Acreage response functions for wheat are fitted to aggregate data and pooled time-series and cross-sectional data for the Northwest. It was hypothesized that the pooled data approach provides a useful alternative to using aggregate data since it requires fewer timer-series observations for reliable parameter estimation and it does not require the assumption of constant acreage response elasticities throughout the region. The results of this study verify this hypothesis as well as indicate that regional response elasticities for Northwest wheat acreage may differ greatly from national estimates.Crop Production/Industries,

Whittaker, James K.

Winter, John R.

English

Research Papers in Economics

Estimation of Wheat Acreage
Response  Functions  for the Northwest
John R.  Winter and James K.  Whittaker
Acreage  response  functions for wheat are fitted to aggregate data and pooled time-
series  and cross-sectional  data for  the Northwest.  It was  hypothesized that the  pooled
data approach provides  a useful alternative to using aggregate data since it requires fewer
time-series  observations  for  reliable parameter  estimation and  it does not require  the
assumption of constant acreage response elasticities throughout the region. The results of
this study verify this hypothesis  as well as  indicate that regional response  elasticities for
Northwest wheat  acreage  may  differ  greatly from  national estimates.
In  the  Northwestern  states  of  Oregon,
Washington  and  Idaho,  fifty  percent  of all
planted acreage  is sown to wheat (1975-1977
average).  The  importance  of wheat  in  the
Northwest  indicates  that  the responsiveness
of wheat acreage  to changes in product prices
and  government  programs  has  a  significant
regional impact on farm  income,  demand for
storage  and  marketing  facilities,  and the  re-
gional  balance  of payments.  National  esti-
mates of wheat acreage responsiveness to var-
ious  independent  variables  may  not  be  ap-
propriate  for  discerning  or  predicting
changes in regional wheat acreages.  If a given
region's  response  to changes  in independent
variables  differs  from the  national  response,
then the use of national models to determine
regional  impacts on farm  income and demand
for  storage  and marketing  facilities  will give
misleading  results.
In  1973,  Hoffman  developed  acreage  re-
sponse functions for five wheat producing re-
gions of the U.S.  Generally,  his models were
successful both in terms of explaining a large
John  R.  Winter  and James  K.  Whittaker  are  graduate
research assistant and assistant professor,  respectively,  in
Agricultural  and  Resource  Economics  at  Oregon  State
University.
Oregon Agricultural Experiment Station Technical Paper
No.  4908.  The authors  wish to acknowledge  the helpful
comments  of  R.  F.  Brokken,  R.  A.  Oliveira,  three
anonymous  reviewers,  and the Editor.
proportion  of  regional  variation  in  wheat
acreage  and in determining the structural re-
sponse  to  various  independent  variables.
However,  for  the  Northwest  region,  his
model failed to meet expectations  in terms of
R 2 and the significance levels of the estimated
coefficients.
The objective of this paper  is to estimate a
regional wheat acreage  response function for
the  Northwest  and compare  parameter  esti-
mates to those  from national models.  Results
of two  approaches  are  compared.  First,  the
parameters  of an  aggregate  regional  model
are estimated using annual time series obser-
vations from 1954 to 1977.  One disadvantage
of estimating an  aggregate  acreage  response
model is  the  need  for  a  fairly  lengthy time
series (usually a minimum of twenty observa-
tions)  in order  to have  sufficient  degrees  of
freedom  for  reliable  parameter  estimation.
Unfortunately,  the parameter estimates from
data  spanning  several  major  policy  regimes
are  somewhat  suspect.  In this analysis,  1954
was  chosen  as  the  first  time  series  observa-
tion for the aggregate model, because it is the
first  post-war  year  following  a major  wheat
policy change and,  in addition,  it provides  a
sufficient  number of observations  for param-
eter  estimation.  The  observations  are  re-
'Hoffman  defined  the  Northwest  region  to  include
Washington,  Oregon,  Idaho,  Nevada,  California,  and
Arizona.
83Western Journal  of Agricultural  Economics
gional  totals  or weighted  regional  variables.
The aggregate  model implicitly  assumes that
the  acreage  response  elasticities  are
homogeneous  across the  three  states.  If this
assumption  is  not  valid,  aggregation  error
and bias are inherent in the estimated coeffi-
cients.
The  second  approach  uses  pooled  time-
series  and cross-sectional  data for parameter
estimation.  The  estimation  period  for  this
model  is  1964  to  1977.  The  year  1964  was
chosen  as  the  starting  point  for  these  data
since it,  too,  was the first  year after a  major
change  in  the  government  programs  for
wheat.
There  are  two major  advantages  of using
pooled data.  The first is that pooling enables
the researcher  to estimate the parameters  of
a model using a shorter historical time period
than  is  necessary  for  an  aggregate  regional
model.  In  addition  to  the  disadvantage  al-
ready  mentioned,  measuring  the  effects  of
changes  in technology  is  a common problem
in  supply  analyses.  The  longer  the  time
period under analysis,  the greater the chance
of significant  changes  in  technology.  While
shortening  the  time  period  used for  param-
eter  estimation  likely will  not  eliminate  the
effects  of changing  technology,  it  should
greatly  reduce  the problem.  The  second  ad-
vantage  of pooled data  is that it enables  the
researcher to relax the assumption that acre-
age  response  elasticities  are  constant
throughout  the region being studied.
Following sections of the paper discuss the
specification  of  the  aggregate  and  pooled
models and then present and compare empir-
ical  results for the two regional  models.
Model  Specification
The  aggregate  regional  wheat  acreage
model  used  in this  analysis  is  similar to  the
model presented by  Houck, et al. However,
a risk variable is added following the formula-
tion  used by  Lin.  The  model is  specified  as
follows:
(1)  AWt  =  f(PWt_-,  EWSPt,  WDt, Risk);
where,  AWt =  acres of wheat planted for the
region in year t,  in thousands of acres; PW-_1
=  regional  price  of wheat  in  year t-l,  in
dollars  per  bushel2;  EWSPt  =  wheat  price
support  rate  weighted  by  percent  of wheat
acreage eligible  for this payment  in year t, in
dollars  per bushel3; WDt  =  voluntary wheat
diversion  payment rate weighted by percent
of wheat acreage  eligible  for this payment in
year t, in dollars per bushel; and Riskt = mov-
ing average  of the standard  deviation  of the
regional gross income per acre from wheat for
the three previous years. 4
The  model  specification  for  the  pooled-
data model is similar to the  aggregate  model
with  the  addition  of  binary  variables  for
Washington and Idaho.  The model  specifica-
tion is:
(2)  AWi,t =  g(PWi,t-_,  EWSPt, WDt,
Riski,t,  BW,  BI);
where,  AWit  =  acres  of wheat  planted  for
state i in year t,  in thousands  of acres; PWi,t-1
=  price of wheat  for state  i  in year t-1, in
dollars  per  bushel;  EWSPt  =  wheat  price
support  rate  weighted  by  percent  of wheat
acreage eligible for this payment in year t, in
dollars  per bushel;  WDt =  voluntary wheat
diversion payment rate weighted by the per-
cent  of wheat  acreage  eligible  for  this  pay-
ment in year t,  in dollars per bushel; Riski,t =
moving average  of the  standard  deviation  of
2The  regional wheat  price  was calculated  as  the sum  of
the  lagged  state  wheat  prices,  with  each  state  price
weighted  by  the proportion of regional wheat  acreage
attributed to  the  state in  that year.
3For a detailed  account of the  construction of these  var-
iables under each policy regime,  see  Houck, et al. One
reviewer questioned  the economic rationale of this pol-
icy  variable  formulation.  The  variables  formulated  by
Houck et al. were chosen for this study because they are
the most prevalent in the literature.  For alternative pol-
icy variable formulations,  see Lidman and Bawden,  Just
(1973),  and Danin.
4Regional  gross  income  per  acre  was  calculated  as  the
sum  of the  state  per  acre  gross  incomes  with  each
weighted  by the  proportion of regional wheat  acreage
attributable  to the state in that year.
84
December 1979Wheat Acreage Response
per acre gross income for state i for the previ-
ous three years; BW  = binary intercept shift
variable  for Washington  (= 1 if the  observa-
tion is for Washington,  and 0 otherwise);  and
BI = binary intercept shift variable  for Idaho,
(=1  if the  observation  is  for  Idaho,  and  0
otherwise).
The lagged price of wheat is assumed to be
a proxy variable for producers'  price expecta-
tions at planting time. The coefficient on this
variable  is expected to be positive; that is, an
increase  in the expected  price of wheat with
all  other  variables  remaining  constant  is
hypothesized  to  result  in  an  increase  in
planted wheat acreage.
Likewise,  the coefficient  of the wheat sup-
port rate is hypothesized  to be positive.  This
variable  may  be  viewed  as  a  guaranteed
minimum price  for wheat.  If this guaranteed
price  is increased with all other variables  re-
maining  constant,  planted  acreage  is  ex-
pected to increase.
The weighted voluntary diversion payment
rate  is hypothesized  to  be negatively  corre-
lated with  planted wheat acreage.  This vari-
able represents  an  alternative  to wheat  pro-
duction; that is, leaving the land idle in order
to  receive  the  diversion  payment.  As  the
price of this production  alternative increases,
one would expect a shift from wheat produc-
tion to diversion.
As producers are generally  assumed to be
risk averse [see,  for example,  Just (1974) and
Lin],  the coefficient  of the risk variable is ex-
pected to be negative.  An increase in the var-
iability  of per acre  gross  income from  wheat
production  is  hypothesized  to  induce  a  de-
crease  in wheat acreage  planted.
The  shift  variables  in  the  pooled-data
model  account  for  differences  in  the  mean
planted  wheat  acreage  among  the  three
states.  The  coefficients  on  these  variables
represent  differences  in planted  acreage  be-
tween  Oregon  and  each  of the other  states.
Since  both  Washington  and  Idaho  produce
more  wheat than  Oregon the  coefficients  on
both  shift variables  are  expected  to be posi-
tive.
Both  the  aggregate  model  and  the
pooled-data  model  are  estimated  using  a
double  logarithmic  functional  form.  The
pooled-data  model  implicitly  assumes  that
the  relationship  between  wheat acreage  and
the independent  variables  is the same  for all
three  states.  If this equation were estimated
in the linear functional form,  this assumption
implies  that  a given  change  in  an  indepen-
dent variable  would change acreage of wheat
equally  in  all  three  states.  Since  planted
wheat acreage varies considerably among the
three  states,  it  is  not  reasonable  to assume
that  the change  in acreage  from some  given
change  in  price  is equal  across  states.  The
double  logarithmic  functional  form  enforces
the  more  reasonable  assumption  that  the
acreage  elasticities  are  equal  across  states.
Therefore,  the double  logarithmic functional
form  was  used  for  parameter  estimation  in
the pooled-data model. The aggregate  model
was  also  estimated  in  double  logarithmic
form  to  maintain  comparability  to  the
pooled-data model.
Empirical Results
Aggregate Model
The ordinary least squares (OLS) estimates
of the  parameters  of equation  1  in  double
logarithmic form are presented below.5
(3)  LnAWt  =  8.11  +  .094 LnPWt_-
(128.7)  (1.46)
- .032 LnWDt  +  .508 LnEWSPt
(-.299) (4.50)
+  .032  LnRiskt
(1.34)
R2 =  .716 DW  =  1.77
All  coefficients  have  the  anticipated  sign
except for the  risk variable,  but it is not  sig-
nificant at  the five percent level of probabil-
ity.  Only  the weighted  support price coeffi-
5Numbers  in  parentheses  below  the  estimated  coeffi-
cients are t-values and DW is the Durbin-Watson  statis-
tic.
85
Winter and WVhittakerWestern Journal  of Agricultural Economics
cient  is  significant  at five  percent.  The esti-
mated  elasticity of planted  acreage  with  re-
spect  to the weighted wheat support price  is
.508 which is  very similar  to Houck,  et al.'s
national estimate  of .58.  The estimated elas-
ticity  with  respect  to  wheat  price  is  .094,
which  is  much  smaller  than  national  esti-
mates  obtained  by  Nerlove  (his  estimates
were in the range  .35 to  .48)  and by Houck,
et al.  (.39).  However,  this coefficient  is not
significant  in the model estimated  here.  The
Durbin-Watson  statistic  indicates  that
serial-correlation  is not a problem.
Pooled-Data Model
The OLS estimates of equation 2 in double
logarithmic form  are presented below.
cant,  and equation  4 was  then re-estimated
with  this  variable  (BWLnPWiti) included.
The  results are presented  as equation  5.
(5) LnAWi,t  =  6.68  +  .376LnPWi,t_l
(100.3)  (5.31)
- .157 BWLnPWi,t_
(-2.30)
+  .242  LnEWSPt  - .029 LnWDt
(2.60) (-  .110)
- .060 LnRiski,t  +  1.13 BW  +  .367  BI
(-2.37)  (19.53)  (6.17)
R2 =  .967
(4)  LnAWi,t  =  6.71  +  .299 LnPWi,t_
(96.2)  (4.53)
+  .246 LnEWSPt  - .013 LnWDt
(2.50) (-.049)
- .049 LnRiski,t
(-1.85)
+  1.03BW
(27.11)
+  .222 BI
(5.78)
R2 =  .962
It was  suggested earlier  in the  paper that
the  pooled-data model allows the  researcher
to relax the assumption that acreage response
elasticities are constant throughout the three
state  region.  If the  elasticities  are  not  con-
stant,  the parameter estimates  of equation  4
are  biased due  to model misspecification.  In
order  to  test  the  assumption  of elasticity
homogeneity  across  states,  variables  were
created  by multiplying  the  binary intercept
shift  variables by the wheat,  wheat support,
and  wheat  diversion  price  variables.  The
wheat price  elasticity shift variable  for Wash-
ington  was  found  to  be  statistically  signifi-
86
All of the  coefficients  in equation  5 have
the anticipated  signs and all are significant at
the  five  percent  level  of probability  except
the  coefficient  for  the  weighted  price  of
wheat diversion  (WD).  The  only coefficients
that exhibit a major change  when compared
to  those  in  equation  4  are  those  for  wheat
price  (PW)  and  the  intercept  shifter  for
Washington  (BW).  These  changes  were  an-
ticipated  because  these  coefficients  were
previously  based  on  a  model  that  excluded
the elasticity  shift variable.
The error terms  from  equation 5  were  in-
itially  assumed to  be serially  correlated  and
heteroskedastic,  and a method suggested by
Kmenta (pp. 509-10) was employed to obtain
consistent  estimates  of the  first  order  au-
tocorrelation  coefficient  for each of the three
states.  None  of the  estimates  were  statisti-
cally significant.  Therefore,  serial correlation
is not a problem in this study.  Estimated var-
iances of the error terms were calculated for
each  state  (Kmenta,  pp.  510-11),  and  the
original data were  transformed  to  adjust for
heteroskedasticity.  Ordinary  least  squares
was  then applied to the  transformed  data  to
obtain  asymptotically  efficient  estimates  of
the parameters  in the acreage response  func-
tion.  The  results  of this  regression  are
December 1979Wheat Acreage Response
virtually  identical  to those  in equation 5  and
therefore are not presented.  The fact that the
parameters  and  the  standard  errors  did  not
change  significantly  indicates  that  hetero-
skedasticity was not a major problem.
For Oregon and Idaho,  the estimated elas-
ticity of planted  acreage  with respect  to  ex-
pected  price  is  .376  for  the  pooled  model.
The  estimate  for Washington  is  .219 (.376-
.157).  These  estimates  are  considerably
larger than the  .095 estimated for the  aggre-
gate  region,  but are  in line with the national
estimates made by Nerlove and Houck, et al.
The  regional  estimate  of the  elasticity  of
planted acreage with respect to the weighted
support  rate  for  the  pooled-data  model  is
.242.  This  estimate  is  considerably  smaller
than either national estimates or the estimate
from  the  aggregate  regional  model.  The  es-
timated  elasticity  of weighted  wheat  diver-
sion is  -. 029  for the pooled-data  model  and
is virtually  identical  to the  aggregate  model
estimate,  but again  is not  statistically  signifi-
cant.  The estimated  elasticity of the risk vari-
able  is  - .06 for the pooled model as opposed
to .032 for the  aggregate  model.  The  pooled
data estimate  of this coefficient  is,  however,
identical  to  the  estimate  made  by  Lin  for
Kansas.  The  sign on this coefficient  is consis-
tent with the  assumption  of risk  averse  be-
havior  by  producers.  The  magnitude  of the
estimated  risk coefficient  suggests  that  a  10
percent  increase  in  the  three  year  moving
average of the  standard deviation  of per acre
gross income from wheat production  induces
a  .6 percent  reduction  in planted acreage.
The  aggregate  and  pooled-data  models
were  also  compared  with  respect  to  their
abilities to correctly predict regional acreages
during  the  time  period  1964  to  1977.  The
prediction  errors  were  calculated  by  trans-
forming the residuals from equations  3 and 5
to the original  units of measurements  (acres)
and dividing these  transformed  residuals  by
the  actual  planted  acreages.  The  aggregate
model had an average prediction  error of 6.5
percent.  The  prediction  error  for  the
pooled-data  model was 5.8 percent,  a reduc-
tion of 11  percent over  that of the aggregate
model.
The differences  between  regional  and na-
tional estimates of the acreage response elas-
ticities  support the hypothesis that the use of
national models for regional analysis may give
misleading  results,  and  greater  emphasis
should  be  placed  on  regional  acreage  re-
sponse functions.  Furthermore,  the results of
this study indicate  that the use of the pooled
time-series  and cross-sectional  data approach
to  acreage  response  function  estimation  is
clearly  a viable  alternative  to  the  previously
used aggregate  approach.
References
Danin,  Y. A  Simple  Analysis  of Acreage  Response  to
Some Agricultural  Programs, Staff Paper P76-27,  De-
partment  of Agricultural  and  Applied  Economics,
University  of Minnesota,  August  1976.
Hoffman,  R.  G.  "Wheat-Regional  Supply  Analysis,"
Wheat Situation, ERS,  USDA,  August  1973.
Houck,  J.  P.,  M.  E.  Abel,  M.  E.  Ryan,  P.  W.  Gal-
lagher,  R.  G.  Hoffman,  and J.  B.  Penn. Analyzing the
Impact  of Government Programs on Crop Acreage,
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Just,  R.  E. "A Methodology  for Investigating  the Impor-
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Just,  R.  E.  "An Investigation  of the Importance  of Risk
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Kmenta,  J. Elements of Econometrics,  New  York,  The
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87
Winter and WhittakerWestern Journal  of Agricultural  Economics
88
December 1979

ESTIMATION OF WHEAT ACREAGE RESPONSE FUNCTIONS FOR THE NORTHWEST

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