business cycle}, Business cycles were split into two major phases; expansion years and contraction years. The single equation model used was linear in the original variables since no particular Justification for using curvilinear forms was apparent. Since comparison of regression coefficients of corresponding variables for contraction and expansion years was the primary objective of the study, the model was constructed with this end in mind. "Splitting out" contrac- tion years and expansion years and computing multiple correlations separ- ately would raise serious problems in the comparison of regression coeffi- cients by a common test. To avoid these problems, and to obtain pester efficiency in computation, synthetic variables were constructed so that both contraction years and expansion years could be treated as being from a single sample. Using this method, it was possible to compare regression 8 coefficients for corresponding variables in contraction years and expansion years for significant difference. The single equation model used which incorporated this capability was linear in the original variables, of the form: Y'801101 Ml02102 +"’11"11‘”’1.2=‘12 * 'mbnl‘nl H’n21‘n2 in where _Y. is gross expenditure on, or shipment of , tractors and machinery, _a_ is the constant value, _b is an estimated parameter, _x_ is an independent variable, l_l_ is the number of independent variables, and g is the unexplained residual. The model includes independent variables x1......xn which are divided into sub-variables, so that variables x11” .12 ------ xnl“ .112 are used. Very simply stated, the model includes corresponding variables for contraction years and expansion years so that comparison of the regression coefficients of corresponding variables can be made. As an example, variable x1 is income, and divided in this manner, x11 and x12 take the following values: 1. During contractions 2. During expansions (a) x11 takes the value of x1 (a) :11 takes the value of zero (b) x12 takes the value of zero , (b) x12 takes the value of 1:1 To obtain a double constant a value, 1's and zeros were used in a similar manner, where 10 is considered to be 1. The model, thus formulated, is based upon the assumption that the error term (u) is independent, i.e. , that the unexplained residual has a similar distribution for expansion and contraction years. These residuals are examined in Chapter III to check the validity of this assmnption. The equations are fitted using ordinary least square techniques. Classification of Years The use of this model requires that the years included in the study be classified individually as being either a contraction year or an expan- sion year. This classification was made with the use of the turning points of business activity developed by the National Bureau of Economic Research3 and gross national product estimates. Since data pertaining to agricul- t1n°e is reported on an annual basis, it was necessary to classify an entire year as being a year of contraction or a year of expansion though obviously turning points are not at the end of the year in all cases. These turning points and gross national product figures are given in Table 2.0. The method of classification used was to observe the time in the year in which the turning point occurred, if at all, for the year being classified. Years in which turning points did not take place near the middle of the year were classified as follows: (1) if a peak in business activity occurred before mid-year, the year was classified as a contrac- tion year, (2) if a trough occurred before mid—year, the year was class- ified as being an expansion year, (3) if a peak occurred after mid-year, the year was classified as being an expansion year, (h) if a trough occ- urred after mid-year, the year was classified as being a contraction year, (5) if neither peak nor trough occurred in the year being classified, it was classified as an expansion year if the last preceding turning point was a trough and as being a contraction year if the last preceding turning point was a peak. 3. For deveth of reference cycles for the general economy see burns, Arthur F., and Mitchell, Wesley C., Measurgg ageiness Cycles, National Bureau of Economic Research, New York, 1 7. 10 TABLE 2.0 - CLASSIFICATION OF THE YEARS USED IN THE ANALYSIS (1) Classi- Turning Point GNP Year fication* Peak Trough Bi1.$ (3) (1) ' Classi- Turning Point GNP Year fication* Peak Trough Bil.$ 1910 0 Jan - 36.7 1932:. E - - 65.0 1911 c - - 36.8 1935 E - - 72.5 1912 E - Jan 38.5 1936 E - - 82.7 1913 C Jan - 1+0. 0 1937 E Mu - 90 . 8 1911; c - Dec 38.5 1938 c - June 85.2 1915 E - - 112.1 1939 E - - 91.1 1916 E - - 117.8 19% E - - 100.6 1917 E - - 59.5 19111 E - - 125.8 1918 E Aug - 65.5 191:.2 E - - 159.1 1919 E - Apr 77 . 1 19$ 3 E - - 192 . 5 1920 E Jan - 86.2 191111 E - - 211.11 1921 c - July 70.3 19115 0 Feb Oct 213.6 1922 E - - 72.5 1916 c - - 209.2 1923 E May - 811.3 191w E - - 232.2 19211 c - July 83.h l9h8 E Nov - 257.3 1925 E - - 90.0 19149 c Oct 257.3 1926 E Oct - 95.3 1950 E - 285.1 1927 c - Nov 93.5 1951 E - 328.2 1928 E - - 95.6 1952 E - - 3115.11 1929 E June - 10M; 1953 E July - 363.2 1930 c - - 91.1 19511 c - Aug 361.2 1931 C - - 76. 3 1955 E - 391.7 1932 C - - 58.5 1956 E - hlh.7 1933 E - Mar 56.0 *C denotes contraction, E denotes expansion. ~- J Source: Col. 2, Mills, Frederick. C. , Introduction to Statistics, Henry Holt Company, New York, 1956, Table 12-3, p. 353. 4 Basic Economic Statistics, Economic Statistics Bureau of Washington, D.C. , Col. 3, Handbook of Julyl5,l ,p. 22. 11 When classifying years in which the turning point occurred near mid- year, the change in gross national product was used as an additional criterion. For years with this characteristic, the classification was as follows: (1) if the gross national product for the year exceeded the gross national product for the preceding year, it was classified as being an expansion year, (2) if the gross national product estimate declined from the level of the preceding year, it was classified as being a contraction year. Exceptions to this system of classification are the years 1920 and 1916. The turning point in 1920 occurred in January, which was a peak. This would cause the year to be classified as a contraction based upon the turning point criterion. Gross national product rose substantially over the 1919 level, so the year was classified as an expansion year. The year 1916 would be classified as an expansion using the turning point criterion, but was classified as a contraction because gross national product declined from the 19115 level. Complete classification of the years 1910 to 1956 is given in Column 1 of Table 2.0. Using this system of classification, there are fifteen years of contra3tion and thirty-two years of expansion included in the forty- seven years covered by the study: The Dependent Variable The dependent variable which is to be explained by other independent variables in the single equation model must be such that it reflects the purchases of tractors and machinery, for agricultural use. To obtain a measure of the physical pmhases of farm tractors and machinery, gross expenditures on farm tractors and machinery were deflated by an index of 12 farm tractor and machinery prices. Deflation of the expenditure figures adJusts the estimates for price changes, thus giving a more accurate measure of plwsical purchases than would expenditure figures, not adJusted. While the components of this input mix (i.e., types of machines, etc.) have been changing rapidly over the period under study, this is a problem which we are not presently capable of handling and is regarded as being beyond the scope and purpose of this study. Rather, the primary concern was in what the relationships between independent variables and investment in farm tractors and machinery as a broad category have been, with an under- standing that specific items included in the category as to kind and number (i.e. , the mix) have changed from your to year. The goss capital expendi- ture figures are derived by marking up shipment figures to retail and making an adjustment for dealer inventory changes.“ These mark-ups have been computed at relatively constant rates, while mark-ups by dealers most likely vary with the business cycle. This would tend to amplify errors in the shipment estimates. Shipments to dealers was used as an alternative dependent variable in several of the fittings. With this variable, there is the problem of dealers' inventories; dealers do not necessarily sell all the tractors and machinery shipped to them in any given year. Dealers may, in some years, have to carry stocks above their planned inventory into the following year. Each of these two variables have been used in the analysis to deter- mine which was more capable of prediction within the limits of the formu- lations used. Values of tractor and machinery shipments have been deflated by the index of farm tractor and machinery prices as with the case of goes expenditure figures . h. Magor Statistical Series of the U. S. De artmnt of iculture 2“" “—‘fl EFT—us‘bia. , Vol. 3 Gross and Net an Income, Agiculture Handbook, No.11 DOC. J’pé‘j'?’ p0 8. 13 The Underlying Investment Theory The crucial problem involved in this study is the choice of explana- tory, "independent" variables which are used in the model to explain why farmers purchase tractors and machinery. This prdblem is not unique in character from other studies in which explanation of phenomena are the goal. Variables which are chosen for this purpose must be the more important ones selected from among the many relevant ones. It is here that theory guides the investigator in determining what variables possess these characteris- tics. On this subject Koopmans has written: But "good" choices means relevant choices....The choices as to what variables to study....call (s) for a systematic argument to show that the best use has been.made of available data in re- lation to the most important aspects of the phenomena studied.5 This clearly outlines the present task of the author, who, following Koopmans' advice, shall try to set down such "systematic argument" which displays the reasoning behind the choice of the variables which have been related to farmers' investments in tractors and.machinery. At the outset of this discussion, it should be pointed out that the author recognizes that "we have as yet no thoroughly satisfactory theory of investment,"6 so that what follows is by no means presumed to be "the" theory of investment. This weakness does not prevent investigations of an empirical nature from being made; indeed, many times such investigations provide insights which lead to norther clarification of the relevant theory, through rejection of invalid parts and indications as to needed additions. The primary concern in choosing variables for explanation of 5. Xoopmans, T. C., "Measurement'flithout Theory", in.Review of Economic Statistics, Vol. XXIX, No. 3, Aug. l9h7, p. 16h. 6. Ackley, op. cit., ch. XII , p. 28. 1h investment is with the selection of those which appear to be relevant and important, using as a guiding reference existing investment theory. The present context in which investment is being explained deals with aggregate gross investment in tractors and machinery for the farm sector of the economy. The macrotheory involved in the study is derived from microtheory by the use of the analogy approach. Thus, the theory which is discussed deals with the theory of the firm, assuming that the aggregates used reflect the simple summed effects of the variables for individual firms which go into the make-up of the aggregative variables. The decision to make investment on the part of individual farm managers involves many considerations such as the age of the Operator, the number of children and the amount of responsibility which the manager bears, to list but a few. HOwever, most of these tend to "cancel out" when investment is considered in the aggregate, so that many of the variables which are highly relevant to the decision of the individual manager are not particularly germane when aggregate investment is considered. Thus, only those vari- ables which affect aggregate investment in a regular and systematic fash- ion need be included. The discussion which has evolved to this point has been preliminary in character, leading up to the question of why capital investments are made by farmers. The investment theory used in the selection of variables is advanced in the discussion that follows. One of the more useful concepts in explaining the nature of invest- ment, the marginal efficiency of capital, was developed by Keynes.7 As contrasted to the marginal value productivity of capital, which is the _— _- 7. Keynes, J. M., The General Theory_pf;§§ploymsnt,_Interest_and Money, Harcourt, Brace and Company, 1935, :h. ll. 15 addition to total revenue resulting from using more of a capital input, marginal efficiency of capital as defined by Keynes refers to the expected rate of return over cost over a period of time from using capital assets.8 A closer comparison between these two concepts is deemed necessary so that confusion between them may be eliminated. When using the marginal value product, we are interested in comparing this (MVP) with the marginal factor cost (MFG). Considering one ixqaut, greatest profit can be obtained by using that level of input where MVP :- MFG since additions of the input prior to this level add more to goss income than to total cost and addi- tions after this level add more to cost than to return. Thus, in using the MVP concept, we must compare cost and return simultaneously. The marginal efficiency of capital (MEG) is the expected rate of return over cost. In this case, both costs and returns have been looked at to obtain the return over cost, so the same elements concerned in W? : MFC have been involved. Thus, we see in total that both concepts are used in con- Junction with costs and returns; these costs and returns being the expected values in each case. From this discussion, it can be seen that the two concepts are highly complementary, marginal efficiency of capital being considered the longer run of the two. The concept of the marginal effici- ency of capital is the basic prOposition of the theory used. Assuming rationality, more of the capital asset should be employed, so long as the expected percentage return, discounted for uncertainty, exceeds the rate of interest. This follows because if the marginal effi- ciency of capital exceeds the rate of interest, invested capital leaves a return over the rate of interest. Conversely, if the marginal effici- ency of capital is below the rate of interest, not enough return would be 8. Ibid, p. lhO-hl. 16 made to pay the rate of interest. Interest charges must be covered whether the capital is borrowed or owned, since with owned capital there is the alternative of loaning the money to others (to banks, through pur- chase of securities, etc.) and collecting the rate of interest. Ability to obtain loans is another issue discussed below. Expectations relating to the future play a very important role in investment decisions (to invest or not to invest). Prospective yields from capital investments are nothing more nor less than the expectations which investors hold. These expectations are conditioned by what has happened in the recent past and what is happening in the present, particu- larly in shorter lengths of run. Longer run expectations are highly unstable with much emphasis placed on the things which are known at the present time and not much weigit attached to uncertain matters. Expecta- tions in reference to decisions on purchasing machinery would probably be concerned with some intermediate length of run depending upon the use intended for the machine, the expected durability of the machine, and other such factors. The ability to obtain loans with which to make investment is another consideration which must be made along with the marginal efficiency of capital. It is not sufficient that the marginal efficiency of capital be attractive to investment; in addition the farmer must be able to provide funds or obtain credit to make the investment. While the rate of interest must be covered by the return on the investment for investment to be profitable, "since the rate of interest is relatively 'sticky' , fluctuations in the inducement to invest depend primarily upon changes in the marginal efficiency of capital" ,9 and not 9. Dillard, Dudley, The Economics of J. M. hm Prentice-Hall, Inc., New York l9h8 , p . 1&2 . . 17 on the rate of interest.10 In relation to tractor and nachinery purchases, Cromarty also reached this conclusion and states "interest rates, Judging from their stability, have not been effective in varying equipment salss."-u Arguments elong this line dismiss the importance of the interest rate in determining investment. Furthermore, if one does allow that the inter- est rate should be included as a determining variable, the relevant rate of interest to use as a determinant is unaccertainable. Using the mort- gage rate of interest would assum that this is the relevant rate, but farm tractors and machinery are financed by and large from non-mortgage type loans. A report in a recent Federal Reserve Bulletin giving the findings of the Agicultural Loan Survey made in 1956 by the Federal Reserve System gave the following: Among loans to finance intermediate -term investments, the difference in rates was most pronounced for the smaller classes where loans to buy fann machinery and consumer durable goods were concentrated . 12 This statemnt provides a strong indication of the difficulty invol- ved in obtaining a relevant rate of interest for use as a determinant of investment. Probably the most suitable published series in this regard would be the series on interest rates for intermediate credit to farmers. However, since the rate of interest is relatively "sticky" and the marginal 10. See also in this regard Shackle, G.L.S. , Uncertain‘tl in Economics, Cambridge University Press, 1955, p . l28-hh. ll. Cromarty, op. cit. 12. Morelle, Wilellyn, "Interest Rates on Farm Loans", {arm Loans at Connercial Banks, Board of Governors of the Federal Reserve System, Washington, D. C., 1957, p. ’49. 18 efficiency of capital fluctuates to a great degree with changes in‘bus- iness activity, changes in the marginal efficiency of capital are consid- ered to be the dominating factor of these two variables. It is more reasonable to expect changes in investment because of (say) a change in the marginal efficiency of capital from 0% to 10% or 15% than to expect a change in the interest rate from 6% to 7% to have much effect. ‘Because of these considerations, rates of interest were not used as variables in the analysis. The factors which would appear to be important in the determination of investment are summarized schematically in the Figure 2.0. The vari- ables used in the analysis of investment in tractors and.machinery need necessarily be related to these factors. The selection of independent variables is discussed in the following section. Figure 2.0 Factors Considered to be Important in the Determination of Investment ICost of the Asset ' Marginal Efficiency lExpe cted Returns of Capital _ EQuity and Internal ‘4 pglnvestment Financing Availability of Credit The Indsgsndent Variables The selection of variables that are related to changes in farmera' investment in tractors and machinery was made with the assistance of the theory which was presented in the preceding section. In making these choices, it is very difficult to be certain exactly what a particular variable measures, so that in essence intuitive reasoning many times pro- 19 vides the only link between a variable and a factor which the theory said was important. Exploration of alternative variables must be made to find those which give the "best fit" and are logically consistent. Statistical measures of association and tests of significance then provide some indic- ation of the (apparent) relevance of the variables used. The reasoning underlying the use of particular variables is discussed in each of the following cases. Farm income. Farm income was used as a variable that is associated with farmers' investment in tractors and machinery. Farm income consti- tutes a crucial element in farm capital outlays13 and should provide a measure of the marginal efficiency of capital in agriculture. This seems to be fairly plausible in that lower incomes appear to be consistent with lower marginal efficiency of capital, given the cost of the asset, and higher incomes represent higher marginal efficiency of capital. The marginal efficiency of capital was defined as being the expected rate of returns over costs. Assuming that farmers' expectations of the future are largely conditioned by outcomes of the present, net farm in- come, or the excess of goes farm incme over costs, appears to be quite closely related to the marginal efficiency of capital in agiculture. It is not argued that expectations of return over cost for the coming year are based completely on the outcome of the present year, but rather that this aspect probably has an important influence on the expectations which are formed. Apart from this, farm income provides a stock of funds which may be used for machinery purchases. Net income was used to represent that part of farm income which is available for investment purposes. Further, because farmers cannot invest 13. Monthly Review, Federal Reserve Bank of San Francisco, July 1956, 20 "realized nonmoney" income, a net-cash-income concept was considered most fitting. Net cash farm income was obtained by subtracting current oper- ating expenses (excluding hired labor), taxes on farm preperty, and inter- est on farm mortgage debt from the total of cash receipts from marketing and. government payments. To put this income in terms of "real" net cash income, the estimates have been deflated by the index of prices paid by farmers. Farm income, along with providing some measure of the marginal effi- ciency of capital in agriculture, is probably important from the standpoint of farmers' ability to obtain loans with which to invest. Ackley has written in connection with this point: We can still relate total investment to current (or recent) profits if we assume that the amount of outside capital which a firm can attract depends upon the amount of internal financing that its owners can supply (or that increases in the ratio of game's: Z; flagelczggiifihinvolve appreciable increases in This idea is closely related to the danger of "illiquidity" when too much credit is taken so that the rate of interest that must be paid is pushed upward.15 Higher incomes provide savings which can be used for investment, thus reducing the ratio of external to internal financing. Capital gains and losses. Capital gains and losses which come about as a result of changes in the prices of assets in which farmrs have an equity, may be another variable important in the determination of farmers' investments in tractors and machinery. The potential importance of capital 1h. Ackley, 0p. cit., ch. XII, p. 27. 15. Kalecki, 14., "The Principle of Increasing Risk", Economics, New Series Vol. Iv, 1937, p. M2. 21 gains in agricultural capital formation has been stressed by Johnson.16 Such gains may expand the credit base for farmers as they occur and thus make credit more available for'machinery purchases. Capital gains and losses have been computed fer real estate, live- stock, and crOps, and the total of these used in the analysis. Computa- tion of these gains and losses is given.in.Appendix.II. The stock of machinegy. The stock of’machinery on farms was included as a variable in the analysis with the thought that the need fer additional (new) machinery has been conditioned in part by the amount of existing stocks. Famere can continue to use machinery until it wears out. To obtain an approximation of the stock of machinery on farms, expenditures in constant dollar terms were weighted linearly for the eight previous years and totaled. This was done because examination of Figure 3.0 in Chapter III, machinery expenditures charted over time, indicated a cycle of highs and lows about eight years in duration. Cromarty also considered a replacement time of eight years as being a valid approximation of the length of time which elapsee between the time a farmer purchases a parti- cular piece of machinery and the time when he re-entsrs the market to make an additional purchase. As he points out, this is only a rough approxi- mation because the life of a piece of machinery may be extended if supplies are restricted or if farm purchasing power falls to a low level.17 This still appears to be a better approximation of machinery stocks on farms than a depreciated book value, such as the value of machinery on farms after depreciation. Such depreciation is done for income tax and 16. Johnson, G. L., "Sources of Expanded Agricultural Production" in Pplicy for Commercial Agriculture,gIts Relation to Economic Growth and Stability, op. cit., p. 1h1-2. 17. Cromarty, 0p. cit. 22 accounting purposes and is not considered as being a good indicator of the "sets" of machinery actually on farms. The use of weighted sums of pre- vious years purchases, while being a rough approximation admittedly, appears to be more useful for this purpose. The weighting has been done linearly, giving the expenditure of the most recent year a weight of eight times its value and giving the expenditure of the eight years pre- vious a weight of one times its value. The "real" price of machinery. In order to Obtain a measure of the real price of machinery, the price of machinery relative to the prices received by farmers was included. Changes in expenditures for tractors and machinery should come about when this relative price changes as farmers compare the prices they receive with the price they must pay for the machinery. The rate that was used was Obtained by dividing the retail index of farm tractor and machinery prices by the index of prices reserved by farmers. The "real" price of labor. The price of labor relative to the price of machinery was used in the analysis to obtain the effect of the substi- tution of capital, in the form of machinery, for labor, when labor becomes more expensive relative to machinery prices. Considering labor and mach- inery as substitutes to some degree in production, one would expect mach- inery to be substituted for labor as the ratio of farm labor prices to machinery prices increases. Since the salvage value of farm machinery out- side agriculture is very low, we would not expect machinery once purchased to be replaced.by hired labor until the marginal value product of the machinery drOps to the point where it equals its salvage value. In this respect, we would not expect hired labor to substitute for machinery as the ratio of farm labor prices to machinery prices decreases, unless additional inputs are being used to expand production. 23 The Optimum combination of machinery and labor is reached when the ratio of the marginal physical product from machinery use to the price of machinery is equal to the ratio of the marginal physical product from labor use to the price of labor. This may be written in equation form as follows: MPP Machinery _ MPP Labor P Machinery " P Labor This condition defines the least cost combination for producing a given output and also the highest Output from a given outlay.18 ‘When.the price ratio between labor and machinery prices change, the Optimum combination of machinery and labor changes. while we cannot expect the optimum to be obtained in a world of uncertainty, the tendency should be in that dir- ection, it appears. This variable was obtained by dividing the index of farm wage rates by the index of tractor and machinery prices. This variable, of course, only considers hired labor. Family labor has constituted a very important portion of the agricultural labor fOrce in the United States. When has machinery replaced family labor? It is impossible to place a price applicable to family labor such as that for hired labor because of its fixed nature. Hence, we must look to other sources for measurement. Employment Opportunities in the nonfarm economy are pointed out by Schultz” as being important in the movement of labor, both family and hired, from agriculture to Jobs in urban communities. Machinery may be used, in turn, to replace labor which has left agricul- ture as a result of improved Job Opportunities. On the importance of 18. Bradford, L. A. and Johnson, G. L., Farm.Mangggment Analysis, Wiley and Sons, Inc., New'York, 1953, p. 127-130. 19. Schultz, Theodore‘W., Agriculture In An.Uhstab1e Economy, McGrawbHill, New'York, l9h5, p. 130. '2h employment Opportunities as affecting the rate of machinery investment, wilcox and Cochrane have written: There is considerable evidence that mechanization in recent years primarily replaced labor that had already left the rural community for nonfarm Jobs, rather than that machinery took Jobs away from local workers. At first, inclusion of an employment variable, based on the percent of the labor force employed, was considered for use in the analysis because of these speculations. However, because of the close association by definition between the classification, based upon business cycles, and the percent of the labor ferce employed, it was decided that inclusion of such a variable would not be useful. (See Appendix II, Table 8, for an employment series.) Time as a variable. In addition to the preceding variables, a time variable (l9lO:l) was used in the analysis of machinery purchases. Time used as a variable has been referred to as a "catchall factor" that allows for the factors which change over time for which data are non-available.21 Writing on technological change and its relation to forecasting in this connection, Siegel has said in regard to the use of calendar time as a variable: In such a case, time serves two purposes; it is a conglom- erate variable representing all the Omitted.pertinent factors of production, and it is a parameter reflecting the continuous change in the structure of the productive process. 2 20. Wilcox, w w., and Cochrane, w w., op. cit., p. 83-h. 21. Thomson, F. L. and Foote, R. J.,.Agriculture Prices,‘McGraw~Hill, New‘York, 1952, p. 287. 22. Siegel, Irving 3., "Technological Change And LongéRun Forecasting", The Journal of'Business of The university of Chicago,‘Volume 26, July, 1953, p. 152. 25 The second purpose which Siegel points out was the primary purpose for including the time variable. Probably the thing which best typifies agri- culture in the United States since the turn of the century has been the improvements which have been made in the production process. Development of new technology must have had a great impact on the purchase of new machinery. Therefore, the reasoning behind the inclusion of a time vari- able was to capture some of the influence of "technological trend" with the passage of time. The magnitude of the coefficient for this variable should give some indication of the rate of adoption of technology in contractions as compared to expansions. The Use Of Legged‘Variables "Time lags are used whenever the effect of a given independent variable takes place in a later time interval ....23 Some of the inde- pendent variables utilized in this study were considered as (possibly) being in this classification, and because of this, certain variables were lagged. Considering farm income, for example, the use of a lag seems very apprOpriate. .....while income is, to a great extent, determined in the fall as crops are harvested, machinery purchases reach a fairly high.peak in the spring months as farm operations get underway. Fur this reason, income of the previous year may have more effect on current machinery purchases than does current income.2 From this same line of reasoning, it would also appear to be more appro- priate to use lagged capital gains rather than current capital gains. ‘When a "lagged" variable is referred to, it means the estimate of the 23. Thomsen, F. L. and Foote, B. J., op. cit., p. 286. 2h. Cromarty, op. cit. 26 variable for the previous year is related to the dependent variable for the current year. Similarly "current" variables are estimates of the variable for the same year as the dependent variable. There must exist a logical basis for using a lagged.variable rather than a current variable if one is to be used in an analysis. ‘Variables used based on logical grounds can then be scrutinized on statistical grounds for apprOpriateness. This was the approach used in regards to the possibilities of lagged relationships. No attempt has been made to employ distributed lags, which was considered to be beyond.the scope of this investigation.25 Prediction Versus Different Relationships Between the'Variables The construction of a demand.model for farm.machinery and tractors suggest that a great deal of attention should be given to the development of a precise prediction equation. While this is a noteworthy objective in itself, the efforts of this study are directed more toward Obtaining indications as to possible differences in the relationships of variables considered relevant in aggregate investment decisions during upswings and downswings of the general business economy. In this way the study separ- ates from studies which have investigated machinery investment in the 26 conventional time series method. 25. For the most recent discussion on the methodological aspects of using distributed lags, see Nerlove, Marc, Distributed Lagg and Demand Analysis for Agricultural and Other Commodities, Agriculture Handbook No. l l, AMS, USDA, June 1958. - 26. As an example, see Cromarty, William A., The Demand for Farm Machinery and Tractors, Agricultural Experiment Station, East Lansing, Tech, Bul.(ln Processl. 27 This accounts in part for the lack of attempt to refine the analysis by using simultaneous equations, distributed lags, et cetera, simply be- cause the purpose was not to construct an accurate predictive model. Such a model if sought, would be difficult to construct, largely because of limitations as to accuracy and availability of data. In this connec- tion, Miss Burk has made the admonishment". ....I always feel called upon to warn against reliance on overly refined methods applied to rough data"?7 The data used in this study would be classified as being in this "rough" category and it was felt that the maximum return, in terms of time and effort, would be obtained by using the methods that were employed. These methods provide some indication of the differences of the relationships of corresponding variables for contraction years and expansion years. The statistical test of significance for difference between corresponding variables is given in Appendix I. Criteria for Evaluation of Regression Coefficients In reviewing the results from the use of alternative equations in the single equation formulations, the interest was in, first of all, the consistency of the signs of the estimated parameters with expected signs from the guiding theory. These expected signs are given in Table 2.1. Reasons for these expected signs, when the variables are considered separately, are fairly obvious and discussion of their derivation is considered unnecessary. However, inconsistencies in signs which appear in the analysis may sometimes be explained in terms of other factors. 27. Burk, Marguerite, "Studies of the Consumption of Food and Their Uses," Journal of Farm Economics, Vol. 38, 1956, p. 17’41. 28 Interpretations of this general nature are made when they are considered appropriate. TABLE 2.1 - EXPECTED SIGNS OF ESTIMNTED PARAMETERS Variable 318D Farm Income 4 Capital Gains Machinery Stocks - Relative Price of Machinery - Relative Price of Labor 4 Time + M M Equations that do not fulfill the criteria of economic theory, i.e., the expected signs of the regression coefficients, must be regarded with suspicion. In some cases these discrepancies can be explained by the margin of error in the data used. Wrong signs at levels not significantly different from zero can be tolerated as not contradicting economic theory. Such results, though undesirable, appear in many cases to be inevitable. In other cases, discrepancies may be exPlained by some other factor exerting an influence on the association. From this, we see the necessity of examining results on both.statistical and economic grounds. CHAPTER III m RESULTS OF THE ANALYSIS The purpose of the study, as previously indicated, was to determine if the relationships between variables associated with farm tractor and machinery purchases have been different during different phases of the business cycle. Several equations were fitted to obtain indications of the relationships of variables during contractions as compared to the relationships of corresponding variables during expansions in general business activity. Since primary interest was in relationships of variables rather than in accurate prediction in putting together formu- lations, it was not expected that "the" prediction equation would be achieved. Undoubtedly, it was not. However, this is a matter of pur- pose 3 some "feel" toward the relations of the variables included, thus the relationships involved, was obtained from the consistencies produced by these fittings. This was the focal point of interest in the examina- tion of the results of the fitted equations. The Results Presented The equations that were fitted are divided into four groups on the basis of major differences in the variables included in the equations. Between equations within these groups, there were changes of a lesser nature in the form of the variables included. The results of each group ~re presented in tabular ton and discussed from the standpoint of rela- tionships indicated by the results. Overall results and interpretations are discussed after the results of all four groups have been presented. 29 30 Gray I. The first group of equations contains one basic equation and five variations. One variable in the basic equation was changed in each of these variations. The variables included in each of these equations, along with the coefficient of multiple determination (a?) for each equation, are given in Table 3.0. ms 3.0 - VARIABLES mcnmsn AND Tm councmm or mm DETERMINATION, EACH EQUATION, GROUP I 2 Dependent Equation R Variable Independent Variables l . 809 Machinery Expenditures 2 . 705 Machinery Shipments 3 . 8&9 Machinery Expenditures h . 830 Machinery Expenditures 5 . 810 Machinery Expenditures 6 . 72h Machinery Expenditures Current year's income, current year‘s capital gain, stocks of machinery, the relative price of machinery and the relative price of labor. Same as equation 1. Same as equation 1, except that pre- ious year's income is used in place of current year's income. Same as squat ion 1, except that current year's capital gains are deflated by the index of prices of farm tractors and machinery. Same as equation 1., except that pre- vious year's capital gain is used in place of current year's capital gain. Same as equation 1, except that stocks of machinery are dropped. In addition to the variables given in Table 3.0, the constant term (a value) was also fitted as a "double" variable in the first two equations. Splitting of the a value resulted in values very close to each other 31 (41108 for contractions and 4368 for expansions in equation one; -l285 for contractions and -l2h6 for expansions in equation two and nonsignifi- cant fran zero in each case), so in the remainder of the equations, the constant tam was fitted as a single value in the usual manner. The results from using each variable in Group I are given in Tables 3.1 to 3.5. These regression coefficients were examined for consistency with economic theory, significant difference from zero, and significant difference between corresponding regression coefficients. In reading these tables, it should be remembered from Chapter II that odd numbered variables are for contractions and even numbered variables are for expan- sions. The test statistics used are for two purposes: (1) the (tb) test statistic is used to test the regression coefficient for significant difference from zero in the conventional manner, and (2) the “bi b3) test statistic is used to test corresponding regression coefficients for significant difference. The (tb) test statistic is obtained by dividing the regression coefficient by its standard error (9b)' The derivation of the (tbi 13.3) test statistic is given in Appendix I. In Table 3.1, we see that the use of farm income as an independent variable in Group I resulted in coefficients consistent in sign with economic theory. 'These cOefficients were significantly different from zero as evidenced by the (tb) test statistic. The regression coefficients of the farm income variable for contractions were always larger than the corresponding coefficients for expansions. This was true in all cases , whether the current year's income or the previous year's income was used, and suggests that changes in farm income are more closely associated with machinery purchases in contractions than in expansions. 32 There is a definite indication that income changes are more closely related to machinery purchases in contractions than in expansion, and the (tum) test statistic indicates that the difference is statistically sign- ificant . was 3.1 - seams m USING FARM moons AS an mmm mamas, (moor I Form of Regression Standard Test statistics Equation variable coefficient error (3b) tb tbibJ 1 Current Year's x11 .1620 .oaho 3.00 1 Income x12 .0696 .0253 2.75 '55 2 Current Year's xn .1153 .0h39 2.63 1 99 Income :12 .0188 .0206 .91 ' 3 Previous Year's ‘11 .1528 .0h57 3.3!; 8 Income :12 .1091; .0256 n.27 ' 3 h Current Year's x11 .1763 .0562 3.1h 1 Income 1:12 .0938 .0263 3.56 '33 5 Current Year‘s x11 .1160 .0822 1.1+1 82 Income x12 .ot62 .0222 2.08 ' 6 Current Year's x11 .2222 .0575 3.86 2 Income x12 . 068k . 030h 2 . 25 ' 37 Table 3.2 gives the results from using capital gains as an indepen— dent variable in Group I. First of all, in checking these results, it should be noticed that the use of the current year's capital gain aims resulted in regression coefficients, both in expansions and in contrac- tions, which have negative signs. This is inconsistent with the theory developed in Chapter II. However, when the capital gain for the previous year was used, the regression coefficients for both expansions and con- 33 tractions take the correct sign. Thus, we have an indication that the capital gain from the previous year is the more correct variable to use. TABIE 3.2 - RESUIES ROM USIIB CAPHAI. GAINS All) LOSSES AS AN INDEPENDENT VARIABIE, GROUP I Form of Regression Standard Test statistics Equation variable coefficient error (ab) tb tbibJ 1 Current Year's 1:21 «0208* .0121 1.73 1 26 Capital Gain :22 -.ooh1* .0056 .73 ° 2 Current Year's x21 -.0095* .0098 .97 79 Capital Gain :22 -.0009* .0016 .20 ° 3 Current Year's x21 -.0067* .0092 .73 3h Capital Gain :22 -.oo32* .0015 .72 ° h Current Year's :21 -.022h* .0135 1.66 1,5 Capital Gain x22 -.015lr* .007h 2.09 ° Deflated 5 Previous Year's 121 .0006 .0208 .03 .39 Capital Gain :22 .0090 .0056 1.60 6 Current Year's :21 -.0321* .0133 2.h1 2 11 Capital Gain x22 -.0007* .0301 .11 ' *Inconsistent with expectations When the previous year's capital gain was used in equation five, the regression coefficient for expansions was larger than for contractions, indicating that capital gains and losses were more closely associated with purchases of tractors and machinery in expansions than during contractions. The regression coefficient for expansions had some significance from zero while the regression coefficient for contractions did not. However, there was not a significant difference between the regression coefficient for expansions as compared to the corresponding coefficient for contractions. 3h The results from using stocks of machinery as an independent variable in Group I are given in Table 3.3. Examdnation of these results reveals that the regression coefficients fer both contractions and expansions have positive signs. TABEE 3.3 - RESUETS FROM USING STOCKS 0F MACHINERY AS AN INDEPENDENT VARIABLE, GROUP I Form of Regression Standard Test Statistics Equation variable coefficient error (ab) ”b tbibJ 1 Stocks as x31 .0169 .0079 2.15 .03 Defined x32 .0172 . 00118 3 . 61 2 Stocks as x31 .0093 .006h 1.h5 7h 3 $00” 88 X31 e 0137 e 0071 1. 92 6“ Defined 132 .0187 .0038 h.87 ' h Stocks as x31 .0162 .0073 2.22 8 Defined x32 .0192 .00h1 1+. 7k ‘3 5 Stocks as x31 .0209 .0113 1.8h 18 Defined. 132 e 0187 . 00,43 ’4 e 38 . The theory in Chapter II suggested the coefficients fer the stocks variable would be negative, particularly during contractions of general business activity. After farmers had acquired.machinery stocks, their needs for additoaal machinery would be reduced.until they must replace that which exists. However, this relation appears to be overpowered.by the trend in new technology that has occurred in agriculture. ‘Wilcox and Cochrane apparently anticipated this result when they wrote: ...unless important technological advance keeps reoccurring a heavy volume of investment must decline after a few'years.1 In Wilcox, w. w., and Cochrane, w.‘w., op. cit., p. h59. 35 The positive sign on the stocks of machinery coefficients appear to attest to the importance of tschnolbgical trend. Interpreted in this manner, this result is consistent with theory. All of the recession coefficients were significantly different from zero, tending to be a little larger in expansions than in contractions. However, the difference between regression coefficients for expansions and contractions was not statistically significant. Table 3.1; gives the results from using the relative price of mach- inery as an independent variable in Group I. The signs of the recession coefficients are as expected, with the exception of equations five and six. Equation five has coefficients not significantly different from zero and equation six has coefficients which do have some significance from zero. Equation six doesn't include the stocks variable, giving some indication of the importance of the inclusion of a variable reflecting trend, as stocks apparently do. In general, the first four equations have coefficients for the relative price of machinery which are larger in contractions than in expansions. This suggests that farmers pay closer attention to machinery prices compared to prices they receive during contractions than during expansions. This difference was not statistically significant, however. 36 TABLE 3.h - RESULTS FROM USING THE RELATIVE PRICE OF MACHINERY AS AN INDEPENDENT VARIABLE, GROUP I Form of Regression Standard Test Statistics Equation variable coefficient error (ab) tb tbibJ 1 Relative Price of Machinery in -227.3h 206.61 1.10 82 as Defined xhe - 10.1w 163.81 .06 ' 2 Relative Price of Machinery 1&1 -ll3.23 168.11 .67 .12 as Defined ‘h2 -l38.3l 133.28 1.0h 3 Relative Price of Machinery xhl -205.96 lh7.39 l.h0 1.06 as Defined xh2 - 71.06 115.0% .62 h Relative Price of Machinery 2“ -203.11 167.55 1.21 .hI as Defined xh2 -1h5.70 125.99 1.16 5 Relative Price of Machinery ‘hl 3.95* 172.0h .02 .08 as Defined xh2 - 7.79 136.21 .06 6 Relative Price of Machinery xhl 98.12* 187.68 .52 62 as Defined 27,2 205.21% 139.30 1.147 ‘ *Inconsistent with expectations The results from using the price of labor relative to the price of ‘machinery in Group I are given in Table 3.5. The regression coefficients for this variable had these characteristics in general: (1) the coeffici- ent for contractions was always a large negative, and (2) the coefficient for expansions was either a smaller negative, or positive. A negative regression coefficient for the price of labor relative to the price of machinery is inconsistent with the theory developed in Chapter II. The negative coefficients in contractions were significantly 37 different from zero; while in expansions, in two cases negative coeffi- cients, and in one case a positive coefficient, were significantly diff- erent from zero. There was a significant difference between the regres- sion coefficient for contractions as compared to the regression coefficient for expansions. Possible interpretations of this result are delayed until the discussion of overall results in the latter part of this chapter. TEBLE 3.5 - RESUDTS EROMIUSING THE RELNTIVE PRICE OF LABOR AS AN INDEPENDENT VARIABDE, GROUP I Form of Regression Standard Test statistics Equation variable coefficient error (ab) tb tbibJ 1 Relative Price Of Labor :51 -392009'. 205-95 1090 1 57 as Defined x52 111.01 156.60 .09 ' 2 Relative Price Of LBDOI‘ 351 '330-1‘0" 167057 1°97 1 1,9 as Defined x52 - l6.7h* 127.h1 .13 ' 3 Relative Price of Labor x51 -352.51* 176.97 1.99 7,2 as Defined x52 -266.88* lh1.5h 1.89 ° h Relative Price of Labor x51 4:32.054: 1911.15 2.23 1 2.). as Defined x52 -l53.57* 1h0.h8 1.09 ° 5 Relative Price of Labor X51 ‘313-30* 229°23 1°39 1 26 as Defined x52 - 9.2h* 126.71 .07 ' 6 Relative Price of Labor :51 «217.5% 235-06 -92 2 21 as Defined :52 356.77 129.53 2.75 ° *Inconsistsnt with expectations 38 Group II. This coup differs from Group I in that instead of including the relative price of machinery as one variable, the index of machinery prices and the index of prices received by farmers were included as separate variables. The variables included in the equations of this coup along with the coefficient of multiple determination (R2) for each equation are given in Table 3.6. TABLE 3.6 - VARIABLES INCLUDED AND THE COEFFICIENT 01“ mm DETERMINPRION, EACH EQUATION, (300? II Dependent Equation R2 variable Independent variables 1 .830 Machinery Previous year's income, previous Expenditures year's capital gain deflated, index of machinery prices, index of prices received. 2 .8113 Machinery Same as equation 1, plus the time Expenditures variable . m Table 3.7 gives the results of the equations used in Group II. Before examining these results, it should be pointed out that using the indexes of machinery prices and prices received involves high intercorrelation between the two indexes as well as inter-correlation between each of the indexes and farm income. Using the relative price of machinery did not present this problem. Thus, the results from this coup are believed to be highly distorted because of the inconsistent signs for several of the recession coefficients compared with the results in Group I. The signs for coefficients of prices received and of machinery prices were inconsistent in all cases. Results such as these raise serious 39 questions as to the usefulness of formulations including the two price indexes separately. It is interesting to note the difference in the coefficients of the time variable, however, which suggests a difference in the influence of the passage of time, or rather variables which change over time, in contractions as compared to expansions. This variable was examined in greater detail in.Group IV. TIBLE 3.7 - RESUDTS FROM GROUP II Form of Regression Standard Test statistics Equation variable coefficient error (ab) tb tbibJ 1 Previous Year's x11 .0790 .l29h .61 .08 Income :12 .0892 .022h 3.97 2 Previous Year's x11 .0886 .0h07 2.18 Income ‘12 .09h3 .0292 3.23 -1“ 1 Previous Year's Capital Gain .017h .0127 1.36 Deflated :3: .0022 .007h .30 1°06 2 Previous Year's Capital Gain x21 .0202 .0123 1.6h 1 ho Deflated x22 .oooh .0072 .06 ' 1 Current Prices x71 -1.335* 2.053 .65 u Received 272 - .550* 1.067 .52 '3 2 Current Prices 171 -l.868* .200 .93 61 Received x72 - .hh1* 1.h89 .30 ° 1 Current Price x81 h.801* 2.359 2.0% h9 of Machinery x82 3.53h* 1.115 3.17 ° 2 Current Price x81 7.5h3* 2.586 2.92 1 h of Machinery x82 3.h09* 2.082 1.6% '3 2 Tile (1910.1) x -9.712 h.355 2.2 xg; .731 h.u28 .17 1'88 *Inconsistent with expectations ho Group III. Because of the results obtained in Group II, it was decided that efforts along the lines of Group I would be more fruitful than continuance of Group II. In Group III, the equations included both income of the previous year and income of the present year as variables. This was done to Obtain a (possible) better measure of the influence of expectations on tractor and machinery purchases. The equations are dif- ferent from the equations in Group I in this respect. Also, stocks of machinery was not included as a variable in the formulations of this coup. There are five equations in the coup. The variables included in each equation, along with the coefficient of multiple determination (R2) are given in Table 3.8. TABLE 3.8 - VARIABLES INCLUDED AND THE COEFFICIENT OF WLTIPIE DETERMINATION, EACH EQUATION, GROUP III Dependent Equation B2 variable Independent variables 1 .7hl Machinery Current year's income, previous year's Expenditures income, previous year's capital gains ' deflated by the price of machinery, the relative price of machinery, and the relative price of labor. 2 .6h3 Machinery Same as equation 1. Shipments 3 .Th'j Machinery Same as equation Lexcept that previous Expenditures year's capital gains were not deflated by price of machinery. h .657 Machinery Same as equation 3. Shipments 5 .6h8 Machinery Same as equation 3, only the relative Shipments price of labor was drapped. 1+1 The results from using farm income in Group III are given in Table 3.9. It should.be pointed out that the two incomes, the previous year's and the current year's, are highly inter—correlated, thus perhaps dis- torting the results of either looked.upon.separately; ‘With this word of caution, we see the regression coefficient for the current year's income was positive in all contractions and negative in all expansions. The regression coefficient for the previous year's income was always consis- tent in sign in‘both expansions and contractions. The possible reason for this result is discussed in the general interpretations after all four groups are presented. Hare again, as in Group I, the indications are that income changes in contractions are more important than in expansions in.farmers' deci- sions to purchase machinery. However, the pattern is not as clear in the case of the previous year's income in this coup as in Group I, and this is possibly a result of the inter-correlation.that exists with the current year's income. The coefficients in general were signifi- cantly different from zero, but were not significantly different in expansions and contractions. TABLE 3.9 - RESUDTS FROM USING FARM INCOME AS AN INDEPENDENT'VARIABLE, GROUP III FOrm of Regression Standard Test statistics Equation variable coefficient error (ab) tb “mm 1 Current Year's x11 .0395 .1191 .33 hh Income x12 - . 015M . 0ho6 . 38 ' 2 Current Year's x11 .0953 .0915 1.0h 1 52 Income :12 - . 0515* . 0312 1. 65 ' 3 Current Year's x11 .0712 .1153 .62 69 Income x12 -.0127* .0h03 .32 ° h Current Year's x11 .1052 .0876 1.20 1 67 Income :12 -.0h89 .0306 1.60 ‘ 5 Current Year's x11 .0387 .0793 .h9 1.06 Income :12 -.05oh* .0305 1.65 1 Previous Year's x11 .1810 .1007 1.80 .35 Income 112 .1h10 .0556 2.5% 2 Previous Year's x11 .052h .077h .68 75 Income x12 .1189 .0h27 2.78 ' 3 Previous Year's x11 .l59h .1010 1.58 .36 Income x12 .1188 .05h1 2.20 h Previous Year's x11 .Ohhl .0767 .57 .69 Income x12 .103h .0h11 2.51 5 Previous Year's x11 .0372 .0775 .hB .99 Income x12 .1203 .O30h 3.96 *Inconsistent with expectations Table 3.10 gives the results from using capital gains as an inde- pendent variable in Group III. deflated‘by the index of tractor and machinery prices in equations one and two resulted in inconsistent signs for the regression coefficients for both expansions and contractions. ‘When capital gains were not Use of the previous year's capital gain deflated.in the other three equations, the sign in expansions was con- sistent, while the sign in contractions was inconsistent. TABLE 3.10 - RESULTS FROM USING CAPITAL GAINS AND LOSSES AS AN INDEPENDENT VARIABLE, GROUP III h3 Form of Regression Standard Test statistics Equation variable coefficient error (9b) tb tbibJ 1 Previous Year's Capital Gain x21 -.0118* .0181 .65 .28 Deflated :22 -.0063* .0093 .68 2 Previous Year's Capital Gain x21 -.0081* .0139 .58 52 Deflated x22 -.0003* .0071 .Oh ' 3 Previous Year's 3:21 -.0175* .0156 1.12 12 Capital Gain :22 .0029 .0069 .h2 ' h Previous Year's x21 -.0095* .0119 .80 1 17 Capital Gain x22 .0056 .0053 1.07 ° 5 Previous Year's x21 -.OO20* .0110 .19 58 Capital Gain :22 .0050 .0052 .96 ' *Inconsistent with expectations The three equations using non-deflated capital gains did not give statistically significant recession coefficients and there was not a significant difference between the recession coefficient of capital gains for contractions and expansions. The results from using the price of machinery relative to prices received by farmers in Group III are given in Table 3.11. The striking feature of this table is that in all cases the recession coefficient has an inconsistent sign. Mt TABLE 3.11 - RESULTS FROM USING THE RELATIVE PRICE OF MACHINERY AS AN INDEPENDENT VARIABLE, GROUP III __—_ Form of Recession Standard Test statistics Equation variable coefficient error (31,) tb tbibJ 1 Relative Price of Machinery ‘hl h9.33* 205.03 .21; . 1,2 as Defined :7“, 120.97* 16h.83 .73 2 Relative Price ' of Machinery x141 h7.99* 157.59 .30 .26 as Defined x112 81.96* 126.69 .65 3 Relative Price of Machinery in 62.87* 187.53 .3h 88 as Defined 1112 205.97* lh5.70 1A1 ' h Relative Price of Machinery xhl 59.’+9* 1h2.51 .h2 .58 as Defined n+2 131.51” 110.72 1.19 5 ‘ Relative Price Of “30th X!”- 38.97* 137.27 .28 .90 as Defined 21,2 150.13% 107.81 1.39 *Inconsistent with expectations The inconsistent sign is very difficult to explain. However, in Group I, the relative price of machinery had the correct sign, excepting when the stocks variable was drapped from the formulation. This indicates the need for a variable which reflects trend. Such a variable was used in Group IV. It appears to be unavailing to discuss a variable which dis- plays such an inconsistent sign, but if we recognize the variable as such, having in mind a possible remedy, it is rather interesting to note certain consistencies. The regression coefficient was always larger in expansions. This indicates the factor used to correct this inconsistency has a "larger Job to do" in expansions than in contractions. The (”bibj) test statistic “5 indicates there was not a significant difference between recession co- efficients for expansions and contractions. The results from using the price of labor relative to the price of machinery in Group III are given in Table 3.12. In this coup of equa- tions, the coefficient for contractions was always a large negative, inconsistent with theory. The sign of the coefficient for expansions was always consistent with theory, but the coefficient was not sicificantly different from zero in each case. TABIE 3.12 - RESUITS FROM USING THE RELATIVE PRICE OF LABOR AS AN INDEPENDM VARIABLE, GROUP III M Form of Recession Standard Test statistics Equation variable coefficient error (ab) t1, tbibJ 1 Relative Price of Labor x 1 -359.22* 268.29 1.3h- 1 39 as Defined :22 h7.oo 16h.76 .29 ° 2 Relative Price of Labor x 1 -305.80* 206.21 1A8 1 50 as Defined xge 31.h0 126.63 .25 ‘ 3 Relative Price of Labor x51 -370.70* 250.87 1.h8 1.69 as Defined x52 102.75 156.h0 .66 h Relative Price of Labor x l -301.9h* 190.6h 1.58 1 72 as Defined x22 6h.ho 118.86 .5h ‘ *Inconsistent with expectations Results here, using the relative price of labor, correspond closely with the results in Group I. The test statistic for difference between regression coefficients indicates there was a significant difference between the recession coefficients for expansions and contractions. 1&6 Group IV. This group continues along the lines of Group III, differ- ing from Group III in that a time variable (1910.1) was added to the variables included in the formulations. Also, because of the intercor- relation between succeeding years' incomes, three equations were used which included onZLv one of the two incomes, current or previous year's. There were seven equations included in Group IV. The variables used, along with the coefficient of multiple detemination (R2), for each equation are given in Table 3.13. TABLE 3.13 - vmnmss INCLUDED AND THE comm-10m or immune mmmn, nos EQUATION, GROUP 1v Dependent Equation R2 variable Independent variables l .793 Machinery Current year's income, previous year's Expenditures income, previous year's capital gain, the relative price of machinery, and the time variable. 2 .691 Machinery Same as equation 1. Shipments 3 .823 Machinery Same as equation 1, with the relative Expenditures price of labor added. 14 .731 Machinery Same as equation 3. Shipments 5 .672 Machinery Same as equation ’4, with current Shipments year's income dropped. 6 .658 Machinery Same as equation 5, with the relative Shipments price of labor drapped. 7 .635 Machinery Same as equation 2, with previous Shipments year ' s income drOpped. h? The results from using farm income in Group IV given in Table 3.1h correspond very closely to the results in Groups I and III. In general, the regression coefficients for the current year's income in expansions were always negative and during contractions, positive. With the previous year's income, the coefficients were always positive in both expansion and contraction and generally larger in contractions, as in Groups I and III. There was not a significant difference between the recession coefficients for farm income during expansions and contractions in most of these equations. To check the effoct of the intercorrelation between the current year's income and the previous year's income, equations five and six were fitted using the previous year's income only, and equation seven was fitted using the current year's income only. The previous year's income used alone in equations five and six gave coefficients consistent in sign in‘both expansions and contractions while the current year's income used alone in equation seven yielded a consistent sign in contractions and an inconsistent sign in.expansions. This is the same result as when both the current year's income and the previous year's income were used together. The coefficients for the current year's income used alone in equation seven were nonsignificant in both contractions and expansions. The co- efficients for the previous year's income used alone in equation six were significantly different from zero, but not significantly different in contractions and expansions. However, in equation five, the previous year's income used alone gave a coefficient for expansions that was signif- icantly different from zero while the coefficient for contractions was not. There was a significant difference between the regression coeffici- ents for expansions and contractions. This suggests that the intercor- #8 relation between the current and the previous years' incomes has possibly distorted the magnitude of the income coefficients and.that only one of the two (prdbably the previous year's) incomes should.be included. TABLE 3.1h - RESULTS FROM'USING FARM INCOME AS AN INDEPENDENT VARIABLE, GROUP IV Form of Regression Standard Test statistics Equation variable coefficient error (3b) tb t’bibJ 1 Current Year's x11 -.0655* .09h3 ' .69 16 Income x12 -.0h99* .0376 1.33 ' 2 Current Year's x11 .006h .075h .09 1 02 Income x12 -.0737* .0301 2.h5 ’ 3 Current Year's x11 .0522 .0966 .51: 1 12 Income 1:12 -.6317* .0367 1.72 ° h Current Year's xll .0958 .0780 1.23 2 18 Income :12 -.0853* .0296 2.88 ° 7 Current Year's ‘ xn .0081 .0299 .27 95 Income :12 -.0133* .0237 .56 ° 1 Previous Year's x11 .1585 .0968 1.6h Income :12 .102h .0385 2.66 '55 2 Previous Year's 1:11 .0307 .077h .hO ~ Income :12 .0912 .0308 2.96 '07 3 Previous Year's x11 .1669 .0898 1.86 1 Income x12 .0953 .0h56 2.09 '7 h Previous Year's x11 .0362 .0725 .50 Income x12 .0896 .0368 2.h3 '65 5 Previous Year's x11 .1221 .0h62 2.6h 1 8 Income x12 .0172 .0298 .58 '9 6 Previous Year's xl1 .0550 .0302 1.82 72 Income 2.15 .0388 .0233 1 . 66 ' *Inconsistent with expentations #9 Table 3.15 presents the results from using capital gains and losses as an independent variable in.Group IV. As in Group III, the regression coefficient in contractions‘was negative in all cases but one and positive in expansions. There was not a significant difference between the regres- sion coefficient for contractions as compared to expansions. TABLE 3.15 - RESULTS FROM USING CAPITAL GAINS AND LOSSES AS AN INDEPENDENT VARIABLE, GROUP IV Form of Regression Standard Test statistics Equation variable coefficient error (s-b) tb tub, 1 Previous Year's :21 -.0069* .013h .52 .55 Capital Gains x22 .0012 .0061 .20 2 Previous Year's x21 -.00002* .0107 .001 39 3 Previous Year's x21 -.0209* .0133 1.57 1 h8 Capital Gains x22 .0006 .0058 .10 ‘ h Previous Year's x21 -.0106* .0108 .98 1 22 Capital Gains :22 .0038 .00h7 .81 ' 5 Previous Year's x21 -.0036* .0100 .36 80 Capital Gains x22 .0055 .0052 1.06 'n 6 Previous Year's x2l -.0002* .0100 .02 h6 Capital Gains x22 .0050 .0051 .98 ‘ 7 Previous Year's x21 .0012 .0112 .11 1 Capital Gains x22 .0076 .0052 Lt? '5 *Inconsistent with expectations The results from using the relative price of machinery as a variable in Group IV are given in Table 3.16. The introduction of the time variable changed.the signs of the coefficients in.both expansions and contractions from Group III. The regression coefficients were statistically signifi- 50 cant from zero and of about equal magnitude in.contractions and expansions. Since in some cases the coefficient for contractions was larger than for expansions and in other cases the coefficient for expansions was larger than for contractions and the two about balance out, the difference bet- ween regression coefficients could.not be considered significant. The test statistic for significant difference (”bibJ) lends credence to this conclusion. TABLE 3.16 - RESULTS FROM USDI} TEE RELATIVE PRICE 02? MACHINERY AS AN INDEPENDENT'VARIABIE, GROUP IV Form of Regression Standard Test statistics Equation variable coefficient error (ab) tb PbibJ 1 Relative Price of Machinery ‘h1 -365.2u 211.77 1.72 6 as Defined rhe -310.01 229.52 1.35 '3 2 Relative Price of Machinery ‘hl -231.18 169.33 1.37 10 as Defined xh2 -218.89 183.52 1.19 ' 3 Relative Price of Machinery ’hi -h89.96 225.71 2.17 2h as Defined xhz -525.35 2h6.58 2.13 ' h Relative Price of Machinery xhl -3h0.2h 182.30 1.87 h8 as Defined ’h2 -396.73 199.15 1.99 ° 5 R;l;:i;: Price 8h h o c nary x -l72.97 1 .95 .9 as Defined 1:: -2l9. 01 208 .113 1. 05 ' 36 6 Relative Price of’Machinery ‘hl -l3l.h7 167.01 .79 05 as Defined mu, -137.h9 186.81 .7h ' 7 Relative Price of Machinery 1&1 -385.23 173.61 2.22 h2 as Defined ‘h2 -h37.77 182.16 2.h0 ' W 51 Table 3.17 gives the results from using the price of labor relative to machinery prices in Group IV. Similarly to Groups I and III, the re- gression coefficient for contractions was, in each case, a large negative, and the regression coefficient for expansions was not significantly differ- ent from zero. The difference between the regression coefficient for contractions as compared to expansions was very significant, statistically. TABLE 3.17 - RESULTS FROM USING THE RELATIVE PRICE OF LKBOR AS AN INDEPENDENT VARIABLE, GROUP IV Form of Regression Standard Test statistics Equation variable coefficient error (81,) t'b tble 3 Relative Price of Labor 1 1 -621.98* 219.81; 2.83 2 o as Defined x22 - 31.78* 1129!; .22 '5 h Relative Price of Labor x 1 -h78.72* 177.55 2.70 2 28 as Defined x; - h3.29* 115.15 .38 ° 5 Relative Price . of Labor x -301.59* l7h.99 1.72 51 1.85 as Defined x52 55.20 121.55 .h5 *Inconsistent with expectations The results from using time as an independent variable in Group IV are given in Table 3.18. The signs of the coefficients were positive in all cases for both contractions and expansions. The regression coeffici- ents for expansions were always larger than the ones fer contractions with the use of this variable. This difference was statistically significant. This finding, along with the other results are interpreted in the follow- ing section. 52 TABLE 3.18 - RESULTS FROM USING TIDE AS AN INDEPENDENT VARIABLE, GROUP IV Form of Regression Standard Test statistics Equation variable coefficient error (ab) tb tbibj 1 I1310=1) :2: 1::23 2.3% 3:33 2-25 2 $1330.1) :2; 8:3; §;§2 2:2; 1.h7 3 11330-1) :2; 122$: 32%: $233 2-62 h $1310.1) :2; 12:22 §:i2 §j§2 1.72 5 ?i330-1> fig; #23; §:%3 2:32 1.61 6 ?:;;o-1) :2; $233 3233 1:33 1.31 7 $i33021) :2; 12:22 §i§$ iii; 1.52 53 Recapitulation and Interpretation of Results The results from the preceding groups of equations are summarized and interpreted from.an overall standpoint under the heading of each indepen- dent variable. ‘Emphasis is placed upon interpretations of differences in the relationships of variables over the business cycle that occurred in the analysis since this was the purpose of the investigation. Fanm income. The results from the fitted equations indicated that income changes during contractions are more closely related to machinery purchases than similar changes in expansions. Farm income changes may have a greater influence on machinery purchases during contractions be- cause: (1) farmers may be more careful or pessimistic as a result of a beneral business decline and (2) credit may be harder to Obtain with lower incomes, thus multiplying the effect of the income decline. we expect expenditures on machinery to be reduced as income is reduced; however, the reduction in expenditures appears to be more then.propor- tional to income decreases, Judging from the regression coefficients. When both income of the current year and of the preceding year were used as variables, it was found that the previous year's income had con- sistent signs during contractions and inconsistent signs during expan- tions. Examination of the relation between farm income and farmers' expenditures on tractors and machinery in Figure 3.0 suggests that farmers reduce expenditures as a result of farm income decreases more rapidly (in the current year) than they increase expenditures as a re- sult of farm income increases (involves a lag of about one year). While this phenomenon has not occurred.in all cases of farm income increases and decreases, the relation does appear to have some degree of regularity. 7., Farm Income (% of 37-hl) H t‘ Figure 3.0 - Machinery Purchases by Farmers Related to Net Cash Farm Income, United States, 1910-56. 1 c1 a --- a Net Cash Farm Income d 00_ 8 Machinery Purchases d 75% 7 50% ’55, p :)}~ 75 t q 50% .4 L: l l l l 1 i 1910 1920 193a 19uo Source: See Appendix II, Tables 1 and 3. 1950 1956 275 250 225 *‘ ’3 d 8 8 Machinery Purchases UT 0 |\) W 55 The relation found here could well be the reason for a positive coeffi- cient for current farm income in contractions and a negative coefficient in expansions. Since farm income was selected in part as a measure of the marginal efficiency of capital, why does a different relation hold between income increases and decreases and the rate of machinery purchase? Dillard gives a very plausible answer in this connection. The turning point from.expansion to contraction is thus explain- ed by a collapse in the marginal efficiency of capital. The change from an upward to downward tendency takes place suddenly, and in this respect differs from the turning point from contraction to expansion, which occurs more gradually and often imperceptibly.2 This appears to be a fairly substantial reason for the results Obtained and the relation evident in Figure 3.0. The relation suggests that per- haps variables pertaining to direction of income change should.be included in the analysis. Also involved would be investigation of the duration of such changes. Unfortunately, no systematic approach exists for the treat- ment of variables of this nature. Using such variables requires specific assumptions which might prove incorrect. This would, of course, lead to classifications which are incorrect since other classifications would fit the case equally well. Since no systematic method of examining the re- sults of alternative classifications has been developed, no attempts at including variables dealing with direction and duration have been made. CapitalZgains and losses. Indications from the fitted equations suggest that capital gains and losses were associated with machinery pur- chases during expansions, but that capital gains and losses were not as 2. Dillard, op. cit., p. 270. 56 closely related to machinery purchases during contractions. Figure 3.1 shows the relation between capital gains and losses and machinery pur- chases plotted over time. This relation exhibits a lag of about one year between the capital gain or loss which leads machinery purchases. The results from the fitted equations also indicated this relation, The relation in Figure 3.1 appears to have been closer befOre World War II than since, but the relation between the previous year's capital gain and the current year's machinery purchase has still moved generally in the same direction. This may be caused by a reduction in the importance of external credit as a source of capital formation since the war, for in- come and savings accumulated during the war period.may have been.more important.3 The regression coefficients were, in some cases, significantly dif- ferent from zero, particularly in expansions, and were not significantly different from zero during contractions. This could.be caused by one of two things; either capital gains were not important in machinery purchases, or the measure cf capital gains used was not accurate enough, There does not appear to be any particular reason for favoring either of these causes over the other. In general, however, more support is marshalled for the hypothesis that capital gains and losses have been.important during ex- pansions with respect to machinery purchases than the hypothesis that capital gains and losses have been important during contractions in influ- enging machinery purchases. Since capital gains and losses. are of the "paper" variety, and as such are not realized as income by those who hold properties on which they 3. In this regard, see Tostlebe, Alvin 3., Capital in Agriculture: Its Formation and Financing;since 1870, a study by the National Bureau of Economic Research, Princeton, University Press, 1957, pp. lhh-l53. 57 Gains and Losses in Holding Real Estate, Crops, and Livestock, Figure 3.1 - Machinery Purchases by Farmers Related to Capital United States, 1910-56. ‘ 275 4 225 AHJINM ..HO *v DOOGSUHSAH tgfiroflz 5 O O 7. Ad 1 1 a 150 12 O 7 5 1956 1950 l9h0 1930 1920 1910 3 5 3 8 ”w a O .m 8 a ,m C mm 8 57. r 1m 8 t .lh mac no ”m :I u. n. P. b . . a .P p _ a _ _ » 505050505050 5.07.5 2570 film; 2 ...4 A» Hamv common can assoc advance See Appendix II, Tables 1 and 3. Source: 58 accrue, there may be some degree of "money illusion" in such gains. This observation is suggested by the improved results from using capital gains in current dollars rather than in deflated (constant) dollars. ‘Why should this illusion Operate in connection with capital gains? Equity positions of farmers are in money terms; thus a $10,000 mortgage on a $20,000 hold- ing seems very serious both to the farmer and to financial institutions. However, let the value of this property increase to $30,000 through price level increases, and the $10,000 mortgage does not appear to be nearly so serious. As a result of the capital gain, the farmer is more likely to use more credit which is now more available. If capital gains are truly.nonsignificant in the determination of machinery purchases, perhaps the nonsignificant regression coefficients of equations one and two in Group III which used deflated capital gains are the correct answer. Con- versely, capital gains and losses, more accurately measured, may be of more importance than indicated.by the results. It appears that this is an area which should.be investigated in greater detail. Stocks of machinery on farms. The results from the use of the stocks of machinery variable in the first group of equations have been inter- preted in that section as a reflection of the influence of new technology in agriculture. The relation between estimated stocks of machinery and machinery purchases as shown in Figure 3.2 has been close by definition. Technological advances have continued over the period studied, thus overpowering the relationship between stocks of machinery on hand and machinery purchases. The influence of technology on the coefficients of the stock variable appeared to be greater in expansions than in contrac- tions. Since the time variable was included in later analyses to obtain a measure of the relationship between technological trend and machinery 59 Figure 3.2 - Machinery Purchases by Farmers Related to Estimated Stocks of Machinery on Farms, United States, 1910-56. 1 275 300*” -1 250 3. ‘ 225 $7» M250 . --- = Estimated Stocks of Machinery -200 0 on Farms 3.“: 17 E’ __ -.- Machinery Purchases 5 §200 _ - 150 ,d O «‘3 ~ 125 a. O 3150- ‘leO '0 a? a . ,/" \ _ I, \ \ / 75 \ / a I \\ I, 100 , ‘“ 50 I, . s 25 60 “I 0‘; L l l I: l 1 O 1910 1920 1930 19140 1950 1956 Source: See Appendix II, Tables 1 and 5. Machinery Purchases (% of 37-hl) 60 purchases, further discussion of the stocks variable appears to be superfluous. The "real" price of machinery. The use of the price of machinery relative to prices received by farmers resulted in the conclusion that this variable is associated with machinery purchases in contractions and in expansions in about the same manner. In the first group of equations, the relative price of machinery appeared to be of more importance in con- tractions. This tendency was not produced in all of the equations of the group, however. In Group III, the regression coefficients were inconsis- tent in sign. This inconsistency was cleared up for some reason‘hy the inclusion of the time variable in.croup VI. Inclusion of the time vari- able did not affect either the sign or magnitude of other variables in- cluded in the equations, however. The regression coefficients in Group IV indicated no pattern of consistency in greater magnitude for either con- traction or expansion. Figure 3.3 shows the relation between the relative price of machinery and machinery purchases plotted over time. The relationship appears to be a quite consistent inverse one, with purchases of machinery rising and falling as the relative price of machinery falls and rises respectively. From the findings of the analysis, it appears that farmers respond to changes in the relative price of machinery in a similar manner in contrac- tions and expansions. The "real" price of labor. In each of the groups of equations, the price of labor relative to the price of machinery had regression coeffici- ents for contractions that were inconsistent and significently different from zero and regression coefficients for expansions that were either positive or negative and nonsignificant from zero. These results indicate Relative Price (Ratio) 1.50 H N) \fi H Figure 3.3 - Machinery Purchases by Farmers Related to the Relative Price of Machinery, United States, 1910-56. 61 --- = Relative Price of Machinery 1"" ~250 I Machinery Purchases : l 4225 l f -200 :I J '7 l V“ ~175 ”‘ l «H l O l ‘4150 3% ' U) ' 3 } “125 m ..n I o p --100 :5 r» n -+ 75 a: :8 U l ‘ J l l O 1910 1920 1930 19u0 1950 1956 Source: See Appendix II, Tables 1 and 6. 62 that there is a possible substitution of machinery for labor in expansions, although the results were not significant, statistically. On the other hand, in contractions, there are influences present that are not conducive to this substitution. This may be explained in part by the magnitude of the outlay that must be made for machinery as contrasted to hired labor, i.e., machinery purchases require a much greater outlay than labor, thus committing more resources and increasing the dangers of illiquidity. Another possible exPlanation for the apparent lack of substitution of machinery for labor in contractions is that since the marginal effici- ency of capital is low, machinery is not purchased, and, in addition, neither is labor hired. Checking this hypothesis requires aggregative labor input data in a form not now available. The price of hired farm labor relative to the price of machinery is related to machinery purchases over time in Figure 3.h. The contractions other than 1921 and the early 30's appear to be quite important in the formation of the regression coefficients since these two periods appear to display a direct relationship in Figure 3.h. While the relative price of labor and farm income are intercorrelated, it is doubtful if the intercorrelation distorts the results with this variable so seriously. Exclusion of the relative price of labor from some of the equations did not appear to alter the results of farm income significantly, hence we would not expect the results of the relative price of labor to be changed significantly if income were dropped from the form- ulations. Further interpretation of the results Obtained from.the use of the relative price of hired farm labor is deemed necessary. In Cromarty's investigation of the demand for farm tractors and machinery, a negative 63 Figure 3.h - Machinery Purchases by Farmers Related to the Relative Price of Farm Labor, United States, 1910-56 ‘250 ?.50" «2‘25 2.25“ 1900 ‘ Relative Price of Farm Labor 1" e) O I Machinery Purchases ’9? .p c 5 §1.75L « 150 331 50- «125 0 .3 f; 1.25r- “ 100 H a? 1.00 q 75 .7 d 50 .5 4 25 0 n L L l l a O 1910 1920 1930 19ho 1950 1956 Source: See Appendix II, Tables 1 and 7. Machinery Purchases (% of 37-hl) 6b. regression coefficient for the relative price of farm labor was obtained, corresponding with the results obtained in this study. Here, negative coefficients were obtained for contractions and nonsignificant positive coefficients were obtained for expansions. Cromarty interpreted the nega- I tive coefficient as being the result of the price of hired farm labor being an endogenous, rather than independent, variable. This in effect means that the relative price of hired farm labor is not important in the substitution of machinery for labor, other influences being much more im- portant. On this basis, he used the industrial wage rate as a variable, to get the effect of higher nonfarm wages (thus attracting labor from farms) on farm machinery purchases. In this case he obtained consistent results.” An observation in connection with the importance of the rela- tive price of hired labor in.machinery purchases appears apprOpriate. Suppose a farmer has a tractor and.other tractor powered.machinery on his farm. NOw suppose the price Of hired labor decreases relative to the price of machinery. The farmer would be more likely, it appears, even under these conditions to buy, say, a cultivator fer the tractor, than to hire labor to work in its place. It should be pointed out that hired labor has prObably not been the important part Of the farm labor force, family labor being considered much more important. Thus, we cannot expect to Obtain the important part Of machinery - labor substitution.by looking only at hired labor prices. As previously mentioned, employment Opportunities in the nonfarm economy are probably very important in the movement Of‘both hired and family labor from the farm. These Opportunities are in turn closely related to the classification of expansion and contraction used in this study; Thus, we h. Cromarty, Op. cit. 65 expect the greatest movement of labor from the farm during expansions and hence the greatest substitution of machinery for labor during those times. Time as a variable. One Of the features which has characterized American agriculture has been the rapid development of new technology. Technological advances become available for adoption as they are discov- ered over time. However, adoption is not automatic -- conditions must be favorable for adOption to take place. These conditions are considered to be more favorable in expansions than in contractions. To obtain a measure Of the relationship between the "trend" of tech- nological development and farm tractor and machinery purchases, the time variable was introduced into the formulations in Group IV. The result from this addition was that the regression coefficient fer expansions was larger and significantly different from the regression coefficient fer contractions. Thus, it appears that the effect of technological develop- ment has been greater in.expansions than in contractions, meaning that these have been the periods when new'technologies were adopted.because Of conditions present. This result lends credence to the hypothesis that the rate at which new inputs are purchased varies over the business cycle, indicating that inputs in agriculture are added at a faster rate during business expansions than during business contractions. It suggests the presence of new technology has had a much greater influence during expan- sions when conditions have lead to better expectations Of the future and the means of purchase were available. Expenditures versus shipments. The question Of‘VhiCh is more appro- priate dependent variable -- expenditures on.mechinery by farmers, or machinery shipments to dealers -- should.be resolved. 66 In the fitted equations, there were four sets of equations, each set including the same independent variables. One Of each set had expendi- tures as the dependent variable, while the other had shipments as the dependent variable. The results of these equations were very similar whether fitted with expenditures or shipments. From this we may conclude that either is equally good for our purposes. This is what we would expect from appendix Tables 1 and 2 which show that these two series move closely together over time. Variation in the unexplained residual. The use of the model employ- ing synthetic variables was based upon the assumption that the error term or unexplained residual of predicted from actual machinery purchase was from the same distribution in contractions and expansions. That is to say, the unexplained residual for contraction years was assumed not to differ in magnitude in a regular pattern from the unexplained residual for expansion years. Due to the enormity of the task of computing the residuals for each Of the fitted equations, it was decided that only a limited number of equations should.be examined in this regard. It was felt that the residuals Of the equations which were examined gave a fair indication of the results of the other equations. Equations from Groups I, III and IV were selected for this purpose. N0 equation was selected from Group II because the formulations there were not investigated exten- sively for reasons given.when that group was discussed. The residuals from equation one, Group I, are given in Figure 3.5 (A). The residuals for contractions do not appear to differ in a regular pattern in magnitude from those for expansions in this equation. There does appear to be some relation between these residuals and time. Time as a variable was not included in this equation, it will be remembered. 67 Figure 3.5 - Unexplained.Residuals (Mil $) A. Equation 1, Group I B. Equation h, Group III 25q- '1 A 1 1' o i ' i i - - '1'r 11 ”1' ' O 11‘;'_ , '_-1 :11 1,2,- riff, _{T 1 ,1-, E I [gill : l .1: 1 l ' i i I - L . ' --- = Contraction 1 = Expansion 350r L 4 L l 1 P 1 _l 1910 1920 1930 19ho 1950 1956 300r ‘ 1 + B ' ‘ t . . , : I .. ' . l .l . 0 .111}1r 1 11" L _J, 1:11 ,_.1 . l 1 l_ i .1 1111117 "W 1.1] .. | ‘ I IL ‘ 1 l l ' --- = Contraction -—-= Expansion 350L - 1 L L 1 1 1910 1920 1930 19uo 1950 1956 6B The greatest deviation, as in the residuals of other equations that were plotted, was in 19h3 when there were serious wartime shortages. Figure 3.5 (B) gives the residuals from equation four, Group III. These residuals appear to demonstrate a cyclical behavior and.were not considered to be random from the pattern they displayed. The cyclical pattern of these residuals indicate that the formulation in this case was not satisfactory. The residuals from equation six, Group Iv, are given in Figure 3.6 (A). The residuals in this case appear to be more random in nature, and there does not appear to be a consistent difference in the magnitude of contrac- tion year residuals as compared to expansion year residuals. Purchases were over~estimated during the war years when there were shortages and under-estimated after the war when backlogs of machinery orders existed. Figure 3.6 (B) gives the residuals from equation five, Group IV, which was the same as equation six when the relative price of labor added. Residuals for contractions are of about equal magnitude as those for expan» sions in this equation. The distribution of residuals appears to be fairly random with over-estimation occurring during the war and under- estimation following the war. In general, from the inspection of these residuals, it appears that the assumption necessary for the use of the model employed in this study was valid; the residuals for contractions do not appear to be of different magnitude from those for contractions. Addition of the time variable in Group IV improved the pattern of the residuals considerably from Group I and Group III, further indicating the usefulness of the time variable. 69 rigure 3.6 - Unexplained Residuals (Mil t) A. Equation 6, Group IV' B. Equation 5, Group IV 250r < :0 A I + i J: I ._ f I I 3 0 1:.1J“IJ’v it] 11‘ [I t'1 7:1 1 1 5H {5 I .1 g: i ‘ 'L I: I l l --- 8 Contraction I Expansion L “00- L - l9l0 igéo 1930 19ho 1950 1956 250. 1 B + .-----. [In .--. o :1111. I] ‘ 1 ’ITIA, " , *1 :Ilulgglli' ,- ' z 1 . ' i - --- = Contraction ___::Exmnuuon hooL_ . L 1 L 1 1 1910 1920 1930 who 195p 1956 CHAPTER IV SUMMARY AND CONCLUSIONS The study was develcped to determine if different relationships exist between variables associated with farmers' purchases of tractors and mach- inery and these purchases during different phases of the business cycle. The period of time included in the investigation covered the years 1910 through 1956. Twenty equations in all, linear in the original variables, were fitted.by least squares techniques in the four groups of equations examined in the analysis. The single equation models were constructed with the use of synthetic variables so that relationships of variables during contractions could be compared.with the relationships of corres- ponding variables during expansions. ‘Using such models, it was possible to Obtain indications of the differences in the relationships between.the independent variables and machinery purchases during expansions and con- tractions of the general economy. The results of the analysis indicated that the relationships between variables have differed in different phases of the business cycle. With respect to each independent variable, these differences may be summarized as follows: 1. Changes in farm tractor and.machinery purchases appear to have a closer relationship with changes in farm income in contractions than in expansions. Regression coefficients for the income variable during con- tractions were consistently larger than those for expansions. The results also suggest farm income has been of major importance in financing new capital investment in recent decades. 70 71 2. Farm tractor and.machinery purchases appear to be related to capital gains and losses during expansions, but the statistical results failed to support the hypothesis that these purchases are associated.with capital gains and losses during contractions. The relation between capital gains and losses and farm tractor and machinery purchases appears to have been closer in years prior to‘Horld.War II than since. This suggests that perhaps external credit sources have played a less important role in agricultural capital fermation after the war than.prior to that time. ‘Vhile this may be the case, there is not reason for assuming that external sources will continue to be less important than internal sources of finance. 3. The stock of machinery on farms as used in this study is admitt- edly a roughapproximation, at best. Results indicated.that "technological trend" has overpowered the relation of this variable with farm tractor and machinery purchases. This appears to be the case, more so in.expansions than in contractions. h. Regarding the "real" price of machinery, the results did not reveal a consistent difference in the relationship during contractions as compared to expansions. The results from the first group of equations suggested that this variable is more closely related'with machinery pur- chases during contractions; however, results from other groups did.not display this consistency. The series, when plotted, indicated.the relation has been consistently inverse. when one assesses these findings, the conclusion.which appears to be lost tenable is that the relationship during expansions.and contractions has been.spproxinately the ease. 5. There was a significant difference betweon.the regression coeffi- cient for the relative price of hired farm labor during contractions and expansions. However, the sign of the coefficient for contractions was inconsistent and the coefficient significant, while the coefficient for expansions was consistent in sign but nonsignificant. Thus, the hypothe- sis that the relative price of hired farm labor has been.important in machinery-labor substitution was not supported.by these findings. However, hired labor probably has not been the important part of the labor involved in machinery-labor substitution. 6. The time variable, insofar as it reflects the development of technology for use in agriculture, indicates that farm tractor and.mach- inery purchases during expansions have been more closely related to the presence of new technology than during contractions. Hew'technology appears to have been adopted at a faster rate during expansions than during contractions. The classification used in this study appears to be useful since consistent differences in the relationships of variables were found in the analysis. Apparently farmers do respond differently to certain changes during different phases of the nonfarm'business cycle. This appears to be particularly so in the case of technological development, as repre- sented by calendar time, and the results in the cases of income and cap- ital gains displayed consistent differences between contractions and ex- pansions. There was a statistically significant difference between the regression coefficients for the relative price of hired farm labor in expansions and contractions. However, it does not appear that the price of hired farm labor relative to the price of farm tractors and.machinery is an important factor in the purchase of farm machinery and tractors. This conclusion in itself is important, but the significant difference between contractions and expansions does not appear to be an important finding. In total, it does appear the relationships between variables 73 have not been the same during expansions and contractions from the find- ings of this study. Reference cycles of the general economy developed by the National Bureau of Economic Research, along with changes in gross national product, were used in making the classification. Thus, periods of contraction and periods of expansion are in terms of the general economy rather than in terms of agriculture itself. Upswings and downswings in the farm economy have not always been concurrent with similar changes in the nonfarm eccnonw. This suggests the need for the develOpment of reference cycles for the farm economy based upon series in agriculture similar to those used in develOping series for the general econom'. Then, using these as a basis for classification, it would be possible to investigate the res- ponse of agricultural producers to changes in variables in upswings and downswings in the farm economy to determine if the reactions of agricul- tural producers during contractions were different from those made during expansions. It appears that this method would give clues to whether reactions of farmers during periods of contraction were reversals of the actions taken during expansion periods. This, of course, refers to the non-reversible nature of the supply curve for agriculture which has been discussed at several points in recent literature. Much of the success of using this method in an overall sense will depend upon ability to measure input flows into and out of agriculture, which is a very difficult problem in itself. In the case of tractors and machinery, flows out of agricul- ture were seemed to be negligible because of their low salvage value outside of agriculture. There is also a need to develop methods of examining alternative - classifications in doing studies of this nature; so that the most useful 7h classification, in terms of the purpose of the study, is selected. For exmle, the farm income variable appears to exhibit a lag in expusions from contraction periods, but not in contractions from expansion periods. The classifications, then, would have to deal with direction and duration of the change being classified. The results from the use of the method outlined in this study suggest that the use of time series analysis in the usual manner may tend to mask the difference in relationships between independent and dependent variables during expansions and contractims and that perhaps sons of these relation- ships should be re-exsmined in this regard. However, limitations of form and accuracy of data encountered in conventional time series methods are not alleviated here. In addition, particularly when onILv a small number of observations are available, the use of twice as any variables makes statistically significant results harder to obtain because of the literal "burning up" of degrees of freedom. This latter point may be compensated in part by closer fits from using "split variables" although this aspect was not checked in this study. It should be recognized that the relationships analyzed in this study are associations between variables as they have been estimated to occur over time. Thus, the findings fall. short of the most desired goal -- that of determing cause-effect relationships. However, limitations as to a suitable theory to use in this regard, along with accurate data to test the theory, make the determination of the lines of causality imposs- ible to achieve. These problems are inherent in investigations of this nature; hence, these shortcomings are by no means unique to this study. The demand models used in this analysis are admittedly naive in nature and probably far too simplified. This is probably particularly 75 true with respect to expectations of the future which agricultural pro- ducers hold, represented by farm income, primarily, in this study. How- ever, there are no apparent reasons why the techniques used in this study cannot be applied to more refined models in investigations of agricultural producers responses during different phases of the business cycle. BIBLIOGRAPHY Ackley, Gardner, An Introduction to Macroeconomic Theory, preliminary edition for student use, Gardner Ackley, University of Michigan, Sept. 1957. Bradford, L. A. and Johnson, G. L., Farm Management Analysis,‘Wiley and Sons, Inc., New York, 1953. Burk, Marguerite, "Studies of the Consumption of Food and Their Uses," Journal of Farm Economics, Vol. 38, 1956. Burns, Arthur F., and Mitchell, Wesley C., Measuring4Business Cycles, National Bureau of Economic Research, New York, l9h7. Cromarty, William A., The Demand for Farm Machinery and Tractors, Agricultural Experiment Station, East Lansing, Technical Bulletin (In Process). Dillard, Dudley, The Economics of J. M. Keynes, Prentice-Hall, Inc., New York, l9h8, p. 132. Economic Statistics Bureau of‘Washington, D.C., Handbook of Basic Economic Statistics, July 15, 1958. Federal Reserve Bank of San Francisco, Monthly Review, July 1956. Goldsmith, RaymondflW., A Study of Saving in the United States, Vol. 1 Princeton University Press, 1955. Goulden, Cyril 3., Methods of Statistical Analysis,‘Wiley, New York, 1952 Hathaway, Dale E., "Agriculture and the Business Cycle", Policy for Commercial Agriculture, Its Relation to Economic Growth and Stability, Joint Economic Committee Print, November 22, 1957. Johnson, Glenn L., "Allocative Efficiency of Agricultural Prices -- As Affected by Changes in the General Level of Employment", unpublished doctor of philosophy dissertation, Department of Economics, University of Chicago, l9h9. . "Sources of Expanded Agricultural Production" in.Policz for Commercial Agriculture, Its Relation to Economic Growth and Stability, Joint Economic Committee Print, November 22, 1957. . "Supply Function - Some Facts and Notions", Agricultural Adjustment PrOblems in a Growing Economy, edited by Heady, et al., Iowa State College Press, 1958} 76 77 Kalecki, M., "The Principle of Increasing Risk", Economics, New Series Vol. IV, 1937. Keynes, J. Mt, The General Theory of Emplgyment, Interest and Money, Harcourt, Brace and Company, 1935. Koopmans, T. C., "Measurement Without Theory", Review of Econcmic Statistics, Vol. XXIX, No. 3, Aug. 19A7. Mills, Fredrick C., Introduction to Statistics, Henry Helt Company, New York, 1956. Morelle, Wilellyn, "Interest Rates on Farm Loans", Farm Loans at Commer- cial Banks, Board of Governors of the Federal Reserve System, Washington, D. C., 1957. Nerlove, Marc, Distributed Legs and Demand Analysis for Agricultural and Other Commodities, Agriculture Handbook No. lhl, AMS, USDA, June, 1958. Schultz, Theodore W., Agriculture In An unstable Economy, McGraw-Hill, New York, 1945. Shackle, G. L. S , Uncertainty in.Economics, Cambridge University Press, 1955- Siegel, Irving H., "Technological Change And Long-Run Forecasting", The Journal of Business of The University of Chicago, velume 26, July: 1953- Snedecor, George W., Statistical Methods, The Iowa State College Press, Ames , Iowa, 1956. Theil, 3., Linear Agggegation of Economic Relations, North-Holland Publishing Company, Amsterdam, 195k. Thomsen, F. L. and Foote, R. J., Agricultural Prices, McGraw-Hill, New York, 1952. Tostlebe, Alvin 3., Capital in*Agriculture: Its Formation and Financing since 1870, a study by the National Bureau of Economic Research, Princeton, University Press, 1957. United States Department of Agriculture, Balance Sheet of Agriculture, Agricultural Research Service, Washington, 1951-57 annual issues. . Farm Income Situation 16%, Agricultural Marketing Service, July 1957. , . Farm Real Estate Market, Agricultural Marketing Service, July 1956. 78 United States Department of Agriculture, Esme Parithor Agiculture, Part II - Expenses of Agricultural Production, Sec. 3, Washington, 19140. . Mailer Statistical Series of thi U. S. Department of Agriculture, Vol. 3, mac an e arm ncome, gr c ure Handbook, No. 118, December 1957. United States Government Printing Office, Economic Report of the President, Washington, 1957. Wilcox, W. W., and Cochrane, W. W., Economics of American Agiculture, Prentice-Hall, 1951. APPENDIX I STATISTICAL TEST OF SIGNIFICANT DIFFERENCE BETWEEN CORRESPONDIM REGRESSION COEFFICIENTS 79 TEST OF SIGNIFICANT DIFTERENCE BETWEEN CORRESPONDING REGRESSION COEFFICIENTS The regression coefficients for corresponding variables were tested for significant difference by using the test statistic: bi - bj Sflii“ s“ - 2a” where the _i_._ th and 1 th regression coefficients are for corresponding variables in contraction and expansion years, §_ is the standard error of the estimate, and 81.1 is an element of the inverse matrix (siJYl, moments being defined as: N 813.2 lXin XJn . n- the appropriateness of the elements under the radical was derived from the expected value: E[(bi -31); (b3 4.13:. E[(b1 -91)2+m 41.1)2 - 2(b1 - 61)(b.1- 3.1)] where (31 and a.) are the true regression coefficients. This test is given 1 in Snedecor. Also included in Snedecor's book is a discussion of elements of an inverse matrix? 1. Snedecor, George W. , Statistical Methods, The Iowa State College Press, Ames, Iowa, 1956, p.’+h2. 2. Ibid., pp.h38-hhl. See also in this regard, Goulden, Cyril H., Methods of Statistical Analflig, Wiley, New York, 1952, Chapter 8. APPENDIX II THE SERIES USED IN THE ANALYSIS 80 TABLE 1 - EXPENDITURES on FARM morons m MACHINERY, v.3. , 1910-56 _‘ m Gross Gross expend- Index of mach- expend- Index of mach- Year iture inary and Machinery Year iture inary and Machinery current tractor prices purchases current tractor prices purchases Mil.$ (193741.100) Mil.$ (1937-h1g100) (1) (2) (3) (1) (2) (3) 1910 26h 6h.5 h09 193k 135 90.5 1&9 1911 265 6h.5 h11 1935 278 9h.6 29h 1912 269 6h.5 #17 1936 383 97.5 393 1913 263 6h.5 h08 1937 50h 100.1 50h 191% 272 6h.5 u22 1938 389 10h.o 37h 1915 272 66.5 h09 1939 366 99.1 369 1916 267 69.7 383 19h0 h38 99.5 tho 1917 282 79J+ 357 19111 6&9 99.8 650 1918 359 100.0 359 19h2 816 1oh.8 779 1919 h06 103. 2 393 1913 199 106 .9 h67 1920 629 107.1 587 19th 1,016 111.3 913 1921 229 103.2 222 1915 990 113.3 87h 1922 21k 92.3 232 19h6 685 119.5 573 1923 289 96.0 301 1917 1,2uu 137.6 90h 192k 2&3 96.0 253 19h8 1,820 158.9 1,115 1925 31h 96.2 326 19h9 2,022 176.1 1,1h8 1926 357 96.5 370 1950 1.957 178.0 1.099 1927 366 96.9 378 1951 2,270 192.0 1,182 1928 36h 96.6 377 1952 2,033 196.8 1,033 1929 It21 95.9 1‘39 1953 1.890 195.7 966 1930 351 96.1 365 1951‘ 1.793 197.5 908 1931 156 9u.2 166 1955 1,778 200.8 885 1932 61 90.0 68 1956 1,722 208.1 827 1933 59 97.8 60 Source: Col. 1, Farm Income Situation 16h, July, 1957, Table 19, p.36. Col. 2, 1910-1922, Policy for Commercial AEiculture, op. cit., Table C-9, 1). 853, 1923-56, AMS Constructed Index for Retail Tractor and Machinery Prices, from the files of William Cromarty, Agricultural Economics Department, M.S.U.. Col. 3, Col. 1 divided by Col. 2. 81 TABIE 2 - TRACTOR AND MACHINERY SHIPMENTS 'TO DEALERS, U.S. , 1910-56 Index of Index of Shipments tractor and Shipments tractor and Year current machinery Shipments Year current machinery Shipments Mil.$ prices Mil.$ prices (1937-11.100) (1937-11.100) (1) (2) (3) (1) (2) (3) 1910 207 6h.5 381 1931 221 90.5 2th 1911 212 61.5 389 1935 272 9h.6 288 1912 237 61.5 he? 1936 366 97.5 375 1913 231 61.5 h18 1937 #63 100.1 163 1911; 217 61.5 396 1938 381 101.0 369 1915 196 66.5 355 1939 379 99.1 382 1916 196 69 . 7 311 19110 387 99 . 5 389 1917 261 79.1 389 1911 535 99.8 536 1918 3142 100.0 102 1912 512 101.8 189 1919 1137 103.2 1183 1913 296 106.9 277 1920 530 107.1 555 1911; 516 111.3 h91 1921 177 103.2 232 1915 606 113.3 535 1922 173 92 . 3 2h7 1916 718 119.5 601 1923 298 96.0 310 1917 1,082 137.6 786 1921 263 96.0 27h 19h8 1,153 158. 9 911 1925 329 96 .2 31:2 1919 1,192 176. 1 8&7 1926 316 96.5 359 1950 1,196 178.0 810 1927 366 96.9 378 1951 1.852 192.0 965 1928 376 96.6 389 1952 1.589 196 8 807 1929 I#20 95.9 I#38 1953 1.1171 195 7 752 1930 290 96.1 302 195k 1,229 197 5 622 1931 195 91.2 207 1955 1,102 200 8 698 1932 167 90.0 186 1956 1,173 208 1 561 1933 153 97-8 156 Source: Col. 1, 1910-22, Income Parity for Agriculture, Part II - Expenses of Agriculture Production, Sec. 3, U.S.D.A. , Washington, D.C. , 19110, Table 28, p.65 sdJusted to 1923 -56 estimates by adding the mean difference between the series for 1923-30 which is 60; 1923-56 reproduced from Fact for Industg from the files of William Cromarty, Agricultural Economics Department, M.S.U. Col. 2, same as for Col. 2, Table 1. Col. 3, Col. 1 divided by Col. 2. 82 man: 3 - m CASH rm moons, 11.3., 1910-56 Prices paid Prices paid Farm ‘ Earn by Year income farmers Income Year income farmers Income 1411.3 (1937-11.100) Mil.$ Mil.$ (1937-11.100) n11.$ (1) (2) (3) (1) (2) (3) 1910 3.710 76.1 1,395 1931 3.718 91.5 3.931 1911 3.535 77.2 11.579 1935 1,118 97.6 11.527 1912 3.776 79.5 21.750 1936 5.071 97.6 5.199 1913 3.890 79.5 1,893 1937 5,267 103.1 5.109 1911 3,618 81.1 1,198 1938 1,171 97.6 1,581 1915 3.967 82.7 11.797 1939 h 1621 96.9 1.769 1916 1,915 91.3 5,116 1910 1,629 97.6 1,713 1917 7,310 116.5 6,275 1911 6,750 101.7 6,117 1918 9,058 136.2 6,651 1912 10,161 119.7 8,191 1919 9,690~ 155.1 6,218 1913 13,252 131.6 9,815 1920 7,268 168.5 1,313 1911 13,825 113. 3 9,618 1921 3.937 122.0 3,227 1915 11,186 119. 6 9,182 1922 1.396 118.9 3.697 1916 16,312 163.8 9,977 1923 5.123 125.2 1.092 1917 18.979 189.0 10,012 1921 ' 5.509 126.0 11,372 1918 18.251 201 7 8.917 1925 6,296 129.1 1,877 1919 16,528 197. 6 8,361 1926 5,813 126.0 1,637 1950 16,086 201. 6 7,979 1927 6,001 125.2 1,796 1951 18,112 222.0 8,291 1928 5,950 127.6 1,663 1952 18,022 226.0 7,971 1929 6,383 126.0 5,066 1953 17,691 219.7 8,051 1930 1.599 113.9 3.868 1951 16.192 221.3 7.317 1931 2.788 102.1 2.723 1955 15 .695 221.3 7.092 1932 1,763 88.2 1,999 1956 16,118 225.2 7,290 1933 2.568 85-8 2,993 Source: 001. 1, Farm Income Situation 161, Total of cash receipts, Table 11, p. 28 minus the_ sum of taxes on fan: prOperty, interest on farm mortgage debt, Table 15, p. 32 and current farm operating expenses excluding hired labor, Table 16, p.33. Col. 2, P_9_l.i 52 for Comercial miculture, op.cit., Table C-9, p. 853. Col. 3, 001.1 divided by Col. 2. M 1909 «4956 83 TABLE 1 - CAPITAL earns AND LOSS av FARMERS IN HOLDING REAL. ESTATE, LIVESTOCK AND asap INVENTORIES,‘U.S., Year Real Estate Livestock Crops Total n11.$ ‘Mil.$ ruins Mil.$ (1) (2) (3) (1) 1909 900 676 117 .722 1910 900 298 - 237 961 1911 932 - 155 323 1,100 1912 822 591 - 510 903 1913 815 318 131 ,591 1911 - 315 115 - 315 - 805 1915 2,357 155 68 2.270 1916 2,922 571 898 1,191 1917 1 ,016 1,291 1,712 7,079 1918 1,153 178 281 1,915 1919 11,311 - 280 89 11,150 1920 '5:369 '19896 '23879 -10,lhh 1921 -7,029 -1,291 - 906 - 9,226 1922 - 929 271 650 - 8 1923 -2,031 - 182 233 - 1.980 1921 - 516 188 555 197 1925 - 182 536 591 - 238 1926 -1,871 220 318 - 2,002 1927 819 1189 223 310 1928 - 217 519 - 52 280 1929 719 158 75 - 802 1930 :us765 :19707 ' 553 ' 7:025 1931 '79118 '13125 '12030 ' 9:573 1932 -6,899 - 666 - 571 - 8,136 1933 999 123 785 1.907 1931 611 601 816 2,061 1935 597 .723 4.057 1.261 1936 881 - 32 866 1,718 1937 - 78 50 4.359 1.016 1938 -1,120 - 32 - 335 - 1,187 1939 - 183 - 188 362 - 309 1910 697 136 - 16 817 1911 2,597 1,161 786 1,811 1912 3.191 2.080 593 6.167 19h3 6:01“ ‘ 362 0372 72021.. *1911 5,009 - 102 - 30 1 ,877 1915 6.351 1,018 11 7,116 1916 7.231 2.611 897 10.775 1917 1.996 1.916 2.821 9.763 1918 2,738 1,393 -3,515 617 19h9 '13597 ‘12992 5&7 ' 1"29135 1950 11,316 1,227 1,181 16,721 1951 9.1971383 .320 11.900 TABLE 1 - (Continued) 81 Year Real Estate Livestock Crepe Total Mil.$ Mil.$ Mil.$ Mil.$ (1) (2) (3) (1) 1952 611 -5,132 200 - 1,290 1953 ~1.918 -2.697 -1.289 - 5.931 1951 1,092 - 660 - 636 2.796 1955 3.872 - 732 -1.220 1.920 1956 6,817 303 517 7,666 Source: Col. 1, from Col. 6, Table 1a. Col. 2 from 001. 6 Table 1b. ‘ Col. 3, from Col. 6, Table 1c. TABLE 1!! - COMPUTATION OF CAPITAL GAINS AND IDSSES BY FARMERS IN sommc FARM REAL ESTATE, 0.3. , 1909-1956 85 Change due Change we Annual change Value Value in 5 year was to physical to price Year in value current constant of previous chany change current year -100 current current 1411.3 Mil.$ M11.$ at Mil.$ Mil.$ (1) (2) (3) (1) (5) (6) 1909 - - - - - 900B 1910 1:21‘9 31‘3793 279857 ' ‘ 9008 1911 1,256 36,012 28,111 0.9 321 932 1912 1,158 37,298 28,363 0.9 336 822 1913 1,123 38,156 28.592 0.8 308 815 1911 11 39.579 28.818 0.9 356 - 315 1915 2.671 39.590 29.089 0.8 317 2.357 1916 3,260 12,261 29,330 0.8 338 2,922 1917 1,156 15,521 29,580 0.9 110 1,016 1918 1.553 19,980 29,821 0.8 100 1,153 1919 11,777 51,533 30,062 0.8 136 11,311 1920 -1.839 66.310 30.306 0.8 530 -5.369 1921 -7.159 61.171 30.089 ~0.7 -130 -7.029 1922 ’1: 307 51" .9012 29 .9890 ‘0 . 7 '378 " 929 1923 -2,212 52,705 29,760 -0.1 -211 -2,031 1921 -1.000 50.163 29.193 -o.9 -151 516 1925 - 179 119.163 29.320 -0.6 497 - 182 1926 -1,237 18,981 29,687 1.3 637 -1,871 1927 - 133 17.717 30.121 1.5 716 - 819 1928 351 17,611 . 30,183 1.2 571 - 217 1929 95 h71%8 30,887 1-3 621‘ "' 719 1930 4.113 I+7.873 31.290 1.3 622 41.765 1931 -6.550 13.730 31.711 1.3 568 -7. 118 1932 -6.378 37.180 32,163 1.1 521 -6 ,899 1933 1.399 30.802 32.595 1.3 100 999 1931 1,063 32,201 33,027 1.3 119 611 1935 996 33.261 33.131 1.2 399 597 1936 953 31.260 33.190 0.2 69 881 1937 - 13 35.213 33.536 0.1 35 - 78 1938 -1.085 35.170 33.559 0.1 35' -1.120 1939 - 119 31. 085 33.581 0.1 31 - 183 1910 761 33.636 33.637 0.2 67 697 1911 3,117 31,100 31,161 1.6 550 2,597 1912 11.057 37.517 31.669 1.5 563 3.191 1913 6,596 11,601 35.168 1.1 582 6,011 1911 5.681 18. 200 35.677 1.1 675 5.009 1915 7.162 53.881 36.212 1.5 808 6.351 1916 7,117 61, 016 36,315 0.3 183 7,231 1917 5,201 68,163 ,1 0.3 205 , 86 TABLE 1a - (Continued) Change due Change due Annual change Value Value in ‘fi year was to ptwsical to price Year in value current constant of previous change change current year -100 current current Mil.$ M114 Mil.$ 1. 1411.3 M11.$ (1) (2) (3) (1) (5) (6) 1918 2.959 73.661 36.522 0. 3 221 2 .738 1919 4.367 76.623 36.627 0.3 230 4.597 1950 11,512 75, 36 ,728 0. 3 226 11,316 1951 9.197 86.798 36.732 0-0 0 9.197 1952 1 95,995 ,737 0.0 0 611 1953 ‘199‘4’8 96.9636 36 9730 0 o 0 O '1 ,9158 1951 11.092 91.688 36.729 0.0 0 1.092 1955 3.872 98.780 36.721 0.0 o 3.872 1956 6,817 102,652 36,727 0.0 0 6,817 1957 ' 109:1‘69 36 3722 " " ‘ ”Estimated at 1911 rate Source: Col. 1, computedfrom Col. 2. Col. 2, Fm 3221 Estate Market, July 1956, p. 9, value on March 1. Col. 3, obtained by dividing Co . by index of value per acre (1910.100), Farm Real Estate Market July 1956, p.9. Col. 1, computed from Col. 3. Col. 5, Col. times Col. 2. Col. 6, Col. 1 minus Col. 5. 87 TABLE 1&1) - COWIOR OF CAPITAL GAINS AND IDSSES BY FARMERS IN ROI-DIN} LIVESTOCK WORIES, U. S. , 1909-1956 ‘Value Total Change due Change due Annual change beginning inventory % year use to physical to price Year in value of year in.constant of previous change change current current and of year year ~lOO current current Mil.$ 1111.3 Mil.$ 1. Mil.$ 1111.3} (1) (2) (3) (h) (5) (6) 1908 - - 6,626 - - - 1909 598 h,316 6,506 -1.8 - 78 676 1910 352 h,91h 6,577 1.1 58 298 1911 - 229 5,266 6,h8h -1.h - 7h - 155 1912 611 5,037 6,513 0.u 20 591 1913 500 5,6h8 6,687 2.7 153 3&8 1911; 11m 6,1h8 6,999 h.7 289 11.5 1915 65 6,292 7,286 3.5 220 155 1916 707 6.357 7,396 2.1 13h 57h 1917 1,h89 7.06h 7,601 2.8 198 1,291 1918 #69 8.553 7.597 -0.1 - 9 #78 1919 - 5&2 9,022 7,376 -2.9 -262 - 280 1920 -2,100 8,h80 7,201 -2.h -20h -1,896 1921 -1,310 6,380 7,181 -0.3 - 19 -1,291 1922 296 5,070 7,216 0.5 25 271 1923 - 295 5.365 7.063 -2-1 4-13 - 182 192k - ~50 5,071 6,732 -h.7 -238 188 1925 365 5.021 6.501 -3.h -171 536 1926 13h 5,386 6.396 -1.6 - 86 220 1927 506 5,520 6,h18 0.3 17 #89 1928 567 6,026 6,836 0.3 18 5&9 1929 - 79 6.593 6.51“ 1.2 79 - 158 1930 4.655 6.5M 6.565 0.8 52 4.707 1931 -1,3oh h,859 6,729 2.5 121 -1,u25 1932 - 572 3.555 6.989 3.9 139 - 666 1933 186 2.983 7.137 2.1 63 123 1931; 309 3,169 6,h81 -9.2 -292 601 1935 1.706 3.1178 6.160 -o.5 - 17 1.723 1936 - 120 5,18h 6.338 -1.7 - 88 - 32 1937 - 31 5,068 6,238 -1.6 - 81 50 1938 59 5.033 6.352 1.8 91 32 1939 M1 5,092 6,6h1 h.5 229 -- 188 19h0 192 5,133 6,711 1.1 56 136 19h1 1,7h9 5,325 7,075 5.h 288 1,h61 19h2 2,568 7,07h 7.562 6.9 #88 2,080 19h3 113 9,612 7,880 h.2 M5 - 362 19hh - 673 9,685 7.h18 -5.9 -571 - 102 1915 730 9,012 7,182 -3.2 -288 1,018 19h6 ' 2,235 9,712 6,880 -h.2 -h09 2,6hh 19h? 1.1107 11.977 6.569 4.5 -539 1.9% 88 TABLE h‘b - (Continued) ‘Value Total Change due Change due Annual change beginning inventory $ year was to physical to price Year in value of year in constant of previous change change current current end of year year -100 current current 2411.3 1411.3 1411.45 1. Mil.$ 1111.45 (1) (2) (3) (h) (5) (6) 19h8 1.273 13.38!» 6.507 ~o.9 -120 1.393 19119 4,757 1h,657 6,61h 1.6 235 -1,992 1950 £1,227 12,900 h,800 0.0 0 £1,227 1951 2,162 17,127 5,100 6.3 1,079 1,383 1952 '2‘ ,7’40 19 3 589 5 3200 2 0 0 392 '5 5132 1953 -2,979 1h,8h9 5,100 -1.9 -282 -2,697 1951:. - 660 11,870 5,100 0.0 0 - 660 1955 - 508 11,210 5,200 2.0 22k - 732 1956 506 10,702 5,100 -1.9 203 303 1957 ‘ ’ 5:000 ’ " ' Source: Col. 1, computed from Col. 2. Col. 2, l909-h9, Goldsmith, Raymond W., A Studyrof Saving in the United States, vei. I, Princeton Univ. Press, 1955, Table A-32, p. 797; 1950-57, Balance Sheet of A iculture, ABS, USDA, ‘Washington, D.C., 1951-57 annual issues. Col. 3, 190 4H5, Goldsmith, Raymond W., Op cit., Table 11.31, p. 795 ; 1950-56, Balance Sheet of 531cm- ture, 0p. cit., 1951-57 annual issues. Col. h, computed from Col. 3. Col. 5, Col. 2 times Col. h. Col. 6, Col. 1 minus Col. 5. 89 TABLE he - COMPUTATION 0r CAPITAL.GAINS Ann LOSSES B!“ranunss IN HOLDING CROP INVENTORIES, 0.3., 1909-1956 Value Illrotal _ Change due Change due Annual change beginning inventory '5 year was to physical to price Year in value of year in constant of previous change change current current end of year year -100 current current 1111.45 Mil.$ Mil.$ 5 M11.$ Mil.$ (1) (2) (3) (h) (5) (6) 1908 - - 2,818 - - - 1909 336 2,203 3,061 8.6 189 117 1910 - 130 2,539 3,191 h.2 107 - 237 1911 31 2,109 2,808 -12.0 289 323 1912 115 2,113 3,561 26.8 655 - 510 1913 - 19 2,588 2,910 -17.h 150 131 1911 101 2,569 3,115 16.2 116 - 315 1915 212 2,670 3,599 5.1 111 68 1916 365 2 .882 2.932 -18-5 533 898 1917 2.251 3 2&7 3.392 15.7 510 1.712 1918 152 5,198 3,312 - 2.h 132 281 1919 72 5.650 3.302 - 0.3 17 89 1920 -1,h77 5,722 1,111 21.5 1,102 -2 ,879 1921 -1,836 1,2h5 3,211 -21.9 930 906 1922 679 2 ,109 3,250 1.2 29 650 1923 239 3, 088 3,256 0.2 6 233 1921‘ 252 35327 2: " 901 303 555 1925 - 19“ 3.579 3.288 11-1 397 591 1926 ' 1‘80 3:385 39160 " 309 132 ' 3118 1927 159 2.905 3.090 - 2.2 62 223 1928 3 3 061 3.116 1.8 55 - 52 1929 - 9“ 3.067 2.97% - 5.5 169 75 1930 " 776 2:973 2:752 ' 7-5 223 " 553 1931 - 533 2.197 3.37% 22.6 #97 -1.030 1932 - I+63 1.66h 3.593 6.5 108 - 571 1933 576 1,201 2,968 -17.h 209 785 193k 230 1.777 1,988 -33.0 586 816 1935 - 39 2.007 2.995 50.7 1.018 -1.057 1936 218 1,968 2,056 -31.h 618 866 1937 ho 2 .216 3.280 59.5 .319 -1.359 1938 270 2,176 3.378 3.0 65 - 335 1939 265 1.906 3.206 - 5-1 97 362 191‘0 93 2 .9171 3 .9365 5 o 0 109 " 16 1911 926 2,261 3,575 6.2 110 786 1912 1,17h 3,190 1,221 18.2 581 593 1913 1,110 1,361 3,876 - 8.2 262 .372 19th 205 5.h7h 3.971 h-3 235 - 30 19h5 - #7 5.679 3.909 - 1.6 91 h“ 1916 1,201 5,632 1,121 5.1 301 897 19h7 1.912 6.833 3.573 ~13.3 909 2.821 TABLE 1c - (Continued) Value Total 90 Change due Change due Annual change beginning inventory 5 year was to physical to price Year in value of year in constant of previous change change current current end of year year -100 current current Mil.$ Mil.$ Mil.$ 5 Mil.$ Mil.$ (l) (2) (1) (5) (6) 1918 -1,215 8,715 1,511 26.3 2,300 -3.515 19h9 “1:571 7:530 3:901 ‘13°6 '19021" " 5“? 1950 981 6,567 3,200 - 3.0 - 197 1,181 1951 852 7,551 3,000 - 6.2 - 168 1,320 1952 77 8 ,103 2,900 - 3.3 - 277 200 1953 715 8,326 3 .9100 6° 9 575 ’1 3290 1951 102 7,611 3,100 9.7 738 - 636 1955 - 765 7.713 3.600 5.9 155 4.220 1956 352 . 3.500 - 2.8 - 195 5h7 1957 - 7.300 - - - Source: Col. 1, computed from Col. 2. culture, op. cit. , 1951-57 annual issues. Col. 5, computed from Col. 3. minus Col. 5. Col. 3, Col. 5, Col. 2 times Col. 1. Col. 2, 1909-1919, Goldsmith, Raymond W., op. cit., Table A-32, p.797; 1950-56, Balance Sheet of 55!;- same source as Col. 2. Col. 6, Col. 91 TABLE 5 - STOCKS OF MACHINERY ON FARMS, U.S., 1910-1956 Expenditures Machinery stocks on tractors & (sum of 8 previous Expenditures Machinery stocks on tractors & (sum of 8 previous machinery years weighted machinery years weighted Year (constant $) linearly) Year (constant $) linearly) (1) (2) (1) (2) 1902 356 - 1930 365 13.166 1903 271 - 1931 166 13,110 1901 298 - 1932 68 11,929 1905 302 - 1933 60 9.799 1906 362 - 1931 119 7.790 1907 363 - 1935 291 6.759 1908 311 - 1936 393 7.109 1909 112 - 1937 503 8.335 1910 109 12,692 1938 371 10,125 1911 111 13,256 1939 369 11,119 1912 117 13,783 1910 110 12,361 1913 108 11,218 1911 650 13,671 1911 g 122 11,162 1912 779 16,292 1915 109 11,712 1913 167 19,352 1916 383 11.798 1911 913 19,286 1917 355 11,630 1915 871 22,615 1918 359 11,199 1916 573 25,112 1919 393 13.857 1917 901 21.830 1920 587 13.837 1918 1.115 26.997 1921 222 15,387 1919 1,118 30,557 1922 232 13.817 1950 1.099 33.136 1923 301 12.573 1951 1.182 35.125 1921 253 12.011 1952 1.033 37.758 1925 326 11.233 1953 966 38.181 1926 370 11.139 1951 908 37.9511 1927 378 11.126 1955 885 37.168 1928 377 11.766 1956 827 35.863 1929 l+39 12.113 Source: 001. 1, 1902-1909. Goldsmith, Raymond W., 0p. cit., tractors, Table A-18, p.777 and machinery Table A-l6, p.773 adjusted to FIS series by subtracting the mean difference between the series from 1910-18 which was 193; 1910-56, from 001. 3, Table 1. Col. 2, Obtained by weighting eight previous years expenditure linearly, i.e. for 1910 value, 1902 expenditure times one, 1903 expenditure times two, etc. 92 TABLE 6 - REIMIV'E PRICE OF MACHINERY, 11.8. ,-1910-56 Index of Index of tractor and Prices Ratio tractor and Prices Ratio machinery re ce ived (relative machinery received ( relative Year prices by farmers price) Year prices by farmers price) (1937-11.100) (1937-11.100) (1) (2) (3) (1) <2) (3) 1910 61.5 97 .66 1931 90.5 81 1.08 1911 61.5 87 .71 1935 91.6 101 .91 1912 61.5 92 .70 1936 97.5 106 .92 1913 61.5 95 .68 1937 100.1 113 .89 1911 61.5 91 .69 1938 101.0 90 1.16 1915 66.5 92 .70 1939 99.1 88 1.13 1916 69.7 111 .63 1910 99.5 93 1.07 1917 79.1 165 .18 1911 99.8 115 .87 1918 100.0 191 .52 1912 101.8 118 .71 1919 103.2 202 .51 1913 106.9 179 .60 1920 107.1 196 .55 1911 111.3 183 .61 1921 103.2 115 .93 1915 113.3 192 .59 1922 92. 3 122 .76 1916 119.5 219 .55 1923 96.0 132 .73 1917 137.6 257 .51 1921 96.0 133 .72 1918 158.9 267 .60 1925 96.2 115 .66 1919 176.1 232 .76 1926 96.5 135 .71 1950 178.0 210 .71 1927 96.9 130 .75 1951 192.0 281 .68 1928 96.6 138 .70 1952 196.8 268 .73 1929 95.9 138 .69 1953 -195.7 210 .81 1930 96.1 116 .83 1951 197.5 231 .85 1931 91.2 81 1.16 1955 200.8 219 .92 1932 90.0 60 1.50 1956 208.1 218 .95 1933 97.8 65 1.50 Source: Col. 1, same as Col. 2, Table l. AEiculture, 0p. cit., Table C-8, p.852. Col. 3, Col. 1 divided by Col. 2. Col. 2, Policy for Conercial 111311: 7 - RELATIVE PRICE OF FARM LABOR, U.S. , 1910-56 93 Index of Index of tractor and Ratio Index of Index of tractor and Ratio farm wage machinery (relative farm wage machinery (relative Year rates prices price) Year rates prices price) (1937-11.100) (1937-11.100) (1) (2) (3) (1) (2) (3) 1910 72.0 61.5 1.12 1931 71.3 90.5 .82 1911 73.5 61.5 1.11 1935 80.3 91.6 .85 1912 75.8 61.5 1.18 1936 85.5 97.5 .88 1913 78.0 61.5 1.21 1937 96.8 100.1 .97 1911 75.8 61.5 1.18 1938 97.5 101.0 .91 1915 75.8 66.5 1.11 1939 95.3 99.1 .96 1916 81.0 69.7 1.21 1910 96.8 99.5 .97 1917 105.8 79.1 1.33 1911 113.3 99.8 1.11 1918 132.8 100.0 1.33 1912 117.8 101.8 1.11 1919 151.5 103.2 1.50 1913 196.5 106.9 1.81 1920 180.8 107.1 1.69 1911 238.5 111.3 2.11 1921 117.0 103.2 1.13 1915 269.3 113.3 2.38 1922 115.5 92.3 1.25 1916 290.3 119.5 2.13 1923 129. 0 96 . 0 1. 31 1917 311. 3 137.6 2 . 28 1921 136.5 96.0 1.12 1918 331.5 158.9 2.09 1925 135.8 96.2 1.11 1919 322.5 176.1 1.83 1926 137.3 96.5 1.12 1950 318.8 178.0 1.79 1927 138.0 96.9 1.12 1951 352.5 192.0 1.81 1928 138.0 96.6 1.13 1952 377.3 196.8 1.92 1929 139. 5 95.9 1.15 1953 381.8 195.7 1.97 1930 132.8 96 .‘1 1. 38 1951 382.5 197.5 1.91 1931 101.3 91.2 1.11 1955 387.0 200.8 1.93 1932 78.0 90.0 .87 1956 102.0 208.1 1.93 1933 66.0 97.8 .67 Source: Col. 1, Policy for Commercial Agriculture, op. cit., Table C-9, p.853. Col. 2, same source as fer Col. 2, Table 1. divided by Col. 2. man: 8 - mm 0F IABOR FORCE EMPLOYED, 0.3. , 1910-56 5. labor 91 % labor Year force employed Year force employed 1910 100 1931 78 1911 97 1935 80 1912 99 1936 83 1913 99 1937 86 1911 91 1938 81 1915 93 1939 83 1916 98 1910 85 1917 103 1911 92 1918 105 1912 ' 101 1919 99 1913 109 1920 97 1911 111 1921 87 1915 108 1922 91 1916 96 1923 96 1917 96 1921 93 1918 97 1925 95 1919 91 1926 96 1950 95 1927 95 1951 97 1928 95 1952 97 1929 97 1953 98 1930 91 1951 95 1931 83 1955 96 1932 77 1956 96 1933 75 Source: 1910-15, Johnson, Glenn L. , ”Allocative Efficiency of Agricultural Prices -- As Affected by Changes in the General Level of’Employment”, unpublished doctor of philosophy dissertation, Department of Economics, University of Chicago, 1919, Plate VI, p.61; 1916-56, Economic Report of the President, united States Government Printing Office,'washington, 1957, Table E-17, p.110. 0005 ”CD” USE ONLY ‘IOL Capt: 8 Jun 59 20 11159 Esq/TY “‘ 1 FEB 8 1800 a W FP.I201350: MAn ,5 1:00 a! W m ”USE. ONLY 7’_ «1’1“. N‘r“‘“ P HICHIGQN STQTE UNIV. LIBRRRIE 101l7lllslll7||l3|l3|5 ls