PRESENT VALUES 0F EXPECTED FUTURE {NCOME STREAMS AND THEIR REVELANCE T0 MOBILITY 0F FARM WORKERS TO THE NGNFARM SECTOR N THE UNITED STATES, 1917-62 Thesis far the Degree of Ph. D. MliHIGAN STATE UNIVERSITY Chennarezfiy Venkéreddy 1965 .A ‘- ‘ L13 ‘9. A Y ’v'slihng-ln .. 3m University _ This is to certify that the thesis entitled Present Values of Expected Future Income Streams and Their Revelance to Mobility of Farm Workers to the Nonfarm Sector in the United States, 1917-62 presented by Chennareddy Venkareddy has been accepted towards fulfillment i of the requirements for i Ph.D. degree in Agricultural Economics \ W Major professor \./ Date November 214, 1965 0-169 5. ABSTRACT PRESENT VALUES OF EXPECTED FUTURE INCOME STREAMS AND THEIR RELEVANCE TO MOBILITY OF FARM WORKERS TO THE NONFARM SECTOR IN THE UNITED STATES, 1917—62 by Chennareddy Venkareddy The major objectives in this study were to estimate the present values of the expected future income stream for a 25 year old and 45 year old worker in the farm sector and in four nonfarm occupations: manufacturing, construction, laundries and retail trade. To formulate a model for estimating the supply function of farm workers. To formulate a model for estimating the mobility of farm Operators of different ages from the farm sector to the non-farm sector. To utilize the estimated relationships for projecting age composition of farm operators to 1970. To estimate the number of farm workers in the future. Among the monetary variables, the ratio of the present value of the expected future income stream of a worker in the non- farm sector to the same in the farm sector was considered to be the basis upon which farm workers decide their Chennareddy Venkareddy occupational choice. This is a variable which has not been estimated and used in the previous studies. Since age is one of the main factors related to mo- bility of farm workers, data were developed on the pre— sent values of the expected future income stream for workers, age 25 and A5. Since unemployment in the nonfarm sector can seriously reduce the expected income stream of a potential off- farm migrant, an adjustment of the annual wage in the non— farm sector was made for this factor. Since annual wage data in retail trade and laundries are not available from 1917 to 1938 and from 1917 to 1933 respectively, they were estimated on the basis of the regression line with the annual wage data in the concerned occupation as the dependent variable and the annual wage data in construction as the independent variable. Expected unemployment rates in individual years up to nine years in the future were estimated so that an average of the estimates is an estimate of the average. On and after the tenth year ahead from the current year, the estimated average in the next nine years was used. In the case of annual wage estimates a similar pro— cedure was used up to nine years ahead. Beyond the ninth year, and up to (nl—l)th year (n1 is the remaining life expectancy of a 45 year old worker) an estimated increment Alin the annual wage was added to the estimate of the Chennareddy Venkareddy annual wage in the ninth year ahead. From nlth year ahead to (n2-1)th year ahead, an estimated increment A2 in the annual wage was added every year to the estimate of the annual wage in the (nl-l)th year ahead. After adjustment of annual wage rates for the unemploy- ment rate, present values of the expected future income stream from each year, 1917 to 1962, were calculated for both the A5 and 25 year old worker in each occupation. The present values in expected future income stream seems to be consistent with the economic and political events overtime since 1917 to 1962. The present value of the expected future income stream for a 25 year old worker increased from $19,381 in 1917 to $56,U23 in 1962 in farming; from $27,278 in construction; from $13,007 to $57,271 in laundries and, finally, from $17,090 to $78,303 in retail trade. The present value for a H5 year old worker increased from $13,u79 in 1917 to $43,709 in 1962 in farming; from $18,516 to $88,705 in manufacturing; from $17,747 to $112,581 in construction; from $8,888 to $u4,136 in laundries and, finally, from $12,173 to $59,229 in retail trade. As a method of testing the validity of the estimates of present values of the expected future income stream, lin— ear and logarithmic regression lines were fitted (one in each age group) with the ratio of the number of farm operators Chennareddy Venkareddy to the number or rural survived farm males, as the de- pendent variable and the ratio of present value in the appropriate nonfarm occupation to the same in farming, as the independent variable. These regression lines were based on the data in four census years (1930-1960)- The tests revealed that the mobility of younger farm Operators are respondent to the ratio of present value of’expected future wages in manufacturing to the same in farming and in the case of older farm operators, laundries, rather than manufacturing is relevant. 0n the basis of the fitted regression lines and the projected present values, the number of farm operators was projected in each age group for 1970. For the United States, the estimate of total number of farm operators for 1970 in this study is 2.607 million by linear regression method and 2.616 million by the "linear in logarithms" method as compared to the 1960 enumeration of 3.701 million. On the basis of two different regression lines total number of agricultural workers was projected to 1980. They are 4.93 million and b.87 million. Most of previous studies projecting the number of farm operators in different age groups were based either directly or indirectly on the hypothesis that the mobility of farm workers to nonfarm occupations is responsive to the ratio of the current nonfarm wage rate to the current wage Chennareddy Venkareddy rate in farming. This assumption is not entirely correct. Farm workers (or anybody else) in changing occupations can be expected to think in terms of lifetime expected returns and their present values, rather than simply in terms of the current years annual wage. In this study, the mobility of farm workers was assumed to be responsive to the ratio of present value of the expected future income stream in nonfarm occupations to the same in farming. The projected number of farm operators in each age group for 1970 indicates that the trend of aging farm operators is not going to be reversed. According to the projected number of farm operators for 1970, the number of farm operators will decrease by about 1.15 million the period 1960 to 1970. PRESENT VALUES OF EXPECTED FUTURE INCOME STREAMS AND THEIR RELEVANCE TO MOBILITY OF FARM WORKERS TO THE NONFARM SECTOR IN THE UNITED STATES, 1917-62 By Chennareddy Venkareddy A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1965 ACKNOWLEDGMENTS This study is a part of a larger project concerned with the impact of government policy on resource flows in and out of agriculture. This larger project is being carried on under the auspices of a grant from Resources for the Future, Inc. The project leader is Dr. Glenn L. Johnson. The author gratefully acknowledges the assistance of the following in making this study possible. Dr. Glenn L. Johnson suggested the topic and guided at various phases of development of this study. The author is particularly grateful to him for the patience and con— fidence he displayed throughout the author's graduate program. Dr. L. V. Manderscheid showed a great deal of patience in laboring through the earlier draft and offered several useful suggestions for improving the presentation of this thesis. His friendly attitude in helping the author through— out the graduate program was highly appreciated. Dr. Robert L. Gustafson served as a member of the author's guidance committee and also as an alternate major professor during Dr. Johnson's absence from the 0.8. His suggestions and advice throughout the author's graduate program are greatly appreciated. ii Drs. Kenneth J. Arnold and Paul Straussman served as members of the author's guidance committee. Dr. Lawrence L. Boger, the chairman of the Department of Agricultural Economics, and Resources for the Future, Inc.,provided the financial assistance which made possible the author's graduate study at Michigan State University. The author thanks all the staff in the computer pool of the Department of Agricultural Ecbnomics for their compe- tent help in the computational work. The author is particularly grateful to Mrs. Anne Ryan for her patience in typing the earlier draft of this thesis. The author's heartfelt appreciation goes to his wife, Mrs. Sulochana, for the invaluable role she played in help- ing the author to complete his graduate work at Michigan State University. The author assumes full responsibility for any errors in this study. iii To My Parents, My Teachers, and My Wife iv TABLE OF CONTENTS LIST OF TABLES. . . . . . . . . . . . LIST OF FIGURES . . . . . . . . . . . . . LIST OF APPENDICES Chapter I. II. INTRODUCTION. . . . . . . . . . . . Introduction . . . . . . . . Need for this Study. . . . . . . Previous Studies. . . . . . . . . Objectives of this Study . . Outline. . . . . . . METHODOLOGY . . . . . . . . . . . Introduction . . . . The Model And An Estimating Procedure. Sources of Off- farm Employment . . Age Classification Expected Remaining Number of Years of .Life of a Worker. . . . . . . . . . . Rate of Interest. . . . . . . . . Type of Wage Rate . . . . Definition of Price of Farm Worker. . . Construction of Annual Wage From 1917 to 2007 Introduction Backward Projection of Annual Wage Rate in Laundries and in Retail Trade Forward Projection of Annual Wage Rates in All the Occupations Construction of Unemployment Rates in the Nonfarm Occupations from 1917 to 1962 Expectation Models . . . Expectations of Unemployment Rate and Annual Wage . . . . . . . . . . . . Present Values . . . . . . . . . . Page viii ix xi H FJH romnocoH 15 15 l7 l9 19 2O 2O 22 23 23 25 26 27 28 3A Chapter III. SOURCES AND LIMITATIONS OF THE DATA. Introduction. Interest Rate Expectancy of Life. Annual Wage Rate Per Worker. Source and Estimation of Annual Wage Farming Manufacturing, Laundries and Retail. Trade . . . Backward Extrapolation in Laundries and in Retail Trade. Construction Forward Projection of Annual Wage Source and Estimation of Unemployment Rate. IV. UNEMPLOYMENT RATE EXPECTATIONS Introduction. Discussion of Results. V. ANNUAL WAGE EXPECTATIONS IN VARIOUS OCCUPATIONS . . . . Introduction. . Discussion of Results. VI. PRESENT VALUES AND SUPPLY FUNCTIONS. Introduction. Present Values of the Expected Future Income Stream. Consistency of Present values with the Political and Economic Events . Testing the Validity of Present Values Introduction . . First Method of Testing the Validity of the Estimates . . . Second Method of Testing the Validity of Present Values. . . . . . vi Page 100 102 102 104 112 Chapter Trend in the Expected Present Value of the Future Income Stream . Projection of Number of Agricultural Workers and Comparisons with the Previous Projections. Projection of Number of Farm operators and Comparison with the Previous Projections. VII. SUMMARY AND CONCLUSIONS. LIST OF REFERENCES APPENDICES. vii Page 112 118 121 132 144 149 10. LIST OF TABLES Page Farm employment, United States, 1910-19 to 1950—59. 0 o o o e o o o o o g Average interest rates charged on mortgage loans for farmers by all lenders in the U.S., 1917-62. . “8 Expected number of years of remaining life of white male worker at the age of 45 and 25 in the U. S. 1917- 62 . . . . . . . . 50 Estimated annual wage rate (in current dollars) in retail trade and in laundries in the U.S., 1917-38. . . . . . . . . . . . . . 58 Unemployment as a percentage of nonfarm em- ployees in the U.S., 1917-60. . . . . . . 67 Current and expected unemployment rate in the future years in various occupations, U.S., selected years . . . . . . . . . . . 83 Current and expected annual wage in the next year, 5th year, 9th year, and expected incre- ments in the annual wage in various occupa- tions, U.S., selected years . . . . . . . 96 Estimated ratios of present values and total number of agricultural workers in the U.S., 1963-80. . . . . . . . . . . . . . 120 Number of farm operators by age group by census years (1920—60) and projections of number of farm operators for 1970 according to 1950 census definitions, U.S. . . . . . . . . . . . . . . 123 Number Of farm Operators by age group in the years 1960 and 1970 according to 1960 census definition, U.S. . . . . . . . . 126 viii Figure LIST OF FIGURES The relationship between annual wage (in current dollars) per worker in retail trade, and annual wage (in current dollars) per worker in construction in the U.S., 1939-51 The relationship between annual wage (in current dollars) per worker in laundries and annual wage (in current dollars) per worker in construction in the U.S., Trend in annual hired wage (in current dollars) per farm worker in the U.S., 1950—62 Trend in annual per worker in 1950—62 Trend in annual per worker in 1950-62 Trend in annual per worker in 1950—62 Trend in annual per worker in 1950—62 wage (in current dollars) manufacturing in the U.S., wage (in current dollars) construction in the U.S., wage (in current dollars) retail trade in the U.S., wage (in current dollars) laundries in the U.S., The relationship between unemployment in manufacturing and unemployment as a per- centage of nonfarm employees in the U.S., 1948-60 The relationship between unemployment rate in construction and unemployment as a percentage of U.S., 1948-60 nonfarm employees in the ix 1934-47 Page 55 56 61 62 63 64 65 69 70 Figure Page 10. The relationship between unemployment rate in trade and unemployment as a per— centage of nonfarm employees in the U.S.,l948-60. . . . . . . . . . . .71 11. The relationship between the unemployment rate in laundries and unemployment as a percentage of nonfarm employees in the U.S., 1948-60. . . . . . . . . . 72 Appendix A. 1. Percentage of unemployment LIST OF APPENDICES Available annual wage (in current dollars) data from published sources in the U.S., 1917—62. . . . . . . . Projected annual wage rates (in current dollars) per worker in farming, manu- facturing, construction, retail trade and in laundries in the U.S., 1963-2007 . . . . . . . . . the period 1917-47 and actual for the period 1948—62) in manufacturing, con- struction, retail trade and in laundries in the U.S., 1917-62 . Estimates of the annual wage (in current dollars) in the (t+n)th year ahead (n=0,l. . . .9) and the increments in in the annual wage (A and A ) ex- pected in each currené year rom 1917 to 1962 in farming in the U.S. . . . . . . . . . . Estimates of the annual wage (in current dollars) in the (t+n)th year ahead (n=0,l. . . .9) and the increments in the annual wage Al and A2) ex— pected in each current year from 1917 to 1962 in manufacturing in in the U.S. . . . . . . . Estimates of the annual wage (in current dollars) in the (t +n) year ahead (n=0,1. . . .9) and the increments in the annual wage of (A and A ) ex- pected in each current year rom 1917 to 1962 in construction in the U.S. . . . . . . . . . . xi (estimated for Page . 151 . 153 155 . 157 159 161 Appendix 4. Estimates of the annual wage (in current dollars) in the (t + n)t year ahead (n=0,l. . . .9) and the increments in the annual wage (Aland A2) ex- pected in each current year from 1917 to 1962 in retail trade in the U.S. . . . . . . . . . . . Estimates of the annual wage (in current dollars) in the (t + n)t year ahead (n=0, 1. . . .9) and the increments in the annual wage (A and A ) ex- pected in each curren$ year rom 1917 to 1962 in laundries in the U. S. . . . . . Estimates of the unemployment rate (per- centage) in the (t+n)th year ahead (n=0,1,2. . . .9) expected in each current year from 1917 to 1962 in manufacturing in the U.S. . . . Estimates of the unemployment rate (per- centage) in the (t+n)th year ahead (n=0,1,2. . . .9) expected in each current year from 1917 to 1962 in construction in the U.S. . . . . Estimates of the unemployment rate (per- centage) in the (t+n)th year ahead (n=0,1,2. . . .9) expected in each current year from 1917 to 1962 in retail trade in the U. S. . . . Estimates of the unemployment rate (per- centage) in the (t+n)th year ahead (n=0,1,2. . . .9) expected in each current year from 1917 to 1962 in laundries in the U.S. Present value of the expected future income stream in the remaining years of life of 25 year Old worker in various occupa— tions in the U.S., 1917-62 Index of present value of the expected future income stream for a 25 year Old worker with the present value in 1917 as the basis in various occupations in the U.S., 1917—62 . . . . xii Page - 163 . 165 168 . 170 172 174 . 177 179 Appendix 3. 4. E. l. 2. F. 1. Present value of the expected future income stream in the remaining years of life of 45 year Old worker in various occupations in the U.S., 1917-62. Index of present value of the expected future income stream for a 45 year old worker with the present value in 1917 as the basis in various occpa— tions in the U.S., 1917—62. Number of farm Operators by age group in the U.S., 1920-60. Estimates Of survived rural farm males by age group in the U.S., 1920—70 Some results from the solutions Of the equations 9 to 13 on page 110. xiii Page 181 183 186 187 189 CHAPTER I INTRODUCTION Introduction A conspicuous characteristic Of American agriculture is the dramatic decline in farm labor input and increase in farm output. The phenomena Of declining farm labor input is not new, but it is more pronounced in recent decades. Total farm labor input in the period 1910—1919 averaged 23,343.7 million man hours per year and decreased to l2,888.3 million man hours in the period 1950-1959. TABLE 1.-—Farm employment, United States 1910-19 to 1950-5‘. Average NO. Average Period Of Farm Workers Farm Labor Input Percent Million Percent 1000's (1910—19) hours (1910:12) 1910—1919 l3,523.l 100.00 23,343.7 lt0.00 1920-1929 l3,046.8 96.48 23,255.4 99.62 1930-1939 12,342.6 91.27 21,658.0 92.78 1940-1949 10,382.1 76.77 18,87l.0 80. 4 1950—1959 8,481.4 62.72 l2,888.3 55.21 Source 1 Farm Employment U.S.D.A. Stat. Bul. NO. 334. Source 2 Changes in Farm Production and Efficiency, J.S.D.A. Stat. Bul. NO. 233. Total farm labor input in the period l950~59 was only 55.21% of the 1910-1919 level. Total farm workers, both 1 2 hired and family, decreased from 13, 23.1 thousands in the period 1910-1919 to 8,481.4 thousands in the period 1950-59. However, the number of farm workers did not decrease in the same proportion as total farm labor. In 1917, labor input was 51.9 per cent Of the total input used in agriculture; by 1962, it accounted for only 24.2 per cent. The supply Of and demand for labor input in the farm sector depends on, firstly, the demand for labor in the non— farm economy, secondly, the technology Of farm production and, thirdly, the demand for farm products. As the nonfarm sector became more and more industrialized, an enormous increase in demand for labor in the nonfarm sector increased the wage rate in the nonfarm sector. The increased wage for labor in the nonfarm sector in turn induced further out—movement of labor from the farm sector. The increased outmovement of labor from the farm sector to the nonfarm sector caused scarcity of labor in the farm sector. The scarcity of labor in the farm sector in turn created a necessity for labor saving and capital intensive farm tech— nology. The rapid growth in farm technology caused a further decline in the demand for labor because of the in— crease in the marginal productivity of capital relative to that of labor. Hence, rapid industrialization in the non- farm sector and tremendous advances in labor saving farm technology are two reasons for the decline in the use of the labor input in the farm sector. The third reason is the inelasticity of the final demand for farm products. Because of the feasibility of large scale (but still mainly family Operated) farms due to the tremendous advances in labor saving as well as output increasing farm technology, farmers increased their size of operation and produced higher levels of farm output. The tremendous increase in the farm output and the existence of a highly inelastic demand for farm pro- ducts caused the farm price level to fall. The decrease in prices caused a subsequent further decline in the demand for labor input. Despite the recent unparallelled decline in farm labor input, farm output continues in excess over what is demanded at "fair prices." The farm surplus problem has continued to be a serious problem for the agricultural policy makers in the American economy. In spite of the various forms of gov— ernment intervention in the free market for farm products to increase the returns to farm labor, farm labor input con- tinues to earn less than its counterpart in the nonfarm sector after giving allowance for differences between the sectors. The gap in the labor earnings between the sectors indicates the malallocation of labor resource between the sectors. Under the assumptions of the perfect competition model in the labor market i.e., (l) homogeneity of labor, (2) perfect mobility of labor, (3) large number of buyers and sellers of labor, (4) perfect knowledge of labor market con— ditions, labor moves out of agriculture in which it earns less until the returns for labor are equal in both sectors. In other words, the price system is the mechanism through which signals are transmitted for allocating production re- sources. In the absence of friction and transfer costs (acquisition costs in excess of salvage values), maximum efficiency can be attained.1 But contrary to this situation of perfect competition and frictionless transfers, much evi— dence reveals that more labor remains in agriculture than needed, despite low returns for labor. That indicates that flows of labor between the sectors are not producing an equ— alization of wage rates throughout the system. This may occur for reasons mentioned by Gallaway: (l) the existence of nonprice barriers to mobility of workers, (2) the exist— ence of positive private economic costs associated with the movement of labor from sector to sector, (3) non- homogeniety of labor units involved, (4) a failure of workers to maximize their utility function; and/or (5) difference in workers' preference functions.2 In addition, Hathaway explains the continuous disequilibrium in terms of the com— bined elements such as (1) highly inelastic demand for products, (2) a low income elasticity for products, lRalph Arthur Loomis, Occupational Mobility in Rural Michigan, an unpublished Ph. D. thesis. Department of Agricultural Economics, Michigan State University (1964). 2Lowell E. Gallaway, "Labor Mobility, Resource Allocation and Structural Unemployment," American Economic Review, Vol. LIII, No. 4 (September, 1963), pp. 694-715. (3) rapid rate of technological change, (4) competitive structure and (5) a high degree of asset fixity. Haver3 believes that factor market imperfections and institutional rigidities tend to misallocate resources, impeding adjustments in agriculture. He also believes that uncertainty causes inefficient production. He further stated that price support and production control programs also have impeded adjustments to achieve optimal resource allocation. The relative immobility of labor in agriculture with its attendant problems of surplus production and low farm prices and incomes has long been a concern to agricultural economists and rural sociologists. During recent years, a conviction has grown among these researchers that the de— clining economic position of agriculture is closely associa- ted with an inadequate rate of migration from farming. This judgment is succinctly expressed in Schultz's statement ". . . the hard core of the United States farm problem is a n5 labor transfer problem. The over-commitment of labor 3Cecil B. Haver, "Institutional Rigidities and Other Imperfections in the Factor Markets," Agricultural Adjust- ment Problems in a Growing Economy (E. O. Heady, et al., eds.) Iowa State College Press, Ames, Iowa, U.S.A. (1958). “H. W. Baumgartner, "Potential Mobility in Agriculture: Some Reasons of the Existence of a Labor—transfer Problem," Journal of Farm Economics, Vol. 47 (February, 1965), p. 74, 5Theodore W. Schultz, "The United States Farm Problena in Relation to the Growth and DeveIOpment of the United States Economy," Policy for Commercial Agriculture: Its Pkg- lation to Economic Growth and Stability, Washington Joiht?‘ Economic Committee (1957), p. 4. resource in agriculture can be avoided by impeding the labor resource flow into agriculture and by inducing labor flows from the farm sector. However transfer of farm labor re— source to the nonfarm sector is not an easy and quick pro— cess. Several studies reveal that quite a few factors other than monetary incentives may influence the out mobility of farm workers. D. Gale Johnson6 has suggested that a study of farmer mobility should include a reasonable explanation of the important motivating factors both monetary and non- monetary. Mobility of farm workers to the nonfarm sector is not only subject to monetary influence but also to various other sociological, psychological and institutional factors. In the literature, among the variables which significantly influence the mobility of the farm workers, the important categOries are economic status, age, and attitudes toward farming. As the present study does not pay much attention to nonmonetary factors other than age, time, unemployment and occupations, a brief review of literature relating to the effect of such factors on the mobility of farm workers is presented below. Age, an important independent variable, was considered to be the most effective in influencing the mobility of 6D. Gale Johnson, "Mobility as a Field of Economic Research," Southern Economic Journal, Vol. XV (October, 1948), p. 152. 7 farm workers. Bowles writes that migration rates were con- sistently lower among younger people. Roy8 found by a chi- square test that both husbands and wives among the high aspirants, were consistently of the younger age groups. In this context aspiration is a measure of a farmer's desire to seek a better paying job and, hence, modifies the monetary 9 pull-factor for farmers to leave agriculture. Heady reports that the number of subjects indicating that "no amount" would move them out of agriculture rose sharply with the increasing age. Baumgartnerlo concludes that under a variety of personal, economic, social, and psychological conditions, age is more closely associated with migration than any other independent variable. Potential mobility was significantly greater among farmers under 45 than among those aged 45 or over. Among all the other variables, nonfarm work 7Gladys K. Bowles, "Migration Patterns of the Rural- Farm Population, Thirteen Economic Regions of the United States, 1940—50," Rural Sociology, Vol. 22 (March, 1957), p. 3, Chart 1. 8Roy Prodipto,_ "Factors Related to Leaving Farming," Journal of Farm Economics, Vol. 43 (August, 1961). 9E. O. Heady, W. B. Back, and G. A. Peterson, Inter~ dependence Between the Farm Business and the Farm Houshold with Implications on Economic Efficiency, Res. Bul. 398, Iowa Ag. Expt. Sta. (1953), p. 421, N. 27. 10H. W. Baumgartner, "Potential Mobility in Agriculture: Some Reasons for the Existence of a Labor—Transfer Problem," Journal of Farm Economics, Vol. 47, No. 1 (Feb., 1965), pp. 715-82 0 experiences also appeared to be closely associated with mobility. Nonfarm experience was associated positively with potential mobility among farmers irrespective of age.11 Some of the monetary factors are (a) present costs of training to fit themselves to nonfarm work, (b) costs of moving to the nonfarm centers, (c) expected returns in the nonfarm sector as compared to the expected returns in the farm sector. Institutional factors are (a) various govern- ment programs relating to farm production, (b) wars. Need For This Study Any policy study for labor resource transfer for farm adjustments needs knowledge of the ease or difficulty with which reductions in number of farm workers can be achieved. This achievement depends partly, if not mainly, upon the res- ponse of the farm workers to the relative monetary incentives in the nonfarm sector and the farm sector. If the response of the mobility of farm workers to relative monetary incen- tives in the farm and nonfarm sector is low, it is very dif- ficult to make the necessary changes in the policies to in- duce transfer of labor. Hence, knowledge about the supply function of farm workers in agriculture is of immense need for better understanding of the future farm adjustment. Agricultural workers include operator, family and hired workers. Previous studies indicated that reductions in farm Operators are not easily brought about when farm operators 11Baumgartner, Op. Cit., p. 82. are largely older persons who are less likely to shift to other employment. Not only information about the response of supply of total number of farm workers to monetary incen- tives but also information about the responses of different aged farm operators is needed. Projections Of the total number of farm workers and farm operators would be an aid in designing programs to facilitate adjustment. This study is intended to supply data on monetary incentives influencing the behavior of farm operators in two age groups. The data pertain to the two age groups, 25 and 45 year old operators, and to five occupations: farming, laundries, retail trade, construction and manu- facturing. Previous Studies Schuhl2 has studied the demand and supply for hired labor. Johnson and Ready13 have investigated the market for both hired and family labor. Recently, several studies emphasizing cohort analysis for projecting the future number of farm Operators were done (Kanel, 1961, Clawson, 1963; 12G. E. Schuh, "An Econometric Investigation of the Market for Hired Labor in Agriculture," Journal of Farm Economics, 44 (2) (1962), 307-321. 138. S. Johnson, and E. 0. Heady, Demand for Labor in Agriculture, C.A.E./Report 13T, Center for Agricultural and Economic Adjustment, Iowa State University, Ames, Iowa (1962). 10 Tolley and Hjort, 1963; Kanel, 1963, Johnston, 1963). Tolley and Hjort (1963) attempted to measure directly the effect of changing farm numbers on the response of different aged farm Operators. The regression model assumes that the number of farm Operators in a given age group depends on the number of cohort members a decade earlier and on the ratio of the total number of farmers of all ages to total numbers 10 years previously. The regression is the logarithmic transformation of b i r 2 f it _ a 1 it i . . f1-1,t—1 Zifi—l,t-l is the number of farm operators in the ith age t group for tth census year. For each age group there are where fi five observationspiegt goes from 1 to 5 corresponding to the five censuses of 1920, 1930, 1940, 1950, 1960. If there were no change in farm operator numbers from census to census, the independent variable would be unity and the parameter a would then measure the cohort pattern i of net entry and withdrawal without changes in the total number of farm operators overtime. The bi may be interpre- ted as the elasticity of farm operators of a given age group with respect to total number of farm operators. For all regions the regression coefficients tend to decline with age. Large bi values for younger age groups substantiates their greater occupational mobility. For most regions and for the national aggregate, occupational mobility was not 11 found to be significant after age group 45-54. Johnston (1963) has formulated the following supply model for pro- jecting the future number of farm operators by age group. Bi fit = diztsitUit B. 1 fit = diztuit Sit where fit is the number of farm operators classified ac- cording to 1th age group in tth census period. Sit is the number of survived rural for males who were ten years younger in the preceding census. Sit is considered a supply shifter. Zt is the ration of farm to nonfarm earnings facing potential farm operators in year t and Uit is a random error. Both farm operator numbers (f ) and survived rural it farm male estimates (Sit) are readily available. Since a suitable measure of the farm to nonfarm earnings ratio (Zt's) is not available for the regions, (such a measure is available for the nation). Johnston adopted an iterative Z procedure to estimate 61, 8 simultaneously. The i’ t’ iterative procedure begins with the assumption that the ra- tio of total farm operator numbers in a given decade to the number of survived rural farm males is a crude approximation of the farm—nonfarm earnings ratio. Using these ratios for each decade as approximations of the Zt's, the first step of the initital iteration yields a set of 61 and 81's. The Bi's are then used in the second step of the first iteration to t's. The Zt's are then used to obtain a new set of 61's 8 's in the first step of the yield new estimates of Z 1 second iteration and so on until estimators are approxi- h h mately identical from the Kt to the K+lt iterations. The Objectives of This Study Are 1. To estimate the present values of the expected future income stream for a 25 year old and 45 year old worker in the farm sector and in four different occupations in the nonfarm sector. 2. To formulate a model for estimating the supply function of farm workers. 3. To formulate a model to estimate age—specific relations for farm operators in agriculture. 4. To utilize the estimated relationships for projecting age composition of farm Operators to 1970. 5. To project the number of farm workers in the future. Outline of This Study To fulfill the above objectives the organization of this thesis is as follows. Chapter II: Methodology. In this chapter the pro— cedure adopted for estimating the expected annual wage and the expected unemployment rate in various occupations in the remaining years of life of a 45 year old and 25 year Old worker is discussed. The method for calculating 13 present values is also given. An explanation of the supply models for farm Operators and total farm workers is also given. Chapter III: Sources and Limitations of Data. In this chapter, sources of all the variables, i.e. annual wage per worker in various occupations, unemployment rate in various occupations, interest rate, expected remaining years of life at a specific age, and their limitations are dis— cussed. If data on the variables were not available during the period 1917 to 1962, methods for projecting the series backwards to 1917 are also discussed. In all cases, the method of projecting the series forward to 2007 is also discussed. Chapter IV deals with a method of estimating expected unemployment rate in the next nine years from each current year from 1917 to 1962. For the tenth year ahead onwards, the estimated average unemployment rate for the next nine years is used. Chapter V deals with a method of estimating the ex- pected annual wage in the next nine years. A method to estimate an average increment in annual wage from the ninth year to the 26th year ahead from the current year and an average increment from the 26th year to the 44th year ahead from the current year is also given. The expected annual wage in any year ahead up to nine years and the first and second increment are derived as a function of the current year and the past year Observations. 14 Chapter VI deals with the present values of the ex— pected future income stream in various occupations. It also deals with the supply models for farm operators and farm workers and empirical estimates. Projections of farm Oper- ators and the total farm workers are also given in this chapter. Chapter VII deals with the summary and conclusions of the entire work described in the previous six chapters. CHAPTER II METHODOLOGY Introduction This chapter first specifies the supply model for farm operators and for total agricultural workers. It also specifies the method for estimating the ratio of the present value of the expected future income stream in a non- farm occupation to the present value of the expected future income stream in farming. The Model and An Estimating Procedure Theoretically, a supply model for any commodity or service is specified with the quantity of the commodity or service under study as a function of price for that commodity or service. To this relationship, one usually adds one or more variables to explain shifts in the supply curve. The supply model used in this thesis for farm operators specifies the farm Operators in a specific age group as the quantity variable. The relevant "price" for farm workers making occupational decisions as to whether or not they should be farmers is assumed as the ratio of the present value of the future income stream in nonfarm occupations to 15 16 the same in farming. This price is used as an independent variable in the supply model. The supply shifter in this study is survived rural farm males. This measure takes rural farm males ten years younger in the previous decennial census and adjusts the numbers for deaths and intercensus enumeration errors by use of agewspecific survival ratios. The rationale for this choice of shifter variable is that it approximates the number of potential farmers if there were no net migration. The foregoing discussion leads to the following supply model for farm operators: 8 . 1 fit = “izt Situit (1) where f is the number of farm operators classified accord- it ing to 1th age group and enumerated in the Census of Agriculture for tth time period. Sit is the number of survived rural farm males who were ten years younger in the preceding census. Zt is the ratio of present value in non— farm occupation to the same in farming, expected by the potential farm Operators in the census year t. Both farm operator numbers (fit's) and survived rural farm male estimates (si 's) are readily available for t quantification of the relationship expressed in equation (1). Zt can also be treated as the ratio of opportunity price in the nonfarm sector to the price in the farm sector. Uit is a random term. 17 The supply function for the total number of farm workers is as follows. Nt = f(Zt, t) (2) where Nt is the total number of farm workers and Zt is the ratio of the present value of expected future income stream in the nonfarm sector to the same in the farm sector. Though this is a general form, different forms of functions are tried. 't' is the time variable. The present values of the expected future income stream are also fitted as a func— tion of time in different forms. Pt = f(t) (3) Different forms of functionsgl, 2, 3 will be discussed with empirical results in Chapter VI. The most important variable to be quantified is the ratio of present values of the expected future income stream in the nonfarm sector to the same in the farm sector. This is a variable not esti- mated and used in the previous studies. Hence, the method of calculating the present values of the future income stream is discussed in detail in this chapter. Sources of Off—farm Employment In the calculation of the present value of the ex- pected future income stream in the nonfarm sector, a question arises as to what kind of jobs farm workers usually take when they move to the nonfarm sector. l.) 03 Perkins found that four industries employed over three- fourths of all the farm workers who transferred to nonfarm employment. The four industries were construction, manufac- turing, wholesale and retail trade, and government. Manu— facturing was most important in 1957 and only slightly less important in 1958 than wholesale and retail trade.1 A survey in 1957 of State Employment Service managers in Kansas by Schnittker and Owens reports similar types of jobs most commonly available to farmers. Managers listed jobs in order of importance as (1) construction labor, (2) machine shop and mechanical work, (3) factory work, (4) retail trade employment, and (5) wholesale trade employment.2 Other jobs available to farm workers included: truck driving, service station attendant, custodial work, farm equipment sales, oil field work, feed milling and mixing and heavy equipment Operator. A survey of the literature indicates that the nonfarm occupations which the majority of farm workers have been taking are (1) building trades (helpers and laborers), (2) manufacturing, (3) service industries (laundries), (4) trade (retail). The sub-occupations (l) helpers and laborers in building trades, (2) laundries in service industries, 1Brian B. Perkins, The Mobility of Labor Between the Farm and Nonfarm Sector,(an unpublished Ph. D. thesis, Department of Agricultural Economics, Michigan State Uni- versity, 1964). 2John A. Schnittker and Gerald P. Owens, Farm to Cipy Migration: Perspective and Problems, Ag. Ec. Report NO. 84, Kansas Ag. Exp. Sta. (1959), p. 28. l9 (3) retail trade under 'trade' are chosen in the light of availability of wage rate data for a longer period. Since age is one of the main factors which affects the mobility of farm workers, data on the present values of the expected future income stream in relation to the age of the farm workers are also constructed. Age Classification All workers were classified into two categories. The first category consists of all the workers belonging to the age group 15—40 with a range of 25 years. The second category consists of all workers of age 40 and above. The first category indicates a group of younger farmers and the second category represents a group of older farmers. Among the ages in each group, two typical ages were selected, 25 in the first category and 45 in the second category. Expected Remaining_Number of Years of Life of a Worker The expected remaining years of life of a worker of a specific age increased gradually though not dramatically from 1917 to 1962. The remaining expected number of years of life of a 25 year Old worker in the United States in the year 1917 was 41. It steadily increased to 46 years in the year 1962. The remaining expected number of years of life of a 45 year old worker in the United States only increased from 25 in the year 1917 to 27 in the year 1962. It is |\) assumed in this study that workers continue to earn until their death. Briefly speaking, workers retire through death. The source and the limitations of these data and assumptions will be discussed in detail in Chapter III (p. 45 to 73). Rate of Interest One of the variables included in the calculation of the present value of the expected future income stream is the current rate of interest. A crucial part of the calculation of present value is the decision as to what rate of interest is to be selected among various rates of interest, charged by different agencies for various trans- actions. A near ideal concept of rate of interest, for our purpose, would be a weighted average of the contract interest rates on currently negotiated mortgage loans. However, in the light of paucity of the desired data over a long period of time, deviation from the ideal concept is justified. The sources and procedure for construction of interest rate series overtime are given in Chapter III. Type of Wage Rate An important aspect of the calculation of the ex— pected income stream is the formulation of expectations of an annual wage in the remaining years of life of a worker. A 25 year old worker in the year 't' can expect up to n (n 2 2 ranges from 41 to 46) remaining years of life. A 45 year old worker can formulate expectations of earnings for up to nl (nl ranges from 25 to 27) remaining years of life. In this study, it was assumed that both workers of age 25 and 45 in the year 't' have the same expectation of the future income stream for a given occupation up to nl years (n1r is the estimate of the expected annual wage in the kth year ahead from the current year 't' in farming. CHAPTER III SOURCES AND LIMITATIONS OF THE DATA Introduction The data for this study are largely taken from pub- lished sources. But some of the series, which are not available throughout the period from 1917 to 1962, were generated by fitting regression lines and making backward projections. All the annual wage series were projected to 2007 by fitting a linear regression with time as an indepen- dent variable for the period 1950-1962. Interest Rate In the published reports, a distinction is made be- tween the average rate of interest on currently negotiated farm mortgage loans and the average rate on farm mortgage loans outstanding. The former is used in this study. An ideal interest rate should be an average of the contract rates on currently negotiated loans weighted by the total quantity for all the farm mortgage loans closed during the year. A project conducted during 1936 and 1937 under the Joint sponsorship of the Bureau of Agricultural Economics and the Work Projects Administration provided estimates of 45 46 the annual average rates of interest charged on farm mort- gage recordings in the United States for the period 1910 to 1935.1 The estimates are weighted averages for each year, based on a sample of about 20 per cent of the coun- ties in the United States. The U.S.D.A. has published bienniel estimates from 1941 to 1959.2 The estimates are weighted averages based on a sample of 1,000 to 1,200 counties which contain 38 to 45 per cent of the farms in the United States. The data are from farm mortgage recordings for these counties during the month of March on alternate years from 1941 to 1953 and for the first quarter of each alternate year from 1955 to 1957. Thus, the rates are based on a sampling of each year, and particularly the month of March, which represents the time of heaviest activity in the farm mortgage market. While it would be better to have estimates based on activity for the entire year, any difference in the average rates would be small. No estimates were available for the years from 1936 3 to 1940 and for the even numbered years thereafter. Leon 1Bureau of Agricultural Economics, Average Rates of Interest Charged on Farm Mortgage Recordings of Selected Lender Groups (Washington, D.C., 1940), 60 pp. 2U. S. Department of Agriculture, Major Statistical Series of the U.S. Department of Agriculture, Land Values and Farm Finance, Agricultural Handbook No. 118, Vol. 6 (1957). 3The U.S.D.A. has published quarterly estimates of average contract rates beginning in 1960. 47 F. Hesser in an econometric study“ felt it necessary to estimate average rates of interest on farm mortgage loans in those years for which published data were not available. Detailed procedure of estimation of interest rates for the interim years adOpted by Hesser can be seen in his bulletin. A continuous series of average annual interest rates for the 40 year period was constructed for all lenders as follows. The available published series was used to 1935. The biennial rates after 1940 were used as benchmarks. Interest rates on farm mortgage loans by all lenders for the interim years were calculated by making the change for the interim year proportional to the percentage change in the rates charged on mortgage loans by insurance companies for the same year. This was done because major portions of mortgaged loan amounts were lent by insurance companies. Though these interest rate series are not an ideal series, they still serve our purpose, in View of a paucity of published data. The following table gives the estimated rate of interest from 1917 to 1962. ”Leon F. Hesser, The Market for Farm Mortgage Credit - An Econometric Study, Research Bulletin No. 770 (December, 1963). Purdue University Agricultural Experiment Station, Lafayette, Indiana. Table 2.—-Average interest rates charged on mortgage loans for farmers by all lenders in the U.S., 1917—62 Rate of Rate of Rate of Year Interest Year Interest Year Interest 333 cent Pg; cent Pg; cent 1917 6.22 1932 6.38 1947 4.48 1918 6.31 1933 5.84 1948 4.56 1919 6.36 1934 5.33 1949 4.73 1920 6.40 1935 5.43 1950 4.73 1921 6.95 1936 5.15 1951 4.74 1922 6.67 1937 5.11 1952 4.92 1923 6.33 1938 5.08 1953 4.97 1924 6.34 1939 5.06 1954 5.00 1925 6.29 1940 4.99 1955 4.87 1926 6.26 1941 4.94 1956 4.92 1927 6.22 1942 4.90 1957 5.19 1928 6.23 1943 4.83 1958 5.36 1929 6.30 1944 4.74 1959 5.41 1930 6.36 1945 4.69 1960 5.60 1931 6.38 1946 4.52 1961 5.79 1962 5.72 fi v v—vv— w- Source: Research Bulletin No. 770, Purdue Agr. Expt. Sta., 1963, Lafayette, Indiana and Finance Review, U.S.D.A., 1959, 1961, 1963. Expectancy of Life The most relevant data for our study would be the data on the number of expected remaining years of life of a rural male worker and an urban male worker of 25 years of age from 1917 to 1962. Due to lack of availability of this type of data, we have to resort to '1ife tables' - vital statistics of the United States.5 This source gives the life expectancy at each age, for white and nonwhite and for 5United States Department of Health and Education and Welfare, Vital Statistics of the United States - Life Tables Vol. II, Section 2 (1960), p. 11 both sexes. It does not give the breakdown by rural and urban. In addition to the coverage not being uniform throughout the period 1910 to 1962, this source gives the data only at an interval of ten years. During the period 1900-1902 to 1919-1921, only death registration states were covered. Only in the period 1929-31 to 1962 were all the states covered. For our purpose, we used the expected num— ber of years of remaining life of white male workers in the United States as a whole at ages 25 and 45. Since life tables give the data at an interval of ten years, the dif- ference was distributed evenly over ten years. The results are presented in the following table. The expected number of years of remaining life of a 45 year old worker did not change much from 1917 to 1962. It increased from 25 in the year 1917 to 27 in the year 1962. The expected number of years of remaining life of a 25 year old worker increased from 41 in the year 1917 to 46 in the year 1962. Annual Wage Rate Per Worker Source and Estimation of Annual Wage Farming Wage rate statistics for agriculture in the United States date back to 1866 when the U. S. Department of Agriculture first surveyed average rates paid to hired farm workers. From 1866 to 1908, 19 surveys were made at TABLE 3.—-Expected number of years of remaining life of white male worker at the age of 45 and 25 in the U.S., 1917-62. 45 years 25 years 45 years 25 years Year (n1) (n2) Year n1 n2 Number Number Number Number 1917 25 41 1941 26 44 1918 25 41 1942 26 44 1919 25 41 1943 26 44 1920 26 42 1944 26 44 1921 26 42 1945 26 44 1922 26 42 1946 26 44 1923 25 42 1947 26 45 1924 25 42 1948 26 45 1925 25 42 1949 26 45 1926 25 42 1950 26 45 1927 25 42 1951 26 45 1928 25 42 1952 26 45 1929 25 42 1953 26 45 1930 25 42 1954 26 45 1931 25 42 1955 26 45 1932 25 42 1956 26 45 1933 25 42 1957 27 46 1934 25 42 1958 27 46 1935 25 42 1959 27 46 1936 25 42 1960 27 46 1937 26 43 1961 27 46 1938 26 43 1962 27 46 1939 26 43 1940 26 43 Source: Life Tables - Vital Statistics of the United States, 1960, Vol. Health and Education and Welfare. II, Section 2, p. 11. U.‘ .D. 51 irregular intervals, followed by annual surveys for the period 1909-22. From 1923 to date, wage rate information has been collected quarterly on about January 1, April 1, July 1, and October 1. Wage rate data are collected on a questionnaire, and farmers are asked to report "average rates being paid to hired farm labor in your locality." Wage rates reported by farmers are summarized in the offices of the state agri- cultural statisticians and are forwarded to Washington together with the statistical evaluation of the reported average. State averages are reviewed and adjusted whenever necessary, on the basis of related data, in Washington. For an extended discussion of the construction of the farm wage series, Major Statistical Series6 may be seen. The farm wage rate series is subject to three principal limitations. First, it is a composite of averages reported by farmers for their localities rather than of actual rates paid by the individuals reporting. Second, piece wage rates, which are particularly important in some agricultural areas, are not included. Third, in relation to the probable impor- tance of hired farm employment, certain types of farms are over-represented, and others are under represented in the Series. v— 6U.S. Department of Agriculture, Major\Statistica1 éfizgies of the U.S.D.A. How They are Constructed and Used. V131. 7. Farm Population, Employment and Levels of Living, Ag. Handbook No. 118-(1957). I I \J‘l I‘J Even though farm wage series before 1948 and after 1948 are not strictly comparable, farm wage rate per month without board (without board or room) constructed before 1948 and farm wage rates per week without board or room constructed after 1948, when converted to annual basis are more comparable than any other series. Therefore, the series of farm wage rate per month without board before 1948 is multiplied by 12, and the series of farm wage rate per week without board or room after 1948 is multiplied by 52, to arrive at an annual farm' wage rate throughout the period 1917 to 1962. Annual farm wage rate per hired worker is given in the appendix. Manufacturing, Laundries,,and Retail Trade The Bureau of Labor Statistics publishes each month average weekly hours, average hourly earnings and average weekly earnings relating to production or non-supervisory workers. The hours and earnings data are based upon monthly mail reports provided by cooperating establishments. The coverage of employees in cooperating establishments in manu- facturing is 65 per cent of the total number of employees. The percentage coverages in trade and services are 20 and 18 respectively. The sample design used in the B.L.S. estab— lishment employment and labor turnover statistics programs is that of a modified cut-off sample. In a cut-off design, all establishments in a category are listed in sequence by number of employees. A cut—off point is selected in terms of the number of employees in an establishment, and only 53 establishments above the cut-off point are included in the design. At present, sample selections are made by the co- Operating state agencies at the area level. The state agencies mail the forms to the establish— ments and examine the returns for consistency, accuracy and completeness. The state offices use the information to prepare state and area series and then send the establishment data to the B.L.S. for use in preparing the national series. In general, the establishment reports contain information on (1) the number of all full and part time production workers or nonsupervisory employees who worked during or re— ceived pay for any part of the period reported, (2) total gross payrolls for such workers, (3) total man—hours actually worked by the full or part time workers, necessary for the computation of the hours and earnings averages. Average hourly earnings for manufacturing and non- manufacturing industries are on a 'gross' basis, re- flecting not only changes in basic hourly and incentive wage rates, but also such variable factors as premium pay for overtime and late shift work, and changes in output of workers paid on an incentive plan.7 Averages or hourly earnings differ from wage rates. Earnings are the actual return to the worker for a stated period of time, while rates are the amounts stipulated for a given unit of work or time. The work week information relates to the average hours for which pay was received and is different from standard or 7U. S. Department of Labor, Bureau of Labor Statistics, Employment and Earnings Statistics for the United States, 1909-62, Bulletin No. 1312-1 (19635, p. 626. 5'55 5* schedule hours. Gross average weekly earnings are derived by multiplying average weekly hours by average hourly earnings. Therefore, weekly earnings are affected not only by changes in the length of the work week caused by part time work stoppages for varying causes, labor turnover and absenteeism. The annual wage per worker is derived by multiplying the average weekly earnings by 52. The payroll figures exclude payment in kind, contri- butions to welfare funds and insurance or pension plans, and bonuses, unless earned and paid regularly each pay period. In calculating the annual wage rate, it was assumed that the worker is fully employed throughout 52 weeks. The sources and limitations are applicable to all the annual wage series in manufacturing, laundries, and retail trade. In the following sections, we discuss the backward and forward extrapolation of the data in each occupation. Backward Extrapolation in Laundries and Retail Trade The data on annual earnings of a nonsupervisory worker in ratail trade and in laundries are available only from 1939 and 1934 respectively. Since the present study required data from 1917, a backward extrapolation of the reSpective series was essential. From the graphs drawn (Fig. 1, Fig. 2) it is reasonably clear'tmmt the relationship between the annual earnings of a Figure l.--The relationship between annual wage (in current dollars) per worker in retail trade and annual wage (in current dollars) per worker in construction in the U. S., 1939-51. (1) S 2500 ~ I/ g / H [D .H / m / p 2250 — ’ 3 B c ff «'1 .. ,5 m 'g 2000 _ / o / 3 Q/ t / Q / A 1750 — / U) Q) / 3* / m S / o ,/ U / p 1500 _ o /' c g / g, o/ 3 / C) c: 1250 — lg 3 , o 0) /® 2? x659 3 / H 1000 n 1 1 . . . g 1200 1600 2000 2400 2800 3200 3600 4000 c .g Annual wage (in current dollars) per worker in construction. 56 Figure 2.——The relationship between annual wage (in current dollars) per worker in laundries and annual wage (in current dollars) per worker in construction in the U. 8., 1934-47. 2000 » 3 . / £1 / 3 1800 ~ / 53 / H 0 c / H / (:13 1600 - // ”23' 0/ O 3 // z: 9 / Q 1400 — / A / a e ’ m // H H _ I/ g 1200 g / e / g x L / 9 5:5 / »- / O 1000 I o C: / ~H / V .6 9‘3. 0’ Ct! 800 — G/ 3 C9 H I, CU / 13 E < 600 1 I l 1 I 1200 1500 1800 2100 2400 2700 3000 Annual wage (in current dollars) per worker in construction 57 worker in retail trade and in laundries are linearly re- lated to the annual earnings of a worker in building trades for the periods 1939-51 and 1934-1947 respectively. Hence a straight line of the form Y = a + bX was fitted for both the series. X is the annual wage in building trades. Results 'a' 'o' d.f. 52 Period Retail trade: 44.25 0.6509 11 0.9805 1939-51 (67.2075) (0.0265) Laundries —200.9561 0.7106 12 0.8976 1934-47 (123.6148) (0.0663) The independent variable in annual wage per worker in building trades explains about 98 per cent of the variation in the annual wage in retail trade during the period 1939—51 and 89.8 per cent of the variation in the annual wage in laundries during the period 1934-47. The regression coef— ficient of the time variable is significantly different from zero at the one per cent level in both the regression equa- tions. Annual wage in retail trade and laundries increases by 0.6509 and 0.7106 dollars for a dollar increase in the annual wage in building trades respectively. The extra- polated annual wage per worker in retail trade and in laundries are given in Table 4. Fri.\..1 . \ \JT 00 TABLE 4.-—Estimated annual wage rate (in current dollars) in retail trade and in laundries in the U.S., 1917—38. A_‘ Y" Annual wage in Year Retail trade Laundries Current Current dollars dollars 1938 1129.72 1937 1050.85 1936 964.54 1935 906.67 1934 911.07 1933 911.40 745.66 1932 959.13 797.76 1931 1143.93 999.50 1930 1151.38 1007.63 1929 1091.53 970.68 1928 1123.28 976.96 1927 1123.28 976.96 1926 1091.81 942.60 1925 1015.99 859.83 1924 986.54 827.69 1923 908.15 742.11 1922 859.28 688.76 1921 939.50 776.33 1920 908.15 742.11 1919 661.95 473.35 1918 587.49 392.07 1917 509.64 307.08 Construction The suboccupation considered for this study under construction is "Helpers and Laborers.” Annual wage per worker data in this occupation are not as readily available as they are in some of the other occupations. However, in- fornuition on the union scales and hours prevailing in each CitY' is available through Bureau of Labor Statistics.8 8U.S. Department of Labor, Bureau of Labor Statistics, %Q$231_Wages and Hours: Building Trades, July 1, 1963 and .1EEZSL1907-63. Bull. No. 1397, 1963. 59 Union scales are those agreed on through collective bargain- ing between trade unions and employers and defined as (1) the basic wage (minimum) scale (excluding holiday, vacation, or other benefit payments regularly made or credited to the worker each pay period), and (2) the maximum schedules of hours at straight time rates. Data are obtained by the USDL primarily from local union officials by mail question— naire. In some instances, economists of the Bureau of Labor Statistics visit local union officials to obtain the de— sired information. Average hourly scales as well as working hours are weighted by the number of union members at each rate. The indexes of union hourly wage rates as well as the indexes of union weekly hours for the helpers and laborers with the base period 57—59 are given for the period 1907-63 in bulletin no. 1397 of the Bureau of Labor Statistics. From these indexes, actual union average wage rate and aver— age weekly hours are calculated for the period 1917 to 1962. The average weekly wage per worker in the occupation "Helpers and Laborers" was derived by multiplying the aver- age weekly hours by the average hourly wage rate. The annual wage per worker was estimated by multiplying the average weekly wage by 52. The annual wage derived by the method explained above does not indicate the actual annual wage earned by all the workers. The averages calculated by the Bureau of Labor 60 Statistics are not designed for precise year to year com— parisons because of fluctuations in union membership. The estimated annual average wage per worker who comes under "helpers and laborers," in construction for the period 1917 to 1962 is given in the appendix. Forward Projection of Annual Wage As pointed out in the methodology chapter this study required annual wage data in each occupation from 1963 to 2007. Hence projection of annual wage data was done on the basis of regression lines fitted with annual wage in the concerned occupation as the dependent variable and time as the independent variable. The period considered is 1950-62. The explanation for the choice of the functional form and time period were given in the Methodology Chapter. The following are the regression equations fitted for annual wage data in farming, manufacturing, construction, retail trade and laundries. (See Figures 3, 4, 5, 6, and 7 respectively.) d.f. 82 w: = 1695.99 + 66.00 t 11 0.9689 (24.12) (3.41) 9% = 3121.65 + 156.69 t 11 0.9908 (30.81) (4.36) 05 = 3374.30 + 254.49 t 11 0.9959 (33.31) (4.71) 03 = 2282.70 + 96.05 t 11 0.9981 (8.66) (1.23) WE = 1855.25 + 62.64 t 11 0.9841 (16.22) (2.29) FIGURE 3.—-Trend in annual wage Annual hired wages (in current dollars) per farm worker 2500 2400 2300 2200 2100 2000 1900 1800 1700 1600 (in current dollars) per farm worker in the U.S., 1950-62. ,6 6 _ / 91’ / / e / " / / / / _ //® 6 l / / / o / 1 / <3 0 /’ /0 1 (9 / / / / / / / .1 § 1 1 1 I J l i L l 4 1 O H (\3 (V) :1' L0 \O [\ (X3 0\ O H (\1 m Ln L0 L0 L0 LO LO LO L0 Ln \0 \O C ON 0\ O\ O\ O\ O'\ C\ O\ O\ C“. 0\ O\ O\ H #1 H H H H «H H H .H H H .4 Year Annual wage (in current dollars) per worker in manufacturing 4200 4100, 4000 3900 3800 3700 3600 3500 62 Year “t3 4.-—Trend in annual wage (in current dollars) per worker in manufacturing in the U.S., 1950—b2. / / / / A) - / C) / ” / p _ / 1 / 0 __ 0 / / 1— G/ / 4»— I 9/ / _. / / _ / o /o / / / / r / / _ <9/ / 1’ / / (9’ r 1 1 1 1 1 1 1 1 1 1 1 O H (\l m :1” Ln \0 [\ CD 0\ O H (\1 L0 L0 Ln L0 LO LO LO LO LO LO \0 \O \O O\ O\ O\ O\ O\ O\ O\ O\ O\ O\ O\ O\ O\ H H r-i H H H H t—i r—1 r—i H :—-l r—1 100 Annual wage (in current dollars) in construct .3500 worker in construction in the U.S., 6500 6300 _ 6100 _ 5900 e 5700 _ 5500 _ 5300 _ 5100 .— 14900_ U”700 _ 14500- 4300L 4100_ :BSQCDO 13'7CDO _ 330o? 0 Ln O\ r--{ 1951 _ 1952 _ 1953 _' 63 FIGURE 5.—-Trend in annual wage (in current dollars) per 1954 _ 1955 _ Year 1956 L - 1957 1950-62. ~ 1958 — 1959 F. 1960 P"- 1961 .54?!" 1962 64 FIGURE 6.--Trend in annual wage (in current dollars) per worker in retail trade in the U.S., 1950-62. 3450 ll 3... ,8 3300 3200 3100 3000 / 2900”. 2800 ’ per worker in retail trade ‘\ 2700m I 2600.. l 2500- , 2400 o’ T \ 2300- Annual wage (in current dollars) _ 2200 W 1951 . 1952 . 1953 - 1954 F 31955 .. . $1956 . 1957.. 1958. 1959 - 1960 . 1961 - 196:»— 65 nv/ 1 / / O./ l / /0 1.. / /o / / / /0 A / //o 1 / / / my 1 / / /AU 1 / / 0./ 1 / / nu / 1 / / / 1 nu / / . p _ _ _ . _ p // 1 mVIll O O O O O O O O O O O O O O O O O O O O n! ,6 5, .4 3o «2 11 no 0, RV A2 21 Q. 9. 9. 22 52 n2 11 .1 mofipocsmq CH poxpoz pom AmpmHHom pcohpzo :Hv ommz Hmscc¢ mmmH HmmH ommH mmmH wmmH ummH \0 Ln O\ 1—1 Year mmmH :mmH mmmH mmmH HmmH ommH 1950-62. 9 Fl: CRIJPIE3 7.--Trend in annual wage (in current dollars) per worker in laundries in the U. S. 6* 2 annual wage per worker in farming 3 annual wage per worker in manufacturing . 51: ’1‘. VS = annual wage per worker in construction 0: = annual wage per worker in retail trade W% = annual wage per worker in laundries t = time variable The constant and the regression coefficient in the :regression equation in each occupation are significantly (different from zero even at the one per cent level. The t:ime variable explains about 98 per cent of the variation .iIi annual wage per worker in each occupation during the guerriod 1950—62. The annual wage rate per worker increases Ifrnom 1950 by an average of 66 dollars per year in farming; ZlESES.7 dollars per year in manufacturing; 254.49 dollars {3631? year in construction; 96.05 dollars per year in retail t:I?51de; and 62.64 dollars per year in laundries. Table 2 1rd Appendix A gives projected annual wages per worker in SfEirnning; in manufacturing, in construction, in retail ‘tl?Eude, and in laundries from 1963 to 2007. Source and Estimation of Unemployment Rate Unemployment rates9 in the concerned nonfarm occupa- tliCDrls are only available from 1948. As pointed out in the WRETSYIOdology Chapter, data on unemployment rates were \ 9U. S. Department of Labor, Bureau of Labor Statistics, %%§%E%§31_Force Employment and Unemployment Statistics, 1947-61 9 2), Table 16. . F7 J reqlired for each occupation from 1917 to 1962. Hence, backward projection of the unemployment rate to 1917 in each nonfarm occupation was done on the basis of fitted regres- sion equations. The dependent variable is the unemployment rate in the concerned nonfarm occupation, and the indepen- dent variable is the unemployment as a percentage of nonfarm enmloyees. The explanation for the method and the time 13eriod used in fitting these regression equations was given ir1 the Methodology Chapter. The following table presents the unemployment rates gxiven by Lebergott for the period 1917 to 1960. (PIXBIE 5.--Unemp1oyment as a percentage of nonfarm employees in the U. 8., 1917-60. Unemployment Unemployment Unemployment Year rate Year rate Year rate per cent per cent per cent 169:17 8.2 1932 36-3 1947 5.4 3159iL8 2.4 1933 37.6 1948 5-1 119:19 2.4 1934 32.6 1949 8.0 4159220 8.6 1935 30.2 1950 7.1 .159231 19.5 1936 25.4 1951 4.4 159232 11.4 1937 21.3 1952 4.0 1923 4.1 1938 27.9 1953 3.8 -15922L1 8.3 1939 25.2 1954 7.1 1925 5.4 1940 21.3 1955 5.7 1926 2.9 1941 14.4 1956 5.4 14922'7 5.u 1942 6.8 1957 5.6 1928 5,9 1943 2.7 1958 8.7 11592259 5.3 1944 1.7 1959 7.0 1930 14.2 1945 2.7 1960 7.1 1931 25.2 1946 2.7 :\ QOuPoe: Stanley Lebergott, Manpower in Economic Growth; the American Record Since 1800 (New York: McGraw- Hill, 1964), Appendix. ( I (T? The following are the regression equations fitted for unemployment rate data in manufacturing, retail trade and laundries. and 11.) = -2.2653 + 1.2057 U N p E M (0.5325) (0.0851) ' ' ' = -o.5727 + 1.6575 U C (0.8389) (0.1341) N'F'E' u = 0.2994 + 0.7381 U N.p E. T (0.3117) (0.0498) 0.6936 + 0.5074 U N.F.E. L (0.3961) (0.0633) is the unemployment rate in is the unemployment rate in is the unemployment rate in is the unemployment rate in is the unemployment as employees construction, (Also see Figures 8, 9, 10, d.f. E2 11 0.9433 11 0.9267 11 0.9479 11 0.8404 manufacturing construction retail trade laundries a percentage of nonfarm The regression coefficient of the independent variable iri each occupation is significantly different from zero eVen at the one per cent level. A one per cent increase in ‘tlfiee unemployment as a percentage of nonfarm employees is aSisociated with an increase in the unemployment rate of 1-.22057 in manufacturing; 1.6575 per cent in construction; C)-'738l per cent in retail trade and of 0.5074 per cent in 3— aundries . 10.0 / G) / 9.0~ // / I, 8.0— // g / 6 3 / .5 7.0- / .53 l g / Z ' / :2 I 0 £3 / g / O / 1. ’0‘” g / c... ’0 o @l <11 / 1.0 3.0_ / C“ G) e / C <4 ¢ C) 5 / m 2 0— / / / 1.0 1 1 1 I 1 1 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 Unemployment as a Percentage of Non Farm Employees F‘i ‘t égllre 8.—-The relationship between unemployment in manufac- Lll‘ilig and unemployment as a percentage of nonfarm employees U. 8., 1948-60. 14.0 L / ,o l / 13.0- /’ / I I 0 / 12.0* C) 5 / 0 -1-1 / ‘5 / 3 I L I J.) a 11.0 / 8 [/0 S I C) / g 10.0- / 9 O ’ 2 / 2 / e 9’ 8 9.0- ,’ é / c... / o a, 9 :2" 8.0— ’ p / S /o g) / >1 / 5: 2 .1 (01“ / / / 0.0t GD/ 9 / ’CD / / 5.0 l 11 1,___ 1 1 1 1 _ 4.0 5.0 6.0 7.0 8.0 9.0 10.0 Unemployment as a Percentage of NonFarm Employees Figure 9.-—The relationship between unemployment rate in construction and unemployment as a percentage of nonfarm employees in the U. 8., 1948—60. 7.0 1 / l )6) / 605- I / / / 6 0- o / / w/ o / o 2 / U 5.5 § /’ C) E. / 49 5.0~ / é / 0 ,’ Fé L1 5 a, g / o o/o 0 lo go 4.0.. / E ,’ 9 94 3.5.. / / / / /<9 3 0- /© / / I 2.5 l 1 1 1 1 1 4.0 5.0 6.0 7.0 8.0 9.0 10.0 Unemployment as a Percentage of Non Farm Employees Figure 10.--The relationship between unemployment rate in trade and unemployment as a percentage of nonfarm employees in the U. 8., 1948-60. 6.0 5.5 ' I 8 / 'Ei / .0 - I m / H / / .5 / <3 13 4.5- / g l s W .9 x g / 0 a 4.0- / C) 8 / :3 o / “a / (D 3.5~ 69 / 51? lo 9 / C. 8 / 0 0 w/ .0- a. 3 / / / /’° 2.5~ /' / C) / 2.0 I 1 J 1 1 1 4.0 5.0 6.0 7.0 8.0 9.0 10.0 Unemployment as a percentage of nonfarm employees Figure 11.——The relationship between the unemployment rate in laundries and unemployment as a percentage of nonfarm employees in the U. 8., 1848-60. 73 The percentages of unemployment (estimated for the period 1917 to 1947 and actual for the period 1948- 1962) in manufacturing, construction, retail trade and in laundries are given in Table 3 in Appendix A. CHAPTER IV UNEMPLOYMENT RATE EXPECTATIONS The procedure for estimating expected unemployment rates in the next n years ahead was discussed in the chapter on "Methodology." However, a brief explanation is given in this chapter. Introduction In this study it was assumed that the expected future unemployment rates in each nonfarm occupation are a linear function of current and past unemployment rates. An indirect method was used for estimating expected unemployment rates in the lst, 2nd. . .(n2-l)th year ahead. The number n is the expected remaining number of 2 years of life of a 25 year old worker. The general formula is as follows. The following regression equation gives an estimate of an average unemployment rate in the next n years ahead. n n n k Un=00+ij- BiUt_i+e...1 1—o th e is the random error in the n equation I1 U = l 2 U = an average unemployment rate in the n 2:1 t+£ next n years ahead. 7“ ‘3 U7 n=l,2,3. . .9. After estimating these n regression equations, an estimate of the expected unemployment rate in any jth year ahead was derived as follows. 0.='A.-°-1A.. t+j JUJ (J ) U(J-1) The assumption in the above formula is that an estimate of the average unemployment rate in the next n years ahead is the average of the estimates of unemployment rate for the individual years up to the nth year ahead. This procedure was designed to ensure that the average of all the estimates of the expected unemployment rate up to the nfig year ahead from the current year is equal to the estimate of the average of all the expected unemployment rates in the n years ahead from the current year. Discussion of Results In this section, empirical results for all the non— farm occupations considered are discussed. For each non— farm occupation, the following decisions were made. On the basis of R2, n was determined as 9 because, beyond n=9, the regression equation explains less than 18 per cent of the variance in the expected average unemployment rate. In all the regression equations, k was determined as 1, because the regression coefficients of U where k:2 t—k were not significantly different from zero even at the 10 76 per cent level. Hence, all the regression equations were fitted only with the two independent variables U U t’ t-l' The fitted regression equations for estimating the average unemployment rate in the next n years ahead (n=1, 2,. . .9) for each nonfarm occupation are given in the following pages. The constants for the regression equations for laundries, retail trade were significantly different from zero even at the one per cent level. The regression coefficients of the current year unemployment rate in all the regression equations in each nonfarm occupation con- sidered were significantly different from zero at the one per cent level. The regression coefficient of the past year unemployment rate is significantly different from zero at the five per cent level in the first four regression equations in manufacturing, construction, trade and in the first five regression equations in trade and at the ten per cent level in the rest of the regression equations in all the nonfarm occupations considered. The percentage of variation of the dependent variable explained by the independent variables in each nonfarm occupation decreases from about 82 per cent in the first regression equation to about 18 per cent in the ninth regression equation. 77 The following are the estimated regression equations used to derive an estimate of the average unemployment rate in the n years ahead (n=l,2,. - .9) Manufacturing d.f. 82 01 = 1.8067 + 1.2387 0t — 0.3953 Ut—l 43 0.8139 (1.0814) (0.1374) (0.1373) 02 = 2.9756 + 1.1636 Ut - 0.4168 Ut_l 42 0.6959 (1.3708) (0.1723) (0.1724) 03 = 4.0846 + 1.0931 0t — 0.4358 Ut_l 41 0.5974 (1-5577) (0.1934) (0.1935) 04 = 5.1019 + 1.0041 Ut — 0.4284 Ut_l 40 0.5022 (1.7024) (0.2100) (0.2098) 05 = 6.1686 + 0.9173 Ut - 0.4180 Ut_l 39 0.4182 (1.8121) (0.2219) (0.2224) 06 = 7.0065 + 0.8498 Ut - 0.4194 Ut_l 38 0.3472 (1.9025) (0.2292) (0.2300) 07 = 7.8562 + 0.8061 Ut - 0.4441 Ut_l 37 0.2899 (1.9672) (0.2330) (0.2340) ‘08 = 8.7284 + 0.7535 Ut — 0.4587 Ut_l 36 0.2341 (2.0182) (0.2358) (0.2363) 119 = 9.7495 + 0.7020 Ut — 0.4768 Ut_l 35 0.1868 (2.0562) (0.2363) (0.2381) 78 The following are the estimated regression equations used to derive an estimate of the average unemployment rate in the n years ahead (n=l,2,. . .9) Construction d.f. E2 01 = 2.9289 + 1.2559 Ut — 0.4132 Ut_l 43 0.8195 (1.5855) (0.1359) (0.1358) 02 = 4.7850 + 1.1764 0t — 0.4306 0t_l 42 0.6986 (2.0292) (0.1724) (0.1724) 03 = 6.5400 + 1.1037 Ut - 0.4473 Ut_l 41 0.5997 (2.3056) (0.1939) (0.1939) 0“ = 8.1859 + 1.0136 Ut - 0.4393 Ut-l 40 0.5052 (2.5189) (0.2099) (0.2098) 05 = 9.7687 + 0.9168 Ut - 0.4179 Ut-l 39 0.4178 (2.6903) (0.2220) (0.2224) 06 = 11.0956 + 0.8496 0t — 0.4194 Ut_l 38 0.3473 (2.8211) (0.2293) (0.2301) ‘07 = 12.4026 + 0.8057 Ut - 0.4428 Ut_1 37 0.2901 (2.9135) (0.2332) (0.2339) ‘08 = 13.7988 + 0.7552 Ut — 0.4600 Ut_l 36 0.2358 (2.9844) (0.2355) (0.2360) 1J9 = 15.3474 + 0.7007 Ut - 0.4745 Ut_l 35 0.1870 (3-0427) (0.2361) (0.2379) 79 The following are the estimated regression equations used to derive an estimate of the average unemployment rate in the n years ahead (n=l,2,. . .9) Laundries .f. E2 01 1.0349 + 1.2699 Ut - 0.4292 Ut_l 43 .8210 (0.5269) (0.1351) (0.1346) 02 1.7025 + 1.1991 Ut - 0.4575 Ut-l 42 .7016 (0.6738) (0.1712) (0.1709) 03 2.3172 + 1.1318 Ut — 0.4807 Ut_l 41 .6041 (0.7652) (0.1923) (0.1920) 64 2.9055 + 1.0452 Ut - 0.4775 Ut_l 40 .5113 (0.8352) (0.2078) (0.2074) 05 3.4650 + 0.9501 Ut - 0.4589 Ut_l 39 .4245 (0.8926) (0.2197) (0.2198) 06 3.9325 + 0.8801 Ut — 0.4580 Ut_l 38 .3534 (0.9370) (0.2270) (0.2274) 67 4.3900 + 0.8301 Ut — 0.4750 Ut_l 37 .2954 (0.9674) (0.2311) (0 2311) 68 4.8852 + 0.7740 Ut - 0.4865 Ut_l 36 .2414 (0-9893) (0-2331) (0-2330) 09 5.4333 + 0.7219 Ut — 0.5038 Ut_l 35 .1961 (1.0062) (0.2332) (0.2346) 80 The following are the estimated regression equations used to derive an estimate of the average unemployment rate in the n years ahead (n=l,2,. . .9) Retail Trade 1.1; 82 01 = 1.4013 + 1.2507 Ut — 0.4085 Ut_l 43 0.8178 (0.7370) (0.1360) (0.1360) 02 = 2.2909 + 1.1749 Ut — 0.4300 Ut_l 42 0.6981 (0.9391) (0.1723) (0.1723) 03 = 3.1147 + 1.1020 Ut - 0.4463 Ut_1 41 0.5988 (1.0672 (0.1938) (0.1939) 84 = 3.8895 + 1.0138 Ut - 0.4404 Ut_l 40 0.5047 (1.1649) (0 2098) (0.2096) 05 = 4.6092 + 0.9192 Ut - 0.4220 Ut_l 39 0.4174 (1.2442) (0.2221) (0.2227) 06 = 5.2678 + 0.8505 Ut - 0.4217 Ut_l 38 0.3462 (1.3058) (0.2295) (0.2304) 07 = 5.8940 + 0.8062 Ut - 0.4452 Ut_l 37 0.2890 (1-3489) (0-2333) (0-2342) 168 = 6.5469 + 0.7541 Ut - 0.4606 Ut_l 36 0.2339 (1-3821) (0-2357) (0-2363) 139 = 7.2868 + 0.7002 Ut — 0.4763 Ut_1 35 0.1856 (1.4086) (0.2364) (0.2383) 81 The increase in the expected average unemployment rate associated with a one per cent increase in the current year unemployment rate decreases from 1.2387 per cent in the next year to 0.7020 in the next nine years, in manu- facturing; from 1.2559 per cent in the next year to 0.7007 per cent in the next nine years in construction; 1.2699 in the next year to 0.7219 in the next nine years in laundries; :from 1.2507 per cent to 0.7002 per cent in the next nine years in retail trade. The decrease in the expected average unemployment Irate due to a one per cent increase in the past year unem- L>loyment rate increases from 0.3953 per cent in the next ywear to 0.4768 per cent in the next nine years in manu- fflacturing; from 0.4132 per cent in the next year to 0.4745 puer cent in the next nine years in construction; from C).4292 per cent in the next year to 0.5038 per cent in tlie next nine years in laundries; from 0.4085 per cent in tflue next year to 0.4763 per cent in the next nine years iri retail trade. The expected unemployment rate in each nonfarm cxzcupation considered in any nth year ahead up to the 9th YeEU? ahead and also in the 10th year ahead from each current year during the period 1917-62 are given in the appendix. The unemployment rate from the 10th year ahead was estimated as the expected average unemployment rate A in the Iiext nine years (Ut+n = 09 for all n110)- However, 82 the expected unemployment rate from the 10th year ahead onwards from the current year 1962, was taken as the average unemployment rate in the last 15 years (1948—62). A brief explanation of the expected unemployment rates in the years ahead from four current years, 1917, 1933, 1944, 1962 in each occupation is presented here. (For (data, see next page.) These four current years are selected 1:0 represent end years of the time period (1917-62) con- sxidered in this study and the years of the highest (year 1&933) and the lowest (year 1944) current unemployment rwecorded in the data. The percentage of unemployment in manufacturing ffluctuates from the lowest figure 0 in 1944 to the highest 433.10 in 1933; it fluctuates from 2.30 to 61.20 in con- stzruction, from 1.60 to 19.80 in laundries, and from 1.60 tca 28.10 in retail trade. The fluctuations in unemploy- Inerit rate in manufacturing and in construction are higher truan those in laundries and retail trade. The expected unennployment rates for the next year, 5th year ahead, and the: 9th year ahead from the current year 1944 (year lowest unenualoyment recorded) are higher than the unemployment rateezrecorded in 1944. The expected unemployment rates in the next year, 5th year ahead, and the 9th year ahead, from the current year 1933 (year of highest unemployment recorded) are lower than the unemployment rate recorded in l933- Tflaese two statements are true in each nonfarm 83 TABLE 6.--Current and expected unemployment rate in the future years in various occupations, U. 8., selected years. Percentage of unemployment in the 10th year Current Next 5th year 9th year ahead and Year year year ahead ahead onwards Per Cent Per Cent Per Cent Per Cent Per Cent Manufacturing 1917 7.60 7.78 11.49 14.72 10.94 1933a 43.10 38.79 19.39 4.63 20.22 1944b 0.00 1.41 10.06 17.30 9.27 1962 5.80 5.95 10.84 14.82 5.29c Construction il9l7 13.00 13.26 18.17 22.62 17.58 :L933a 61.20 55.92 29.02 8.90 30.37 Il944b 2.30 4.21 16.02 26.04 15.11 3.962 12.00 12.17 17.77 22.59 9.97c Laundries 21917 4.90 4.98 6.46 7.91 6.30 Il933a 19.80 17.98 9.64 3.59 10.10 :1944b 1.60 ' 2.17 5.81 8.96 5.53 :1962 4.30 4.39 6.27 7.98 3.89c Retail Trade 21917 6.40 6.55 8.51 10.71 8.43 16933a 28.10 25.48 13.24 4.45 14.05 19LHH) 1.60 2.46 7.55 12.25 7.31 21962 6.30 6.34 8.39 10.57 5.05c ii Year of highest unemployment rate recorded in data. 13 Year of lowest unemployment rate recorded in data. C: Average unemployment rate during the period 1948—62. Source: These figures are taken from the Appendix. 84 occupation considered. Extending these two statements, two generalizations with some exceptions can be made for all the nonfarm occupations considered. The expected unemployment rate in any year in the future (up to 9th year ahead) is lower than the current unemployment rate when the current unemployment rate is high. The expected unemployment rate in any year in the future (up to 9th ;year ahead) is higher than the current year unemployment :rate when the current unemployment rate is low. CHAPTER V ANNUAL WAGE EXPECTATIONS IN VARIOUS OCCUPATIONS The general procedure for estimating the expected annual wage in the remaining years of life of a 45 year old and a 25 year old worker in both the farm and nonfarm sectors that applies to all the occupations was discussed in the chapter on "Methodology." However, a brief outline of the method adopted is given in this chapter. Introduction Firstly, the following regression equations were fitted to annual wage data: “ _ “n “n “n “n Wn — 60 + BOWt + Blwt—l’ . . . + Bkwt-k INhere n=1, 2, . . . , 9 and 8? represents the coefficient of‘the annual wage with lag i (i=0,1, . . .,k) in the equation fitted for estimating the average annual wage in A ‘the next n years ahead. From these fitted equations, Wt+J estinmted expected annual wage in the nth year ahead, is derived. Two other regression equations ‘ _ ‘26 ‘26 “26 W26 — 60 + 80 wt, . . . + 8k wt-k ‘ _ “44 “44 ‘44 W44 - 60 + Bo wt, . . . + Bk wt-k 85 86 are also fitted to give an estimate of the average annual wage in the next 26 years ahead and 44 years ahead. From these two and other previous equations, the following two equations are derived. * *26-9 *26-9 026-9 W = 6 + 8 . . . + 8 26—9 0 o wt_l’ k wt_k where W26“9 is the estimate of the average annual wage from the ninth to the 26th year ahead. Similarly “ _ “44—26 “44—26 ‘44-26 w44-26 — 6o + 80 wt + Bo wt—l’ “44-26 + Bk wt-k where 844-26 gives an estimate of the average annual wage in the period from the 26th year to the 44th year ahead. A A A ZFrom the regression equations for W26_9, w44-26’ Wt+9 and A W' two average annual wage increments (Al and A2) are t+26’ cierived as follows: A A A _ 2 Al - I7 [W26—9 - w .0 t-l-9:l A _ l ‘ ‘ A1 ' 9 [W44—26 ‘ wt+26J A A A ' A l is added to W 17 times to arrive at wt+26' A2 is t+9’ added to W 6 18 times to arrive at Qt+44’ which gives t+2 an estimate of the expected annual wage in the 44th year ahead. Thus, W for all i=0,1,2,. . .(n2-1) are de— t+i rived fku'each year from 1917 to 1962 in each of the five 87 occupations. The number n2 is the expected number of years of remaining life of a 25 year old worker. Discussion of Results In this section, empirical results for all the oc— cupations considered are discussed. For each occupation the following decisions were made. In all the regression equations for each occupation, R was determined as 1, because the regression coefficients of W where k l 2 were not significantly different from t—k zero, even at the ten per cent level. Hence, all the regression equations were fitted only with the two indev pendent variables, Wt and wt—l' The number n was deter— Inined as nine even though R2 in the (n+1)th regression equation where n>9 is as high as .80. This was done for ‘two reasons; firstly, to make this procedure consistent tvith the procedure adopted in the case of unemployment rate eexpectations; secondly, to reduce the computations. The fitted regression equations to estimate the aver- éage annual wage rate in the next n years ahead (n=l,2, . . .9) :for each occupation (farming, manufacturing, construction, laundries, retail trade) are given in the following pages. The constant in all the first nine regression equations is not significantly different from zero even at the tens per cent level in all the occupations. But it is Significantly different from zero even at the one per cent 88 in the regression equations estimating the average annual wage in the next 26 and 44 years. The regression coefficient of the current year annual wage is significantly different from zero even at the one per cent level in all the regression equations except the one for estimating the average annual wage in the next 44 years. This is true in each occupation. The regression coefficient of the past year annual vvage is significantly different from zero at the one per (zent level only in the first three regression equations in :farming; in the first regression equation in manufacturing; eat the one per cent level in the first regression equation, sand at the five per cent level in the second regression eequation in construction; at the five per cent level in the thirst regression equation in laundries; at the one per cent lxevel in the first regression equation, and at the five per (ment level in the second, third, fourth and fifth regression exquation in retail trade. All the regression equations in each occupation except true one for estimating average annual wage in the next 44 yeuars in farming explain over 80 per cent of the variation ill'the dependent variable. The regression equation for estimating the average annual wage in the next 44 years in the farming occupation explains about 78.5 per cent of the variation in the dependent variable. 89 The increase in the expected average annual wage in the future years, due to a one dollar increase in the current year annual wage, increases from 1.4857 dollars in the next year to 2.2878 dollars in the next nine years ahead in farming; from 1.3478 dollars in the next year to 1.7078 dollars in the next nine years in manufacturing; from 1.4589 dollars in the next year to 1.9438 dollars in the next nine years in construction; from 1.3465 dollars in the next year to 1.6380 dollars in the next nine years in laundries; from 1.4271 dollars in the next year to 1.9523 dollars in the next nine years in retail trade. The decrease in the expected average annual wage due to a one dollar increase in the past year annual wage increases from 0.4761 dollars in the next year to 1.2412 dollars in the next nine years in farming; from 0.3213 dollars in the next year to 0.4831 in the next nine years in manufacturing; from 0.4325 dollars in the next year to 0.6324 dollars in the next nine years in construction; :from 0.3436 dollars in the next year to 0.6190 dollars in ‘the next nine years in laundries; from 0.4133 dollars in the next year to 0.7997 dollars in the next nine years in retail trade. Expected annual wages in any nth year ahead (up to n=9) and the expected first and second increment in the annua1.wage from each current year during the period 1917- 62:h1 each occupation are given in the Appendix. However, 90 Farming The following are the estimated regression equations to derive an estimate of the average annual wage in the d. n years ahead (n=l,2, . . .9) 01 = 14.1347 + 1.4857 Wt — 0.4761 wt_l (19.1412) (0.13561) (0.1407) 82 = 23.6702 + 1.6024 wt — 0.5853 wt_l (26.1966) (0.1850) (0.1928) w3 = 30.8440 + 1.6887 wt - 0.6594 wt__l (33.2712) (0.2312) (0.2416) 0, = 35.8971 + 1.7739 wt ; 0.7291 wt_l (40.1684) (0.2740) (0.2863) 85 = 43.7789 + 1.8583 wt - 0.8030 wt_l (47.1397) (0.3157) (0.3309) 86 = 52.5094 + 1.9471 wt — 0.8807 wt_l (54.6230) (0.3583) (0.3758) 07 = 66.8818 + 2.0357 wt - 0.9539 wt_l (62.6687) (0.4023) (0.4228) 08 = 88.3503 + 2.1452 wt - 1.0801 48—1 (71.3010) (0.4495) (0.4765) W9 = 116.6466 + 2 2878 wt — 1.2412 wt_l (81.3444) (0.5078) (0.5478) 601.1184 + 2.13215 Wt - 1.05668 wt-l (79.6285) (0.6728) (0.6841) 2) ll 44 1213.3940 + 1.86532 Wt - 0.76793 wt-l (113.2449) (0.8294) 1(0.8575) 43 42 41 40 39 38 37 36 35 63 45 f. 5UI .9902 .9813 -9699 .9564 .9403 .9203 .8956 .8664 .8318 .92432 .7852 91 Manufacturing The following are the estimated regression equations used to derive an estimate of the average annual wage in the n years ahead (n=l,2, 1 (37.3683) (0.1451) (47-5911) (0-1893) W = 41.6270 + 1.3912 W (58.7884) (0.2303) t w“ = 33.4594 + 1.4250 w (68.4557) (0.2631) t (78.3267) (0.2960) W6 = 27.8930 + 1.4876 Wt — 0.3511 W (89.0997) (0.3261) (101.3050)(0.3574) W8 = 0.1016 + 1.6312 W (114.2754)(0.3914) t \O (131.3263)(0.4397) A W26 = 1069.4624 + 2.0384 — 0.8816 wt_ (130.6944) (0.6635) 0 = 4.8116 + 1.3478 wt - 0.3213 wt_ W = 33.0029 + 1.3925 Wt - 0.3562 Wt_ W = 36.8249 + 1.4558 Wt — 0.3502 Wt_ w = 10.0147 + 1.7078 wt - 0.4831 wt_ .9). w = 16.5045 + 1.5296 wt - 0.3593 Wt_l 1 (0.1512) 1 (0.1972) — 0.3354 wt_l (0.2415) — 0.3399 48.1 (0.2747) 1 (0.3114) t—l (0.3444) (0.3789) — 0.4247 48—1 (0.4128) 1 (0.4714) 1 (0.6764) 0,, = 2037.5675 + 1.5903 wt - 0.2181 w (207.8165) (0.8760) (0-9089) 43 42 41 40 39 38 37 36 35 63 45 WI .9912 .9842 .9760 .9677 .9583 .9472 .9336 .9174 .8957 .9574 .8642 92 Construction The following are the estimated regression equations used to derive an estimate of the average annual wage in the next n years ahead (n=l,2, . . .9). d.f. 82 01 = 9.0837 + 1.4589 wt - 0.4325 wt_l 43 0.9953 (31.5310)(0.1405) (0.1490) 42 = 4.8787 + 1.4998 wt - 0.4447 wt_l 42 0.9906 (44.5387)(0.1923) (0.2042) w3 = —1.0518 + 1.5473 wt — 0.4624 wt_l 41 0.9849 (56.6682) (0.2363) (0.2517) 0, = -15.1982 + 1.6183 wt — 0.4991 wt_1 40 0.9780 (68.6042) (0.2766) (0.2942) 85 = -26.3325 + 1.6868 wt — 0.5357 wt_l 39 0.9693 (81.6169) (0.3162) (0.3373) w6 = —46.2414 + 1.7646 wt - 0.5763 wt_l 38 0.9588 (95-6797) (0-3550) (0.3792) w7 = —69.4649 + 1.8401 wt - 0.6109 wt_l 37 0.9452 (111.5680) (0.3962) (0.4229) 08 = -83.5469 + 1.8991 wt - 0.6332 wt_l 36 0.9279 (130.5273) (0.4408) (0.4733) 09 = —108.1538 + 1.9438 wt — 0.6324 wt_l 35 0.9067 (153-2137) (0-4879) (0-5290) w26 = 1284.79016 + 3.92312 wt — 2.74090 wt-163 0.9615 (177.9759) (0.9567) (0.9808) W44 = 2441.2619-+2.32940 wt—-0.69526 wt_l 45 0.8644 (301.9383) (1.4004) (1.4719) 93 Laundries The following are the estimated regression equations used to derive an estimate of the average annual wage in the next n years ahead (n=l,2,3, . . .9). d.f. wl = 30.7954 + 1.3465 wt - 0.3436 wt_l ”3 (22.4460) (0.1430) (0.1458) 82 = 51.9897 + 1.3660 wt - 03603 wt_l 42 (29.9190) (0.1868) (0.1907) 83 = 70.7593 + 1.4177 wt - 0.4083 wt__l 41 (36.5246) (0.2232) (0.2276) w” = 92.0853 + 1.4676 wt - 0.4577 wt_l 40 (43.2329) (0.2585) (0.2639) 45 = 106.4602 + 1.5078 wt - 0.4915 wt_l 39 (50.2942) (0-2941) (0-2995) 86 = 123.4582 + 1.5503 wt — 0.5315 wt_l 38 (57.1658) (0.3267) (0.3331) 87 = 139.8237 + 1.5824 wt - 0.5595 wt_l 37 (64.6691) (0.3607) (0.3671) 88 = 161.9980 + 1.6141 wt - 0.5939 wt_l 36 (72.2606) 0.3940) (0.4025) w9 = 183.2212 + 1.6380 wt-0.6190 wt_l 35 (80.5335) (0.4283) (0.4402) 426 = 571.71970 + 1.05970 wt + 0.03757 wt_l 63 (58.1184) (0.47039) (0.47482) A ”44 = 1040.8409 + 0.87423 wt + 0.31332 wt_l 45 (85.8099) (0.5654) (0.5749) .9594 .9450 .9288 .9091 .8862 .8596 .96435 .90232 94 Retail Trade The following are the estimated regression equations used to derive an estimate of the average annual wage in the next n years ahead (n=l,2,3, 4682 + 1. 5160) (0. 4019 + 1. .8875) (O. 8592 + 1. 0192) (O. .8875 + 1. 0110) (O. 6231 + 1. 6272) (0. 4260 + 1. 6676) (O. 4136 + 1. 6330) (0. 5836 + 1. «0379) (0. 8471 + 1. 1410) (0. W26 = 687.5397 + (85.6793) ( 41 = 17. (21. w2 = 29. (29 W3 = 39. (37. W4 - 47 (45. WS = 51. (53. W6 = 520 (62. W7 = 55. (72- w8 = 58. (84 W9 = 59. (97. w44 = (133-3482) 4271 wt - 0.4133 wt_l 13952) (0.1444) 4950 wt — 0.4701 wt_l 1878) (0.1948) 5891 wt - 0.5527 wt_l 2295) (0.2388) 6745 wt - 0.6238 wt_l 2711) (0.2827) 7412 wt - 0.6727 wt_l 3130) (0.3272) 8093 wt — 0.7204 wt_l 3533) (0.3698) 8772 wt - 0.7691 wt_l 3945) (0.4142) 9243 wt — 0.7955 wt-l 4381) (0.4620) 9523'Wt - 0 7997 Wt_l 4834) (0.5133) 2.0368 wt — 0.9288 wt_ 0.7052) (0.7170) (0.9317) .9). 1301.1088 + 1.5008 Wt - 0.1832 W (0.9022) 1 t—1 43 42 41 40 39 38 37 36 35 WI -9938 .9881 .9815 .9728 .9620 .9490 .9331 .9132 .8892 .9597 .8797 95 the expected annual wages in the years ahead and the ex- pected increments in the annual wages from four current years 1917, 1933, 1944, 1962 are given on the next page. These four years are selected to represent the starting year of the time period, depression year, year in the Second World War and the end year of the time period. Broadly speaking, the expected annual wage in any nth year ahead (n=l,2, . . .9) from any current year during the period 1917—62 is higher than the current year annual wage. This is true in each occupation considered in this study. Another generalization with an exception can be made in regard to the expected average increments in the annual wage. The expected increment in the annual wage from the tenth year to the (nl-l)th year ahead, decreases in all the occupations except in farming and laundries as the current year annual wage increases. The expected increment in the annual wage from the nlth to the (n2-l)th year ahead increases in all the occupations except in farming and laundries as the current year annual wage increases. In farming and in laundries the relationships are reversed. 00.000 55.50 1 050.03 00m.0 035.0 053.0 N003 05.0mm 00.303 ~00.m 503.m 0m0.m 000.3 3303 m3.00m 30.003 300.3 m00.3 03m.3 mmm.3 mm03 00.5m 30.m0m 5mm N00 355 035 5303 COHuoShmeOO mm.3m3 00.5m 053.5 000.0 0mm.m 3m0.0 N003 30.m3m 30.m33 353.m 000.0 503.0 05m.m 3303 03.033 00.003 00m.3 350.3 000 000 mm03 m0.m5 03.003 05m.3 000.3 N30 055 5303 wdHLSpomadcmz m0.30 00.00 0m5.m 500.m 000.0 m03.N 0003 00.05 00.m0 035.3 3m3.3 503.3 000.3 3303 3m00 00.00 030 0mm m0m 00m mm03 33.05 00.50 500.3 500 030 003 5303 wcHEme m< 30 300% com 300» com 300% pxm: 300% 5005 map 30% on» mom on» how pcmphzo owmz 303ccm pmpomdxm Umpomdxm Umpomdxm map :3 600 c3 mpCmEGLOCH Umpomdxm Amnmfiaovv mwmz 303cc¢ .mpmmw @mpomHQm ..m.D .mcofipmdsooo 030330> :3 mwmz amazed on» :3 mucoEmpocH ompoodxm 0cm 33mm» gum .300» cpm .pmmm pxmc map CH mwmz Hmsccm Umpoodxm cam pcm335011.5 mqm¢e 000302503 .m xflpcwmad ”mopsom 00.050 00.00 005.3 300.3 000.0 003.0 0003 55.033 03.05 000.0 035.3 353.3 000.3 3303 00.503 30.50 000.3 000.3 300 330 .0003 .05.00 00.00 305 000 300 030 5303 00000 330000 00.05 03.00 000.0 030.0 300.0 000.0 0003 30.05 00.03 500.3 000.3 003.3 030.3 3303 30.00 30.00 000.3 000 305 035 0003 33.30 00.53 005 030 000 500 5303 CHAPTER VI PRESENT VALUES AND SUPPLY FUNCTIONS Introduction In this chapter the present values of the expected future income streams for 25 and 45 year old workers in all the occupations from 1917 to 1962 are discussed. Consistency of present values with the political and economic events is also discussed. The supply function of total number of agricultural workers and the supply function of total number of farm Operators in each age group of farm Opera- tors are estimated. The independent variable in all the types of supply function was taken as the ratio of present value of the expected future income stream in the nonfarm occupation to the same in farm occupation. Present Values of the Expected Future IncomegStream The method of estimation of present value was dis— anssed in the second chapter on "Methodology." However, a bITief explanation is given here. Present value consists Of‘ four components: (1) expected annual wage, (2) expected Luuemployment rate, (3) interest rate, and (4) expected Pennaining years of life. Given all of these four types of 98 99 data, the present values in the nonfarm occupation and in farming, were estimated by the formulas given in Chapter II on "Methodology." The present values in various occupations are given in Appendix D. The present value of the eXpected future income stream for a 25 year old worker increased from $19,381 in 1917 to $56,423 in 1962 in farming; from $27,278 to $117,827 in manufacturing; from $27,412 to $155,543 in construction; from $13,007 to $57,271 in laun- dries; and finally, from $17,909 in 1917 to $78,303 in 1962 in retail trade. The present value of a 45 year old worker increased from $13,479 in 1917 to $43,709 in 1962 in farming; from $18,516 to $88,705 in manufacturing, from $17,747 to $112,581 in construction; from $8,888 to $44,136 in laun- dries; and finally from $12,173 in 1917 to $59,229 in 1962 in retail trade. Apart from fluctuations in the present value of the expected future income stream due to major political or eeconomic events, they showed a phenomenal increase from £1917 to 1962. This phenomenal increase can be attributed tc3 (1) the price level increase, (2) to the increase in tkie productivity of the worker, finally (3) to the quality 017 the worker which was increased by the general level of eciucation and knowledge. The present value of the expected fWIture income stream for a 45 year old worker increased by atNDut 324 per cent in farming, by about 479 per cent in Inarn1facturing, by about 634 per cent in construction, by 100 about 497 per cent in laundries, and by about 487 per cent in retail trade. The present value of the expected future income stream for a 25 year old worker increased by 291 per cent in farming, by about 432 per cent in manufacturing, by about 567 per cent in construction, by about 440 per cent in laundries and by about 437 per cent in retail trade. Consistency of Present Values with Political and Economic Events The present values of the expected future income stream are consistent with major economic and political events. After the end of the First World War in 1918, the expected annual wage fell in retail trade. This was reflected in the low present value of the expected future income stream in all the occupations and in the case of both workers of age 25 and 45 in the year 1921. The onset of the depression in the American economy in the early thirties was followed by low wage expectations. In ‘the post depression and in the beginning of the Second Edorld War, present values increased for almost all occupa- ‘tions and for both 25 and 45 year old workers. The Pearl Harbor attack by the Japanese and the IDaITicipation of America in the Second World War in the yfaar 1941 had a tremendous impact on the expectations EflDout the future income stream. Present values rose in 101 1941 in almost all the occupations and in the case of both 25 and 45 year old workers. ESpecially in manufacturing and in construction, present values suddenly increased from $44,730 in the year 1940 to $53,391 in the year 1941 and from $54,415 in the year 1940 to $61,603 in the year 1941 respectively in the case of a 25 year old worker. In the case of a 45 year old worker, present value suddenly increased from $29,367 in the year 1940 to $36,235 in the year 1941 and from $34,561 in 1940 to $39,893 in 1941 respectively, in manufacturing and construction. The Korean War was associated with increases in the value of expected future income streams. The present value for a 25 year old worker increased from $47,129 in 1950 to $54,824 in 1951 in farming; from $89,805 to $96,593 in manufacturing; from $104,231 to $114,879 in construction; from $49,377 to $52,518 in laundries; and from $52,124 to $68,013 in retail trade. In the case of a 45 year old 'worker, the present value of the expected future income stream increased from $30,601 in 1950 to $38,922 in 1951 in farming; from $61,232 to $66,376 in manufacturing; from $67,810 to $76,132 in construction; from $34,706 to $37,319 in laundries; and from $65,662 to $47,045 in retail trade. The end of the Korean War was followed by reductions in the present values of the future income stream. In the case of a 25 year old worker, the present value decreased 102 from $53,068 in 1953 to $50,680 in 1954 in farming; from $99,288 to $94,572 in manufacturing; from $119,062 to $115,824 in construction; from $52,087 to $51,516 in laundries and from $68,914 to $68,725 in retail trade. In the case of a 45 year old worker, the present value of the expected future income stream decreased from $38,160 in 1953 to $36,264 in 1954 in farming; from $69,315 to $65,422 in manufacturing; from $80,997 to $77,577 in con- struction; from $37,519 to $37,122 in laundries; and from $48,504 to $48,339 in retail trade. After 1954, present values in all occupations which cannot be attributed to any specific major event, increased with minor fluctuations to 1962. The present value of the expected future income stream in the year 1962 reached 43,709 dollars in farming, 88,705 dollars in manufacturing, 112,581 dollars in construction; 44,138 dollars in laun- dries and 59,229 dollars in retail trade. The present values estimated in this thesis .’2 probably have been underestimated in some years and over- estimated in other years. In addition to the current and past annual wages, outlook information supplied by the government and other research agencies might have been taken into account by the workers in estimating the future expected annual wages. The outlook information might be Concerned with the expected gross national product, imports, EEXports, consumer prices, and changes in the labor legislation. 103 The major political and economic events that occurred in the recent past and expected events in the future might greatly influence the expected annual wages. Hence, in the light of the past and future events, present values estimated in this study might be subjectively adjusted to yield better estimates of "actual" expectations held by workers. Testing the Validity of the Present Values Introduction One way of testing the validity and relevance of the present values of the expected future income stream in the nonfarm and the farm sector is to test the hypothesis that the number of agricultural workers in the agricultural sector depends upon the ratio of the present value of the expected future income stream in the nonfarm sector to the same in the farm sector. Over time, this ratio has been increasing. In addition to other factors, if this vari- able is found to be significantly related to the decreasing numbers of farm workers, then it is safe to conclude that the estimates of the present values have some validity and are relevant in the context of migration of workers. Another method of finding the validity of the esti- Inates of the present values of the expected future income Stream is to test the hypothesis that decisions of farm 104 operators to continue or leave farming depends upon the ratio of expected present value in the nonfarm sector to the same in the farm sector. If the relationship between the ratio of the expected present value in the nonfarm sector to the same in the farm sector and the number of farm operators is found to be significantly different from zero at an acceptable probability level, then the estimates of present values can be considered to be at least partially validated and relevant. First Method of Testing the Validity of the Estimates The following regression equations are fitted with the ratio of number of agricultural workers in the year t to the number of agricultural workers in the base year 1917 as the dependent variable. The emphasis in this section is On testing the rele- vance of the present values in the context of supply function of total number of agricultural workers. In this context, it is to be pointed out that these relationships are merely an outcome of a preliminary analysis and full analysis of these relationships must await a full scale effort on the part of another investigator. All the regressions fitted with the ratio of present Values as the independent variables, explain a high degree Of‘variation in the dependent variable. Almost all of the iPegression coefficients in all the regressions are signifi- <3ant1y different from zero at the one per cent level. The 1(35 1(a) 8 1.101902 — 0.160820 88, + 0.080882 28- — 0.010162 t ._t.;_ = 4 C- ) ’t L8.) ,t to (0.05650) (0. 05 2343) (0. 013209) (0.000421) d.f. = 42 82 = 0. 965335 . h 0. 031391 - 0 350302 16g RM + 0.224432 log BL, - 0.013255 t (b) 109 —£ 25’t 45,t e no =(0. 028093) (0.13.3235) (0.042399) (0.000754) __') . . d.f. = 42 R“ = 0.937765 2(a) Nt 1.08829 - 0.141230 R,,) t + 0.090103 885 t - 0.01055 t _ = , , .— 3 ’ ,. 80 (0.064493)(0. 06L1855 ) (0.020793) (0.000466) _'3 d.f. = 42 R“ = 0.95466 - - , _ .4 . T . 8 0.064436 - 0.264706 102 R? + 0.197040 log R . - 0.013970 t (b) 166 t — 7 :5.t ‘ 45,t 0 NO (0.030415 (0.141941) (0.05825) (0.000834) __’7 _ d.f. = 42 at = 0.918459 3(a) at 1.050768 - 0.13 7160 a: t + 0 102606 88% t - 0.009508 t _ = ( , ‘ _. , . 80 (0.032741) (0.031633) (0,014305) (0.000451) _'D . d.f. = 42 R“ = 0.970796 (b) 162 w 0.0 22787 - 0.411072 10? RC + 0 324538 102 RL — 0 011744 . t) ‘—t— = I— ~ -2L~;,t ._ ._.; '1 u5,t o t 80 (0.023190) (0.081720) (0.044983) (0.000761) _"J , d.f. = 42 R‘ = 0.95369 4(2) 8 1 0.7800 0 17 or > PC + 0 148471 PT 0 00U f t (Ci mt - ,JJU_,‘/ - . 11L 135,36 0 7) I “5,1: - 0 ),)3.) 7; ‘(0.036532) (0.041122) (0.025025) (0.000622 d.f. = 4) 8‘ = 0.9637104 ‘ N O 06 M00 — 0 481970 103 RC + 0 307613 109 RT - 0 011848 (b) log _3 = ' ' " ‘ 5 25,0 '7’ ‘ 2 45,0 ' “ HO (0.024788) (0.113663) (0.07 4623) (0.000926) _'3 d.f. = 42 R8 = 0.938121 KWiere Ratio of the present value in manufacturing for a 25 year 010 w rk~~ 3 in the year t to its base value in thegyear 1917 R75 t = Ratio of the presen' value in farming for a 25 year old worker t6 ‘- « 9 its base value in the year 1917 C Ratio of the pr resent value in construction for a 25 year old worker R30 = in the year t to its base value in the year 1917 “ Ratio of the present value in far ing for a 25 year old worker its base value in the year 1917 Ratio of the present value in laundries for a 4?) year old worker R.. = in the year t to its base value in the year 191/ ’ latio of the present value in farming for a 4‘ year old worker tu its base value in the year 1917 T Ratio of present value in trade for a 45 year old worker in the yea? R45 t = t to its base value in the year 1917 ’ Ratio of present value in farming for a 45 year old worker to its base value in the year 1917 N t Total nu ber of a: icultura 1 workers in the year t L.’ — _40 ,- .2 r Total number of a ricultural workers in the year 1917 o 't' is the time variable. This variable is included as a proxy for many factwru, norlmonetary, which are highly correlated with the time, such as average level of 6110611»» anCi aspiration to live in 1rban area. 106 regression coefficients of the ratio of present value in nonfarm occupations to the same in farming for 25 year old workers have the right sign in all the regression equations. The regression coefficients of the present value in nonfarm occupations to the same in farming for a 45 year old worker shows generally the wrong sign. The regression coefficients of the time variable have the right sign in all the regres- sion equations. For further explanation the linear regres- sion equation 1(a) is used. The explanation for this equation applies more or less to all the other regression equations. Regression equation 1(a) explains over 96.5 per cent of the variation in the ratio of the number of agricultural workers in the year t to the number of agricultural workers in the base year 1917. The regression coefficient of the ratio of expected present value in manufacturing to the expected present value in farming for a 25 year old worker is significantly different from zero at the l per cent level. The ratio of the present value in manufacturing to the present value in farming for a 25 year old worker has steadily increased over time. The regression coefficient of this variable indicates that as the ratio increases over time, the ratio of the number of agricultural workers to the number of agricultural workers in the base year decreases. This is quite consistent with the normally expected behavior of agricultural workers. In other words, 'When the present value of the expected future income stream Sin manufacturing for a 25 year old worker increases over 107 time as compared to its counterpart in farming, rational agricultural workers, move to manufacturing to maximize their income. The number of entrants in the younger age group into farming decreases and the exits in the younger age group out of farming increases, resulting in a net decrease in the number of younger farm workers. The regression coefficient of the ratio of the expected present value in laundries to the expected present value in farming for a 45 year old worker is also signifi- cantly different from zero at the l per cent level. The sign of the regression coefficient is negative. This sign does not seem to be inconsistent with reasonable theoretical models under some Special conditions. The consistency of this negative relationship (between the total number of agricultural workers and the ratio of present values of the expected future income stream in laundries to the same in farming, in the case of a 45 year old workers) with the reasonable theoretical models is discussed below. The following theoretical model,1 represents one possible explanation for the observed negative relationship (between the total number of agricultural workers and the ratio of present values of the expected future income stream in laundries to the same in farming in the case of 45 year old worker) brought out in this study. 1This development was suggested by Dr. Robert L. Gustafson., Let 1 WF = a1 + bl (025 + Q45); bl< O 2 Q25 = a2 + b2 RM b2< 0 3 Q45 ‘ a3 + b3 RL b3< O R = WM/WF RL = WL/WF Assumptions: WM, wL exogenous variables WF, RM, RL, Q25, Q45 endogeneous variables WF: wage rate in farming Q25: number of 25 year old farm workers 045: number of 45 year old farm workers WM: wage rate in manufacturing WL: wage rate in laundries ai (i=l,2,3) and bi (i=l,2,3) are constants. The first equation denotes a form of demand equation in farming. The second and third equations denote supply functions. The interpretation of these equations are as follows. The farm wage rate is a decreasing function of total number of farm workers. The higher the total number of farm workers, the lower is the farm wage rate and the lower is the total number of farm workers, the higher is the farm wage rate. The farm wage rate is determined by the total number of farm workers. Hence farm wage rate is endogeneous variable because it is determined by the ratio of wage rates in the nonfarm occupations to the same in farming. Wage rates in nonfarm occupations are assumed to be exogeneous variables. 109 The higher the ratio of manufacturing wage rate to the farm wage rate, the higher is the off—farm mobility of 25 year old farm workers and hence the lower number of 25 year old farm workers in farming. the ratio of wage rate in laundries to the wage farming, the higher the off-farm mobility of 45 workers and hence the lower is the total number old farm workers in farming. is the total The higher rate in year old farm of 45 year Now suppose there is a change in WM, manufacturing wage rate (exogeneous variable) and WL’ wage rate in laun- dries is constant. dWF = E" Q E 3 dQ25 bl( dW ll 0‘ II 0" dQu5 dWM Differentiating with respect to WM 110 Now the equations 4 to 8 can be written as follows. 9 X1 — le2 - le3 = 0 11 x3 - 63x5 = 0 12 x“ + WM x _ 1 .5 l - W— W? F 13 x + WL x '= 0 5 -—2' l v F Solving these five linear equations (9-13) in five unknowns for the variables of interest and applying the assumed signs of b'S we obtain the following results. (See Appendix F) If w increases and W is constant M L WM dRM R =.__ increases since ——— > 0 M W dW F M WL dRL R = —— decreases since ——— < 0 L w dw F M d025 Q25 decreases Since dW§_ < 0 wL Q increases since —— decreases 45 WP d’Q +0 ) . ‘ 45 25 Q25 + Q45 decreases Since de < 0 WF increases Since Q25+Q45 decreases and therefore there is negative correlation between (Q25+Q45)’ RM and a positive correlation between (Q25+Q45)’ RL. However, by symmetry, if WL increases and WM is constant the following conclusions are true. 111 W W R = —£ increases, R = _fl decreases L WF M WF ’ Q45 decreases, 025 increases, 014518025 decreases, WF increases, and therefore there is positive correlation between (Q25+Q45)’ RM and negative correlation between (Q25+Q45)’ RL. Since the positive correlation between (Q25+Q45)’ RL and negative correlation between (Q45+Q25)’ RM are observed, the probable implication in this model might be the variation in the WM (present value of the expected future income stream in manufacturing) is higher than the variation in WL (Present value of the expected future income stream). The calculated data on WM and WL (present values, of course) support this implication. All the regression equations even with different variables, support the argument that the Signs of the regression coefficients of the concerned variables are consistent and validate the relevancy of the estimates of the present values in various occupations insofar as they are considered as indicators for decision making for farm workers whether to stay on farm or move out off—farm. The same arguments need not be repeated in repeated dis- cussions of all the other regression equations. 112 Trend in the Expected Present Value of the Future Income Stream Projections of the number of agricultural workers into the future required as a first step projection of the expected present values in the nonfarm and farm sector. The following sections deal with two types of functional form for fitting the trend in the present values for a 45 year old and 25 year old worker. P Both the linear regressions of the form $3 = 60 0 Pt + at + Ut in actual values and of the form log P_ = 60 o + at + Ut’ where Pt is the present value and PO is the present value in 1917 and 60, B are the parameters and t is the time variable, were fitted to the present values during the period 1917-62. These fitted regression equa- tions were used for projecting the present values into the future. The foregoing analysis required the projections of present values only in the occupations; farming, manu- facturing and construction in the case of a 25 year old worker and in farming, laundries and retail trade in the case of a 45 year old worker, hence the trends in those occupations were fitted. However, Similar trends can be fitted for the present values in the other occupations. The fitted regression equations in various occupations in the case of 25 year and 45 year old worker are given below. F M C L T Pt’ Pt’ Pt’ Pt’ Pt’ are the present values in the year t in farming, manufacturing, construction, laundries and in 2.a. Cr PF = 0 F 10 P g t P: = 0 (0 M lo P g t C P = O t (0 C l P og t PF = 0 (0 10g PE t 23:. (0 ‘ L log Pt PT - 0 t - (0. 103 P 113 Trend in the Present Values in the Case of a.25 year old Worker 1. Farming ,. F d.f. .44704 P‘ + 0.05829 P t 44 .10151) (0.00389) = -o.33529 + log PF + 0.03344 t 44 (0.06731) (0.00258) 2. Manufacturing M M .434230 PO + 0.080224 P t 44 .122320) (0.004882) 0 M = -0.154250 + log P + 0.038837 t 44 (0.059794) 0 (0.002289) 3. Construction c - c .353858 P + 0.102069 P t 44 .149401) (0.005719) 0 = -0.055943 + log PC + 0.039142 t 44 (0.052354) (0.002004) Trend in the Present Values in the Case of a 45 year old Worker 1. Farming F _ . F .351845 P + 0.061146 P t 44 .119091) (0.004559) = -0.394113 + log PF + 0.035403 t 44 (0.080723) (0.003090) 2. Laundries L L .83305 P + 0.08789 P t 44 .10512) (0.00402) = 0.205415 + log PL + 0.032444 t 44 (0.038828) (0.001410) 3. Retail trade T T .590924 P + 0.088181 P t 44 123988) (0.004741)‘ = 0.042410 + log Pg + 0.034274 t 44 (0.042628) (0.00163?) *0 0.8227 0.7882 0.8667 0.8501 0.8759 0.8942 0.7991 0.7433 0.9137 0.9216 0.8798 0.9073 11M . F M C L T retail trade respectively. P0, P0, P0, P0, P0 are the present values in the year 1917 in farming, manufacturing, construction, laundries and in retail trade respectively. 't' is the time variable. The constant and the regression coefficient of the time variable in each functional form and in each occupation in the cases of a 25 year old and U5 year old worker, are significantly different from zero even at the one per cent level. All the fitted regression equations explain above 7“ per cent of the variation in the dependent variables. These fitted regression equations with time as an independent variable will be used in the following sections for pro- Jecting the present values. These projected present values will be used for projecting the total number of agricultural workers and also total number of farm operators in each age group. Second Method of Testing the Validity of the Estimates of Present Values The second test involves the relationship between the number of farm operators by age group and the ratio of present values in the nonfarm and farm occupations. For each age group two estimates, one linear and the other lOgarithmic, are given. For each age group regression equations were fitted with the ratio of the number of farm Operators to the number of rural survived males who were 115 10 years younger in the previous census period as the dependent variable and the ratio of present value in the nonfarm occupation to the same in farming as the indepen- dent variable. The dependent variable relate to the four census years 1930, 1940, 1950, 1960. The independent variable is the ratio of the average present value in nonfarm occupation to the same in farming. The present values are averaged in the previous 10 years from the cen- sus year. For example, the corresponding independent variable for the dependent variable in the census year 1930 is the ratio of average present value during the period 1920-29 in the nonfarm occupation to the same in farming. Since present values for the entire period l9l0- 19 were not available, the census year 1920 was eliminated from the census years used in this study. Therefore the number of observations for this study is only four. For each age group and for each functional form, four regression equations were fitted. The independent variable in each regression is the ratio of present value in the corresponding nonfarm occupation to the same in farming. On the basis of the results, one occupation for each age group was selected for further use. The results revealed that the ratio of present value in manufacturing to the same in farming was highly correlated with the dependent variable in the lower age groups and the ratio of present value in laundries to the same in farming was highly corre- lated with the dependent variable in the higher age groups. These findings are quite consistent with economic reasoning having to do with acquisition costs and salvage values of laborers in the farm sector. The young farm workers are more attracted to the high paid nonfarm occupations like manufacturing. Older people cannot get jobs in manufac- turing because of technical educational, experience and training requirements associated with the jobs. Hence, older farm workers are likely to get only low paid nonfarm jobs in occupations like laundries or retail trade. The following are the empirical results in each age group. In the first two age groups, the sign of the regression coefficient is negative, which indicates that as the ratio of present value in manufacturing to the present value in farming increases over time, the number of farm operators will decrease, given the number of survived rural males. This is due to the fact that the number of young peOple who enter farming decreases due to the attractiveness of urban jobs, and the number of young people who leave farming increases for the same reason. Therefore it is reasonable to conclude that the ratio of present values is playing its expected role as a guide for directing the flow of young peOple. Hence, estimates of present values are relevant in explaining the occupational choice of the farm operators. In the rest of the age groups, the sign of the regression coefficient is positive which it can be inter- preted in a reasonably way. The ratio of the present value 117 Age Group: 15-2U Years A i M (Ft/St) = 0.996250 — 0.5158U8 R25,t (0.359899) (0.194970) . logfl(ft/St) = 3.764719 - 19.319177 10g RS5 t (1.086341) (9.176811) . Age Group: 25-BU Years _ 6,1, M (ft/St) - 2.421993 - 1.162381 R25,t (0.929187) (0.510U72) log (ft/St) = 1.U15935 - 7.954133 log R75 t (0.730098) (2.807110) L ’ gge Group: 35—44 Years A L ft/st - 0.348837 + 0.294460 Ru5,t (0.143499) (0.120707) A ., , » L 10g (ft/St) = -0.19M052 + 0.524089 log R45,t (0.018170) (0.199822) gge Group: Ub—Su Years *0 _ - ,--, L ft/Ut - 0.97125U + 0.305632 RUS’t (0.170337) (0.1U3282) log (ft/St) = -0.1l2303 + 0.96270 log 8&5 t (0.017596) (0.193498) ’ Age Group: 55-6U Years ‘ _ . L (rt/st) - 0.358671 + 0.417370 Ru5,t (0.133708) (0.112971) (10% (ft/St) = —0.112250 + 0.603165 16g REC t (0.013448) (0.147884) 2’ fige Group: 65 Years and Above (ft/St = 0.1U5261 + 0.91U028 R95 t (0.119527) (0.1005U3) ’ . O - L log (ft/st) - -O.254853 + 0.797935 log R95,t (0.016717) (0.18383“) .66465 .871761 .582466 .668560 .66465 .662715 .5U1985 .61302 .80978 .839015 .8U1750 .85605 118 in laundries to the present value in farming has been decreasing over time. This tendency is not only exhibited in the case of laundries but also in many occupations similar to laundries in which older farmers have been able to enter. Even though the ratio has been decreasing, the magnitude of present value in the laundries has been greater than the present value in farming. Hence, the older farmers who find occupations similar to laundries and retail trade as the only occupations in which they can enter, are inclined to move into these occupations because they do not possess the higher skills and technical training to enter other occupations. One possible explanation for the positive relationship is that both the number of older farmers, mainly because of deaths, retirement and other reasons, and the ratio of expected present values have been declining over time. Since both are highly negatively correlated with time, these two variables are positively correlated. What- ever may be the cause, the relationships are fairly strong, and most of the regression coefficients are significantly different from zero at the five per cent level in most of the age groups. Projection of Number of Agricultural Workers and Comparisons With the Previous Projections For the purpose of projection of number of agricul- tural workers to 1980, two of the estimated regression 119 equations 1(a) and 2(a) in the page 105are used. For the ratios, only linear trends are used 1(a) _E = 1 101902 - 0 160820 RM + 0 080882 RL -0 01062 t NO 0 .0 25’t ' “5,t ° 0 2(8) 12 = 1 088290 — 0 141230 RM + 0 090103 RT '0 01055 t No . . 253t . “53t . N (NE) can be derived as a function of time only by simply o substituting estimated functions of time for RM and BL . 25,t 25,t N One method of projecting (NE) for any year in the future o is tn) simply substituting the number of year in the future N_t. N 0 after derivation of ( ) as simply a function of time. An equivalent method is a two stage procedure. Firstly, M an 25,t are substituted for each year in the future to arrive at N NE in the future. The following table gives the estimated o R d R35 t are projected in the future. These values 3 values for each variable in the future. The ratio of present value of the expected future income stream in manufacturing to the same in farming for a 25 year old worker increased from 1.35837 in 1963 to 1.3721“ in 1980. The rate of increase seems to be very low and is decreasing over time. The ratio of present value of the expected future income stream in laundries to the same in farming for a 95 year old worker is decreasing Over time. 120 TABLE 8.--Estimated ratios of present values and total number of agricultural workers in the U. 8., 1963-80. # 1’4 M .1 .1 83:29:. ”(3‘50“ ““533?“ Year 25,t 45,t 45,t the year) (in thousands) 1963 1.35837 1.54081 1.43906 46 7,335 7,338 1964 1.35958 1.53885 1.43859 47 7,192 7,192 1965 1.36076 1.53696 1.43804 48 7,050 7,046 1966 1.36189 1.53514 1.43751 49 6,908 6,900 1967 1.36298 1.53339 1.43700 50 6,765 6,754 1968 1.36404 1.53169 1.43651 51 6,623 6,608 1969 1.36505 1.53006 1.43604 52 6,481 6,462 1970 1.36604 1.52848 1.43558 53 6,340 6,317 1971 1.36700 1.52696 1.43514 54 6,198 6,171 1972 1.36792 1.52548 1.43471 55 6,057 6,026 1973 1.36882 1.52406 1.43429 56 5,915 5,880 1974 1.36969 1.52268 1.43389 57 5,774 5,735 1975 1.37053 1.52134 1-43350 58 5,633 5,590 1976 1.37134 1.52004 1.43313 59 5,492 5,445 1977 1.37214 1.51878 1.43276 60 5,351 5,300 1978 1.37291 1.51756 1.43241 61 5,210 5,155 1979 1.37365 1.51638 1.43206 62 5,069 5,010 1980 1.37438 1.51523 1.43173 63 4,928 4,865 121 Heady and Tweetenl have pointed out that projecting 1950-60 trends yields a prediction that the farm labor force will decline from 7.1 million in 1960 to 4 million in 1980, a 44 per cent decline. In an alternative proce- dure, they estimated the number of workers required in 1980 to be 3.6 million. This result was based on the compound interest formula assuming annual increases in output and output per man-hour to be 1.8 and 5 per cent respectively. In the present study, total number of agricultural workers is projected to 1980 using two regression equations. On the basis of regression equation (1a), the estimate of total number of workers 1111980:is 4.93 million, and on the basis of regression equation (2a) it is 4.87 million. The estimates in this study are higher than what Heady and Tweeten estimated. The total number of workers will decline from 6.70 million in 1962 to 4.93 or 4.87 million in 1980 if these projections were true. These estimates indicate that there will be at least a reduction of 1.77 million agricultural workers. Projection of Number of Farm Operators and 'Comparison With the Previous PrOjections The number of farm operators in each age group is projected for 1970. The projected total number of farm lEarl O. Heady, Luther Y. Tweeten, Resource Demand and Structure of the Agricultural Industry (Ames, Iowa: Iowa State University Press, 1963). 122 Operators is obtained by adding all the projected number of farm Operators in each age group. The projection of the number of farm operators in each age group is made as follows. From the projections Of the present values in the farm and some of the nonfarm occupations, the average present values in each occupation during the period 1960- 70 is estimated. Then the ratio Of average present values in the nonfarm occupation to the same in farming is used in the regression equation for estimating the ratio Of farm Operators to the survived rural farm males in each age group. After obtaining these ratios in the age groups, they are multiplied by the estimates of rural survived males in the corresponding age group to Obtain the estimates of farm operators in each age group for 1970. The estimates of rural survived males for 1970 are given in the Appendix D- Table 9, on the next page, gives the number of farm Operators in each age group from census year 1920 to census year 1960 and also projected number of farm Operators for 1970 along with previous projections. Bishop and Tolley estimated the total number of farm Operators for 1970 at 2.65 million. This figure given in terms Of the 1960 census definition of a farm, is equivalent to approximately 2.82 millhm1"l950" farms when adjusted by the total U. S. farm definitional change weight of 0.941. Fox (1962) has estimated that there will be 1.4 million commercial farms selling $2,500 worth or more of 123 oup by census years (1920-60) for 1970 according to 1950 U. S. T.BLE 9.-—Number Of farm Operators by age gr and projections Of number of farm Operators census definition, Farm Operators Total <25 25—34 35-44 45-54 55-64 65+ Year (thousands) 1920 6,448 388 1,305 1,608 1,502 1,007 592 1930 6,289 384 1,085 1,504 1,512 1,103 701 1940 6,097 244 992 1,207 1,491 1,198 865 1950 5,379 175 844 1,286 1,234 1,066 794 1960 3,933 65 428 858 1,047 851 683 Y‘ ., 1920, 1930, 1940, 1950, 1960 C") Source: Agricultural Census, Estimated for 1970 by Other Studies Bishopa and 2,820 58 283 424 716 728 611 Tolley (1963) Foxb 7 g (1962) 2,657 45 247 404 683 696 563 JohnstonC (1963) 2,756 52 267 421 702 715 599 Marion ‘7 p . Clawson 2,787 8 200 475 764 720 548 (3,440) (50) (150) (400) (690) (650) (500) Estimated for 1970 on the Basis Of this Study Linear 2,770 27 212 442 736 740 613 CObb- , Doublass 2,780 31 234 439 729 737 610 a C. E. Bishop and G. S. Tolley, «. ‘ ‘ . , occupations, Education for a changing w r11 of work. Appendix II. Report Of the panel of consultants on vocational education, (Washington D.C.z U. S. Department of Health, Education and Welfare, U. S. Government Printing Office, 1963). b I I I I C h. A. Fox, "Commer01al Agriculture: Perspectives and Prospect1ves," in Farming, Farmers and Market for Farm Goods, Supplementary Paper NO. 15 (New York: Committee for Economic Development, 1962) c W. E. Johnston, The Supply Of Farm Operators, an unpublished thesis, North Carolina State Of the University Of North Carolina, Raleigh, North Carolina, 1963). dMarion Clauson, "Aging Farmers and Agricultural Policy," Journal of Farm Economics, Vol. 45 (February, 1963), p. 15, Table 1. The Figures in this bracket are low estimates. The figures in this study relate to only the number of farm Operators reporting age. 124 farm products in 1970. If, as in the case Of 1960, commer- cial farms were to make up 56 per cent Of the total farm population, there would be 2.5 million farms in 1970 according to 1960 definition. This estimate would be equi- valent to about 2.657 million "1950" farms. Johnston, utilizing an iterative procedure, estimated the number Of total farm Operators. He estimated the total number of farm Operators as 2.593 and 2.756 million as per 1960 and 1950 census definition respectively. Marion Clawson (1963) assuming that the same rates of entry and withdrawal in each age group in the past censuses, will continue in the future, estimated the total number of farm operators for 1970. He provided high and low estimates in each age group. The number of farm operators in the age group 15-24 in the 1960 census is 62 thousand. The number Of farm operators projected for 1970 in this study is 26 thousand by linear regression method and 30 thousand by the log linear method as compared to 56, 43, 50 thousand estimated by Bishop and Tolley, Fox and Johnston respectively. The estimates of this number made in this study are low rela- tive to other estimates, they may very well be nearer correct. The highly favorable nonfarm Opportunities for :farm youth will reduce the number Of entrants to and EEncourage the number of withdrawals from farming Operations. lif we compare the decrease in number of farm Operators in 125 the age group 15—24 from 175 thousand in 1950 census to 65 thousand in 1960 census, the estimated decrease from 62 thousand in the 1960 census to 26 or 30 thousand in 1970 does not seem to be unnatural or unreasonable. In the light Of this fact, the estimated decrease from the 1960 census to the 1970 census in the number Of farm Operators in the age group l5-24 by other studies appears too low. From the same point of view, the estimated decrease in number of farm Operators for 1970 in the age group 25-34 by other studies also appears underestimated as compared to the estimated decrease of this study. The estimates made in this study in the higher age groups are higher than the estimates made in the previous studies. Table 10, on the following page, gives the age com— position Of farm Operators in the 1960 census and the pro— jected number Of farm Operators according to the definition Of 1960 census. For the United States, according to 1960 census definition the estimate Of total number Of farm Operators for 1970 in this study is 2.607 million by linear regression method and 2.616 million by the log linear method as com- pared to the 1960 enumeration Of 3.701 million. The total number Of farm operators projected for 1970 on the basis Of methods used in the previous studies by BishOp and Tolley, Fox, Johnston and Clawson and in this study do not deviate much from each other. Even though the 126 m mwamsom 6mm Hos wwo ma: mmm om ©H©.N -6660 H LOOCHQ mmm nos mom was Ham om aoo.m osmfi N@:pm pcmmmpm mam owe moo mam :mm om mam.m osmfi Ameaflv 66866668 Hmm New mam mmm mmm m: oom.m osmfi Ammmav xom smm mam mew Ho: mom om :mo.m oama Ammmfic smaaoe 6cm dogmam mmaespm pampmecfio s6 osmfi toe mmpeeflpwm mmo mom was mam No: we Hoa.m coma Amocmmsonpv Leo» +mo moumm :mnm: azumm amamm mmv H6669 mLOOmLOQo Spam .m .D .COfipHchoo mamcoo coma Op wcHOLooom osma .omma mhmom 639 CH adopm Own an mpOpmpOQo 89mm mo LopESZII.oH mqm2©a mmo.m .aa www.mw aoa om mm .ma oama \ . : 000 0: 000 00 000.00 000.0: 0:00 000 0: 0.0.00 .. d. .;J. . a J.u 40 .-r maa.m© mar am $00 ea aama 00.0: m00.m0 000.00 000.00 00..00 0:00 000.mm .00.00 000.00 :00.00 0:0.00 0:00 000.“. 0:0 00 000 00 000.00 0:0.00 0.00 000 00 000.00 00:.:0 00 .:: 000.00 0000 00HH00 000H00 000.00 000.0: 000.00 0000 000.00 000 00 000.0: 000.00 000.00 0000 000 00 000.00 000.00 0; ., 0 .0 .0.. oa\.om 0.0:. q0 . .konma mam Cm moaa 000.00 0..._0 000.0: :00 00 000.00 0000 00 .00 n::.mm :00.00 0:0.:0 000.00 0000 :00..m 0::.0m 000.0: 000.00 000.00 :000 000.:_ 00:.00 000.00 0:0.00 000.00 0000 0.0.mm 000.00 000.00 000.00 000.00 0000 www.mc W00.m0 :00.:0 000.00 00:.:0 0000 d A .J a. .0. 000. o 000 00 000 00 :00.00 0000 d -J .n n ,I wM0.mm 000.0m 000.0: :00 0: 000.00 0000 m0 . w 000.00 000 0: 0:0.00 000.00 0000 :«00 000 0 000.0: 000.00 00 .00 0. 000.00 000.00 000.0: 000.00 00w.00 wmww 0:0 00 0:0.00 000.0: 00 .00 00 . 000 :00..0 000. . 0. 0 00 0.00 00 .04 0.0m 0:0.00 000 00 :00.00 :000 -0. w 000.0. 000 0: 0:0.00 :00.00 0000 m0mm0w 000.00 000.00 000.00 000.00 0000 .00.00 000 00 000.00 000.:0 000.00 000 000 00 000. 0 000.0 00 .00 J. ..J .0: as .o . .. a r a :r mmm mo Gama .: 0 0::.00 \\0.00 000.00 . . . ... .. -- 000 00 0000 www.mw W00Hm0 000H0 000M00 000. 0 0000 .00 -0 00: 00 000 00 000.00 0000 Aw..00waaOU 000090.030 Gav AwkwaaOU pCQPHLSU CHV AmLmaaOU 0.0090030 Gav nmhmaaOU 00:97:00 Gav. AmLmaaOU 02.00.00.030 Gav «00000.0. maam> pcmmmpm maam> pcmmmgm mzaw> pcwmwpm maam> 0cmmmgm maam> 0:00000 . mswpfi aam0mm 00000::mq scauosgpwcoo m20030000320a mc0figmm - .0050000 .0 .0 0:0 :0 m: ifim» pi 00 muaa go mgwmw mgaCamem ecu :a Esmg. z o 00uwmzoo; 030000> :0 000003 saw 0m mfioocH 002030 Umpommxu mzp 00 03a0> 0Cmmmznll.0 0000M i178 .HHH Lmuamco mmm pmmLmuC0 000.00m>0pomammp m U20 < x0ncwaa< mmm mmpw 0 ucms>o0aamcs 0cm mmwmz 003ccm 00000000 00 mmpma0pmm co mums pom .m000 mo 00 empowaxm 3cm mum .meawco 0000000500? 020 :0 cm>0m mm300> pcmmmpa pom mm0zrgou was ”mopzom rL 000.00 000.00 000.:0 000.00 000.00 000.00 000.:0 000.00 000100 :00.00 000.00 000.00 :00.00 000.00 000. 000.00 000.00 020.19 000.:0 \m..0 -wamm 000. 00 000.00 000.00 >02. . mafiamm 000.0: mxn. m@s. 00m 000. :00. O>zn 000. 000. :00. 000. 02m 000. 000. 000 000 000 0:0 wmfi HmH :MH Nma 300 $00 .000 :00 :00 O\O\C‘\ C\ E\ OJ C1330? :0QJ C‘\ .') —9- . own 4:0:rwm0 (‘0) CU r—‘1 'v‘l I a CC. 05.3.0712?- LIZWOC‘ :VM‘J 1"\ I 03 0 000 $90 $00 8 fl 0‘ NHH SCH 030 £30 ccfl ”:0 CO ”as O? .00 A A 0‘ \ rm N no 00H” :0 .0uo 0U .0 "\ .\ 000..00 00.0%” ::.0 000. 000.00 T$m0mm 0000 0000 0000 Odha “000000000 5000 OQOH 3:00 :30H mmma mmaa amaa ooma 179 mm.m:m mm.m>m ::.Hnm mm.mmm Hm.O:m mama oo.mzm :O.fiOm Om.mxm m:.OHm Or.OOm OOOH H0.0mm aa.:Om O0.0nm OO.:Om \m.r:m wzmfi mm.mOm aa.m:m >O.HOm Hm.Omm OH.OON OOOH :O.mOm O0.0Hm HO.HOO O:.Onm O9.0Hm OOOH m .Hmm m>.HOm O0.0:O mm.axm m0.00m ::OH NO.mmm N0.00N mm.m:m OO.>OO HH.:OH mOOH aa.:mm ma.apm >O.>nm rm.O:m :m.mofi mama H0.000 O0.0mm m>.:mm O0.00H OO.MMH HOOH mO.mOfl nu.OHm O0.00H :0.00H O:.OHH OOOH oo.mma oo.mflm oo.mmfi om.mnH O0.0HH OOOH Hm.OO~ oo.mOm pm.m>H ma.mwfi O0.00H OmOH m:.OOH m>.OOm O0.00H O0.00H mm.OHH >mmfi :O.H>H :>.OOH O0.0>H am.mzfi O0.00H OmOH >m.anfi OO.OOfi :O.N:H Om.naH O0.00 mmm” m:.onfl. pm.OOH mm.m:fl >H.Oma OH.OO :mOH Om.zma O0.00a O0.0HH Om.OO ~:.O> mmma OO.>HH aa.:3H ma.aa OH.OO OH.OO mmmfl OO.m:H OH.O>H am.amfi OO.OO 09.:O _mOH m>.mnfi OO.>OO OH.H:fl HO.OOH ma.ma OmOH om.mnH :O.HOH >0.0nfl :O.Hma :0.00H OOOH m:.OmH O0.00H Ofl.OOH OH.OOH NO.HOH OOOH O0.00H a:.mwfi m>.OOH >m.nmfl OO.HOH OOOH N0.00H mm.amfl OO.>OH mm.mmfi O>.HOH OOOH O0.0:H OO.OOH OO.mmH :0.0ma m0.00 OOOH mm.m:fl OO.HOfi O>.Hzfi O0.0mH O0.00H OOOH :O.N:H :H.Omfi OO.O:H OO.:MH HO.HOH mmOH OO.mmH O0.0mH Om.OmH Om.MHH m0.00 mmOH M0.0HH O:.oma mm.mOH p0.00 O:.HO amaa mm.m:a aa.:mfl OO.HOH O0.0mH mm.mmH OOOH >0.0HH MO.OHH N0.0HH :x.mmH mr NHH OHOH m0.00H am.afia O0.0HH :fi.OmH O0.00H OHOH O0.00H O0.00H O0.00fi O0.00H O0.00H OHOH OOH u OHOH OOfl u OHOH OOH u OHOH OOH n OHOH OOH u OHOH Lam» mzam> pcmwwcfim msfiw> ucmmmLa ejam> ucmmem wzflm> ucmmmcfim ®3Hm> pcwmmLm LO X®UCH LO XQUEH LO XQUCH LO xmeCH no meCH mUMLE mepmm mmwgcczma sewuusppwcco mcHLSOOmmzcmz mCHEme OOH: meL03 5H0 .nonFHOH ..m .O mg: .4 3 Lo,“ m20HJmazooo 14 £QO:H ¢L3p3O Ompcoaxw ozp no mzam> pcmmmga no wacHlo. wzcflgm> CH mfimwn mgp mm maaa :fl maam> pcmwmgu mLp M uqmqh 180 .xHOOmOO< chp O0 H mHOme mmm ”moLzom om.mm: Hm.::: an.&©m :m.am: @©.H©m moaa mu OO: O;.OH: O:.OOO OO.OOO ma.mwm HOOH OH mH: O>.mm: OO.OO9 OO.HOm OH.OHO OOOH mo.mm: OO.:O: O0.0HO O0.0H: Om.:OO OOOH H: “O: am.mH: O0.0H: m .OOH O:.OOO DOOH an NH: O0.0H: OO.OH: OO.Omm mm.bwm OOOH HH.$H: OO.mm: OO.OO: O0.000 mm.mm“ OOOH OH fifl: m$.fiflq ©H.F@ 0@.$mm 3%.:NJ mfimfi OH mmm OO.OOH mm.mm: HO.OHH \O.HOO :nOH Ow OOW ::.OO: :m.:m: OO.MOH OO.HHO mmm o A H 0 x . ,\1 Iv o ‘ 4 a v. x .. WW.WMW ©W.M©n 00 man NR JIM ®©.:%m mfiOH L 3 c», o H) 1.-.. 1V V\ OO.HHU m.. Om mm.~Hm HO OOH :3 amp HOOH H Or Hf (Lo 00 or? :H.Omw aa.mHm QmmH me.m: :mm.mz OOH.H: OOm.:w me.mO HOH.HH HOH.HH www.mo OHO.Hn . OOO.Hm mOO.Hm mmO.mO OHO.HO Om: mm ‘ momaom HHO.ON HHo.mm Hon.nn HOO.HH mHmH onz.mm ONO.NN mm:.mz Omm.n: Omm.m{ WOOH OOO.Om OOH.OO ~O2.a: :O:.O: nO0.0m .OOH HOH.mm 03>.mm OOO.NH OOHAOO 3:5.0m MHOH SOHO. 9348 m8? Sm"? ::.: LMH OOH. HHO.OH oO0.0m H:H.O: OHO.OO H .H \ NW HOD.“ H‘m.un 1 3H H n \JQH Om .J O d" K, :m ;.c Om GOO Hm d x maam mean . Nefiaom 00$.0H 0:0H U h u. f ._C x JHOAMP stnwfi WHH.NM U ,n OfflaJH HSQH Hz: ON :ON OH .OO Om FOO Hm OzmH mHO.Om :HO.OH mOm.:m mmm.mm OOm.mH ,-\ 1i mmm.OH O:O.OH OHO.O~ HOE.OO O:O.mH OWOH oo www.mH OOO.OH OOanm OmO.mm OOmamH OWOH 1i nHmazH . HOO.:H OHO.HO :Omamm H:O.OH WWOH OHO.OH O m.mH OanOm Hm:.Hm mOO.HH WHOH :OO.mH NOO.OH O:O.:H OOO.HH OOO.HH mmmH Omm.m H:O.HH OOH.mm TOO.:H HHHaO mwuH mOH. H OO_.O NOO.OO OOm.>H HOO.H ONOH RON NNA H n H©~ a U WONAO h...‘.0.fi NH: Om NO: OH amm OO O c mmu.g HHOH OmwaOm OOOaOH Hm>.wm O:O.:m c OH OmOH OOH.OH OOn.OH HmO.OO :O:.:m OHO.OH Hux ONO.OH OOH.OH NOO.Hm :OO.:O OOO.MH meH HOOaOH OHHROH NHO.ON OOO.OO OHH.MH mmoH ONO.mH HOH.HH OOOnOO OOH.HO :HHnHH :mmH HMH.OH HO:.HH ONO. O OOOfimO OOH.HH mmCH :OO.OO Oom.mH mmH.mm O:>.OO OOOamH mmmH OO:.HH m»n.nH OmHaOm OOm.mm Ow>an ammm mmm.m ooo. mon.Hm mooama or? HH wa m ..H O ”HH . Omm.cx :x0.0 omcH OH OH pm OH OHO Hm .g‘ OOO,OH HLOH www.w wnr.am >OH.:N .mw. omOH mgm L .“ ONH x a; n \ H Wwou Ocmggso cHO ngm HO OH OHO.WW OmHamw OHOH Hm> Ocmmmpm HHOO Ocmppso cHO . O\ .L OHOH mUmL9 HHmumm msHm> ucmmmpm . AwHOHHOU ucmgpzo :Hv Hopm WQHLUCSGQ . ®3H6> Pcmwwfifl . 0 HHOU PCWLLSU CHV J)4 COHUOSLUWCOU U QDHNNV DCUWQLAW . .HOQV LCHLSpowuscmE d mCHEme Lamw x . .NOINHm . . 2 L: .m, rHO ®%Hs H m D m3 1 c .H no mpmmw mchHmme mflp.mmmcoHpma:Ooo msoHpm> cH pm . .‘ H megpm oncocH mgspsw O xpoz OHO mpomaxl w 3 Lu no QSHU c> UC®W®LQII.W HA. 6 Lqmib All-a. u¢nuw 182 pmwgmpcfi Low .HHH meqmzo mmm .mmHH go mocmpomaxm Ucm mpwg .sz>Hpowqm®L m 62w < xflncmaa< mmm wopmg pcmEmoHQEwc: Ucm mmwmz Hmsccm Umpoqum mo mmpwEHpmm co mpmu pom .pmpamco xmoHocpmz mgp CH cm>flw wmsHm> pcmwmpa Lou mmH5ELom mmm “mopzom mm.mm OOH.:: HOO.OHH OOO.OO OOO.mz OOOH OOm.mm HmO.H: OOOMOOH OMOMOO OOOMH: HOOH OO0.00 OHOAO: OOO HOH OOO OH mm» m OOOH OHO.OO HOH.H: m::.mOH OOOaOO Rpm.m: OOOH OOH.mn HO .O: OcmaHO OOOAMO OOO.H: OOOH HOH.:O Omm.O: HOO.OO Ozmnwm OOO.H: OOOH OOO.OO OHOnOm :OOnHO OOO.OO HOO.O: OOOH Hm>.Hn OO0.0M mmm.:x :moanH OO0.0m OOOH OOm.O: OOH.Om ON0.00 mm:.mO :Om.Om OOOH :OO.O: OHOaHm HOO OO OHM.OO OOH.Om mnOH mOO.H: OOH.OO OOH.OO OOH.OO OHH.Om OOOH OOO.$O OHm.~m OMH.OO OHm.OO mmmamm HmOH OOO.OM OOH.:m OHO.HO mmm.HO HOO.Om OOOH 183 OO.OOM OO.OOH O0.0:m O0.000 O0.000 OOOH OH.O:m O0.00m O0.000 OO.HHH ::.csx OOOH 20.5mm 50.0Im aa....HFO, ACUFTN ma.mfnfi \‘.:$H OO.OOm OH.mOm O0.0HO O;.r:m :3.Hmz OOOH OO.HOO mm.mmm mm.mmm OO.O;O mm.mHa IOOH OO.OOO O0.0HM OO.OOO a .HOO O0.00H OOOH :>.mmm Om.mmm OH.wa O:.H>u OO.HOH “OOH OO.HOO O0.000 0.0;O O0.0zu OH.OOH «OOH m .OOO O0.0mO OO.OOO OO.OOH mH.;OH HOOH >O.mOH rO.mmm 2%.: H OO.OgH H0.00H OOOH OO.HOH O.>Hm O0.00H OO.OOH O«.HO OmOH Om.OOH O0.000 OO.OOH HH.:xH Ha.xO LHOH O0.00H HH.HHm O0.00H L .OOH OO.OOH OMOH O0.00H O0.00H OH.OOH MOH.:HH OO.HH, OHJH OO.OOH OH.NOH «H.cmH mm.OaH OO.OO :NOH OO.OOH OO.HOH OO.OOH O0.0HH HH.OO OHOO O0.0mH O0.00H mfi.mHH O0.00 H0.00 meH O>.OHH OO.OOH OO.OO OO.OH OO.OO FOOH OH.OOH OO.OOH OO.OHH mO.:O OO.OO OWOH mm.mOH OO.OOH OH.OOH OO.OHH OO.HO OHOH OO.OOH am.OOH H:.nOH HH.OOO O:.HOH OOHH OH.OOH OH.OOH OH.OOH OH.HmH m:.OO OOOO O0.00H OH.OOH O0.00H OO.OOH OO.OO OOOO OO.HOH OO.OOH O0.00H a:.;HH H».OOH OHOH Om.»mH OO.HOH >5.00H m:.HmH O:.»O OOOO OH.OOH OO.:HH H:.H:H OO.OOO Om.OO :mcH O0.00H ::.OOH _O.O;O OO.O,H mO.HOH HOOH O0.00 OO.H:H aa.:wd OO.OOH OO.OO OOOH m.OOH hOOH Wm.mHO ::.:: O0.00 HOOH H0.00H O0.00H OO.OOH O;.HOH OO.OOH OOOH OO.OHH OO.OOH OO.OOH OHOOH O.H.OHH OHOH H0.00H OO.OHO Oz. OH OH.OOO OO.OOH OHOH OO.OOH OO.OOH OO.OOH OO.OOH OO OOH HHOH OOH n NHOH OOH u HHOH OOH n OHOO OOH u OHOH OOH u HHOH Lam» msHm> pcwmmpm msz> ucmmmpm mch> Hcmmagm 1:Hm> O: m;;a wsHmp ucmwtum Lo xofizH no xLfiOH no meLH Lo waH:« no xmrzp mumpb Hampmm mmHLtcsmH ccwpw LHmccc mzHaposL:cmr . MCHEme .NOIOHmH ..w .2 map :H muoHuwasuao njoHHu> :H andu vgp mm w..H :4 33Hw> Oslmmna mzp :pH3 Lmuno; 34c Lam: :: a mom Fabupm meoozH ¢O2L3L On counb ax; Lu LOHm> ucmuoLg go xmficHll.O .afizq . .,L 184 .xHOOOOOO OHOO O0 m OHOOO Hm.Ox: O0.00: O0.000 HO.OOO Hm. mm :O.mfi: oo.mw: Oh.wwm ma.am: ®M.MHM OO.OOO OO.OOO O0.000 H:.Om: O0.0Hm HH.OO: OO.OOH HO.HHO O .HO: HH.HOH OO.H:: O0.00: HO.HHO OH.HOM OH.OOH m:.::: :..m;: OO.OOO HH.OHH OO.OOH OH.Nm: >0.x:~ mm.wam :m.m©: am.acm OO.OOH OH.HH: OO.OHO HO.OO: OO.HOO OO.OOH OO.OHO OH.O~O am.mmm HO.OOO HO.OOO m..mm: Om.cnz Om.:Om O0.000 OO.OOm OO.OHO HO.OO: OO.OOm OH. Om m:.OOm OO.OH: OO.OO: H:.Onm O0.000 mO.mOO OO.OOH OO.OOO O0.0m: O0.000 \ OHf—‘J ““ ' v} T Ox p. L (‘\ Or%CJUM3U\ APPENDIX E 185 T. TABLE l.--Number of farm operators by age group in the U.S., 1920-1960. Farm Operators by age Total <25 25-3u 35-“4 “5-54 55-64 65+ Year (thousands) 1920 6,uu8 388 1,305 1,608 1,502 1,007 592 1930 6,289 384 1,085 1,50“ 1,512 1,103 701 1940 6,097 244 992 1,207 1,491 1,198 865 1950 5,379 175 '8uu 1,266 1,23“ 1,066 794 1960 3,933 65 428 858 1,047 851 683 187 .H mHOmeuum xHOcmOO< .mOOH .OpHmpm>HcO mumpm mcHHome appoz "mcHHome nppoz .cmeHmmv manocoom HOLSuHSoHLw< mo unmsppmamo on» on coppHEQSm mHmmnu .Q.cm cmanHnsoc: .mLOpwmeo ammm mo zHoasm one .3 .m .COpmczom "mopsom umm.aOa.O Ham.OOO.H mOO,OOO mmm,msm mHO.OOO HHH.:mm.H NOO.~OO.H OOOH OOH.mam.m Oma.Omm.H MOO.OHH.H amm.mOm.H OOO.HOm.H OO:.O~O.H mm0.0m=.m OOOH OOO.Omm.mH mmO,ONH.H OOO.mom.H OOO.mOm.H NOO.~OO.N OOO.OOO.m mam.OOH.m OOOH Osm.mam.mH OmO.OOH.H :ON.OON,H OmmaHOm.H HON.ONN.H mmm.amm.m emo.mmm.m OOOH OOO.HON.NH MOO.mmO.H OHH.mHm.H NOO.ONO.H mmm.~OO.H OOO.OmO.m Omm.OOO.m OMOH Hma.H~O.HH mmm,mam mom.OOO,H OOO.HOm.H OmO.OHO.H MOO,OHN.N Om~.Omm.m ONOH Hmpoe +mO :Oumm am-m: aa-mm am-mm mmv mmm an .mmHmE Spam HMpSL Um>fi>pzm .owmalommH ..m.D mgp CH asopw mmm an mmHmE Spam HOLSL cm>H>p3m mo mopmefipmmst.m mqm¢9 APPENDIX F 188 189 Refer to the equations 9—13 on page The equations notation. ‘F— 1 —b1 —b1 0 1 0 O O l A O O B O O L_ This matrix manageable form as determinant T— 1 —b1 -b1 0 1 O O O 1 O Abl Abl El Bbl Bbl (9-13) can be written in a matrix ._ T‘" _[ . .._., O 0 X1 [—0 —b2 0 X2 0 _ = O 0 b3 X3 1 0 X“ C l X 0 O - 1_ 5 J .L. _JL of coefficients can be reduced to a follows for easy calculation of the -—1r y—- —-r 'r— n 0 O X Om1 1 -b2 0 X2 0 ._ = O 0 b3 X3 1 O X“ C O 1 X 0 —-——J i'—‘ 5 .......n J...— —L 190 -r—- _ — F—-—'1 -'—-—‘P l O «bl blb2 0 X1 0 O l 0 -b2 0 X2 0 O O l O -b = 0 3 X3 0 O Abl (1+Ablb2) O X“ C “0 O Bbl Bblb2 1 _fi 1E5_1 L_D_i "r— 711”“ “m" l O O -blb2 —blb3 X1 1 O O l 0 —b2 0 X2 0 O O 1 O —b X = O 3 3 O O O (1+Ablb2)Ablb3 X14 0 O O O Bb b 1+Bb b X 0 12 l 5 1. :O’J LJ- 1.._L The determinant of the matrix of coefficients _ 2 D - (1 + Ablb2) (l + Bblb3) — ABblb2b3 = l + blb2A + blb3B D > 0 since bl < 0; b2 < O: A < O; B < O X=lC(1+Bbb)>O A D l 3 since C > O; B > 0, b1 < 0, b3 < O x =l(—CBbb) 5 D 12 = l CBb b < O D' 1 2 since D > 0, C > 0, B > 0, b1 < 0, b2 < O 1" w WT b L L 2 + = —. _ :— X2 X3 b2 + blb3 W2 b1b3 W2 D < O F F L. D .1 since D > O, b < 0 our