Historic note
 Front Cover
 Title Page
 Table of Contents
 List of Tables
 Center information

Group Title: Technical report / Florida Agricultural Market Research Center ; 81-1
Title: The market for winter tomatoes
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00049262/00001
 Material Information
Title: The market for winter tomatoes a rational expectations interpretation
Series Title: Technical report Florida Agricultural Market Research Center
Physical Description: ii, 22 p. : ; 28 cm.
Language: English
Creator: Shonkwiler, J. S ( John Scott )
Emerson, Robert D
Florida Agricultural Market Research Center
Publisher: Food and Resource Economics Dept., Agricultural Experiment Stations, Institute of Food and Agricultural Sciences, University of Florida
Place of Publication: Gainesville
Publication Date: [1981]
Subject: Tomatoes -- Marketing -- Florida   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
non-fiction   ( marcgt )
Bibliography: Includes bibliographical references (p. 20-22).
Statement of Responsibility: by J. Scott Shonkwiler, Robert D. Emerson.
General Note: "October 1981"--Cover.
Funding: Technical report (Florida Agricultural Market Research Center) ;
 Record Information
Bibliographic ID: UF00049262
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: aleph - 001752610
oclc - 26812835
notis - AJG5565

Table of Contents
    Historic note
        Historic note
    Front Cover
        Front cover
    Title Page
        Title page
    Table of Contents
        Page i
    List of Tables
        Page ii
    Center information
        Page iii
        Page 1
        Page 2
        Page 3
        Page 4
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        Page 6
        Page 7
        Page 8
        Page 9
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        Page 15
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        Page 22
Full Text


The publications in this collection do
not reflect current scientific knowledge
or recommendations. These texts
represent the historic publishing
record of the Institute for Food and
Agricultural Sciences and should be
used only to trace the historic work of
the Institute and its staff. Current IFAS
research may be found on the
Electronic Data Information Source

site maintained by the Florida
Cooperative Extension Service.

Copyright 2005, Board of Trustees, University
of Florida

The Maret for
A RAt v, ona

Wit." er Fmotoes
txpectati os

-ntert .e.oreta o s

The Market for Winter Tomatoes:
A Rational Expectations Interpretation

J. Scott Shonkwiler
Robert D. Emerson

J. Scott Shonkwiler is an Assistant Professor and Robert D. Emerson
1s an Associate Professor, Food and Resource Economics Department,
University of Florida, Gainesville, Florida 32611



List of Tables ........................... ...........1ii

Model Specification ..................................3

Modeling Expectations ................................ 5

Estimation Results .... ............................. 8

Model Implications .................................11

Conclusions ............................. ........... 13

Footnotes ...........................................18

References ..........................................20



Table 1. Maximum Likelihood Estimates .............. 15

Table 2. Derived Reduced Form Results .............. 16

Table 3. Impact, Interim and Long-run
Acreage Elasticities ..................... 17

The Florida Agricultural Market Research Center

A Service of
the Food and Resource Economics Department
of the
Institute of Food and Agricultural Sciences

The purpose of this Center is to provide timely, applied research

on current and emerging marketing problems affecting Florida's agri-

cultural and marine industries. The Center seeks to provide research

and information to production, marketing, and processing firms, groups

and organizations concerned with improving and expanding markets for

Florida agricultural and marine products.

The Center is staffed by a basic group of economists trained in

agriculture and marketing. In addition, cooperating personnel from

other IFAS units provide a wide range of expertise which can be applied

as determined by the requirements of individual projects.

The Market for Winter Tomatoes:
A Rational Expectations Interpretation

Florida produces about 90 percent of domestic fresh tomato supplies

during the November to mid-June season. Since the Cuban trade embargo

of February 1962, Mexico has become the major foreign supplier of fresh

winter tomatoes. The fresh winter tomat- market in the U.S. has been

almost equally shared by Florida and Mexico in recent years. The

rivalry for this tirket reached the point in 1979 that Florida growers

charged that Mexican producers were dumping their product on the U.S.

market. Many Florida growers suggest that unless Mexican tomato imports

are limited the Florida tomato industry will effectively disappear. /

Primary attention in this paper is focused on domestic tomato

acreage allocations in light of the increasing Mexican influence on the

winter tomato market. The paper does not attempt to evaluate the

welfare effects of Mexican imports on the Florida tomato industry. In

addition to the emphasis on acreage response, the domestic quantity and

price effects are also considered.

Most efforts to explain acreage devoted to agricultural crops

utilize some variant of a cobweb model since the ultimate price of the

crop cannot be ascertained until the completion of the production

cycle. Nevertheless, if our supply and demand framework is truly

representative of the way the market works, an alternative to lagged

price for representing the anticipated price for the crop is the price-

prediction of the supply and demand model itself. Thus, acreage would

be argued to be dependent on the expected price of the crop; and

expected price would be quite simply the solution of the supply and

demand model for price on the basis of information available at planting

time. The underlying hypothesis is that producers are acting in

accordance with the information available to them at planting time and

in a way represented by the interaction in the supply and demand

model. Viewed in this way, planted acreage decisions would be based on

such factors as anticipated Mexican imports and their attendant effect

on the price of tomatoes. One distinction between this and the

traditional cobweb framework is that in the latter case lagged imports

may influence planted acreage via their effect on lagged prices, but any

impact expected imports might have on current price is ignored in the

acreage relationship. Additionally, by utilizing the expected price to

explain acreage, all information in the supply and demand model

including expected imports is brought to bear to assist in explaining

acreage. This concept is referred to in the economics literature as the

rational expectations hypothesis as introduced by Muth-1/

An economic model of the winter tomato market incorporating the

rational expectations hypothesis is specified in the following

section. This is followed by a discussion of alternative price

expectation hypotheses. The parameters of the supply and demand model

are then estimated for the rational expectations and the cobweb

models. The final section of the paper presents an evaluation of the

results and assesses their implications.

Model Specification

We specify a supply and demand model for Florida tomatoes since

Florida produces nearly all of the domestic winter fresh tomatoes. The

demand equation is an aggregate U.S. demand function. The supply side

is decomposed into an acreage equation and a yield equation. The

rationale for the latter is that the decision to plant must be made

considerably before the market time. Nevertheless, a number of factors

can alter the yield once acreage is devoted to tomatoes.

The structural model is specifi-d Ly the following four equation

system with all variables in logarithms:

(1) At = + aa t + a2Ct + a3Rt + a At-+ It

(2) Yt 0 + Pt Lt + 2Wt + + 2t

(3) = Y + YiPt Y1Dt + Y2Mt + Y31t + 3t

(4) Qt = At + Yt


At = acreage of tomatoes planted;

Pt = expected price per carton of tomatoes;

Ct = expected cost of a carton of tomatoes;

Rt = prime interest rate prevailing during the time planting

decisions are made (July through January);

Yt = yield of 30 pound cartons per planted acre;

Pt = season average price per carton of tomatoes;

Lt = hourly wage of piece-rate farm workers in Florida


Wt = weather index constructed from the detrended yields of

cucumbers and green peppers two vegetable crops grown in

many of the same areas as tomatoes during the winter season;

Xt = adoption of plastic mulch: 0 prior to 1973 season; 1


Qt = quantity of tomatoes shipped;

Dt = U.S. personal consumption expenditures price deflator (October

through June);

Mt = quantity of Mexican tomatoes imported (October through June);

It = U.S. total real disposable income (October through June).

Since product prices and production costs are uncertain at the time

the acreage decision is made, we argue that decisions are made on

expected price and expected cost. The specification of expectations is

treated in the following section. Much of the land used to grow

tomatoes is rented. Consequently, the tomato grower may be less

interested in the production of other crops than in the opportunity cost

of funds used on purchased inputs, as reflected by the prime rate

(Rt). Finally, the producer may not be able to fully adjust acreage to

an optimum level due to mistakes or increased costs, thus he can only

make a partial adjustment as reflected by the inclusion of At-I.2/

Tomato yields (Y ) are strongly influenced by the number of times

the crop is harvested. Because tomatoes do not mature uniformly, fields

of staked tomatoes may be picked five times and ground plants may be

picked twice depending on crop and market conditions (Zepp and

Simmons). The harvesting decision is argued to depend on current

product price (the price is known at harvest time in contest to the

acreage question) and the wage rate. Furthermore, the specification

assumes that it is the ratio of price to wage rate that is important.

They thus have the same coefficient except for sign. Tomato yields are

also highly affected by cold weather which can either destroy the plant

or inhibit the fruit from setting. The introduction of full-bed plastic

mulch during the 1970s represented aun laporLant change in technology as

reflected through an increase in yields.

The demand for tomatoes (Qt) is specified at the wholesale level

including the usual economic variables, deflated price and deflated

disposable income. In addition, Mexican imports are included as a

demand shifter for Florida tomatoes-./ The final equation (4) closes

the system with the identity that quantity demanded is equal to yield

per acre times the number of acres planted.

Modeling Expectations

Two expectational variables are utilized in our supply response

model, both of which occur in the acreage equation. These are expected

price and expected cost of production, neither of which can be known at

the time the crop is planted. Typically ad hoc extrapolative models for

expectation variables of the form

(5) Zt ti
i t-i.

are used. The number of lags and the types of restrictions to put on

the A1 are usually subjectively determined. Moreover, such procedures

ignore the information specified in the structural model for how prices

are determined in the market. Nerlove has recently argued that supply

response models have not become more "econometrically relevant" since

his work of over two decades ago. Shonkwiler similarly comments that:

A fundamental difficulty with such expectation formation

models concerns their arbitrariness and lack of theoretical

basis. These models are not necessarily accurate

representations of economic behavior implied by the underlying

economic structure.

The rational expectations model presented in this paper is offered as an

alternative to the traditional agricultural supply response approaches.

Despite Muth's original casting of the rational expectations model

in terms of market supply and demand relations, empirical applications

of the rational expectations hypothesis (REH) have almost exclusively

appeared in the macroeconomics province (vid. Shiller's review). In the

agricultural sector where fixed biological lags separate the production

decision and consequent output, supply response models have typically

employed extrapolative mechanisms to represent expected prices or

returns (c.f. Askari and Cummings, Nerlove). By contrast, the REH

maintains that participants in the market act as if they were solving

the supply and demand system in forming their price expectations. Thus,

the rational expectations model and models incorporating extrapolative

types of expectations are two competing frameworks for explaining

acreage variations.

There are several reasons to expect that Florida tomato growers

form rational expectations. Note first that production is found in a

small geographic area which implies that producers face similar economic

and climatic environments. The highly commercial and concentrated

nature of the Florida tomato industry may produce a situation more

conducive to the use of rational expectations by producers (DeCanio).

Finally, the intense competition with Mexican imports and the

information collection and dissemination service of the Florida Tomato

Committee suggest that growers take important supply and demand forces

into account when making production decisions.

In its most general form, the rational expectations interpretation

of expected price, Pt is the mathematical expectation of Pt given all

information available when the expectation is formed. In a structural

economic model this information consists of the predetermined variables

and the model's reduced form parameters (Wallis). Specifically, the

econometric model presented in equations (1)-(4) yields the following

reduced form equation for the price variable4 /

(6) aP + BPt + YPt a a2C 3Rt At-+ 0 Lt

-2 Wt 3Xt + YO Dt+ Y2Mt + Y3 t

Taking the expectation of the above equation, the expected price, Pt, is

given by

S- 1* *
(7) P t ( + 1 Y-1) (- a2Ct 33Rt 4 At-1 0 1 t

-W X + Y YD + YM + YI
-82 t t 0 1 t 2Mt 3 t

where asterisks on the right-hand-side of (7) denote the expectations of

the current exogenous variables.

The consequences of expression (7) are immediate since it

explicitly shows that expected price depends not only upon expected

levels of imports but also upon the other predetermined variables or

forecasted exogenous variables in the system. And, this dependence is

given exactly as a function of the structural model's parameters.

The values of the exogenous variables are forecasted by the

following relations:

(8) Zit = 6io + 611 it-I + it

since there is no other structural information concerning their

generation (Wallis). The exception to (8) occurs for the weather index

which is created with zero mean. Because this variable is not expected

to have any systematic component, we assume that its forecasted value is

identical to its mean value.

The alternative cobweb model is specified by substituting Pt-1 for

P in the acreage equation (1). The model is dynamic since lagged

acreage is included as an explanatory variable. This particular form

for acreage response models has been found to explain tomato acreage

fairly well (Morris).

Estimation Results

The data used are the nineteen winter seasons from 1961-62 through

1979-80.-! Under the REH the variables exogenous to the system, Ct, L ,
A it t
Dt, Mt and It, were predicted using (8) and had squared correlations

with their actual values of .80, .98, .998, .86, and .994

respectively. Substituting these predicted series in (7) gives an

expression for P which is linear in the variables but non-linear in

terms of the structural parameters. Estimation of the four equation

system (1)-(4) is accomplished by replacing Pt in (1) with expression

(7). The resulting acreage equation under the REH is then:

(9) At 0 + a R Y- aA

80 + t 8 t + Y t 2 t + t
+ 2Ct + 3R + 4 At-1 It

Under the alternative of a dynamic cobweb model the acreage equation

appears as

(10) At = a0 + t- + a2Ct + a3Rt + a At-1 + t

Under the REH the system is highly non-linear in the parameters in

addition to having parameter restrictions across equations. Although

limited information methods such as two stage least squares could be

utilized to estimate the parameters equation by equation, the occurrence

of cross-equation parameter restrictions make this much less attractive

than usual. A particularly appropriate method for this simultaneous

equations model is full information maximum likelihood (although still

conditional on the forecasts of C L D M and It)-/ The

disturbances pit' 2t' p3t as well as ult', 2t' 3t are assumed to

follow joint normal distributions.

The maximum likelihood parameter estimates for both expectations

models are presented in Table 1. Note that the parameters may also be

interpreted as elasticities since all variables are in logarithmic

form. It is apparent that the REH "fits" the data better than the

cobweb hypothesis since its calculated likelihood is greater. In fact

using a test suggested by Revankar, the variable Pt-_ was included in

the REH acreage model and the full system was reestimated. The

rationale for inclusion of Pt-, was that the REH model was now nested

within a model with an extrapolative component. The likelihood ratio

test of the restricted rational expectations model versus the more

general expectations model yielded a calculated chi-square value of

.0134 with one degree of freedom. The critical value for rejecting the

rational expectations model at the .05 level would require a chi-square

value greater than 3.84.

The REH and the cobweb model parameter estimates, however, show

many close similarities. The results for the acreage equation appear

reasonable in terms of the coefficients' signs and magnitudes. The

rational expectations variable Pt-_ enters the equation quite

significantly and with a magnitude twice that of the naive

expectation. As expected, the opportunity costs associated with the

rate of interest and the expected production costs have a negative

effect on the acreage planted.

The yield equation illustrates the sensitivity of supply to current

prices and labor costs. While the price elasticity of yield may appear

unduly large, recall that this is essentially a structural supply

equation. Thus, a sharp increase in yields acts to depress price

through the resulting increase in supply.7/

The demand equation shows an own price elasticity of about -.8 for

Florida tomatoes which appears reasonable in terms of other studies

(Nuckton). The effect of Mexican imports on the demand for Florida

tomatoes is extremely significant and the -.8 parameter suggests they are

very close substitutes. The high income elasticity of demand is not

surprising given that fresh winter tomatoes may be considered somewhat

of a luxury item.

Model Implications

The structural models were solved for their reduced forms so that

each endogenous variable could be expressed as a function of only the

predetermined variables. The calculated reduced form parameters are

presented in Table 2 along with their associated validation measures.

Again, recall that all coefficients may also be interpreted as


As discussed above, the REH variable, P may be expressed as a

linear combination of all predetermined and forecasted exogenous

variables (except Wt). Since Pt is consistent with the reduced form

forecast of Pt from the original model, their reduced forms should be

related. This relationship is immediate if we assume that each

forecasted exogenous variable is an unbiased estimate. Then, for

example, we see that the coefficient on M in the expectations equation

equals the sum of the coefficients on Mt and Mt in the price equation.

The reduced form results in Table 2 underscore the importance of

imports on expected prices and quantities in the Florida tomato

industry. With regard to Florida tomato prices and quantities sold, a

10 percent increase in observed imports reduced price by 2.68% (1.66%)

and quantity by 5.91% (6.53%) under the REH (dynamic cobweb). In other

words, a 10 percent increase in Mexican tomato imports, ceteris paribus,

has the effect of reducing total Florida tomato revenues by 8.59%

(8.19%). This relationship highlights the competitive nature of the

winter tomato market.

The reduced form thus suggests that the dominant effect of Mexican

tomato imports is on the reduction of domestic supply, not domestic

price. As Mexican imports increase, not only does this reduce domestic

supply, but correctly anticipated increases in imports (or lagged

imports under the cobweb model) reduce domestic acreage. This strongly

suggests that Mexican imports have had a significant influence on the

contraction of the Florida industry in terms of acres planted.

Moreover, the reduced form equation for acreage is the one equation that

reveals a difference in predictive ability between the REH and the

cobweb models. The R2 is somewhat over twice as high as for the REH and

the mean absolute error is about one-third less with the REH model as

compared to the cobweb. Thus, although the REH does not offer

significant improvements in predicting price or quantity over the

simpler cobweb, the predictive ability for acreage is greatly improved

with the additional information brought to bear through the rational

expectations interpretation.

The long runeffects of Mexican imports on Florida tomato acreage

are illustrated with a dynamic analysis of the reduced forms. (Table 3).

The long run response of acreage to imports is nearly four times as

great under the REH model as compared to the cobweb model (-.447 vs.

-.123). The results thus suggest considerably more acreage adjustment

to anticipated imports, for example, than would be reflected by the

simpler cobweb model. Moreover, the REH estimates suggest that 42

percent of the acreage adjustment due to changes in anticipated imports

occurs in the current time period. By contrast the cobweb model cannot

reflect any adjustment in the current period.


The primary focus of this paper is interpreting the effect of

Mexican tomato imports on the highly structured and centralized Florida

winter tomato market. The unique feature of the approach taken in this

paper is the specification of a rational. expectations framework on the

producers' expected price in the acreage decision. Previous efforts at

estimating acreage and supply equations have typically assumed ad hoc

price expectation specifications in order to compensate for the

production time lag in the acreage decision equation. The most common

of these is the cobweb model. By contrast, the rational expectations

specification allows for the possibility that producers utilize all

information available to them at the time planting decisions are made.

They subsequently adjust their plantings on the basis of this

information and in accordance with its implications as reflected through

the supply and demand model.

We find that the rational expectations specification is consistent

with the data for the winter tomato market. Moreover, the results

suggest superior performance in interpreting acreage decisions than for

the more typical cobweb model. As might be anticipated, the differences

in yield and price predictions are not greatly different in the two

cases. The reason is simply that the essential difference in the two

approaches is in the specification of the acreage equation. There is

very little difference between the two models in either the composition

or the coefficients of the reduced form equations other than acreage.

The significance of the rational expectations statement is that

producers can and do adjust not only to historic price information, but

more importantly to current information not necessarily reflected in

past prices. If anticipated imports are higher than previously,

domestic producers adjust in part by reducing plantings. As trade

restrictions on tomatoes are reevaluated with Mexico, it is significant

to note that the results of this paper suggest that Florida producers

quickly and correctly adjust to the anticipated level of Mexican

imports. Moreover, the impact is primarily on quantities rather than

prices, and furthermore, a significant part of the quantity impact is

attributed to acreage rather than the complete impact being absorbed by

economic abandonment and the ensuing waste of resources once the crop

has been planted.

Table 1. Maximum Likelihood Estimates

Equation Parameters Variable REH Model Cobweb Model



































































aEstimated asymptotic standard errors are in parentheses.

bThis is Pt-I under the cobweb model.

Table 2. Derived Reduced Form Results

Dependrat Predetermined Variables
Variables Model Intercept PV C 1 A -1 L1 U I DL Mt 1 1 R2a tAIb

t RER -.549 -.560 -.361
Cobweb 2.116 .460 -.484 -.256

Yt R -3.89 .413 .266 -.427 -.580 .055
Cobweb -7.05 -.380 .400 .211 -.449 -.691 .056

t RE -4.44 -.147 -.095
Cobweb -4.93 .081 -.085 -.045

.152 -.580 .055
.095 -.691 .056

P RH -2.03 .187 .121 -.193 .737 -.070
Cobweb -1.78 -.096 .101 .054 -.114 .825 -.067


.184 -.188 .489 .518 .624 1.862
.268 2.88Z

.093 .580 -.591 1.54 -.136 .138 -.361 -.382
-.003 .691 -.653 1.74

.043 .580 -.591 1.54 .048 -.050 .128 .136
-.003 .691 -.653 1.74

-.055 .263 -.268 .697 -.062 .063 -.163 -.173
.003 .175 -.166 .442

.897 4.362
.924 3.532

.839 1.10Z
.834 1.102

.906 6.26Z
.924 6.08Z

REX -2.03

.187 .121 -.193


.201 -.205 .534 .564

aSquared correlation between predicted reduced form and actual values.
"Mean absolute percentage error of predicted series.

Table 3. Impact, Interim and Long-run Acreage Elasticities

Period REH Cobweb

s %AAt/%AM* %AAt/%AMt__s

Impact Interim Impact Interim

0 -.188 -.188 -.0671 -.0671

1 -.109 -.297 -.0300 -.9071

2 -.063 -.360 -.0139 -.111

3 -.036 -.396 -.0064 -.1174

4 -.021 -.417 -.0030 -.1204

0 -.447 0 -.1230



1/ Nelson has mentioned that "'rational' has deteriorated in current

usage to little more than a synonym for 'unbiased' or 'optimal

extrapolative'," (p. 331). Our usage conforms with Muth's

definition that rational expectations "are essentially the same as

predictions of the relevant theory," (p. 316).

2/ Kennan has shown that when a decision-maker is faced with a

quadratic loss function containing both a disequilibrium cost and an

adjustment cost the partial adjustment model can serve as a

description of optimal behavior.

3/ One can logically argue that the demand equation should be specified

as the demand for domestic and imported tomatoes. However, this

introduces additional severe non-linearities into the system as well

as the requirement for data to explain the level of exports from

Mexico. This is beyond the scope of this paper and is left for

future work.

4/ The disturbance terms have been deleted here since they will

disappear upon taking expectations.

5/ Data on P and A were from Florida Vegetable Summary, C was from

Costs and Returns from Vegetable Crops in Florida, R, D, and I were

from Department of Commerce, L was from Walker and Florida Farm

Labor, Q was from Annual Report of the Florida Tomato Committee, and

M was from Preview of Mexico's Vegetable Production for Export.

6/ See, for example, Intriligator, p. 412.

7/ In fact, if the underlying harvesting production function is assumed

to be of the form

Y = aH

where H represents the labor input, thb elasticities from the

estimated supply equation

Y p2.208 L-2.208

imply that the elasticity of production for the labor input be 8 =



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