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U.S. farm numbers, sizes, and related structural dimensions

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U.S. farm numbers, sizes, and related structural dimensions projections to year 2000
Series Title:
Technical bulletin - Dept. of Agriculture no. 1625
Creator:
Lin, William
Coffman, George W. ( joint author )
Penn, J. B. ( joint author )
United States -- Dept. of Agriculture. -- Economics, Statistics, and Cooperatives Service
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[Washington]
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Dept. of Agriculture, Economics, Statistics, and Cooperatives Service
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English
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iv, 79 p. : ill. ; 26 cm.

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Farms -- United States ( lcsh )
Farms, Size of -- United States ( lcsh )
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bibliography ( marcgt )
federal government publication ( marcgt )
non-fiction ( marcgt )

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Bibliography:
Bibliography: p. 65-66.
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Issued July 1980.
Funding:
Technical bulletin (United States. Dept. of Agriculture) ;
Statement of Responsibility:
William Lin, George Coffman, J. B. Penn.

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U.S. FARM NUMBERS, SIZES, AND RELATED STRUCTURAL DIMENSIONS: Projections to Year 2000. William Lin, George Coffman, and J.B. Penn. National Economics Division; Economics, Statistics, and Cooperatives Service; U.S. Department of Agriculture. Technical Bulletin No. 1625.
ABSTRACT
The number of U.S. farms is projected to continue to decline through the end of the century--from 2.9 million in 1974 to 1.8 million in 2000. The proportions of small and large farms will change as well, with large farms increasing'and dominating agricultural production. Farm production, farmland, and farm wealth will become more concentrated; farm operators will rent more of their farmland and will produce more of their commodities under contractual arrangements with food processors. The projections are based on four analytical methods: trend extrapolation, negative exponential functions, Markov process, and age cohort analysis.
Keywords: Farm structure, Farm numbers, Farm sizes, Trend extrapolation,
Negative exponential functions, Markov process, Age cohort analysis,
Concentration of ownership, Specialization, Capital requirements.
The following reports published by ESCS also deal with the structure of U.S. agriculture.
Status of the Family Farm: Second Annual Report to the Congress.
AER-434. September 1979.
Structure Issues of American Agriculture. AER-438. November 1979.
Another Revolution in U.S. Farming? Lyle P. Schertz and others.
AER-441. December 1979.
ACKNOWLEDGMENTS
The authors acknowledge with thanks the comments and suggestions of
Emerson Babb, Dave Harrington, Levi Powell, Donn Reimund, Allen Smith, and Alan Walter. Tom McDonald edited the manuscript. Appreciation is also due Ronald Miller for his computation assistance for the negative exponential functions chapter, and Roy Hatch for his preparation of an earlier version of the Markov process chapter. Several technical support people made important contributions. They include: Dana Anthony, Carol Collins, Angie Kennedy, Virginia Minter, Terry Salus, Jennifer Reed, and Sandy Swingle.
Washington, D.C. 20250 July 1980




CONTENTS
Page
Summary. .. ........ .. .. .. .. .. .. .. .. .. .i.
Introduction .. ........... .. .. .. 1
Overview of Structure and Structural Change .. . ..... 3
Numbers and Sizes. .. ........ . .. .. .. .. .. . . 3
Concentration of Production . .. .. .. .#. .. .. .. .. 3
Concentration of Farmland Ownership .. ...... . #.. .. .. .. ..7
Form of Business Organization. . .. .. .. . .** . . . 8
Financial Structure. .. ........ . . .. .. .. .. .. ....9
Prospects for Farm Organization . . . . .. .. .. .. .. ....10
Numbers and Sizes .. .. ........ . . . . . . . 10
Concentration and Specialization of Production .* . .. .. .. 10
Concentration of Farmland Ownership . .. .. .. . .. .. .14
Form of Business Organization ... . . . .. .. .. .. 14
Financial Structure .. ................. .. .. ... 15
Age of Farm Operators and Replacement Rates . . . .. .. .. 15
Tenure of Farm Operators . . . . . . . . .. .. ..18
Trend Extrapolation .. ...... . . . .. .. .. .. .. .. .. 20
Technical Overview .. .. .. .. . .. .. .. . .* . 20
Data Adjustments . . . ... . . .. .. . . 20
Projections......... . ... .. .. .. . o.. 0 0. .. ....21
Negative Exponential Functions. ......... . .. .. .. .. . 24
Technical Overview .. ............ .. .. .. .. .. 24
Projections .. .. .. .. .. .. .. .. .. .. . . . 27
Markov Process . . .* . .. .... . . .. .. . . 33
Technical Overview. .. .. . .. .. .. . . . . . 33
Data Adjustments .. ......... . . . . . . .& . .1 34
Projections. ................. .. .. .. .. ... 36
Age Cohort Analysis ..... . .. .. ..... . 45
Technical Overview....... ..... . .. .. .. .. .. .. .. 45
Data Adjustments . . . .. . .*0. .. .. .. .47
Projections. .. .. .. ... . .. .. .. .. . . . . 47
Comparison of Alternative Projections .. ...... . . .. .. .. .. 54
Conclusions and Implications...... . . . . . 62
Literature Cited..... ... .. .. .. .. .............. 65
Appendices. .. .. . .. .. .. .. .. .. .. .. .. . . 67




SUMMARY
The total number of farms in the United States will decline from 2.9
million in 1974 to 2.1 million in 1990 and to 1.8 million in 2000 if present trends continue. The farms will probably be arranged in a bimodal distributioni--a large proportion of small farms, an ever-increasing proportion of large farms, and a declining proportion of medium-size farms. Small farms (gross sales of less than $20,000) will constitute about 50 percent of all farms in 2000, a decline from 72 percent in 1974, while the proportion of large farms (gross sales of more than $100,000) will increase from 5 percent to 32 percent.
The projections deemed most likely to be realized are summarized as follows:
Sales class 1974 1985 1990 2000
1,000 farms
Less than $20,000 2,070 1,416 1,193 889
$20,000 -$99,999 655 563 450 301
$100,000 -$499,999 139 290 358 344
$500,000 and over 11 51 88 .217
All farms 2,875 2,320 2,090 1,750
Much of the shift to larger farms will be due to the expected rise in t he index of prices received by farmers rather than a rise in the real output per farm. For example, the number of farms with sales of $100,000 or more is projected to increase four times between 1974 and 2000 in current prices compared with an increase of 2.7 times in that period if constant (1964 -)_prices are
-used. If the rate of price increases through the year 2000 is less than that projected, the numbers of farms in each sales class will change: the number offarms in the larger sales classes will be reduced and the number of farms in the smaller sales classes will be increased.
The decline in farm numbers and the increase in farm size will probably be accompanied by other changes in the structural characteristics of the U.S. farm sector. The highlights are:
*Agricultural production and farmland ownership will be dominated by fewer
and fewer farms. By 2000, the largest 1 percent of farms will account for
abot hlfof all farm production. By contrast, 50 percent of the
farms-the smaller ones--will produce only 1 percent.
; Almost two-thirds of the production will likely come from the largest
50,000 farms and nearly all farm products will be produced by the largest
1 million farms in 2000.




" By 2000, about 96 percent of total farm production is projected to. come from
farms with sales of at least $100,000. About 54 percent came from such large
farms in 1974.
* About 57 percent of the farmland will be operated by farms containing at
least 2,000 acres. The corresponding percentage in 1974 was 42 percent.
" Half of the farmland will be farmed by the largest 50,000 farms, and almost
all of the land will be operated by the largest 1 million farms.
* Capital requirements will rise to about $2 million of capital assets per
farm for farms with sales of more than $l00,000--nearly double what was
required in 1978.
* The accelerating capital requirements imply that the low-equity, young, potential farmers will have even more difficulty getting started in farming.
" Large capital requirements and large farms will tend to concentrate farm
wealth in the hands of a few. By 2000, two-thirds of the wealth in the farm sector will be in the hands of those who have an interest in farms
with more than $100,000 in sales.
" The number of new farmers under 35 years of age will shrink from 475,000 in
1964-74 to 284,000 in 1994-2004, a 40-percent decrease.
" The number of corporations in farming will continue to increase, while the
number of partnerships will decline. Multiownership farms (corporations
and partnerships) may account for half of all farm sales by the end of the
century. The number of corporations might nearly triple by that time; even if they did so, however, farm corporations would still constitute
less than 4 percent of the total farms.
" Part owners will account for a third of all farms by 2000 and more than
two-thirds of large farms (sales of more than $100,000). In 1974, part
owners accounted for 27 percent of all farms and 57 percent of large
farms. (Part ownership means that a farmer owns some farmland but rents
the remainder from others,.)
iv




U.S. Farm Numbers, Sizes, and
Related Structural Dimensions:
Projections to Year 2000
William Lin
George Coff man
A.B. Penn
INTRODUCTION
The U.S. farming sector has undergone significant structural changes over the past few decades, and is expected to continue changing. Perhaps the most obvious of the changes is in farm numbers and sizes. The Census of Agriculture counted 4 million farms in 1959 and 2.9 million in 1974; that number is expected to decline to 1.8 million in 2000. The average farm size is increasing as farm numbers decline, with the consequent concentration reflected in production. The largest 4 percent of the farms accounted for about a third of the value of farm products sold in 1959 and 43 percent in 1974. By 2000, the largest
1 percent of the farms will account for about half of all farm production. l/
This trend toward greater concentration--fewer but larger farms--is the result of the interaction of many factors: technology, economies of size, tax laws, returns to resources, price instability, operator's managerial ability, capital requirements, market conditions, farm programs, credit availability, exchange arrangements, government regulations, and the like. While it is recognized that these factors have immediate effects on the farm sector, their effects on the structure of agriculture are of a longer term nature.
1/ The projections in this report are based on historical data--up to and including data from the 1974 Census of Agriculture, the most recent available. Another Census of Agriculture was conducted in 1978, but data from that census are not expected to be fully compiled and available until late 1980.
1-




Thus, an interesting question is: What will the farm structure of the future be, barring major shifts in the course of events or the underlying causes? This report addresses that question by using four analytical methods (trend extrapolation, negative exponential functions, Markov process, and age cohort analysis) to project future farm numbers and sizes.
These methods are compared and evaluated in terms of the accuracy of their projections. From this examination, a set of most likely projections was selected, and the implications of the projections for size-related structural dimensions examined--how they relate to current structural concerns, including the concentration of production, control of land resources, form of business organization, barriers to entry, capital requirements, distribution of wealth, separation of resource ownership and use, contracting arrangements, and farm specialization.
The projections presented are not forecasts; that is, they are not best judgment estimates of what will actually exist at the turn of the century.
Rather, they are most useful as providing a boundary notion of where the present trends are likely to lead, in the absence of significant changes in the underlying forces. It is certain, however, that changes not yet anticipated will occur.
The projections and implications presented here, even with their acknowledged limitations, may prove useful for long-term planning by agribusiness, academicians, and government institutions. Agribusiness may find them useful for planning business activities related to input supply and product processing. The projections may also suggest research and extension activities. Government may find the projections of use for planning research, for projecting revenues and expenditures, and for examining long-term public policy options to influence the structure of agriculture.
2




OVERVIEW OF STRUCTURE AND STRUCTURAL CHANGE
This chapter describes the current situation for some elements of the structure of U.S. agriculture and recent changes in structural characteristics, emphasizing those related to size. The reader then can compare the current situation with that projected for the future described in the next chapter.
The land in farms declined only slightly between 1940 and 1974, but that relatively constant land base was occupied by fewer and fewer farms. Thus, the average farm size increased by one-third between 1940 and 1974. This change-also implies increasing concentration of production and control of land resources into fewer and fewer hands.
Contrary to frequent assertion, the remaining farms, although larger, continued to be family-operated farms. Corporations still had an insignificant role in farm production and in farmland ownership. The average age of farm operators did not change noticeably from 1969 to 1974. Big farms appeared to have an edge over small farms in net farm income, payments from Government farm programs, and capital gains on farm physical assets. In 1969, off-farm income per farm was about the same for the very large and small farms. The situation differed significantly in 1974, however. Off-farm income per farm almost doubled for small farms, but no appreciable change was evident for large farms.
Although this study focuses on farm numbers and size, there are other important structural characteristics related to size, such as concentration ofproduction and farmland, form of business organization, age and tenure arrangments of operators (discussed in the next chapter), and financial structure.
Numbers and Sizes
The land in farms increased slightly after 1940, but declined somewhat between 1950 and 1974. The number of farms, however, decreased by 60 percent while the average size(measured by acres) increased by 128 percent (table 1). The decline in the number of small farms perhaps contributed most to the increase in average size. Historically, the number of farms with less than 500 acres has steadily declined, while the number with more than 500 acres has increased (table 2). The decline in farm numbers since 1959 has been at a lower rate than that from 1940 to 1959. Many farmers left voluntarily for better opportunities in the nonfarm sectors; others who retired or died were not replaced by new farmers. The remaining farmers were often motivated by prospects of increased returns by enlarging their lands or consolidating their operations with neighboring ones. The historical trend when farms are measured by gross sales is similar to that for acreage sizes (table 3).
Concentration of Production
A major aspect of the public concern about farm structure is the concentration of farm production and control of the Nation's land. The concentration of farm production between 1969 and 1974 is shown graphically by the Lorenz curve in figure 1 (tabular data are in app. table 1). In 1969, the largest 24 percent ~of3




Table 1--Number of farms, land in farms, and acres per farm
Year Number : Land in farms Average size
1,000 Million acres Acres
1940 6,102 1,065 175
1945 5,859 1,141 195
1950 : 5,388 1,161 216
1954 4,782 1,158 242
1959 3,711 1,124 303
1964 3,158 1,110 352
1969 2,730 1,063 389
1974 l/ 2,466 1,026 416
l/ Not adjusted for census underenumeration.
The number of farms reported by the.Bureau of the Census is
based on the 1959 definition of a farm: any place from which $250
or more of agricultural products are sold, or normally would have
been sold, during the census year, or any place of 10 acres or
more from which $50 or more of the agricultural products were
sold, or norn~ally would have been sold, during the census year.
The definition was changed in 1974 to exclude places with
less than $1,000 of gross receipts in the census year. The effect of this change was to reduce the number of farms in 1974
from the 2.5 million to 2.3 million.
Source: U.S. Department of Commerce, 1974 Census of Agriculture,
Vol. II, Part 2, June 1978.
the farms produced 80 percent of the total output. In 1974, only 20 percent of the farms were required to produce the same output. In other words, 80 percent of-the output came from 655,000 farms in 1969 and from 493,000 farms in 1974. The shift of the Lorenz curve to the right illustrates this further concentration of production.
The increasing concentration of production on larger farms carries implications beyond just the numbers. Larger farms are becoming more involved with vertical integration and contractual arrangements; such arrangements suggest that farm management decisions may gradually become controlled by the nonfarm sector.
While the concentration of total farm production increased, the, extent
of that concentration varied widely among farm commodities. Vegetable, poultry, nursery, and greenhouse farms were more concentrated than other types of farms in 1969 (table 4). In addition, considerable increase in concentration occurred in grain, cotton, and dairy industries. Production of tobacco and forest products, as in the past, was not dominated by big farms. The same pattern of concentration was evident in 1974.
4




Table 2--Number of farms, by size of farm l/
Size of farm 1974 1969 1964 1959 1954 2/ 1950 1945 2/ 1940 1935 2/
Number of farms
1 to 9 acres 168,925 162,111 182,581 244,328 484,291 488,530 594,561 509,347 570,831
10 to 49 acres 453,690 473,465 637,434 813,216 1,212,831 1,479,596 1,654,404 1,782,061 2,123,595
50 to 69 acres 160,702 177,028 211,398 258,195 346,323 427,025 472,415 510,585 581,352
70 to 99 acres 244,494 282,914 331,032 399,795 517,740 621,050 684,905 780,743 862,655
100 to 139 acres 235,056 278,752 324,652 394,505 491,458 579,244 633,851 688,479 754,076
140 to 179 acres 217,826 263,012 308,288 378,003 461,651 523,659 565,958 621,578 683,941
180 to 219 acres 137,591 165,209 191,254 225,576 257,189 275,049 282,839 279,577 294,309
220 to 259 acres 118,346 141,733 164,188 188,899 206,509 212,344 210,376 206,759 212,238
260 to 499 acres 365,369 419,421 451,301 471,547 482,246 478,170 473,184 459,003 473,239
500 to 999 acres 208,375 215,659 210,437 200,012 191,697 182,297 173,777 163,711 167,452
1,000 to 1,999 acres 93,203 91,039 84,999 136,427 130,481 121,473 112,899 100,574 88,662
2,000 acres and over 62,546 59,907 60,293
All farms 2,466,123 2,730,250 3,157,854 2,610,503 4,782,416 5,288,437 5,859,169 6,102,417 6,812,350
l/ No adjustment for the undercounting of farm numbers by the Census Bureau was made.
Z/ Alaska and Hawaii not included.




Table 3--Number of farms, by sales class, selected years 1/
Sales class 1974 1969 1964 1959 Sales class 2/ 1954 1950
Number N.rumber
Less than $2,500 768,838 994,456 1,338,239 1,637,849 Less than $1,200 462,427 717,201
$2,500-4,999 289,983 395,104 443,918 617,677 Part-time 574,575 639,230
$5,000-9,999 296,373 390,425 504,614 653,881 Residential 878,136 1,029,392
$10,000-19,999 310,011 395,472 467,096 483,004 $1,200-2,400 763,348 901,316
$20,000-39,999 321,771 330,992 259,898 210,402 $2,500-9,999 811,965 882,302
$40,000-99,999 324,310 169,695 110,513 82,120 $5,000-9,999 706,929 721,211
$100,000-199,999 101,153 35,308 21,148 14,201 $10,000-24,999 448,945 381,151
$200,000-499,999 40,034 12,608 7,760 4,570 $25,000 and over 134,003 103,231
$500,000 and over 11,412 4,079 2,493 1,208
All farms 2,463,885 2,728,139 3,155,679 3,704,912 All farms 4,783,021 5,379,250
1/ No adjustment for the undercounting of farm numbers by the Census Bureau was made. 2/ The sales classification was changed after 1954 by the U.S. Census Bureau to more adequately reflect need of users.




Concentration of Farmland Ownership
Concentration of farmland operations did not change greatly between 1969 and 1974. Eighty percent of the farmland was operated by the largest 28 percent of the farms in 1969 and the largest 23 percent in 1974 (fig. 2). This means that 80 percent of the farmland was operated by 600,000 farms in 1974. Conversely, the other 1.9 million farms controlled the remaining 20 percent of the farmland.
The concern over control of the land goes beyond the domination of large
farms. It includes the extent of foreign ownership of farmland, corporate ownership, and absentee ownership in general. According to a *1978 U.S. landownership survey by the U.S. Department of Agriculture, foreigners owned 0.1 percent of all land, although the percentage varied widely in different parts of the country (19~). 2/ About 30 percent of farm and ranch land was owned by only 1 percent of the landowners. Most owners were white males between the ages of 50 to 64. Sole proprietors and husbands and wives held almost three-fourths of the land in farms and ranches. Corporations held about 9 percent of farm and ranch land and nonfamily corporations held only 2.4 percent. Less than one-half of 1 percent of American farmland was owned by foreigners or U.S. corporations with 5 percent or more foreign ownership.
2/ Underscored numbers in parentheses refer to items listed in the Literature Cited, beginning on p. 65.
Figure 1 Figure 2
Concentration of Farm Concentration of Farmland
Production in the United States, among Farms, 1969 and 1974
1969 and 1974
______________Percentage of land in farms Percentage of sales
80
80
60
60
40-1994
20 20V417
20 40 60 76 80 100 0 20 40 60 707780 100
Percentage of farms Percentage of farm numbers
7




Form of Business Organization
Contrary to common assertion that corporations are taking over farming today, the Census of Agriculture data clearly show that noncorporate farms continue to be the dominant form of business organization. Corporations were still relatively insignificant in farm production and control of the land. Moreover, more than 90 percent of the farm corporations were family-held or closely-held corporations (16 or fewer stockholders).
Corporate farms (including the family-held corporations) constituted 1 percent of the total number of farms in 1969 and 1.7 percent in 1974. These were, however, relatively large farms. The average size of corporate farms was about 3,400 acres in 1974, eight times larger than the average sole proprietorship farm. Corporate farms constituted 4 percent of the 493,000 farms which produced 80 percent of the total farm production in 1974. Overall, corporations produced 18 percent of the value of agricultural sales in 1974.
The amount of farmland controlled by corporations has never been significant and it is unlikely to become so in the near future. In 1969, corporate farms controlled about 8 percent of all farmland; that control rose to 10 percent in 1974. By comparison, the amount controlled by sole proprietorships increased from 74.5 to 76.9 percent over the same period. Farms organized as partnerships appeared to lose ground, both-in terms of total farm numbers and control of farmland. During the 1969-74 period, the proportion of partnership farms declined from 11 to 7 percent; control of farmland by partnership farms declined from 17 to 13 percent.
Table 4--Concentration of production by type of farm
*Percentage of val ue of products
* sold by class 1 farms I/
Type of farm
1969 1974.
Percent
Cotton and cottonseed 56.5 85.4
Dairy 42.2 74.5
Field seeds, hay, forage silage 41.5 64.5
Forest products 36.6 53.4
Fruit, nuts, and berries 68.9 82.8
Grain 38.9 75.0
Livestock 61.1 78.9
Nursery and greenhouse 85.5 90.2
Other field crops 73.5 94.1
Po ultry 82.9 96.2
Tobacco .21.0 46.1
Vegetables, sweet corn,-and melons 82.6 91.3
1/ "Value of products" refers to the total value of products sold by faTns having $2,500 or more of sales. Class 1 farms were defined by the census as those with sales of $40,000 and over.
8




Financial Structure
Farm income, off-farm income, and government farm program payments constitute the major components of net income per farm (app. table 1). As would be expected, large farms had a considerably larger amount of net farm income, government farm program payments, and capital gains on farm physical assets than small farms. Although the significant reduction in Federal farm program payments in 1974 made the differences proportionally less obvious, a recent ESCS study reaffirms what is widely known about the programs--that benefits are closely proportional to production volume: the larger farms, although few in numbers, have the highest production and thus receive a disproportionate share of the program benefits (24). Of $2 billion in program payments in 1978, almost half the payments went to only 10 percent of the participants, those with the largest farms. By contrast, 50 percent of the farms--the smaller units--received only 10 percent of the payments.
In 1969, the amount of off-farm income per farm for farms with sales of more than $100,000 and less than $2,500 were about the same. This changed drastically, however, in 1974. Off-farm income per farm in sales classes of less than $2,500 almost doubled, while no significant change occurred in the top sales classes. In fact farmers in sales classes of less than $40,000 all increased their offfarm income significantly. Preliminary data indicate that this trend continued into 1978. This suggests that small farmers are supplementing their family income through off-farm employment and investment, and that off-farm income has become more important as a source of farm family income.
Another characteristic of agriculture is the increasing ratio of debts to
assets as farm size increases. In 1969, farms with sales of $20,000 or less had a ratio of 13.2 (13.2 cents of debts for each $1 of assets); farms with $100,000 or more of sales had a ratio of 24.6. By 1974, the ratio for small farms had decreased, while the ratio increased to 30.2 for the largest farms.
9




PROSPECTS FOR FARM ORGANIZATION
This chapter summarizes the projections to indicate where the future U.S.
farm numbers and sizes are heading, and the size-related implications pertaining to the structure of U.S. farming in the following categories: concentration of farm production, contracting arrangements, specialization in farm production,. concentration of farmland, form of business organization, capital requirements, distribution of wealth, age of operators and replacement rates, and tenure of farm operators.
Numbers and Sizes
The most reliable of the projections, which are described in more detail in ensuing chapters, suggest that farm numbers are likely to decline from 2.87 million in 1974 to 2.32 million in 1985, 2.09 million in 1990, 1.89 million in 1995, and 1.75 million in 2000.
The projections further reveal that future farm numbers are likely to follow a bimodal distribution--a large proportion of small farms, an ever-increasing proportion of large farms, and a declining segment of medium-size farms (fig. 3). By 2000, small farms (less than 220 acres) are projected to account for about 65 percent of the total, a slight decrease from 70 percent in 1974. By contrast, large farms (1,000 acres and over) are projected to account for about 10 percent, double their proportion in 1974 (table 5). %nen sales are used as the size measure, small farms (sales of less than $20,000) are projected to account for about 50 percent, a decrease from 72 percent in 1974. On the other hand, large farms (sales of more than $100,000) are projected to increase from 5 percent in 1974 to 32 percent in 2000 (table 6). The number of farms in the $l00,OOO-to-$199,999 sales class is likely to begin declining by the turn of the century, indicating that a farm with sales of $100,000 may not be an economically viable unit in farming.
Of course, the number of farms would be still lower if the new definition of a farm, which requires minimum sales of $1,000,. were applied (see table 1 footnote for new and old definitions of a farm). Using the new definition, farm numbers are likely to decline from the 2.37 million in 1978 to 2.05 million in 1985, 1.85 million in 1990, 1.66 million in 1995, and 1.54 million in 2000. The difference in the number of farms between the new and old definitions is the number of farms included in the lowest sales class (less than $2,500) by the old definition, but excluded by the new definition.
Concentration and Specialization of Production
One direct and important implication of the projections is the further concentration of agricultural production. In 1974, about half of the total farm cash receipts were received by farms with sales over $100,000. About 30 percent of the total farm production was produced by the largest 50,000 farms (2 percent of the total farms) and 60 percent by the largest 200,000 farms (7 percent of the total). Projections show that this pattern is likely to continue to 2000, and that big farms are likely to control agricultural production even more so than in the past. By 2000, about 96 percent of the total production is projected to
10




Table 5--Most likely projection of the nuber of farms, by size of farm
Actual
Size of farm 1974 1985 1990 1995 2000
1,000 farms
1-99 acres : 1,356.9 1,096.2 989.6 894.9 826.9
100-219 acres 649.9 475.6 404.4 345.9 301.9
200-499 acres 502.1 387.4 338.6 295.8 264.3
500-999 acres 210.7 201.8 193.3 187.1 182.9
1,000-1,999 acres 93.3 97.4 98.2 100.2 102.4
2,000 acresand over 62.0 65.0 65.8 67.1 70.9
All farms 2,874.9 2,320.0 2,090.0 1,890.0 1,750.0
Table 6--Most likely projection of the number of farms, by sales class
Act ual
Sales class 1974 1985 1990 1995 2000
1,000 farms
Less than $2,500 1,100.6 793.5 752.4 723.0 603.7
$2,500-9,999 642.4 421.1 296.8 211.7 185.5
$10,000-19,999 326.9 201.8 144.2 94.5 99.8
$20,000-39,999 327.6 204.2 158.8 111.5 87.5
$40,000-99,999 327.5 358.4 291.6 233.4 213.5
$100,000-.199,999 99.4 190.2 211.1 193.7 161.0
$200,000-499,999 39.3 99.8 147.3 176.7 182.5
$500,000 and over 11.2 51.0 87.8 145.5 216.5
All farms 2,874.9 2,320.0 2,090.0 1,890.0 1,750.0
11




come from farms with sales of at least Figure 3
$100,000. This means that the 50,000 largest farms will probably produce Distribution of Farm Numbers by
almost two-thirds of all agricultural Sales: Actual 1974 and Projected for products, and the largest 1 million 2000
farms (57 percent of the total) will produce almost all agricultural pro- Million farms
*ducts (table 7). 3/ 17
Concentration of farm production
can further be put into perspective by a Lorenz curve (fig. 4). In 1974, the largest 20 percent of farms produced 1.5
about 80 percent of farm production. By 2000, the same percentage of farm production will likely come from the largest 12 percent of farms. More dramatically, about half the production will likely be produced by the largest 1 percent of farms. By con- 0
trast, 50 percent of the farms--the1. smaller ones--will produce only about
1 percent of the production.
Concentration of production is also related to two other structural factors: co ntractual arrangements 0.5
and the economic advantages of different sizes of firms for various commodities.
ContractingArrangements 0
Agricultural production under 1.0
contractual arrangements has in- 2000
creased gradually. The percentage of farms having contracts increased from 4.5 percent in 1960 to 9 percent in 1974. Furthermore, the proportion of farms having contracts
was much higher for large farms:0. the proportion of small farms (less than $20,000 in sales) having contracts in 1974 was less than 5 per3/ The concentration of agricultural production differs from com- 0
modity to commodity. Industries such Less Than $10,000- $40,000- $200,000
as egg, poultry, and sugarcane may $10,000 $39,999 $199,999 or more
actually have higher concentrations Sales groups
than the aggregate portrayed in table 7. _________________12




Figure 4. cent, while the proportion was more
_______________________________than 30 percent for large farms
Concentration of Farm ($100,000 sales or more).
Production in 1974, 1985, The projected increase in farm
and 2000 size by 2000 indicates that more
_______________ farms perhaps as many as a quarter Percentage of sales to one-third of all farms, will mar..1974 ket their products under contractual
-- 1985 arrangements. Virtually all produc80.. 2000 tion of sugarbeets and dairy products
are now marketed under contractual arrangements. By 2000, contracts are 60 -likely to increase in marketing
I: vegetables, fruits, cotton, and
1 poultry and poultry products. 40
Size Variability by Commodity
20
Historically, some farm commodities have been dominated by large farms, and others by small farms
0 20 40 60 80 100 (table 4). The changes in the farm
Percentage of farms sector reflected by our data suggest
that farm production of vegetables and poultry will continue to be dominated by large farms. Other industries, such as livestock and cotton, which have recently become much more concentrated, are likely to be dominated by large farms in the future.
Table 7--Comparison of historical and projected concentration of production, by sales class and largest farms
Sales class Cash receipts by the
Year: : :largest
: $500,000:$100,000 to :$20,000 to :Less than :50,000: 200,000 :1 million
: and over: $499,999 :$99,999 :$20,000 :farms: farms :farms
Percent
1969 : 19.5 14.1 42.6 23.8 30 50 89
1974 : 31.2 22.5 36.0 10.3 31 57 94
1985 : 47.1 34.0 15.7 3.2 54 72 98
2000 : 77.3 18.5 3.6 .6 63 78 99
1/ Concentration of production is expressed by the percentage of cash receipts produced by farms in a given size class; the size of farms is ranked by sales recei pts.
13




Concentration of Farmland Ownership
Related to the concentration of production is the concentration of farmland. About 42 percent of the farmland was operated by farms having at least 2,000 acres in 1974. That meant that 35 percent of the farmland was operated by the largest 50,000 farms (2 percent of total), and 58 percent of the farmland was operated by the largest 200,000 farms (7 percent of total). The projections show continued concentration of land resources among the big farms. About 57 percent of farmland is projected to be operated by farms with 2,000 or more acres in 2000; less than 10 percent of the farmland will be in farms with less than 220 acres (table 8). Thus, half of the land will be farmed by the largest 50,000 farms (3 percent of total) and almost all farmland will be operated by the largest
1 million farms (57 percent of total).
Form of Business Organization
The number of corporations in farming is expected to continue to increase while the number of partnerships will decline slightly. Overall, the sales of multiownership farms (corporations and partnerships) could account for half of the farm sales before the end of the century. The number of corporations is projected to nearly triple, but still account for less than 4 percent of the farms.
Most of these multiownership farms will likely continue to be multifamily
farms. Most new corporations will likely represent the incorporation of existing farms rather than the entry of corporations not now farming. In fact, the number of corporations could well exceed the present trends because of changes in income tax laws, more rapid rise in asset values, and new technology. Few nonfarm corporations are likely to be attracted to farming unless the profitability of farming improves greatly.
Table 8--Comparison of historical and projected concentration of U.S.
farmland, by size of farm
Farmland operated by
Size of farm the largest
Year:::
:2,000 :1,000 acres: 220 acres : Less : .. 1
:acres : to : to : than :50,000:200,000 : million
:and over:l,999 acres: 999 acres :220 acres: farms: farms : farms
Percent
1969 : 42.8 11.6 31.1 14.5 30 50 80
1974 : 45.7 12.4 29.4 12.5 35 58 88
1985 : 47.7 13.6 27.0 11.7 40 65 93
2000 : 56.6 14.1 20.8 8.5 50 74 98
14




Financial Structure
Farms with sales of $20,000 to $99,999 required about $390,000 worth of physical and financial assets in 1978. Capital requirements were more than $1 million per farm for farms with sales of more than $100,000. Increasing farm7land value and farm machinery costs will make capital requirements for farming even higher in the future. If the trend of asset-sales ratio continues, farms with sales of $20,000 to $99,999 will have assets valued at nearly $1 million per farm by the year 2000 (table 9). This is nearly triple what was required in 1978. More important, economically viable farms probably will require assets valued at almost $2 million per farm--nearly double what was required in 1978.
Much of the increase in asset values will likely result from appreciation, especially in land values. Some additional expansion of equity would arise from reinvestment of savings from income flows. These increases in equity could provide a base for additional debt. The increased debt and equity could be used to purchase more land and other capital'items. Such soaring capital requirements in farming create barriers to entry, especially for low-equity, young, potential farmers.
The change in farm structure in the future will have a far-reaching effect
on the distribution of wealth among farms and households that have an interest in farming.
Capital assets were dispersed about evenly among various sizes of farms in 1978--one-third each for farms with sales of: (1) less than $20,000,_,(2) $20,000 to $99,999, and (3) more than $100,000. The average farm required assets valued at about $267,000. By 2000, about two-thirds of the farm assets will go to farms with sales of more than $100,000, with the remaining one-third spread evenly among farms of less than $20,000 in sales and those with $20,000 to $99,999 in sales. Farm assets for all farms will -average about $930,200--more than triple the 1978 figure. By 2000, two-thirds of the wealth in the farm sector will be in the hands of these farms with more than $100,000 in sales.
Age of Farm Operators and Replacement Rates
The average age of farm operators is projected to drop from 51.9 in 1974 to 50.2 by 2004 (table 10). Although this is counter to the trend up to 1974, the shift in average age reflects the higher actual entry rate of young people in the 1964-74 period. By 2004, these operators will be the middle age group, resulting in an increase in the number of farm operators in the 35 to 54 age range--from 43 percent in 1974 to nearly half in 2004. By contrast, a slight decline in the proportion of operators 55 years of age and over is projected. The projected decline in the average age of farm operators is counter to the trend observed through 1974, although the increase in average age from 1969 to 1974 was barely noticeable--from 51.2 in 1969 to 51.7 in 1974. Similarly, the percentage of farmers 55 years and over (and probably approaching retirement) increased, with the increases being especially significant in the large sales classes.
As farms become fewer and larger, fewer new farmers are needed to replace existing farm operators on adequate size farms. Therefore, the total number of net entries by persons under 35 years of age is projected to shrink from 475,000
15




Table 9--Balance sheet of the farming sector, by sales class
Item Unit : Less than $20,000 $20,000 to $99,999 : $100,000 and over : All farms
Total
Farm assets:
1978 M il. dol. :218,512 278,096 216,357 712,965
2000 do. 273,238 292,027 1,062,600 1,627,865
Debt/asset ratio.
1978 : Percent :9.5 17.8 22.7 16.7
2000 do. :6.3 17.0 26.0 21.1
Farm debt:
1978 Nil. dol. 20,E60 49,468 49,145 119,273
2000 do. :17,214 49,645 276,276 343,135
S Equity:
1978 M il. dol. 197,852 228,628 167,212 593,692
2000 do. :256,024 242,382 786,324 1,284,730
Distribution of
equity:
1978 : Percent :33.3 38.5 28,2 100.0
2000 do. :19.9 18.9 61.2 100.0
Per farm
Farm assets:
1978 : 1,000 dol. :123.3 390.0 1,157 266.8
2000 do. :307.4 9,701.9 1,894.1 930.2
Farm debt:
1978 : 1,000 dol. :11.7 69.4 262.8 446.6
2000 do. 19.4 164.9 492.5 196.1
Farm equity:
1978 : 1,000 dol. :111.7 320.7 894.2 222.2
2000 do. :288.0 805.3 1,401.6 734.1




in the 1964-74 period to 284,000 during the 1984-2004 period, a 40-percent decline in entries.
Since only a few large farming operations will be required to produce the
total farm output, many of the younger entries will be on small, part-time farms, and will depend primarily on nonf arm income sources. Expectations of nonf arm income will likely encourage young people associated with what are now marginal or inadequate size farms to choose nonfarm occupations. Therefore, farm numbers will continue to decline as fewer young people enter farming to replace older operators who leave farming.
The replacement rate of young for old operators has been considerably higher for larger farms with sales exceeding $100,000 (table 11). But since there were so many more small farms, 90 percent of the entries from 1964 to 1974 were on farms with sales less than $100,000. By 2000, however, only about half of the entries will be on such smaller farms.
Many of the small farms of retiring farm operators will be consolidated into existing farms, increasing the-proportion of large farms. These large farms will require significant amounts of'.capital. Therefore, the farming opportunities will be limited to a few entries on larger farms. Many of the younger persons entering farming will probably do so on established farms as partners or shareholders with-other family members.
Table 10--U.S. farm operator age distribution
Age 1974 1984 1994 2004"
Percent
Less than 25 years 2.2 2.0 1.8 2.1
25 to 34 years 10.9 13.5 11.0 11.2
35 to 44 years 17.8 19.4 24.5 21.2
45 to 54 years : 25.3 22.0 23.5 28.2
55 to 64 years 25.3 24.1 20.6 21.6
65 years and older 18.5 19.0 18.6 15.6
Total 100.0 100.0 100.0 100.0
Years
Estimated average age 1/: 51.9 51.2 50.8 50.3
1/ The weighted average was calculated from the age distribution by
muTtiplying the weighting factor (the fraction of the farmers in each
age group) by the midpoint of each age group. For the youngest age group,
the assumed midpoint was 22; for the oldest age group, the assumed midpoint was 71.
Source: Adjusted 1974 Census of Agriculture and age cohort projections.
17




Tenure of Farm Operators
Tenure patterns in farming have changed. Part6-owner-operators have increased as a percentage of all farmers. The proportion of full owners has declined only slightly, while the percentage of tenant-operated farms has declined significantly.
The proportion of tenants in each sales class and for all farms decreased from 1969 to 1974, reflecting farmers' long-held desire to acquire farmland and the ability to do so. But at the same time, the proportion of full owners declined only slightly. In 1974, 62 percent of farms were classified as full owners, 27 percent as part owners, and 11 percent as tenants. Full owners mostly dominated in farms with sales of less than $20,000 (73.4 percent), and accounted for less than one-third of the farms with sales of more than $100,000. By contrast, part owners were the majority in farms with sales of more than $100,000-accounting for nearly 60 percent (table 12).
This trend in resource ownership structure is projected to continue into the future. Part owners are likely to account for more than one-third of all farms, while the share of tenants will decline from 11 percent in 1974 to 7 percent in 2000. The share of full owners is likely to remain the same. Full owners will be concentrated mostly in small farms and will account for only 16 percent of
Table 11--Farm operator replacement rates
Item 1964-74 1974-84 1984-94 1994-2004
Percent
Replacement rate on farms
with sales of: 1/29292314
$100,000 or m-ore29292314
less than $100,000 44 47 42 32
Total 51 56 63 53
Thousands
Net entry of operators
under 35 years 475 452 405 284
Net exit of operators
over 55 years 930 811 650 537
1/ Percentage of exiting operators over 55 years of age replaced in the foTlowing decade by entering operators under 35 years at the beginning of the decade.
Source: Adjusted 1974 Census of Agriculture and Projection. See text
for details.
18




farms with sales of more than $100,000. Part owners, on the other hand, will
account for about 72 percent of farms with sales of more than $100,000.
Ownership and use of farmland, therefore, will be separated more than is the case now. Farmers will be more likely to rent additional farmland to enlarge their farming operations.
Table 12--Tenure structure by sales class
* Less $20,000 :$100,000 :
Item than : to and :All farms
*$20,000 $99,999 over
Percent
Full owners:
1964 61.8 31.5 34.2 57.9
1969 69.4 35.1 35.3 62.5
1974 74.3 39.3 29.3 61.5
2000 93.0 59.0 16.0 63.0
Part owners:
1964 : 21.7 50.3 51.6 24.9
1969 26.9 47.8 51.4 24.6
1974 16.6 44.8 57.2 27.2
2000 : 4.0 28.0 72.0 30.0
Tenants:
1964 16.5 18.1 14.1 17.2
1969 : 17.1 17.1 13.3 12.9
1974 : 9.1 15.9 13.5 11.3
2000 : 3.0 12.0 12.0 7.0
19




TREND EXTRAPOLATION
This chapter describes the projections obtained from simple extrapolations of trends, and the adjustment of the census data to take account of overenumeration and underenumeration. Again, the central question is: If we assume that the current trends are going to continue into the future, what will the structure of agriculture likely be by the year 2000?
Technical Overview
The functional specification for projecting the number of farms in each acre size and sales class was selected on the basis of the R2 (coefficient of determination) goodness-of-fit criterion, consistency, reasonableness in comparison to the past trend, and, to some degree, our own subjective judgment. To illustrate, a linear trend equation was rejected because: (1) the linear specification frequently projected a much faster rate of decline in farm numbers than one would normally expect. In fact, a linear equation will project the number of farms in the 100-219 acres class to completely disappear by the late 1990's and to be negative in the year 2000; and (2) this form did not generally yield a higher R2 than a semilog specification, the form eventually selected. Conversely, a polynomial specification was rejected for the opposite reason--it frequently projected trend reversal. Instead of a decline in the number of farms in the l-to-99-acre size class, it projected an increasing trend into the future.
This left a choice between the log-linear and the semilog forms. The semilog form was chosen because it generally gave a better fit in terms of the R2 criterion, and it produced expected results better than the log-linear form. For example, the number of farms in the l-to-99-acre size group historically had declined at a high rate--311,O00 farms between 1959 and 1964 and 133,000 between 1969 and 1974. If this trend continues, one would reasonably expect the number of farms in this size group to decline from the 1.36 million in 1974 to about 1.2 million in 1980. Yet, the log-linear specification would project virtually no decline. For similar reasons, we chose the semilog form to project the number for sales classes of less than $20,000, and the log-linear form for sales classes of more than $20,000.
Data Adjustments
The data used throughout this study came primarily from the 1974 Census of Agriculture and earlier censuses; data from other sources are specifically noted. Because of incomplete counting in the census and the importance of capturing the effects of changes in commodity prices on shifts in farm numbers from one sales class to a higher one, adjustments were made to the data used in this study to account for underenumeration and overcounting, and for the effects of price inflation. No adjustments were made to the data for trend projections because the effects of price inflation were assumed to be captured in the trend equations. However, this adjustment was explicitly made for the Markov process and age cohort projections discussed subsequently.
20




Prior to 1969, all censuses were conducted by personal interview in a complete canvass of rural areas. In 1969, a mailout-mailback, self-enumerated national census was conducted. The change in survey procedure, along with other factors, contributed to the underenumeration problem, that is, an incomplete farm count, espe'cially for small farms (26). Conversely, overcounting sometimes occurred for large farms.
Without adjustment of the census data to account for underenumeration and occasional overcounting, the number of farms reported differs considerably from another primary data source, namely the Farm Income Statistics of the U.S. Department of Agriculture (23). For example, the Farm Income Statistics reported 2.8 million farms in 1974 while the Census of Agriculture estimated 2.47 million farms, a difference of 330,000 farms. 4/ To avoid confusion and maintain the comparability of the census data with _USDA estimates, it was necessary to adjust the census data.
The detailed adjustment process for the 1974 Census of Agriculture data by sales class and acre size is shown in append 'ix tables 2 and 3. In general, the adjustment process for acres and sales was te same. However, slight differences result from the nature of the census data. Abnormal farms are reported separately by sales class, but are included in the number of farms by acreage. 5/ Since abnormal farms could be expected to respond quite differently from normal farms to factors that cause the changes in farm structure, they were excluded from the numbers for purposes of this study. Adjusted Census of Agriculture data by sales class and by acre size for years 1959, 1964, 1969, and 1974, based on procedures illustrated in appendix tables 2 and 3, are shown in tables 13 and 14.
Projections
The estimated trend equations, based on the adjusted census data in tables 13 and 14, are shown in appendix tables 4 and 5. Projections of the farm numbers by acre and sales size are shown in tables 15 and 16.
Farm numbers by acre size are projected to decline from 2.9 million in 1974 to 2.6 million in 1980 and to 1.7 million in 2000. The simple trend projections show the numbers of farms with less than 1,000 acres to continue declining, while those of 1,000 acres or more to continue increasing. Similarly, the number of farms by sales class is projected to decline from 2.9 million in 1974 to 2.6 million in 1980 and 2.1 million in 2000. As expected, the number of small farms (sales less than $20,000) continues to decline, while the number of big farms increases.
4/ The 1959 Census definition of a farm is used in both data sources and throughout this study (see table 1).
5/ Abnormal farms include institutional farms, experimental and research
farms, and Indian reservations. Institutional farms include those operated by hospitals, penitentiaries, schools, grazing associations, government agencies, and others.
21




Table 13--Census of Agriculture data on number of farms, by sales class,
adjusted for underenumeration
Sales class : 1959 1964 1969 1974
1 ,000 farms
Less than $2,500 1,896.4 1,657.2 1,417.1 1,100.6
$2,500-$4,999 646.0 473.9 432.8 322.9
$5,000-$9,999 683.8 528.6 410.9 319.5
$10,000-$19,999 496.8 484.1 399.5 326.9
$20,000-$39,999 216.4 266.9 329.8 327.6
$40,000-$99,999 84.5 113.5 168.0 327.5
$100,000-$199,999 : 14.6 21.8 35.0 99.4
$200,000-$499,999 4.7 8.0 12.4 39.3
$500.,000 and over. 1.2 2.6 4.0 11.2
All farms : 4,044.5 3,556.7 3,209.6 2,874.9
Table 14--Census of Agriculture data on number of farms, by size of farm, adjusted for underenumeration
Size of farm 1959 : 1964 1969 : 1974
1,000 farms
1-9 acres 301.9 217.8 268.0 244.4
10-49 acres 890.3 760.3 675.8 636.1
50-69 acres 291.6 252.2 210.2 188.9
70-99 acres 452.0 394.8 335.8 287.5
100-139 acres 410.0 350.5 301.5 258.7
140-179 acres 392.8 332.8 284.5 239.8
180-219 acres 234.4 206.5 178.7 151.4
220-259 acres 203.1 177.5 148.2 122.9
260-499 acres 507.4 487.7 438.5 379.3
500-999 acres 214.7 225.1 218.4 210.7
1,000-1,999 acres 84.9 89.8 90.7 93.3
2,000 acres and over: 61.2 61.6 59.2 62.0
All farms : 4,044.5 3,556.7 3,209.6 2,874.9
22




It is significant to note that the total number of farms projected by sales class exceeds the total projected by acre size starting in 1985. By 2000, the difference is about 400,000 farms. That difference, to a large extent, can be attributed to the trend projections procedures. For farms in the $20,000-$39,999 sales class, the trend first pointed to an upward shift, then a decline in 1974. The estimated trend equation for this sales class, which has a positive coefficient for the time variable, apparently failed to capture the downturn in 1974. Thus, trend projections by sales class are likely to overestimate the total number of farms and the number in the :$20,000-$39,959 sales class.
Table 15--Trend projections of the number of farms, by size of farm
Size of farm 1980 1985 1990 1995 2000
1 ,000 farms
1-99 acres 1,190.4 1,060.8 945.3 842.4 750.6
100-219 acres 558.1 477.7 409.0 350.1 299.7
220-499 acres 456.3 406.0 361.3 321.5 286.1
500-999 acres 212.6 210.5 208.9 207.1 205.3
1,000-1,999 acres 96.3 99.3 102.2 105.3 108.4
2,000 acres and over: 60.9 60.9 60.9 60.9 60.8
All farms 2,574.6 2,315.4 2,087.5 1,887.2 1,711.0
Table 16--Trend projections of the number of farms, by sales class
Sales class : 1980 1985 1990 1995 2000
1 ,000 farms
Less than $2,500 : 951.4 795.6 665.3 556.3 456.2
$2,500-$4,999 264.3 212.8 171.3 137.8 110.9
$5,000-$9,999 : 247.7 192.2 149.2 115.8 89.8
$10,000-$19,999 : 293.2 253.6 219.5 189.9 164.3
$20,000-$39,999 : 366.2 388.5 408.5 426.6 443.2
$40,000-$99,999 : 316.9 373.7 429.6 484.8 539.4
$100,000-$199,999 : 90.1 113.3 137.4 162.5 188.3
$200,000-$499,999 : 36.0 46.3 57.2 68.8 81.0
$500,000 and over : 11.4 14.9 18.7 22.7 27.0
All farms :2,577.1 2,390.9 2,256.6 2,165.2 2,109.2
23




NEGATIVE EXPONENTIAL FUNCTIONS
This chapter presents an empirical examination of farm size distribution projections to the year 2000 derived by use of negative exponential functions. The farm size distribution, using this projection method, was found to be stable, that is, no significant shifts occur in the distribution over time. However, the size distribution estimated by negative exponential functions deviates from the actual one in that a relatively large proportion of the number of farms goes to the medium-size and large farms (200 acres and more), and a rather small percentage goes to the small farms (less than 100 acres).
Technical Overview
Negative exponential functions have been used by Dovring (,8 )
Boxley (1), Ching (3), and Dixon and Sonka (6) to estimate farm size distributions. If the farm size distribution has been stable around a moving average over time, this would suggest that, if the distributions could be adequately reppresented by a functional form, the projections problem would be reduced to that of estimating future average sizes. It would also suggest that the diversity of farm size characteristics of past and present is likely to extend into the future. And finally, it would suggest that causal economic studies could be conducted to explain this underlying stability.
Although farm numbers have been declining rapidly and average size has been increasing substantially, small farms have not disappeared nor been amalgamated into a few large operations. Dovring (8) suggested that processes influencing farm sizes produced distributions that may be characterized by specific functional forms. The relatively constant land base means that changes in farm numbers of a given size require an offsetting change in numbers in other size categories. That is, the land base is a physical constraint on the number of farms of a given size, and the number possible is inversely related to size. Noting the inverse relationship between frequency of occurrence and farm size categories, Dovring suggested the size distribution of farm numbers should resemble the inverse exponential distribution (7, 8, 9).
The general form of exponential function is ex where e is the irrational
number 2.71828... and x is the manifest variable. The inverse exponential function (e-x) may represent a decumulative size distribution written as:
y = Yoe -Bx (1)
where y is the percentage of farms remaining above a given size limit, x. The size limits can be and are expressed as fractions or multiples of average size in this study, and when x =0, e _Bx 1. The function monotonically decreases asymptotically to zero as x increases. When Bx = 10, e -Bx = .005 of 1 percent.
Boxley (1) utilized a logarilthmic (base 10) transformation of equation (1) as follows:
log y =log Yo Bx log e (2)
24




In more general terms:
log y = Bo + Blx (3)
where Bo = log yo and B1 = -B log e.
The estimated function was forced through the point representing 100 percent of the farms and the smallest fractional size (that is, restricting 100 percent of the farms to lie above the lower limits of the smallest category). Using the logarithmic transformation (base 10) of the data, this is the point with coordinates (xi/x, 2.0), where x, is the lower limit of the smallest size category and
3 is the average farm size. This follows, noting that from:
log y = Bo + Bvx
log y = 2.0 when x = xl/ = xo. That is,
2.0 = Bo + BlX
Bo = 2.0 Blx
log y = (2.0 BlxO) + Blx
= 2.0 + B1(x xO)
The last expression is equivalent to (log y 2.0) = Bl(x xO), which indicates operations performed on the data prior to estimation. The value of the constant term for the estimated equation is calculated according to the relationship
Bo = 2.0 B1x
This is not a severe restriction and simply results in the estimated distribution reflecting that all farms are 1 acre or larger in size.
Census of Agriculture data (without adjustment for underenumeration) for the years of 1959, 1964, 1969, and 1974 showing farm numbers by acreage categories were used to estimate distribution functions (as described by equation 3 above) for the United States, nine geographic regions, and each of the 50 States. 6/ The equations, estimated by ordinary least squares, for the four census periods and for the periods combined, with related statistics, are shown in table 17 for the United.States and the nine regions.
6/ The States in each region were as follows:
New England: Maine, New Hampshire, Vermont, Massachusetts, Rhode Island,
Connecticut
Middle Atlantic: New York, New Jersey, Pennsylvania East North Central: Ohio, Indiana, Illinois, Michigan, Wisconsin West North Central: Minnesota, Iowa, Missouri, North Dakota, South Dakota,
Nebraska, Kansas
South Atlantic: Delaware, Maryland, Virginia, West Virginia, North Carolina,
South Carolina, Georgia, Florida
East South Central: Kentucky, Tennessee, Alabama, Mississippi West South Central: Arkansas, Louisiana, Oklahoma, Texas Mountain: Montana, Idaho, Wyoming, Colorado, New Mexico, Arizona, Utah, Nevada Pacific: Washington, Oregon, California, Alaska, Hawaii
25




Table 17--Estimated size distribution function, United States and regions
CoeffiRegion Year Intercept Slope cient R2 F statistic
* .standard
error
United States 1959 2.00107 -0.3260 0.0411 0.913
* 1964 2.00101 -.3554 .0426 .921
* 1969 2.00096 -.3754 .0418 .931 0.405
* 1974 2.00092 r.3844 .0431 .930
* 1959-74 2.00097 -.3549 .0203 .919
New England 1959 2.001 55 -.2810 .0241 .950
* 1964 2.001 45 -.2684 .0246 .952
* 1969 2.00152 -.2914 .0219 .967 .364
* 1974 2.00144 -.2763 .0224 .962
* 1959-74 2.00147 -.2721 .0113 .956
Middle Atlantic 1959 2.00287 -.2524 .0268 .937
1964 2.00181 -.2735 .9261 .948
1969 2.001 76 -.2868 .0255 .955 .352
1974 2.001 65 -.2773 .0236 .958
1959-74 2.00175 -.2704 .0124 .947
East North Central 1959 2.00200 -.3096 .0272 .966
1964 2.00185 -.3209 .0254 .964
1969 2.001 72 -.3171 .0232 .969 .090
1974 2.001 58 -.3030 .0198 .975
1969-74 2.00780 -.3130 .0116 .964
West North Central 1959 2.00098 -.3644 .0282 .965
1964 2.00094 -.3799 .0277 .969
1969 2.00089 .3904 .0261 .974 .213
1974 2.00085 -.3896 .0263 .973
1959-74 2.00091 -.3794 .0130 .969
South Atlantic 1959 2.001 42 -.1993 .0277 .896
1964 2.00142 -.1993 .0292 .902
1969 2.00127 -.2337 .0291 .915 .364
1974 2.00122 -.2348 .0298 .912
1959-74 2.00128 -.2176 .0139 .901
East South Central 1959 2.00150 -.1821 .0251 .897
1964 2.00141 -.1944 .0260 .903
1969 2.00137 -.2119 .0261 .916 .351
1974 2.001 30 -.2138 .0266 .915
1959-74 2.00137 -.1975 .0124 .903
West South Central 1959 2.00093 -.3901 .0450 .926
1964 2.00088 -.4138 .0446 .935
1969 2.00084 .4299 .0406 .949 .282
1974 2.00080 -.4434 .0440 .944
1959-74 2.00085 -.4152 .0210 .935
Mountain 1959 2.00049 -.8717 .1063 .918
1964 2.00046 -.9228 .1121 .919
1969 2.00044 -.9487 .1141 .920 .1311
1974 2.00045 -.9611 .1277 .904
1959-74 2.00046 -.9205 .0544 .914
Pacific 1959 2.00090 -.3601 .0629 .845
1964 2.00085 -.4046 .0704 .846
1969 2.00082 -.422. .0726 .849 .2131
1974 2.00082 -.4253 .0760 .839
1959-74 2.00089 -.3973 .0333 .841
26




Few of the regions or States have size distributions that conform exactly to the theoretical negative exponential distribution. This is as expected, since the distribution for most States reflects unique characteristics of the State, such as geographic conditions, types of agriculture, and institutional constraints (for example, large number of small tobacco farms in North Carolina). 7/ It is also expected that long-established, traditional farming areas (with few physical, economic, or institutional constraints) which have undergone fragmentation and reconsolidation of farming units from original settlement patterns would tend to more nearly approximate the inverse exponential distribution.
While the usefulness of estimated equations of this form for projection depends upon the magnitude of deviation from the theoretical distributions, it is also dependent upon the stability of the farm size distribution over time. To determine statistically the stability of the estimated equations, an analysis of the covariance was conducted (3, 4). This involves comparison of the sum of squared residuals from the individual equations and the equation estimated for all groups. The hypothesis tested is that the data used in estimating the parameters of each equation belong to the same regression equation, that is, the data are subsamples of the same population--no significant shifts occur in the distribution over time. The F ratio calculated was expressed as:
(A B C D E) / P (k 1)
F =
(B + C + D + E) / (n1 + n2 + n3 + n4 4P)
Where ni = the number of observations (7) (i = 1, ... 4)
p = number of parameters estimated (1 slope)
k = number of classes (4 1959, 1964, 1969, 1974)
A = total group sum of squares of n, + n2 + n3 + n4 observations with
n, + n2 + n3 + n4 P degrees of freedom
B, C, D, E, = individual group sum of squares on ni deviations of the dependent
variable from the regression estimated by ni observations with
ni P degrees of freedom.
A comparison of the calculated F (table 17) with tabular F at the 0.05 level of significance indicates the null hypothesis is rejected for only one State, Rhode Island, in the New England region. Thus, the distributions appear stable over time and, if adequately portrayed by the estimated equations, projections may be made with some confidence.
Projections
To maintain the consistency of our data series for projection purposes, it was necessary for us to adjust the Census of Agriculture data for underenumeration and reestimate the negative exponential functions for the United States by using the adjusted census data, as shown in table 2.
7/ For further discussion of why deviations occur, see Dovring (7).
27




Acreage Distributions
Based on the combined and adjusted 1969 and 1974 census data, the following negative exponential function was estimated:
in y 2.0 = -0.4160 R2= 0.885 (4)
(-13.30)L J
where: y = percentage of farms lying above a size limit, xi,
Xi = the lower size class limit in acres,
R = average farm size in acres, and
R2= the coefficient of determination.
The slope of the function is -0.4160, and the t ratio is shown in parentheses. After calculating the intercept term, the estimated equation can also be written:
in y = 2.0011 0.4160 xi/-x (5)
The intercept term was estimated by using the average farm sizes from 1969 and 1974 census data, after adjusting both land in farms and number of farms for und erenumeration (fig. 5). A test for structural change between the two census years again Indicated. that the hypothesis .of no structural change cannot be rejected.
Figure 5
Negative Exponential Curves of the Acreage Distribution, 1974
100-----------80 60
40 -.
E
~ 0
10
(L 4 Observed distribution
Theoretical distribution
2
1 II I I I I
.01 .02 .04 .06.08.1 .2 .4 .6 .81 2 4 6 810
Average size
Relative size of farm (ratio to average farm size)
28




To the extent that size distribution around a moving average is stable over time, the information required for projecting future farm size distributions is minimal--the projected land in farms and average farm size in acreage distributions, and the projected total sales receipts and average sales receipts in sales distributions. Strictly speaking, however, the rationale for using the negative exponential function is not as strong for size distributions defined by sales. Thus, caution is advised in use of these equations for obtaining precise projections of sales distribution. Nevertheless, for comparison purposes and to maintain consistency throughout this report, sales distributions and their projections are also projected in this section.
Projections of acreage distributions to 2000 were obtained from the estimated equations by dividing the trend average farm size into the lower limits of each of the size categories to obtain new x variable values and the constant term, calculated as described previously. The resulting values are used to obtain the projected decumulative distribution, and the percentage of farms in each size category is found by subtracting each category from the previous one. Projected annual mean sizes were obtained from a linear time trend equation estimated from data for the 1957-77 period. The estimated equation is:
M =363.39 +3.02 T R2-=0.96 (6)
(0.20)
where M is mean size in acres, T is the time variable (1957 = 1. 0, ..),and the value in parentheses is the standard error of the estimate.
While the above information is sufficient to project future farm size distributions, projections of total number of farms require additional information on expected land in farms in the future. Land in farms was fitted by a linear trend equation based on census data (adjusted for undercoverage) for the years of 1959, 1964, and 1974. The estimated equation is:
L = 1233.80 8.16 T R2= 0.971 (7)
(0.13)
where L is land in farms and T is the time variable (1959= 1, 1964 = 6, etc.). Total number of farms is projected by dividing the projected average farm size into land in farms.
As expected, the number of farms was projected to continue to decline; a decrease from the actual 2.9 million farms in 1974 to 1.8 million farms in 2000 (table 18). The general pattern of decline in farm numbers is similar to that projected by historical trends reported in the previous section. However, the rate of decline after 1980 slows. During the 1974 to 2000 period, the negative exponential functions projected farm numbers to decrease at an annual average rate of 1.8 percent. Farms less than 220 acres in size show a continued decline in numbers, especially farms of less than 50 acres in size. The projected size distributions in the 220 to 2,000-acre range, although generally continuing a declining trend, present a discontinuity to recent trends: Instead of projecting smaller farm numbers in 1980 than that in 1974, the numbers are projected to increase. This discontinuity becomes more obvious in the 220 to 2,000-acre range. On the other hand, the numbers projected for the size class of over 2,000 acres present the opposite kind of discontinuity, even though the increasing trend is maintained.
29




Table 18--Projected number of U.S. farms, by size of farm, negative exponential function Size of farm: 1974 (actual) :1980 :1985 :1990 :1995 :2000
:Thousands Percent Thousands Percent Thousands Percent Thousands Percent Thousands Percent Thousands Percent
1-9 acres : 244.4 8.5 48.6 2.0 43.6 1.9 39.2 1.9 35.2 1.8 31.7 1.7
10-49 acres : 636.1 22.1 204.5 8.3 184.0 8.1 165.6 7.8 149.1 7.6 134.3 7.4
50-69 acres : 188.9 6.6 95.7 3.9 86.3 3.8 77.8 3.7 70.2 3.6 63.3 3.5..
70-99 acres : 287.5 10.0 135.8 5.5 122.6 5.4 110.8 5.2 100.2 5.1 90.5 5.0
100-139 acres: 258.7 9.0 167.5 6.8 151.8 6.6 137.5 6.5 124.5 6.3 112.2 6.2
CD 140-179 acres: 239.8 8.3 153.3 6.2 139.3 6.1 126.5 6.0 114.9 5.8 104.3 5.7
180-219 acres: 151.4 5.3 140.3 5.7 127.9 5.6 116.5 5.5 106.0 5.4 96.5 5.3
220-259 acres: 122.9 4.3 128.3 5.2 117.3 5.1 107.2 5.1 97.9 5.0 89.3 4.9
260-499 acres: 379.3 13.2 571.3 23.2 527.3 23.1 486.1 22.9 447.6 22.7 411.5 22.5
500-999 acres: 210.7 7.3 544.9 22.2 515.7 22.6 486.7 22.9 458.2 23.3 430.2 23.6
1 ,000-1 ,999
acres : 93.3 3.2 239.2 9.7 237.2 10.4 234.0 11.0 229.6 11.7 224.3 12.4
2,000 acres
and over : 62.0 2.2 29.3 1.2 31.6 1.4 33.7 1.6 35.7 1.8 37.4 2.1
All farms :2,874.9 100.0 2,458.8 100.0 2,284.5 100.0 2,121.7 100.0 1,969.1 100.0 1,825.9 100.0




Sales Distributions
Based on the 1974 adjusted census data, the equation below does not estimate the sales class distributions as well as the acreage distributions:
In y 2.0 = -0.18961 R2~~0 = 0.846 (8)
where: y = percentage of farms that lie above a size limit x1,
X= the lower size class limit in sales receipts,
x=the average sales receipts per farm, and
R2- the coefficient of determination.
The slope of the function is -0.18961, and the t ratio is shown in parentheses. After calculating the intercept term, the estimated equation for 1974 sales distribution can be written alternatively as:
ln y =2.00029 0.18961 xi/i- (9)
The constant term was estimated by using the average sales receipts per farm ($33,077) in 1974.
It is necessary to have projected average sales per farm to project the future sales distribution. A linear trend equation for this purpose was estimated for the period 1970-77:
a=2152.47 + 4645.33 T R 056 (10)
where: Sa = average sales receipts per farm,
T = time (1970 =1.0, 1971 =2.0, etc.),
and the t ratios are in parentheses. In addition, total sales receipts are needed so that the number of all farms can be projected. Another linear trend equation for this purpose was estimated:
St = 44,998.3 + 7,303.13 T R2= 0.841 (11)
(6.878) (5.637)
where St is total sales receipts, and the other values are as defined above. Projected total farm numbers again continue to decline, with the pattern similar to that of acreage distributions (table 19).
The projected sales distributions, however, appear to depart from the historical trends in several important-aspects. First, the negative exponential function projects far too many farms with sales of more than $100,000. Second, small farms (sales less than $20,000) are projected to disappear at a rapid rate--a decline from 72 percent of the total number of farms in 1974 to 6 percent in 2000. Third, the number of farms in the $40,000-to-$99,999 sales class is projected to be smaller in 2000 than the number in 1974.
31




Table 19--Projected number of U.S. farms, by sales class, negative exponential
functions
Sales class : Actual 1974 1980 .1985
Thousands Percent Thousands Percent Thousands Percent
Less than $2,500 1,100.6 38.3 46.8 2.0 29.0 1.4
$2,500-4,999 322.9 11.2 46.8 2.0 33.4 1.6
$5,000-9,999 319.5 11.1 90.6 3.9 55.9 2.6
$10,000-19,999 326.9 11.4 170.9 7.3 111.7 5.3
$20,000-39,999 327.6 11.4 302.2 12.8 '201.3 9.5
$40,000-99,999 327.5 11.4 659.0 28.0 489.5 23.1
$100,000-199,999 99.4 3.5 580.4 24.7 520.0 24.6
$200,000-499,999 39.3 1.4 417.8 17.8 553.8 26.2
$500,000 and over: 11.2 .4 39.1 1.7 121.7 5.8
All farms :2,874.9 100.0 2,353.6 100.0 2,116.3 100.0
1990 1995 :2000
Thousands Percent Thousands Percent Thousands Percent
Less than $2,500 22.7 1.1 17.6 .9 12.8 .7
$2,500-4,999 : 22.7 1.1 17.4 .9 12.6 .7
$5,000-9,999 : 39.8 2.0 34.4 1.8 29.3 1.6
$10,000-19,999 81.6 4.1 62.5 3.3 53.1 2.9
$20,000-39,999 : 152.6 7.7 122.5 6.4 101.6 5.5
$40,000-99,999 385.6 19.4 316.2 16.2 270.9 14.6
$100,000-199,999 455.2 22.9 402.4 21.1 353.7 19.1
$200,000-499,999 606.8 30.5 614.3 32.2 606.1 32.6
$500,000 and over: 222.6 11.2 323.7 16.9 416.7 22.4
All farms 1,989.5. 100.0 1,910.7 100.0 1,856.9 100.0
32




MARKOV PROCESS
This chapter reviews the use of Markov processes for projecting farm number and size distributions, describes the process of adjusting the census data for the effects of price inflation, and presents projections to the year 2000. As a result of an 80-percent increase in prices received by farmers between 1969 and 1974, about 90 percent of the apparent increase in the numbers of farms with sales of $100,000 and more is attributed to the effects of price inflation. Of the projected 1.9 million farms in 2000, small farms (less than $20,000) will constitute 50 percent, a decrease from the 72 percent in 1974. By contrast, large farms (sales of $100,000 and more) will constitute 33 percent, an increase from 5 percent in 1974.
Technical Overview
Markov processes have been used to estimate the number and size distribution of firms for a number of industries, including agriculture. 8/ These applications have often used modifications or variants of a Markov process. Many of the modifications are concerned with the estimation of a transition matrix (that is, a description of how firms move among size categories over time) and are necessitated by limited data describing the movement of firms from one time period to another (for example, see 16, 18, 20).
The Markov chain process assumes that a population can be classified into
various groups (S, S2, ... I Sn) and that movements between states over time can be regarded as a stochastic process that can be quantified by probabilities. The states must be defined so that an individual can only be in one state at any point in time. A transition occurs when an individual shifts from one state to another.
A crucial step in the use of Markov processes is estimation of the transition probability--the probability of movement from one state to another in a specified time period. The transition probabilities, Pij, can be expressed in the form of transition matrix, P:
S1 S2 ... Sn
S 1 PII P 12 Pln
$2 P 21 P22 P2n
Sn P nl Pn2 Pnn
where: j Pij 1.0 and P > 0, for all i and j.
The elements of P (the Pi) indicate the probability of moving from state Si to S in the next period. Since the elements of the matrix are nonnegative and the sum of the elements in any row is unity, each row of the matrix is a probability
8/ Illustrative studies include (5, 12, 16, 20).
33




vector, and P is a stochastic matrix. The matrix, P, in combination with an initial starting state completely defines a Markov chain process.
A chain is irreducible if all states are required to be accessible, that is, there is a nonzero probability of moving from state i to state j in a finite number of time periods. A sufficient condition for the transition matrix P to be irreducible is that some power of the matrix have only positive components.
Traditional Markov analysis projects future farm numbers by multiplying the row vector of farm numbers in the base period by the transition matrix which was constructed from actual farm numbers in the past. This analytical approach implicitly assumes that changes in prices received by farmers can be ignored or that farm product prices change little between periods. Historicially, that was a valid assumption--the index of prices received by farmers has remained relatively stable, increasing by less than 1 percent annually between 1954 and 1969. However, a changing economic environment resulted in a nearly 80-percent increase in the prices received by farmers between 1969 and 1974, thus requiring that explicit attention be given to product prices.
Data Adjustments
The general approach in this study to adjust the census data for the effects of price inflation explicitly differentiates and quantifies the changes in farm numbers into two components: (1) changes due to price inflation; and (2) changes due to "real" factors such as technological change, economies of size, farm commodity programs, production and market instabilities, land enlargement, and the like.
The percentage increase in the index of prices received by farmers is used to quantify the shift from current (1974) to a constant (1969) dollar sales distribution of farm numbers. The sales distribution was approximated by a decumulative polynomial function with both sales and farm numbers expressed in logarithuic values. That is:
N
FN(s) = cexp E n (ln s)n
n=1
where FN(s) = cumulative farm numbers that produce sales receipts
in excess of s,
s = sales receipts,
n = degree of the polynomial function, and
a, Sn = parameters of the distribution.
This distribution function differs from the traditional Pareto distribution of income and wealth in that a negatively sloped nonlinear functional relation, instead of linear, is assumed to exist between the cumulative number of farms and
34




the sales receipts, with both variables expressed in natural logarithmic values. 9/ The nonlinear specification gives a closer fit to observed data than the linear function.
The 80-percent increase in the index of prices received by farmers between 1969 and 1974 implies that $1 worth of agricultural products sold in 1974 car.ied a price tag of $0.56 in 1969. The cumulative distribution of farm numbers by sales class in 1974, therefore, was transformed into a comparable sales distribution in 1969 constant dollars by multiplying 0.56 by the sales value associated with each observation on the current dollar sales distribution. 10/ Based on the estimated polynomial functions of the two sales distributions, predicted cumulative distributions of 1974 farm numbers (both in 1974 current dollars and 1969 constant dollars) are shown in figure 6 and columns 5 and 6 in
9/ The Pareto law of income distribution asserts that "the logarithm of the
percentage of units with an income in excess of some value is a negatively sloped linear function of the logarithm of that value" (15). Mathematically, it has the form:
P(y) = A Y-'
P(y) = percentage of units with income in excess of Y,
Y = income level
A,a = parameters of the distribution
10/ This approach implicitly assumes that farms within a sales class are uniformly distributed.
Figure 6
1974 Farm Numbers in 1974 and 1969 Farm Prices
Decumulative number of farms (100,000)
20
10 HC
8
F D I
6 P" 1974 Prices
4 1969 Prices P 1%
2
1 I f I I I I 1 I 1 1
.05 .1 .2 .4 .6 .81.0 2 4 6 810 20 40 6080100 200
Sales ($1,000)
Decumulative means that the distance along the y-axls between points A and C, for example, Is the number of farms In the sales class of $10,000 to $19,999.
35




table 20. For example, while there were about 800,000 farms with sales of $20,000 and more in 1974 (point A in fig. 6), the number of farms dropped to about 500,000 when the sales were expressed in 1969 dollars (point B in fig. 6).
The next step is to figure out the shifts in farm numbers for each sales class through this deflationary process. That is, to determine the numbers of farms that remain in the same sales class and those that move to the lower sales classes. For example, the 327,000 farms with sales of $10,000 to $19,999 in 1974 would have had sales ranging from $5,600 to $11,200 if they had not had an 80-percent increase in prices received due to inflation. In other words, the same 327,000 farms which are measured by the vertical distance CD for segment CA in the current dollar distribution, now can be measured by the vertical distance EF for segment EG in the 1969 constant dollar distribution (fig. 6).
It is clear that distance DH (60,900 farms) measures the number of farms with sales of $10,000 to $19,999 that remain in the same size class after the deflation, a difference between point H (853,600 farms) and point A (792,700 farms). In the meantime, distance CH- or EI (265,400 farms) measures the number of farms that move to the lower sales class ($5,000 to $9,999), a difference between point C (1,118,900 farms) and point H. Thus, the 80-percent increase in prices received by farmers due to inflation is estimated to have moved 265,400 farms up statistically from the sales class of $5,000 to $9,999 to the next higher sales class ($10,000 to $19,999), a gain in the number of farms with sales of $10,000 to $19,999 (column 8 in table 16). Repeating the same deflationary process for farms in the next higher sales class ($20,000 to $39,999), we estimated that the price inflation moved 281,200 farms up from the sales class of $10,000 to $19,999 to the next higher sales class ($20,000 to $39,999), a loss
in the number of farms with sales of $10,000 to $19,999 (column 9' in table 20). Therefore, the 80-percent increase in prices received by farmers due to inflation had the net effect of reducing the number of farms in the sales class of $10,000 to $19,999 by 15,800 farms. Table 20 shows that the number of farms in this sales class declined by 72,600 from 1969 to 1974. The preceding interpretation of that decline, however, tells us that about 22 percent of it (15,800 farms) was attributed to the price inflation and the remainder (56,800 farms) was due to other "real" factors.
Performing the same analysis for each sales class, we obtained a gain-loss array of the changes in farm numbers due to price inflation as shown in table 20. In general, price inflation has a net effect of reducing the number of small farms and increasing the number of large farms. As a result of an 80-percent increase in prices received by farmers between 1969 and 1974, about 90 percent of the apparent increase in the numbers of farms with sales of $100,000 and more is attributed to the effects of price inflation. Farms with sales of $100,000 and more increased by 98,500, but 88,200 of those were pushed into the higher sales classes because of the price inflation.
Projections
The Markov process, as employed in this study, enables projecting the future number of farms by acreage by multiplying the transition probability matrix by the row vector of farm numbers in the base year. The projection proceeds in two steps, however, when sales are used to measure the size of farms. First, a
36




Table 20--Calculation of change in farm numbers due to price inflation and other factors, by sales, 1969-74
Fam umes umti ve of is7tfrmbu Number of: : Change 1974 farm
Famnumbers farms Change due to inflation :det ubr
Sales : eand::other without
in class ::factors price
inflation
194 :Actual 1969 : 1974 :Percent Percent
* 1969 1974 Gain :Loss : Net
*changer dollars: dollars. gain 2/ loss 3/
Thousands
$500,000 and over 4.03 11.21 7.18 5.73 10.88 5.73 5.15 --5.15 46 --2.03 6.06
$0,0-9999 : 12.46 39.33 26.87 18.51 48.70 7.63 30.19 5.15 25.04 77 41 18 42
$100,000-199,999 : 34.97 99.38 64.41 59.51 147.71 10.81 88.20 30.19 58.01 89 86 6.40 41.37
$40,000-99,999 : 168.01 327.52 159.51 237.48 456.42 89.42 218.94 88.20 130.74 67 52 28.77 196.78
$2,0-999 : 329.79 327.57 -2.22 511.54 792.72 55.12 281.18 218.94 62.24 86 66-6.6 253
$10,000-19,999 : 399.52 326.90 -72.62 853.59 1,118.98 60.87 265.39 281.18 -15.79 81 70 -56.83 342.69
$5,000-9,999 : 410.93 319.47 -91.46 1,173.21 1,408.81 54.23 235.60 265.39 -29.79 74 65 -61.67 342.69
$2,500-4,999 : 432.80 322.95 -109.85 1,462.89 1,751.64 54.08 288.75 235.60 53.15 89 54 -163.00 269.80
Less than $2,500 :1,417.06 1,100.60 -316.46 2,750.00 2,873.13 998.36 123.13 288.75 -165.62 11 20 -150.84 1,266.32
Total :3,209.57 2,874.93 -334.64 --- ---- --- 2,751.80
1/ These are cumulative farm numbers distributions predicted by a fifth-degree polynomial function wi~th both sales receipts. and farm numbers expressed in natural logarithms.
2/ Column 8 divided by column 3.
3/ Column 9 divided by column 2.
--=Not applicable.




projection is obtained by multiplying the transition probability matrix (which is constructed from constant dollar distributions of farm numbers),by the row vector of farm numbers in the base year. Second, effects of anticipated increase in prices received by farmers on the number of farms in each sales class are then incorporated into the projection results obtained in step one.
In the absence of more detailed data on entry, exit, and farm movement
among size classes, we relied on aggregate census data in recent years to construct and approximate the transition probability matrix. The guiding principle in developing this matrix was to select numerical values that minimized the residual sun of squares, computed from the projected and actual number of farms by size class. Analytically, this problem can be solved with a quadratic programming framework (18). This study, however, employed a less formal, trialand-error iterative procedure and, in part, assumed traditional farm movement patterns underlying the Markov process to construct the transition probability matrix. 11/ Farms were permitted to expand their size or to exit from farming, but not to' contract. En addition, we assumed that the number of farms in the largest size class would remain in that category and that any increase in the number of farms in a size class came from the immediately smaller size class. 12/
To illustrate, all the farms of 2,000 acres and more in 1969 (59,167- -see
table 14) were assumed to remain in the same size category in 1974--they neither ceased operations nor moved to a smaller size class. Thus, the same 59,167 farms were placed in the diagonal element of the farm movement matrix between 1969 and 1974, the cell intersecting row vector A10 and column vector A10 (table 21). The numerical value in row A9 and column A1O is then the estimate of farms (2,827) moving up from size class A9 to A1O.
The number of farms lost in the consolidation process in size class A9 (farmland of 1,000 to 1,999 acres) is then estimated as 11,135. Before the consolidation took place, the 2,827 farms that moved up from size class A9 to A10 operated about 3.83 million acres of farmland. By contrast, the same 2,827 farms operated about 18.93 million acres of farmland after the expansion. This implies that about 15.1 million acres of farmland were consolidated from size class A9 to A1O in the process of structural change between 1969 and 1974. Translating the consolidated farmland into the number of farms lost in the consolidation process means that 11,135 farms moved out of farming in size class A9 (15,100,000 / 1,356). Mechanically, this net exit estimate (column AO) can be computed as:
11,135 = [(6,697/1,356) 11 x 2,827
The number of farms that remain in size class A9 is then computed as the difference between the 1969 number of farms in size class A9 and the sum of the number of farms that move up to the higher class (MlO) and those in the net exit category.
11/ The combined use of the iterative procedure and traditional farm movement assumptions results in a projection error of less than 1 percent.
12/ This is what is known as the 100-0-0 transition pattern as illustrated by Dfaly, Dempsey, and Cobb (5). This assumption was found to give a better fit to actual data than other alternatives, including 40-40-20 and 60-40-0 patterns.
38




Continuing this process, we have shown that a number of farm movement matrix elements can be constructed. Starting from the size category of 260 to 499 acres and continuing on to the smallest size class, this process breaks down, however; it begins to yield nonpositive diagonal elements. 13/ A trialand-error iterative procedure is thus employed to identify the remaining matrix elements that minimize the residual sum of squares, computed from the projected and actual number of farms by size class. The off-diagonal elements, again, reflect the number of farms moving to the upper classes. As a result, the diagonal elements are all positive--with the numerical value ranging from about 82 percent to 93 percent of the number of farms in 1969.
Following the same procedure, we constructed a movement matrix by sales class between 1969 and 1974 (table 22). The transition probability matrices, obtained by dividing the number of farms in the farm movement matrix by the 1969 number of farms in each size class, are shown in tables 23 and 24.
The transition probability matrix is the crux of the Markov process;
therefore, its stability over time willcontribute to the accuracy of projections. The probabilities were so stable that there were virtually no differences between the two transition matrices, one for the 1969 to 1974 period and another for the 1964 to 1969 period. In this way, the transition probability matrix used for projections actually represents the synthesis of the two periods: 1964 to 1969 and 1969 to 1974.
Acreage Distribution
The number of farms is projected to decline .to 2.1 million in 1990 and
1.7 million in 2000. Of the projected 1.7 million farms in 2000, large farms (those with 1,000 acres or more) will account for about 10 percent, an increase from 5 percent in 1974. By contrast, the proportion of small farms (those with less than 220 acres) is projected to remain high, 68 percent as compared to 70 percent in 1974 (table 25).
Historically, the number of farms with less than 500 acres h~s been declining since 1945. Projected acreage distributions based on the Markov process show that this trend is likely to continue into the year 2000. In addition, the decline of the number of farms with 400 to 999 acres, beginning in 1969, is projected to continue. About 90 percent of all farms in 2000 will likely have less than 1,000 acres.
Sales Distribution
The transition probability matrix by sales class was intended to reflect the physical change in farm structure, discounting any effects of price inflation. Thus, multiplying the transition probability matrix by the base period (say 1969) number of farms does not result in the projected number of farms in 1974. Instead, the projection is derived by adding the effects of price infla13/ This finding appears to have economic meaning. It could suggest that the-farm growth and consolidation process may not start from the very small size classes as is implied in the traditional Markov process. Rather, consolidation may actually begin from a larger, more economically viable size level, such as 500 acres or larger.
39




Table 21--Farm movement matrix by acreage, 1969-74: 100-0-0 movement assumption
:1974:
:average: :
Size of farm :farm : A0 : Al. : A2 : A3 : A4 : A5 : A6 : A7 : A8 : Ag : A10
: size : : : : : : :
Acres Numbers of farms
1-69 acres (Al) : 32 84,257 l/ 1,069,433 335
70-99 acres (A2) : 82 47,814 2/ 287,137 882
100-139 acres (A3) : 117 42,923 2/ 257,808 799
140-179 acres (A4) : 158 44,146 3/ 238,987 1,375
180-219 acres (A5) : 198 27,270 3/ 150,072 1,315
220-259 acres (A6) : 238 20,075 4/ 121,536 6,604
260-499 acres (A7) : 359 40,964 5/ 372,693 24,805
500-999 acres (A8) : 687 16,055 185,897 16,487
1,000-1,999 acres (Ag) :1,356 11,135 76,777 2,827
2,000 acres and over (A1o) :6,697 0 59,167
I/ Computed as 92.7 percent of the number of farms in 1969.
2/ Computed as 85.5 percent of the number of farms in 1969.
3/ Computed as 84.0 percent of the number of farms in 1969.
- 4/ Computed as 82.0 percent of the number of farms in 1969.
0 5/ Computed as 85.0 percent of the number of farms in 1969.
Table 22-Farm movement matrix by sales class, 1969-74: 100-0-0 movement assumption
Sales class : : S1 : S2 3 : S4 : S5: S6 : S7: S8: S9
1 ,000 farms
Less than $2,500 : 147.21 1/ 1,266.85 3.00
$2,500-4,999 : 154.33 2/ 266.17 12.30
$5,000-9,999 : 50.80 3/ 336.96 23.07
$10,000-19,999 : 56.05 4/ 319.62 23.85
$20,000-39,999 : 30.32 241.48 57.99
$40,000-99,999 : 12.12 138.79 17.10
$100,000-199,999 : 4.62 24.27 6.08
$200,000-499,999 : 2.16 8.21 2.03
$500,000 and over : 0 4.03
1/ 89.4 percent of the number of farms in 1969.
2-/ 61.5 percent of the number of farms in 1969.
T/ 82 percent of the number of farms in 1969.
_/ 80 percent of the number of farms in 1969.




Table 23--Farm transition matrix by size of farm, 1969-74: 100-0-0 movement assumption
Size of farm : A0 : Al : A2 A3 : A4 : A5 A6 : A7 : A8 A9 A10
Probabilities
1-69 acres (Al) .073 .927 .0003
70-99 acres (A2) .142 .855 .003
100-139 acres tA3) : .142 .855 .003
140-179 acres (A4) : .155 .840 .005
180-219 acres (A5) .153 .840 .007
220-259 acres (A6) : .135 .820 .045
260-499 acres (A7) .093 ,850 .057
500-999 acres (A8) .073 .851 .075
1,000-1,999 acres (A9) .123 .846 .031
2,000 acres and over (Al0) 0 1.000
Table 24--Farm transition matrix by sales class, 1969-74: 100-0-0 movement assumption
Sales class SO S : S 2 : 3 S4 S5 S : S7 S8 S 9
Probabilities
Less than $2,500 (Sl) : 0.104 0.894 0.002
$2,500-4,999 (S2) : .357 .615 0.028
$5,000-9,999 (S3) .124 .820 0.056
$10,000-19,999 (S4) .140 .800 0.060
$20,000-39,999 (S5) .092 .732 0.176
$40,000-99,999 (S6) : .072 .826 0.102
$100,000-199,999 (S7) .132 .694 0.174
$200,000-499,999 (S8) .174 .662 0.164
$500,000 and over (S) 0 1.000




tion or number of farms to the aforementioned results. This process must also be repeated through the projection periods and we must assume what the rate of future price inflation will be.
In this study, we assumed the following changes in farm prices received by farmers:
Projection Percentage increase in prices
period received by farmers
1974-85 68.2
1985-90 42.0
1990-95 34.*0
1995-2000 27.0
These assumptions between 1974 and 1990 are based on the National-Interregional Agricultural Projections (NIRAP) high demand and low supply projections. After 1990, the increasing trend of prices received by farmers (evident since 1972) is assumed to continue (see figure 7).
The number of farms is projected to decline to 2.2 million in 1990 and
1.86 million in 2000. The number of small farms (those with sales of less than
- $20,000) is projected to decline from 72 percent of the total in 1974 to 56 percent in 1990, and 50 percent by the turn of the century. By contrast, the number of farms having sales of 'over Fgr
$100,000 is projected to increase from Flue
the 5.2 percent in 1974 to 21 percent in 1990, and about 33 percent in 2000 Actual and Projected Prices
(table 26). Received by Farmers
For comparison, another set of pro- 800
jections is shown in table 27 based on High price
the following low price inflation assump- Inflation ~
tions 14/:
600
Projection Percentage increase
period in prices
1974-85 32.5 40-J
1985-90 24.5/
1990-95 27.0
195200274200 0 Low price
Inflation
14/ These-assumptions were obtained 0
from the National-Interregional Agricul- 190 90 170 98 190 20
tural Projections (NIRAP) baseline of Percentage of 1967
May 1, 1978.
42




The main effect of the low price inflation assumptions is to shift the projected number of farms from large sales classes to smaller classes. Under the low price inflation assumption, the number of small farms is projected to decline at only a moderate rate, from 72 percent of the 1974 total to 63 percent in 1990, and to 56 percent in 2000. Similarly, percentage increases in large farms are projected to increase less drastically. The number of farms with sales of over $100,000 is projected to increase to 14 percent of the total in 1990, and to 24 percent in 2000.
Table 25--Projected number of farms, by size of farm, Markov chain analysis
Actual
Size of farm : 1974 1980 1985 : 1990 1995 2000
1,000 farms
1-69 acres 1,069.4 991.4 919.0 851.9 789.7 732.1
70-99 acres 287.5 246.1 210.7 180.4 154.5 132.4
100-139 acres 258.7 222.0 190.6 163.6 139.9 121.0
140-179 acres : 239.8 202.2 170.5 143.8 121.3 102.3
180-219 acres 151.4 128.4 108.9 92.3 78.3 66.3
220-259 acres 122.9 101.8 84.4 69.9 580l 48.1
260-499 acres 379.3 327.9 283.3 244.6 211.1 182.0
500-999 acres 210.7 200.9 189.7 177.6 165. 152.5
1,000-1,999 acres : 93.3 94.7 95.2 94.8 93.5 91.5
2,000 acres and over: 62.0 64.9 67.8 70.8 73.7 76.6
All farms 2,974.9 2,580.4 2,320.1 2,089.7 1,885.0 1,704.8
Table 26--Projected number of farms, by sales class, Markov process, high price inflation (7.5 percent per year)
: Actual
Sales class 1974 : 1980 : 1985 1990 : 1995 : 2000
1,000 farms
Less than $2,500 : 1,100.6 928.9 855.4 794.7 760.5 639.9
$2,500-$4,999 : 323.0 185.8 176.1 115.4 82.6 72.3
$5,000-$9,999 : 319.5 251.0 179.0 141.7 129.4 108.4
$10,000-$19,999 : 326.9 274.4 210.6 166.5 126.1 108.1
$20,000-$39,999 327.6 269.4 213.7 176.1 .123.9 88.3
$40,000-$99,999 : 327.5 392.7 388.8 338.8 290.8 262.0
$100,000-$199,999 : 99.4 131.5 184.5 217.9 205.8 167.5
$200,000-$499,999 39.3 69.8 96.1 150.8 187.7 190.1
$500,000-and over : 11.2 20.6 49.5 90.3 155.0 225.8
All farms 2,874.9 2,524.1 2,354.0 2,193.2 2,061.8 1,862.4
43




Table 27--Projected number of farms by sales class: Markov process, low price inflation
1974
Sales Class 1980 : 1985
Actual : Projection
1,000 farms
Less than $2,500 1,100.6 1,101.2 998.0 894.5
$2,500-$4,999 : 323.0 322.2 202.7 197.3
$5,000-$9,999 : 319.5 319.3 270.9 233.1
$10,000-$19,999 : 326.9 326.8 279.0 211.9
$20,000-$39,999 : 327.6 327.6 260.4 193.9
$40,000-$99,999 : 327.5 327.6 331.1 371.4
$100,000-$199,999 : 99.4 99.4 104.0 143.0
$200,000-$499,999 : 39.3 39.3 44.1 67.0
$500,000 and over
All farms : 2,874.9 2,874.7 2,508.2 2,341.6
Sales Class : 1990 : 1995 : 2000
1,000 farms
Less than $2,500 : 881.2 865.0 750.0
$2,500-$4,999 : 135.6 102.0 50.0
$5,000-$9,999 189.4 155.8 140.0
$10,000-$19,999 : 165.7 124.2 100.0
$20,000-$39,999 : 147.0 101.9 100.0
$40,000-$99,999 370.2 350.6 275.0
$100,000-$199,999 : 161.7 178.1 181.5
$200,000-$499,999 : 90.1 113.2 132.0
$500,000 and over : 51.0 83.0 121.5
All farms : 2,191.9 2,069.6 1,850.0
44




AGE COHORT ANALYSIS
This chapter presents an overview of analysis by age cohorts (people born in the same decade), cohort adjustments by size class and projections obtained by this method. The number and sizes of farms change through time as farm operators enter, adjust the size of their operations, and leave agriculture. The life cycle of the farm operator has long been related to the concurrent phases of entry, expansion,and exit from the farm business: (1) young farmers (less than 35 years)--entry and establishment phase; (2) middle-aged farmers (35 to 54 years)--expansion phase; and (3) older farmers (55 and older)--exit, transfer, or close-out phase.
Technical Overview
Figure 8 shows the decreasing number and increasing age of farm operators. The age distribution shifts because the numbers of young persons entering farming are fewer than the numbers of older persons retiring or leaving farming. Also, many older operators continue to farm past the usual retirement age, when they are not replaced by a younger generation. Occupational mobility decreases as farm operators advance in age, further contributing to the shift in age distribution (2, 10, 11, 13) and the long-term adjustment process for farm operator number and farm size.
Age cohorts can be traced through successive agricultural censuses to determine the net change in the number in each age cohort by size of farm.
Figure 8
Farm Operator Age Distribution, 1920.74
Thousands
1,400
1,200 -0000 1940
S -- ......
1,000 0. 1954 --" .
8000f/
600 t..60 -.. 96 -- tfff
400 / o.. o 1974
200 o 00
0 I I II
Under 25 25-34 35-44 45-54 55-64 65 or
Age Group over
Source: (25).
45




Kanel found that most of the adjustments occur as the older operators leave farms (14). Using Kanel's age cohort framework, Tolley stratified farm operators by size of farm and further examined mobility (22). He found considerable variation in entry and exit rates by age group and sales class.
Age cohort analysis centers on identifying the common pattern of entry and exit related to operator age. From census of agriculture data, the same cohort group of farm operators with common birthdates can be identified in successive censuses and the changes in net entry and exits for each age group can be estimated (figure 9). For example, for the cohort born from 1876 to 1885, some 1.4 million were farm operators when they reached the ages of 25 to 34 (in the 1910 Census). The number increased in the next decade to 1.6 million (1920) and declined slightly by 1930, by which time the cohort was 45 to 54 years old. This cohort declined to 1 million farm operators by 1940 (ages 55 to 64) and to 745,000 to 1950 (ages 65 to 75). All are assumed to have exited by 1960 as they reached 75 years of age. A few of these older operators may have continued farming, but beyond this point the Census does not provide data.
A similar pattern for other cohorts is shown in figure 9. The number of farmers in each group expands to a peak at 35 to 44 years and then declines through death or retirement. Some differences in slopes are revealed for individual cohorts. For example, the cohort born in 1916-25 was disrupted by World War II, and a new pattern seems to have emerged. Younger operators entered farming at previous rates, but a large number left farming after 35 years of age--10 years younger than previous age groups began to leave farming.
Figure 9
Farm Operator Age Cohort Movements, 1910-69
Thousands
1,400 -1
1,200
8190
600 1921-96-19165
1,200 --0 .---.' so
600 After 1945 %
Under 25 25-34 35-44 45-54 55-64 65 or over
Age Group
Source: (25).
46




Data Adjustments
Farm numbers declined 682,000 between 1964 and 1974 to 2.9 million; but the numbers in some age groups increased while those in others decreased (table 28). Also, farms with sales of $40,000 or more increased but smaller farms declined. The data in this as well as most of the following tables have been adjusted to the 1964 price level by a process similar to that described in the previous chapter. However, for the age-cohort sales class data, it was necessary to deflate each group separately (see appendix C for details).
The net entry rates for some sales classes for some age groups probably result from shifts to larger or smaller size classes. For example, table 28 shows that between 1964 and 1974, the 1920-29 cohort group declined in total numbers and in sales classes of $5,000 to $39,999 but increased in number for the two sales classes of $40,000 and above and the two smallest sales classes. The 22,100 increase in farm operators in the two larger sales classes probably represented not new entries but operators with increased sales during the period. The increased number of operators with sales of less than $5,000 in this cohort group in this period probably resulted from reductions in size of farming operations as the operators approached retirement, or increased nonfarm employment.
The replacement ratio of entering to exiting farm operators between 1964 and 1974 was about 0.23 for all farm operators (that means that about five operators left for each new entry) and less than 1 for farms with sales of less than $40,000. However, the ratio becomes 7 or higher for farms with sales of more than $40,000. Younger persons are apparently unwilling to enter farming on the smaller farms in sufficient numbers to replace older operators who leave, because of the inadequate levels of income from small farms. There were substantial entries of young operators on farms with sales of less than $2,560, but most of these are probably part-time operations. However, t le 141,500 net entries of younger farmers (age 35 or less) on farms of that size were far less than the 611,800 older operators (age 55 or more) who departed.
Table 29 presents similar data for age cohorts by acreage with similar patterns of entry and exit related to size and age. The totals in tables 28 and 29 differ because the farm operator numbers by sales class for 1974 were deflated to 1964 price levels. This resulted in some of the smaller farms not meeting the minimum sales requirement when the sales were deflated.
Projections
Future farm numbers can be projected if one assumes that future adjustments and phases of successive cohorts will follow the patterns of the previous. ones. The adjustments in the cohort groups are computed as the ratio of two periods and the ratios are applied to the succeeding base-period cohorts.
Figure 10 shows the cohort movements, number changes, and projected farm operator numbers by age group. For example, if we trace the 1920-29 cohort by 10-year periods starting with 1964, we find 740,000 farm operators in the 35-44 ye r group. By 1974, 98 percent of the group remained in farming, namely 72t,300 farm operators of the age of 45-54 years old. This implies a cohort
47




Table 28--Change in farm operator numbers by age cohort, by sales class, 1964-74 Cohort by year : Age at Less than $2,500 to $5,000 to :$10,000 to :$20,000 to $40,000 to $100,000 Total
of birth : 1974 Census :$2,500 4,999 9,999 19,999 39,999 99,999 or more
Years .Farmers
After 1949 Less than 25: 22.8 8.5 10.6 9.1 5.4 2.4 0.4 59.3
1940 to 1949 25 to 34 : 118.7 21.9 30.2 30.6 24.8 16.8 4.8 243.8
1930 to 1939 35 to 44 95.5 7.7 10.1 1.2 10.3 19.5 9.0 153.3
1920 to 1929 45 to 54 12.6 12.8 -13.1 -27.7 -4.8 15.4 6.7 -23.7
1910 to 1919 : 55 to 64 -83.3 -37.5 -50.7 -53.8 -15.8 3.4 0 -237.7
1900 to 1909 : 65 to 74 :-101.7 -51.2 -7.8 -62.3 -43-6.9 -2.1 -326.5
Before 1900 : 75 or -426.8 -88.9 -63.8 -37.2 -7.0 -7.7 -2.7 -644.1
older 1/
Total : NA -362.2 -152.3 -154.7 -140.1 -21.4 43.0 16.1 -771.6
Net entry : NA : 249.6 50.9 50.9 40.9 40.5 100.6 37.0 456.4
Net exits NA 974.0 329.9 290.1 321.1 73.3 14.6 4.8 2,003.6
Replacement rate: NA : .26 .15 .18 .13 .55 6.89 7.71 .23
1/ Assumed all operators 65 years and older in 1964 would have exited by 1974 or before the age of 75.
NA = Not applicable.
Source: U.S. Dept. of Commmerce, Bureau of the Census, Census of Agriculture; adjusted for reported undercounting; excludes abnormal farms; 1974 sales classes adjusted to 1964 prices.




ratio of 0.98 for the group born between 1920 and 1929. To project the number
in this cohort to 1984, cohort ratio for the 45-54 years age group in 1964 and
the 55-64 years age group in 1974 (0.77) is multiplied by the number of farm operators of the 45-54 years age group in 1974 (728,300). Therefore, 563,000 farm operators are projected for the 55-64 age group in 1984. Following the same procedure, 366,000 farm operators of age 65-74 are projected for 1994. No farm operators in this cohort will remain in farming by the year 2004, since we assume that all farm operators will leave farming by age 75. 15/
The projected numbers of farm operators by age group to the year 2004 are shown in figure 10. Summing the numbers in each group for each year indicates that the total number of farm operators is likely to continue to decline. The number is projected to decline from 2.9 million in 1974 to about 2.4 million in 1984, 2 million in 1994, and 1.6 million in 2004.
15/ The cohort ratios for the under 25-year old group are calculated differently. The Census reports no data for this group as they would have been less than 15 years old in the earlier period. To calculate their entry rates we assumed that these youngest entries were replacing their fathers and we allowed up to a 40-year age difference, as suggested by Tolley (21). So the ratio became the number of farm operators who are less than 25 years old in a specific year divided by the total of the farm numbers in the 35-44 and 45-54 age group enumerated 10 years earlier.
Table 29--Change in farm operator numbers, by age cohort and farm size, 1964-74
Cohort by Age at 1- 100- 220- :500- 1,000- 2,000
year of 1974 Census 99 219 449 999 1,999 acres Total
birth acres acres acres :acres acres and over
Years 1,.000 farmers
After 1949 Less than 25 29.4 15.2 11.6 3.7 1.3 .7 61.9
1940-49 25-34 123.1 52.7 43.2 19.7 8.4 4.7 251.8
1930-39 35-44 :89.9 25.8 14.3 16.2 8.8 55.9 160.9
1920-29 :45-54 :13.4 -17.5 -22.1 5.3 5.6 3.6 11.7
1910-19 55-64 -67.9 -70.1 -58.6 -13.1 -2.9 -1.6 -214.2
1900-09 65-74 :-93.0 -89.4 -71.8 -21 .4 -7.0 -3.8 -286.4
Before 1900 75 or older 1/ :-363.1 -156.7 -79.6 -25.3 -10.4 -9.0 -644.1
Total : NA :-268.2 -240.0 -163.0 -14.9 3.8 .5 -681.8
Net entry NA 242.4 93.7 69.1 39.6 18.5 11.3 474.6
Net exits : NA 456.1 246.1 151.4 46.7 17.4 12.8 930.5
Replacement rate NA .53 .38 .46 .85 1.06 .88 .51
NA = Not applicable.
1/ Assumed all operators 65 years and older in 1964 would have exited in 1974 before the age of 75.
Source: (25), adjusted for reported undercounting, excludes abnormal farms.
49




Sales Distribution
Following the same procedure, the numbers of farm operators by sales class and acreage can be projected based on the age cohort ratios presented in tables 30 and 31. The entry rates are higher for the larger size groups as indicated by the larger cohort ratios. On the other hand, the ratios are higher for the smaller classes than the mid-classes, suggesting a real possibility of a bimodal distribution of the number of farms in the future. Also, the retention rates for older operators are higher in the larger and smallest size classes.
Of the projected 1.7 million farms in 2004, large farms (sales of at least $100,000) will account for about 38 percent, an increase from 5 percent in 1974. By contrast, small farms (sales of less than $20,000) will account for 49 percent, down from 72 percent in 1974 (table 32). However, part of the increase in the percentage of large farms is due to the anticipated price inflation. When sales receipts are expressed in 1964 price levels, the proportion reduces to only 9 percent. The number of farms reduces from the projected 620,000 to 129,300 in 2004 (table 33).
Figure 10
Farm Operator Age Cohiort Movements, 10 Year Periods
1964 1974* 19840 1994 0 2004e
Cohort Ratio
Current Age (Years) .037,& .037 .037 .3
Less than 25 61.2 5.12 61.9 5.12 45.6 5.12 35. 5.12 33.6I
35-44 740.0 0.98 0.98 098 61 0.98 34.
45-54 942. 62. 0. 4. 5.
55-64 818.8 0.5 728.4 65 563.0 0.5 388.6 3476 6
65-74 644.153.47.360226
75 or older 00 0
Total 3,556.7 2,874.9 2,358.2 1,934.9 1,609.7
*Data rounded after calculations.
A The ratio Is defined as all new entrants under 25 years divided by the number of operators who, 10 years earlier, were
35-54 years old (see text for more detail).
o0 Assume all exits by age 75.
*1984, 1994, and 2004 are projections.
Nu.mbsrs--in boxes are In thousands.
50




Table 30--Ratio of 1974 farmers to 1964 farmers by age cohort and sales class 1/
Cohort Age in : Less : :
birth 1974 than $2,500- $5,000- : $10,000- : $20,000- $40,000- $100,000 Total
year : Census $2,500 : 4,999 9,999 19,999 39,999 : 99,999 or more
Years Ratio 2/
After 1949 : Under 25 3/: 0.03 0.04 0.04 0.03 0.03 0.04 0.02 0.04
1940-49 : 25-34 : 5.54 3.38 3.85 4.22 6.83 14.48 23.17 5.05
1930-39 35-44 : 1.69 1.19 1.19 1.02 1.27 2.29 3.56 1.14
1920-29 45-54 1.04 .85 .88 .78 .94 1.45 1.70 .97
1910-19 55-64 .79 .70 .67 .64 .80 1.10 1.00 .75
1900-09 65 or more .73 .59 .44 .40 .49 .65 .66 .60
1/ 1974 sales class data adjusted to 1964 prices.
7/ The number of 1974 farmers in each sales class and each age cohort divided by the number of 1964 farmers in the same sales class and age cohort.
3/ The ratio for this age cohort is defined as all new entrants under 25 divided by the number of operators who, 10 years earlier, were 35-54 years old (see text for more detail).
Table 31--Ratio of 1974 farmers to 1964 farmers, by age cohort and size of farm 1/
Cohort : Age in : : : : 1,000- : 2,000
birth : 1974 : 1-99 : 100-219 : 220-499 : 500-999 : 1,999 : or more : Total
year : Census : acres : acres : acres : acres : acres : acres
Years : Ratio 2/
After 1949 : Under 25 3/: 0.04 0.04 0.03 0.03 0.03 0.02 0.04
1940-49 : 25-34 : 4.99 4.52 4.89 7.83 10.74 10.20 5.12
1930-39 : 35-44 : 1.59 1.31 1.19 1.64 1.91 2.05 1.46
1920-29 : 45-54 : 1.04 .90 .86 1.10 1.25 1.25 .98
1910-19 : 55-64 : .83 .71 .70 .81 .89 .91 .77
1900-09 : 65 or more : .75 .59 .51 .56 .64 .72 .65
1/ Ratios for acre size differ slightly from those by sales classes because sales class data were deflated to 1964 prices.
2/ The number of 1974 farmers in each sales class and each age cohort divided by the number of 1964 farmers in the same sales class and age cohort.
3/ The ratio for this age cohort is defined as all new entrants under 25 divided by the number of operators who, 10 years earlier, were 35-54 years old (see text for more detail).
51




Table 32--U.S. farm operators by sales class, selected years and projections
Yer Less than: $2,500- $5,000- $10,000- $20,000- $40,000- $100,000 Total
Yer $2,500 :$4,999 :$9,999 :$19,999 :$39,999 :$99,999 :or more:
1 ,000 farmers
1964 1,657.3 473.9 528.6 484.1 266.9 113.5 32.4 3,556.7
1974 1,400.6 322.9 319.5 326.9 327.6 327.5 149.9 2,874.9
1984 750.0 250.0 250.0 200.0 200.0 335.0 365.0 2,350.0
1994 820.0 158.0 100.0 80.0 120.0 220.0 580.0 2,078.0
2004 490.0 80.0 100.0 120.0 80.0 160.0 620.0 1,650.0
Percent
1964 46.6 13.3 14.9 13.6 7.5 3.2 .9 100.0
1974 38.3 11.2 11.1 11.4 11.4 11.4 5.2 100.0
1984 31.9 10.6 10.6 8.5 8.5 14.3 15.5 100.0
1994 39.6 7.3 4.8 3.9 5.8 10.6 28.0 100.0
2004 29.7 4.8 6.1 7.3 4.8 9.7 37.6 100.0
Table 33--U.S. farm operators by sales class, in 1964 prices, selected years and projections
Less than: $2,500- $5,000- :$10,000- :$20,000- :$40,000- :$100,000 Toa
Year $2,500 :$4,999 :$9,999 :.$19,999 :$39,999 $99,999 or more Toa
1 ,000 farmers
1964 1,657.3 473.9 528.6 484.1 266.9 13532.4 3,556.7
1974 .1,295.1 321.6 373.9 344.0 245.5 156.5 48.5 2,785.1
1984 1,068.1 207.9 252.4 225:'0 208.2 203.1 68.8 2,233.5
1994 859.1 129.9 165.7 135.9 160.2 249.5 96.6 1,796.9
2004 663.7 80.4 107.5 78.9 114.6 291.0 129.3 1,465.4
Percent
1964 46.6 13.3 14.9 13.6 7.5 3.2 .9 100.0
1974 46.5 11.6 13.4 12.4 8.8 5.6 1.7 100.0
1984 47.8 9.3 11.3 10.1 9.3 9.1 3.1 100.0
1994 47.8 7.2 9.2 7.6 8.9- 13.9 5.4 100.0
2004 45.3 5.5 7.3 5.4 7.8 19.9 8.8 100.0
52




Acreage Distribution
Table 34 presents the distribution of farm operator numbers by acre size group for 1964, 1974, and projections for 1984, 1994, and 2004. The projections show declining numbers in all acre sizes, except the 1,000 to 1,999 acre size, through 2004. The numbers of farm operators who farm more than 1,000 acres account for 10 percent of the total number, an increase from 5.5 percent in 1974. By contrast, the proportion of small farm operators with less than 220 acres is projected to remain the same in 2004, about 70 percent. Actually, the number of farm operators with less than 100 acres is projected to account for an increasing percentage of the total.
Table 34--U.S. farm operators, by size of farm, selected years and projections
100- 220- : 500- :1,000- :2,000
Year :1-99 : 219 500 : 999 :1,999- :or more: Total
:acres acres :acres acres : acres : acres
1,000 farms
1964 : 1,625.1 890.0 665.1 225.1 89.8 61.6 3,556.7
1974 : 1,356.9 649.9 502.1 210.3 93.6 62.1 2,874.9
1984 : 1,171.2 472.7 366.4 120 95.5 60.4 2,358.2
1994 : 1,005.1 345.0 258.4 .172.8 96.5 57.1 1,934.9
2004 : 862.4 256.8 182.5 156.1 98.0 53.9 1,609.7
Percent
1964 : 45.7 25.0 18.7 6.3 2.5 1.8 100.0
1974 : 47.2 22.6 17.4 7.3 3.3 2.2 100.0
1984 : 49.7 20.0 15.5 8.1 4.1 2.6 100.0
1994 : 51.9 17.8 13.4 8.9 5.0 3.0 100.0
2004 : 53.5 16.0 11.3 9.7 6.1 3.4 100.0
53




COMPARISON OF ALTERNATIVE PROJECTIONS
Up to this point, we have presented projections of farm numbers and size distributions to 2000 for each of the four most frequently used projection methods. This chapter summarizes those projections and compares them for accuracy and reasonableness. A set of "most likely" projections were presented earlier.
All the projections point to a continuous decline in farm numbers, to about 1.75 million farms by 2000, although the estimate varies by the method used and whether the projection is by acreage or sales size. The trend extrapolation and Markov process analysis closely aprallel one another for acreage distribution, while the negative exponential function performs erratically. For sales distributions, the Markov process and age cohort analysis give very consistent projections; negative exponential functions again perform poorly.
Acreage distributions projected to 2000 by trend extrapolation, Markov process, and age cohort analysis are very consistent. Negative exponential functions probably underestimate the percentage of small farms, and overestimate that for medium-size and large farms (table 35). The projected total number of farms, based on the acreage distribution, varies from 1.7 million to
1.8 million in 2000. The small deviations among the methods give confidence in projecting the acreage distributions of farm numbers (fig. 11). Unfortunately, farmland acreage is not the best size measure. Frequently, sales receipts are preferred to farmland acreage as a size measure. Furthermore, the new definition of a farm adopted by the U.S. Department of Agriculture in 1978 makes it almost necessary to base projections on sales.
Total farm number projections based on the sales distribution vary more widely, however, ranging from 1.9 million to 2.1 million in 2000 (fig. 12). The large number of farms obtained from trend extrapolation is partly due to the erratic trend equation for farms with $20,000 to $39,999 in sales. Instead of projecting a downturn (a trend established from 1969 to 1974), an upward increasing trend is projected. Markov process and age cohort analysis, on the other hand, give very consistent projections.
Table 35--Comparison of alternative projections by size class in 2000
Size of farm (acres) Sales class
Alternative
projections Less than: 220 to 1,000 Less than: $20,000- $100,000 220 999 and over: $20,000 $99,999 and over
Percent of total farms
1974 actual 69.8 24.8 5.4 72.0 22.8 5.2
Trend extrapolation 61.4 28.7 9.9 39.1 46.8 14.1
Negative exponential:
functions : 34.6 51.0 14.4 5.8 20.1 74.1
Markov process 67.7 22.4 9.9 49.9 18.8 31.3
Age cohort analysis 69.5 21.7 8.8 51.8 15.5 32.8
54




Figure 11 Figure 12
Projected Numbers of Farms Projected Numbers of Farms
Based on Acreage Distribution Based on Sales Distribution
Million farms Million farms
Trend extrapolation and .Trend extrapolation
4.0 Markov process 4.0 Markov process
--Negative exponential *---Negative exponential
functionfunction
3. ...Age cohort analysis 3.5 ...Age cohort analysis
3.0 -3.0
2.5 2.5.
2.0 -2.0
199 4 9 4 0 5 0 5 000 1959 64 69 748 590 9 000
The decline in the percentage of small farms (less than 220 acres) 'and the increase in large farms (1,000 acres and more) are less apparent than the changes in the total number of farms would lead us to believe. While the U.S. farm sector experienced a 19-percent decline-in the number of all farms between 1964 and 1974, the decline in the percentage of small farms was negligible-from 71 percent in-1964 to 70 percent in 1974. Similarly, the percentage of the large farms increased by only 1 point, from 4 percent in 1964 to 5 percent in 1974. This size configuration of American farm structure is projected to continue into 2000.
The sales distribution of farm numbers is projected to have a more apparent shift from those with low sales to those with high, partly due to the anticipated high price inflation. By 2000, small farms (sales of less than $20,000) are likely to account for 50 percent of the total, a decline from 72 percent in 1974. By contrast, the percentage of large farms (sales of $100,000 and more) is projected to increase to 32 percent, a rise from 5 percent in 1974.,
The procedure used to measure the percentage error between the actual and projected number of farms is the inequality coefficient (U) developed by Theil
(21):
55




where ~U = th (hi inqalt coffcin,2
1974e nubr wi=th precins.alt Tofrthendiaetetereopoeto
accuracy in each size class, the simple percentage differences are also shown.
The accuracy of the projections differs among the four projection methods. In general, projections of farm numbers and size distributions by acreage tend to be more accurate than those by sales. This is understandable since projections by sales are complicated by the inflation factor. Even though specific attempts were made to account for the effects of inflation in changes in farm numbers of the Markov chain and age cohort analyses, some errors of measurement probably remain.
Simple trend extrapolation typically gives fairly accurate projections by acreage, but commits a larger error of projections by sales (tables 36 and 37). A 13.2-percent error rate was found for the projections by sales in 1974, but the error rate was greater for farms with sales of $40,000 and over. 16/ This partly reflects the fact that the simple trend extrapolation tended tunderestimate the shifts in farm numbers from low to high sales as a result of the 80-percent increase in prices received by farmers during the 1969-74 period. The projected numbers of small farms do not differ significantly from actual 1974 numbers.
The simple trend extrapolation method in years other than 1974 yielded a similar accuracy and pattern. Theil-U inequality coefficients of 0.0151 and 0.0084 were computed for 1964 and 1969 projections based on acreage. Those
low numbers reflect the insignificant changes in prices received by farmers in the sixties.
The negative exponential function is a procedure to project the size distribution, especially when acreage is used as the size measure. As we indicated before, this method was not very satisfactory for projections based on
*-16/ The U coefficient of 0.13 for the trend extrapolation by sales class means that there is an average difference of 13 percent between actual and projected farm numbers in 1974. The smaller the U coefficients, the better is the projection accuracy.
56




Table 36--Projected number of fat-ins by acreage in 1974, simple trend extrapolation
Actual Projected Percent
Size of farm 1974 1974 difference I/
N umber Percent
1-99 acres 1,356,905 1,336,748 -1.49
100-219 acres 649,923 652,620 +0.41
220-499 acres 502,148 512,344 +2.03
500-999 acres 210,702 214,218 +1.67
1,000-1,999 acres 93,264 83,599 +0.36
2,000 acres and over 61,994 60,947 -1.69
All farms 2,874,936 2,870.476 -0.15
1/ Theil-U = 0.0144 or 1.44 percent.
Table 37--Projected number of farms by sales in 1974, simple trend extrapolation
Actual Projected Percent
Sales class 1974 1974 difference l/
Number Percent
Less than $2,500 1,100,597 1,136,826 3.29
$2,500-$4,999 322,949 328,651 1.77
$5,000-$9,999 319,474 319,576 0.03
$10,000-$19,999 326,905 338,660 3.60
$20,000-$39,999 327,567 340,698 4.01
$40,000-$99,999 327,516 258,785 -20.99
$100,000-$199,999 99,385 68,101 -31.48
$200,000-$499,999 39,335 26,390 -32.91
$500,000 and over 11,206 8,232 -26.54
All farms 2,874.934 2,825.919 -1.70
I/ Theil-U = 0.1316 or 13.16 percent.
57




sales, yielding a 94-percent error for 1974 sales projections (table 38). 17/ This procedure proved equally unsatisfactory to project farm numbers based on acreage, yielding errors of 68 percent (table 39). Those results suggest that considerable discrepancies still exist between the actual and estimated distribution functions obtained by the negative exponential function. As shown in table 38, there are significant underestimates in the smaller size classes and overestimates in the medium and larger classes. Also, this function overestimates the numbers of farms with sales between $10,000 and $500,000 by factors rangingfrom 1.5 to 4.5, and underestimates the number of farms with sales less than $10,000.
Markov chain analysis, modified somewhat in this study to adjust for the effects of price inflation on changes in farm numbers, appears to be promising. The errors of projection, by both acreage and sales, in 1974 were about 4 and
0.1 percent (tables 40 and 41). In contrast to previous applications, there are no gross estimation errors evidenced in these projections. It is essential to capture the effects of price inflation-in-ane-ra of price instability to avoid gross distrotions and inaccuracies in projections of farm numbers by sales.
In addition, those results suggest that the underlying assumption of the Markov process on the growth of farms is questionable. Instead of a farm's growing from the smallest to the largest size, the census data suggest that the largest farms tend to come from smaller farms of a minimum viable size, and not from the smallest size classes.
Age cohort projections tend to be similar to those from the Markov process. Compared with 1969 actual farm numbers by both acreage and sales, age cohort analysis yielded a 10.9-percent and a 16-percent error according to the Theil-U coefficient (tables 42 and 43). 18/ Age cohort analysis appears to underestimate farms with $2,500 to $4,999 sales and to overestimate those with $20,000 to $39,999 sales.
17/ The percentage error is derived from comparing actual proportions of 1974 farm numbers by size class with projected percentages. In this way, the comparison is not complicated by projections on land in farms and acreage farm size.
18/ In projecting the 1969 number of farms by acreage, the cohort ratios constructed from the 1950-59 period were multiplied by the age-size distributions in 1959. For sales, a 1959-69 cohort-ratio matrix was multiplied by the 1964 age-size matrix to project the 1974 farm numbers by sales class. This procedure overlapped 5 years of calculation of the age cohort ratios and the projection period. This was necessary because different sales class intervals were published by the Bureau of the Census before 1959.
58




Table 38--Projected proportions of 1974 farm numbers by sales, class,
negative exponential function
Sales class Actual Projection Percentage difference l/
Percent
Less than $2,500 38.3 4.5 -88.3
$2,500-$4,999 11.2 4.3 -61.6
$5,000-$9,999 11.1 6.2 -44.1
$l0,000-$19,999 11.4 14.3 25.4
$20,000-$39,999 11.4 20.7 81.6
$40,000-$99,999 11.4 32.3 183.3
$I00,000-$199,999 3.4 14.5 326.4
$200,000-$499,999 1.4 2.2 57.1
$500,000 and over .4 1.0 150.0
All farms 100.0 100.0 NA
NA means not applicable.
1/ Theil-U = 0.941 or 94.1 percent.
Table 39--Projected proportions of 1974 farm numbers by size of farm, negative exponential functions
Size of farm Actual Projection Percentage difference l/
Percent
1-69 acres 37.2 14.7 -60.5
70-99 acres 10.0 5.7 -43.0
100-139 acres 9.0 7.0 -22.2
140-179 acres 8.3 6.4 -22.9
180-219 acres 5.3 5.7 7.5
220-259 acres 4.3 5.3 23.3
260-499 acres 13.2 23.4 77.3
500-999 acres 7.3 21.7 197.3
1,000-1,999 acres 3.2 9.1 184.4
2,000 acres and over 2.2 1.0 -54.5
All farms 100.0 100.0 NA
NA means not applicable.
1/ Theil-U = 0.681 or 68.1 percent.
59




Table 40--Projected number of farms, by size of farm, 1974, Markov process
Size of farm : Actual Projected Percent
difference
Number
1-69 acres : 1,069,433 1,027,082 -3.96
70-99 acres 287,472 287,137 -0.12
100-139 acres 258,690 265,079 2.47
140-179 acres 239,786 245,530 2.40
180-219 acres 151,447 155,180 2.46
220-259 acres 122,851 127,105 3.38
260-499 acres 379,297 392,479 3.47
500-999 acres 210,702 219,227 4.04
1,000-1,999 acres 93,264 93,898 0.68
2,000 acres and over 61,994 61,889 -0.17
All farms : 2,874,936 2,874,506 -0.01
1/ Theil-U = 0.0367 or 3.67 percent.
Table 41--Projected number of farms by sales class, 1974, Markov process
Sales class Act ual Projected Percent
difference
1,000 Farms Percent
Less than $2,500 1,100.6 1,109.7 .8
$2,500-4,999 322.9 322.9 0
$5,000-9,999 319.5 320.4 .3
$10,000-19,999 326.9 328.2 .4
$20,000-39,999 327.6 322.3 -1.6
$40,000-99,999 327.5 322.1 -1.6
$100,000-199,999 99.4 97.3 -2.1
$200,000-499,999 : 39.3 38.5 -2.0
$500,000 and over : 11.2 11.0 -1.8
All farms : 2,874.9 2,872.4 -.1
1/ Theil-U = 0.0007 or 0.07 percent.
60




Table 42--Projected 1969 farm numbers, by size of farm, age-cohort analysis I/
Size of farm Actual Projected Percent
difference
:- Number ------------------Percent---Less than 10 acres 162,111 120,221 25.8
10-49 acres 473,465 407,655 13.9
50-69 acres 177,028 140,847 20.4
70-99 acres 282,914 231,065 18.3
100-139 acres : 278,752 240,448 13.7
140-179 acres : 263,012 244,752 6.9
180-219 acres 165,209 164,682 3.2
220-259 acres 141,733 149,074 5.2
260-499 acres 419,421 419,189 .1
500-999 acres 215,659 194,967 9.6
1,000 acres or more 150,946 137,432 9.0
Total 2,730,250 2,450,332 10.3
1/ Not adjusted for census underenumerati'on; Theil-U is 0.1087 or 10.9 percent.
Table 43--Projected 1974 farm numbers by sales class, age-cohort analysis 1/
Sales Class Actual Projected Percent
difference
:. Number-------------- ----Percent---Less than $2,500 768,838 800,000 4.1
$2,500-$4,999 289,983 155,000 -45.6
$5,000-$9,999 296,373 260,000 -12.3
$10,000-$19,999 310,011 355,000 14.5
$20,000-$39,999 : 321,771 390,000 21.2
$40,000-$99,999 324,310 345,000 6.4
$100,000 or more : 152,599 165,000 8.1
All farms 2,463,885 2,450,000 .6
1/ Not adjusted for census underenuieration; the Theil-U is 0.16 or 16 percent. The accuracy for the farm operator age distribution was very good, only 2.1 percent error of projection was computed. Projections presented in this table have )been adjusted to take into account the effects of price inflation.
61




CONCLUSIONS AND IMPLICATIONS
The techniques employed in this study used several kinds of data and assumptions in projecting farm numbers and size distributions. The specific projections are, therefore, contingent upon the techniques, assumptions, and data employed. The different techniques are not necessarily equally valid for examining the same questions. The results, however, provide different perspectives and suggest some common tendencies and regularities.
Although the four frequently used techniques project future number and size of farms with some regularity, their accuracy varies. In addition, the projected size distributions may differ considerably from one procedure to another, even though the projected totals are similar. For example, farm numbers by acreage projected by trend extrapolation, Markov process, and age cohort analysis are reasonably comparable. However, trend extrapolation and age cohort analysis both project a slight decline in the number of farms of 2,000 acres and over, but Markov process projects a continuous, slow increase in the number of such farms (table 44).
Trend extrapolation gives fairly accurate projections by acreage, but commits a large projection error in sales distribution. Unlike the continuous trends for the acreage distribution, some of the trends for the sales distribution occasionally reverse. Trend projections, under this circumstance, could lead to an incorrect direction. For example, the number of farms with sales of $20,000 to $39,999 increased from 1959 to 1969, but then declined after 1969. Once a new trend is established, it is likely to continue to project an increasing trend for the number of such farms.
Table 44--Alternative projections of farm numbers, by size of farm, 2000
Negative
Size of farmn 1974 Trend :exponential :Markov Age
Actual extrapolation functions process :cohort
1 ,000 farms
1-99 acres :1,356 751 320 864 934
100-139 acres 259 113 121
140-179 acres 240 300 104 102 301
180-219 acres 151 96 66
220-259 acres 123 286 89 48 220
260-499 acres 379 712 182
500-999 acres 211 205 430 152 164
1,000-1,999 acres 93 108 224 91 97
2,000 acres and over: 62 61 37 77 56
All1 farms :2,875 1,711 1,826 1,705 1,772
62




Projected total numbers of farms and those for the medium-size groups
(sales of $20,000 to $99,999) obtained from the trend extrapolation appear to be overestimated. This reflects another serious problem with this technique. Even though there was a consistent, increasing trend which occurred in the past, the number of farms may begin to decline at some point in the future. For example, despite the continuous, increasing trend for the number of farms with sales of $40,000 to $99,999, a decline in the number is projected by other techniques (table 45). Thus, a simple trend extrapolation fails to foresee that the trend can be reversed. Finally, the trend extrapolation, by failing to capture the effects of inflation on changes in farm numbers, makes a larger projection error. If inflation is higher in the future, then the number of farms in the upper sales classes is likely to be underestimated as evidenced in table 45.
The numbers of farms projected by negative exponential functions differ significantly from those obtained by other procedures and apparently have larger percentage errors. The number of projected small farms (sales of less than $20,000) is too low and the number of projected large farms (sales of $100,000 and over) is too high. The large projection errors when this technique is applied to sales distributions are expected, but projections by acreage distribution are not much better. The projected numbers of farms with 1 to 99 acres and 2,000 acres and over are much smaller than those projected by other procedures. On the other hand, the projected numbers of farms with 260 to 1,999 acres appear to be much too large, and present a discontinuity to the recent trends. In short,, evidence suggests that while the distributional functions are stable over time, an empirical approximation of the true theoretical function shows a considerable discrepancy.
Table 45--Alternative projections of farm numbers by sales class, 2000
:1974 Trend :Negative :Markov :Age
Sales class :actual extrapolation :exponential :process :cohort
:functions:
1 ,000 farms
Less than $2,500 1,101 456 13 640 655
$2,500-4,999 323 ill 13 72 119
$5,000-9,999 319 90 29 108 100
$10,000-19,999 327 164 53 108 100
$20,000-39,999 328 443 102 88 100
$40,000-99,999 328 539 271 262 190
$100,000-199,999 99 188 354 168
$200,000-499,999 39 81 606 190 600
$500,000 and over 11 27 417 226
All farms 2,875 2,109 1,857 1,862 1,864
63




The Markov process and age cohort techniques give very similar projections. However, we found that the traditional farm growth assumption, underlying the Markov process is questionable. Census data suggest that firms tend to enter farming at an economically viable size and then expand. The age cohort techniques incorrectly project a slight decline in the number of farms with 2,000 acres and over. By contrast, the Markov process projects a moderate increase-a trend more consistent with the past. In sum, Markov process and age cohort techniques appear to be more promising for projecting sales distributions.
The most likely projections for the number of farms are synthesized from projections based on the acreage distribution from trend extrapolation and Markov process. The small deviations between the two methods and the fact that the projections are free of any estimation errors in accounting for the effects of price inflation, gives us confidence in projecting the total number of farms. Farm numbers are, therefore, projected to decline from 2.87 million in 1974 to 2.32 million in 1985, 2.09 million in 1990, 1.89 million in 1995, and 1.75 million in 2000.
Projections on farm numbers by acreage are computed by multiplying the
most likely total number of farms by a synthesized distribution of farm numbers obtained from trend expolation and Markov process projections, since the two methods yield a higher degree of accuracy in reproducing historical data. Similarly, projections on farm numbers by sales class are computed by multiplying the most likely total number of farms by a synthesized distribution of farm numbers obtained from Markov process and age cohort analysis. The most likely projections on number of farms by acreage and sales class are given in tables 5 and 6.
Most of the projections in this study are trend related, with the exception of assumptions to account for the effects of inflation on changes in farm numbers by sales. However, studies that base projections on causal economic relationships are needed. One such approach is to link the transition probabilities, as employed in the Markov process, and the cohort ratios, as used in age cohort analysis, to factors that cause structural changes. This, however, requires more detailed structural data on a longitudinal basis--that is, a data base linking the "true" structural changes from one census year to the others, and the associated factors that have caused the changes.
Further specificity is also needed for production regions and farm commodity subsectors--each of which tends to have its own unique characteristics. To make projections of the number of farms and size distribution more useful, it would also be desirable to disaggregate the study by region and by commodity subsector. Implications for other structural characteristics drawn from such projections would be more useful than those based on national averages.
64




LITERATURE CITED
(1) Boxley, Robert F., "Farm Size and the Distribution of Farm Numbers," Agricultural Economics Research, Vol. 23, No. 4, Oct. 1971.
(2) Chennareddy, Venkareddy, and Glen L. Johnson, "Projections of Age Distribution of Farm Operation in the United States Based Upon Estimates of Present Value of Income," American Journal of Agricultural Economics,
Vol. 50, No. 3, Aug. 1968.
(3) Ching, C. T. K., "A Note on the Stability of Firm Size Distribution Functions for Western Cattle Ranches," American Journal of Agricultural
Economics, Vol. 55, No. 3, Aug. 1973.
(4) Chow, Gregory C., "Tests of Equality Between Sets of Coefficients in Two Linear Regressions," Econometrica, Vol. 28, No. 3, July 1960.
(5) Daly, Rex F., J. A. Dempsey, and C. W. Cobb, "Farm Numbers and Sizes in the Future," in Size, Structure, and Future of Farms, ed. by
A. Gordon Ball and Earl 0. Heady, Ames, Iowa State University Press,
1972, pp. 314-332.
(6) Dixon, B. L., and S. T. Sonka, "A Note on the Use of Exponential Functions for Estimating Farm Size Distributions," American Journal of
Agricultural Economics, Vol. 61, No. 3, Aug. 1969.
(7) Dovring, Folke, "Distribution of Farm Size and Income: Analysis by Exponential Functions," Land Economics, Vol. 49, No. 2, May 1973.
(8) "Income and Wealth Distributions: The Exponential Functions," AE-4212, Dept. of Agr. Econ., Univ. of Illinois, June 1969.
(9), "Farm Size Data: Frequency Distribution, Interpolation, and Projection," AERR-50, Dept. of Agr. Econ., Univ. of Illinois,
May 1962.
(10) Guither, Harold D., "Factors Influencing Farm Operators Decision to Leave
Farming," Journal of Farm Economics, Vol. 45, No. 3, Aug. 1963.
(11) Hill, Lowell D., "Characteristics of the Farmers Leaving Agriculture in
Iowa County," Journal of Farm Economics, Vol. 44, No. 2, May 1962.
(12) Judge, G. G., and Earl R. Swanson, Markov Chains: Basic Concepts and Suggested Uses in Agricultural Economics, Dept. of Agr. Econ., AERR-49,
Univ. of Illinois, Dec. 1961.
(13) Kaldor, Donald R., and William M. Edwards, Occupational Adjustment of
Iowa Farm Operators who Quit Farming in 1959-1961, Agr. and Home Econ.
Exper. Sta., Iowa State Univ., Special Bul. No. 75, March 1975.
(14) Kanel, Don, "Farm Adjustments by Age Groups, North Central States,
1950-1959," Journal of Farm Economics, Vol. 45, No. 1, Feb. 1963.
65




(15) Klein, L. R., An Introduction to Econometrics, Prentice-Hall, Inc.,
Englewood Cliffs, N.J., 1972, p. 150.
(16) Krenz, R. D., "Projections of Farm Numbers for North Dakota with Markov
Chains," Agricultural Economics Research, Vol. 16, No. 3, July 1964.
(17) Kyle, L. R., W.B. Sundquist, and H. D. Guither, "Who Controls Agriculture Now?-The Trends Underway" in Who Will Control U.S. Agriculture?
ed. by H. D. Guither, North Central Regional Extension Publication 32,
Urbana, Illinois, Aug. 1972.
(18) Lee, T. C., G. G. Judge, and T. Takayama, "On Estimating the Transition
Probabilities of a Markov Process," Journal of Farm Economics,
Vol. 47, No. 3, Aug. 1965.
(19) Lewis, James A., Landownership in the United States. 1978, AIB-435,
U.S. Dept. of Agr., Econ. Stat. Coop. Serv., April 1980.
(20) Padberg, Daniel I., "The Use of Markov Process in Measuring Changes in
Market Structure," Journal of Farm Ecomonics, Vol. 44, No. 1,
Feb. 1962.
(21) Theil, H., Applied Economic Forecasting, Amsterdam: North-Holland
Publishing Co., 1966.
(22) Tolley, G. S., "Management Entry into U.S. Agriculture," American
Journal of Agricultural Economics, Vol. 52, No. 4, Nov. 1970.
(23) U.S. Department of Agriculture, Economics, Statistics, and Cooperatives
Service, Farm Income Statistics, SB-609, July 1978.
(24) U.S. Department of Agriculture, Economics, Statistics, and Cooperatives
Service, Status of the Family Farm: Second Annual Report to the
Congress, AER-434, Sept. 1979.
(25) U.S. Department of Commerce, Bureau of Census, Census of Agriculture,
General Reports, 1959, 1964, and 1974.
(26) U.S. Department of Commerce, Bureau of Census, Census of Agriculture,
Special Reports on Evaluation of Coverage, 1959, 1964, 1969, 1974.
66




Appendix table 1--Selected structural characteristics of U.S. farms, by sales class
: $100,000 : $40,000 to : $20,000 to : $10,000 to $5,000 to : $2,500 to : Less than
Item Unit : and over : $99,999 : $39,999 : $19,999 : $9,999 : $4,999 : $2,500 : All
: (.lass IA) : (class IB) : (class II) : (class III): (class IV) : (class V) : (class VI): Farms
Number of farms: :
1969 : 1,000 52.0 169.7 331.0 395.5 390.4 395.1 994.5 2,728.1
: Percent 1.9 6.2 12.1 14.5 14.3 14.5 36.5 100
1974 : 1,000 : 152.6 324.3 321.8 310.0 296.0 290.0 768.8 2,463.9
: Percent : 6.2 13.2 13.1 12.6 12.0 11.8 31.2 100
Cash receipts:
1969 :Bil. dol.: 15.3 10.1 9.3 5.7 2.8 1.3 .98 45.48
Percent : 33.6 22.2 20.4 12.5 6.2 2.9 2.2 100
1974 :Bil. dol.: 43.7 20.1 9.2 4.5 2.1 .98 .74 888.32
Percent : 53.7 24.7 11.3 5.5 2.6 1.2 .9 100
Cash receipts per:
farm:
1969 : Dols. : 293,915 59,364 27,999 14,396 7,208 2,626 953 16,689
1974 : Dols. : 286,268 61,890 28,737 14,387 7,215 3,640 1,143 25,234
Form of organiza-:
tion:
Sole proprietorships:
1969 : Farms : 30,683 131,418 277,233 341,063 344,063 356,105 896,005 2,376,570
: Percent : 59.0 77.4 83.8 86.1 88.1 90.1 90.1 87.1
1974 : Farms : 108,463 280,824 290,596 284,521 277,272 275,897 731,165 1/ 2,248,738
: Percent : 71.1 86.6 90.3 91.8 93.6 95.1 95.1 91.3
Partnerships: .
1969 : Farms : 13,049 33,104 49,236 49,990 41,878 34,278 86,518 308,053
Percent : 25.1 19.5 14.9 12.6 10.7 8.7 8.7 11.3
1974 : Farms : 27,811 37,107 27,671 22,801 17,180 12,399 33,060 1/ 178,029
Percent : 18.2 11.4 8.6 7.4 5.8 4.3 4.3 7.2
See footnotes at end of table. -----.Continued ----




Appendix table 1--Selected structural characteristics of U.S. farms, by sales class--Continued
*:$100,000 :$40,000 to :$20,000 to $10,000 to :$5,000 to $2,500 to : Less than
Item :Unit and over $99,999 $39,999 $19,999 $9,999 : $4,999 :$2,500 All
(class IA) (class 18) :(class II) :(class III) :(class IV) (class V) :(class VI) farms
Corporations:
1969 :Farms 8,049 4,306 2,847 2,262 1,984 2,062 4,972 2,648
Percent : 15.5 2.5 0.8 0.6 0.5 0.5 0.5 1.0
1974 :Farms 15,787 5,630 2,768 1,988 1,335 1,148 3,075 1/ 31,731
Percent : 10.3 1.7 .9 .6 .4 .4 .4 1.3
Other:
1969 :Farms : 214 867 1,673 2,157 2,500 2,659 6,961 17,031
Percent : .4 .5 .5 .6 .7 .7 .7 .8
1974 :Farms : 538 749 736 701 586 539 1,538 1/ 5,387
Percent : .4 .2 .2 .2 .2 .2 .2 .2
Land farmed by:
Sole proprietor-:
a, ships:
1969 :Mlil. acre: 69.27 127.12 166.63 144.24 92.43 66.01 125.85 1/ 791.55
Percent : 40.3 68.6 80.4 84.3 86.5 87.0 87.0 74.5
1974 :Mil. acre: 147.52 193.08 138.65 90.73 59.80 48.31 109.06 1/ 787.15
Percent : 53.3 78.3 86.2 88.6 91.0 90.6 90.6 76.7
Partnerships:
1969 :Mil. acre: 44.04 41.12 35.08 23.33 12.23 7.59 14.47 1/ 177.86
Percent : 25.6 62.2 16.9 13.6 11.4 10.0 10.0 16.7
1974 :Mil. acre: 56.45 34.18 16.52 9.17 4.77 3.38 7.70 l/ 132.17
Percent : 20.4 13.9 10.3 9.0 7.3 6.4 6.4 12.9
Corporations: :
1969 :Mil. acre: 55.94 15.49 4.15 2.57 1.15 1.55 2.89 1/ 83.74
Percent : 32.6 8.4 2.0 1.5 1.1 2.0 2.0 7.9
1974 :Mil. acre: 69.73 18.10 4.83 2.10 0.88 1.14 2.53 1/ 99.3
Percent : 25.2 7.3 3.0 2.0 1.3 2.1 2.1 9.7
See footnotes at end of table. ---Continued --




Appendix table 1--Selected structural characteristics of U.S. farms, by sales class--Continued
: $100,000 :$40,000 to :$20,000 to $10,000 to $5,000 to :$2,500 to Less than
Item Unit :and over $99,999 :$39,999 $19,999 .: $9,999 :$4,999 $2,500 All
:(class IA): (class IB) :(class II): (class III): (class IV) : (class V) (class VI): farms
Other:
1969 :Mil. acre: 2.58 1.56 1.44 1.07 1.03 0.73 1.45 1/ 9.86
Percent : 1.5 0.8 0.6 1.0 1.0 1.0 1.0 0.9
1974 :Mil. acre: 3.11 1.28 0.71 0.41 0..28 0.50 1.08 1/7.37
Percent : 1.1 .5 .4 .4 .4 .9 .9 .4
Average size of
farm:
1969 :Acres : 3304.7 1091.9 626.2 432.9 273.6 192.0 90.3 389.0
1974 : do. : 1,814.0 761.0 499.0 330.0 222.0 184.0 84.5 416.0
Farm operator age
distribution:
(1969)
Less than 35 yrs: Percent : 11.3 13.8 14.3 12.4 11.4 10.9 11.4 12.0
35 to 54 years : do. : 60.3 59.8 56.3 48.5 42.4 40.9 41.0 45.7
55 yrs. and over: do. : 28.4 26.4 29.4 39.1 46.2 48.2 47.6 42.4
Average age :Years : 48.1 47.4 47.7 50.0 51.9 52.8 52.0 51.2
Farm operator age
distribution :
(1974)
Less than 35 yrs: Percent : 12.0 14.2 14.0 13.2 12.3 11.7 12.3 12.6
35 to 54 years : do. : 56.4 51.4 44.7 40.5 36.9 37.6 41.1 43.2
55 yrs. and over: do. : 31.6 34.4 41.3 46.4 50.8 50.7 46.7 43.6
Average age :Years : 48.8 48.9 50.4 51.9 53.5 53.6 52.7 51.7
Net farm income
per farm:
1969 :Dols. : 31,959 13,168 7,490 3,767 1,603 -551 -268 2,940
1974 : do. : 63,287 20,453 9,499 4,135 1,401 -1,039 -412 8,890
See footnotes at end of table. ---Continued -




Appendix table 1--Selected structural characteristics of U.S. farms, by sales class--Continued
: $100,000 : $40,000 to : $20,000 to :$10,000 to $5,000 to :$2,500 to :Less than
Item : Unit :and over : $99,999 :$39,999 :$19,999 : $9,999 :$4,999 : $2,500 All
:(class IA) : (class 18) : (class II) : (class III): (class IV) : (classV) : (class VI): farms
0ff-farm income
per farm: 1
1969 Dols. : 7,471 3,865 3,212 3,858 5,094 5,757 6,964 5,537
1974 do. : 8,060 4,997 5,512 7,444 9,640 11,566 12,411 9,487
Payments government farm programs per farm:
1969 : do. : 15,018 5,679 3,407 2,330 1,511 1,028 565 2,242
1974 : do. : 3,890 1,677 1,336 1,083 811 715 400 1,305
Capital gains on :
farm assets per :
farm:
1969 : do. : 36,765 12,655 7,442 4,848 3,167 2,314 1,333 4,106
1974 : do. : 71,273 30,560 18,541 12,289 8,074 6,242 4,209 13,770
Total net income;
per farm 2/:
1969 : do. : 54,448 22,712 14,109 9,955 8,208 6,234 7,261 10,719
1974 : do. : 75,237 27,127 16,347 12,662 11,852 11,242 12,399 19,682
Assets, debts per
farm, 1969:
Assets : do. : 852,456 314,949 181,773 119,426 80,395 60,969 40,991 106,780
Debts : do. : 210,088 65,101 33,439 20,331 10,821 5,267 3,458 17,981
Debt/asset ratio: Percent : 24.6 21.4 18.4 17.0 13.5 8.6 8.4 16.8
Assets, debts per
farm, 1974
Assets :Dols. : 954,326 380,511 224,328 150,760 108,299 91,770 73,746 186,472
Debts : do. : 287,830 58,549 29,712 16,027 8,892 5,039 3,375 29,575
Debt/asset ratio: Percent : 30.2 15.4 13.2 10.6 8.2 5.5 4.6 15.9
See footnotes at end of table. ---Continued --




Appendix table 1--Selected structural characteristics of U.S. farms, by sales class--Continued
: $100,000 $40,000 to $20,000 to $10,000 to $5,000 to : $2,500 to Less than All
Item Unit and over $99,999 $39,999 $19,999 $9,999 : $4,999 $2,500 fa
(class IA) (class IB) (class II) (class III) (class IV) : (class V) (class VI) farms
Tenure of farm
operators--1969
Full owners Percent 35.3 32.6 36.4 45.9 59.3 69.4 82.8 62.5
Part owners do. 51.4 51.3 45.4 36.8 25.7 17.9 9.0 24.6
Tenants do. 13.3 16.1 18.2 17.3 15.0 12.7 8.2 12.9
Tenure of farm
operators--1974
Full owners do. 29.3 33.3 45.4 58.8 69.1 75.3 84.0 61.5
Part owners do. 57.2 50.8 38.7 27.3 19.8 15.7 10.1 27.2
Tenants do. 13.5 15.9 15.9 13.9 11.1 9.0 5.9 11.3
l/ Number of farms estimated by the authors by assuming that the number of farms and land in farms in this sales class follow the same distribution pattern among the various types of organization in sales class V where sales range from $2,500 to $4,999. Direct census data on these items are not available.
2/ Total net income per farm include net farm income, off-farm income, and farm program payments. Capital gains on farm assets are excluded.




APPENDIX A
Data Adjustments for Underenumeration of the 1974 Census of Agriculture Data
This adjustment process uses the evaluation of coverage results reported by the U.S. Census Bureau, specifically the percentage of farms enumerated by farm size (24). An estimate of missed farms is then computed for each size class. But, the sum of the estimated missed farms frequently exceeds the total of missed farms, suggesting that another round of adjustments is needed. The second-round estimates of missed farms are computed by assuming that the discrepancy between the two estimates can be eliminated in proportion to the firstround estimates of missed farms in each size class. The adjusted farm numbers are then obtained by adding the revised estimates of missed farms to the numbers of farms reported by the census. This implies, however, that the number of
abnormal farms, after adjusting for underenumeration (column 9 in appendix table 2), should be deducted from column 8. Therefore, a complete comparability
is maintained for column 8 in appendix table 2 and column 10 in appendix table 3, with each showing the number of farms by size class adjusted for underenumeration and excluding normal farms.
72




Appendix table 2--Adjustment process for underenumeration of the 1974 Census of Agri-culture data by sales class
*.: First-round : First-round Second-round Adjusted
Sales : Number of Farms included :adjustment of :estimate of Total missed estimates of number of
class :farms 1/ in census number of :missed farms farms missed farms farms 5/
*. farms 3/ 4/
() : (2) (3) (4) (5) (6) : (7) (8)
Number Percent Number Percent Number
Less than $2,500 : 768,838 67.2 1,144,104 375,266 80.71 331,759 1,100,597
$2,500-4,999 289,983 88.6 327,295 37,312 8.02 32,966 322,949
$5,000-9,999 296,373 91.9 322,495 26,122 5.62 23,101 319,474
$10,000-19,999 310,011 94.2 329,099 19,088 4.11 16,894 326,905
$20,000-39,999 321,771 98.0 328,338 6,567 1.41 5,796 327,567
$40,000-99,999 324,310 98.9 327,917 3,607 0.78 3,206 327,516
$100,000-199,999 : 101,153 102.0 99,170 -1,983 -0.43 -1,768 99,385
$200,000-499,999 : 40,034 102.0 39,249 -785 -.0.17 -699 39,335
$500,000 and over: 11,412 102.0 11,188 -224 -0.05 -206 11,206
All farms 2,463,885 85.7 2,928,855 464,970 100.00 411,049 2,874,934
1/ Based on 1959 definition, for which see footnote to table 1.
2/Column (4) is obtained by dividing column (3) into column (2).
3/Column (5) is computed by subtracting column (2) from column (4).
4/ Column (7) is computed by multiplying column (6) by 411,051, the overall missed farms. ThE: overall missed farms is obtained as follows: 411,051=(2,463,855+-2,238)/0.857 2,238/0.833, where 2,238 is the number of abnormal farms reported in the Census of Agriculture and 0.833 refers to 83.3% of those farms included in the Census.
5/ Column (8) is computed by adding column (7) to column (2).




Appendix table 3--Adjustment process for underenumeration of the 1974 Census of Agriculture data, by farm size
Nubr Farms First-round First-round Total :Second-round Adjusted aubr djusted ffa ms, e
Farm size f include adjustment estimates missed :estimates of numeof ajsd ofar ,ex
farm 1/br o mse missed farms meof abnormal cluding abnorFarmrm siz/o in cnudes fnme fmse farms ~fa rms 5/
:of f arms 2/: farms 3/ :: 4/ farms 6/: mal farms
Number Percent Number Percent Number
1 to 9 acres 168,925 66.6 253,641 84,716 18.36 75,551 244,476 89 244,387
10 to 49 acres :453,690 68.9 658,476 204,786 44.37 182,583 636,273 176 636,097
50 to 69 acres :160,'702 83.5 192,457 31,755 6.88 28,311 189,013 64 188,949
70 to 99 acres :244,494 83.5 292,807 48,313 10.47 43,084 287,578 106 287,472
100-1 39 acres :235,056 89.8 261 ,755 26,699 5.78 23,785 258,841 151 258,690
140 to 179 acres :217,826 89.8 242,568 24,742 5.36 22,056 239,882 96 239,786
180 to 219 acres :137,591 89.8 153,219 15,628 5.39 13,950 151,541 94 151,447
220 to 259 acres :1189346 95.8 123,534 5,188 1.12 4,609 122,955 104 122,851
260 to 499 acres 365,369 95.8 381 ,387 16,018 3.47 14,279 379,648 351 379,297
500 to 999 acres :209,187 99.0 211,300 2,113 0.46 1,893 211,080 378 210,702
1,000 to 1,999
acres : 92,712 99.0 93,648 936 0.20 823 93,535 271 93,264
2,000 acres and
over : 62,225 99.0 62,854 629 0.14 576 62,801 807 61,994
All farms :2,466,123 85.7 2,927,646 461 ,523 100.00 411 ,500 2,877,623 2,687 2,874,936
1/ Based on the 1959 definition
2/ Column 4 is obtained by dividing column 3 by column 2.
'T/ Column 5 is computed by subtracting column 2 from column 4.
T/ Column 7 is computed by multiplying column 6 by 411,500; the overall missed farms is obtained as follows: 411,500=
(27,466,123/0.857) 2,466,123.
5/ Column 8 is computed by adding column 7 to column 2.
C/ Number of abnormal farms divided by its inclusion factor, 0.833.




APPENDIX B
Estimated Simple Trend Equations by Size Class
Appendix table 4--Estimated simple trend equations by average size: 1959, 1964, 1969, 1974 l/
Size of farm : Estimated trend equations :R2
1-99 acres In FN = 7.658 0.115T 0.969
(192.57) (-7.94)
100-219 acres : In FN2 = 7.101 0.155T 0.9997
(1489.62) (-59.27)
220-499 acres : In FN3 = 6.707 0.117T 0.971
(171.27) (-8.16)
500-999 acres In FN4 = 5.402 0.0087T 0.159
(140.02) (-0.62)
1,000-1,999 acres : In FN5 = 4.423 + 0.029T 0.912
(251.45) (4.55 )
2,000 acres and over : In FN6 = 4.112 0.0004T 0.000.5
(131.38) (-0. 033)
1/ The time variable (T) is: 1959 = 1, 1964 = 2, etc; R2 is the coefficient of determination. Figures in parentheses are t ratios.
75




Appendix table 5--Estimated simple trend equations by sales class: 1959, 1964, 1969, 1974 1/
Sales class : Estimated trend equations : R2
Less than $2,500 : In FN1 = 7.752 0.179T 0.977
(146.09) (9.23)
$2,500-$4,999 : In FN2 = 6.663 0.217T 0.964
(81.40) (-7.26)
$5,000-$9,999 : ln FN3 = 6.779 0.253T 1.000
(2537.51) (-259.83)
$10,000-$19,999 : In FN4 = 6.405 0.145T 0.922
(78.54) (-4.86)
$20,000-$39,999 : ln FN5 = 5.381 + 0.3251n T 0.953
(111.22) (6.38)
$40,000-$99,999 : In FN6 = 4.312 + 0.905In T 0.862
(17.71) -(3.54)
$100,000-$199,999 In FN7 = 2.483 + 1.2541n T 0.830
(6.52) (3,13)
$200,000-499,999 : In FN8 = 1.358 + 1.382In T 0.846
(3.43) (3.32)
$500,000 and over In FN = 0.079 + 1.404In T 0.913
(0.260) (4.574)
1/ The time variable (T) is: 1959 = 1, 1964 = 2, etc; R2 is the coefficient of determine. Figures in parentheses are t ratios.
76




APPENDIX C
Adjustments for Age Cohort Projections
Several adjustments were necessary in order to use the census data within the age cohort framework to project the total farm numbers by size. These adjustments are summarized in appendix table 6.
The least adjustment was required for the 1964 sales distribution where only estimated missed farms were added to the census published data. These missed farms were published in Evaluation of Coverage (24), which presented the data by age group, acre size, and sales. Therefore, it was necessary to establish the numbers in each cell. The estimated number (E) was determined by the formula, Ei= N.Nj IN for the i,j th cell. Where Ni., Nj., and N represent
the totals of the i th row, the j th column, and the grand total. This formula was also used for the abnormal farm matrix (line 3, appendix table 5), the 1974 farms with sales of less than $1,000 (line 4), and the corporate and other (line 5). The age distribution for corporate and other operations was obtained from the 1969 Census of Agriculture.
Another adjustment was made to the sales data to remove the impact of price inflation for farm commodities. The sales distribution was deflated for each age group as described in the data adjustment section, except that 1964 constant prices were used. The projections were made in constant prices, then reinflated to the expected price levels as described in the data adjustment section. A log polynomial of the 4th degree was used. A peculiar kink developed at the lower end of the size curve that caused a rapid increase in small farms when the curve was shifted for reinflation. This did not correspond to the historical shape in 1964 or 1974. The fit did not improve by changing the degree of polynomial. Therefore, the data were plotted on log paper and smoothed for the lower sales classes in each age group.
The cohort ratio shown in tables 24 and 25, when multiplied by the base period data, resulted in projections where the individual cells in the row summed to more than the row total except for farm operators younger than 25 years old. The row total was obtained by multiplying the age group total by the cohort ratio for the age group in the last column in tables 24 and 25.
The individual projected numbers for each cell was forced to equal the projected totals for each age group (see appendix table 7 for adjustment factors).
77




Appendix table 6--Adjustments to census data and projects for acres and sales, 1964 and 1974
Acres : Sales
Item : Projec-: : Projec1964 1974 : tions 1964 1974 : tions
1. Estimated missed farms : I/ x 1/ x
2. Estimated age-size matrix
for missed farms x
3. Estimated age-size for abnormal farms in order to subtact
them : x x
4. Farms with sales of less than
$1,000 not included in 1974 x x
5. Corporations and others without
opertor age-distributed by size: x X
6. Deflation with decumulative log
polynomial curve x
7. Reinflation to current prices x x
8. Adjust cell total to equal cohort total 2/ x 2/ x
1/ 401,000 farms reported in Census Evaluation Coverage by Age, Acres and Sales Distribution.
2/ See appendix table 4 for amount of adjustment required.
78




Appendix table 7--Ratios of adjustment used for acre and sale projection by age
: Acres : Sales
Age
1984 1994 2004 1984 1994 2004
Ratios
Less than 25 0.999 0.991 0.993 1.028 1.050 1.040
25-34 .983 .967 .958 .861 .861 .790
35-44 .984 .979 .963 .915 .915 .845
45-54 .987 .977 .980 .931 .931 .890
55-64 .991 .980 .972 .943 .943 .919
65 and older .999 .991 .975 .978 .984 .952
*U.S. GOVERENqT PRINTING OFICE : 1980 0-310-94V/ESCS-218
79




Full Text

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CONTENTS Page Summary. .. ........ ... .. .. ... ... .. .. .. .. ..i. Introduction .. ........... ...... ... ... ....1 Overview of Structure and Structural Change ..... ....... 3 Numbers and Sizes. .. ........ .... .. .. .. ... ....3 Concentration of Production .... .. ... .#. .. .. .. ... .3 Concentration of Farmland Ownership .. ...... ..#.. .. .. .. ..7 Form of Business Organization. .... .. .. ....** ......8 Financial Structure. .. ........ ...... .. .. .. .. ....9 Prospects for Farm Organization ........... .. .. .. .. ....10 Numbers and Sizes .. .. ........ ...............10 Concentration and Specialization of Production .* .... .. ... .10 Concentration of Farmland Ownership ..... .. ... .... .. ..14 Form of Business Organization ... ......... .. .. ... .14 Financial Structure .. ................. .. .. .... .15 Age of Farm Operators and Replacement Rates ......... .. ... 15 Tenure of Farm Operators .....* .............. .. ..18 Trend Extrapolation .. ...... ........ .. .. .. .. .. .. .20 Technical Overview .. .. .. ... ..... .. ... ...* ...20 Data Adjustments ......... ......... .. ....20 Projections......... ..... ... .. .. ...o.. 0 0. .. ....21 Negative Exponential Functions. ......... .... .. .. .. ...24 Technical Overview .. ............ ... .. .. .. ... .24 Projections .. ... .. .. .. .. .. .. .. ... ........27 Markov Process ......* .... .... ....... .. .....33 Technical Overview. .. ... ..... .. ... ..........33 Data Adjustments .. ......... .............& ....1 34 Projections. ................. .... .. .. .. ... 36 Age Cohort Analysis ..... .... .. ...... .......45 Technical Overview....... ..... .... .. .. .. ... .... ... 45 Data Adjustments .......... .....*0. .. .. .. ..47 Projections. ... .. .. ... .... .. .. ... .........47 Comparison of Alternative Projections .. ...... ...... .. .. .. 54 Conclusions and Implications...... .............62 Literature Cited..... ... .. .. .. .. .............. 65 Appendices. ... .. .... .. .. .. .. .. .. .. ... ....67



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Tenure of Farm Operators Tenure patterns in farming have changed. Part6-owner-operators have increased as a percentage of all farmers. The proportion of full owners has declined only slightly, while the percentage of tenant-operated farms has declined significantly. The proportion of tenants in each sales class and for all farms decreased from 1969 to 1974, reflecting farmers' long-held desire to acquire farmland and the ability to do so. But at the same time, the proportion of full owners declined only slightly. In 1974, 62 percent of farms were classified as full owners, 27 percent as part owners, and 11 percent as tenants. Full owners mostly dominated in farms with sales of less than $20,000 (73.4 percent), and accounted for less than one-third of the farms with sales of more than $100,000. By contrast, part owners were the majority in farms with sales of more than $100,000-accounting for nearly 60 percent (table 12). This trend in resource ownership structure is projected to continue into the future. Part owners are likely to account for more than one-third of all farms, while the share of tenants will decline from 11 percent in 1974 to 7 percent in 2000. The share of full owners is likely to remain the same. Full owners will be concentrated mostly in small farms and will account for only 16 percent of Table 11--Farm operator replacement rates Item 1964-74 1974-84 1984-94 1994-2004 Percent Replacement rate on farms with sales of: 1/29292314 $100,000 or m-ore29292314 less than $100,000 44 47 42 32 Total .51 56 63 53 Thousands Net entry of operators under 35 years .475 452 405 284 Net exit of operators over 55 years .930 811 650 537 1/ Percentage of exiting operators over 55 years of age replaced in the foTlowing decade by entering operators under 35 years at the beginning of the decade. Source: Adjusted 1974 Census of Agriculture and Projection. See text for details. 18



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(15) Klein, L. R., An Introduction to Econometrics, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1972, p. 150. (16) Krenz, R. D., "Projections of Farm Numbers for North Dakota with Markov Chains," Agricultural Economics Research, Vol. 16, No. 3, July 1964. (17) Kyle, L. R., W.B. Sundquist, and H. D. Guither, "Who Controls Agriculture Now?-The Trends Underway" in Who Will Control U.S. Agriculture? ed. by H. D. Guither, North Central Regional Extension Publication 32, Urbana, Illinois, Aug. 1972. (18) Lee, T. C., G. G. Judge, and T. Takayama, "On Estimating the Transition Probabilities of a Markov Process," Journal of Farm Economics, Vol. 47, No. 3, Aug. 1965. (19) Lewis, James A., Landownership in the United States. 1978, AIB-435, U.S. Dept. of Agr., Econ. Stat. Coop. Serv., April 1980. (20) Padberg, Daniel I., "The Use of Markov Process in Measuring Changes in Market Structure," Journal of Farm Ecomonics, Vol. 44, No. 1, Feb. 1962. (21) Theil, H., Applied Economic Forecasting, Amsterdam: North-Holland Publishing Co., 1966. (22) Tolley, G. S., "Management Entry into U.S. Agriculture," American Journal of Agricultural Economics, Vol. 52, No. 4, Nov. 1970. (23) U.S. Department of Agriculture, Economics, Statistics, and Cooperatives Service, Farm Income Statistics, SB-609, July 1978. (24) U.S. Department of Agriculture, Economics, Statistics, and Cooperatives Service, Status of the Family Farm: Second Annual Report to the Congress, AER-434, Sept. 1979. (25) U.S. Department of Commerce, Bureau of Census, Census of Agriculture, General Reports, 1959, 1964, and 1974. (26) U.S. Department of Commerce, Bureau of Census, Census of Agriculture, Special Reports on Evaluation of Coverage, 1959, 1964, 1969, 1974. 66



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farms with sales of more than $100,000. Part owners, on the other hand, will account for about 72 percent of farms with sales of more than $100,000. Ownership and use of farmland, therefore, will be separated more than is the case now. Farmers will be more likely to rent additional farmland to enlarge their farming operations. Table 12--Tenure structure by sales class Less $20,000 :$100,000 : Item than : to and :All farms *$20,000 $99,999 over Percent Full owners: 1964 61.8 31.5 34.2 57.9 1969 69.4 35.1 35.3 62.5 1974 74.3 39.3 29.3 61.5 2000 93.0 59.0 16.0 63.0 Part owners: 1964 : 21.7 50.3 51.6 24.9 1969 26.9 47.8 51.4 24.6 1974 16.6 44.8 57.2 27.2 2000 : 4.0 28.0 72.0 30.0 Tenants: 1964 16.5 18.1 14.1 17.2 1969 : 17.1 17.1 13.3 12.9 1974 : 9.1 15.9 13.5 11.3 2000 : 3.0 12.0 12.0 7.0 19



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CONCLUSIONS AND IMPLICATIONS The techniques employed in this study used several kinds of data and assumptions in projecting farm numbers and size distributions. The specific projections are, therefore, contingent upon the techniques, assumptions, and data employed. The different techniques are not necessarily equally valid for examining the same questions. The results, however, provide different perspectives and suggest some common tendencies and regularities. Although the four frequently used techniques project future number and size of farms with some regularity, their accuracy varies. In addition, the projected size distributions may differ considerably from one procedure to another, even though the projected totals are similar. For example, farm numbers by acreage projected by trend extrapolation, Markov process, and age cohort analysis are reasonably comparable. However, trend extrapolation and age cohort analysis both project a slight decline in the number of farms of 2,000 acres and over, but Markov process projects a continuous, slow increase in the number of such farms (table 44). Trend extrapolation gives fairly accurate projections by acreage, but commits a large projection error in sales distribution. Unlike the continuous trends for the acreage distribution, some of the trends for the sales distribution occasionally reverse. Trend projections, under this circumstance, could lead to an incorrect direction. For example, the number of farms with sales of $20,000 to $39,999 increased from 1959 to 1969, but then declined after 1969. Once a new trend is established, it is likely to continue to project an increasing trend for the number of such farms. Table 44--Alternative projections of farm numbers, by size of farm, 2000 Negative Size of farmn 1974 Trend :exponential :Markov Age Actual extrapolation functions process :cohort 1 ,000 farms 1-99 acres :1,356 751 320 864 934 100-139 acres 259 113 121 140-179 acres 240 300 104 102 301 180-219 acres 151 96 66 220-259 acres 123 286 89 48 220 260-499 acres 379 712 182 500-999 acres 211 205 430 152 164 1,000-1,999 acres 93 108 224 91 97 2,000 acres and over: 62 61 37 77 56 All1 farms :2,875 1,711 1,826 1,705 1,772 62



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Table 9--Balance sheet of the farming sector, by sales class Item Unit : Less than $20,000 $20,000 to $99,999 : $100,000 and over : All farms Total Farm assets: 1978 M il. dol. :218,512 278,096 216,357 712,965 2000 do. 273,238 292,027 1,062,600 1,627,865 Debt/asset ratio. 1978 : Percent :9.5 17.8 22.7 16.7 2000 do. :6.3 17.0 26.0 21.1 Farm debt: 1978 Nil. dol. 20,E60 49,468 49,145 119,273 2000 do. :17,214 49,645 276,276 343,135 S Equity: 1978 M il. dol. 197,852 228,628 167,212 593,692 2000 do. :256,024 242,382 786,324 1,284,730 Distribution of equity: 1978 : Percent :33.3 38.5 28,2 100.0 2000 do. :19.9 18.9 61.2 100.0 Per farm Farm assets: 1978 : 1,000 dol. :123.3 390.0 1,157 266.8 2000 .do. :307.4 9,701.9 1,894.1 930.2 Farm debt: 1978 : 1,000 dol. :11.7 69.4 262.8 446.6 2000 do. 19.4 164.9 492.5 196.1 Farm equity: 1978 : 1,000 dol. :111.7 320.7 894.2 222.2 2000 .do. :288.0 805.3 1,401.6 734.1



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Prior to 1969, all censuses were conducted by personal interview in a complete canvass of rural areas. In 1969, a mailout-mailback, self-enumerated national census was conducted. The change in survey procedure, along with other factors, contributed to the underenumeration problem, that is, an incomplete farm count, espe'cially for small farms (26). Conversely, overcounting sometimes occurred for large farms. Without adjustment of the census data to account for underenumeration and occasional overcounting, the number of farms reported differs considerably from another primary data source, namely the Farm Income Statistics of the U.S. Department of Agriculture (23). For example, the Farm Income Statistics reported 2.8 million farms in 1974 while the Census of Agriculture estimated 2.47 million farms, a difference of 330,000 farms. 4/ To avoid confusion and maintain the comparability of the census data with _USDA estimates, it was necessary to adjust the census data. The detailed adjustment process for the 1974 Census of Agriculture data by sales class and acre size is shown in append 'ix tables 2 and 3. In general, the adjustment process for acres and sales was te same. However, slight differences result from the nature of the census data. Abnormal farms are reported separately by sales class, but are included in the number of farms by acreage. 5/ Since abnormal farms could be expected to respond quite differently from normal farms to factors that cause the changes in farm structure, they were excluded from the numbers for purposes of this study. Adjusted Census of Agriculture data by sales class and by acre size for years 1959, 1964, 1969, and 1974, based on procedures illustrated in appendix tables 2 and 3, are shown in tables 13 and 14. Projections The estimated trend equations, based on the adjusted census data in tables 13 and 14, are shown in appendix tables 4 and 5. Projections of the farm numbers by acre and sales size are shown in tables 15 and 16. Farm numbers by acre size are projected to decline from 2.9 million in 1974 to 2.6 million in 1980 and to 1.7 million in 2000. The simple trend projections show the numbers of farms with less than 1,000 acres to continue declining, while those of 1,000 acres or more to continue increasing. Similarly, the number of farms by sales class is projected to decline from 2.9 million in 1974 to 2.6 million in 1980 and 2.1 million in 2000. As expected, the number of small farms (sales less than $20,000) continues to decline, while the number of big farms increases. 4/ The 1959 Census definition of a farm is used in both data sources and throughout this study (see table 1). 5/ Abnormal farms include institutional farms, experimental and research farms, and Indian reservations. Institutional farms include those operated by hospitals, penitentiaries, schools, grazing associations, government agencies, and others. 21



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Sales Distribution Following the same procedure, the numbers of farm operators by sales class and acreage can be projected based on the age cohort ratios presented in tables 30 and 31. The entry rates are higher for the larger size groups as indicated by the larger cohort ratios. On the other hand, the ratios are higher for the smaller classes than the mid-classes, suggesting a real possibility of a bimodal distribution of the number of farms in the future. Also, the retention rates for older operators are higher in the larger and smallest size classes. Of the projected 1.7 million farms in 2004, large farms (sales of at least $100,000) will account for about 38 percent, an increase from 5 percent in 1974. By contrast, small farms (sales of less than $20,000) will account for 49 percent, down from 72 percent in 1974 (table 32). However, part of the increase in the percentage of large farms is due to the anticipated price inflation. When sales receipts are expressed in 1964 price levels, the proportion reduces to only 9 percent. The number of farms reduces from the projected 620,000 to 129,300 in 2004 (table 33). Figure 10 Farm Operator Age Cohiort Movements, 10 Year Periods 1964 1974* 19840 1994 0 2004e Cohort Ratio Current Age (Years) .037,& .037 .037 .3 Less than 25 61.2 5.12 61.9 5.12 45.6 5.12 35. 5.12 33.6I 35-44 740.0 0.98 0.98 098 61 0.98 34. 45-54 942. 62. 0. 4. 5. 55-64 818.8 0.5 728.4 65 563.0 0.5 388.6 3476 6 65-74 644.153.47.360226 75 or older 00 0 Total 3,556.7 2,874.9 2,358.2 1,934.9 1,609.7 *Data rounded after calculations. A The ratio Is defined as all new entrants under 25 years divided by the number of operators who, 10 years earlier, were 35-54 years old (see text for more detail). o0 Assume all exits by age 75. *1984, 1994, and 2004 are projections. Nu.mbsrs--in boxes are In thousands. 50



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Financial Structure Farm income, off-farm income, and government farm program payments constitute the major components of net income per farm (app. table 1). As would be expected, large farms had a considerably larger amount of net farm income, government farm program payments, and capital gains on farm physical assets than small farms. Although the significant reduction in Federal farm program payments in 1974 made the differences proportionally less obvious, a recent ESCS study reaffirms what is widely known about the programs--that benefits are closely proportional to production volume: the larger farms, although few in numbers, have the highest production and thus receive a disproportionate share of the program benefits (24). Of $2 billion in program payments in 1978, almost half the payments went to only 10 percent of the participants, those with the largest farms. By contrast, 50 percent of the farms--the smaller units--received only 10 percent of the payments. In 1969, the amount of off-farm income per farm for farms with sales of more than $100,000 and less than $2,500 were about the same. This changed drastically, however, in 1974. Off-farm income per farm in sales classes of less than $2,500 almost doubled, while no significant change occurred in the top sales classes. In fact farmers in sales classes of less than $40,000 all increased their offfarm income significantly. Preliminary data indicate that this trend continued into 1978. This suggests that small farmers are supplementing their family income through off-farm employment and investment, and that off-farm income has become more important as a source of farm family income. Another characteristic of agriculture is the increasing ratio of debts to assets as farm size increases. In 1969, farms with sales of $20,000 or less had a ratio of 13.2 (13.2 cents of debts for each $1 of assets); farms with $100,000 or more of sales had a ratio of 24.6. By 1974, the ratio for small farms had decreased, while the ratio increased to 30.2 for the largest farms. 9



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Table 2--Number of farms, by size of farm l/ Size of farm 1974 1969 1964 1959 1954 2/ 1950 1945 2/ 1940 1935 2/ Number of farms 1 to 9 acres 168,925 162,111 182,581 244,328 484,291 488,530 594,561 509,347 570,831 10 to 49 acres 453,690 473,465 637,434 813,216 1,212,831 1,479,596 1,654,404 1,782,061 2,123,595 50 to 69 acres 160,702 177,028 211,398 258,195 346,323 427,025 472,415 510,585 581,352 70 to 99 acres 244,494 282,914 331,032 399,795 517,740 621,050 684,905 780,743 862,655 100 to 139 acres 235,056 278,752 324,652 394,505 491,458 579,244 633,851 688,479 754,076 140 to 179 acres 217,826 263,012 308,288 378,003 461,651 523,659 565,958 621,578 683,941 180 to 219 acres 137,591 165,209 191,254 225,576 257,189 275,049 282,839 279,577 294,309 220 to 259 acres 118,346 141,733 164,188 188,899 206,509 212,344 210,376 206,759 212,238 260 to 499 acres 365,369 419,421 451,301 471,547 482,246 478,170 473,184 459,003 473,239 500 to 999 acres 208,375 215,659 210,437 200,012 191,697 182,297 173,777 163,711 167,452 1,000 to 1,999 acres 93,203 91,039 84,999 136,427 130,481 121,473 112,899 100,574 88,662 2,000 acres and over 62,546 59,907 60,293 All farms 2,466,123 2,730,250 3,157,854 2,610,503 4,782,416 5,288,437 5,859,169 6,102,417 6,812,350 l/ No adjustment for the undercounting of farm numbers by the Census Bureau was made. Z/ Alaska and Hawaii not included.



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Financial Structure Farms with sales of $20,000 to $99,999 required about $390,000 worth of physical and financial assets in 1978. Capital requirements were more than $1 million per farm for farms with sales of more than $100,000. Increasing farm7land value and farm machinery costs will make capital requirements for farming even higher in the future. If the trend of asset-sales ratio continues, farms with sales of $20,000 to $99,999 will have assets valued at nearly $1 million per farm by the year 2000 (table 9). This is nearly triple what was required in 1978. More important, economically viable farms probably will require assets valued at almost $2 million per farm--nearly double what was required in 1978. Much of the increase in asset values will likely result from appreciation, especially in land values. Some additional expansion of equity would arise from reinvestment of savings from income flows. These increases in equity could provide a base for additional debt. The increased debt and equity could be used to purchase more land and other capital'items. Such soaring capital requirements in farming create barriers to entry, especially for low-equity, young, potential farmers. The change in farm structure in the future will have a far-reaching effect on the distribution of wealth among farms and households that have an interest in farming. Capital assets were dispersed about evenly among various sizes of farms in 1978--one-third each for farms with sales of: (1) less than $20,000,_,(2) $20,000 to $99,999, and (3) more than $100,000. The average farm required assets valued at about $267,000. By 2000, about two-thirds of the farm assets will go to farms with sales of more than $100,000, with the remaining one-third spread evenly among farms of less than $20,000 in sales and those with $20,000 to $99,999 in sales. Farm assets for all farms will -average about $930,200--more than triple the 1978 figure. By 2000, two-thirds of the wealth in the farm sector will be in the hands of these farms with more than $100,000 in sales. Age of Farm Operators and Replacement Rates The average age of farm operators is projected to drop from 51.9 in 1974 to 50.2 by 2004 (table 10). Although this is counter to the trend up to 1974, the shift in average age reflects the higher actual entry rate of young people in the 1964-74 period. By 2004, these operators will be the middle age group, resulting in an increase in the number of farm operators in the 35 to 54 age range--from 43 percent in 1974 to nearly half in 2004. By contrast, a slight decline in the proportion of operators 55 years of age and over is projected. The projected decline in the average age of farm operators is counter to the trend observed through 1974, although the increase in average age from 1969 to 1974 was barely noticeable--from 51.2 in 1969 to 51.7 in 1974. Similarly, the percentage of farmers 55 years and over (and probably approaching retirement) increased, with the increases being especially significant in the large sales classes. As farms become fewer and larger, fewer new farmers are needed to replace existing farm operators on adequate size farms. Therefore, the total number of net entries by persons under 35 years of age is projected to shrink from 475,000 15



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Table 18--Projected number of U.S. farms, by size of farm, negative exponential function Size of farm: 1974 (actual) :1980 :1985 :1990 :1995 :2000 :Thousands Percent Thousands Percent Thousands Percent Thousands Percent Thousands Percent Thousands Percent 1-9 acres : 244.4 8.5 48.6 2.0 43.6 1.9 39.2 1.9 35.2 1.8 31.7 1.7 10-49 acres : 636.1 22.1 204.5 8.3 184.0 8.1 165.6 7.8 149.1 7.6 134.3 7.4 50-69 acres : 188.9 6.6 95.7 3.9 86.3 3.8 77.8 3.7 70.2 3.6 63.3 3.5.. 70-99 acres : 287.5 10.0 135.8 5.5 122.6 5.4 110.8 5.2 100.2 5.1 90.5 5.0 100-139 acres: 258.7 9.0 167.5 6.8 151.8 6.6 137.5 6.5 124.5 6.3 112.2 6.2 CD 140-179 acres: 239.8 8.3 153.3 6.2 139.3 6.1 126.5 6.0 114.9 5.8 104.3 5.7 180-219 acres: 151.4 5.3 140.3 5.7 127.9 5.6 116.5 5.5 106.0 5.4 96.5 5.3 220-259 acres: 122.9 4.3 128.3 5.2 117.3 5.1 107.2 5.1 97.9 5.0 89.3 4.9 260-499 acres: 379.3 13.2 571.3 23.2 527.3 23.1 486.1 22.9 447.6 22.7 411.5 22.5 500-999 acres: 210.7 7.3 544.9 22.2 515.7 22.6 486.7 22.9 458.2 23.3 430.2 23.6 1 ,000-1 ,999 acres : 93.3 3.2 239.2 9.7 237.2 10.4 234.0 11.0 229.6 11.7 224.3 12.4 2,000 acres and over : 62.0 2.2 29.3 1.2 31.6 1.4 33.7 1.6 35.7 1.8 37.4 2.1 All farms :2,874.9 100.0 2,458.8 100.0 2,284.5 100.0 2,121.7 100.0 1,969.1 100.0 1,825.9 100.0



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Appendix table 1--Selected structural characteristics of U.S. farms, by sales class--Continued : $100,000 :$40,000 to :$20,000 to $10,000 to $5,000 to :$2,500 to Less than Item Unit :and over $99,999 :$39,999 $19,999 .: $9,999 :$4,999 $2,500 All :(class IA): (class IB) :(class II): (class III): (class IV) : (class V) (class VI): farms Other: 1969 :Mil. acre: 2.58 1.56 1.44 1.07 1.03 0.73 1.45 1/ 9.86 Percent : 1.5 0.8 0.6 1.0 1.0 1.0 1.0 0.9 1974 :Mil. acre: 3.11 1.28 0.71 0.41 0..28 0.50 1.08 1/7.37 Percent : 1.1 .5 .4 .4 .4 .9 .9 .4 Average size of farm: 1969 :Acres : 3304.7 1091.9 626.2 432.9 273.6 192.0 90.3 389.0 1974 : do. : 1,814.0 761.0 499.0 330.0 222.0 184.0 84.5 416.0 Farm operator age distribution: (1969) Less than 35 yrs: Percent : 11.3 13.8 14.3 12.4 11.4 10.9 11.4 12.0 35 to 54 years : do. : 60.3 59.8 56.3 48.5 42.4 40.9 41.0 45.7 55 yrs. and over: do. : 28.4 26.4 29.4 39.1 46.2 48.2 47.6 42.4 Average age :Years : 48.1 47.4 47.7 50.0 51.9 52.8 52.0 51.2 Farm operator age distribution : (1974) Less than 35 yrs: Percent : 12.0 14.2 14.0 13.2 12.3 11.7 12.3 12.6 35 to 54 years : do. : 56.4 51.4 44.7 40.5 36.9 37.6 41.1 43.2 55 yrs. and over: do. : 31.6 34.4 41.3 46.4 50.8 50.7 46.7 43.6 Average age :Years : 48.8 48.9 50.4 51.9 53.5 53.6 52.7 51.7 Net farm income per farm: 1969 :Dols. : 31,959 13,168 7,490 3,767 1,603 -551 -268 2,940 1974 : do. : 63,287 20,453 9,499 4,135 1,401 -1,039 -412 8,890 See footnotes at end of table. ---Continued --



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Table 13--Census of Agriculture data on number of farms, by sales class, adjusted for underenumeration Sales class : 1959 1964 1969 1974 1 ,000 farms Less than $2,500 1,896.4 1,657.2 1,417.1 1,100.6 $2,500-$4,999 646.0 473.9 432.8 322.9 $5,000-$9,999 683.8 528.6 410.9 319.5 $10,000-$19,999 496.8 484.1 399.5 326.9 $20,000-$39,999 216.4 266.9 329.8 327.6 $40,000-$99,999 84.5 113.5 168.0 327.5 $100,000-$199,999 : 14.6 21.8 35.0 99.4 $200,000-$499,999 4.7 8.0 12.4 39.3 $500.,000 and over. 1.2 2.6 4.0 11.2 All farms : 4,044.5 3,556.7 3,209.6 2,874.9 Table 14--Census of Agriculture data on number of farms, by size of farm, adjusted for underenumeration Size of farm 1959 : 1964 1969 : 1974 1,000 farms 1-9 acres 301.9 217.8 268.0 244.4 10-49 acres 890.3 760.3 675.8 636.1 50-69 acres 291.6 252.2 210.2 188.9 70-99 acres 452.0 394.8 335.8 287.5 100-139 acres 410.0 350.5 301.5 258.7 140-179 acres 392.8 332.8 284.5 239.8 180-219 acres 234.4 206.5 178.7 151.4 220-259 acres 203.1 177.5 148.2 122.9 260-499 acres 507.4 487.7 438.5 379.3 500-999 acres 214.7 225.1 218.4 210.7 1,000-1,999 acres 84.9 89.8 90.7 93.3 2,000 acres and over: 61.2 61.6 59.2 62.0 All farms : 4,044.5 3,556.7 3,209.6 2,874.9 22



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AGE COHORT ANALYSIS This chapter presents an overview of analysis by age cohorts (people born in the same decade), cohort adjustments by size class and projections obtained by this method. The number and sizes of farms change through time as farm operators enter, adjust the size of their operations, and leave agriculture. The life cycle of the farm operator has long been related to the concurrent phases of entry, expansion,and exit from the farm business: (1) young farmers (less than 35 years)--entry and establishment phase; (2) middle-aged farmers (35 to 54 years)--expansion phase; and (3) older farmers (55 and older)--exit, transfer, or close-out phase. Technical Overview Figure 8 shows the decreasing number and increasing age of farm operators. The age distribution shifts because the numbers of young persons entering farming are fewer than the numbers of older persons retiring or leaving farming. Also, many older operators continue to farm past the usual retirement age, when they are not replaced by a younger generation. Occupational mobility decreases as farm operators advance in age, further contributing to the shift in age distribution (2, 10, 11, 13) and the long-term adjustment process for farm operator number and farm size. Age cohorts can be traced through successive agricultural censuses to determine the net change in the number in each age cohort by size of farm. Figure 8 Farm Operator Age Distribution, 1920.74 Thousands 1,400 1,200 -0000 1940 S -....... 1,000 0. 1954 --" -. 8000f/ 600 t..60 -.. 96 -tfff 400 / o.. o 1974 200 o 00 0 I I II Under 25 25-34 35-44 45-54 55-64 65 or Age Group over Source: (25). 45



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Appendix table 2--Adjustment process for underenumeration of the 1974 Census of Agri-culture data by sales class *.: First-round : First-round Second-round Adjusted Sales : Number of Farms included :adjustment of :estimate of Total missed estimates of number of class :farms 1/ in census number of :missed farms farms missed farms farms 5/ *. farms 3/ 4/ () : (2) .(3) (4) (5) (6) : (7) (8) Number Percent Number Percent Number Less than $2,500 : 768,838 67.2 1,144,104 375,266 80.71 331,759 1,100,597 $2,500-4,999 289,983 88.6 327,295 37,312 8.02 32,966 322,949 $5,000-9,999 296,373 91.9 322,495 26,122 5.62 23,101 319,474 $10,000-19,999 310,011 94.2 329,099 19,088 4.11 16,894 326,905 $20,000-39,999 321,771 98.0 328,338 6,567 1.41 5,796 327,567 $40,000-99,999 324,310 98.9 327,917 3,607 0.78 3,206 327,516 $100,000-199,999 : 101,153 102.0 99,170 -1,983 -0.43 -1,768 99,385 $200,000-499,999 : 40,034 102.0 39,249 -785 -.0.17 -699 39,335 $500,000 and over: 11,412 102.0 11,188 -224 -0.05 -206 11,206 All farms 2,463,885 85.7 2,928,855 464,970 100.00 411,049 2,874,934 1/ Based on 1959 definition, for which see footnote to table 1. 2/Column (4) is obtained by dividing column (3) into column (2). 3/Column (5) is computed by subtracting column (2) from column (4). 4/ Column (7) is computed by multiplying column (6) by 411,051, the overall missed farms. ThE: overall missed farms is obtained as follows: 411,051=(2,463,855+-2,238)/0.857 -2,238/0.833, where 2,238 is the number of abnormal farms reported in the Census of Agriculture and 0.833 refers to 83.3% of those farms included in the Census. 5/ Column (8) is computed by adding column (7) to column (2).



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Table 5--Most likely projection of the nuber of farms, by size of farm Actual Size of farm 1974 1985 1990 1995 2000 1,000 farms 1-99 acres : 1,356.9 1,096.2 989.6 894.9 826.9 100-219 acres 649.9 475.6 404.4 345.9 301.9 200-499 acres 502.1 387.4 338.6 295.8 264.3 500-999 acres 210.7 201.8 193.3 187.1 182.9 1,000-1,999 acres 93.3 97.4 98.2 100.2 102.4 2,000 acresand over 62.0 65.0 65.8 67.1 70.9 All farms 2,874.9 2,320.0 2,090.0 1,890.0 1,750.0 Table 6--Most likely projection of the number of farms, by sales class Act ual Sales class 1974 1985 1990 1995 2000 1,000 farms Less than $2,500 1,100.6 793.5 752.4 723.0 603.7 $2,500-9,999 642.4 421.1 296.8 211.7 185.5 $10,000-19,999 326.9 201.8 144.2 94.5 99.8 $20,000-39,999 327.6 204.2 158.8 111.5 87.5 $40,000-99,999 327.5 358.4 291.6 233.4 213.5 $100,000-.199,999 99.4 190.2 211.1 193.7 161.0 $200,000-499,999 39.3 99.8 147.3 176.7 182.5 $500,000 and over 11.2 51.0 87.8 145.5 216.5 All farms 2,874.9 2,320.0 2,090.0 1,890.0 1,750.0 11



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Table 1--Number of farms, land in farms, and acres per farm Year Number : Land in farms Average size 1,000 Million acres Acres 1940 6,102 1,065 175 1945 5,859 1,141 195 1950 : 5,388 1,161 216 1954 4,782 1,158 242 1959 3,711 1,124 303 1964 3,158 1,110 352 1969 2,730 1,063 389 1974 l/ 2,466 1,026 416 l/ Not adjusted for census underenumeration. The number of farms reported by the.Bureau of the Census is based on the 1959 definition of a farm: any place from which $250 or more of agricultural products are sold, or normally would have been sold, during the census year, or any place of 10 acres or more from which $50 or more of the agricultural products were sold, or norn~ally would have been sold, during the census year. The definition was changed in 1974 to exclude places with less than $1,000 of gross receipts in the census year. The effect of this change was to reduce the number of farms in 1974 from the 2.5 million to 2.3 million. Source: U.S. Department of Commerce, 1974 Census of Agriculture, Vol. II, Part 2, June 1978. the farms produced 80 percent of the total output. In 1974, only 20 percent of the farms were required to produce the same output. In other words, 80 percent of-the output came from 655,000 farms in 1969 and from 493,000 farms in 1974. The shift of the Lorenz curve to the right illustrates this further concentration of production. The increasing concentration of production on larger farms carries implications beyond just the numbers. Larger farms are becoming more involved with vertical integration and contractual arrangements; such arrangements suggest that farm management decisions may gradually become controlled by the nonfarm sector. While the concentration of total farm production increased, the, extent of that concentration varied widely among farm commodities. Vegetable, poultry, nursery, and greenhouse farms were more concentrated than other types of farms in 1969 (table 4). In addition, considerable increase in concentration occurred in grain, cotton, and dairy industries. Production of tobacco and forest products, as in the past, was not dominated by big farms. The same pattern of concentration was evident in 1974. 4



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MARKOV PROCESS This chapter reviews the use of Markov processes for projecting farm number and size distributions, describes the process of adjusting the census data for the effects of price inflation, and presents projections to the year 2000. As a result of an 80-percent increase in prices received by farmers between 1969 and 1974, about 90 percent of the apparent increase in the numbers of farms with sales of $100,000 and more is attributed to the effects of price inflation. Of the projected 1.9 million farms in 2000, small farms (less than $20,000) will constitute 50 percent, a decrease from the 72 percent in 1974. By contrast, large farms (sales of $100,000 and more) will constitute 33 percent, an increase from 5 percent in 1974. Technical Overview Markov processes have been used to estimate the number and size distribution of firms for a number of industries, including agriculture. 8/ These applications have often used modifications or variants of a Markov process. Many of the modifications are concerned with the estimation of a transition matrix (that is, a description of how firms move among size categories over time) and are necessitated by limited data describing the movement of firms from one time period to another (for example, see 16, 18, 20). The Markov chain process assumes that a population can be classified into various groups (S, S2, ... I Sn) and that movements between states over time can be regarded as a stochastic process that can be quantified by probabilities. The states must be defined so that an individual can only be in one state at any point in time. A transition occurs when an individual shifts from one state to another. A crucial step in the use of Markov processes is estimation of the transition probability--the probability of movement from one state to another in a specified time period. The transition probabilities, Pij, can be expressed in the form of transition matrix, P: S1 S2 ... Sn S 1 PII P 12 Pln $2 P 21 P22 P2n Sn P nl Pn2 Pnn where: j Pij 1.0 and P > 0, for all i and j. The elements of P (the Pi) indicate the probability of moving from state Si to S in the next period. Since the elements of the matrix are nonnegative and the sum of the elements in any row is unity, each row of the matrix is a probability 8/ Illustrative studies include (5, 12, 16, 20). 33



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Table 3--Number of farms, by sales class, selected years 1/ Sales class 1974 1969 1964 1959 Sales class 2/ 1954 1950 Number N.rumber Less than $2,500 768,838 994,456 1,338,239 1,637,849 Less than $1,200 462,427 717,201 $2,500-4,999 289,983 395,104 443,918 617,677 Part-time 574,575 639,230 $5,000-9,999 296,373 390,425 504,614 653,881 Residential 878,136 1,029,392 $10,000-19,999 310,011 395,472 467,096 483,004 $1,200-2,400 763,348 901,316 $20,000-39,999 321,771 330,992 259,898 210,402 $2,500-9,999 811,965 882,302 $40,000-99,999 324,310 169,695 110,513 82,120 $5,000-9,999 706,929 721,211 $100,000-199,999 101,153 35,308 21,148 14,201 $10,000-24,999 448,945 381,151 $200,000-499,999 40,034 12,608 7,760 4,570 $25,000 and over 134,003 103,231 $500,000 and over 11,412 4,079 2,493 1,208 All farms 2,463,885 2,728,139 3,155,679 3,704,912 All farms 4,783,021 5,379,250 1/ No adjustment for the undercounting of farm numbers by the Census Bureau was made. 2/ The sales classification was changed after 1954 by the U.S. Census Bureau to more adequately reflect need of users.



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Concentration of Farmland Ownership Concentration of farmland operations did not change greatly between 1969 and 1974. Eighty percent of the farmland was operated by the largest 28 percent of the farms in 1969 and the largest 23 percent in 1974 (fig. 2). This means that 80 percent of the farmland was operated by 600,000 farms in 1974. Conversely, the other 1.9 million farms controlled the remaining 20 percent of the farmland. The concern over control of the land goes beyond the domination of large farms. It includes the extent of foreign ownership of farmland, corporate ownership, and absentee ownership in general. According to a *1978 U.S. landownership survey by the U.S. Department of Agriculture, foreigners owned 0.1 percent of all land, although the percentage varied widely in different parts of the country (19~). 2/ About 30 percent of farm and ranch land was owned by only 1 percent of the landowners. Most owners were white males between the ages of 50 to 64. Sole proprietors and husbands and wives held almost three-fourths of the land in farms and ranches. Corporations held about 9 percent of farm and ranch land and nonfamily corporations held only 2.4 percent. Less than one-half of 1 percent of American farmland was owned by foreigners or U.S. corporations with 5 percent or more foreign ownership. 2/ Underscored numbers in parentheses refer to items listed in the Literature Cited, beginning on p. 65. Figure 1 Figure 2 Concentration of Farm Concentration of Farmland Production in the United States, among Farms, 1969 and 1974 1969 and 1974 ______________Percentage of land in farms Percentage of sales 80 80 60 60 40-1994 20 20V417 20 40 60 76 80 100 0 20 40 60 707780 100 Percentage of farms Percentage of farm numbers 7



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vector, and P is a stochastic matrix. The matrix, P, in combination with an initial starting state completely defines a Markov chain process. A chain is irreducible if all states are required to be accessible, that is, there is a nonzero probability of moving from state i to state j in a finite number of time periods. A sufficient condition for the transition matrix P to be irreducible is that some power of the matrix have only positive components. Traditional Markov analysis projects future farm numbers by multiplying the row vector of farm numbers in the base period by the transition matrix which was constructed from actual farm numbers in the past. This analytical approach implicitly assumes that changes in prices received by farmers can be ignored or that farm product prices change little between periods. Historicially, that was a valid assumption--the index of prices received by farmers has remained relatively stable, increasing by less than 1 percent annually between 1954 and 1969. However, a changing economic environment resulted in a nearly 80-percent increase in the prices received by farmers between 1969 and 1974, thus requiring that explicit attention be given to product prices. Data Adjustments The general approach in this study to adjust the census data for the effects of price inflation explicitly differentiates and quantifies the changes in farm numbers into two components: (1) changes due to price inflation; and (2) changes due to "real" factors such as technological change, economies of size, farm commodity programs, production and market instabilities, land enlargement, and the like. The percentage increase in the index of prices received by farmers is used to quantify the shift from current (1974) to a constant (1969) dollar sales distribution of farm numbers. The sales distribution was approximated by a decumulative polynomial function with both sales and farm numbers expressed in logarithuic values. That is: N FN(s) = cexp E n (ln s)n n=1 where FN(s) = cumulative farm numbers that produce sales receipts in excess of s, s = sales receipts, n = degree of the polynomial function, and a, Sn = parameters of the distribution. This distribution function differs from the traditional Pareto distribution of income and wealth in that a negatively sloped nonlinear functional relation, instead of linear, is assumed to exist between the cumulative number of farms and 34



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LITERATURE CITED (1) Boxley, Robert F., "Farm Size and the Distribution of Farm Numbers," Agricultural Economics Research, Vol. 23, No. 4, Oct. 1971. (2) Chennareddy, Venkareddy, and Glen L. Johnson, "Projections of Age Distribution of Farm Operation in the United States Based Upon Estimates of Present Value of Income," American Journal of Agricultural Economics, Vol. 50, No. 3, Aug. 1968. (3) Ching, C. T. K., "A Note on the Stability of Firm Size Distribution Functions for Western Cattle Ranches," American Journal of Agricultural Economics, Vol. 55, No. 3, Aug. 1973. (4) Chow, Gregory C., "Tests of Equality Between Sets of Coefficients in Two Linear Regressions," Econometrica, Vol. 28, No. 3, July 1960. (5) Daly, Rex F., J. A. Dempsey, and C. W. Cobb, "Farm Numbers and Sizes in the Future," in Size, Structure, and Future of Farms, ed. by A. Gordon Ball and Earl 0. Heady, Ames, Iowa State University Press, 1972, pp. 314-332. (6) Dixon, B. L., and S. T. Sonka, "A Note on the Use of Exponential Functions for Estimating Farm Size Distributions," American Journal of Agricultural Economics, Vol. 61, No. 3, Aug. 1969. (7) Dovring, Folke, "Distribution of Farm Size and Income: Analysis by Exponential Functions," Land Economics, Vol. 49, No. 2, May 1973. (8) "Income and Wealth Distributions: The Exponential Functions," AE-4212, Dept. of Agr. Econ., Univ. of Illinois, June 1969. (9), "Farm Size Data: Frequency Distribution, Interpolation, and Projection," AERR-50, Dept. of Agr. Econ., Univ. of Illinois, May 1962. (10) Guither, Harold D., "Factors Influencing Farm Operators Decision to Leave Farming," Journal of Farm Economics, Vol. 45, No. 3, Aug. 1963. (11) Hill, Lowell D., "Characteristics of the Farmers Leaving Agriculture in Iowa County," Journal of Farm Economics, Vol. 44, No. 2, May 1962. (12) Judge, G. G., and Earl R. Swanson, Markov Chains: Basic Concepts and Suggested Uses in Agricultural Economics, Dept. of Agr. Econ., AERR-49, Univ. of Illinois, Dec. 1961. (13) Kaldor, Donald R., and William M. Edwards, Occupational Adjustment of Iowa Farm Operators who Quit Farming in 1959-1961, Agr. and Home Econ. Exper. Sta., Iowa State Univ., Special Bul. No. 75, March 1975. (14) Kanel, Don, "Farm Adjustments by Age Groups, North Central States, 1950-1959," Journal of Farm Economics, Vol. 45, No. 1, Feb. 1963. 65



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tion or number of farms to the aforementioned results. This process must also be repeated through the projection periods and we must assume what the rate of future price inflation will be. In this study, we assumed the following changes in farm prices received by farmers: Projection Percentage increase in prices period received by farmers 1974-85 68.2 1985-90 42.0 1990-95 34.*0 1995-2000 27.0 These assumptions between 1974 and 1990 are based on the National-Interregional Agricultural Projections (NIRAP) high demand and low supply projections. After 1990, the increasing trend of prices received by farmers (evident since 1972) is assumed to continue (see figure 7). The number of farms is projected to decline to 2.2 million in 1990 and 1.86 million in 2000. The number of small farms (those with sales of less than -$20,000) is projected to decline from 72 percent of the total in 1974 to 56 percent in 1990, and 50 percent by the turn of the century. By contrast, the number of farms having sales of 'over Fgr $100,000 is projected to increase from Flue the 5.2 percent in 1974 to 21 percent in 1990, and about 33 percent in 2000 Actual and Projected Prices (table 26). Received by Farmers For comparison, another set of pro800 jections is shown in table 27 based on High price the following low price inflation assumpInflation ~ tions 14/: 600 Projection Percentage increase period in prices 1974-85 32.5 40-J 1985-90 24.5/ 1990-95 27.0 195200274200 -0 Low price Inflation 14/ These-assumptions were obtained 0 from the National-Interregional Agricul190 90 170 98 190 20 tural Projections (NIRAP) baseline of Percentage of 1967 May 1, 1978. 42



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Appendix table 5--Estimated simple trend equations by sales class: 1959, 1964, 1969, 1974 1/ Sales class : Estimated trend equations : R2 Less than $2,500 : In FN1 = 7.752 -0.179T 0.977 (146.09) (9.23) $2,500-$4,999 : In FN2 = 6.663 -0.217T 0.964 (81.40) (-7.26) $5,000-$9,999 : ln FN3 = 6.779 -0.253T 1.000 (2537.51) (-259.83) $10,000-$19,999 : In FN4 = 6.405 -0.145T 0.922 (78.54) (-4.86) $20,000-$39,999 : ln FN5 = 5.381 + 0.3251n T 0.953 (111.22) (6.38) $40,000-$99,999 : In FN6 = 4.312 + 0.905In T 0.862 (17.71) -(3.54) $100,000-$199,999 .In FN7 = 2.483 + 1.2541n T 0.830 (6.52) (3,13) $200,000-499,999 : In FN8 = 1.358 + 1.382In T 0.846 (3.43) (3.32) $500,000 and over .In FN = 0.079 + 1.404In T 0.913 (0.260) (4.574) 1/ The time variable (T) is: 1959 = 1, 1964 = 2, etc; R2 is the coefficient of determine. Figures in parentheses are t ratios. 76



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SUMMARY The total number of farms in the United States will decline from 2.9 million in 1974 to 2.1 million in 1990 and to 1.8 million in 2000 if present trends continue. The farms will probably be arranged in a bimodal distributioni--a large proportion of small farms, an ever-increasing proportion of large farms, and a declining proportion of medium-size farms. Small farms (gross sales of less than $20,000) will constitute about 50 percent of all farms in 2000, a decline from 72 percent in 1974, while the proportion of large farms (gross sales of more than $100,000) will increase from 5 percent to 32 percent. The projections deemed most likely to be realized are summarized as follows: Sales class 1974 1985 1990 2000 1,000 farms Less than $20,000 2,070 1,416 1,193 889 $20,000 -$99,999 655 563 450 301 $100,000 -$499,999 139 290 358 344 $500,000 and over 11 51 88 .217 All farms 2,875 2,320 2,090 1,750 Much of the shift to larger farms will be due to the expected rise in t he index of prices received by farmers rather than a rise in the real output per farm. For example, the number of farms with sales of $100,000 or more is projected to increase four times between 1974 and 2000 in current prices compared with an increase of 2.7 times in that period if constant (1964 -)_prices are -used. If the rate of price increases through the year 2000 is less than that projected, the numbers of farms in each sales class will change: the number offarms in the larger sales classes will be reduced and the number of farms in the smaller sales classes will be increased. The decline in farm numbers and the increase in farm size will probably be accompanied by other changes in the structural characteristics of the U.S. farm sector. The highlights are: *Agricultural production and farmland ownership will be dominated by fewer and fewer farms. By 2000, the largest 1 percent of farms will account for abot hlfof all farm production. By contrast, 50 percent of the farms-the smaller ones--will produce only 1 percent. ; Almost two-thirds of the production will likely come from the largest 50,000 farms and nearly all farm products will be produced by the largest 1 million farms in 2000.



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Table 27--Projected number of farms by sales class: Markov process, low price inflation 1974 Sales Class 1980 : 1985 Actual : Projection 1,000 farms Less than $2,500 1,100.6 1,101.2 998.0 894.5 $2,500-$4,999 : 323.0 322.2 202.7 197.3 $5,000-$9,999 : 319.5 319.3 270.9 233.1 $10,000-$19,999 : 326.9 326.8 279.0 211.9 $20,000-$39,999 : 327.6 327.6 260.4 193.9 $40,000-$99,999 : 327.5 327.6 331.1 371.4 $100,000-$199,999 : 99.4 99.4 104.0 143.0 $200,000-$499,999 : 39.3 39.3 44.1 67.0 $500,000 and over All farms : 2,874.9 2,874.7 2,508.2 2,341.6 Sales Class : 1990 : 1995 : 2000 1,000 farms Less than $2,500 : 881.2 865.0 750.0 $2,500-$4,999 : 135.6 102.0 50.0 $5,000-$9,999 189.4 155.8 140.0 $10,000-$19,999 : 165.7 124.2 100.0 $20,000-$39,999 : 147.0 101.9 100.0 $40,000-$99,999 370.2 350.6 275.0 $100,000-$199,999 : 161.7 178.1 181.5 $200,000-$499,999 : 90.1 113.2 132.0 $500,000 and over : 51.0 83.0 121.5 All farms : 2,191.9 2,069.6 1,850.0 44



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It is significant to note that the total number of farms projected by sales class exceeds the total projected by acre size starting in 1985. By 2000, the difference is about 400,000 farms. That difference, to a large extent, can be attributed to the trend projections procedures. For farms in the $20,000-$39,999 sales class, the trend first pointed to an upward shift, then a decline in 1974. The estimated trend equation for this sales class, which has a positive coefficient for the time variable, apparently failed to capture the downturn in 1974. Thus, trend projections by sales class are likely to overestimate the total number of farms and the number in the :$20,000-$39,959 sales class. Table 15--Trend projections of the number of farms, by size of farm Size of farm 1980 1985 1990 1995 2000 1 ,000 farms 1-99 acres 1,190.4 1,060.8 945.3 842.4 750.6 100-219 acres 558.1 477.7 409.0 350.1 299.7 220-499 acres 456.3 406.0 361.3 321.5 286.1 500-999 acres 212.6 210.5 208.9 207.1 205.3 1,000-1,999 acres 96.3 99.3 102.2 105.3 108.4 2,000 acres and over: 60.9 60.9 60.9 60.9 60.8 All farms 2,574.6 2,315.4 2,087.5 1,887.2 1,711.0 Table 16--Trend projections of the number of farms, by sales class Sales class : 1980 1985 1990 1995 2000 1 ,000 farms Less than $2,500 : 951.4 795.6 665.3 556.3 456.2 $2,500-$4,999 264.3 212.8 171.3 137.8 110.9 $5,000-$9,999 : 247.7 192.2 149.2 115.8 89.8 $10,000-$19,999 : 293.2 253.6 219.5 189.9 164.3 $20,000-$39,999 : 366.2 388.5 408.5 426.6 443.2 $40,000-$99,999 : 316.9 373.7 429.6 484.8 539.4 $100,000-$199,999 : 90.1 113.3 137.4 162.5 188.3 $200,000-$499,999 : 36.0 46.3 57.2 68.8 81.0 $500,000 and over : 11.4 14.9 18.7 22.7 27.0 All farms :2,577.1 2,390.9 2,256.6 2,165.2 2,109.2 23



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Figure 11 Figure 12 Projected Numbers of Farms Projected Numbers of Farms Based on Acreage Distribution Based on Sales Distribution Million farms Million farms Trend extrapolation and -.Trend extrapolation 4.0 Markov process 4.0 -Markov process --Negative exponential *---Negative exponential functionfunction 3. ...Age cohort analysis 3.5 -...Age cohort analysis 3.0 -3.0 2.5 2.5. 2.0 -2.0 199 4 9 4 0 5 0 5 000 1959 64 69 748 590 9 000 The decline in the percentage of small farms (less than 220 acres) 'and the increase in large farms (1,000 acres and more) are less apparent than the changes in the total number of farms would lead us to believe. While the U.S. farm sector experienced a 19-percent decline-in the number of all farms between 1964 and 1974, the decline in the percentage of small farms was negligible-from 71 percent in-1964 to 70 percent in 1974. Similarly, the percentage of the large farms increased by only 1 point, from 4 percent in 1964 to 5 percent in 1974. This size configuration of American farm structure is projected to continue into 2000. The sales distribution of farm numbers is projected to have a more apparent shift from those with low sales to those with high, partly due to the anticipated high price inflation. By 2000, small farms (sales of less than $20,000) are likely to account for 50 percent of the total, a decline from 72 percent in 1974. By contrast, the percentage of large farms (sales of $100,000 and more) is projected to increase to 32 percent, a rise from 5 percent in 1974., The procedure used to measure the percentage error between the actual and projected number of farms is the inequality coefficient (U) developed by Theil (21): 55



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Table 38--Projected proportions of 1974 farm numbers by sales, class, negative exponential function Sales class Actual Projection Percentage difference l/ Percent Less than $2,500 38.3 4.5 -88.3 $2,500-$4,999 11.2 4.3 -61.6 $5,000-$9,999 11.1 6.2 -44.1 $l0,000-$19,999 11.4 14.3 25.4 $20,000-$39,999 11.4 20.7 81.6 $40,000-$99,999 11.4 32.3 183.3 $I00,000-$199,999 3.4 14.5 326.4 $200,000-$499,999 1.4 2.2 57.1 $500,000 and over .4 1.0 150.0 All farms 100.0 100.0 NA NA means not applicable. 1/ Theil-U = 0.941 or 94.1 percent. Table 39--Projected proportions of 1974 farm numbers by size of farm, negative exponential functions Size of farm Actual Projection Percentage difference l/ Percent 1-69 acres 37.2 14.7 -60.5 70-99 acres 10.0 5.7 -43.0 100-139 acres 9.0 7.0 -22.2 140-179 acres 8.3 6.4 -22.9 180-219 acres 5.3 5.7 7.5 220-259 acres 4.3 5.3 23.3 260-499 acres 13.2 23.4 77.3 500-999 acres 7.3 21.7 197.3 1,000-1,999 acres 3.2 9.1 184.4 2,000 acres and over 2.2 1.0 -54.5 All farms .100.0 100.0 NA NA means not applicable. 1/ Theil-U = 0.681 or 68.1 percent. 59



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Table 21--Farm movement matrix by acreage, 1969-74: 100-0-0 movement assumption :1974: :average: : Size of farm :farm : A0 : Al.: A2 : A3 : A4 : A5 : A6 : A7 : A8 : Ag : A10 : size : : : : : : : Acres Numbers of farms 1-69 acres (Al) : 32 84,257 l/ 1,069,433 335 70-99 acres (A2) : 82 47,814 2/ 287,137 882 100-139 acres (A3) : 117 42,923 2/ 257,808 799 140-179 acres (A4) : 158 44,146 3/ 238,987 1,375 180-219 acres (A5) : 198 27,270 3/ 150,072 1,315 220-259 acres (A6) : 238 20,075 4/ 121,536 6,604 260-499 acres (A7) : 359 40,964 5/ 372,693 24,805 500-999 acres (A8) : 687 16,055 185,897 16,487 1,000-1,999 acres (Ag) :1,356 11,135 76,777 2,827 2,000 acres and over (A1o) :6,697 0 59,167 I/ Computed as 92.7 percent of the number of farms in 1969. 2/ Computed as 85.5 percent of the number of farms in 1969. 3/ Computed as 84.0 percent of the number of farms in 1969. -4/ Computed as 82.0 percent of the number of farms in 1969. 0 5/ Computed as 85.0 percent of the number of farms in 1969. Table 22-Farm movement matrix by sales class, 1969-74: 100-0-0 movement assumption Sales class : : S1 : S2 3 : S4 : S5: S6 : S7: S8: S9 1 ,000 farms Less than $2,500 : 147.21 1/ 1,266.85 3.00 $2,500-4,999 : 154.33 2/ 266.17 12.30 $5,000-9,999 : 50.80 3/ 336.96 23.07 $10,000-19,999 : 56.05 4/ 319.62 23.85 $20,000-39,999 : 30.32 241.48 57.99 $40,000-99,999 : 12.12 138.79 17.10 $100,000-199,999 : 4.62 24.27 6.08 $200,000-499,999 : 2.16 8.21 2.03 $500,000 and over : 0 4.03 1/ 89.4 percent of the number of farms in 1969. 2-/ 61.5 percent of the number of farms in 1969. T/ 82 percent of the number of farms in 1969. _/ 80 percent of the number of farms in 1969.



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ratio of 0.98 for the group born between 1920 and 1929. To project the number in this cohort to 1984, cohort ratio for the 45-54 years age group in 1964 and the 55-64 years age group in 1974 (0.77) is multiplied by the number of farm operators of the 45-54 years age group in 1974 (728,300). Therefore, 563,000 farm operators are projected for the 55-64 age group in 1984. Following the same procedure, 366,000 farm operators of age 65-74 are projected for 1994. No farm operators in this cohort will remain in farming by the year 2004, since we assume that all farm operators will leave farming by age 75. 15/ The projected numbers of farm operators by age group to the year 2004 are shown in figure 10. Summing the numbers in each group for each year indicates that the total number of farm operators is likely to continue to decline. The number is projected to decline from 2.9 million in 1974 to about 2.4 million in 1984, 2 million in 1994, and 1.6 million in 2004. 15/ The cohort ratios for the under 25-year old group are calculated differently. The Census reports no data for this group as they would have been less than 15 years old in the earlier period. To calculate their entry rates we assumed that these youngest entries were replacing their fathers and we allowed up to a 40-year age difference, as suggested by Tolley (21). So the ratio became the number of farm operators who are less than 25 years old in a specific year divided by the total of the farm numbers in the 35-44 and 45-54 age group enumerated 10 years earlier. Table 29--Change in farm operator numbers, by age cohort and farm size, 1964-74 Cohort by Age at 1100220:5001,0002,000 year of 1974 Census 99 219 449 999 1,999 acres Total birth acres acres acres :acres acres and over Years 1,.000 farmers After 1949 Less than 25 29.4 15.2 11.6 3.7 1.3 .7 61.9 1940-49 25-34 123.1 52.7 43.2 19.7 8.4 4.7 251.8 1930-39 35-44 :89.9 25.8 14.3 16.2 8.8 55.9 160.9 1920-29 :45-54 :13.4 -17.5 -22.1 5.3 5.6 3.6 11.7 1910-19 55-64 -67.9 -70.1 -58.6 -13.1 -2.9 -1.6 -214.2 1900-09 65-74 :-93.0 -89.4 -71.8 -21 .4 -7.0 -3.8 -286.4 Before 1900 75 or older 1/ :-363.1 -156.7 -79.6 -25.3 -10.4 -9.0 -644.1 Total : NA :-268.2 -240.0 -163.0 -14.9 3.8 .5 -681.8 Net entry NA 242.4 93.7 69.1 39.6 18.5 11.3 474.6 Net exits : NA 456.1 246.1 151.4 46.7 17.4 12.8 930.5 Replacement rate NA .53 .38 .46 .85 1.06 .88 .51 NA = Not applicable. 1/ Assumed all operators 65 years and older in 1964 would have exited in 1974 before the age of 75. Source: (25), adjusted for reported undercounting, excludes abnormal farms. 49



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Kanel found that most of the adjustments occur as the older operators leave farms (14). Using Kanel's age cohort framework, Tolley stratified farm operators by size of farm and further examined mobility (22). He found considerable variation in entry and exit rates by age group and sales class. Age cohort analysis centers on identifying the common pattern of entry and exit related to operator age. From census of agriculture data, the same cohort group of farm operators with common birthdates can be identified in successive censuses and the changes in net entry and exits for each age group can be estimated (figure 9). For example, for the cohort born from 1876 to 1885, some 1.4 million were farm operators when they reached the ages of 25 to 34 (in the 1910 Census). The number increased in the next decade to 1.6 million (1920) and declined slightly by 1930, by which time the cohort was 45 to 54 years old. This cohort declined to 1 million farm operators by 1940 (ages 55 to 64) and to 745,000 to 1950 (ages 65 to 75). All are assumed to have exited by 1960 as they reached 75 years of age. A few of these older operators may have continued farming, but beyond this point the Census does not provide data. A similar pattern for other cohorts is shown in figure 9. The number of farmers in each group expands to a peak at 35 to 44 years and then declines through death or retirement. Some differences in slopes are revealed for individual cohorts. For example, the cohort born in 1916-25 was disrupted by World War II, and a new pattern seems to have emerged. Younger operators entered farming at previous rates, but a large number left farming after 35 years of age--10 years younger than previous age groups began to leave farming. Figure 9 Farm Operator Age Cohort Movements, 1910-69 Thousands 1,400 -1 1,200 8190 600 1921-96-19165 1,200 --0 .---.' .so 600 After 1945 % Under 25 25-34 35-44 45-54 55-64 65 or over Age Group Source: (25). 46



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TREND EXTRAPOLATION This chapter describes the projections obtained from simple extrapolations of trends, and the adjustment of the census data to take account of overenumeration and underenumeration. Again, the central question is: If we assume that the current trends are going to continue into the future, what will the structure of agriculture likely be by the year 2000? Technical Overview The functional specification for projecting the number of farms in each acre size and sales class was selected on the basis of the R2 (coefficient of determination) goodness-of-fit criterion, consistency, reasonableness in comparison to the past trend, and, to some degree, our own subjective judgment. To illustrate, a linear trend equation was rejected because: (1) the linear specification frequently projected a much faster rate of decline in farm numbers than one would normally expect. In fact, a linear equation will project the number of farms in the 100-219 acres class to completely disappear by the late 1990's and to be negative in the year 2000; and (2) this form did not generally yield a higher R2 than a semilog specification, the form eventually selected. Conversely, a polynomial specification was rejected for the opposite reason--it frequently projected trend reversal. Instead of a decline in the number of farms in the l-to-99-acre size class, it projected an increasing trend into the future. This left a choice between the log-linear and the semilog forms. The semilog form was chosen because it generally gave a better fit in terms of the R2 criterion, and it produced expected results better than the log-linear form. For example, the number of farms in the l-to-99-acre size group historically had declined at a high rate--311,O00 farms between 1959 and 1964 and 133,000 between 1969 and 1974. If this trend continues, one would reasonably expect the number of farms in this size group to decline from the 1.36 million in 1974 to about 1.2 million in 1980. Yet, the log-linear specification would project virtually no decline. For similar reasons, we chose the semilog form to project the number for sales classes of less than $20,000, and the log-linear form for sales classes of more than $20,000. Data Adjustments The data used throughout this study came primarily from the 1974 Census of Agriculture and earlier censuses; data from other sources are specifically noted. Because of incomplete counting in the census and the importance of capturing the effects of changes in commodity prices on shifts in farm numbers from one sales class to a higher one, adjustments were made to the data used in this study to account for underenumeration and overcounting, and for the effects of price inflation. No adjustments were made to the data for trend projections because the effects of price inflation were assumed to be captured in the trend equations. However, this adjustment was explicitly made for the Markov process and age cohort projections discussed subsequently. 20



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Few of the regions or States have size distributions that conform exactly to the theoretical negative exponential distribution. This is as expected, since the distribution for most States reflects unique characteristics of the State, such as geographic conditions, types of agriculture, and institutional constraints (for example, large number of small tobacco farms in North Carolina). 7/ It is also expected that long-established, traditional farming areas (with few physical, economic, or institutional constraints) which have undergone fragmentation and reconsolidation of farming units from original settlement patterns would tend to more nearly approximate the inverse exponential distribution. While the usefulness of estimated equations of this form for projection depends upon the magnitude of deviation from the theoretical distributions, it is also dependent upon the stability of the farm size distribution over time. To determine statistically the stability of the estimated equations, an analysis of the covariance was conducted (3, 4). This involves comparison of the sum of squared residuals from the individual equations and the equation estimated for all groups. The hypothesis tested is that the data used in estimating the parameters of each equation belong to the same regression equation, that is, the data are subsamples of the same population--no significant shifts occur in the distribution over time. The F ratio calculated was expressed as: (A -B -C -D -E) / P (k -1) F = (B + C + D + E) / (n1 + n2 + n3 + n4 -4P) Where ni = the number of observations (7) (i = 1, ... 4) p = number of parameters estimated (1 -slope) k = number of classes (4 -1959, 1964, 1969, 1974) A = total group sum of squares of n, + n2 + n3 + n4 observations with n, + n2 + n3 + n4 -P degrees of freedom B, C, D, E, = individual group sum of squares on ni deviations of the dependent variable from the regression estimated by ni observations with ni -P degrees of freedom. A comparison of the calculated F (table 17) with tabular F at the 0.05 level of significance indicates the null hypothesis is rejected for only one State, Rhode Island, in the New England region. Thus, the distributions appear stable over time and, if adequately portrayed by the estimated equations, projections may be made with some confidence. Projections To maintain the consistency of our data series for projection purposes, it was necessary for us to adjust the Census of Agriculture data for underenumeration and reestimate the negative exponential functions for the United States by using the adjusted census data, as shown in table 2. 7/ For further discussion of why deviations occur, see Dovring (7). 27



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Table 20--Calculation of change in farm numbers due to price inflation and other factors, by sales, 1969-74 Fam umes umti ve of is7tfrmbu Number of: : Change 1974 farm Famnumbers farms Change due to inflation :det ubr Sales : eand::other without in class ::factors price inflation 194 :Actual 1969 : 1974 :Percent Percent 1969 1974 Gain :Loss : Net *changer dollars: dollars. gain 2/ loss 3/ Thousands $500,000 and over 4.03 11.21 7.18 5.73 10.88 5.73 5.15 --5.15 46 --2.03 6.06 $0,0-9999 : 12.46 39.33 26.87 18.51 48.70 7.63 30.19 5.15 25.04 77 41 18 42 $100,000-199,999 : 34.97 99.38 64.41 59.51 147.71 10.81 88.20 30.19 58.01 89 86 6.40 41.37 $40,000-99,999 : 168.01 327.52 159.51 237.48 456.42 89.42 218.94 88.20 130.74 67 52 28.77 196.78 $2,0-999 : 329.79 327.57 -2.22 511.54 792.72 55.12 281.18 218.94 62.24 86 66-6.6 253 $10,000-19,999 : 399.52 326.90 -72.62 853.59 1,118.98 60.87 265.39 281.18 -15.79 81 70 -56.83 342.69 $5,000-9,999 : 410.93 319.47 -91.46 1,173.21 1,408.81 54.23 235.60 265.39 -29.79 74 65 -61.67 342.69 $2,500-4,999 : 432.80 322.95 -109.85 1,462.89 1,751.64 54.08 288.75 235.60 53.15 89 54 -163.00 269.80 Less than $2,500 :1,417.06 1,100.60 -316.46 2,750.00 2,873.13 998.36 123.13 288.75 -165.62 11 20 -150.84 1,266.32 Total :3,209.57 2,874.93 -334.64 --------2,751.80 1/ These are cumulative farm numbers distributions predicted by a fifth-degree polynomial function wi~th both sales receipts. and farm numbers expressed in natural logarithms. 2/ Column 8 divided by column 3. 3/ Column 9 divided by column 2. --=Not applicable.



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Appendix table 6--Adjustments to census data and projects for acres and sales, 1964 and 1974 Acres : Sales Item : Projec-: : Projec1964 1974 : tions 1964 1974 : tions 1. Estimated missed farms : I/ x 1/ x 2. Estimated age-size matrix for missed farms x 3. Estimated age-size for abnormal farms in order to subtact them : x x 4. Farms with sales of less than $1,000 not included in 1974 x x 5. Corporations and others without opertor age-distributed by size: x X 6. Deflation with decumulative log polynomial curve .x 7. Reinflation to current prices x x 8. Adjust cell total to equal cohort total 2/ x 2/ x 1/ 401,000 farms reported in Census Evaluation Coverage by Age, Acres and Sales Distribution. 2/ See appendix table 4 for amount of adjustment required. 78



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table 20. For example, while there were about 800,000 farms with sales of $20,000 and more in 1974 (point A in fig. 6), the number of farms dropped to about 500,000 when the sales were expressed in 1969 dollars (point B in fig. 6). The next step is to figure out the shifts in farm numbers for each sales class through this deflationary process. That is, to determine the numbers of farms that remain in the same sales class and those that move to the lower sales classes. For example, the 327,000 farms with sales of $10,000 to $19,999 in 1974 would have had sales ranging from $5,600 to $11,200 if they had not had an 80-percent increase in prices received due to inflation. In other words, the same 327,000 farms which are measured by the vertical distance CD for segment CA in the current dollar distribution, now can be measured by the vertical distance EF for segment EG in the 1969 constant dollar distribution (fig. 6). It is clear that distance DH (60,900 farms) measures the number of farms with sales of $10,000 to $19,999 that remain in the same size class after the deflation, a difference between point H (853,600 farms) and point A (792,700 farms). In the meantime, distance CHor EI (265,400 farms) measures the number of farms that move to the lower sales class ($5,000 to $9,999), a difference between point C (1,118,900 farms) and point H. Thus, the 80-percent increase in prices received by farmers due to inflation is estimated to have moved 265,400 farms up statistically from the sales class of $5,000 to $9,999 to the next higher sales class ($10,000 to $19,999), a gain in the number of farms with sales of $10,000 to $19,999 (column 8 in table 16). Repeating the same deflationary process for farms in the next higher sales class ($20,000 to $39,999), we estimated that the price inflation moved 281,200 farms up from the sales class of $10,000 to $19,999 to the next higher sales class ($20,000 to $39,999), a loss in the number of farms with sales of $10,000 to $19,999 (column 9' in table 20). Therefore, the 80-percent increase in prices received by farmers due to inflation had the net effect of reducing the number of farms in the sales class of $10,000 to $19,999 by 15,800 farms. Table 20 shows that the number of farms in this sales class declined by 72,600 from 1969 to 1974. The preceding interpretation of that decline, however, tells us that about 22 percent of it (15,800 farms) was attributed to the price inflation and the remainder (56,800 farms) was due to other "real" factors. Performing the same analysis for each sales class, we obtained a gain-loss array of the changes in farm numbers due to price inflation as shown in table 20. In general, price inflation has a net effect of reducing the number of small farms and increasing the number of large farms. As a result of an 80-percent increase in prices received by farmers between 1969 and 1974, about 90 percent of the apparent increase in the numbers of farms with sales of $100,000 and more is attributed to the effects of price inflation. Farms with sales of $100,000 and more increased by 98,500, but 88,200 of those were pushed into the higher sales classes because of the price inflation. Projections The Markov process, as employed in this study, enables projecting the future number of farms by acreage by multiplying the transition probability matrix by the row vector of farm numbers in the base year. The projection proceeds in two steps, however, when sales are used to measure the size of farms. First, a 36



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in the 1964-74 period to 284,000 during the 1984-2004 period, a 40-percent decline in entries. Since only a few large farming operations will be required to produce the total farm output, many of the younger entries will be on small, part-time farms, and will depend primarily on nonf arm income sources. Expectations of nonf arm income will likely encourage young people associated with what are now marginal or inadequate size farms to choose nonfarm occupations. Therefore, farm numbers will continue to decline as fewer young people enter farming to replace older operators who leave farming. The replacement rate of young for old operators has been considerably higher for larger farms with sales exceeding $100,000 (table 11). But since there were so many more small farms, 90 percent of the entries from 1964 to 1974 were on farms with sales less than $100,000. By 2000, however, only about half of the entries will be on such smaller farms. Many of the small farms of retiring farm operators will be consolidated into existing farms, increasing the-proportion of large farms. These large farms will require significant amounts of'.capital. Therefore, the farming opportunities will be limited to a few entries on larger farms. Many of the younger persons entering farming will probably do so on established farms as partners or shareholders with-other family members. Table 10--U.S. farm operator age distribution Age 1974 1984 1994 2004" Percent Less than 25 years 2.2 2.0 1.8 2.1 25 to 34 years 10.9 13.5 11.0 11.2 35 to 44 years 17.8 19.4 24.5 21.2 45 to 54 years : 25.3 22.0 23.5 28.2 55 to 64 years 25.3 24.1 20.6 21.6 65 years and older 18.5 19.0 18.6 15.6 Total 100.0 100.0 100.0 100.0 Years Estimated average age 1/: 51.9 51.2 50.8 50.3 1/ The weighted average was calculated from the age distribution by muTtiplying the weighting factor (the fraction of the farmers in each age group) by the midpoint of each age group. For the youngest age group, the assumed midpoint was 22; for the oldest age group, the assumed midpoint was 71. Source: Adjusted 1974 Census of Agriculture and age cohort projections. 17



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APPENDIX A Data Adjustments for Underenumeration of the 1974 Census of Agriculture Data This adjustment process uses the evaluation of coverage results reported by the U.S. Census Bureau, specifically the percentage of farms enumerated by farm size (24). An estimate of missed farms is then computed for each size class. But, the sum of the estimated missed farms frequently exceeds the total of missed farms, suggesting that another round of adjustments is needed. The second-round estimates of missed farms are computed by assuming that the discrepancy between the two estimates can be eliminated in proportion to the firstround estimates of missed farms in each size class. The adjusted farm numbers are then obtained by adding the revised estimates of missed farms to the numbers of farms reported by the census. This implies, however, that the number of abnormal farms, after adjusting for underenumeration (column 9 in appendix table 2), should be deducted from column 8. Therefore, a complete comparability is maintained for column 8 in appendix table 2 and column 10 in appendix table 3, with each showing the number of farms by size class adjusted for underenumeration and excluding normal farms. 72



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Appendix table 1--Selected structural characteristics of U.S. farms, by sales class--Continued : $100,000 : $40,000 to : $20,000 to :$10,000 to $5,000 to :$2,500 to :Less than Item : Unit :and over : $99,999 :$39,999 :$19,999 : $9,999 :$4,999 : $2,500 All :(class IA) : (class 18) : (class II) : (class III): (class IV) : (classV) : (class VI): farms 0ff-farm income per farm: 1 1969 Dols. : 7,471 3,865 3,212 3,858 5,094 5,757 6,964 5,537 1974 do. : 8,060 4,997 5,512 7,444 9,640 11,566 12,411 9,487 Payments government farm programs per farm: 1969 : do. : 15,018 5,679 3,407 2,330 1,511 1,028 565 2,242 1974 : do. : 3,890 1,677 1,336 1,083 811 715 400 1,305 Capital gains on : farm assets per : farm: 1969 : do. : 36,765 12,655 7,442 4,848 3,167 2,314 1,333 4,106 1974 : do. : 71,273 30,560 18,541 12,289 8,074 6,242 4,209 13,770 Total net income; per farm 2/: 1969 : do. : 54,448 22,712 14,109 9,955 8,208 6,234 7,261 10,719 1974 : do. : 75,237 27,127 16,347 12,662 11,852 11,242 12,399 19,682 Assets, debts per farm, 1969: Assets : do. : 852,456 314,949 181,773 119,426 80,395 60,969 40,991 106,780 Debts : do. : 210,088 65,101 33,439 20,331 10,821 5,267 3,458 17,981 Debt/asset ratio: Percent : 24.6 21.4 18.4 17.0 13.5 8.6 8.4 16.8 Assets, debts per farm, 1974 Assets :Dols. : 954,326 380,511 224,328 150,760 108,299 91,770 73,746 186,472 Debts : do. : 287,830 58,549 29,712 16,027 8,892 5,039 3,375 29,575 Debt/asset ratio: Percent : 30.2 15.4 13.2 10.6 8.2 5.5 4.6 15.9 See footnotes at end of table. ---Continued --



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Appendix table 1--Selected structural characteristics of U.S. farms, by sales class--Continued : $100,000 $40,000 to $20,000 to $10,000 to $5,000 to : $2,500 to Less than All Item Unit and over $99,999 $39,999 $19,999 $9,999 : $4,999 $2,500 fa (class IA) (class IB) (class II) (class III) (class IV) : (class V) (class VI) farms Tenure of farm operators--1969 Full owners Percent 35.3 32.6 36.4 45.9 59.3 69.4 82.8 62.5 Part owners do. 51.4 51.3 45.4 36.8 25.7 17.9 9.0 24.6 Tenants do. 13.3 16.1 18.2 17.3 15.0 12.7 8.2 12.9 Tenure of farm operators--1974 Full owners do. 29.3 33.3 45.4 58.8 69.1 75.3 84.0 61.5 Part owners do. 57.2 50.8 38.7 27.3 19.8 15.7 10.1 27.2 Tenants do. 13.5 15.9 15.9 13.9 11.1 9.0 5.9 11.3 l/ Number of farms estimated by the authors by assuming that the number of farms and land in farms in this sales class follow the same distribution pattern among the various types of organization in sales class V where sales range from $2,500 to $4,999. Direct census data on these items are not available. 2/ Total net income per farm include net farm income, off-farm income, and farm program payments. Capital gains on farm assets are excluded.



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Table 28--Change in farm operator numbers by age cohort, by sales class, 1964-74 Cohort by year : Age at Less than $2,500 to $5,000 to :$10,000 to :$20,000 to $40,000 to $100,000 Total of birth : 1974 Census :$2,500 4,999 9,999 19,999 39,999 99,999 or more Years .Farmers After 1949 Less than 25: 22.8 8.5 10.6 9.1 5.4 2.4 0.4 59.3 1940 to 1949 25 to 34 : 118.7 21.9 30.2 30.6 24.8 16.8 4.8 243.8 1930 to 1939 35 to 44 95.5 7.7 10.1 1.2 10.3 19.5 9.0 153.3 1920 to 1929 45 to 54 12.6 12.8 -13.1 -27.7 -4.8 15.4 6.7 -23.7 1910 to 1919 : 55 to 64 -83.3 -37.5 -50.7 -53.8 -15.8 3.4 0 -237.7 1900 to 1909 : 65 to 74 :-101.7 -51.2 -7.8 -62.3 -43-6.9 -2.1 -326.5 Before 1900 : 75 or -426.8 -88.9 -63.8 -37.2 -7.0 -7.7 -2.7 -644.1 older 1/ Total : NA -362.2 -152.3 -154.7 -140.1 -21.4 43.0 16.1 -771.6 Net entry : NA : 249.6 50.9 50.9 40.9 40.5 100.6 37.0 456.4 Net exits NA 974.0 329.9 290.1 321.1 73.3 14.6 4.8 2,003.6 Replacement rate: NA : .26 .15 .18 .13 .55 6.89 7.71 .23 1/ Assumed all operators 65 years and older in 1964 would have exited by 1974 or before the age of 75. NA = Not applicable. Source: U.S. Dept. of Commmerce, Bureau of the Census, Census of Agriculture; adjusted for reported undercounting; excludes abnormal farms; 1974 sales classes adjusted to 1964 prices.



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projection is obtained by multiplying the transition probability matrix (which is constructed from constant dollar distributions of farm numbers),by the row vector of farm numbers in the base year. Second, effects of anticipated increase in prices received by farmers on the number of farms in each sales class are then incorporated into the projection results obtained in step one. In the absence of more detailed data on entry, exit, and farm movement among size classes, we relied on aggregate census data in recent years to construct and approximate the transition probability matrix. The guiding principle in developing this matrix was to select numerical values that minimized the residual sun of squares, computed from the projected and actual number of farms by size class. Analytically, this problem can be solved with a quadratic programming framework (18). This study, however, employed a less formal, trialand-error iterative procedure and, in part, assumed traditional farm movement patterns underlying the Markov process to construct the transition probability matrix. 11/ Farms were permitted to expand their size or to exit from farming, but not to' contract. En addition, we assumed that the number of farms in the largest size class would remain in that category and that any increase in the number of farms in a size class came from the immediately smaller size class. 12/ To illustrate, all the farms of 2,000 acres and more in 1969 (59,167-see table 14) were assumed to remain in the same size category in 1974--they neither ceased operations nor moved to a smaller size class. Thus, the same 59,167 farms were placed in the diagonal element of the farm movement matrix between 1969 and 1974, the cell intersecting row vector A10 and column vector A10 (table 21). The numerical value in row A9 and column A1O is then the estimate of farms (2,827) moving up from size class A9 to A1O. The number of farms lost in the consolidation process in size class A9 (farmland of 1,000 to 1,999 acres) is then estimated as 11,135. Before the consolidation took place, the 2,827 farms that moved up from size class A9 to A10 operated about 3.83 million acres of farmland. By contrast, the same 2,827 farms operated about 18.93 million acres of farmland after the expansion. This implies that about 15.1 million acres of farmland were consolidated from size class A9 to A1O in the process of structural change between 1969 and 1974. Translating the consolidated farmland into the number of farms lost in the consolidation process means that 11,135 farms moved out of farming in size class A9 (15,100,000 / 1,356). Mechanically, this net exit estimate (column AO) can be computed as: 11,135 = [(6,697/1,356) -11 x 2,827 The number of farms that remain in size class A9 is then computed as the difference between the 1969 number of farms in size class A9 and the sum of the number of farms that move up to the higher class (MlO) and those in the net exit category. 11/ The combined use of the iterative procedure and traditional farm movement assumptions results in a projection error of less than 1 percent. 12/ This is what is known as the 100-0-0 transition pattern as illustrated by Dfaly, Dempsey, and Cobb (5). This assumption was found to give a better fit to actual data than other alternatives, including 40-40-20 and 60-40-0 patterns. 38



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To the extent that size distribution around a moving average is stable over time, the information required for projecting future farm size distributions is minimal--the projected land in farms and average farm size in acreage distributions, and the projected total sales receipts and average sales receipts in sales distributions. Strictly speaking, however, the rationale for using the negative exponential function is not as strong for size distributions defined by sales. Thus, caution is advised in use of these equations for obtaining precise projections of sales distribution. Nevertheless, for comparison purposes and to maintain consistency throughout this report, sales distributions and their projections are also projected in this section. Projections of acreage distributions to 2000 were obtained from the estimated equations by dividing the trend average farm size into the lower limits of each of the size categories to obtain new x variable values and the constant term, calculated as described previously. The resulting values are used to obtain the projected decumulative distribution, and the percentage of farms in each size category is found by subtracting each category from the previous one. Projected annual mean sizes were obtained from a linear time trend equation estimated from data for the 1957-77 period. The estimated equation is: M =363.39 +3.02 T R2-=0.96 (6) (0.20) where M is mean size in acres, T is the time variable (1957 = 1. 0, ..),and the value in parentheses is the standard error of the estimate. While the above information is sufficient to project future farm size distributions, projections of total number of farms require additional information on expected land in farms in the future. Land in farms was fitted by a linear trend equation based on census data (adjusted for undercoverage) for the years of 1959, 1964, and 1974. The estimated equation is: L = 1233.80 -8.16 T R2= 0.971 (7) (0.13) where L is land in farms and T is the time variable (1959= 1, 1964 = 6, etc.). Total number of farms is projected by dividing the projected average farm size into land in farms. As expected, the number of farms was projected to continue to decline; a decrease from the actual 2.9 million farms in 1974 to 1.8 million farms in 2000 (table 18). The general pattern of decline in farm numbers is similar to that projected by historical trends reported in the previous section. However, the rate of decline after 1980 slows. During the 1974 to 2000 period, the negative exponential functions projected farm numbers to decrease at an annual average rate of 1.8 percent. Farms less than 220 acres in size show a continued decline in numbers, especially farms of less than 50 acres in size. The projected size distributions in the 220 to 2,000-acre range, although generally continuing a declining trend, present a discontinuity to recent trends: Instead of projecting smaller farm numbers in 1980 than that in 1974, the numbers are projected to increase. This discontinuity becomes more obvious in the 220 to 2,000-acre range. On the other hand, the numbers projected for the size class of over 2,000 acres present the opposite kind of discontinuity, even though the increasing trend is maintained. 29



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OVERVIEW OF STRUCTURE AND STRUCTURAL CHANGE This chapter describes the current situation for some elements of the structure of U.S. agriculture and recent changes in structural characteristics, emphasizing those related to size. The reader then can compare the current situation with that projected for the future described in the next chapter. The land in farms declined only slightly between 1940 and 1974, but that relatively constant land base was occupied by fewer and fewer farms. Thus, the average farm size increased by one-third between 1940 and 1974. This change-also implies increasing concentration of production and control of land resources into fewer and fewer hands. Contrary to frequent assertion, the remaining farms, although larger, continued to be family-operated farms. Corporations still had an insignificant role in farm production and in farmland ownership. The average age of farm operators did not change noticeably from 1969 to 1974. Big farms appeared to have an edge over small farms in net farm income, payments from Government farm programs, and capital gains on farm physical assets. In 1969, off-farm income per farm was about the same for the very large and small farms. The situation differed significantly in 1974, however. Off-farm income per farm almost doubled for small farms, but no appreciable change was evident for large farms. Although this study focuses on farm numbers and size, there are other important structural characteristics related to size, such as concentration ofproduction and farmland, form of business organization, age and tenure arrangments of operators (discussed in the next chapter), and financial structure. Numbers and Sizes The land in farms increased slightly after 1940, but declined somewhat between 1950 and 1974. The number of farms, however, decreased by 60 percent while the average size(measured by acres) increased by 128 percent (table 1). The decline in the number of small farms perhaps contributed most to the increase in average size. Historically, the number of farms with less than 500 acres has steadily declined, while the number with more than 500 acres has increased (table 2). The decline in farm numbers since 1959 has been at a lower rate than that from 1940 to 1959. Many farmers left voluntarily for better opportunities in the nonfarm sectors; others who retired or died were not replaced by new farmers. The remaining farmers were often motivated by prospects of increased returns by enlarging their lands or consolidating their operations with neighboring ones. The historical trend when farms are measured by gross sales is similar to that for acreage sizes (table 3). Concentration of Production A major aspect of the public concern about farm structure is the concentration of farm production and control of the Nation's land. The concentration of farm production between 1969 and 1974 is shown graphically by the Lorenz curve in figure 1 (tabular data are in app. table 1). In 1969, the largest 24 percent ~of3



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Acreage Distribution Table 34 presents the distribution of farm operator numbers by acre size group for 1964, 1974, and projections for 1984, 1994, and 2004. The projections show declining numbers in all acre sizes, except the 1,000 to 1,999 acre size, through 2004. The numbers of farm operators who farm more than 1,000 acres account for 10 percent of the total number, an increase from 5.5 percent in 1974. By contrast, the proportion of small farm operators with less than 220 acres is projected to remain the same in 2004, about 70 percent. Actually, the number of farm operators with less than 100 acres is projected to account for an increasing percentage of the total. Table 34--U.S. farm operators, by size of farm, selected years and projections 100220: 500:1,000:2,000 Year :1-99 : 219 500 : 999 :1,999:or more: Total :acres acres :acres acres : acres : acres 1,000 farms 1964 : 1,625.1 890.0 665.1 225.1 89.8 61.6 3,556.7 1974 : 1,356.9 649.9 502.1 210.3 93.6 62.1 2,874.9 1984 : 1,171.2 472.7 366.4 120 95.5 60.4 2,358.2 1994 : 1,005.1 345.0 258.4 .172.8 96.5 57.1 1,934.9 2004 : 862.4 256.8 182.5 156.1 98.0 53.9 1,609.7 Percent 1964 : 45.7 25.0 18.7 6.3 2.5 1.8 100.0 1974 : 47.2 22.6 17.4 7.3 3.3 2.2 100.0 1984 : 49.7 20.0 15.5 8.1 4.1 2.6 100.0 1994 : 51.9 17.8 13.4 8.9 5.0 3.0 100.0 2004 : 53.5 16.0 11.3 9.7 6.1 3.4 100.0 53



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Table 40--Projected number of farms, by size of farm, 1974, Markov process Size of farm : Actual Projected Percent difference Number 1-69 acres : 1,069,433 1,027,082 -3.96 70-99 acres 287,472 287,137 -0.12 100-139 acres 258,690 265,079 2.47 140-179 acres 239,786 245,530 2.40 180-219 acres 151,447 155,180 2.46 220-259 acres 122,851 127,105 3.38 260-499 acres 379,297 392,479 3.47 500-999 acres 210,702 219,227 4.04 1,000-1,999 acres 93,264 93,898 0.68 2,000 acres and over 61,994 61,889 -0.17 All farms : 2,874,936 2,874,506 -0.01 1/ Theil-U = 0.0367 or 3.67 percent. Table 41--Projected number of farms by sales class, 1974, Markov process Sales class Act ual Projected Percent difference 1,000 Farms Percent Less than $2,500 1,100.6 1,109.7 .8 $2,500-4,999 322.9 322.9 0 $5,000-9,999 319.5 320.4 .3 $10,000-19,999 326.9 328.2 .4 $20,000-39,999 327.6 322.3 -1.6 $40,000-99,999 327.5 322.1 -1.6 $100,000-199,999 99.4 97.3 -2.1 $200,000-499,999 : 39.3 38.5 -2.0 $500,000 and over : 11.2 11.0 -1.8 All farms : 2,874.9 2,872.4 -.1 1/ Theil-U = 0.0007 or 0.07 percent. 60



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APPENDIX C Adjustments for Age Cohort Projections Several adjustments were necessary in order to use the census data within the age cohort framework to project the total farm numbers by size. These adjustments are summarized in appendix table 6. The least adjustment was required for the 1964 sales distribution where only estimated missed farms were added to the census published data. These missed farms were published in Evaluation of Coverage (24), which presented the data by age group, acre size, and sales. Therefore, it was necessary to establish the numbers in each cell. The estimated number (E) was determined by the formula, Ei= N.Nj IN for the i,j th cell. Where Ni., Nj., and N represent the totals of the i th row, the j th column, and the grand total. This formula was also used for the abnormal farm matrix (line 3, appendix table 5), the 1974 farms with sales of less than $1,000 (line 4), and the corporate and other (line 5). The age distribution for corporate and other operations was obtained from the 1969 Census of Agriculture. Another adjustment was made to the sales data to remove the impact of price inflation for farm commodities. The sales distribution was deflated for each age group as described in the data adjustment section, except that 1964 constant prices were used. The projections were made in constant prices, then reinflated to the expected price levels as described in the data adjustment section. A log polynomial of the 4th degree was used. A peculiar kink developed at the lower end of the size curve that caused a rapid increase in small farms when the curve was shifted for reinflation. This did not correspond to the historical shape in 1964 or 1974. The fit did not improve by changing the degree of polynomial. Therefore, the data were plotted on log paper and smoothed for the lower sales classes in each age group. The cohort ratio shown in tables 24 and 25, when multiplied by the base period data, resulted in projections where the individual cells in the row summed to more than the row total except for farm operators younger than 25 years old. The row total was obtained by multiplying the age group total by the cohort ratio for the age group in the last column in tables 24 and 25. The individual projected numbers for each cell was forced to equal the projected totals for each age group (see appendix table 7 for adjustment factors). 77



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U.S. Farm Numbers, Sizes, and Related Structural Dimensions: Projections to Year 2000 William Lin George Coff man A.B. Penn INTRODUCTION The U.S. farming sector has undergone significant structural changes over the past few decades, and is expected to continue changing. Perhaps the most obvious of the changes is in farm numbers and sizes. The Census of Agriculture counted 4 million farms in 1959 and 2.9 million in 1974; that number is expected to decline to 1.8 million in 2000. The average farm size is increasing as farm numbers decline, with the consequent concentration reflected in production. The largest 4 percent of the farms accounted for about a third of the value of farm products sold in 1959 and 43 percent in 1974. By 2000, the largest 1 percent of the farms will account for about half of all farm production. l/ This trend toward greater concentration--fewer but larger farms--is the result of the interaction of many factors: technology, economies of size, tax laws, returns to resources, price instability, operator's managerial ability, capital requirements, market conditions, farm programs, credit availability, exchange arrangements, government regulations, and the like. While it is recognized that these factors have immediate effects on the farm sector, their effects on the structure of agriculture are of a longer term nature. 1/ The projections in this report are based on historical data--up to and including data from the 1974 Census of Agriculture, the most recent available. Another Census of Agriculture was conducted in 1978, but data from that census are not expected to be fully compiled and available until late 1980. 1-



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Acreage Distributions Based on the combined and adjusted 1969 and 1974 census data, the following negative exponential function was estimated: in y -2.0 = -0.4160 R2= 0.885 (4) (-13.30)L J where: y = percentage of farms lying above a size limit, xi, Xi = the lower size class limit in acres, R = average farm size in acres, and R2= the coefficient of determination. The slope of the function is -0.4160, and the t ratio is shown in parentheses. After calculating the intercept term, the estimated equation can also be written: in y = 2.0011 -0.4160 xi/-x (5) The intercept term was estimated by using the average farm sizes from 1969 and 1974 census data, after adjusting both land in farms and number of farms for und erenumeration (fig. 5). A test for structural change between the two census years again Indicated. that the hypothesis .of no structural change cannot be rejected. Figure 5 Negative Exponential Curves of the Acreage Distribution, 1974 100-----------80 60 40 -. E ~ 0 10 (L 4 -Observed distribution Theoretical distribution 2 1 II I I I I .01 .02 .04 .06.08.1 .2 .4 .6 .81 2 4 6 810 Average size Relative size of farm (ratio to average farm size) 28



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come from farms with sales of at least Figure 3 $100,000. This means that the 50,000 largest farms will probably produce Distribution of Farm Numbers by almost two-thirds of all agricultural Sales: Actual 1974 and Projected for products, and the largest 1 million 2000 farms (57 percent of the total) will produce almost all agricultural proMillion farms *ducts (table 7). 3/ 17 Concentration of farm production can further be put into perspective by a Lorenz curve (fig. 4). In 1974, the largest 20 percent of farms produced 1.5 about 80 percent of farm production. By 2000, the same percentage of farm production will likely come from the largest 12 percent of farms. More dramatically, about half the production will likely be produced by the largest 1 percent of farms. By con0 trast, 50 percent of the farms--the1. smaller ones--will produce only about 1 percent of the production. Concentration of production is also related to two other structural factors: co ntractual arrangements 0.5 and the economic advantages of different sizes of firms for various commodities. ContractingArrangements 0 Agricultural production under 1.0 contractual arrangements has in2000 creased gradually. The percentage of farms having contracts increased from 4.5 percent in 1960 to 9 percent in 1974. Furthermore, the proportion of farms having contracts was much higher for large farms:0. the proportion of small farms (less than $20,000 in sales) having contracts in 1974 was less than 5 per3/ The concentration of agricultural production differs from com0 modity to commodity. Industries such Less Than $10,000$40,000$200,000 as egg, poultry, and sugarcane may $10,000 $39,999 $199,999 or more actually have higher concentrations Sales groups than the aggregate portrayed in table 7. __________________ 12



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Table 32--U.S. farm operators by sales class, selected years and projections Yer Less than: $2,500$5,000$10,000$20,000$40,000$100,000 Total Yer $2,500 :$4,999 :$9,999 :$19,999 :$39,999 :$99,999 :or more: 1 ,000 farmers 1964 1,657.3 473.9 528.6 484.1 266.9 113.5 32.4 3,556.7 1974 1,400.6 322.9 319.5 326.9 327.6 327.5 149.9 2,874.9 1984 750.0 250.0 250.0 200.0 200.0 335.0 365.0 2,350.0 1994 820.0 158.0 100.0 80.0 120.0 220.0 580.0 2,078.0 2004 490.0 80.0 100.0 120.0 80.0 160.0 620.0 1,650.0 Percent 1964 46.6 13.3 14.9 13.6 7.5 3.2 .9 100.0 1974 38.3 11.2 11.1 11.4 11.4 11.4 5.2 100.0 1984 31.9 10.6 10.6 8.5 8.5 14.3 15.5 100.0 1994 39.6 7.3 4.8 3.9 5.8 10.6 28.0 100.0 2004 29.7 4.8 6.1 7.3 4.8 9.7 37.6 100.0 Table 33--U.S. farm operators by sales class, in 1964 prices, selected years and projections Less than: $2,500$5,000:$10,000:$20,000:$40,000:$100,000 Toa Year $2,500 :$4,999 :$9,999 :.$19,999 :$39,999 $99,999 or more Toa 1 ,000 farmers 1964 1,657.3 473.9 528.6 484.1 266.9 13532.4 3,556.7 1974 .1,295.1 321.6 373.9 344.0 245.5 156.5 48.5 2,785.1 1984 1,068.1 207.9 252.4 225:'0 208.2 203.1 68.8 2,233.5 1994 859.1 129.9 165.7 135.9 160.2 249.5 96.6 1,796.9 2004 663.7 80.4 107.5 78.9 114.6 291.0 129.3 1,465.4 Percent 1964 46.6 13.3 14.9 13.6 7.5 3.2 .9 100.0 1974 46.5 11.6 13.4 12.4 8.8 5.6 1.7 100.0 1984 47.8 9.3 11.3 10.1 9.3 9.1 3.1 100.0 1994 47.8 7.2 9.2 7.6 8.913.9 5.4 100.0 2004 45.3 5.5 7.3 5.4 7.8 19.9 8.8 100.0 52



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the sales receipts, with both variables expressed in natural logarithmic values. 9/ The nonlinear specification gives a closer fit to observed data than the linear function. The 80-percent increase in the index of prices received by farmers between 1969 and 1974 implies that $1 worth of agricultural products sold in 1974 car.ied a price tag of $0.56 in 1969. The cumulative distribution of farm numbers by sales class in 1974, therefore, was transformed into a comparable sales distribution in 1969 constant dollars by multiplying 0.56 by the sales value associated with each observation on the current dollar sales distribution. 10/ Based on the estimated polynomial functions of the two sales distributions, predicted cumulative distributions of 1974 farm numbers (both in 1974 current dollars and 1969 constant dollars) are shown in figure 6 and columns 5 and 6 in 9/ The Pareto law of income distribution asserts that "the logarithm of the percentage of units with an income in excess of some value is a negatively sloped linear function of the logarithm of that value" (15). Mathematically, it has the form: P(y) = A Y-' P(y) = percentage of units with income in excess of Y, Y = income level A,a = parameters of the distribution 10/ This approach implicitly assumes that farms within a sales class are uniformly distributed. Figure 6 1974 Farm Numbers in 1974 and 1969 Farm Prices Decumulative number of farms (100,000) 20 10 HC 8 F D I 6 P" 1974 Prices 4 1969 Prices P 1% 2 1 I f I I I I 1 I 1 1 .05 .1 .2 .4 .6 .81.0 2 4 6 810 20 40 6080100 200 Sales ($1,000) Decumulative means that the distance along the y-axls between points A and C, for example, Is the number of farms In the sales class of $10,000 to $19,999. 35



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Figure 4. cent, while the proportion was more _______________________________than 30 percent for large farms Concentration of Farm ($100,000 sales or more). Production in 1974, 1985, The projected increase in farm and 2000 size by 2000 indicates that more _______________ farms perhaps as many as a quarter Percentage of sales to one-third of all farms, will mar..1974 ket their products under contractual -1985 arrangements. Virtually all produc80.. 2000 tion of sugarbeets and dairy products are now marketed under contractual arrangements. By 2000, contracts are 60 -likely to increase in marketing I: vegetables, fruits, cotton, and 1 poultry and poultry products. 40 Size Variability by Commodity 20 Historically, some farm commodities have been dominated by large farms, and others by small farms 0 20 40 60 80 100 (table 4). The changes in the farm Percentage of farms sector reflected by our data suggest that farm production of vegetables and poultry will continue to be dominated by large farms. Other industries, such as livestock and cotton, which have recently become much more concentrated, are likely to be dominated by large farms in the future. Table 7--Comparison of historical and projected concentration of production, by sales class and largest farms Sales class Cash receipts by the Year: : :largest : $500,000:$100,000 to :$20,000 to :Less than :50,000: 200,000 :1 million : and over: $499,999 :$99,999 :$20,000 :farms: farms :farms Percent 1969 : 19.5 14.1 42.6 23.8 30 50 89 1974 : 31.2 22.5 36.0 10.3 31 57 94 1985 : 47.1 34.0 15.7 3.2 54 72 98 2000 : 77.3 18.5 3.6 .6 63 78 99 1/ Concentration of production is expressed by the percentage of cash receipts produced by farms in a given size class; the size of farms is ranked by sales recei pts. 13



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Table 19--Projected number of U.S. farms, by sales class, negative exponential functions Sales class : Actual 1974 1980 .1985 Thousands Percent Thousands Percent Thousands Percent Less than $2,500 1,100.6 38.3 46.8 2.0 29.0 1.4 $2,500-4,999 322.9 11.2 46.8 2.0 33.4 1.6 $5,000-9,999 319.5 11.1 90.6 3.9 55.9 2.6 $10,000-19,999 326.9 11.4 170.9 7.3 111.7 5.3 $20,000-39,999 327.6 11.4 302.2 12.8 '201.3 9.5 $40,000-99,999 327.5 11.4 659.0 28.0 489.5 23.1 $100,000-199,999 99.4 3.5 580.4 24.7 520.0 24.6 $200,000-499,999 39.3 1.4 417.8 17.8 553.8 26.2 $500,000 and over: 11.2 .4 39.1 1.7 121.7 5.8 All farms :2,874.9 100.0 2,353.6 100.0 2,116.3 100.0 1990 1995 :2000 Thousands Percent Thousands Percent Thousands Percent Less than $2,500 22.7 1.1 17.6 .9 12.8 .7 $2,500-4,999 : 22.7 1.1 17.4 .9 12.6 .7 $5,000-9,999 : 39.8 2.0 34.4 1.8 29.3 1.6 $10,000-19,999 81.6 4.1 62.5 3.3 53.1 2.9 $20,000-39,999 : 152.6 7.7 122.5 6.4 101.6 5.5 $40,000-99,999 385.6 19.4 316.2 16.2 270.9 14.6 $100,000-199,999 455.2 22.9 402.4 21.1 353.7 19.1 $200,000-499,999 606.8 30.5 614.3 32.2 606.1 32.6 $500,000 and over: 222.6 11.2 323.7 16.9 416.7 22.4 All farms 1,989.5. 100.0 1,910.7 100.0 1,856.9 100.0 32



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U.S. FARM NUMBERS, SIZES, AND RELATED STRUCTURAL DIMENSIONS: Projections to Year 2000. William Lin, George Coffman, and J.B. Penn. National Economics Division; Economics, Statistics, and Cooperatives Service; U.S. Department of Agriculture. Technical Bulletin No. 1625. ABSTRACT The number of U.S. farms is projected to continue to decline through the end of the century--from 2.9 million in 1974 to 1.8 million in 2000. The proportions of small and large farms will change as well, with large farms increasing'and dominating agricultural production. Farm production, farmland, and farm wealth will become more concentrated; farm operators will rent more of their farmland and will produce more of their commodities under contractual arrangements with food processors. The projections are based on four analytical methods: trend extrapolation, negative exponential functions, Markov process, and age cohort analysis. Keywords: Farm structure, Farm numbers, Farm sizes, Trend extrapolation, Negative exponential functions, Markov process, Age cohort analysis, Concentration of ownership, Specialization, Capital requirements. The following reports published by ESCS also deal with the structure of U.S. agriculture. Status of the Family Farm: Second Annual Report to the Congress. AER-434. September 1979. Structure Issues of American Agriculture. AER-438. November 1979. Another Revolution in U.S. Farming? Lyle P. Schertz and others. AER-441. December 1979. ACKNOWLEDGMENTS The authors acknowledge with thanks the comments and suggestions of Emerson Babb, Dave Harrington, Levi Powell, Donn Reimund, Allen Smith, and Alan Walter. Tom McDonald edited the manuscript. Appreciation is also due Ronald Miller for his computation assistance for the negative exponential functions chapter, and Roy Hatch for his preparation of an earlier version of the Markov process chapter. Several technical support people made important contributions. They include: Dana Anthony, Carol Collins, Angie Kennedy, Virginia Minter, Terry Salus, Jennifer Reed, and Sandy Swingle. Washington, D.C. 20250 July 1980



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sales, yielding a 94-percent error for 1974 sales projections (table 38). 17/ This procedure proved equally unsatisfactory to project farm numbers based on acreage, yielding errors of 68 percent (table 39). Those results suggest that considerable discrepancies still exist between the actual and estimated distribution functions obtained by the negative exponential function. As shown in table 38, there are significant underestimates in the smaller size classes and overestimates in the medium and larger classes. Also, this function overestimates the numbers of farms with sales between $10,000 and $500,000 by factors rangingfrom 1.5 to 4.5, and underestimates the number of farms with sales less than $10,000. Markov chain analysis, modified somewhat in this study to adjust for the effects of price inflation on changes in farm numbers, appears to be promising. The errors of projection, by both acreage and sales, in 1974 were about 4 and 0.1 percent (tables 40 and 41). In contrast to previous applications, there are no gross estimation errors evidenced in these projections. It is essential to capture the effects of price inflation-in-ane-ra of price instability to avoid gross distrotions and inaccuracies in projections of farm numbers by sales. In addition, those results suggest that the underlying assumption of the Markov process on the growth of farms is questionable. Instead of a farm's growing from the smallest to the largest size, the census data suggest that the largest farms tend to come from smaller farms of a minimum viable size, and not from the smallest size classes. Age cohort projections tend to be similar to those from the Markov process. Compared with 1969 actual farm numbers by both acreage and sales, age cohort analysis yielded a 10.9-percent and a 16-percent error according to the Theil-U coefficient (tables 42 and 43). 18/ Age cohort analysis appears to underestimate farms with $2,500 to $4,999 sales and to overestimate those with $20,000 to $39,999 sales. 17/ The percentage error is derived from comparing actual proportions of 1974 farm numbers by size class with projected percentages. In this way, the comparison is not complicated by projections on land in farms and acreage farm size. 18/ In projecting the 1969 number of farms by acreage, the cohort ratios constructed from the 1950-59 period were multiplied by the age-size distributions in 1959. For sales, a 1959-69 cohort-ratio matrix was multiplied by the 1964 age-size matrix to project the 1974 farm numbers by sales class. This procedure overlapped 5 years of calculation of the age cohort ratios and the projection period. This was necessary because different sales class intervals were published by the Bureau of the Census before 1959. 58



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Continuing this process, we have shown that a number of farm movement matrix elements can be constructed. Starting from the size category of 260 to 499 acres and continuing on to the smallest size class, this process breaks down, however; it begins to yield nonpositive diagonal elements. 13/ A trialand-error iterative procedure is thus employed to identify the remaining matrix elements that minimize the residual sum of squares, computed from the projected and actual number of farms by size class. The off-diagonal elements, again, reflect the number of farms moving to the upper classes. As a result, the diagonal elements are all positive--with the numerical value ranging from about 82 percent to 93 percent of the number of farms in 1969. Following the same procedure, we constructed a movement matrix by sales class between 1969 and 1974 (table 22). The transition probability matrices, obtained by dividing the number of farms in the farm movement matrix by the 1969 number of farms in each size class, are shown in tables 23 and 24. The transition probability matrix is the crux of the Markov process; therefore, its stability over time willcontribute to the accuracy of projections. The probabilities were so stable that there were virtually no differences between the two transition matrices, one for the 1969 to 1974 period and another for the 1964 to 1969 period. In this way, the transition probability matrix used for projections actually represents the synthesis of the two periods: 1964 to 1969 and 1969 to 1974. Acreage Distribution The number of farms is projected to decline .to 2.1 million in 1990 and 1.7 million in 2000. Of the projected 1.7 million farms in 2000, large farms (those with 1,000 acres or more) will account for about 10 percent, an increase from 5 percent in 1974. By contrast, the proportion of small farms (those with less than 220 acres) is projected to remain high, 68 percent as compared to 70 percent in 1974 (table 25). Historically, the number of farms with less than 500 acres h~s been declining since 1945. Projected acreage distributions based on the Markov process show that this trend is likely to continue into the year 2000. In addition, the decline of the number of farms with 400 to 999 acres, beginning in 1969, is projected to continue. About 90 percent of all farms in 2000 will likely have less than 1,000 acres. Sales Distribution The transition probability matrix by sales class was intended to reflect the physical change in farm structure, discounting any effects of price inflation. Thus, multiplying the transition probability matrix by the base period (say 1969) number of farms does not result in the projected number of farms in 1974. Instead, the projection is derived by adding the effects of price infla13/ This finding appears to have economic meaning. It could suggest that the-farm growth and consolidation process may not start from the very small size classes as is implied in the traditional Markov process. Rather, consolidation may actually begin from a larger, more economically viable size level, such as 500 acres or larger. 39



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Table 36--Projected number of fat-ins by acreage in 1974, simple trend extrapolation Actual Projected Percent Size of farm 1974 1974 difference I/ N umber Percent 1-99 acres 1,356,905 1,336,748 -1.49 100-219 acres 649,923 652,620 +0.41 220-499 acres 502,148 512,344 +2.03 500-999 acres 210,702 214,218 +1.67 1,000-1,999 acres 93,264 83,599 +0.36 2,000 acres and over 61,994 60,947 -1.69 All farms 2,874,936 2,870.476 -0.15 1/ Theil-U = 0.0144 or 1.44 percent. Table 37--Projected number of farms by sales in 1974, simple trend extrapolation Actual Projected Percent Sales class 1974 1974 difference l/ Number Percent Less than $2,500 1,100,597 1,136,826 3.29 $2,500-$4,999 322,949 328,651 1.77 $5,000-$9,999 319,474 319,576 0.03 $10,000-$19,999 326,905 338,660 3.60 $20,000-$39,999 327,567 340,698 4.01 $40,000-$99,999 327,516 258,785 -20.99 $100,000-$199,999 99,385 68,101 -31.48 $200,000-$499,999 39,335 26,390 -32.91 $500,000 and over 11,206 8,232 -26.54 All farms 2,874.934 2,825.919 -1.70 I/ Theil-U = 0.1316 or 13.16 percent. 57



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Table 23--Farm transition matrix by size of farm, 1969-74: 100-0-0 movement assumption Size of farm : A0 : Al : A2 A3 : A4 : A5 A6 : A7 : A8 A9 A10 Probabilities 1-69 acres (Al) .073 .927 .0003 70-99 acres (A2) ..142 .855 .003 100-139 acres tA3) : .142 .855 .003 140-179 acres (A4) : .155 .840 .005 180-219 acres (A5) .153 .840 .007 220-259 acres (A6) : .135 .820 .045 260-499 acres (A7) .093 ,850 .057 500-999 acres (A8) .073 .851 .075 1,000-1,999 acres (A9) .123 .846 .031 2,000 acres and over (Al0) 0 1.000 Table 24--Farm transition matrix by sales class, 1969-74: 100-0-0 movement assumption Sales class SO S : S 2 : 3 S4 S5 S : S7 S8 S 9 Probabilities Less than $2,500 (Sl) : 0.104 0.894 0.002 $2,500-4,999 (S2) : .357 .615 0.028 $5,000-9,999 (S3) .124 .820 0.056 $10,000-19,999 (S4) .140 .800 0.060 $20,000-39,999 (S5) .092 .732 0.176 $40,000-99,999 (S6) : .072 .826 0.102 $100,000-199,999 (S7) .132 .694 0.174 $200,000-499,999 (S8) .174 .662 0.164 $500,000 and over (S) 0 1.000



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APPENDIX B Estimated Simple Trend Equations by Size Class Appendix table 4--Estimated simple trend equations by average size: 1959, 1964, 1969, 1974 l/ Size of farm : Estimated trend equations :R2 1-99 acres In FN = 7.658 -0.115T 0.969 (192.57) (-7.94) 100-219 acres : In FN2 = 7.101 -0.155T 0.9997 (1489.62) (-59.27) 220-499 acres : In FN3 = 6.707 -0.117T 0.971 (171.27) (-8.16) 500-999 acres In FN4 = 5.402 -0.0087T 0.159 (140.02) (-0.62) 1,000-1,999 acres : In FN5 = 4.423 + 0.029T 0.912 (251.45) (4.55 ) 2,000 acres and over : In FN6 = 4.112 -0.0004T 0.000.5 (131.38) (-0. 033) 1/ The time variable (T) is: 1959 = 1, 1964 = 2, etc; R2 is the coefficient of determination. Figures in parentheses are t ratios. 75



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Appendix table 1--Selected structural characteristics of U.S. farms, by sales class : $100,000 : $40,000 to : $20,000 to : $10,000 to $5,000 to : $2,500 to : Less than Item Unit : and over : $99,999 : $39,999 : $19,999 : $9,999 : $4,999 : $2,500 : All : (.lass IA) : (class IB) : (class II) : (class III): (class IV) : (class V) : (class VI): Farms Number of farms: : 1969 : 1,000 52.0 169.7 331.0 395.5 390.4 395.1 994.5 2,728.1 : Percent 1.9 6.2 12.1 14.5 14.3 14.5 36.5 100 1974 : 1,000 : 152.6 324.3 321.8 310.0 296.0 290.0 768.8 2,463.9 : Percent : 6.2 13.2 13.1 12.6 12.0 11.8 31.2 100 Cash receipts: 1969 :Bil. dol.: 15.3 10.1 9.3 5.7 2.8 1.3 .98 45.48 Percent : 33.6 22.2 20.4 12.5 6.2 2.9 2.2 100 1974 :Bil. dol.: 43.7 20.1 9.2 4.5 2.1 .98 .74 888.32 Percent : 53.7 24.7 11.3 5.5 2.6 1.2 .9 100 Cash receipts per: farm: 1969 : Dols. : 293,915 59,364 27,999 14,396 7,208 2,626 953 16,689 1974 : Dols. : 286,268 61,890 28,737 14,387 7,215 3,640 1,143 25,234 Form of organiza-: tion: Sole proprietorships: 1969 : Farms : 30,683 131,418 277,233 341,063 344,063 356,105 896,005 2,376,570 : Percent : 59.0 77.4 83.8 86.1 88.1 90.1 90.1 87.1 1974 : Farms : 108,463 280,824 290,596 284,521 277,272 275,897 731,165 1/ 2,248,738 : Percent : 71.1 86.6 90.3 91.8 93.6 95.1 95.1 91.3 Partnerships: 1969 : Farms : 13,049 33,104 49,236 49,990 41,878 34,278 86,518 308,053 Percent : 25.1 19.5 14.9 12.6 10.7 8.7 8.7 11.3 1974 : Farms : 27,811 37,107 27,671 22,801 17,180 12,399 33,060 1/ 178,029 Percent : 18.2 11.4 8.6 7.4 5.8 4.3 4.3 7.2 See footnotes at end of table. -----.Continued ----



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The main effect of the low price inflation assumptions is to shift the projected number of farms from large sales classes to smaller classes. Under the low price inflation assumption, the number of small farms is projected to decline at only a moderate rate, from 72 percent of the 1974 total to 63 percent in 1990, and to 56 percent in 2000. Similarly, percentage increases in large farms are projected to increase less drastically. The number of farms with sales of over $100,000 is projected to increase to 14 percent of the total in 1990, and to 24 percent in 2000. Table 25--Projected number of farms, by size of farm, Markov chain analysis Actual Size of farm : 1974 1980 1985 : 1990 1995 2000 1,000 farms 1-69 acres 1,069.4 991.4 919.0 851.9 789.7 732.1 70-99 acres 287.5 246.1 210.7 180.4 154.5 132.4 100-139 acres 258.7 222.0 190.6 163.6 139.9 121.0 140-179 acres : 239.8 202.2 170.5 143.8 121.3 102.3 180-219 acres 151.4 128.4 108.9 92.3 78.3 66.3 220-259 acres 122.9 101.8 84.4 69.9 580l 48.1 260-499 acres 379.3 327.9 283.3 244.6 211.1 182.0 500-999 acres 210.7 200.9 189.7 177.6 165. 152.5 1,000-1,999 acres : 93.3 94.7 95.2 94.8 93.5 91.5 2,000 acres and over: 62.0 64.9 67.8 70.8 73.7 76.6 All farms 2,974.9 2,580.4 2,320.1 2,089.7 1,885.0 1,704.8 Table 26--Projected number of farms, by sales class, Markov process, high price inflation (7.5 percent per year) : Actual Sales class 1974 : 1980 : 1985 1990 : 1995 : 2000 1,000 farms Less than $2,500 : 1,100.6 928.9 855.4 794.7 760.5 639.9 $2,500-$4,999 : 323.0 185.8 176.1 115.4 82.6 72.3 $5,000-$9,999 : 319.5 251.0 179.0 141.7 129.4 108.4 $10,000-$19,999 : 326.9 274.4 210.6 166.5 126.1 108.1 $20,000-$39,999 327.6 269.4 213.7 176.1 .123.9 88.3 $40,000-$99,999 : 327.5 392.7 388.8 338.8 290.8 262.0 $100,000-$199,999 : 99.4 131.5 184.5 217.9 205.8 167.5 $200,000-$499,999 39.3 69.8 96.1 150.8 187.7 190.1 $500,000-and over : 11.2 20.6 49.5 90.3 155.0 225.8 All farms 2,874.9 2,524.1 2,354.0 2,193.2 2,061.8 1,862.4 43



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The Markov process and age cohort techniques give very similar projections. However, we found that the traditional farm growth assumption, underlying the Markov process is questionable. Census data suggest that firms tend to enter farming at an economically viable size and then expand. The age cohort techniques incorrectly project a slight decline in the number of farms with 2,000 acres and over. By contrast, the Markov process projects a moderate increase-a trend more consistent with the past. In sum, Markov process and age cohort techniques appear to be more promising for projecting sales distributions. The most likely projections for the number of farms are synthesized from projections based on the acreage distribution from trend extrapolation and Markov process. The small deviations between the two methods and the fact that the projections are free of any estimation errors in accounting for the effects of price inflation, gives us confidence in projecting the total number of farms. Farm numbers are, therefore, projected to decline from 2.87 million in 1974 to 2.32 million in 1985, 2.09 million in 1990, 1.89 million in 1995, and 1.75 million in 2000. Projections on farm numbers by acreage are computed by multiplying the most likely total number of farms by a synthesized distribution of farm numbers obtained from trend expolation and Markov process projections, since the two methods yield a higher degree of accuracy in reproducing historical data. Similarly, projections on farm numbers by sales class are computed by multiplying the most likely total number of farms by a synthesized distribution of farm numbers obtained from Markov process and age cohort analysis. The most likely projections on number of farms by acreage and sales class are given in tables 5 and 6. Most of the projections in this study are trend related, with the exception of assumptions to account for the effects of inflation on changes in farm numbers by sales. However, studies that base projections on causal economic relationships are needed. One such approach is to link the transition probabilities, as employed in the Markov process, and the cohort ratios, as used in age cohort analysis, to factors that cause structural changes. This, however, requires more detailed structural data on a longitudinal basis--that is, a data base linking the "true" structural changes from one census year to the others, and the associated factors that have caused the changes. Further specificity is also needed for production regions and farm commodity subsectors--each of which tends to have its own unique characteristics. To make projections of the number of farms and size distribution more useful, it would also be desirable to disaggregate the study by region and by commodity subsector. Implications for other structural characteristics drawn from such projections would be more useful than those based on national averages. 64



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Table 42--Projected 1969 farm numbers, by size of farm, age-cohort analysis I/ Size of farm Actual Projected Percent difference :Number ------------------Percent---Less than 10 acres 162,111 120,221 25.8 10-49 acres 473,465 407,655 13.9 50-69 acres 177,028 140,847 20.4 70-99 acres 282,914 231,065 18.3 100-139 acres : 278,752 240,448 13.7 140-179 acres : 263,012 244,752 6.9 180-219 acres 165,209 164,682 3.2 220-259 acres 141,733 149,074 5.2 260-499 acres .419,421 419,189 .1 500-999 acres 215,659 194,967 9.6 1,000 acres or more 150,946 137,432 9.0 Total 2,730,250 2,450,332 10.3 1/ Not adjusted for census underenumerati'on; Theil-U is 0.1087 or 10.9 percent. Table 43--Projected 1974 farm numbers by sales class, age-cohort analysis 1/ Sales Class Actual Projected Percent difference :. Number-----------------Percent---Less than $2,500 768,838 800,000 4.1 $2,500-$4,999 289,983 155,000 -45.6 $5,000-$9,999 .296,373 260,000 -12.3 $10,000-$19,999 310,011 355,000 14.5 $20,000-$39,999 : 321,771 390,000 21.2 $40,000-$99,999 324,310 345,000 6.4 $100,000 or more : 152,599 165,000 8.1 All farms 2,463,885 2,450,000 .6 1/ Not adjusted for census underenuieration; the Theil-U is 0.16 or 16 percent. The accuracy for the farm operator age distribution was very good, only 2.1 percent error of projection was computed. Projections presented in this table have )been adjusted to take into account the effects of price inflation. 61



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Appendix table 1--Selected structural characteristics of U.S. farms, by sales class--Continued *:$100,000 :$40,000 to :$20,000 to $10,000 to :$5,000 to $2,500 to : Less than Item :Unit and over $99,999 $39,999 $19,999 $9,999 : $4,999 :$2,500 All (class IA) (class 18) :(class II) :(class III) :(class IV) (class V) :(class VI) farms Corporations: 1969 :Farms 8,049 4,306 2,847 2,262 1,984 2,062 4,972 2,648 Percent : 15.5 2.5 0.8 0.6 0.5 0.5 0.5 1.0 1974 :Farms 15,787 5,630 2,768 1,988 1,335 1,148 3,075 1/ 31,731 Percent : 10.3 1.7 .9 .6 .4 .4 .4 1.3 Other: 1969 :Farms : 214 867 1,673 2,157 2,500 2,659 6,961 17,031 Percent : .4 .5 .5 .6 .7 .7 .7 .8 1974 :Farms : 538 749 736 701 586 539 1,538 1/ 5,387 Percent : .4 .2 .2 .2 .2 .2 .2 .2 Land farmed by: Sole proprietor-: a, ships: 1969 :Mlil. acre: 69.27 127.12 166.63 144.24 92.43 66.01 125.85 1/ 791.55 Percent : 40.3 68.6 80.4 84.3 86.5 87.0 87.0 74.5 1974 :Mil. acre: 147.52 193.08 138.65 90.73 59.80 48.31 109.06 1/ 787.15 Percent : 53.3 78.3 86.2 88.6 91.0 90.6 90.6 76.7 Partnerships: 1969 :Mil. acre: 44.04 41.12 35.08 23.33 12.23 7.59 14.47 1/ 177.86 Percent : 25.6 62.2 16.9 13.6 11.4 10.0 10.0 16.7 1974 :Mil. acre: 56.45 34.18 16.52 9.17 4.77 3.38 7.70 l/ 132.17 Percent : 20.4 13.9 10.3 9.0 7.3 6.4 6.4 12.9 Corporations: : 1969 :Mil. acre: 55.94 15.49 4.15 2.57 1.15 1.55 2.89 1/ 83.74 Percent : 32.6 8.4 2.0 1.5 1.1 2.0 2.0 7.9 1974 :Mil. acre: 69.73 18.10 4.83 2.10 0.88 1.14 2.53 1/ 99.3 Percent : 25.2 7.3 3.0 2.0 1.3 2.1 2.1 9.7 See footnotes at end of table. ---Continued --



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Table 17--Estimated size distribution function, United States and regions CoeffiRegion Year Intercept Slope cient R2 F statistic ..standard error United States 1959 2.00107 -0.3260 0.0411 0.913 1964 2.00101 -.3554 .0426 .921 1969 2.00096 -.3754 .0418 .931 0.405 1974 2.00092 r.3844 .0431 .930 1959-74 2.00097 -.3549 .0203 .919 New England 1959 2.001 55 -.2810 .0241 .950 1964 2.001 45 -.2684 .0246 .952 1969 2.00152 -.2914 .0219 .967 .364 1974 2.00144 -.2763 .0224 .962 1959-74 2.00147 -.2721 .0113 .956 Middle Atlantic 1959 2.00287 -.2524 .0268 .937 1964 2.00181 -.2735 .9261 .948 1969 2.001 76 -.2868 .0255 .955 .352 1974 2.001 65 -.2773 .0236 .958 1959-74 2.00175 -.2704 .0124 .947 East North Central 1959 2.00200 -.3096 .0272 .966 1964 2.00185 -.3209 .0254 .964 1969 2.001 72 -.3171 .0232 .969 .090 1974 2.001 58 -.3030 .0198 .975 1969-74 2.00780 -.3130 .0116 .964 West North Central 1959 2.00098 -.3644 .0282 .965 1964 2.00094 -.3799 .0277 .969 1969 2.00089 .3904 .0261 .974 .213 1974 2.00085 -.3896 .0263 .973 1959-74 2.00091 -.3794 .0130 .969 South Atlantic 1959 2.001 42 -.1993 .0277 .896 1964 2.00142 -.1993 .0292 .902 1969 2.00127 -.2337 .0291 .915 .364 1974 2.00122 -.2348 .0298 .912 1959-74 2.00128 -.2176 .0139 .901 East South Central 1959 2.00150 -.1821 .0251 .897 1964 2.00141 -.1944 .0260 .903 1969 2.00137 -.2119 .0261 .916 .351 1974 2.001 30 -.2138 .0266 .915 1959-74 2.00137 -.1975 .0124 .903 West South Central 1959 2.00093 -.3901 .0450 .926 1964 2.00088 -.4138 .0446 .935 1969 2.00084 -.4299 .0406 .949 .282 1974 2.00080 -.4434 .0440 .944 1959-74 2.00085 -.4152 .0210 .935 Mountain 1959 2.00049 -.8717 .1063 .918 1964 2.00046 -.9228 .1121 .919 1969 2.00044 -.9487 .1141 .920 .1311 1974 2.00045 -.9611 .1277 .904 1959-74 2.00046 -.9205 .0544 .914 Pacific 1959 2.00090 -.3601 .0629 .845 1964 2.00085 -.4046 .0704 .846 1969 2.00082 -.422. .0726 .849 .2131 1974 2.00082 -.4253 .0760 .839 1959-74 2.00089 -.3973 .0333 .841 26



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Form of Business Organization Contrary to common assertion that corporations are taking over farming today, the Census of Agriculture data clearly show that noncorporate farms continue to be the dominant form of business organization. Corporations were still relatively insignificant in farm production and control of the land. Moreover, more than 90 percent of the farm corporations were family-held or closely-held corporations (16 or fewer stockholders). Corporate farms (including the family-held corporations) constituted 1 percent of the total number of farms in 1969 and 1.7 percent in 1974. These were, however, relatively large farms. The average size of corporate farms was about 3,400 acres in 1974, eight times larger than the average sole proprietorship farm. Corporate farms constituted 4 percent of the 493,000 farms which produced 80 percent of the total farm production in 1974. Overall, corporations produced 18 percent of the value of agricultural sales in 1974. The amount of farmland controlled by corporations has never been significant and it is unlikely to become so in the near future. In 1969, corporate farms controlled about 8 percent of all farmland; that control rose to 10 percent in 1974. By comparison, the amount controlled by sole proprietorships increased from 74.5 to 76.9 percent over the same period. Farms organized as partnerships appeared to lose ground, both-in terms of total farm numbers and control of farmland. During the 1969-74 period, the proportion of partnership farms declined from 11 to 7 percent; control of farmland by partnership farms declined from 17 to 13 percent. Table 4--Concentration of production by type of farm *Percentage of val ue of products sold by class 1 farms I/ Type of farm 1969 1974. Percent Cotton and cottonseed 56.5 85.4 Dairy 42.2 74.5 Field seeds, hay, forage silage 41.5 64.5 Forest products 36.6 53.4 Fruit, nuts, and berries 68.9 82.8 Grain 38.9 75.0 Livestock 61.1 78.9 Nursery and greenhouse 85.5 90.2 Other field crops 73.5 94.1 Po ultry 82.9 96.2 Tobacco .21.0 46.1 Vegetables, sweet corn,-and melons 82.6 91.3 1/ "Value of products" refers to the total value of products sold by faTns having $2,500 or more of sales. Class 1 farms were defined by the census as those with sales of $40,000 and over. 8



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Concentration of Farmland Ownership Related to the concentration of production is the concentration of farmland. About 42 percent of the farmland was operated by farms having at least 2,000 acres in 1974. That meant that 35 percent of the farmland was operated by the largest 50,000 farms (2 percent of total), and 58 percent of the farmland was operated by the largest 200,000 farms (7 percent of total). The projections show continued concentration of land resources among the big farms. About 57 percent of farmland is projected to be operated by farms with 2,000 or more acres in 2000; less than 10 percent of the farmland will be in farms with less than 220 acres (table 8). Thus, half of the land will be farmed by the largest 50,000 farms (3 percent of total) and almost all farmland will be operated by the largest 1 million farms (57 percent of total). Form of Business Organization The number of corporations in farming is expected to continue to increase while the number of partnerships will decline slightly. Overall, the sales of multiownership farms (corporations and partnerships) could account for half of the farm sales before the end of the century. The number of corporations is projected to nearly triple, but still account for less than 4 percent of the farms. Most of these multiownership farms will likely continue to be multifamily farms. Most new corporations will likely represent the incorporation of existing farms rather than the entry of corporations not now farming. In fact, the number of corporations could well exceed the present trends because of changes in income tax laws, more rapid rise in asset values, and new technology. Few nonfarm corporations are likely to be attracted to farming unless the profitability of farming improves greatly. Table 8--Comparison of historical and projected concentration of U.S. farmland, by size of farm Farmland operated by Size of farm .the largest Year::: :2,000 :1,000 acres: 220 acres : Less : .. 1 :acres : to : to : than :50,000:200,000 : million :and over:l,999 acres: 999 acres :220 acres: farms: farms : farms Percent 1969 : 42.8 11.6 31.1 14.5 30 50 80 1974 : 45.7 12.4 29.4 12.5 35 58 88 1985 : 47.7 13.6 27.0 11.7 40 65 93 2000 : 56.6 14.1 20.8 8.5 50 74 98 14



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Projected total numbers of farms and those for the medium-size groups (sales of $20,000 to $99,999) obtained from the trend extrapolation appear to be overestimated. This reflects another serious problem with this technique. Even though there was a consistent, increasing trend which occurred in the past, the number of farms may begin to decline at some point in the future. For example, despite the continuous, increasing trend for the number of farms with sales of $40,000 to $99,999, a decline in the number is projected by other techniques (table 45). Thus, a simple trend extrapolation fails to foresee that the trend can be reversed. Finally, the trend extrapolation, by failing to capture the effects of inflation on changes in farm numbers, makes a larger projection error. If inflation is higher in the future, then the number of farms in the upper sales classes is likely to be underestimated as evidenced in table 45. The numbers of farms projected by negative exponential functions differ significantly from those obtained by other procedures and apparently have larger percentage errors. The number of projected small farms (sales of less than $20,000) is too low and the number of projected large farms (sales of $100,000 and over) is too high. The large projection errors when this technique is applied to sales distributions are expected, but projections by acreage distribution are not much better. The projected numbers of farms with 1 to 99 acres and 2,000 acres and over are much smaller than those projected by other procedures. On the other hand, the projected numbers of farms with 260 to 1,999 acres appear to be much too large, and present a discontinuity to the recent trends. In short,, evidence suggests that while the distributional functions are stable over time, an empirical approximation of the true theoretical function shows a considerable discrepancy. Table 45--Alternative projections of farm numbers by sales class, 2000 :1974 Trend :Negative :Markov :Age Sales class :actual extrapolation :exponential :process :cohort :functions: 1 ,000 farms Less than $2,500 1,101 456 13 640 655 $2,500-4,999 323 ill 13 72 119 $5,000-9,999 319 90 29 108 100 $10,000-19,999 327 164 53 108 100 $20,000-39,999 328 443 102 88 100 $40,000-99,999 328 539 271 262 190 $100,000-199,999 99 188 354 168 $200,000-499,999 39 81 606 190 600 $500,000 and over 11 27 417 226 All farms 2,875 2,109 1,857 1,862 1,864 63



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Appendix table 3--Adjustment process for underenumeration of the 1974 Census of Agriculture data, by farm size Nubr Farms First-round First-round Total :Second-round Adjusted aubr djusted ffa ms, e Farm size f include adjustment estimates missed :estimates of numeof ajsd ofar ,ex farm 1/br o mse missed farms meof abnormal cluding abnorFarmrm siz/o in cnudes fnme fmse farms ~fa rms 5/ :of f arms 2/: farms 3/ :: 4/ farms 6/: mal farms Number Percent Number Percent Number 1 to 9 acres 168,925 66.6 253,641 84,716 18.36 75,551 244,476 89 244,387 10 to 49 acres :453,690 68.9 658,476 204,786 44.37 182,583 636,273 176 636,097 50 to 69 acres :160,'702 83.5 192,457 31,755 6.88 28,311 189,013 64 188,949 70 to 99 acres :244,494 83.5 292,807 48,313 10.47 43,084 287,578 106 287,472 100-1 39 acres :235,056 89.8 261 ,755 26,699 5.78 23,785 258,841 151 258,690 140 to 179 acres :217,826 89.8 242,568 24,742 5.36 22,056 239,882 96 239,786 180 to 219 acres :137,591 89.8 153,219 15,628 5.39 13,950 151,541 94 151,447 220 to 259 acres :1189346 95.8 123,534 5,188 1.12 4,609 122,955 104 122,851 260 to 499 acres 365,369 95.8 381 ,387 16,018 3.47 14,279 379,648 351 379,297 500 to 999 acres :209,187 99.0 211,300 2,113 0.46 1,893 211,080 378 210,702 1,000 to 1,999 acres : 92,712 99.0 93,648 936 0.20 823 93,535 271 93,264 2,000 acres and over : 62,225 99.0 62,854 629 0.14 576 62,801 807 61,994 All farms :2,466,123 85.7 2,927,646 461 ,523 100.00 411 ,500 2,877,623 2,687 2,874,936 1/ Based on the 1959 definition 2/ Column 4 is obtained by dividing column 3 by column 2. 'T/ Column 5 is computed by subtracting column 2 from column 4. T/ Column 7 is computed by multiplying column 6 by 411,500; the overall missed farms is obtained as follows: 411,500= (27,466,123/0.857) -2,466,123. 5/ Column 8 is computed by adding column 7 to column 2. C/ Number of abnormal farms divided by its inclusion factor, 0.833.



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In more general terms: log y = Bo + Blx (3) where Bo = log yo and B1 = -B log e. The estimated function was forced through the point representing 100 percent of the farms and the smallest fractional size (that is, restricting 100 percent of the farms to lie above the lower limits of the smallest category). Using the logarithmic transformation (base 10) of the data, this is the point with coordinates (xi/x, 2.0), where x, is the lower limit of the smallest size category and 3 is the average farm size. This follows, noting that from: log y = Bo + Bvx log y = 2.0 when x = xl/ = xo.That is, 2.0 = Bo + BlX Bo = 2.0 -Blx log y = (2.0 -BlxO) + Blx = 2.0 + B1(x -xO) The last expression is equivalent to (log y -2.0) = Bl(x -xO), which indicates operations performed on the data prior to estimation. The value of the constant term for the estimated equation is calculated according to the relationship Bo = 2.0 -B1x This is not a severe restriction and simply results in the estimated distribution reflecting that all farms are 1 acre or larger in size. Census of Agriculture data (without adjustment for underenumeration) for the years of 1959, 1964, 1969, and 1974 showing farm numbers by acreage categories were used to estimate distribution functions (as described by equation 3 above) for the United States, nine geographic regions, and each of the 50 States. 6/ The equations, estimated by ordinary least squares, for the four census periods and for the periods combined, with related statistics, are shown in table 17 for the United.States and the nine regions. 6/ The States in each region were as follows: New England: Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, Connecticut Middle Atlantic: New York, New Jersey, Pennsylvania East North Central: Ohio, Indiana, Illinois, Michigan, Wisconsin West North Central: Minnesota, Iowa, Missouri, North Dakota, South Dakota, Nebraska, Kansas South Atlantic: Delaware, Maryland, Virginia, West Virginia, North Carolina, South Carolina, Georgia, Florida East South Central: Kentucky, Tennessee, Alabama, Mississippi West South Central: Arkansas, Louisiana, Oklahoma, Texas Mountain: Montana, Idaho, Wyoming, Colorado, New Mexico, Arizona, Utah, Nevada Pacific: Washington, Oregon, California, Alaska, Hawaii 25



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Appendix table 7--Ratios of adjustment used for acre and sale projection by age : Acres : Sales Age 1984 1994 2004 1984 1994 2004 Ratios Less than 25 0.999 0.991 0.993 1.028 1.050 1.040 25-34 .983 .967 .958 .861 .861 .790 35-44 .984 .979 .963 .915 .915 .845 45-54 .987 .977 .980 .931 .931 .890 55-64 .991 .980 .972 .943 .943 .919 65 and older .999 .991 .975 .978 .984 .952 *U.S. GOVERENqT PRINTING OFICE : 1980 0-310-94V/ESCS-218 79



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Thus, an interesting question is: What will the farm structure of the future be, barring major shifts in the course of events or the underlying causes? This report addresses that question by using four analytical methods (trend extrapolation, negative exponential functions, Markov process, and age cohort analysis) to project future farm numbers and sizes. These methods are compared and evaluated in terms of the accuracy of their projections. From this examination, a set of most likely projections was selected, and the implications of the projections for size-related structural dimensions examined--how they relate to current structural concerns, including the concentration of production, control of land resources, form of business organization, barriers to entry, capital requirements, distribution of wealth, separation of resource ownership and use, contracting arrangements, and farm specialization. The projections presented are not forecasts; that is, they are not best judgment estimates of what will actually exist at the turn of the century. Rather, they are most useful as providing a boundary notion of where the present trends are likely to lead, in the absence of significant changes in the underlying forces. It is certain, however, that changes not yet anticipated will occur. The projections and implications presented here, even with their acknowledged limitations, may prove useful for long-term planning by agribusiness, academicians, and government institutions. Agribusiness may find them useful for planning business activities related to input supply and product processing. The projections may also suggest research and extension activities. Government may find the projections of use for planning research, for projecting revenues and expenditures, and for examining long-term public policy options to influence the structure of agriculture. 2



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PROSPECTS FOR FARM ORGANIZATION This chapter summarizes the projections to indicate where the future U.S. farm numbers and sizes are heading, and the size-related implications pertaining to the structure of U.S. farming in the following categories: concentration of farm production, contracting arrangements, specialization in farm production,. concentration of farmland, form of business organization, capital requirements, distribution of wealth, age of operators and replacement rates, and tenure of farm operators. Numbers and Sizes The most reliable of the projections, which are described in more detail in ensuing chapters, suggest that farm numbers are likely to decline from 2.87 million in 1974 to 2.32 million in 1985, 2.09 million in 1990, 1.89 million in 1995, and 1.75 million in 2000. The projections further reveal that future farm numbers are likely to follow a bimodal distribution--a large proportion of small farms, an ever-increasing proportion of large farms, and a declining segment of medium-size farms (fig. 3). By 2000, small farms (less than 220 acres) are projected to account for about 65 percent of the total, a slight decrease from 70 percent in 1974. By contrast, large farms (1,000 acres and over) are projected to account for about 10 percent, double their proportion in 1974 (table 5). %nen sales are used as the size measure, small farms (sales of less than $20,000) are projected to account for about 50 percent, a decrease from 72 percent in 1974. On the other hand, large farms (sales of more than $100,000) are projected to increase from 5 percent in 1974 to 32 percent in 2000 (table 6). The number of farms in the $l00,OOO-to-$199,999 sales class is likely to begin declining by the turn of the century, indicating that a farm with sales of $100,000 may not be an economically viable unit in farming. Of course, the number of farms would be still lower if the new definition of a farm, which requires minimum sales of $1,000,. were applied (see table 1 footnote for new and old definitions of a farm). Using the new definition, farm numbers are likely to decline from the 2.37 million in 1978 to 2.05 million in 1985, 1.85 million in 1990, 1.66 million in 1995, and 1.54 million in 2000. The difference in the number of farms between the new and old definitions is the number of farms included in the lowest sales class (less than $2,500) by the old definition, but excluded by the new definition. Concentration and Specialization of Production One direct and important implication of the projections is the further concentration of agricultural production. In 1974, about half of the total farm cash receipts were received by farms with sales over $100,000. About 30 percent of the total farm production was produced by the largest 50,000 farms (2 percent of the total farms) and 60 percent by the largest 200,000 farms (7 percent of the total). Projections show that this pattern is likely to continue to 2000, and that big farms are likely to control agricultural production even more so than in the past. By 2000, about 96 percent of the total production is projected to 10



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where ~U = th (hi inqalt coffcin,2 1974e nubr wi=th precins.alt Tofrthendiaetetereopoeto accuracy in each size class, the simple percentage differences are also shown. The accuracy of the projections differs among the four projection methods. In general, projections of farm numbers and size distributions by acreage tend to be more accurate than those by sales. This is understandable since projections by sales are complicated by the inflation factor. Even though specific attempts were made to account for the effects of inflation in changes in farm numbers of the Markov chain and age cohort analyses, some errors of measurement probably remain. Simple trend extrapolation typically gives fairly accurate projections by acreage, but commits a larger error of projections by sales (tables 36 and 37). A 13.2-percent error rate was found for the projections by sales in 1974, but the error rate was greater for farms with sales of $40,000 and over. 16/ This partly reflects the fact that the simple trend extrapolation tended tunderestimate the shifts in farm numbers from low to high sales as a result of the 80-percent increase in prices received by farmers during the 1969-74 period. The projected numbers of small farms do not differ significantly from actual 1974 numbers. The simple trend extrapolation method in years other than 1974 yielded a similar accuracy and pattern. Theil-U inequality coefficients of 0.0151 and 0.0084 were computed for 1964 and 1969 projections based on acreage. Those low numbers reflect the insignificant changes in prices received by farmers in the sixties. The negative exponential function is a procedure to project the size distribution, especially when acreage is used as the size measure. As we indicated before, this method was not very satisfactory for projections based on *-16/ The U coefficient of 0.13 for the trend extrapolation by sales class means that there is an average difference of 13 percent between actual and projected farm numbers in 1974. The smaller the U coefficients, the better is the projection accuracy. 56



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Data Adjustments Farm numbers declined 682,000 between 1964 and 1974 to 2.9 million; but the numbers in some age groups increased while those in others decreased (table 28). Also, farms with sales of $40,000 or more increased but smaller farms declined. The data in this as well as most of the following tables have been adjusted to the 1964 price level by a process similar to that described in the previous chapter. However, for the age-cohort sales class data, it was necessary to deflate each group separately (see appendix C for details). The net entry rates for some sales classes for some age groups probably result from shifts to larger or smaller size classes. For example, table 28 shows that between 1964 and 1974, the 1920-29 cohort group declined in total numbers and in sales classes of $5,000 to $39,999 but increased in number for the two sales classes of $40,000 and above and the two smallest sales classes. The 22,100 increase in farm operators in the two larger sales classes probably represented not new entries but operators with increased sales during the period. The increased number of operators with sales of less than $5,000 in this cohort group in this period probably resulted from reductions in size of farming operations as the operators approached retirement, or increased nonfarm employment. The replacement ratio of entering to exiting farm operators between 1964 and 1974 was about 0.23 for all farm operators (that means that about five operators left for each new entry) and less than 1 for farms with sales of less than $40,000. However, the ratio becomes 7 or higher for farms with sales of more than $40,000. Younger persons are apparently unwilling to enter farming on the smaller farms in sufficient numbers to replace older operators who leave, because of the inadequate levels of income from small farms. There were substantial entries of young operators on farms with sales of less than $2,560, but most of these are probably part-time operations. However, t le 141,500 net entries of younger farmers (age 35 or less) on farms of that size were far less than the 611,800 older operators (age 55 or more) who departed. Table 29 presents similar data for age cohorts by acreage with similar patterns of entry and exit related to size and age. The totals in tables 28 and 29 differ because the farm operator numbers by sales class for 1974 were deflated to 1964 price levels. This resulted in some of the smaller farms not meeting the minimum sales requirement when the sales were deflated. Projections Future farm numbers can be projected if one assumes that future adjustments and phases of successive cohorts will follow the patterns of the previous. ones. The adjustments in the cohort groups are computed as the ratio of two periods and the ratios are applied to the succeeding base-period cohorts. Figure 10 shows the cohort movements, number changes, and projected farm operator numbers by age group. For example, if we trace the 1920-29 cohort by 10-year periods starting with 1964, we find 740,000 farm operators in the 35-44 ye r group. By 1974, 98 percent of the group remained in farming, namely 72t,300 farm operators of the age of 45-54 years old. This implies a cohort 47



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" By 2000, about 96 percent of total farm production is projected to. come from farms with sales of at least $100,000. About 54 percent came from such large farms in 1974. About 57 percent of the farmland will be operated by farms containing at least 2,000 acres. The corresponding percentage in 1974 was 42 percent. Half of the farmland will be farmed by the largest 50,000 farms, and almost all of the land will be operated by the largest 1 million farms. Capital requirements will rise to about $2 million of capital assets per farm for farms with sales of more than $l00,000--nearly double what was required in 1978. The accelerating capital requirements imply that the low-equity, young, potential farmers will have even more difficulty getting started in farming. Large capital requirements and large farms will tend to concentrate farm wealth in the hands of a few. By 2000, two-thirds of the wealth in the farm sector will be in the hands of those who have an interest in farms with more than $100,000 in sales. The number of new farmers under 35 years of age will shrink from 475,000 in 1964-74 to 284,000 in 1994-2004, a 40-percent decrease. The number of corporations in farming will continue to increase, while the number of partnerships will decline. Multiownership farms (corporations and partnerships) may account for half of all farm sales by the end of the century. The number of corporations might nearly triple by that time; even if they did so, however, farm corporations would still constitute less than 4 percent of the total farms. Part owners will account for a third of all farms by 2000 and more than two-thirds of large farms (sales of more than $100,000). In 1974, part owners accounted for 27 percent of all farms and 57 percent of large farms. (Part ownership means that a farmer owns some farmland but rents the remainder from others,.) iv



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NEGATIVE EXPONENTIAL FUNCTIONS This chapter presents an empirical examination of farm size distribution projections to the year 2000 derived by use of negative exponential functions. The farm size distribution, using this projection method, was found to be stable, that is, no significant shifts occur in the distribution over time. However, the size distribution estimated by negative exponential functions deviates from the actual one in that a relatively large proportion of the number of farms goes to the medium-size and large farms (200 acres and more), and a rather small percentage goes to the small farms (less than 100 acres). Technical Overview Negative exponential functions have been used by Dovring (,8 ) Boxley (1), Ching (3), and Dixon and Sonka (6) to estimate farm size distributions. If the farm size distribution has been stable around a moving average over time, this would suggest that, if the distributions could be adequately reppresented by a functional form, the projections problem would be reduced to that of estimating future average sizes. It would also suggest that the diversity of farm size characteristics of past and present is likely to extend into the future. And finally, it would suggest that causal economic studies could be conducted to explain this underlying stability. Although farm numbers have been declining rapidly and average size has been increasing substantially, small farms have not disappeared nor been amalgamated into a few large operations. Dovring (8) suggested that processes influencing farm sizes produced distributions that may be characterized by specific functional forms. The relatively constant land base means that changes in farm numbers of a given size require an offsetting change in numbers in other size categories. That is, the land base is a physical constraint on the number of farms of a given size, and the number possible is inversely related to size. Noting the inverse relationship between frequency of occurrence and farm size categories, Dovring suggested the size distribution of farm numbers should resemble the inverse exponential distribution (7, 8, 9). The general form of exponential function is ex where e is the irrational number 2.71828... and x is the manifest variable. The inverse exponential function (e-x) may represent a decumulative size distribution written as: y = Yoe -Bx (1) where y is the percentage of farms remaining above a given size limit, x. The size limits can be and are expressed as fractions or multiples of average size in this study, and when x =0, e _Bx -1. The function monotonically decreases asymptotically to zero as x increases. When Bx = 10, e -Bx = .005 of 1 percent. Boxley (1) utilized a logarilthmic (base 10) transformation of equation (1) as follows: log y =log Yo Bx log e (2) 24



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Sales Distributions Based on the 1974 adjusted census data, the equation below does not estimate the sales class distributions as well as the acreage distributions: In y -2.0 = -0.18961 R2~~0 = 0.846 (8) where: y = percentage of farms that lie above a size limit x1, X= the lower size class limit in sales receipts, x=the average sales receipts per farm, and R2the coefficient of determination. The slope of the function is -0.18961, and the t ratio is shown in parentheses. After calculating the intercept term, the estimated equation for 1974 sales distribution can be written alternatively as: ln y =2.00029 -0.18961 xi/i(9) The constant term was estimated by using the average sales receipts per farm ($33,077) in 1974. It is necessary to have projected average sales per farm to project the future sales distribution. A linear trend equation for this purpose was estimated for the period 1970-77: a=2152.47 + 4645.33 T R 056 (10) where: Sa = average sales receipts per farm, T = time (1970 =1.0, 1971 =2.0, etc.), and the t ratios are in parentheses. In addition, total sales receipts are needed so that the number of all farms can be projected. Another linear trend equation for this purpose was estimated: St = 44,998.3 + 7,303.13 T R2= 0.841 (11) (6.878) (5.637) where St is total sales receipts, and the other values are as defined above. Projected total farm numbers again continue to decline, with the pattern similar to that of acreage distributions (table 19). The projected sales distributions, however, appear to depart from the historical trends in several important-aspects. First, the negative exponential function projects far too many farms with sales of more than $100,000. Second, small farms (sales less than $20,000) are projected to disappear at a rapid rate--a decline from 72 percent of the total number of farms in 1974 to 6 percent in 2000. Third, the number of farms in the $40,000-to-$99,999 sales class is projected to be smaller in 2000 than the number in 1974. 31



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Table 30--Ratio of 1974 farmers to 1964 farmers by age cohort and sales class 1/ Cohort Age in : Less : : birth 1974 than $2,500$5,000: $10,000: $20,000$40,000$100,000 Total year : Census $2,500 : 4,999 9,999 19,999 39,999 : 99,999 or more Years Ratio 2/ After 1949 : Under 25 3/: 0.03 0.04 0.04 0.03 0.03 0.04 0.02 0.04 1940-49 : 25-34 : 5.54 3.38 3.85 4.22 6.83 14.48 23.17 5.05 1930-39 35-44 : 1.69 1.19 1.19 1.02 1.27 2.29 3.56 1.14 1920-29 45-54 1.04 .85 .88 .78 .94 1.45 1.70 .97 1910-19 55-64 .79 .70 .67 .64 .80 1.10 1.00 .75 1900-09 65 or more .73 .59 .44 .40 .49 .65 .66 .60 1/ 1974 sales class data adjusted to 1964 prices. 7/ The number of 1974 farmers in each sales class and each age cohort divided by the number of 1964 farmers in the same sales class and age cohort. 3/ The ratio for this age cohort is defined as all new entrants under 25 divided by the number of operators who, 10 years earlier, were 35-54 years old (see text for more detail). Table 31--Ratio of 1974 farmers to 1964 farmers, by age cohort and size of farm 1/ Cohort : Age in : .: : : 1,000: 2,000 birth : 1974 : 1-99 : 100-219 : 220-499 : 500-999 : 1,999 : or more : Total year : Census : acres : acres : acres : acres : acres : acres Years : Ratio 2/ After 1949 : Under 25 3/: 0.04 0.04 0.03 0.03 0.03 0.02 0.04 1940-49 : 25-34 : 4.99 4.52 4.89 7.83 10.74 10.20 5.12 1930-39 : 35-44 : 1.59 1.31 1.19 1.64 1.91 2.05 1.46 1920-29 : 45-54 : 1.04 .90 .86 1.10 1.25 1.25 .98 1910-19 : 55-64 : .83 .71 .70 .81 .89 .91 .77 1900-09 : 65 or more : .75 .59 .51 .56 .64 .72 .65 1/ Ratios for acre size differ slightly from those by sales classes because sales class data were deflated to 1964 prices. 2/ The number of 1974 farmers in each sales class and each age cohort divided by the number of 1964 farmers in the same sales class and age cohort. 3/ The ratio for this age cohort is defined as all new entrants under 25 divided by the number of operators who, 10 years earlier, were 35-54 years old (see text for more detail). 51



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COMPARISON OF ALTERNATIVE PROJECTIONS Up to this point, we have presented projections of farm numbers and size distributions to 2000 for each of the four most frequently used projection methods. This chapter summarizes those projections and compares them for accuracy and reasonableness. A set of "most likely" projections were presented earlier. All the projections point to a continuous decline in farm numbers, to about 1.75 million farms by 2000, although the estimate varies by the method used and whether the projection is by acreage or sales size. The trend extrapolation and Markov process analysis closely aprallel one another for acreage distribution, while the negative exponential function performs erratically. For sales distributions, the Markov process and age cohort analysis give very consistent projections; negative exponential functions again perform poorly. Acreage distributions projected to 2000 by trend extrapolation, Markov process, and age cohort analysis are very consistent. Negative exponential functions probably underestimate the percentage of small farms, and overestimate that for medium-size and large farms (table 35). The projected total number of farms, based on the acreage distribution, varies from 1.7 million to 1.8 million in 2000. The small deviations among the methods give confidence in projecting the acreage distributions of farm numbers (fig. 11). Unfortunately, farmland acreage is not the best size measure. Frequently, sales receipts are preferred to farmland acreage as a size measure. Furthermore, the new definition of a farm adopted by the U.S. Department of Agriculture in 1978 makes it almost necessary to base projections on sales. Total farm number projections based on the sales distribution vary more widely, however, ranging from 1.9 million to 2.1 million in 2000 (fig. 12). The large number of farms obtained from trend extrapolation is partly due to the erratic trend equation for farms with $20,000 to $39,999 in sales. Instead of projecting a downturn (a trend established from 1969 to 1974), an upward increasing trend is projected. Markov process and age cohort analysis, on the other hand, give very consistent projections. Table 35--Comparison of alternative projections by size class in 2000 Size of farm (acres) Sales class Alternative projections Less than: 220 to 1,000 Less than: $20,000$100,000 220 999 and over: $20,000 $99,999 and over Percent of total farms 1974 actual 69.8 24.8 5.4 72.0 22.8 5.2 Trend extrapolation 61.4 28.7 9.9 39.1 46.8 14.1 Negative exponential: functions : 34.6 51.0 14.4 5.8 20.1 74.1 Markov process 67.7 22.4 9.9 49.9 18.8 31.3 Age cohort analysis 69.5 21.7 8.8 51.8 15.5 32.8 54