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 centuryfrom 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 in
creasing 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.
AER434. September 1979.
Structure Issues of American Agriculture. AER438. November 1979.
Another Revolution in U.S. Farming? Lyle P. Schertz and others.
AER441. 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, Angle Kennedy,
Virginia Minter, Terry Salus, Jennifer Reed, and Sandy Swingle.
Washington, D.C. 20250 July 1980
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 centuryfrom 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 in
creasing 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.
AER434. September 1979.
Structure Issues of American Agriculture. AER438. November 1979.
Another Revolution in U.S. Farming? Lyle P. Schertz and others.
AER441. 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, Angle Kennedy,
Virginia Minter, Terry Salus, Jennifer Reed, and Sandy Swingle.
Washington, D.C. 20250 July 1980
CONTENTS
Page
Summary . . ..... . . ....... iii
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. . .. ........... .... . 21
Negative Exponential Functions . .. . .. .. 24
Technical Overview . . . ..... .. .. 24
Projections. . . . . ... . . 27
Markov Process . . . . . . 33
Technical Overview . . . . .. 33
Data Adjustments . .. . . . .. 34
Projections . ... . . . . . 36
Age Cohort Analysis. . . . . . 45
Technical Overview . . . ....... . .. 45
Data Adjustments .. . . . . 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 distri
butiona large proportion of small farms, an everincreasing proportion of
large farms, and a declining proportion of mediumsize 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 the
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 pro
jected 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
of farms 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
about half of all farm production. By contrast, 50 percent of the
farmsthe smaller oneswill produce only 1 percent.
Almost twothirds 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 $100,000nearly double what was
required in 1978.
* The accelerating capital requirements imply that the lowequity, young, po
tential 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, twothirds 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
196474 to 284,000 in 19942004, a 40percent 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
twothirds 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.)
U.S. Farm Numbers, Sizes, and
Related Structural Dimensions:
Projections to Year 2000
William Lin
George Coffman
J.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 pro
duction. 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. 1f
This trend toward greater concentrationfewer but larger farmsis the re
sult 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 dataup to and in
cluding 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.
Thus, an interesting question is: What will the farm structure of the fu
ture be, barring major shifts in the course of events or the underlying causes?
This report addresses that question by using four analytical methods (trend ex
trapolation, 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 se
lected, and the implications of the projections for sizerelated structural
dimensions examinedhow 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 under
lying 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 longterm planning by agribusiness, academicians,
and government institutions. Agribusiness may find them useful for planning busi
ness activities related to input supply and product processing. The projections
may also suggest research and extension activities. Government may find the pro
jections of use for planning research, for projecting revenues and expenditures,
and for examining longterm public policy options to influence the structure of
agriculture.
OVERVIEW OF STRUCTURE AND STRUCTURAL CHANGE
This chapter describes the current situation for some elements of the struc
ture of U.S. agriculture and recent changes in structural characteristics, empha
sizing 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 rel
atively constant land base was occupied by fewer and fewer farms. Thus, the
average farm size increased by onethird between 1940 and 1974. This changealso
implies increasing concentration of production and control of land resources into
fewer and fewer hands.
Contrary to frequent assertion, the remaining farms, although larger, con
tinued to be familyoperated 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, offfarm income per farm was
about the same for the very large and small farms. The situation differed signi
ficantly in 1974, however. Offfarm 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 impor
tant structural characteristics related to size, such as concentration of produc
tion and farmland, form of business organization, age and tenure arrangements of
operators (discussed in the next chapter), and financial structure.
Numbers and Sizes
The land in farms increased slightly after 1940, but declined somewhat be
tween 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 far
mers. The remaining farmers were often motivated by prospects of increased
returns by enlarging their lands or consolidating their operations with neigh
boring 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 concentra
tion 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 tabularr data are in app. tabl e 1). In 1969, the largest 24 percent of
OVERVIEW OF STRUCTURE AND STRUCTURAL CHANGE
This chapter describes the current situation for some elements of the struc
ture of U.S. agriculture and recent changes in structural characteristics, empha
sizing 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 rel
atively constant land base was occupied by fewer and fewer farms. Thus, the
average farm size increased by onethird between 1940 and 1974. This changealso
implies increasing concentration of production and control of land resources into
fewer and fewer hands.
Contrary to frequent assertion, the remaining farms, although larger, con
tinued to be familyoperated 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, offfarm income per farm was
about the same for the very large and small farms. The situation differed signi
ficantly in 1974, however. Offfarm 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 impor
tant structural characteristics related to size, such as concentration of produc
tion and farmland, form of business organization, age and tenure arrangements of
operators (discussed in the next chapter), and financial structure.
Numbers and Sizes
The land in farms increased slightly after 1940, but declined somewhat be
tween 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 far
mers. The remaining farmers were often motivated by prospects of increased
returns by enlarging their lands or consolidating their operations with neigh
boring 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 concentra
tion 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 tabularr data are in app. tabl e 1). In 1969, the largest 24 percent of
Table 1Number 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 : 1/ 2,466 1,026 416
1/ 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 normally 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 ef
fect 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 concentra
tion of production.
The increasing concentration of production on larger farms carries implica
tions beyond just the numbers. Larger farms are becoming more involved with ver
tical 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.
Table 2Number of farms, by size of farm 1/
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
the undercounting of farm numbers by the Census Bureau was made.
not included.
1/ No adjustment for
2/ Alaska and Hawaii
Table 3Number of farms, by sales class, selected years 1/
Sales class 1974 1969 1964 1959 :: Sales class 2/ 1954 : 1950
Number Number
Less than $2,500 768,838 994,456 1,338,239 1,637,849 Less than $1,200 462,427 717,201
$2,5004,999 289,983 395,104 443,918 617,677 :Parttime 574,575 639,230
$5,0009,999 296,373 390,425 504,614 653,881 :Residential 878,136 1,029,392
$10,00019,999 : 310,011 395,472 467,096 483,004 :$1,2002,400 : 763,348 901,316
$20,00039,999 321,771 330,992 259,898 210,402 :$2,5009,999 811,965 882,302
$40,00099,999 324,310 169,695 110,513 82,120 :$5,0009,999 706,929 721,211
$100,000199,999 : 101,153 35,308 21,148 14,201 :: $10,00024,999 448,945 381,151
$200,000499,999 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
2/ The sales classification was changed after 1954 by the
the Census Bureau was made.
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 per
cent 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 owner
ship, 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 threefourths of the land in farms
and ranches. Corporations held about 9 percent of farm and ranch land and non
family corporations held only 2.4 percent. Less than onehalf 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
Cited, beginning on p. 65.
Figure 1
Concentration of Farm
Production in the United States,
1969 and 1974
20 40 60 76 80
Percentage of farms
refer to items listed in the Literature
Figure 2
Concentration of Farmland
among Farms, 1969 and 1974
Percentage of land in farms
20 40 60 707780
Percentage of farm numbers
Form of Business Organization
Contrary to common assertion that corporations are taking over farming to
day, the Census of Agriculture data clearly show that noncorporate farms con
tinue 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 familyheld or closelyheld
corporations (16 or fewer stockholders).
Corporate farms (including the familyheld corporations) constituted 1 per
cent 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 farm
land. During the 196974 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 4Concentration of production by type of farm
: Percentage of value of products
: sold by class 1 farms 1/
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
Poultry : 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
farms having $2,500 or more of sales. Class 1 farms were defined by the
census as those with sales of $40,000 and over.
Financial Structure
Farm income, offfarm income, and government farm program payments consti
tute 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 re
affirms what is widely known about the programsthat benefits are closely pro
portional 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 pay
ments went to only 10 percent of the participants, those with the largest farms.
By contrast, 50 percent of the farmsthe smaller unitsreceived only 10 percent
of the payments.
In 1969, the amount of offfarm 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. Offfarm 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 off
farm income significantly. Preliminary data indicate that this trend continued
into 1978. This suggests that small farmers are supplementing their family in
come through offfarm employment and investment, and that offfarm 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 de
creased, while the ratio increased to 30.2 for the largest farms.
PROSPECTS FOR FARM ORGANIZATION
This chapter summarizes the projections to indicate where the future U.S.
farm numbers and sizes are heading, and the sizerelated 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 mil
lion 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 distributiona large proportion of small farms, an everincreasing
proportion of large farms, and a declining segment of mediumsize 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). When sales are used as the size mea
sure, 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 $100,000to$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 con
centration 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
PROSPECTS FOR FARM ORGANIZATION
This chapter summarizes the projections to indicate where the future U.S.
farm numbers and sizes are heading, and the sizerelated 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 mil
lion 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 distributiona large proportion of small farms, an everincreasing
proportion of large farms, and a declining segment of mediumsize 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). When sales are used as the size mea
sure, 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 $100,000to$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 con
centration 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
PROSPECTS FOR FARM ORGANIZATION
This chapter summarizes the projections to indicate where the future U.S.
farm numbers and sizes are heading, and the sizerelated 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 mil
lion 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 distributiona large proportion of small farms, an everincreasing
proportion of large farms, and a declining segment of mediumsize 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). When sales are used as the size mea
sure, 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 $100,000to$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 con
centration 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
Table 5Most likely projection of the number of farms, by size of farm
:Actual
Size of farm 1974 :1985 : 1990 1995 2000
1,000 farms
199 acres : 1,356.9 1,096.2 989.6 894.9 826.9
100219 acres : 649.9 475.6 404.4 345.9 301.9
200499 acres 502.1 387.4 338.6 295.8 264.3
500999 acres 210.7 201.8 193.3 187.1 182.9
1,0001,999 acres : 93.3 97.4 98.2 100.2 102.4
2,000 acres.and 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 6Most 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
$2,5009,999 642.4 421.1 296.8 211.7 185.5
$10,00019,999 : 326.9 201.8 144.2 94.5 99.8
$20,00039,999 327.6 204.2 158.8 111.5 87.5
$40,00099,999 327.5 358.4 291.6 233.4 213.5
$100,000199,999 : 99.4 190.2 211.1 193.7 161.0
$200,000499,999 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
come from farms with sales of at least
$100,000. This means that the 50,000
largest farms will probably produce
almost twothirds of all agricultural
products, and the largest 1 million
farms (57 percent of the total) will
produce almost all agricultural pro
ducts (table 7). 3/
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
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 produc
tion will likely be produced by the
largest 1 percent of farms. By con
trast, 50 percent of the farmsthe
smaller oneswill produce only about
1 percent of the production.
Concentration of production is
also related to two other structural
factors: contractual arrangements
and the economic advantages of dif
ferent sizes of firms for various
commodities.
Contracting Arrangements
Agricultural production under
contractual arrangements has in
creased gradually. The percentage
of farms having contracts increased
from 4.5 percent in 1960 to 9 per
cent in 1974. Furthermore, the
proportion of farms having contracts
was much higher for large farms:
the proportion of small farms (less
than $20,000 in sales) having con
tracts in 1974 was less than 5 per
3/ The concentration of agricul
tural production differs from com
modity to commodity. Industries such
as egg, poultry, and sugarcane may
actually have higher concentrations
than the aggregate portrayed in table 7.
Figure 3
Distribution of Farm Numbers by
Sales: Actual 1974 and Projected for
2000
Million farms
I
1.0 l
0.5 I
0 L
U I    
Less Than $10,000 $40,000 $200,000
$10,000 $39,999 $199,999 or more
Sales groups
1974
Figure 4.
Concentration of Farm
Production in 1974, 1985,
and 2000
Percentage of sales
.1974
1985
80 ..... 2000
20 40 60 80
Percentage of farms
cent, while the
than 30 percent
($100,000 sales
proportion was more
for large farms
or more).
The projected increase in farm
size by 2000 indicates that more
farms, perhaps as many as a quarter
to onethird of all farms, will mar
ket their products under contractual
arrangements. Virtually all produc
tion of sugarbeets and dairy products
are now marketed under contractual
arrangements. By 2000, contracts are
likely to increase in marketing
vegetables, fruits, cotton, and
poultry and poultry products.
Size Variability by Commodity
Historically, some farm com
modities have been dominated by large
farms, and others by small farms
(table 4). The changes in the farm
sector reflected by our data suggest
that farm production of vegetables
and poultry will continue to be dom
inated by large farms. Other indus
tries, such as livestock and cotton,
which have recently become much more
concentrated, are likely to be dom
inated by large farms in the future.
Table 7Comparison of historical and projected concentration of production,
by sales class and largest farms
Sales class Cash receipts by the
: :largest
Year :
Year: $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
receipts.
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 farm
land 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 pro
jected 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 cor
porations are likely to be attracted to farming unless the profitability of
farming improves greatly.
Table 8Comparison 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:1,999 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
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 farm
land 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 pro
jected 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 cor
porations are likely to be attracted to farming unless the profitability of
farming improves greatly.
Table 8Comparison 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:1,999 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
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 farm
land value and farm machinery costs will make capital requirements for farming
even higher in the future. If the trend of assetsales 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 farmnearly 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 pro
vide 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 lowequity, young, potential
farmers.
The change in farm structure in the future will have a farreaching 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
1978onethird 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 twothirds of the farm assets will go to farms
with sales of more than $100,000, with the remaining onethird 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 $930,200more than triple
the 1978 figure. By 2000, twothirds 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
196474 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 rangefrom
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 de
cline 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
noticeablefrom 51.2 in 1969 to 51.7 in 1974. Similarly, the percentage of far
mers 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
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 farm
land value and farm machinery costs will make capital requirements for farming
even higher in the future. If the trend of assetsales 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 farmnearly 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 pro
vide 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 lowequity, young, potential
farmers.
The change in farm structure in the future will have a farreaching 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
1978onethird 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 twothirds of the farm assets will go to farms
with sales of more than $100,000, with the remaining onethird 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 $930,200more than triple
the 1978 figure. By 2000, twothirds 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
196474 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 rangefrom
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 de
cline 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
noticeablefrom 51.2 in 1969 to 51.7 in 1974. Similarly, the percentage of far
mers 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
Item : Unit
Farm assets:
1978
2000
Debt/asset ratio:
1978
2000
Farm debt:
1978
2000
0' Equity:
1978
2000
Distribution of
equity:
1978
2000
Farm assets:
1978
2000
Farm debt:
1978
2000
Farm equity:
1978
2000
Mil. dol.
do.
Percent
do.
Mil. dol.
do.
Mil. dol.
do.
Percent
do.
1,000 dol.
do.
1,000 dol.
do.
1,000 dol.
do.
Table 9Balance sheet of the farming sector, by sales class
: Less than $20,000 : $20,000 to $99,999 : $100,000 and over
Total
218,512 278,096 216,357
: 273,238 292,027 1,062,600
S9.5 17.8 22.7
: 6.3 17.0 26.0
S20,660 49,468 49,145
S17,214 49,645 276,276
197,852 228,628 167,212
256,024 242,382 786,324
33.3
19.9
123.3
307.4
11.7
19.4
111.7
288.0
38.5
18.9
Per farm
390.0
9,701.9
69.4
164.9
320.7
805.3
28,2
61.2
1,157
1,894.1
262.8
492.5
894.2
1,401.6
All farms
712,965
1,627,865
16.7
21.1
119,273
343,135
593,692
1,284,730
100.0
100.0
266.8
930.2
446.6
196.1
222.2
734.1

in the 196474 period to 284,000 during the 19842004 period, a 40percent de
cline 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, parttime farms,
and will depend primarily on nonfarm income sources. Expectations of nonfarm in
come 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 op
erators 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 en
tries 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 op
portunities 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 10U.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 mid
point was 71.
Source: Adjusted 1974 Census of Agriculture and age cohort projections.
Tenure of Farm Operators
Tenure patterns in farming have changed. Partowner operators have in
creased as a percentage of all farmers. The proportion of full owners has de
clined only slightly, while the percentage of tenantoperated farms has de
clined significantly.
The proportion of tenants in each sales class and for all farms decreased
from 1969 to 1974, reflecting farmers' longheld desire to acquire farmland and
the ability to do so. But at the same time, the proportion of full owners de
clined 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 onethird of the farms with sales of more than $100,000. By con
trast, 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 onethird 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 11Farm operator replacement rates
Item :196474 :197484 :198494 :19942004
Percent
Replacement rate on farms
with sales of: 1/
$100,000 or more 296 299 293 145
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.
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 12Tenure structure by sales class
S 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
TREND EXTRAPOLATION
This chapter describes the projections obtained from simple extrapolations
of trends, and the adjustment of the census data to take account of overenumera
tion and underenumeration. Again, the central question is: If we assume that
the current trends are going to continue into the future, what will the struc
ture 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) goodnessoffit criterion, consistency, reasonableness in com
parison 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 num
bers than one would normally expect. In fact, a linear equation will project
the number of farms in the 100219 acres class to completely disappear by the
late 1990's and to be negative in the year 2000; and (2) this form did not gen
erally yield a higher R2 than a semilog specification, the form eventually
selected. Conversely, a polynomial specification was rejected for the opposite
reasonit frequently projected trend reversal. Instead of a decline in the
number of farms in the lto99acre size class, it projected an increasing
trend into the future.
This left a choice between the loglinear 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 loglinear
form. For example, the number of farms in the lto99acre size group histor
ically had declined at a high rate311,000 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 loglinear 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 loglinear
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.
TREND EXTRAPOLATION
This chapter describes the projections obtained from simple extrapolations
of trends, and the adjustment of the census data to take account of overenumera
tion and underenumeration. Again, the central question is: If we assume that
the current trends are going to continue into the future, what will the struc
ture 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) goodnessoffit criterion, consistency, reasonableness in com
parison 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 num
bers than one would normally expect. In fact, a linear equation will project
the number of farms in the 100219 acres class to completely disappear by the
late 1990's and to be negative in the year 2000; and (2) this form did not gen
erally yield a higher R2 than a semilog specification, the form eventually
selected. Conversely, a polynomial specification was rejected for the opposite
reasonit frequently projected trend reversal. Instead of a decline in the
number of farms in the lto99acre size class, it projected an increasing
trend into the future.
This left a choice between the loglinear 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 loglinear
form. For example, the number of farms in the lto99acre size group histor
ically had declined at a high rate311,000 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 loglinear 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 loglinear
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.
TREND EXTRAPOLATION
This chapter describes the projections obtained from simple extrapolations
of trends, and the adjustment of the census data to take account of overenumera
tion and underenumeration. Again, the central question is: If we assume that
the current trends are going to continue into the future, what will the struc
ture 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) goodnessoffit criterion, consistency, reasonableness in com
parison 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 num
bers than one would normally expect. In fact, a linear equation will project
the number of farms in the 100219 acres class to completely disappear by the
late 1990's and to be negative in the year 2000; and (2) this form did not gen
erally yield a higher R2 than a semilog specification, the form eventually
selected. Conversely, a polynomial specification was rejected for the opposite
reasonit frequently projected trend reversal. Instead of a decline in the
number of farms in the lto99acre size class, it projected an increasing
trend into the future.
This left a choice between the loglinear 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 loglinear
form. For example, the number of farms in the lto99acre size group histor
ically had declined at a high rate311,000 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 loglinear 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 loglinear
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.
Prior to 1969, all censuses were conducted by personal interview in a com
plete canvass of rural areas. In 1969, a mailoutmailback, selfenumerated
national census was conducted. The change in survey procedure, along with other
factors, contributed to the underenumeration problem, that is, an incomplete
farm count, especially 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 re
ported 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 main
tain 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 appendix tables 2 and 3. In general, the
adjustment process for acres and sales was tne same. However, slight differ
ences 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 num
bers 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.
Table 13Census 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 14Census of Agriculture data on number of farms, by size of farm,
adjusted for underenumeration
Size of farm 1959 : 1964 1969 : 1974
1,000 farms
19 acres : 301.9 217.8 268.0 244.4
1049 acres : 890.3 760.3 675.8 636.1
5069 acres 291.6 252.2 210.2 188.9
7099 acres 452.0 394.8 335.8 287.5
100139 acres : 410.0 350.5 301.5 258.7
140179 acres : 392.8 332.8 284.5 239.8
180219 acres : 234.4 206.5 178.7 151.4
220259 acres 203.1 177.5 148.2 122.9
260499 acres 507.4 487.7 438.5 379.3
500999 acres 214.7 225.1 218.4 210.7
1,0001,999 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
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 coeffi
cient for the time variable, apparently failed to capture the downturn in 1974.
Thus, trend projections by sales class are likely to overestimate the total num
ber of farms and the number in the :$20,000$39,999 sales class.
Table 15Trend projections of the
number of farms, by size of farm
Size of farm : 1980 1985 1990 : 1995 : 2000
1,000 farms
199 acres :1,190.4 1,060.8 945.3 842.4 750.6
100219 acres : 558.1 477.7 409.0 350.1 299.7
220499 acres 456.3 406.0 361.3 321.5 286.1
500999 acres 212.6 210.5 208.9 207.1 205.3
1,0001,999 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 16Trend 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
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 mediumsize and large farms (200 acres and more), and a rather small per
centage goes to the small farms (less than 100 acres).
Technical Overview
Negative exponential functions have been used by Dovring (7, 8, 9),
Boxley (1), Ching (3), and Dixon and Sonka (6) to estimate farm size distribu
tions. If the farm size distribution has been stable around a moving average
over time, this would suggest that, if the distributions could be adequately rep
presented 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 con
ducted 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 func
tional 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 re
semble 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 func
tion (ex) 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 x = 1. The function monotonically decreases
asymptotically to zero as x increases. When Bx = 10, e Bx = .005 of 1 percent.
Boxley (1) utilized a logarithmic (base 10) transformation of equation (1)
as follows:
log y = log yo Bx log e (2)
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 mediumsize and large farms (200 acres and more), and a rather small per
centage goes to the small farms (less than 100 acres).
Technical Overview
Negative exponential functions have been used by Dovring (7, 8, 9),
Boxley (1), Ching (3), and Dixon and Sonka (6) to estimate farm size distribu
tions. If the farm size distribution has been stable around a moving average
over time, this would suggest that, if the distributions could be adequately rep
presented 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 con
ducted 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 func
tional 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 re
semble 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 func
tion (ex) 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 x = 1. The function monotonically decreases
asymptotically to zero as x increases. When Bx = 10, e Bx = .005 of 1 percent.
Boxley (1) utilized a logarithmic (base 10) transformation of equation (1)
as follows:
log y = log yo Bx log e (2)
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 coordi
nates (x1/x, 2.0), where xl is the lower limit of the smallest size category and
X is the average farm size. This follows, noting that from:
log y = Bo + Bl:
log y = 2.0 when x = xl/x = xo. That is,
2.0 = Bo + Blxo
Bo = 2.0 Blxo
log y = (2.0 BlxO) + Blx
= 2.0 + Bl(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 B1 xo
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
Table 17Estimated size distribution function, United States and regions
Coeffi
Region Year Intercept :Slope cientdard R2 F statistic
standardror
error
United States
New England
Middle Atlantic
East North Central
West North Central
South Atlantic
East South Central
West South Central
Mountain
Pacific
1959
1964
1969
1974
195974
1959
1964
1969
1974
195974
1959
1964
1969
1974
195974
1959
1964
1969
1974
196974
1959
1964
1969
1974
195974
1959
1964
1969
1974
195974
1959
1964
1969
1974
195974
1959
1964
1969
1974
195974
1959
1964
1969
1974
195974
1959
1964
1969
1974
195974
2.00107
2.00101
2.00096
2.00092
2.00097
2.00155
2.00145
2.00152
2.00144
2.00147
2.00287
2.00181
2.00176
2.00165
2.00175
2.00200
2.00185
2.00172
2.00158
2.00780
2.00098
2.00094
2.00089
2.00085
2.00091
2.00142
2.00142
2.00127
2.00122
2.00128
2.00150
2.00141
2.00137
2.00130
2.00137
2.00093
2.00088
2.00084
2.00080
2.00085
2.00049
2.00046
2.00044
2.00045
2.00046
2.00090
2.00085
2.00082
2.00082
2.00089
0.3260
.3554
.3754
.3844
.3549
.2810
.2684
.2914
.2763
.2721
.2524
.2735
.2868
.2773
.2704
.3096
.3209
.3171
.3030
.3130
.3644
.3799
,.3904
.3896
.3794
.1993
.1993
.2337
.2348
.2176
.1821
.1944
.2119
.2138
.1975
.3901
.4138
.4299
.4434
.4152
.8717
.9228
.9487
.9611
.9205
.3601
.4046
.422:
.4253
.3973
0.0411
.0426
.0418
.0431
.0203
.0241
.0246
.0219
.0224
.0113
.0268
.9261
.0255
.0236
.0124
.0272
.0254
.0232
.0198
.0116
.0282
.0277
.0261
.0263
.0130
.0277
.0292
.0291
.0298
.0139
.0251
.0260
.0261
.0266
.0124
.0450
.0446
.0406
.0440
.0210
.1063
.1121
.1141
.1277
.0544
.0629
.0704
.0726
.0760
.0333
0.913
.921
.931
.930
.919
.950
.952
.967
.962
.956
.937
.948
.955
.958
.947
.966
.964
.969
.975
.964
.965
.969
.974
.973
.969
.896
.902
.915
.912
.901
.897
.903
.916
.915
.903
.926
.935
.949
.944
.935
.918
.919
.920
.904
.914
.845
.846
.849
.839
.841
0.405
.364
.352
.090
.213
.364
.351
.282
.1311
.2131
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 longestablished, 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 de
pends 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 para
meters of each equation belong to the same regression equation, that is, the data
are subsamples of the same populationno significant shifts occur in the distri
bution over time. The F ratio calculated was expressed as:
(A B C D E) / P (k 1)
F =
(B + C + D + E) / (nl + 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 n1 + n2 + n3 + n4 observations with
n1 + 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, pro
jections 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 underenumera
tion 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).
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 1*
(13.30) x
R2 = 0.885
where: y
xi
R2
percentage of farms lying above a size limit, xi,
the lower size class limit in acres,
average farm size in acres, and
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
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
underenumeration (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
o \
10 
S8
c 1
0 6
(
a. 4 Observed distribution
 Theoretical distribution
2
1
1I I I I I I I I I I I 1 1 I I
.01 .02 .04 .06.08.1 .2 .4 .6 .81 2
Average size
Relative size of farm (ratio to average farm size)
4 6 8 10
To the extent that size distribution around a moving average is stable over
time, the information required for projecting future farm size distributions is
minimalthe projected land in farms and average farm size in acreage distribu
tions, 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 projec
tions of sales distribution. Nevertheless, for comparison purposes and to
maintain consistency throughout this report, sales distributions and their pro
jections are also projected in this section.
Projections of acreage distributions to 2000 were obtained from the esti
mated 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 ob
tain the projected decumulative distribution, and the percentage of farms in each
size category is found by subtracting each category from the previous one. Pro
jected annual mean sizes were obtained from a linear time trend equation esti
mated from data for the 195777 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 dis
tributions, 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 2,000acre 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 in
crease. This discontinuity becomes more obvious in the 220 to 2,000acre 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.
Table 18Projected number of U.S. farms, by size of farm, negative exponential function
Size of farm: 1974 (actual) : 1980 : 1985 : 1990 : 1995 : 2000
:Thousands
19 acres : 244.4
1049 acres
5069 acres
7099 acres
100139 acres:
o 140179 acres:
180219 acres:
220259 acres:
260499 acres:
500999 acres:
1,0001,999
acres
2,000 acres
and over
636.1
188.9
287.5
258.7
239.8
151.4
122.9
379.3
210.7
93.3
62.0
Percent
8.5
22.1
6.6
10.0
9.0
8.3
5.3
4.3
13.2
7.3
Thousands
48.6
204.5
95.7
135.8
167.5
153.3
140.3
128.3
571.3
544.9
3.2 239.2
2.2 29.3
Percent
2.0
8.3
3.9
5.5
6.8
6.2
5.7
5.2
23.2
22.2
Thousands
43.6
184.0
86.3
122.6
151.8
139.3
127.9
117.3
527.3
515.7
Percent
1.9
8.1
3.8
5.4
6.6
6.1
5.6
5.1
23.1
22.6
Thousands
39.2
165.6
77.8
110.8
137.5
126.5
116.5
107.2
486.1
486.7
Percent
1.9
7.8
3.7
5.2
6.5
6.0
5.5
5.1
22.9
22.9
Thousands
35.2
149.1
70.2
100.2
124.5
114.9
106.0
97.9
447.6
458.2
9.7 237.2 10.4 234.0 11.0 229.6
1.2 31.6
1.4 33.7
35.7
Percent
1.8
7.6
3.6
5.1
6.3
5.8
5.4
5.0
22.7
23.3
Thousands
31.7
134.3
63.3
90.5
112.2
104.3
96.5
89.3
411.5
430.2
11.7 224.3
1.8 37.4
100.0 2,284.5 100.0 2,121.7 100.0 1,969.1 100.0 1,825.9 100.0
Percent
1.7
7.4
3.5..
5.0
6.2
5.7
5.3
4.9
22.5
23.6
12.4
2.1
All farms :2,874.9 100.0 2,458.8
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 xi 10] R2 = 0.846 (8)
(6.627) x
where: y = percentage of farms that lie above a size limit xl,
xl = 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 paren
theses. After calculating the intercept term, the estimated equation for
1974 sales distribution can be written alternatively as:
In y = 2.00029 0.18961 xl/x (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 esti
mated for the period 197077:
2
S, = 2152.47 + 4645.33 T R = 0.569 (10)
(0.259) (2.815)
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 his
torical 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
ratea decline from 72 percent of the total number of farms in 1974 to 6
percent in 2000. Third, the number of farms in the $40,000to$99,999 sales
class is projected to be smaller in 2000 than the number in 1974.
Table 19Projected number of U.S. farms, by sales
functions
class, negative exponential
Sales class : Actual 1974 1980 1985
: Thousands Percent
Less than $2,500
$2,5004,999
$5,0009,999
$10,00019,999
$20,00039,999
$40,00099,999
$100,000199,999
$200,000499,999
$500,000 and over:
All farms
1,100.6
322.9
319.5
326.9
327.6
327.5
99.4
39.3
11.2
2,874.9
38.3
11.2
11.1
11.4
11.4
11.4
3.5
1.4
.4
100.0
Thousands Percent
46.8
46.8
90.6
170.9
302.2
659.0
580.4
417.8
39.1
2.0
2.0
3.9
7.3
12.8
28.0
24.7
17.8
1.7
2,353.6 100.0
Thousands Percent
29.0
33.4
55.9
111.7
201.3
489.5
520.0
553.8
121.7
1.4
1.6
2.6
5.3
9.5
23.1
24.6
26.2
5.8
2,116.3 100.0
1990 1995 2000
Thousands Percent
Less than $2,500
$2,5004,999
$5,0009,999
$10,00019,999
$20,00039,999
$40,00099,999
$100,000199,999
$200,000499,999
$500,000 and over:
All farms
22.7
22.7
39.8
81.6
152.6
385.6
455.2
606.8
222.6
1,989.5.
1.1
1.1
2.0
4.1
7.7
19.4
22.9
30.5
11.2
100.0
Thousands Percent
17.6
17.4
34.4
62.5
122.5
316.2
402.4
614.3
323.7
.9
.9
1.8
3.3
6.4
16.2
21.1
32.2
16.9
1,910.7 100.0
Thousands Percent
12.8
12.6
29.3
53.1
101.6
270.9
353.7
606.1
416.7
.7
.7
1.6
2.9
5.5
14.6
19.1
32.6
22.4
1,856.9 100.0
MARKOV PROCESS
This chapter reviews the use of Markov processes for projecting farm num
ber 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 80percent 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 distribu
tion of firms for a number of industries, including agriculture. 8/ These ap
plications 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 (SI, S2, ..., 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 transi
tion probabilitythe 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
Sl P11 12 PIn
S2 P21 P22 2n
P = .
Sn P1 n n2 Pnn
where: Pij = 1.0 and Pi > 0, for all i and j.
The elements of P (the P.) indicate the probability of moving from state Si to
Sj 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).
MARKOV PROCESS
This chapter reviews the use of Markov processes for projecting farm num
ber 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 80percent 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 distribu
tion of firms for a number of industries, including agriculture. 8/ These ap
plications 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 (SI, S2, ..., 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 transi
tion probabilitythe 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
Sl P11 12 PIn
S2 P21 P22 2n
P = .
Sn P1 n n2 Pnn
where: Pij = 1.0 and Pi > 0, for all i and j.
The elements of P (the P.) indicate the probability of moving from state Si to
Sj 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).
vector, and P is a stochastic matrix. The matrix, P, in combination with an ini
tial 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 num
ber 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 im
plicitly 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 assumptionthe index of prices received by farmers has remained rela
tively stable, increasing by less than 1 percent annually between 1954 and 1969.
However, a changing economic environment resulted in a nearly 80percent increase
in the prices received by farmers between 1969 and 1974, thus requiring that ex
plicit 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 decumu
lative polynomial function with both sales and farm numbers expressed in loga
rithmic values. That is:
N
FN(s) = aexp E (In 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, 8n = 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, in
stead of linear, is assumed to exist between the cumulative number of farms and
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 80percent increase in the index of prices received by farmers between
1969 and 1974 implies that $1 worth of agricultural products sold in 1974 car
.ried 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 dis
tribution in 1969 constant dollars by multiplying 0.56 by the sales value asso
ciated 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 uni
formly distributed.
Figure 6
1974 Farm Numbers in 1974 and 1969 Farm Prices
Decumulative number of farms (100,000)
20
10 H
8
F D
6 " 1974 Prices
4 1969 Prices %
1 I f I I I I I I I I I I I
.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 yaxis between points A and C, for example, is the number of farms In
the sales class of $10,000 to $19,999.
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
80percent 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 El (265,400 farms) measures the number
of farms that move to the lower sales class ($5,000 to $9,999), a difference be
tween point C (1,118,900 farms) and point H. Thus, the 80percent 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 esti
mated 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 80percent 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 attrib
uted 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 gainloss
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 80percent
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 fu
ture 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
Table 20Calculation of change in farm numbers due to price inflation and other factors, by sales, 196974
Cumulative distribu: of
tion of 1974 farm Number ofrhane 1974 farm
Farm numbers : farms : Change due to inflation due t : number
Sales retained : other without
i; in class : :factors : price
inflation
S Actual 1969 1974 Percent Percentnfatn
Change dollars dollars Gain Loss Net 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
$200,000499,999 : 12.46 39.33 26.87 18.51 48.70 7.63 30.19 5.15 25.04 77 41 1.83 14.29
$100,000199,999 : 34.97 99.38 64.41 59.51 147.71 10.81 88.20 30.19 58.01 89 86 6.40 41.37
$40,00099,999 : 168.01 327.52 159.51 237.48 456.42 89.42 218.94 88.20 130.74 67 52 28.77 196.78
$20,00039,999 : 329.79 327.57 2.22 511.54 792.72 55.12 281.18 218.94 62.24 86 66 64.46 265.33
$10,00019,999 : 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
$5,0009,999 : 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
$2,5004,999 : 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
pressed in natural logarithms.
2/ Column 8 divided by column 3.
3/ Column 9 divided by column 2.
 = Not applicable.
distributions predicted by a fifthdegree polynomial function with both sales receipts. and farm numbers ex
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 in
crease 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 con
struct and approximate the transition probability matrix. The guiding prin
ciple 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, trial
anderror 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. In 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 (59,167see
table 14) were assumed to remain in the same size category in 1974they 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 A10 is then the estimate
of farms (2,827) moving up from size class A9 to A10.
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 A10 in the process of structural change between 1969 and 1974.
Translating the consolidated farmland into the number of farms lost in the con
solidation 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) 1] x 2,827
The number of farms that remain in size class A9 is then computed as the dif
ference 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 (A10) and those in the net
exit category.
11/ The combined use of the iterative procedure and traditional farm move
ment assumptions results in a projection error of less than 1 percent.
12/ This is what is known as the 10000 transition pattern as illustrated
by Daly, Dempsey, and Cobb (5). This assumption was found to give a better fit
to actual data than other alternatives, including 404020 and 60400 patterns.
Continuing this process, we have shown that a number of farm movement ma
trix 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 trial
anderror 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 offdiagonal elements, again,
reflect the number of farms moving to the upper classes. As a result, the di
agonal elements are all positivewith 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 be
tween 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 has been de
clining 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 pro
jected 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 infla
tion. 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 infla
13/ 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, consoli
dation may actually begin from a larger, more economically viable size level,
such as 500 acres or larger.
Table 21Farm movement matrix by acreage, 196974: 10000 movement assumption
: 1974 : :
:average:
Size of farm :farm : AO : A : A2 : A3 : A4 : A : A A7 : A : A : A10
: size : ::::::
:Acres Numbers of farms
169 acres (Al) : 32 84,257 1/ 1,069,433 335
7099 acres (A2) 82 47,814 2/ 287,137 882
100139 acres (A3) :117 42,923 2/ 257,808 799
140179 acres (A4) :158 44,146 3/ 238,987 1,375
180219 acres (A5) :198 27,270 3/ 150,072 1,315
220259 acres (A6) :238 20,075 4/ 121,536 6,604
260499 acres (A) : 359 40,964 5/ 372,693 24,805
500999 acres (A8) :687 16,055 185,897 16,487
1,0001,999 acres (A9) :1,356 11,135 76,777 2,827
2,000 acres and over (A10) :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.
5/ Computed as 85.0 percent of the number of farms in 1969.
Table 22Farm movement matrix by sales class, 196974: 10000 movement assumption
Sales class : S S1 : S2 : S3 : S S S6 : S7 : S8 : S
1,000 farms
Less than $2,500 :147.21 1/ 1,266.85 3.00
$2,5004,999 : 154.33 2/ 266.17 12.30
$5,0009,999 : 50.80 3/ 336.96 23.07
$10,00019,999 : 56.05 4/ 319.62 23.85
$20,00039,999 : 30.32 241.48 57.99
$40,00099,999 : 12.12 138.79 17.10
$100,000199,999 : 4.62 24.27 6.08
$200,000499,999 : 2.16 8.21 2.03
$500,000 and over : 0 4.03
1/ 89.4 percent of the number of farms in 1969.
/ 61.5 percent of the number of farms in 1969.
3/ 82 percent of the number of farms in 1969.
/ 80 percent of the number of farms in 1969.
Table 23Farm transition matrix by size of farm, 196974: 10000 movement assumption
Size of farm : A : Al : A2 A3 : A4 : A5 A6 : A7 A : Ag : A10
Probabilities
169 acres (Al) .073 .927 .0003
7099 acres (A2) .142 .855 .003
100139 acres (A3) : .142 .855 .003
140179 acres (A4) .155 .840 .005
180219 acres (A5) .153 .840 ,007
220259 acres (A6) .135 .820 .045
260499 acres (A7) .093 ,850 .057
500999 acres (A8) .073 .851 .075
1,0001,999 acres (Ag) .123 .846 .031
2,000 acres and over (A10) 0 1.000
Table 24Farm transition matrix by sales class, 196974: 10000 movement assumption
Sales class : S S 1 S 2 : 3 S S S S S8 S9
Probabilities
Less than $2,500 (Sl) : 0.104 0.894 0.002
$2,5004,999 (S2) .357 .615 0.028
$5,0009,999 (S3) .124 .820 0.056
$10,00019,999 (S4) .140 .800 0.060
$20,00039,999 (SS) .092 .732 0.176
$40,00099,999 (S6) .072 .826 0.102
$100,000199,999 (S7) : .132 .694 0.174
$200,000499,999 (S8) .174 .662 0.164
$500,000 and over (Sg) 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
period
Percentage increase in prices
received by farmers
197485 68.2
198590 42.0
199095 34.0
19952000 27.0
These assumptions between 1974 and 1990 are based on the NationalInter
regional 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
1.86 million in 2000. The number of small farms (those
$20,000) is projected to decline from 72 percent of the
cent in 1990, and 50 percent by the turn of the century.
ber of farms having sales of over F
$100,000 is projected to increase from
the 5.2 percent in 1974 to 21 percent
in 1990, and about 33 percent in 2000 Actual and Pro
(table 26). Received by Fa
million in 1990 and
with sales of less than
total in 1974 to 56 per
By contrast, the num
jected Prices
rmers
For comparison, another set of pro
jections is shown in table 27 based on
the following low price inflation assump
tions 14/:
Projection
period
197485
198590
199095
19952000
Percentage increase
in prices
32.5
24.5
27.0
27.4
14/ Theseassumptions were obtained
from the NationalInterregional Agricul
tural Projections (NIRAP) baseline of
May 1, 1978.
800
Hig
infl
600
400
200 O L
rI
0 I I
1950 1960 1970 1980
Percentage of 1967
1990 2000
The main effect of the low price inflation assumptions is to shift the pro
jected 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 25Projected number of farms, by size of farm, Markov chain analysis
:Actual
Size of farm : 1974 :1980 : 1985 : 1990 :1995 :2000
1,000 farms
169 acres :1,069.4 991.4 919.0 851.9 789.7 732.1
7099 acres 287.5 246.1 210.7 180.4 154.5 132.4
100139 acres : 258.7 222.0 190.6 163.6 139.9 121.0
140179 acres : 239.8 202.2 170.5 143.8 121.3 102.3
180219 acres : 151.4 128.4 108.9 92.3 78.3 66.3
220259 acres 122.9 101.8 84.4 69.9 5801 48.1
260499 acres 379.3 327.9 283.3 244.6 211.1 182.0
500999 acres 210.7 200.9 189.7 177.6 165.1 152.5
1,0001,999 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 26Projected 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
$500,000and 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
Table 27Projected
number of farms by sales
low price inflation
class: Markov process,
: 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
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 op
erators 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) middleaged farmers (35 to
54 years)expansion phase; and (3) older farmers (55 and older)exit, trans
fer, or closeout 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 retire
ment 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 longterm adjustment pro
cess for farm operator number and farm size.
Age cohorts can be traced through successive agricultural censuses to de
termine the net change in the number in each age cohort by size of farm.
Figure 8
Farm Operator Age Distribution, 192074
Thousands
1920
1,400 
1,200 ,0 1940* 4
/ ...... ......
1,000_ 0 1954 *...
1,000 / .....1
600 / / .  ....
/ .*. *..
400 / 1974
/ .*** *' 
200 *
o I I I I
Under 25 2534 3544 4554 5564 65 or
Age Group over
Source: (25).
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 op
erators 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) middleaged farmers (35 to
54 years)expansion phase; and (3) older farmers (55 and older)exit, trans
fer, or closeout 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 retire
ment 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 longterm adjustment pro
cess for farm operator number and farm size.
Age cohorts can be traced through successive agricultural censuses to de
termine the net change in the number in each age cohort by size of farm.
Figure 8
Farm Operator Age Distribution, 192074
Thousands
1920
1,400 
1,200 ,0 1940* 4
/ ...... ......
1,000_ 0 1954 *...
1,000 / .....1
600 / / .  ....
/ .*. *..
400 / 1974
/ .*** *' 
200 *
o I I I I
Under 25 2534 3544 4554 5564 65 or
Age Group over
Source: (25).
Kanel found that most of the adjustments occur as the older operators leave
farms (14). Using Kanel's age cohort framework, Tolley stratified farm opera
tors 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 suc
cessive 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 in
dividual cohorts. For example, the cohort born in 191625 was disrupted by
World War II, and a new pattern seems to have emerged. Younger operators en
tered farming at previous rates, but a large number left farming after 35 years
of age10 years younger than previous age groups began to leave farming.
Figure 9
Farm Operator Age Cohort Movements, 191069
Thousands
Born 187685
1,400 188695
~1,200 /* *,18961905
1,200  ..00. '
1,000 **
190615 **.
800 / .. *
400
 193645
200
4 After 1945
Under 25 2534 3544 4554 5564 65 or over
Age Group
Source: (25).
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 agecohort 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 192029 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 peri
od. 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 non
farm 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 op
erators 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 sub
stantial entries of young operators on farms with sales of less than $2,500, but
most of these are probably parttime operations. However, the 141,500 net en
tries 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 baseperiod cohorts.
Figure 10 shows the cohort movements, number changes, and projected farm
operator numbers by age group. For example, if we trace the 192029 cohort by
10year periods starting with 1964, we find 740,000 farm operators in the 3544
year group. By 1974, 98 percent of the group remained in farming, namely
728,300 farm operators of the age of 4554 years old. This implies a cohort
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 agecohort 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 192029 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 peri
od. 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 non
farm 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 op
erators 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 sub
stantial entries of young operators on farms with sales of less than $2,500, but
most of these are probably parttime operations. However, the 141,500 net en
tries 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 baseperiod cohorts.
Figure 10 shows the cohort movements, number changes, and projected farm
operator numbers by age group. For example, if we trace the 192029 cohort by
10year periods starting with 1964, we find 740,000 farm operators in the 3544
year group. By 1974, 98 percent of the group remained in farming, namely
728,300 farm operators of the age of 4554 years old. This implies a cohort
Table 28Change in farm operator numbers by age cohort, by sales class, 196474
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
: : :
After 1949
1940 to 1949
1930 to 1939
1920 to 1929
4. 1910 to 1919
CO
1900 to 1909
Before 1900
Total
Net entry
Net exits
Replacement
:
:
:
:
:
:
:
:
:
*
:
rate *
Years
Less than 25:
25 to 34
35 to 44
45 to 54
55 to 64
65 to 74
75 or
older / :
NA
NA
NA
NA
22.8
118.7
95.5
12.6
83.3
101.7
426.8
362.2
249.6
974.0
.26
8.5
21.9
7.7
12.8
37.5
51.2
88.9
152.3
50.9
329.9
.15
10.6
30.2
10.1
13.1
50.7
7.8
63.8
154.7
50.9
290.1
.18
Farmers
9.1
30.6
1.2
27.7
53.8
62.3
37.2
140.1
40.9
321.1
.13
1/ Assumed all operators 65 years and
NA = Not applicable.
older in 1964 would have exited by 1974 or before the age of 75.
Source: U.S. Dept. of Commmerce, Bureau of the Census, Census of Agriculture;
normal farms; 1974 sales classes adjusted to 1964 prices.
adjusted for reported undercounting; excludes ab
5.4
24.8
10.3
4.8
15.8
24.3
7.0
21.4
40.5
73.3
.55
2.4
16.8
19.5
15.4
3.4
6.9
7.7
43.0
100.6
14.6
6.89
0.4
4.8
9.0
6.7
0
2.1
2.7
16.1
37.0
4.8
7.71
59.3
243.8
153.3
23.7
237.7
326.5
644.1
771.6
456.4
2,003.6
.23

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 4554 years age group in 1964 and
the 5564 years age group in 1974 (0.77) is multiplied by the number of farm op
erators of the 4554 years age group in 1974 (728,300). Therefore, 563,000 farm
operators are projected for the 5564 age group in 1984. Following the same
procedure, 366,000 farm operators of age 6574 are projected for 1994. No farm
operators in this cohort will remain in farming by the year 2004, since we as
sume 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 25year old group are calculated differ
ently. 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 as
sumed that these youngest entries were replacing their fathers and we allowed up
to a 40year 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 3544 and 4554 age group enu
merated 10 years earlier.
Table 29Change in farm operator numbers, by age cohort and farm size, 196474
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
194049 :2534 : 123.1 52.7 43.2 19.7 8.4 4.7 251.8
193039 :3544 : 89.9 25.8 14.3 16.2 8.8 55.9 160.9
192029 : 4554 : 13.4 17.5 22.1 5.3 5.6 3.6 11.7
191019 :5564 : 67.9 70.1 58.6 13.1 2.9 1.6 214.2
190009 :6574 : 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.
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 midclasses, 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 per
cent, 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 Cohort Movements, 10 Year Periods
1964 1974 1984 1994 *
2004*
Cohort Ratio
Age (Years) \ .037
ess than 25 1. 5.12
2534 350 1.46 3
3544 0.98 5
4554 942.6 77
5564 818 0.65 7
6574 644.1 5
75 or older
Total 3,556.7 2,E
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
3554 years old (see text for more detail).
o Assume all exits by age 75.
* 1984, 1994, and 2004 are projections.
Numbers in boxes are in thousands.
Current
L
Table 30Ratio 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
194049 : 2534 : 5.54 3.38 3.85 4.22 6.83 14.48 23.17 5.05
193039 :3544 : 1.69 1.19 1.19 1.02 1.27 2.29 3.56 1.14
192029 :4554 :1.04 .85 .88 .78 .94 1.45 1.70 .97
191019 :5564 : .79 .70 .67 .64 .80 1.10 1.00 .75
190009 :65 or more : .73 .59 .44 .40 .49 .65 .66 .60
1/ 1974 sales class data adjusted 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 3554 years old (see text for more detail).
Table 31Ratio of 1974 farmers to 1964 farmers, by age cohort and size of farm 1/
Cohort : Age in : : : : 1,000 : 2,000
birth : 1974 : 199 : 100219 : 220499 : 500999 : 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
194049 : 2534 : 4.99 4.52 4.89 7.83 10.74 10.20 5.12
193039 : 3544 : 1.59 1.31 1.19 1.64 1.91 2.05 1.46
192029 : 4554 : 1.04 .90 .86 1.10 1.25 1.25 .98
191019 : 5564 : .83 .71 .70 .81 .89 .91 .77
190009 : 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 3554 years old (see text for more detail).
Table 32U.S. farm operators by sales class, selected years and projections
: Less than: $2,500 : $5,000 : $10,000 : $20,000 : $40,000 : $100,000 : To
Year : $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 33U.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 : To
Year : $2,500 : $4,999 : $9,999 : $19,999 : $39,999 $99,999 or more T
1,000 farmers
1964 :1,657.3 473.9 528.6 484.1 266.9 113.5 32.4 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
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 projec
tions 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 34U.S. farm operators, by size of farm, selected years and projections
S100 220 : 500 :1,000 : 2,000
Year :199 : 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 : 1,171.2 472.7 366.4 192.0 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
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 ac
curacy 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 dis
tributions, the Markov process and age cohort analysis give very consistent pro
jections; 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 overesti
mate that for mediumsize and large farms (table 35). The projected total num
ber 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 defini
tion 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 in
creasing trend is projected. Markov process and age cohort analysis, on the
other hand, give very consistent projections.
Table 35Comparison 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
80 85 90 95 200005
Year
Figure 12
Projected Numbers of Farms
Based on Sales Distribution
Figure 11
Projected Numbers of Farms
Based on Acreage Distribution
Million farms
3.5 
3.0
2.5
2.0
*. Trend extrapolation and
Markov process
 Negative exponential
Function
..... Age cohort analysis
 V

 i I I I I i i
80 85
Year
90 95 2000 05
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 19percent 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 per
cent 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 appar
ent shift from those with low sales to those with high, partly due to the antic
ipated 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):
Million farms
4.0
3.5
3.0
2.5
2.0
1.5
1.5 1 I 1 I
1959 64 69 74
 Trend extrapolation
 Markov process
.. Negative exponential
function
....... Age cohort analysis
n. J
'I*~
I I I I I
195964
69 74
m
I I I I I i i
I
I
" Yi)A
Z (Yi Yi)2
i=1
n
E Yi2
i=1
where ^U = the Theil inequality coefficient,
Yi = projected number of farms in size class i, and
Yi = actual number of farms in size class i.
The accuracy of projections is determined primarily by comparing actual
1974 numbers with projections. To further indicate the degree of projection
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 projec
tions 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 13.2percent 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 to underes
timate the shifts in farm numbers from low to high sales as a result of the
80percent increase in prices received by farmers during the 196974 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. TheilU 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 dis
tribution, especially when acreage is used as the size measure. As we indi
cated 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 pro
jected farm numbers in 1974. The smaller the U coefficients, the better is the
projection accuracy.
Table 36Projected number of farms by acreage in 1974,
simple trend extrapolation
Actual : Projected : Percent
Size of farm 1974 :1974 : difference 1/
Number Percent
199 acres : 1,356,905 1,336,748 1.49
100219 acres : 649,923 652,620 +0.41
220499 acres 502,148 512,344 +2.03
500999 acres 210,702 214,218 +1.67
1,0001,999 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/ TheilU = 0.0144 or 1.44 percent.
Table 37Projected number of farms by sales in 1974,
simple trend extrapolation
Actual Projected Percent
Sales class 1974 1974 difference 1/
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
1/ TheilU = 0.1316 or 13.16 percent.
sales, yielding a 94percent 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 distri
bution 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 overesti
mates the numbers of farms with sales between $10,000 and $500,000 by factors
ranging from 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 inflationinan era 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 a
nalysis yielded a 10.9percent and a 16percent error according to the TheilU
coefficient (tables 42 and 43). 18/ Age cohort analysis appears to underesti
mate 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 compar
ison 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 con
structed from the 195059 period were multiplied by the agesize distributions
in 1959. For sales, a 195969 cohortratio matrix was multiplied by the 1964
agesize 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 pub
lished by the Bureau of the Census before 1959.
Table 38Projected
proportions of 1974 farm numbers by sales, class,
negative exponential function
Sales class Actual Projection Percentage difference 1/
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
$10,000$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
$100,000$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/ TheilU = 0.941 or 94.1 percent.
Table 39Projected proportions of 1974 farm numbers by size of farm,
negative exponential functions
Size of farm Actual Projection Percentage difference 1/
Percent
169 acres : 37.2 14.7 60.5
7099 acres 10.0 5.7 43.0
100139 acres : 9.0 7.0 22.2
140179 acres : 8.3 6.4 22.9
180219 acres : 5.3 5.7 7.5
220259 acres 4.3 5.3 23.3
260499 acres 13.2 23.4 77.3
500999 acres 7.3 21.7 197.3
1,0001,999 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/ TheilU = 0.681 or 68.1 percent.
Table 40Projected number of farms, by size of farm, 1974, Markov process
Size of farm Actual Projected : Percent
Difference
Number
169 acres : 1,069,433 1,027,082 3.96
7099 acres 287,472 287,137 0.12
100139 acres :258,690 265,079 2.47
140179 acres :239,786 245,530 2.40
180219 acres :151,447 155,180 2.46
220259 acres 122,851 127,105 3.38
260499 acres 379,297 392,479 3.47
500999 acres 210,702 219,227 4.04
1,0001,999 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/ TheilU = 0.0367 or 3.67 percent.
Table 41Projected 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
$2,5004,999 322.9 322.9 0
$5,0009,999 319.5 320.4 .3
$10,00019,999 :326.9 328.2 .4
$20,00039,999 327.6 322.3 1.6
$40,00099,999 327.5 322.1 1.6
$100,000199,999 :99.4 97.3 2.1
$200,000499,999 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/ TheilU = 0.0007 or 0.07 percent.
Table 42Projected 1969 farm numbers, by size of farm, agecohort analysis 1/
Size of farm Actual : Projected Percent
: difference
N umberPercent
Less than 10 acres 162,111 120,221 25.8
1049 acres : 473,465 407,655 13.9
5069 acres 177,028 140,847 20.4
7099 acres 282,914 231,065 18.3
100139 acres : 278,752 240,448 13.7
140179 acres : 263,012 244,752 6.9
180219 acres : 165,209 164,682 3.2
220259 acres 141,733 149,074 5.2
260499 acres 419,421 419,189 .1
500999 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 underenumeration; TheilU is 0.1087 or 10.9 per
cent.
Table 43Projected 1974 farm numbers by sales class, agecohort analysis 1/
Sales Class Actual : Projected : Percent
: : difference
N umberPercent
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
Not adjusted for
accuracy for the fa
error of projectic
adjusted to take i
census underenumeration; the TheilU is 0.16 or 16 percent.
rm operator age distribution was very good, only 2.1 per
>n was computed. Projections presented in this table have
nto account the effects of price inflation.
1/
The
cent
been
CONCLUSIONS AND IMPLICATIONS
The techniques employed in this study used several kinds of data and as
sumptions in projecting farm numbers and size distributions. The specific pro
jections are, therefore, contingent upon the techniques, assumptions, and data
employed. The different techniques are not necessarily equally valid for ex
amining the same questions. The results, however, provide different perspec
tives 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 com
mits a large projection error in sales distribution. Unlike the continuous
trends for the acreage distribution, some of the trends for the sales distribu
tion 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 in
creasing trend for the number of such farms.
Table 44Alternative projections of farm numbers, by size of farm, 2000
:Negative
Size of farm 1974 : Trend : exponential : Markov Age
:Actual : extrapolation : functions :process : cohort
1,000 farms
199 acres : 1,356 751 320 864 934
100139 acres : 259 113 121
140179 acres : 240 300 104 102 301
180219 acres : 151 96 66
220259 acres 123 286 89 48 220
260499 acres 379 712 182
500999 acres 211 205 430 152 164
1,0001,999 acres 93 108 224 91 97
2,000 acres and over: 62 61 37 77 56
All farms : 2,875 1,711 1,826 1,705 1,772
Projected total numbers of farms and those for the mediumsize 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 sig
nificantly 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 ap
plied to sales distributions are expected, but projections by acreage distribu
tion 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 proce
dures. 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 45Alternative 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
$2,5004,999 323 111 13 72 119
$5,0009,999 319 90 29 108 100
$10,00019,999 327 164 53 108 100
$20,00039,999 328 443 102 88 100
$40,00099,999 328 539 271 262 190
$100,000199,999 : 99 188 354 168
$200,000499,999 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
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 tech
niques 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 multi
plying 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 ex
ception 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, how
ever, requires more detailed structural data on a longitudinal basisthat 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 commod
ity subsectorseach 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.
LITERATURE CITED
(1) Boxley, Robert F., "Farm Size and the Distribution of Farm Numbers," Agri
cultural Economics Research, Vol. 23, No. 4, Oct. 1971.
(2) Chennareddy, Venkareddy, and Glen L. Johnson, "Projections of Age Distri
bution 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 Func
tions 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 O. Heady, Ames, Iowa State University Press,
1972, pp. 314332.
(6) Dixon, B. L., and S. T. Sonka, "A Note on the Use of Exponential Func
tions 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 Expo
nential Functions," Land Economics, Vol. 49, No. 2, May 1973.
(8) "Income and Wealth Distributions: The Exponential Func
tions," AE4212, Dept. of Agr. Econ., Univ. of Illinois, June 1969.
(9) "Farm Size Data: Frequency Distribution, Interpolation,
and Projection," AERR50, 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 Sug
gested Uses in Agricultural Economics, Dept. of Agr. Econ., AERR49,
Univ. of Illinois, Dec. 1961.
(13) Kaldor, Donald R., and William M. Edwards, Occupational Adjustment of
Iowa Farm Operators who Quit Farming in 19591961, 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,
19501959," Journal of Farm Economics, Vol. 45, No. 1, Feb. 1963.
(15) Klein, L. R., An Introduction to Econometrics, PrenticeHall, 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 Agricul
ture 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, AIB435,
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: NorthHolland
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, SB609, July 1978.
(24) U.S. Department of Agriculture, Economics, Statistics, and Cooperatives
Service, Status of the Family Farm: Second Annual Report to the
Congress, AER434, 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.
Appendix table
: $100,000
Item :Unit : and over
: : (lass IA)
Number of farms:
1969 : 1,000 : 52.0
: Percent : 1.9
1974 : 1,000 : 152.6
: Percent : 6.2
Cash receipts:
1969 :Bil. dol.: 15.3
:Percent : 33.6
1974 :Bil. dol.: 43.7
:Percent : 53.7
Cash receipts per:
farm:
1969 : Dols. : 293,915
1974 : Dols. : 286,268
Form of organiza:
tion:
Sole proprie
torships:
1969 : Farms : 30,683
: Percent : 59.0
1974 : Farms : 108,463
: Percent : 71.1
Partnerships:
1969 : Farms : 13,049
:Percent : 25.1
1974 : Farms : 27,811
:Percent : 18.2
See footnotes at end of table.
1Selected structural characteristics of U.S. farms, by sales class
: $40,000 to : $20,000 to : $10,000 to : $5,000 to : $2,500 to : Less than
: $99,999 : $39,999 : $19,999 : $9,999 : $4,999 : $2,500 : All
: (class IB) : (class II) : (class III) : (class IV) : (class V) : (class VI) : Farms
169.7
6.2
324.3
13.2
10.1
22.2
20.1
24.7
59,364
61,890
131,418
77.4
280,824
86.6
33,104
19.5
37,107
11.4
331.0
12.1
321.8
13.1
9.3
20.4
9.2
11.3
27,999
28,737
277,233
83.8
290,596
90.3
49,236
14.9
27,671
8.6
395.5
14.5
310.0
12.6
5.7
12.5
4.5
5.5
14,396
14,387
341,063
86.1
284,521
91.8
49,990
12.6
22,801
7.4
390.4
14.3
296.0
12.0
2.8
6.2
2.1
2.6
7,208
7,215
344,063
88.1
277,272
93.6
41,878
10.7
17,180
5.8
395.1
14.5
290.0
11.8
1.3
2.9
.98
1.2
2,626
3,640
356,105
90.1
275,897
95.1
34,278
8.7
12,399
4.3
994.5
36.5
768.8
31.2
.98
2.2
.74
.9
953
1,143
896,005
90.1
731,165 1/
95.1
86,518
8.7
33,060 1/
4.3
Continue
2,728.1
100
2,463.9
100
45.48
100
888.32
100
16,689
25,234
2,376,570
87.1
2,248,738
91.3
308,053
11.3
178,029
7.2
d 
Appendix table 1Selected structural characteristics of U.S. farms, by sales classContinued
Item : Unit :
Corporations:
1969 : Farms
:Percent
1974 : Farms
:Percent
Other:
1969 : Farms
:Percent
1974 : Farms
:Percent
Land farmed by:
Sole proprietor:
a ships:
1969 :Mil. acre:
:Percent :
Partnerships:
1969
1974
Corporations:
1969
1974
:Mil. acre:
:Percent
:Mil. acre:
: Percent :
$100,000 : $40,000 to : $20,000 to : $10,000 to : $5,000 to : $2,500 to : Less than :
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
8,049
15.5
15,787
10.3
214
.4
538
.4
69.27
40.3
147.52
53.3
44.04
25.6
:Mil. acre: 56.45
: Percent : 20.4
:Mil. acre:
:Percent
:Mil. acre:
: Percent
55.94
32.6
69.73
25.2
4,306
2.5
5,630
1.7
867
.5
749
.2
127.12
68.6
193.08
78.3
41.12
62.2
34.18
13.9
15.49
8.4
18.10
7.3
2,847
0.8
2,768
.9
1,673
.5
736
.2
166.63
80.4
138.65
86.2
35.08
16.9
16.52
10.3
4.15
2.0
4.83
3.0
2,262
0.6
1,988
.6
2,157
.6
701
.2
144.24
84.3
90.73
88.6
23.33
13.6
9.17
9.0
2.57
1.5
2.10
2.0
1,984
0.5
1,335
.4
2,500
.7
586
.2
92.43
86.5
59.80
91.0
12.23
11.4
4.77
7.3
1.15
1.1
0.88
1.3
2,062
0.5
1,148
.4
2,659
.7
539
.2
66.01
87.0
48.31
90.6
7.59
10.0
3.38
6.4
1.55
2.0
See footnotes at end of table.
4,972
0.5
2,648
1.0
3,075 1/ 31,731
.4 1.3
6,961
.7
17,031
.8
1,538 1/ 5,387
.2 .2
125.85 1/ 791.55
87.0 74.5
109.06 1/ 787.15
90.6 76.7
14.47 1/ 177.86
10.0 16.7
7.70 1/ 132.17
6.4 12.9
2.89 l/ 83.74
2.0 7.9
2.53 1/ 99.3
2.1 9.7
Continued
Appendix table 1Selected structural characteristics of U.S. farms, by sales classContinued
:$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 1Selected structural characteristics of U.S. farms, by sales classContinued
: $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
Offfarm income
per farm: 1/
1969 : ols. : 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 govern
ment farm pro
grams 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:
S 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 1Selected structural characteristics of U.S. farms, by sales classContinued
: $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 : Al
:(class IA) : (class IB) : (class II) : (class III): (class IV) : (class V) :(class VI) farms
Tenure of farm
operators1969
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
operators1974
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, offfarm 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
secondround estimates of missed farms are computed by assuming that the dis
crepancy between the two estimates can be eliminated in proportion to the first
round 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 underenu
meration and excluding normal farms.
Appendix table 2Adjustment process for underenumeration of the 1974 Census of Agriculture data by sales class
S: Firstround : Firstround : : Secondround :Adjusted
Sales : Number of :Farms included : adjustment of : estimate of :Total missed :estimates of :number of
class : farms / : in census : number of : missed farms : farms :missed farms : farms 5/
Sfarms 3/ 4/
(1) : (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
$2,5004,999 289,983 88.6 327,295 37,312 8.02 32,966 322,949
$5,0009,999 296,373 91.9 322,495 26,122 5.62 23,101 319,474
$10,00019,999 : 310,011 94.2 329,099 19,088 4.11 16,894 326,905
$20,00039,999 321,771 98.0 328,338 6,567 1.41 5,796 327,567
$40,00099,999 324,310 98.9 327,917 3,607 0.78 3,206 327,516
$100,000199,999 : 101,153 102.0 99,170 1,983 0.43 1,768 99,385
$200,000499,999 : 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 3Adjustment process for underenumeration of the 1974 Census of Agriculture data, by farm size
N r Farms Firstround : Firstround Total : Secondround : : Number of :Adjusted number
Number Farmof included adjustment estimates missed : estimates of nu adjusted of farms, ex
Farm size of included of number : of missed ssed missed farms : mr abnormal : cluding abnor
farms sz in census n m farms farms 5/
: of farms 2/ : farms 3/ : 4/ : farms 6/: mal farms
(1) (2) (3) (4) (5) (6) (7) : (8) : (9) : (10)
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
100139 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 : 118,346 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.
3/ Column 5 is computed by subtracting column 2 from column 4.
4/ Column 7 is computed by multiplying column 6 by 411,500; the
(27466,123/0.857) 2,466,123.
5/ Column 8 is computed by adding column 7 to column 2.
~/ Number of abnormal farms divided by its inclusion factor, 0.8
overall missed farms is obtained as follows: 411,500 =
APPENDIX B
Estimated Simple Trend Equations by Size Class
Appendix table 4Estimated simple trend equations by average size: 1959, 1964,
1969, 1974 1/
Size of farm : Estimated trend equations R2
199 acres In FN1 = 7.658 0.115T 0.969
(192.57) (7.94)
100219 acres : In FN2 = 7.101 0.155T 0.9997
(1489.62) (59.27)
220499 acres : In FN3 = 6.707 0.117T 0.971
(171.27) (8.16)
500999 acres In FN4 = 5.402 0.0087T 0.159
(140.02) (0.62)
1,0001,999 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.
APPENDIX B
Estimated Simple Trend Equations by Size Class
Appendix table 4Estimated simple trend equations by average size: 1959, 1964,
1969, 1974 1/
Size of farm : Estimated trend equations R2
199 acres In FN1 = 7.658 0.115T 0.969
(192.57) (7.94)
100219 acres : In FN2 = 7.101 0.155T 0.9997
(1489.62) (59.27)
220499 acres : In FN3 = 6.707 0.117T 0.971
(171.27) (8.16)
500999 acres In FN4 = 5.402 0.0087T 0.159
(140.02) (0.62)
1,0001,999 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.
Appendix table 5Estimated
Sales class
Less than $2,500
$2,500$4,999
$5,000$9,999
$10,000$19,999
$20,000$39,999
$40,000$99,999
$100,000$199,999
$200,000499,999
$500,000 and over
1/ The time variable (T) i
of determine. Figures in par
simple trend equations by sales class:
1969, 1974 1/
Estimated trend equations
In FN1 = 7.752 0.179T
(146.09) (9.23)
In FN2 = 6.663 0.217T
(81.40) (7.26)
In FN3 = 6.779 0.253T
(2537.51) (259.83)
In FN4 = 6.405 0.145T
(78.54) (4.86)
In FN5 = 5.381 + 0.325In T
(111.22) (6.38)
In FN6 = 4.312 + 0.905In T
(17.71) (3.54)
In:FN7 = 2.483 + 1.254In T
(6.52) .(3,13)
In FN8 = 1.358 + 1.382In T
(3.43) (3.32)
In FN9 = 0.079 + 1.404In T
(0.260) (4.574)
s: 1959 = 1, 1964 = 2, etc; R2 is the
entheses are t ratios.
1959, 1964,
0.977
0.964
1.000
0.922
0.953
0.862
0.830
0.846
0.913
coefficient
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 ad
justments 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 estab
lish the numbers in each cell. The estimated number (E) was determined by the
formula, Eij = Ni.N /N 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 poly
nomial. 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 pro
jected totals for each age group (see appendix table 7 for adjustment factors).
Appendix table 6Adjustments to census data and projects for acres and sales,
1964 and 1974
:Acres Sales
Item : : : Projec: : : Projec
:1964 : 1974 : tions :1964 : 1974 : tions
1. Estimated missed farms : 1/ x 1/ x
2. Estimated agesize matrix
for missed farms x x
3. Estimated agesize for abnor
mal 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
operator agedistributed 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 co
hort 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.
Appendix table 7Ratios of adjustment used for acre and sale projection by age
SAcres Sales
Age
:1984 : 1994 2004 1984 1994 : 2004
Ratios
Less than 25 0.999 0.991 0.993 1.028 1.050 1.040
2534 .983 .967 .958 .861 .861 .790
3544 .984 .979 .963 .915 .915 .845
4554 .987 .977 .980 .931 .931 .890
5564 .991 .980 .972 .943 .943 .919
65 and older .999 .991 .975 .978 .984 .952
*U.S. GOVERiOMET PRINTING OFFICE t 1980 0310945/ESCS218
