Monke, James D.

Onal, Hayri

English

Research Papers in Economics

Journal of Agricultural and Applied Economics, 28,1(July 1996):211-213
@ 1996 Southern Agricultural Economics Association
Incorporating the 1990 Farm Bill into
Farm-Level Decision Models: An
Application to Cotton Farms: Comment
Hayri Onal and James D. Monke
The 1990 Farm Bill introduced planting flexibility
options while at the same time imposing slightly
different program participation provisions from
those of the previous farm bill. An article published
by Duffy, Cain, and Young (1993) in this journal
presents a methodology to model farm-level deci-
sion making and program participation. Their
model does not truly represent the set-aside and
flex requirements when compared to actual pro-
gram provisions. This comment addresses those
shortcomings and proposes appropriate modifica-
tions to the model,
The 1990 Farm Bill provisions related to par-
ticipation requirements introduced two important
changes with respect to the 1985 Farm Bill: (a) set-
aside land (ARP) for each program crop is propor-
tionately related to the established program crop
base rather than to the participating acreage, and
(b) a portion of the crop base (designated normal
flex acres) can be planted to any crop without re-
ceiving deficiency payments and without altering
the crop base in the subsequent year. Similarly, an-
other fixed percentage of the crop base, called op-
tional flex acres, can also be flexed and planted to
any crop, but will earn deficiency payments only if
planted to the original program crop.
The new program provisions are best illustrated
by a simple example. Suppose a farmer has estab-
lished a crop base of 100 acres and participates in
the program for that crop. The farmer has to set
The authors are assistant professor, Department of Agri-
cultural Economics, University of Illinois at Urbana–
Champaign, and adjunct assistant professor, Department of
Economics and Finance, University of Wyoming.
aside 10 acres and may flex 15 acres when the ARP
and normal flex ratios are 10 and 15%, respectively.
This leaves 90 acres that can be planted to the
program crop, of which 75 will earn deficiency
payments if the farmer decides to fully participate
on all of the crop base, As long as set-aside and
flex requirements are met (which are dependent on
base acreage), the farmer may choose to plant any
amount not exceeding 90 acres. For instance, the
farmer may choose to plant only 25 acres to the pro-
gram crop—all of which would receive deficiency
payments. Any other crop may be planted on the
remaining portion of the plantable base; however,
the farmer would be “considered” to have planted
only 60 acres when computing base acres in future
years (25 planted + 10 optional flex + 15 normal
flex + 10 ARP). The difference of 40 acres (100 –
60) represents the result of partial participation and
the farmer’s intention to voluntarily reduce program
benefits and future base allocations, In the cases of
full participation or no participation, the new and
old set-aside requirements are identical. In the case
of partial participation under the 1990 Farm Bill,
however, the amount of land to be idled is fixed and
larger than the amount required by the 1985 Farm
Bill provisions.
The Problem
Previous farm program participation rules required
complex modeling techniques when farm-level
resource allocation and government program par-
ticipation were modeled using mathematical pro-
gramming, The 1990 Farm Bill introduced further
modeling complexities, mainly because of the two
changes noted above, again requiring integer pro-212 Journal of Agricultural and Applied Economics, July 1996
gramming methods. The 1993 model developed by
Duffy, Cain, and Young was basically an extension
of the earlier model presented by Perry et al., except
that it included additional constraints to model flex
acreage provisions and base expansion limitations.
Those additional constraints will work properly if
the farmer either participates on the entire base or
does not participate at all. However, in the case of
partial participation (which will be justified later in
our comment), the model will result in a lesser
amount of land to be idled and flexed than the
amount actually required by the program pro-
visions.
To observe this, consider the equation associ-
ated with the ARP3 row in the matrix representa-
tion of the Duffy, Cain, and Young model (p. 122).
Using their notation, the equation states that
ACP3 = arp x AP3,
where ACP3 is the land to be idled, arp is the set-
aside requirement, and AP3 is the total program
acres including those planted, set aside, and fiexed.
The actual program provision must consider
BASE3 rather than the participating acres (AP3) as
specified in the model.
Replacing AP3 with BASE3, however, will not
correct the equation. If the farmer chooses not to
participate, set-aside land should be zero, whereas
the equation would imply that a portion of the base
would be set aside. Therefore, neither the above
equation nor one replacing AP3 with BASE3 will
correctly represent the actual participation require-
ment. A proper algebraic formulation must include
the binary participation variable Y3in a linear inte-
ger programming framework.
The equations given by (NFAT3) and (OFAT3)
also are not proper representations of normal and
optional flex acreage provisions because of the
same reasons. Both the normal flex and optional
flex acres must be related to the total crop base, not
the participating acreage.
The implications of these equations can be seen
by considering the example given above, When the
farmer chooses to partially participate on 60 acres
of the crop base, the 1990 Farm Bill provisions re-
quire 10 acres to be set aside. This leaves 50 acres
that can be planted to the program crop, of which
35 acres may receive deficiency payments (60 –
10 set-aside – 15 normal flex). According to the
formulation by Duffy, Cain, and Young, however,
the farmer has to set aside six acres, and can plant
up to 54 acres, of which 45 may receive deficiency
payments (60 – 6 set-aside – 9 normal flex). The
set-aside and flex equations therefore will not work
properly and need to be modified.
An Appropriate Formulation
A correct and linear formulation of the set-aside
provision is provided below:
(ARP3) M X (1 – Y3)+ ACP3 > arp X BASE3,
where Y3 equals 1 if the farmer enrolls in the pro-
gram and zero otherwise, and M is an arbitrarily
specified large number.
To see how the above equation works, consider
the case for Y3 = 0. When M is large enough, the
constraint is satisfied without necessitating positive
set-aside, ACP3 > 0. Since the set-aside variable
appears only in this equation and in the objective
function with a negative objective coefficient, the
model will always set this variable at its lower
bound. Therefore, ACP3 = O in the optimal solu-
tion, and there is no set-aside. Now consider the
case for Y3 = 1. The first term in the equation van-
ishes, and the lower bound (also the level) of ACP3
becomes the fixed portion of the base that must be
idled, as required.
A critical argument here is that the set-aside
variable ACP3 appears only in equation (ARP3)
and the objective function, and a negative objective
coefficient is assigned to it. This is not true for the
normal flex and optional flex variables, NFA3 and
0FA3, which are revenue items. Therefore, a differ-
ent approach must be used to model the flex activ-
ities.
We use an indirect relationship that ties the flex
variables to the set-aside variable, which in turn is
correctly related to the crop base variable through
the revised set-aside equation. The relationship for
normal flex is given below:
(NFAT3) NFA3 = njlex X (ACP3/arp),
where njlex is the normal flex parameter. If the
farmer does not participate in the government
program, the revised equation (ARP3) impliesOnal and Monke: Incorporating the 1990 Farm Bill into Farm-Level Decision Models: Comment 213
ACP3 = O, which in turn implies that NFA3 = O,
as required. Conversely, if the farmer decides to
participate, then Y3 = 1, and ACP3 = arp X
BASE3, as explained above. When this is substi-
tuted into revised equation (NFAT3), we obtain the
required result, i.e., NFA3 = njlex X BASE3.
Revised equation (NFAT3) creates a complexity
when arp = O,because the division involved in that
equation cannot be carried out. This difficulty can
be overcome, however, by specifying a very small
positive arp value instead of zero. This implies a
negligibly small positive set-aside variable that will
not have a significant effect on the optimum land
allocation, In the case of participation, we have
ACP3 = arp X BASE3. When this is substituted
into revised equation (NFAT3), the normal flex
variable NFA3 will again be correctly tied to
BASE3.
The revised model allows for positive set-aside
under nonparticipation, i.e., ACP3 >0, and Y3 =
O.Although no set-aside is required in this case, the
model may choose ACP3 > 0, so that a positive
NFA3 value might more than compensate for the
loss from positive set-aside. However, this will
never occur since the model has an alternative ac-
tivity, namely, nonparticipating crop acreage (AF3),
which yields the same return as flex (NFA3) with-
out incurring a positive cost due to set-aside. There-
fore, this anomaly is ruled out.
Another similar consideration is the allowance
for excessive set-aside when program participation
is chosen, particularly when the arp requirement is
zero. In this case, the model may choose an exces-
sive value of set-aside so that flex acres may be in-
creased beyond their permitted level through the
use of equation (NFAT3). This may occur because
our revised equation (ARP3) is defined as greater
than inequality, and the value of flex acres (beyond
that legally permitted) may compensate for the ad-
ditional cost of set-aside. By adding the following
constraint, the set-aside variable ACP3 is effec-
tively prohibited from exceeding its required level
when modeled in tandem with the revised inequal-
ity equation (ARP3):
(ARP3a) ACP3 s arp X BASE3.
Optional flex activities can be modeled in ex-
actly the same way by revising equation (OFAT3)
in a parallel fashion to (NFAT3).
One final revision to the Duffy, Cain, and Young
model is necessary to correctly compute eiigible
program acres, PAC3, now that set-aside and flex
acres have been redefined. Equation (PLIM3)
should be rewritten as follows:
(PLIM3) AP3 – ACP3 – NFA3 – 0FA3 2 PAC3.
The above inequality permits partial program par-
ticipation when optimal, but limits program acres
to those permitted by governmental provisions.
The Case for Partial Participation
Duffy, Cain, and Young may not have found partial
program participation to be a viable outcome be-
cause strict profit maximization in a linear program
would imply either full or zero participation. Be-
cause their model indicated full participation to be
optimal, their results were not affected by the im-
proper model specifications explained above. How-
ever, partial participation may be optimal in some
cases, such as nonlinear formulations involving risk
in farm-level decision making behavior. If the ob-
jective function includes penalties for risky behav-
ior because of risk aversion (Monke), partial pro-
gram participation may be an optimal solution for
resource allocation. Highly risk-averse producers
may select a crop rotation which does not utilize
the entire allocation of base acres, but instead ex-
changes program benefits for the risk reduction
offered by crop diversification. In this case, crop
diversification may be the final risk-management
objective or the means to reduce base acreage in
future years by participating in the government pro-
gram with less than full use of their base acreage.
References
Duffy, P. A., D. L. Cain, and G. J. Young. “Incorporating
the 1990 Farm Bill into Farm-Level Decision Mod-
els: An Application to Cotton Farms.” 1 Agc and
Appl. .Eccwr. 25(December 1993): 119–33.
Monke, J. D. “Farmer Participation in Government Com-
modity Programs: A Multiyear Risk-Management
Analysis.” Unpublished Ph.D. dissertation, Univer-
sity of Illinois, August 1995.
Perry, G. M., B. A. McCarl, M. E. Rister, and J. W. Rich-
ardson. “Modeling Government Program Participa-
tion Decisions at the Farm Level.” Amez J. Agz Econ.
7l(November 1989): 1011-20.

INCORPORATING THE 1990 FARM BILL INTO FARM-LEVEL DECISION MODELS: AN APPLICATION TO COTTON FARMS: COMMENT

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