Group Title: econometric analysis of the Florida grapefruit industry
Title: An Econometric analysis of the Florida grapefruit industry
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Title: An Econometric analysis of the Florida grapefruit industry
Physical Description: 123 leaves : ill. ; 28 cm.
Language: English
Creator: Parker, Arthur Findlay, 1943-
Publication Date: 1973
Copyright Date: 1973
 Subjects
Subject: Grapefruit   ( lcsh )
Citrus fruit industry -- Florida   ( lcsh )
Food and Resource Economics thesis Ph. D
Dissertations, Academic -- Food and Resource Economics -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (Ph. D.)--University of Florida, 1973.
Bibliography: Includes bibliographical references (leaves 120-122).
Additional Physical Form: Also available on World Wide Web
General Note: Typescript.
General Note: Vita.
Statement of Responsibility: by Arthur Findlay Parker.
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Bibliographic ID: UF00097586
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000414737
oclc - 37847525
notis - ACG1922

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AN ECONOMIETRIC ANALYSIS OF
THE FLORIDA GRAPEFRUIT INDUSTRY





By



ARTHUR F. PARKER, JR.


A Dissertation Presented to the Graduate Council
of the University of Florida
in Partial F-ulfillment of the Requirements for the
Degree of Doctor of Philosophy



UNIVERSITY OF FLORIDA


1973




















II1 ||||11:1 11 1 l lill IIII1 liil il l1 11111











ACKN~OW~LEDGMENTS


The author wishes to express sincere appreciation to

his chairman, Dr. W. W\. MlcPherson, for his guidance through-

out his graduate program. Also, a debt of gratitude is

owed to Dr. Lester Mlyers for his invaluable assistance dur-

ing the course of the research for this study. The other

members of his committee, Dr. Max Langham and Dr. F. 0.

Goddard, are also due a special word of appreciation. The

author wishes to thank the various members of the Food and

Resource Economics Department faculty, andi especially Dr.

W. B. Lester, of the Florida Department of Citrus, for their

assistance.

The author is grateful to Mlrs. Jane Mioore for typing

the various drafts of the study and to Mlrs. Elizabeth Godey

for her typing of the final copy. Appreciation is also

extended to the Florida Department of Citrus for financing

the computer time.

Finally, the author thanks his wife, Sandy, for her

Patience and understanding during the years spent in graduate

study.













TABLE OF CONTENTS


Page

. . . . . ii


ACKNOWLEDGMENTS .....

LIST OF TABLES ...


LIST OF FIGURES .. ... .. .. .. .. .. viii

ABSTRACT .. .. ... .. .. .. . ... ix


CHAPTER


I INTRODUCTION ......


Objectives .. ....
Literature RevIiew .........
Organization of Presentation ....

II MODEL DEVELOPMENT

lo del I . . . .
Price of Grapefruit for Packing.
Price of Grapefruit for Processing..
Utilization or Pack.. ......
Storage . . .
FOB Demand
Supply to Buyers at FOB Level ...
Identities . . . . . .
Model II . . . . . .
Storage
FOB Demand . ... .
Supply to Buyers at FOB Level ...
Identities . . . . . .

III STATISTICAL CONSIDERATIONS ......

Statistical Mlodel... .....
Mo del I . . . . . .
Model II . . . . .
General Model . . . . . .
Identification ..... .....
Estimation Procedure ...... ..
Selection of Time Unit and Period..
Data . . . . .





TABLE OF CONTENTS (continued)


Page

CHAPTER

IV STATISTICAL RESULTS .. .. .. 49

Model I . . . . . . . . 49
On-Tree Price Equations ........ 49
Pack Equations .. .. .. . ... 51
Storage Equations .. ... . . 53
FOB Domand . .. ... .. .. .. 55
Model II . . . . . . . . 58
Storage Equations ...... .... 58
FOB Demand . ... .. .. .. .. 59

V ECONOMIC IMPLICATIONS .. .. .. .. 61

Elasticities 61
Implications from the Derived
Reduced Forms .. .... .. .. 67
Short-Term Forecasting .. ... .. 74

VI SUMMFARY AND CONCLUSIONS .. .. .. .. 84

Summary .. .. ... ... .. .. 84
Conclusions ....... 88
Suggestions for Further Research .... 90

APPENDIX . .... .. .. .. .. ... 92

BIBLIOGRAPHY .. .. .. . ... .. ... 120

BIOGRAPHICAL SKETCH ... .. .. .. .. .. 123










LIST OF TABLES


.ble Page

1 Percent of the Grapefruit Crop Accounted
for by Each Product Form, 1967-68
Through 1970-71 Seasons .... .. 6

2 Elasticities and Cross Elasticities of
Demand at the FOB Level for Grapefruit
in Various Forms, Computed at Mlean
Values of the Variables, Moadel I,
1964-71 .. .. .. ... .. . . 64

3 Elasticities and Cross Elasticities of
Demand at the FOB Level for Grapefruit
in Various Processed Forms, Computed at
Mlean Values of the Variables Mlodel II,
1964-70 .. .. .. ... . . 66

4 Coefficients of Derived Reduced Form
Equations for M~odel I .. .. .. .. 68

5 Coefficients of Derived Reduced Form
Equations for M~odel II .. . ... .. 71

6 Endogenous Variables : Actual Values,
Predicted Values Based on the Reduced
Form Estimated Directly and Deviations,
December, 1971, Through March, 1972 .. 78

7 Theil's Inequality Coefficients for
Predicted Yalues of the Endogeneous
Variables, Based on Reduced Form
Estimated Directly, December, 1971,
Through M~arch, 1972 ..... 8

8 Endogeneous Variables: Actual Values,
Predicted Values Based on the Derived
Reduced Form and Deviations, August
and September, 1971 . .. ... . . 82

9 On-Tree and FOB Prices: Mlonthly Data
Used in Estimating the Structural
Models, 1964-71 ...... 93





LIST OF TABLES (continued)


Table Page

10 FOB Prices and Canned Single-Strength
Grapefruit Juice Quantities: M~onthly
Data Used in Estimating the Structural
Models, 1964-71 ... .. .. . 95

11 Grapefruit Sections and Frozen Concen-
trated Grapefruit Juice Quantities:
Monthly Data Used in Estimating the
Structural Models, 1964-71 .. .. . 97

12 Inventory of Frozen Concentrated
Grapefruit Juice and Grapefruit
Quantities : Mlonthly Data Used in
Estimating the Structural Mlodels,
1964-71 ... .. .. .. .. .. 99

13 Exogenous Variables: Mionthly Data
Used in Estimating the Structural
Models, 1964-71 .. . . .. 101

14 Retail Price of Frozen Concentrated
Orange Juice and Demand Shifters:
Monthly Data Used in Estimating the
Structural Mlodels, 1964-71. .. .. 103

15 Coefficients, Standard Errors and
Coefficients of Determination of
Reduced Form Equations from First
Stage of Two-Stage Least Squares,
Model I .. .. .. ... .. .. .. 105

16 Endogenous Variables: Actual Values,
Predicted Values Based on the Derived
Reduced Form and Deviations, December,
1971, Through Miarch, 1972 .. .. . 110

17 Theil's Inequality Coefficients for
Predicted Values of the Endogenous
Variables, Based on Derived Reduced
Form, December, 1971, 'Through Mlarch,
1972 .. .. .. .. ... .. 112

18 Data Used in Forecasting and Evalu-
ating Mlodel I, by Mlonths, November,
1971, Through Mlarch, 1972.. .. . .. 113




LIST OF TABLES (continued)


Table Page

19 Coefficients, Standard Errors and
Coefficients of Determination of
Reduced Form Equations from First
Stage of Two-Stage Least Squares,
Model II .. .. ... .. .. .. .. 115

20 Endogenous Variables: Actual Values,
Predicted Values Based on the Reduced
Form Estimated Directly and Deviations,
August and September, 1971 . ... .. 118

21 Data Used in Forecasting for Model II,
by Months, July, August and September,
1971 . . . 119











LIST OF FIGURES


Figure Page

1 Distribution of commercial grapefruit
acreage, by counties, as of December,
1969, and delineation of Indian River
district . ... .. .. .. .. .. 4


V111




Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy



ANZ ECONON\ETRIC ANALYSIS OF
THE FLORIDA GRAPEFRUIT INDUSTRY


By

Arthur F. Parker, Jr.

March, 1973


Chairman: Dr. WI. W. MlcPherson
Co-chairman: Dr. L. H. Myers
M~aj or Departmnent: Food and Resource Economics



The objectives of this study were (1) to quantitatively

describe, by means of a simultaneous equation model, the

Florida grapefruit industry from the grower transactions

at harvest to the FOB level for canned single-strength juice,

canned sections, frozen concentrated juice and fresh grape-

fruit, (2) to measure the effects of factors exogenous to

the Florida grapefruit industry on the production and sale

of the four products listed above, and (3) to develop a model

for forecasting values of the variables endogenous to the

Florida grapefruit industry.

Two models were developed: one for the months in which

fruit was harvested and thus available for processing and

for fresh pack (Mlodel I) and one for the months when no

fruit was available (Model II). Model I consisted of 11

behavioral equations and seven identities for the crop years





1964-65 to 1970-71. Model II consisted of six behavioral

equations and six identities for the crop years 1963-64 to

1969-70. Included in Mlodel I wJere behavioral relationships

for (1) on-tree prices for grapefruit for packing and for

processing, (2) pack for each of canned sections and frozen

concentrated juice, (3) storage of each of the processed

products, and (4) FOB demand for each of the processed prod-

ucts, as well as FOB demand for fresh grapefruit. The

behavioral relationships for Miodel II included (1) storage

of each of the processed products and (2) FOB demand for

eachz of the processed products. The behavioral equations

were estimated by means of two-stage least squares. Monthly

data wjere used.

The supply of fruit to packers and processors was

assumed to be predetermined. In the processor and packer

on-tree price equations, both the quantity available and the

prices of the products to be derived from the fruit were

shown to affect on-tree prices. For fresh fruit, the margin

between the on-tree price and the FOB price was found to

increase with advances in the price level.

The pack and storage equations contained price expecta-

tion relationships. The results indicated that current

prices had more influence on pack and storage than did

expected prices.

The FOB demand equations w~ere each estimated with the

quantity of a product demanded as a function of its FOB

price, the prices of substitutes, disposable personal income





per capital, the FOB quantity in the previous month and the

month. In general, seasonality in demand was found to

exist, the income effects were positive and the own-price

slopes were negative.

Average values were used to calculate elasticities.

For Model I, price elasticities of demand at the FOB level

were -0.392 for single-strength juice, -2.101 for canned

sections, 0.163 for frozen concentrated juice and -12.268

for fresh grapefruit. For Mlodel II, the elasticities for

the first three products above were -1.254, -2.636 and

-2.096, respectively. For both Model I and Model II, cross

elasticities indicated that single-strength juice and fro-

zen concentrated juice were substitutes.

Direct and derived reduced form estimates were obtained

for the two models. Implications of the derived reduced

forms were discussed.

Finally, predictions were obtained for each model using

both the direct and derived reduced form estimates. Pre-

dictions were made for December, 1971, to Mlarch, 1972, for

Model I and for August and September, 1971, for Mlodel II.

Model I predictions were evaluated using Theil's inequality

coefficients. Because there w~ere only tw\o data points,

Model II predictions were not evaluated. The predictions

for Mlodel II appeared to be considerably more accurate than

were those for Mlodel I.











CH-APTER I

INTRODUCTION



During the past decade, Florida growers have produced

approximately 76 percent of the grapefruit produced in the

United States. The amount produced annually has varied from

26 to 44 million boxes, with an annual average of over 34

million boxes. California, Texas and Arizona produce average

annual quantities of 4.1, 3.9 and 2.7 million boxes, respec-

tively, and are the only other states that produce grape-

fruit. In terms of total value of farm production in Florida,

grapefruit ranks third, among different commodities, behind

oranges and tomatoes, with an annual average farm value of

over 44 million dollars. During the 1970-71 season the

value of the production of oranges, the primary agricultural

commodity in the state, was approximately 1S9 million dollars

[19, 1971 issue,p. 18].

Varieties of Florida grapefruit are classified, based

on physical characteristics, into white seedy, white seed-

less and pink seedless grapefruit. The white seedless type

is primarily composed of the M~arsh variety. The Duncan

variety is the predomiinant white seedy type. In December,

1969, 26.8 percent of the bearing acreage was of the pink







seedless type, 47.8 percent was of the white seedless type

and the other 25.4 percent was white seedy [20]. The harvest

of each type usually begins in September, but it is October

before any appreciable quantity is available for market.

Harvest of the seedy type peaks in October, tapers off

through the succeeding months and ends in April or May..

The white seedless type is available in large quantities in

October; thereafter the production decreases for a month or

two and then increases. In February or March, production

neaks and then tapers off until June or July, at which time

picking ceases. The seasonal production pattern for pink

seedless fruit is similar to that for the white seedless

type.

The fact that these patterns exist tends to complicate

the decision-making process for processors and packers. For

example, except for a very few~ products, pink grapefruit is

not desirable for processing because of the color that it

imparts to the products. On the other hand, the Duncan

variety is preferred for use in canned grapefruit sections

because of its fairly large sections. The matter of storage

of processed products also enters the decision-making pro-

cess, as there is no fresh fruit available during the summer

months.

Florida grapefruit production may also be categiorized

with respect to geographic location. Grapefruit is gener-

ally produced in the lower twso-thirdls of the state, from







Putnam, Flagler and Mlarion counties south to Collier and

Brow~ard counties (Fig. 1.). The two general areas are

referred to as the Indian River district and the Interior

district [22, p. 40]. During the crop years 1966-67 through

1970-71, 27.8 percent of the grapefruit produced in Florida

was produced in the Indian River district, while the other

72.2 percent was produced in the Interior district.~r c

Efforts to establish a differentiation between Indian

River and Interior grapefruit have been highly successful.

For years, Indian River packers have advertised fresh Indian

River fruit as being of a higher quality than fruit from the

other region. This campaign w~as successful, as shown by the

fact that, for the past five years, grapefruit from the

Indian River district has commanded an on-tree price aver-

aging over 75 cents per box more than Interior district

prices. However, it has been shown that product differen-

tiation has decreased in the last year or two [24, p. ii].

Prices of grapefruit for processing in the tw~o districts

have tended to be about equal.

SThe grapefruit industry is organized along the follow-

ing lines. The growJers sell the grapefruit either to packers,

for sale later as fresh fruit, or to processors for process-

ing into 10 processed grapefruit products. There are at

present approximately 34 firms that process citrus. Mlost

of these firms produce at least some of the products derived

from grapefruit. Some firms produce only single-strength
































3
$;.
a





d


,,,,.
a


5-1,000 acres


I~] 1,000-10,000 acres



6~Over 10,000 acres


II1I1ii~
'd-%," '


Figure 1. Distribution of commercial girapefruit acreage,
by counties, as of Decemnber, 1969, and
delineation of Indian River district.







juices, othersproduce almost all of the products except

canned sections. During 1970-71, approximately 120 to 130

firms packed fresh grapefruit. The number has varied from

year to year as a number of the smaller firms have ceased

packing operations or merged with larger firms. Also, small

firms are continually being formed. During the crop years

1967-68 to 1970-71, approximately 38.3 percent of the grape-

fruit crop was delivered to the packers, with the rest going

to the processors. The products that are derived from grape-

fruit, as well as the relative importance of each, are shown

in Table 1. Processors pack the 10 processed products and

move them into the warehouse to be sold at a later date or

they sell them immediately to buyers (i.e., chain stores and

wholesalers). During the months w~hen grapefruit is avail-

able for processing, processors build up inventories for the

summer months when fresh fruit is not available. During the

months of no grapefruit production, processed products are

moved from the warehouse and into the marketing channels for

final consumption.

Fresh grapefruit, canned juice, canned sections and

frozen concentrated juice, wJhich account annually for about

89 percent of the total crop, were included in this study.

The other seven products account for the other 11 percent,

the most important of the seven, chilled juice, accounted

for an average of less than 5 percent over the four years

included in Table 1. Although chilled juice is a relatively















































*Less than .1 percent.

Source: Florida Citrus Mlutual, Annual
Report, Lakeland, Florida, 1970-71 issue.


Statistical


Table 1. Percent of the Grapefruit Crop Accounted
for by Each Product Form, 1967-68
Through 1970-71 Seasons


Fresh

Canned Juice

Frozen Concentrate

Chilled Juice

Canned Sections

Canned Blend

Chilled Salad

Chilled Sections

Canned Salad

Processed Concentrate

Frozen Blend


TOTAL


Percent
1970-71

34.8

34.0

15.7

5.5

5.4

1.6

1.5

1.1

0.2

0.2




100.0


of Total
1969-70

38.0

32.8

12.1

4.9

6.6

2.0

1.9

1.2

0.4

0.1




100.0


Grapefruit Crop
1968-69 1967-68

35.2 45.0

29.7 30.2

16.5 5.4

4.1 3.9

7.6 7.9

2.1 2.1

2.7 3.9

1.5 1.0

0.5 0.6

0.1 0.0




100.0 100.0


Product Form








new product, it is currently more important than canned

sections. However, a lack of data for the earlier years

included in the study precluded its use in this analysis.

The other processed products as a group, represent such a

small proportion of the total that they were omitted in this

study.

There are three main types of arrangements for the sale

of fruit to packers and processors. Cash buyers deal

directly with growers and an agreement is reached as to

price and quantity to be exchanged. The participation plan

type of contract is a hedge against a loss of markets result-

ing from an oversupply of fruit. Mlost plans contain pro-

visions whereby a grower binds all or a portion of his fruit

to a processor. The price of the fruit is determined at the

end of the pool period and is based upon a formula specified

in the contract. Generally, the pool periods end either at

the end of the crop year or approximately midway through it,

depending on the contract. Thus, the processor pays the

grower at the end of the year only for the fruit used, based

on the price that the processor receives for the processed

products derived from the fruit. This type of arrangement

is advantageous to growers in that they are assured of a

market for all or part of their fruit. The processor bene-

fits in that he is assured, of both a source of supply and a

locked-in profit margin. The third type of arrangement is

the cooperative. Member growers pool their fruit and sell







it as a group rather than individually. At the end of the

operating year, profit received by the cooperative from the

sale of products derived from the fruit, including byproducts,

is divided among the members in proportion to the quantity

each member put into the pool. In some cases, cooperatives

have started their own processing plants. They benefit from

an assured market, even though the fruit is unpriced until

the end of the year. Also, members share in the profits of

the cooperative's processing plants. Similarly, packers and

processors that deal with the cooperative are fairly certain

of a source of rawJ fruit.

Each of the three arrangements has a different effect

on the allocation of the fruit to be packed or processed.

The participation plan member has no choice as to how his

fruit is allocated; that is, price does not play a role in

the decision to supply the fruit to a packer or to a pro-

cessor. The same is true for the cooperative member. Only

the cash seller has this option. During the 1970-71 season,

almost 28 million boxes of grapefruit were utilized by pro-

cessors for the production of various processed grapefruit

products. Of this total, nearly 10 million boxes, or almost

35 percent, were moved to the processors as priced fruit [4].

The Florida grapefruit industry is constantly faced

with the possibility of widely fluctuating supplies of fruit

combined with a more or less steadily increasing demand for

grapefruit products. This condition results in substantial








year-to-year variations in prices and net revenues to growers.

Unlike industrial production, where the flow of raw materials

can be adjusted as conditions require, the supply of grape-

fruit is a rather long-term proposition. Trees will produce

fruit for many years, so that short-run variations in sup-

plies are primarily the result of weather and basically

beyond the control of producers.

Growers, then, as well as packers and processors, are

faced with constraints on the volume of fruit available at

a particular point in time within the season as well as that

for the total season. Both of these constraints make utili-

zation and marketing decisions more difficult. The more

information that is available to decision makers, the better

the industry can adjust to the factors over which it has no

control.



Objectives


Necessary inputs into the decision-making process

include empirical estimates of the supply and demand relation-

ships at each transaction point in the system. Also needed

are estimates of economic relationships, such as price-

quantity relationships and the effects of inventory levels,

which determine the allocation of grapefruit among various

products and between storage and current sales.







The objectives of this study follow:

(1) To quantitatively describe, by means of an
econometric model, the Florida grapefruit
industry from the grower transactions at
harvest to the FOB level for canned single-
strength juice, canned sections, frozen
concentrated juice and fresh grapefruit.

(2) To measure the effects of factors exogenous
to the Florida grapefruit industry on the
production and sale of the four products
included in the study.

(3) To develop a model for forecasting values
of the variables endogenous to the Florida
grapefruit industry.


Literature Review


Research dealing with the Florida citrus subsector has

dealt primarily wlith the orange industry. The grapefruit

industry w~as included. only when it was necessary for the

quantification of economic relationships dealing with orange

products, such as substitutes in demand equations. This

emphasis on oranges has possibly been due to the fact that

the orange industry has historically been of much greater

economic importance than has the grapefruit industry.

Shafer has conducted several studies relating to the

annual demand for Texas grapefruit. Estimates of the demand

for Florida grapefruit were obtained as a byproduct of his

studies. In An Analysis of Season- Average prices for Texas

Grapefruit, 1949-1967 [14], Shlafer and Gutierrez analyzed

grapefruit prices for the years fromn 1949 to 1967. They

found that the Florida crop values generally tended to move








inversely with the size of the Florida crop. A 1 percent

change in Florida production on a U. S. per capital basis

was associated with a 1.68 percent change of opposite sign

in the Florida price for fresh grapefruit. In the case of

grapefruit for processing, a 1 percent change in production

per capital was found to be associated with a 2.3 percent

change in price in the opposite direction.

A later study by Shafer [13] updated the previous study.

It was found that the quantity of Florida production allo-

cated to fresh use exerted a significant negative effect on

the season average FOB price for Texas grapefruit. From

this information, it w~as concluded that fresh Florida grape-

fruit and fresh Texas grapefruit w~ere substitutes for one

another.

In a study by Ward [25], detailed price-quantity rela-

tionships were estimated for grapefruit from the Indian

River district. In particular, it was found that over one-

third of the weekly variation in the FOB price of Indian

River grapefruit was explained by weekly changes in shipments

from Indian River, Interior Florida and Texas. Further,

Texas shipments were found to have a greater influence on

the Indian River price than did Interior shipments.

Another study by Wlard [24], conducted a year later,

generally confirmed the results of the previous study. H

found, however, that Indian River grapefruit prices had

become more responsive to Interior Florida and Texas








shipments, with the increased price responsiveness to Texas

shipments far exceeding the response to Interior shipments.

A study with objectives similar to those of the present

study was conducted by Vanderborre [23] for the soybean

economy. He described the markets for soybean oil and soy-

bean meal by means of a simultaneous equation model. A pri-

mary objective of that study was the estimation of the

demand relationships for both domestic and export markets

for soybean products. The model consisted of equations for

the wholesale demands for crude soybean oil and for soybean

meal, as well as equations for the export demand for those

two commodities. Pricing, margin and stock equations w~ere

also included. First differences were used in all of the

equations in an effort to reduce the possibility of auto-

correlation and multicollinearity. Conclusions were reached

with respect to the effects of the ex(ogenous variables on

the endogoenous variables by algebraic manipulation of the

structural equations which were estimated by means of two-

stage least squares. At the time of the publication of the

article, the model had not yet been tested for its predic-

tive ability.

K'ulshreshtha and Wilson [9 ] presented a simultaneous

equation model of the Canadian beef cattle industry as a

first attempt to examine the interdependent nature of demand,

sunply and price relationships in that industry. The comn-

plete system included six behavioral equations and three








identities. Behavioral equations were estimated by means

of two-stage least squares and included relationships for

the demand for beef, the demand for live cattle for export,

retail prices, slaughter, dressed weight and inventory.

One of the major purposes of the study was to derive a model

for predicting changes in the beef cattle sector. For pre-

dictions, the authors converted the structural equations

and the identities into reduced form equations. The pre-

dictive ability of the model was evaluated with Theil's

U-coefficient [16, p. 28, and 17, p. 32].

Another study with objectives and methodology similar

to the present one was conducted by Myers, Havlicek and

Henderson [11]. The objective was to obtain a simultaneous

equation model of the monthly structure of the hog-pork

sector of the United States. The model consisted of eight

behavioral equations and two identities. The behavioral

equations represented the supply and demand relationships,

as well as margin equations, that existed within the hog-

pork sector from the farm level to the retail level. Two-

stage least squares was used to estimate the parameters of

the model. Then, using the second-stage structural equations

and the first-stage reduced form equations, values of the

endogenous variables were predicted for 18 months for which

the data had not been used in the original estimates. The

ability of the model to predict was evaluated by several

means. As in the previously mentioned study, Theil's








U-coefficient was calculated for each endogenous variable.

Also, the predictive ability of the model wa~s evaluated by

means of its ability to predict changes in direction in the

endogenous variables.



Organization of Presentation


The economic model of the Florida grapefruit industry

is described in the second chapter. The third chapter con-

tains the statistical model, as well as a discussion of the

statistical procedures used. The statistical results of the

study are presented in the fourth chapter. The fifth chap-

ter consists of implications drawn from the results of the

statistical analysis, including elasticity estimates and a

prediction model. In the final chapter the results and

conclusions are summarized.











CHAPTER II

MODEL DEVELOPMENT



At each level of exchange of fruit or processed product,

there are relationships that interact to determine price and

quantity. In addition, each level affects each other level

in that changes in orices and quantities at one level cause

repercussions in other levels. For example, a change in the

FOB price of a product affects pack decisions of that prod-

uct, which in turn affects the pack of the other products.

Hence, the system was formulated as a simultaneous one.

There are several months of each year when all four

Products included in this study are produced. Model I

represents these months. However, grapefruit is not picked

year round, nor can it be stored in fresh~ form for very

long. Model II represents the months when there is no har-

vest. Finally, there are months during which some, but not

all, of the products are produced. These months were dis-

tributed between the two models according to the following

criteria. If canned single-strength grapefruit juice, which

normally accounts for approximately 55 percent of all pro-

cessed grapefruit, w~as produced during a month, that months

wJas placed in Mlodel I. Fresh pack usually coincides with

the months during which single-strengith juice is produced.







On this basis, Model I included the nine months from October

to June, while Model II included July, August and September.

Retail prices were deflated by the consumer price

index, while all other prices wJere deflated by the wholesale

price index for farm products. Also, all quantities, after

the raw fruit was supplied to the packers and to the pro-

cessors, wJere converted to the equivalent of gallons of

single-strength juice. This conversion was made to facili-

tate direct comparisons among products.



Model I


Price of Grapefruit for Packing

Thie quantity of grapefruit that growers are willing to

supply to packers was assumed to be determined outside of

the system. Rather than supply being a function of economic

variables, it is a function of the month of the season, with

a constant quantity being supplied in a particular month.

For example, it was found that the average quantities going

to fresh use, during the years included in this study, in

December, January, February and Mlarch were 1.555, 1.757,

1.650 and 2.102 million boxes, respectively. The correspond-

ing standard deviations were 0.172, 0.143, 0.161 and 0.280,

respectively. Thus an economic supply function was not

specified for the system. The same reasoning wias applied

for the quantity of grapefruit supplied for processing.







W~hen the supply of fruit is predetermined, price becomes

the critical variable for equating supply with demand.

Therefore, the equation w~as formulated wLith on-tree price as

an endogenous variable and quantities supplied as a pre-

determined explanatory variable. Since the packers purchase

the fruit to vack and then sell at the FOB level, the FOB

rice was also hynothesized as influencing on-tree prices.

The relationship is shown below~.


(2-1) PGKms = FlPFFGms,GKms)

wdh ere PGhas = deflated on-tree price of grapefruit for
fresh packing in month m and year s
(dollars per 1 3/5-bushiel box).

PFFGs = deflated FOB price of fresh grapefruit in
month m and year s (dollars per 1
3/5-bushel box).

GKs = qua"ntity of gracefruit for packing in
msmonth m and year s (million 1 3/5-
bushel boxes).

It was expected that the FOB price and the on-tree

price would change in the same direction. Also, since supply

was predetermined, the price was expected to fluctuate in-

versely with the quantity of fruit available in a particular

month. Therefore, aPGKms/aGKm < 0.


Price of Granefruit for Processing

The equation for the price of grapefruit for processing

was similar to that for packing in that it was derived from

the FOB level. The price that the processors pay for the

fruit was expressed as a function of, among other things,







the quantity of fruit going to the processors. Because of

the various contractual arrangements within the industry

whereby the price growers receive is determined by the FOB

prices received for the output and the processing cost, the

on-tree price was also a function of the FOB prices of the

three processed products and the average cost of processing.

The year was used in other equations in the model.
Both the year and processing costs w~ere exogenous variables.

Since the system was formulated as a simultaneous one, no

predetermined variables should be highly correlated. To

violate this principle could result in a singular matrix of

exogenous variables. The correlation coefficient between

the year and procecssing costs was found to be 0.91. Because

of this close relationship, the year was used in place of

processing costs.

The equation for the price is given below.


(2-2) PGRms = f(PFCSms,PFCGms,PFFCms,GRms's)

where PGRms = deflated on-tree price of grapefruit for
processing in nonth m and year s (dollars
per 1 3/5-bushel box).

PFCSms = deflated F0B price of canned single-strength
grapefruit juice in month m and year s
(dollars per case of twelve 46-ounce cans).

PFCGms = deflated FOB price of canned grapefruit
sections in nonth m and year s (dollars
per case of 24 number 303 cans).

PFFCs = deflated FOB price of frozen concentrated
grapefruit juice in month m and year s
(dollars per case of twelve 6-ounce cans).







GR = quantity of grapefruit for processing in
msmonth m and year s (million 1 3/5-bushel
boxes).

s = harvest season (1964-65 season = 1).


Utilization or Pack

After processors have purchased the fruit, a decision

must be made with regard to allocating the fruit among alter-

native products. Products produced will be either sold to

buyers immediately or stored for later sale. Thus, the

quantity packed was expected to be a function of both the

current FOB price of the product (in the event that the

product is sold during the current time period) and the

expected FOB price of the product (in the event that it is

stored for later sale). The expected price is the current

expectation of the price that the processor feels he will

receive if he sells his current output at a later date.

Since the fruit can be used in the production of more than

one product, FOB prices of alternative products were con-

sidered. Further, the quantity of product currently in

storage must be considered. It w7as expected that producers

desire to reduce the pack of a particular product when inven-

tories exceed certain levels. It was anticipated that the

increased popularity of frozen food products during the

years included in the study had resulted in an increase in

the production of frozen concentrated grapefruit juice. It

was also expected that the production patterns of the other

two processed products had been altered over time. To







measure these effects, time, as measured by numbering the

marketing seasons, was included as an independent variable

in the relationships.

As discussed in Chapter I, some varieties of grapefruit

are better suited for use in certain processed products,

while other varieties are best suited to other products.

Since different varieties mature during different months of

the season, the pack of a product depends somewhat upon the

month of the year. Finally, in making production decisions,

the best public information available as to crop size is the

United States Department of Agriculture (USDA) crop esti-

mate. The pack relationships for canned sections and frozen

concentrated juice are shown below. The equation for canned

single-strength juice is discussed subsequently in this
section.

(2-3) PCG = f(PFCS ,PFCSL ,PFCG ,PFCG" ,PFFC S,
ms ms ms ms ms m

PFFC ~,BCG ,s,S'm2m2,GE ,)


(2-4) PFC, = f(PFCSm ,PFCS" ,PFCG PFCGX PFFCms

PFC,BFC ,s,m,m2,GE)
ms ms ms

where PCGm = quantity of canned grapefruit sections
produced during month m in year s
(million gallons single-strength).

PFCs = quantity of frozen concentrated grapefruit
juice produced during month m in year s
(million gallons single-strength).







PFCSms = the expectation, during month m in year s,
of the FOB price that will be received for
canned single-strength grapefruit juice
sold at a later date (dollars per case of
twelve 46-ounce cans).

PFCGms = the expectation, during month m in year s,
of the FOB price that will be received for
canned grapefruit sections sold at a later
date (dollars per case of 24 number 303 cans).

PFFCms = the expectation, during month m in year s,
of the FOB price that will be received for
frozen concentrated grapefruit juice sold
at a later date (dollars per case of twelve
6-ounce cans).

BCGms = inventory of canned grapefruit sections at
beginning of month m in year s (million
gallons single-strength).

BFCms = inventory of frozen concentrated grapefruit
juice at beginning of month m in year s
(million gallons single-strength).

GEms = official USDA estimate, during month mn in
year s, of the size of the grapefruit crop
for year s (million 1 3/5-bushel boxes).
The other variables have been defined previously.

Since producers are assumed to be profit maximizers,

it w\as expected that they react to increased current and

expected prices by attempting to increase output, thus it

was expected that aPCG s/aPFCGm and aPCGs/aPFCG woul
be > 0. Since the three processed products are viewed by

the industry as alternatives, it was anticipated that an

increase in either the current or expected FOB price of one

of the alternative products results in a shift of productive

resources to the product withi the higher price. There fore ,

it w~as expected, a priori, that aPCG n/aPFCSs ,, 8PG/BFS
aPCGSaPFFms ms ms~m ms
BPCms/PF~msan BP~m/aPFFCs < 0. The reasoning behind








aPCGms/aBCGms < 0 was explained above. Because of the pat-
tern of production whereby the quantity produced increases

one or more months and then decreases, it w\as expected that

aPCGms/am > 0 and aPCGms/am2 < 0. Finally, it was expected
that the annual size of the crop and the production of each

of the products would be directly related. The foregoing

discussion involved primarily relationship (2-3), but the

relationships in (2-4) were expected to be similar to those

in (2-3).

Over the past several years, the quantity of canned

sections produced annually has decreased, while the produc-

tion of frozen concentrated juice has increased. This gav~e

rise to the expectation of aPCGms/3s < 0 and aPFCms/as > 0.

Expected prices appear in the above relationshiips.

However, it is difficult, if not impossible, to obtain data

relating to price expectations. The expected FOB price of

a product is the expectation, in time period ms, of the

average FOB price for that product expected for the remainder

of the year beyond time period ms and as such is a reflection

of the expected future supply and demand conditions for that

product. Future supply expectations are based on the current

crop estimate for that year. Demand expectations are based

on the current FOB price of the product. Since FOB prices

do not vary widely over the course of a crop year, the cur-

rent price should reflect fairly accurately the expected FOB

price. The price expectation relationships are given below.








(2-5) PFCSS = g (PFCS s,GE )


(2-6) PFCGS = g (PFCG sG,GE


(2-7) PFFCs = g (PFFC G, E ))

These variables were defined previously.

Since GE, was included in relationship (2-5) to reflect

future supply expectations, it was expected that aPFCSms/aGEms
< 0 because a larger supply in the future would generally

lead to lower future prices. PFCSs was included to reflect

demand expectations so aPFCSk /aPFCS > 0. Similar rela-
ms ms
tionships were expected for (2-6) and (2-7).

W~hen the expected price relationships w~ere substituted

into that for the pack of canned sections, the following

equation was obtained.


(2-8) PCGm~s = f [PF:CSms' 11gPFCSms, GEms) ,PFCGms'

82(PFCGms,GEms),PFFCms'83(PFFCms,GEm

BCGms,s,m,m2,GEms]
or

(2-9) PCG = h(PFCS ,PFCG ,PFFC ,GE ,BCG ,s,m,m )
ms ms ms ms' ms ms

From (2-8) it can be seen that PFCG has an effect
ms
both directly and indirectly through PFCGms. To determine

a priori what effect the combination will have on the quan-

tity backed, it w~as necessary to examine the effects sepa-
rately and then put them together. The effect through the








expected price was

aPCG BPFCGk aPCG
ms ms ms
>0Oor ->0
aPFCG* aPFCG aPFCG
ms ms ms

as both partial derivatives are positive. Wvhen the direct

effect, which has a positive partial derivative, is added

to the above, the total effect is > 0. The other variables

were analyzed in a similar manner to determine if the rela-

tionship (i.e., whether direct or inverse) had changed with

the introduction of the expected price. It was found that,

with the exception of the crop estimate, all sign expecta-

tions were unchanged from those discussed earlier.

In the case of GEms the combined effect of the esti-

mate directly and through each of the three expected prices

could not be determined a priori. Again, this relationship

can be derived from (2-8) above. The total effect, composed

of the sum of four parts, is

aPCG aPFCS* aPCG, aPFCGS
aPFCS* aGE aPFCG* aGE
ms ms ms ms
aPCG aPFFC~ aPCG
ms ms ms >
+ + -- -
aPFFCf ms mGEs ams

The first effect is negative, while the other three are

positive. Thus the total effect depends upon the relative

magnitudes of the partial derivatives. The relationships

for the pack of frozen concentrated juice were analyzed in

an analogous manner and yielded essentially similar results.







Since the total quantity of grapefruit purchased for

processing is predetermined, it is possible to determine the

pack of canned single-strength juice if the pack of the

other two processed products is known. Since the fruit

cannot be stored very long after it is picked, it is reason-

able to assume that the sum of the quantities of the three

products that are produced is equal to the quantity of fruit

purchased for processing. Because GRs is given in boxes

and quantities packed are given in gallons single-strength,

it was necessary to convert pack to boxes. This was done

by dividing the pack of each product by the average yield

of grapefruit used for that product times the number of

gallons per case (3.375 for single-strength juice and canned

sections and 4.0 for frozen concentrated juice). Hence

PCSs PCGs PFCs
(2-10) GR -+ +
msYCS-3.375 YCG-3.375 YFC-4.0
or
PCS PCG PFC
ms ms ms
(21)Gms 4.54410 4.01547 4.02932

where PCS = quantity of canned single-strength grapefruit
ms juice produced during month m in year s
(million gallons).

YCS = average yield of canned single-strength
grapefruit juice (cases of number 2 cans
per box of fruit).

YCG = average yield of canned grapefruit sections
(cases of number 2 cans per box of fruit).

YFC = average yield of frozen concentrated grape-
fruit juice (gallons per box of fruit).

The other variables wJere defined previously.







While the yields vary slightly from year to year, the

variation is small enough so that the yields were treated as

constant. The average yields and standard deviations,

respectively, were 1.3464 and 0.0394 for single-strength

juice, 1.2164 and 0.1436 for canned sections and 1.0198 and

0.0790 for frozen concentrated juice.

The pack of canned juice was chosen to be represented

by the identity because of the error introduced by the use of

average yields. Since the pack of the product is a residual

in the identity, the resulting percentage error is smaller

for that product since it accounts for a relatively larger

share of the processed fruit.


stores

Storage here refers to the inventory in processor ware-

houses at the end of a time period. Grapefruit products

packed but not sold are placed in storage. The quantity in

storage at the end of a time period was hypothesized to be

a function of the FOB price of the product, the expected FOB

price of the product and storage costs. Als in the case of

processing costs in the pack equations, storage costs and

time w~ere highly correlated. The correlation coefficient

between storage costs and time was 0.89, so the year was

used in place of storage costs. Finally, quantities of a

product packed( should influence inventory levels since any

excess pack over current sales would move into storage. The

storage relationships are given below.







(2-12) SCS = f(PFCSm ,PFCS* ,PCS ,s)

(2-13) SCGn = f(PFCG ,PFCG ,PCG ,s)
ms ms ms ms

(2-14) SFC, = f(PFFC ,sPFFC ,PFC m, s)

where SCSms = quantity of canned single-strength grapefruit
juice in storage at end of month m in year s
(million gallons).

SCGmns = quantity of canned grapefruit sections in
storage at end of month m in year s (million
gallons single-strength).

SFCs = quantity of frozen concentrated grapefruit
juice in storage at end of month m in year s
(million gallons single-strength).

The other variables were defined previously.

Current and expected prices of a product were expected

to have opposite effects on the quantity of that product.

An increase in the current price should cause more of the

product to be sold in the current time period, whereas a

rise in the expected price should cause more of the product

to be stored for sale at a later date at the expected

higher price. Thus aSCSms/aPFCSs < 0, while aSCSms/aPFCSm

and aSCSms/as > 0. Relationships for (2-13) and (2-14) were

expected to be similar to those described for (2-12).

Relationships for the expected prices were substituted

into the equation of the storage of canned single-strength

juice to obtain


(2-15) SCSms = f[PFCSms'81(PFCSms ,GEms) ,PCSms,s]


(2-16) SCSmIs = f(PFCSmsGEms ,PCSms,s)







Again the expected effect of the FOB price was both
direct and indirect.

aSCS aPFCS aSCS
ms ms ms>
i< 0
aPFCSm aPFCSm aPFCSm

since the product was positive and aSCSms/aPFCSms < 0. The

relative magnitudes of the partial derivatives determine

the sign. aSCSms/aGEms was expected to be < 0. The other

sign expectations were unchanged. Similar reasoning was

applied to (2-13) and (2-14), with similar results.

FOB Demand

FOB demand is directly related to retail demand.

While the FOB level was hypothesized to be the critical

pricing point throughout the industry, demand for a product

at the FOB level is derived from the demand at the retail

level. Therefore,


(2-17) QFCSmsI = f(PFCSms, retail demand for canned

single-strength grapefruit juice)


(2-18) QFCGms = f(PFCGms, retail demand for canned

grapefruit sections)


(2-19) QFFCm = f(PFFCms retail demand for frozen

concentrated grapefruit juice)


The formlulationn for the FOB demand for fresh grapefruit

was somewhat different. Since the quantity of fresh








grapefruit going to packers was hypothesized to be predeter-

mined, the quantity at the FOB level was also predetermined.

Consequently, the relationship was formulated with the FOB

price of the product as a function of the FOB quantity and
the retail demand.


(2-20) PFFGms = f(QFFGms,realdmnfofes

Grapefruit)


where QFCSms = quantity of canned single-strength grapefruit
juice demanded by buyers at the FOB level
during month m of year s (million gallons).

QFCGms = qu~antity of canned grapefruit sections
demanded by buyers at the FOB level during
month m in year s (million gallons single-
,fstrength).

QFFCms = quantity oE frozen concentrated grapefruit
juice demanded by buyers at: the FOB level
during month m in year s (million gallons
single-strength).

QFFGms = quantity of fresh grapefruit available at
the FOB level during month m in year s
(million gallons single-strength).

Retail demand for each of the processed, products wdas

reflected by the retail quantity of the product, per capital

disposable personal income and the retail prices of each of

the products thought to be substitutes for the product.

Also, to reflect seasonality in the demand for the product,

the month and the month squared were included. For fresh

grapefruit, retail. quantities, rather than retail prices,

w~ere included. In the absence of retail quantity data, the

preceding month's FOB sales for processed products, were








included as an approximate estimate of retail sales. A

comparison of the turning points for FOB movement with those

for household purchases, as reported by the Mlarket Research

Corporation of Amnerica [11], revealed approximately a one-
month lag between FOB and retail sales. Income and retail

price of substitutes wjere included as demand shifters.

Texas grapefruit has been shown to be a substitute for

Florida grapefruit [25]. The quantity of Texas grapefruit

shipped was used, rather than the retail price, because

there were no data available on retail prices of Texas grape-

fruit. Since retail prices w~ere not available for the var-

ious grapefruit products the corresponding FOB prices were

used in place of the retail prices of the substitute products.

Dummy variables were added to the equations after a

graphical analysis of prices and quantities revealed that

there may have been a shift in demand for three of the prod-

ucts. If a shift had actually occurred, and this shift w~as

not accounted for, erroneous results could be generated.

For example, a shift may have occurred during the time period

under consideration which would require two demand curves,

one reflecting the demand before the shift and the other

reflecting the demand after the shift. To ignore this

shift would lead to a demand equation which did not reflect

reality.

The FOB demand equations are given below.








(2-21) QFCSms = f(PFCSms,QFCSm-1,s,I~msPO~ms'
PFFC ms~mm2


(2-22) QFCGm = f(PFCGmsQCGm-sINms,PFFGms

TGms,m,m2,D1)


[2-23) QFFCm = f(PFFCms,QFFCm-1~'I,sImsPFCSms'

POJ S,m,m ,D2)

(2-24) PFFG = f(QFFG ,IN :QFCG ,TG ,m,m ,D3)
ms ms' ms ms ms

w~h ere INm = deflated per capital disposable personal
income in month m and year s (thousands
of dollars).

POJs = deflated retail price of frozen concentrated
orange juice during month m in year s
(dollars per case of 6-ounce cans).

TGms = shipments of Texas grapefruit during month m
of year s (million cartons).

s1 0 ( ~~;8,""" '""if otherwise

D ={1 if 1965-66 or 1966-67
s 0 if otherwise

D ={1 if 1967-68
s 0 if otherwise

The other variables w~ere defined previously.

For each of the products the income effect was expected

to be positive. The own-price slopes were expected to be

negative for the processed products, as was the own-quantity

slope for fresh grapefruit. Since the lagged quantities

were introduced as proxy variables for retail sales, they

wcere expected to have positive slopes. There were no








complementary relationships hypothesized, so each cross-

product w~as viewed as a substitute product. As such, the

cross-price slopes were expected to be positive. In equa-

tion (2-24), the cross-quantity slopes were expected to be

negative. The expectations for the slopes of the dummy

variables were aQFCGms/3D1s and aPFFGms/aD3s > 0 and

aQFFCms/3D2s < 0.


Supply to Buyers at FOB Level
If the quantity of a product produced and the storage

of that product are known, then the quantity supplied by

processors for sale at the FOB level can be derived by

tying together the three quantities via an identity. Thus,

for each product there would be three equations with three

unknowns, from which a solution can be obtained. The supply

for each product is shown below~ to be equal to the inventory

at the beginning of time period ms plus the pack of the

product during time period ms minus the quantity in storage
at the end of time period ms.


(2-25) SUCSm = BCSs + PCSm SCSs


(2-26) SUCGm = BCGs + PCGm SCGm


(2-27) SUF'C = BFCs + PFC SFC

where SUCS = quantity of canned single-strength grapefruit
msjuice supplied to buyers at the FOB level
during month m in year s (million gallons)








SUCGm = quantity of canned grapefruit sections
supplied to buyers at the FOB level during
month m in year s (million gallons single-
strength).

SUFCms = quantity of frozen concentrated grapefruit
juice supplied to buyers at the FOB level
during month m in year s (million gallons
single-strength).

BCSms = inventory of canned single-strength grape-
fruit julce at beginning of month m in
year s (million gallons).

The other variables were defined previously.

Identities

To assume that, at the FOB level, supply equals demand,

identities are nooded in order to equate the two.


(2-28) QFCSms = SUCSms


(2-29) QFCGs = SUCGm


(2-30) QFFCs = SUFCm



Model II


During the months included in Mlodel II, there is no

grapefruit available for supply to packers or processors.

Since fresh grapefruit cannot be stored, there can be no

production of any of the products being considered in this

study. Therefore, grower supply, processor demand, pack

and fresh relationships that are part of Mlodel I are no

longer appropriate. Model II includes only the behavioral







equations for storage and FOB demand plus the necessary
identities.


Storage

The storage equations in Mlodel I were formulated with

the quantity of a product stored as a function of the FOB

price of the product, the expected FOB price of the prod-

uct, the quantity of the product packed and the storage

cost. The quantity stored for Mlodel II was hypothesized to

be a function of the FOB price of the product, the expected

FOB price of the product, storage cost and the month. As

in Model I, the year was used in place of storage cost.

Processors must insure that they are able to supply products

at all times of the year, despite the fact that there is no

production with which to replenish inventories. Therefore,
the month becomes very important. The storage relation-

ships are shown below.

(2-31) SCSm = f(PFCSmsPFCSms,s,m)

ms ms ms



(2-33) SFC = f(PFFCn ,PFFCh ,s ,m)

The variables are as defined previously.

The anticipated signs were similar to those for the

storage equations for M~odel I. The fact that some of each

product is sold each month implied that aSCSms/am,

aSCGms/am and BSF~Cms/3m < 0.







As in Mlodel I, the expected price relationships were

substituted into the storage equations. However, for Mlodel

II, the USDA crop estimate in the expected price equations
was replaced by the actual size of the grapefruit crop, for
the harvest period had ended. After the substitution,

storage for canned single-strength juice became


(2-34) SCSms = f(PFCSms,s,Qs,m)

where Q5 = size of the Florida grapefruit crop in year s
s(million 1 3/5-bushel boxes).
It was not possible to determine the sign of

aSCms /aPFCSm a priori for the sam~e reasons given in Model I.
The other three coefficients were expected to be negative.

FOB Demand

The reasoning for the FOB demand relationships during

the months when there is no production was similar to that

in Model I. There were only the three processed products ,

because of the nonavailability of fresh grapefruit during

this period. The FOB demand equations are given belowv.


(2-35) QFCSms = f(PFCSmsPFFmFCsQFSm-1s'~m,s msPOm

(2-36) QFCGms = f(PFCGmsQFCGm-1,sINms)

(2-37) QFFCms = f(PFFCmsQFFCm-1,sINmsPFCSmsPOJms)

The variables have been defined Dreviously. The expected

signs of the coefficients were similar to those for the

respective equations in Mlodel I.




36


Supply to Buyers at FOB Level

The FOB supply identities were similar to those in

Model I. However, there was no new pack in the months of

Model II.


(2-38) SUCSs BCSm SCSm

(2-39) SUCG =BCG SCS
msms ms

(2-40) SUFCm = BFC -SFC
msms ms


Identities

The following three identities show~ that FOB supply

equals FOB demand.


(2-41) QFCSs = SUCSm


(2-42) QFCG =SUCG
ms ms


(2-43) QFFC, = SUFCm











CHAPTER III

STATISTICAL CONSIDERATIONS



Statistical Model


The statistical models that w~ere estimated are given

below~. The variables were defined in Chapter II. Endo-

genous variables are those variables whose values are deter-

mined jointly within the system. These variables are pre-

ceded by "6" coefficients. Exogenous variables, those whose

values are determined outside of the system, are preceded by

"y" coefficients.

M\o del I

FOB Price Equations:
(3-1) 611PGKm 12BPFFGm 10 yl 11GKms 1 ~ms


(3-2) 821PGRms C 22PFCSms + 23PFCGms 2 B4PFFCms

+ 20 + 21s + Y22GRms = 2ms

Pack:
PCSs PCG PFC
(3)Gms 4.5 4;1 4.01547 4.0m932=0







(3-4) 831PCSms + 632PFCSms 33aPFCGm 34BPFFCm

f 30 + 31GEms + 32BCSms Y33s + Y34m

SY35m2 =3ms

(3-5) 641PCGms + 42PFCSms + 43PFCGms + 44PFFCms

+ 40 + 41GEms + 42BCGms Y43s + Y44m

SY45m2 = 4ms

Storage:

(3-6) B51SCSms + 52PFCSms + 53PCSms + 50

51YSGEms + 52s = v5ms

(3-7) B61SCGms 6 B2PFCGms + 63PCGms + 60

+ 61GEms + 62s = v6ms

(3-8) B71SFCms + 72PFFCms 7 B3PFCms 70Y?

+ 71GEms 7 Y2s = v7ms

FOB Demand:
(3-9) 881QFCSs + 682PFCSm 835PFFCm 80YQ

SY81QFCSm-1,s 8 Y2INms f 83POJms Y84m

SY85m- 2 8ms

(3-10) B91QFCGms 9 a2PFCGms + 93PFFGms 9g0

SY91QFCGm-1,s 9 Y2INms Y93TGms 94Ygm

79Y5m2 9 Y6D1s = 9ms




39


(11 101QFFms 102PFFms 103PFCms 100

C 101QFFCm-1,s + 102INms + 103POJms C 104m

10m2 106D~ 10ms

(-2 111PFFms 112QFCms 110 Y111QFFms

112IITGms r 113I~ms t 114m + Yll5m2

+ 116D3s 11ms

Identities :

(3-13) SUCSS BCS, PCSs + SCSS = 0

(3-14) SUCG -BCG PCG + SCG = 0
ms ms ms ms

(3-15) SUFC -BFC -PFC + SFC =0
ms mns ms ms

(3-16) QFCSs SUCSm = 0

(3-17) qFCG SUCG = 0
ms ms

(3-18) QFFCms SUFCms = 0

Model II

Storage:

(3-19) 8121SCSms + 122PFCSms + 120 +121 s

+ 122s + Yl23m = 1-l2ns

(3-20) B 3 SCG m 132 PFCGms 130j 131 Q s


13s+y33m = 3ms




40

(3-21) B141SFms 6142PFm 14 11s


+ 142s + Yl43m = pl4ms

FOB Demand:

(3-22) B151QFCSms + 152PFCSms + 153PFFCms + 150

f 151QFCSmls 1 s 152INms Y153POJms 1 ~5ms

(3-23) Bl61QFCGms + 162PFCGms + 160 161QFCGm-1,s

+ 162INms = 16ms

(3-24) B171QFFCms + 172PFFCms + 173PFCSms + 170

+ 171QFFCm 1,s + 172INms + 173POJms = 17ms

Identities:

(3-25) SUCS -BCSS + SCS =0

(3-26) SUCGm BCG + SCG = 0

(3-27) SUFCS BFCs + SFCS = 0

(3-28) QFCS, SUCS = 0

(3-29) QFCG -SUCG = 0

(3-30) QFFCS SUFCm = 0








General Mlodel


The two models can each be stated in matrix notation as


BY + TX = p


where B is the JxJ matrix of coefficients of the J endo-
genous variables,

Y is the Jx1 vector of endogenous variables,

r is the JxK; matrix of coefficients of the K
exogenous variables,

X is the Kx1 vector of exogenous variables, and

v is the Jx1 Vector of disturbance terms.

For Model I, J = 18 and K; = 19. For Mlodel II, J = 12 and

K= 11.

The following assumptions were made regarding the model.

(1) The matrix 6 is assumed to be non-singular,
so that the system can be solved for the
endogenous variables.

(2) Plm -1 X'X = Ex where Ex is the non-
singular contemporaneous covariance matrix.

(3) The p's are random variables w~ith E(vjms) = 0
(for j=1,..., J-L; s=1,..., S; for each value
of s ,m=1,..., MI). L is defined as the number
of identities, S is the number of years and
M is the number of months per year. The L
identities are excluded because the coeffi-
cients are known.

(4) ~pjs9 n) =0 ,if and only if i=j m=n
and s=t tfor 1,j=1.. -;st1..
and m,n=1,..., M for each s).

(5) E(lsjms9 int) = 0 wjhen ifj or mfn or sft
(for i,3=1,..., J-L, s,t=1,..., S and
m,n=1,..., Mi for each s).







Identification


The problem of identification must be considered prior
to estimation of the structural coefficients of the model.

If the parameter values in a relationship can be uniquely

estimated, the relationship is said to be identified.

Consider one equation from a system of equations. The

necessary or order condition for identifiability is that the

number of exogenous variables excluded from the equation

must be at least as great as the number of endogenous vari-

ables included minus one. This can be calculated as


H -h g -


where H = the number of exogenous variables in the system,

h = the number of exogenous variables in the equation,

and g = the number of endogenous variables in the equation.

If H-h = g-1, the equation is said to be just-identified.

If H-h > g-1, the equation is over-identified. In the event

that H-h < g-1, the equation is not identified and the

parameters cannot be uniquely estimated. The necessary con-

ditions for identification indicate that each of the equa-

tions in M~odel I and Mlodel II is over-identified.

Trhe necessary and sufficient condition for identifica-

tion is known as the rank condition. For an equation to be

identified, it must be possible to form at least one non-zero

determinant of rank J-1 from the coefficients of the







variables excluded from the equation of interest, but which

occur elsewhere in the system. J is the number of endo-

genous variables in the system.1


Estimation Procedure


Estimation of the coefficients of over-identified equa-

tions by ordinary least squares yields biased and inconsis-

tent estimates. Estimates obtained by two-stage least

squares (2SLS) are biased but consistent. Three-stage

least squares (3SLS) is superior to 2SLS in its asymptotic

efficiency because 3SLS incorporates restrictions associated

with the specification of the structural equations in the

system. Since the whole system of equations is estimated

simultaneously, 3SLS estimates are more subject to specifi-

cation errors. The list of all variables in the equation

of interest plus the list of all exogenous variables in the

system is needed for 2SLS. However, 3SLS requires the

specification of all zero elements of the parameter matrix

[T'B'], not just the row of that matrix corresponding to the

par ti cular equation. Thus, if an element is hypothesized to

be zero when it is actually non-zero, this affects the 2SLS

estimates of that particular equation only. In the case of

3SLS, estimates in all equations are affected [21, pp.528-529].



For a more detailed discussion of identification in the
case of simultaneous equations, see Johnston [8, pp. 240-
252].







However, the overriding consideration in the choice of

estimation Drocedure was the unavailability of a 3SLS com-

puter program capable of handling a model as large as that

specified in Chapter II. Therefore, 2SLS was used to esti-

mate the parameters in the two models.



Selection of Time Unit and Period


The time unit selected for this study was a month. At

the FOB level, processors generally announce price increases

two weeks in advance of the actual change. This gives

buyers time to make their adjustments within the month.

Also, the nature of the production pattern for grapefruit

ruled out time units of less than a month. The quantity of

grapefruit available in a particular month can be predicted

more reliably than can the quantity available in a particu-

lar week. In other words, the production pattern over time

is more constant from month to month than from weiek to week.

An additional consideration was the availability of

data. Several data series are published on a monthly basis.

While it w~as possible to sum the weekly data series to obtain

monthly observations it w~as not possible to convert the

monthly observations to a weekly basis.







Data

Most of the data used in this study hiad to be trans-

formed in some way before it could be used. The monthly

data, after transformations, are given in Tables 9 to 14.

All prices, w~ith the exception of the retail price of frozen

concentrated orange juice, were deflated by the wholesale

price index (1957-59 = 100). On-tree prices and shipment

data for grapefruit for fresh use are reported on a monthly

basis by the Growers Administrative Committee and Shippers

Advisory Committee [7]. Retail prices of frozen concen-

trated orange juice are reported monthly by Florida Citrus

Mutual [6]. All other prices are reported weekly. Prices

for seedy, white seedless and pink seedless grapefruit

going to processors are reported by the United States Depart-

ment of Agriculture (19], while the corresponding shipment

data are reported by the Grow~ers Administrative Committee

and Shippers Advisory Committee [7]. To obtain a single

price, the price of each of the three types of grapefruit
was multiplied by its respective shipment quantity and the

re sults were summe d. This sum was then divided by the sum

of the shipments for that month to yield a weighted average

price.

FOB prices of processed products are published weekly

by various processors in the form of price cards [1,2,12].

The prices for the different size containers and the various

product forms, such as sugar added or sugarless, are reported.








For this study, the largest-selling container size and form

w~as chosen as the representative one. Since the prices are

reported, on a weekly basis, it w~as necessary to weight the

weekly prices by the respective FOB sales to obtain a single

price for each month. FOB prices for fresh grapefruit are

published as prices for Interior fruit and for Indian River

fruit on a weekly basis by the Growers Administrative Com-

mittee and Shippers Advisory Committee [7]. To obtain a sin-

gle price for each month, the product of the weekly prices

times their quantities were summed and then divided by the

total quantity for the month. After the monthly FOB prices

and on-tree prices were derived, they were deflated by the

monthly wholesale price index to convert them to constant

dollars. The retail price of frozen concentrated orange

juice was deflated by the consumer rice index (1957-59

= 100).

The measure used for income was disposable personal

income per capital, which is not reported directly. The

series wJas obtained by subtracting reported personal taxes

and non-tax payments from personal income each month and

then dividing this by the population of the United States.

Both population and personal income are reported monthly by

the United States Department of Commerce [21], while per-

sonal income per capital was deflated by the consumer price

index to adjust for the effect of inflation on income.








Data on pack, FOB movement and inventories for pro-

cessed products are published in weekly series by the Florida

Canners Association [3,5]. Beginning inventories and quanti-

ties in storage can be taken directly from the series. Pack

and movement figures must be summed over the weeks in the

month. The quantities of canned single-strength grapefruit

juice and canned grapefruit sections, as reported, were in

cases of 24 number 2 cans. Frozen concentrated grapefruit

juice quantities are reported in gallons of 400 brix con-

centrate. To make all of the quantities comparable, they

wvere converted to gallons of single-strength equivalent by

multiplying single-strength juice and canned sections quan-

tities by 3.375 and frozen concentrate juice quantities by

4.0. The conversion factor 3.375 converts cases of 24

number 2 cans to gallons of single-strength juice. The

factor 4.0 converts concentrated juice to single-strength

juice.

The quantities of fresh grapefruit at the FOB and grove

levels are published as a monthly series by Florida Citrus

MIutual [6] as boxes shipped. To convert boxes of fresh

grapefruit to cases of 24 number 2 cans of single-strength

juice, it was necessary to multiply the number of boxes

times the yield of canned single-strength grapefruit juice.

The yield for each month is available in published form from

the Florida Canners Association [4]. To convert the cases

of 24 number 2 cans to gallons it was necessary to multiply

by a factor of 3.375.







The quantity of grapefruit going to processors is the

sum of thle grapefruit, in boxes used in each of the pro-

cossed products. The quantity going to each product is

published by Florida Canners Association [4] on a weekly

basis in terms of cases of 24 number 2 cans. To get a

monthly series, the weekly quantities were summed over the

period of each month. The number of boxes were then ob-

tained by dividing the number of cases packed by the respec-

tive yield for each product.

The shipments of Texas grapefruit are reported monthly

by the Growers Administrative Committee and Shippers Advi-

sory Committee [7].

Finally, the monthly United States Departmnent of A~gri-

culture's estimate of the size of the crop is published in

the weekly report of the Florida Canners Association (3,5].











CHAlPTER IV

STATISTICAL RESULTS



The results of the estimation of the coefficients are

presented in this chapter. The standard errors are given

in parenthesis below the respective coefficients. Consider-

ation of the statistical significance of more than one

coefficient in a particular equation requires a joint

hypothesis. In the absence of a joint hypothesis, the test-

ing of more than one coefficient results in a change in the

probability of a Type I error. Therefore, no statistical
tests were made.



Model II


On-Tree Price Equations

(4-1) PGK = -1.639 + 0.906 PFFG 0.173 GKs
ms ~(0.046) m (0.127) m


(4-2) PGR =-1.797 + 0.665 PFCS 0.039 PFCG
ms (0.067) ms (0.109) ms

+ 0.117 PFFCS + 0.067 GR 0.039 s
(0.088) ms(0.028) ms (0.018)







The equations for the prices of grapefruit for packing

and for processing were normalized on the on-tree price of

grapefruit. The signs of the coefficients were in keeping

with a priori expectations.

The coefficient of the FOB price of fresh grapefruit

(PFFG) indicates that the on-tree price and the FOB price

tend to move together. The importance of the FOB price in

the relationship is shownm by the fact that its estimated

coefficient w~as more than 19 times as large as its standard

error. The coefficient of the FOB price w\as 0.906. The

margin between prices can be examined using the estimated

equation above. K~ere the coefficient to be 1.0, margins

would be unaffected by price levels, for a rise in the FOB

price would correspond to an equal rise in the price that

the growers receive. The coefficient of 0.906 implies that,

as the price level increases, the absolute margin between

the on-tree price and the FOB price increases slightly.

Miore than half of the grapefruit that is processed goes

into the packing of canned single-strength grapefruit juice.

Thus, it was expected that the on-tree price that the pro-

cessors are willing to pay for grapefruit would be affected

more by the canned single-strength juice FOB price than by

the FOB prices of the other two processed products--canned

sections and frozen concentrated juice. This w~as indeed the

case. The coefficient of the F~OB price of single-strength

juico (PFCS) was over 17 times as large as that for the







price of canned sections (PFCG), and almost six times as

large as that for frozen concentrated juice (PFFC). The

signs of the FOB price coefficients were as expected, with

the exception of the FOB price of canned sections.

The year (s) was included as a proxy variable for pro-

cessing costs, which were assumed to increase steadily from

year to year. However, since the coefficient of the year

was opposite of expectations, it may also represent other

variables that have not been included but that also change

steadily over time. One such variable might be changes in

technology that reduce the cost of producing frozen concen-

trated grapefruit juice. Since the on-tree price is

derived from the FOB prices of the three products, a cost-

reducing change in technology would affect the price of the

input, that input being grapefruit.


Pack Equations

(4-3) PCG
ms








(4-4) PFC
ms


= 0.166 0.411 PFCS + 0.755 PFCG
(0.265) ms(0.452) m

-0.133 PFC + 0.184 BCG 0.199 s
(0.346) ms (0.182) ms (0.087)

+ 0.121 m 0.133 m2 + 0.079 GE
(0.929) (0.079) (0.033) m"s


=16.100 + 0.807 PFCS 1.931 PFCG
(1.030) ms (2.235) ms

+ 1.447 PFFC 0.304 BFCm + 0.575 s
(1.389) m"s (0.246) ms 0.366)

-5.821 m + 0.886 m2 0.148 GEm
(2.892) (0.307) (0.139) m








While the signs of the coefficients of the prices in

equation (4-3) were as expected, equation (4-4) was less

satisfactory in this respect. FOB prices entered the equa-

tions to measure tw\o effects. One was the effect that the

current FOB prices have on the pack of the products. The

other was the effect on pack of the FOB prices that the

processor expects to obtain for the products at a later

date. It was shown earlier that the own-price slope should

be positive whilee the cross-price slopes should be negative.

In equation (4-4), the coefficient of the price of canned

single-strength juice (PFCS) had a sign opposite from

expectations. However, its coefficient wias relatively

small compared to its standard error.

Since canned sections is a product of declining impor-

tance and frozen concentrated juice an emerging one, the

negative and positive, respectively, annual trends were in

keeping with a priori expectations.

The net influence of the USDA crop estimate was com-

posed of a negative component from the expected price rela-

tionship and a positive direct component. Since the coeffi-

cient of GEm in equation (4-3) was positive it was con-

cluded that the expected FOB price of the product had a

less important impact on the production decision-maker than

did the current USDA crop estimate. However, the sign of

the coefficient in equation (4-4) wjas negative, implying

the opposite relationship of that above.








Storage Equations

(4-5) SCS =1.458 + 0.280 PFCS +- 1.749 PCS
ms ~(2.044) ms(0.325) m

+ 0.117 s 0.101 GE
(0.690) (0.240) m


(4-6) SCG = 17.280 1.538 PFCG 0.397 PCGs
ms (0.752) ms (0.186) m

+ 0.161 s 0.083 GE
(0.161) (0.058) ms

(4-7) SFC =14.600 0.430 PFFC + 1.008 PFC
ms (11.272) ms(0.141) m

+ 1.014 s 0.369 GE
(0.332) (0.130) m


In equations (4-5) and (4-7), the coefficients for

pack (PCS and PFC) are greater than one. It may appear

unrealistic for inventory to increase by more than the

quantity packed. It becomes much more reasonable w\hen the

meaning of the variables is made clear. A change in inven-

tory, of course, refers to a change in the total quantity

of the product in storage. However, a change in the pack

refers to a change in the rate of pack, and not the change

in the cumulative quantity packed in the year. Consider

the case of canned single-strength juice for December, 1964,

to January, 1965. The pack in December was 1,450,937 cases

of number 2 cans while the pack in January was 1,756,995.

The inventory at the end of each month was 1,618,112 and

2,643,230 cases, respectively. From December to January,

the inventory increased by 1,025,118 cases, the rate of pack







increased by 306,058 cases, and the cumulative pack in-

creased by 1,756,995 cases. Thus, an increase of 306,058

cases in the rate of pack corresponded to an increase of

1,025 ,118 cases in inventory. Thus, it is not unreasonable

for the inventory to increase by more than the rate of

change in pack.

As in the pack equations above, FOB prices of the prod-

ucts were both a reflection of the FOB prices in the current

time period and the expected FOB prices of the products.

The direct effect was expected a priori to be negative,

while it wans expected that producers would respond to

changes in expected prices by adjusting inventories in the

same direction as the price changes. The fact that the FOB

price of canned single-strength juice (PFCS) had a positive

coefficient, while the other twJo FOB prices (PFCG and PFFC)

had negative coefficients implies that the expected FOB

price is relatively more important to processors w~hen making

storage decisions concerning single-strength juice, but

that current prices are more important in decisions con-

cerning the other two products.

The year was included as a proxy for storage costs.

One normally expects storage costs and quantity stored to

move in opposite directions. However, the coefficient of

the year w~as positive in each equation. This indicates that

the variable was possibly measuring the effect of one or

more other variables, in addition to storage costs. One







possible effect in the case of canned sections might be a
declining sales trend and a failure to fully coordinate

production with sales, with a resulting build-up of inven-

tories. For the other two products, it is possible that

the year variable was also measuring the increase in storage
needed to meet increased demand.

The USDA crop estimate (GE) was found to have a negative

relationship with storage. This was expected. Since the

crop estimate entered the relationship via the expected

price equation with an expected negative coefficient in that

equation, the variable was also measuring the effect of the

expected price on storage. An increase in the crop esti-
mate would presumably affect storage decisions through the

expectation of a fall in the whole spectrum of grapefruit

product prices. This would cause a desire on the part of

producers to sell more of the products in the current time

period and put less into storage for sale at a later date
when prices are expected to be low~er.

FOB Demand

(4-8) QFCS = -10.380 -0.549 PFCS + 0.456 PFFC
ms ~(0.509) ms(0.856) m
+ 6.590 IN 0.085 POJ
(4.097) ms (0.161) ms

+ 0.092 QFCS 0.338 m -0.027 m
(0.274) m-1,s (1.350) (0.138)







(4-9) QFCG
ms








(4-10) QFFC
ms








(4-11) PFFG
ms


=0.335 0.554 PFCG 0.080 PFFG
(0.358) ms (0.099) ms

+ 0.643 INs + 0.334 D1 0.272 TG
(1.066) ms(0.216) s(0.216) ms

+ 0.607 QFCG + 0.898 m 0.105 m
(0.149) m-1,s (0.409) (0.042)


= 6.382 + 0.290 PFCS + 0.076 PFFC
(0.221) ms (0.420) ms

-1.531 IN 0.063 POJ 0.284 D25
(1.605) m (0.070) ms (0.321)

+ 0.212 QFFC 1.109 m +0.149 m
(0.240) m-1,s (0.526) (0.055)


=8.257 0.042 QFFG -0.368 QFCG
(0.075) ms 0.234) m
+ 0.441 TG 2.346 IN + 0.817 m
(0 .418) ms(181 ms(06)

-0.094 m2 + 1.963 D3s
(0.679) (0.394)s


The estimation of the FOB demand equations yielded

very acceptable results. The own-price slopes for single-

strength juico, canned sections and fresh grapefruit (PFFG)

were negative, as theory would lead one to expect. The own-

price slope of frozen concentrated juice (PFFC), however,

was positive, indicating that there is possibly an identifi-

cation problem whereby supply has not been completely iso-

lated from demand. However, the estimated coefficient for

the FOB price of frozen concentrated juice was considerably

smaller than its estimated standard error.








In equations (4-8) and (4-10), the signs of the coeffi-

cients of two products hypothesized as competing were posi-

tive as expected, implying that single-strength juice and

frozen concentrated juice are indeed substitutes. In both

equations, the coefficient of the price of concentrated

orange juice (POJ) w~as negative. However, the estimated

coefficient in each case was less than its estimated stan-

dard error.

It was anticipated that fresh grapefruit and canned

grapefruit sections would be substitutes for one another.

Also, since it has been shown that fresh Texas grapefruit

(TG) and fresh Florida grapefruit substitute for one another

to some extent [25], it was expected that canned sections

and fresh Texas grapefruit would also substitute for one

another. While the signs of the coefficients for fresh

grapefruit in equation (4-9) and Texas grapefruit in (4-11)

were the opposite of expectations, Texas grapefruit was

found to substitute for canned sections.

Seasonality in the demand for each of the products

was found to exist. For single-strength juice and canned

sections, there is a tendency for demand to first increase

and then decrease as the season progresses. The opposite

seasonal effect was found for concentrated juice and fresh

grapefruit with the demand increasing later in the season.

Disposable personal income (IN), as expected, exerts a

positive influence on the demand for the first two products.







The negative coefficient for income in equation (4-10) was

unexpected. However, the estimated coefficient of the dis-

posable personal variable was less than the estimated stan-

dard error for that variable.

The coefficient of income in equation (4-11) was also

negative. It is possible that consumers shift away from

fresh grapefruit in favor of the more convenient processed

grapefruit products as their income increases. Weisenborn,

M~cPherson and Polopolus found that consumption of fresh

oranges decreases with increases in income [26, pp. 19-20].

Since the value of the dummy variable (D2) in the con-

centrated juice equation was 1 in the early years of the

study, the negative coefficient was as expected for an emerg-

ing product. The coefficient indicates that the demand has

shifted upward during the later years of the study. Though

canned sections has declined in importance, the sign of the

coefficient of the dummy variable (DI) indicates that the

demand for that product has also shifted upwdards. The value

of this variable was 0 in the earlier years of the study.

This shift after the 1966-67 crop year possibly resulted

from the large crop in 1966-67 and the resulting low prices.

With the low prices, consumers may hiave become attached to

the products and continued buying them in succeeding years.

The demand for fresh grapefruit shifted upw~ards during

the 1967-68 crop year. This possibly w~as caused by the fact

that the quality of the citrus crop in that year was








especially good, resulting in consumers demanding more of

the product at each price.


Model II


Storage Equations

(4-12) SCS
ms





(4-13) SCG S





(4-14) SFC
ms


= 43.142 6.235 PFCSm + 0.980 s
(3.517) ms(0.925)

S0.390 Q 0.770 m
(-.619) s(1.931)


=4.060 0.530 PFCG + 0.142 s
(0.762) ms(0.119)

+ 0.076 Q -0.952 m
(0.041) s (0.194)


=-36.765 + 3.474 PFFC 1.262 s
(1.476) ms(0.312)

+ 1.094 Q_ 0.940 m
(0.166) s (0.483)


In theory, the storage equations for M~odel II were

similar to those for Mlodel I. The primary difference w~as

that there was no pack during the months in Mfodel II.

In the first two equations, the negative coefficients

for the prices of the products imply that the current FOB

price is a more important consideration in the decision-

making process than is the expected price of the product.

However, since M[odel II covered only the last three months

of each season, it is possible that producers assume that

the current price is the expected price.







As explained earlier, the positive trend for sections

is possibly due to the fact that the processors have not

fully coordinated their storage decisions with the declining

importance of the product. The negative coefficient for the

year in equation (4-14) was consistent with theory, since

the year was included as a proxy variable for storage costs.

In each equation, the month had a negative coefficient,

as expected. Since there is no pack, all of the sales must

come from inventory, so it is expected to decrease from

month to month. The coefficients of the quantity of grape-

fruit in a year were as expected in the latter two equations.


FOB Demand

(4-15) QFCS
ms


=1.088 1.018 PFCSm + 0.769 PFFCm
(0.841) ms 2.064) m

+ 0.148 QFCS +- 2.017 INmS
(0.74) m-1,s (7.695) s

-0.121 POJ
(0.307) m


(4-16) QFCGmIs = 2.0988 0.554 PFCGm 0.581 QFCGm-,
(0.173) (0.227)

+ 0.879 IN
(0.338) m


(4-17) QFFCms


= -9.320 0.718 PFFCS + 0.327 PFCSm
(0.996) ms(0.365) m

+ 0.200 QFFC + 4.224 INs
(0.92) m-1,s (4.004) m

+ 0.092 POJ
(0.1.54) m





61


The estimated coefficients in the equations for FOB

demand for both single-strength juice and canned sections

for Model II were very similar to those for Mlodel I, especi-

ally with respect to signs. However, the equation for

frozen concentrated juice was closer to expectations than

was the equation in Model I. The own-price slope for con-

centrated grapefruit juice was found to be negative. The

resulting demand elasticities for Model I and M~odel II are

compared in the next chapter.









CHAPTER V

ECONOMIIC IMPLICATIONS



This chapter is divided into three sections. In the

first section, estimates of elasticities and implications

based on these estimates are presented. The second section

deals with an analysis of the derived reduced forms for the

two models. Finally, in the third section, the results of

short-term forecasting based on the reduced forms are pre-

sented.



Elasticities


The estimates of the demand elasticities and cross elas-

ticities for grapefruit products at the FOB level for Mlodel I

are presented in Table 2.1 The elasticities for processed

grapefruit products at the FOB level were calculated directly

from the demand equations as estimated. Since the FOB demand

equation for fresh grapefruit was estimated with price as a

function of quantity, it w~as necessary to solve it for the

quantity demanded in terms of prices and income.


1Elasticity estimates should be interpreted with caution
in the case of simultaneous equation models. Elasticities
are based on the assumption of ceteris paribus. However, in
a simultaneous equation model, a change in an endogenous
variable would result in changes in other endogenous variables
wJithin the system to restore the equilibrium. Hence, the
assumption that all other endogenous variables remain con-
stant is not fulfilled.
62








Table 2. Elasticities and Cross Elasticities of
Demand at the FOB Level for Grapefru~it
in Various Forms, Computed at Mrean V'alues
of the Variables, Mlodel I, 1964-71



Elasticities or Cross Elasticities
Normaizedwith Resp3ect to:
Variable PFCS PFCG PFFC PFFG POJ IN

QFCS -0.392 -- 0.309 ---0.268 3.216
qFCG -- -2.101 -- -0.270 -- 1.219
QFFC 0.654 -- 0.163 -- -0.622 -2.357
QFFG -- 2.874a -- -12.268a -- -1.667a


aComputed by solving the estimated demand function
for the quantity in terms of prices and income.





The cross elasticity estimates presented in Table 2

indicate that none of the products are very strong substi-

tutes for one another at the FOB level. A positive cross

elasticity is required for substitute goods and a negative

one for complementary goods. Based on the measures given in

Table 2, frozen concentrated grapefruit juice and canned

single-strength juice are substitutes for each other. This

is really not surprising since they are simply two forms of

the same product.

The cross elasticity measures for canned sections and

fresh grapefruit conflict somewhat. One elasticity measure

indicates that the two products are substitutes, while the

other indicates that they are complementary.








Based on the cross elasticity estimates, concentrated

orange juice is shown to be complementary to both single-

strength juice and frozen concentrated juice. However, as

indicated earlier, the estimated coefficients for concen-

trated orange juice were less than their respective esti-

mated standard errors.

The income elasticities given in Table 2 show~ that in

a period of rising income, the quantity demanded of canned

single-strength juice and canned sections would increase,

while the quantity demanded of frozen concentrated juice

and fresh granefruit would decrease. An increase in dis-

posable personal income per cavita of 1 percent would result

in increases in the FOB demand of single-strength juice and

canned sections of slightly over 3 percent and 1 percent,

respectively. Also, the FOB demand for frozen concentrated

juice and fresh grapefruit would decrease by more than 2

percent and 1.5 percent, respectively.

The elasticities and cross elasticities of demand for

the three products in MIodel II are given in Table 3. In

each case, the equation was normalized on the quantity

variable for estimation, making the price-quantity slope,

as estimated, appropriate for computing elasticities

directly.

The elasticities for M~odel II are much closer to the-

oretical expectations than were those for M~odel I in that

all elasticity measures have the expected signs. In








Table 3. Elasticities and Cross Elasticities of
Demand at the FOB Level for Grapefruit
in Various Processed Forms, Computed at
Mean Values of the Variables, Mlodel II,
19641-70



Elasticities or Cross Elasticities
Normalized with Respect to:
Variable PFCS PFCG PFFC IN

QFCS -1.254 -- .825 1.532
QFCG -- -2.636 -- 2.094
QFFC 1.097 ---2.096 8.734


contrast to Mlodel I, all of the products have negative

demand elasticities.

The demand for each of the products is shown to be more

elastic during the months of M~odel II. During these months,

the demand for canned sections and frozen concentrated

juice is more responsive to changes in income. The demand

for single-strength juice responds about half as much as

during the months of Mlodel I.

As in Model I, canned single-strength juice and frozen

concentrated juice are shown to be substitutes. Both elas-

ticity measures are larger than their respective measures

in Model 1, implying that, during the months in M~odel II,

consumers respond more readily to changes in the prices of

the substitutes.







The elasticities of the two models can be compared.

In general, consumers are more responsive to changes in

prices and income during July, August and September th~an

during the other nine months of th-e year. This possibly

results from the importance that consumers place on the cold-

preventing properties inherent in citrus products. During

the summer months, consumers are less interested in prevent-

ing colds than they are in the winter months, so they may

choose to substitute carbonated beverages and other fruit

drinks for the grapefruit beverages as thirst quenchers.

Thereforec, during the months of M~odel II, there are more

substitute prIoducts available, which typically has the

effect of making con-sumers more responsive to price.



Implications fr~om th~e
Derived Reduced Form Estimates


Reduced form equations describe each endogenous variable

in terms of all exvogenous variables in the system. The

direct reduced form is identical to the first stage of the

two-stage least squares procedure. It is obtained from


Y = X + 9


where r is the matrix of direct estimates of the reduced

form. The derived reduced form estimates are obtained from


Yi = -B yX + D


where -B y = is the matrix of derived reduced form esti-








The derived and direct reduced form estimates for

Model I are given in Tables 4 and 15, respectively. Those

for Mlodel II are given in Tables 5 and 19, respectively. In

this section, implications based on the derived reduced form

are discussed for M~odel I. A similar discussion follows for

Model II, at which time the two models are compared.

In Model I, increases in personal disposable income

per capital would increase the FOB demand for each of the

products, with the exception of canned sections. For single-

strength juice and frozen concentrated juice, the FOB prices

and quantities demanded would increase. Also, the FOB3 price

of fresh grapefruit would increase. For canned sections,

the FOB price would increase, but there would be a corre-

sponding decrease in the quantity demanded.

The increases in revenue would not be restricted to

processors. Growers would also benefit. Whereas the quan-

tity of grapefruit going to processing and to packing is

predetermined, increased on-tree prices would mean increased

returns for the growers. Thus, in a period of rising in-

come, such as has consistently occurred in recent years, the

Florida grapefruit industry as a whole would receive in-

creased revenues.

The effect of beginning inventories can also be exam-

ined. If the industry w~ere to initiate a program to in-

crease inventories, perhaps to be able to provide more of

the products during the months of Mlodel II or to provide a

cushion in the event of a freeze, the result would be an














Exogenous Endogenous Variablea
Variable PGR PGK PFCS PFCG PFFC PFFG


Table 4. Coefficients of Derived Reduced Form
Equations for M~odel I


IN
BCS
BCG
BFC
m
m2


TG
POJ
GE
Dl
D2
D3

QFCSb
qF~cb
QFFCb
GR
GK

QFFG


7.149
-0.810
-0.437
1.285
5.585
-0.684
-1.187
-0.078
-0.002
0.315
0.085
0.305
-0.040
0.075
0.154
-0.227
2.823
0.000
0.001


1.959
-0.047
-0.102
0.062
0.806
-0.085
-0.027
0.481
-0.001
0.002
-0.089
0.014
1.820
0.004
-0.161
-0.011
0.160
-0.173
-0.039


10.208
-1.072
-0.600
2.143
7.911
-0.972
-1.962
-0.109
0.025
0.577
0.119
0.529
-0.055
0.100
0.216
-0.394
3.647
0.000
0.001
-57.386


2.372
-0.248
-0.535
0.325
1.852
-0.172
-0.142
-0.125
-0.005
0.009
0.136
0.074
-0.064
0.023
0.247
-0.055
0.845
0.000
0.001
-4.263


4.262
-0.918
-0.496
-1.090
3.392
-0.378
1.286
-0.089
-0.161
-0.583
0.097
-0.375
-0.045
0.085
0.176
0.280
3.122
0.000
0.001
12.216


2.163
-0.052
-0.112
0.068
0.889
-0.093
-0.030
0.532
-0.001
0.002
-0.098
0.016
2.009
0.005
-0.178
-0.012
0.177
0.000
-0.043
7.855


Constant -38.353 5.141













Exogenous Endogenous Variablea
Variable PCS QFCS,SUCS SCS PCG QFCG,SUCG


Table 4. (continued)


IN
BCS
BCG
BFC
m
m2

s
TG
POJ
GE
D1
D2
D3

QFCSb
QFC~b
QFFCb
GR
GK

QFFG


-7.723
1.508
0.086
1.433
0.327
-0.083
-1.643
0.015
0.221
0.670
-0.016
0.418
0.008
-0.139
-0.029
-0.312
-0.589
0.000
-0.001


2.924
0.171
0.104
-1.674
-2.462
0.335
1.664
0.019
-0.172
-0.583
-0.021
-0.461
0.010
0.077
-0.038
0.344
-0.581
0.000
-0.001


-10.647
2.338
-0.018
3.107
2.789
-0.418
-3.307
-0.005
0.393
1.279
0.005
0.880
-0.002
-0.216
0.009
-0.656
-0.009
0.000
0.000


-2.968
0.375
0.092
-0.490
-2.181
0.187
0.329
-0.038
0.007
-0.074
0.041
-0.112
-0.019
-0.035
0.075
0.083
-1.275
0.000
0.000


-0.499
0.142
0.305
-0.185
-0.198
-0.002
0.081
-0.245
0.003
-0.005
0.266
-0.042
-0.125
-0.013
0.484
0.031
-0.482
0.000
0.003


Constant -16.136 26.708


42.884 18.564 2.101













ExognousEndogenous Variablea
Variable SCG PFC QFFC,SUFC SFC


a~,ariables are as defined in Chapter II.

bQuantity lagged one month.


Table 4. (continued)


-2.469
0.233
0.787
-0.305
-1.982
0.190
0.248
0.207
0.005
-0.068
-0.225
-0.069
0.105
-0.022
-0.410
0.052
-0.793
0.000
-0.002
16.464


9.826
-1.713
-0.169
-0.779
1.898
-0.114
1.127
0.025
-0.203
-0.544
-0.027
-0.259
0.013
0.158
-0.049
0.193
5.830
0.000
-0.001
-4.315


1.753
-0.381
-0.212
0.538
1.443
-0.162
-0.470
-0.038
-0.068
0.123
0.042
-0.159
-0.020
0.035
0.076
0.119
1.296
0.000
0.000
-9.314


8.073
-1.333
0.043
-0.317
0.454
0.047
1.597
0.063
-0.135
-0.667
-0.069
-0.100
0.032
0.123
-0.125
0.074
4.535
0.000
-0.001
4.999


IN
BCS
BCG
BFC
m
m2

s
TG
POJ
GE
Dl
D2
D3

QFCSb
QFCcb
QFFCb
GR
GK

QFFG
Constant
















































































CO U
UUL
m m 0


SOL4CA
uoECV ACTCYC








increase in the level of pack. Also, FOB sales would be

increased. However, perhaps because the impetus would come

from the supply side, the FOB prices of each of the prod-

ucts would decrease. The price of single-strength juice,

which accounts for about 55 percent of the grapefruit pro-

cessed, would decrease by approximately one-third, while

the movement would increase by less than 4 percent. In

addition, though not given in the reduced forms, there would

likely be increases in the cost of storing the increased

inventories. Therefore, during the months of Mlodel I, it

appears that revenue to producers would decrease. However,

as shown later, revenues during the months represented by

Modell II would increase.

Increases in Texas grapefruit is shown to adversely

affect the Florida industry. Increases in Texas grapefruit

shipments would depress prices for all three processed

grapefruit products and, consequently, the price that

growers receive for grapefruit going to processing would

decline. Also, the price of grapefruit for fresh sales

would decrease. Fortunately for the Florida industry, Texas

shipments are annually only about 3 percent as large as the

Florida crop.

Based on the coefficients for the FOB prices in the

reduced form equations, increases in the price of frozen

concentrated orange juice would adversely affect the prices

of canned sections and frozen concentrated grapefruit juice.

The fresh market for grapefruit would be unaffected by

changes in the price of frozen concentrated orange juice.








Finally, changes in the FOB quantity of fresh grapefruit

would have virtually no effect on the other products in the

study. The effect of a decrease in the FOB quantity, per-

haps caused by a freeze, would be an increase in both the

on-tree and FOB price for fresh grapefruit.

For Model II, increases in income would result in in-

creased demand for single-strength juice and canned sections,

with prices anid quantities both increasing. Income increases

would result in an increased volume of sales of frozen con-

centrated juice; however, there would be a net decrease in

price. Since frozen concentrated juice represents a rela-

tively small share of the grapefruit market, rising income

would clearly result in increased revenues to the industry.

Whereas in Mlodel I, single-strength juice w~as shown to

be a substitute for frozen concentrated orange juice, the

reduced form for M~odel II tends to substantiate the findings

based on the cross elasticity for the tw\o products. The

cross elasticity was negative, indicating complementarity.

Were the price of the orange product to increase, both the

quantity and the price of single-strength juice would de-

crease while the storage of the product would increase.

Further, the price of frozen concentrated grapefruit juice

would decline while the FOB movement would increase.

In Model I, it w~as shown that the gains from increased

inventories would be questionable. However, if they were

to be increased during the months in Mlodel I and w\ere carried

over to give high-er inventory levels during the months of








Model II, net revenue to producers would increase. For

single-strength juice and canned sections, sales would be

increased, while prices would decline. However, based on the

elasticity estimates decreases in the prices would be more

than offset by increases in sales.


Short-Term Forecasting


Forecasts of the values of the variables endogenous to

the Florida grapefruit industry can prove invaluable to the

growers, packers and processors wiithin the industry by

reducing uncertainties. Based on the expected values of the

exogenous variables, the decision makers within the industry

could determine the economic consequences of following their

established decision criteria. For example, once the size

of the grapefruit crop for the coming year is predicted, the

values of all of the endogenous variables can be forecast.

This assumes that it is possible to obtain acceptable pre-

dictions for the other exogenous variables.

To avoid the necessity of having to actually simultane-

ously solve the equations in the model to determine the

values of the endogenous variables each time a change occurs

in the exogenous variables, the reduced form of the system

is used. The forecasts based on these reduced form equa-

tions are only for the short term. W\hen forecasting w~ith

a static model, the assumption is made that the structure

of the system will remain as it was during the period of

data used for estimation of the structure. Thus, a model







that yields satisfactory forecasts for the short term may

be inadequate for long-term predictions because of changes

in the structure.

There are several methods that can be used to evaluate

the resulting forecasts. Each method requires that pre-

dictions be made for a period in which the values for both

the endogenous and exogenous variables are known, so that

the model's predicted values can be compared with the actual

values that occurred. To avoid biasing the comparison, data

used in testing the model should not have been used in the

estimation of the model. One test involves the ability of

the model to predict turning points. The turning points

that are predicted are compared with the turning points that

actually occurred. This test w~as inappropriate to the pros-

ent study because of the lack of turning points over the

r-ange of the data for each production season.

Another test attempts to give an objective measure of

how close the predictions are to the actual values by con-

sidering the magnitude of the predictions relative to the

actual values. In addition, the ability of the model to

predict changes in the endogenous variables is also included.

This measure is known as Theil's inequality coefficient

[16, p. 28 and 17, p. 32].


C(P-A)
U. = v

(A-j 1 Tj-Aj-0)










C(P -A )


2 -(A -jQ


where P. is the predicted value of the endogenous variable

and A. is the actual value.2

U1 is confined to values between 0 and 1. A value of
0 imlie tht P = A.j for all j, so that the forecasts are

perfect. A value of U1 = 1 implies the extreme case where
nonzero predictions are made of actual values that are 0 or

vice-versa (i.e., P. = 0 for all j or A. = 0 for all j).
Or it means that there is a nonpositive proportionality
between the P's and the A's.

A value of 0 for U2 likewise denotes perfect forecast-

ing. If a no-change extrapolation is applied (i.e., that

the value in time period j is predicted to be the same as

occurred in time period j-1), then P = Aj-1. In thzat case,
the numerator and the denominator are equal and UZ = 1. The


The coefficients, U1 and U2, are typically given as


1 i 1 V
and
U2 i-A )2 (A )


where the Ai and Pi refer to changes in the actual value
and the predicted value, respectively. The A- and P- that
annear in the formulations in the text are ac ual va ues,
rather than changes. For the derivation of the formulations
in the text, see Stekler [15, p. 4139].








coefficient has no upper bound, so a value greater than 1

implies that the forecast is worse than could be obtained

by using a no-change extrapolation.

Thus, in the cases of both U1 and U2, values close to
0 are indicative of accuracy in forecasting, whereas values

approaching 1 indicate that a no-change extrapolation would

have performed about as well. If U2 > 1, a no-change

extrapolation would have been preferable.

The predicted values of the endogenous variables for

Model I, based on the estimated reduced form, are given in

Table 6. Table 6 also includes the actual values for the

variables and the deviations of the predicted values from

the actual values. Predictions based on the estimated

reduced forms rather than on the derived reduced forms are

presented in the text because, evaluated on the basis of the

inequality coefficients, they were closer to the actual

values. The calculated inequality coefficients, U1 and U2'

are given in Table 7. While the discussion in the text is

based on the results presented in Tables 6 and 7, predicted

values and inequality coefficients based on the derived

reduced forms are presented in Tables 16 and 17. Data used

in forecasting are given in Table 18.

Based on the inequality coefficients, the model pre-

dicted the storage of canned single-strength juice fairly

well. Also, the values for storage and FOB quantity of

frozen concentrated juice were fairly accurate. However,








Table 6. Endogenous Variables: Actual Values,
Predicted Values Based on the Reduced
Form Estimated Directly and Deviations,
December, 1971, Through Mlarch, 1972



Month

Variable December January February Mlarch


.92
.41
.51

1.54
1.61
-.07


.92 .88
.23 -.16
.69 1.04


Actual
Predicted
Deviationb

Actual
Predicted
Deviation

Actual
Predicted
Deviation

Actual
Predicted
Deviation

Actual
Predicted
Deviation

Actual
Predicted
Deviation

Actual
Predicted
Deviation


.93
.24
.69

1.49
1.60
-.11


1.44
2.00
-.56


1.34
2.13
-.79


4.72
3.85
.87

5.46
5.01
.45

3.97
3.37
.60

5.40
3.22
2.18

10.007
11.264
-1.256

5.494
8.539
-3.044

10.511
8.753
1.759

2.706
3.073
-0.367


4.58
3.30
1.28

5.30
5.28
.02

3.85
3.61
.24

5.24
3.10
2.14

11.853
14.476
-2.624

5.087
10.109
-5.022

17.277
14.910
2.367

2.064
3.979
-1.915


4.51
3.15
1.36

5.37
5.42
-.05

3.80
4.07
-.27

5.10
3.45
1.65

13.202
14.866
-1.664

4.978
10.629
-5.651

25.501
21.546
3.954

1.361
3.317
-1.956


4.07
2.38
1.69

5.41
5.80
-.39

3.83
4.27
-.44

4.90
3.35
1.55

15.416
21.338
-5.923

6.728
13.892
-7.164

34.188
32.984
1.204

0.448
3.622
-3.174


gal.)


PFCS, SUCS Actual
(mil. gal.) Predicted
Deviation

SCS Actual
(mil. gal.) Predicted
Deviation

PCG Actual
(mil. gal.) Predicted
Deviation












Month
Variablea December January February March

QFCG, SUCG Actual 0.935 0.824 0.978 0.948
(ml.ga.)Predicted -0.599 0.301 0.853 0.945
Deviation 1.535 0.523 0.126 0.003

SCG Actual 4.610 5.850 6.233 5.732
(mil. gal.) Predicted 6.496 8.265 8.292 8.887
Deviation -1.885 -2.415 -2.059 -3.155

PFC Actual 4.528 3.495 4.043 13.891
(mil. gal.) Predicted 0.172 -2.479 -0.121 4.518
Deviation 4.356 5.974 4.164 9.373

QFFC, SUFC Actual 2.248 1.265 1.389 2.867
(mil. gal.) Predicted 2.328 1.583 1.839 1.884
Deviation -0.080 -0.319 -0.451 0.984

SFC Actual 6.871 9.102 11.756 22.779
(mil. gal.) Predicted 2.437 2.817 7.154 14.406
Deviation 4.434 6.284 4.601 8.373


aVariables are as defined in Chapter II.

Actual value minus predicted value.


Table 6. (continued)








Table 7. Theil's Inequality Coefficients for
Predicted V'alues of the Endogenous
Variables, Based on Reduced Form
Estimated Directly, December, 1971,
Through Mlarch, 1972


U~b

33.5867
7.931.8
5.3877
2.1762
4.2819
10.6775
2.1020
5.7869
0.3466
3.1768
2.7952
3.2185
1.1968
0.6337
0.9896


Ula

0.9520
0.9919
0.7407
0.5946
0.7445
0.8440
0.5168
0.7851
0.2034
0.9978
0.6495
0.6858
0.6662
0.4045
0.6817


Endogenous Variable

PR
PK
PFCS
PFCG
PFFC
PFFG
PCS
QFCS, SUCS
SCS
PCG
QFCG, SUCG
SCG
PFC
QFFC, SUFC
SFC


aUI = P-A) 4C (AAj- >2

j=2 j=2

where A. = actual value (j = 2, 3, 4)

P. = predicted value (j = 2, 3, 4]


bU2 =~ j ~ ~ 4 P A 2 (A -Aj-
j=2 j=2


+4 (P -Aj-1 2c
;=7





81


for all the other variables, the values of U~2 w~ere > 1. :

This implies that a no-change extrapola-tiopn~would have beenrk

preferable to the predicted values.

If evaluated with respect to the values of UI, the

model performs somewhat better. The clcosr- the..value;EiF. oE

is to 1, the closer the predictions get to th~e ;ro -chang~e--

extrapolation value. Eight of the 18 variables had U1

values less than 0.7, indicating that the predictions may

not be as bad as indicated by the U2 values. Th7iS is-no~t` -'

to imply that 0.7 is the value below which the predictive

ability of the model is acceptable; there is no.test.to : .

indicate how much better a particular value of U1 is thaa r

another. Overall, with the few exceptions noted, it appears

that the predictive ability of Mlodel I is not very sharp..:

The predicted values based on the derived reduced forms,

actual values and deviations for Mlodel II are presen~ted.ia> .

Table 8, while the predictions based on thze,cs;sinrtted-1..

reduced form are presented in Table 20. The data used in

obtaining the predictions are given in Table:-2"p.; -:-No ingrt-.

equality coefficients wecre calculated foS.-Medell II be-casuse

there w~ere only tw~o months of data available that were ,not ..

used in the estimation. Any attempts to draw~ conclusions

as to the predictive ability of the model would be sus.pect,

However, several observations can be made. In general, the

predictions based on the two reduced forms did not.dItEfes

widely, though, based on observation alone, the precdictions
















Month

Variable August September


aActual value minus predicted value.


Table 8. Endogenous Variables: Actual
Predicted Values Based on the
Reduced Forms and Deviations,
and September, 1971


Values,
Derived
August


4.51
3.53
0.98

5.22
5.90
-.68

3.80
3.09
0.71

3.875
3.953
0.078

0.751
0.594
0.157

2.099
1.831
0.268

9.798
9.719
0.078

3.100
3.257
-0.157

8.899
10.167
-1.268


4.68
3.88
0.80

5.42
5.72
-.30

3.941
2.56
1.38

4.454
3.042
1.412

0.987
0.703
0.284

2.710
2.504
0.206

5.343
6.756
-1.412

2.113
2.397
-0.284

7.189
7.395
-0.206


Actual
Predicted
Deviations

Actual
Predicted
Deviation

Actual
Predicted
Deviation

Actual
Predicted
Deviation

Actual
Predicted
Deviation

Actual
Predicted
Deviation

Actual
Predicted
Deviation

Actual
Predicted
Deviation

Actual
Predicted
Deviation


PFCG
($/gal.)


QFCS, SUCS
(mil. gal.)


QFCG, SUCG
(mil. gal.)


QFFC, SUFC
(mil. gal.)


SCS
(mil.


gal.)



gal.)



gal.)


SFC
(mil.





83


using the derived reduced form were slightly more accurate.

Also, both reduced forms for Model II predicted better than

did either reduced form for Model I.













CHAPTER VI

SUMME-ARY AND CONTCLUSIONTS



The first part of the present chapter consists of a

summary of the objectives and findings of the study. Con-

clusions based on the findings are presented in the second

section. Finally, suggestions are made as to further

research that is needed for a fuller understanding of the

Florida grapefruit indus try.



Summary


The objectives of this study were (1) to quantitatively

describe, by means of an econometric model, the Florida

grapefruit industry from the grower transactions at harvest

to the FOB level for canned single-strength juice, canned

sections, frozen concentrated juice and fresh grapefruit;

(2) to measure the effects of factors exogenous to the

Florida grapefruit industry on the production and sale of

the four products listed above; and (3) to develop a model

for forecasting values of the variables endogenous to the

Florida grapefruit industry.

Twio models were developed: one for the months in which

fruit was harvested and thus available for processing and








for fresh pack (Mlodel I) and one for the months when no

fruit was harvested (Mlodel II). Model I consisted of 11

behavioral equations and 7 identities for the crop years

from 1964-65 to 1970-71. Model II consisted of six behav-

ioral equations and six identities for the crop years

1963-64 through 1969-70. Included in Mlodel I were behav-

ioral relationships for (1) on-tree prices for grapefruit

for packing and for processing, (2) pack for each of canned

grapefruit sections and frozen concentrated grapefruit

juice, (3) storage of each of the processed products, and

(4) FOB demand for each of the processed products, as well

as FOB demand for fresh grapefruit. The behavioral rela-

tionships for Mlodel II include (1) storage of each of the

processed products and (2) FOB demand for each of the pro-

cessed products. All of the behavioral equations were over-

identified and w~ere estimated using two-stage least squares.

Monthly data w~ere used.

The processor and packer on-tree price equations were

each formulated w~ith the on-tree price as a function of thle

other variables. All of the other equations were normalized

on quantity. Both the quantity demanded and the prices of

the products to be derived from the fruit were shown to

affect the prices that the buyers were willing to pay, Also,

for fresh fruit, the margin between the on-tree and FOB

price was found to increase with advances in the price

level. The year was also included in the equation for the

price of fruit for processing.








The packs of canned sections and frozen concentrated

juice were hypothesized to be a function of the FOB price

of the product and the FOB price of the other two products

that compete for the fruit, as well as the inventory level

of the product and the USDA estimate of the size of the

grapefruit crop for the year. The year was included to cap-

ture the effects of the emergence and decline of frozen con-

centrated juice and canned sections, respectively. Included

in each equation w~ere price expectation relationships con-

sisting of the USDA crop estimate (to reflect expected

supply) and the FOB price of the product (to reflect

expected demand). The results did not indicate that expected

prices influence pack decisions.

The storage equations also contained expected price

relationships. Generally, the results did not indicate

that expected prices influence storage decisions. Not sur-

prisingly, the quantity of each of the products that was

packed wvas found to affect the storage of the products in

Model I. Also, the equations included the year and the USDA

estimate. In Mlodel II there was no pack, so the pack vari-

ables were omitted.

In Model I, the FOB demand for each of the products

was estimated with the quantity of a product demanded as a

function of its FOB price, the prices of substitutes, dis-

posable personal income per capital, the FOB quantity in the

previous month and the month. In Mlodel II, the month








variable dropped out because it covered such a short period

of tine. Seasonality in the demand for the products wvas

found to exist. Also, generally, income had a positive

effect on demand. W~ith the exception of frozen concentrated

juice, the own-price slopes were negative. It was suggested

that the positive own-price slope for concentrated juice

resulted from an identification problem.

The estimates of the structural coefficients, average

prices and average quantities were used to calculate price

elasticities. Also, measures of average disposable personal

income per capital were used to calculate income elasticities.

For M~odel I, the price elasticities of demand obtained at

the FOB level were -0.392 for single-strength juice, -2.101

for canned sections, 0.163 for frozen concentrated juice

and -12.268 for fresh grnpefruiit. The income elasticities

for the first two products listed above were positive, while

they wecre negative for the other twao products. Based on the

cross elasticities, single-strength juice and frozen concen-

trated juice were found to be substitutes. Cross elastici-

ties for single-strength juice and concentrated grapefruit

juice with respect to frozen concentrated orange juice were

-0.268 and -0.622, respectively. For Mlodel II, the demand

elasticities were -1.254, -2.636 and -2.096 for single-

strength juice, canned sections and frozen concentrated

juice, respectively. The income elasticities for the prod-

ucts were all positive. Cross elasticities indicated that








single-strength juice and frozen concentrated grapefruit

juice were substitutes.

Direct and derived reduced form estimates were obtained

for the two models. Implications of the derived reduced

form estimates were discussed.

Finally, predictions were obtained for each of the

models using both the estimated and derived reduced forms.

Predictions were made for December, 1971, to March, 1972,

for Model I and for August and September, 1971, for Mlodel II.

Model I predictions were evaluated using Theil's inequality

coefficients. The reduced form estimated directly produced

more accurate predictions that did the derived reduced form

estimates. Because there wrere only tw\o data points, the

predictions for Mlodel II were not evaluated. Based on

observations, however, the derived reduced form estimates

appeared to give more accurate predictions that did the

reduced form estimated directly. Also, the predictions for

Model II appeared to be considerably more accurate than

those for M~odel I.



Conclusions


Based on the results obtained in the study, the follow~-

ing conclusions were drawn.

(1) During periods of rising disposable personal
income per capital, such as has occurred in
the years included in the study, both growers
and processors experience increased returns
through increases in prices and sales.




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