Journal of Agricultural and App ied Economics, 30,1(July 1998):21–33 0 1998 Souther nAgricultura lEconomic sAssociation Estimating Price Variability in Agriculture: Implications for Decision Makers Daryll E. Ray, James W. Richardson, Daniel G. De La Terre Ugarte, and Kelly H. Tiller ABSTRACT Using a stochastic version of the POLYSYS modeling framework, an examination of pro- jected variability in agricultural prices, supply, demand, stocks, and incomes is conducted for corn, wheat, soybeans, and cotton during the 1998–2006 period. Increased planting flexibility introduced in the 1996 farm bill results in projections of signif cantly higher planted acreage variability compared t recent historical level . Varia ility of ending stocks and stock-to-use ratios is projected to be higher for com and soybeans and lower for wheat and cotton compared to the 1986-96 period. Significantly higher variability is projected for corn prices, with wheat and soybean prices also being more variable. No significant change in cotton price variability is projected. Key Words: POLYSYS model, price variability, stochastic simulation. The economic well-being of production agri- culture and agribusiness is influenced by a number of forces beyond the control of eco- n om ic agents in agriculture. Producers and an- alysts ca n for mu la te r ea son able expectations about the influences of some of these exoge- n ou s fa ct or s, s u ch as population, per capita in- com es, t ech nology, and cu rr en t gover nmen t policies and programs, wh en making produc- t ion plans. Other exogen ou s fa ct or s cannot be expressly incorporated into the decision-mak- ing process, but st ron gly in fluen ce domestic and global a gr icu lt ur al supplies—including random effect s of weather, biological phenom- Rayis BlasingameChairof Excellenceprofessor,Uni- versityofTennesseeAgriculturalPolicy AnalysisCen- ter,Richardsonis a professorin theDepartmentof Ag- riculturalEconomics, Texas A&M University.De La TerreUgarteis a researchassistantprofessor,andTiller is post-doctoralresearchassociate,bothwith the Uni- versityofTennesseeAgriculturalPolicy AnalysisCen- ter. ens, changes in in st it ut ion al structures among trading partners, and natural phenomena. A la rge portion of the historical va ria bilit y in agricultural prices, supplies, exports, and re- turns can be attributed to factors over which in dividu al p r od u cer s h ave n eit her con tr ol n or r elia ble predictive ability. For more than a half century, various government programs specif- ica lly designed in part to reduce the variability of agricultural prices, supplies, exports, and fa rm in com es h ave a ffect ed U.S. a gr icu lt ur e. Since passage of the Federal Agriculture Im- provement and Reform (FAIR) Act in 1996, a dismantling of government supply controls and price stabilizing programs has begun, with movem en t t owa rd fr eer agricultural p r od u c- tion and markets. Now that government sup- ply controls and price stabilizing tools are no lon ger a va ila ble, it has become even m or e cr it - ical that producers, policy makers, and ot h er agricultural decision makers a re cogn izan t of the sources and magnitude of variability around a gr icu lt ur al yields and exports, and on
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n om ic a gen ts in a gr icu lt ur e. P rodu cer s a nd a n-
a lyst s ca n formu la te r ea son able expect at ion s
about the influences of some of t hese exoge-
n ou s fa ct or s, su ch a s popu la tion , per ca pit a in -com es, t ech nology, a nd cu rr en t gover nmen t
policies a nd pr ogr ams, wh en makin g produ c-
t ion pla ns. Ot her exogen ou s fa ct or s can not be
exp res sly in cor por a ted in t o t h e decis ion -mak -
ing pr ocess, bu t st ron gly in fluen ce domest ic
a nd globa l a gr icu lt ur al su pplies—in clu din g
r an dom effect s of wea th er , biologica l ph en om -
Ray is BlasingameChairof Excellenceprofessor,Uni-versityof Tenn esseeAgricultu ra lPolicy AnalysisCen-ter,Richar dsonis a professorin the Departmentof Ag-riculturalEconomics, Texas A&M University.De LaTerr eUgart eis a resea rchass ista ntprofessor,andTilleris a post-doctoralresearchassociate,both with the Uni-versityof Tenn esseeAgricultu ra lPolicy AnalysisCen-ter.
en s, ch an ges in in st it ut ion al st ru ct ur es amon g
t ra din g pa rt n er s, a n d n at ur al ph en omen a.
A la rge por tion of t he h ist or ica l va ria bilit y
in a gr icu lt ur al pr ices, s upp lies, exp or ts, a nd r e-
turns can be at t r ibu ted to factors over which
in dividu al pr odu cer s h ave n eit her con tr ol n or
r elia ble pr edict ive a bilit y. F or m or e t ha n a h alfcen t ur y, va riou s gover nmen t p rogr am s specif-
ica lly design ed in pa rt t o r ed uce t he va ria bilit y
of agr icu ltura l pr ices, supplies, expor ts, and
fa rm in com es h ave a ffect ed U.S. agr icu lt ur e.
Since passage of the Federa l Agricu lture Im-
provement and Reform (FAIR) Act in 1996, a
dismant ling of government supply cont rols
a nd pr ice st abilizin g pr ogr am s h as begu n, wit h
movem en t t owa rd fr eer a gr icult ur al pr odu c-
t ion and markets. Now that government sup-
ply cont rols and pr ice stabilizing tools a re no
lon ger a va ila ble, it h as becom e even mor e cr it -
ica l th at producers, policy makers, and oth er
agr icu lt ura l decision ma ker s a re cogn izan t of
the sou rces and magnitude of var iability
a rou nd a gr icu lt ur al yields a nd expor ts, a nd on
22 Journal of Agricultural and Applied Economics, July 1998
decision-m aking va ria bles such a s pr ices a nd
net retu rns. Also of considerable in terest is
whether price and net return variabilityy are
less or greater in the South than for the U.S.
a s a whole.A number of determin ist ic, la rge-sca le
models of the U.S. agr icultura l sector have
pr oven t o be u sefu l t ools for pr oject in g pr ices
and incomes with an “average sta te” of
wea ther , unchanged in t erna tiona l in st it u tiona l
st r uctur es, a nd other exogenous condit ions. ]
But producers, policy makers, agricultura l
lender s, a gr ibu sin esses, a nd ot h er s a r e in cr ea s-
ingly in terested in the range and rela t ive fre-
quencies of pr ices given the var ia bility a sso-ciated with yields and expor t s. Stochast ic
simulat ion techniques allow est imat ion of
pr oba bilit y dist ribu tion s for en dogen ou s va ri-
ables such as prices and net returns, given
pr oba bility dist r ibut ions for uncert ain va ri-
ables in the system. Uncer ta inty in the agri-
cultura l system may be in the form of proba-
bility dist r ibut ions on the r andom va riables,
such as yields and expor ts, or on the distur -
ba nce t erms for pa rt icu la r equ at ion s. St och as-
t ic simula t ion of such a model results in an
est imat e of t he pr oba bilit y dist ribu tion s on t he
endogenous var iables, and thus provides an
im por ta nt dim ension to the inform at ion base
for decision maker s.
Th is a dded dimen sion of va ria bilit y a rou nd
key indica t or s of agr icu lt ur a l per formance will
be esp ecia lly impor t an t for examin ing agr icu l-
tural sector impacts of the FAIR Act . This pa-per r epr esen t s an in it ia l examin at ion of supply,
dem and, pr ice, a nd income var ia bility using a
stocha st ic sim ulat ion model of th e U.S. agr i-
cultura l sect or , ba sed on the P olicy An alysis
Syst em (POLYSYS) n at ion al simula tion mod-
el (Ra y et a l. 1997). A 10-yea r st och ast ic ba se-
lin e simula tion is per formed u sin g t he Novem-
ber 1997 Food and Agriculture Policy
Resea rch In st it ut e (FAPRI) a gr icu lt ur e ba se-
lin e. All of t he ba selin e a ssumpt ion s r ega rdin g
1Examples of large-scale deterministic structuralmodels that are often used for policy analysis includemodels such as AGMOD (Ferris), COMGEM (Pensonand Chen), FAPRI (Devadoss et al.), AGSIM (Taylor1993), and CARD LP (English et al.).
agr icu lt ur a l policies, domest ic and globa l eco-
nomic condit ions, wea ther , technologica l
ch an ge, a nd ot her in flu en ces a lso ch ar act er ize
t he st och ast ic ba selin e simula tion , except t ha t
stochast ic yield and expor t shocks are int ro-
duced. Examinat ion of the result s focuses on
crops of pr imary importance to southern ag-
r iculture, including cor n, soybea ns, cot ton ,
and whea t . For s elect ed commodit ies, st a tist ics
on va ria bilit y a re pr esen ted for h ar vest ed a cr e-
a ge, yield, su pply, feed u se, expor t u se, en din g
stocks, season average pr ice, and net returns
per a cr e. Th e pr oba bilit y dist ribu tion s a ssoci-
a ted wit h t he 10- yea r simula tion a re compa red
to t he historica l va ria tion of cr op pr ices, sup-plies, demands, and returns to allow an ex-
amin at ion of t he ch an ge in pr oject ed va ria bil-
ity in agr iculture compared to observed
va ria bilit y in r ecen t yea rs.
Methodology
The POLYSYS nat ion al agr icu lt ur e simula tion
model is anchored to a nat ional baseline of
pr oject ion s for a gr icu lt ur e. Ba selin e pr ojec-
t ions for cr op a cr ea ges, pr ices, a nd expendi-
t ur es a re r et ailor ed for 305 pr odu ct ion r egion s
corr espondin g t o Agr icultur al Sta tist ic Dis-
t nict s (ASDS). Ch an ges t o t he ba selin e t hen a re
int roduced exogenously, and the model est i-
mates the impact s of changes to the baseline
for r egion al cr op su pply, na tion al cr op pr ices
and demand, livestock supply and demand,
a nd agr icultur al income. En dogenou s modelcrops include corn, soybeans, cot ton, gra in
sor ghum, ba rley, oa ts, wheat , a nd rice. Seven
livestock commodit ies also are included as a
complement to the feed dem an d componen t of
the crop sector . The calculat ion of most na-
t ional var iables in POLYSYS is dr iven by de-
via tion s fr om a ba selin e a nd ela st icit y pa ram-
eters. POLYSYS incorpora tes 305 regional
linear pr ogr amming cr op supply m odels a nd a
cr op deman d a nd pr ice simult an eou s block forthe est im at ion of en dogenous cr op var ia bles.
Th e r egion al cr op su pply models a re design ed
to alloca te margina l changes in acreage over
the ba seline cr op a crea ge within ea ch r egion,
Ray et al.: Estimating Price Variability in Agriculture 23
u la tion yields a dyn am ic per forma nce pa th for
cr op a nd livestock supply, dem and, pr ice, a nd
agr icu lt u ra l income var iables .
An implicit a ssumpt ion ch ar act er izin g r e-
su lt s from determinist ic simula t ion models
like POLYSYS is t ha t simula tion r esu lt s differ
from the baseline only to the extent tha t
ch an ges a re in tr odu ced t o defin e a simula tion .
Th us, det ermin ist ic models gener ally a re lim -
it ed to providing point est imates of endoge-
nous variables. It is possible to use a deter -
minist ic model to examine the impact s of
ch an ges fr om t he ba selin e for model va ria bles
character ized by high levels of uncer ta inty.
For example, the sensit ivity of agr icultura lvariables to baseline expor t project ions has
been the subject of several POLYSYS simu-
la tion a na lyses (e.g., Ra y a nd Tiller ; Ra y; Ra y
et al. 1995). But unless specific cha nges to the
ba selin e expor t pr oject ion s a re simula ted, t he
en dogen ou s va ria bles a re est im at ed u nder t he
assumpt ion that there is no range of values
a ssocia ted wit h ba selin e expor t pr oject ion s.
While a determinist ic model cou ld be used to
perform mult iple simula tions t ha t int roducer andomness to desir ed va ria bles, stocha st ic
t ech niqu es pr ovide a st at ist ica l fr am ewor k t o
per form a ser ies of simula tion s in a n efficien t
a nd syst emat ic man ner (Ta ylor 1994; Rich ar d-
son a nd Nixon ).
A POLYSYS stochast ic baseline simula-
t ion is developed by in tr odu cin g va ria bilit y in
(a) nat ional crop export project ions, and (b)
yield est im at es for ea ch of t he 305 r egion s in to
t he POLYSYS ba selin e simula tion . St och ast icexpor t s for eight crops were simula ted from a
mult iva ria te empir ica l (MVE ) dist ribu tion of
devia tion s fr om a t ren d. Th e MVE dist ribu tion
for expor ts wa s est im at ed u sin g da ta for 1982–
96. Historica l values of crop expor t s over the
1982–96 per iod wer e r egr essed on a t im e t ren d
for each of the eight model crops to obta in the
er ror t erms (va ria bilit y) fr om h ist or ica l t ren d
expect a tion s.z The per cen t age devia t ion s fr om
2Export data are available prior to 1982, but evi-dence of a structural change in U.S. exports around1982 exists. An alternative to truncating historical ex-ports at 1982 would be inclusion of additional histor-ical export data with an estimation of structural change
included in the regression of historical exports on atime trend.
the t rend for each crop were used to specify
empir ica l pr obabilit y dist r ibu t ion s for cr op ex-
por t devia tions. A corr ela tion ma tr ix of cr op
export deviat ions for eight crops was calcu-
la ted and used in con junct ion with the h istor -
ical percen ta ge devia tions fr om t rend t o sim-
u la te cor rela ted r an dom devia tes t o t he a nn ua l
ba selin e expor t va lu es in t he st och ast ic simu-
lation.
A mult iva ria te empirica l dist ribut ion for
crop yields was not used to genera te random
yields due to the sheer size of the correlat ion
mat r ix for simulat ing eight crops in each of
305 regions. The histor ica l variability of re-
gional crop yields, 1972–96, was used to de-velop empir ica l dist ribu tion s for pr odu ct ion
for each crop in each region. Percentage de-
viat ion st r uctur es a re preser ved by year t o r e-
flect cor rela tion a cr oss cr ops a nd r egion s. Cor -
rela ted yields were simply simula ted by
randomly select ing rows from the matr ix of
a nn ua l per cen ta ge yield devia tion s for t he 305
regions and eight crops. Once a row in the
mat r ix (year ) was selected randomly, the de-
via tion s wer e a pplied t o t heir r espect ive ba se-
lin e va lu es t o ca lcu la te t he st och ast ic yield.3
In the fir st yea r of a POLYSYS simula tion,
the model randomly selects a percentage de-
viat ion for init ial export sh ocks for ea ch cr op
and applies it to the baseline value for crop
expor ts in t ha t year . Simila rly, a r andom year
is chosen from 1972 through 1996, and the
yield percentage devia t ions for each of eight
crops in each of 305 regions for that year area pplied t o t he ba selin e yield pr oject ion s. Sim -
ilar random draws of export shocks and yield
percentage devia t ions are made in each suc-
cessive year of the simulat ion. In a 10-year
simula tion , 10 r an dom a nn ua l dr aws of expor t
shocks and yield percentage devia t ions are
m ade a nd a pplied to their respect ive baseline
va lu es. Th e model solves t he 10-yea r h or izon
3Historical crop yields were regressed on a timetrend to calculate the annual percentage deviationsfrom trend. The regional nature of the crop supply sec-tor of the model requires complete historical yield dataat the county level, which were not available electron-ically prior to 1972. Thus, historical data available for
estimation of yield deviations from a trend are limitedto 25 years.
26 Journal of Agricultural and Applied Economics, July 1998
Table 1. Summar y St at ist ics of H ist or ica l Aver age (1986–96) a nd Sim ula tion Aver age ( 1997–
2006) Resu lt s for Cr op Va ria bles
corn Wheat Soybeans Cottonc
1986- 1997– 1986– 1997– 1986– 1997– 1986- 1997-
Item 9&l 06b 96 oeb 96a ofjb 9tP oeb
Plant ed Acreage
Mean (rnil. at.) 74.1
Std. Dev. 3.9
Coef. of Variation 0.053
Production
Mean (roil. bu., bales) 7,800
Std. Dev. 1,332
Coef. of Variation 0.171
Total Use
Mean (roil. bu., bales) 8,096
Std. Dev. 425
Coef. of Variation 0.053
Endin g Stocks
Mean (roil. bu., bales.) 1,897
Std. Dev. 877
Coef. of Variation 0.462
Stocks-to-Total Use Ratio
Mean (ratio) 0.24
Std. Dev. 0.11
Coef. of Variation 0.468Season Average Price
Mean ($/bu., lb.) 2.34
Std. Dev. 0.31
Coef. of Variation 0.133
Net Retur ns (value of pr odu ction
minus va riable expen ses)
Mean ($ rnil.) 7,825
Std. Dev. 1,461
Coef. of Variation 0.187
82.3
7.7
0.094
10,238
1,526
0.149
10,211
633
0.062
1,271
684
0.538
0.12
0.06
0.508
2.65
0.64
0.242
11,422
3,427
0.300
71.5 69.6
3.8 6.2
0.053 0.089
2,220 2,484
238 271
0.107 0.109
2,220 2,543
134 203
0.060 0.080
735 683
276 192
0.375 0.281
0.36 0.28
0.13 0.09
0.353 0.338
3.35 3.55
0.49 0.71
0.146 0.200
3,533 3,708
648 1,620
0.183 0.437
60,3
1.4
0,023
2,037
188
0.092
2,077
171
0.082
265
72
0.270
0.13
0.03
0.231
6.06
0.75
0.124
7,412
1,130
0.152
68.0
6.2
0.091
2,692
331
0.123
2,681
204
0.076
310
147
0.473
0.11
0.05
0.437
6.43
1.00
0.156
10,182
1,619
0.159
12.7
1.0
0.080
15
1.7
0.107
16
1.1
0.068
4
1.2
0.316
0.26
0.10
0.375
0.64
0.06
0.101
1,317
551
0.418
13.7
1.0
0.075
18
2.4
0.129
18.5
1.2
0.065
4.6
1.3
0.282
0.25
0.07
0.288
0.69
0.07
0.102
1,467
380
0.259
‘ For the 1986–96 historical period, the mean is the historical mean; the standard deviation is the deviation of residualsfrom detrended historical data; and the coefficient of variation is calculated using that deviation from trend and thehistorical mean.bFor the 1997–2006 simulation period, the mean is the simulation mean; the standard deviation is the deviation of
residuals from detrended simulation data; and the coefficient of variation is calculated using that deviation from trend
and the overall simulation mean.
c For prices and returns, 1986 was removed from the historical period to avoid an extreme price impact resulting from
the first year of the cotton marketing loan program in 1986.
The coefficien t of var ia ion for corn produc-
1
t ion actua lly declines fr m its respect ive his-
tor ical measure by 13%. Some port ion of th is
apparent decline in var”ability for corn may
stem from a significan t y higher mean level
of product ion repor t e for the projected
years. If the standard d viat ions are used to
compare var iability, th n table 1 shows a
higher standard devia t ion (and thus higher
nominal var iability) for project ed corn pro-
du ct ion du rin g t he 1997–2006 simu lat ion pe-
r iod compared to the histor ical devia t ion .
Va riabilit y in wh ea t pr odu ct ion r ises by n ear -
ly 2% from the histor ical per iod, while var i-
ability in soybean product ion r ises by more
t ha n 33~0. Cot ton var iabilit y is sligh tly m ore
Figure 2. H ist ogr am s of sim ula tion per iod pr ice coefficien ts of va ria tion
2.4 Comparing the historical period to the sim-
ulation period, figure 2 shows that corn price
experiences the most dramatic increase in vari-
ability during 1997–2006. The probability of
achieving a level of variability greater than the
historical level (mean historical coefficient of
variation of O.133) is greater than 95%. Sim-ulation period corn prices were less variable
than historical period prices in fewer than five
of the 100 iterations. Soybean prices were
more variable in the simulation period in more
than 76% of the iterations, and wheat prices
were more variable in more than 86% of the
iterations. Average cotton price variability
during the simulation period was approxi-
4 Note that the coefficients of variation presented
in figure 2 are calculated as the percentage of the re-
siduals from trend to the period expected value, an
analogous calculation to the coefficients of variation
presented in table 1. The annual coefficients of varia-tion presented in table 3, however, are the sample stan-dard deviation as a percentage of the mean,
mately equal to variability during the histori-
cal period.
A statistical test was performed to test the
hypothesis that the mean of the simulation co-
efficient of variation for price is greater than
or equal to the coefficient of variation of ac-
tual prices experienced from 1986–96. The
simulation mean coefficient of variation for
corn price (0.242) was significantly different
from the coefficient of variation for corn price
over 1986–96 (O. 133) (figure 2) at the 0.01
significance level (t = 18.8). The simulation
mean coefficients of variation for wheat price
(0.20) and soybean price (O. 156) were also
significantly different from the historical co-
efficients of variation (O. 146 and 0.124, re-spectively) at the 0.01 significance level (t =