This article develops a model to forecast monthly alfalfa hay prices before the first harvest. This is done by linking an annual model, which forecasts the initial May price, with a system of monthly equations that track the monthly seasonal price pattern, given the forecasted May price.Crop Production/Industries, Demand and Price Analysis,

Blake, Martin J.

Clevenger, Tom

English

Research Papers in Economics

A Linked Annual  and Monthly
Model  for Forecasting  Alfalfa
Hay Prices
Martin J.  Blake  and Tom  Clevenger
This article  develops a model to forecast  monthly alfalfa  hay prices before the first  harvest.
This is  done by linking  an annual model,  which  forecasts  the  initial May  price,  with a system
of monthly equations  that track  the monthly  seasonal  price pattern,  given  the forecasted  May
price.
In  much  of  the  western  United  States,
alfalfa  hay is a  cash crop.  Before  the first
cutting  each  year,  growers  and  users  of
alfalfa  hay  spend  considerable  time  and
effort gathering information to help estab-
lish their  initial  price  offers.  Buyers  con-
tact other  buyers  and  sellers,  and  sellers
do  the same  as they  try to arrive  at mu-
tually agreeable  prices.
Currently,  neither annual  nor monthly
forecasts of New Mexico alfalfa hay prices
are published before the first cutting.  Such
forecasts  would  help producers  and users
of alfalfa hay plan their operations for the
coming  year.  These  forecasts  would  also
be an independent information source that
users and growers could  use in the process
of price  discovery.  The  forecasts  can  also
be the basis to initiate more  formal price
negotiations.  This article develops  a mod-
el  for  forecasting  monthly  alfalfa  hay
prices for the season,  before the first har-
vest.
The level of alfalfa hay prices has been
volatile  while  the  seasonal  price  pattern
has  remained  fairly  stable.  Under  these
conditions,  determining  prices  can  be
viewed  as a two-step  procedure.  The first
Martin  J.  Blake  and  Tom  Clevenger  are  Associate
Professor and  Professor,  respectively,  in the  Depart-
ment  of  Agricultural  Economics  and  Agricultural
Business at New  Mexico  State  University.
New  Mexico  State  University,  Agricultural  Experi-
ment  Station,  Journal  Article  1045.
step  is  to  forecast  that point  from which
the seasonal price pattern  starts.  This was
done using an annual  model.  The  second
step  is to identify  the seasonal  price  pat-
tern.  In  this article,  this was done using  a
system of monthly equations.  Linking the
annual  model  with  the  monthly  price
forecasting relationships incorporates both
these elements  of the price determination
process in forecasting monthly  alfalfa hay
prices.
Literature
No published  studies to forecast  alfalfa
hay  prices  were found.  Although  an im-
portant input in beef, dairy and horse pro-
duction,  alfalfa  hay  price  forecasting  has
received  scant  attention  in the literature.
Only one unpublished study by Myer and
Yanagida  was  found on this topic.*  They
combined  an  annual  econometric  model
with  a  quarterly  ARIMA  model  to fore-
cast quarterly  alfalfa hay prices in the 11-
state western  region.
Annual Model
Forecasts  of monthly  alfalfa  hay prices
in New  Mexico are generated through the
use  of a linked model.  The  linked model
* This  and  the following  article,  while  dealing  with
similar  issues, were prepared  independently  of each
other.
Western Journal of Agricultural Economics, 9(1):  195-199
© 1984 by  the Western  Agricultural  Economics  AssociationWestern Journal of Agricultural  Economics
consists of a model estimated using annual
data to forecast the price of alfalfa  hay in
May,  the  month  of  first  harvest  in  New
Mexico,  and  a  system  of  equations  esti-
mated using monthly data to forecast  sub-
sequent  monthly  prices  using  the  May
price  as a starting point.
The  annual  model  is  formulated  as  a
four-equation,  recursive,  supply  and  de-
mand  model.  This  four-equation  annual
model  is estimated using  real  prices.  Real
prices are calculated using the annual GNP
implicit  price  deflator  for  the  United
States, with 1972 as base year. Because  the
annual  model  is recursive,  it is  estimated
using  ordinary  least  squares  (OLS).  The
annual  model  was  estimated  using  May
1960 through May  1982 data. The t-values
for  each  estimated  regression  coefficient
are  in parentheses.
The  first  two  equations  in  the  model
determine  the  annual  alfalfa  hay  supply
in New Mexico.  Equation  (1) estimates the
New  Mexico  alfalfa  hay  acreage  in  the
current  year  as  a  function  of  last  year's
alfalfa hay  acreage.
Equation  (1) is:
AA, = 16,267.825  + 0.943AAt_l  (1)
(1.05)  (12.51)
R
2 = 0.882,  F = 156.41
where:
AAt = New  Mexico alfalfa hay acreage,
year  t.
Because alfalfa is a perennial,  it was ex-
pected  that  the  sign  of  AAt_1  would  be
positive and close to 1. This is the case and
the  coefficient  for  AAt  is  significant  at
the a = 0.0001  level.  This  simple  autore-
gressive  equation  accounted  for  about 88
percent  of the variation  in annual  alfalfa
hay  acreage in New Mexico.
Although  producers  undoubtedly  con-
sider factors  other than  last year's  alfalfa
acreage  to  determine  this  year's  alfalfa
acreage,  reasonable alternatives  proved to
be  statistically  insignificant.  Last  year's
196
cotton and grain sorghum prices were both
tried  with poor  results,  as was  the  alfalfa
hay  price  in  the  previous  year.  Because
alfalfa  is  a perennial  crop,  it  is  typically
left in production for at least 5 years, once
it is established. Such cultural practices as-
sure the success of a simple autoregressive
model, because  much of what was in pro-
duction last year will also be in production
this year.
Equation  (2)  estimates  annual  alfalfa
hay  production  as  a  function  of  current
alfalfa hay  acreage.  The  second  equation
is:
PAt  =  -189,710.042  + 5.278AAt
(-2.75)  (15.88)
R2 = 0.920,  F  = 252.18
(2)
where:
PA, = New  Mexico  alfalfa  hay  produc-
tion in tons,  year  t.
The coefficient of alfalfa hay acreage  (AA 1)
was  positive,  as  expected,  and  significant
at  the a = 0.0001  level.  The equation  ex-
plained  about  92  percent  of the variation
in  annual  New  Mexico  alfalfa  hay  pro-
duction.
Both range conditions and a trend vari-
able  for  technology  were  examined  for
possible  use in equation  (2).  Neither  vari-
able entered was significant.  A variable to
account  for  weather  influences  upon  al-
falfa hay production  was not included for
two  reasons.  Because  most  alfalfa  pro-
duced in New Mexico  is irrigated,  drought
has  little  impact  upon  production.  Fur-
ther, even  if weather  or range  conditions
did enter  as  significant  supply  shifters,  a
user would have  to forecast these weather
variables  for use in price  forecasting.
Equation  (3)  in  the  annual  model  is  a
price-dependent  demand  equation  for
New  Mexico  alfalfa  hay.  The  price-de-
pendent  formulation  for  alfalfa  hay  de-
mand  is  appropriate  because  supply  en-
ters  as  a  given  from  equation  (2).  In
equation  (3), the real May price for alfalfa
July 1984Blake and Clevenger
in the current year is estimated as a func-
tion of current alfalfa hay production,  the
real  April  1  price  of  a  September  corn
futures contract,  and a trend  variable.
Equation  (3)  is:
RP,  =  -1,596.52  + 0.116RCFP,
(-2.83)  (4.16)
- 0.00001435PA,  + 0.827YR,  (3)
(-1.36)  (2.83)
2 =  0.713,  F =  16.59
where:
RCFPt  =  The April  1 price  of a Septem-
ber  corn  futures  contract  in
cents  per bushel,  Chicago,  de-
flated  by  the  GNP  implicit
price  deflator, year  t; and
YR,  =  Year.
Because  most  feed  ration  ingredients
are, to a large extent, substitutes, prices of
these  ingredients  tend  to  move  together.
The  April  1 price  of  a  September  corn
futures  contract  was  used  to  reflect  the
price  of an  important  feed  ration  ingre-
dient and the expected price  of feedstuffs
in general. The futures price was assumed
to indicate  market  expectations  for  live-
stock feed inputs for the coming year.  This
coefficient  was  significant  at  the  a =
0.0005  level in equation  (3).
Corn  and  soybean  futures  prices  for
various contract  delivery dates were eval-
uated in  equation  (3),  and the September
corn futures contract  was the most signif-
icant.  A possible explanation for this is that
the  hay  price  formation  process  may  be
related to both the old and new corn crops.
Some hay demand  in early  summer is for
immediate  consumption.  This  demand
would be higher if old crop corn is in short
supply. Hay prices can  also be influenced
by the  expected  feed  availability  for  the
coming winter, after the new corn crop is
available.  The September futures price for
corn  may  work  well  because  it  is  influ-
enced by both old and new crop feed sup-
plies.  Livestock prices were  also evaluated
in equation  (3) and  found to have no sig-
nificant relationship.
Year  was  included  as  a  trend  variable
and  was  significant  at  the  a = 0.01  level
in equation  (3).  This variable  may  be  in-
fluenced  by  several  other  variables  that
have increased over this time period, such
as cattle numbers.
The estimated coefficient  for alfalfa hay
production was negative, as expected, and
was  significant  at  the  a = 0.19  level.  Al-
though  the  alfalfa  hay  production  vari-
able  in  equation  (3)  appears  to be  statis-
tically  weak,  exclusion  of  this  variable
from the equation resulted in poorer fore-
casts.  Because  this  variable  had  the  ex-
pected  sign  and  its  inclusion  resulted  in
better  forecasts,  it  was  retained  in  the
model.
Because  real prices  are used in the an-
nual  model,  an  equation  to  forecast  the
GNP  implicit  price  deflator  is  needed  to
forecast  with  the  annual  model.  This
equation  is:
GNPD, =  -664.092  + 1.062GNPDt_,
(-2.17)  (38.40)
+ 0.337YR,
(2.15)
R2  =  0.998,  F =  6,572.19
(4)
where:
GNPDt = Gross  National  Product  im-
plicit  price  deflator,  1972 =
100.
Although this  is  a simple  model for fore-
casting the GNP implicit price deflator,  it
yielded good  results.
Monthly Model
The  relationships  for  forecasting  the
seasonal price pattern for alfalfa hay were
estimated  using OLS  with data from Jan-
uary  1960  through December  1982.  The
monthly  model  consists  of  11  price  fore-
casting  equations  in  which  the  current
197
Linked Hay ModelWestern Journal of Agricultural Economics
monthly  price  is  estimated  as  a  function
of the  previous  monthly  price.  These  re-
lationships are estimated using  real prices
and can be used  to track the price pattern
throughout  the  season.  The  11  monthly
price forecasting  relationships  are:
JUN =  1.921  + 0.877MAY
(0.64)  (11.70)
JUL =  1.622  + 0.923JUN
(1.01)  (21.16)
AUG  = -1.626  + 1.051JUL
(-0.48)  (11.11)
SEP =  1.227  + 0.991AUG
(0.51)  (14.79)
OCT =  -0.203  + 1.078SEP
(-0.09)  (18.08)
NOV =  5.833  + 0.9330CT
(2.80)  (17.78)
DEC  =  0.423  + 1.074NOV
(0.13)  (13.86)
JAN  = 7.864  + 0.806DEC
(3.38)  (15.97)
FEB =  5.218  + 0.895JAN
(1.85)  (14.27)
MAR  =  0.626  + 0.987FEB
(0.20)  (14.00)
APR  =  5.217  + 0.873MAR
(1.42)  (10.84)
R
2 = 0.872,
F =  136.85
R
2 = 0.957,
F = 447.95
R
2 = 0.860,
F  = 123.33
R
2 =  0.916,
F =  218.80
R
2 = 0.942,
F = 326.83
R
2 = 0.940,
F = 316.03
R
2 = 0.906,
F  = 192.15
R
2 = 0.927,
F =  255.02
R
2 =  0.911,
F =  203.70
R
2 =  0.907,
F =  195.95
R
2 = 0.854,
F  =  117.40
All estimated  regression coefficients  for
the previous month's price are statistically
significant  at  the  a = 0.0001  level.  The
lowest  R2 is  0.854  for  the  April  equation
(15).  These  estimated  relationships  indi-
cate a  stable  price pattern  for alfalfa  hay
throughout the season.
Linking the  Models
Forecasts of average monthly alfalfa hay
prices  in  New  Mexico  are  generated  in
two stages. First, the annual model is used
to forecast  the  real  May  price  of  alfalfa
hay. This real price forecast could be con-
verted to a nominal price forecast using a
forecast of the GNP implicit price deflator
from  equation  (4).  All  the  information
needed to forecast the May price  is avail-
able  by April  1. This  provides  price pro-
jections well in advance of the first alfalfa
hay cutting. These price  projections could
be  used by the  industry in price negotia-
tions for the coming year.
Second,  the  forecasted  real  May  price
from the annual model is used in equation
(5)  to  forecast  the  real  June  price.  Equa-
tions  (5) through  (15)  are used iteratively
to generate subsequent real monthly price
forecasts  through  April  of  the  following
year.  Again,  the  real  monthly  prices  can
be  converted  to  nominal  monthly  prices
by using  equation  (4).  The  use of the an-
nual and monthly  models in tandem pro-
vides both a forecast  of the season starting
price  and subsequent  monthly  prices.
Even if the May price forecast from the
annual  model  is  fairly accurate,  mechan-
ical  generation  of  subsequent  monthly
prices may err due to factors  not included
in the monthly  models, such as a drought
or insect infestations. If actual monthly al-
falfa hay  prices are incorporated  into the
monthly models as they become available,
forecasting errors for the remainder of the
season  can  be  substantially  reduced.  Al-
though  the  monthly  models  do  not  in-
clude  such  exogenous  factors  as  drought,
actual alfalfa  hay prices incorporate  these
influences.  Hence, use of actual alfalfa hay
price  information  as it  becomes available
incorporates  these  exogenous  factors  into
the price  forecasts.  This continued  updat-
ing of monthly price forecasts  keeps them
on  track and  enhances  the linked model's
usefulness  to buyers and  sellers  of alfalfa
hay.
Error Analysis  and Model
Validation
Because an  annual  model and monthly
models were combined to form the linked
model,  the  root  mean  square  error  was
calculated  separately for the annual mod-
el, the system of monthly  models and the
linked model using January  1960 through
December  1982  data.  The  root  mean
square  error  from  the  annual  model
(equations  (1) through  (4))  for the  nomi-
nal May alfalfa hay price was $3.20. With
198
July 1984Blake and Clevenger
TABLE 1.  New  Mexico Alfalfa Hay Prices per
Ton:  Actual,  Forecasted  and  Re-
sidual,  May  1983-October  1983.
Using  Four Equation
Annual  Model
Fore-
Month  Actual  casted  Residual
May 1983  92.00  93.36  -1.36
June 1983  87.00  86.15  0.85
July 1983  89.00  83.13  5.87
August  1983  87.00  83.75  3.25
September 1983  87.00  85.74  1.26
October  1983  90.00  91.98  -1.98
Source: Actual  prices from  U.S.  Department  of Agri-
culture, Statistical Reporting Service,  Las Cruces,  New
Mexico.
a nominal mean  May price of $44.21,  the
root  mean  square  error  for  the  annual
model  was  7.2  percent  of the  mean  May
price.
For  the  system  of  monthly  models
(equations  (5)  through  (15)),  which  fore-
cast  the  seasonal  price  pattern,  the  root
mean square error was $5.58 and the mean
monthly  price  for the period was  $46.36.
The root mean square error for the system
of monthly  price forecasting  relationships
was  12.0  percent  of  the  mean  monthly
price.
The  root  mean  square  error  for  the
linked model  (equations (1)  through  (15))'
was $5.30.  With  a mean monthly  price of
$46.36, the root mean square error for the
linked model was 11.4 percent of the mean
monthly  price.
The  performance  of  the  linked  model
outside  the  sample  was  examined  (Table
1).  The  root  mean  square  error  for  May
1983  through  October  1983  using  the
linked model was $2.97. This was 3.3 per-
cent of the mean actual nominal price for
these 6 months. Performance of the linked
model outside of the sample compares  fa-
vorably  with the in-sample  performance.
Conclusions
Two  problems  were  identified in  fore-
casting New Mexico alfalfa hay prices.  The
first  was  forecasting  the  initial  starting
price  for  each  season.  The  second  was
forecasting  the  subsequent  monthly  sea-
sonal price pattern. The technique used in
this study was to develop separate  models
that would  best  forecast each  of  these  as-
pects  and  then link  the resulting  models.
This  technique  seemed  to  work  well  in
this case. It is suggested that the technique
might  be  applicable  in  forecasting  other
commodity prices where the initial season
price  establishes  a  level  from  which  the
subsequent  seasonal price pattern  begins.
The  linked  model  developed  in  this
study can  serve  as an independent  source
of information  to  help  growers  and  users
in the initial  price discovery  process  each
season.  It also  provides  detailed  monthly
price information,  which can be useful in
making  storage  and  forward  contracting
decisions.
References
Myer,  G.  L.  and J.  F.  Yanagida.  "A  Methodology  of
Combining  Annual  Econometric  Forecasts  with
Quarterly  ARIMA  Forecasts."  Contributed paper,
Western  Agricultural  Economics  Association  An-
nual Meeting,  Lincoln,  Nebraska, July  19-21,  1981.
United  States  Department  of  Agriculture,  Statistical
Reporting  Service  and  New  Mexico  Department
of  Agriculture.  New  Mexico Agricultural Statis-
tics, various  issues.
199
Linked Hay Model

A Methodology of Combining Annual Econometric Forecasts with Quarterly ARIMA Forecasts.&quot; Contributed paper, Western Agricultural Economics Association Annual Meeting,

A LINKED ANNUAL AND MONTHLY MODEL FOR FORECASTING ALFALFA HAY PRICES

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