The paper outlines an approach to estimation of rational expectations acreage response model for US soybeans that explicitly takes into account government payments. Numerical methods are used to recompute the model equilibrium at each iteration of the log-likelihood optimization routine. Estimation results allow one to measure market distortion introduced by the government support programs.Production Economics,

Vedenov, Dmitry V.

English

Research Papers in Economics

“Irrational” Planting Behavior as Rational Expectations of  
Government Support 
 
 
 
 
 
Dmitry V. Vedenov 
Dept. of Ag. and Applied Economics 
University of Georgia 
315C Conner Hall, Athens, GA 30602 
e-mail: dvedenov@agecon.uga.edu 
 
 
 
 
 
Selected Paper prepared for presentation at the Southern Agricultural Economics Association 
Annual Meeting, Mobile, Alabama, February 1-5, 2003  
 
Research in progress. Do not quote without author’s permission. 
 
 
© Copyright 2002 by Dmitry Vedenov. All rights reserved. Readers may make verbatim copies of 
this document for non-commercial purposes by any means, provided that this copyright notice 
appears on all such copies. Abstract 
The paper outlines an approach to estimation of rational expectations acreage response model for 
US soybeans that explicitly takes into account government payments. Numerical methods are 
used to recompute the model equilibrium at each iteration of the log-likelihood optimization rou-
tine. Estimation results allow one to measure market distortion introduced by the government 
support programs. 
Introduction 
Government farm support programs have been available to producers since late 1930s. However, 
major changes in the program introduced by the Federal Crop Insurance Act of 1980 and subse-
quent Acts of Congress significantly expanded the scope of the program. Introduction of new in-
surance products in mid-1990s and increasing government subsidies led to dramatic increase in 
program participation. In 2001, over 200 million acres were enrolled in the program, compared 
with only 26 million in 1980. Since 1980 total liability has increased almost ten-fold to $36.7 bil-
lion in 2001 (FCIC Summary of Business Report, 2001). 
While government crop insurance programs provide a vital support to nation’s producers, it also 
introduces  market distortion. Planting decisions made by crop producers incorporate expecta-
tions of government payments and result in behavior which may seem “irrational”. For example, 
while harvest prices of  soybeans (as reported by NASS) steadily declined between 1995 and 
2001 at an average rate of 3.7% a year, the acreage planted just as steadily moved in the opposite 
direction at an average rate of 2.7% a year.  While counterintuitive at the first glance, such plant-
ing behavior makes perfect sense if one takes into account that the harvest prices during the same period were below commodity loan rate, i.e. the latter effectively served as a price floor. There-
fore, government support payments need to be taken into account in modeling acreage supply. 
Various approaches to analysis of acreage supply have been presented in the literature (Gardner; 
Morzuch, Weaver, and Helmberger; Askari and Cummings; Chavas, Pope, and Kao; McIntosh 
and Shideed; Shideed and White; Parrott and McIntosh)  While different models consider differ-
ent factors influencing producers’ decisions, the one common variable present in all models is 
the expected future price of the commodity. The latter is not observed at the decision time and 
thus has to be somehow deduced based on current information.  
Several proxies have been developed for the expected output price including  “naïve expecta-
tions” or lagged cash price (e.g. Shumway and Chang), various forecasts based on historical cash 
prices (e.g. McIntosh and Shideed), futures prices (e.g. Morzuch, Weaver, and Helberger), com-
binations of futures and cash prices (Chavas, Pope, and Kao), and so on. While each of the ap-
proaches above has its merits, they all share the same disadvantage that the price model is disso-
ciated from the decision model in the sense that expected future price is an exogenous variable in 
the acreage supply equation. 
The rational expectations approach, on the other hand, provides a way to derive the expectations 
of model variables as conditional forecasts based on the model itself (Muth; Fair and Taylor). 
Thus a rational expectations model of acreage supply would reflect the fact that while the acre-
age decision is based on the present expectation of future commodity price, the realization of this 
future price is, in turn, affected by the planted acreage. In other words, the way the expectations 
of future prices are formed is determined by the structure of the acreage supply model. The effect 
of government support programs may then be analyzed by explicitly incorporating government 
payments into expected future prices. The practical applications of rational expectations models have been limited due to their compu-
tational complexity and lack of closed form solution. However, recent developments in computa-
tional techniques have made such applications a distinct possibility. Fair and Taylor suggested a 
numerical strategy for solution and estimation of nonlinear rational  expectations models. 
Miranda and Glauber attempted to implement this strategy  in order to estimate a commodity 
market model. Finally, Miranda has outlined an approach to numerical solution of rational ex-
pectations models using the collocation method. 
The present paper attempts to estimate a model of acreage supply set in the rational expectations 
framework. The model is similar to that of Miranda and Glauber, but puss less emphasis on the 
dynamics of government stockholding and instead explicitly accounts for government payments 
to producers. Numerical approach used to recompute model equilibrium at each step of likeli-
hood maximization routine incorporate recent advances in computational methods.  
The paper proceeds as follows. The next section presents the rational expectations model of acre-
age supply followed by outlines of estimation procedure and numerical solution approach. Then 
the data to be used for estimation are described. The paper will be updated as the estimation 
results become available. 
Rational Expectations Model of Acreage Supply 
Let  t Q be the available supply of a commodity at the beginning of year
1 t, let  t S  be the total 
stock (both government and private) at the end of the same year, and let  t C  be consumption in-
                                                 
1 Here we consider crop marketing years which for most commodities begin on September 1. cluding domestic demand, export, and seed utilization during the year. The material balance re-
quires that 
(1)          t t t S C Q + = . 
Assume that the overall consumption is governed by
2 
(2)               t t
C
t t u P X C + + = 2 1 a a , 
where  t P  is the average market price, 
C
t X  are exogenous variables to be specified later, and ut is 
a random shock. 
Under the no-arbitrage assumption, the stockholding is driven by the trade-off between the cur-
rent price, expected future price, and the cost of storage. Thus the current stock can be described 
by 
(3)        t t
t
E
S
t t v P
r
P
X S + ￿ ￿
ł
￿
￿ ￿
Ł
￿
-
+
+ =
) 1 (
2 1 b b , 
where  t P  again is the average market price,  t r  is a one-period discount factor,  1 + = t t
E P E P  is the 
expectation of the next period price conditional on current information, 
S
t X  are exogenous vari-
ables to be specified later, and vt is a random shock.  
Finally, assume that the decision of planted acreage is driven mainly by the price the producer 
expects to receive for commodity in the next year. The latter may differ from the market price if 
the farmer receives payments from government support programs. Due to a wide variety of such 
                                                 
2 An alternative way to specify equations (2) through (4) is to express all variables in logs. Both variant will be esti-
mated in the final version of the paper. programs that existed for different commodities in the past, it is impossible to incorporate them 
all in an estimable model. Therefore, I choose to concentrate on commodity loan programs be-
cause of its relatively simple structure and availability of relevant data. In addition historically 
this was the only form of government support for soybeans in the U.S. that resulted in direct 
payments to farmers. Thus the effect of the program on acreage decisions can be clearly identi-
fied. 
While commodity loan programs have changed over the years, the basic principle remained the 
same. Producers can receive loans from the government at a predefined rate per unit of produc-
tion by pledging future harvest as collateral. The loan has to be repaid unless the market prices at 
harvest are lower than the loan rate. In this case, depending on the specific program the produc-
ers can either forfeit the collateral or repay the loan at a lower rate. In either case, the net effect is 
that the loan rate effectively serves as a price floor because the actual price received by produc-
ers never drops below it. 
Formally, the effective price received by producers under a commodity loan program can be ex-
pressed as  } , max{ t t P P F = , where  t P  is the market price and  P  is the loan rate. It is this effec-
tive price that ultimately drives the acreage planting decisions made by the farmers. Thus the 
acreage response equation can be written as 
(4)        t
t
E
A
t t w
r
F
X A +
+
+ =
1
2 1 g g , 
where  1 + = t t
E F E F  is the current expectation of the next period effective price,  t r  again is a one-
period discount factor, 
A
t X are appropriate exogenous variables, and wt is a random shock. 
The available supply at the beginning of the next period is then determined as (5)        1 1
~
+ + ￿ + = t t t t Y A S Q , 
where  1
~
+ t Y  is the random yield unknown at the planting time. 
Equations (2) through (4) define current market price P as well as the effective price F as func-
tions of available supply Q and the vector of exogenous variables X = {X
C, X
S, X
A}. The rational 
expectations principle then requires that 
(6)   
)}. , ~ ( , max{ ) , ( ) , (
), , ~ ( ) , ( ) , (
1 1 1 1
1 1 1 1
+ + + +
+ + + +
+ = =
+ = =
t t t t t t t t t t
E
t t t t t t t t t t
E
Y A S P P E Q F E Q F
Y A S P E Q P E Q P
X X X
X X X
 
Estimation Methodology 
The acreage supply model is estimated using the full-information maximum likelihood method. 
The estimable model consists of equations (2) through (4). The random variables  t t t w v u , ,  are 
assumed to be normally distributed with zero mean and stationary variance-covariance matrix W. 
The material balance equation (1) can be used to eliminate the commodity stock from equations 
(2)–(4) so that the likelihood of observations  } , , { t t t A P C  can be derived from the joint density of 
random shocks  } , , { t t t w v u . Following Fair and Taylor, the corresponding full information  log-
likelihood function can be written as 
(7)    ￿ ￿
= =
- W - + W - =
T
t
T
t
t t t J
T
L
1 1
1 ˆ ' ˆ
2
1
| | log | | log
2
e e , 
where  2 2 | | a b - = t J  is the determinant of Jacobian of the transformation 
} , , { } , , { t t t t t t A P C w v u ﬁ , and (8)     
￿ ￿
￿
￿
￿
￿
￿
￿
ł
￿
￿ ￿
￿
￿
￿
￿
￿
￿
Ł
￿
+
- -
￿ ￿
ł
￿
￿ ￿
Ł
￿
-
+
- - -
- -
=
t
E
t A
t t
t
t
E
t S
t t t
t
C
t t
t
r
F
X A
P
r
P
X C Q
P X C
1
) 1 (
ˆ
2 1
2 1
2 1
g g
b b
a a
e . 
The maximum likelihood estimates can be then obtained by maximizing (7) with respect to the 
parameter vector  } , , { i i i g b a = d and W.  
The standard optimization techniques could be used to optimize the log-likelihood function (7). 
However, the latter  includes the unknown expectations of future prices, which cannot be ex-
pressed in a closed form in terms of model parameters but instead have to recomputed at each 
perturbation of the optimization algorithm. 
Numerical Solution of Rational Expectations Model 
For any given value of the parameter vector  d, equations (1)–(6) represent a closed system of 
functional equations that  needs to  be solved for  the unknown functions  ) , ( X Q P P =  and 
) , ( X Q F F = . This can be done by using a numerical strategy called collocation method 
(Miranda). The strategy involves three steps. First, the unknown functions are replaced by linear 
combinations of known basis functions  } ,..., , { 2 1 n f f f  with unknown coefficients 
(9)       
￿
￿
=
=
=
=
n
j
j
F
j
n
j
j
P
j
s c s F
s c s P
1
1
), ( ) (
, ) ( ) (
f
f
 
where  } , { X Q s =  is the vector of state variables. Second, a finite number of points or collocation 
nodes  n s s s ,..., , 2 1   are selected. Finally, Gaussian quadrature method (Judd) is used to discretize 
the continuous yield distribution by replacing it with a set of discrete values of yields } ,..., , { 2 1 m y y y  and corresponding probability weights } ,..., , { 3 2 1 w w w . The unknown coefficients 
c
P and c
F are then fixed by requiring (9) to exactly satisfy equations (1)–(6) at the collocation 
nodes. 
For the practical purposes, the Chebychev polynomials (Judd) can be chosen as the basis func-
tions. The collocation nodes are selected so that to cover the historically observed range of state 
variables. The number of basis function and collocation nodes is determined by the dimensional-
ity of the problem and desired accuracy of approximation. The unknown coefficients then can be 
calculated by using a relatively simple iteration algorithm (Miranda). 
Data Description 
The presented acreage supply model is estimated using historical data for U.S. soybeans for 
1970–2001. The relevant data have been collected from NASS, Analytical Database of U.S. Ag-
riculture (APAC), Federal Reserve Bank, and U.S. Department of Labor.  
The prices used in all equations are measured as season average prices in $/bu adjusted for infla-
tion using Consumer Price Index (CPI). The one-period discount factor is measured as annual-
ized return on 6-month commercial papers. 
In the consumption equation (2), consumption is total disappearance in billions of bushels in-
cluding domestic demand, export, and seed utilization. The vector of exogenous variables in-
cludes constant term, domestic livestock-poultry population index measured in grain consuming 
animal equivalent units, and foreign exchange rate measured as broad index of U.S. exchange 
rates. 
In the stock equation (3), the stock variable is the total stockholding (government and private) in 
billions of bushels. The exogenous variables are constant term and annual time trend.  Finally, in the acreage supply equation (4), the planted acreage is total acreage under soybeans in 
the U.S. in millions of acres and the support price is the Commodity Credit Corporation an-
nounced loan rate inflation-adjusted by CPI. The vector of exogenous variables includes constant 
term, lagged acreage, and cost of production measured as the index of all prices paid for farm 
production also inflation-adjusted by CPI. 
Expected Results and Discussion 
At the writing time, all relevant data have been collected and the numerical algorithm for solving 
rational expectations model has been implemented. The estimation results will be available in the 
near future and will include elasticities of acreage supply with respect to loan rate and other rele-
vant factors.  
The model will also be estimated under a counterfactual assumption of no government payments 
in order to determine the degree of market distortion introduced by the support payments and 
subsidies. It is hypothesized that setting more realistic levels of loan rates may reduce the level 
of distortion introduced in the planting decisions, while at the same time providing adequate pro-
tection to farmers. The results of the paper will provide policymakers with an additional insight 
into the side effects of existing and proposed farm support programs. This, in turn, may help to 
improve the efficiency of the programs both in terms of benefits to the crop producers and tax-
payers cost. 
References 
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Gardner, B. “Futures Prices in Supply Analysis.” American Journal of Agricultural Economics 
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"IRRATIONAL" PLANTING BEHAVIOR AS RATIONAL EXPECTATIONS OF GOVERNMENT SUPPORT

"IRRATIONAL" PLANTING BEHAVIOR AS RATIONAL EXPECTATIONS OF GOVERNMENT SUPPORT

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