A SEASONAL COINTEGRATION APPROACH MOHAMMED IBRAHIM

THE RELATIONSHIP BETWEEN PECAN PRICE AND COLD STORAGE INVENTORIES:

A SEASONAL COINTEGRATION APPROACH

by

MOHAMMED IBRAHIM

(Under the Direction of Wojciech J. Florkowski)

ABSTRACT

Little is known about the behavior of shelled pecan prices and the pivotal role the sheller

plays in the pecan industry. Available literature on pecans is mostly concentrated on pecan

growers and the prices they receive. Although agricultural data are known to have some form of

seasonality, economists frequently model by assuming seasonality to be approximately constant.

This dissertation employs an alternative approach to examine the time series behavior between

shelled pecan prices and inventories, at both the zero and seasonal frequencies, using a seasonal

cointegration technique. The study employs both seasonally unadjusted and adjusted quarterly

data (1991-2002). Results suggest that, first, pecan cold storage inventories and shelled pecan

prices are seasonally integrated. Second, shelled pecan prices and pecan cold storage inventories

(shelled only or total) are seasonally cointegrated only at the biannual frequency when

unadjusted data are used. Finally, the speeds of adjustment are greater than one implying rapid

adjustment to any short-term seasonal deviation in cold storage inventories.

INDEX WORDS: Cold Storage Inventories, Pecans, Seasonal Cointegration, Speed of

Adjustment, Shelled, Inshell, Prices



by

MOHAMMED IBRAHIM

B.A., International Islamic University (Malaysia), 1993

M.A., Clark Atlanta University, 1999

A Dissertation Submitted to the Graduate Faculty of The University of Georgia in Partial

Fulfillment of the Requirements for the Degree

DOCTOR OF PHILOSOPHY

ATHENS, GEORGIA

2005

© 2005

Mohammed Ibrahim

All Rights Reserved



by

MOHAMMED IBRAHIM

Major Professor: Wojciech J. Florkowski

Committee: Timothy Park Cesar Escalante

Electronic Version Approved: Maureen Grasso Dean of the Graduate School The University of Georgia May 2005

iv

This dissertation is dedicated to the memory of my mother,

Azaara and Ruhaina Halid

v

ACKNOWLEDGEMENTS

I would like to acknowledge and sincerely thank the members of my committee for their

patience, understanding, support and guidance throughout the dissertation process. I owe them an

incalculable debt.

I am deeply indebted to my major professor, Dr. Wojciech J. Florkowski, for his extreme

patience and assistance throughout my program, for cheering me on during hard times and for

encouraging me to strive for excellence. I would like to thank Dr. Timothy Park and Dr. Cesar

Escalante for their thought provoking comments that further improved my research. I also thank

them for editing and ensuring the quality in presentation of the dissertation as well as its content.

I would like to thank and acknowledge Dr. Michael Wezstein, Dr. William Lastrapes, Dr.

Jeffrey Dorfman, Dr Robert Kunst and Dr Walter Labys for their time to answer my questions. I

am very grateful to Dr Donald Mcllelan, Dr Ivery Clifton and Dr Gerald F. Arkin for helping

make my dream come true. To Jo Anne Norris, Chris Peters, Kim Waters, Laura Alfonso,

Christy Porterfield and Yanping Chen, thank you.

I would like to thank all of my fellow graduate students at the Department of Agricultural

and Applied Economics for their support and encouragement. I would especially express my

appreciation to Daniel Ngugi, and Cristina Caligario. Special thanks go to Marionnette C.

Holmes and Yvonne J. Acheampong for their friendship, support and guidance.

Special thanks to all my friends for their encouragement and support, especially Afa Iddi,

Nasir Ibrahim (Nash), Abdulai Iddrisu, Alhassan Umar, Kuleyawura Shelly and Dr Zaki Ibrahim.

To the Amenyah family, I thank you very much for your support and friendship during my stay

vi

in Athens. To my dad, Ibrahim Ziblem, I owe the deepest gratitude for his understanding. I

thank my sister, Abiba, for her understanding and belief in me. Finally, but most importantly, I

would like to express my gratitude to Allah (SWT) for giving me the strength, patience and the

perseverance to complete this terminal degree.

vii

TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS.............................................................................................................v

TABLE OF CONTENTS.............................................................................................................. vii

LIST OF TABLES...........................................................................................................................x

LIST OF FIGURES ....................................................................................................................... xi

CHAPTER

1 INTRODUCTION .........................................................................................................1

Problem Statement ....................................................................................................2

Objectives..................................................................................................................6

Methodology .............................................................................................................7

Organization of the Dissertation................................................................................8

2 OVERVIEW OF THE PECAN INDUSTRY................................................................9

The U. S. Pecan Production.......................................................................................9

Characteristics of the Pecan Crop .............................................................................9

Pecan Marketing......................................................................................................11

Role of the Pecan Sheller in the U. S. Pecan Industry ............................................12

Pecan Cold Storage Inventories ..............................................................................16

Motives for Storing Pecans .....................................................................................18

Duration of Storage .................................................................................................18

viii

Pecan Prices.............................................................................................................20

Prices Received by the Grower ...............................................................................20

Prices Received by the Sheller ................................................................................21

3 LITERATURE REVIEW ............................................................................................22

Introduction .............................................................................................................22

Perennial Crop Inventories ......................................................................................22

Production Smoothing.............................................................................................25

Time Series Analysis of Price-Inventory Relationship ...........................................26

Summary of Literature Review ...............................................................................26

4 THEORETICAL FRAMEWORK...............................................................................28

Introduction .............................................................................................................28

Commodity Price Behavior .....................................................................................29

The Supply of Storage Theory ................................................................................30

The General Model..................................................................................................31

Price Determined by the Supply of Storage Function.............................................32

5 EMPIRICAL MODEL AND RESULTS.....................................................................35

Introduction .............................................................................................................35

Seasonal Unit Roots in Prices and Inventories........................................................36

The HEGY Procedure .............................................................................................36

Cointegration and Seasonal Cointegration ..............................................................38

Seasonal Error Correction Model............................................................................40

U. S. Pecan Market Data .........................................................................................41

Descriptive Statistics of the Time Series.................................................................42

ix

Graphical Analysis of Seasonality and Nonstationarity..........................................48

Integration and Seasonal Integration.......................................................................55

Results of Cointegration and Seasonal Cointegration Test .....................................59

Error Correction Models and Price-inventory Relationships ..................................63

6 SUMMARY, CONCLUSIONS AND FUTURE RESEARCH...................................71

Research Themes.....................................................................................................71

The Literature and Econometric Analysis...............................................................72

Conclusions and Implications .................................................................................73

Literature and Future Research ...............................................................................76

REFERENCES ..............................................................................................................................78

x

LIST OF TABLES

Page

Table 1: Selected Pecan Shellers in the United States...................................................................14

Table 2: Quarterly-average Shelled Pecan Cold Storage Inventories, 1991-2002 ........................43

Table 3: Quarterly-average Inshell Pecan Cold Storage Inventories, 1991-2002 .........................44

Table 4: Quarterly-average Total Pecan Cold Storage Inventories, 1991-2002............................45

Table 5: Quarterly-average Prices for Fancy Halves, 1991-2002..................................................46

Table 6: Summary Statistics on Price and Pecan Inventory Series ...............................................47

Table 7: Characteristics of Pecan Cold Storage Inventory and Price Behavior ............................47

Table 8: Results of Testing Pecan Inventory Series and Price Series for Seasonal Unit Roots ....57

Table 9: Results for Unit Root Test ...............................................................................................60

Table 10: Results for (Seasonal) Cointegration .............................................................................62

Table 11: Estimation Results for the Shelled Pecan Price and Shelled Pecan and Total Pecan

Inventories.......................................................................................................................64

Table 12: Error Correction Models and Instability Tests ..............................................................68

Table 13: Error Correction Models................................................................................................69

xi

LIST OF FIGURES

Page

Figure 1: U. S. per capita Pecan Consumption ................................................................................3

Figure 2: Annual Production of Pecans in the United States, 1990-2003 .......................................4

Figure 3: Production of Pecans in Georgia, Texas and New Mexico between 1997 and 2003.....10

Figure 4: Volume of Shelled, Inshell and Total Pecan Cold Storage Inventories in 2001 ............17

Figure 5: Monthly Shelled Pecan Prices in the Southeast, 2001 ...................................................19

Figure 6: Plotted Inventories of Shelled, Inshell, and Total Cold Storage Inventories of Pecans

and the Shelled Pecan Prices .........................................................................................49

Figure 7: Plotted Natural Logarithm Values of the Shelled, Inshell, and Total Cold Storage

Inventories and the Shelled Pecan Prices for Fancy Halves, 1991-2001 ......................50

Figure 8: Graphical Representation of Seasonality in Shelled Pecan Cold Storage Inventories...51

Figure 9: Graphical Representation of Seasonality in the Inshell Pecan Cold Storage Inventories

Inventories .....................................................................................................................52

Figure 10: Graphical Representation of Seasonality in Total Pecan Cold Storage Inventories ....53

Figure 11: Graphical Representation of Seasonality in Shelled Pecan Cold Storage Inventories.54

1

CHAPTER 1

INTRODUCTION

The pecan is one of the most popular tree nuts in the U.S. A member of the hickory

family, the pecan tree is the only commercially grown nut tree indigenous to North America

(Johnson, 1998). Large-scale pecan production in the U.S. started in the late 1880s along the

Mississippi delta. Soon, pecan production spread all over the southern United States. Currently,

the U.S. is the world-leading producer of pecans, producing, on average, 75 % of the total world

pecan supply, followed by Mexico, Australia, Israel and the Republic of South Africa,

respectively (Herrera, 2003; Johnson, 1998).

Pecans have historically been part of the diet of the Native Americans. The early

European settlers also made pecans part of their diet and pecans have since become a seasonal

product served during the Thanksgiving holidays. In addition to traditional uses such as pecan

pies, pecans are ingredients in a variety of food products.

Pecans contribute significantly not only to the agricultural economies of the producing

states but also to the U.S gross domestic product (GDP). The industry is reported to make an

annual contribution of about $400 million to the U.S. economy (Crocker, 1989). The value of

production, at the farm level, $259 million, $191million, and $239 million in 1997, 1998, and

2000, respectively (USDA-ERS, 2001). The U.S. pecan industry operates on a competitive free-

market basis. The industry is considered competitive because neither the state nor the federal

governments pay subsidies to influence the supply or price of pecans (Wood, 2000).

2

Problem Statement

Bought by food manufacturers in large volume, pecans are used in a number of products

ranging from ice cream to breakfast cereals. In addition, retailers market raw shelled pecans to

consumers, who use pecans in home baked goods and other dishes. In recent years, major fast

food chains have begun using pecans (e.g., Wendy’s uses roasted pecans for their salads). Food

manufacturers, supermarket chains, and fast food chains contract their pecans from shellers or

ingredient distributors. The profit motive of the shellers dictates the range of shelled pecan prices

in response to the available supply. Although new pecan uses broaden the market for shelled

pecans, the demand for pecans has remained consistent with population growth (see Figure1.1),

indicating a relatively stable demand curve.

With the fixed acreage of commercial production, maximum production is

predetermined. Changes in the volume produced each year result from pecan physiology and

weather conditions during the growing season. The pecan tree has a natural tendency to alternate

bearing; a relatively large crop in one year is often followed by a relatively small crop in the next

year (see Figure 1.2). For example, in 1998, the annual inshell pecan production was 150 million

pounds; it rose to over 400 million pounds the next year before falling to a little over 200 million

pounds the following year. The alternate bearing pattern is often exacerbated by the vagaries of

supply (i.e., unfavorable weather conditions, pests, or diseases). Due to fluctuating production,

prices received by growers fluctuate widely from one crop year to the next.

Shellers are the primary owners of pecan inventories in cold storage. Shellers hold both

inshell pecans for processing and shelled pecans to meet their contractual obligations.

In order not to run out of either inshell or shelled pecans, shellers ration the available

supply of pecans held in storage throughout the year and carry over some inventories into the

3

Figure 1 U.S. Per Capita Pecan Consumption. Source: USDA - Economic Research Service (2003).

0

0.1

0.2

0.3

0.4

0.5

0.619

89/9

0

1990

/91

1991

/92

1992

/93

1993

/94

1994

/95

1995

/96

1996

/97

1997

/98

1998

/99

1999

/00

2000

/01

2001

/02

Seasons

Per

Cap

ita C

onsu

mpt

ion

PecansWalnuts

4

050

100150200250300350400450

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

Year

Mill

ion

lbs

Production

Figure 2 Annual Production of Inshell Pecans in the U.S., 1990-2003, mln lbs. Source: USDA - Economic Research Service (2004).

5

new crop season. This approach to inventory management helps smooth the supply of pecans for

shelling plants and assures pecan availability.

While the supply of pecans is predetermined, demand is relatively stable. As a result,

gathering information about inventory levels is essential. This information however, is reported

on a voluntary basis and little can be done to change it. Growers have expressed a great deal of

dissatisfaction with the voluntary reporting system. Some have been suggesting that the

inventory figures are inaccurate and, consequently, offer little informational value to the market

and that inaccurate and insufficient information is used in the discovery of prices paid to growers

and paid by end users.

In the general absence of similar studies for other perennial crops, this study provides

insights into the potential role of perennial crop inventory. A formal analysis of the effects of

inventory on prices should improve understanding of the complexities of the pecan market and

dispel some of the misinterpretations and uncertainty.

The pivotal role of shellers as input buyers and output suppliers leads some growers to

perceive the price paid by shellers to be low. The need to shell pecans prior to sale combined

with the cost of storage technology, the fluctuating crop size, and a fairly stable demand

exacerbates wide price swings. Specifically, this study investigates the response of in-shell and

shelled prices to the reported inventory levels. The results should shed light on the response of

shelled pecan prices to inventory of shelled and inshell pecans. Knowledge of inventory-price

relationships should be useful to the whole pecan industry and pecan users.

Results of this study should enable shellers to develop superior inventory management

strategies. Knowledge of price-inventory relationship will help them better anticipate the

direction of these two major variables. Pecan shellers may use this information to enhance their

6

planning of financial flows and marketing tactics. Growers gain insight into the influence of

inshell pecan cold storage influence on shelled pecan prices at the wholesale market level. In

addition, understanding the price–inventory relationship enables manufacturers to plan their

procurement programs efficiently, and reduce large and disruptive fluctuations in production.

Objectives

Shellers play a pivotal role in the pecan industry; shelled pecans are the primary product

traded on the market and their prices are said to dictate the range of prices paid to growers

(Florkowski and Hubbard, 1994). At harvest, inshell pecans are purchased by shellers from

growers who, in general, do not have cold storage facilities necessary for the extended storage of

nuts. Inshell pecans are accumulated to assure the operation of shelling plants. The final

products, shelled pecans, are kept by shellers to meet the demand of food manufactures,

wholesalers, and retailers. Assuming that price fluctuations result from changes in supply and

that supply is predetermined, pecan inventories play an essential role in shaping prices for

shelled pecans. Therefore, the general objective of this study was to determine the relationship

between the cold storage inventory of pecans and pecan prices. Specific objectives included the

following:

1. To test the interaction between the inshell pecan cold storage inventories and shelled

pecan prices;

2. To test the interaction of shelled pecan cold storage inventory and shelled pecan

prices;

3. To examine the effects of total pecan cold storage inventories on shelled pecan prices;

4. To determine the existence and form of seasonality in the pecan price and inventory

data.

7

Methodology

This dissertation applies the concept of seasonal cointegration to the U.S. pecan market to

determine the relationship between pecan prices and cold storage inventories. The cointegration

concept is appropriate for this study because it is able to capture concomitantly both long and

short run effects of univariate variables. The empirical estimation is carried out as follows. First,

seasonal unit root tests are conducted to investigate the nature of seasonality in the variables

involved using the procedure developed by Hylleberg, Engle, Granger and Yoo (1990). The

procedure divides data into frequencies, namely, zero or long run, biannual and annual,

respectively. Failure to reject the null hypothesis of unit roots implies the existence of unit roots

at a given frequency.

Second, a univariate seasonal cointegration approach is adopted to determine whether

long run and seasonal equilibrium relationships exist between shelled pecan prices and cold

storage inventory series. The seasonal cointegration test follows the first step only if unit roots

are found at the corresponding frequencies. For example, in a bivariate case, both variables must

have unit roots at the non-seasonal or seasonal frequencies before cointegration can be estimated.

This test procedure is superior to that of Engle and Granger (1987) because it provides

cointegration analysis at the seasonal frequencies.

The final step is the error correction mechanism which determines the short run dynamics

and adjustment process of the cointegrating variables. The error term from the cointegrating

variable is used in estimating the speed of adjustment coefficient.

Data used in this study come from U.S. Department of Agriculture sources. The pecan

cold storage inventory data are that of all pecan producing areas. The shelled pecan prices,

however, are that of ‘fancy halves’ reported in the southeastern region of the United States.

8

Organization of the Dissertation

The remaining chapters of this dissertation are organized as follows. Chapter 2 discusses

the nature and scope of the pecan industry, focusing mainly on the sheller’s role. Chapter 3

reviews studies on perennial agricultural crops such as pecans. Chapter 4 presents the conceptual

framework and discusses the supply of storage, which is the underlying concept for the

theoretical model. Chapter 5 introduces the time series model and the estimated results. Chapter

6 concludes the study and makes suggestions for future research.

9

CHAPTER 2

AN OVERVIEW OF THE PECAN INDUSTRY

The U.S. Pecan Production

The majority of pecans are grown in the “pecan belt”: the Southwestern and Southeastern

U.S. A substantial volume of pecan is produced in the states of Georgia, Texas, New Mexico,

Arizona, Alabama, Oklahoma, Louisiana, Mississippi, Florida, North Carolina, South Carolina,

Arkansas, California, and Kansas. Georgia currently accounts for about 40 percent of the total

U.S. pecan production (USDA-ERS, 2003). Texas is the second leading producer of pecans (22

percent) followed by New Mexico, Arizona, Louisiana, and Oklahoma (see Figure 3). Pecans are

divided into two general types, natives or seedling and improved.

Pecan harvesting has evolved from manual to mechanized throughout the U.S. Pecans are

gathered by mechanical shakers. Some growers spread sheets under trees to collect the pecans

while others use sweepers to gather them. Harvesting occurs during the fall and winter months,

usually from October to January, and pecans are sold for shelling soon after.

Characteristics of the Pecan Crop

Because the pecan is a long-lived perennial, any investment in a commercial orchard is

considered a long-term investment. Price and Wetzstein (1999) observed that investment in

perennial crops involves a relatively large sunk cost. Hence, perennial crops such as pecans are

characterized by irreversibility of investment, meaning resources cannot be reallocated to another

enterprise once committed. This risk can be considered a barrier to entry into large scale pecan

production.

10

Figure 3 Production of Pecans in Georgia, Texas, and New Mexico between 1997 and 2003. Source: Based on USDA - National Agricultural Statistics Service (2004).

0

20

40

60

80

100

120

1997 1998 1999 2000 2001 2002 2003

Year

Milli

on lb

s

GATXNM

11

Pecans are divided into two general types, natives (or seedlings) and improved. Native

pecan trees are found primarily west of the Mississippi river, in river valleys in Oklahoma and

Texas, where the tree is indigenous (Wood et al., 1994). Native trees are propagated directly

from pecan nuts. East of the Mississippi and throughout the Southeastern United States, pecan

trees are either seedlings or improved. Seedlings are trees propagated from nuts and may display

characteristics of the parent to some degree. Improved or grafted trees, on the other hand, show

characteristics of the parent from which a graft originated. In general, improved varieties

produce a more consistent volume of nuts with desired quality attributes, including the size of a

kernel and the color of the skin.

Like many tree crops, the pecan crop is characterized by a prolonged period before

reaching the fruit bearing age (usually 6 to 7 years). Pecan trees then produce output for a long

period of time (usually decades or generations) (French and Matthews, 1971). The pecan crop is

characterized by alternate bearing: a large crop in one year is followed by a small crop in the

next (Wood, 2000). Finally, like most perennial crops, pecans must be processed before they are

marketed.

Pecan Marketing

The pecan is classified as a specialty crop1 and has a niche market. The players in the

pecan industry include growers, accumulators, and shellers (Lillywhite et al., 2003). Growers

include small scale, backyard operations and commercial orchards extending over thousands of

acres. Large growers sell their harvest (inshell) directly to shellers. Large growers tend to use

forward contracting with greater frequency than do small growers (Lillywhite et al., 2003). A

1 A specialty crop, in this instance, follows the congressional definition as any agricultural crop except wheat, feed grains, oilseeds, cotton, peanuts, rice, and tobacco (USDA- Farm Service Agency, 2003). The pecan market is considered a niche market because the industry supplies pecans of specific characteristics that are required by certain food industries to meet specific needs (Pepper, 1995).

12

forward contract is a written agreement between a grower and a pecan sheller relating to the

delivery and acceptance of pecans at some future date. Forward contracts specify what volume

the grower will deliver. The shellers promise payment for the nuts, either by specifying the price

or detailing how the price will be determined.

Accumulators buy pecans from small-scale pecan growers in small quantities until they

accumulate a sufficiently large lot (usually a truckload) to sell to shellers or wholesalers.

Accumulators are the middlemen between small-scale growers and shellers. Some accumulators

also shell pecans (Herrera, 2002; Herrera and Gorman, 1991).

The shellers are the pecan processors. The sheller converts inshell nuts into the tradable

form of shelled pecans. Based on the fact that the majority of accumulators sell their inshell

pecans to a sheller, the term sheller in this study refers only to commercial shellers. Also, the

terms processor and sheller are used interchangeably throughout the study. Pecan shellers tend to

forward contract with end users. The contracting parties agree to the delivery and acceptance of

pecans at some future date. The mode of payment for the pecans is also agreed upon at the time

of closing the contract. Shellers benefit from forward contracts by having assured access to a

market, the potential for increased operational efficiency, and reduced price risk. The sheller

will, however, suffer a loss should an unexpected price increase occur during the remainder of

the marketing season. The contracting period for the sheller-buyer usually extends from the

fifteenth of October to the fifteenth of March.

Role of the Pecan Sheller in the Pecan Industry

The pecan sheller is responsible for removing or separating the pecan shell and inner

packing material from the nut meat (shelled pecans). Furthermore, the pecan sheller performs a

13

pivotal role in the pecan industry by being the final point of sale for both accumulators and

commercial growers.

Like most nut crops, pecans are highly dependent on processing to be marketed. Over 80

percent of pecans are sold shelled (Taylor, 2001). Pecans require special postharvest handling

by the sheller, include cleaning, in-shell size sorting, shelling, grading, and storage. Size sorting

before shelling ensures optimal and efficient processing and a more uniform output. Pecan

storage is very important in the pecan industry because pecans are semi-perishable nuts and they

need proper care. Improperly cared for pecans easily become rancid and inedible, resulting in an

economic loss.

Although inshell pecans can be stored for a few months in ambient temperature without a

detectable loss of quality by consumers, refrigeration is preferred. Shellers place pecans in cold

storage immediately after harvest because refrigeration helps maintain freshness and also

prevents insects from invading the harvested nuts.

Shellers either operate year-round or operate on seasonal basis. Seasonal shelling

coincides with the harvesting season each fall. Seasonal shellers process all inshell pecans and

store the shelled pecans. Shellers that operate year round usually have large cold storage

facilities to hold millions of pounds of both inshell and shelled pecans. The cold storage space

can also be rented from warehouse operators. Storage of pecans in both forms assures a

continuous supply of input throughout the marketing year. For example, on average, large

shellers shell about 150,000 pounds of pecans a day and about 30 million pounds per season

(Taylor, 2001). Most shelling plants are located in the pecan producing regions, namely the

southeastern and southwestern United States (see Table 1).

14

Table 1 Selected Pecan Shellers in the United States. Company name Location

Louisville Pecan Co., Inc. Louisville, AL

Priester Pecan Co. Fort Deposit, AL

Tucker Pecan Co. Montgomery, AL

Whaley Pecan Co., Inc, Troy, AL

The Green Valley Pecan Co. Sahuarita, AZ

Hamilton Ranches, Inc. Visalia, CA

J.W. Rentroe Pecan Co. Pensacola, FL

Atwell Pecan Co., Inc Wrens, GA

Mascot Pecan Shelling Co., Inc Glenville, GA

Sunnyland Farms Inc. Albany, GA

Harrell Nut Company Camilla, GA

Terri Lynn, Inc. Cordele, GA

H.J. Bergeron Pecan Shelling Plant, Inc. New Roads, LA

Delta Pecan Orchards Tutwiler, MS

Stahmann Farms San Miguel, NM

Golden Kernel Pecan Co., Inc. Cameron, SC

Orangeburg Pecan Co., Inc. Orangeburg, SC

Young Pecan Co. Florence, SC

Sun Valley Pecan Co. Fabens, TX

San Saba Pecan San Saba, TX

John B. Sanfilippo & Son, Inc Selma, TX

15

Company name Location

Atkins Farms El Paso, TX

Southwest Nut Co. Fabens, TX

Source: National Association of Pecan Shellers, http://www.ilovepecans.org/ (2002); Herrera (2002)

http://www.ilovepecans.org/

16

Pecan Cold Storage Inventories

Pecans are stored in cold storage to prevent rancidity, which lowers the kernel quality.

Cold storage, however, requires a high initial investment. The majority of pecan growers do not

hold their pecans in cold storage. Instead, growers sell almost all their output to shellers during

harvest. Due to the high initial cost of constructing cold storage facilities, many shellers rent cold

storage space for their inshell pecan inventory. Shelled pecans kept in cold storage represent

inventories used to meet contractual commitments of shellers. The shelled pecan inventory is

replenished by processing inshell pecans.

After cleaning and shelling, the sheller then sizes halves (small, large, jumbo and

chipped) and pieces, and packages the nuts before marketing. The shelled pecans are either

packaged for direct outlets in small packages (usually between 2 and 12 ozs.) or in 30-pound

boxes. The 30-pound boxes are sold to manufacturing companies such as ice cream

manufacturers and bakers (Herrera and Gorman, 1996). Other marketing channels include

wholesalers, retailers, and export markets.

The short and contracted harvest period of the pecan crop is followed by a prolonged

marketing period during which the quantity sold comes from inventories held in cold storage.

The sheller becomes the primary owner of the pecan cold storage inventories soon after the

harvesting season. It is, therefore, assumed that pecan inventories are held for production

smoothing purposes and also to meet contractual commitments. The majority of the pecans in

cold storage are located in major production regions.

The volume of inshell pecans in cold storage starts to increase during the harvesting

season (October to December) and peaks in February. This pattern is shown in Figure 4 using

data for the 2001 calendar year. In Figure 4, the volume of shelled pecans begins to increase

17

Figure 4 Volume of Shelled, Inshell and Total Pecan Cold Storage Inventories in 2001. Source: Economic Research Service, USDA (2002).

020406080

100120140160180

Jan-

01

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ion

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Shelled PecansInshell PecansTotal Pecans

18

during the latter part of the harvesting season, peaks in July, and reaches its lowest point in

November. Figure 5 shows the behavior of shelled pecan prices in 2001. Shelled pecan prices

peaked in January and continued to decline until June. Prices increased slightly in July and

remained constant until October when prices began to drop sharply.

Motives for Storing Pecans

Generally, inventories are held for two reasons, either for speculative purposes, where the

inventory owner expects the future price to change in his/her favor, or as “pipeline stocks” held

for production smoothing. The speculator holds inventories to profit from arbitrage

opportunities. The processor, on the other hand, keeps inventories to assure continuous

production and also to meet contractual obligations. This study assumes pecan shellers hold

inventories for production smoothing purposes based on finding that majority of shellers are not

speculators (Hall and Shafer, 1998).

Duration of Storage

Inshell pecans can be stored in a cool and dry place for a few months without a detectable

loss of quality. Storing inshell or shelled pecans under refrigeration at near freezing temperatures

will maintain pecan freshness for nine months. Pecans stored at 0o F or lower temperatures

maintain their quality for two or more years. Shelled pecans can be stored indefinitely with the

appropriate procedure (Florkowski, 2003). In this study, however, it is assumed that shelled

pecans can only be stored for two years based on the fact that costs (labor, utilities, etc.) and the

risk of quality loss (e.g., due to absorption of foreign odors) limit the duration of storage.

Furthermore, the alternate bearing of pecans, although not occurring in a perfect pattern, creates

expectations of a large crop every other year, forcing the removal of some inventories to be

replaced with a new crop.

19

0.000.501.001.502.002.503.003.504.004.50

Jan-0

1

Mar-01

May-01

Jul-0

1

Sep-01

Nov-01

Dolla

r / lb

s

Shelled prices

Figure 5 Monthly Shelled Pecan Prices in the Southeast, 2001. Source: Based on data from Economic Research Service, USDA (2002).

.

20

Pecan Prices

Shelled pecan sales carry the pecan industry as a whole because shelled pecans are

subject to trade. Prices received by the grower depend on prices paid to the sheller. Factors such

as demand, total supply, and expectation of crop size are very important in pecan price

discovery. For example, expectations drive buyer willingness to accept sheller asking prices and

sheller prices offered to growers. Similarly, a large crop year reflects low prices and a short crop

year results in higher prices. In addition, higher pecan prices will result in a decrease in the

demand for pecans. Prices received by growers and shellers determine, in the long run, changes

in the pecan industry.

Prices Received by the Grower

Although prices paid to growers are expected to reflect prices paid to shellers for shelled

pecans, prices for inshell pecans are influenced by several other factors: total expected seasonal

production, shell-out ratio, carry-in inventories of shelled pecans, and kernel quality (Florkowski

and Hubbard, 1994; Wood, 2000; Shafer, 1997). These and other factors have led to a wide

variation in the average inshell pecan price paid to the grower. For instance, in years of a short

crop, shellers may be willing to bid higher prices for inshell pecans, while in years of a large

crop, prices offered to growers may be rather low. The pricing behavior in years of short and

large crop years, as described, reflects the expectations of shellers who need an adequate supply

of inshell pecans to operate their processing plants. Because the inshell market is defunct outside

the harvest season, inshell pecan buyers (mostly shellers) offer prices in response to the crop size

and available inventories.

21

Price Received by the Sheller

The shelled pecan market is competitive. The price is determined by demand and supply

and their expected changes. Specifically, the price received by the sheller is influenced by the

end user, quality attributes, the price of competing nuts (walnuts) and nut-meat on-hand (carry-

in). Like many other agricultural commodities, shelled pecans are sorted and graded using a

variety of grading standards (Florkowski and Hubbard, 1994). Beside the USDA standards for

shelled pecans, several other systems of grading have been developed by industry organizations

and individual shelling firms. However, published information about prices for shelled pecans is

scarce. Asking sheller prices for shelled pecans are available, but with the exception of the

highest grade (“fancy halves”), price series are incomplete.

22

CHAPTER 3

LITERATURE REVIEW

Introduction

Literature related to price and inventory studies of pecans is sparse. Pecans and other

specialty crops represent a relatively small portion of agricultural crops in the U.S. Moreover,

specialty crops are often considered to be important only to local economies. This perception is

reflected in the scarcity of studies related to specialty crops and the absence of any study on the

behavior of pecan shellers. For example, public pecan inventory data collection started only in

the early 1970s. The data were first used in the empirical study of the pecan market by Wells et

al. (1986). Furthermore, not only are inventories in the pecan industry held privately but

inventory reporting is also voluntary. Voluntary reporting may be inconsistent because of the

lack of any enforcement or accountability. Another reason there are so few studies focused on

the relationship between pecan crop inventories and price is the perennial nature of the crop.

Among perennial crop price studies, most have concentrated on primary commodities such as

cocoa, coffee, and tea. These primary commodities have well-established spot and futures

markets that provide a relatively good database. Finally, the infrequency of perennial crop

studies has resulted from the lack of application of recently developed estimation techniques.

Perennial Crop Inventories Few empirical studies related to price-inventory relationships of perennial crops are

found in the economic literature. Several of these studies concentrate on primary commodities

with well-developed markets. Florkowski and Wu (1990) conducted an econometric study of the

Georgia pecan industry. The purpose of the study was to determine the impact of the on-farm

23

storage technology on prices received by growers and grower income in Georgia. Florkowski

and Wu (1990) described the nature of the pecan industry and the marketing strategies of

growers. The theoretical profit maximizing condition they derived stated that growers maximize

profits when expected gain in marginal revenue equals marginal cost of storage. The model was

estimated using a 3SLS method, and all the parameters were estimated using annual time series

data. The results showed that storage stabilized prices but that if the storage volume increased

above a certain level, gains in income decreased because price differences from year to year

decreased.

Weymar (1968) conducted an econometric analysis of cocoa prices. Based on the theory

of price, the study developed an empirical model suitable for the cocoa market. Weymar (1968)

proposed a model in which the spot price of cocoa was approximated by a function of the current

inventory ratio, the market forecast inventory ratio for a given period, and the expected long-run

equilibrium levels of price and inventory ratio. All the parameters were estimated both the

ordinary least squares (OLS) and the generalized least squares (GLS) methods. The GLS

estimates were found to be consistent with the supply theory of storage, confirming the behavior

of long-run price expectations. The results were also consistent with observed cocoa price

behavior.

Shepherd (1998) conducted a feasibility study of optimal storage decisions by pecan

growers in Georgia, the dominant producer of pecans in the U.S. The overall objective was to

evaluate the practicality for Georgia pecan growers of forming cooperatives and adopting storage

technology that would increase their market power and eventually increase profits. To estimate

the Bayesian model, Shepherd (1998) first estimated the demand and supply models. The

demand model was estimated using the linear regression method. The supply model was divided

24

into a dominant firm and a competitive fringe firm. The dominant firm referred to the state of

Georgia, the largest area of the commercial pecan production, while all other pecan producing

states were defined together as the competitive fringe firm. One-period ahead forecasts were

made for both firms. The estimates from the demand and supply forecasts were used to

determine the dominant firm’s optimal storage strategy. Results showed that storage at the farm-

level is not economically feasible because it is inefficient. In some cases, excessive storage

seemed to have reduced profits.

Antonini (1988) conducted an empirical analysis of price and inventory dynamics of

primary commodities in order to build and test a rational expectations model. The maximum

likelihood method was used to estimate the cocoa model. Antonini (1988) first built a theoretical

model and then tested the assumptions of the model. The results showed that the coefficients for

the cocoa model had good fit but failed the Granger causality test. The study also confirmed the

widely held notion that price elasticities of supply for agricultural crops are very small in the

short term.

Trivedi (1989) in a study of the role of rational expectations on commodity storage,

proposed a semi-structural price model for tea and cocoa. The explanatory variables included

total world inventory, exchange rates, and other exogenous variables. The model was estimated

using the generalized instrumental variable procedure because inventories were considered

endogenous. The study showed that inventories of both commodities had the expected negative

signs, indicating an inverse relationship. Results indicated that the cocoa model had a better fit

and was more robust than the tea model. Trivedi (1989) noted that cocoa prices were sensitive to

intertemporal demand for inventories.

25

Deaton and Laroque (1992) studied commodity price behavior from a rational

expectations perspective. The purpose of the study was to determine whether the theory of

speculative storage could explain actual price behavior. Deaton and Laroque (1992) explicitly

incorporated the behavior of the speculator into the theoretical model and assumed that the

speculator would hold inventories in order to maximize profits. A combination of numerical and

general method of moment (GMM) procedures was used to estimate the model. The study

showed that most of the actual commodity price behavior confirmed the predictions of the theory

of competitive storage.

Peterson and Willett (2000), in their analysis of the supply and demand of U.S. kiwifruit,

developed a modeling framework for specialty crops with the limited available data. The authors

used the 3SLS procedure to estimate the model. In the study, inventory level at the end of the

month was the sum of the beginning inventory, incoming harvest, and monthly imports, less the

total quantity of shipments during the month. The study, however, focused on change in

inventory. The results of the study showed that the model replicated seasonal patterns of

inventory fluctuation.

Production Smoothing Eichenbaum (1989) studied firms’ motives for holding inventories. The purpose of the

study was to determine empirically whether firms hold inventories to smooth production level or

production cost. Production-level smoothing occurs when inventories of finished goods are held

to smooth production in the face of fluctuating demand and convex cost functions. Production-

cost smoothing occurs when firms use inventories to smooth production costs. Eichenbaum

(1989) estimated both production level and production cost smoothing models using econometric

time series methods. Results indicated that firms likely hold inventories for production-cost

smoothing rather than for production-level smoothing purposes.

26

Pindyck (1994) used cost functions to explain the economic gains of holding inventories.

The objective of the study was to examine the importance of inventory holdings in the short run

dynamics of production and price. The study showed that in the short term, firms tend to engage

in production and cost smoothing. In the long term, however, inventories were used primarily to

minimize marketing cost rather than to smooth production.

Revoredo (2000) conducted a rational expectations analysis of commodity storage when

both speculators and processors hold stocks. The purpose of the study was to develop a model

that incorporates both speculative storage and processor’s storage. Revoredo (2000) replaced the

convenience yield motive with manufacturing inventories in the model. The manufacturing

inventories were considered factors of production because processors carry a significant portion

of raw material inventories during the production process. The study concluded that the new

model outperformed other models in explaining commodity dynamics.

Time Series Analysis of Price-Inventory Relationships

The limited availability of data on perennial crops has resulted from the paucity of time

series analysis of price and inventory studies. Trivedi (1989) conducted a time series analysis of

coconut and palm oils to determine the relationship between price and inventories of vegetable

oil. The study applied the cointegration test approach to examine the price-inventory

relationship. The unit root test showed that all variables had the unit root property. The

hypothesis of non-cointegration was accepted in almost all cases.

Summary of Literature Review

The review of literature revealed little research that explored price and inventory relations

in the pecan industry. While a few studies examined price-inventory relationships from the

grower’s standpoint, none have accounted for the position of the sheller. The reviewed studies

27

were mostly done from the rational expectations perspective. Similarly, prices and inventories

were considered only at the macro level, and annual data were applied most often. The lack of

price and inventory related studies from the shellers’ perspective makes the present study an

important contribution.

Few studies have conducted quantitative analysis of the pecan industry. Both Florkowski

and Wu (1990) and Shepherd (1998) conducted an analysis of optimal storage by growers in

Georgia. In addition, Florkowski and Lai (1997) tested for cointegration between prices of

different grades of tree nuts. Ibrahim and Florkowski (2003) also used the cointegration concept

to study the relationship between pecan prices and cold storage inventories. The other studies,

however, dealt with optimal storage from the growers view point.

This dissertation differs from earlier studies in the following ways. First, storage is

addressed from the sheller’s point of view. Second, the study examines the role of pecan cold

storage inventories in pecan price determination. Finally, the study does not consider seasonality

a nuisance and applies seasonal cointegration methodology in the estimation process.

28

CHAPTER 4

THEORETICAL FRAMEWORK

Introduction

This chapter presents the theoretical underpinnings of the examination of pecan price

relationships, especially with inventories. Few studies have attempted to describe the relationship

between price and inventory. Weymar (1968) explicitly incorporated the supply of storage

function to explain both spot and futures prices of cocoa. Later, Miranda and Glauber (1993)

extended the model to annual crops (soybeans). Antonini (1988) used a macroeconomic

approach to describe price and inventory dynamics by assuming rational expectations. Similarly,

Deaton and Laroque (1992) used the rational expectations model to describe commodity price

behavior. Among the models used in the various studies, Weymar’s model seems to be most

appropriate for this study; this research, therefore, borrows heavily from his work.

Pecan shellers are motivated not only by profit maximization but also want to assure the

operation of shelling plants. Assuming that price fluctuations result from changing supply and

that supply is predetermined (due to the crop’s perennial nature), pecan inventories may play an

essential role in shaping prices for shelled pecans. Shelled pecans are the primary product traded

on the market, and their prices are said to dictate the range of prices paid to growers for their

delivery of inshell pecans.

The remaining parts of this chapter are organized as follows: The next section describes

the behavior of primary commodity prices; the third section explains the theory of supply of

storage; sections 4 and 5 describe the general and specific models, respectively.

29

Commodity Price Behavior

Commodity price behavior has its roots in Working’s 1933 and 1949 seminal papers

(Labys, 1973). The primary commodity price behavior literature concentrated on commodities

with futures markets. Most of the studies in the literature, however, explain price behavior in the

macroeconomic context (e.g., Antonini, 1988; Trivedi, 1989).

The commodity market model used to formulate price behavior contains a set of

relationships pertaining to the demand for a commodity, its supply, and the inventory. The level

of commodity prices influences each of these relationships. A review of the literature indicates

that many agricultural markets are more appropriately described as dynamic rather than static.

For example, consumer behavior does not respond instantaneously to an income or price change.

Rather, the full effect of consumer responses spreads over a period of time. Therefore, a price

change influences consumption in the short and in the long run.

Modeling demand for agricultural commodities poses some difficulties (Tomek, 2000).

First, agricultural commodities have multiple uses. For example, pecans are used in baking,

confections, and salads, to mention only a few. Second, demand for inventories is difficult to

determine because holders may have varied reasons for keeping inventories. In this study, it is

assumed that inventories of inshell pecans are held by shellers for processing, whereas most

studies have concentrated on the speculative motives of holding agricultural commodity

inventories (e.g., Working, 1949; Brennan, 1958; Deaton and Laroque, 1992; Miranda and

Glauber, 1993).

On the supply side of agricultural commodities, the agronomic and biological nature of

commodities heavily influences the specification of relationships useful for market models. Yet

the agricultural supply analysis is deeply rooted in microeconomic theory. For instance,

30

producers are assumed to maximize expected discounted profits though subject to some

constraints (Tomek and Myers, 1993). The major challenges in modeling agricultural

commodities include the gestation period, physical factors, and economic considerations. As a

result, the choice of a dynamic specification in itself becomes a challenge.

The biological nature of the production process of perennial crops also influences price

behavior. The output of perennial crops is constrained in the short run by the number of full

bearing trees. An expected rise in profits will not result in an instantaneous increase in supply.

As a result, there is a lag between the timing of the initial investment and the moment output is

produced. For example, production in any given period tends to be affected by decisions made in

the past.

Various studies have incorporated different price expectation variables (e.g., naïve,

adaptive, and rational) into supply functions. But assumptions about how expectations are

formed can alter empirical results (Antonovitz and Greene, 1990). Whereas the simplest

expectations model implies naïve expectations, according to which the current expectations equal

the previous actual price, inventory behavior plays a vital role in explaining commodity price

behavior. The ability to carry stocks from one period to the next indicates a dynamic nature of

inventories. In this context, the use of the supply of storage concept helps to describe commodity

prices as a function of inventories. However, the ability to carry stocks through time contributes

to possible autocorrelation in prices, including both intra- and inter–year variability (Deaton and

Laroque, 1992).

The Supply of Storage Theory

The supply of storage theory has its origins in the works of Working (Labys, 1973).

Weymar (1968) extended and applied the supply of storage theory to a theory of spot price

31

behavior. The current objective of the supply of storage theory is to explain intertemporal price

difference between spot and expected future spot prices. Most of the studies of inventory

behavior have concentrated on explaining inventory holding in terms of adjustment to

transactions or speculative motives (Working, 1949; Brennan, 1958; Deaton and Laroque, 1992;

Miranda and Glauber, 1993). Some processors, however, are willing to hold certain minimum

inventory levels even though they expect negative price spreads because of the “marginal

convenience yield” those inventories provide to them (Kaldor, 1939). The marginal convenience

yield is the difference between carrying charge and intertemporal spread (Kaldor, 1939). The

supply of storage theory is based on the premise that firms adjust their individual levels to a

point where marginal revenue of holding inventories equals the marginal holding cost.

The processor keeps inventory for two main reasons (Kaldor, 1939). First, processing a

primary commodity in many cases involves enormous capital investment. The more inventories

held, the lower the possibility of having capital equipment sitting idle as a result of temporary

outages. This behavior is referred to as “the avoidance of stockout”; the processor in effect

reduces cost adjustment through production smoothing. Second, a processor may wish to sustain

a relatively stable but competitive output price. By increasing the normal level of inventory

coverage, the processor can change prices less often and still remain competitive at the industry

level. Inventory coverage yields a return known as coverage yield.

The General Model

Assuming a competitive market organization, the general model for any given

commodity may be written in the following form, involving three behavioral equations and a

market clearing identity:

(1) ( )ttttt uzppcC ,,, 1−=

32

(2) ( )ttttt vzpphH ,,, 1−=

(3) ( )ttttt ezsfPP ,,* =−

(4) tttt CHss −+= −1

where, tC is current consumption, tH is current production, tp is current price, tz represents

exogenous variables, ts represents inventories, and tv , tu , and te are random shocks. tC and tH

are functions of both tp and lagged price ( 1−tp ). Furthermore, ts is inventory level, and

*tP denotes the expected price.

The expected price-spread relationship in equation (3) represents the supply of storage

curve, which indicates whether stockholders are willing to hold large stock for speculative

purposes if future prices are expected to increase. Some stockholders, however, are still willing

to hold stocks at negative price spreads to ensure adequate volume for processing. The

processing motive plays a major role in the pecan shelling industry (Hall and Shafer, 1998).

Weymar (1968) extended the supply of storage function to explain spot price behavior

via long-run price expectations and inventory holding expectations. As such, the model is

appropriate in describing the relationship between shelled pecan prices and pecan inventory.

Price Determined by the Supply of Storage Function

This researcher is interested in explaining quarterly pecan spot price behavior despite the

short data interval relative to production and consumption lags. Even though this discrepancy

does not meet all the conditions of Weymar’s model, this researcher can still incorporate the

supply of storage function in determining prices because pecan inventories fluctuate

considerably. Also, by assuming that both production and consumption are functions of lagged

prices, the spot price can be estimated using equation (4) (Weymar, 1968).

33

Suppose the supply of storage function is stated in a way such that the expected fraction

change in price becomes a linear function of the inventory level:

(5) [ ] ttt

tt essP

PP+−=

−α

*

where, 0>α and s represents the unknown volume of pecans in cold storage not owned by the

sheller. Inventory levels are used in this study as opposed to inventory ratios. The adopted linear

form represents an approximation of the usual supply of storage curve shown in equation (3).

The system is in equilibrium when the inventory level equals the volume not available to the

market and the current price equals the expected price (Weymar, 1968).

Taking the natural log of the left hand side of equation (5) results in

(6) [ ] ttt

t essPP

+−=⎟⎟⎠

⎞⎜⎜⎝

⎛α

*

ln

where ⎟⎟⎠

⎞⎜⎜⎝

⎛

t

t

PP*

ln is defined as the expected price ratio. Substituting for ts , equation (6) becomes

(7) [ ] ttttt

t esCHsPP

+−−+=⎟⎟⎠

⎞⎜⎜⎝

⎛− )(ln 1

*

α

Expanding the right hand side (RHS) of equation (7) and some rearrangements result in

(8) ( )[ ] ( ) tttttt esCHsPP +−+−+= −1* )()(lnln αααα

Suppose ( )[ ]sPt α+*ln is assumed to be a constant and the coefficients of tC and tH are required

to be equal in magnitude. Thus, equation (8) becomes

(9) ( ) tttt esHaP ++−= −1ln α

34

where, a is a constant. The model indicates that a reduction or growth in pecan cold storage

inventories will result in an increase or decrease in the shelled pecan price. The theoretical model

is, therefore, consistent with microeconomic theory.

Given the nonlinear relationship between price and inventory (Tomek, 1994), the

theoretical model cannot be estimated by ordinary least squares (OLS). Moreover, prices are

known to have seasonal components, and coupled with shellers’ reaction to expected price

changes, prices could be both inter-year and intra-year autocorraleted. Due to the dynamic nature

of inventories, changing seasonal patterns in agriculture may involve stochastic seasonality

(seasonal unit roots). Thus, it seems appropriate to apply the newly developed seasonal

cointegration procedures to the model. The seasonal cointegration technique allows for the joint

modeling of short run economic reactions, trends, and seasonal and long run equilibria.

35

CHAPTER 5

EMPIRICAL MODEL AND RESULTS

Introduction

Most agricultural time series exhibit seasonal behavior. Seasonality is either deterministic

or stochastic. Following Tomek and Robinson (2003), seasonality may be defined as a pattern

that repeats itself on a regular basis (e.g., once every twelve months or every four quarters).

Seasonality in many agricultural commodities is either supply- or demand-influenced but is

considered principally supply-influenced (Tomek and Robinson, 2003; Jumah and Kunst, 1996).

The supply-side seasonality results from the biological production cycle. Many agricultural crops

produce output only once a year. Because some crops can be stored between harvests, the

available supply consists of the current production and the carry-in inventory from the previous

year. Demand-influenced seasonality in agriculture is caused by such factors as traditionally

celebrated holidays or the pattern of weather changes. For example, the U.S. demand for pecans

peaks during the Thanksgiving and Christmas holidays and tapers off in subsequent months.

Box and Jenkins (1976) treated seasonality as a nuisance. Engle, Granger, and Hallman

(1989) have argued that the disadvantages of using the Box and Jenkins approach include (a) loss

of significant information on important seasonal behavior and (b) unintended mistakes regarding

inferences with respect to economic relationships among the data. Inspired by these observations,

Hylleberg et al., (1990) developed a time series model that allows for changes in the seasonal

pattern. This procedure, henceforth termed the HEGY procedure, is designed to test for the

presence of seasonal unit roots (integration) in quarterly data.

36

Having established that most agricultural commodities exhibit seasonal behavior, it is

appropriate to adopt the HEGY procedure in the study of pecans. Moreover, because the HEGY

procedure has been able to distinguish between stationary I (0), unit roots of order one I (1), and

seasonal unit roots of order one SI (1), it has become a standard tool of analysis. The next three

sections describe the tests for seasonal integration, seasonal cointegration, and the error

correction model (ECM). Section 5 describes the data, and section 6 reports the results of the

study.

Seasonal Unit Roots in Prices and Inventories

The early work of Engle et al. (1989) led to the development of a number of seasonal

cointegration procedures. These techniques can be divided into two approaches. The first

approach is residual-based and was applied by, for example, Hylleberg et al. (1990), Engle et al.

(1993), Joyeux (1992) and Cubbada (1995). The second approach based on maximum likelihood,

was first proposed by Lee (1992). Lee’s procedure is an extension of the Johansen (1988)

technique to the seasonal case. The maximum likelihood technique allows for the analysis of a

multivariate system.

The HEGY Procedure

The first step in testing for seasonal cointegration is to test for unit roots at the non-

seasonal and seasonal frequencies. The appropriate technique used to test for seasonal unit roots

is the HEGY procedure. The HEGY procedure tests for unit roots at each frequency separately

without maintaining the assumption that unit roots are present at other frequencies. The

underlying assumption of the HEGY test is that seasonal behavior is stochastic. The procedure

may or may not fail to reject the hypothesis of the existence of seasonal unit roots in such series.

37

A given time series tx , with unit roots at the long-run and seasonal frequencies, is

assumed to be generated by an autoregression process of the form

ttxB εϕ =)( ( )2,0~ σiid , t = 1, 2, T,

where )(Bϕ = ( )41 B− and B is the lag operator. To determine the order of integration and/or

seasonal integration, the following regression model for quarterly data is estimated:

(10) tttttt yyyyx εππππ ++++=∆ −−−− 1342331221114 .

Here 4∆ = ( )41 B− and tε is an error term. Each ity (i=1, 2, 3) is a transformed series for unit

roots at various frequencies. The ity is designed such that ty1 is trending but non-seasonal, while

ty2 and ty3 are non-trending and display seasonal cycles at π and 2π , respectively.

The transformations ity of tx removes the seasonal unit roots at certain frequencies

while preserving them at other frequencies. For example, ( ) tt xBBBy 321 1 +++= removes all

seasonal unit roots, while preserving the long run or zero frequency unit roots. Next,

( ) tt xBBBy 322 1 −+−−= preserves unit roots at the biannual frequency, which corresponds to a

six-month period. Finally, the ( ) tt xBy 23 1−−= transformation eliminates the unit roots at zero

and biannual frequencies while preserving potential seasonal unit roots at the annual frequency.

Additional lags of tx4∆ are usually added to whiten the errors. Similarly, deterministic

terms (a constant, seasonal dummies, and a trend) may also be added to the equation. Thus,

equation (10) can be rewritten as

(11) 1342331221114 −−−− +++=∆ ttttt yyyyx ππππ ptntt xaxatD −− ∆++∆++++ 4141 ...δπµ .

38

Here µ is a constant term, and tD is a vector of three seasonal dummy variables. Under the

HEGY technique, equation (11) is estimated using the ordinary least squares (OLS) method.

The tests for the presence of a unit root at each frequency is based on the t-statistics for

iπ (i=1, 2, 3, 4) or joint F-test for iπ (i=3, 4), where equation (11) is the model under the null

hypothesis. If 1π is not significantly different from zero, then the procedure fails to reject the

existence of a unit root at the zero frequency. If 2π is not significantly different from zero, it

fails to reject a seasonal unit root at the biannual,π , frequency. If 43 ππ ∩ is not significantly

different from zero, then the null hypothesis fails to reject a seasonal unit root at the annual, 2π ,

frequency. In effect, a failure to reject the null hypothesis implies the presence of unit roots. The

procedure, therefore, requires tests for 01 =π , 02 =π , and a joint test 043 == ππ . Critical

values are obtained from Hylleberg et al. (1990).

Cointegration and Seasonal Cointegration

Seasonal cointegration may apply between two or more variables at the seasonal

frequencies if these variables contain unit roots at the seasonal frequencies. Hylleberg et al.

(1990) developed a seasonal cointegration methodology to test whether two series share a

common unit root at each frequency. Engle, Granger, Hylleberg and Lee, (henceforth EGHL),

(1993), improved the technique and applied Engle and Granger (1987) type 2-step procedure to

appropriately filtered data.

Assuming two series, tp and ty , have unit roots at both zero and seasonal frequencies, the

variables will be transformed accordingly and used in the test procedure. In order to test for

cointegration and seasonal cointegration, the following regression equations for quarterly data

are estimated:

39

(12a) ttt yp 11211 αω −=

(12b) ttt yp 22222 αω −=

(12c) 1,3421,34133233 −− −−−= ttttt ypyp αααω .

Here itp and ity ( =i 1, 2, 3) represent the transformed series at various frequencies. The linear

combinations of these variables are, therefore, expected to be stationary, I (0), at all frequencies.

Cointegration of tp1 and ty1 , at the zero frequency implies that equation (12a) is a unique

linear combination such that t1ω ~I(0). Similarly, seasonal cointegration of ty2 and tp2 occurs at

the biannual frequency if the null hypothesis of noncointegration is rejected. This means that

equation (12b) has a unique stationary linear combination. The OLS estimates of equations (12a)

and (12b) are expected to be “superconsistent” (EGHL, 1993). In addition, the residuals of the

cointegrating equations are used directly in the ECM. Tests for cointegration at the zero and

semiannual frequencies are conducted by testing the residuals from the cointegrating regressions.

The test is meant to detect any remaining unit roots at the zero and biannual frequencies,

respectively.

Equation (12c) is, however, treated differently. The cointegrating relation between

tp3 and ty3 is estimated by regressing tp3 on ty3 and 1,3 −tty . Also, in this case, the residuals will

be used to test for seasonal cointegration at the annual frequency. The estimates are

superconsistent, and the error terms are used in the ECM.

Let us denote the residuals obtained from regressing tp1 on ty1 , tp2 on ty2 , and tp3 on

ty3 and 1,3 −tty as tε , tµ and tν , respectively. The test of noncointegration at the zero frequency

can be performed by an auxiliary regression of tε∆ on 1−∆ tε . The regression can be run with or

40

without deterministic parts. Similarly, the regression can also be augmented by the necessary

lagged values of tε∆ . The critical values are obtained from Engle and Yoo (1987).

Seasonal Error Correction Model (SECM)

The seasonal error correction mechanism or model (SECM) is the second stage of the

EGHL (1993) two-step type cointegration procedure. This is similar to the Engle and Granger

(1987) two-step cointegration procedure. The SECM can be estimated as part of the two-stage

procedure only if cointegration is found for each frequency. The lagged residuals from the

cointegrating residuals are used in the SECM. Assuming that cointegration is established at the

long run and seasonal frequencies, the SECM is then written as

(13a) ttttttp 11342331221114 εωλωλωλωλ ++++=∆ −−−− ,

and

(13b) tttttty 21342331221114 εωλωλωλωλ ++++=∆ −−−− ,

where itω ( i = 1, 2, 3) are residuals from the cointegrating equations, kλ ( k = 1, 2, 3, 4) are

coefficients and jtε ( j = 1, 2) are stationary disturbances. Lagged variables can also be added to

measure short run dynamics. Equation (13) can be rewritten as

(14a) 1342331221114 −−−− +++=∆ tttttp ωλωλωλωλ

t

k

iiti

q

jjtj yp 1

11

141 εδα ++∆+ ∑∑

=−

=− ,

and

(14b) 1342331221114 −−−− +++=∆ ttttty ωλωλωλωλ

t

k

iiti

q

jjtj yp 2

142

142 εδα +∆+∆+ ∑∑

=−

=− .

The SECM can be used to determine both the speed of adjustment and Granger causality

(Enders, 1995; 1996). The speed of adjustment determines the rate at which the dependent

41

variable corrects short run deviations. The Granger causality, however, determines the lead

variable.

The advantage of using the SECM is that it provides an interpretation that is amenable to

economic theory. Similarly, the clear separation between long- and short-run parameters in the

SECM makes it an excellent framework for assessing the validity of the long-run implications of

a theory and the dynamic processes involved. Among the disadvantages of the SECM, one often

mentioned limitation of the Engle-Granger two-step procedure is the identification problem. For

example, Gonzalo (1994) demonstrated that the identification problem may lead to weak and

biased results when the model has more than one cointegrating relationship. Another limitation is

that if the cointegration is wrongly estimated, then an error is introduced into the ECM.

Fortunately, we do not expect to encounter identification problems since the study involves two

univariate time series. Therefore, the Engle-Granger two-step type approach is the appropriate

procedure for this study.

U.S. Pecan Market Data

Pecan cold storage inventory and price series both have 132 monthly observations

covering the period from January 1991 through December 2001. The data include three pecan

cold storage inventory series (inshell, shelled, and total) and shelled pecan price series (PFHP).

PFHP series are price quotes from published industry sources for the highest shelled pecan

grade. PFHP used in this study are prices for “Fancy Halves.” These prices reflect sheller asking

prices (i.e., free on board (FOB) for shipments from the southeastern United States) (Florkowski,

2003). The total pecan series (TPCSI) (shelled basis) is the sum of the volume of shelled pecan

cold inventories (SHPCSI) and the volume of inshell pecan cold storage inventories (ISHPCSI).

42

Note that the inshell cold storage volume was converted to the shelled pecan volume by

assuming a 40% shell-out ratio.

The original monthly pecan inventory data were converted into quarterly data. From the

practical standpoint, the pecan industry and pecan buyers may view quarterly data as adequate

given the timing of their marketing decisions. The conversion from monthly to quarterly figures

was done in the following fashion. The first quarter starts in October and ends in December

because the pecan-harvesting season falls within this period. The second quarter is from January

to March, and the third quarter is from April to June. Finally, the period from July to September

is designated as the fourth quarter. The cold storage inventory volume for each quarter was the

sum of both the inshell and shelled pecan volume, respectively. The quarterly pecan cold

storage data are reported in Tables 2, 3, and 4.

For PFHP, the simple quarterly average was based on monthly quotations of the three

consecutive months aggregated into a quarter (see Table 5). The final quarterly data set ranges

from the second quarter of 1991 through the first quarter of 2002.

Descriptive Statistics of the Time Series

The coefficient of variation (CV) indicates the relative variation of the time series. In

Table 6, the highest value of the CV is for the ISHPSCI for monthly data. The price series show

the least variation. In the case of the quarterly series, however, price series has the highest CV

values. In the pecan cold storage inventory series, on the other hand, despite a reduction in value,

the CV still follows the same pattern (i.e., the ISHPSCI series has the highest CV value among

inventory series).

Table 7 reports the inventory instability and price instability indices. The inventory

instability indices suggest that inshell pecan cold storage inventories were relatively unstable,

43

Table 2 Quarterly-Average Shelled Pecan Cold Storage Inventories (SHPCSI) (Million Lbs), 1991-2002.

Year Quarter I Quarter II Quarter III Quarter IV 1991 - 67.84 87.22 73.10

1992 53.10 70.27 93.64 88.87

1993 56.93 71.79 95.99 80.60

1994 43.92 75.73 96.73 92.67

1995 51.07 70.98 92.38 91.35

1996 61.88 103.12 137.06 145.03

1997 98.33 117.99 127.16 97.97

1998 49.24 99.02 134.14 132.52

1999 72.02 93.49 101.25 77.18

2000 41.89 87.79 110.15 104.44

2001 87.48 129.69 150.30 140.09

2002 91.70 - - -

Source: Own calculations based on USDA-NASS (2003).

44

Table 3 Quarterly-Average In-shelled Pecan Cold Storage Inventories (ISHPCSI) (Million Lbs), 1991-2002.


1992 134.72 310.37 177.45 72.55

1993 118.56 247.59 143.40 34.04

1994 149.04 483.21 374.66 191.80

1995 177.93 323.84 199.63 72.95

1996 151.02 435.57 302.70 133.10

1997 113.77 287.48 159.01 39.52

1998 125.08 542.34 419.39 218.23

1999 164.90 318.00 161.01 41.40

2000 179.12 751.49 630.77 408.80

2001 390.67 491 301.69 111.72

2002 143.33 - - -

Source: Own calculations based on USDA-NASS (2003).

45

Table 4 Quarterly-Average Total Pecan (shelled basis) Cold Storage Inventories (TPCSI) (Million Lbs), 1991-2002.


1992 106.99 194.42 164.62 117.89

1993 104.35 170.82 153.35 94.22

1994 103.54 269.02 246.59 169.39

1995 122.24 200.51 172.23 120.53

1996 122.28 277.34 258.14 198.27

1997 143.84 232.99 190.76 113.78

1998 99.27 315.96 301.90 219.81

1999 137.98 220.68 165.65 93.74

2000 113.54 388.38 362.45 267.96

2001 243.74 326.29 270.98 184.77

2002 149.03 - - -

Source: Own calculations based on USDA-NASS (2003). Note: Inshell cold storage volume was converted to shelled pecan volume, assuming 40 percent shell-out ratio, and added to shelled cold storage inventory.

46

Table 5 Quarterly-Average Prices for Fancy Halves (PFHP) (dollars per lb), 1991-2002. Year Quarter I Quarter II Quarter III Quarter IV 1991 - 4.57 4.57 4.57

1992 4.27 3.50 3.53 3.71

1993 4.37 4.55 4.45 4.45

1994 3.65 2.15 2.23 2.51

1995 4.12 4.03 3.74 3.67

1996 3.20 3.10 2.81 2.24

1997 2.31 2.58 3.04 3.31

1998 3.39 2.94 3.01 3.10

1999 3.68 4.25 4.57 4.71

2000 4.10 2.88 3.04 3.78

2001 3.87 3.75 3.42 3.45

2002 2.95 - - -

Source: Own calculations based on USDA-ERS (2003).

47

Table 6 Summary Statistics on Pecan Inventory and Price Series 1991 to 2001.

Coefficient of Variation

Monthly Data

1991.1 to 2001.12 Quarterly Data

1991:II to 2002:I

SHPCSI 0.31485 0.07169

ISHPCSI 0.72385 0.1436

TPCSI 0.4334 0.0784

PFHP 0.21144 0.1755

Note: CV=Std. dev. / mean.

Table 7 Characteristics of Pecan Cold Storage Inventory and Price Behavior. Commodity Instability Index Pecan Inventory Index /

Price Index SHPCSI 7.16 0.41

ISHPCSI 14.36 0.82

TPCSI 7.84 0.45

PFHP 17.55 -

Note: Computed instability index = (std. dev. / mean) * 100.

48

followed by TPSCI and by the SHPSCI. The price instability index of the shelled pecan prices

suggests a relatively unstable series. When comparing the pecan cold storage inventory

instability to that of PFHP, the relative instability of the former was less, with all the pecan cold

storage inventories having a ratio of less than one.

Graphical Analysis of Seasonality and Nonstationarity

Seasonality and nonstationarity are the two most important properties of economic time

series. Figures 6 through 11 were examined to check for properties. Each of the figures shows

four plots. Panels 1-3 of Figure 6 plot pecan cold storage inventories in millions of pounds. All

the series appear to be nonstationary in both their variances and means. The plots also appear to

have positive trends. Panel 4 of Figure 6 plots shelled pecan prices during the period under

consideration.

Figure 7 shows the log transformation of data plotted in Figure 6. Panels 1-3 show the log

transformations of the shelled, inshell, and total pecan cold storage inventories, respectively. The

log transformation reduced the trend, but the variances and means remain nonstationary. The

price series do not show any trend.

Panel 1 of Figures 8 - 11 plot long run frequencies of the shelled cold storage,

inshell cold storage, total cold storage and shelled pecan price series, respectively. The long run

frequency represents the series transformed by the lag-polynomial ( )321 BBB +++ , which

eliminates all potential unit roots at the seasonal frequencies, while preserving unit roots at the

zero frequency. A stochastic or deterministic trend in the graph is an indication of the presence

of unit roots in levels at a specific frequency. For example, all the inventory series indicate, in

49

Figure 6 Plotted Inventories of Shelled, Inshell, and Total Cold Storage Inventories (million lbs) of Pecans and Shelled Pecan Prices (in $ per lb).

50

Figure 7 Plotted Natural Logarithm Values of Shelled, Inshell and Total Pecan Cold Storage Inventories and Shelled Pecan Prices for “Fancy Halves,” 1991- 2001.

51

Figure 8 Graphical Representation of Seasonality in Shelled Pecan Cold Storage Inventories.

52

Figure 9 Graphical Representation of Seasonality in Inshell Pecan Cold Storage Inventories.

53

Figure 10 Graphical Representation of Seasonality in Total Pecan Cold Storage Inventories.

54

Figure 11 Graphical Representation of Seasonality in Shelled Pecan Prices.

55

general, a positive trend; prices show both positive and negative trends. Thus, all the series of

interest may have a unit root at the zero frequency.

Panel 2 of Figures 8-11, shows the series in logs transformed with the lag-

polynomial ( )321 BBB −+−− . This filter preserves the unit roots only at the biannual frequency

but eliminates all potential unit roots at other frequencies. A nonstationary behavior of any of the

series indicated a possible presence of unit roots at biannual frequencies. All of biannual

transformation of cold storage inventory and shelled price series show a nonstationary behavior

in variances.

Panel 3 on Figures 8-1 shows the series in logs transformed with the lag-polynomial

( )21 B−− . The transformation removed all potential unit roots at other frequencies except the

one at the annual frequency (one cycle per annum). The presence of nonstationarity signals the

presence of unit roots at the annual frequency in the series in logs. None of the series show a

clear nonstationary behavior in this study.

Finally, the fourth panel on Figures 8–11 depicts the fourth difference filtered

series ( )41 B− . The fourth difference filter eliminates all possible unit roots at seasonal

frequencies. The plots of the filtered series are expected to exhibit a stationary behavior if the

series in logs are seasonally integrated of order one. A stationary behavior in mean and variance

is observed in this study.

Integration and Seasonal Integration

The HEGY (1990) integration tests were first applied to the raw series. To whiten the

residuals, the auxiliary regressions were only augmented with significant lags as recommended

by Ghysels et al. (1993). Statistically significant lags of up to two years were added because

shellers store pecans for up to two years. Deterministic terms, including a constant (I), a linear

56

trend (T), and seasonal dummies (SD), were also added. All regressions have seasonal dummies

included. According to Beaulieu and Miron (1993), the omission of seasonal dummies when they

are necessary may bias results.

The HEGY test results for ISHPCSI, TPCSI, SHPCSI, and PFHP are summarized in

Table 8. Only significant lags were included in the auxiliary regressions to remove

autocorrelation in the residuals. Table 8 shows the results of the HEGY test application to the

pecan cold storage inventories and shelled pecan prices. Results for the ISHPCSI series indicates

the presence of unit roots at the zero frequency, except when I and SD or I, SD and T were

included in the regression. Similarly, the null hypothesis of no unit roots was rejected at the

annual frequency only when I and SD or I, SD and T are added to the auxiliary regression.

However, no unit roots were present at the biannual frequency regardless of the deterministic

terms added.

The results in Table 8 also show that for the TPCSI variable, unit roots were found at the

zero frequency except with the inclusion of I and T or I, SD and T deterministic components.

The TPCSI variable rejected the null hypothesis of no unit roots only when I, SD and T

deterministic terms were used. In the case of the annual frequency, no unit roots were found

when the regression was augmented with I and SD or I, SD and T.

Results of the HEGY tests for the SHPCSI variable in Table 8 indicate the presence of

unit roots at both the zero and biannual frequencies. The presence of unit roots was, however,

rejected when all the deterministic terms are included in the auxiliary regression at the same

time. For the annual frequency, the tests rejected the null hypothesis of no unit roots when I and

SD or I, SD and T were added to regression.

57

Table 8 Results of Testing Pecan Inventory Series and Price Series for Seasonal Unit Roots Using HEGY Procedure. Variable Auxiliary

regression ‘t’:π1

(Zero frequency)‘t’:π2

(Bi-annual)‘F’: π3 ∩ π4

None 2.5937 3.1498** 1.9369

I 0.4312 2.7389** 1.2738

ISHPCSI I, SD -3.8639** 4.1419** 21.7962**

I, T -3.6051 6.6989** 3.8186

I, SD, T -6.2394** 5.1410** 35.4848**

None 1.7717 0.3930 0.1021

I -0.1781 0.3859 0.0792

TPCSI I, SD -0.3755 3.3147 37.5490**

I, T -7.4686** 0.9607 0.6799

I, SD, T -4.8886** 5.6876** 14.8343**

None 0.8634 0.1475 0.2689

I -1.4223 0.1258 0.4186

SHPCSI I, SD -1.94731 3.6638 17.698**

I, T -4.1131 0.7612 0.5402

I, SD, T -4.7894** 5.2146** 22.7493**

None -0.7433 3.4438** 8.4925**

I -3.0687 3.5044** 15.8450**

PFHP I, SD -2.8694 3.4163 13.6388**

58

Variable Auxiliary regression

‘t’:π1 (Zero frequency)

‘t’:π2 (Bi-annual)

‘F’: π3 ∩ π4

I, T -3.0311 3.4689** 15.3598**

I, SD, T -2.8583 3.3938 13.0947**

Note: ** indicates the rejection of the null hypothesis in question at 1% significance level. Null hypotheses: 01 =π , 02 =π , 03 =π , 04 =π , and 043 =∩ππ .

59

The last part of Table 8 presents the results of unit roots tests for PFHP. Unit roots appear

to be present at the zero frequency regardless of the deterministic terms included in the auxiliary

regression. At the biannual frequency, unit roots were found only when the regression was

augmented by I and SD, or I, SD and T deterministic components. Finally, no unit roots were

found at the annual frequency.

Results for the adjusted Dickey Fuller (ADF) test for unit root presence at the zero

frequency are shown in Table 9. The data used in the tests were seasonally adjusted. In each of

the series, the ADF test found unit roots at zero frequency. Constant terms were added in the

tests.

In sum, all series had unit roots at zero frequency, whether the data were adjusted or not.

With the exception of the ISHPCSI series, all other series showed the presence of biannual

seasonal units. In a similar fashion, all series had annual seasonal unit roots except for the PFHP

series. Since the seasonal unit root of PFHP at the biannual frequency were present when

seasonal dummies were included, this researcher concluded that SHPCSI, TPCSI and PFHP

contain seasonal unit roots at the biannual frequency. Thus, the presence of seasonal unit roots at

biannual frequency is an indication of varying stochastic seasonal patterns (Hylleberg, 1992).

The results suggest that seasonally adjusting data without knowing the nature of the seasonality

may bias the outcome. Discovering seasonality in the unadjusted data is consistent with the

nature of agricultural economic time series (Tomek, 2000).

Results of Cointegration and Seasonal Cointegration Tests

The evidence of the presence of unit roots in SHPCSI, TPCSI and PFHP led to an

examination of whether the series shared a common unit root at each frequency. Following the

EGHL procedure, the Engle and Granger (1987) technique was applied to appropriately adjusted

60

Table 9 Results of Unit Roots Test. Variable Lags ‘t’:π1

(Zero frequency)ISHPCSI: Inshell Pecan Inventories 4 -2.753

TPCSI: Total Pecan inventories 4 -2.504

SHPCSI: Shelled Pecan Inventories 4 -1.361

PFHP: Prices for Fancy halves 5 -2.829

Note: Critical value at the 5% significance level is 2.93.

61

series. For the zero frequency unit roots were removed at the biannual frequency by applying a

seasonal filter, S(B) = (1+B), to each series. The resulting filtered series, tSSHPCSI =

( )B+1 tSHPCSI , tSTPCSI = ( )B+1 tTPCSI and tSPFHP = ( )B+1 tPFHP , had unit roots only

at the zero frequency. The biannual frequency was adjusted by first differencing the series to

remove possible unit roots at the zero frequency.

The results in Table 10 suggest that the null hypothesis of noncointegration at the long

run frequency cannot be rejected in both price-inventory relationships. The null hypothesis of the

absence of seasonal cointegration is, however, rejected at the 5% significance level at the

biannual frequency in both cases. The absence of cointegrating relationship at the zero frequency

implies that there is no long run equilibrium between shelled pecan prices and cold storage

inventories. However, the presence of a seasonal cointegrating relationship at the biannual

frequency suggests that seasonal fluctuations in shelled pecan prices may be a reflection of

seasonal variations in pecan inventories.

The regression results for the seasonal static model are as follows:

(16) tPFHPI∆ = 0.114 – 0.484 tSHPCSI∆ - 0.340 1D - 0.140 2D + 0.004 3D (1.470) (-3.111) (-2.242) (-1.402) (0.071) where R2 = 0.27, DW= 1.12; t-values are in parentheses; ∆= ( )B−1 is a filter; all variables are in logs. (17) tPFHPI∆ = 0.247 – 0.478 tTPCSI∆ - 0.293 1D - 0.415 2D - 0.301 3D (3.194) (-4.953) (-3.121) (-3.519) (-3.129) where R2 = 0.44, DW= 1.35; t-values are in parentheses; ∆= ( )B−1 is a filter; all variables are in logs.

Although we should avoid drawing overly strong conclusions from the above results, the

following observations are in order. Equations (16) and (17) indicate an inverse relationship

62

Table 10 Results for (Seasonal) Cointegration. Deterministic term

Lags Long run frequency

Lags Bi-annual frequency

Shelled Pecan Price and Shelled Pecan Inventory

None 1,2,3,4,5,6,7,8 -1.91921 0 -3.93437*

I 1,2,3,4,5,6,7 -2.48430 0 -3.96010*

I, SD 1,2 -2.68242 1 -4.39597*

I, T 1,2,3,4,5,6,7 -2.54261 1 -4.84719*

I, SD, T 1,2 -3.01185 1,2,3 5.29495*

Shelled Pecan Price and Total Pecan Inventory

None 1,2,3,4,5,6,7,8 -2.12449 0 -3.98823*

I 1,2,3,4,5,6,7 -2.34461 0 -4.01643*

I, SD 1,2,3,4 -1.53934 0 -4.43838*

I, T 1,2,3,4,5,6,7 -2.45525 0 -4.01193*

I, SD, T 1,2,3,4 -1.74357 0 -4.43889*

* Indicates the rejection of the null hypothesis of noncointegration at 5% significance level.

63

between shelled pecan prices and pecan cold storage inventories (i.e., shelled and total). The

signs of the coefficient estimates obtained for both shelled and total pecan cold storage inventory

variables are consistent with prior expectations.

Table 11 reports the results for conventional cointegration using the Engle-Granger

(1987) procedure. The underlying assumption of the conventional cointegration is that unit roots

are only found at the zero frequency. The results show that shelled and total pecan cold storage

inventories were conitegrated with shelled pecan prices at the zero frequency. Shelled pecan

prices, however, were not cointegrated with total pecan cold storage inventories only when no

deterministic term or only a constant term was added.

Error Correction Models and Price-Inventory Relationships

Given the presence of seasonal cointegration at the biannual frequency, the Engle-

Granger (1987) two-step procedure can be used to determine the speed of adjustment and

Granger causality. The absence of cointegration at the zero frequency means that the ECM to be

estimated originates from the following:

(18a) 1222 −=∆ ttp ωλ t

k

iiti

q

jjtj yp 1

121

121 εδα +∆+∆+ ∑∑

=−

=−

and

(18b) 1222 −=∆ tty ωλ t

k

iiti

q

jjtj yp 2

122

122 εδα +∆+∆+ ∑∑

=−

=− ,

where 2∆ = ( )21 B− and B is a lag term.

Once the seasonal cointegration relationships were established, the SECM could be

estimated. Seasonal error correction terms, obtained from the first stage (i.e., from equations 16

and 17), were lagged one quarter period and substituted as explanatory variables in the SECM.

As in the EGHL (1993) procedure, the regressions were augmented with deterministic terms.

64

Table 11 Estimation Results for the Shelled Pecan Price and Shelled Pecan and Total Pecan Inventories. Deterministic term

Lags Long- run frequency

Shelled Pecan Price and Shelled Pecan Inventory

I 1 8.1937*

I, T 1 8.2957*

Shelled Pecan Price and Inshell Pecan Inventory

I 1, 3 -3.8561*

I, T 1, 3 -3.8690*

Shelled Pecan Price and Total Pecan Inventory

I 1 -4.1210*

I, T 1 -4.1141*

Note: * indicates the rejection of the null hypothesis of noncointegration at 5% significance level.

65

The deterministic terms were added in the cointegrating equations but not to the auxiliary

regressions. The coefficients of the seasonal error correction terms were interpreted as the speed

of adjustment. The results from estimating the SECM with appropriately adjusted data are as

follows:

(19a) tPFHP2∆ =- 0.022 + 0.153 12 −∆ tPFHP + 0.097 12 −∆ tSHPCSI + 1.3650 1ˆ −tz (-0.980) (1.055) (1.782) (5.090) R2 = 0.68, DW= 1.53; t-values are in parentheses.

In the SECM (19a), the t-statistic for the seasonal error correction term, 1ˆ −tz , turned out to be

significant, while the lagged values for tPFHP2∆ and tSHPCSI2∆ did not differ significantly

from zero.

(19b) tSHPCSI2∆ = 0.001 - 1.229 12 −∆ tPFHP -0.114 12 −∆ tSHPCSI + 1.349 1ˆ −tz (0.013) (-2.730) (-0.676) (0.828) R2 = 0.18, DW= 1.85; t-values in parentheses.

In the case of equation (19b), all variables were not significantly different from zero. The results

imply that in the process of discovering shelled pecan prices, short run dynamics of shelled

pecan prices and total pecan cold storage inventories do not occur.

Equations (20a and 20b) represent the SECM results for the shelled pecan price discovery

process with respect to total pecan cold storage inventories.

(20a) tPFHP2∆ = -0.018 +0.340 12 −∆ tPFHP + 0.018 12 −∆ tTPCSI + 0.981 1ˆ −tε (-0.600) (1.743) (0.227) (2.563) R2 = 0.47, DW= 1.50; t-values are in parentheses.

In the SECM (20a), the t-statistic for the seasonal error correction term, 1ˆ −tε , appeared to be

significant while that of the lagged values for tTPCSI2∆ and tPFHP2∆ were both insignificant.

66

The lack of statistical significance implies that there is no relationship between prices and the

short run dynamics of prices and total pecan inventories.

The results in equation (20b) show that the t-statistic for 1ˆ −tε and the lagged values for

tPFHP2∆ and tTPCSI2∆ all appear not to be significantly different from zero.

(20b) tTPCSI2∆ = -0.0002 -0.9401 12 −∆ tPFHP - 0.0147 12 −∆ tTPCSI + 1.2480 1ˆ −tε (-0.0026) (-1.4763) (-0.0741) (0.9648) R2 = 0.08, DW= 1.77; t-values in parentheses. The speeds of adjustment in equations (19a) and (19b) indicate the variable that adjusts

after a deviation is price. Similarly, equations (20a) and (20b) show that the price adjustment

follows a disequilibrium. The positive speeds of adjustment in equations (19) and (20), however,

do not mean the adjustment will cause the system to deviate gradually from the equilibrium. In

the case of SECM, the sign of the speed of adjustment does not make any difference (Lee, 1992;

Shen and Huang, 1999). For example, Shen and Huang (1999) stated that the average speed of

adjustment of the seasonal error correction terms can be interpreted as moving toward

equilibrium even if it is positive.

Unlike most studies (e.g., Blinder, 1986; Lee, 1996; and Lee and Siklos, 1997), this study

has high speeds of adjustment (1.36 for the shelled pecan market and 0.98 for the total pecan

market). Although most of the studies with slow speeds of adjustment have used macroeconomic

data, this study used microeconomic data. But the use of microeconomic data does not explain

the high values of the speeds of adjustment. Generally, the high speed of adjustment may be due

to a rapid adjustment or misspecification. There is, however, no indication that the model is

misspecified because only two variables were involved in the study.

A stability test (Hansen, 1992) was conducted to determine the stability of the parameters

in equations (19) and (20). The stability test results for the error correction coefficients in

67

equations (19a) and (20a) are 0.0599 and 0.0946, respectively (see Table 12). In each case, we

failed to reject the null hypothesis of stability at the 5 percent significance level (critical value of

0.470). The result of the joint stability test result for equation (19a) was found not to be

significantly different from zero. Also, the joint stability test for equation (20a) was found to be

insignificant. Thus, the high coefficient of the speed of adjustment in equation (19a) implies a

rapid adjustment to a seasonal equilibrium from deviations between shelled pecan prices and

shelled pecan cold storage inventories (Kunst, 2004). Similarly, the high coefficient of the speed

of adjustment in equation (20a) indicates a rapid adjustment after a seasonal equilibrium

deviation between shelled pecan and total pecan prices and shelled pecan cold storage

inventories. The high adjustment coefficients, therefore, were caused by neither model

misspecification nor explosive data.

Table 13 shows the result of the Engle-Granger two-step test for error correction model.

The speed of adjustment of a deviation from the long run equilibrium between shelled pecan

prices and shelled pecan inventory was -0.411. The speed of adjustment means that shelled pecan

prices partially adjusted to the deviation at the rate of 41%. Similarly, the adjustment rate for

shelled pecan prices to long run equilibrium deviation in inshell or total cold storage inventories

is 44%.

In summary, SHPCSI, ISHPCSI, TPCSI and PFHP were found to have unit roots at the

zero frequency. But only SHPCSI, TPCSI and PFHP had common seasonal unit roots at the

biannual frequency, indicating stochastic seasonality. Next, the cointegration test found that

pecan prices seasonally cointegrated with pecan cold storage inventories (i.e., SHPCSI and

TPCSI) at the biannual frequency. In addition, the study found that prices adjusted at a fast rate

to a seasonal equilibrium deviation in models (19a) and (20a). The

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Table 12 Seasonal Error Correction Models (SECM) and Instability Tests. SECM1 SECM2

Parameter tPFHP2∆ tSHPCSI2∆ Parameter tPFHP2∆ tTPCSI2∆

0β -0.0229 (-0.9807)

-0.0009 (-0.0132)

0α -0.0184 (-0.6006)

-0.0002 (-0.0026)

1L 0.0758 0.0332 1L 0.0356 0.0290

1β 0.1537 (1.0551)

-1.2295 (-2.7306)

1α 0.3404 (1.7431)

-0.9401 (-1.4763)

2L 0.0964 0.0758 2L 0.0374 0.0457

2β 0.0977 (1.7823)

-0.1145 (-0.6765)

2α 0.0184 (0.2272)

- 0.0147 (-0.0741)

3L 0.1498 0.0425 3L 0.1498 0.0108

1γ 1.3650 (5.0909)

1.3491 (0.8283)

2γ 0.9813 (2.5636)

1.2480 (0.9648)

4L 0.0599 0.0749 4L 0.0946 0.0897

2σ 0.1133 0.0539 2σ 0.0614 0.0979

2R 0.69 0.18 2R 0.47 0.08

Joint cL 0.6377 0.4386 Joint cL 0.6433 0.4005

Note: SECM1 represents price-shelled pecan inventories; SECM2 represents price- total pecan inventories; the asymptotic critical value at 5% is 0.470 (Hansen, 1992).

iγ are error correction parameters and iL denote stability test statistics.

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Table 13 Error Correction Models (ECM). Independent Variables Dependent Const 1−∆ tPFHP 1−∆ tSHPCSI 1−∆ tISHPCSI 1−∆ tTPCSI 1−tε

tPFHP1∆ -0.003 (-0.126)

0.970 (7.531)

0.588 (4.103)

-0.411 (-4.137)

tPFHP2∆ 0.003 (0.108)

0.625 (3.534)

-0.018 (-0.323)

-0.440 (-3.043)

tPFHP3∆ 0.007 (0.198)

0.859 (3.778)

0.231 (1.417)

-0.438 (-2.630)

Note: t-statistics are in parentheses.

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parameters were found to be stable. In contrast, long run equilibria between shelled pecan prices

and pecan cold storage inventories were found using adjusted data. In addition, speeds of

adjustment were found to be -0.411, -0.44 and -0.43 for shelled pecan price-shelled, shelled

pecan price-inshell, and shelled pecan price-total cold storage inventories, respectively. The

other parameter coefficients simply indicated the short run dynamic relations between the

variables. According to the results in Table 12, the short run changes in the past shelled pecan

prices and shelled pecan cold storage inventories had significant effects on shelled pecan prices.

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CHAPTER 6

SUMMARY, CONCLUSIONS AND FUTURE RESEARCH

The seasonal cointegration methodology has not been used widely by agricultural

economists in empirical research even though it has been established that agricultural economic

data have seasonality problems. This dissertation contributes to the literature by applying

seasonal cointegration methodologies (e.g., Hylleberg et al., 1990; Engle et al., 1993; Lee, 1992)

to the study of pecan price relationships.

This chapter summarizes the content of the dissertation, highlights the main conclusions,

and outlines areas of immediate research interest. The organization of the rest of the chapter is as

follows: Section 1 outlines the objectives that were described in Chapter 1. The overview of the

pecan industry, literature review, economic theory, and econometric literature are summarized in

Section 2. Section 3 outlines the specific conclusions of the dissertation. The limitations and

suggestions for future research are described in Section 4.

Research Themes

The first theme focused on the role of the pecan sheller in the pecan market. This issue is

considered timely because the pecan sheller plays a vital role in the pecan industry, yet very little

research has been conducted from the sheller’s perspective. The role of the pecan cold storage

inventories in determining the price of shelled pecan prices can be interpreted as being analogous

to the role of the sheller in the pecan industry because the sheller becomes the sole owner of a

major portion of the pecan supply soon after harvest.

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The second theme focused on applying recent econometric developments to the study of

perennial agricultural commodity price relationship with inventories. The study employed

seasonal cointegration methodologies (HEGY, 1990; EGHL, 1993) to determine the relationship

between shelled pecan price and pecan cold storage inventory.

The Literature and Econometric Analysis

Chapter 2 described the pecan industry with specific reference to the role of the sheller.

The sheller plays the role of middleman between the grower and the end user of shelled pecans.

By shelling and storing both the shelled and inshell pecans, the sheller is strategically positioned

in the pecan marketing chain. Next, Chapter 3 reviewed the existing literature on the study of

perennial agricultural crops. Several of these studies used various methodologies such as

cointegration, OLS, GLS, and two stage least squares. The few studies that investigated price-

inventory relationships focused mostly on the macroeconomic relationships and international

trade issues. The relevant contribution of this dissertation is that no study has formally applied

seasonal cointegration methodology to explain the pecan price relationship to pecan cold storage

inventories.

Chapter 4 introduced the theoretical underpinnings of price behavior in relation to

inventories. Following Weymar (1968), the chapter showed how the supply of storage function

was explicitly used to build an economic theory consistent with spot price behavior. Finally,

chapter 5 explained the use of seasonal cointegration methodology in the empirical analysis. The

estimated results were also presented in Chapter 5. Employing the HEGY (1990) procedure and

the use of quarterly pecan data, this study first examined the nature of seasonality in the pecan

data. Next, the seasonal cointegration test was conducted using the EGHL (1993) procedure.

Finally, the short run dynamics were examined using the ECM.

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Conclusions and Implications

This study successfully applied seasonal cointegration methodology to pecan price

analysis. The researcher has gained insight on price relationship with pecan cold storage

inventories. Specifically, the influence that cold storage inventories have on shelled pecan prices

was uncovered using time series modeling techniques.

The findings of the study are divided into two categories, namely, methodological and

practical. The methodological, findings can be classified, generally, into three groups: (a) unit

roots, (b) cointegration, and (c) error correction. The tests for unit roots confirmed the presence

of unit roots at the zero frequency when both unfiltered and filtered data were used. The results

suggest that pecan data are nonstationary at the zero frequency. But the presence of seasonal unit

roots when unadjusted data are used suggests that pecan data are characterized by varying and

stochastic seasonal patterns. In contrast, the unit root at the zero frequency for the adjusted data

may not only be inconsistent but also lack power due to over differencing (Hylleberg et al.,

1990). In addition, these findings are consistent with the observation that most agricultural

economic time series have seasonal components (Tomek, 1994).

From the biannual seasonal cointegration model, the shelled pecan price-shelled pecan

cold storage inventories and shelled pecan price-total pecan cold storage were found to be

cointegrated. The results reveal that both shelled and total pecan cold storage inventories have a

seasonal influence on shelled pecan prices. Thus, pecan wholesale prices are seasonal in nature.

Results in Tables 8 and 9 indicate the existence of inconsistencies between the seasonally

adjusted data and unadjusted data. These inconsistencies have serious implications. The

conclusions about the long run relationship between price and inventory are obviously sensitive

to whether the data have been seasonally adjusted or not. Seasonal adjustment seems to have a

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distorting effect on the outcome of the Engle-Granger (1987) type tests in favor of long-run

cointegration.

The absence of cointegration at the zero frequency, however, means there is no long run

equilibrium in the pecan market, when only cold storage inventories are considered. The lack of

long run equilibrium may be due to the following reasons. First, the structural changes observed

in the pecan industry over the study period may have disrupted the process. For example, the

number of the U.S. pecan shelling plants declined from 30 to about 20 in 2003. Second, the

grower tree removal in the Southeast may also be, in part, responsible for the observed lack of

long run equilibrium. For instance, growers are known to remove trees or reduce the application

of fertilizers after receiving lower prices, expecting higher prices the following year from a

smaller harvest. Finally, climatic conditions, such as periodic droughts, may have also influenced

the lack of long run equilibrium. Note, however, that the above mentioned possible problems

may have had only regional, rather than national, impacts.

The coefficient for the speed of seasonal price adjustment in the case of shelled pecan

price-shelled pecan inventories was greater than one. This result implies that the seasonal

disequilibrium adjusts at a rapid pace (Kunst, 2004). For the price-total cold storage inventory

relationship, the significant coefficient for the speed of seasonal adjustment was 0.98. This result

also suggests a rapid adjustment to any deviation in the seasonal price equilibrium.

The finding of seasonal cointegration relationship between price and inventory in the

pecan market has important practical implications. This study found that the influence of cold

storage inventory on shelled pecan price is seasonal. As a result, we can conclude that the sheller

plays a vital role in the pecan industry by storing pecans. The significance of the finding to the

pecan industry can be illustrated by an explanation of forward contracts.

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Most pecan shellers engage in forward contracting. Shellers forward contract a large

portion of their pecan inventories. As a result, shellers may not have as much influence on pecan

prices as perceived by pecan growers. Shellers benefit from forward contracts on shelled pecans

through assured access to a market, the potential for increased operational efficiency, and

reduced price risk. We do not know, however, what portion of the inventories is still owned by

the sheller. The study also benefits the sheller in the decision making process regarding the use

of forward contracts. A sheller can choose to continue with forward contracts which will reduce

or eliminate the price risk by selling on cash basis.

Since growers are not able to store pecans, this study enables them to understand the

timing of sales in order to obtain higher prices for their crop. Studies have shown that prices paid

to growers by shellers directly reflect prices they receive from end users. Also, because shellers

report volume without differentiating between the volumes of pecans readily available to the

market and those already sold to end users, voluntary reporting is not likely to provide all

relevant information for the price discovery process.

End users such as commercial bakers, ice cream manufacturers, retailers, and

confectioners can benefit from this study by improving their understanding of the seasonal nature

of prices created, possibly, by forward contracting in the pecan market. End users usually initiate

forward contracts to guarantee their pecan supply throughout the pecan marketing year. For

example, commercial bakers purchase the major portion of shelled pecans and, because they

have to meet the seasonal demand (Thanksgiving and Christmas) and beyond, they would do

well to forward contract during the harvesting period. Delivery should be spread over the rest of

the marketing season. Ice cream manufacturers can benefit by forward contracting after the

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seasonal demand peaks in November and December. Like the commercial bakers, retailers and

confectioners should not restrict themselves to any part of the contracting period.

The finding of seasonal components in the pecan inventory data also suggests that

shellers may be holding pecan inventories, for the most part, to meet contractual obligations.

Moreover, the detection of seasonal components and appropriate data transformation could result

in efficient pecan price forecasts to the benefit of all agents in the pecan industry.

Limitations and Future Research

The quality of empirical studies is often influenced by the quantity and quality of

available data. This study may be limited by factors such as the paucity of data and the averaging

problem. The USDA only started collecting monthly data on pecan cold storage inventories in

1991. Because shellers are assumed to make decisions on a quarterly rather than a monthly basis,

quarterly data were necessary for this study. Since the quarterly data were not readily available,

they had to be created using monthly data. The created quarterly data are monthly averages,

aggregation that may have caused autocorrelation and heteroskedasticity problems (Tomek,

1994). Another data problem is highlighted in the results shown in Table 6: shelled pecan prices

varied the least when monthly data were used. However, when converted into quarterly, shelled

pecan prices varied the most.

Canova and Hansen (1995) noted that the HEGY test is limited by its low power in

moderate sized samples. In such a case, a non-rejection of the null hypothesis unfortunately

cannot be interpreted as evidence for the presence of a seasonal unit root. Thus, rejection of the

null hypothesis strongly indicates that a stationary seasonal pattern is present.

This study was not exhaustive and can be extended to include other aspects of price

analysis. One possible area of research is the use of multivariate models that will allow for the

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inclusion of other price determining factors such as the price of close substitutes (e.g., walnuts).

The maximum likelihood approach could then be employed to measure seasonal cointegration

(e.g., Lee, 1992). The maximum likelihood approach allows the testing of several null

hypotheses separately for each case, without having any prior knowledge about cointegration

relations at other frequencies.

Besides increasing the number of explanatory variables, the Beaulieu and Miron (1993)

or Franses (1991) seasonal cointegration techniques could be applied using monthly data.

Because the USDA reports pecan cold storage inventories on a monthly basis, a study of pecan

price relations with pecan inventories using the monthly data is possible.

Finally, the seasonal error correction term could be used in forecasting pecan prices.

According to Lee and Siklos (1997), having a significant error correction term suggests that

seasonality can be explicitly used in the forecasting process. A seasonal cointegration forecasting

technique could be a viable method in forecasting prices received by shellers in the pecan

industry.

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A SEASONAL COINTEGRATION APPROACH MOHAMMED IBRAHIM

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