An economic analysis of corn yield, corn profitability, and risk at the edge of the Corn Belt


Chavas, J.P.; Kim, K.S.; Lauer, J.G.; Klemme, R.M.; Bland, W.L.

Journal of Agricultural and Resource Economics 26(1): 230-247

2001


This study investigates the recent evolution of corn yield, with a special focus on the tradeoff between corn profitability and risk. The analysis relies on time-series data from Wisconsin experimental farms at the edge of the Corn Belt. An econometric model of corn yield, corn grain moisture, and corn profitability is specified. Both conditional means and conditional variances are estimated for different sites in Wisconsin. The empirical analysis shows the changes in corn yield and profit over time and across space. The evidence suggests that yield trends are due mostly to technical progress, with smaller effects generated by climate change. On average, corn yield and profitability have improved faster in northern Wisconsin than in the Corn Belt. However, risk has also increased faster. Results show that the choice of corn hybrid maturity makes it easier to manage risk in the Corn Belt than in northern Wisconsin.

Journal
of
Agricultural
and
Resource
Economics
26(1):230-247
Copyright
2001
Western
Agricultural
Economics
Association
An
Economic
Analysis
of
Corn
Yield,
Corn
Profitability,
and
Risk
at
the
Edge
of
the
Corn
Belt
Jean
-Paul
Chavas,
Kwansoo
Kim,
Joseph
G.
Lauer,
Richard
M.
Klemme,
and
William
L.
Bland
This
study
investigates
the
recent
evolution
of
corn
yield,
with
a
special
focus
on
the
tradeoff
between
corn
profitability
and
risk.
The
analysis
relies
on
time
-series
data
from
Wisconsin
experimental
farms
at
the
edge
of
the
Corn
Belt.
An
econometric
model
of
corn
yield,
corn
grain
moisture,
and
corn
profitability
is
specified.
Both
conditional
means
and
conditional
variances
are
estimated
for
different
sites
in
Wisconsin.
The
empirical
analysis
shows
the
changes
in
corn
yield
and
profit
over
time
and
across
space.
The
evidence
suggests
that
yield
trends
are
due
mostly
to
technical
progress,
with
smaller
effects
generated
by
climate
change.
On
average,
corn
yield
and
profit-
ability
have
improved
faster
in
northern
Wisconsin
than
in
the
Corn
Belt.
However,
risk
has
also
increased
faster.
Results
show
that
the
choice
of
corn
hybrid
maturity
makes
it
easier
to
manage
risk
in
the
Corn
Belt
than
in
northern
Wisconsin.
Key
words:
climate,
corn,
crop
yield,
farm
profitability,
management
practices,
risk,
technology
Introduction
Many
factors
influence
the
evolution
of
agricultural
productivity.
First,
a
substantial
amount
of
research
has
focused
on
climate
change
and
its
effects
on
crop
yields
(e.g.,
Adams
et
al.;
Baker,
Rushy,
and
Skaggs;
Houghton
and
Woodwell;
Thompson
1969,
1975, 1986,
1988).
These
effects
involve
changes
in
yield
trend
as
well
as
yield
variabil-
ity.
Second,
there
is
strong
evidence
showing
rapid
technological
change
has
contributed
to
a
significant
increase
in
average
yield
over
time
(e.g.,
Baker,
Rushy,
and
Skaggs;
Ramirez).
Thompson
(1975,
1986)
and
Cardwell
found
that
only
a
small
portion
of
yield
trends
can
be
attributed
to
evolving
weather
patterns
in
recent
years.
This
stresses
the
important
effects
of
technological
progress
on
yield
and
crop
productivity.
However,
there
is
also
evidence
of
a
significant
increase
in
yield
variability
over
the
last
few
decades
(e.g.,
Thompson
1988;
Ramirez).
Part
of
this
increase
has
been
attributed
to
climatic
changes
(Baker,
Rushy,
and
Skaggs),
which
suggests
farmers
are
now
exposed
to
greater
production
uncertainty.
There
is
a
need
to
investigate
farmers'
changing
risk
exposure
and
to
reassess
farm
management
strategies
dealing
with
production
risk.
Jean
-Paul
Chavas
is
professor
and
Kwansoo
Kim
is
research
associate,
Department
of
Agricultural
and
Applied
Economics;
Joseph
G.
Lauer
is
associate
professor,
Department
of
Agronomy;
Richard
M.
Klemme
is
associate
dean,
College
of
Agri-
cultural
and
Life
Sciences;
and
William
L.
Bland
is
associate
professor,
Department
of
Soil
Science,
all
at
the
University
of
Wisconsin,
Madison.
This
project
was
funded
by
a
Hatch
grant
from
the
College
of
Agricultural
and
Life
Sciences,
University
of
Wisconsin,
Madison.
The
authors
acknowledge
the
contribution
of
Ren
Zhong
for
research
assistance,
and
thank
two
anonymous
reviewers
for
useful
comments
on
an
earlier
draft
of
this
paper.
Review
coordinated
by
Gary
D.
Thompson.
Chavas
et
al.
Economic
Analysis
of
Corn
Yield,
Profitability,
and
Risk
231
Accumulations
of
greenhouse
gases
(particularly
CO
2
)
contribute
to
climatic
changes
and
global
warming
(Houghton
and
Woodwell;
U.S.
Department
of
Commerce/NOAA).
The
effects
of
global
warming
on
agricultural
productivity
have
generated
much
interest.
Mendelsohn,
Nordhaus,
and
Shaw
found
evidence
showing
global
warming
(through
generation
of
both
higher
temperatures
and
higher
precipitations)
would
be
harmful
to
the
traditional
U.S.
grain
-producing
regions
(such
as
the
Corn
Belt)
while
benefiting
the
northern
fringe
of
the
United
States.
Thus
climatic
changes
have
differential
impacts
across
regions,
suggesting
a
need
to
investigate
how
agricultural
productivity
has
recently
changed
over
space.
This
study
investigates
the
recent
evolution
of
corn
yield,
with
a
special
focus
on
the
tradeoff
between
corn
profitability
and
risk.
Our
analysis
relies
on
time
-series
data
from
Wisconsin
experimental
farms
at
the
edge
of
the
Corn
Belt
for
the
period
1974-1997.
An
econometric
model
of
corn
yield,
corn
grain
moisture,
and
corn
profitability
is
specified
for
three
different
sites
in
Wisconsin.
The
analysis
provides
useful
insights
on
the
eco-
nomics
and
uncertainty
of
corn
production
in
the
northern
Corn
Belt
and
the
northern
fringe
of
the
United
States,
reflecting
the
effects
of
changes
in
climate
as
well
as
tech-
nology.
We
focus
on
an
ex
ante
analysis
at
planting
time,
when
the
farmer
does
not
know
the
weather
conditions
during
the
growing
season.
In
this
context,
corn
yield
is
treated
as
a
random
variable,
conditional
on
decisions
made
at
planting
time.
We
analyze
the
effects
of
choosing
corn
hybrid
maturity
on
corn
yield,
corn
grain
moisture
at
harvest,
and
corn
profitability.
The
choice
of
hybrid
maturity
is
an
important
management
tool
for
dealing
with
production
uncertainty.
For
example,
for
a
given
length
of
the
growing
season,
planting
longer
(shorter)
season
hybrids
tends
to
increase
(decrease)
expected
yield,
but
also
increases
(decreases)
production
risk.
These
effects
can
vary
across
sites
(e.g.,
with
changes
in
the
corn
growing
season).
Effects
also
vary
over
time
due
to
tech-
nological
progress
and
climate
change.
An
important
objective
of
this
research
is
to
evaluate
the
effectiveness
of
choosing
corn
hybrid
maturity
as
a
risk
management
tool,
and
to
observe
how
this
effectiveness
has
varied
both
over
time
and
across
sites.
Evaluated
ex
ante
at
planting
time,
corn
yield,
corn
grain
moisture
at
harvest,
and
corn
profitability
are
random
variables
that
depend
on
weather
patterns
during
the
growing
season.
Thus,
there
is
a
need
to
specify
and
estimate
their
respective
distribu-
tion
functions,
conditional
on
technology,
climate,
and
the
choice
of
corn
hybrid
maturity.
This
can
be
done
using
biophysical
models
of
corn
yield,
which
evaluate
the
effects
of
weather
on
corn
growth
(Runge;
Coelho
and
Dale;
Dixon
et
al.;
Kaufmann
and
Snell).
Alternatively,
econometric
methods
can
be
used
to
estimate
the
distribution
functions
more
directly
(Nelson
and
Preckel;
Kaylen,
Wade,
and
Frank;
Gallagher;
Goodwin
and
Ker;
Ramirez).
As
noted
by
Goodwin
and
Ker,
and
by
Ramirez,
these
distribution
func-
tions
can
be
complex.
Here,
we
rely
on
central
-moment
measurements.
Following
Antle,
and
Antle
and
Goodger,
this
method
provides
a
fl
exible
and
convenient
basis
for
evalu-
ating
the
effects
of
risk
on
production
decisions.
It
gives
the
framework
for
estimating
conditional
means
and
conditional
variances
of
the
relevant
variables
over
time
and
at
different
Wisconsin
sites.
The
remainder
of
the
article
is
organized
as
follows.
We
first
develop
a
model
of
decision
making
under
uncertainty
and
review
the
moment
-based
representation
of
the
uncertainty
under
risk
aversion.
The
data
and
application
to
corn
at
the
edge
of
the
Corn
Belt
are
then
considered,
followed
by
a
presentation
of
the
empirical
analysis.
232
July
2001
Journal
of
Agricultural
and
Resource
Economics
empirical
analysis
demonstrates
how
corn
yield
and
profit
have
changed
over
time,
and
how
they
are
affected
by
the
choice
of
corn
hybrid
maturity
across
sites.
The
evidence
suggests
yield
trends
are
due
mostly
to
technical
progress,
with
smaller
effects
gener-
ated
by
climate
change.
Based
on
our
results,
corn
yield
and
corn
profitability
have
improved
faster
in
northern
Wisconsin
than
in
the
Corn
Belt.
However,
risk
has
also
increased
faster.
Further,
we
found
that
the
choice
of
corn
hybrid
maturity
makes
it
easier
to
manage
risk
in
the
Corn
Belt
than
in
northern
Wisconsin.
Concluding
remarks
are
presented
in
the
final
section.
Decision
Making
Under
Uncertainty
Consider
a
farm
producing
under
uncertainty.
Under
technology
t,
farm
profit
is
repre-
sented
by
the
stochastic
function
n(x,
t,
e),
where
x
is
an
(n
x
1)
vector
of
inputs
and
e
is
a
vector
of
uncontrollable
factors
that
are
not
known
to
the
decision
maker
at
the
time
x
is
chosen.
The
vector
e
is
treated
as
a
random
vector
with
a
given
probability
distri-
bution
G.
It
includes
the
unpredictable
effects
of
weather
on
farm
production.
In
this
context,
the
influence
of
input
choice
x
on
farm
profit
depends
on
both
weather
effects
e
and
technology
t.
Assume
that
inputs
are
chosen
to
maximize
the
expected
utility
of
profit,
EU(it)
=
f
U(it)
dG,
where
E
is
the
expectation
operator
based
on
the
information
available
at
the
time
decisions
are
made.
The
von
Neumann
-Morgenstern
utility
function
U(it)
represents
the
risk
preferences
of
the
decision
maker,
with
a
Wait
>
0.
1
Thus,
we
assume
that
farm
decision
making
is
represented
by
the
following
optimization
problem:
(1)
x*(t)
solves
max
{EU[n(x,
t,
e)]}.
Making
(1)
empirically
tractable
requires
information
about
the
expected
utilityEU(it).
A
convenient
approach
is
to
rely
on
the
moments
of
stochastic
profit
it.
Let
11
17
,(x,
t)
=
En(x,
t,
e)
=
f
n(x,
t,
e)dG(e)
the
mean
profit
or
first
moment
of
profit.
Then,
assuming
differentiability,
expanding
U(it)
in
an
mth-order
Taylor
series
about
11
17
,
and
taking
expectation
gives
m
(2)
EU(n)
U(1.1
1
„)
+
E
i
=2
aiu
)•
E[(Tu
-
i!
an
m
{1
aiu
=
E
(311,c)
I
l
ini
i
=2
i!
aTe
where
p
i
,
c
(x,
t)
=
E[(n(x,
t,
e)
-
11
17
,(x,
0)1
is
the
ith
central
moment
of
it
=
2,
...,
m}.
Equation
(2)
shows
how
expected
utility
depends
on
mean
profit
11
17
,(x,
t),
on
the
variance
of
profit
p
27
,(x,
t),
on
the
skewness
of
profit
1.1
37
,(x,
t),
etc.
In
turn,
each
moment
of
profit
depends
on
the
input
decision
x
and
on
technology
t.
Note
that
equation
(2)
applies
under
very
general
conditions.
It
requires
only
that
the
first
m
moments
of
it
are
finite.
As
such,
it
allows
for
many
probability
distribution
functions
for
the
random
variables
e,
thus
providing
a
flexible
representation
of
the
uncertainty.
A
linear
function
U(n)
would
represent
risk
neutrality,
while
risk
aversion
implies
that
U(a)
is
a
concave
function
(Pratt).
Chavas
et
al.
Economic
Analysis
of
Corn
Yield,
Profitability,
and
Risk
233
Under
risk
neutrality,
the
utility
function
U(n)
is
linear,
and
maximizing
(2)
reduces
to
maximizing
expected
profit
11
1
,,(x,
t)
=
Erc(x,
t,
e).
However,
there
is
strong
empirical
evidence
suggesting
most
farmers
are
risk
averse
(Young;
Lin,
Dean,
and
Moore;
Saha,
Shumway,
and
Talpaz;
Chavas
and
Holt).
Under
risk
aversion,
8
2
U/an
t
<
0
means
that
the
variance
of
profit
1.1
27
,
becomes
relevant
in
(1),
indicating
a
need
to
estimate
the
moments
of
profit
p,„(x,
t)
i
=
1,
2,
...,
m}.
This
can
be
done
by
specifying
a
parametric
form
for
each
A
T
,
and
estimating
the
corresponding
parameters.
Let
A
i
,
=
f
i
(x,
t,
13,),
where
13,
is
a
vector
of
parameters
representing
the
effects
of
x
and
t
on
the
ith
moment
of
profit
i
=
1,
2,
...,
m}.
Then,
consider
the
econometric
model
(3)
rc
=
f
i
(x,
t,
13
1
)
+
where
v
17
,
is
an
error
term
distributed
with
mean
zero,
E(v,,,)
=
0.
Assume
that
we
obtain
a
sample
of
observations
on
profit
n
and
on
the
variables
(x,
t).
Then,
treating
(x,
t)
as
exogenous
variables,
equation
(3)
is
a
standard
regression
model
where
the
parameters
1,
can
be
consistently
estimated
by
the
least
squares
method.
Let
137
be
the
least
squares
estimator
of
13
1
in
(3),
giving
vi
n
=
it
- f
1
(x,
t,
137)
as
the
least
squares
residual.
Because
14
is
a
consistent
estimator
of
13,,
it
follows
that
vi
n
is
a
consistent
estimator
of
Using
(3),
we
obtain
E[(v
D
)l]
=
E
[(Tc
-
=
A.
It
follows
that
(v
h
)
i
=
f
i
(x,
t,
13,)
+
where
v
in
is
an
error
term
distributed
with
mean
zero,
E(v
in
)
=
0,
and
i
z
2.
This
suggests
the
following
model
specification:
(4)
(vin)`
=
f
i
(x,
t,
13
i
)
+
v
in
,
i
z
2.
Again,
assuming
a
sample
of
observations
on
profit
n
and
on
the
exogenous
variables
(x,
t),
consider
(4)
as
a
regression
model
and
let
P
i
e
be
the
least
squares
estimator
of
13,
in
(4).
Because
4
T
,
is
a
consistent
estimator
of
v
1
„,
it
follows
that
137
is
a
consistent
esti-
mator
of
13,
in
(4),
where
i
z
2
(Antle).
Thus,
the
least
squares
estimation
of
(3)
and
(4)
gives
consistent
estimates
of
the
central
moments
of
profit,
including
mean
profit
11
17
,
=
f
1
(x,
t,
137),
and
the
variance
of
profit
p
=
f
2
(x,
t,
14).
This
provides
a
framework
for
the
empirical
investigation
of
the
distribution
of
profit
as
it
changes
with
technology
t
and
the
input
choices
x.
Under
risk
neutrality,
expression
(1)
implies
the
input
choice
x
would
be
chosen
so
as
to
maximize
expected
profit
E(n)
=
t,
137).
Alternatively,
under
risk
aversion,
production
decisions
in
(1)
would
take
into
consideration
both
mean
profit
f
1
(x,
t,
137),
and
the
variance
of
profit
f
2
(x,
t,
(4).
If
we
restrict
our
attention
only
to
these
first
two
moments,
then
risk
aversion
will
imply
some
tradeoff
between
expected
profit
and
the
variance
of
profit
(Meyer).
Under
risk
aversion,
the
decision
maker
will
always
choose
to
obtain
the
highest
pos-
sible
expected
profit
for
a
given
variance,
or
the
smallest
possible
variance
for
a
given
expected
profit
(Anderson,
Dillon,
and
Hardaker).
This
defines
the
"mean
-variance
frontier"
or,
equivalently,
a
"mean
-standard
deviation"
frontier.
Without
information
on
the
exact
risk
preferences
of
the
decision
maker,
the
optimal
decision
in
(1)
will
be
a
point
on
this
frontier.
Under
risk
neutrality,
it
would
correspond
to
the
point
where
the
expected
profit
is
the
largest
possible.
Under
extreme
risk
aversion,
it
would
correspond
to
the
point
where
the
variance
(or
standard
deviation)
of
profit
is
the
smallest
possible
(which
is
typically
associated
with
lower
expected
profit).
Under
intermediate
situations,
it
would
trade
off
increases
in
expected
profit
with
decreases
in
variance
(or
standard
deviation)
depending
on
the
degree
of
risk
aversion
of
the
decision
maker.
234
July
2001
Journal
of
Agricultural
and
Resource
Economics
It
is
often
of
interest
to
know
in
more
detail
how
input
choice
x,
technology
t,
and
uncertainty
e
affect
farm
profit
7t
.
These
effects
can
take
place
through
outputs
and/or
inputs.
On
the
output
side,
these
effects
can
be
represented
by
a
stochastic
production
function:
y
=
y(x,
t,
e),
where
y
denotes
farm
output,
and
e
represents
the
effects
of
production
uncertainty
(e.g.,
weather)
on
agricultural
production.
On
the
input
side,
cost
effects
can
be
represented
by
a
stochastic
function:
C
=
C(x,
t,
e),
which
allows
cost
to
vary
with
input
choice
x,
technology
t,
and
production
uncertainty
e
(e.g.,
weather).
2
Denoting
byp
the
price
of
output
y,
then
farm
profit
is
specified
as
7r
(x,
t,
e)
=
py(x,
t,
e)
-
C(x,
t,
e).
Based
on
the
above
discussion,
we
decompose
the
effects
of
(x,
t,
e)
on
farm
profit
rc
into
two
effects:
(a)
production
effects
through
the
production
function
y(x,
t,
e),
and
(b)
cost
effects
through
the
function
C(x,
t,
e).
3
Both
functions
are
stochastic
because
they
depend
on
the
random
variables
e.
Like
the
profit
function
t,
they
can
each
be
repre-
sented
by
their
central
moments
—mean,
variance,
etc.
The
empirical
analysis
of
these
moments
can
be
conducted
in
a
manner
similar
to
the
approach
discussed
above
for
the
profit
function.
In
particular,
the
central
moments
of
the
production
function
y(x,
t,
e)
can
be
parameterized
as
E(y)
=
g
i
(x,
t,
a)
for
average
production,
E[(y
-
101
=
p
2y
=g
2
(x,
t,
a
2
)
for
the
variance
of
production,
and
so
forth.
Furthermore,
given
sample
data
on
output
y,
and
the
variables
(x,
t)
are
treated
as
exogenous
variables,
the
functions
g
i
(x,t,
{
i
=
1,
2,
...,
ml
can
be
consistently
estimated
by
standard
econometric
methods.
Similarly,
the
central
moments
of
the
function
C(x,
t,
e)
can
be
parameterized
as
E(C)
=
31
1c
=
t,
y
1
)
for
expected
cost,
E[(C
-
p,
c
)
2
]
= =
h
2
(x,
t,
y
2
)
for
the
variance
of
cost,
etc.
Again,
given
appropriate
sample
data,
the
functions
h
i
(x,t,yd
{
i
=1,
2,
...,
m}
can
be
consistently
estimated
using
standard
econometric
methods.
This
procedure
can
provide
useful
insights
on
the
effects
of
management
practices
on
crop
yield,
agricultural
produc-
tivity,
cost,
farm
profitability,
and
risk
exposure.
While
least
squares
estimation
provides
consistent
estimates
of
the
parameters
of
the
conditional
moments
[e.g.,
in
(3)
and
(4)],
it
will
be
of
interest
to
test
hypotheses
about
these
parameters.
In
general,
the
conditional
-moment
specifications
suggest
the
presence
of
heteroskedasticity
(Just
and
Pope;
Yang,
Koo,
and
Wilson).
This
factor
must
be
taken
into
consideration
when
conducting
hypothesis
testing.
We
address
this
issue
by
imple-
menting
the
procedure
proposed
by
White,
which
gives
consistent
estimates
of
the
standard
errors
in
the
presence
of
general
heteroskedasticity.
This
estimation
and
testing
procedure
is
applied
in
the
investigation
of
corn
production,
discussed
in
the
next
section.
An
Application
to
Corn
The
effects
of
technology
and
climatic
changes
on
corn
yield
have
been
the
subjects
of
much
research.
These
effects
are
particularly
interesting
at
the
edge
of
the
Corn
Belt,
where
it
is
well
known
that
corn
production
has
a
large
comparative
advantage.
Corn
is
grown
in
this
region
under
a
broad
range
of
economic
and
climatic
scenarios.
However,
2
Note
that
this
allows
for
cost
to
depend
directly
on
output
y
[e.g.,
c(y,
x,
t,
e)].
An
example
is
the
case
of
storage
and
drying
cost
considered
below,
cost
that
varies
with
output.
In
this
case,
after
substituting
the
stochastic
production
function
y
=
y(x,
t,
e),
we
obtain
C(x,
t,
e)
=
c(y(x,
t,
e),
x,
t,
e).
3
For
simplicity,
we
focus
our
attention
on
production
and
cost
uncertainty.
This
neglects
the
possible
effects
of
price
uncer-
tainty.
Incorporating
price
risk
into
the
analysis
would
be
straightforward.
This
is
not
done
here
given
our
focus
on
weather
and
technology
effects.
Chavas
et
al.
Economic
Analysis
of
Corn
Yield,
Profitability,
and
Risk
235
Table
1.
Description
of
Data:
Annual
Experimental
Observations,
1972-1997
Wisconsin
Research
No.
of
Average
Yield
Average
Moisture
Relative
Maturity
(RM)
(days)
Min.
Max.
Station
Site
(Location)
Observ.
(bu./acre)
(%)
Arlington
(South)
2,484
166.3
25.9
85
120
Marshfield
(North
Central)
1,591
119.5
27.5
75
110
Spooner
(North)
2,335
109.0
27.9
70
110
changing
technology
and
weather
patterns
can
have
significant
effects
on
corn
produc-
tion
in
more
marginal
areas
around
the
Corn
Belt.
Indeed,
such
changes
can
contribute
to
either
expanding
or
contracting
the
region
where
corn
is
profitably
grown,
depending
on
how
they
affect
corn
yield,
production
cost,
and
risk
exposure.
In
this
analysis,
we
investigate
the
effects
of
changing
technology
and
weather
pat-
terns
using
corn
production
data
generated
from
several
research
stations
in
Wisconsin.
The
stations
in
southern
Wisconsin
are
located
in
the
northern
Corn
Belt,
but
the
research
stations
in
central
or
northern
Wisconsin
are
not
located
in
traditional
corn
-
producing
regions.
As
one
moves
north
in
Wisconsin,
the
length
of
the
growing
season
gets
shorter,
it
becomes
more
difficult
for
corn
grain
to
reach
maturity
before
the
first
frost,
and
corn
yields
tend
to
decline.
However,
farmers
can
deal
with
the
reduced
growing
season
by
planting
shorter
-season
corn
hybrids.
These
hybrids
face
a
higher
probability
of
reaching
maturity
before
the
end
of
the
growing
season
and
have
lower
drying
costs,
but
generate
lower
expected
yield.
This
tradeoff
and
its
evolution
over
the
last
few
decades
are
evaluated
empirically
below
using
the
approach
discussed
in
the
previous
section.
The
data
were
generated
from
long-term
studies
of
corn
yields
conducted
by
the
University
of
Wisconsin
Agricultural
Experiment
Station
(AES).
The
data
set
used
for
our
analysis
was
obtained
from
agronomic
trials
designed
to
measure
corn
hybrid
performance.
The
trials
evaluated
yield
and
grain
moisture
for
a
large
selection
of
corn
hybrids.
Since
1972,
the
experiment
has
been
conducted
at
several
agricultural
research
locations
throughout
Wisconsin.
The
experiment
controlled
for
other
input
conditions
by
using
similar
cultural
practices
at
each
site.
As
a
result,
yield
variations
in
each
location
are
due
to
the
choice
of
hybrid
maturity,
to
genetic
improvements,
and
to
uncontrollable
factors
(in
particular,
weather
effects).
The
data
set
from
the
AES
trials
provides
the
basis
for
evaluating
the
changing
distribution
of
corn
yield.
To
the
extent
that
agronomic
trials
represent
situations
similar
to
farm
conditions,
the
findings
can
help
farmers
decide
which
hybrid
maturity
to
choose
at
planting
time.
The
data
set
consists
of
26
years
(1972-1997)
of
yield
and
relative
maturity
(RM)
information.
Corn
hybrid
maturity
is
measured
using
the
"Minnesota
relative
maturity
rating,"
a
standardized
index
(measured
in
days)
characterizing
each
hybrid.
The
data
are
summarized
in
table
1
for
three
research
stations:
Arlington
(in
south
Wisconsin),
Marshfield
(in
north
central
Wisconsin),
and
Spooner
(in
northern
Wisconsin).
It
reports
the
number
of
observations,
average
yield
(bushels/acre),
average
corn
moisture
at
harvest
(%),
and
the
range
of
maturity
ratings
(RM)
for
each
location.
The
number
of
observations
varies
across
sites.
For
example,
the
Arlington
station
has
2,484
obser-
vations,
while
Marshfield
has
1,591
observations.
Note
that
the
expected
yield
ove
ie
236
July
2001
Journal
of
Agricultural
and
Resource
Economics
sample
period
decreases
as
one
moves
north.
In
contrast,
average
corn
moisture
is
distributed
evenly
across
sites,
except
in
the
northern
region
where
it
is
higher.
Relative
maturity
ranges
from
85
to
120
days
in
the
south,
and
from
70
to
110
days
in
the
north,
reflecting
the
different
climatic
conditions
experienced
at
the
sites.
Empirical
Results
The
empirical
analysis
focuses
on
three
issues.
First,
the
determinants
of
the
distribu-
tion
of
corn
yield
are
investigated.
Second,
the
factors
affecting
the
moisture
of
corn
grain
at
harvest
are
analyzed.
Cost
is
also
affected,
since
drying
cost
increases
with
corn
grain
moisture.
Third,
the
distribution
of
profit
and
its
evolution
(both
over
time
and
across
space)
are
examined.
Analysis
of
the
Mean
and
Variance
of
Corn
Yield
The
implications
of
technology
and
uncertainty
for
agricultural
production
are
examined
here.
Our
analysis
focuses
on
corn
yield.'
As
discussed
in
the
earlier
section
on
decision
making
under
uncertainty,
we
estimate
the
factors
influencing
both
the
mean
and
variance
of
corn
yield.
First,
we
consider
the
stochastic
production
function
representing
corn
yield,
y
=
g
l
(x,
t,
a
l
)
+
v
ly
,
where
v
ly
is
an
error
term
distributed
with
mean
zero.
The
expected
yield
function
g
l
(•)
is
specified
and
estimated
as
a
linear
function
of
relative
maturity
(RM),
the
square
of
relative
maturity
(RM
2
),
and
a
time
trend
(T).
Introducing
RM
2
allows
for
a
nonlinear
relationship
between
relative
maturity
and
expected
corn
yield.
The
time
trend
T
captures
two
effects:
the
impact
of
technological
change
(e.g.,
genetic
progress)
on
yield
(Cardwell),
as
well
as
the
impact
of
climatic
change
(Baker,
Rushy,
and
Skaggs;
Mendelsohn,
Nordhaus,
and
Shaw).
Attempting
to
assess
these
two
effects
separately
is
addressed
below.
The
error
term
v
ly
accounts
for
unobserved
weather
effects
and
other
uncontrollable
factors
affecting
corn
yield.
Note
that
while
using
least
squares
estimation
gives
consistent
estimates,
it
involves
a
possible
heteroskedasticity
problem
(Yang,
Koo,
and
Wilson).
As
noted
previously,
we
adopt
White's
method,
which
provides
consistent
estimates
of
the
standard
errors
under
heteroskedasticity.
5
Second,
in
order
to
examine
the
effects
of
relative
maturity
on
the
risk
associated
with
corn
production,
we
consider
the
variance
of
yield
112y
=
g
2
(x,
t,
a
2
)
+
v
2y
.
Following
the
approach
discussed
earlier,
we
specify
and
estimate
the
variance
of
corn
yield
as
a
linear
function
of
relative
maturity
(RM)
and
a
time
trend
(T).
The
regression
results
are
presented
in
table
2
for
the
three
selected
Wisconsin
sites.
The
Arlington
site
(South)
represents
the
growing
conditions
in
the
northern
area
of
the
Corn
Belt.
The
Marshfield
(North
Central)
and
Spooner
(North)
sites
are
outside
the
Corn
Belt,
and
represent
increasingly
difficult
conditions
for
corn
production
due
to
a
shorter
growing
season.
At
the
farm
level,
this
amounts
to
treating
corn
acreage
as
given.
Then,
corn
production
is
simply
corn
yield
multiplied
by
corn
acreage.
The
effects
of
climate
change
on
corn
acreage
are
not
explored
in
our
study.
This
appears
to
be
a
good
topic
for
further
research.
Note
that
there
may
also
be
nonzero
covariance
in
the
error
terms
across
observations.
While
this
would
not
affect
the
consistency
of
the
parameter
estimates
reported
below,
it
would
influence
their
efficiency
(meaning
that
standard
errors
of
the
parameters
may
be
upward
biased).
Chavas
et
al.
Economic
Analysis
of
Corn
Yield,
Profitability,
and
Risk
237
Table
2.
Estimated
Relationship
Between
Yield
and
Relative
Maturity
at
the
Three
Wisconsin
Sites
(A)
Expected
Yield
=
g,(RM,
RM
2
,
T)
Site
No.
of
Parameter
R
2
Observ.
Constant
RM RM
2
T
Arlington
2,484
-77.98
3.58*
-0.014
1.84***
0.245
(98.35)
(1.879)
(0.0089)
(0.073)
Marshfield
1,591
-
140.30
4.91***
-0.026**
1.89***
0.249
(85.35)
(1.884)
(0.010)
(0.080)
Spooner
2,335
-540.76***
13.93***
-0.078***
2.19***
0.232
(90.25)
(2.116)
(0.012)
(0.086)
(B)
Variance
of
Yield
=
g
2
(RM,
T)
Site
No.
of
Parameter
R
2
Observ.
Constant
RM
T
Arlington
2,484
-785.18***
11.795***
3.155
0.0094
(276.60)
(2.59)
(2.607)
Marshfield 1,591
-21.75
5.599*
7.684***
0.0110
(259.57)
(2.955)
(2.061)
Spooner
2,335
-530.72
13.808***
8.777***
0.0075
(350.39)
(4.068)
(2.879)
Notes:
Single,
double,
and
triple
asterisks
(*)
denote
significance
at
the
10%,
5%,
and
1%
levels,
respectively.
Numbers
in
parentheses
are
standard
errors.
The
coefficient
estimates
in
the
expected
yield
equation
[table
2(A)]
have
anticipated
signs
and
a
high
level
of
significance.
The
model
explains
about
25%
of
the
variation
in
corn
yields.
This
low
R
2
value
is
due
to
the
important
effects
of
unpredictable
weather
variations
captured
in
the
error
term.
Note
that
this
is
appropriate
for
ex
ante
analysis,
where
production
decisions
(e.g.,
the
choice
of
relative
maturity)
are
made
at
planting
time
when
relevant
weather
conditions
during
the
growing
season
are
still
unknown.
The
coefficients
associated
with
RM
are
all
statistically
significant.
At
all
three
sites,
we
find
a
positive
relationship
between
relative
maturity
and
corn
yield,
confirming
the
conventional
wisdom
widely
shared
by
agronomists-i.e.,
short
-season
hybrids
tend
to
produce
lower
expected
yield.
Moreover,
we
also
identify
a
nonlinear
and
concave
rela-
tionship
between
relative
maturity
and
expected
corn
yield.
The
relative
maturity
length
which
maximizes
expected
yield
at
Arlington,
Marshfield,
and
Spooner
is
calculated
as
125.9,
96.0,
and
89.0
days,
respectively.
These
values
imply
that,
in
the
south,
risk
-
neutral
farmers
would
plant
long
-season
corn
hybrids.
As
one
moves
north,
the
calcu-
lated
RM
value
decreases,
reflecting
the
shorter
growing
season.
The
coefficients
of
the
time
trend
(T)
are
all
statistically
significant
at
the
1%
level.
They
are
positive,
indicating
expected
corn
yield
increases
over
time.
T
measures
the
joint
effects
of
climate
change
and
productivity
growth
due
to
genetic
and
technology
improvements.
Note
that
the
magnitude
of
the
time
trend
effects
increases
as
one
moves
north.
The
average
annual
output
increase
at
Arlington
is
1.84
bushels/acre,
whereas
it
is
2.19
bushels/acre
at
Spooner.
238
July
2001
Journal
of
Agricultural
and
Resource
Economics
Growing
Degree
Days
(GDD)
3,500
3,000
2,500
2,000
1,500
1,000
500
0
--s—
Arlington
Marshfield
Spooner
N.
Cc)
N.
LO
CO
N.
CO
0)
0
01
Cc)
LO
CO
.
CO
0)
0
•c—
0.1
N. N. N. N. N. N. N.
N.
CO CO CO CO CO CO CO
a)
co co
0) 0) 0) 0)
0) 0) 0) 0)
0) 0) 0) 0) 0) 0) 0) 0) 0)
0) 0) 0) 0) 0) 0) 0) 0) 0)
0) 0) 0) 0) 0) 0) 0) 0)
Figure
1.
Annual
data
on
growing
degree
days
(GDD)
for
the
three
Wisconsin
sites
(1972-1997,
April
-October)
Table
2(B)
reports
estimation
results
for
the
variance
of
yield.
The
R
2
is
fairly
low,
implying
a
large
part
of
the
variance
remains
unexplained.
However,
the
variance
of
yield
tends
to
increase
over
time.
While
not
significant
in
Arlington,
this
effect
becomes
more
positive
and
significant
as
one
moves
north
—confirming
that
technological
and
climatic
changes
have
increased
production
risk
for
corn
at
the
edge
of
the
Corn
Belt.
While
these
results
show
significant
increases
in
both
the
mean
and
variance
of
yield
over
time,
can
we
assess
how
much
is
due
to
technological
change
versus
climate
change?
To
answer
this
question,
consider
the
evolution
of
growing
degree
days
(GDD)
reported
in
figure
1
for
Arlington,
Marshfield,
and
Spooner.
GDD
is
a
temperature
-based
index
6
commonly
used
as
a
summary
measure
of
the
length
of
the
growing
season
for
corn.
Figure
1
shows
how
the
GDD
index
fluctuates
over
time
as
well
as
across
space.
A
trend
analysis
of
GDD
over
the
period
1972-1997
is
reported
in
table
3.
Three
regression
equations
(each
employing
GDD
as
a
dependent
variable
and
time
trend
T
as
an
independent
variable)
were
estimated
using
a
seemingly
unrelated
regression
(SUR)
method
to
account
for
the
possible
contemporaneous
correlation
between
unex-
plained
variations
in
GDD
across
locations.
Table
3
shows
a
positive
and
significant
trend
in
GDD
for
Marshfield,
but
no
significant
trend
for
Arlington
or Spooner.
Thus,
for
Arlington
and
Spooner,
there
is
no
strong
evidence
of
a
longer
growing
season
(as
measured
by
GDD).
For
these
stations,
this
weak
evidence
of
global
warming
effects
suggests
that
most
of
the
yield
trends
could
be
attributed
to
technological
change.
The
results
for
Marshfield
indicate
an
average
annual
increase
in
GDD
of
10.15°F,
showing
a
significant
lengthening
of
the
growing
season
of
0.37%
per
year
—a
fmding
consistent
with
beneficial
effects
of
global
warming
in
the
northern
fringe
of
the
United
For
a
given
location
and
growing
season,
the
GDD
index
for
corn
is
defined
as
GDD
=
E,
i(1/2)[max(Tmin„
50)
+
min(Tmax„
86)1
-
50),
where
Train,
(Tmax,)
is
the
minimal
(maximal)
temperature
on
day
i
(in
degree
F).
It
reflects
the
absence
of
appreciable
corn
growth
for
temperatures
below
50°F
or
above
86°F.
Chavas
et
al.
Economic
Analysis
of
Corn
Yield,
Profitability,
and
Risk
239
Table
3.
Seemingly
Unrelated
Regression
Analysis
of
Growing
Degree
Days
(GDD)
at
the
Three
Wisconsin
Sites,
1972-1997
[GDD
=
f(T)]
Site
No.
of
Parameter
Observ.
Constant
Arlington
25
2,877.40***
-1.817
0.0052
(75.79)
(4.91)
Marshfield
25
2,508.48***
10.150**
0.1388
(67.18)
(4.35)
Spooner
25
2,541.56***
3.326
0.0158
(79.44)
(5.14)
Notes:
Double
and
triple
asterisks
(*)
denote
significance
at
the
5%
and
1%
levels,
respectively.
Numbers
in
parentheses
are
standard
errors.
States
(Mendelsohn,
Nordhaus,
and
Shaw).
This
can
be
compared
with
the
annual
yield
increase
of
+1.89
bushels/acre/year
(or
+1.14%/year)
reported
for
Marshfield
in
table
2(A).
Therefore,
to
the
extent
that
GDD
increases
are
expected
to
generate
proportional
changes
in
expected
corn
yield,
about
32%
of
productivity
gains
in
Marshfield
would
be
attributed
to
a
longer
growing
season.
The
remaining
68%
of
productivity
gain
may
be
associated
with
technological
change.'
In
agreement
with
earlier
results
reported
by
Thompson
(1975,
1986)
and
Cardwell,
our
findings
indicate
only
a
small
proportion
of
yield
trend
can
be
attributed
to
evolving
weather
patterns.
Thus,
for
all
three
sites,
technological
progress
seems
the
dominant
factor
influencing
productivity
trends
in
corn
production.
If
the
above
conclusion
is
correct,
the
results
presented
in
table
2(A)
reveal
techno-
logical
progress
in
corn
production
(e.g.,
genetic
progress
in
the
form
of
new
hybrids)
has
improved
faster
in
the
marginal
corn
production
areas
compared
to
the
Corn
Belt.
This
fi
nding
is
consistent
with
the
observed
expansion
of
corn
production
outside
the
Corn
Belt
over
the
last
few
decades.
More
specifically,
the
development
of
new
hybrids
has
allowed
farmers
to
grow
corn
relatively
more
profitably
outside
the
traditional
Corn
Belt
(Cardwell).
Next,
we
evaluate
the
role
of
climatic
change
on
production
risk.
We
would
like
to
determine
whether
the
length
of
the
growing
season
has
become
more
unpredictable.
For
that
purpose,
we
investigate
the
variance
of
the
error
term
in
the
GDD
regression
reported
in
table
3.
We
test
whether
this
variance
is
higher
in
the
second
half
of
the
sample
(compared
to
the
first
half).
The
corresponding
F
-statistic
is
4.18,
2.23,
and
1.79
for
Arlington,
Marshfield,
and
Spooner,
respectively.
With
(12,
12)
degrees
of
freedom
and
a
5%
significance
level,
the
critical
value
for
the
F
-test
is
3.28.
This
shows
a
significant
increase
in
the
variance
of
GDD
for
Arlington,
but
no
significant
change
for
Marshfield
or
Spooner.
Thus,
for
Marshfield
and
Spooner,
there
is
no
strong
evidence
that
the
length
of
the
growing
season
has
become
more
unpredictable;
i.e.,
at
these
stations,
it
is
not
clear
whether
global
warming
is
contributing
to
increasing
corn
yield
uncertainty.
Never
-
It
should
be
noted,
however,
that
there
might
be
other
factors
which
potentially
explain
the
proportion
of
the
trend
not
associated
with
weather
patterns.
Including
other
factors
in
the
model
would
require
a
more
refined
analysis
of
how
technological
change
affects
yield
variations.
This
appears
to
be
a
good
topic
for
further
research.
240
July
2001
Journal
of
gricultural
and
Resource
Economics
theless,
significant
increases
in
yield
risk
are
reported
in
table
2(B)
for
Marshfield
and
Spooner.
To
the
extent
that
they
are
not
associated
with
climatic
fluctuations,
such
changes
can
be
attributed
to
changing
technology;
along
with
higher
expected
yields,
improved
technologies
also
bring
an
increased
exposure
to
production
risk
(for
example,
improved
short
-season
hybrids
with
better
average
yield
but
more
sensitivity
to
weather
shocks).
The
findings
differ
in
the
northern
Corn
Belt
(Arlington).
At
the
Arlington
site,
the
variance
test
result
indicates
a
significant
increase
in
the
unpredictability
of
the
length
of
the
growing
season.
Consistent
with
Baker,
Rushy,
and
Skaggs,
our
investigation
found
global
warming
may
contribute
to
production
uncertainty.
Yet,
as
seen
from
table
2(B),
while
the
variance
of
yield
has
increased
over
time
in
Arlington,
this
effect
is
not
statistically
significant.
How
can
we
explain
that
this
significant
increase
in
weather
variability
is
associated
with
no
significant
changes
in
yield
variation?
One
possible
explanation
can
be
offered:
In
Arlington,
technological
change
may
have
counter-
balanced
the
exposure
to
production
risk.
For
example,
new
long
-season
corn
hybrids
may
be
less
sensitive
to
some
weather
shocks.
In
this
context,
our
results
could
be
interpreted
as
indirect
evidence
showing
technological
change
may
have
contributed
to
reducing
exposure
to
production
risk
in
the
Corn
Belt.
Thus,
for
all
three
sites,
tech-
nological
progress
seems
an
important
factor
influencing
corn
production
uncertainty.
The
results
presented
in
table
2(B)
indicate
global
warming
and
technological
change
appear
to
interact
with
each
other
as
they
affect
production
risk,
but
in
a
way
that
varies
across
regions.
Finally,
in
table
2(B),
the
relationship
between
relative
maturity
and
variance
of
yield
is
found
to
be
statistically
significant
and
positive,
suggesting
a
tradeoff
between
expected
yield
increases
and
risk.
For
example,
a
larger
RM
value
tends
to
increase
yields,
but
it
also
increases
production
risk
(as
measured
by
the
variance
of
yield).
By
stressing
the
role
of
risk,
this
tradeoff
can
make
farmers'
ex
ante
production
decisions
more
complex.
We
explore
this
issue
in
more
detail
below.
Analysis
of
the
Mean
and
Variance
of
Corn
Moisture
Next,
we
examine
the
changes
in
corn
grain
moisture
at
harvest.
Corn
grain
moisture
is
affected
both
by
weather
conditions
toward
the
end
of
the
growing
season
and
by
the
choice
of
hybrid
maturity.
Expected
moisture
and
variance
of
moisture
equations
are
specified
and
are
estimated
econometrically.
Results
are
reported
in
table
4
for
the
Arlington,
Marshfield,
and
Spooner
sites.
The
expected
moisture
equation
is
specified
as
a
linear
function
of
relative
maturity
RM
and
its
square,
RM
2
[see
table
4(A)]
.
8
This
allows
for
a
nonlinear
relationship
between
RM
and
moisture.
The
coefficients
associated
with
relative
maturity
are
all
statistically
significant
except
the
RM
term
at
the
Marshfield
site.
Even
though
the
selected
sites
do
not
share
the
same
pattern
of
quadratic
relation
between
RM
and
moisture
(concave
relationship
for
Arlington
and
convex
relationship
for
the
others),
they
all
show
positive
relationships
between
RM
and
moisture
in
the
range
of
the
data.
8
Note
that
the
moisture
equation
does
not
include
a
time
trend.
This
is
justified
based
on
a
priori
agronomic
information.
The
calculation
of
RM
depends
on
the
moisture
of
hybrids
tested
against
standard
hybrids.
As
a
result,
one
can
expect
a
stable
relationship
between
moisture
and
RM.
In
addition,
inclusion
of
a
time
trend
in
the
moisture
equation
yielded
insignificant
coefficient
estimates
for
RM
variables,
which
is
not
consistent
with
a
priori
agronomic
information.
Chavas
et
al.
Economic
Analysis
of
Corn
Yield,
Profitability,
and
Risk
241
Table
4.
Estimated
Relationship
Between
Corn
Moisture
and
Relative
Matur-
ity
at
the
Three
Wisconsin
Sites
(A)
Expected
Moisture
=
h
i
(RM,
RM
2
)
Site
No.
of
Observ.
Parameter
R
2
Constant
RM
RM
2
Arlington
2,484
-41.14**
0.937***
-0.0029*
0.155
(16.72)
(0.319)
(0.0015)
Marshfield 1,591
53.50**
-0.811
0.0057*
0.071
(25.69) (0.570)
(0.0032)
Spooner
2,335
-59.69***
-1.110**
0.0086***
0.094
(20.49)
(0.482)
(0.0028)
(B)
Variance
of
Moisture
=
h
2
(RM)
Site
No.
of
Observ.
Parameter
R
2
Constant
RM
Arlington
2,484
-33.804***
0.499***
0.0094
(8.73)
(0.083)
Marshfield
1,591
-46.540***
0.876***
0.0189
(17.70)
(0.199)
Spooner
2,335
-38.606**
0.894***
0.0071
(19.67) (0.235)
Notes:
Single,
double,
and
triple
asterisks
(*)
denote
significance
at
the
10%,
5%,
and
1%
levels,
respectively.
Numbers
in
parentheses
are
standard
errors.
This
means
that
increasing
relative
maturity
tends
to
increase
expected
moisture
in
all
three
sites.
The
coefficient
ofRM
2
and
its
significance
suggest
the
degree
of
nonlinearity
becomes
more
important
as
one
moves
north.
In
particular,
the
convex
relationship
between
RM
and
expected
moisture
implies
the
(positive)
marginal
impact
of
RM
on
expected
moisture
becomes
greater
as
one
gets
further
away
from
the
Corn
Belt
toward
shorter
growing
seasons.
The
variance
of
moisture
is
specified
as
a
linear
function
of
relative
maturity
RM.
The
corresponding
estimation
results
are
reported
in
table
4(B)
for
the
three
sites.
The
coefficients
ofRM
are
all
statistically
significant
at
the
1%
level.
Within
the
range
of
the
data,
they
show
a
positive
relationship
between
relative
maturity
and
the
variance
of
corn
moisture.
The
increasing
magnitude
of
these
coefficients
as
one
moves
north
reveals
that
the
impact
of
RM
on
the
variability
of
corn
moisture
increases
as
one
moves
away
from
the
Corn
Belt
toward
shorter
growing
seasons.
Analysis
of
the
Mean
and
Variance
of
Income
Finally,
we
explore
the
implications
of
technology
and
uncertainty
on
income
from
corn
production.
Since
cultural
practices
are
similar
across
plots
at
a
given
location,
we
measure
income
as
corn
revenue
minus
drying
cost,
all
on
a
per
acre
basis.
Income
uncertainty
involves
both
production
uncertainty
and
uncertainty
in
the
cost
of
drying
(which
depends
on
the
moisture
of
corn
grain
at
harvest).
Corn
price
is
assumed
t
be
242
July
2001
Journal
of
Agricultural
and
Resource
Economics
$2
per
bushel.'
The
drying
cost
varies
depending
on
corn
moisture
at
harvest
as
well
as
farm
type.
We
consider
three
farm
types:
a
livestock
farm
where
corn
is
fed
directly
to
livestock,
a
grain
farm
using
on
-farm
drying
facilities,
and
a
grain
farm
relying
on
commercial
drying.
On
a
livestock
farm,
drying
costs
are
zero
and
corn
moisture
varia-
tions
have
no
impact
on
income.
In
contrast,
corn
drying
affects
cost
under
commercial
drying,
with
a
drying
cost
of
0.030
per
bushel
per
percentage
moisture
in
excess
of
15.5%.
On
-farm
drying
represents
an
intermediate
situation,
with
a
drying
cost
of
0.0150
per
bushel
per
percentage
moisture
in
excess
of
15.5%.
Expected
income
and
its
variance
are
specified
and
estimated
as
discussed
previously.
The
econometric
results
are
presented
in
table
5.
Table
5(A)
summarizes
the
estimation
results
for
expected
income
by
farm
type
and
by
location
(Arlington,
Marshfield,
and
Spooner).
The
results
are
consistent
with
those
obtained
in
the
analysis
of
expected
yield
(see
table
2
and
the
related
discussion).
For
example,
the
coefficients
associated
with
relative
maturity
RM
and
time
trend
T
are
statistically
significant
(except
the
square
of
RM
for
Arlington
for
a
livestock
farm)
and
have
expected
signs.
Following
the
analy-
sis
of
the
mean
and
variance
of
corn
yield,
summarized
above,
these
coefficients
confirm
that
technological
change
has
contributed
to
increases
in
expected
corn
profitability
over
time,
with
the
rate
of
increase
being
faster
as
one
moves
north.
However,
the
patterns
of
variance
in
corn
profitability
become
more
complex.
For
example,
only
in
northern
Wisconsin
(Spooner)
does
profit
risk
increase
significantly
over
time
for
all
farm
types.
The
rate
of
increase
is
largest
for
the
Spooner
farm
using
commercial
drying,
and
smallest
for
the
livestock
farm.
In
the
other
two
locations,
the
results
vary
across
farm
types,
emphasizing
the
significant
role
of
drying
cost.
This
stresses
the
need
for
analysts
to
go
beyond
yield
effects
in
the
investigation
of
how
technology
and
climate
affect
the
economics
of
corn
production.
The
results
in
table
5(A)
enable
us
to
examine
these
relationships
by
farm
type.
For
each
site,
we
calculated
the
RM
value
that
maximizes
expected
income
(corresponding
to
a
risk
-neutral
farmer).
At
Arlington
this
equals
125.9
for
the
livestock
farm,
110.9
for
on
-farm
drying,
and
98.7
for
commercial
drying.
The
respective
values
at
Marshfield
are
96.0,
90.1
and
84.9,
and
at
Spooner
are
89.0,
87.3,
and
85.3.
Therefore,
as
one
moves
north,
the
drying
cost
effects
are
important,
and
maximum
expected
profit
is
achieved
at
a
lower
value
of
RM.
In
addition,
the
fact
that
these
RM
values
tend
to
decline
as
drying
cost
increases
(particularly
in
the
south)
confirms
the
significant
role
played
by
drying
cost.
Based
on
these
findings,
under
commercial
drying,
switching
to
a
lower
maturity
rating
provides
farmers
an
opportunity
to
reduce
their
drying
cost
and
to
increase
expected
profit.
But
how
would
that
affect
the
farmer's
risk
exposure?
If
this
plan
involves
greater
production
risk,
then
a
risk
-averse
farmer
would
choose
a
different
production
plan,
provided
the
costs
associated
with
risk
increase
offset
the
benefits
associated
with
expected
profit
increase.
Indeed,
as
seen
in
table
5(B),
there
is
a
statistically
significant
and
positive
relationship
between
the
variance
of
income
(risk)
and
relative
maturity
RM.
The
effects
of
drying
cost
on
expected
income
and
variance
of
income
by
location
and
by
farm
type
are
discussed
next.
9
The
analysis
was
also
conducted
under
alternative
corn
-price
scenarios.
While
higher
corn
price
increased
corn
profita-
bility,
the
empirical
fi
ndings
presented
below
were
found
to
be
fairly
robust
to
the
corn
-price
scenario.
Chavas
et
al.
Economic
Analysis
of
Corn
Yield,
Profitability,
and
Risk
243
Table
5.
Estimated
Relationship
Between
Profit
and
Relative
Maturity
at
the
Three
Wisconsin
Sites
(A)
Expected
Profit
=
f
i
(RM,
RM
2
,
T)
Site
Farm
Type
Parameter
R
2
Constant
RM RM
2
T
Arlington
Livestock
-155.96
7.151*
-0.0284
3.688***
0.245
(196.70)
(3.758)
(0.018)
(0.145)
On
-farm
-
116.53
7.039**
-
0.032*
2.534***
0.136
(185.64)
(3.548)
(0.017)
(0.146)
Commercial
-77.108
6.928**
-0.035**
1.380***
0.048
(182.90)
(3.50)
(0.017)
(0.153)
Marshfield
Livestock
-280.60
9.816***
-0.051**
3.771***
0.249
(170.71)
(3.77)
(0.021)
(0.160)
On
-farm
-
274.27*
9.805***
-0.054***
3.868***
0.253
(163.39)
(3.602)
(0.020)
(0.147)
Commercial
-267.94
9.794**
-0.058***
3.965***
0.249
(164.51)
(3.627)
(0.020)
(0.142)
Spooner
Livestock
-1,081.50***
27.850***
-0.156***
4.373***
0.232
(178.20)
(4.19)
(0.025) (0.163)
On
-farm
-988.56***
26.110***
-0.149***
4.130***
0.215
(172.70)
(4.05)
(0.024)
(0.154)
Commercial
-915.63***
24.370***
-0.143***
3.880***
0.192
(171.30)
(4.012)
(0.024)
(0.151)
(B)
Variance
of
Profit
=
f
2
(RM,
T)
Site
Farm
Type
Parameter
R
2
Constant
RM
T
Arlington
Livestock
-3,140.70***
47.183***
12.62
0.0094
(1,106.6)
(10.37)
(10.43)
On
-farm
-3,106.70***
48.425***
-11.29
0.0099
(1,057.5)
(9.95)
(10.80)
Commercial
-3,709.60***
56.210***
-24.93**
0.0133
(1,114.4)
(10.58)
(11.87)
Marshfield
Livestock
-86.99
22.400*
30.74***
0.0110
(1,038.3)
(11.82)
(8.243)
On
-farm
261.01
19.830*
9.52
0.0037
(955.76)
(10.86)
(7.782)
Commercial
161.20
23.570**
-8.06
0.0028
(953.37)
(10.84)
(8.334)
Spooner
Livestock
-2,122.90
55.230***
35.11***
0.0075
(1,410.5)
(16.27)
(11.51)
On
-farm
-2,392.50
52.510***
61.14***
0.0127
(1,413.2)
(16.45)
(10.59)
Commercial
-2,967.90**
54.480***
92.92***
0.0218
(1,507.8)
(17.61)
(10.28)
Notes:
Single,
double,
and
triple
asterisks
(*)
denote
significance
at
the
10%,
5%,
and
1%
levels,
respectively.
Numbers
in
parentheses
are
standard
errors.
244
July
2001
Journal
of
Agricultural
and
Resource
Economics
Expected
Profit
400
380
360
340
320
300
280
260
240
220
200
180
160
140
85
110
105
90
95~~_?00
On
-farm
85
85
,may
90
95
98
Commercial
90
95
100
105
110
115
120
Livestock
Arlington
95
85
Livestock
85
90
85
84
7>#
0
"'"
On
-farm
87
75
Co
n
-fa
Commercial
75
80
rm
89
li
vestock
Marshfield
70
70
80
75
80
85
7
75
Spooner
20
25
30
35
40
45
50
55
60
65
70
Standard
Deviation
Note:
Numbers
above
each
frontier
denote
maturity
days.
Figure
2.
Expected
profit
-standard
deviation
frontiers
for
the
three
Wisconsin
sites
(with
T
set
at
1997
level)
Tradeoff
Between
Expected
Income
and
Risk
The
expected
income
-standard
deviation
frontiers
are
shown
in
figure
2.
These
frontiers
illustrate
the
tradeoff
that
exists
between
per
acre
expected
income
and
risk
(repre-
sented
by
the
standard
deviation
of
income)
by
location
and
by
farm
type,
for
different
relative
maturity
ratings.
Figure
2
is
constructed
from
the
information
reported
in
table
5,
with
the
time
trend
value
T
set
at
its
1997
level
(the
most
recent
year
in
the
data
set).
A
move
along
each
frontier
is
obtained
by
changing
corn
hybrids
and
their
associated
RM
ratings
(expressed
in
days).
The
positive
slope
of
the
frontier
functions
indicates
that
expected
income
cannot
increase
without
also
increasing
risk.
Alternatively,
risk
cannot
be
reduced
without
sacrificing
expected
income.
In
the
northern
Corn
Belt
(represented
by
the
Arlington
site),
the
growing
season
is
longer.
There,
the
tradeoff
between
risk
and
expected
return
varies
across
farm
types.
Indeed,
each
farm
exhibits
a
different
slope
of
its
frontier
function.
The
livestock
farm
shows
a
relatively
large
tradeoffbetween
expected
return
and
risk,
whereas
the
tradeoff
is
less
pronounced
under
commercial
drying.
This
means
that,
under
commercial
drying,
risk
can
be
reduced
without
much
reduction
in
expected
profit
by
choosing
hybrids
with
lower
relative
maturity.
For
example,
even
a
moderately
risk
-averse
farmer
would
choose
a
low
RM
to
avoid
risk
while
not
sacrificing
much
in
expected
profit.
On
the
other
hand,
for
a
livestock
farm,
the
mean
profit
-risk
tradeoff
is
more
significant,
and
the
choice
of
relative
maturity
would
depend
on
farmers'
risk
preferences.
For
example,
a
risk
-averse
farmer
would
have
incentive
to
plant
hybrids
with
low
relative
maturity
(e.g.,
RM
=
85).
But
a
risk
-neutral
farmer
would
choose
an
RM
of
120
because
this
production
plan
substantially
increases
expected
profit.
These
large
difference
Zg
Chavas
et
al.
Economic
Analysis
of
Corn
Yield,
Profitability,
and
Risk
245
farm
types
originate
from
drying
cost
differentials.
When
there
is
no
drying
cost
(as
with
the
livestock
farm),
planting
a
high
RM
produces
both
higher
expected
profit
and
higher
risk.
Alternatively,
when
drying
cost
becomes
significant
(as
under
commercial
drying),
using
a
high
RM
hybrid
has
only
a
modest
effect
on
expected
net
return
while
signifi-
cantly
increasing
the
farmer's
risk
exposure.
In
contrast,
under
a
short
growing
season,
Spooner
(in
northern
Wisconsin)
shows
much
more
significant
tradeoff
between
risk
and
expected
return.
This
is
illustrated
by
a
much
steeper
mean
-standard
deviation
frontier
in
figure
2.
Also,
figure
2
shows
the
mean
-standard
deviation
frontiers
have
a
similar
shape
for
all
Spooner
farm
types,
indicating
similar
risk
tradeoff
across
farm
types.
In
this
case,
risk
-neutral
farmers
have
an
incentive
to
use
long
-season
hybrids
for
all
farm
types.
But,
across
all
drying
cost
scenarios,
risk
-averse
farmers
have
an
incentive
to
switch
to
short
-season
hybrids
as
a
means
of
reducing
significantly
their
risk
exposure.
Finally,
the
results
obtained
in
north
central
Wisconsin
(Marshfield)
are
intermediate
between
the
other
two
sites.
The
risk
tradeoff
is
not
as
pronounced
as
in
the
north,
but
is
more
pronounced
than
in
the
south.
These
findings
stress
the
role
of
risk
management
in
corn
production,
especially
as
one
moves
away
from
the
Corn
Belt
toward
the
north-
ern
fringe
of
the
United
States.
Our
results
emphasize
the
role
of
choosing
corn
hybrids
and
their
relative
maturity
as
a
means
of
managing
risk.
They
also
reveal
that
risk
exposure
can
vary
significantly
both
across
sites
and
across
farm
types.
Consequently,
risk
management
strategies
are
expected
to
differ
depending
on
the
location
and
the
farm
type,
as
well
as
on
the
decision
maker's
degree
of
risk
aversion.
Concluding
Remarks
This
study
has
investigated
the
recent
evolution
of
corn
yield
focusing
on
the
tradeoff
between
corn
profitability
and
risk.
The
analysis
relied
on
time
-series
data
from
Wisconsin
research
stations
and
farm
test
sites
at
the
edge
of
the
Corn
Belt.
Both
conditional
means
and
conditional
variances
for
corn
yield,
corn
grain
moisture,
and
corn
profitability
were
specified
and
estimated
for
different
sites
in
Wisconsin.
The
empirical
analysis
demonstrates
how
corn
yield
and
profit
have
changed
over
time,
and
how
they
are
affected
by
the
choice
of
corn
hybrid
maturity
across
sites.
The
results
indicate
that,
on
average,
corn
yield
and
profitability
have
improved
faster
in
northern
Wisconsin
than
in
the
Corn
Belt,
suggesting
a
slow
northward
expansion
of
the
Corn
Belt.
However,
we
also
found
that
both
yield
risk
and
profit
uncertainty
have
increased
faster
in
northern
Wisconsin
than
in
the
Corn
Belt.
Our
empirical
results
show
the
choice
of
corn
hybrid
maturity
makes
it
easier
to
manage
risk
in
the
Corn
Belt
than
in
northern
Wisconsin.
Thus,
the
tradeoffbetween
risk
and
expected
return
appears
to
be
site
specific.
Finally,
our
investigation
points
to
the
importance
of
drying
costs.
While
higher
drying
cost
tends
to
reduce
expected
profit,
it
also
makes
reducing
risk
easier
through
switching
to
shorter
-season
hybrids.
This
finding
identifies
the
need
for
adapting
risk
manage-
ment
strategies
to
both
the
location
and
type
of
farm.
Our
analysis
stresses
the
increased
importance
of
risk
management
in
response
to
climatic
and
technological
change.
Although
there
is
strong
evidence
that
both
technological
progress
(Cardwell)
and
cli-
mate
change
(Baker,
Rushy,
and
Skaggs;
Mendelsohn,
Nordhaus,
and
Shaw)
affect
the
economics
of
corn
production,
our
results
identify
technological
change
as
the
d
246
July
2001
Journal
of
Agricultural
and
Resource
Economics
factor.
In
northern
Wisconsin,
we
find
large
productivity
gains,
but
such
gains
are
also
associated
with
significant
increases
in
production
risk.
This
contrasts
with
the
Corn
Belt,
where
productivity
gains
are
positive
but
smaller.
There,
we
fi
nd
indirect
evidence
that
technological
change
may
have
contributed
to
reducing
exposure
to
production
risk
(e.g.,
new
long
-season
hybrids
exhibiting
less
sensitivity
to
adverse
weather
shocks).
This
seems
particularly
relevant
in
a
context
where
global
warming
contributes
to
increasing
weather
uncertainty.
Indeed,
the
development
of
new
agricultural
tech-
nologies
can
create
new
options
to
deal
with
climate
changes.
Future
research
might
benefit
from
more
in-depth
analysis
of
these
important
issues.
[Received
April
2000;
final
revision
received
December
2000.]
References
Adams,
R.
M.,
C.
Rosenzweig,
R.
M.
Pearl,
J.
T.
Richie,
B.
A.
McCarl,
J.
D.
Glyer,
R.
B.
Curry,
J.
W.
Jones,
K.
J.
Boote,
and
L.
H.
Allen,
Jr.
"Global
Climate
Change
in
U.S.
Agriculture."Nature
345,
no.
6271
(1990):219-24.
Anderson,
J.
R.,
J.
Dillon,
and
B.
Hardaker.
Agricultural
Decision
Analysis.
Ames
IA:
Iowa
State
Uni-
versity
Press,
1977.
Antle,
J.
M.
"Testing
the
Stochastic
Structure
of
Production:
A
Flexible
Moment
-Based
Approach."
J.
Bus.
and
Econ.
Statis.
1(1983):192-201.
Antle,
J.
M.,
and
W.
J.
Goodger.
"Measuring
Stochastic
Technology:
The
Case
of
Tulare
Milk
Produc-
tion."
Amer.
J.
Agr.
Econ.
66(1984):342-50.
Baker,
D.
G.,
D.
L.
Rushy,
and
R.
H.
Skaggs.
"Agriculture
and
Recent
'Benign
Climate'
in
Minnesota."
Bull.
Amer.
Meteorological
Society
74(June
1993):1035-40.
Cardwell,
V.
B.
"Fifty
Years
of
Minnesota
Corn
Production:
Sources
of
Yield
Increase."
Agronomy
J.
74(November/December
1982):984-90.
Chavas,
J.
-P.,
and
M.
T.
Holt.
"Economic
Behavior
Under
Uncertainty:
A
Joint
Analysis
of
Risk
Pref-
erences
and
Technology."
Rev.
Econ.
and
Statis.
78(1996):329-35.
Coelho,
D.
T.,
and
R.
F.
Dale.
"An
Energy
-Crop
Growth
Variable
and
Temperature
Function
for
Pre-
dicting
Corn
Growth
and
Development:
Planting
to
Silking."
Agronomy
J.
72(1980):503-10.
Dixon,
B.
L.,
S.
E.
Hollinger,
P.
Garcia,
and
V.
Tirupattur.
"Estimating
Corn
Yield
Response
Models
to
Predict
Impacts
of
Climate
Change."
J.
Agr.
and
Resour.
Econ.
19(July
1994):58-68.
Gallagher,
P.
"U.S.
Corn
Yield
Capacity
and
Probability:
Estimation
and
Forecasting
with
Non
-
Symmetric
Disturbances."
N.
Cent.
J.
Agr.
Econ.
8(1986):109-22.
Goodwin,
B.
K,
and
A.
P.
Ker.
"Nonparametric
Estimation
of
Crop
Yield
Distributions:
Implications
for
Rating
Group
-Risk
Crop
Insurance
Contracts."
Amer.
J.
Agr.
Econ.
80(1998):139-53.
Houghton,
R.
A.,
and
G.
M.
Woodwell.
"Global
Climatic
Change."
Scientific
American
260(1989):36-44.
Just,
R.
E.,
and
R.
D.
Pope.
"Production
Function
Estimation
and
Related
Risk
Considerations."Amer.
J.
Agr.
Econ.
61(1979):277-84.
Kaufmann,
R.
K,
and
S.
E.
Snell.
"A
Biophysical
Model
of
Corn
Yield:
Integrating
Climatic
and
Social
Determinants."
Amer.
J.
Agr.
Econ.
79(1997):178-90.
Kaylen,
M.
S.,
J.
W.
Wade,
and
D.
B.
Frank.
"Stochastic
Trend,
Weather,
and
U.S.
Corn
Yield
Vari-
ability."
Appl.
Econ.
24(1992):513-18.
Lin,
W.,
G.
W.
Dean,
and
C.
V.
Moore.
"An
Empirical
Test
of
Utility
versus
Profit
Maximization
in
Agri-
culture
Production."
Amer.
J.
Agr.
Econ.
56(1974):497-508.
Mendelsohn,
R.,
W.
D.
Nordhaus,
and
D.
Shaw.
"The
Impact
of
Global
Warming
on
Agriculture:
A
Ricardian
Analysis."
Amer.
Econ.
Rev.
84(1994):753-71.
Meyer,
J.
"Two
-Moment
Decision
Models
and
Expected
Utility
Maximization."
Amer.
Econ.
Rev.
77(1987):421-30.
Nelson,
C.
H.,
and
P.
V.
Preckel.
"The
Conditional
Beta
Distribution
as
a
Stochastic
Production
Func-
tion."
Amer.
J.
Agr.
Econ.
71(1989):370-78.