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
THE RELATIONSHIP BETWEEN PECAN PRICE AND COLD STORAGE INVENTORIES:
A SEASONAL COINTEGRATION APPROACH
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
THE RELATIONSHIP BETWEEN PECAN PRICE AND COLD STORAGE INVENTORIES:
A SEASONAL COINTEGRATION APPROACH
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)
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
Feb-
01
Mar
-01
Apr-0
1
May
-01
Jun-
01
Jul-0
1
Aug-
01
Sep-
01
Oct
-01
Nov-
01
Dec-
01
Months
Mill
ion
Lbs
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 in- shell 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.
Year Quarter I Quarter II Quarter III Quarter IV 1991 - 231.95 134.46 40.34
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.
Year Quarter I Quarter II Quarter III Quarter IV 1991 - 160.62 141.00 89.24
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
74
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.
75
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
76
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
77
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.
78
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