Document ID: EPA-HQ-OAR-2003-0012-0999
Agency: epa
Document Type: Supporting & Related Material
Title: 
Posted Date: 2004-04-23T04:00Z

1
Draft
Regulatory
Impact
Analysis,
EPA420­
R­
03­
008,
April
2003.
See
www.
epa.
gov/
nonroad/.

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2004
MEMORANDUM
SUBJECT:
Population
Growth
Projections
for
Nonroad
Diesel
Equipment
FROM:
NONROAD
Emissions
Modeling
Team
Assessment
and
Standards
Division,
Office
of
Transportation
and
Air
Quality
TO:
Environmental
Protection
Agency
(
EPA),
Air
Docket
A­
2001­
28;
E­
DOCKET
OAR­
2003­
0012
DATE:
April
23,
2004
1.
Background
EPA
presented
diesel
fuel
consumption
projections
in
Chapter
3
(
Table
3.1­
8)
of
the
Draft
Regulatory
Impact
Analysis
(
DRIA)
associated
with
the
proposed
rule
"
Control
of
Emissions
of
Air
Pollution
From
Nonroad
Diesel
Engines
and
Fuel,"
(
68
FR
28327,
May
23,
2003).
1
These
fuel
consumption
projections
were
also
implicit
in
the
pollutant
benefits
projected,
in
that
nonroad
diesel
equipment
only
emit
exhaust
pollutants
during
operation.
More
or
less
fuel
consumption
inherently
means
more
or
less
emissions,
other
factors
being
equal.

During
the
public
comment
process
for
the
proposed
rule,
several
commenters
raised
questions
concerning
the
equipment
population
growth
projections
used
in
EPA's
inventory
modeling,
which
are
higher
than
broadly
analogous
diesel
fuel
consumption
projections
published
by
the
Energy
Information
Administration
(
EIA).
To
address
these
comments
EPA
investigated
many
of
the
important
parameters
upon
which
the
growth
estimates
in
Draft
NONROAD2004
were
based.

This
memo
describes
the
key
analyses
designed
to
investigate
the
EPA
growth
estimates,
particularly
the
relationships
among
equipment
sales,
expected
equipment
life,
scrappage,
and
equipment
populations.
In
the
end,
on
the
basis
of
methods
and
assumptions
similar
to
those
used
in
the
NONROAD
model,
we
were
unable
to
reasonably
reconcile
the
relatively
high
growth
in
equipment
populations
and
work
output
projected
in
our
analyses
with
EIA's
growth
projections
for
diesel
fuel
consumption.
Thus,
the
draft
NONROAD2004
model
has
retained
its
current
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2
equipment
population
growth
projections.
However,
for
purposes
of
the
final
rule,
the
Final
Regulatory
Impact
Analysis
includes
a
sensitivity
analysis
in
which
fuel
consumption
and
emissions
projections
from
Draft
NONROAD2004
are
adjusted
to
match
corresponding
fuel
consumption
projections
derived
from
EIA
sources.
This
analysis
will
allow
an
assessment
of
the
appropriateness
of
the
new
standards
under
the
assumption
that
the
EIA­
based
projections
were
correct.

These
analyses
covered
the
four
largest
diesel
equipment
segments
in
the
NONROAD
model,
which
would
account
for
the
bulk
of
nonroad
diesel
fuel
use.
These
four
segments
are:
agricultural
(
e.
g.,
farm
tractors,
combines,
etc.),
construction
(
e.
g.,
earth­
moving
equipment),
commercial
(
e.
g.,
generator
sets,
pumps,
etc.),
and
industrial
(
e.
g.,
mobile
refrigeration,
forklifts,
sweepers,
etc.).

2.
Sales
Growth
Projection
Methods
The
Data.
These
analyses
were
performed
using
diesel
equipment
sales
histories
obtained
from
the
commercially
available
OELink
 
database,
produced
by
Power
Systems
Research/
Compass
International,
Inc.,
(
PSR).
The
database
contains
estimates
of
annual
sales
for
a
wide
variety
of
equipment
types
produced
and
sold
into
the
U.
S.
market,
over
a
27­
year
period
(
1973­
2000).
Before
examination
and
analysis
of
trends,
we
summed
the
data
by
equipment
type
and
size
class,
where
engine
size
is
defined
in
terms
of
rated
horsepower.
Sixteen
of
the
18
engine
size
classes
used
in
NONROAD
and
relevant
to
this
analysis
are
presented
in
Table
1.

Approach.
Because
the
NONROAD
model
projects
growth
in
equipment
populations,
and
because
the
available
data
represent
historical
equipment
sales,
we
elected
to
estimate
population
growth
from
sales
growth
by
means
of
a
sales
and
scrappage
model.
The
first
step
in
this
process
was
to
derive
sales
growth
rates
from
historical
sales
trends,
for
specific
combinations
of
equipment
type
and
size
class.
The
approach
employed
was
to
fit
trends
to
time
series
representing
equipment
sales
histories,
and
to
extrapolate
the
derived
trends
over
the
forecast
horizon
of
the
NONROAD
model
(
2000­
2050).

The
Analysis.
To
derive
sales
growth
rates,
the
following
steps
were
performed:

­
The
time
series
for
each
equipment
type
and
size
class
was
plotted
and
examined.

­
Decisions
were
made
concerning
the
approach
to
curve
fitting.
­
Within
some
agricultural
equipment
types,
size
classes
were
combined
to
increase
sample
sizes.
­
For
each
of
the
other
three
equipment
categories
all
equipment
types
of
that
category
were
combined
by
size
class.
­
Visual
evaluation
also
governed
the
selection
of
the
form
of
the
trend
to
be
fit.

­
A
trend
was
fit,
with
the
optimal
fit
determined
by
minimization
of
least­
squares.
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Trend
Forms.
The
trends
fit
to
the
data
were
selected
to
follow
linear,
exponential
or
logistic
forms.
Visual
examples
of
these
trends
are
shown
in
Figure
1.
The
form
for
the
linear
fit
is
where
y
t
is
the
projected
sales
growth
in
year
t,
and
c
and
m
are
the
intercept
and
slope
coefficients,
respectively.
When
expressed
in
percentage
terms
relative
to
each
prior
year's
population,
the
resulting
annual
growth
rate
declines
gradually
over
time.

The
form
for
the
exponential
fit
is
Unlike
the
linear
trend,
the
percentage
growth
rate
in
each
year
relative
to
the
preceding
year
for
the
exponential
trend
remains
constant
over
time,
but
relative
to
a
single
year
the
percentage
growth
increases
over
time
for
a
positive
trend
or
decreases
for
a
negative
trend.
For
declining
sales
trends,
the
exponential
trend
has
the
advantage
that
the
predicted
sales
can
never
go
negative.

As
a
third
alternative,
logistic
trends
were
fit
to
six
time
series
(
four
agricultural
and
two
construction)
showing
rapid
growth
during
the
last
one
third
to
one
half
of
the
sales
history.
This
approach
is
consistent
with
approaches
currently
used
to
model
phenomena
such
as
the
introduction
of
new
products
to
market.
The
logistic
function
is
described
using
three
to
four
parameters,
as
where
K,
A
and
L
are
empirically
derived
coefficients
and
 
is
an
exponential
growth
rate,
also
empirically
derived.
The
logistic
function
describes
a
characteristic
sigmoid
or
"
s­
shaped"
curve,
in
which
projected
sales
follow
exponential
growth
patterns
between
the
lower
bound
L
and
the
upper
bound
K.
y
c
mt
t
=
+
(
1)

log
(
)
y
c
mt
y
t
t
c
mt
=
+
=
+
or
10
(
2)

y
K
Ae
L
t
t
=
+
+
 
1
 
(
3)
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Example
Trend
Fits
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
Year
Relative
Sales
per
Year
Linear
Exponential
Logistic
Figure
1.
General
examples
of
linear,
negative
exponential
and
logistic
trends.

2.1
Agricultural
Equipment
Sales
Projection
Methods
An
initial
analysis
focused
on
equipment
types
that
the
NONROAD
model
classifies
as
"
agricultural
engines,"
since
these
engines
constitute
a
substantial
portion
of
the
nonroad
diesel
equipment
population,
fuel
consumption,
and
thus
emissions.
Selected
equipment
types
in
this
category
are
listed
in
Table
2.
The
sales
growth
analysis
for
agricultural
equipment
was
performed
under
contract
by
Research
Triangle
Institute
(
RTI).
The
analysis
is
further
described
in
a
memo
drafted
by
RTI
to
summarize
their
work,
which
is
appended
to
this
document
as
Appendix
A.

Within
each
agricultural
equipment
type,
engines
were
further
classified
by
size,
as
presented
above
(
Table
1).
However,
during
the
analysis,
specific
size
classes
used
for
each
equipment
type
were
aggregated
as
necessary
to
provide
adequate
sample
sizes
for
each
time
series.

Truncation
of
Time
Series.
Prior
to
curve­
fitting,
some
time
series
were
truncated
to
remove
the
effects
of
a
serious
macroeconomic
shock
in
the
equipment
market.
Specifically,
the
1970s
boom
in
grain
sales
to
the
Soviet
Union
attracted
many
new
entrants
into
farm
operations.
Subsequently,
the
embargo
imposed
on
grain
sales
to
the
Soviet
Union
in
1980
led
to
a
crash
in
new
equipment
sales
over
the
ensuing
six
to
10
years.
However,
the
presence
of
such
an
event
in
the
time
series
could
not
be
considered
typical,
and
would
have
an
undue
influence
on
a
time
series
intended
for
projection
over
several
decades.
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Linear
fits
were
used
for
three
agricultural
time
series
that
showed
steady
growth
over
the
sales
history.
Exponential
trends
were
fit
to
two
time
series
showing
very
slow
growth
and
14
series
showing
sales
declines.
Logistic
trends
were
fit
to
four
time
series
showing
rapid
growth
during
the
last
one
third
to
one
half
of
the
sales
history.
Table
3
below
lists
which
trend
forms
applied
to
specific
equipment­
types/
size­
class
combinations.
The
specific
time
period
used
to
derive
each
trend
is
also
indicated.

Using
the
sales
trend
fits
described
above,
absolute
sales
were
projected
into
the
future
for
each
size
class
in
each
of
the
seven
agricultural
equipment
types
examined.
Because
these
sales
projections
were
derived
using
variable
size
classes
(
Table
3),
they
could
not
be
used
directly
to
project
sales
for
NONROAD
size
classes
within
equipment
types,
unless
the
size
class
used
for
trend
fitting
exactly
matched
that
used
for
projection.
For
example,
regression
coefficients
derived
for
50­
75
hp
tractors
can
be
applied
directly
to
project
sales
for
this
size
class.
However,
the
coefficients
derived
for
175+
hp
tractors
cannot
be
used
directly
to
project
sales
for
300­
600
hp
tractors
without
erroneous
results.
Therefore,
to
adapt
the
broad­
level
sales
projections
to
narrower
size
classes
within
individual
equipment
types,
the
projections
were
converted
from
absolute
sales
to
"
relative
sales."
In
the
case
of
linear
trend
fits,
absolute
sales
were
expressed
as
a
single
annual
percentage
increase
relative
to
the
1996
sales
data
point
(
g
linPct),
as
in
equation
(
4)
below,

where
m,
c
and
S
1996
are
the
regression
slope
term
(
engines/
year),
intercept
(
engines)
and
projected
sales
in
1996
for
a
given
combination
of
equipment
type
and
size
class
(
e.
g.,
tractors,
50­
75
hp),
respectively.
Averaging
annual
sales
over
a
specific
time
period
and
using
the
year
1996
as
a
fixed
reference
point
express
the
linear
growth
in
relative
terms
as
a
constant
value
over
the
projection
period.

In
the
case
of
exponential
fits,
the
resulting
percentage
growth
rate
was
applied
directly
in
all
years,
since
a
constant
growth
rate
in
percentage
terms
is
a
defining
characteristic
of
an
exponential
trend.

In
the
case
of
logistic
fits,
the
absolute
sales
projections
were
expressed
as
fractional
changes
in
each
year
relative
to
the
preceding
year
(
g
log%,
y),
starting
with
the
year
1996,

where
S
y
and
S
y­
1
are
projected
sales
in
years
y
and
y­
1,
respectively.
g
m
S
m
c
m
linPct=
=
+
1996
1996
(
4)

g
S
S
S
y
y
y
y
log%,
=
 








 
 

 
1
1
100
(
5)
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2.2
Construction,
Commercial,
and
Industrial
Equipment
Sales
Projection
Methods
Subsequent
analyses
focused
on
equipment
types
classified
by
NONROAD
as
belonging
to
"
construction,"
"
industrial,"
and
"
commercial"
segments.
As
with
agricultural
engines,
we
fit
trends
to
sales
histories.
The
treatment
of
engines
in
these
three
segments
differs
with
respect
to
the
level
of
detail.
Before
examining
sales
trends,
we
summed
sales
for
all
equipment
types
in
each
segment
(
construction
equipment,
etc.)
by
NONROAD
size
classes,
rather
than
for
individual
size
classes
within
equipment
types.
All
the
trend
fits
were
linear,
except
for
two
size
classes
for
construction
engines
(
75­
100
hp,
100­
175
hp).
Due
to
the
strong
growth
seen
in
these
classes
during
the
1990'
s,
we
projected
sales
growth
using
logistic,
rather
than
linear
fits.
For
most
trends
modeled,
the
entire
sales
history
from
1973
to
2000
was
modeled,
except
for
commercial
equipment,
for
which
we
modeled
the
period
1973­
1997.
For
commercial
engines,
we
omitted
sales
during
1998­
2000,
which
showed
a
sharp
spike
in
sales
of
small
generators,
apparently
due
to
concerns
related
to
Y2K.
The
forms
of
the
equations
are
the
same
as
those
used
for
agricultural
engines,
as
described
above.

Using
the
sales
trend
fits
described
above,
absolute
sales
were
projected
into
the
future
for
each
size
class
in
each
of
the
three
industry
segments
examined
(
construction,
industrial,
commercial).
Because
these
sales
projections
were
for
broad
groupings
including
multiple
equipment
types,
they
could
not
be
used
directly
to
project
sales
for
individual
equipment
types
or
size
classes
within
equipment
types.
For
example,
if
the
slope
coefficient
for
16­
25
hp
construction
equipment
were
10,000
engines
per
year,
this
value
could
not
be
directly
applied
to
16­
25
hp
trenchers
(
which
have
a
total
population
of
several
hundred),
without
erroneous
results.
Therefore,
to
adapt
the
broad
segment­
level
sales
projections
to
individual
equipment
types,
the
projections
were
converted
from
absolute
sales
to
"
relative
sales."
In
the
case
of
linear
trend
fits,
absolute
sales
were
expressed
as
a
single
annual
percentage
increase
relative
to
the
2000
sales
data
point
(
or
1997
for
commercial
equipment)
(
g
linPct),
as
in
equation
(
4)
above.

In
the
cases
of
the
two
size
classes
of
construction
engines
for
which
logistic
fits
were
used,
different
relative
growths
were
needed
for
each
future
year.
Thus,
for
these
trends,
the
absolute
sales
projections
for
each
year
were
converted
to
ratios
to
the
year
1996
sales
data
point
(
r
log,
y).

These
relative
growth
values
(
linear
or
logistic)
by
industry
segment
and
power
size
class
were
then
applied
to
each
specific
equipment
type
within
the
corresponding
segment
and
size
class
to
generate
projected
sales
for
each
equipment
type
and
size
class.
Section
3.2
below
details
the
trends
applied
to
each
equipment
type.
r
S
S
y
y
log,
=
1996
(
6)
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Table
1
Diesel
Equipment
Size
Classes
Represented
in
the
Draft
NONROAD2004
Model
(
rated
horsepower)

3
<
hp

6
6
<
hp

11
11
<
hp

16
16
<
hp

25
25
<
hp

40
40
<
hp

50
50
<
hp

75
75
<
hp

100
100
<
hp

175
175
<
hp

300
300
<
hp

600
600
<
hp

750
750
<
hp
<=
1000
1000
<
hp
<=
1500
1500
<
hp
<=
2000
2000
<
hp
<=
3000
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Table
2
Important
Agricultural
Equipment
Types
Represented
in
the
NONROAD
Model
Agricultural
Tractors
Balers
Combines
Irrigation
Sets
Sprayers
Windrowers
Other
Agricultural
Equipment
3.
Sales
Growth
Trend
Fit
Results
Results
of
sales
trend
fitting
are
presented
below,
first
for
agricultural
equipment
and
then
for
the
other
three
equipment
segments
considered
in
this
analysis.

3.1
Agricultural
Equipment
Sales
Trend
Projections
For
each
combination
of
equipment
type
and
size
class,
Table
3
shows
the
time
period
modeled
and
the
type
of
fit.
Tables
4­
6
show
the
trend
fit
coefficients
and
the
corresponding
growth
rates.

3.2
Construction,
Commercial,
Industrial
Equipment
Sales
Trend
Fit
Results
Tables
7­
9
present
linear
regression
coefficients
and
equivalent
annual
percentage
sales
growth
rates
by
NONROAD
size
class
for
construction,
industrial
and
commercial
engines,
respectively.
Table
10
presents
parameters
for
the
two
size
classes
of
construction
engines
for
which
sales
were
projected
using
logistic
trends.
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Table
3
Agricultural
Equipment
Sales
Trend
Types
Application
Engine
Size
Class
(
rated
hp)
Time
Period
Type
of
Fit
Agricultural
Tractors
11­
25
1980­
2000
Logistic
Agricultural
Tractors
25­
50
1973­
2000
Logistic
Agricultural
Tractors
51­
75
1973­
2000
Exponential
Agricultural
Tractors
75­
100
1973­
2000
Exponential
Agricultural
Tractors
100­
175
1982­
2000
Linear
Agricultural
Tractors
175
+
1982­
2000
Linear
Combines
75­
100
1973­
2000
None
Combines
100­
175
1982­
2000
Exponential
Combines
175
+
1982­
2000
Linear
Windrowers
all
1977­
2000
Exponential
Bakers
all
1982­
2000
Exponential
Sprayers
11­
100
1977­
2000
Exponential
Sprayers
100
+
1973­
2000
Logistic
Irrigation
Sets
11­
25
1973­
2000
Exponential
Irrigation
Sets
25­
50
1973­
2000
Exponential
Irrigation
Sets
50­
75
1973­
2000
Exponential
Irrigation
Sets
75­
100
1973­
2000
Exponential
Irrigation
Sets
100­
175
1973­
2000
Exponential
Irrigation
Sets
175
+
1973­
2000
Exponential
Other
Ag
Equipment
11­
50
1973­
2000
Exponential
Other
Ag
Equipment
50­
75
1973­
2000
Exponential
Other
Ag
Equipment
75­
100
1977­
2000
Exponential
Other
Ag
Equipment
100­
175
1989­
2000
Exponential
Other
Ag
Equipment
175­
300
1989­
2000
Exponential
Other
Ag
Equipment
300
+
1989­
2000
Logistic
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Table
4
Fit
Parameters
and
Annual
Growth
Rates
for
Agricultural
Equipment
with
Linear
Sales
Trends1
Application
Size
Class
(
rated
hp)
intercept
(
c
)
slope
(
m)
Linear
Sales
Growth
Rate
(%
)
2
Agricultural
Tractors
100­
175
­
1,433,278
727.82
3.74%

Agricultural
Tractors
175
+
­
1,726,573
877.7807
3.45%

Combines
175
+
­
176,357
91.3632
0.03%

1
See
Equation
1.
Time
t
is
entered
into
the
linear
equation
as
calendar
year,
e.
g.,
"
2010."
2
Calculated
in
relative
terms
as
the
constant
linear
rate
relative
to
1996­
year
sales
,
i.
e.,
glinPct(
See
Equation
4).

Table
5
Fit
Parameters
and
Annual
Growth
Rates
for
Agricultural
Equipment
with
Logistic
Sales
Trends1
Application
Size
Class
(
rated
hp)
Upper
bound
(
K)
Linear
coefficient
(
A)
Growth
Rate
(
 )
Lower
Bound
(
L)
Annual
Sales
Growth
Rate
(%

2001­
10
2011­
20
2021­
30
2031
Agricultural
Tractors
11­
25
68,000
200
0.1337
0
8.01%
4.22%
1.56%
0.4
Agricultural
Tractors
25­
50
75,000
9
0.0900
0
2.37%
1.17%
0.52%
0.2
Sprayers
100
+
4,310
7,000
0.4190
90
0.89%
0.03%
0.00%
0.0
Other
Ag
Equipment
300
+
560
27
0.612
0
0.31%
0.00%
0.00%
0.0
1
See
Equation
3.
Time
t
is
entered
into
the
logistic
equation
as
(
t
­
1970),
i.
e.,
"
1970"
is
treated
as
t=
0.
2
Calculated
as
fraction
change
from
year
to
year
(
glog%,
y),
as
in
Equation
(
5).
Values
presented
are
averages
for
the
periods
indicate
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Table
6
Fit
Parameters
and
Annual
Growth
Rates
for
Agricultural
Equipment
with
Exponential
Sales
Trends1
Application
Size
Class
(
rated
hp)
intercept
(
c
)
slope
(
m)
Annual
Sales
Growth
Rate
(%/
year)

Agricultural
Tractors
50­
75
7.9087
­
0.001921
­
0.44%

Agricultural
Tractors
75­
100
29.0167
­
0.01255
­
2.9%

Combines
100­
175
129.2412
­
0.06327
­
14%

Windrowers
all
22.5105
­
0.009609
­
2.2%

Balers
all
­
2.7593
0.002562
0.59%

Sprayers
10­
100
9.7729
­
0.00367
0.84%

Irrigation
Sets
11­
25
49.67554
­
0.02415
­
5.4%

Irrigation
Sets
25­
50
99.9526
­
0.04919
­
11%

Irrigation
Sets
50­
75
99.9796
­
0.04925
­
11%

Irrigation
Sets
75­
100
3.0417
0.00006454
0.015%

Irrigation
Sets
100­
175
17.8374
­
0.007347
­
1.7%

Irrigation
Sets
175
+
4.5922
­
0.0009645
­
0.22%

Other
Ag
Equipment
11­
50
20.7211
­
0.009219
­
2.1%

Other
Ag
Equipment
50­
75
116.07813
­
0.05758
­
12%

Other
Ag
Equipment
75­
100
14.8355
­
0.006342
­
1.4%

Other
Ag
Equipment
100­
175
27.9645
­
0.1262
­
2.9%

Other
Ag
Equipment
175­
300
5.8907
­
0.001526
­
0.35%

1
See
Equation
2.
Time
t
is
entered
into
the
exponential
equation
as
calendar
year,
e.
g.,
"
2010."
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Table
7
Fit
Parameters
and
Annual
Growth
Rates
for
Linear
Equipment
Sales
Trends
for
Construction
Engines1
Segment
Size
Class
(
rated
hp)
2
intercept
(
c
)
slope
(
m)
Linear
Sales
Growth
Rate
(%
of
calculated
1996
sales)
3
Construction
3­
6
­
340.0
128.1
4.91%

6­
11
415.6
79.5
3.54%

11­
16
237.2
123.3
4.01%

16­
25
­
2636.5
601.4
5.37%

25­
40
­
905.9
775.8
4.58%

40­
50
­
347.4
385.6
4.53%

50­
75
13999.8
354.9
1.60%

75­
100
Logistic
fit
used,
see
Table
10
100­
175
Logistic
fit
used,
see
Table
10
175­
300
9351.2
586.3
2.57%

300­
600
4302.0
233.9
2.42%

600­
750
­
21.3
87.7
4.39%

750­
1,000
198.9
19.6
3.02%

1,000­
1,500
­
114.6
23.4
5.53%

1,500­
2,000
­
118.1
21.5
5.71%

2,000­
3,000
­
22.8
4.8
5.49%

1
See
Equation
1.
Time
t
is
entered
into
the
linear
equation
as
(
t
­
1973),
i.
e.,
"
1973"
is
treated
as
t=
0,
unlike
the
agricultural
linear
fit.
2
Defined
as
lower­
bound

rated
power
<
upper
bound.
3
Calculated
in
relative
terms
as
the
constant
linear
rate
relative
to
1996­
year
sales
,
i.
e.,
glinPct
(
See
Equation
4).
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Table
8
Fit
Parameters
and
Annual
Growth
Rates
for
Linear
Equipment
Sales
Trends
for
Commercial
Engines1
Segment
Size
Class
(
rated
hp)
2
intercept
(
c
)
slope
(
m)
Linear
Sales
Growth
Rate
(%
of
calculated
1996
sales)
3
Commercial
3­
6
­
73.4
116.4
4.47%

6­
11
178.3
352.4
4.25%

11­
16
1909.2
123.6
2.60%

16­
25
340.4
392.8
4.19%

25­
40
3405.2
164.0
2.28%

40­
50
1724.5
265.0
3.39%

50­
75
4933.4
240.5
2.30%

75­
100
3297.8
346.1
3.07%

100­
175
6662.2
116.6
1.25%

175­
300
3172.6
177.3
2.45%

300­
600
3377.5
12.8
0.35%

600­
750
644.4
4.5
0.60%

1
See
Equation
1.
Time
t
is
entered
into
the
linear
equation
as
(
t
­
1973),
i.
e.,
"
1973"
is
treated
as
t=
0,
unlike
the
agricultural
linear
fit.
2
Defined
as
lower
bound

rated
power
<
upper
bound.
3
Calculated
in
relative
terms
as
the
constant
linear
rate
relative
to
1996­
year
sales
,
i.
e.,
glinPct
(
See
Equation
4).
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Table
9
Fit
Parameters
and
Annual
Growth
Rates
for
Linear
Equipment
Sales
Trends
for
Industrial
Engines1
Segment
Size
Class
(
rated
hp)
2
intercept
(
c
)
slope
(
m)
Linear
Sales
Growth
Rate
(%
of
calculated
1996
sales)

Industrial
3­
6
­
104.9
22.1
5.48%

6­
11
­
450.4
75.0
5.88%

11­
16
372.5
172.1
3.97%

16­
25
­
859.5
383.9
4.82%

25­
40
2416.4
75.6
1.82%

40­
50
273.3
351.1
4.21%

50­
75
12763.1
462.8
1.98%

75­
100
4766.8
90.8
1.32%

100­
175
2135.5
156.0
2.73%

175­
300
63.5
115.4
4.25%

300­
600
­
64.5
15.3
5.32%

600­
750
­
1.6
0.40
5.21%

1
See
Equation
1.
Time
t
is
entered
into
the
linear
equation
as
(
t
­
1973),
i.
e.,
"
1973"
is
treated
as
t=
0,
unlike
the
agricultural
linear
fit.
2
Defined
as
lower­
bound

rated
power
<
upper
bound.
3
Calculated
in
relative
terms
as
the
constant
linear
rate
relative
to
1996­
year
sales
,
i.
e.,
glinPct
(
See
Equation
4).
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Table
10
Fit
Parameters
and
Annual
Growth
Rates
for
Logistic
Equipment
Sales
Trends
for
Construction
Equipment
1
Size
Class
(
rated
hp)
Upper
bound
(
K)
Linear
coefficient
(
A)
Growth
Rate
(
 )
Lower
Bound
(
L)
Ratio
of
Sales
in
Year
to
Sales
in
2000
(
ry)
2
2001
2010
2020
2030
2040
2050
75­
100
98,000
21.5
0.104
0.0
1.010
1.403
1.675
1.798
1.847
1.864
100­
175
33,400
12,000
0.38
18,200
1.059
1.118
1.120
1.120
1.120
1.120
1
See
Equation
3.
Time
t
is
entered
into
the
logistic
equation
as
(
t
­
1970),
i.
e.,
"
1970"
is
treated
as
t=
0.

2
See
Equation
5.
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4.0
Population
and
Hp­
Hour
Growth
Projection
Methods
The
equipment
sales
growth
projections
described
above
were
used
to
generate
equipment
population
projections,
which
were
then
combined
with
activity,
hp,
and
load
factors
to
generate
total
activity
(
hp­
hour)
growth
rates
for
comparison
to
NONROAD's
fuel
consumption
growth
rates.
Two
versions
of
this
basic
approach
were
used.
In
Method
#
1,
the
sales
growth
rates
by
size
class
were
translated
directly
into
corresponding
population
growth
rates
by
size
class.
This
method
is
described
in
Section
4.1
below.
Method
#
2
included
the
revised
sales
and
population
growth
by
size
class
as
in
Method
#
1,
but
also
placed
a
maximum
limit
on
the
expected
life
of
equipment
in
the
calculation
of
the
populations,
as
described
in
Section
4.2
below.

4.1
Method
1:
Estimating
Equipment
Population
Growth
from
Sales
Growth
by
Size
Class
To
convert
sales
growth
into
population
growth,
we
input
sales
estimates
for
the
period
1950
­
2045
to
an
attrition
model
that
applied
scrappage
rates
to
engines
sold
in
successive
years,
using
the
same
scrappage
curves,
median
lives,
activities
and
load
factors
used
in
NONROAD.
In
the
sales
history,
the
period
1973­
2000
is
represented
by
reported
sales
(
except
as
noted),
the
period
2001
to
2050
is
represented
by
projected
future
sales,
and
the
period
1950
to
1972
is
represented
by
constant
sales
equal
to
the
1973
values.
After
applying
appropriate
scrappage
rates
to
all
sales
cohorts
(
equipment
sold
in
a
given
model
year)
present
in
each
year,
the
sum
of
remaining
(
not
yet
scrapped)
engines
in
each
evaluation
year
constitutes
the
equipment
population
for
that
year
(
N
y).
These
calculations
were
performed
individually
for
each
hp
size
class
within
each
equipment
type
to
estimate
equipment
populations
in
each
year
from
1996
to
2045.

For
purposes
of
comparison
to
population
growth
in
the
existing
NONROAD
model,
these
detailed
population
projections
by
equipment
type
or
hp
size
class
were
then
summed
by
industry
segment
for
each
of
the
four
segments
considered
in
this
analysis.
For
each
segment,
a
constant
annual
average
growth
rate
for
the
period
1996­
2030
was
calculated
(
g
Pct9630),
using
the
1996
population
as
a
fixed
reference,
similar
to
that
calculated
for
linear
sales
projections.

This
approach
follows
that
used
in
NONROAD
to
project
populations,
allowing
direct
comparisons
to
projections
from
draft
NONROAD2004,
as
well
as
among
the
different
segments.
To
allow
similar
comparisons
of
growth
trends
over
time,
projected
populations
were
also
scaled
to
a
relative
basis
as
used
in
the
NONROAD
growth
inputs.
To
put
all
projections
on
the
same
scale,
each
segment
was
assigned
a
`
reference
population'
i
y
of
1,000
in
1996.
For
years
following
1996,
i
y
is
projected
as
the
product
of
i
1996
(=
1,000)
and
the
ratio
of
projected
populations
in
1996
and
a
given
future
year
y,
N
1996
and
N
y,
respectively.
In
equation
form,
this
calculation
is
g
N
N
N
Pct9630
=
 
 






1
2030
1996
1996
2030
1996
(
7)

i
i
N
N
y
y
=






1996
1996
(
8)
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For
example,
if
the
projected
diesel
construction
population
in
2015
(
N
2015)
were
2
million,
and
the
corresponding
1996
population
(
N
1996)
were
1
million,
then
the
`
reference
population'
would
be
1,000
for
1996
(
i
1996)
and
2,000
for
2015
(
i
2015).
Use
of
the
reference
populations
is
another
way
of
making
direct
comparisons
to
NONROAD's
growth
rates
across
multiple
equipment
segments.

4.2
Method
2:
Estimating
Equipment
Population
Growth
with
Bounded
Median
Lives
This
method
is
essentially
the
same
as
Method
1,
except
that
the
sales/
scrappage/
population
calculation
modified
the
median
life
values,
capping
them
at
an
equivalent
of
16
years.
The
NONROAD
model
assigns
the
age
distributions
of
equipment
in
a
given
simulation
year
using
the
"
annualized
median
life."
We
calculate
annualized
life
(
l
y,
years)
from
median
life
at
full
load
(
l
h,
hours)
as
where
A
is
the
annual
activity
(
hours/
year)
and
L
is
the
load
factor,
which
represents
the
average
fraction
of
the
engine's
rated
power
used
during
operation.
Thus,
in
addition
to
engine
life,
annualized
life
is
dependent
on
assumptions
regarding
how
much
and
how
hard
equipment
is
used.
Examination
of
annualized
life
in
relation
to
activity
and
load,
shows
that
certain
combinations
of
median
life
(
l
h),
activity
and
load
factor
give
values
of
annualized
median
life
that
appear
implausible.
For
example,
as
shown
in
Table
11,
low
values
of
load
factor
or
activity,
especially
in
combination,
tend
to
result
in
long
annualized
lives,
as
in
the
case
of
welders,
pressure
washers
or
combines.
On
the
other
hand,
high
values
of
activity
or
load
factor
can
give
annualized
lives
that
appear
implausibly
short
as
in
the
case
of
forklifts.
Increasing
the
annualized
life
increases
the
persistence
of
engines
in
the
population,
slowing
fleet
turnover,
and
resulting
in
rapid
population
growth.

To
address
the
possibility
that
long
annualized
median
lives
for
some
equipment
types
and
size
classes
could
be
contributing
to
high
population
growth
rates
in
NONROAD,
we
manipulated
median
life
in
the
spreadsheet
attrition
model.
Specifically,
we
constrained
annualized
median
life
to
a
maximum
of
16
years
for
any
equipment
type
or
size
class.
Thus,
because
the
scrappage
curve
is
always
symmetric
about
its
median,
the
longest
any
engine
could
survive
would
be
32
years.
These
modifications
to
annualized
median
life
were
applied
by
equipment
type
and
size
class,
as
discussed
above
in
Method
1.
l
l
AL
y
h
=
(
9)
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Table
11
Annualized
Median
Lives
for
Selected
Diesel
Equipment
Types
Application
Load
factor
(
L)
Activity
(
A,
hr/
yr)
Annualized
Life
(
ly,
years)

<=
50
hp
(
lh
=
2,500
hr)
50­
300
hp
(
lh=
4,667
hr)
300
+
hp
(
lh=
7,000
hr)

Other
Materials
Handling
0.21
421
28.3
52.8
79.2
Welders
0.21
643
18.5
34.6
51.8
Skid­
steer
loaders
0.21
818
14.6
27.2
Backhoes
0.21
1,135
10.5
19.6
Pressure
washers
0.43
145
40.1
74.9
112.3
Generators
0.43
338
17.2
32.1
48.2
Refrigeration/
AC
Units
0.43
1,341
4.3
8.1
Combines
0.59
150
52.7
79.1
Agricultural
tractors
0.59
475
8.9
16.7
25.0
Crawler
tractors
0.59
936
4.5
8.5
12.7
Off­
Highway
trucks
0.59
1,641
4.8
7.2
Forklifts
0.59
1,700
2.5
4.7
7.0
5.0
Population
and
Hp­
Hour
Growth
Projection
Results
Table
12
and
Figures
2­
5
present
comparisons
of
the
diesel
equipment
growth
projections
from
the
NONROAD
model
to
the
alternative
methods
described
above.
The
table
presents
annual
average
percentage
growth
rates
with
respect
to
the
1996
base­
year
population
(
g
Pct9630,
Equation
7),
as
well
as
an
analogous
growth
rate
for
work
output
(
total
hp­
hr).
Work
output
is
estimated
as
the
product
of
total
population
(
N
y),
activity
rates
(
hr/
yr),
average
rated
power
(
hp)
and
load
factor,
and
provides
a
more
direct
surrogate
for
comparison
to
fuel
consumption
as
projected
by
the
NONROAD
model.
The
figures
present
the
growth
index
i
y
(
Equation
8)
for
all
methods,
as
a
direct
comparison
of
trends
through
2045.

Based
on
our
updated
assessment
of
historic
equipment
sales,
populations
of
some
important
equipment
types
are
projected
to
grow
at
a
fairly
high
rate
over
the
next
30
years,
e.
g.,
3­
5%/
year.
In
contrast,
the
EIA
Annual
Energy
Outlook
(
AEO)
projects
fuel
use
as
growing
more
slowly,
e.
g.,
<
1.5%/
year.
Assumptions
and
approaches
used
in
the
analysis
that
account
for
the
results
obtained
are
discussed
below.
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At
the
outset,
projected
sales
growth
is
quite
rapid
for
some
size
classes
or
equipment/
size
combinations
in
the
different
segments.
Strong
sales
growth
would
in
itself
result
in
rapid
population
growth,
other
factors
being
equal.

In
addition,
some
important
equipment
types
having
high
sales
growth
and
large
populations
also
have
long
annualized
median
lives.
These
factors
in
combination
would
also
tend
towards
rapid
population
growth,
as
the
sales
"
inputs"
are
large,
and
the
scrappage
"
outgo"
is
relatively
small.
Rapid
growth
combined
with
a
large
population
and
moderate
to
high
activity
or
load
factor
would
imply
substantial
contributions
to
projected
fuel
consumption.
At
the
same
time,
activity
is
assumed
constant
over
the
entire
expected
life
for
all
equipment
types,
which
in
combination
with
long
annualized
lives
would
again
increase
contributions
to
work
output
(
hp­
hrs)
and
fuel
consumption.

Finally,
there
is
an
important
interaction
in
the
sales/
scrappage
model
between
annualized
life
and
the
base­
year
population
that
influences
projected
future
population
growth
rates.
A
central
feature
of
the
development
of
base­
year
populations
and
growth
rates
for
use
in
NONROAD
is
that
the
same
annualized
life
estimates
are
used
to
project
both
base­
year
and
future
populations.
Thus,
if
a
given
set
of
sales
projections
is
accepted
as
given,
and
if
an
estimated
population
growth
rate
appears
high
relative
to
an
external
counterpart,
such
as
EIA's
fuel
consumption
projections,
one
possibility
is
that
scrappage
rates
are
low,
i.
e.,
annualized
life
may
be
too
long.
However,
if
annualized
lives
are
reduced
by
adjusting
activity
estimates
or
load
factors,
or
by
imposing
maximum
limits
(
as
in
Method
2),
resulting
decreases
in
growth
rates
are
smaller
than
might
be
expected,
given
the
size
of
the
reductions
in
annualized
life.

To
account
for
this
counterintuitive
result,
it
is
important
to
remember
that
reducing
annualized
life
accelerates
scrappage
in
the
"
past"
(
prior
to
the
base
year)
as
well
as
in
the
"
future,"
(
following
the
base
year).
As
a
result,
the
base­
year
population
also
decreases,
which
has
a
compensating
effect
on
the
population
growth
rate
because
the
rate
is
calculated
with
respect
to
N
1996
as
a
fixed
reference
point
(
see
Equation
7),
and
a
reduction
in
N
1996
has
the
effect
of
increasing
the
growth
rate.
This
effect
can
be
seen
in
a
comparison
of
Methods
1
and
2
in
Table
12.
Population
growth
rates
are
consistently
lower
for
Method
2
relative
to
Method
1,
but
the
margins
are
small.
Base­
year
populations
in
each
segment
are
also
lower
for
Method
2.
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Table
12
Comparison
of
Growth
Rates
used
in
Draft
NONROAD2004
and
Alternative
Sales­
Based
Approaches
(
This
Analysis)

Method
Backcast3
(
N1996)
Population
Growth
(
gPct9630)
5
Hp­
Hour
Growth4
(
gPct9630)
5
Agricultural
Method
11
1,864,716
2.6%
4.4%

Method
22
1,507,722
2.7%
3.9%

Base
=
NONROAD2004
1,724,156
2.9%
2.9%
Construction
Method
1
1,362,150
7.0%
4.7%

Method
2
1,290,283
5.9%
4.3%

Base
=
NONROAD2004
1,463,829
3.2%
3.2%
Commercial6
Method
1
668,484
5.4%
4.1%

Method
2
561,597
4.8%
3.7%

Base
=
NONROAD2004
773,213
4.5%
4.5%
Industrial
Method
1
353,031
4.8%
3.5%

Method
2
344,221
3.9%
3.4%

Base
=
NONROAD2004
394,240
3.5%
3.5%

1
"
Method
1"
=
May
2003
sales
data,
sales
projected
linear
&
logistic
by
hp
size
class.
2
"
Method
2"
=
Method
1,
but
with
annualized
median
life
capped
at
16
years.
3
"
Backcast"
1996
populations
show
that
methods
differ
in
past
as
well
as
future
projections.
4
Hp­
Hour
growth
is
used
here
as
a
surrogate
to
approximate
growth
in
fuel
consumption.
5
Average
annual
growth
rates
(
gPct9630)
are
given
for
year
2030
relative
to
1996
(
Equation
7).

6Hydro
Power
Units
are
reclassified
into
the
Commercial
category
for
this
analysis.
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Agricultural
Equipment
Growth
500
1000
1500
2000
2500
3000
3500
4000
1990
2000
2010
2020
2030
2040
2050
Year
Relative
Growth
Index
Method
1
Population
Method
1
Pop*
Hp
Method
2
Population
Method
2
Pop*
Hp
NONROAD
Model
Figure
2.
Projected
relative
growth
trends
for
agricultural
equipment
populations
and
total
work
output
(
hp­
hr).
The
growth
index
iy
(
Equation
9)
is
used
to
allow
comparisons
between
Method
1,
Method
2
and
Draft
NONROAD2004.

Construction
Equipment
Growth
500
1000
1500
2000
2500
3000
3500
4000
1990
2000
2010
2020
2030
2040
2050
Year
Relative
Growth
Index
Method
1
Population
Method
1
Pop*
Hp
Method
2
Population
Method
2
Pop*
Hp
NONROAD
Model
Figure
3.
Projected
relative
growth
trends
for
construction
equipment
populations
and
total
work
output
(
hp­
hr).
The
growth
index
iy
(
Equation
9)
is
used
to
allow
comparisons
between
Method
1,
Method
2
and
Draft
NONROAD2004.
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Industrial
Equipment
Growth
500
1000
1500
2000
2500
3000
3500
4000
1990
2000
2010
2020
2030
2040
2050
Year
Relative
Growth
Index
Method
1
Population
Method
1
Pop*
Hp
Method
2
Population
Method
2
Pop*
Hp
NONROAD
Model
Figure
5.
Projected
relative
growth
trends
for
industrial
equipment
populations
and
total
work
output
(
hp­
hr).
The
growth
index
iy
(
Equation
9)
is
used
to
allow
comparisons
between
Method
1,
Method
2
and
Draft
NONROAD2004.
Commercial
Equipment
Growth
500
1000
1500
2000
2500
3000
3500
4000
1990
2000
2010
2020
2030
2040
2050
Year
Relative
Growth
Index
Method
1
Population
Method
1
Pop*
Hp
Method
2
Population
Method
2
Pop*
Hp
NONROAD
Model
Figure
4.
Projected
relative
growth
trends
for
commercial
equipment
populations
and
total
work
output
(
hp­
hr).
The
growth
index
iy
(
Equation
9)
is
used
to
allow
comparisons
between
Method
1,
Method
2
and
Draft
NONROAD2004.
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6.
Conclusions
In
the
course
of
these
analyses,
we
developed
revised
growth
rates
for
nonroad
equipment
populations.
The
revised
population
growth
rates
were
derived
in
turn
from
sales
growth
rates
developed
at
higher
levels
of
detail
than
those
currently
used
in
the
NONROAD
model,
i.
e.,
rates
were
developed
to
represent
individual
equipment
types
or
size
classes,
or
combinations
of
equipment
type
and
size.
While
the
revised
rates
may
better
represent
possible
trends
in
populations
of
smaller
equipment,
they
do
not
reduce
projected
growth
in
fuel
consumption
in
nonroad
equipment
to
levels
comparable
to
projections
published
by
the
Energy
Information
Administration.
Due
to
the
difficulties
in
achieving
such
reconciliation,
we
have
not
modified
the
growth
rates
used
in
Draft
NONROAD2004
for
purposes
of
the
final
rulemaking
for
diesel
engines.
However,
as
mentioned,
we
have
performed
a
sensitivity
analysis
in
which
NONROAD's
fuel
consumption
and
emissions
estimates
were
adjusted
to
match
fuel
consumption
projections
for
nonroad
equipment
derived
from
EIA's
Annual
Energy
Outlook
2003
(
Chapter
8,
Appendix
A.
2).
This
sensitivity
case
is
designed
to
assess
the
appropriateness
of
the
new
emission
standards
under
an
assumption
that
EIA's
projections
were
correct.
Additionally,
we
will
continue
to
evaluate
the
estimation
of
growth
in
nonroad
equipment
populations
in
the
future.
As
EPA
incorporates
nonroad
emissions
into
the
MOVES
model,
we
hope
to
resolve
these
issues
to
improve
our
confidence
in
current
and
future
projections
of
nonroad
emissions.
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APPENDIX
A
Memorandum
describing
Development
of
Sales
Projections
for
Agricultural
Nonroad
Equipment
performed
by
Research
Triangle
Institute
International
TO:
Todd
Sherwood,
EPA
Office
of
Transportation
Air
Quality
FROM:
Andrea
Thomas
Bill
White
DATE:
August
25,
2003
SUBJECT:
Horsepower­
Based
Growth
Rates
for
Agricultural
Engines
­
Final
Report
This
memo
presents
projected
growth
rates
for
sales
of
diesel­
powered
agricultural
equipment
for
the
period
2001­
2050.
In
completing
this
work,
we
have
used
a
variety
of
standard
statistical
techniques
to
analyze
the
30
years
of
sales
data
provided
by
EPA
and
to
project
these
historical
sales
trends
into
the
future.
This
effort
is
consistent
in
technique
and
results
with
recent
estimates
generated
by
EPA's
Office
of
Transportation
Air
Quality.
An
alternative
approach,
involving
creation
of
a
new
model
that
would
link
agricultural
equipment
purchases
to
projections
of
changes
in
underlying
technological
and
economic
aggregates,
was
not
pursued,
because
of
concerns
about
complexity
and
cost.

This
memorandum
is
divided
into
three
major
sections.
The
first
section
contains
an
analysis
of
the
engine
sales
database
EPA
provided
to
RTI
to
use
in
this
analysis.
In
the
second
section,
we
discuss
the
statistical
techniques
that
we
used
to
generate
sales
projections
based
on
the
historical
data
and
the
reasons
for
selecting
the
chosen
techniques.
In
the
final
section,
we
present
the
resulting
growth
estimates
for
each
application
area
and
engine
size
class.
To
make
this
report
more
useful,
we
have
included
two
appendices
containing
tables
of
the
year­
by­
year
sales
projections
for
each
application/
size
class
and
a
third
appendix
with
thumbnail
graphs.

I.
Summary
and
Analysis
of
Diesel­
Powered
Agricultural
Equipment
Database
As
the
source
material
for
new
long­
run
growth
estimates,
the
database
EPA
provided
us
includes
approximately
30
years
of
sales
data
for
nonroad
agricultural
engines,
with
detailed
information
on
engine
size
and
application
area.
This
database,
known
as
PSR
OE­
LinkTM,
is
compiled
and
provided
to
EPA
by
PSR
(
Power
Systems
Research,
2003).
We
used
this
data
source
extensively
for
our
analysis,
in
which
we
looked
at
trends
in
reported
sales,
separated
into
application
areas
and
horsepower
classes
as
used
by
EPA
in
the
EIA
for
the
proposed
rule.

Broad
Trends
in
Equipment
Aggregates.
The
most
striking
feature
of
the
important
tractor
and
combine
segments,
as
well
as
for
several
of
the
smaller
application
groups,
is
the
huge
increase
in
Todd
Sherwood
August
25,
2003
Page
2
40,000
60,000
80,000
100,000
120,000
140,000
160,000
180,000
200,000
220,000
240,000
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
Annual
Units
Sold
PSR
Data
Census:
Apparent
Consumption
Figure
1.
Sales
Agriculture
Tractor
 
1970­
2000
sales
during
the
1970s
and
subsequent
crash
during
the
early
1980s.
Figure
1
shows
these
impacts
quite
clearly
for
the
agricultural
tractor
application
area.
These
unusual
trends
resulted
primarily
from
the
agricultural
boom
fueled
by
the
1970s
grain
sales
to
the
Soviet
Union,
which
attracted
many
new
entrants
into
farm
operations.
These
newcomers
needed
to
purchase
or
lease
new
equipment
to
get
into
the
business;
many
also
borrowed
money
to
lease
farmland
as
well.
After
the
Soviet
invasion
of
Afghanistan
in
1979,
President
Carter
placed
an
embargo
on
grain
sales
to
Russia,
and
markets
for
grain,
farmland,
and
farm
equipment
all
crashed.
It
took
several
years
for
the
equipment
glut
to
clear
through
the
used
equipment
market
and
for
sales
of
new
machines
to
recover
to
equilibrium
levels.

The
second
significant
overall
trend
is
one
of
strong
growth
from
the
mid­
1990s
through
the
present,
which
Figure
1
also
shows.
Combines,
sprayers,
and
irrigation
equipment
also
show
this
recent
increase
in
sales,
although
there
is
considerable
variation
between
horsepower
class
segments.
A
ready
explanation
is
not
available
for
this
recent
time
period,
unlike
the
1975
to
1985
period.
In
fact,
farming
has
reportedly
been
in
almost
continual
crisis
since
passage
of
the
1996
Freedom
to
Farm
Act,
which
attempted
to
reform
the
nation's
price
support
system.
It
is
Todd
Sherwood
August
25,
2003
Page
3
quite
possible
that
these
increases
may
have
resulted
from
increased
liquidity
among
farm
operators
following
large
"
emergency
payments"
voted
by
Congress
each
year
from
1997
onward.
Although
a
definitive
explanation
is
beyond
the
scope
of
this
task,
the
potential
of
liquidity­
induced
purchases
suggests
that
care
should
be
exercised
in
extrapolating
recent
data
out
many
years
into
the
future.

Figure
1
also
provides
some
indication
of
the
comparability
of
the
PSR
database
for
farm
tractors
to
another
source
of
historical
shipments
data,
the
Census
Bureau's
annual
industrial
reports
on
farm
tractor
production
and
consumption
(
U.
S.
Department
of
Commerce,
1985;
U.
S.
Department
of
Commerce,
1990).
In
these
reports,
domestic
production,
exports,
and
imports
for
consumption
are
listed
separately,
allowing
a
calculation
of
"
apparent
consumption"
for
each
year.
Unfortunately,
the
Census
Bureau
changed
its
method
of
calculating
the
totals
several
times
during
the
1970s
and
1980s
and
discontinued
the
report
completely
after
1989.
Nonetheless,
the
two
sources
track
fairly
well
during
the
period
of
overlap,
except
for
the
first
4years
of
PSR
data;
this
issue
is
discussed
further
in
the
second
section
of
this
memorandum.

Trends
in
Sales
by
Size
and
Application
Areas.
When
the
database
information
is
broken
down
by
horsepower
class
within
each
application
area,
other
concerns
emerge.
It
appears
that
detailed
model­
specific
data
are
only
available
in
the
database
from
1990
to
2000.
Before
that
time,
there
is
only
one
record
for
each
year
in
each
size
class,
which
suggests
that
units
of
varying
size
were
lumped
together
in
the
record.
The
resulting
"
heaping"
of
data
around
the
reported
horsepower
values
makes
statistically
valid
inferences
more
difficult.
More
importantly,
however,
the
reported
horsepower
values
change
at
intervals
during
the
30­
year
time
period,
often
jumping
from
one
size
segment
to
another.
Figure
2
shows
this
phenomena
for
windrowers;
note
that
the
50
to
75
hp
category
drops
to
zero
in
the
reported
data
after
1985,
at
which
point
the
adjacent
75
to
100
hp
category
immediately
increases.
The
large
engine
100
to
175
hp
class,
which
is
close
to
zero
for
most
of
the
period,
jumps
to
more
than
500
units
per
year
once
model­
level
data
became
available
in
1990.
This
is
accompanied
by
corresponding
drop
in
the
75
to
100
hp
range.

These
heaping
and
size­
class
instability
phenomena
make
independent
estimation
of
growth
rates
by
horsepower
size
class
difficult.
In
addition,
the
small
sample
sizes
noted
in
the
1998
EPA
memorandum
that
summarized
a
previous
version
of
these
growth
projections
are
unchanged
as
an
estimation
issue
(
Dolce,
1998).
We
have
found,
however,
that
some
reaggregation
of
size
classes
can
yield
consistent
time
series,
with
decent
sample
sizes,
at
least
for
a
few
of
the
application
areas.
For
example,
combining
all
of
the
windrower
size
classes
removes
the
anomalous
jumps
noted
earlier,
revealing
a
much
smoother
underlying
trend.
Todd
Sherwood
August
25,
2003
Page
4
0
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
4,500
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
Annual
Units
Sold
50­
75hp
75­
100hp
100­
175hp
Figure
2.
Windrower
Sales
by
HP
Class
1973­
2000
Suitability
for
Development
of
Requested
Growth
Estimates.
With
the
qualification
noted
above,
we
concluded
that
the
PSR
database
provided
will
be
more
than
adequate
to
provide
a
basis
for
creating
growth
estimates
for
the
2001­
2050
time
horizon.
Truncation
of
some
of
the
early
years'
data
will
help
avoid
distortions
caused
by
the
Soviet
grain
bubble
and
mitigate
any
effects
of
the
PSR's
low
sales
figures
in
the
1973­
1976
period.
Selective
combining
of
adjacent
size­
class
series
will
eliminate
heaping
and
data
instability
issues.
The
results
of
these
modifications
will
be
discussed
in
more
detail
in
the
next
section
of
this
memorandum.

Other
Potential
Databases.
We
are
not
aware
of
any
comprehensive
sources
of
agricultural
equipment
data
that
report
unit
sales
by
model,
as
the
PSR
does.
The
Agricultural
Equipment
Manufacturers
(
AEM)
trade
group
reports
monthly
tractor
sales
by
major
type
and
size
group,
including
two­
wheel
drive
(
2WD)
units
under
100
hp,
2WD
over
100
hp,
and
4WD.
The
AEM
also
reports
on
combines.
Unfortunately,
AEM
does
not
release
historical
data,
because
their
Todd
Sherwood
August
25,
2003
Page
5
focus
is
primarily
to
highlight
current
market
conditions.
We
did
not
believe
that
it
would
be
advisable
to
contact
this
group
directly
to
ask
if
they
maintained
and
would
be
willing
to
share
long­
run
data.

Until
recently,
the
Census
Bureau's
annual
reports
series
noted
above,
along
with
their
predecessor,
Current
Industrial
Reports
(
CIR),
would
have
been
quite
useful
in
providing
aggregate
sales
of
tractors
and
other
major
pieces
of
farm
equipment.
The
Economic
Census
reports,
published
every
5
years,
have
also
been
helpful
in
the
past
to
supplement
the
annual
CIR
data.
With
the
long­
term
decline
and
recent
consolidation
of
the
agricultural
equipment
industry,
there
are
so
few
producing
firms
remaining
that
the
Census
Bureau
has
stopped
publishing
unit
volume
information.
Likewise,
the
annual
Agricultural
Statistics
published
by
the
U.
S.
Department
of
Agriculture
also
no
longer
contains
unit
production
and
sales
figures
for
tractors,
although
they
report
on
several
classes
of
minor
equipment.

II.
Approach
for
Generating
Growth
Estimates
EPA
has
used
a
variety
of
methods
to
estimate
near­
term
movements
in
sales
and
equipment
populations,
most
notably
projections
of
economic
indicators
and
historic
trend
analysis.
The
Bureau
of
Economic
Analysis's
(
BEA's)
periodic
regional
projections
proved
especially
useful
in
supporting
the
former
in
that
they
provided
a
50­
year
look
ahead
at
growth
rates
by
industrial
sector.
If
the
researcher
were
willing
to
assume
that
each
equipment
category's
share
of
total
output
would
remain
unchanged
over
half
a
century,
the
aggregate
economic
trends
could
be
converted
into
equipment­
specific
ones.
Unfortunately
for
our
purposes,
the
BEA
eliminated
their
regional
projections
program
in
1996,
and
their
last
report,
containing
1995
to
2045
projections,
is
now
quite
out
of
date.

In
the
absence
of
the
BEA
economic
forecasts,
it
might
still
be
possible
to
use
long­
term
estimates
of
national
GDP
or
population
to
generate
projections
for
sales
of
diesel­
powered
agricultural
equipment.
By
understanding
the
way
this
equipment
is
used
and
uncovering
the
technical
relationships
between
inputs,
outputs,
and
economic
or
demographic
drivers,
it
would
be
possible
to
bring
appropriate
economic
variables
to
bear
on
the
estimation
task.
In
fact,
the
Census
Bureau
published
100­
year
population
projections
for
the
U.
S.
after
every
decennial
census
and
makes
them
available
on
its
website
(
U.
S.
Department
of
Commerce,
2000).

Embarking
on
a
new
modeling
effort,
involving
the
complex
relationships
between
population,
food
consumption,
imports
and
exports,
crop
yields,
and
equipment
inputs,
would
be
quite
costly
and
complex.
The
assumptions
needed
to
inform
such
a
model
carry
sufficient
uncertainty
that
it
is
possible
that
such
estimates
would
be
more
speculative
that
extrapolation
of
recent
trends.
For
Todd
Sherwood
August
25,
2003
Page
6
this
reason,
RTI
and
EPA
elected
to
adopt
the
simpler
approach
recommended
by
the
previous
Dolce
report.

Overall
Approach
By
electing
to
use
statistical
methods
to
analyze
the
sales
data
and
create
projections,
our
task
became
that
of
fitting
the
data
to
a
smooth
curve
and
extrapolating
that
curve
over
the
2001
to
2050
time
period.
Still,
decisions
were
necessary
about
a
number
of
data
and
analytical
issues,
including
decisions
on
combining
size
classes
into
aggregate
series;
potential
truncation
in
the
early
years;
and,
most
importantly,
the
type
of
equation
to
use
in
fitting
the
trends.
As
EPA
had
noted
in
previous
communication
with
RTI,
the
raw
data
were
not
amenable
to
simple
leastsquares
regression,
either
to
fit
linear
trends
or
constant­
growth­
rate
(
exponential)
projections.
Although
we
did
not
modify
any
of
the
data
presented
to
us,
we
truncated
or
combined
several
series
in
an
attempt
to
make
the
data
series
more
consistent
and
to
eliminate
distortions
created
by
macroeconomic
shocks
and
defects
in
the
PSR
data.
We
describe
each
of
these
steps
in
the
text
that
follows.

Combining
Data
Series
We
described
in
the
first
section
of
this
memorandum
one
of
several
instances
in
which
there
were
discontinuities
in
adjacent
PSR
data
series,
appearing
to
result
from
changes
in
definition
or
perhaps
re­
testing
or
re­
engineering
of
popular
equipment
models.
By
combining
these
series,
and
therefore
using
a
common
growth
rate
for
both
size
classifications,
more
consistent
and
precise
trends
could
be
estimated.
Of
the
35
equipment/
engine
size
categories
for
which
RTI
was
given
PSR
data
(
excluding
hydraulic
power
units,
which
were
later
excluded),
we
created
24
separate
50­
year
estimates.

Truncating
Data
Series
Where
we
had
information
that
inclusion
of
data
from
the
early
years
of
the
1970­
2000
time
period
would
likely
distort
the
curve
fitting,
we
opted
to
truncate
the
data
series.
This
was
done
for
two
reasons:
distortions
from
the
late
1970s
boom/
early
1980s
bust
in
grain
sales,
which
affected
tractors,
combines,
and
a
couple
of
other
equipment
types,
and
apparent
incomplete
records
for
several
equipment
categories
in
the
first
few
years
of
the
PSR
database.
As
we
discussed
in
the
Task
8
memorandum,
for
instance,
tractor
totals
do
not
match
census
values
until
the
late
1970s,
and
many
other
series
have
very
low
numbers
in
the
mid­
1970s.
A
total
of
five
data
series
were
truncated
prior
to
1982
to
eliminate
the
boom/
bust
distortion;
in
three
series,
we
eliminated
extremely
low
sales
estimates
from
the
1973­
1976
period.
Todd
Sherwood
August
25,
2003
Page
7
Selection
of
Equation
for
Fitting
the
Data
In
previous
projections
of
future
equipment
sales,
EPA
has
most
often
estimated
a
constant
growth
rate
over
time,
which
is
equivalent
to
fitting
the
data
to
an
exponential
growth
curve.
The
following
equation
describes
this
type
of
fit:

y
=
exp
©
+
mT)
(
1)

where
y
is
the
unit
sales
for
year
T,
and
c
and
m
are
intercept
and
slope
parameters,
respectively.
The
constant
growth
rate
function
has
the
advantage
of
simplicity
of
estimation
and
use.
For
those
data
series
where
sales
are
declining
over
the
period
in
question,
it
has
a
second
advantage
of
preventing
the
estimation
of
negative
sales
values
out
in
the
distant
future.
Nonetheless,
for
long­
range
extrapolation,
exponential
growth
fits
tend
to
produce
unreasonably
large
projected
sales
in
the
out
years,
unless
the
underlying
growth
rate
is
very
small.
In
the
present
study,
all
of
the
declining
series
and
two
of
the
(
very
slowly)
growing
series
were
estimated
using
the
constant
growth
rate
equation.

For
a
data
series
that
is
increasing
through
time,
a
linear
fit
can
avoid
the
tendency
of
the
estimates
to
explode
in
the
long
run.
Such
a
fit
can
be
described
by
Eq.
(
2):

y
=
c
+
mT
(
2)

where
each
of
the
variables
has
the
same
meaning
as
in
Eq.
(
1).
For
a
series
growing
in
a
linear
fashion,
the
steady
increase
in
the
number
of
units
compared
with
an
increasing
base
means
that
the
growth
rate
falls
slowly
over
time.
The
projected
behavior
is
consistent
with
much
of
the
last
50
to
60
years
of
agricultural
experience.
We
judged
that
three
of
the
agricultural
equipment
data
series
were
best
fitted
to
a
linear
equation.

Unfortunately,
neither
exponential
nor
linear
models
are
very
useful
for
estimating
the
long­
run
behavior
of
products
that
are
experiencing
rapid
growth
during
the
base
period.
The
new
products
literature
in
economics
and
business
management,
along
with
studies
of
biological
growth
processes,
have
increasingly
stressed
the
use
of
equations
that
trace
out
the
S­
shaped
growth
curve
most
often
experienced.
Several
of
these
equations,
including
the
logistic,
Gompertz,
and
Richards
functions,
can
be
described
with
three
or
four
parameters,
making
them
suitable
for
the
present
task,
where
we
have
a
limited
number
of
observations.
The
logistic
function
can
be
modeled
using
the
following
equation:

y
=
{
K
/
[
1
+
A
*
(
exp
(­
B
*
T)]}
+
L
(
3)
Todd
Sherwood
August
25,
2003
Page
8
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
1975
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
K
­
Asymptote
=
65,000
B
­
Maximum
Slope
A
­
Onset
Figure
3.
Illustration
of
Logistic
Curve
with
y
and
T
as
before,
and
K,
A,
B,
and
L
empirically
derived
parameters.
In
the
simplest
logistic
formulations,
L
is
excluded;
its
presence
allows
the
base
of
the
S­
shaped
curve
to
be
lifted
above
zero.

Each
of
the
other
parameters
has
an
interpretation
in
the
logistic
model,
as
illustrated
in
Figure
3.
The
value
of
K
determines
the
maximum
value
the
logistic
function
will
attain
(
i.
e.,
the
asymptote
of
the
function).
(
If
L
is
greater
than
zero,
the
asymptote
is
actually
L
+
K.)
The
B
parameter
affects
the
slope
of
the
function
at
its
inflection
point,
the
time
at
which
the
slope
is
the
greatest.
The
value
of
A
determines
the
onset
of
growth
or
the
position
of
the
S­
curve
along
the
time
axis.

Empirically,
the
values
of
the
four
parameters
are
estimated
by
minimizing
the
mean
square
error
of
the
fit,
a
process
that
can
be
done
by
any
of
a
number
of
readily
available
equation
solvers
(
Cavallini,
1993).
RTI
judged
that
four
rapidly
growing
series,
including
the
two
smallest
agricultural
tractor
classes,
were
best
described
by
logistic
fits.
Upon
EPA's
request,
RTI
also
Todd
Sherwood
August
25,
2003
Page
9
elected
to
provide
linear
fits
for
these
data
series
(
which
are
included
in
the
alternate
projections
in
Appendix
B
and
illustrated
in
the
thumbnail
graphs
in
Appendix
C).

III.
Growth
Rate
and
Sales
Projections
The
growth
rate
estimates
appear
in
Tables
1,
2,
and
3.
For
those
series
fitted
to
an
exponential
function,
the
constant
growth
rates
are
included
in
Table
1.
Representative
growth
rates
for
each
decade
over
the
next
50
years
are
shown
for
the
series
fitted
to
a
linear
model
in
Table
2
and
for
logistic
models
in
Table
3.
It
should
be
noted
that
sales
projections
for
a
number
of
these
declining
series
approach
zero
over
the
50­
year
time
horizon.
At
the
other
extreme,
the
use
of
linear
or
logistic
curves
to
describe
the
rapidly
growing
application/
size
classes
prevented
2050
estimates
for
these
categories
from
exceeding
the
total
population
of
agricultural
equipment
in
place
or
the
number
of
farms
being
operated
today.
The
four
series
we
fitted
to
logistic
curves
show
a
close
correspondence
to
the
existing
data
and
yield
growth
projections
that
we
find
to
be
very
reasonable.
Figure
4
illustrates
a
comparison
between
the
projections
of
the
three
types
of
curve
fits
and
shows
the
hazard
of
using
constant
growth
rates
to
project
future
sales
for
series
that
show
rapid
growth
over
the
recent
horizon.

In
the
appendices
to
this
memorandum,
we
have
included
tables
containing
sales
projections
by
application
area,
by
engine
class,
for
each
year
from
2001
to
2050,
along
with
the
PSR
totals
for
each
category
and
the
parameters
estimated
statistically
for
each
model
fit.
RTI's
recommended
projections,
including
constant
growth
rate
(
exponential),
linear,
and
logistic
fits,
appear
as
the
base
case
in
Appendix
A.
An
alternative
set
of
projections,
substituting
linear
fits
for
those
initially
fitted
to
logistic
functions,
is
included
]
as
Appendix
B.
Finally,
Appendix
C
contains
thumbnail
graphs
of
all
24
series,
with
both
base
and
alternate
fit
lines
included
for
comparison.
Todd
Sherwood
August
25,
2003
Page
10
Table
1.
Annual
Growth
Rates
for
Agricultural
Equipment
Data
Series
Application
Engine
Size
Base
Period
Type
of
Fit
Annual
Growth
Rate
Agricultural
Tractors
11­
25
hp
1980­
2000
Logistic
See
Table
3
Agricultural
Tractors
26­
50
hp
1973­
2000
Logistic
See
Table
3
Agricultural
Tractors
51­
100
hp
1973­
2000
Exponential
­
1.68
%

Agricultural
Tractors
101­
175
hp
1982­
2000
Linear
See
Table
2
Agricultural
Tractors
176
hp
and
up
1982­
2000
Linear
See
Table
2
Combines
76­
100
hp
1973­
2000
None
Nil
Combines
101­
175
hp
1982­
2000
Exponential
­
14.5
%

Combines
175
hp
and
up
1982­
2000
Linear
See
Table
2
Windrowers
all
hp
1977­
2000
Exponential
­
2.21
%

Balers
all
hp
1982­
2000
Exponential
+
0.59
%

Sprayers
11­
100
hp
1977­
2000
Exponential
­
0.85
%

Sprayers
101
hp
and
up
1973­
2000
Logistic
See
Table
3
Irrigation
Sets
11­
25
hp
1973­
2000
Exponential
­
5.56
%

Irrigation
Sets
26­
50
hp
1973­
2000
Exponential
­
11.32
%

Irrigation
Sets
51­
75
hp
1973­
2000
Exponential
­
11.33
%

Irrigation
Sets
76­
100
hp
1973­
2000
Exponential
+
0.01
%

Irrigation
Sets
101­
175
hp
1973­
2000
Exponential
­
1.69
%

Irrigation
Sets
175
hp
and
up
1973­
2000
Exponential
­
0.22
%

Other
Ag
Equipment
11­
50
hp
1973­
2000
Exponential
­
2.12
%

Other
Ag
Equipment
51­
75
hp
1973­
2000
Exponential
­
13.24
%

Other
Ag
Equipment
76­
100
hp
1977­
2000
Exponential
­
1.46
%

Other
Ag
Equipment
101­
175
hp
1989­
2000
Exponential
­
2.90
%

Other
Ag
Equipment
176­
300
hp
1989­
2000
Exponential
­
0.35
%
Todd
Sherwood
August
25,
2003
Page
11
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
100,000
1970
1975
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
Annual
Units
Sold
PSR
Data
Logistic
Linear
Exponential
Figure
4.
Projected
Sales
of
26­
50hp
Ag
Tractors
Figure
4.
Projected
Sales
of
26­
50hp
Ag
Tractors
Other
Ag
Equipment
301
hp
and
up
1989­
2000
Logistic
See
Table
3
Table
2.
Annual
Growth
Rates
by
Decade
for
Linear
Series
Projections
Application
Engine
Size
2001­
10
2011­
20
2021­
30
2031­
40
2041­
50
Agricultural
Tractors
101­
175
hp
+
2.76
%
+
2.16
%
+
1.78
%
+
1.51
%
+
1.31
%

Agricultural
Tractors
176
hp
and
up
+
2.60
%
+
2.06
%
+
1.71
%
+
1.46
%
+
1.27
%

Combines
175
hp
and
up
+
1.33
%
+
1.17
%
+
1.05
%
+
0.95
%
+
0.85
%

Table
3.
Annual
Growth
Rates
by
Decade
for
Logistic
Series
Projections
Application
Engine
Size
2001­
10
2011­
20
2021­
30
2031­
40
2041­
50
Agricultural
Tractors
11­
25
hp
+
8.01
%
+
4.22
%
+
1.56
%
+
0.46
%
+
0.13
%

Agricultural
Tractors
26­
50
hp
+
2.37
%
+
1.17
%
+
0.52
%
+
0.22
%
+
0.09
%

Sprayers
101
hp
and
up
+
0.89
%
+
0.03
%
nil
nil
nil
Todd
Sherwood
August
25,
2003
Page
12
Other
Ag
Equipment
301
hp
and
up
+
0.31
%
nil
nil
nil
nil
References
Cavallini,
Fabio.
1993.
"
Fitting
a
Logistic
Curve
to
Data."
College
Mathematics
Journal
24(
3):
247­
53.

 
Dolce,
Gary
J.
1998.
"
Nonroad
Engine
Growth
Estimates."
U.
S.
Environmental
Protection
Agency,
Office
of
Mobile
Sources,
Report
No.
NR­
008.
Washington,
DC:
EPA.

Power
Systems
Research
(
PSR).
2003.
OELink
 
.
<
http://
www.
powersys.
com/
OELink.
htm>.

U.
S.
Department
of
Commerce,
Bureau
of
the
Census.
1985.
"
Tractors
(
Except
Garden
Tractors)."
M35S(
83)­
13,
and
previous
annual
summaries.
Washington,
DC:
U.
S.
Department
of
Commerce.

U.
S.
Department
of
Commerce,
Bureau
of
the
Census.
1990.
"
Farm
Machinery
and
Lawn
and
Garden
Equipment."
MA35A(
89)­
1,
and
previous
annual
summaries.
Washington,
DC:
U.
S.
Department
of
Commerce.

U.
S.
Department
of
Commerce,
Bureau
of
the
Census.
2000.
"
Annual
Projections
of
the
Total
Resident
Population
as
of
July
1:
Middle,
Lowest,
Highest,
and
Zero
International
Migration
Series,
1999­
2100."
Washington:
Population
Projections
Program,
Population
Division.
Todd
Sherwood
August
25,
2003
Page
13
Appendix
A.
Tables
of
Sales
Projections
Data
 
Base
Case
Ag
Tractor
Combines
Windro
wers
Balers
Sprayers
Irrigation
Sets
Other
Ag
Ag
Mowers
Year
10<
x#
2
5
25<
x#
5
0
50<
x#
7
5
75<
x#

100
100<
x#
1
75
>
175
75<
x#
1
00
100<
x#

175
>
175
All
All
10<
x#
1
00
>
100
10<
x#
25
25<
x#
50
50<
x#
75
75<
x#
10
0
100<
x#
1
75
>
175
10<
x#
5
0
50<
x#
7
5
75<
x#
1
00
100<
x#

175
175<
x#

300
>
300
All
Historical
1973
0
13,805
11,388
9,698
30,545
8,097
595
3,584
2,633
718
15
42
118
14
302
182
744
779
209
230
86
17
Data
1974
0
13,849
13,703
12,159
35,372
9,725
785
3,568
3,100
983
44
44
137
27
571
160
806
870
376
220
80
35
(
from
PSR)
1975
0
9,881
13,442
16,465
43,681
13,399
1,178
4,025
4,557
697
111
62
69
37
668
264
1,078
1,123
578
147
119
49
1976
0
9,713
11,199
18,007
50,847
17,175
1,587
6,307
6,077
208
126
71
65
73
1,316
300
1,229
1,567
746
197
147
51
1977
0
8,816
9,993
20,038
60,145
28,152
1,133
13,456
8,288
736
194
119
80
211
979
468
1,733
2,307
687
292
178
143
172
1978
0
7,715
9,551
18,061
53,740
26,933
778
14,017
8,201
3,447
313
144
130
90
187
717
2,282
4,198
624
564
261
219
151
1979
2
11,643
12,175
20,207
57,395
33,776
1,446
14,557
8,456
2,828
308
197
160
158
480
802
2,912
5,176
797
653
268
290
173
1980
1,091
21,630
20,778
20,105
44,232
28,052
1,651
10,456
7,868
3,678
118
617
227
218
286
719
3,087
4,765
910
583
168
259
147
11
1981
1,088
22,852
18,323
19,367
29,834
22,544
1,510
9,630
7,712
3,924
264
609
130
182
280
685
2,468
3,673
555
450
564
226
122
15
1982
1,087
25,484
17,201
17,903
24,551
20,394
964
6,509
6,653
2,007
263
555
122
127
294
512
1,851
2,756
427
381
634
245
125
17
1983
1,089
26,396
16,231
15,833
18,682
17,396
808
5,748
6,026
1,887
296
612
130
169
262
506
1,745
2,499
357
304
604
242
129
16
1984
1,883
25,788
15,470
14,478
16,075
16,246
1,263
6,471
5,830
2,082
142
344
139
140
358
429
1,427
2,196
315
277
257
144
103
3
60
1985
2,045
24,169
14,535
12,656
8,346
11,538
758
4,152
3,515
3,304
147
353
154
145
374
352
1,411
2,170
380
293
272
128
74
4
64
1986
2,191
23,416
13,854
11,369
7,237
6,302
0
4,991
2,339
3,297
189
367
128
141
388
154
1,467
1,864
362
251
115
97
56
0
65
1987
3,617
21,686
11,963
10,657
8,727
8,107
16
5,999
5,266
4,102
180
336
115
95
228
112
1,350
1,622
418
254
119
94
55
0
58
1988
3,843
20,171
11,534
10,645
9,600
17,221
13
2,895
4,501
2,725
235
204
627
107
237
110
1,597
1,799
501
277
133
103
59
0
58
1989
2,605
20,714
11,534
10,565
9,013
23,217
15
2,637
7,669
2,614
212
232
658
118
259
121
1,377
1,687
471
178
4
334
489
504
70
50
1990
6,314
30,260
9,154
13,420
10,032
30,550
11
2,629
4,444
2,270
307
275
1,125
4
18
11
870
1,030
405
189
0
171
808
735
17
47
1991
6,951
37,759
9,951
12,346
7,738
21,022
16
2,228
4,253
2,128
234
271
1,617
5
43
39
1,221
1,272
422
200
0
138
740
796
15
45
1992
6,771
39,100
8,245
8,207
8,811
19,494
10
2,119
4,095
1,963
228
281
2,063
6
40
42
1,066
1,083
398
200
4
145
733
810
172
45
1993
7,761
39,983
6,534
5,504
11,091
19,763
9
681
5,316
2,147
229
278
2,336
25
56
42
1,284
1,155
437
211
4
156
686
739
191
45
1994
7,880
38,761
9,082
5,753
13,881
22,911
7
378
5,092
2,231
237
322
2,508
29
61
46
1,435
1,261
476
220
3
162
750
780
222
45
1995
8,135
34,458
10,803
6,290
14,657
24,525
3
346
5,542
2,302
225
281
2,580
33
68
54
1,572
1,385
501
233
3
171
828
754
248
45
1996
8,744
38,158
12,541
7,881
16,392
29,731
5
1,329
7,569
2,273
208
332
2,981
34
71
55
1,575
1,439
517
203
29
168
630
665
473
44
1997
8,129
42,609
13,723
9,344
28,487
31,362
3
809
7,933
2,280
230
324
4,040
35
73
55
1,577
1,502
532
188
43
161
518
780
463
45
1998
11,049
41,423
12,685
11,077
31,884
31,603
6
860
8,885
2,018
254
235
4,254
36
75
56
1,622
1,548
549
200
48
147
541
758
559
47
1999
14,086
45,959
15,687
11,401
26,980
28,846
5
873
5,780
1,918
211
194
4,012
180
50
143
493
643
540
2000
15,522
54,773
16,849
12,271
28,072
20,435
0
989
4,673
1,927
212
204
4,015
179
42
167
499
556
480
Projection
s
2001
16,308
49,275
11,616
7,971
23,081
29,865
0
443
6,460
1,917
233
264
4,246
23
33
27
1,482
1,366
460
188
7
140
522
687
550
38
2002
18,023
50,774
11,565
7,744
23,809
30,743
0
383
6,551
1,875
234
261
4,298
22
29
24
1,482
1,343
459
184
6
138
507
685
555
37
2003
19,849
52,226
11,514
7,523
24,537
31,621
0
331
6,643
1,834
235
259
4,332
20
26
21
1,482
1,320
458
180
6
136
493
682
557
36
2004
21,779
53,627
11,463
7,309
25,265
32,499
0
286
6,734
1,794
237
257
4,355
19
23
19
1,483
1,298
457
176
5
134
479
680
558
35
2005
23,803
54,976
11,412
7,101
25,992
33,376
0
248
6,825
1,755
238
255
4,370
18
21
17
1,483
1,276
456
172
4
132
465
678
559
34
2006
25,911
56,269
11,362
6,898
26,720
34,254
0
214
6,917
1,717
239
253
4,380
17
19
15
1,483
1,255
455
169
4
130
452
675
560
33
2007
28,087
57,505
11,312
6,702
27,448
35,132
0
185
7,008
1,679
241
251
4,387
16
17
14
1,483
1,234
454
165
3
128
439
673
560
32
2008
30,313
58,683
11,262
6,511
28,176
36,010
0
160
7,100
1,642
242
248
4,392
15
15
12
1,484
1,213
453
162
3
126
426
671
560
31
2009
32,573
59,803
11,212
6,325
28,904
36,888
0
138
7,191
1,606
244
246
4,394
15
13
11
1,484
1,193
452
158
3
125
414
668
560
30
2010
34,844
60,864
11,163
6,145
29,631
37,765
0
119
7,282
1,571
245
244
4,396
14
12
10
1,484
1,173
451
155
2
123
402
666
560
30
2011
37,109
61,868
11,114
5,970
30,359
38,643
0
103
7,374
1,537
247
242
4,398
13
11
9
1,484
1,153
450
152
2
121
391
663
560
29
2012
39,346
62,814
11,065
5,800
31,087
39,521
0
89
7,465
1,503
248
240
4,398
12
9
8
1,484
1,134
449
148
2
119
379
661
560
28
2013
41,536
63,705
11,016
5,635
31,815
40,399
0
77
7,556
1,470
250
238
4,399
12
8
7
1,485
1,115
448
145
2
117
369
659
560
27
2014
43,663
64,542
10,967
5,474
32,543
41,276
0
67
7,648
1,438
251
236
4,399
11
8
6
1,485
1,096
447
142
1
116
358
657
560
27
2015
45,710
65,326
10,919
5,318
33,271
42,154
0
58
7,739
1,407
253
234
4,400
10
7
5
1,485
1,078
446
139
1
114
348
654
560
26
2016
47,665
66,059
10,871
5,167
33,998
43,032
0
50
7,830
1,376
254
232
4,400
10
6
5
1,485
1,060
445
136
1
112
338
652
560
25
2017
49,519
66,744
10,823
5,020
34,726
43,910
0
43
7,922
1,346
256
230
4,400
9
5
4
1,486
1,042
444
134
1
111
328
650
560
24
2018
51,262
67,382
10,775
4,877
35,454
44,788
0
37
8,013
1,316
257
228
4,400
9
5
4
1,486
1,024
443
131
1
109
319
647
560
24
2019
52,891
67,977
10,727
4,738
36,182
45,665
0
32
8,105
1,287
259
226
4,400
8
4
3
1,486
1,007
442
128
1
108
310
645
560
23
2020
54,404
68,529
10,680
4,603
36,910
46,543
0
28
8,196
1,259
260
224
4,400
8
4
3
1,486
990
441
125
1
106
301
643
560
22
2021
55,800
69,042
10,633
4,472
37,637
47,421
0
24
8,287
1,232
262
223
4,400
8
3
3
1,486
974
440
123
1
105
292
641
560
22
2022
57,082
69,517
10,586
4,344
38,365
48,299
0
21
8,379
1,205
263
221
4,400
7
3
2
1,487
957
439
120
0
103
284
638
560
21
2023
58,253
69,957
10,539
4,221
39,093
49,177
0
18
8,470
1,178
265
219
4,400
7
3
2
1,487
941
438
118
0
102
276
636
560
21
2024
59,317
70,364
10,493
4,100
39,821
50,054
0
16
8,561
1,153
266
217
4,400
6
2
2
1,487
925
437
115
0
100
268
634
560
20
(
continued)
Todd
Sherwood
August
25,
2003
Page
14
Appendix
A.
Tables
of
Sales
Projections
Data
 
Base
Case
(
continued)

Ag
Tractor
Combines
Windro
wers
Balers
Sprayers
Irrigation
Sets
Other
Ag
Ag
Mowers
Year
10<
x#
2
5
25<
x#
5
0
50<
x#
7
5
75<
x#

100
100<
x#
1
75
>
175
75<
x#
1
00
100<
x#

175
>
175
All
All
10<
x#
1
00
>
100
10<
x#
25
25<
x#
50
50<
x#
75
75<
x#
10
0
100<
x#
1
75
>
175
10<
x#
5
0
50<
x#
7
5
75<
x#
1
00
100<
x#

175
175<
x#

300
>
300
All
2025
60,280
70,741
10,446
3,984
40,549
50,932
0
13
8,653
1,127
268
215
4,400
6
2
2
1,487
910
436
113
0
99
260
632
560
20
2026
61,149
71,088
10,400
3,870
41,276
51,810
0
12
8,744
1,103
269
213
4,400
6
2
2
1,488
895
435
110
0
97
253
629
560
19
2027
61,930
71,409
10,354
3,760
42,004
52,688
0
10
8,835
1,079
271
212
4,400
5
2
1
1,488
880
434
108
0
96
245
627
560
18
2028
62,629
71,704
10,309
3,653
42,732
53,565
0
9
8,927
1,055
273
210
4,400
5
2
1
1,488
865
433
106
0
94
238
625
560
18
2029
63,255
71,977
10,263
3,549
43,460
54,443
0
8
9,018
1,032
274
208
4,400
5
1
1
1,488
850
432
104
0
93
232
623
560
17
2030
63,812
72,227
10,218
3,448
44,188
55,321
0
6
9,110
1,009
276
206
4,400
5
1
1
1,488
836
431
101
0
92
225
621
560
17
2031
64,308
72,458
10,173
3,349
44,916
56,199
0
6
9,201
987
278
205
4,400
4
1
1
1,489
822
430
99
0
90
218
618
560
17
2032
64,748
72,670
10,128
3,254
45,643
57,077
0
5
9,292
966
279
203
4,400
4
1
1
1,489
808
429
97
0
89
212
616
560
16
2033
65,137
72,865
10,083
3,161
46,371
57,954
0
4
9,384
945
281
201
4,400
4
1
1
1,489
795
428
95
0
88
206
614
560
16
2034
65,482
73,044
10,039
3,071
47,099
58,832
0
4
9,475
924
282
199
4,400
4
1
1
1,489
781
427
93
0
86
200
612
560
15
2035
65,787
73,208
9,994
2,984
47,827
59,710
0
3
9,566
904
284
198
4,400
3
1
1
1,490
768
426
91
0
85
194
610
560
15
2036
66,056
73,359
9,950
2,899
48,555
60,588
0
3
9,658
884
286
196
4,400
3
1
1
1,490
755
425
89
0
84
189
608
560
14
2037
66,293
73,497
9,906
2,816
49,282
61,465
0
2
9,749
865
288
194
4,400
3
1
0
1,490
743
424
87
0
83
183
606
560
14
2038
66,502
73,624
9,863
2,736
50,010
62,343
0
2
9,840
846
289
193
4,400
3
0
0
1,490
730
423
86
0
82
178
603
560
14
2039
66,686
73,741
9,819
2,658
50,738
63,221
0
2
9,932
827
291
191
4,400
3
0
0
1,490
718
422
84
0
80
173
601
560
13
2040
66,848
73,847
9,776
2,582
51,466
64,099
0
2
10,023
809
293
190
4,400
3
0
0
1,491
706
421
82
0
79
168
599
560
13
2041
66,990
73,945
9,733
2,509
52,194
64,977
0
1
10,115
791
294
188
4,400
2
0
0
1,491
694
421
80
0
78
163
597
560
12
2042
67,115
74,035
9,690
2,437
52,922
65,854
0
1
10,206
774
296
186
4,400
2
0
0
1,491
682
420
79
0
77
159
595
560
12
2043
67,224
74,117
9,647
2,368
53,649
66,732
0
1
10,297
757
298
185
4,400
2
0
0
1,491
671
419
77
0
76
154
593
560
12
2044
67,320
74,192
9,604
2,300
54,377
67,610
0
1
10,389
740
300
183
4,400
2
0
0
1,492
660
418
75
0
75
150
591
560
11
2045
67,405
74,261
9,562
2,235
55,105
68,488
0
1
10,480
724
301
182
4,400
2
0
0
1,492
649
417
74
0
74
145
589
560
11
2046
67,479
74,324
9,520
2,171
55,833
69,365
0
1
10,571
708
303
180
4,400
2
0
0
1,492
638
416
72
0
73
141
587
560
11
2047
67,543
74,382
9,478
2,109
56,561
70,243
0
1
10,663
693
305
179
4,400
2
0
0
1,492
627
415
71
0
72
137
585
560
11
2048
67,600
74,434
9,436
2,049
57,288
71,121
0
0
10,754
678
307
177
4,400
2
0
0
1,492
617
414
69
0
70
133
583
560
10
2049
67,650
74,483
9,394
1,991
58,016
71,999
0
0
10,845
663
309
176
4,400
2
0
0
1,493
606
413
68
0
69
129
581
560
10
2050
67,694
74,527
9,353
1,934
58,744
72,877
0
0
10,937
648
310
174
4,400
1
0
0
1,493
596
412
66
0
68
126
579
560
10
Model
Type
Logisti
c
Logistic
Expone
ntial
Expon
ential
Linear
Linear
None
Expone
ntial
Linear
Expone
ntial
Expone
ntial
Expone
ntial
Logistic
Exponent
ial
Exponent
ial
Exponent
ial
Exponent
ial
Exponent
ial
Exponent
ial
Expone
ntial
Expone
ntial
Expone
ntial
Expone
ntial
Expone
ntial
LogisticExponenti
al
Years
Used
All
All
All
All
(
1982­

2000)
(
1982­

2000)
(
1982­
2000)
(
1982­

2000)
(
1978­

2000)
(
1982­

2000)
(
1977­

2000)
All
All
All
All
All
All
All
All
All
(
1977­

2000)
(
1989­

2000)
(
1989­

2000)
(
1989­

2000)
All
Model
FitInterce
pt
(
c)
7.91
29.02
­

1,433,27
8
­

1,726,5
74
129.24
­

176,358
22.51
­
2.76
9.77
49.68
99.95
99.98
3.04
17.84
4.59
20.72
116.08
14.84
27.96
5.89
25.80
Parameter
s
Slope
(
m)
­

0.00192
1
­

0.0125
51
727.82
877.78
­

0.06326
6
91.36
­

0.00960
9
0.00256
2
­

0.00367
4
­

0.024147
­

0.049194
­

0.049252
0.000065
­

0.007347
­

0.000964
­

0.00921
9
­

0.05757
6
­

0.00634
2
­

0.01261
7
­

0.00152
6
­
0.012105
Todd
Sherwood
August
25,
2003
Page
15
Appendix
B.
Tables
of
Sales
Projections
Data
 
Alternate
Case
Ag
Tractor
Combines
Windro
wers
Balers
Sprayers
Irrigation
Sets
Other
Ag
Year
10<
x#
2
5
25<
x#
5
0
50<
x#
7
5
75<
x#
1
00
100<
x#

175
>
175
75<
x#
1
00
100<
x#

175
>
175
All
All
10<
x#
1
00
>
100
10<
x#
25
25<
x#
50
50<
x#
75
75<
x#
100
100<
x#
17
5
>
175
10<
x#
5
0
50<
x#
7
5
75<
x#
1
00
100<
x#

175
175<
x#

300
>
300
Historica
l
1973
0
13,805
11,388
9,698
30,545
8,097
595
3,584
2,633
718
15
42
118
14
302
182
744
779
209
230
86
17
Data
1974
0
13,849
13,703
12,159
35,372
9,725
785
3,568
3,100
983
44
44
137
27
571
160
806
870
376
220
80
35
(
from
PSR)
1975
0
9,881
13,442
16,465
43,681
13,399
1,178
4,025
4,557
697
111
62
69
37
668
264
1,078
1,123
578
147
119
49
1976
0
9,713
11,199
18,007
50,847
17,175
1,587
6,307
6,077
208
126
71
65
73
1,316
300
1,229
1,567
746
197
147
51
1977
0
8,816
9,993
20,038
60,145
28,152
1,133
13,456
8,288
736
194
119
80
211
979
468
1,733
2,307
687
292
178
143
172
1978
0
7,715
9,551
18,061
53,740
26,933
778
14,017
8,201
3,447
313
144
130
90
187
717
2,282
4,198
624
564
261
219
151
1979
2
11,643
12,175
20,207
57,395
33,776
1,446
14,557
8,456
2,828
308
197
160
158
480
802
2,912
5,176
797
653
268
290
173
1980
1,091
21,630
20,778
20,105
44,232
28,052
1,651
10,456
7,868
3,678
118
617
227
218
286
719
3,087
4,765
910
583
168
259
147
11
1981
1,088
22,852
18,323
19,367
29,834
22,544
1,510
9,630
7,712
3,924
264
609
130
182
280
685
2,468
3,673
555
450
564
226
122
15
1982
1,087
25,484
17,201
17,903
24,551
20,394
964
6,509
6,653
2,007
263
555
122
127
294
512
1,851
2,756
427
381
634
245
125
17
1983
1,089
26,396
16,231
15,833
18,682
17,396
808
5,748
6,026
1,887
296
612
130
169
262
506
1,745
2,499
357
304
604
242
129
16
1984
1,883
25,788
15,470
14,478
16,075
16,246
1,263
6,471
5,830
2,082
142
344
139
140
358
429
1,427
2,196
315
277
257
144
103
3
1985
2,045
24,169
14,535
12,656
8,346
11,538
758
4,152
3,515
3,304
147
353
154
145
374
352
1,411
2,170
380
293
272
128
74
4
1986
2,191
23,416
13,854
11,369
7,237
6,302
0
4,991
2,339
3,297
189
367
128
141
388
154
1,467
1,864
362
251
115
97
56
0
1987
3,617
21,686
11,963
10,657
8,727
8,107
16
5,999
5,266
4,102
180
336
115
95
228
112
1,350
1,622
418
254
119
94
55
0
1988
3,843
20,171
11,534
10,645
9,600
17,221
13
2,895
4,501
2,725
235
204
627
107
237
110
1,597
1,799
501
277
133
103
59
0
1989
2,605
20,714
11,534
10,565
9,013
23,217
15
2,637
7,669
2,614
212
232
658
118
259
121
1,377
1,687
471
178
4
334
489
504
70
1990
6,314
30,260
9,154
13,420
10,032
30,550
11
2,629
4,444
2,270
307
275
1,125
4
18
11
870
1,030
405
189
0
171
808
735
17
1991
6,951
37,759
9,951
12,346
7,738
21,022
16
2,228
4,253
2,128
234
271
1,617
5
43
39
1,221
1,272
422
200
0
138
740
796
15
1992
6,771
39,100
8,245
8,207
8,811
19,494
10
2,119
4,095
1,963
228
281
2,063
6
40
42
1,066
1,083
398
200
4
145
733
810
172
1993
7,761
39,983
6,534
5,504
11,091
19,763
9
681
5,316
2,147
229
278
2,336
25
56
42
1,284
1,155
437
211
4
156
686
739
191
1994
7,880
38,761
9,082
5,753
13,881
22,911
7
378
5,092
2,231
237
322
2,508
29
61
46
1,435
1,261
476
220
3
162
750
780
222
1995
8,135
34,458
10,803
6,290
14,657
24,525
3
346
5,542
2,302
225
281
2,580
33
68
54
1,572
1,385
501
233
3
171
828
754
248
1996
8,744
38,158
12,541
7,881
16,392
29,731
5
1,329
7,569
2,273
208
332
2,981
34
71
55
1,575
1,439
517
203
29
168
630
665
473
1997
8,129
42,609
13,723
9,344
28,487
31,362
3
809
7,933
2,280
230
324
4,040
35
73
55
1,577
1,502
532
188
43
161
518
780
463
1998
11,049
41,423
12,685
11,077
31,884
31,603
6
860
8,885
2,018
254
235
4,254
36
75
56
1,622
1,548
549
200
48
147
541
758
559
1999
14,086
45,959
15,687
11,401
26,980
28,846
5
873
5,780
1,918
211
194
4,012
180
50
143
493
643
540
2000
15,522
54,773
16,849
12,271
28,072
20,435
0
989
4,673
1,927
212
204
4,015
179
42
167
499
556
480
Projectio
ns
2001
12,545
47,693
11,616
7,971
23,081
29,865
0
443
6,460
1,917
233
264
3,569
23
33
27
1,482
1,366
460
188
7
140
522
687
636
2002
13,182
49,132
11,565
7,744
23,809
30,743
0
383
6,551
1,875
234
261
3,730
22
29
24
1,482
1,343
459
184
6
138
507
685
690
2003
13,819
50,572
11,514
7,523
24,537
31,621
0
331
6,643
1,834
235
259
3,890
20
26
21
1,482
1,320
458
180
6
136
493
682
744
2004
14,455
52,011
11,463
7,309
25,265
32,499
0
286
6,734
1,794
237
257
4,051
19
23
19
1,483
1,298
457
176
5
134
479
680
797
2005
15,092
53,451
11,412
7,101
25,992
33,376
0
248
6,825
1,755
238
255
4,212
18
21
17
1,483
1,276
456
172
4
132
465
678
851
2006
15,729
54,890
11,362
6,898
26,720
34,254
0
214
6,917
1,717
239
253
4,372
17
19
15
1,483
1,255
455
169
4
130
452
675
905
2007
16,366
56,329
11,312
6,702
27,448
35,132
0
185
7,008
1,679
241
251
4,533
16
17
14
1,483
1,234
454
165
3
128
439
673
958
2008
17,002
57,769
11,262
6,511
28,176
36,010
0
160
7,100
1,642
242
248
4,693
15
15
12
1,484
1,213
453
162
3
126
426
671
1,012
2009
17,639
59,208
11,212
6,325
28,904
36,888
0
138
7,191
1,606
244
246
4,854
15
13
11
1,484
1,193
452
158
3
125
414
668
1,066
2010
18,276
60,648
11,163
6,145
29,631
37,765
0
119
7,282
1,571
245
244
5,015
14
12
10
1,484
1,173
451
155
2
123
402
666
1,120
2011
18,913
62,087
11,114
5,970
30,359
38,643
0
103
7,374
1,537
247
242
5,175
13
11
9
1,484
1,153
450
152
2
121
391
663
1,173
2012
19,550
63,527
11,065
5,800
31,087
39,521
0
89
7,465
1,503
248
240
5,336
12
9
8
1,484
1,134
449
148
2
119
379
661
1,227
2013
20,186
64,966
11,016
5,635
31,815
40,399
0
77
7,556
1,470
250
238
5,496
12
8
7
1,485
1,115
448
145
2
117
369
659
1,281
2014
20,823
66,406
10,967
5,474
32,543
41,276
0
67
7,648
1,438
251
236
5,657
11
8
6
1,485
1,096
447
142
1
116
358
657
1,334
2015
21,460
67,845
10,919
5,318
33,271
42,154
0
58
7,739
1,407
253
234
5,818
10
7
5
1,485
1,078
446
139
1
114
348
654
1,388
2016
22,097
69,285
10,871
5,167
33,998
43,032
0
50
7,830
1,376
254
232
5,978
10
6
5
1,485
1,060
445
136
1
112
338
652
1,442
2017
22,733
70,724
10,823
5,020
34,726
43,910
0
43
7,922
1,346
256
230
6,139
9
5
4
1,486
1,042
444
134
1
111
328
650
1,495
2018
23,370
72,164
10,775
4,877
35,454
44,788
0
37
8,013
1,316
257
228
6,300
9
5
4
1,486
1,024
443
131
1
109
319
647
1,549
2019
24,007
73,603
10,727
4,738
36,182
45,665
0
32
8,105
1,287
259
226
6,460
8
4
3
1,486
1,007
442
128
1
108
310
645
1,603
2020
24,644
75,043
10,680
4,603
36,910
46,543
0
28
8,196
1,259
260
224
6,621
8
4
3
1,486
990
441
125
1
106
301
643
1,656
2021
25,281
76,482
10,633
4,472
37,637
47,421
0
24
8,287
1,232
262
223
6,781
8
3
3
1,486
974
440
123
1
105
292
641
1,710
2022
25,917
77,921
10,586
4,344
38,365
48,299
0
21
8,379
1,205
263
221
6,942
7
3
2
1,487
957
439
120
0
103
284
638
1,764
2023
26,554
79,361
10,539
4,221
39,093
49,177
0
18
8,470
1,178
265
219
7,103
7
3
2
1,487
941
438
118
0
102
276
636
1,817
2024
27,191
80,800
10,493
4,100
39,821
50,054
0
16
8,561
1,153
266
217
7,263
6
2
2
1,487
925
437
115
0
100
268
634
1,871
Todd
Sherwood
August
25,
2003
Page
16
Appendix
B.
Tables
of
Sales
Projections
Data
 
Alternate
Case
(
continued)

Ag
Tractor
Combines
Windrow
ers
Balers
Sprayers
Irrigation
Sets
Other
Ag
Year
10<
x#
25
25<
x#
50
50<
x#
75
75<
x#
10
0
100<
x#
1
75
>
175
75<
x#
10
0
100<
x#
1
75
>
175
All
All
10<
x#
10
0
>
100
10<
x#
25
25<
x#
50
50<
x#
75
75<
x#
100
100<
x#
175
>
175
10<
x#
50
50<
x#
75
75<
x#
10
0
100<
x#
1
75
175<
x#
3
00
>
300
2025
27,828
82,240
10,446
3,984
40,549
50,932
0
13
8,653
1,127
268
215
7,424
6
2
2
1,487
910
436
113
0
99
260
632
1,925
2026
28,464
83,679
10,400
3,870
41,276
51,810
0
12
8,744
1,103
269
213
7,585
6
2
2
1,488
895
435
110
0
97
253
629
1,978
2027
29,101
85,119
10,354
3,760
42,004
52,688
0
10
8,835
1,079
271
212
7,745
5
2
1
1,488
880
434
108
0
96
245
627
2,032
2028
29,738
86,558
10,309
3,653
42,732
53,565
0
9
8,927
1,055
273
210
7,906
5
2
1
1,488
865
433
106
0
94
238
625
2,086
2029
30,375
87,998
10,263
3,549
43,460
54,443
0
8
9,018
1,032
274
208
8,066
5
1
1
1,488
850
432
104
0
93
232
623
2,139
2030
31,012
89,437
10,218
3,448
44,188
55,321
0
6
9,110
1,009
276
206
8,227
5
1
1
1,488
836
431
101
0
92
225
621
2,193
2031
31,648
90,877
10,173
3,349
44,916
56,199
0
6
9,201
987
278
205
8,388
4
1
1
1,489
822
430
99
0
90
218
618
2,247
2032
32,285
92,316
10,128
3,254
45,643
57,077
0
5
9,292
966
279
203
8,548
4
1
1
1,489
808
429
97
0
89
212
616
2,300
2033
32,922
93,756
10,083
3,161
46,371
57,954
0
4
9,384
945
281
201
8,709
4
1
1
1,489
795
428
95
0
88
206
614
2,354
2034
33,559
95,195
10,039
3,071
47,099
58,832
0
4
9,475
924
282
199
8,870
4
1
1
1,489
781
427
93
0
86
200
612
2,408
2035
34,195
96,635
9,994
2,984
47,827
59,710
0
3
9,566
904
284
198
9,030
3
1
1
1,490
768
426
91
0
85
194
610
2,461
2036
34,832
98,074
9,950
2,899
48,555
60,588
0
3
9,658
884
286
196
9,191
3
1
1
1,490
755
425
89
0
84
189
608
2,515
2037
35,469
99,513
9,906
2,816
49,282
61,465
0
2
9,749
865
288
194
9,351
3
1
0
1,490
743
424
87
0
83
183
606
2,569
2038
36,106
100,953
9,863
2,736
50,010
62,343
0
2
9,840
846
289
193
9,512
3
0
0
1,490
730
423
86
0
82
178
603
2,623
2039
36,743
102,392
9,819
2,658
50,738
63,221
0
2
9,932
827
291
191
9,673
3
0
0
1,490
718
422
84
0
80
173
601
2,676
2040
37,379
103,832
9,776
2,582
51,466
64,099
0
2
10,023
809
293
190
9,833
3
0
0
1,491
706
421
82
0
79
168
599
2,730
2041
38,016
105,271
9,733
2,509
52,194
64,977
0
1
10,115
791
294
188
9,994
2
0
0
1,491
694
421
80
0
78
163
597
2,784
2042
38,653
106,711
9,690
2,437
52,922
65,854
0
1
10,206
774
296
186
10,155
2
0
0
1,491
682
420
79
0
77
159
595
2,837
2043
39,290
108,150
9,647
2,368
53,649
66,732
0
1
10,297
757
298
185
10,315
2
0
0
1,491
671
419
77
0
76
154
593
2,891
2044
39,926
109,590
9,604
2,300
54,377
67,610
0
1
10,389
740
300
183
10,476
2
0
0
1,492
660
418
75
0
75
150
591
2,945
2045
40,563
111,029
9,562
2,235
55,105
68,488
0
1
10,480
724
301
182
10,636
2
0
0
1,492
649
417
74
0
74
145
589
2,998
2046
41,200
112,469
9,520
2,171
55,833
69,365
0
1
10,571
708
303
180
10,797
2
0
0
1,492
638
416
72
0
73
141
587
3,052
2047
41,837
113,908
9,478
2,109
56,561
70,243
0
1
10,663
693
305
179
10,958
2
0
0
1,492
627
415
71
0
72
137
585
3,106
2048
42,474
115,348
9,436
2,049
57,288
71,121
0
0
10,754
678
307
177
11,118
2
0
0
1,492
617
414
69
0
70
133
583
3,159
2049
43,110
116,787
9,394
1,991
58,016
71,999
0
0
10,845
663
309
176
11,279
2
0
0
1,493
606
413
68
0
69
129
581
3,213
2050
43,747
118,227
9,353
1,934
58,744
72,877
0
0
10,937
648
310
174
11,440
1
0
0
1,493
596
412
66
0
68
126
579
3,267
Model
Type
Linear
Linear
Exponent
ial
Exponent
ial
Linear
Linear
None
Exponent
ial
Linear
Exponent
ial
Exponent
ial
Exponent
ial
Linear
Exponentia
l
Exponentia
l
Exponentia
l
Exponentia
l
Exponentia
l
Exponentia
l
Exponent
ial
Exponent
ial
Exponent
ial
Exponent
ial
Exponent
ial
Linear
Years
Used
All
All
All
All
(
1982­

2000)
(
1982­

2000)
(
1982­
2000)
(
1982­

2000)
(
1978­

2000)
(
1982­

2000)
(
1977­

2000)
All
All
All
All
All
All
All
All
All
(
1977­

2000)
(
1989­

2000)
(
1989­

2000)
(
1989­

2000)

Model
Fit
Intercept
­
1,261,65
0
­

2,832,68
1
7.91
29.02
­
32.05
­

1,726,57
4
129.24
­
176,358
22.51
­
2.76
9.77
­
317,836
49.68
99.95
99.98
3.04
17.84
4.59
20.72
116.08
14.84
27.96
5.89
­
106,774
Parameter
s
Slope
636.8
1439.5
­

0.001921
­

0.012551
0.018179
877.78
­

0.063266
91.36
­

0.009609
0.002562
­

0.003674
160.62
­
0.024147
­
0.049194
­
0.049252
0.000065
­
0.007347
­
0.000964
­

0.009219
­

0.057576
­

0.006342
­

0.012617
­

0.001526
53.68
Todd
Sherwood
August
25,
2003
Page
17
Ag
Tractor
Sales
100
<
x
<
175hp
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Units
Sold
PSR
Data
Linear
Fit
AG
Tractor
Sales
50
<
x
<
75hp
6,000
8,000
10,000
12,000
14,000
16,000
18,000
20,000
22,000
1970
1975
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Units
Sold
Sales
Exponential
Fit
Ag
Tractor
Sales
10
<
x
<
of
<
25hp
Logistic
and
Linear
Projections
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
1975
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Units
Sold
PSR
Data
Logistic
Fit
Linear
Fit
Appendix
C:
Thumbnail
Graphs
of
Projections
Todd
Sherwood
August
25,
2003
Page
18
AG
Tractor
Sales
>
175hp
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Units
Sold
PSR
Data
Linear
Fit
AG
Tractor
Sales
75
<
x
<
100hp
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
20,000
22,000
1970
1975
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Units
Sold
PSR
Data
Exponential
Fit
Ag
Tractor
Sales
25
<
x
<
50hp
Logistic,
Linear,
and
Exponential
Projections
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
100,000
1970
1975
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
Annual
Units
Sold
PSR
Data
Logistic
Linear
Exponential
Todd
Sherwood
August
25,
2003
Page
19
Combine
Sales
101<
x
<
175hp
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Units
Sold
PSR
Data
Exponential
Fit
Combine
Sales
>
175hp
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
10,000
11,000
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Units
Sold
PSR
Data
Linear
Fit
Total
Windrower
Sales
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
4,500
1975
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Units
Sold
PSR
Data
Exponential
Fit
Total
Baler
Sales
125
150
175
200
225
250
275
300
325
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Units
Sold
PSR
Data
Exponential
Fit
<
100hp
Sprayer
Sales
and
Projections
0
100
200
300
400
500
600
700
1975
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Units
Sold
PSR
Data
Exponential
Fit
Sprayers
>
100hp
Logistic
and
Linear
Projections
­
2,000
0
2,000
4,000
6,000
8,000
10,000
12,000
1970
1975
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Units
Sold
PSR
Data
Logistic
Fit
Series3
Todd
Sherwood
August
25,
2003
Page
20
Irrigation
Sets
100
<
x
<
175hp
0
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
4,500
5,000
5,500
1970
1975
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Units
Sold
PSR
Data
Exponential
Fit
Irrigation
Sets
>
175hp
0
100
200
300
400
500
600
700
800
900
1,000
1970
1975
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Units
Sold
PSR
Data
Exponential
Fit
Irrigation
Sets
50
<
x
<
75hp
0
100
200
300
400
500
600
700
800
900
1970
1975
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Units
Sold
PSR
Data
Exponential
Fit
Irrigation
Sets
75
<
x
<
100hp
0
500
1,000
1,500
2,000
2,500
3,000
3,500
1970
1975
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Units
Sold
PSR
Data
Exponential
Fit
Irrigation
Sets
10
<
x
<
25hp
0
20
40
60
80
100
120
140
160
180
200
220
240
1970
1975
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Units
Sold
PSR
Data
Exponential
Fit
Irrigation
Sets
25
<
x
<
50hp
0
200
400
600
800
1,000
1,200
1,400
1970
1975
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Units
Sold
PSR
Data
Exponential
Fit
Todd
Sherwood
August
25,
2003
Page
21
Other
Ag
Equip
10
<
x
<
50hp
0
100
200
300
400
500
600
700
1970
1975
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Units
Sold
PSR
Data
Exponential
Fit
Other
Ag
Equip
50
<
x
<
75hp
0
100
200
300
400
500
600
700
1970
1975
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Units
Sold
PSR
Data
Exponential
Fit
Other
Ag
Equip
75
<
x
<
100hp
0
50
100
150
200
250
300
350
400
1975
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Units
Sold
PSR
Data
Exponential
Fit
Other
Ag
Equip
100
<
x
<
175hp
0
100
200
300
400
500
600
700
800
900
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Units
Sold
PSR
Data
Exponential
Fit
Other
Ag
Equip
175
<
x
<
300hp
400
450
500
550
600
650
700
750
800
850
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Units
Sold
PSR
Data
Exponential
Fit
Other
Ag
Equipment
>
300hp
Logistic
and
Linear
Projections
0
500
1,000
1,500
2,000
2,500
3,000
3,500
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Annual
Unit
Sales
PSR
Data
Logistic
Fit
Series3