A BIO-ECONOMETRIC ANALYSIS OF THE
GULF OF MEXICO COMMERCIAL REEF FISH FISHERY
BY
TIMOTHY GORDON TAYLOR
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR
THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1980
ACKNOWLEDGMENTS
To acknowledge all who have assisted in my graduate career would be
an impossible task. I wish to express my appreciation and thanks to my
many unrecognized colleagues.
My greatest debt of gratitude is to my wife, Keri, whose patience,
support and love carried me through many trying times.
Fred Prochaska served not only as chairman of the supervisory
committee, but also as a close friend. His insight has enhanced my
ability as an economist. Jim Cato gave freely of his time in providing
an excellent critique of this dissertation which greatly improved the
final draft. I also wish to thank the other members of my supervisory
committee, Tom Spreen, John Reynolds and Bill Seaman, for their many
contributions to this study. To many of my fellow students who provided
help and friendship during my tenure as a graduate student, I wish to
say thanks.
I also wish to thank Leo Polopolus, Chairman of the Food and
Resource Economics Department of the University of Florida, and George
Maddala, Director of the Center for Econometrics and Decision Sciences,
for providing financial assistance during my graduate career.
I am also greatly indebted to Leigh Parsons and Janet Eldred for
their help in the seemingly impossible task of typing and putting this
dissertation into its present form.
ii
TABLE OF CONTENTS
ACKNOWLEDGMENTS .. . ...
LIST OF TABLES . .
LIST OF FIGURES .. .......... .
ABSTRACT ...........
CHAPTERS
I INTRODUCTION .. ...........
Objectives . .
Scope .
II THEORETICAL FOUNDATIONS ............
Biological Theory .........
Sustainable Yield. .. .......
Stock Production Models .. ......
Basic Bioeconomic Models of the Fishery .
Static Bioeconomic Fishery Models .. ...
Dynamic Bioeconomic Fishery Models ...
Theoretical Extensions .. ..
Fishing Effort and Equilibrium Yield .
Variable Product Price ....
A Multi-Sector Fishery ....
III EMPIRICAL MODEL .......
Introduction . .
Catch Equation Specification and Estimation .
Specification of Fishing Effort .. ....
Within Region Specification Considerations
Stochastic Approximation of Resource Stock
Effects . .
iii
Page
ii
vi
ix
xi
1
6
8
9
10
10
14
18
19
24
33
34
38
43
51
51
52
53
55
57
TABLE OF CONTENTS (Continued)
Page
Cross-Sectional Specification
Considerations .... .. ..... ... .. 59
Choice of Estimator for the Catch
Equations . .. 63
Price Equation Specification and Estimation ...... 68
Aggregation Across Species .... ..... .69
Choice of Estimator for the Price Equation ... 74
IV EMPIRICAL RESULTS .................. .. 77
Analysis of Production in the Gulf of Mexico Reef
Fish Fishery .. ... ................ 77
Fishing Power .................... 81
Catch Equations .............. 88
Derived Equilibrium Catch Equations ......... 89
Productive Interdependence and Average
Productivity . 91
Analysis of the Price Equations ............ 94
Gulf of Mexico Reef Fish Optimization Model ...... 100
Total Revenue Equations .............. 101
Cost Equations ............. .... 102
Catch Equation Constraints ............ 106
Maximum Economic Yield .. .. ........... 107
Exogenous Changes in Fishing Power ......... 114
Comparison with Previous Studies ......... 119
V SUMMARY AND CONCLUSION ................ 123
Theoretical Conclusions ... ....... .125
Estimated Parameters ........... 127
Condition and Management of the Fishery ......... 134
APPENDICES
A SPECIES COMPOSITION OF THE FISHERY AND THE
DISTRIBUTION OF FISHING ACTIVITY ........... 140
B DATA UTILIZED IN ANALYZING THE GULF OF MEXICO
COMMERCIAL REEF FISH FISHERY ......... 144
iv
TABLE OF CONTENTS (Continued)
Page
C DERIVATION OF EFFORT LEVELS FOR MAXIMUM
SUSTAINABLE YIELD AND MAXIMUM ECONOMIC YIELD .... 154
D GRAPHICAL DERIVATION OF THE DOUBLE HUMPED
SUSTAINABLE REVENUE CURVE ...... ......... .157
E IDENTIFICATION OF THE ORDER OF THE AUTOREGRESSIVE
PROCESSES IN THE CATCH EQUATIONS ............ .159
Bartlett Test .. .. .......... 159
Max x2 Test .... .. ..... 160
Akaike's Final Prediction Error (FPE) Test ..... 160
Durbin-Watson Test ................. .161
F MARKETING AND PRICE INFORMATION CONCERNING GULF
OF MEXICO RED SNAPPER AND GROUPER ........... 163
G RESOURCE STOCK ADJUSTMENT FOR FIXED LEVELS OF
EFFORT . 166
H THE GULF OF MEXICO OPTIMIZATION MODEL AND
RESULTS OF EXOGENOUS CHANGES IN FISHING POWER ..... 169
BIBLIOGRAPHY .... ... ................ ...... 172
BIOGRAPHICAL SKETCH .................. .. 176
LIST OF TABLES
Table Page
1 Ordinary least squares with dummy variables parameter
estimates for the Gulf of Mexico Reef Fish Fishery
catch equations .................. ... 79
2 Four state Aitken's parameter estimates for the Gulf
of Mexico Reef Fish Fishery catch equations ....... 80
3 Estimated relative fishing power indices by state,
1957-75 ..... ..... .. .. ... ... 84
4 Estimated number of standardized reef fish vessels
and actual number of reef fish vessels in the Gulf
of Mexico Reef Fish Fishery by state, 1957-1975 ...... 85
5 Estimated differences in intercepts for the Gulf of
Mexico Reef Fish Fishery state catch equations ..... 93
6 Ordinary least squares parameter estimates for the
Gulf of Mexico Reef Fish Fishery price equations ..... 96
7 Two stage Aitken's parameter estimates for the Gulf
of Mexico Reef Fish Fishery price equations ....... 97
8 Estimated within and across state price flexibilities
for states participating in the Gulf of Mexico Reef
Fish Fishery ........ ......... .. 99
9 Estimated annual operating and maintenance costs for
reef fish vessels by state, 1979 .... ... .. 105
10 Adjusted and unadjusted intercepts for the estimated
Gulf of Mexico Reef Fish Fishery catch equations by
state ..... ......... .... .108
11 Estimated catch, profits and effort levels cor-
responding to maximum economic yield in the Gulf of
Mexico Reef Fish Fishery ... .. ..... .. 109
12 Number of reef fish vessels in 1975 and the
economically optimum number of vessels by state ...... 110
vi
LIST OF TABLES (Continued)
Table
13 Estimated species composition of MEY catch of reef
fish . .
14 Fishing power components for proportional increases
along rays defined by constant vessel size-crew
size ratios . .
A-1 Species in the management unit ....
A-2 Species included in the fishery but not in the
management unit .
B-1 Red Snapper catch by countries, 1970-1973 .. .
B-2 Grouper catch by countries, 1970-1973 .. ...
B-3 Estimated catch and effort in Gulf of Mexico
recreational reef fishery for selected years .
B-4 Estimated number and weight of reef fish caught by
recreational fishermen in the Gulf of Mexico, 1975
B-5 Estimated catch of reef fish per handline vessel
in the Gulf of Mexico, 1957-1975 .. ......
B-6 Catch of reef fish by handline vessels in the Gulf
of Mexico Reef Fish Fishery, 1957-1975 .. ....
B-7 Average crew size of reef fish vessels by state,
1957-1975 . .
B-8 Average size of reef fish vessels by state, 1957-
1975 . .
B-9 Number of reef fish vessels by state, 1957-1975 .
F-1 Domestic marketing of grouper and snapper by Gulf
of Mexico commerical fish dealers, 1977 .. ..
F-2 Two stage Aitken's parameter estimates for Red
Snapper and Grouper price equations .. ......
H-1 Maximum economic yield in the reef fishery given
a 10 percent increase in average fishing power
per vessel . .
Page
. 115
S. 116
S. .. .140
. 141
S. 144
. ... 145
. 146
. .. 147
. 148
S. .. 149
S.... 150
S. ... 151
. 152
. 163
. 164
. 170
vii
LIST OF TABLES (Continued)
Table Page
H-2 Maximum economic yield in the reef fishery given
a 15 percent increase in average fishing power
per vessel ................ .... .. 170
H-3 Maximum economic yield in the reef fishery given
a 20 percent increase in average fishing power
per vessel ................... ..... 171
H-4 Maximum economic yield in the reef fishery given
a 25 percent increase in average fishing power
per vessel .............. ...... .. 171
viii
* 0
Vill
LIST OF FIGURES
Figure
ix
Page
11
13
18
20
22
1 Relationship between population size and mature
progeny .. .
2 Quadratic sustainable yield function .........
3 Equilibrium yield relationships for various
values of m . .. .
4 Allocation of fishing effort between fishing
grounds of different productivity or location .. ...
5 Cost and revenue in an unregulated fishery with
constant product price .. ........
6 Phase diagram for equilibria between vessels and
resource stock in an open access fishery ...
7 Open access equilibrium and maximum economic yield
in a fishery with constant product price ...
8 Open access equilibria and maximum economic yield
in a fishery with variable product price ....
9 Equilibrium in a multi-sector fishery with
variable price and pecuniary externalities ..
10 Principal fishing grounds in the Gulf of Mexico
Reef Fish Fishery . .
11 Estimated relative fishing power for proportionate
increases in average crew size and vessel size ...
12 Iso-fishing power contours for selected levels of
relative fishing power .......
13 Derived equilibrium catch equations for the Gulf
of Mexico Reef Fish Fishery .. ...
14 Optimum number of vessels corresponding to maximum
economic yield for increasing levels of average
fishing power . .
S. 30
S. 38
39
48
. 62
. 82
.. 87
. 92
S. 117
Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philsosphy
A BIO-ECONOMETRIC ANALYSIS OF THE
GULF OF MEXICO COMMERCIAL REEF FISH FISHERY
By
Timothy Gordon Taylor
December, 1980
Chairman: Frederick J. Prochaska
Major Department: Food and Resource Economics
Commercial reef fish landings (primarily grouper and red snapper)
from the Gulf of Mexico have declined fairly consistently since the mid-
sixties while the number of reef fish vessels has increased in all
coastal states except Louisiana. Declining catch per unit of effort has
caused concern in the industry. The main objective of this dissertation
was to construct an aggregate econometric model of the commercial sector
of the Gulf of Mexico Reef Fish Fishery and estimate maximum economic
yield. The basic theoretical model developed was a multi-sector model
with variable production prices and pecuniary externalities. Each
state participating in the fishery constituted a single sector. An
alternative methodology for obtaining equilibrium catch functions was
developed and utilized.
Stochastic processes were identified and incorporated into the
residual components of the estimated catch equations to account for the
unobservable resource stock effects. Derived equilibrium catch func-
tions were obtained by taking the limit of the catch equations over
time, with fishing effort held constant. A non-linear optimization
model for the Gulf of Mexico Reef Fish Fishery was constructed through
xi
incorporation of the derived equilibrium catch functions with a system
of estimated price and cost equations.
Maximum economic yield of reef fish was estimated to be 11.5
million pounds. The economically efficient number of nominal vessels
corresponding to this level of catch was estimated to be 180. This
result was conditioned by exogenously fixed average fishing power per
vessel at 1975 reported levels. Fishing power was systematically
changed to determine the effects of such changes on maximum economic
yield and the corresponding optimum number of vessels.
The results of the analysis implied that the reef fish fishery in
1975 was overfished biologically and economically. To support this
implication, a Schaefer type sustainable yield function was estimated
for the domestic Gulf of Mexico Reef Fish Fishery. Maximum sustainable
yield was estimated to be 13.7 million pounds which is consistent with
the implication of overfishing.
xii
CHAPTER I
INTRODUCTION
The Gulf of Mexico Reef Fish Fishery is one of the oldest
(Carpenter, 1965) and most important of the Gulf fisheries in terms of
both quantity landed and total dockside value. The fishery encompasses
a wide variety of fishes, including 15 species of snappers, 15 species
of groupers and 3 species of sea basses. Although the above species
constitute the management unit as defined by the Gulf of Mexico Fishery
Management Council (GMFMC, 1979), several additional species of fish are
taken incidentally. These incidental species include several species
each of tilefishes, jacks, tiggerfishes, wrasses, grunts, porgies and
sand perches (Appendix A). In spite of the sizable number and variety
of species taken, three species, red snapper (Lutjanus campechanus), red
grouper (Epinephelus morio) and black grouper (Mycteroperca bonaci), are
the most desired species and hence the most abundant in commercial
catches (Moe, 1963). All of the Gulf Coastal States participate in the
reef fishery with fishing activity widely dispersed throughout the Gulf
of Mexico.
The Gulf of Mexico Reef Fish Fishery (GMRFF) is the primary domes-
tic producer of reef fish, accounting annually for an average of 93
percent of total domestic catch. Total landings (U.S. NMFS, 1979) in
1The Gulf Coastal States include Florida West Coast, Alabama,
Mississippi, Louisiana and Texas.
1979 were reported to be 10.3 million pounds with a total dockside value
of $10.4 million. Red snapper landings were 4.2 million pounds with a
dockside value of $5.6 million, while grouper landings were reported to
be 6.0 million pounds at $4.7 million. The importance of red snapper
and grouper to the GMRFF can be seen from these figures. In 1976, red
snapper and grouper accounted for 82 percent of all reef fish landings
by weight and 86 percent of the total revenue generated in the commer-
cial Gulf of Mexico Reef Fish Fishery.
Three nations, Cuba, Mexico and the United States, are responsible
for the bulk of the world supply of reef fish (grouper and red snapper).
The U.S. is the leading producer of red snapper, accounting for approxi-
mately 52 percent of the world catch in 1973 (Klima, 1976). In that
same year the United States ranked third in grouper production, behind
Mexico and Cuba which accounted for 52 and 29 percent of the world
catch, respectively (Appendix B).
The Gulf of Mexico reef fish stocks also support a significant
recreational fishery. The recreational sector is composed of three
distinct segments: party or head boats, charter boats and privately
owned and operated boats.2 Although data pertaining to the recreational
fishery are somewhat scant, there is sufficient evidence to suggest
that it is larger, in terms of catch, than the commercial fishery.
Surveys conducted in 1960, 1965 and 1970 indicated recreational catches
of 122.6, 70.9 and 76.8 million pounds of reef fish, respectively
(Clark, 1963; Duel and Clark, 1968; Duel, 1973). Total recreational
2Party or head boats generally carry over 20 passengers while
private charter boats carry six passengers or less.
catch, however, dropped to 39.5 million pounds in 1975 (GMFMC, 1979).
The proportion of groupers and red snapper present in recreational reef
fish catches declined significantly over the 1960 to 1970 period. In
1960, approximately 69 percent of the total weight of the recreational
catch was comprised of these primary species. By 1970, this proportion
dropped to only 39 percent of the total. Preliminary data for 1975
indicated that this proportion rose to 64 percent of the 1970-1975
period, however (Appendix B).
Within the fishery the Florida West Coast is the dominant producer
with respect to both catch levels and industry size. In 1976, Florida's
West Coast accounted for 81 percent of total Gulf of Mexico reef fish
landings. In terms of the primary species, Florida's West Coast
accounted for 57 percent by weight and 67 percent by value of the total
red snapper catch and 96 percent by both weight and value of all grouper
landed in the Gulf of Mexico in that same year. Industry size, as
measured by the number of vessels reported by states, also illustrates
the dominant position of Florida. In 1976, 509 vessels were reported in
the reef fishery. Of these vessels, 449 fished out of Florida Gulf of
Mexico ports. During the 1970 to 1976 period, 82 percent of all GMRFF
vessels originated from Florida West Coast ports.
The Gulf of Mexico reef fishery is a hook and line fishery. The
fishing process mainly involves the location of high concentrations of
reef fish and the capture of these fish using hand or mechanically
operated fishing reels. Generally, each crewman on a vessel operates
only one reel. Fishing activity in the Gulf of Mexico occurs over a
wide geographic area ranging from the West Florida shelf to the Western
Gulf off Texas and as far south as the Campeche shelf near Mexico
(Appendix A). Given the ."search and capture" nature of the fishing
process, two of the most important "inputs" in the reef fish fishery are
the size of vessels and the crew sizes corresponding to fishing vessels.
Average vessel sizes are heterogeneous across states. Florida vessels
are the smallest, having an average size of 24.7 gross registered tons
in 1976. Vessels originating from Mississippi ports are the largest,
averaging 73 gross registered tons per vessel in the same year (GMFMC,
1979). Crew sizes also exhibit considerable variation across states
ranging from an average of three men per vessel for Florida vessels to
nine men per vessel aboard Mississippi vessels in 1976.
Very little information is available on costs and revenues of
commercial reef fish vessels in general. Some data, however, have been
accumulated for Florida vessels for the years 1974 and 1975 (Cato and
Prochaska, 1977). While these data cannot be assumed representative of
vessels originating from states other than Florida, they nevertheless
provide some indication as to the magnitude of costs and revenues cor-
responding to reef fishery vessels. During 1974 and 1975, the average
annual total revenue for Florida vessels operating in the reef fish
fishery was estimated to be $56,484. In general, $11,680 of the revenue
went to crew shares with the captain and/or owner receiving an average
of $22,752. The remaining revenue was used for payment of fixed and
variable vessel expenses. During this period average investment per
vessel ranged from $26,526 to $67,267.
Total commercial landings in the GMRFF have exhibited a fairly
consistent decline from a peak of 24.7 million pounds in 1965 to approxi-
mately 18.3 million pounds in 1972. Since 1972, reef fish landings have
shown no significant trend, fluctuating between 16.7 and 17.7 million
pounds. This appearance of constancy is somewhat misleading, however,
in that from 1972 to 1976 the total landings of the primary target
species, red snapper and grouper, continued to decline. Combined land-
ings of these primary species have decreased 37 percent from 22.5
million pounds in 1965 to 14.0 million pounds in 1976. Thus, the
apparent constancy of total reef fish landings is attributable to in-
creased landings of the less desired reef species. The behavior of
total landings since 1972 is especially interesting given the fact that
fishing effort as measured by the number of vessels operating in the
fishery has increased consistently during this time. Within the 1957
to 1976 period covered by current available data, three states--Florida,
Alabama and Mississippi--experienced their lowest average catch per
vessel in 1976 (Appendix B).
In spite of the trends in total catch and catch per vessel, only
partial conclusions can be offered with respect to the biological status
of the reef fish stocks and the extent to which economic efficiency
exists in the fishery. The Gulf of Mexico reef fish stocks are typical
of biological populations in that any given level of stock size
(measured by either numbers or weight) is capable of producing a sus-
tainable yield. That is, a given proportion of the population may be
harvested in any given time period while leaving the underlying stock
size unchanged. Biological theory has maintained that, in general,
sustainable yields can range from zero to some unique maximum level,
termed maximum sustainable yield (MSY) (Gulland, 1965). Furthermore,
this body of theory when used in conjunction with economic theory has
suggested that the common property nature of the fishery in combination
with the interdependency of producing units would, under a competitive
6
regime, lead to economically inefficient levels of catch and fishing
effort (Gordon, 1954). Generally, a fishery is said to be biologically
overfished if fishing effort being expended is greater than that
required to capture MSY, while the fishery is considered to be economi-
cally overfished if aggregate fishing effort exceeds the point where the
3
marginal cost of effort equals marginal revenue.
Production in the GMRFF has followed a competitive regime through-
out most of its long history.4 Whether or not his competition has led
to a situation of economic and/or biological overfishing remains largely
unanswered. To date, only limited aggregate economic analysis has been
conducted on this fishery. The most notable exception has been the pre-
liminary management plan constructed by the Gulf of Mexico Fishery
Management Council (GMFMC, 1979). Although some basic MSY calculations
presented in the plan suggest that the fishery is currently operating
near MSY, the bulk of the study is descriptive in nature. The basic
questions of economic efficiency, price structure and possible conse-
quences of instituting various management strategies on catch and effort
levels remain unanswered.
Objectives
The passage of the Fishery Conservation and Management Act of 1976
(PL94-265) has made it necessary to develop management plans for all
3The yield from a fishery that results from a level of fishing
effort such that marginal cost equal marginal revenue is called maximum
economic yield (MEY).
4Minimum legal size limits for certain species of reef fish have
been instituted in some states.
domestic commercial fisheries (U.S. Department of Commerce, 1976).
These management plans are to be constructed from the best available
scientific data and directed toward achieving an "optimum yield" from
all fisheries. While the precise economic and biological definition of
optimum yield is still unclear, the necessity to develop empirical
fishery models describing the interrelationships between relevant
economic and biological agents is clear. The primary objective of this
study is to provide an econometric model of the Gulf of Mexico Reef Fish
Fishery to serve as an analytical framework within which a wide variety
of management questions may be analyzed. Specific objectives include:
1. Development of a conceptual and empirical fishing power
function for vessels operating in the Gulf of Mexico
Reef Fish Fishery.
2. Specification and estimation of aggregate catch equations
for each participating state in the GMRFF. Both produc-
tive interdependence between states and the unobserva-
bility of the fish stock will be explicitly considered by
means of stochastic specifications.
3. Identification of the price structure of the reef fishery
and estimation of a system of dockside price equations.
4. Development of a framework within which the concept of
fishing power and the estimated catch and price equations
can be integrated to analyze economic efficiency in the
Gulf of Mexico Reef Fish Fishery.
The results of this analysis will provide valuable information to these
individuals charged with the responsibility to make management decisions
in the Gulf of Mexico Reef Fish Fishery. Furthermore, it is hoped that
the results of this study will further the state of the art in the
statistical specification and estimation of empirical models describing
production in an ocean fishery.
Scope
The scope of the analysis is confined solely to the commercial
fishing sectors for Florida West Coast, Alabama, Mississippi, Louisiana
and Texas. In spite of the size of the recreational fishery in terms of
catch, severe data limitations preclude any detailed analysis of this
sector. This, however, should have only minimal effects on the analysis
of the commercial sector. The GMFMC has established that the commercial
and recreational sectors are, to a large extent, geographically distinct
in regard to the location of fishing activity.
The data utilized in this study consist primarily of secondary
data reported annually by the National Marine Fisheries Service. While
these data constitute the "best available" data, its highly aggregate
nature has forced considerable simplification in building the empirical
models. Within the context of limited data, it is anticipated that some
of the theoretical and statistical formulations presented will prove
useful to others engaged in the empirical analysis of the fisheries
under similar data confines.
Chapter II presents a review of current bioeconomic theory and
develops a theoretical model of a multi-sector fishery with variable
output prices. Chapter III presents the empirical specification of the
catch and price equations for each state participating in the GMRFF.
Also included is a discussion of the estimators utilized in estimating
these equations. The resulting estimated equations are discussed and
used to estimate maximum economic yield in Chapter IV. Chapter V con-
tains a summary of this study and all conclusions which have been
rendered. Also included are suggestions for further research.
CHAPTER II
THEORETICAL FOUNDATIONS
The analysis of fishery production has led to the development of a
conceptual framework known as the bioeconomic theory of the fishery.
The term bioeconomics as used here refers to the theoretical integration
of biological and economic theory. Under this general definition, there
are several variations of theoretical models describing fishery
production. The main thrust of bioeconomics has been to create a
conceptual framework that enables the determination of economically
efficient input levels at the firm and/or industry level while simul-
taneously maintaining the underlying resource at some fixed level.
The first section of this chapter discusses the biological bases of
bioeconomic models. Specifically, the notion of sustainable yield will
be developed and some of the main stock production models will be
presented. Section two builds upon the technical biological relation-
ships by introducing prices and concepts dealing with economic effi-
ciency in production. Included in this section is a review of several
specific bioeconomic models of fishery production. The final section of
this chapter extends these basic bioeconomic models by presenting a
theoretical bioeconomic model of a multi-sector fishery with variable
product price and pecuniary externalities.
Industry here refers to the aggregate of all vessels operating in
a given fishery.
10
Biological Theory
The need to consider the biological characteristics of fish popula-
tions in economic analyses of fisheries becomes immediately evident when
the nature of the resource (fish population) is considered. Fish popu-
lations can be placed in the category of use-dependent flow resources
with a critical zone (Schaefer, 1957). A critical zone as used here is
defined to be a rate of decrease in flow which cannot be reversed
economically or technologically. Thus, in terms of fish population, a
critical zone would correspond to that level of population which has an
insufficient reproductive potential to remain viable.
Sustainable Yield
The main aspect of biological theory that is relevant to production
analysis of a fishery is that of population dynamics. More precisely,
the notion of sustainable yield (SY) is one of the cornerstones of bio-
economic theory.
The size of a non-exploited fish population (biomass) can, in
general, be assumed to be a function of three factors: growth, recruit-
ment and natural mortality (Gulland, 1965). Each of these variables, in
turn, is a function of the biomass. Individual growth is generally
assumed to be at a maximum at low levels of population and to decrease
as the population size increases. Natural mortality acts in the oppo-
site manner, being low at low levels of population. As, population size
increases, natural mortality increases due to increased competition for
food and other such factors. Recruitment, the rate at which individuals
enter into the fishable population, is generally assumed to be low at
11
both high and low populations, reaching a maximum at some intermediate
biomass. These three factors can be combined to yield a general func-
tional relationship between the population in time period t and mature
progeny in time period t + 1. This relationship is described by the
h(P) function shown in Figure 1. The h(P) function corresponds to the
actual production of mature progeny. For example, if the population at
time t is equal to P1, the mature progeny entering in the fishery will
be equal to MP,. The r(P) function is the replacement line representing
the production of progeny necessary to maintain the population at its
present level.
r(P)
C MP
I I
450 I I I
I I
p p* p p Population (t)
1 max N
Figure 1. Relationship between population size and mature
progeny
A population of P1 need only produce MPr progeny to maintain
itself. The difference between MP1 and MPr (A B in Figure 1) cor-
responds to a yield of fish which can be harvested while maintaining
12
the population at a level of P1. This is the basis from which the
notion of sustainable yield derives. Before proceeding to a discussion
of sustainable yield, several aspects of the model in Figure 1 merit
comment. Under a given set of environmental conditions, a given popula-
tion will approach some natural equilibrium size. This equilibrium
occurs at the population size corresponding to the intersection of the
r(P) and h(P) functions. This population size is given by PN in the
diagram. The h(P) function is assumed to possess a unique maximum pro-
duction of mature progeny, corresponding to the underlying population,
P max As will be shown presently, the population size corresponding to
micax
the maximum production of mature progeny is not the same as that cor-
responding to maximum sustainable yield.
Sustainable yield represents, for any given population level, the
surplus production of mature progeny over that needed to just maintain
the population at a fixed level. In terms of Figure 1, sustainable
yield for any given population is then simply the difference between the
h(P) function and the r(P) function. Mathematically, this can be
represented by
SY(Pi) = h(Pi) r(Pi) 0 < P< P (1)
where SY(Pi) refers to sustainable yield corresponding to population Pi"
Equation (1) defines a single valued function relating sustainable yield
to population size. Figure 2 illustrates one possible shape of the
sustainable yield function.2 This function can be seen to rise from a
20ther possible shapes of the sustainable yield curve are discussed
below.
13
MSY
rJ
1 SY
SP P P2 Population
0 0
Figure 2. Quadratic sustainable yield function
level of zero at zero population to a unique maximum, and then back to
zero at the natural equilibrium level.
The maximum point on the curve, maximum sustainable yield (MSY),
I I
1 2
occurs at population P This is precisely the same P as shown in
Figure 1. Thus, it can be seen that maximum sustainable yield occurs at
a population level which is smaller than that which produces the maximum
number of mature progeny, max in Figure 1.
The form of the sustainable yield function in Figure 2, the
inverted U-shape, corresponds to any population that obeys a logistic
growth process. While other shapes are possible, there is no loss of
generality in considering the above curve. Before proceeding to a
mathematical discussion of biological stock production models, two
aspects of the above sustainable yield curve need mention. First,
inspection of Figure 2 reveals that the same sustainable yield can cor-
respond to two different population levels. For example, populations
PO and P2 both produce a sustainable yield of SYO. The importance of
14
this fact will become obvious when costs and revenues are incorporated
into the theoretical models. More precisely, it is this property of the
sustainable yield function which leads to many conclusions rendered by
economists with respect to the workings of perfect competition.
Secondly, any given sustainable yield function is defined for a given
set of environmental and ecological parameters. Any change in these
parameters will bring about a shift in the sustainable yield function
(Schaefer, 1957).
Stock Production Models
The mathematical models describing the sustainable yield concepts
have mainly been in the form of biological stock production models. Two
of the more prominent models in fisheries theory are the Schaefer model
(Schaefer, 1957) and the Generalized Stock Production Model (Pella and
Tomlinson, 1969). These models are, in general, empirically oriented.
This orientation has resulted primarily from the lack of time series
data on population sizes. Thus, these models generally invoke several
assumptions which make it possible to express sustainable yields as a
function of fishing effort. While the term fishing effort is more
specifically dealt with in the following sections, it should suffice
here to define effort simply as some measure of fishing activity
directed toward the resource stock.
The Schaefer model is actually a special case of the Generalized
Stock Production Model. The following discussion will deal with the
most general model while in the process pointing out its relation to the
Schaefer formulation.
15
The Generalized Stock Production Model (GSPM) as developed by Pella
and Tomlinson (1969) is composed of two functions. These are a popula-
tion growth function and a catch function. These functions are combined
in such a manner as to create a function relating sustainable yield to
fishing effort. The rate of change in any given fish population over
time can be expressed as a function of the population size by
P(t) = HPm(t) KP(t) (2)
where H, K, m are constant parameters and P(t) is the time derivative of
population or biomass, P(t). Equation (2) is a general functional rep-
resentation of the sustainable yield function shown in Figure 2. For
populations to have an absolute maximum rate of growth or maximum sus-
tainable yield, the above equation must satisfy certain conditions on
3
the parameters. These conditions are H, K < 0 if m > 1 and H, K > 0
if m < 1.
Fishing effort is introduced into the GSPM by using the equation
C(t) = qE(t)P(t) (3)
where q is a constant, E(t) is fishing effort expended in time period t
and C(t) is the time derivative of catch. This relationship is hypothe-
sized under the assumption that effort units operate independently.
Equation (3) can be seen to represent the production function for the
fishery under non-equilibrium conditions. Equilibrium conditions are
3The m parameter in equation (2) measures the skewness of the popu-
lation growth function. A value of m = 2 leads to a symmetric function.
As will be shown presently, a value of m = 1 is not permissable.
16
defined to be those levels of effort and population that yield a catch
equal to sustainable yield.
The introduction of fishing into the GSPM necessitates that equa-
tion (2) be modified to
P(t) = HPm(t) KP(t) qE(t)P(t) (4)
where all terms have been previously defined. Equation (4) implies the
rate of increase of any given population over time is decreased pre-
cisely by the rate at which fish are caught through fishing activity.
The imposition of the equilibrium conditions described above can be
accomplished by constraining P(t) = 0 in equation (4). This constraint,
in effect, requires that catch always equal sustainable yield. By solv-
ing the equation
HPm(t) KP(t) E(t)P(t) = 0 (5)
for P(t) and substituting the result into equation (3), the equilibrium
effort yield function
1
C = qE(qE + m (6)
is obtained. This equation represents the Generalized Stock Production
Model relating equilibrium catch to fishing effort. Note that a value
of m = 1 would make equation (6) undefined.
The Schaefer model, which is a special case of the above model
named after its originator, M. B. Schaefer, was developed in 1954
(Schaefer, 1954). This model is based upon a logistic population growth
17
function. Using this function, the natural rate of increase as a func-
tion of population size can be expressed by
P(t) = K1 P(t) [M P(t)] (7)
where K and M are constants and all other terms are defined as above.
It can be easily shown that this equation corresponds to equation (2)
of the GSPM with m = 2, H = -K1, and K = -K1M. Thus, it becomes appar-
ent that the basis of the Schaefer model is merely a specific form of
the GSPM, with parameter m = 2. The Schaefer model also provides an
equation expressing equilibrium catch as a function of fishing effort.
Utilizing equation (3) once again as the non-equilibrium catch function,
the function
C = qE (M E) (8)
K1
can be derived. As before, the appropriate redefinition of constants
(H = -K1, K = -KIM) illuminates the fact that equation (8) is merely a
specific form of equation (6) with m = 2.
The above has shown the widely used Schaefer model to be a special
case of the Generalized Stock Production Model. In part, one of the
primary goals of developing the GSPM was aimed at relaxing the con-
straint of the symmetric yield function generated by the Schaefer model
(Pella and Tomlinson, 1969). Figure 3 presents several possible equi-
librium yield functions that are possible utilizing the GSPM. It can be
seen that the shape of the equilibrium yield function takes a wide
variety of shapes as m varies.
18
50
50 m = .27
E 40
So 30
S 20 m = .80
10 \\ m = 4.94
m=11.1 2.0 m= 1.4
200 400 600 800 1000 1200 Effort
Figure 3. Equilibrium yield relationships for various values
of m
The foregoing has presented a brief introduction to the biological
bases underlying the bioeconomic models currently utilized in fisheries
management. The Generalized Stock Production Model provides a framework
which is more general than Schaefer's formulation, but still enables the
expression of equilibrium catch as a function of fishing effort. As
noted above, the type of result is significant in that the generally
unobservable population variable is eliminated in favor of those
variables (catch and effort) which are observable.
Basic Bioeconomic Models of the Fishery
The previous section of this chapter presented the basic biological
relationships that create the framework within which the economic
aspects of fisheries production may be analyzed. The biological rela-
tionships it will be recalled, led to the concept of sustainable yield,
and suggested that the harvest of any given fishery be restricted to be
19
equal to some sustainable yield in equilibrium. The economic models of
the fisheries have built upon this restriction and have attempted to
define the sustainable yield which is optimum in terms of economic effi-
ciency for both industry components (vessels) and society as a whole.
As would be expected, considerable debate has been generated over what
is the true socially optimum yield. This section presents a discussion
of several of the more popular theoretical bioeconomic models of the
fishery. The ensuing discussion of these models does not attempt to
derive the "true" optimum catch and effort levels of a fishery, but
rather provides a description of current theoretical models.
Static Bioeconomic Fishery Models
Common to all bioeconomic models is the recognition of the unique
aspects of the resource and its productive setting. Three aspects of
any given fishery, the use-dependence of the resource, the lack of
property rights (common property) and interdependence of producing
units, provide the motivation behind the development of bioeconomic
models of fishing. Using these aspects, bioeconomic models have almost
universally resulted in the conclusion that the workings of unregulated
competition in a fishery generally lead to a higher level of effort and
lower sustainable yield than that which is socially optimal.
The first attempt at constructing a bioeconomic model of a fishery
was done by H. Scott Gordon (1954). Gordon's analysis begins with the
assumption that a fishing ground can be treated in a manner similar to a
parcel of land in the traditional economic analysis of rents. Thus, the
conclusion reached is that the optimum degree of utilization of a fish-
ing ground occurs at the level of fishing effort which equates value of
20
the marginal product of effort (VMPE) with its marginal (average) cost,
r. To demonstrate how the common property nature of an unregulated
fishery encourages non-optimal levels of effort, Gordon (1954) analyzes
a fishery which is composed of two grounds of different productivity or
location and constant product price. Figure 4 depicts this situation.
$ a $ b
r \ r
VMP VAP1 VMP2 j\VAP2
SI Effort Efor
0 E1 E Effort 0 E2 E E2 Effort
Ground 1 Ground 2
Figure 4. Allocation of fishing effort between fishing
grounds of different productivity or location
The optimum degree of utilization of the fishery will, according
to Gordon, occur with OE1 units of effort being used on Ground 1 and OE2
units of effort on Ground 2. Under this allocation of effort, each
ground yields a rent corresponding to the shaded areas. This pattern of
fishing, however, does not represent a stable position for the fishery.
The reason for this instability relates to the lack of property rights
on any given fishing ground. Fishermen venturing from port are inter-
ested in grounds with the highest average productivity. Given the
constant marginal cost of effort, this is where the fisherman will
21
receive the highest return. Thus, in the case depicted by Figure 4,
fishermen will enter the fishery and allocate their effort such that the
value of average productivity (VAP) of the two grounds is equal to
average cost (r) and, hence, equal on all grounds. Thus, OE' units of
effort will fish on Ground 1 and OE2 units will produce on Ground 2.
Effort levels, El and E2, correspond to the effort levels that would
produce a catch equal to maximum sustainable yield. This makes it
apparent that the result of unregulated competition in this common
property resource industry leads to effort levels greater than that
necessary to harvest maximum sustainable yield. One final point of
note is that on both grounds, effort is employed past the point of nega-
tive marginal productivity. This represents Gordon's (1954) theory
explaining the results of production from a common property resource
under a competitive regime.
Gordon also proposed a bioeconomic model of the fishery at the
industry level. Schaefer (1957) presented essentially the same model.
Due to the wide use of the so-called Schaefer model in fishery theory
and its similarity to Gordon's formulations, the following analysis
follows Schaefer.
The Schaefer model begins with the definition of the long-run
equilibrium industry production function. This function, based on a
logistic population growth function, was shown in equation (8) to be a
special case of the GSPM. Equation (9) restates equilibrium catch
function as
C = aE(b E) (9)
2 K1M
where a and b in terms of the constants in equation (8), and
K1 q
22
E is defined as fishing effort. Further assumptions of the model are as
follows. The demand curve facing the industry is assumed to be infi-
nitely elastic, which implies a constant price, p, and industry costs
are proportional to effort. Thus, the cost function can be written as
K = rE
(10)
where r corresponds to average and marginal cost of effort. These
equations are shown in Figure 5. Given the constant production price,
the total revenue curve shown is simply the catch function in equation
(9) multiplied by the product price p. Recalling Gordon's (1954)
result that all profit in a common property fishery is dissipated
through entry of new firms, the equilibrium position of an unregulated
fishery will occur at the point where total revenue is equal to total
cost.
Effort
optm E
Figure 5. Cost and revenue in an unregulated fishery
with constant product price
23
The level of effort corresponding to this point can be derived from
the profit equation
n = paE(b E) rE (11)
Setting 0 = 0 and solving for E yields the open access equilibrium
effort level E= b r (see Figure 5). As shown in the above figure,
1e pa
the open access level of effort is greater than that needed to harvest
maximum sustainable yield (revenue), Em. The implications of this are
that a decrease in effort will not only free resources to be used in
other productive processes, but also an increase in equilibrium catch
will result as effort is decreased from the open access level of
E = b --, to the MSY level of effort E = (Appendix C). While
I pa 2
this is true in terms of Figure 5, this conclusion in fact depends upon
the average (marginal) cost of providing effort. It can be shown that
if average cost, r > bpa, any decrease in effort will result in a de-
crease in equilibrium yield. Further, if r = bpa- the effort levels
corresponding to MSY and open access equilibrium will coincide.
The economically optimum yield, termed maximum economic yield
(MEY), requires the maximization of the profit function shown in
equation (11). Differentiating and solving the first-order condition
for E yields the MEY effort level, Eopt = !(b ). A comparison of
Eopt and E1, the open access effort level, illustrates that it is always
necessary to restrict effort if returns to the resource are to be
maximized.
The seminal paper by Gordon (1954) and the ensuing analysis by
Schaefer (1957) have provided the basis from which subsequent bio-
economic formulations have proliferated. These additional works have
24
both criticized and extended these basic models. In spite of these
extensions, the basic conclusions of Gordon's model have been maintained
in nearly all bioeconomic models. These conclusions are that the common
property nature of the resource creates a situation in which the open
access equilibrium in the fishery generates socially undesirable levels
of catch and effort and that some type of restrictions on the fishery
are necessary as a means of correction. Commensurate with this is
Gordon's creation of the management goal of attaining maximum economic
yield rather than the more traditional goal of maximum sustainable
yield generally proposed by the biological discipline.
Dynamic Bioeconomic Fishery Models
One of the first criticisms of the traditional model was made by
Scott (1955) and later extended by others, most notably Clark (1976).
This criticism was aimed at the concept of the static MEY. More pre-
cisely, it was argued that since catch was a function of population and
population was a function of catch, a dynamic concept of MEY was needed.
To attack this problem, Scott developed the concept of user cost.4
Basically, Scott argues that the feedback relationship between catch and
population size implies that "correct" regulation of a fishery requires
an examination of the discounted present value of returns in the
fishery. Thus, any increase in marginal current revenue (catch) must be
weighed against the cost of such an increase in terms of diminished
present value. Scott defines user cost to be the "effect of succeeding
4Scott's argument was couched in terms of the sufficiency of sole
ownership of the fishery with the attainment of MEY. The essence of his
argument, however, involves the optimality of static versus dynamic MEY.
25
units of current output on the present value of the enterprise" (Scott,
1955, p. 123). Dynamic MEY, therefore, occurs where marginal current
revenue is equal to marginal user cost. The determination of the catch
and effort levels necessary to achieve dynamic MEY is thus a function of
the discount rate. In general, as the discount rate rises, lower valua-
tion is put on landings in the future. Clark (1976) has shown that
dynamic MEY is bounded by static MEY levels of catch and effort and the
open access equilibrium position. More precisely, a discount rate of
zero would result in an equilibrium position identical with the open
access position while a discount rate of infinity would result in the
attainment of static MEY.
The bioeconomic models discussed above represent what can be termed
aggregate models. Aggregate as used here refers to the treatment of the
entire industry as the unit of analysis. One limitation of this type of
5
model is that the basic producing unit of any given fishery, the vessel,
is not explicitly included other than in its nebulous relationship with
the variable termed fishing effort. In answer to this problem, V. L.
Smith developed the first bioeconomic model which incorporated firm
behavior into the analysis (Smith, 1969). Others, most notably
Fullenbaum et al. (1971) and Anderson (1975) have all criticized and
sought to extend Smith's work. The following discussion is confined to
Smith's analysis.
Smith's formulation centers on dealing with three key aspects of a
fishery. These are the renewable nature of the resource stock, the
feedback relationship between industry catch and stock growth rate and
The term vessel and firm are used interchangeably.
26
the externalities of production. Three different types of production
externalities are said to exist. Stock externalities are assumed to
represent shifts in the firm cost function due to changes in the stock
size. Crowding externalities result from direct interdependence of pro-
duction (fishing) activities. Finally, Smith (1968) considers mesh
externalities which correspond to both the economic and biological
effects of changing mesh size. It should be noted that in any given
fishery, some or all of these externalities may or may not exist.
The general formulation of the model centers on the assumption of
V homogeneous vessels, each producing x units of output. Total industry
catch is thus equal to Vx. The sustainable yield function used is
defined in general function form to be f(X) where X corresponds to the
resource stock size. This function is assumed to possess the following
properties: f(X) = f(X) = 0 where X and X are the maximum and minimum
viable populations, respectively, f x0 = 0 for some X < X < X, an
d2f
interior maximum growth rate (MSY) exists, and finally 2 < 0 ruling
dx
out any inflection point in the sustainable yield function. As noted
previously, the most common specific form of f(X) is the quadratic form
which corresponds to a logistic growth law.
To bring fishing activity into the model, Smith expresses f(X) X
as
X = f(X, m, Vx) (12)
where m = mesh size and other variables are defined as above. Equation
(12) thus states that sustainable yield, X, is a function of population
size, mesh size and total industry catch. It is further assumed that X
is an "inverted U" shape with f3 V < 0. By ruling out any type of
27
interaction between industry catch and the population growth rate,
equation (12) can be rewritten as
X = f(X, m) Vx (13)
This form of equation (13) can be interpreted to mean that the sus-
tainable yield produced by any given stock and fixed mesh size is
reduced by an amount precisely equal to industry catch.
In dealing with the individual firm, Smith (1969) chooses to define
behavior in terms of the firm's long-run cost function. It should be
emphasized that the firm's production function is implicity in the cost
function. The general form of the cost function is
c = 5(x, X, m, V) + ( (14)
where T is defined to be the firm's opportunity cost. Partial effects
are hypothesized to be, c = > 0, c2 0, c3 > 0 and
-1 a-x > 01c X = am
c4 E > 0. Of interest here is the fact that stock externality
4 aV -
effects, c2, and productive interdependency effects, c4, can be equal to
zero.
Industry revenue (R) is defined to be a function of industry catch
and mesh size. Mathematically, this relationship is expressed by
R = R(Vx, m) (15)
From this relationship the price of output received by individual firms
in the industry can be shown to be
P(m) R(Vx, m) (16)
P(m) = Vx
28
The use of the notation P(m) here implies that price is constant with
respect to variations in firm output, but does vary with changes in mesh
size due to the change in the size of fish caught.
Individual firm behavior is assumed to follow a profit maximization
goal with vessel catch rate, x, and mesh size, m, being the decision
variables. The profit function for the individual firm can thus be
expressed as
S= P(m)x ((x, X, m, V) v (17)
Maximization of this function yields the following first-order
conditions:
P(m) = cl(x, X, m, V) (17a)
P'(m)x < c3(x, X, m, V) if < m = m (17b)
The inequality occurring in equation (17b) holds when the solution is
such that mesh size is below the point of technological feasibility.
Equation (17a) states the familiar profit maximization condition that
marginal cost equals price. Interpretation of equation (17b) is less
clear. In general, it states that the marginal revenue of varying mesh
size must equal the marginal cost of doing so. It may be, however, that
the mesh size which satisfies this condition is below that which is
technologically feasible. Hence, the inequality becomes effective in
this case and the optimal mesh size is assumed to be mrn.
The foregoing illustrates the determination of the optimal (profit
maximizing) levels of firm catch and mesh size. The rate of exit or
entry of firms operating at these levels is given by
29
61 Tr Tr > 0
S= { o (18)
62r ir < O
where 9 = dV
where 6, 62 are constants of proportionality and = firm
profit. Equation (18) illustrates that the entry and exit of firms is
asymmetrically proportional to profit. Generally, it is assumed that
firms leave the industry at a slower rate than firms enter.
Equations (17), (17a), (17b) and (18) provide a system of equations
in which the entire workings of the fishery can be analyzed.
Specifically, equations (17a) and (17b) provide unique values of catch
and mesh size for any given population size and industry size. Thus,
once the catch rate per vessel and mesh size is determined, changes in
industry output can be seen to be a function of changes in the industry
size and stock size. These effects are summarized by
X = F(X, V) (19a)
V = I(X, V) (19b)
Equation (19a) states that the change in the resource stock over time is
a function of both the stock size and the number of efficiently operat-
ing vessels in the fishery. When X = 0, a biological equilibrium occurs
in the sense that the industry harvest rate is equal to sustainable
yield. In equation (19b), the change in the number of participating
vessels is also seen to be a function of stock size and industry size.
The set of solutions represented by V = 0 correspond to those in which
investment in the fishery is in equilibrium in relation to alternative
Industry size here refers to the number of efficiently operating
vessels in the fishery.
30
productive uses. Thus, when equations (19a) and (19b) are simultaneously
zero, an open access bioeconomic equilibrium is said to exist.
An example of such a system of equations is pictured in Figure 6.
Points above the I(X, V) = 0 curve correspond to points where industry
profits are negative while the converse holds for points below the
function.
I (X, V) = 0
( A
F(X, V) = 0
Resource stock (X)
Figure 6. Phase diagram for equilibria between vessels and
resource stock in an open access fishery
Similarly, points above the F(X, V) = 0 curve correspond to harvest
rates in excess of sustainable yield. The arrows in the diagram cor-
respond to the direction of change in vessels and resource stock.
Immediately obvious is the fact that there are three potential equi-
librium positions (points A, B and C). Only points A and C represent
stable solutions, however. The instability of point B can be seen by
examination. Any displacement from this point would result in a new
equilibrium being established at point A or C.
31
The above discussion has provided a review of Smith's (1969) steady
state representation of an unregulated commercial fishery. As with
previous writers, Smith's conclusion is that the unrestricted operation
of a fishery results in levels of catch and effort which exceed those
necessary to maximize returns to the resource. Furthermore, Smith
assumes if the fishery were managed by a sole owner, the appropriate
levels of catch and effort would result. These levels are harmonious
with previous writers in that they result in maximizing returns to the
resource; in other words, static MEY results.
The profit function for a sole owner can be written as
S = P(m)Vx VQ(x, X, m, V)
(20)
where all terms are defined as above. In contrast to the firm which
considers only m and x as decision variables, the sole owner must maxi-
mize equation (20) with respect to the arguments x, m, X, and V.
Furthermore, to insure that the stock remains in equilibrium, maximiza-
tion of equation (20) is constrained such that f(x, m, Vx) = 0.
Constrained maximization of the above profit function leads to the first-
order conditions
P(m) = c1 x f3
xf
xp' (m) + 2 < c3
V_ 3 c
if < m = m
Vc2
f
S= P(m) x- c = Vc f3x
V3
F(X, m, Vx) = 0
(20a)
(20b)
(20c)
(20d)
(20e)
32
where X represents the undetermined lagrange multiplier. Equation (20a)
states that the vessel catch rate be adjusted to the point where price
equals direct and user cost. Similarly, equation (20b) states that mesh
size should be adjusted to the point where marginal private and social
revenue is less than or equal to the cost of changing mesh size.
Condition equation (20c) states that the marginal profitability of total
industry catch equals the marginal social cost of adding a vessel to the
fishery. Using these criteria, the socially optimal levels of the
decision variables will be realized. Of course, this assumes that the
socially optimal position of a fishery is achieved by catching MEY.
As with previous writers, Smith (1969) concludes that in the
absence of sole ownership, an open access fishery must be regulated to
achieve economically efficient production. Smith proposes that an
extraction fee of -f3 on each pound of fish landed and a license fee of
Vc4 on each vessel would be sufficient to insure social and economic
efficiency (MEY) in an open-access fishery.
The main goal of bioeconomic theory can be seen to be that of
representing the productive activities of fishing within the bio-
technical constraints created by the growth pattern of the resource
stock. The works discussed above are by no means exhaustive. They
merely serve to illustrate the historical development of bioeconomic
theory and the general conclusions derived concerning economic effi-
ciency in fisheries production. Under the stated assumptions of con-
stant product price, a well-behaved growth law, and homogeneous units of
effort, be they vessels or some other economic entity, the above models
all arrive at the conclusion that in the absence of restrictions of
some type, suboptimal levels of catch and effort will result.
33
The economically "correct" degree of utilization of effort in the
fishery is shown to correspond to some form of maximum economic yield
(dynamic MEY or static MEY). Further, the failure to achieve MEY under
perfect competition was universally attributed to the common property
nature of the resource and externalities in production.
While the preceding analysis may seem to indicate that the "book
has been closed" on bioeconomic theory, the converse is true. As with
most theoretical constructs, when the assumptions change, so do the
conclusions. Thus, Anderson (1973) has shown that when price becomes
variable, the elasticity of demand becomes an important determinant in
defining the socially efficient production level for a fishery.
Furthermore, Bromley (1969) has eloquently questioned whether or not
externalities do, in fact, exist in fisheries production. By differ-
entiating between productive interdependence and externalities, Bromley
argues that perfect competition may not be as inefficient as the tradi-
tional writers above would lead one to believe. He also questioned the
social optimality of maximizing returns to the resource, suggesting that
maximizing net social benefits is perhaps more appropriate.
Theoretical Extensions
The foregoing has provided a review of the basic notions and
principles underlying the bioeconomic models used in analyzing fisheries
production. As suggested by the term bioeconomics, the models are char-
acterized by incorporating prices and costs into the biological surplus
stock production models. The resulting analysis then proceeded in the
neo-classical economic tradition to derive the results of the undesira-
bility of unregulated competition, the economic inefficiency of MSY
34
regulation and the "economically efficient" management goal of attaining
maximum economic yield. In all cases, these results were obtained from
models which treated the fishery as a single aggregate operating with a
constant product price. The purpose of this section is to first relax
the assumption of a constant product price and then extend the results
to consider the case of a multi-sector fishery where each sector cor-
responds to a sub-industry defined on regional or state basis.
Fishing Effort and Equilibrium Yield
Before pursuing these extensions, a brief digression on the concept
of fishing effort and equilibrium versus non-equilibrium production
functions will be useful. Prior to this discussion, a specific defini-
tion of fishing effort has been omitted, being defined only as some
measure of fishing activity. Traditionally, this measure has been
defined to be a composite of physical inputs in the fishery. Gulland
(1965) and Rothchild (1977) have noted that the notion of fishing effort
to the biologist and economist are different, especially in the long run.
This difference can be seen by comparing the effects of doubling effort
under the biological definition of effort as opposed to that of the
economist. Biological definitions of fishing effort are generally
couched in terms of catch. This results in the conclusion that a doubl-
ing of effort, other things being equal, must necessarily result in a
doubling of catch. In contrast, the economic definition of effort is
independent of catch. Under this definition a doubling of effort does
not necessitate a doubling of catch. Thus, it can be seen that the
concept of fishing effort can indeed be quite different to different
disciplines.
35
In spite of these apparent conceptual differences, effort is still
generally considered as a single composite input. The present analysis
diverges from this notion and considers that any measure of effort must
be composed of several components. Paralleling Gulland (1965), fishing
effort can be thought of as being composed of three basic components.
These are normal fishing effort, fishing power and fishing intensity.
Nominal fishing effort can be thought of as a unit of measure or perhaps
an industry size measure such as the number of vessels. Fishing power
is a measure of the input characteristics of firms (vessels) in the
fishery. Finally, fishing intensity can be thought of as some type of
time measure such as days fished. Fishing intensity is often implicit,
in the data, being defined by the observation interval.
To make this notion more explicit, assume that fishing intensity is
implicit in the interval of observation. Fishing power can then be
represented by
Ep = g(X1, ... Xn) (21)
when E denotes fishing power and the X i = 1, ..., n are input char-
acteristics of firms in the fishery. If g(X1, ..., Xn) is assumed to be
the same for all firms, total fishing effort is then given by
E = EN g(X1, ..., Xn) (22)
where EN denotes nominal effort. This notion of effort will be main-
tained throughout the remainder of this study. Further discussion will
follow in the empirical analysis to be presented.
36
Having briefly clarified the definition of fishing effort, it
remains to draw a distinction between the equilibrium yield functions
such as those developed by Pella and Thomlinson (1969) and Schaefer
(1957) and non-equilibrium yield functions. Equilibrium yield functions,
as shown above, are derived in such a manner as to produce a relation-
ship between fishing effort and sustainable yield. It is precisely
this relationship between catch and effort that has resulted in the
term equilibrium yield function. The catch resulting from any level of
effort along these functions corresponds to equilibrium (sustainable)
yield.
The significance of such functions in the analysis of fishery
production is twofold. First, the use of such functions implicitly
ensures that biological equilibrium is achieved. This means that catch
rates are always equated to sustainable yield. A note of caution should
go with such a strong statement, however. In the empirical estimation
of such functions, the degree to which such estimated equilibrium yields
and actual equilibrium yields coincide rests largely on the adherence of
certain underlying assumptions (Pella and Tomlinson, 1969). Thus,
empirically estimated equilibrium yield functions may not incorporate
the biological equilibrium condition of catch equals sustainable yield
to any reasonable degree. Secondly, equilibrium yield functions gen-
erally impose specific functional forms on the observed relationship
between catch and effort. This is significant in that the set of valid
equilibrium yield functions is fairly limited.
In contrast to the notion of equilibrium yield functions is that of
non-equilibrium yield functions. In this study, the term non-equilib-
rium implies that no biological equilibrium condition of catch equal to
37
sustainable yield is imposed on the relationship between catch and
effort. Very little attention has been given to equations of this type.
The most notable exception is a paper by Bell et al. (1973) wherein they
addressed the question of constant versus decreasing returns in an
essentially non-equilibrium framework. Within the framework of bio-
economics it may seem objectionable to consider analyzing fishery pro-
duction without implicitly incorporating biological concepts in the form
of population dynamics. A closer examination of non-equilibrium yield
functions may serve to lessen these objections.
One of the primary reasons for analyzing fishery production is to
develop analytic models which can be used in studying the effects of
various management alternatives. Non-equilibrium yield functions are
very amenable to such types of analysis for two reasons. First, this
class of functions provides a much wider range in the choice of func-
tional relationships between catch and effort. This is especially
significant in that equilibrium yield functions generally treat fishing
effort as a single variable or composite measure. Non-equilibrium
models, however, can be specified in several variables which serve to
decompose effort into components which greatly enhance the analytic
ability of the model with respect to management questions. Secondly,
with the appropriate stochastic incorporation of unobservable population
effects, non-equilibrium yield functions can be used to derive equilib-
rium yield relationships.7 Unless otherwise stated, all yield (catch)
equations in the ensuing analysis will be non-equilibrium in nature.
7The notion of derived equilibrium yield equations is developed in
the following chapters.
38
Variable Product Price
Since most fishery analyses are done at the aggregate or industry
level, the validity of a constant product price is questionable.
Relaxing the assumption of constant product prices complicates some of
the traditional theoretical results in the context of equilibrium yield
functions. Anderson (1976) has shown that both the derivation of maxi-
mum economic yield (MEY) and the results of unregulated competition are
obscured when product price is variable. Consider Figure 7 which illus-
trates the MEY and open access solutions under the assumption of a
constant product price, p.
C-)
V
a)
w4
E E
m c
Figure 7.
Effort
Open access equilibrium and maximum economic yield
in a fishery with constant product price
The curve labeled TR is the "monetized" sustainable yield functions
and the line labeled TC corresponds to total cost. In that price is
constant, it is important to note that the sustainable yield function
retains its shape. There are unique effort levels corresponding to
39
MEY (E ) and the open access solution (Ec). Now consider Figure 8,
where price is variable. It can be seen that the total revenue function
no longer retains the shape of the sustainable yield function, but
rather has become "doubled-humped" (Anderson, 1973).8 If the relevant
total cost curve is TCI, there still is a unique open access solution.
However, there are now three effort levels (El, E2 and E3) wherein
marginal cost equals marginal revenue.
,TC
C 2
I A TC1
1 TR
a,
E2 E3 E
Figure 8.
Open access equilibria and maximum economic yield
in a fishery with a variable product price
Thus, the task of finding the correct solution requires finding a
global optimum from several local solutions where marginal revenues and
costs are equated. If the relevant cost curve is TC2, in addition to
multiple MEY solutions, there now exists three points (A, B and C) where
8
A graphical derivation of the "double-humped" sustainable revenue
function is presented in Appendix D for the case of a linear demand
function.
40
the open access result of total cost equals total revenue holds. Thus,
it can be seen that relaxation of the constant price assumption does
indeed confuse and complicate many of the theoretical results derived by
using equilibrium yield functions.
Utilizing non-equilibrium yield functions can avoid some of these
complications. Let the yield function for a fishery be defined by
C = f(X1, ..., Xn) (23)
where C denotes output and the X. corresponds to n inputs. It is
1
further assumed that f(X1, ..., X ) is such that
> 0 i = 1 ..., n (23a)
aXi
i
2
< 0 i = 1, ..., n (23b)
aX
Equations (23a) and (23b) merely assert that the marginal product func-
tion is everywhere positive and declining. The price of output is now
defined to be a declining function of catch
P = P(C) (24)
dP
where d < 0. Finally, the cost equation is defined by
dC
n
K = r. X. (25a)
i=1 l 1
where the input prices, ri, are assumed constant. From equation (25a),
the marginal cost of Xi is then given by
41
aK
Sr.
aX.
i = 1, ..., n
Given these assumptions on the technical relationship between catch,
inputs and product and input prices, the profit maximization problem or
equivalently the MEY problem can be stated in the form
n
MAX 7 = P(C)C z r X.
i=1
(26)
s.t. C = f(X, ..., Xn)
Equation (26) can be seen to be a constrained maximization problem with
9
the constraint being the yield equation. Utilizing the method of
lagrange multipliers, equation (26) can be restated by
n
MAX L = P(C)C z r. x X[C f(X1, .., X )] (27)
i=l n
Differentiation of equation (27) yields the first order conditions
aL p + dP
= + C-x = o
aC dC
L = -r + X 0
ax. ax.
1 1
i = 1, ..., n
a = f(X .. X ) -C =0
ax 1 n
Examination of the first equation indicates that the lagrange multiplier,
dP
X, is equal to P + -C C, which is precisely marginal revenue.
9 s section draws upon Intri gator (1971
This section draws upon Intrilligator (1971).
(25b)
(27a)
(27b)
(27c)
42
Substitution of P + P C into equation (27b) for X yields
(P+ CdP C- r. i 1 n (28)
The expression in equation (28) states that in equilibrium, the marginal
+th
revenue product of the thinput must be equated to its price, or
equivalently, its marginal cost. Equation (28) can be rewritten in an
alternative and perhaps more illuminating fashion as
(P + C) r/i= ,..., n (29)
dC 1 X."
af / f
From equation (29) it is readily seen that r / = r. / for all
i e ji
i and j. Now, in equilibrium, ri / is precisely equal to the
marginal cost of output. Hence, equation (29) states the well-known
result that, in equilibrium, marginal cost equals marginal revenue.
Equation (29) provides a convenient way of examining some possible
consequences of various management goals. One can consider the implica-
tions with respect to input usage levels under various management goals.
In this case, the industry is treated as a single firm and the manage-
ment goal is defined to be profit maximization. The relevant equations
to be solved in this case are given by equations (27a-27c). Assume
that the input levels resulting from this solution are denoted by Xi,
i = 1, ..., n. Consider now the relationship between these input levels
and those that would result if the fishery was managed at price equals
marginal cost. Under this regime, the equilibrium equations analogous
to equation (29) would be
43
P r/ i = .., n (30)
1 r X.
dP
From equation (24) it can be shown that (P + dC C) is always less than
P. This taken in conjunction with equations (23a) and (23b) can be
used to show that the input levels satisfying equation (30), say X ,
must be such that X' > X. for all i. Thus, the obvious result that
input levels under the management strategy of marginal cost pricing are
greater than those corresponding to profit maximization is obtained.
A Multi-Sector Fishery
The term fishery is somewhat synonymous with the traditional
definition of an industry. A sector is defined in this study to be a
sub-industry defined in terms of geographical location. Thus, if a
large fishery is composed of several states or distinct geographic
regions, under the above definition, each state or region can be con-
strued as a single sector.
To begin the analysis of a multi-sector fishery, assume there are
N sectors or regions, each facing a demand function defined by
P = P.(C1, ..., CN) i = 1, ... N (31)
th
where P. is the price received by producers in the i region and the C.
correspond to the outputs of the N regions. It should be emphasized
here that the C. are assumed to be the same product. The subscript
refers to regions rather than commodities. This form of the demand
equation will be discussed later. The demand equations given in equa-
tion (31) are assumed to be such that
44
aP.
< 0 all i, j(31a)
aC
th
Turning to the yield equations, let the i region's catch function
be defined by
C = f (X, ..., Xni) (32)
where the X.. refer to the jth input used in the ith region. It is
u'
further assumed that fi (Xi' ..., Xni) i = 1, ..., N satisfy the con-
ditions stated in equations (23a) and (23b). Finally, assume that the
cost equation for the ithregion is given by
n
Ki = z r.X.. i = 1, ..., N (33)
j=l j J1
where the r. are fixed input prices assumed the same for all regions.
The profit maximization problem for the entire fishery can be
stated as
N N
MAX ~r = Pi(C1', ... CN) C. K. (34)
i=l i=l
s.t. Yi = f(Xli, ..., Xni) i = 1, ..., N
Once again, using the method of lagrange multipliers, equation (34) can
be restated in the form
MAX L = E Pi(C1, ..., CN) Yi K. + [f (X., .,.
i i i
Xi) Ci ] (35)
45
where the are the undetermined lagrange multipliers. Differentiation
1
of equation (35) with respect to C., X.. and x. yields the N(n + 2)
1 3frst-o r c i
first-order conditions
aCi
(35a)
N aP
k
P. + C = 0
k=1 aCi k 1
af.
-r. + *. 1 0
+j 1 aX i
fi (Xli' Xni) Ci
i 1, ..., N
i = 1, ..., N
j = 1, ..., n
= 0
i =1, ..., N
From equation (35a) it can be immediately seen that X. = P. +
i = 1, .
aP.
+
3a. Ci
term on
revenue
output.
(MRi).
N aP
al k Ck'
k=l i
.., N. This expression for A. can be rewritten as X. = (P.
1 1 i
aP
) + z k C. In this form, it can be seen that the first
kfi aCi k.
the right-hand side of the equality is precisely the change in
th th
in the i region with respect to variations in the i region's
th
Thus, this term is equal to the i region's marginal revenue
Now, substituting for Xi in (35b) yields
af. af.
(MR. + E 1 C) =- r.
1 kti Ci k aXji
j = l, ..., n
i = 1, ..., N
Rearranging terms in equation (36) results in the expression for the ith
region
aL
aX..
31
aL
ax.
(35b)
(35c)
(36)
46
aP af.
1R k#i C i k 1 aX Jji
af
This equation can be used to show that in equilibrium, r / = r. /
aff
Small i, j, and that these expressions are in turn equal to the
Xji
marginal cost of output. From equation (37), it can then be seen that
the single result of within region marginal cost equals within region
marginal revenue does not necessarily hold when the industry is composed
of several regions of whose profit is jointly maximized.
The reason for this apparent divergence between each region's
marginal cost and revenue can be explained by examining the second term
aP
on the left-hand side of equation (37), E k C This term is equal
kfi 3Ci k
to the sum of the change in total revenues in the N 1 regions induced
by a change in the output of the ith region. From this, the non-equality
of within region marginal costs and within region marginal revenues makes
more sense. The equating of within region marginal revenues and mar-
gional costs fails to account for interregional price effects. When
maximization deals with all sectors simultaneously, these price effects
are "internalized," resulting in the expression in equation (37).
Having seen that simultaneous maximization of profit in the above
situation does not result in the traditional result in the equality of
each region's marginal cost and marginal revenue, it is of interest to
determine the sign of difference between these two terms. Knowledge of
this sign will enable comparison of input levels obtained under the
above procedure and those obtained by maximization of each region's
profit independently of other regions. Rewriting equation (37) as
47
aP
MR. MC. = Ck C(38)
S 1 kfi aC k
f.
where MCi has replaces the expression r / it can be seen that the
1
sign of the difference between MR. and MC. is given by the sign of
P 9P k
-C Ck. From equation (31a), < 0 for all i, k and Y is
ki aCi k aC k
strictly positive. Therefore, the sign of the right-hand side of equa-
tion (38) must be greater than zero, implying that MRi is greater than
MC.. It should be noted here that a sufficient condition for MRi = MCi
aP
is that 0, i k. In this case, independent maximization of
aC
regional profits is equivalent to maximizing profit in all regions
simultaneously.
.th
The implications of these results on input levels for the i
region can be seen by examining Figure 9. The figure illustrates that
equating MR. and MC. results in an output of Cli, which is greater than
that produced, C2i, under the equilibrium conditions stated in equation
aP
(37). The distance OA-OB is equal to kC- C Taken in conjunction
k=i i 1
with the nature of the yield function (equations (23a) and (23b)), it
can be concluded that inputs are at lower levels when cross-regional
price effects are taken into account.
As in the case of a single sector fishery, the question of produc-
ing at the point where price is equated to marginal cost must be con-
sidered in the multi-sector fishery. As with the single sector fishery,
assume that the desired yield levels have been determined for each
region. In that fixing yield levels results in fixing price, the
profit maximization problem reduces to a cost minimization problem with
48
Price in
Region i
P / MC.
P2i -
A I
kY B I
-kti y K .
kfi i I MRi
I P. (Y ..., YN)
0 Y2iYi Catch in Region i
2 Yii Yl
Figure 9. Equilibrium in a multi-sector fishery with variable
price and pecuniary externalities
constant price and output. The main concern, in so far as the multi-
sector fishery is concerned, is the correct choice of price. Consider,
for example, that C. i = 1, ..., N are the desired yields for the N
1
regions. Now, if the relevant demand curve for region i is given by
P. = P (C., ., Cn) (39)
the resulting expected price will be given P. = E[ P. (Y' Y ) ].
1 1' n
This price reflects the interregional price effects and is used to
derive the appropriate levels of inputs. If, however, interregional
price effects are ignored and the demand function erroneously is assumed
to be of the form
Pi = Pi (Ci) (40)
the resulting expected price, P) ] will not be the
49
Pi I *
correct price. Unless 0 i k, P. will not equal P., which will
k
result in a different set of input levels being chosen. The reason this
is so is that P. fails to reflect between region price effects.
These results are not surprising. In a situation in which each
sector is being managed independently, only costs and revenues specific
to the region will be considered in the decision process. If, in fact,
there exist cross-regional price effects which are not considered, each
region in attempting to maximize its profits will tend to choose higher
levels of output and, hence, higher input levels than would be obtained
if the interregional effects were taken into account. If all regions
were under the control of one central management authority, these inter-
regional price effects would be "internalized" and the appropriate
levels of regional input levels and outputs would be obtained.
As a motivation behind how such a situation as described above
could arise, consider a fishery which is composed of several states
fishing over a fairly large geographic area. Furthermore, assume that
the fishery is such that each state's demand price is determined in
part by the within state supply of fish and in part by a national
market, supplied by shipments from all states in the fishery. Thus, the
price in each state is determined directly within state catch and in-
directly through a national market by the catch of all states in the
fishery. Now, if the management authority is extended over the fishery,
the appropriate method of incorporating management goals becomes a
relevant question. One possible goal of management could be to manage
the fishery in such a manner as to maximize the entire fishery's profit.
A key result of the above analysis is that under these circumstances,
management should not be undertaken on an independent basis by
50
individual states or regions. Rather, management should take into
consideration all states simultaneously.
CHAPTER III
EMPIRICAL MODEL
Introduction
This chapter presents the empirical model for the Gulf of Mexico
Reef Fish Fishery to be utilized in simulating the effects of various
management alternatives. The first section of this chapter deals with
the specification and estimation of the regional catch equations. The
second section contains the regional demand equations facing producers.
Before proceeding with the specification and estimation of the
various empirical relationships, a brief discussion concerning the
nature and type of data employed in this study is in order. As with
many fisheries, data on the GMRFF are extremely limited. Primary data
at the firm level are almost non-existent. While some data of this type
could be collected for perhaps one or two years, this would not be suf-
ficient given the long-run nature of this study. Furthermore, virtually
no consistent continuous set of biological data on resource stock sizes
suitable for econometric analysis exist. Such data could be collected,
but only at extremely high costs in terms of both time and dollars.
The major source of data used in this study is Fishery Statistics
of the United States (U.S. NMFS, 1957-1975). The data used thus cor-
respond to aggregate cross-section time series observations on states
participating in the GMRFF for the years 1957 to 1975 inclusive
(Appendix B). Because of the aggregate nature of these data, the
51
52
relationships discussed are necessarily aggregate in nature. Such
aggregation unfortunately limits the resulting empirical models in many
undesirable ways.
Catch Equation Specification and Estimation
In order to specify state catch equations, the form of the catch
equation for an arbitrary region is first developed in a deterministic
fashion. After developing the typical region's catch equation, the
corss-sectional specification is presented. Commensurate with this
discussion is the stochastic specification of the catch equation. The
presentation concludes with the choice of the appropriate estimator.
A general expression for a fishery catch equation is given by
C = f(E, S) (41)
where C refers to catch, E is effective fishing effort and S denotes the
resource stock size. Since stock size is seldom observable, the catch
equation stated in (41) is often modified for empirical analysis to
C = f*(E) (42)
In equation (42) aggregate catch is expressed as a function of only
effective fishing effort. The f (E) function is used to denote the fact
that the influence of the resource stock is not considered explicitly as
in equation (41) but rather indirectly. The equilibrium yield models
presented in the previous chapter are one such class of models.1
1Consider the Schaefer formula as an example. Equation (41) cor-
responds to C = KEP in the Schaefer model. In this context P is elimi-
nated through algebraic manipulation to derive the Schaefer type
equilibrium yield function C = AE BE2. Here, AE BE2 corresponds to
f*(E) in equation (42) above.
A second class of models which correspond to those defined by equation
(42) are non-equilibrium yield functions. In these types of models,
stock effects are incorporated through stochastic processes.
Specification of Fishing Effort
Central to.the development of an empirical representation of the
ith state's catch function is the notion of effective fishing effort.
Recall from equation (22) that effective fishing effort is primarily
composed of a nominal component and a fishing power component. Further,
fishing power was seen to be a function of input levels.
The aggregate nature of the data must be considered in specifying
the fishing power equation for the ith state in the GMRFF. As such, the
fishing power function relates to the average fishing power correspond-
ing to vessels operating out of ports located in each state. The fish-
ing power function for the ith state is thus given by
Sexp(k) Xl X i = 1, ..., 5 (43)
it lit 2it t = ..., 19
where EP denotes fishing power, Xlit is average crew size, X2it is
it
average vessel size (gross registered tonnage) and k is a constant
parameter.
The choice of average crew size and average vessel size as the
relevant inputs for use in specifying the fishing power function was in
part determined by available data. The nature of the fishing activity
for vessels in the GMRFF suggest that these variables are appropriate
measures of labor and capital inputs which determine fishing power,
however. The general fishing process involves operating hand or power
driven reels which control the fishing line. Average crew size provides
a good aggregate measure of "gear contact" with the resource stock since
each crewman usually operates only one reel. The use of average vessel
size measured in gross registered tonnage is also a reasonable represen-
tation of the capital input in the fishing power equation. In the reef
fishery, factors such as sea conditions and weather can impair or pre-
vent altogether the fishing process. Vessel size is a factor which
affects the ability or certainty of the fishing process to be undertaken.
This measure also is related to the duration of fishing trips and to a
lesser degree, the distance a vessel can travel to fishing grounds.
Thus, the effect of vessel size on fishing power is seen to be related
to the ability of vessels to undertake and sustain the fishing process.
The choice of the functional form was in part due to the ease with
which the Cobb-Douglas type function can capture non-linear production
relationships without a large loss in degrees of freedom. In addition,
this functional form also facilitates testing the hypothesis that the
fishing power function exhibits constant returns to scale. Given that
fishing power is a theoretical construct, it may be that a doubling of
all inputs doubles fishing power. Equation (43) as specified permits a
direct test of this hypothesis. Finally, the ji, j = 1, 2, provide a
convenient means of judging the relative importance of each input with
respect to the "production" of fishing power. A priori, one would
expect that average crew size should have a larger influence on fishing
power than does vessel size, given its relationship to "gear contact"
with the resource stock.
Total effective fishing effort is defined to be the product of the
nominal measure of effort and fishing power.2 It should be noted that
fishing intensity is assumed to be implicit in the observation interval
of the time series data. The nominal effort measure used in this study
is defined to be the number of vessels. The expression for total effort
is then given by
Eit = exp(k) Vit X X (44)
where Eit is total effort and Vit refers to total vessels in state i and
time t. Examination of equation (44) reveals that total effort in
state i and time t is precisely the number of vessels operating in the
corresponding region and time period, "weighted" by the average fishing
power corresponding to those vessels.
Within Region Specification Considerations
The relationship in equation (44) serves to define total effort as
a function of the size of a fishery (number of vessels) and the cor-
responding average levels of capital and labor inputs (fishing power).
This equation, however, is definitional in nature and as such precludes
direct estimation of parameters independently of catch. Thus, it is
necessary to specify the ith region's catch equation.
The empirical form of the catch equation for the ith state is given
by
Ci exp[A(S)it] E = 1, ... 5 (45)
it .. ., 19
2Hereafter, the terms total effort and total effective fishing
effort are used interchangeably.
where Cit represents combined catch of red snapper and grouper, A(S)it
is a stochastic process generated by the resource stock, Eit is total
effort and .i is a constant. The aggregation of red snapper and
grouper into a single catch variable is an unfortunate result of limited
data. While separate catch series are available, input data are not
disaggregated to permit an analysis of the allocation of these inputs
between species.
The form of the catch equation, as with the fishing power equation,
was chosen in part due to the ability of such a function to capture a
non-linear relationship between catch and effort while retaining an
intrinsic linear form for estimation purposes. The form chosen does,
however, lend itself to an approximate test of an interesting hypothesis.
The notion of returns to scale is a somewhat misleading notion with
respect to fisheries production due to the dynamic nature of the
resource stock. It has been used, however, in fishery production
literature (Schaefer, 1957; Scott, 1955). More precisely, the non-
equilibrium catch equations utilized in stock production models gener-
ally assume constant returns to scale as exhibited by the ith state's
catch equation. Acceptance that the stochastic process, A(S)it, in
equation (45) adequately accounts for the effects of the resource stock
on catch allows the utilization of the pi parameter to conduct an ap-
proximate test of the "constant returns" assumption of the stock produc-
tion models of Schaefer (1957) and Pella and Tomlinson (1969).
3The specification of the stochastic nature of A(S)it will be
discussed more fully in the latter portion of this section.
The catch equation in (45) can be expressed in terms of nominal
effort and fishing power by substituting equation (44) into equation
(45) for Eit. The resulting reduced form catch equation is
I i Xli x 2i (46)
it = exp[A'(S)t] V Xlit (46)
where the term A'(S)it denotes the fact that the constant k in equation
(44) has been incorporated into the stochastic process A(S)it and the
reduced form parameters are ji = BiOi' j = 1, 2. To facilitate
further discussion, it is convenient to write equation (46) in an alter-
native form. By defining cit = In Cit, x = In Xi and so on, equation
(46) can be written in double log form as
cit = A'(S)it + i + i li Xlit + 2ix2it (47)
i = 1, ..., 5
t = ..., 19
The nature of the stochastic process A'(S)it can be analyzed in this
form.
Stochastic Approximation of Resource Stock Effects
The expected presence of a stochastic process in the catch equation
derives from the nature of the omitted resource stock variable.4 From
the discussion contained in Chapter II, it is apparent that the change
in the resource stock over time is proportional to the difference
between catch and sustainable yield. An expression for the size of the
4The discussion that follows implicitly assumes that the resource
stock variable is uncorrelated with the included set of regressors.
the resource stock in any given time period can then be given by
St = S + X(C_1 Ct) (48)
where St is the stock size in time t, Ct is sustainable yield produced
by the resource stock in time t, Ct is the corresponding catch and X is
a constant of proportionality. Thus, equation (48) states that the
stock size in time t is equal to the stock size in the preceding time
period plus a proportion of the difference between sustainable yield and
catch in time t-l. While only Ct_1 is observable, equation (48) serves
to suggest that the resource stock variable is at least to a certain
degree, autocorrelated. Thus, the omission of the resource stock vari-
able is expected to generate some systematic variation in the distur-
bances of the catch equation which can be approximated by an
autoregressive process. In particular then, the stochastic process
corresponding to the ith region's catch equation is assumed to take the
general form
A'(S) = A' + U (49)
it 1 it
where A! is constant and the disturbance term, Uit, is postulated to be
characterized by a pth order autoregressive process. On substitution of
equation (49) into equation (47) the ith state's catch equation can be
expressed as
cit = A + Bivt + li xlit + 2ix2it + Uit (50)
where Uit= PliUt- + p2i Ui,t-2 + + Ppi Ut-P + eit and eit is
assumed to be white noise.5 Before proceeding to a more detailed
specification of the stochastic properties of equation (50), it is
necessary to consider the cross-sectional specification of the catch
equations.
Cross-Sectional Specification Considerations
The main consideration which must be addressed in the cross-
sectional specification of the catch equations involves determining what
restrictions exist on the catch equation parameters across states. Both
the nature of the fishing process and the nature of the data must be
considered in determining these restrictions.
Consider the equality or non-equality of the fishing power function
coefficients. In general, the fishing process and input characteristics
of vessels across states are very similar. Given this, it seems reason-
able to assume that the fishing power coefficients are constant across
states in the GMRFF. The fishing power function, incorporating this
restriction is given by
E = exp(k) X t = 1, ..., 19 (51)
it lit 2it
i = 1, ..., 5
The consequences of such a restriction are not without complications,
however. The assumption that aji = ajk for j = 1, 2 and all i, k
requires that non-linear restrictions be placed on the reduced form
parameters of equation (50). More explicitly, these restrictions take
5A white noise process is defined as a sequence of independent
identically distributed random variables with zero mean and constant
variance.
the form of Pk ji = Bj "jk for j = 1, 2 and all i, k. Thus, in the
absence of any a priori assumptions concerning the Bi, i = 1, ..., 5,
parameters across states, non-linear restrictions on the parameters must
be incorporated for correct estimation. If, however, Bi = Pj for all
i, j, this restriction is trivially satisfied and estimation difficul-
ties are greatly reduced.
The Bi parameters measure the marginal response of total state
catch to small changes in vessel numbers holding fishing power constant.
Given the homogeneity of the fishing process across states and the fact
that the fishing power function serves to "weight" vessels according to
the input characteristics of each state's vessels, the assumption that
i = Bj for all i, j may not be an unreasonable assumption to make. As
stated above, making the assumption Bi = .B for all i, j insures that
the non-linear restrictions on the reduced form parameters are met,
There is also an additional gain realized by assuming that the catch
equations for the GMRFF producing states to take the form
cit = Ai + Bvit + Xlit + 2 x2it + Uit (52)
Stated in the manner above, the data on vessels, crew sizes and vessel
sizes can be pooled across states. Not only does such pooling generate
considerably more variation in the vectors of regressors, which aids in
parameter estimation, it also creates a sizeable gain in degrees of
freedom. The final specification of the state catch equations given in
euqation (52) illustrates the cross equation restriction corresponding
6Recall that i.. = i a.. for all i, j. If .. ajk -for all i, k,
it follows that Bki ji = i "jk for all i, j, k.
to the equality of the reduced form (and structural) parameters across
states. It should be noted, however, that the mean of each region's
stochastic process, Ai, is unconstrained across equations. The specifi-
cation and intrepretation of the Ai parameters, in particular, and the
stochastic processes characterizing the regression disturbance, in
general, provide a convenient introduction to the discussion concerning
the choice of the appropriate estimator.
The geographic location of the primary reef fish stocks are
depicted in Figure 10. There is some indication, although there is not
an overwhelming amount of evidence, that the reef fish stocks do not
exhibit a great deal of migratory behavior (GMFMC, 1979). This fact,
taken in conjunction with the large geographic dispersion of fishing
grounds, suggests that the GMRFF is composed of several biologically
independent stocks of reef fish. Additional information on the general
fishing locations of vessels originating from various states' ports
(GMFMC, 1979), indicates that vessels originating from different states
fish on common grounds. This information suggests each state catch
function should have a stochastic process dominated by the stock most
frequently fished, and that these processes should be contemporaneously
correlated due to the intermixing of vessels from different states.
Thus, the overall structure of the system of catch equations is char-
acterized by a system of seemingly unrelated regression equations (SUR)
with cross equation parameter restrictions and autoregressive
disturbances.
The information above also serves to give an interesting interpre-
tation to the Ai parameters. These parameters serve to determine the
"location" of the catch equations for each state in input-output space.
Figure 10. Principal fishing grounds in the Gulf of Mexico
Reef Fish Fishery
Given that all other technical parameters are constrained to be constant
across states, the A. may serve to indicate the relative size or densi-
1
ties of the primary stocks fished by vessels for each state.
Furthermore, testing the difference between the A. constitutes an
approximate test for the degree to which various states' vessels fish
common grounds. The reasoning behind this is that if vessels from dif-
ferent states fish common grounds, the stock densities should eventually
become equal. This can be investigated by testing the hypothesis A. =
1
A. for all i, j.
J
Choice of Estimator for the Catch Equations-
As a prelude to the discussion regarding the estimation of the
catch equations, it is convenient to place the system of equations into
matrix form. This is accomplished by
C = .XB + U (53)
where
C = NT x 1 vector of logged catch variables;
g = (k + N) x 1 vector of parameters to be estimated; and
U = NT x 1 vector of disturbances with EU = 0, EUU = 1.
The NT x (k + N) matrix of regressors is of the form
X = [D X] (53a)
with the NT x N matrix, D, composed of appropriately defined state dummy
variables and X corresponding to the NT x K matrix of logged values of
regressors given in equation (52). Specification of the distrubance
term is given in general form to emphasize the covariance matrix is
non-spherical. The precise form is conditioned by the exact form of the
autoregressive processes corresponding to each state's disturbance
vector.
Estimation of the catch equation parameters must be done in two
basic steps. The first step involves the identification and estimation
of the autoregressive processes for each state generated by the unobserv-
able resource stock. Once this is accomplished, the appropriate form of
the covariance matrix of the disturbances can be ascertained and the
appropriate estimator for the reduced form parameters derived.
Due to the small sample size of each cross section (T = 19), many
of the standard time series identification techniques for determining
the autoregressive order parameter are unsatisfactory. This mainly
results from the fact that most statistical tests on the order parameter
are only asymptotically valid and utilize a variance measure that is
inversely proportional to the sample size. There are, however, several
techniques, such as Akaike's (1969) FPE criterion which do not suffer
from this limitation. Several alternative identification procedures
were used in the identification of the residual autoregressive process.
These procedures are outlined in Appendix E.
The estimated residuals used in the identification process were
generated by applying a two stage Aitken's estimation procedure to
equation (52). More precisely, the NT x 1 vector of residual estimates
is given by
0 = C (54)
where 3 = (X'(i1 aI)X)-" (X'(" a I)C) and E is the N x N matrix of
estimated contemporaneous covariances. The estimated residual vector
was then partioned into N, T x 1 vectors corresponding to the N cross-
sections. The results of the identification procedure indicated that
all sets of estimated residuals were characterized by first order
autoregression.
Having determined the order of the autoregressive processes for
each state catch equation, a complete specification of the distrubances
for the system of catch equations can now be made. Denote the stochas-
tic process of the ith region by
Uit = PiUit-I + e it (55)
The stochastic specification of U in equation (55)7 is then given by
E(Uit) = ii (55a)
E(UitUjt) = (55b)
4ij t = s
E(e ite) = { (55c)
o t t s
E(Uio Ujo) = ij /1 -Pi Pj (55d)
1ii) 1
for i, j = 1, ..., N and Uio N(O, 2) and eit N(O, i).
1 Pi
As a result of the residual identification process, the system of
catch equations can be characterized as a system of seemingly unrelated
regression equations with cross equation parameter restrictions.
Furthermore, the disturbances exhibit first order autoregression. A
great deal of literature pertaining to the estimation of this type of
equation system is available. Most notable is the work done by Parks
(1967), Kmenta (1971), Kmenta and Gilbert (1968) and Zellner (1962).
The most important of these insofar as this study is concerned is the
work done by Kmenta and Gilbert on the small sample properties of alter-
native estimators for systems of equations similar in nature to the
catch equations above. As mentioned previously, data on the catch equa-
tion variables is limited, resulting in rather small sample sizes.
The form of U is given by
U1 = [ Uil ..., UiT, ..., UN1, ..., UNT '
Given that all estimators for the above equation system possesses only
asymptotic properties, it is appropriate to use a relative efficiency
criterion in small samples as a basis for choosing the "best" estimator
for the system of catch equations given in equation (53).
Drawing on the results of Monte Carlo studies conducted by Kmenta
and Gilbert (1968), a four stage Aitken's estimator (FSAE) was chosen as
the appropriate estimator. The formation of this estimator proceeds in
two basic steps. Given that the disturbances in each equation in the
system are known to follow a first order autoregressive process, the
first step involves the application of the two stage Aitken's estimator
to equation (53) to generate a sequence of estimated residuals for each
state catch equation. These residuals correspond to those given in
equation (54). The use of this four stage estimator is the reason that
the residuals estimated using equation (54) were used in the order
parameter identification. The estimation of the autoregressive parame-
ters is accomplished by
N U N
p. it- / Z i = 1, N (56)
t=2 T 1 t=l T
where U is the estimated residual for the ith state and tth time
it
period defi-ned in equation (54).
The second step in deriving the FSAE involves a second application
of the Atiken's two stage estimator. Before this estimator is applied,
however, the data is transformed by
i = 1 p. C i = 1, ..., N (57a)
111 i1
c = Ct pCi i = 1, ..., N (57b)
it it 1 i ,t- t =2, ..., T
^ .
Xi = 1 p X all i, j (57c)
^
Xit = it pixjitl all j (57d)
jt =2, ..., T
where cit and xjit are defined as in equation (53a). In matrix form,
the transformed system can be written as
C = X + U (58)
*
where C is an NT x 1 vector of transformed logged catch values and X
is an NT x (N + K) matrix of transformed regressors in log form. The
effect of the transformation is to remove the autoregressive effects
*I
from the NT x 1 disturbance vector, U Thus, EU U = I IT where
11 h12 "' 1N
S= 21 22 "' 2N (59)
N1l RN2 NN
corresponds to the contemporaneous covariance matrix of the transformed
disturbances. To estimate t, ordinary least squares was applied to
equation (58) to yield
^* *^ (60)
U = C X (60)
where B = (X* X*)- (X*' C*). Estimates of the ij were calculated by
1 T ^. ^.
ij T-k Uit U jt (61)
where Uj., t = 1, ..., T is the estimated residual sequence correspond-
ing to the ith state. The estimated covariance matrix, f, is formed by
replacing j.. with cij in equation (59). Finally, the FSAE for the
system of catch equation is given by
S= (X* (- a I)X)-1 X*( a I)C* (62)
where I is an identity matrix with rank T. Furthermore, the estimated
variance-covariance matrix for B is given by
*' 1 -1
COV e = (X (~ I)X ) (63)
The precise statistical properties of p are somewhat difficult to
ascertain. The primary reason for this relates to the stochastic
specification of the system of equations. Under the assumption that the
true stochastic specification is first order autoregression with con-
temporaneous correlation, the asymptotic covariance matrix for p is
consistent and asymptotically normal and efficient. Unfortunately, the
actual stochastic specification of the system constitutes a pretest.
This seriously clouds the precise statistical properties of the esti-
mated coefficients.
Price Equation Specification and Estimation
The latter part of Chapter II presented a scenario in which pro-
ducing states faced a variable product price. The price faced by
producers in any given state was dependent on the outputs of all
other states. The purpose of this section is to present the specifica-
tion and estimation of a system of interrelated price equations for the
GMRFF which are similar in nature to those discussed in the previous
chapter. The discussion that follows first addresses issues involving
8
the appropriate structure of the price equations. The choice of the
appropriate estimator and the estimation scheme utilized are then
discussed.
Aggregation Across Species
As with the catch equations, the price equations must be specified
in aggregate terms. The basic reason for this relates to the data
limitations which required the catch equations to be specified in terms
of the aggregate catch of reef fish. Thus, to be compatible with the
catch equations, the price relationships must be specified in terms of
an aggregate "price" of reef fish. Within the model "price" of reef
fish serves as a measure of the average value per pound produced by reef
fish vessels.
The degree to which such a "price" can be used in deriving valid
price equation estimates depends on many factors. These factors include
the similarity of the prices and markets for red snapper and grouper,
the relative magnitudes of each species in total catch and the similarity
of the price responses to changes in catch for each species. Since
1957, the dockside price of red snapper has been about twice that of
grouper (U.S. NMFS, 1957-75). Over this period both have exhibited
8The term price in this section pertains to the nominal dockside or
ex-vessel price.
fairly consistent price increases. Both species have exhibited similari-
ties in product form when shipped from dockside although the type and
location of the markets to which they are sent differ. In 1977, 81.6
percent of grouper and 93.7 percent of all red snapper taken in the
GMRFF were shipped from dockside in fresh iced form (GMFMC, 1979).
Similarly, over half of each of these species was shipped to wholesalers.
In terms of market location, 58.4 percent of the red snapper caught was
9
shipped to Northeastern markets, and 24.1 percent was shipped to South-
eastern markets.0 In contrast, only 15 percent of the grouper catch
went to Northeastern markets while 77 percent was shipped to markets in
the Southeast (Appendix F). Thus, while the absolute prices of the two
species differ as do the location of terminal markets, the basic trends
in prices as well as the product form for grouper and red snapper
shipped from dockside are very similar.
In estimating price equations using price of reef fish as the
dependent variable, some bias in the parameter estimates will be
incurred. The degree of bias is related to both the relative magnitudes
of each species in total catch and the similarity of price responses to
changes in catch of each species. Florida is the dominant producer of
grouper in the GMRFF. The proportion of grouper in the total catch of
states other than Florida has been relatively insignificant. No state
other than Florida has accounted for more than 4 percent of the total
grouper catch since 1970 (GMFMC, 1979). Thus, only the price equation
for Florida appears susceptable to significant aggregation bias.
Includes New York, Illinois, Michigan, Maryland, Pennsylvania and
Ohio.
10ncludes South Carolina, Georgia and Florida.
The degree to which this bias is incurred rests on the similarity
or dissimilarity of the price responses to changes in catch for each
species. To see this, let
Pkt = aok + YkCkt k = S, G (65)
denote the price equations for red snapper, (S), and grouper, (G). Now,
if instead of equation (65) the price equation is written as
Pt = a + YCt (66)
where Pt = w1 Pst + W2 P w + 2 = 1 and C = C the estimated
parameters will correspond to a = W aoG + W2aoG and y = wls + W2Yg.
If, however, s = Yg = Yo, the price response parameter in equation (66)
will be y = (wl + w2)Yo = Yo since w1 + w2 = 1. To test the equality
of the price response parameters for grouper and snapper caught by
Florida vessels, separate price equations were estimated for each
species. The results of estimation indicated that the price response
parameters were of very similar magnitude (Appendix F).
The necessity to aggregate across species in specifying the reef
fishery price equations is unfortunate. However, the similarity between
grouper and red snapper as food fish at dockside, the relatively small
size of groupers in the reef fish catches of states other than Florida
and the similarity of the price response parameters of both species for
Florida makes the expected consequences of such aggregation small.
Thus, in the analysis that follows, the price equations are defined in
terms of the aggregate variables, price of reef fish and total catch of
reef fish.
The main product form of reef fish when shipped from dockside is
fresh iced. Thus, reef fish can be considered to be non-storable
products. Furthermore, the direction of causality is such that quantity
produced determines price at dockside. The implication of this is that
the price (demand) equations should be specified in price dependent
form. This specification is harmonious with fishery demand analyses
conducted by others (Cato, 1976; Doll, 1972). Within this context,
price can be considered as determined by factors such as quantity pro-
duced, quantity of substitute products, income and tastes and preferences
of consumers (Tomek and Robinson, 1972). Since the price equations
considered here relate to dockside prices, the empirical price equations
derived below abstract from many of these causal factors.
The price equations in the latter part of Chapter II were presented
in general form and in such manner that the price in each state was a
function of the quantities produced in all states. In spite of this
general form, there is considerable information on the structure of
prices in the GMRFF which suggests some parameter restrictions. Cato
and Prochaska (1976a) have shown that Florida is the dominant producer in
the GMRFF. Their findings suggest that Florida is the only state which
has a significant effect on prices in other participating states. This
result is not surprising in that Florida's catch since 1957 has
accounted annually for an average of 45 percent of all red snapper and
84 percent of all grouper caught in the Gulf of Mexico region.
Furthermore, it appears that all states are net exporters of reef fish.
Since 1975, the GMRFF has accounted annually for approximately 98
percent of all red snapper and 92 percent of all grouper produced in the
United States (U.S. NMFS, 1957-75). Data for 1977 also indicate that
93.3 percent and 89.0 percent of the red snapper and grouper catch,
respectively, was shipped to areas other than the GMRFF states (Appendix
F). The implication of this data is that there should be very little,
if any, interregional trade in reef fish among GMRFF states. This is
significant in that it implies the absence of any systematic price dif-
ferentials across states based on transportation costs, thus simplifying
the price model greatly.
The information above serves to provide the basis for specification
of the empirical price equations. The price equation for Florida is
assumed to have the form
Plt = ^01 + 11 C1t + 21t + elt (67)
where Plt is the ex-vessel Florida "price" of reef fish, Clt is the
corresponding catch and t is a time trend variable. Specification of
the disturbance component, e1t, is discussed below. For other states,
the general form of the price equation for the ith state is given by
it = YOi + li Cit + Y2i Cit + '3it + eit (68)
i = 2, ..., 5
where Pit and Cit are, respectively, the "price" and catch of reef fish
in state i. Once again, the specification of the disturbance term, eit,
is discussed below.
Incorporation of the trend variable in equations (67) and (68) was
done to account for demand shifts over time. This variable is a com-
posit proxy for effects such as population and income. The basic reason
these variables were not explicitly incorporated into the price equation
relates back to data limitations and the utilization of the "price" of
reef fish as the dependent variable. Although grouper and red snapper
are very similar products at dockside, they tend to move through dif-
ferent markets both with respect to type as well as location. Further,
as evidenced by Appendix F, there are also several marketing levels
through which these species pass in moving from dockside to retail.
Thus, any attempts to infer income flexibilities for reef fish would be
necessarily crude. In an effort to avoid such potentially misleading
inference and still capture the effects of such factors, the use of a
time trend variable was employed.
Choice of Estimator for the Price Equation
As with the catch equations, the choice of the appropriate esti-
mator for equations (67) and (68) is oriented toward obtaining desirable
statistical properties for the parameter estimates. Choosing the
appropriate estimator largely rests on the stochastic specifications of
the disturbance terms in equations (67) and (68). The delineation of
the price equations on a state basis is done on the basis of recorded
data rather than on the basis of some other economic factors which would
serve to delineate the appropriate cross-sectional units. In relation
to the economic structure of price determination in the GMRFF, such
division of units on the basis of geographic boundaries is admittedly
arbitrary with respect to the actual economic structure of the GMRFF.
Thus, a considerable degree of contemporaneous correlation in the dis-
turbances of the price equations is anticipated. The disturbance
specification for the price equations in equations (67) and (68) is
given by
E(eit) = 0 for all i, t (69a)
E.. t = s and all i, j
E(eit e) = { 'J (69b)
i s 0 t f s and all i, j
The stochastic specifications given in equations (69a) and (69b)
serve to characterize the price equations as a system of seemingly un-
related regression equations. Zellner (1962) has shown that the best
estimator for this type of equation system in terms of relative effi-
ciency is a two-stage Aitken's estimator. This estimator was utilized
in estimating the price equation parameters. Before proceeding with a
presentation of this estimator, it is convenient to place the price
equations in matrix form. Let P be an NT x 1 vector of prices, Zi be
T x ki matrix of exogenous variables corresponding to the independent
variables given in equations (67) and (68) for the ith region and e be
an NT x 1 vector of disturbances. The price equations in matrix form
are then given by
P = Zy + e (70)
where Z is a NT x (zKi) block diagonal matrix with Zi i = 1, ..., N
constituting the diagonal blocks. Further, E(e) = 0 and E(e e') = Qo IT
where IT is a T x T identity matrix and Q has the form
a11 021 ." alN
n = 21 22 ". 02N (71)
N1 aN2 aNN
The Aitken's estimator for y is then given by
y = (Z'(-I IT)Z) (Z'( l IT) P). (72)
Although this estimator is consistent, asymptotically normal and effi-
cient (Kmenta, 1971), it is not feasible in that n is unknown. The
covariance matrix can, however, be estimated as follows. Let eit be the
estimated residuals from the ordinary least squares regression of the
price equation for the it state alone. The aij can then be estimated
by
1 ^ ^
_i T E eit ejt. (73)
ij T jt
By replacing o.. in equation (71) with .ij, the two-stage Aitken's
estimator (TSAE) for y
S= (Z'(n1 IT)Z)- (C'("-1 IT)P) (74)
is obtained. Zeller (1962) has shown that y has the same asymptotic
properties as y given in equation (72).
CHAPTER IV
EMPIRICAL RESULTS
Previous chapters in this study have developed a theoretical model
indicative of the GMRFF and presented the specification of the empirical
equations to be utilized in analyzing the fishery. The various esti-
mators for the empirical equation were also discussed and derived. This
chapter presents a discussion of the empirical results obtained.
The first section contains an analysis of the estimated state catch
equations. The following section presents a similar analysis for the
estimated state price equations. The third section develops the com-
plete reef fishery model used to determine maximum economic yield.
Further, the results of profit maximization in the fishery are presented
and discussed in detail. The final section of this chapter compares the
results of this analysis with those obtained by the Gulf of Mexico
Fishery Management Council.
Analysis of Production in the
Gulf of Mexico Reef Fish Fishery
The state catch equations were characterized in equation (52) as a
system of seemingly unrelated regression equations with autoregressive
disturbances and cross equation parameter restrictions. As such, a four
stage Aitken's estimator (FSAE) was utilized in estimating the catch
equation parameters. To a certain extent, the validity of the a priori
specification of the catch equations can be measured by the gains in
efficiency obtained by using the FSAE as opposed to the ordinary least
squares with dummy variables (OLSDV) estimator.
An examination of the parameter estimates obtained from the two
estimators indicates that both estimators yield parameter values of
similar magnitude with the exception of the parameter estimate for
vessel size (Tables 1 and 2). Furthermore, both estimators yield
parameter estimates of reasonable magnitude and the expected sign. The
gains from using the systems estimator become apparent when the standard
errors of the parameter estimates are examined. All standard errors
obtained utilizing the FSAE are substantially lower than the correspond-
ing estimated standard errors obtained from the OLSDV estimator with the
1
exception of the standard error of the vessel size parameter. Finally,
examination of the estimated autoregressive parameters illustrates that
the estimated equations for all states, except Louisiana, are charac-
terized by significant first order autoregression (Table 2).
This brief comparison of estimators for the reef fishery catch
equations gives considerable support to the a priori specifications of
the preceding chapter. Given the small sample size employed, the gains
in efficiency obtained by the FSAE coupled with the reasonable magnitude
of the estimated parameters and the strong presence of autoregression,
serve to give heuristic confirmation of the overall specification and
choice of estimator in deriving the empirical catch equations for the
GMRFF.
It should be noted that the slight increase in the standard error
of the vessel size parameter must be considered in light of the fact
that the FSAE estimate is approximately three times larger than the
OLSDV estimate.
Table 1. Ordinary least squares with
Fishery catch equations
dummy variables parameter estimates for the Gulf of Mexico Reef Fish
Dependent variable Intercept an vessels in crew size An vessel sizeb
An Florida catch 3.72581 0.848001 0.756031 0.111163 R2 = 944
(.71085) (.08539) (.22132) (.16841)
An Alabama catch 3.0625 0.848001 0.756031 0.111163
(.86631) (.08539) (.22132) (.16841)
An Mississippi catch 3.3531 0.848001 0.756031 0.11163
(.8558) (.08539) (.22132) (.16841)
An Louisiana catch 1.1514 0.848001 0.75601 0.111163
(.74639) (.08539) (.22132) (.16841)
An Texas catch 2.007 0.848001 0.75601 0.11163
(.7782) (.08539) (.22132) (.16841)
aCatch is measured in thousands of pounds.
Vessel size is measured in gross registered tons.
Table 2. Four state Aitken's parameter estimates for the Gulf of Mexico Reef Fish Fishery catch equations
Dependent variable Intercept an vessels an crew size An vessel sizeb Uit-1
An Florida catch 3.15533 0.740230 0.713178 0.340649 0.44048
(.68466) (.067263) (.18169) (.17306) (.036391)
An Alabama catch 2.374897 0.740230 0.713178 0.340649 0.85468
(.80167) (.067263) (.18169) (.17306) (.022373)
An Mississippi catch 2.747624 0.740230 0.713178 0.340649 0.74216
(.76746) (.067263) (.18169) (.17306) (.028931)
An Louisiana catch 0.52701 0.740230 0.713178 0.340649 0.40764
(.73240) (.067263) (.18169) (.17306) (.40089)
An Texas catch 1.62417 0.740230 0.713178 0.340649 0.44820
(.74008) (.067263) (.18169) (.17306) (.037976)
aCatch is measured in thousands of pounds.
Vessel size is measured in gross registered tons.
Fishing Power
The estimated catch equations represent reduced form expressions.
It can be recalled from equation (44) that total effort was composed of
nominal effort and fishing power, and that the estimated fishing power
function can be derived from the estimated reduced form catch equations.
The estimated fishing power function corresponding to equation (43) for
an arbitrary state in the GMRFF is given by
.9635 .4601 (75)
Pi li 2i
where Xli and X21 are average crew size and average vessel size in the
ith state, respectively.2 Examination of equation (75) indicates that
average crew size has a much larger effect on fishing power than does
average vessel size. This was expected, however, as crew size is a
direct measure of "gear contact" with the resource stock. The estimated
fishing power elasticity corresponding to crew size is 0.9635, implying
a 10 percent increase in average crew size would increase fishing power
approximately 9.6 percent. The corresponding elasticity for average
vessel size is estimated to be 0.4601. Thus, a 10 percent increase in
average vessel size increases fishing power 4.6 percent. To the extent
that vessel size measures the ability of vessels to undertake and
sustain the fishing process, this elasticity may be interpreted as the
effect on fishing power of increased fishing time. This interpretation
It will be recalled that the fishing power function's constant
term was subsumed in the intercept of the catch function. In that the
ensuing discussion proceeds in relative terms, the constant in equation
(75) has been set equal to one with no loss of generality.
is reasonable since factors such as weather and sea conditions can
impair or prevent fishing.
The scale elasticity for the fishing power function in equation
(75) is estimated to be 1.4236. The implication of this elasticity is
that a proportionate increase of average vessel and crew size by some
1.4236
factor, X, would increase fishing power by X .4 Thus, the fishing
power function exhibits increasing returns to scale. The effects on
fishing power of increasing average vessel size and crew size from 10 to
100 percent are shown in Figure 11. The result of increasing returns in
the fishing power function are somewhat surprising. A priori, returns
to scale in the neighborhood of unity were anticipated. This expecta-
tion rested mainly on the definitional nature of the fishing power
2.5
o 2.3
0
2.1
S1.9 -
iu 1.7
1.5
4-I)
S 1.3
1.1
Proportionate Increase
7 lin Average Crew and
.1 .3 .5 .7 .9 1,1 Vessel Size
Figure 11. Estimated relative fishing power for proportionate
increases in average crew size and vessel size3
In Figure 11, average crew size and vessel size are assumed to
take an initial value of 1. While no actual vessels exhibit such input
proportions, choosing such levels alters only the scale of the figure.
expression. The interpretation of the output elasticities, however,
serve to make the appearance of increasing returns a reasonable result.
The primary role of the fishing power function in relation to the
empirical catch equations involves weighting the nominal effort compo-
nent (vessels). The basic notion here is that a standardized measure of
fishing effort can be derived by weighting vessels in the fishery by
certain input characteristics. Such a standardized measure of fishing
effort is extremely important, not only in analyses such as the current
study, but also in estimating Schaefer (1954) type sustainable yield
functions. By weighting vessels according to their relative fishing
power with respect to some base period, a standardized measure of fish-
ing effort such as standardized vessels can be obtained.
The estimated fishing power indices for each state participating in
the GMRFF for the years 1957 to 1975 are shown in Table 3. The fishing
power index is defined by
I Xlit .9635 it .4601(76)
I = ( X X ) (76)
Xlb X2b
where Xlb and X2b are average crew and vessel size in the base year and
state. In Table 3, Florida's 1960 input composition serves as the base.
Examination of the fishing power indices illustrates that Florida
vessels in 1975 are characterized by the lowest average fishing power
per vessel in the fishery. Perhaps more surprising is the fact that in
1975, Florida vessels possessed only about 75 percent of the fishing
power of vessels in the base period. Since 1967, Mississippi vessels,
on average, have had the greatest fishing power. Mississippi vessels in
1975 had slightly over four times the fishing power of Florida vessels.
Table 3. Estimated relative fishing power indices by state, 1957-75
Estimated fishing power index
Year
Florida Alabama Mississippi Louisiana Texas
West Coast
1957 1.064 2.271 1.210 1.315 0.970
1958 1.176 2.361 1.297 1.281 1.154
1959 0.932 2.468 1.514 1.366 0.915
1960 1.000 2.471 1.971 1.423 1.165
1961 1.001 2.729 2.133 1.278 1.102
1962 0.984 2.785 2.487 1.604 1.153
1963 0.994 2.870 2.527 1.623 1.327
1964 0.959 2.755 2.571 1.594 1.585
1965 0.909 2.970 3.057 1.461 1.553
1966 0.937 3.251 3.148 1.554 1.836
1967 0.030 3.119 3.529 1.073 1.657
1968 0.911 2.973 3.328 1.098 1.538
1969 0.960 2.973 3.325 1.098 1.491
1970 0.875 2.404 3.268 1.268 1.377
1971 0.893 2.407 3.299 1.172 1.723
1972 0.783 2.458 3.295 0.963 1.628
1973 0.774 2.447 3.322 1.153 1.547
1974 0.860 2.612 3.309 1.250 1.504
1975 0.766 2.612 3.313 1.229 1.592
aThe fishing power index is calculated by Ip = X95 X45 / X196
Xb where Xl and Xi are, respectively, average crew size and
2b where lit 2it th th
average vessel size in the i state and the tth time period. The 1960
input composition for Florida constitutes the index base.
Utilizing the fishing power indices to create a standardized mea-
sure of fishing effort in the GMRFF has significant implications in
relation to both stock assessment and management questions. A compari-
son of fishing effort measured in nominal terms (vessels) and fishing
effort measured in standardized terms (standardized vessels) is pre-
sented in Table 4. The standardization of vessels results in substantial
Table 4. Estimated number of standardized reef fish vesselsa and actual number of reef fish vessels
in the Gulf of Mexico Reef Fish Fishery by state, 1957-1975
Florida West Coast Alabama Mississippi Louisiana Texas
Year
Standardized vessels Standardized vessels Standardized vessels Standardized vessels Standardized
Vessels vessels vessels vessels veVesse vessels vessels
1957 108 115 11 25 5 6 2 3 129 125
1958 120 141 11 26 7 9 5 6 89 103
1959 300 280 12 30 8 12 12 16 158 145
1960 180 180 12 30 11 -22 13 19 118 138
1961 219 221 13 36 12 26 30 38 151 166
1962 232 228 15 42 12 30 36 58 152 175
1963 280 278 22 63 13 33 30 49 119 158
1964 334 317 22 61 14 36 23 37 93 147
1965 337 306 20 59 14 43 23 34 85 132
1966 274 257 22 72 17 54 13 20 64 113
1967 267 248 19 59 20 71 6 6 66 109
1968 256 233 12 36 21 70 5 6 50 77
1969 242 236 12 36 20 67 5 6 46 69
1970 257 225 11 26 19 62 6 8 23 32
1971 282 252 11 27 20 66 7 8 30 52
1972 306 240 12 30 21 69 11 11 45 73
1973 331 256 11 27 19 63 13 15 41 64
1974 353 304 11 29 18 60 13 16 40 60
1975 425 326 11 29 18 60 14 17 34 54
aStandardized
(Table 3).
reef fish vessels are calculated by multiplying the actual number of vessels by the corresponding fishing power index
increases in estimated fishing effort in all states except Florida.
Standardization of vessels in Florida leads to a downward adjustment in
measured fishing effort for all years since 1962. Thus, it can be seen
that the failure to adjust nominal effort (vessels) by the fishing power
indices can result in serious overestimations of stock assessment mea-
sures such as catch per unit of effort.
The similarity of the fishing power function to the traditional
economic production function facilitates an analysis of the substituta-
bility of average crew and vessel size in "producing" fishing power.
The importance of such substitution relates primarily to questions
involving appropriate management levels of effort. Consider, for
example, a situation where a specified number of vessels with a given
average fishing power per vessel are determined to constitute of appro-
priate amount of effort by management authorities. Any change in average
fishing power per vessel will create a change in effective fishing
effort, even though the actual number of vessels may remain constant.
The implication here is that changes in fishing power determinants
(average crew and vessel size) must be managed such that changes in
these factors do not change average fishing power, or the number of
vessels must be adjusted to reflect these changes.
Constant levels of fishing power may be analyzed with iso-fishing
power contours calculated from the fishing power function in equation
(75). The expression for these contours for a given level of fishing
power, Ep is given by
X E1.0417 i-0.4792 (77)
li Po 2i
87
where Xli and X21 are, respectively, average crew size and average
th
vessel size in the ith state. Several iso-fishing power contours are
shown in Figure 12. The rate of substitution necessary to maintain a
constant level of fishing power depends not only on the ratio of vessel
size to crew size on a given contour, but also on the location of the
contour (Figure 12). Consider point A on the Ep = 1.5 contour. An in-
crease in crew size of one man requires a decrease in vessel size of
approximately 10 gross registered tons to maintain fishing effort at a
constant level (point B). Next, consider point A' on the Ep = 2.0
contour. A one man increase in crew size now requires a decrease in
80
70 -A'
6 60
N W
S. 50 -
S.- 40 A E = 3.0
"I ) p
os-\
> 30 = 2.5
0 Ep = 1.5
0 Ep = 1.5
SEEp = 1.0
0 2 3 4 5 6 7 8 9 10 11 Crew Size
Figure 12. Iso-fishing power contours for selected levels of
relative fishing power4
The contours are expressed in terms of the fishing power index
described in equation (76). This changes only the scale of measure.
The contours shown in the figure ignore any technological limitations on
substitution. Thus, the ranges of substitution shown in all probability
exceed the limits of the feasible range of substitution. For example, a
10 ton vessel with 11 crew is clearly an infeasible input composition
for the fishery.
in vessel size of 20 gross registered tons to maintain fishing power at
the same level (point B).
These aspects of the substitutability between crew size and vessel
size are significant in regards to managing the GMRFF. Management mea-
sures must focus on regulating nominal fishing effort (vessels), fishing
power or both. Figure 12 demonstrates that significant changes in the
average input composition in each state may be required to maintain
fishing power at constant levels. Furthermore, given the substantial
differences in the average fishing power of vessels across states in the
GMRFF, it can be seen that management measures aimed at maintaining
fishing power at constant levels must be formulated on an individual
state basis.
Catch Equations
The catch equations derived in equation (45) expressed catch as a
function of effective fishing effort, with effective fishing effort
defined to be the product of nominal effort (vessels) and fishing power.
This section centers on catch equations conditioned by fixed levels of
fishing power. Thus, each state's catch becomes a function of the
number of vessels fishing power being fixed.
The output elasticity of vessels with given fishing power is esti-
mated to be 0.74023 (Table 2). Recalling that this parameter is con-
strained to be constant across states, it may be interpreted to estimate
a 7.4 percent increase in catch in each state given a 10 percent increase
in vessels holding fishing power in each state at a fixed level. Given
the manner in which fishing power has been defined, this output elas-
ticity is synomous with returns to scale in the fishery. The notion of
returns to scale must be used with caution within the context of fishery
production, however.
Scale elasticities measure the percentage change in output given a
1 percent change in all inputs. Within the context of fishery produc-
tion, the resource stock constitutes an unobservable input. A simulta-
neous increase in all physical inputs which serves to increase catch
must necessarily alter the resource stock size. Thus, any true measure
of returns to scale in terms of only measured physical inputs is con-
founded by unobserved stock size changes. Given the incorporation of
the autoregressive process to account for such unobserved changes, the
estimated scale elasticity of 0.74023 can be considered as a reasonable
approximation.
The catch equations underlying all stock production models have
assumed constant returns to fishing effort as pointed out in Chapter II.
If one is willing to accept that the autoregressive processes in the
estimated catch equations adequately account for changes in the resource
stock, the estimated scale elasticity for vessels may be used to conduct
an approximate test of the "constant returns" hypothesis. A t-test of
the null hypothesis of 0.74023 equal to one versus the alternative of
less than one can be rejected at the .05 level of significance. Given
the rejection of this hypothesis and the large absolute difference
between the estimated parameter and unity, it is apparent that the GMRFF
is characterized by diminishing returns to scale.
Derived Equilibrium Catch Equations
The estimated catch equations in the form presented in Table 2
correspond to non-equilibrium equations. Non-equilibrium functions
|
PAGE 1
$ %,2(&2120(75,& $1$/<6,6 2) 7+( *8/) 2) 0(;,&2 &200(5&,$/ 5(() ),6+ ),6+(5< %< 7,027+< *25'21 7$25 $ ',66(57$7,21 35(6(17(' 72 7+( *5$'8$7( &281&,/ 2) 7+( 81,9(56,7< 2) )/25,'$ ,1 3$57,$/ )8/),//0(17 2) 7+( 5(48,5(0(176 )25 7+( '(*5(( 2) '2&725 2) 3+,/2623+< 81,9(56,7< 2) )/25,'$
PAGE 2
$&.12:/('*0(176 7R DFNQRZOHGJH DOO ZKR KDYH DVVLVWHG LQ P\ JUDGXDWH FDUHHU ZRXOG EH DQ LPSRVVLEOH WDVN ZLVK WR H[SUHVV P\ DSSUHFLDWLRQ DQG WKDQNV WR P\ PDQ\ XQUHFRJQL]HG FROOHDJXHV 0\ JUHDWHVW GHEW RI JUDWLWXGH LV WR P\ ZLIH .HUL ZKRVH SDWLHQFH VXSSRUW DQG ORYH FDUULHG PH WKURXJK PDQ\ WU\LQJ WLPHV )UHG 3URFKDVND VHUYHG QRW RQO\ DV FKDLUPDQ RI WKH VXSHUYLVRU\ FRPPLWWHH EXW DOVR DV D FORVH IULHQG +LV LQVLJKW KDV HQKDQFHG P\ DELOLW\ DV DQ HFRQRPLVW -LP &DWR JDYH IUHHO\ RI KLV WLPH LQ SURYLGLQJ DQ H[FHOOHQW FULWLTXH RI WKLV GLVVHUWDWLRQ ZKLFK JUHDWO\ LPSURYHG WKH ILQDO GUDIW DOVR ZLVK WR WKDQN WKH RWKHU PHPEHUV RI P\ VXSHUYLVRU\ FRPPLWWHH 7RP 6SUHHQ -RKQ 5H\QROGV DQG %LOO 6HDPDQ IRU WKHLU PDQ\ FRQWULEXWLRQV WR WKLV VWXG\ 7R PDQ\ RI P\ IHOORZ VWXGHQWV ZKR SURYLGHG KHOS DQG IULHQGVKLS GXULQJ P\ WHQXUH DV D JUDGXDWH VWXGHQW ZLVK WR VD\ WKDQNV DOVR ZLVK WR WKDQN /HR 3RORSROXV &KDLUPDQ RI WKH )RRG DQG 5HVRXUFH (FRQRPLFV 'HSDUWPHQW RI WKH 8QLYHUVLW\ RI )ORULGD DQG *HRUJH 0DGGDOD 'LUHFWRU RI WKH &HQWHU IRU (FRQRPHWULFV DQG 'HFLVLRQ 6FLHQFHV IRU SURYLGLQJ ILQDQFLDO DVVLVWDQFH GXULQJ P\ JUDGXDWH FDUHHU DP DOVR JUHDWO\ LQGHEWHG WR /HLJK 3DUVRQV DQG -DQHW (OGUHG IRU WKHLU KHOS LQ WKH VHHPLQJO\ LPSRVVLEOH WDVN RI W\SLQJ DQG SXWWLQJ WKLV GLVVHUWDWLRQ LQWR LWV SUHVHQW IRUP f f Q
PAGE 3
7$%/( 2) &217(176 $&.12:/('*0(176 3DJH f f Q /,67 2) 7$%/(6 YL /,67 2) ),*85(6 L[ $%675$&7 [L &+$37(56 ,1752'8&7,21 2EMHFWLYHV 6FRSH ,, 7+(25(7,&$/ )281'$7,216 %LRORJLFDO 7KHRU\ 6XVWDLQDEOH
PAGE 4
7$%/( 2) &217(176 &RQWLQXHGf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
PAGE 5
7$%/( 2) &217(176 &RQWLQXHGf 3DJH & '(5,9$7,21 2) ())257 /(9(/6 )25 0$;,080 6867$,1$%/( <,(/' $1' 0$;,080 (&2120,& <,(/' *5$3+,&$/ '(5,9$7,21 2) 7+( '28%/( +803(' 6867$,1$%/( 5(9(18( &859( ( ,'(17,),&$7,21 2) 7+( 25'(5 2) 7+( $8725(*5(66,9( 352&(66(6 ,1 7+( &$7&+ (48$7,216 m %DUWOHWW 7HVW 0D[ 7HVW $NDLNHnV )LQDO 3UHGLFWLRQ (UURU )3(f 7HVW 'XUELQ:DWVRQ 7HVW ) 0$5.(7,1* $1' 35,&( ,1)250$7,21 &21&(51,1* *8/) 2) 0(;,&2 5(' 61$33(5 $1' *5283(5 5(6285&( 672&. $'-8670(17 )25 ),;(' /(9(/6 2) ())257 + 7+( *8/) 2) 0(;,&2 237,0,=$7,21 02'(/ $1' 5(68/76 2) (;2*(1286 &+$1*(6 ,1 ),6+,1* 32:(5 %,%/,2*5$3+< %,2*5$3+,&$/ 6.(7&+ Y
PAGE 6
/,67 2) 7$%/(6 7DEOH 3DJH 2UGLQDU\ OHDVW VTXDUHV ZLWK GXPP\ YDULDEOHV SDUDPHWHU HVWLPDWHV IRU WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ FDWFK HTXDWLRQV )RXU VWDWH $LWNHQnV SDUDPHWHU HVWLPDWHV IRU WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ FDWFK HTXDWLRQV (VWLPDWHG UHODWLYH ILVKLQJ SRZHU LQGLFHV E\ VWDWH (VWLPDWHG QXPEHU RI VWDQGDUGL]HG UHHI ILVK YHVVHOV DQG DFWXDO QXPEHU RI UHHI ILVK YHVVHOV LQ WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ E\ VWDWH (VWLPDWHG GLIIHUHQFHV LQ LQWHUFHSWV IRU WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ VWDWH FDWFK HTXDWLRQV 2UGLQDU\ OHDVW VTXDUHV SDUDPHWHU HVWLPDWHV IRU WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ SULFH HTXDWLRQV 7ZR VWDJH $LWNHQnV SDUDPHWHU HVWLPDWHV IRU WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ SULFH HTXDWLRQV (VWLPDWHG ZLWKLQ DQG DFURVV VWDWH SULFH IOH[LELOLWLHV IRU VWDWHV SDUWLFLSDWLQJ LQ WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ (VWLPDWHG DQQXDO RSHUDWLQJ DQG PDLQWHQDQFH FRVWV IRU UHHI ILVK YHVVHOV E\ VWDWH $GMXVWHG DQG XQDGMXVWHG LQWHUFHSWV IRU WKH HVWLPDWHG *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ FDWFK HTXDWLRQV E\ VWDWH (VWLPDWHG FDWFK SURILWV DQG HIIRUW OHYHOV FRUn UHVSRQGLQJ WR PD[LPXP HFRQRPLF \LHOG LQ WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ 1XPEHU RI UHHI ILVK YHVVHOV LQ DQG WKH HFRQRPLFDOO\ RSWLPXP QXPEHU RI YHVVHOV E\ VWDWH YL
PAGE 7
/,67 2) 7$%/(6 &RQWLQXHGf 7DEOH 3DJH (VWLPDWHG VSHFLHV FRPSRVLWLRQ RI 0(< FDWFK RI UHHI ILVK )LVKLQJ SRZHU FRPSRQHQWV IRU SURSRUWLRQDO LQFUHDVHV DORQJ UD\V GHILQHG E\ FRQVWDQW YHVVHO VL]HFUHZ VL]H UDWLRV $O 6SHFLHV LQ WKH PDQDJHPHQW XQLW n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nV SDUDPHWHU HVWLPDWHV IRU 5HG 6QDSSHU DQG *URXSHU SULFH HTXDWLRQV +O 0D[LPXP HFRQRPLF \LHOG LQ WKH UHHI ILVKHU\ JLYHQ D SHUFHQW LQFUHDVH LQ DYHUDJH ILVKLQJ SRZHU SHU YHVVHO YLL
PAGE 8
/,67 2) 7$%/(6 &RQWLQXHGf 7DEOH 3DJH + 0D[LPXP HFRQRPLF \LHOG LQ WKH UHHI ILVKHU\ JLYHQ D SHUFHQW LQFUHDVH LQ DYHUDJH ILVKLQJ SRZHU SHU YHVVHO + 0D[LPXP HFRQRPLF \LHOG LQ WKH UHHI ILVKHU\ JLYHQ D SHUFHQW LQFUHDVH LQ DYHUDJH ILVKLQJ SRZHU SHU YHVVHO + 0D[LPXP HFRQRPLF \LHOG LQ WKH UHHI ILVKHU\ JLYHQ D SHUFHQW LQFUHDVH LQ DYHUDJH ILVKLQJ SRZHU SHU YHVVHO f f f YP
PAGE 9
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
PAGE 10
$EVWUDFW RI 'LVVHUWDWLRQ 3UHVHQWHG WR WKH *UDGXDWH &RXQFLO RI WKH 8QLYHUVLW\ RI )ORULGD LQ 3DUWLDO )XOILOOPHQW RI WKH 5HTXLUHPHQWV IRU WKH 'HJUHH RI 'RFWRU RI 3KLOVRVSK\ $ %,2(&2120(75,& $1$/<6,6 2) 7+( *8/) 2) 0(;,&2 &200(5&,$/ 5(() ),6+ ),6+(5< %\ 7LPRWK\ *RUGRQ 7D\ORU 'HFHPEHU &KDLUPDQ )UHGHULFN 3URFKDVND 0DMRU 'HSDUWPHQW )RRG DQG 5HVRXUFH (FRQRPLFV &RPPHUFLDO UHHI ILVK ODQGLQJV SULPDULO\ JURXSHU DQG UHG VQDSSHUf IURP WKH *XOI RI 0H[LFR KDYH GHFOLQHG IDLUO\ FRQVLVWHQWO\ VLQFH WKH PLGn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n WLRQV ZHUH REWDLQHG E\ WDNLQJ WKH OLPLW RI WKH FDWFK HTXDWLRQV RYHU WLPH ZLWK ILVKLQJ HIIRUW KHOG FRQVWDQW $ QRQOLQHDU RSWLPL]DWLRQ PRGHO IRU WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ ZDV FRQVWUXFWHG WKURXJK [L
PAGE 11
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n LQ ZDV RYHUILVKHG ELRORJLFDOO\ DQG HFRQRPLFDOO\ 7R VXSSRUW WKLV LPSOLFDWLRQ D 6FKDHIHU W\SH VXVWDLQDEOH \LHOG IXQFWLRQ ZDV HVWLPDWHG IRU WKH GRPHVWLF *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ 0D[LPXP VXVWDLQDEOH \LHOG ZDV HVWLPDWHG WR EH PLOOLRQ SRXQGV ZKLFK LV FRQVLVWHQW ZLWK WKH LPSOLFDWLRQ RI RYHUILVKLQJ [L L
PAGE 12
&+$37(5 ,1752'8&7,21 7KH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ LV RQH RI WKH ROGHVW &DUSHQWHU f DQG PRVW LPSRUWDQW RI WKH *XOI ILVKHULHV LQ WHUPV RI ERWK TXDQWLW\ ODQGHG DQG WRWDO GRFNVLGH YDOXH 7KH ILVKHU\ HQFRPSDVVHV D ZLGH YDULHW\ RI ILVKHV LQFOXGLQJ VSHFLHV RI VQDSSHUV VSHFLHV RI JURXSHUV DQG VSHFLHV RI VHD EDVVHV $OWKRXJK WKH DERYH VSHFLHV FRQVWLWXWH WKH PDQDJHPHQW XQLW DV GHILQHG E\ WKH *XOI RI 0H[LFR )LVKHU\ 0DQDJHPHQW &RXQFLO *0)0& f VHYHUDO DGGLWLRQDO VSHFLHV RI ILVK DUH WDNHQ LQFLGHQWDOO\ 7KHVH LQFLGHQWDO VSHFLHV LQFOXGH VHYHUDO VSHFLHV HDFK RInWLOHILVKHV MDFNV WLJJHUILVKHV ZUDVVHV JUXQWV SRUJLHV DQG VDQG SHUFKHV $SSHQGL[ $f ,Q VSLWH RI WKH VL]DEOH QXPEHU DQG YDULHW\ RI VSHFLHV WDNHQ WKUHH VSHFLHV UHG VQDSSHU /XWMDQXV FDPSHFKDQXVf UHG JURXSHU (SLQHSKHOXV PRULRf DQG EODFN JURXSHU 0\FWHURSHUFD ERQDFLf DUH WKH PRVW GHVLUHG VSHFLHV DQG KHQFH WKH PRVW DEXQGDQW LQ FRPPHUFLDO FDWFKHV 0RH f $OO RI WKH *XOI &RDVWDO 6WDWHVn SDUWLFLSDWH LQ WKH UHHI ILVKHU\ ZLWK ILVKLQJ DFWLYLW\ ZLGHO\ GLVSHUVHG WKURXJKRXW WKH *XOI RI 0H[LFR 7KH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ *05))f LV WKH SULPDU\ GRPHVn WLF SURGXFHU RI UHHI ILVK DFFRXQWLQJ DQQXDOO\ IRU DQ DYHUDJH RI SHUFHQW RI WRWDO GRPHVWLF FDWFK 7RWDO ODQGLQJV 86 10)6 f LQ 7KH *XOI &RDVWDO 6WDWHV LQFOXGH )ORULGD :HVW &RDVW $ODEDPD 0LVVLVVLSSL /RXLVLDQD DQG 7H[DV
PAGE 13
ZHUH UHSRUWHG WR EH PLOOLRQ SRXQGV ZLWK D WRWDO GRFNVLGH YDOXH RI PLOOLRQ 5HG VQDSSHU ODQGLQJV ZHUH PLOOLRQ SRXQGV ZLWK D GRFNVLGH YDOXH RI PLOOLRQ ZKLOH JURXSHU ODQGLQJV ZHUH UHSRUWHG WR EH PLOOLRQ SRXQGV DW PLOOLRQ 7KH LPSRUWDQFH RI UHG VQDSSHU DQG JURXSHU WR WKH *05)) FDQ EH VHHQ IURP WKHVH ILJXUHV ,Q UHG VQDSSHU DQG JURXSHU DFFRXQWHG IRU SHUFHQW RI DOO UHHI ILVK ODQGLQJV E\ ZHLJKW DQG SHUFHQW RI WKH WRWDO UHYHQXH JHQHUDWHG LQ WKH FRPPHUn FLDO *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ 7KUHH QDWLRQV &XED 0H[LFR DQG WKH 8QLWHG 6WDWHV DUH UHVSRQVLEOH IRU WKH EXON RI WKH ZRUOG VXSSO\ RI UHHI ILVK JURXSHU DQG UHG VQDSSHUf 7KH 86 LV WKH OHDGLQJ SURGXFHU RI UHG VQDSSHU DFFRXQWLQJ IRU DSSUR[Ln PDWHO\ SHUFHQW RI WKH ZRUOG FDWFK LQ .OLPD f ,Q WKDW VDPH \HDU WKH 8QLWHG 6WDWHV UDQNHG WKLUG LQ JURXSHU SURGXFWLRQ EHKLQG 0H[LFR DQG &XED ZKLFK DFFRXQWHG IRU DQG SHUFHQW RI WKH ZRUOG FDWFK UHVSHFWLYHO\ $SSHQGL[ %f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f 7RWDO UHFUHDWLRQDO 3DUW\ RU KHDG ERDWV JHQHUDOO\ FDUU\ RYHU SDVVHQJHUV ZKLOH SULYDWH FKDUWHU ERDWV FDUU\ VL[ SDVVHQJHUV RU OHVV
PAGE 14
FDWFK KRZHYHU GURSSHG WR PLOOLRQ SRXQGV LQ *0)0& f 7KH SURSRUWLRQ RI JURXSHUV DQG UHG VQDSSHU SUHVHQW LQ UHFUHDWLRQDO UHHI ILVK FDWFKHV GHFOLQHG VLJQLILFDQWO\ RYHU WKH WR SHULRG ,Q DSSUR[LPDWHO\ SHUFHQW RI WKH WRWDO ZHLJKW RI WKH UHFUHDWLRQDO FDWFK ZDV FRPSULVHG RI WKHVH SULPDU\ VSHFLHV %\ WKLV SURSRUWLRQ GURSSHG WR RQO\ SHUFHQW RI WKH WRWDO 3UHOLPLQDU\ GDWD IRU LQGLFDWHG WKDW WKLV SURSRUWLRQ URVH WR SHUFHQW RI WKH SHULRG KRZHYHU $SSHQGL[ %f :LWKLQ WKH ILVKHU\ WKH )ORULGD :HVW &RDVW LV WKH GRPLQDQW SURGXFHU ZLWK UHVSHFW WR ERWK FDWFK OHYHOV DQG LQGXVWU\ VL]H ,Q )ORULGDnV :HVW &RDVW DFFRXQWHG IRU SHUFHQW RI WRWDO *XOI RI 0H[LFR UHHI ILVK ODQGLQJV ,Q WHUPV RI WKH SULPDU\ VSHFLHV )ORULGDnV :HVW &RDVW DFFRXQWHG IRU SHUFHQW E\ ZHLJKW DQG SHUFHQW E\ YDOXH RI WKH WRWDO UHG VQDSSHU FDWFK DQG SHUFHQW E\ ERWK ZHLJKW DQG YDOXH RI DOO JURXSHU ODQGHG LQ WKH *XOI RI 0H[LFR LQ WKDW VDPH \HDU ,QGXVWU\ VL]H DV PHDVXUHG E\ WKH QXPEHU RI YHVVHOV UHSRUWHG E\ VWDWHV DOVR LOOXVWUDWHV WKH GRPLQDQW SRVLWLRQ RI )ORULGD ,Q YHVVHOV ZHUH UHSRUWHG LQ WKH UHHI ILVKHU\ 2I WKHVH YHVVHOV ILVKHG RXW RI )ORULGD *XOI RI 0H[LFR SRUWV 'XULQJ WKH WR SHULRG SHUFHQW RI DOO *05)) YHVVHOV RULJLQDWHG IURP )ORULGD :HVW &RDVW SRUWV 7KH *XOI RI 0H[LFR UHHI ILVKHU\ LV D KRRN DQG OLQH ILVKHU\ 7KH ILVKLQJ SURFHVV PDLQO\ LQYROYHV WKH ORFDWLRQ RI KLJK FRQFHQWUDWLRQV RI UHHI ILVK DQG WKH FDSWXUH RI WKHVH ILVK XVLQJ KDQG RU PHFKDQLFDOO\ RSHUDWHG ILVKLQJ UHHOV *HQHUDOO\ HDFK FUHZPDQ RQ D YHVVHO RSHUDWHV RQO\ RQH UHHO )LVKLQJ DFWLYLW\ LQ WKH *XOI RI 0H[LFR RFFXUV RYHU D ZLGH JHRJUDSKLF DUHD UDQJLQJ IURP WKH :HVW )ORULGD VKHOI WR WKH :HVWHUQ *XOI RII 7H[DV DQG DV IDU VRXWK DV WKH &DPSHFKH VKHOI QHDU 0H[LFR
PAGE 15
$SSHQGL[ $f *LYHQ WKH VHDUFK DQG FDSWXUH QDWXUH RI WKH ILVKLQJ SURFHVV WZR RI WKH PRVW LPSRUWDQW LQSXWV LQ WKH UHHI ILVK ILVKHU\ DUH WKH VL]H RI YHVVHOV DQG WKH FUHZ VL]HV FRUUHVSRQGLQJ WR ILVKLQJ YHVVHOV $YHUDJH YHVVHO VL]HV DUH KHWHURJHQHRXV DFURVV VWDWHV )ORULGD YHVVHOV DUH WKH VPDOOHVW KDYLQJ DQ DYHUDJH VL]H RI JURVV UHJLVWHUHG WRQV LQ 9HVVHOV RULJLQDWLQJ IURP 0LVVLVVLSSL SRUWV DUH WKH ODUJHVW DYHUDJLQJ JURVV UHJLVWHUHG WRQV SHU YHVVHO LQ WKH VDPH \HDU *0)0& f &UHZ VL]HV DOVR H[KLELW FRQVLGHUDEOH YDULDWLRQ DFURVV VWDWHV UDQJLQJ IURP DQ DYHUDJH RI WKUHH PHQ SHU YHVVHO IRU )ORULGD YHVVHOV WR QLQH PHQ SHU YHVVHO DERDUG 0LVVLVVLSSL YHVVHOV LQ 9HU\ OLWWOH LQIRUPDWLRQ LV DYDLODEOH RQ FRVWV DQG UHYHQXHV RI FRPPHUFLDO UHHI ILVK YHVVHOV LQ JHQHUDO 6RPH GDWD KRZHYHU KDYH EHHQ DFFXPXODWHG IRU )ORULGD YHVVHOV IRU WKH \HDUV DQG &DWR DQG 3URFKDVND f :KLOH WKHVH GDWD FDQQRW EH DVVXPHG UHSUHVHQWDWLYH RI YHVVHOV RULJLQDWLQJ IURP VWDWHV RWKHU WKDQ )ORULGD WKH\ QHYHUWKHOHVV SURYLGH VRPH LQGLFDWLRQ DV WR WKH PDJQLWXGH RI FRVWV DQG UHYHQXHV FRUn UHVSRQGLQJ WR UHHI ILVKHU\ YHVVHOV 'XULQJ DQG WKH DYHUDJH DQQXDO WRWDO UHYHQXH IRU )ORULGD YHVVHOV RSHUDWLQJ LQ WKH UHHI ILVK ILVKHU\ ZDV HVWLPDWHG WR EH ,Q JHQHUDO RI WKH UHYHQXH ZHQW WR FUHZ VKDUHV ZLWK WKH FDSWDLQ DQGRU RZQHU UHFHLYLQJ DQ DYHUDJH RI 7KH UHPDLQLQJ UHYHQXH ZDV XVHG IRU SD\PHQW RI IL[HG DQG YDULDEOH YHVVHO H[SHQVHV 'XULQJ WKLV SHULRG DYHUDJH LQYHVWPHQW SHU YHVVHO UDQJHG IURP WR 7RWDO FRPPHUFLDO ODQGLQJV LQ WKH *05)) KDYH H[KLELWHG D IDLUO\ FRQVLVWHQW GHFOLQH IURP D SHDN RI PLOOLRQ SRXQGV LQ WR DSSUR[Ln PDWHO\ PLOOLRQ SRXQGV LQ 6LQFH UHHI ILVK ODQGLQJV KDYH VKRZQ QR VLJQLILFDQW WUHQG IOXFWXDWLQJ EHWZHHQ DQG PLOOLRQ
PAGE 16
SRXQGV 7KLV DSSHDUDQFH RI FRQVWDQF\ LV VRPHZKDW PLVOHDGLQJ KRZHYHU LQ WKDW IURP WR WKH WRWDO ODQGLQJV RI WKH SULPDU\ WDUJHW VSHFLHV UHG VQDSSHU DQG JURXSHU FRQWLQXHG WR GHFOLQH &RPELQHG ODQGn LQJV RI WKHVH SULPDU\ VSHFLHV KDYH GHFUHDVHG SHUFHQW IURP PLOOLRQ SRXQGV LQ WR PLOOLRQ SRXQGV LQ 7KXV WKH DSSDUHQW FRQVWDQF\ RI WRWDO UHHI ILVK ODQGLQJV LV DWWULEXWDEOH WR LQn FUHDVHG ODQGLQJV RI WKH OHVV GHVLUHG UHHI VSHFLHV 7KH EHKDYLRU RI WRWDO ODQGLQJV VLQFH LV HVSHFLDOO\ LQWHUHVWLQJ JLYHQ WKH IDFW WKDW ILVKLQJ HIIRUW DV PHDVXUHG E\ WKH QXPEHU RI YHVVHOV RSHUDWLQJ LQ WKH ILVKHU\ KDV LQFUHDVHG FRQVLVWHQWO\ GXULQJ WKLV WLPH :LWKLQ WKH WR SHULRG FRYHUHG E\ FXUUHQW DYDLODEOH GDWD WKUHH VWDWHV)ORULGD $ODEDPD DQG 0LVVLVVLSSLH[SHULHQFHG WKHLU ORZHVW DYHUDJH FDWFK SHU YHVVHO LQ $SSHQGL[ %f ,Q VSLWH RI WKH WUHQGV LQ WRWDO FDWFK DQG FDWFK SHU YHVVHO RQO\ SDUWLDO FRQFOXVLRQV FDQ EH RIIHUHG ZLWK UHVSHFW WR WKH ELRORJLFDO VWDWXV RI WKH UHHI ILVK VWRFNV DQG WKH H[WHQW WR ZKLFK HFRQRPLF HIILFLHQF\ H[LVWV LQ WKH ILVKHU\ 7KH *XOI RI 0H[LFR UHHI ILVK VWRFNV DUH W\SLFDO RI ELRORJLFDO SRSXODWLRQV LQ WKDW DQ\ JLYHQ OHYHO RI VWRFN VL]H PHDVXUHG E\ HLWKHU QXPEHUV RU ZHLJKWf LV FDSDEOH RI SURGXFLQJ D VXVn WDLQDEOH \LHOG 7KDW LV D JLYHQ SURSRUWLRQ RI WKH SRSXODWLRQ PD\ EH KDUYHVWHG LQ DQ\ JLYHQ WLPH SHULRG ZKLOH OHDYLQJ WKH XQGHUO\LQJ VWRFN VL]H XQFKDQJHG %LRORJLFDO WKHRU\ KDV PDLQWDLQHG WKDW LQ JHQHUDO VXVWDLQDEOH \LHOGV FDQ UDQJH IURP ]HUR WR VRPH XQLTXH PD[LPXP OHYHO WHUPHG PD[LPXP VXVWDLQDEOH \LHOG 06
PAGE 17
UHJLPH OHDG WR HFRQRPLFDOO\ LQHIILFLHQW OHYHOV RI FDWFK DQG ILVKLQJ HIIRUW *RUGRQ f *HQHUDOO\ D ILVKHU\ LV VDLG WR EH ELRORJLFDOO\ RYHUILVKHG LI ILVKLQJ HIIRUW EHLQJ H[SHQGHG LV JUHDWHU WKDQ WKDW UHTXLUHG WR FDSWXUH 06< ZKLOH WKH ILVKHU\ LV FRQVLGHUHG WR EH HFRQRPLn FDOO\ RYHUILVKHG LI DJJUHJDWH ILVKLQJ HIIRUW H[FHHGV WKH SRLQW ZKHUH WKH PDUJLQDO FRVW RI HIIRUW HTXDOV PDUJLQDO UHYHQXH 3URGXFWLRQ LQ WKH *05)) KDV IROORZHG D FRPSHWLWLYH UHJLPH WKURXJK RXW PRVW RI LWV ORQJ KLVWRU\ :KHWKHU RU QRW KLV FRPSHWLWLRQ KDV OHG WR D VLWXDWLRQ RI HFRQRPLF DQGRU ELRORJLFDO RYHUILVKLQJ UHPDLQV ODUJHO\ XQDQVZHUHG 7R GDWH RQO\ OLPLWHG DJJUHJDWH HFRQRPLF DQDO\VLV KDV EHHQ FRQGXFWHG RQ WKLV ILVKHU\ 7KH PRVW QRWDEOH H[FHSWLRQ KDV EHHQ WKH SUHn OLPLQDU\ PDQDJHPHQW SODQ FRQVWUXFWHG E\ WKH *XOI RI 0H[LFR )LVKHU\ 0DQDJHPHQW &RXQFLO *0)0& f $OWKRXJK VRPH EDVLF 06< FDOFXODWLRQV SUHVHQWHG LQ WKH SODQ VXJJHVW WKDW WKH ILVKHU\ LV FXUUHQWO\ RSHUDWLQJ QHDU 06< WKH EXON RI WKH VWXG\ LV GHVFULSWLYH LQ QDWXUH 7KH EDVLF TXHVWLRQV RI HFRQRPLF HIILFLHQF\ SULFH VWUXFWXUH DQG SRVVLEOH FRQVHn TXHQFHV RI LQVWLWXWLQJ YDULRXV PDQDJHPHQW VWUDWHJLHV RQ FDWFK DQG HIIRUW OHYHOV UHPDLQ XQDQVZHUHG 2EMHFWLYHV 7KH SDVVDJH RI WKH )LVKHU\ &RQVHUYDWLRQ DQG 0DQDJHPHQW $FW RI 3/f KDV PDGH LW QHFHVVDU\ WR GHYHORS PDQDJHPHQW SODQV IRU DOO 7KH \LHOG IURP D ILVKHU\ WKDW UHVXOWV IURP D OHYHO RI ILVKLQJ HIIRUW VXFK WKDW PDUJLQDO FRVW HTXDO PDUJLQDO UHYHQXH LV FDOOHG PD[LPXP HFRQRPLF \LHOG 0(
PAGE 18
GRPHVWLF FRPPHUFLDO ILVKHULHV 86 'HSDUWPHQW RI &RPPHUFH f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n WLYH LQWHUGHSHQGHQFH EHWZHHQ VWDWHV DQG WKH XQREVHUYDn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
PAGE 19
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n WDLQV D VXPPDU\ RI WKLV VWXG\ DQG DOO FRQFOXVLRQV ZKLFK KDYH EHHQ UHQGHUHG $OVR LQFOXGHG DUH VXJJHVWLRQV IRU IXUWKHU UHVHDUFK
PAGE 20
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n WDQHRXVO\ PDLQWDLQLQJ WKH XQGHUO\LQJ UHVRXUFH DW VRPH IL[HG OHYHO 7KH ILUVW VHFWLRQ RI WKLV FKDSWHU GLVFXVVHV WKH ELRORJLFDO EDVHV RI ELRHFRQRPLF PRGHOV 6SHFLILFDOO\ WKH QRWLRQ RI VXVWDLQDEOH \LHOG ZLOO EH GHYHORSHG DQG VRPH RI WKH PDLQ VWRFN SURGXFWLRQ PRGHOV ZLOO EH SUHVHQWHG 6HFWLRQ WZR EXLOGV XSRQ WKH WHFKQLFDO ELRORJLFDO UHODWLRQn VKLSV E\ LQWURGXFLQJ SULFHV DQG FRQFHSWV GHDOLQJ ZLWK HFRQRPLF HIILn FLHQF\ LQ SURGXFWLRQ ,QFOXGHG LQ WKLV VHFWLRQ LV D UHYLHZ RI VHYHUDO VSHFLILF ELRHFRQRPLF PRGHOV RI ILVKHU\ SURGXFWLRQ 7KH ILQDO VHFWLRQ RI WKLV FKDSWHU H[WHQGV WKHVH EDVLF ELRHFRQRPLF PRGHOV E\ SUHVHQWLQJ D WKHRUHWLFDO ELRHFRQRPLF PRGHO RI D PXOWLVHFWRU ILVKHU\ ZLWK YDULDEOH SURGXFW SULFH DQG SHFXQLDU\ H[WHUQDOLWLHV n,QGXVWU\ KHUH UHIHUV WR WKH DJJUHJDWH RI DOO YHVVHOV RSHUDWLQJ LQ D JLYHQ ILVKHU\
PAGE 21
%LRORJLFDO 7KHRU\ 7KH QHHG WR FRQVLGHU WKH ELRORJLFDO FKDUDFWHULVWLFV RI ILVK SRSXODn WLRQV LQ HFRQRPLF DQDO\VHV RI ILVKHULHV EHFRPHV LPPHGLDWHO\ HYLGHQW ZKHQ WKH QDWXUH RI WKH UHVRXUFH ILVK SRSXODWLRQf LV FRQVLGHUHG )LVK SRSXn ODWLRQV FDQ EH SODFHG LQ WKH FDWHJRU\ RI XVHGHSHQGHQW IORZ UHVRXUFHV ZLWK D FULWLFDO ]RQH 6FKDHIHU f $ FULWLFDO ]RQH DV XVHG KHUH LV GHILQHG WR EH D UDWH RI GHFUHDVH LQ IORZ ZKLFK FDQQRW EH UHYHUVHG HFRQRPLFDOO\ RU WHFKQRORJLFDOO\ 7KXV LQ WHUPV RI ILVK SRSXODWLRQ D FULWLFDO ]RQH ZRXOG FRUUHVSRQG WR WKDW OHYHO RI SRSXODWLRQ ZKLFK KDV DQ LQVXIILFLHQW UHSURGXFWLYH SRWHQWLDO WR UHPDLQ YLDEOH 6XVWDLQDEOH
PAGE 22
Q ERWK KLJK DQG ORZ SRSXODWLRQV UHDFKLQJ D PD[LPXP DW VRPH LQWHUPHGLDWH ELRPDVV 7KHVH WKUHH IDFWRUV FDQ EH FRPELQHG WR \LHOG D JHQHUDO IXQFn WLRQDO UHODWLRQVKLS EHWZHHQ WKH SRSXODWLRQ LQ WLPH SHULRG W DQG PDWXUH SURJHQ\ LQ WLPH SHULRG W 7KLV UHODWLRQVKLS LV GHVFULEHG E\ WKH K3f IXQFWLRQ VKRZQ LQ )LJXUH 7KH K3f IXQFWLRQ FRUUHVSRQGV WR WKH DFWXDO SURGXFWLRQ RI PDWXUH SURJHQ\ )RU H[DPSOH LI WKH SRSXODWLRQ DW WLPH W LV HTXDO WR 3 WKH PDWXUH SURJHQ\ HQWHULQJ LQ WKH ILVKHU\ ZLOO EH HTXDO WR 03 7KH U3f IXQFWLRQ LV WKH UHSODFHPHQW OLQH UHSUHVHQWLQJ WKH SURGXFWLRQ RI SURJHQ\ QHFHVVDU\ WR PDLQWDLQ WKH SRSXODWLRQ DW LWV SUHVHQW OHYHO )LJXUH 5HODWLRQVKLS EHWZHHQ SRSXODWLRQ VL]H DQG PDWXUH SURJHQ\ $ SRSXODWLRQ RI 3 QHHG RQO\ SURGXFH 03U SURJHQ\ WR PDLQWDLQ LWVHOI 7KH GLIIHUHQFH EHWZHHQ 03 DQG 03U $ % LQ )LJXUH f FRUn UHVSRQGV WR D \LHOG RI ILVK ZKLFK FDQ EH KDUYHVWHG ZKLOH PDLQWDLQLQJ
PAGE 23
WKH SRSXODWLRQ DW D OHYHO RI 3_ 7KLV LV WKH EDVLV IURP ZKLFK WKH QRWLRQ RI VXVWDLQDEOH \LHOG GHULYHV %HIRUH SURFHHGLQJ WR D GLVFXVVLRQ RI VXVWDLQDEOH \LHOG VHYHUDO DVSHFWV RI WKH PRGHO LQ )LJXUH PHULW FRPPHQW 8QGHU D JLYHQ VHW RI HQYLURQPHQWDO FRQGLWLRQV D JLYHQ SRSXODn WLRQ ZLOO DSSURDFK VRPH QDWXUDO HTXLOLEULXP VL]H 7KLV HTXLOLEULXP RFFXUV DW WKH SRSXODWLRQ VL]H FRUUHVSRQGLQJ WR WKH LQWHUVHFWLRQ RI WKH U3f DQG K3f IXQFWLRQV 7KLV SRSXODWLRQ VL]H LV JLYHQ E\ 3A LQ WKH GLDJUDP 7KH K3f IXQFWLRQ LV DVVXPHG WR SRVVHVV D XQLTXH PD[LPXP SURn GXFWLRQ RI PDWXUH SURJHQ\ FRUUHVSRQGLQJ WR WKH XQGHUO\LQJ SRSXODWLRQ 3 $V ZLOO EH VKRUQ SUHVHQWO\ WKH SRSXODWLRQ VL]H FRUUHVSRQGLQJ WR PD[ WKH PD[LPXP SURGXFWLRQ RI PDWXUH SURJHQ\ LV QRW WKH VDPH DV WKDW FRUn UHVSRQGLQJ WR PD[LPXP VXVWDLQDEOH \LHOG 6XVWDLQDEOH \LHOG UHSUHVHQWV IRU DQ\ JLYHQ SRSXODWLRQ OHYHO WKH VXUSOXV SURGXFWLRQ RI PDWXUH SURJHQ\ RYHU WKDW QHHGHG WR MXVW PDLQWDLQ WKH SRSXODWLRQ DW D IL[HG OHYHO ,Q WHUPV RI )LJXUH VXVWDLQDEOH \LHOG IRU DQ\ JLYHQ SRSXODWLRQ LV WKHQ VLPSO\ WKH GLIIHUHQFH EHWZHHQ WKH K3f IXQFWLRQ DQG WKH U3f IXQFWLRQ 0DWKHPDWLFDOO\ WKLV FDQ EH UHSUHVHQWHG E\ 6<3f K3f U3f 331 f ZKHUH 6<3f UHIHUV WR VXVWDLQDEOH \LHOG FRUUHVSRQGLQJ WR SRSXODWLRQ 3A (TXDWLRQ f GHILQHV D VLQJOH YDOXHG IXQFWLRQ UHODWLQJ VXVWDLQDEOH \LHOG WR SRSXODWLRQ VL]H )LJXUH LOOXVWUDWHV RQH SRVVLEOH VKDSH RI WKH VXVWDLQDEOH \LHOG IXQFWLRQ 7KLV IXQFWLRQ FDQ EH VHHQ WR ULVH IURP D 2WKHU SRVVLEOH VKDSHV RI WKH VXVWDLQDEOH \LHOG FXUYH DUH GLVFXVVHG EHORZ
PAGE 24
)LJXUH 4XDGUDWLF VXVWDLQDEOH \LHOG IXQFWLRQ OHYHO RI ]HUR DW ]HUR SRSXODWLRQ WR D XQLTXH PD[LPXP DQG WKHQ EDFN WR ]HUR DW WKH QDWXUDO HTXLOLEULXP OHYHO 7KH PD[LPXP SRLQW RQ WKH FXUYH PD[LPXP VXVWDLQDEOH \LHOG 06
PAGE 25
WKLV IDFW ZLOO EHFRPH REYLRXV ZKHQ FRVWV DQG UHYHQXHV DUH LQFRUSRUDWHG LQWR WKH WKHRUHWLFDO PRGHOV 0RUH SUHFLVHO\ LW LV WKLV SURSHUW\ RI WKH VXVWDLQDEOH \LHOG IXQFWLRQ ZKLFK OHDGV WR PDQ\ FRQFOXVLRQV UHQGHUHG E\ HFRQRPLVWV ZLWK UHVSHFW WR WKH ZRUNLQJV RI SHUIHFW FRPSHWLWLRQ 6HFRQGO\ DQ\ JLYHQ VXVWDLQDEOH \LHOG IXQFWLRQ LV GHILQHG IRU D JLYHQ VHW RI HQYLURQPHQWDO DQG HFRORJLFDO SDUDPHWHUV $Q\ FKDQJH LQ WKHVH SDUDPHWHUV YL EULQJ DERXW D VKLIW LQ WKH VXVWDLQDEOH \LHOG IXQFWLRQ 6FKDHIHU f \\ 6WRFN 3URGXFWLRQ 0RGHOV 7KH PDWKHPDWLFDO PRGHOV GHVFULELQJ WKH VXVWDLQDEOH \LHOG FRQFHSWV KDYH PDLQO\ EHHQ LQ WKH IRUP RI ELRORJLFDO VWRFN SURGXFWLRQ PRGHOV 7ZR RI WKH PRUH SURPLQHQW PRGHOV LQ ILVKHULHV WKHRU\ DUH WKH 6FKDHIHU PRGHO 6FKDHIHU f DQG WKH *HQHUDOL]HG 6WRFN 3URGXFWLRQ 0RGHO 3HOOD DQG 7RPOLQVRQ f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
PAGE 26
7KH *HQHUDOL]HG 6WRFN 3URGXFWLRQ 0RGHO *630f DV GHYHORSHG E\ 3HOOD DQG 7RPOLQVRQ f LV FRPSRVHG RI WZR IXQFWLRQV 7KHVH DUH D SRSXODn WLRQ JURZWK IXQFWLRQ DQG D FDWFK IXQFWLRQ 7KHVH IXQFWLRQV DUH FRPELQHG LQ VXFK D PDQQHU DV WR FUHDWH D IXQFWLRQ UHODWLQJ VXVWDLQDEOH \LHOG WR ILVKLQJ HIIRUW 7KH UDWH RI FKDQJH LQ DQ\ JLYHQ ILVK SRSXODWLRQ RYHU WLPH FDQ EH H[SUHVVHG DV D IXQFWLRQ RI WKH SRSXODWLRQ VL]H E\ 3Wf +3PWf .3Wf f ZKHUH + P DUH FRQVWDQW SDUDPHWHUV DQG 3Wf LV WKH WLPH GHULYDWLYH RI SRSXODWLRQ RU ELRPDVV 3Wf (TXDWLRQ f LV D JHQHUDO IXQFWLRQDO UHSn UHVHQWDWLRQ RI WKH VXVWDLQDEOH \LHOG IXQFWLRQ VKRZQ LQ )LJXUH )RU SRSXODWLRQV WR KDYH DQ DEVROXWH PD[LPXP UDWH RI JURZWK RU PD[LPXP VXVn WDLQDEOH \LHOG WKH DERYH HTXDWLRQ PXVW VDWLVI\ FHUWDLQ FRQGLWLRQV RQ WKH SDUDPHWHUV 7KHVH FRQGLWLRQV DUH + LI P DQG + L I P )LVKLQJ HIIRUW LV LQWURGXFHG LQWR WKH *630 E\ XVLQJ WKH HTXDWLRQ &Wf T(^Wf 3Wf f ZKHUH T LV D FRQVWDQW (Wf LV ILVKLQJ HIIRUW H[SHQGHG LQ WLPH SHULRG W DQG &Wf LV WKH WLPH GHULYDWLYH RI FDWFK 7KLV UHODWLRQVKLS LV K\SRWKHn VL]HG XQGHU WKH DVVXPSWLRQ WKDW HIIRUW XQLWV RSHUDWH LQGHSHQGHQWO\ (TXDWLRQ f FDQ EH VHHQ WR UHSUHVHQW WKH SURGXFWLRQ IXQFWLRQ IRU WKH ILVKHU\ XQGHU QRQHTXLOLEULXP FRQGLWLRQV (TXLOLEULXP FRQGLWLRQV DUH 7KH P SDUDPHWHU LQ HTXDWLRQ f PHDVXUHV WKH VNHZQHVV RI WKH SRSXn ODWLRQ JURZWK IXQFWLRQ $ YDOXH RI P OHDGV WR D V\PPHWULF IXQFWLRQ $V ZLOO EH VKRZQ SUHVHQWO\ D YDOXH RI P LV QRW SHUPLVVDEOH
PAGE 27
GHILQHG WR EH WKRVH OHYHOV RI HIIRUW DQG SRSXODWLRQ WKDW \LHOG D FDWFK HTXDO WR VXVWDLQDEOH \LHOG 7KH LQWURGXFWLRQ RI ILVKLQJ LQWR WKH *630 QHFHVVLWDWHV WKDW HTXDn WLRQ f EH PRGLILHG WR 3Wf +3PWf .3Wf J(Wf 3Wf f ZKHUH DOO WHUPV KDYH EHHQ SUHYLRXVO\ GHILQHG (TXDWLRQ f LPSOLHV WKH UDWH RI LQFUHDVH RI DQ\ JLYHQ SRSXODWLRQ RYHU WLPH LV GHFUHDVHG SUHn FLVHO\ E\ WKH UDWH DW ZKLFK ILVK DUH FDXJKW WKURXJK ILVKLQJ DFWLYLW\ 7KH LPSRVLWLRQ RI WKH HTXLOLEULXP FRQGLWLRQV GHVFULEHG DERYH FDQ EH DFFRPSOLVKHG E\ FRQVWUDLQLQJ 3Wf LQ HTXDWLRQ f 7KLV FRQVWUDLQW LQ HIIHFW UHTXLUHV WKDW FDWFK DOZD\V HTXDO VXVWDLQDEOH \LHOG %\ VROYn LQJ WKH HTXDWLRQ +3PWf .3Wf (Wf 3Wf f IRU 3Wf DQG VXEVWLWXWLQJ WKH UHVXOW LQWR HTXDWLRQ f WKH HTXLOLEULXP HIIRUW \LHOG IXQFWLRQ BF m( Afn n P f LV REWDLQHG 7KLV HTXDWLRQ UHSUHVHQWV WKH *HQHUDOL]HG 6WRFN 3URGXFWLRQ 0RGHO UHODWLQJ HTXLOLEULXP FDWFK WR ILVKLQJ HIIRUW 1RWH WKDW D YDOXH RI P ZRXOG PDNH HTXDWLRQ f XQGHILQHG 7KH 6FKDHIHU PRGHO ZKLFK LV D VSHFLDO FDVH RI WKH DERYH PRGHO QDPHG DIWHU LWV RULJLQDWRU 0 % 6FKDHIHU ZDV GHYHORSHG LQ 6FKDHIHU f 7KLV PRGHO LV EDVHG XSRQ D ORJLVWLF SRSXODWLRQ JURZWK
PAGE 28
IXQFWLRQ 8VLQJ WKLV IXQFWLRQ WKH QDWXUDO UDWH RI LQFUHDVH DV D IXQFn WLRQ RI SRSXODWLRQ VL]H FDQ EH H[SUHVVHG E\ 3Wf A 3Wf >0 3Wf@ f ZKHUH DQG 0 DUH FRQVWDQWV DQG DOO RWKHU WHUPV DUH GHILQHG DV DERYH ,W FDQ EH HDVLO\ VKRZQ WKDW WKLV HTXDWLRQ FRUUHVSRQGV WR HTXDWLRQ f RI WKH *630 ZLWK P + DQG .0 7KXV LW EHFRPHV DSSDUn HQW WKDW WKH EDVLV RI WKH 6FKDHIHU PRGHO LV PHUHO\ D VSHFLILF IRUP RI WKH *630 ZLWK SDUDPHWHU P 7KH 6FKDHIHU PRGHO DOVR SURYLGHV DQ HTXDWLRQ H[SUHVVLQJ HTXLOLEULXP FDWFK DV D IXQFWLRQ RI ILVKLQJ HIIRUW 8WLOL]LQJ HTXDWLRQ f RQFH DJDLQ DV WKH QRQHTXLOLEULXP FDWFK IXQFWLRQ WKH IXQFWLRQ & T( 0 I (f f FDQ EH GHULYHG $V EHIRUH WKH DSSURSULDWH UHGHILQLWLRQ RI FRQVWDQWV + . ,&_0f LOOXPLQDWHV WKH IDFW WKDW HTXDWLRQ f LV PHUHO\ D VSHFLILF IRUP RI HTXDWLRQ f ZLWK P 7KH DERYH KDV VKRZQ WKH ZLGHO\ XVHG 6FKDHIHU PRGHO WR EH D VSHFLDO FDVH RI WKH *HQHUDOL]HG 6WRFN 3URGXFWLRQ 0RGHO ,Q SDUW RQH RI WKH SULPDU\ JRDOV RI GHYHORSLQJ WKH *630 ZDV DLPHG DW UHOD[LQJ WKH FRQn VWUDLQW RI WKH V\PPHWULF \LHOG IXQFWLRQ JHQHUDWHG E\ WKH 6FKDHIHU PRGHO 3HOOD DQG 7RPOLQVRQ f )LJXUH SUHVHQWV VHYHUDO SRVVLEOH HTXLn OLEULXP \LHOG IXQFWLRQV WKDW DUH SRVVLEOH XWLOL]LQJ WKH *630 ,W FDQ EH VHHQ WKDW WKH VKDSH RI WKH HTXLOLEULXP \LHOG IXQFWLRQ WDNHV D ZLGH YDULHW\ RI VKDSHV DV P YDULHV
PAGE 29
BF -' R fLf§ Uf§ UF6 rUf§ 2 FU /8 P )LJXUH (TXLOLEULXP \LHOG UHODWLRQVKLSV IRU YDULRXV YDOXHV RI P 7KH IRUHJRLQJ KDV SUHVHQWHG D EULHI LQWURGXFWLRQ WR WKH ELRORJLFDO EDVHV XQGHUO\LQJ WKH ELRHFRQRPLF PRGHOV FXUUHQWO\ XWLOL]HG LQ ILVKHULHV PDQDJHPHQW 7KH *HQHUDOL]HG 6WRFN 3URGXFWLRQ 0RGHO SURYLGHV D IUDPHZRUN ZKLFK LV PRUH JHQHUDO WKDQ 6FKDHIHUnV IRUPXODWLRQ EXW VWLOO HQDEOHV WKH H[SUHVVLRQ RI HTXLOLEULXP FDWFK DV D IXQFWLRQ RI ILVKLQJ HIIRUW $V QRWHG DERYH WKH W\SH RI UHVXOW LV VLJQLILFDQW LQ WKDW WKH JHQHUDOO\ XQREVHUYDEOH SRSXODWLRQ YDULDEOH LV HOLPLQDWHG LQ IDYRU RI WKRVH YDULDEOHV FDWFK DQG HIIRUWf ZKLFK DUH REVHUYDEOH %DVLF %LRHFRQRPLF 0RGHOV RI WKH )LVKHU\ 7KH SUHYLRXV VHFWLRQ RI WKLV FKDSWHU SUHVHQWHG WKH EDVLF ELRORJLFDO UHODWLRQVKLSV WKDW FUHDWH WKH IUDPHZRUN ZLWKLQ ZKLFK WKH HFRQRPLF DVSHFWV RI ILVKHULHV SURGXFWLRQ PD\ EH DQDO\]HG 7KH ELRORJLFDO UHODn WLRQVKLSV LW ZLOO EH UHFDOOHG OHG WR WKH FRQFHSW RI VXVWDLQDEOH \LHOG DQG VXJJHVWHG WKDW WKH KDUYHVW RI DQ\ JLYHQ ILVKHU\ EH UHVWULFWHG WR EH
PAGE 30
HTXDO WR VRPH VXVWDLQDEOH \LHOG LQ HTXLOLEULXP 7KH HFRQRPLF PRGHOV RI WKH ILVKHULHV KDYH EXLOW XSRQ WKLV UHVWULFWLRQ DQG KDYH DWWHPSWHG WR GHILQH WKH VXVWDLQDEOH \LHOG YKLFK LV RSWLPXP LQ WHUPV RI HFRQRPLF HIILn FLHQF\ IRU ERWK LQGXVWU\ FRPSRQHQWV YHVVHOVf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f DQG LQWHUGHSHQGHQFH RI SURGXFLQJ XQLWV SURYLGH WKH PRWLYDWLRQ EHKLQG WKH GHYHORSPHQW RI ELRHFRQRPLF PRGHOV RI ILVKLQJ 8VLQJ WKHVH DVSHFWV ELRHFRQRPLF PRGHOV KDYH DOPRVW XQLYHUVDOO\ UHVXOWHG LQ WKH FRQFOXVLRQ WKDW WKH ZRUNLQJV RI XQUHJXODWHG FRPSHWLWLRQ LQ D ILVKHU\ JHQHUDOO\ OHDG WR D KLJKHU OHYHO RI HIIRUW DQG ORZHU VXVWDLQDEOH \LHOG WKDQ WKDW YKLFK LV VRFLDOO\ RSWLPDO 7KH ILUVW DWWHPSW DW FRQVWUXFWLQJ D ELRHFRQRPLF PRGHO RI D ILVKHU\ ZDV GRQH E\ + 6FRWW *RUGRQ f *RUGRQnV DQDO\VLV EHJLQV ZLWK WKH DVVXPSWLRQ WKDW D ILVKLQJ JURXQG FDQ EH WUHDWHG LQ D PDQQHU VLPLODU WR D SDUFHO RI ODQG LQ WKH WUDGLWLRQDO HFRQRPLF DQDO\VLV RI UHQWV 7KXV WKH FRQFOXVLRQ UHDFKHG LV WKDW WKH RSWLPXP GHJUHH RI XWLOL]DWLRQ RI D ILVKn LQJ JURXQG RFFXUV DW WKH OHYHO RI ILVKLQJ HIIRUW ZKLFK HTXDWHV YDOXH RI
PAGE 31
WKH PDUJLQDO SURGXFW RI HIIRUW 903Af ZLWK LWV PDUJLQDO DYHUDJHf FRVW U 7R GHPRQVWUDWH KRZ WKH FRPPRQ SURSHUW\ QDWXUH RI DQ XQUHJXODWHG ILVKHU\ HQFRXUDJHV QRQRSWLPD OHYHOV RI HIIRUW *RUGRQ f DQDO\]HV D ILVKHU\ ZKLFK LV FRPSRVHG RI WZR JURXQGV RI GLIIHUHQW SURGXFWLYLW\ RU ORFDWLRQ DQG FRQVWDQW SURGXFW SULFH )LJXUH GHSLFWV WKLV VLWXDWLRQ *URXQG *URXQG )LJXUH $OORFDWLRQ RI ILVKLQJ HIIRUW EHWZHHQ ILVKLQJ JURXQGV RI GLIIHUHQW SURGXFWLYLW\ RU ORFDWLRQ 7KH RSWLPXP GHJUHH RI XWLOL]DWLRQ RI WKH ILVKHU\ ZLOO DFFRUGLQJ WR *RUGRQ RFFXU ZLWK ( XQLWV RI HIIRUW EHLQJ XVHG RQ *URXQG DQG (e XQLWV RI HIIRUW RQ *URXQG 8QGHU WKLV DOORFDWLRQ RI HIIRUW HDFK JURXQG \LHOGV D UHQW FRUUHVSRQGLQJ WR WKH VKDGHG DUHDV 7KLV SDWWHUQ RI ILVKLQJ KRZHYHU GRHV QRW UHSUHVHQW D VWDEOH SRVLWLRQ IRU WKH ILVKHU\ 7KH UHDVRQ IRU WKLV LQVWDELOLW\ UHODWHV WR WKH ODFN RI SURSHUW\ ULJKWV RQ DQ\ JLYHQ ILVKLQJ JURXQG )LVKHUPHQ YHQWXULQJ IURP SRUW DUH LQWHUn HVWHG LQ JURXQGV ZLWK WKH KLJKHVW DYHUDJH SURGXFWLYLW\ *LYHQ WKH FRQVWDQW PDUJLQDO FRVW RI HIIRUW WKLV LV ZKHUH WKH ILVKHUPDQ ZLOO
PAGE 32
UHFHLYH WKH KLJKHVW UHWXUQ 7KXV LQ WKH FDVH GHSLFWHG E\ )LJXUH ILVKHUPHQ ZLOO HQWHU WKH ILVKHU\ DQG DOORFDWH WKHLU HIIRUW VXFK WKDW WKH YDOXH RI DYHUDJH SURGXFWLYLW\ 9$3f RI WKH WZR JURXQGV LV HTXDO WR DYHUDJH FRVW Uf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n WLYH PDUJLQDO SURGXFWLYLW\ 7KLV UHSUHVHQWV *RUGRQnV f WKHRU\ H[SODLQLQJ WKH UHVXOWV RI SURGXFWLRQ IURP D FRPPRQ SURSHUW\ UHVRXUFH XQGHU D FRPSHWLWLYH UHJLPH *RUGRQ DOVR SURSRVHG D ELRHFRQRPLF PRGHO RI WKH ILVKHU\ DW WKH LQGXVWU\ OHYHO 6FKDHIHU f SUHVHQWHG HVVHQWLDOO\ WKH VDPH PRGHO 'XH WR WKH ZLGH XVH RI WKH VRFDOOHG 6FKDHIHU PRGHO LQ ILVKHU\ WKHRU\ DQG LWV VLPLODULW\ WR *RUGRQnV IRUPXODWLRQV WKH IROORZLQJ DQDO\VLV IROORZV 6FKDHIHU 7KH 6FKDHIHU PRGHO EHJLQV ZLWK WKH GHILQLWLRQ RI WKH ORQJUXQ HTXLOLEULXP LQGXVWU\ SURGXFWLRQ IXQFWLRQ 7KLV IXQFWLRQ EDVHG RQ D ORJLVWLF SRSXODWLRQ JURZWK IXQFWLRQ ZDV VKRZQ LQ HTXDWLRQ f WR EH D VSHFLDO FDVH RI WKH *630 (TXDWLRQ f UHVWDWHV HTXLOLEULXP FDWFK IXQFWLRQ DV & D(E (f f .0 ZKHUH D UU DQG E LQ WHUPV RI WKH FRQVWDQWV LQ HTXDWLRQ f DQG LV
PAGE 33
( LV GHILQHG DV ILVKLQJ HIIRUW )XUWKHU DVVXPSWLRQV RI WKH PRGHO DUH DV IROORZV 7KH GHPDQG FXUYH IDFLQJ WKH LQGXVWU\ LV DVVXPHG WR EH LQILn QLWHO\ HODVWLF ZKLFK LPSOLHV D FRQVWDQW SULFH S DQG LQGXVWU\ FRVWV DUH SURSRUWLRQDO WR HIIRUW 7KXV WKH FRVW IXQFWLRQ FDQ EH ZULWWHQ DV U( f ZKHUH U FRUUHVSRQGV WR DYHUDJH DQG PDUJLQDO FRVW RI HIIRUW 7KHVH HTXDWLRQV DUH VKRZQ LQ )LJXUH *LYHQ WKH FRQVWDQW SURGXFWLRQ SULFH WKH WRWDO UHYHQXH FXUYH VKRZQ LV VLPSO\ WKH FDWFK IXQFWLRQ LQ HTXDWLRQ f PXOWLSOLHG E\ WKH SURGXFW SULFH S 5HFDOOLQJ *RUGRQnV f UHVXOW WKDW DOO SURILW LQ D FRPPRQ SURSHUW\ ILVKHU\ LV GLVVLSDWHG WKURXJK HQWU\ RI QHZ ILUPV WKH HTXLOLEULXP SRVLWLRQ RI DQ XQUHJXODWHG ILVKHU\ ZLOO RFFXU DW WKH SRLQW ZKHUH WRWDO UHYHQXH LV HTXDO WR WRWDO FRVW )LJXUH &RVW DQG UHYHQXH LQ DQ XQUHJXODWHG ILVKHU\ ZLWK FRQVWDQW SURGXFW SULFH
PAGE 34
7KH OHYHO RI HIIRUW FRUUHVSRQGLQJ WR WKLV SRLQW FDQ EH GHULYHG IURP WKH SURILW HTXDWLRQ ,7 SD( E (f U( f 6HWWLQJ LW DQG VROYLQJ IRU ( \LHOGV WKH RSHQ DFFHVV HTXLOLEULXP HIIRUW OHYHO (M E f§ VHH )LJXUH f $V VKRZQ LQ WKH DERYH ILJXUH WKH RSHQ DFFHVV OHYHO RI HIIRUW LV JUHDWHU WKDQ WKDW QHHGHG WR KDUYHVW PD[LPXP VXVWDLQDEOH \LHOG UHYHQXHf ( 7KH LPSOLFDWLRQV RI WKLV DUH WKDW D GHFUHDVH LQ HIIRUW ZLOO QRW RQO\ IUHH UHVRXUFHV WR EH XVHG LQ RWKHU SURGXFWLYH SURFHVVHV EXW DOVR DQ LQFUHDVH LQ HTXLOLEULXP FDWFK ZLOO UHVXOW DV HIIRUW LV GHFUHDVHG IURP WKH RSHQ DFFHVV OHYHO RI (Q E f§ WR WKH 06< OHYHO RI HIIRUW ( _U $SSHQGL[ &f :KLOH SD UQ WKLV LV WUXH LQ WHUPV RI )LJXUH WKLV FRQFOXVLRQ LQ IDFW GHSHQGV XSRQ WKH DYHUDJH PDUJLQDOf FRVW RI SURYLGLQJ HIIRUW ,W FDQ EH VKRZQ WKDW LI DYHUDJH FRVW U DQ\ GHFUHDVH LQ HIIRUW ZLOO UHVXOW LQ D GHn FUHDVH LQ HTXLOLEULXP \LHOG )XUWKHU LI U +S WKH HIIRUW OHYHOV FRUUHVSRQGLQJ WR 06< DQG RSHQ DFFHVV HTXLOLEULXP ZLOO FRLQFLGH 7KH HFRQRPLFDOO\ RSWLPXP \LHOG WHUPHG PD[LPXP HFRQRPLF \LHOG 0(
PAGE 35
ERWK FULWLFL]HG DQG H[WHQGHG WKHVH EDVLF PRGHOV ,Q VSLWH RI WKHVH H[WHQVLRQV WKH EDVLF FRQFOXVLRQV RI *RUGRQnV PRGHO KDYH EHHQ PDLQWDLQHG LQ QHDUO\ DOO ELRHFRQRPLF PRGHOV 7KHVH FRQFOXVLRQV DUH WKDW WKH FRPPRQ SURSHUW\ QDWXUH RI WKH UHVRXUFH FUHDWHV D VLWXDWLRQ LQ ZKLFK WKH RSHQ DFFHVV HTXLOLEULXP LQ WKH ILVKHU\ JHQHUDWHV VRFLDOO\ XQGHVLUDEOH OHYHOV RI FDWFK DQG HIIRUW DQG WKDW VRPH W\SH RI UHVWULFWLRQV RQ WKH ILVKHU\ DUH QHFHVVDU\ DV D PHDQV RI FRUUHFWLRQ &RPPHQVXUDWH ZLWK WKLV LV *RUGRQnV FUHDWLRQ RI WKH PDQDJHPHQW JRDO RI DWWDLQLQJ PD[LPXP HFRQRPLF \LHOG UDWKHU WKDQ WKH PRUH WUDGLWLRQDO JRDO RI PD[LPXP VXVWDLQDEOH \LHOG JHQHUDOO\ SURSRVHG E\ WKH ELRORJLFDO GLVFLSOLQH '\QDPLF %LRHFRQRPLF )LVKHU\ 0RGHOV 2QH RI WKH ILUVW FULWLFLVPV RI WKH WUDGLWLRQDO PRGHO ZDV PDGH E\ 6FRWW f DQG ODWHU H[WHQGHG E\ RWKHUV PRVW QRWDEO\ &ODUN f 7KLV FULWLFLVP ZDV DLPHG DW WKH FRQFHSW RI WKH VWDWLF 0(< 0RUH SUHn FLVHO\ LW ZDV DUJXHG WKDW VLQFH FDWFK ZDV D IXQFWLRQ RI SRSXODWLRQ DQG SRSXODWLRQ ZDV D IXQFWLRQ RI FDWFK D G\QDPLF FRQFHSW RI 0(< ZDV QHHGHG 7R DWWDFN WKLV SUREOHP 6FRWW GHYHORSHG WKH FRQFHSW RI XVHU FRVW %DVLFDOO\ 6FRWW DUJXHV WKDW WKH IHHGEDFN UHODWLRQVKLS EHWZHHQ FDWFK DQG SRSXODWLRQ VL]H LPSOLHV WKDW FRUUHFW UHJXODWLRQ RI D ILVKHU\ UHTXLUHV DQ H[DPLQDWLRQ RI WKH GLVFRXQWHG SUHVHQW YDOXH RI UHWXUQV LQ WKH ILVKHU\ 7KXV DQ\ LQFUHDVH LQ PDUJLQDO FXUUHQW UHYHQXH FDWFKf PXVW EH ZHLJKHG DJDLQVW WKH FRVW RI VXFK DQ LQFUHDVH LQ WHUPV RI GLPLQLVKHG SUHVHQW YDOXH 6FRWW GHILQHV XVHU FRVW WR EH WKH HIIHFW RI VXFFHHGLQJ A6FRWWnV DUJXPHQW ZDV FRXFKHG LQ WHUPV RI WKH VXIILFLHQF\ RI VROH RZQHUVKLS RI WKH ILVKHU\ ZLWK WKH DWWDLQPHQW RI 0(< 7KH HVVHQFH RI KLV DUJXPHQW KRZHYHU LQYROYHV WKH RSWLPDOLW\ RI VWDWLF YHUVXV G\QDPLF 0(<
PAGE 36
XQLWV RI FXUUHQW RXWSXW RQ WKH SUHVHQW YDOXH RI WKH HQWHUSULVH 6FRWW S f '\QDPLF 0(< WKHUHIRUH RFFXUV ZKHUH PDUJLQDO FXUUHQW UHYHQXH LV HTXDO WR PDUJLQDO XVHU FRVW 7KH GHWHUPLQDWLRQ RI WKH FDWFK DQG HIIRUW OHYHOV QHFHVVDU\ WR DFKLHYH G\QDPLF 0(< LV WKXV D IXQFWLRQ RI WKH GLVFRXQW UDWH ,Q JHQHUDO DV WKH GLVFRXQW UDWH ULVHV ORZHU YDOXDn WLRQ LV SXW RQ ODQGLQJV LQ WKH IXWXUH &ODUN f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f 2WKHUV PRVW QRWDEO\ )XOOHQEDXP HWA DOB f DQG $QGHUVRQ f KDYH DOO FULWLFL]HG DQG VRXJKW WR H[WHQG 6PLWKnV ZRUN 7KH IROORZLQJ GLVFXVVLRQ LV FRQILQHG WR 6PLWKnV DQDO\VLV 6PLWKnV IRUPXODWLRQ FHQWHUV RQ GHDOLQJ ZLWK WKUHH NH\ DVSHFWV RI D ILVKHU\ 7KHVH DUH WKH UHQHZDEOH QDWXUH RI WKH UHVRXUFH VWRFN WKH IHHGEDFN UHODWLRQVKLS EHWZHHQ LQGXVWU\ FDWFK DQG VWRFN JURZWK UDWH DQG 7KH WHUP YHVVHO DQG ILUP DUH XVHG LQWHUFKDQJHDEO\
PAGE 37
WKH H[WHUQDOLWLHV RI SURGXFWLRQ 7KUHH GLIIHUHQW W\SHV RI SURGXFWLRQ H[WHUQDOLWLHV DUH VDLG WR H[LVW 6WRFN H[WHUQDOLWLHV DUH DVVXPHG WR UHSUHVHQW VKLIWV LQ WKH ILUP FRVW IXQFWLRQ GXH WR FKDQJHV LQ WKH VWRFN VL]H &URZGLQJ H[WHUQDOLWLHV UHVXOW IURP GLUHFW LQWHUGHSHQGHQFH RI SURn GXFWLRQ ILVKLQJf DFWLYLWLHV )LQDOO\ 6PLWK f FRQVLGHUV PHVK H[WHUQDOLWLHV ZKLFK FRUUHVSRQG WR ERWK WKH HFRQRPLF DQG ELRORJLFDO HIIHFWV RI FKDQJLQJ PHVK VL]H ,W VKRXOG EH QRWHG WKDW LQ DQ\ JLYHQ ILVKHU\ VRPH RU DOO RI WKHVH H[WHUQDOLWLHV PD\ RU PD\ QRW H[LVW 7KH JHQHUDO IRUPXODWLRQ RI WKH PRGHO FHQWHUV RQ WKH DVVXPSWLRQ RI 9 KRPRJHQHRXV YHVVHOV HDFK SURGXFLQJ [ XQLWV RI RXWSXW 7RWDO LQGXVWU\ FDWFK LV WKXV HTXDO WR 9[ 7KH VXVWDLQDEOH \LHOG IXQFWLRQ XVHG LV GHILQHG LQ JHQHUDO IXQFWLRQ IRUP WR EH I;f ZKHUH ; FRUUHVSRQGV WR WKH UHVRXUFH VWRFN VL]H 7KLV IXQFWLRQ LV DVVXPHG WR SRVVHVV WKH IROORZLQJ SURSHUWLHV I;f I;f ZKHUH ; DQG ;A DUH WKH PD[LPXP DQG PLQLPXP YLDEOH SRSXODWLRQV UHVSHFWLYHO\ [+[T IRU VRPH ; ;X ; DQ GI LQWHULRU PD[LPXP JURZWK UDWH 06
PAGE 38
LQWHUDFWLRQ EHWZHHQ LQGXVWU\ FDWFK DQG WKH SRSXODWLRQ JURZWK UDWH HTXDWLRQ f FDQ EH UHZULWWHQ DV ; I; Pf 9[ f 7KLV IRUP RI HTXDWLRQ f FDQ EH LQWHUSUHWHG WR PHDQ WKDW WKH VXVn WDLQDEOH \LHOG SURGXFHG E\ DQ\ JLYHQ VWRFN DQG IL[HG PHVK VL]H LV UHGXFHG E\ DQ DPRXQW SUHFLVHO\ HTXDO WR LQGXVWU\ FDWFK ,Q GHDOLQJ ZLWK WKH LQGLYLGXDO ILUP 6PLWK f FKRRVHV WR GHILQH EHKDYLRU LQ WHUPV RI WKH ILUPnV ORQJUXQ FRVW IXQFWLRQ ,W VKRXOG EH HPSKDVL]HG WKDW WKH ILUPnV SURGXFWLRQ IXQFWLRQ LV LPSLFLW\ LQ WKH FRVW IXQFWLRQ 7KH JHQHUDO IRUP RI WKH FRVW IXQFWLRQ LV F c![ ; P 9f LI f ZKHUH LU LV GHILQHG WR EH WKH ILUPnV RSSRUWXQLW\ FRVW 3DUWLDO HIIHFWV DUH K\SRWKHVL]HG WR EH FM _A _\ e FA _A DQG 6 F F 7\ / r 2I LQWHUHVW KHUH LV WKH IDFW WKDW VWRFN H[WHUQDOLW\ HIIHFWV FSM DQG SURGXFWLYH LQWHUGHSHQGHQF\ HIIHFWV FA FDQ EH HTXDO WR ]HUR ,QGXVWU\ UHYHQXH 5f LV GHILQHG WR EH D IXQFWLRQ RI LQGXVWU\ FDWFK DQG PHVK VL]H 0DWKHPDWLFDOO\ WKLV UHODWLRQVKLS LV H[SUHVVHG E\ 5 59[ Pf f )URP WKLV UHODWLRQVKLS WKH SULFH RI RXWSXW UHFHLYHG E\ LQGLYLGXDO ILUPV LQ WKH LQGXVWU\ FDQ EH VKRZQ WR EH 3LQf f
PAGE 39
7KH XVH RI WKH QRWDWLRQ 3Pf KHUH LPSOLHV WKDW SULFH LV FRQVWDQW ZLWK UHVSHFW WR YDULDWLRQV LQ ILUP RXWSXW EXW GRHV YDU\ ZLWK FKDQJHV LQ PHVK VL]H GXH WR WKH FKDQJH LQ WKH VL]H RI ILVK FDXJKW ,QGLYLGXDO ILUP EHKDYLRU LV DVVXPHG WR IROORZ D SURILW PD[LPL]DWLRQ JRDO ZLWK YHVVHO FDWFK UDWH [ DQG PHVK VL]H P EHLQJ WKH GHFLVLRQ YDULDEOHV 7KH SURILW IXQFWLRQ IRU WKH LQGLYLGXDO ILUP FDQ WKXV EH H[SUHVVHG DV LU 3Pf[ c![ ; P 9f WW f 0D[LPL]DWLRQ RI WKLV IXQFWLRQ \LHOGV WKH IROORZLQJ ILUVWRUGHU FRQGLWLRQV 3Pf FM[ ; P 9f Df 3n Pf[ B FA[ ; P 9f LI P P Ef 7KH LQHTXDOLW\ RFFXUULQJ LQ HTXDWLRQ Ef KROGV ZKHQ WKH VROXWLRQ LV VXFK WKDW PHVK VL]H LV EHORZ WKH SRLQW RI WHFKQRORJLFDO IHDVLELOLW\ (TXDWLRQ Df VWDWHV WKH IDPLOLDU SURILW PD[LPL]DWLRQ FRQGLWLRQ WKDW PDUJLQDO FRVW HTXDOV SULFH ,QWHUSUHWDWLRQ RI HTXDWLRQ Ef LV OHVV FOHDU ,Q JHQHUDO LW VWDWHV WKDW WKH PDUJLQDO UHYHQXH RI YDU\LQJ PHVK VL]H PXVW HTXDO WKH PDUJLQDO FRVW RI GRLQJ VR ,W PD\ EH KRZHYHU WKDW WKH PHVK VL]H ZKLFK VDWLVILHV WKLV FRQGLWLRQ LV EHORZ WKDW ZKLFK LV WHFKQRORJLFDOO\ IHDVLEOH +HQFH WKH LQHTXDOLW\ EHFRPHV HIIHFWLYH LQ WKLV FDVH DQG WKH RSWLPDO PHVK VL]H LV DVVXPHG WR EH P 7KH IRUHJRLQJ LOOXVWUDWHV WKH GHWHUPLQDWLRQ RI WKH RSWLPDO SURILW PD[LPL]LQJf OHYHOV RI ILUP FDWFK DQG PHVK VL]H 7KH UDWH RI H[LW RU HQWU\ RI ILUPV RSHUDWLQJ DW WKHVH OHYHOV LV JLYHQ E\
PAGE 40
9 ^ 6L 7 77 2 7 2 f SURILW (TXDWLRQ f LOOXVWUDWHV WKDW WKH HQWU\ DQG H[LW RI ILUPV LV DV\PPHWULFDOO\ SURSRUWLRQDO WR SURILW *HQHUDOO\ LW LV DVVXPHG WKDW ILUPV OHDYH WKH LQGXVWU\ DW D VORZHU UDWH WKDQ ILUPV HQWHU (TXDWLRQV f Df Ef DQG f SURYLGH D V\VWHP RI HTXDWLRQV LQ ZKLFK WKH HQWLUH ZRUNLQJV RI WKH ILVKHU\ FDQ EH DQDO\]HG 6SHFLILFDOO\ HTXDWLRQV Df DQG Ef SURYLGH XQLTXH YDOXHV RI FDWFK J DQG PHVK VL]H IRU DQ\ JLYHQ SRSXODWLRQ VL]H DQG LQGXVWU\ VL]H 7KXV RQFH WKH FDWFK UDWH SHU YHVVHO DQG PHVK VL]H LV GHWHUPLQHG FKDQJHV LQ LQGXVWU\ RXWSXW FDQ EH VHHQ WR EH D IXQFWLRQ RI FKDQJHV LQ WKH LQGXVWU\ VL]H DQG VWRFN VL]H 7KHVH HIIHFWV DUH VXPPDUL]HG E\ ; ); 9f Df Ef 9 ,; 9f (TXDWLRQ Df VWDWHV WKDW WKH FKDQJH LQ WKH UHVRXUFH VWRFN RYHU WLPH LV D IXQFWLRQ RI ERWK WKH VWRFN VL]H DQG WKH QXPEHU RI HIILFLHQWO\ RSHUDWn LQJ YHVVHOV LQ WKH ILVKHU\ :KHQ ; D ELRORJLFDO HTXLOLEULXP RFFXUV LQ WKH VHQVH WKDW WKH LQGXVWU\ KDUYHVW UDWH LV HTXDO WR VXVWDLQDEOH \LHOG ,Q HTXDWLRQ Ef WKH FKDQJH LQ WKH QXPEHU RI SDUWLFLSDWLQJ YHVVHOV LV DOVR VHHQ WR EH D IXQFWLRQ RI VWRFN VL]H DQG LQGXVWU\ VL]H 7KH VHW RI VROXWLRQV UHSUHVHQWHG E\ I FRUUHVSRQG WR WKRVH LQ ZKLFK LQYHVWPHQW LQ WKH ILVKHU\ LV LQ HTXLOLEULXP LQ UHODWLRQ WR DOWHUQDWLYH J LQGXVWU\ VL]H KHUH UHIHUV WR WKH QXPEHU RI HIILFLHQWO\ RSHUDWLQJ YHVVHOV LQ WKH ILVKHU\
PAGE 41
SURGXFWLYH XVHV 7KXV ZKHQ HTXDWLRQV Df DQG Ef DUH VLPXOWDQHRXVO\ ]HUR DQ RSHQ DFFHVV ELRHFRQRPLF HTXLOLEULXP LV VDLG WR H[LVW $Q H[DPSOH RI VXFK D V\VWHP RI HTXDWLRQV LV SLFWXUHG LQ )LJXUH 3RLQWV DERYH WKH ,; 9f FXUYH FRUUHVSRQG WR SRLQWV ZKHUH LQGXVWU\ SURILWV DUH QHJDWLYH ZKLOH WKH FRQYHUVH KROGV IRU SRLQWV EHORZ WKH IXQFWLRQ )LJXUH 3KDVH GLDJUDP IRU HTXLOLEULD EHWZHHQ YHVVHOV DQG UHVRXUFH VWRFN LQ DQ RSHQ DFFHVV ILVKHU\ 6LPLODUO\ SRLQWV DERYH WKH ); 9f FXUYH FRUUHVSRQG WR KDUYHVW UDWHV LQ H[FHVV RI VXVWDLQDEOH \LHOG 7KH DUURZV LQ WKH GLDJUDP FRUn UHVSRQG WR WKH GLUHFWLRQ RI FKDQJH LQ YHVVHOV DQG UHVRXUFH VWRFN ,PPHGLDWHO\ REYLRXV LV WKH IDFW WKDW WKHUH DUH WKUHH SRWHQWLDO HTXLn OLEULXP SRVLWLRQV SRLQWV $ % DQG &f 2QO\ SRLQWV $ DQG & UHSUHVHQW VWDEOH VROXWLRQV KRZHYHU 7KH LQVWDELOLW\ RI SRLQW % FDQ EH VHHQ E\ H[DPLQDWLRQ $Q\ GLVSODFHPHQW IURP WKLV SRLQW ZRXOG UHVXOW LQ D QHZ HTXLOLEULXP EHLQJ HVWDEOLVKHG DW SRLQW $ RU &
PAGE 42
7KH DERYH GLVFXVVLRQ KDV SURYLGHG D UHYLHZ RI 6PLWKnV f VWHDG\ VWDWH UHSUHVHQWDWLRQ RI DQ XQUHJXODWHG FRPPHUFLDO ILVKHU\ $V ZLWK SUHYLRXV ZULWHUV 6PLWKnV FRQFOXVLRQ LV WKDW WKH XQUHVWULFWHG RSHUDWLRQ RI D ILVKHU\ UHVXOWV LQ OHYHOV RI FDWFK DQG HIIRUW ZKLFK H[FHHG WKRVH QHFHVVDU\ WR PD[LPL]H UHWXUQV WR WKH UHVRXUFH )XUWKHUPRUH 6PLWK DVVXPHV LI WKH ILVKHU\ ZHUH PDQDJHG E\ D VROH RZQHU WKH DSSURSULDWH OHYHOV RI FDWFK DQG HIIRUW ZRXOG UHVXOW 7KHVH OHYHOV DUH KDUPRQLRXV ZLWK SUHYLRXV ZULWHUV LQ WKDW WKH\ UHVXOW LQ PD[LPL]LQJ UHWXUQV WR WKH UHVRXUFH LQ RWKHU ZRUGV VWDWLF 0(< UHVXOWV 7KH SURILW IXQFWLRQ IRU D VROH RZQHU FDQ EH ZULWWHQ DV WW 3Pf 9[ 9 M! [ ; P 9f f ZKHUH DOO WHUPV DUH GHILQHG DV DERYH ,Q FRQWUDVW WR WKH ILUP ZKLFK FRQVLGHUV RQO\ P DQG [ DV GHFLVLRQ YDULDEOHV WKH VROH RZQHU PXVW PD[Ln PL]H HTXDWLRQ f ZLWK UHVSHFW WR WKH DUJXPHQWV [ P ; DQG 9 )XUWKHUPRUH WR LQVXUH WKDW WKH VWRFN UHPDLQV LQ HTXLOLEULXP PD[LPL]Dn WLRQ RI HTXDWLRQ f LV FRQVWUDLQHG VXFK WKDW I[ P 9[f &RQVWUDLQHG PD[LPL]DWLRQ RI WKH DERYH SURILW IXQFWLRQ OHDGV WR WKH ILUVW RUGHU FRQGLWLRQV 3Pf FM ; IJ ;I [Sn Pf Zf§ e &J LI P P < 3Pf [ F 9FA [ I [ Df Ef Ff Gf ); P 9[f Hf
PAGE 43
ZKHUH $ UHSUHVHQWV WKH XQGHWHUPLQHG ODJUDQJH PXOWLSOLHU (TXDWLRQ Df VWDWHV WKDW WKH YHVVHO FDWFK UDWH EH DGMXVWHG WR WKH SRLQW ZKHUH SULFH HTXDOV GLUHFW DQG XVHU FRVW 6LPLODUO\ HTXDWLRQ Ef VWDWHV WKDW PHVK VL]H VKRXOG EH DGMXVWHG WR WKH SRLQW ZKHUH PDUJLQDO SULYDWH DQG VRFLDO UHYHQXH LV OHVV WKDQ RU HTXDO WR WKH FRVW RI FKDQJLQJ PHVK VL]H &RQGLWLRQ HTXDWLRQ Ff VWDWHV WKDW WKH PDUJLQDO SURILWDELOLW\ RI WRWDO LQGXVWU\ FDWFK HTXDOV WKH PDUJLQDO VRFLDO FRVW RI DGGLQJ D YHVVHO WR WKH ILVKHU\ 8VLQJ WKHVH FULWHULD WKH VRFLDOO\ RSWLPDO OHYHOV RI WKH GHFLVLRQ YDULDEOHV ZLOO EH UHDOL]HG 2I FRXUVH WKLV DVVXPHV WKDW WKH VRFLDOO\ RSWLPDO SRVLWLRQ RI D ILVKHU\ LV DFKLHYHG E\ FDWFKLQJ 0(< $V ZLWK SUHYLRXV ZULWHUV 6PLWK f FRQFOXGHV WKDW LQ WKH DEVHQFH RI VROH RZQHUVKLS DQ RSHQ DFFHVV ILVKHU\ PXVW EH UHJXODWHG WR DFKLHYH HFRQRPLFDOO\ HIILFLHQW SURGXFWLRQ 6PLWK SURSRVHV WKDW DQ H[WUDFWLRQ IHH RI IA RQ HDFK SRXQG RI ILVK ODQGHG DQG D OLFHQVH IHH RI 9FÂ RQ HDFK YHVVHO ZRXOG EH VXIILFLHQW WR LQVXUH VRFLDO DQG HFRQRPLF HIILFLHQF\ 0(
PAGE 44
7KH HFRQRPLFDOO\ FRUUHFW GHJUHH RI XWLOL]DWLRQ RI HIIRUW LQ WKH ILVKHU\ LV VKRZQ WR FRUUHVSRQG WR VRPH IRUP RI PD[LPXP HFRQRPLF \LHOG G\QDPLF 0(< RU VWDWLF 0(
PAGE 45
UHJXODWLRQ DQG WKH HFRQRPLFDOO\ HIILFLHQW PDQDJHPHQW JRDO RI DWWDLQLQJ PD[LPXP HFRQRPLF \LHOG ,Q DOO FDVHV WKHVH UHVXOWV ZHUH REWDLQHG IURP PRGHOV ZKLFK WUHDWHG WKH ILVKHU\ DV D VLQJOH DJJUHJDWH RSHUDWLQJ ZLWK D FRQVWDQW SURGXFW SULFH 7KH SXUSRVH RI WKLV VHFWLRQ LV WR ILUVW UHOD[ WKH DVVXPSWLRQ RI D FRQVWDQW SURGXFW SULFH DQG WKHQ H[WHQG WKH UHVXOWV WR FRQVLGHU WKH FDVH RI D PXOWLVHFWRU ILVKHU\ ZKHUH HDFK VHFWRU FRUn UHVSRQGV WR D VXELQGXVWU\ GHILQHG RQ UHJLRQDO RU VWDWH EDVLV )LVKLQJ (IIRUW DQG (TXLOLEULXP
PAGE 46
,Q VSLWH RI WKHVH DSSDUHQW FRQFHSWXDO GLIIHUHQFHV HIIRUW LV VWLOO JHQHUDOO\ FRQVLGHUHG DV D VLQJOH FRPSRVLWH LQSXW 7KH SUHVHQW DQDO\VLV GLYHUJHV IURP WKLV QRWLRQ DQG FRQVLGHUV WKDW DQ\ PHDVXUH RI HIIRUW PXVW EH FRPSRVHG RI VHYHUDO FRPSRQHQWV 3DUDOOHOLQJ *XOODQG f ILVKLQJ HIIRUW FDQ EH WKRXJKW RI DV EHLQJ FRPSRVHG RI WKUHH EDVLF FRPSRQHQWV 7KHVH DUH QRUPDO ILVKLQJ HIIRUW ILVKLQJ SRZHU DQG ILVKLQJ LQWHQVLW\ 1RPLQDO ILVKLQJ HIIRUW FDQ EH WKRXJKW RI DV D XQLW RI PHDVXUH RU SHUKDSV DQ LQGXVWU\ VL]H PHDVXUH VXFK DV WKH QXPEHU RI YHVVHOV )LVKLQJ SRZHU LV D PHDVXUH RI WKH LQSXW FKDUDFWHULVWLFV RI ILUPV YHVVHOVf LQ WKH ILVKHU\ )LQDOO\ ILVKLQJ LQWHQVLW\ FDQ EH WKRXJKW RI DV VRPH W\SH RI WLPH PHDVXUH VXFK DV GD\V ILVKHG )LVKLQJ LQWHQVLW\ LV RIWHQ LPSOLFLW LQ WKH GDWD EHLQJ GHILQHG E\ WKH REVHUYDWLRQ LQWHUYDO 7R PDNH WKLV QRWLRQ PRUH H[SOLFLW DVVXPH WKDW ILVKLQJ LQWHQVLW\ LV LPSOLFLW LQ WKH LQWHUYDO RI REVHUYDWLRQ )LVKLQJ SRZHU FDQ WKHQ EH UHSUHVHQWHG E\ (S J;@ ;Qf f ZKHQ ( GHQRWHV ILVKLQJ SRZHU DQG WKH L Q DUH LQSXW FKDUn DFWHULVWLFV RI ILUPV LQ WKH ILVKHU\ ,I J; ;Qf LV DVVXPHG WR EH WKH VDPH IRU DOO ILUPV WRWDO ILVKLQJ HIIRUW LV WKHQ JLYHQ E\ ( (1 f J;M ;5f f ZKHUH ( GHQRWHV QRPLQDO HIIRUW 7KLV QRWLRQ RI HIIRUW ZLOO EH PDLQ 1 WDLQHG WKURXJKRXW WKH UHPDLQGHU RI WKLV VWXG\ )XUWKHU GLVFXVVLRQ ZLOO IROORZ LQ WKH HPSLULFDO DQDO\VLV WR EH SUHVHQWHG
PAGE 47
+DYLQJ EULHIO\ FODULILHG WKH GHILQLWLRQ RI ILVKLQJ HIIRUW LW UHPDLQV WR GUDZ D GLVWLQFWLRQ EHWZHHQ WKH HTXLOLEULXP \LHOG IXQFWLRQV VXFK DV WKRVH GHYHORSHG E\ 3HOOD DQG 7KRPOLQVRQ f DQG 6FKDHIHU f DQG QRQHTXLOLEULXP \LHOG IXQFWLRQV (TXLOLEULXP \LHOG IXQFWLRQV DV VKRZQ DERYH DUH GHULYHG LQ VXFK D PDQQHU DV WR SURGXFH D UHODWLRQn VKLS EHWZHHQ ILVKLQJ HIIRUW DQG VXVWDLQDEOH \LHOG ,W LV SUHFLVHO\ WKLV UHODWLRQVKLS EHWZHHQ FDWFK DQG HIIRUW WKDW KDV UHVXOWHG LQ WKH WHUP HTXLOLEULXP \LHOG IXQFWLRQ 7KH FDWFK UHVXOWLQJ IURP DQ\ OHYHO RI HIIRUW DORQJ WKHVH IXQFWLRQV FRUUHVSRQGV WR HTXLOLEULXP VXVWDLQDEOHf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f 7KXV HPSLULFDOO\ HVWLPDWHG HTXLOLEULXP \LHOG IXQFWLRQV PD\ QRW LQFRUSRUDWH WKH ELRORJLFDO HTXLOLEULXP FRQGLWLRQ RI FDWFK HTXDOV VXVWDLQDEOH \LHOG WR DQ\ UHDVRQDEOH GHJUHH 6HFRQGO\ HTXLOLEULXP \LHOG IXQFWLRQV JHQn HUDOO\ LPSRVH VSHFLILF IXQFWLRQDO IRUPV RQ WKH REVHUYHG UHODWLRQVKLS EHWZHHQ FDWFK DQG HIIRUW 7KLV LV VLJQLILFDQW LQ WKDW WKH VHW RI YDOLG HTXLOLEULXP \LHOG IXQFWLRQV LV IDLUO\ OLPLWHG ,Q FRQWUDVW WR WKH QRWLRQ RI HTXLOLEULXP \LHOG IXQFWLRQV LV WKDW RI QRQHTXLOLEULXP \LHOG IXQFWLRQV ,Q WKLV VWXG\ WKH WHUP QRQHTXLOLEn ULXP LPSOLHV WKDW QR ELRORJLFDO HTXLOLEULXP FRQGLWLRQ RI FDWFK HTXDO WR
PAGE 48
VXVWDLQDEOH \LHOG LV LPSRVHG RQ WKH UHODWLRQVKLS EHWZHHQ FDWFK DQG HIIRUW 9HU\ OLWWOH DWWHQWLRQ KDV EHHQ JLYHQ WR HTXDWLRQV RI WKLV W\SH 7KH PRVW QRWDEOH H[FHSWLRQ LV D SDSHU E\ %HOO HW DB f ZKHUHLQ WKH\ DGGUHVVHG WKH TXHVWLRQ RI FRQVWDQW YHUVXV GHFUHDVLQJ UHWXUQV LQ DQ HVVHQWLDOO\ QRQHTXLOLEULXP IUDPHZRUN :LWKLQ WKH IUDPHZRUN RI ELRn HFRQRPLFV LW PD\ VHHP REMHFWLRQDEOH WR FRQVLGHU DQDO\]LQJ ILVKHU\ SURn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n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f HTXDWLRQV LQ WKH HQVXLQJ DQDO\VLV ZLOO EH QRQHTXLOLEULXP LQ QDWXUH 7KH QRWLRQ RI GHULYHG HTXLOLEULXP \LHOG HTXDWLRQV LV GHYHORSHG LQ WKH IROORZLQJ FKDSWHUV
PAGE 49
9DULDEOH 3URGXFW 3ULFH 6LQFH PRVW ILVKHU\ DQDO\VHV DUH GRQH DW WKH DJJUHJDWH RU LQGXVWU\ OHYHO WKH YDOLGLW\ RI D FRQVWDQW SURGXFW SULFH LV TXHVWLRQDEOH 5HOD[LQJ WKH DVVXPSWLRQ RI FRQVWDQW SURGXFW SULFHV FRPSOLFDWHV VRPH RI WKH WUDGLWLRQDO WKHRUHWLFDO UHVXOWV LQ WKH FRQWH[W RI HTXLOLEULXP \LHOG IXQFWLRQV $QGHUVRQ f KDV VKRZQ WKDW ERWK WKH GHULYDWLRQ RI PD[Ln PXP HFRQRPLF \LHOG 0(
PAGE 50
0(< ( f DQG WKH RSHQ DFFHVV VROXWLRQ ( f 1RZ FRQVLGHU )LJXUH LOO F ZKHUH SULFH LV YDULDEOH ,W FDQ EH VHHQ WKDW WKH WRWDO UHYHQXH IXQFWLRQ QR ORQJHU UHWDLQV WKH VKDSH RI WKH VXVWDLQDEOH \LHOG IXQFWLRQ EXW T UDWKHU KDV EHFRPH GRXEOHGKXPSHG $QGHUVRQ f ,I WKH UHOHYDQW WRWDO FRVW FXUYH LV 7& WKHUH VWLOO LV D XQLTXH RSHQ DFFHVV VROXWLRQ +RZHYHU WKHUH DUH QRZ WKUHH HIIRUW OHYHOV ( ( DQG (Af ZKHUHLQ PDUJLQDO FRVW HTXDOV PDUJLQDO UHYHQXH )LJXUH 2SHQ DFFHVV HTXLOLEULD DQG PD[LPXP HFRQRPLF \LHOG LQ D ILVKHU\ ZLWK D YDULDEOH SURGXFW SULFH 7KXV WKH WDVN RI ILQGLQJ WKH FRUUHFW VROXWLRQ UHTXLUHV ILQGLQJ D JOREDO RSWLPXP IURP VHYHUDO ORFDO VROXWLRQV ZKHUH PDUJLQDO UHYHQXHV DQG FRVWV DUH HTXDWHG ,I WKH UHOHYDQW FRVW FXUYH LV 7&A LQ DGGLWLRQ WR PXOWLSOH 0(< VROXWLRQV WKHUH QRZ H[LVWV WKUHH SRLQWV $ % DQG &f ZKHUH T $ JUDSKLFDO GHULYDWLRQ RI WKH GRXEOHKXPSHG VXVWDLQDEOH UHYHQXH IXQFWLRQ LV SUHVHQWHG LQ $SSHQGL[ IRU WKH FDVH RI D OLQHDU GHPDQG IXQFWLRQ
PAGE 51
WKH RSHQ DFFHVV UHVXOW RI WRWDO FRVW HTXDOV WRWDO UHYHQXH KROGV 7KXV LW FDQ EH VHHQ WKDW UHOD[DWLRQ RI WKH FRQVWDQW SULFH DVVXPSWLRQ GRHV LQGHHG FRQIXVH DQG FRPSOLFDWH PDQ\ RI WKH WKHRUHWLFDO UHVXOWV GHULYHG E\ XVLQJ HTXLOLEULXP \LHOG IXQFWLRQV 8WLOL]LQJ QRQHTXLOLEULXP \LHOG IXQFWLRQV FDQ DYRLG VRPH RI WKHVH FRPSOLFDWLRQV /HW WKH \LHOG IXQFWLRQ IRU D ILVKHU\ EH GHILQHG E\ & I;@ [Qf f ZKHUH & GHQRWHV RXWSXW DQG WKH ; FRUUHVSRQGV WR Q LQSXWV IXUWKHU DVVXPHG WKDW I; ; f LV VXFK WKDW ,W LV 2U L Q Df I r L OQ D[I Ef (TXDWLRQV Df DQG Ef PHUHO\ DVVHUW WKDW WKH PDUJLQDO SURGXFW IXQFn WLRQ LV HYHU\ZKHUH SRVLWLYH DQG GHFOLQLQJ 7KH SULFH RI RXWSXW LV QRZ GHILQHG WR EH D GHFOLQLQJ IXQFWLRQ RI FDWFK 3 3&f f G3 ZKHUH A )LQDOO\ WKH FRVW HTXDWLRQ LV GHILQHG E\ Q ( U ; L L Df ZKHUH WKH LQSXW SULFHV U DUH DVVXPHG FRQVWDQW )URP HTXDWLRQ Df WKH PDUJLQDO FRVW RI ; LV WKHQ JLYHQ E\
PAGE 52
. L Q Ef *LYHQ WKHVH DVVXPSWLRQV RQ WKH WHFKQLFDO UHODWLRQVKLS EHWZHHQ FDWFK LQSXWV DQG SURGXFW DQG LQSXW SULFHV WKH SURILW PD[LPL]DWLRQ SUREOHP RU HTXLYDOHQWO\ WKH 0(< SUREOHP FDQ EH VWDWHG LQ WKH IRUP Q 0$; LU 3&f& ] U ; L O VW & f (TXDWLRQ f FDQ EH VHHQ WR EH D FRQVWUDLQHG PD[LPL]DWLRQ SUREOHP ZLWK WKH FRQVWUDLQW EHLQJ WKH \LHOG HTXDWLRQ 8WLOL]LQJ WKH PHWKRG RI ODJUDQJH PXOWLSOLHUV HTXDWLRQ f FDQ EH UHVWDWHG E\ Q 0$; / 3&f& ] U [ [>& I; ; f@ f mM B L L L L Q 'LIIHUHQWLDWLRQ RI HTXDWLRQ f \LHOGV WKH ILUVW RUGHU FRQGLWLRQV / DF G3 3A&; G& Df / ;L U ; D[ L Q Ef / D[ I; ; f & n Qn Ff ([DPLQDWLRQ RI WKH ILUVW HTXDWLRQ LQGLFDWHV WKDW WKH ODJUDQJH PXOWLSOLHU G3 ; LV HTXDO WR 3 & ZKLFK LV SUHFLVHO\ PDUJLQDO UHYHQXH 7KLV VHFWLRQ GUDZV XSRQ ,QWULOOLJDWRU f
PAGE 53
6XEVWLWXWLRQ RI 3 LQWR HTXDWLRQ Ef IRU $ \LHOGV L Q 7KH H[SUHVVLRQ LQ HTXDWLRQ f VWDWHV WKDW LQ HTXLOLEULXP WKH PDUJLQDO WK UHYHQXH SURGXFW RI WKH L LQSXW PXVW EH HTXDWHG WR LWV SULFH RU HTXLYDOHQWO\ LWV PDUJLQDO FRVW (TXDWLRQ f FDQ EH UHZULWWHQ LQ DQ DOWHUQDWLYH DQG SHUKDSV PRUH LOOXPLQDWLQJ IDVKLRQ DV L Q f )URP HTXDWLRQ f LW LV UHDGLO\ VHHQ WKDW UA U \ IRU DOO I L DQG M 1RZ LQ HTXLOLEULXP U LV SUHFLVHO\ HTXDO WR WKH PDUJLQDO FRVW RI RXWSXW +HQFH HTXDWLRQ f VWDWHV WKH ZHOONQRZQ UHVXOW WKDW LQ HTXLOLEULXP PDUJLQDO FRVW HTXDOV PDUJLQDO UHYHQXH (TXDWLRQ f SURYLGHV D FRQYHQLHQW ZD\ RI H[DPLQLQJ VRPH SRVVLEOH FRQVHTXHQFHV RI YDULRXV PDQDJHPHQW JRDOV 2QH FDQ FRQVLGHU WKH LPSOLFDn WLRQV ZLWK UHVSHFW WR LQSXW XVDJH OHYHOV XQGHU YDULRXV PDQDJHPHQW JRDOV ,Q WKLV FDVH WKH LQGXVWU\ LV WUHDWHG DV D VLQJOH ILUP DQG WKH PDQDJHn PHQW JRDO LV GHILQHG WR EH SURILW PD[LPL]DWLRQ 7KH UHOHYDQW HTXDWLRQV WR EH VROYHG LQ WKLV FDVH DUH JLYHQ E\ HTXDWLRQV DFf $VVXPH fN WKDW WKH LQSXW OHYHOV UHVXOWLQJ IURP WKLV VROXWLRQ DUH GHQRWHG E\ ; L Q &RQVLGHU QRZ WKH UHODWLRQVKLS EHWZHHQ WKHVH LQSXW OHYHOV DQG WKRVH WKDW ZRXOG UHVXOW LI WKH ILVKHU\ ZDV PDQDJHG DW SULFH HTXDOV PDUJLQDO FRVW 8QGHU WKLV UHJLPH WKH HTXLOLEULXP HTXDWLRQV DQDORJRXV WR HTXDWLRQ f ZRXOG EH
PAGE 54
3 UL IW } Q f G3 )URP HTXDWLRQ f LW FDQ EH VKRZQ WKDW 3 A &f LV DOZD\V OHVV WKDQ 3 7KLV WDNHQ LQ FRQMXQFWLRQ ZLWK HTXDWLRQV Df DQG Ef FDQ EH XVHG WR VKRZ WKDW WKH LQSXW OHYHOV VDWLVI\LQJ HTXDWLRQ f VD\ ;r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n VWUXHG DV D VLQJOH VHFWRU 7R EHJLQ WKH DQDO\VLV RI D PXOWLVHFWRU ILVKHU\ DVVXPH WKHUH DUH 1 VHFWRUV RU UHJLRQV HDFK IDFLQJ D GHPDQG IXQFWLRQ GHILQHG E\ 3L 3L& &1f L 1 f WK ZKHUH 3 LV WKH SULFH UHFHLYHG E\ SURGXFHUV LQ WKH L UHJLRQ DQG WKH & FRUUHVSRQG WR WKH RXWSXWV RI WKH 1 UHJLRQV ,W VKRXOG EH HPSKDVL]HG KHUH WKDW WKH & DUH DVVXPHG WR EH WKH VDPH SURGXFW 7KH VXEVFULSW UHIHUV WR UHJLRQV UDWKHU WKDQ FRPPRGLWLHV 7KLV IRUP RI WKH GHPDQG HTXDWLRQ ZLOO EH GLVFXVVHG ODWHU 7KH GHPDQG HTXDWLRQV JLYHQ LQ HTXDn WLRQ f DUH DVVXPHG WR EH VXFK WKDW
PAGE 55
3 & f X R DQ L M Df WK 7XUQLQJ WR WKH \LHOG HTXDWLRQV OHW WKH L UHJLRQ V FDWFK IXQFWLRQ EH GHILQHG E\ &L IL [! fff [QLf f WK WK ZKHUH WKH ; UHIHU WR WKH M LQSXW XVHG LQ WKH L UHJLRQ ,W LV M IXUWKHU DVVXPHG WKDW I ;A M ;Af } L } 1 VDWLVI\ WKH FRQ GLWLRQV VWDWHG LQ HTXDWLRQV Df DQG Ef )LQDOO\ DVVXPH WKDW WKH W K FRVW HTXDWLRQ IRU WKH L UHJLRQ LV JLYHQ E\ .L Q H UM[ML L 1 f ZKHUH WKH U DUH IL[HG LQSXW SULFHV DVVXPHG WKH VDPH IRU DOO UHJLRQV 7KH SURILW PD[LPL]DWLRQ SUREOHP IRU WKH HQWLUH ILVKHU\ FDQ EH VWDWHG DV 1 0$; LU ( 3 & L O 1 &1f & (A .L f VW < I ;@ A ;QLf L 1 2QFH DJDLQ XVLQJ WKH PHWKRG RI ODJUDQJH PXOWLSOLHUV HTXDWLRQ f FDQ EH UHVWDWHG LQ WKH IRUP 0$; / ( 3& & f I ;A L L L [QL! &L@ f
PAGE 56
ZKHUH WKH $ DUH WKH XQGHWHUPLQHG ODJUDQJH PXOWLSOLHUV 'LIIHUHQWLDWLRQ RI HTXDWLRQ f ZLWK UHVSHFW WR & ;A DQG $ \LHOGV WKH 1Q f ILUVWRUGHU FRQGLWLRQV ,N A 1 3 3 ] N O &L &N A Df L 1 / ; f f -7 I U $ ‘ ‘ Z ‘‘‘ ;ML L 9 1 M M m Q Ef BM/B $ f IL ;OLf ffff ;QL` n &L L 1 Ff 1 D3 )URP HTXDWLRQ Df LW FDQ EH LPPHGLDWHO\ VHHQ WKDW $ 3 ] A & L L N W L 1 7KLV H[SUHVVLRQ IRU $ FDQ EH UHZULWWHQ DV $ 3 3 3 &f ] &L ZL NL &L N & ,Q WKLV IRUP LW FDQ EH VHHQ WKDW WKH ILUVW WHUP RQ WKH ULJKWKDQG VLGH RI WKH HTXDOLW\ LV SUHFLVHO\ WKH FKDQJH LQ UHYHQXH LQ WKH LAr UHJLRQ ZLWK UHVSHFW WR YDULDWLRQV LQ WKH LA UHJLRQnV WK RXWSXW 7KXV WKLV WHUP LV HTXDO WR WKH L UHJLRQnV PDUJLQDO UHYHQXH 05f 1RZ VXEVWLWXWLQJ IRU $ LQ Ef \LHOGV I If f§ &O :05 = S n‘nN D[ NAL /L ;ML U M Q L 1 f f WK 5HDUUDQJLQJ WHUPV LQ HTXDWLRQ f UHVXOWV LQ WKH H[SUHVVLRQ IRU WKH L UHJLRQ
PAGE 57
D3 DI KU ] WAF VLU N"Kn &L N ;ML M a Q f IL 7KLV HTXDWLRQ FDQ EH XVHG WR VKRZ WKDW LQ HTXLOLEULXP U U R$ DOO L M DQG WKDW WKHVH H[SUHVVLRQV DUH LQ WXUQ HTXDO WR WKH IL ;ML PDUJLQDO FRVW RI RXWSXW )URP HTXDWLRQ f LW FDQ WKHQ EH VHHQ WKDW WKH VLQJOH UHVXOW RI ZLWKLQ UHJLRQ PDUJLQDO FRVW HTXDOV ZLWKLQ UHJLRQ PDUJLQDO UHYHQXH GRHV QRW QHFHVVDULO\ KROG ZKHQ WKH LQGXVWU\ LV FRPSRVHG RI VHYHUDO UHJLRQV RI ZKRVH SURILW LV MRLQWO\ PD[LPL]HG 7KH UHDVRQ IRU WKLV DSSDUHQW GLYHUJHQFH EHWZHHQ HDFK UHJLRQnV PDUJLQDO FRVW DQG UHYHQXH FDQ EH H[SODLQHG E\ H[DPLQLQJ WKH VHFRQG WHUP D3N RQ WKH OHIWKDQG VLGH RI HTXDWLRQ f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f +DYLQJ VHHQ WKDW VLPXOWDQHRXV PD[LPL]DWLRQ RI SURILW LQ WKH DERYH VLWXDWLRQ GRHV QRW UHVXOW LQ WKH WUDGLWLRQDO UHVXOW LQ WKH HTXDOLW\ RI HDFK UHJLRQnV PDUJLQDO FRVW DQG PDUJLQDO UHYHQXH LW LV RI LQWHUHVW WR GHWHUPLQH WKH VLJQ RI GLIIHUHQFH EHWZHHQ WKHVH WZR WHUPV .QRZOHGJH RI WKLV VLJQ ZLOO HQDEOH FRPSDULVRQ RI LQSXW OHYHOV REWDLQHG XQGHU WKH DERYH SURFHGXUH DQG WKRVH REWDLQHG E\ PD[LPL]DWLRQ RI HDFK UHJLRQnV SURILW LQGHSHQGHQWO\ RI RWKHU UHJLRQV 5HZULWLQJ HTXDWLRQ f DV
PAGE 58
n,5 0& L O (  &L f I ZKHUH 0& KDV UHSODFHV WKH H[SUHVVLRQ U UAU LW FDQ EH VHHQ WKDW WKH R L f VLJQ RI WKH GLIIHUHQFH EHWZHHQ 05 DQG 0&A LV JLYHQ E\ WKH VLJQ RI 3 D3 USf§ &A )URP HTXDWLRQ Df US B IRU DOO L N DQG < LV NMAL /L G8L VWULFWO\ SRVLWLYH 7KHUHIRUH WKH VLJQ RI WKH ULJKWKDQG VLGH RI HTXDn WLRQ f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f ,KH GLVWDQFH $% LV HTXDO WR 3 N U N L &L 7DNHQ LQ FRQMXQFWLRQ ZLWK WKH QDWXUH RI WKH \LHOG IXQFWLRQ HTXDWLRQV Df DQG Eff LW FDQ EH FRQFOXGHG WKDW LQSXWV DUH DW ORZHU OHYHOV ZKHQ FURVVUHJLRQDO SULFH HIIHFWV DUH WDNHQ LQWR DFFRXQW $V LQ WKH FDVH RI D VLQJOH VHFWRU ILVKHU\ WKH TXHVWLRQ RI SURGXFn LQJ DW WKH SRLQW ZKHUH SULFH LV HTXDWHG WR PDUJLQDO FRVW PXVW EH FRQn VLGHUHG LQ WKH PXOWLVHFWRU ILVKHU\ $V ZLWK WKH VLQJOH VHFWRU ILVKHU\ DVVXPH WKDW WKH GHVLUHG \LHOG OHYHOV KDYH EHHQ GHWHUPLQHG IRU HDFK UHJLRQ ,Q WKDW IL[LQJ \LHOG OHYHOV UHVXOWV LQ IL[LQJ SULFH WKH SURILW PD[LPL]DWLRQ SUREOHP UHGXFHV WR D FRVW PLQLPL]DWLRQ SUREOHP ZLWK
PAGE 59
2 \ < L 3L SL A 3&f @ ZLOO QRW EH WKH f
PAGE 60
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n UHJLRQDO SULFH HIIHFWV ZRXOG EH LQWHUQDOL]HG DQG WKH DSSURSULDWH OHYHOV RI UHJLRQDO LQSXW OHYHOV DQG RXWSXWV ZRXOG EH REWDLQHG $V D PRWLYDWLRQ EHKLQG KRZ VXFK D VLWXDWLRQ DV GHVFULEHG DERYH FRXOG DULVH FRQVLGHU D ILVKHU\ ZKLFK LV FRPSRVHG RI VHYHUDO VWDWHV ILVKLQJ RYHU D IDLUO\ ODUJH JHRJUDSKLF DUHD )XUWKHUPRUH DVVXPH WKDW WKH ILVKHU\ LV VXFK WKDW HDFK VWDWHnV GHPDQG SULFH LV GHWHUPLQHG LQ SDUW E\ WKH ZLWKLQ VWDWH VXSSO\ RI ILVK DQG LQ SDUW E\ D QDWLRQDO PDUNHW VXSSOLHG E\ VKLSPHQWV IURP DOO VWDWHV LQ WKH ILVKHU\ 7KXV WKH SULFH LQ HDFK VWDWH LV GHWHUPLQHG GLUHFWO\ ZLWKLQ VWDWH FDWFK DQG LQn GLUHFWO\ WKURXJK D QDWLRQDO PDUNHW E\ WKH FDWFK RI DOO VWDWHV LQ WKH ILVKHU\ 1RZ LI WKH PDQDJHPHQW DXWKRULW\ LV H[WHQGHG RYHU WKH ILVKHU\ WKH DSSURSULDWH PHWKRG RI LQFRUSRUDWLQJ PDQDJHPHQW JRDOV EHFRPHV D UHOHYDQW TXHVWLRQ 2QH SRVVLEOH JRDO RI PDQDJHPHQW FRXOG EH WR PDQDJH WKH ILVKHU\ LQ VXFK D PDQQHU DV WR PD[LPL]H WKH HQWLUH ILVKHU\nV SURILW $ NH\ UHVXOW RI WKH DERYH DQDO\VLV LV WKDW XQGHU WKHVH FLUFXPVWDQFHV PDQDJHPHQW VKRXOG QRW EH XQGHUWDNHQ RQ DQ LQGHSHQGHQW EDVLV E\
PAGE 61
LQGLYLGXDO VWDWHV RU UHJLRQV 5DWKHU PDQDJHPHQW VKRXOG WDNH LQWR FRQVLGHUDWLRQ DOO VWDWHV VLPXOWDQHRXVO\
PAGE 62
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n ILFLHQW JLYHQ WKH ORQJUXQ QDWXUH RI WKLV VWXG\ )XUWKHUPRUH YLUWXDOO\ QR FRQVLVWHQW FRQWLQXRXV VHW RI ELRORJLFDO GDWD RQ UHVRXUFH VWRFN VL]HV VXLWDEOH IRU HFRQRPHWULF DQDO\VLV H[LVW 6XFK GDWD FRXOG EH FROOHFWHG EXW RQO\ DW H[WUHPHO\ KLJK FRVWV LQ WHUPV RI ERWK WLPH DQG GROODUV 7KH PDMRU VRXUFH RI GDWD XVHG LQ WKLV VWXG\ LV )LVKHU\ 6WDWLVWLFV RI WKH 8QLWHG 6WDWHV 86 10)6 f 7KH GDWD XVHG WKXV FRUn UHVSRQG WR DJJUHJDWH FURVVVHFWLRQ WLPH VHULHV REVHUYDWLRQV RQ VWDWHV SDUWLFLSDWLQJ LQ WKH *05)) IRU WKH \HDUV WR LQFOXVLYH $SSHQGL[ %f %HFDXVH RI WKH DJJUHJDWH QDWXUH RI WKHVH GDWD WKH
PAGE 63
UHODWLRQVKLSV GLVFXVVHG DUH QHFHVVDULO\ DJJUHJDWH LQ QDWXUH 6XFK DJJUHJDWLRQ XQIRUWXQDWHO\ OLPLWV WKH UHVXOWLQJ HPSLULFDO PRGHOV LQ PDQ\ XQGHVLUDEOH ZD\V &DWFK (TXDWLRQ 6SHFLILFDWLRQ DQG (VWLPDWLRQ ,Q RUGHU WR VSHFLI\ VWDWH FDWFK HTXDWLRQV WKH IRUP RI WKH FDWFK HTXDWLRQ IRU DQ DUELWUDU\ UHJLRQ LV ILUVW GHYHORSHG LQ D GHWHUPLQLVWLF IDVKLRQ $IWHU GHYHORSLQJ WKH W\SLFDO UHJLRQnV FDWFK HTXDWLRQ WKH FRUVVVHFWLRQDO VSHFLILFDWLRQ LV SUHVHQWHG &RPPHQVXUDWH ZLWK WKLV GLVFXVVLRQ LV WKH VWRFKDVWLF VSHFLILFDWLRQ RI WKH FDWFK HTXDWLRQ 7KH SUHVHQWDWLRQ FRQFOXGHV ZLWK WKH FKRLFH RI WKH DSSURSULDWH HVWLPDWRU $ JHQHUDO H[SUHVVLRQ IRU D ILVKHU\ FDWFK HTXDWLRQ LV JLYHQ E\ & I( 6f f ZKHUH & UHIHUV WR FDWFK ( LV HIIHFWLYH ILVKLQJ HIIRUW DQG 6 GHQRWHV WKH UHVRXUFH VWRFN VL]H 6LQFH VWRFN VL]H LV VHOGRP REVHUYDEOH WKH FDWFK HTXDWLRQ VWDWHG LQ f LV RIWHQ PRGLILHG IRU HPSLULFDO DQDO\VLV WR & Ir(f f ,Q HTXDWLRQ f DJJUHJDWH FDWFK LV H[SUHVVHG DV D IXQFWLRQ RI RQO\ N HIIHFWLYH ILVKLQJ HIIRUW 7KH I (f IXQFWLRQ LV XVHG WR GHQRWH WKH IDFW WKDW WKH LQIOXHQFH RI WKH UHVRXUFH VWRFN LV QRW FRQVLGHUHG H[SOLFLWO\ DV LQ HTXDWLRQ f EXW UDWKHU LQGLUHFWO\ 7KH HTXLOLEULXP \LHOG PRGHOV SUHVHQWHG LQ WKH SUHYLRXV FKDSWHU DUH RQH VXFK FODVV RI PRGHOV &RQVLGHU WKH 6FKDHIHU IRUPXOD DV DQ H[DPSOH (TXDWLRQ f FRUn UHVSRQGV WR & .(3 LQ WKH 6FKDHIHU PRGHO ,Q WKLV FRQWH[W 3 LV HOLPLn QDWHG WKURXJK DOJHEUDLF PDQLSXODWLRQ WR GHULYH WKH 6FKDHIHU W\SH HTXLOLEULXP \LHOG IXQFWLRQ & $( %( +HUH $( %( FRUUHVSRQGV WR Ir(f LQ HTXDWLRQ f DERYH
PAGE 64
$ VHFRQG FODVV RI PRGHOV ZKLFK FRUUHVSRQG WR WKRVH GHILQHG E\ HTXDWLRQ f DUH QRQHTXLOLEULXP \LHOG IXQFWLRQV ,Q WKHVH W\SHV RI PRGHOV VWRFN HIIHFWV DUH LQFRUSRUDWHG WKURXJK VWRFKDVWLF SURFHVVHV 6SHFLILFDWLRQ RI )LVKLQJ (IIRUW &HQWUDO WR WKH GHYHORSPHQW RI DQ HPSLULFDO UHSUHVHQWDWLRQ RI WKH LWK VWDWHnV FDWFK IXQFWLRQ LV WKH QRWLRQ RI HIIHFWLYH ILVKLQJ HIIRUW 5HFDOO IURP HTXDWLRQ f WKDW HIIHFWLYH ILVKLQJ HIIRUW LV SULPDULO\ FRPSRVHG RI D QRPLQDO FRPSRQHQW DQG D ILVKLQJ SRZHU FRPSRQHQW )XUWKHU ILVKLQJ SRZHU ZDV VHHQ WR EH D IXQFWLRQ RI LQSXW OHYHOV 7KH DJJUHJDWH QDWXUH RI WKH GDWD PXVW EH FRQVLGHUHG LQ VSHFLI\LQJ WKH ILVKLQJ SRZHU HTXDWLRQ IRU WKH LA VWDWH LQ WKH *05)) $V VXFK WKH ILVKLQJ SRZHU IXQFWLRQ UHODWHV WR WKH DYHUDJH ILVKLQJ SRZHU FRUUHVSRQGn LQJ WR YHVVHOV RSHUDWLQJ RXW RI SRUWV ORFDWHG LQ HDFK VWDWH 7KH ILVKn LQJ SRZHU IXQFWLRQ IRU WKH Lrnr VWDWH LV WKXV JLYHQ E\ fHN! [P [Q L ,M f f rf W f ZKHUH GHQRWHV ILVKLQJ SRZHU LV DYHUDJH FUHZ VL]H ;A LV DYHUDJH YHVVHO VL]H JURVV UHJLVWHUHG WRQQDJHf DQG N LV D FRQVWDQW SDUDPHWHU 7KH FKRLFH RI DYHUDJH FUHZ VL]H DQG DYHUDJH YHVVHO VL]H DV WKH UHOHYDQW LQSXWV IRU XVH LQ VSHFLI\LQJ WKH ILVKLQJ SRZHU IXQFWLRQ ZDV LQ SDUW GHWHUPLQHG E\ DYDLODEOH GDWD 7KH QDWXUH RI WKH ILVKLQJ DFWLYLW\ IRU YHVVHOV LQ WKH *05)) VXJJHVW WKDW WKHVH YDULDEOHV DUH DSSURSULDWH PHDVXUHV RI ODERU DQG FDSLWDO LQSXWV ZKLFK GHWHUPLQH ILVKLQJ SRZHU KRZHYHU 7KH JHQHUDO ILVKLQJ SURFHVV LQYROYHV RSHUDWLQJ KDQG RU SRZHU
PAGE 65
GULYHQ UHHOV ZKLFK FRQWURO WKH ILVKLQJ OLQH $YHUDJH FUHZ VL]H SURYLGHV D JRRG DJJUHJDWH PHDVXUH RI JHDU FRQWDFW ZLWK WKH UHVRXUFH VWRFN VLQFH HDFK FUHZPDQ XVXDOO\ RSHUDWHV RQO\ RQH UHHO 7KH XVH RI DYHUDJH YHVVHO VL]H PHDVXUHG LQ JURVV UHJLVWHUHG WRQQDJH LV DOVR D UHDVRQDEOH UHSUHVHQn WDWLRQ RI WKH FDSLWDO LQSXW LQ WKH ILVKLQJ SRZHU HTXDWLRQ ,Q WKH UHHI ILVKHU\ IDFWRUV VXFK DV VHD FRQGLWLRQV DQG ZHDWKHU FDQ LPSDLU RU SUHn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f DV VSHFLILHG SHUPLWV D GLUHFW WHVW RI WKLV K\SRWKHVLV )LQDOO\ WKH D M SURYLGH D r FRQYHQLHQW PHDQV RI MXGJLQJ WKH UHODWLYH LPSRUWDQFH RI HDFK LQSXW ZLWK UHVSHFW WR WKH SURGXFWLRQ RI ILVKLQJ SRZHU $ SULRUL RQH ZRXOG H[SHFW WKDW DYHUDJH FUHZ VL]H VKRXOG KDYH D ODUJHU LQIOXHQFH RQ ILVKLQJ SRYHU WKDQ GRHV YHVVHO VL]H JLYHQ LWV UHODWLRQVKLS WR fJHDU FRQWDFW ZLWK WKH UHVRXUFH VWRFN
PAGE 66
7RWDO HIIHFWLYH ILVKLQJ HIIRUW LV GHILQHG WR EH WKH SURGXFW RI WKH QRPLQDO PHDVXUH RI HIIRUW DQG ILVKLQJ SRZHU ,W VKRXOG EH QRWHG WKDW ILVKLQJ LQWHQVLW\ LV DVVXPHG WR EH LPSOLFLW LQ WKH REVHUYDWLRQ LQWHUYDO RI WKH WLPH VHULHV GDWD 7KH QRPLQDO HIIRUW PHDVXUH XVHG LQ WKLV VWXG\ LV GHILQHG WR EH WKH QXPEHU RI YHVVHOV 7KH H[SUHVVLRQ IRU WRWDO HIIRUW LV WKHQ JLYHQ E\ f ZKHUH (AW LV WRWDO HIIRUW DQG 9AW UHIHUV WR WRWDO YHVVHOV LQ VWDWH L DQG WLPH W ([DPLQDWLRQ RI HTXDWLRQ f UHYHDOV WKDW WRWDO HIIRUW LQ VWDWH L DQG WLPH W LV SUHFLVHO\ WKH QXPEHU RI YHVVHOV RSHUDWLQJ LQ WKH FRUUHVSRQGLQJ UHJLRQ DQG WLPH SHULRG ZHLJKWHG E\ WKH DYHUDJH ILVKLQJ SRZHU FRUUHVSRQGLQJ WR WKRVH YHVVHOV :LWKLQ 5HJLRQ 6SHFLILFDWLRQ &RQVLGHUDWLRQV 7KH UHODWLRQVKLS LQ HTXDWLRQ f VHUYHV WR GHILQH WRWDO HIIRUW DV D IXQFWLRQ RI WKH VL]H RI D ILVKHU\ QXPEHU RI YHVVHOVf DQG WKH FRUn UHVSRQGLQJ DYHUDJH OHYHOV RI FDSLWDO DQG ODERU LQSXWV ILVKLQJ SRZHUf 7KLV HTXDWLRQ KRZHYHU LV GHILQLWLRQDO LQ QDWXUH DQG DV VXFK SUHFOXGHV GLUHFW HVWLPDWLRQ RI SDUDPHWHUV LQGHSHQGHQWO\ RI FDWFK 7KXV LW LV W K QHFHVVDU\ WR VSHFLI\ WKH L UHJLRQnV FDWFK HTXDWLRQ 7KH HPSLULFDO IRUP RI WKH FDWFK HTXDWLRQ IRU WKH LWK VWDWH LV JLYHQ E\ } f f f f f f f +HUHDIWHU WKH WHUPV WRWDO HIIRUW DQG WRWDO HIIHFWLYH ILVKLQJ HIIRUW DUH XVHG LQWHUFKDQJHDEO\
PAGE 67
ZKHUH UHSUHVHQWV FRPELQHG FDWFK RI UHG VQDSSHU DQG JURXSHU $L6f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f 0RUH SUHFLVHO\ WKH QRQn HTXLOLEULXP FDWFK HTXDWLRQV XWLOL]HG LQ VWRFN SURGXFWLRQ PRGHOV JHQHUn DOO\ DVVXPH FRQVWDQW UHWXUQV WR VFDOH DV H[KLELWHG E\ WKH LAr VWDWHnV FDWFK HTXDWLRQ $FFHSWDQFH WKDW WKH VWRFKDVWLF SURFHVV K^6fA LQ HTXDWLRQ f DGHTXDWHO\ DFFRXQWV IRU WKH HIIHFWV RI WKH UHVRXUFH VWRFN RQ FDWFK DOORZV WKH XWLOL]DWLRQ RI WKH S SDUDPHWHU WR FRQGXFW DQ DSn SUR[LPDWH WHVW RI WKH FRQVWDQW UHWXUQV DVVXPSWLRQ RI WKH VWRFN SURGXFn WLRQ PRGHOV RI 6FKDHIHU f DQG 3HOOD DQG 7RPOLQVRQ f 2 7KH VSHFLILFDWLRQ RI WKH VWRFKDVWLF QDWXUH RI $6fMW ZLOO EH GLVFXVVHG PRUH IXOO\ LQ WKH ODWWHU SRUWLRQ RI WKLV VHFWLRQ
PAGE 68
7KH FDWFK HTXDWLRQ LQ f FDQ EH H[SUHVVHG LQ WHUPV RI QRPLQDO HIIRUW DQG ILVKLQJ SRZHU E\ VXEVWLWXWLQJ HTXDWLRQ f LQWR HTXDWLRQ f IRU (BMW 7KH UHVXOWLQJ UHGXFHG IRUP FDWFK HTXDWLRQ LV &LW H[3>$nVfLW YLM [LLW ;LW ZKHUH WKH WHUP $f6fA GHQRWHV WKH IDFW WKDW WKH FRQVWDQW N LQ HTXDWLRQ f KDV EHHQ LQFRUSRUDWHG LQWR WKH VWRFKDVWLF SURFHVV $L6fA DQG WKH UHGXFHG IRUP SDUDPHWHUV DUH WWA A FWM M 7R IDFLOLWDWH IXUWKHU GLVFXVVLRQ LW LV FRQYHQLHQW WR ZULWH HTXDWLRQ f LQ DQ DOWHUn QDWLYH IRUP %\ GHILQLQJ FA ,Q &A [A ,Q DQG VR RQ HTXDWLRQ f FDQ EH ZULWWHQ LQ GRXEOH ORJ IRUP DV F LW $n6fLW 9LW OL[OLW r ;LW L W f 7KH QDWXUH RI WKH VWRFKDVWLF SURFHVV $n6f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
PAGE 69
WKH UHVRXUFH VWRFN LQ DQ\ JLYHQ WLPH SHULRG FDQ WKHQ EH JLYHQ E\ VW VWO ; A&W &WA fN ZKHUH 6W LV WKH VWRFN VL]H LQ WLPH W &W LV VXVWDLQDEOH \LHOG SURGXFHG E\ WKH UHVRXUFH VWRFN LQ WLPH W &A LV WKH FRUUHVSRQGLQJ FDWFK DQG $ LV D FRQVWDQW RI SURSRUWLRQDOLW\ 7KXV HTXDWLRQ f VWDWHV WKDW WKH VWRFN VL]H LQ WLPH W LV HTXDO WR WKH VWRFN VL]H LQ WKH SUHFHGLQJ WLPH SHULRG SOXV D SURSRUWLRQ RI WKH GLIIHUHQFH EHWZHHQ VXVWDLQDEOH \LHOG DQG FDWFK LQ WLPH W :KLOH RQO\ &WBM LV REVHUYDEOH HTXDWLRQ f VHUYHV WR VXJJHVW WKDW WKH UHVRXUFH VWRFN YDULDEOH LV DW OHDVW WR D FHUWDLQ GHJUHH DXWRFRUUHODWHG 7KXV WKH RPLVVLRQ RI WKH UHVRXUFH VWRFN YDULn DEOH LV H[SHFWHG WR JHQHUDWH VRPH V\VWHPDWLF YDULDWLRQ LQ WKH GLVWXUn EDQFHV RI WKH FDWFK HTXDWLRQ ZKLFK FDQ EH DSSUR[LPDWHG E\ DQ DXWRUHJUHVVLYH SURFHVV ,Q SDUWLFXODU WKHQ WKH VWRFKDVWLF SURFHVV FRUUHVSRQGLQJ WR WKH LrA UHJLRQnV FDWFK HTXDWLRQ LV DVVXPHG WR WDNH WKH JHQHUDO IRUP $nVfQ $L XQ ZKHUH $M LV FRQVWDQW DQG WKH GLVWXUEDQFH WHUP ,.A LV SRVWXODWHG WR EH IK FKDUDFWHUL]HG E\ D S RUGHU DXWRUHJUHVVLYH SURFHVV 2Q VXEVWLWXWLRQ RI HTXDWLRQ f LQWR HTXDWLRQ f WKH LAr VWDWHnV FDWFK HTXDWLRQ FDQ EH H[SUHVVHG DV FLW $L YLW rOL [OLW ;LW 8LW f ZKHUH 8X 3A8A SL 8LW 3L 8LW3 H DQG H LV fLW LW
PAGE 70
DVVXPHG WR EH ZKLWH QRLVH %HIRUH SURFHHGLQJ WR D PRUH GHWDLOHG VSHFLILFDWLRQ RI WKH VWRFKDVWLF SURSHUWLHV RI HTXDWLRQ f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n DEOH WR DVVXPH WKDW WKH ILVKLQJ SRZHU FRHIILFLHQWV DUH FRQVWDQW DFURVV VWDWHV LQ WKH *05)) 7KH ILVKLQJ SRZHU IXQFWLRQ LQFRUSRUDWLQJ WKLV UHVWULFWLRQ LV JLYHQ E\ (LW H[3Nf [LLW ;LI W f O } R 7KH FRQVHTXHQFHV RI VXFK D UHVWULFWLRQ DUH QRW ZLWKRXW FRPSOLFDWLRQV KRZHYHU 7KH DVVXPSWLRQ WKDW D D IRU M DQG DOO L N UHTXLUHV WKDW QRQOLQHDU UHVWULFWLRQV EH SODFHG RQ WKH UHGXFHG IRUP SDUDPHWHUV RI HTXDWLRQ f 0RUH H[SOLFLWO\ WKHVH UHVWULFWLRQV WDNH $ ZKLWH QRLVH SURFHVV LV GHILQHG DV D VHTXHQFH RI LQGHSHQGHQW LGHQWLFDOO\ GLVWULEXWHG UDQGRP YDULDEOHV ZLWK ]HUR PHDQ DQG FRQVWDQW YDULDQFH
PAGE 71
WKH IRUP RI WW J WWE IRU M DQG DOO L N 7KXV LQ WKH DEVHQFH RI DQ\ D SULRUL DVVXPSWLRQV FRQFHUQLQJ WKH A L SDUDPHWHUV DFURVV VWDWHV QRQOLQHDU UHVWULFWLRQV RQ WKH SDUDPHWHUV PXVW J EH LQFRUSRUDWHG IRU FRUUHFW HVWLPDWLRQ ,I KRZHYHU IRU DOO r L M WKLV UHVWULFWLRQ LV WULYLDOO\ VDWLVILHG DQG HVWLPDWLRQ GLIILFXOn WLHV DUH JUHDWO\ UHGXFHG 7KH SDUDPHWHUV PHDVXUH WKH PDUJLQDO UHVSRQVH RI WRWDO VWDWH FDWFK WR VPDOO FKDQJHV LQ YHVVHO QXPEHUV KROGLQJ ILVKLQJ SRZHU FRQVWDQW *LYHQ WKH KRPRJHQHLW\ RI WKH ILVKLQJ SURFHVV DFURVV VWDWHV DQG WKH IDFW WKDW WKH ILVKLQJ SRZHU IXQFWLRQ VHUYHV WR ZHLJKW YHVVHOV DFFRUGLQJ WR WKH LQSXW FKDUDFWHULVWLFV RI HDFK VWDWHnV YHVVHOV WKH DVVXPSWLRQ WKDW IRU DOO L M PD\ QRW EH DQ XQUHDVRQDEOH DVVXPSWLRQ WR PDNH $V VWDWHG DERYH PDNLQJ WKH DVVXPSWLRQ c IRU DOO L M LQVXUHV WKDW WKH QRQOLQHDU UHVWULFWLRQV RQ WKH UHGXFHG IRUP SDUDPHWHUV DUH PHW 7KHUH LV DOVR DQ DGGLWLRQDO JDLQ UHDOL]HG E\ DVVXPLQJ WKDW WKH FDWFK HTXDWLRQV IRU WKH *05)) SURGXFLQJ VWDWHV WR WDNH WKH IRUP nLW $ Y LW f ; LW [LW X LW f 6WDWHG LQ WKH PDQQHU DERYH WKH GDWD RQ YHVVHOV FUHZ VL]HV DQG YHVVHO VL]HV FDQ EH SRROHG DFURVV VWDWHV 1RW RQO\ GRHV VXFK SRROLQJ JHQHUDWH FRQVLGHUDEO\ PRUH YDULDWLRQ LQ WKH YHFWRUV RI UHJUHVVRUV ZKLFK DLGV LQ SDUDPHWHU HVWLPDWLRQ LW DOVR FUHDWHV D VL]HDEOH JDLQ LQ GHJUHHV RI IUHHGRP 7KH ILQDO VSHFLILFDWLRQ RI WKH VWDWH FDWFK HTXDWLRQV JLYHQ LQ HXTDWLRQ f LOOXVWUDWHV WKH FURVV HTXDWLRQ UHVWULFWLRQ FRUUHVSRQGLQJ J 5HFDO WKDW LU LW IROORZV WKDW LU L D IRU DOO L M ,I D L L7MN IRU DOO L M N -N IRU DOO N
PAGE 72
WR WKH HTXDOLW\ RI WKH UHGXFHG IRUP DQG VWUXFWXUDOf SDUDPHWHUV DFURVV VWDWHV ,W VKRXOG EH QRWHG KRZHYHU WKDW WKH PHDQ RI HDFK UHJLRQnV VWRFKDVWLF SURFHVV $A LV XQFRQVWUDLQHG DFURVV HTXDWLRQV 7KH VSHFLILn FDWLRQ DQG LQWUHSUHWDWLRQ RI WKH $ SDUDPHWHUV LQ SDUWLFXODU DQG WKH VWRFKDVWLF SURFHVVHV FKDUDFWHUL]LQJ WKH UHJUHVVLRQ GLVWXUEDQFH LQ JHQHUDO SURYLGH D FRQYHQLHQW LQWURGXFWLRQ WR WKH GLVFXVVLRQ FRQFHUQLQJ WKH FKRLFH RI WKH DSSURSULDWH HVWLPDWRU 7KH JHRJUDSKLF ORFDWLRQ RI WKH SULPDU\ UHHI ILVK VWRFNV DUH GHSLFWHG LQ )LJXUH 7KHUH LV VRPH LQGLFDWLRQ DOWKRXJK WKHUH LV QRW DQ RYHUZKHOPLQJ DPRXQW RI HYLGHQFH WKDW WKH UHHI ILVK VWRFNV GR QRW H[KLELW D JUHDW GHDO RI PLJUDWRU\ EHKDYLRU *0)0& f 7KLV IDFW WDNHQ LQ FRQMXQFWLRQ ZLWK WKH ODUJH JHRJUDSKLF GLVSHUVLRQ RI ILVKLQJ JURXQGV VXJJHVWV WKDW WKH *05)) LV FRPSRVHG RI VHYHUDO ELRORJLFDOO\ LQGHSHQGHQW VWRFNV RI UHHI ILVK $GGLWLRQDO LQIRUPDWLRQ RQ WKH JHQHUDO ILVKLQJ ORFDWLRQV RI YHVVHOV RULJLQDWLQJ IURP YDULRXV VWDWHVn SRUWV *0)0& f LQGLFDWHV WKDW YHVVHOV RULJLQDWLQJ IURP GLIIHUHQW VWDWHV ILVK RQ FRPPRQ JURXQGV 7KLV LQIRUPDWLRQ VXJJHVWV HDFK VWDWH FDWFK IXQFWLRQ VKRXOG KDYH D VWRFKDVWLF SURFHVV GRPLQDWHG E\ WKH VWRFN PRVW IUHTXHQWO\ ILVKHG DQG WKDW WKHVH SURFHVVHV VKRXOG EH FRQWHPSRUDQHRXVO\ FRUUHODWHG GXH WR WKH LQWHUPL[LQJ RI YHVVHOV IURP GLIIHUHQW VWDWHV 7KXV WKH RYHUDOO VWUXFWXUH RI WKH V\VWHP RI FDWFK HTXDWLRQV LV FKDUn DFWHUL]HG E\ D V\VWHP RI VHHPLQJO\ XQUHODWHG UHJUHVVLRQ HTXDWLRQV 685f ZLWK FURVV HTXDWLRQ SDUDPHWHU UHVWULFWLRQV DQG DXWRUHJUHVVLYH GLVWXUEDQFHV 7KH LQIRUPDWLRQ DERYH DOVR VHUYHV WR JLYH DQ LQWHUHVWLQJ LQWHUSUHn WDWLRQ WR WKH $ SDUDPHWHUV 7KHVH SDUDPHWHUV VHUYH WR GHWHUPLQH WKH ORFDWLRQ RI WKH FDWFK HTXDWLRQV IRU HDFK VWDWH LQ LQSXWRXWSXW VSDFH
PAGE 73
)LJXUH 3ULQFLSDO ILVKLQJ JURXQGV LQ WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ *LYHQ WKDW DOO RWKHU WHFKQLFDO SDUDPHWHUV DUH FRQVWUDLQHG WR EH FRQVWDQW DFURVV VWDWHV WKH $ PD\ VHUYH WR LQGLFDWH WKH UHODWLYH VL]H RU GHQVLn WLHV RI WKH SULPDU\ VWRFNV ILVKHG E\ YHVVHOV IRU HDFK VWDWH )XUWKHUPRUH WHVWLQJ WKH GLIIHUHQFH EHWZHHQ WKH $ FRQVWLWXWHV DQ DSSUR[LPDWH WHVW IRU WKH GHJUHH WR ZKLFK YDULRXV VWDWHVn YHVVHOV ILVK FRPPRQ JURXQGV 7KH UHDVRQLQJ EHKLQG WKLV LV WKDW LI YHVVHOV IURP GLIn IHUHQW VWDWHV ILVK FRPPRQ JURXQGV WKH VWRFN GHQVLWLHV VKRXOG HYHQWXDOO\ EHFRPH HTXDO 7KLV FDQ EH LQYHVWLJDWHG E\ WHVWLQJ WKH K\SRWKHVLV $A $ IRU DOO L M 8
PAGE 74
&KRLFH RI (VWLPDWRU IRU WKH &DWFK (TXDWLRQV $V D SUHOXGH WR WKH GLVFXVVLRQ UHJDUGLQJ WKH HVWLPDWLRQ RI WKH FDWFK HTXDWLRQV LW LV FRQYHQLHQW WR SODFH WKH V\VWHP RI HTXDWLRQV LQWR PDWUL[ IRUP 7KLV LV DFFRPSOLVKHG E\ & ; 8 f ZKHUH & 17 [ YHFWRU RI ORJJHG FDWFK YDULDEOHV N 1f [ YHFWRU RI SDUDPHWHUV WR EH HVWLPDWHG DQG 8 17 [ YHFWRU RI GLVWXUEDQFHV ZLWK (8 e (88 7KH 17 [ N 1f PDWUL[ RI UHJUHVVRUV LV RI WKH IRUP ; >' ;@ Df ZLWK WKH 17 [ 1 PDWUL[ FRPSRVHG RI DSSURSULDWHO\ GHILQHG VWDWH GXPP\ YDULDEOHV DQG ; FRUUHVSRQGLQJ WR WKH 17 [ PDWUL[ RI ORJJHG YDOXHV RI UHJUHVVRUV JLYHQ LQ HTXDWLRQ f 6SHFLILFDWLRQ RI WKH GLVWUXEDQFH WHUP LV JLYHQ LQ JHQHUDO IRUP WR HPSKDVL]H WKH FRYDULDQFH PDWUL[ LV QRQVSKHULFDO 7KH SUHFLVH IRUP LV FRQGLWLRQHG E\ WKH H[DFW IRUP RI WKH DXWRUHJUHVVLYH SURFHVVHV FRUUHVSRQGLQJ WR HDFK VWDWHfV GLVWXUEDQFH YHFWRU (VWLPDWLRQ RI WKH FDWFK HTXDWLRQ SDUDPHWHUV PXVW EH GRQH LQ WZR EDVLF VWHSV 7KH ILUVW VWHS LQYROYHV WKH LGHQWLILFDWLRQ DQG HVWLPDWLRQ RI WKH DXWRUHJUHVVLYH SURFHVVHV IRU HDFK VWDWH JHQHUDWHG E\ WKH XQREVHUYn DEOH UHVRXUFH VWRFN 2QFH WKLV LV DFFRPSOLVKHG WKH DSSURSULDWH IRUP RI WKH FRYDULDQFH PDWUL[ RI WKH GLVWXUEDQFHV FDQ EH DVFHUWDLQHG DQG WKH DSSURSULDWH HVWLPDWRU IRU WKH UHGXFHG IRUP SDUDPHWHUV GHULYHG
PAGE 75
'XH WR WKH VPDOO VDPSOH VL]H RI HDFK FURVV VHFWLRQ 7 f PDQ\ RI WKH VWDQGDUG WLPH VHULHV LGHQWLILFDWLRQ WHFKQLTXHV IRU GHWHUPLQLQJ WKH DXWRUHJUHVVLYH RUGHU SDUDPHWHU DUH XQVDWLVIDFWRU\ 7KLV PDLQO\ UHVXOWV IURP WKH IDFW WKDW PRVW VWDWLVWLFDO WHVWV RQ WKH RUGHU SDUDPHWHU DUH RQO\ DV\PSWRWLFDOO\ YDOLG DQG XWLOL]H D YDULDQFH PHDVXUH WKDW LV LQYHUVHO\ SURSRUWLRQDO WR WKH VDPSOH VL]H 7KHUH DUH KRZHYHU VHYHUDO WHFKQLTXHV VXFK DV $NDLNHnV f )3( FULWHULRQ ZKLFK GR QRW VXIIHU IURP WKLV OLPLWDWLRQ 6HYHUDO DOWHUQDWLYH LGHQWLILFDWLRQ SURFHGXUHV ZHUH XVHG LQ WKH LGHQWLILFDWLRQ RI WKH UHVLGXDO DXWRUHJUHVVLYH SURFHVV 7KHVH SURFHGXUHV DUH RXWOLQHG LQ $SSHQGL[ ( 7KH HVWLPDWHG UHVLGXDOV XVHG LQ WKH LGHQWLILFDWLRQ SURFHVV ZHUH JHQHUDWHG E\ DSSO\LQJ D WZR VWDJH $LWNHQnV HVWLPDWLRQ SURFHGXUH WR HTXDWLRQ f 0RUH SUHFLVHO\ WKH 17 [ YHFWRU RI UHVLGXDO HVWLPDWHV LV JLYHQ E\ & ;J f ZKHUH ;]aA D7f ;ff ;r]aA D ,f &f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n WLF SURFHVV RI WKH LA UHJLRQ E\
PAGE 76
S 8 L H LW LWO LW f VWRFKDVWLF VSHFLILFDWLRQ RI 8 LQ HTXDWLRQ f LV WKHQ JLYHQ E\ (XLWf m Df (XLW9 mX Ef (HLWHMV! W V W I V Ff (8LR9 ALG &O &O Gf IRU L M 1 DQG A 1 f DQG HLW A 1 $V D UHVXOW RI WKH UHVLGXDO LGHQWLILFDWLRQ SURFHVV WKH V\VWHP RI FDWFK HTXDWLRQV FDQ EH FKDUDFWHUL]HG DV D V\VWHP RI VHHPLQJO\ XQUHODWHG UHJUHVVLRQ HTXDWLRQV ZLWK FURVV HTXDWLRQ SDUDPHWHU UHVWULFWLRQV )XUWKHUPRUH WKH GLVWXUEDQFHV H[KLELW ILUVW RUGHU DXWRUHJUHVVLRQ $ JUHDW GHDO RI OLWHUDWXUH SHUWDLQLQJ WR WKH HVWLPDWLRQ RI WKLV W\SH RI HTXDWLRQ V\VWHP LV DYDLODEOH 0RVW QRWDEOH LV WKH ZRUN GRQH E\ 3DUNV f .PHQWD f .PHQWD DQG *LOEHUW f DQG =HOOQHU f 7KH PRVW LPSRUWDQW RI WKHVH LQVRIDU DV WKLV VWXG\ LV FRQFHUQHG LV WKH ZRUN GRQH E\ .PHQWD DQG *LOEHUW RQ WKH VPDOO VDPSOH SURSHUWLHV RI DOWHU QDWLYH HVWLPDWRUV IRU V\VWHPV RI HTXDWLRQV VLPLODU LQ QDWXUH WR WKH FDWFK HTXDWLRQV DERYH $V PHQWLRQHG SUHYLRXVO\ GDWD RQ WKH FDWFK HTXD WLRQ YDULDEOHV LV OLPLWHG UHVXOWLQJ LQ UDWKHU VPDOO VDPSOH VL]HV 7KH IRUP RI 8 LV JLYHQ E\ 8 f§ e 8 M fff} 8\ f f f f m f f
PAGE 77
*LYHQ WKDW DOO HVWLPDWRUV IRU WKH DERYH HTXDWLRQ V\VWHP SRVVHVVHV RQO\ DV\PSWRWLF SURSHUWLHV LW LV DSSURSULDWH WR XVH D UHODWLYH HIILFLHQF\ FULWHULRQ LQ VPDOO VDPSOHV DV D EDVLV IRU FKRRVLQJ WKH EHVW HVWLPDWRU IRU WKH V\VWHP RI FDWFK HTXDWLRQV JLYHQ LQ HTXDWLRQ f 'UDZLQJ RQ WKH UHVXOWV RI 0RQWH &DUOR VWXGLHV FRQGXFWHG E\ .PHQWD DQG *LOEHUW f D IRXU VWDJH $LWNHQnV HVWLPDWRU )6$(f ZDV FKRVHQ DV WKH DSSURSULDWH HVWLPDWRU 7KH IRUPDWLRQ RI WKLV HVWLPDWRU SURFHHGV LQ WZR EDVLF VWHSV *LYHQ WKDW WKH GLVWXUEDQFHV LQ HDFK HTXDWLRQ LQ WKH V\VWHP DUH NQRZQ WR IROORZ D ILUVW RUGHU DXWRUHJUHVVLYH SURFHVV WKH ILUVW VWHS LQYROYHV WKH DSSOLFDWLRQ RI WKH WZR VWDJH $LWNHQnV HVWLPDWRU WR HTXDWLRQ f WR JHQHUDWH D VHTXHQFH RI HVWLPDWHG UHVLGXDOV IRU HDFK VWDWH FDWFK HTXDWLRQ 7KHVH UHVLGXDOV FRUUHVSRQG WR WKRVH JLYHQ LQ HTXDWLRQ f 7KH XVH RI WKLV IRXU VWDJH HVWLPDWRU LV WKH UHDVRQ WKDW WKH UHVLGXDOV HVWLPDWHG XVLQJ HTXDWLRQ f ZHUH XVHG LQ WKH RUGHU SDUDPHWHU LGHQWLILFDWLRQ 7KH HVWLPDWLRQ RI WKH DXWRUHJUHVVLYH SDUDPHn WHUV LV DFFRPSOLVKHG E\ S L 1 = W 8 8 LW L 7 W 1 = W O L 1 f Y IFK WK ZKHUH 8 LV WKH HVWLPDWHG UHVLGXDO IRU WKH L VWDWH DQG W WLPH LW SHULRG GHILQHG LQ HTXDWLRQ f 7KH VHFRQG VWHS LQ GHULYLQJ WKH )6$( LQYROYHV D VHFRQG DSSOLFDWLRQ RI WKH $WLNHQnV WZR VWDJH HVWLPDWRU %HIRUH WKLV HVWLPDWRU LV DSSOLHG KRZHYHU WKH GDWD LV WUDQVIRUPHG E\ r  &LO L f f f Df
PAGE 78
LW 6nW SL &LW L 1 W 7 Ef r MLO f SL ;MLO DOO L M Ff r r fMLW [MLW SL [MLW DOO L M W 7 Gf ZKHUH F DQG [ DUH GHILQHG DV LQ HTXDWLRQ Df ,Q PDWUL[ IRUP & X WKH WUDQVIRUPHG V\VWHP FDQ EH ZULWWHQ DV r r r & ; 8 f r r ZKHUH & LV DQ 17 [ YHFWRU RI WUDQVIRUPHG ORJJHG FDWFK YDOXHV DQG ; LV DQ 17 [ 1 .f PDWUL[ RI WUDQVIRUPHG UHJUHVVRUV LQ ORJ IRUP 7KH HIIHFW RI WKH WUDQVIRUPDWLRQ LV WR UHPRYH WKH DXWRUHJUHVVLYH HIIHFWV LH LW r IURP WKH 17 [ GLVWXUEDQFH YHFWRU 8 7KXV (8 8 D ,M ZKHUH FRUUHVSRQGV WR WKH FRQWHPSRUDQHRXV FRYDULDQFH PDWUL[ RI WKH WUDQVIRUPHG GLVWXUEDQFHV 7R HVWLPDWH e RUGLQDU\ OHDVW VTXDUHV ZDV DSSOLHG WR HTXDWLRQ f WR \LHOG r I! f f f r1 r r r1 r1 f f f f f f r1 r11 f 8 A nN r ZKHUH ; r r r‘ & ; f (VWLPDWHV RI WKH S ZHUH FDOFXODWHG E\ L -
PAGE 79
8 Dr N f ZKHUH 8A} W 7 LV WKH HVWLPDWHG UHVLGXDO VHTXHQFH FRUUHVSRQG LQJ WR WKH LrA VWDWH 7KH HVWLPDWHG FRYDULDQFH PDWUL[ LV IRUPHG E\ $ UHSODFLQJ ZLWK M! LQ HTXDWLRQ f )LQDOO\ WKH )6$( IRU WKH 2 f V\VWHP RI FDWFK HTXDWLRQ LV JLYHQ E\ ?L ; ‘ D ,f ; f rn [ r ; nD,f& f ZKHUH LV DQ LGHQWLW\ PDWUL[ ZLWK UDQN 7 )XUWKHUPRUH WKH HVWLPDWHG YDULDQFHFRYDULDQFH PDWUL[ IRU S LV JLYHQ E\ &29 S ;rn D ,f ;rf B f 7KH SUHFLVH VWDWLVWLFDO SURSHUWLHV RI S DUH VRPHZKDW GLIILFXOW WR DVFHUWDLQ 7KH SULPDU\ UHDVRQ IRU WKLV UHODWHV WR WKH VWRFKDVWLF VSHFLILFDWLRQ RI WKH V\VWHP RI HTXDWLRQV 8QGHU WKH DVVXPSWLRQ WKDW WKH WUXH VWRFKDVWLF VSHFLILFDWLRQ LV ILUVW RUGHU DXWRUHJUHVVLRQ ZLWK FRQ WHPSRUDQHRXV FRUUHODWLRQ WKH DV\PSWRWLF FRYDULDQFH PDWUL[ IRU S LV FRQVLVWHQW DQG DV\PSWRWLFDOO\ QRUPDO DQG HIILFLHQW 8QIRUWXQDWHO\ WKH DFWXDO VWRFKDVWLF VSHFLILFDWLRQ RI WKH V\VWHP FRQVWLWXWHV D SUHWHVW 7KLV VHULRXVO\ FORXGV WKH SUHFLVH VWDWLVWLFDO SURSHUWLHV RI WKH HVWLn PDWHG FRHIILFLHQWV 3ULFH (TXDWLRQ 6SHFLILFDWLRQ DQG (VWLPDWLRQ 7KH ODWWHU SDUW RI &KDSWHU ,, SUHVHQWHG D VFHQDULR LQ ZKLFK SURn GXFLQJ VWDWHV IDFHG D YDULDEOH SURGXFW SULFH 7KH SULFH IDFHG E\ SURGXFHUV LQ DQ\ JLYHQ VWDWH ZDV GHSHQGHQW RQ WKH RXWSXWV RI DOO
PAGE 80
RWKHU VWDWHV 7KH SXUSRVH RI WKLV VHFWLRQ LV WR SUHVHQW WKH VSHFLILFDn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f 2YHU WKLV SHULRG ERWK KDYH H[KLELWHG 2 7KH WHUP SULFH LQ WKLV VHFWLRQ SHUWDLQV WR WKH QRPLQDO GRFNVLGH RU H[YHVVHO SULFH
PAGE 81
IDLUO\ FRQVLVWHQW SULFH LQFUHDVHV %RWK VSHFLHV KDYH H[KLELWHG VLPLODUL WLHV LQ SURGXFW IRUP ZKHQ VKLSSHG IURP GRFNVLGH DOWKRXJK WKH W\SH DQG ORFDWLRQ RI WKH PDUNHWV WR ZKLFK WKH\ DUH VHQW GLIIHU ,Q SHUFHQW RI JURXSHU DQG SHUFHQW RI DOO UHG VQDSSHU WDNHQ LQ WKH *05)) ZHUH VKLSSHG IURP GRFNVLGH LQ IUHVK LFHG IRUP *0)0& f 6LPLODUO\ RYHU KDOI RI HDFK RI WKHVH VSHFLHV ZDV VKLSSHG WR ZKROHVDOHUV ,Q WHUPV RI PDUNHW ORFDWLRQ SHUFHQW RI WKH UHG VQDSSHU FDXJKW ZDV VKLSSHG WR 1RUWKHDVWHUQ PDUNHWV DQG SHUFHQW ZDV VKLSSHG WR 6RXWKn HDVWHUQ PDUNHWVA ,Q FRQWUDVW RQO\ SHUFHQW RI WKH JURXSHU FDWFK ZHQW WR 1RUWKHDVWHUQ PDUNHWV ZKLOH SHUFHQW ZDV VKLSSHG WR PDUNHWV LQ WKH 6RXWKHDVW $SSHQGL[ )f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f 7KXV RQO\ WKH SULFH HTXDWLRQ IRU )ORULGD DSSHDUV VXVFHSWDEOH WR VLJQLILFDQW DJJUHJDWLRQ ELDV J ,QFOXGHV 1HZ
PAGE 82
7KH GHJUHH WR ZKLFK WKLV ELDV LV LQFXUUHG UHVWV RQ WKH VLPLODULW\ RU GLVVLPLODULW\ RI WKH SULFH UHVSRQVHV WR FKDQJHV LQ FDWFK IRU HDFK VSHFLHV 7R VHH WKLV OHW 3NW DRN
PAGE 83
7KH PDLQ SURGXFW IRUP RI UHHI ILVK ZKHQ VKLSSHG IURP GRFNVLGH LV IUHVK LFHG 7KXV UHHI ILVK FDQ EH FRQVLGHUHG WR EH QRQVWRUDEOH SURGXFWV )XUWKHUPRUH WKH GLUHFWLRQ RI FDXVDOLW\ LV VXFK WKDW TXDQWLW\ SURGXFHG GHWHUPLQHV SULFH DW GRFNVLGH 7KH LPSOLFDWLRQ RI WKLV LV WKDW WKH SULFH GHPDQGf HTXDWLRQV VKRXOG EH VSHFLILHG LQ SULFH GHSHQGHQW IRUP 7KLV VSHFLILFDWLRQ LV KDUPRQLRXV ZLWK ILVKHU\ GHPDQG DQDO\VHV FRQGXFWHG E\ RWKHUV &DWR 'ROO f :LWKLQ WKLV FRQWH[W SULFH FDQ EH FRQVLGHUHG DV GHWHUPLQHG E\ IDFWRUV VXFK DV TXDQWLW\ SURn GXFHG TXDQWLW\ RI VXEVWLWXWH SURGXFWV LQFRPH DQG WDVWHV DQG SUHIHUHQFHV RI FRQVXPHUV 7RPHN DQG 5RELQVRQ f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f KDYH VKRZQ WKDW )ORULGD LV WKH GRPLQDQW SURGXFHU LQ WKH *05)) 7KHLU ILQGLQJV VXJJHVW WKDW )ORULGD LV WKH RQO\ VWDWH ZKLFK KDV D VLJQLILFDQW HIIHFW RQ SULFHV LQ RWKHU SDUWLFLSDWLQJ VWDWHV 7KLV UHVXOW LV QRW VXUSULVLQJ LQ WKDW )ORULGDnV FDWFK VLQFH KDV DFFRXQWHG DQQXDOO\ IRU DQ DYHUDJH RI SHUFHQW RI DOO UHG VQDSSHU DQG SHUFHQW RI DOO JURXSHU FDXJKW LQ WKH *XOI RI 0H[LFR UHJLRQ )XUWKHUPRUH LW DSSHDUV WKDW DOO VWDWHV DUH QHW H[SRUWHUV RI UHHI ILVK 6LQFH WKH *05)) KDV DFFRXQWHG DQQXDOO\ IRU DSSUR[LPDWHO\ SHUFHQW RI DOO UHG VQDSSHU DQG SHUFHQW RI DOO JURXSHU SURGXFHG LQ WKH 8QLWHG 6WDWHV 86 10)6 f 'DWD IRU DOVR LQGLFDWH WKDW
PAGE 84
SHUFHQW DQG SHUFHQW RI WKH UHG VQDSSHU DQG JURXSHU FDWFK UHVSHFWLYHO\ ZDV VKLSSHG WR DUHDV RWKHU WKDQ WKH *05)) VWDWHV $SSHQGL[ )f 7KH LPSOLFDWLRQ RI WKLV GDWD LV WKDW WKHUH VKRXOG EH YHU\ OLWWOH LI DQ\ LQWHUUHJLRQDO WUDGH LQ UHHI ILVK DPRQJ *05)) VWDWHV 7KLV LV VLJQLILFDQW LQ WKDW LW LPSOLHV WKH DEVHQFH RI DQ\ V\VWHPDWLF SULFH GLIn IHUHQWLDOV DFURVV VWDWHV EDVHG RQ WUDQVSRUWDWLRQ FRVWV WKXV VLPSOI\LQJ WKH SULFH PRGHO JUHDWO\ 7KH LQIRUPDWLRQ DERYH VHUYHV WR SURYLGH WKH EDVLV IRU VSHFLILFDWLRQ RI WKH HPSLULFDO SULFH HTXDWLRQV 7KH SULFH HTXDWLRQ IRU )ORULGD LV DVVXPHG WR KDYH WKH IRUP 3OW < < &OW \@W HOW f ZKHUH LV WKH H[YHVVHO )ORULGD SULFH RI UHHI ILVK LV WKH FRUUHVSRQGLQJ FDWFK DQG W LV D WLPH WUHQG YDULDEOH 6SHFLILFDWLRQ RI WKH GLVWXUEDQFH FRPSRQHQW HA LV GLVFXVVHG EHORZ )RU RWKHU VWDWHV WKH JHQHUDO IRUP RI WKH SULFH HTXDWLRQ IRU WKH LAr VWDWH LV JLYHQ E\ 3LW nn2L fnOL&LW AL&LW
PAGE 85
UHODWHV EDFN WR GDWD OLPLWDWLRQV DQG WKH XWLOL]DWLRQ RI WKH SULFH RI UHHI ILVK DV WKH GHSHQGHQW YDULDEOH $OWKRXJK JURXSHU DQG UHG VQDSSHU DUH YHU\ VLPLODU SURGXFWV DW GRFNVLGH WKH\ WHQG WR PRYH WKURXJK GLIn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n PDWRU IRU HTXDWLRQV f DQG f LV RULHQWHG WRZDUG REWDLQLQJ GHVLUDEOH VWDWLVWLFDO SURSHUWLHV IRU WKH SDUDPHWHU HVWLPDWHV &KRRVLQJ WKH DSSURSULDWH HVWLPDWRU ODUJHO\ UHVWV RQ WKH VWRFKDVWLF VSHFLILFDWLRQV RI WKH GLVWXUEDQFH WHUPV LQ HTXDWLRQV f DQG f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n WXUEDQFHV RI WKH SULFH HTXDWLRQV LV DQWLFLSDWHG 7KH GLVWXUEDQFH VSHFLILFDWLRQ IRU WKH SULFH HTXDWLRQV LQ HTXDWLRQV f DQG f LV JLYHQ E\
PAGE 86
(HQf IRU DOO L W Df (HLWHMV! f W W I V DQG V DQG DOO L M DOO L M Ef 7KH VWRFKDVWLF VSHFLILFDWLRQV JLYHQ LQ HTXDWLRQV Df DQG Ef VHUYH WR FKDUDFWHUL]H WKH SULFH HTXDWLRQV DV D V\VWHP RI VHHPLQJO\ XQn UHODWHG UHJUHVVLRQ HTXDWLRQV =HOOQHU f KDV VKRZQ WKDW WKH EHVW HVWLPDWRU IRU WKLV W\SH RI HTXDWLRQ V\VWHP LQ WHUPV RI UHODWLYH HIILn FLHQF\ LV D WZRVWDJH $LWNHQnV HVWLPDWRU 7KLV HVWLPDWRU ZDV XWLOL]HG LQ HVWLPDWLQJ WKH SULFH HTXDWLRQ SDUDPHWHUV %HIRUH SURFHHGLQJ ZLWK D SUHVHQWDWLRQ RI WKLV HVWLPDWRU LW LV FRQYHQLHQW WR SODFH WKH SULFH HTXDWLRQV LQ PDWUL[ IRUP /HW 3 EH DQ 17 [ YHFWRU RI SULFHV =c EH 7 [ Nc PDWUL[ RI H[RJHQRXV YDULDEOHV FRUUHVSRQGLQJ WR WKH LQGHSHQGHQW YDULDEOHV JLYHQ LQ HTXDWLRQV f DQG f IRU WKH LAr UHJLRQ DQG H EH DQ 17 [ YHFWRU RI GLVWXUEDQFHV 7KH SULFH HTXDWLRQV LQ PDWUL[ IRUP DUH WKHQ JLYHQ E\ 3 =< H f ZKHUH = LV D 17 [ ].f EORFN GLDJRQDO PDWUL[ ZLWK = L 1 FRQVWLWXWLQJ WKH GLDJRQDO EORFNV )XUWKHU (Hf DQG (H Hnf Q D ,M ZKHUH A LV D 7 [ 7 LGHQWLW\ PDWUL[ DQG KDV WKH IRUP f 7KH $LWNHQnV HVWLPDWRU IRU \ LV WKHQ JLYHQ E\ r U f r DO1 r r r D1 1 f f f m A f D1 D11
PAGE 87
< =nM D ,7f=fB =nB D ,7f 3f f $OWKRXJK WKLV HVWLPDWRU LV FRQVLVWHQW DV\PSWRWLFDOO\ QRUPDO DQG HIILn FLHQW .PHQWD f LW LV QRW IHDVLEOH LQ WKDW Q LV XQNQRZQ 7KH $ FRYDULDQFH PDWUL[ FDQ KRZHYHU EH HVWLPDWHG DV IROORZV /HW HA EH WKH HVWLPDWHG UHVLGXDOV IURP WKH RUGLQDU\ OHDVW VTXDUHV UHJUHVVLRQ RI WKH SULFH HTXDWLRQ IRU WKH LAr VWDWH DORQH 7KH D FDQ WKHQ EH HVWLPDWHG ‘ X E\ DLM f %\ UHSODFLQJ D LQ HTXDWLRQ f ZLWK D WKH WZRVWDJH $LWNHQnV HVWLPDWRU 76$(f IRU \ \ =rLLB ‘ ,7f =f &AB m ,7f 3f f LV REWDLQHG =HOOHU f KDV VKRZQ WKDW \ KDV WKH VDPH DV\PSWRWLF $ SURSHUWLHV DV \ JLYHQ LQ HTXDWLRQ f
PAGE 88
&+$37(5 ,9 (03,5,&$/ 5(68/76 3UHYLRXV FKDSWHUV LQ WKLV VWXG\ KDYH GHYHORSHG D WKHRUHWLFDO PRGHO LQGLFDWLYH RI WKH *05)) DQG SUHVHQWHG WKH VSHFLILFDWLRQ RI WKH HPSLULFDO HTXDWLRQV WR EH XWLOL]HG LQ DQDO\]LQJ WKH ILVKHU\ 7KH YDULRXV HVWLn PDWRUV IRU WKH HPSLULFDO HTXDWLRQ ZHUH DOVR GLVFXVVHG DQG GHULYHG 7KLV FKDSWHU SUHVHQWV D GLVFXVVLRQ RI WKH HPSLULFDO UHVXOWV REWDLQHG 7KH ILUVW VHFWLRQ FRQWDLQV DQ DQDO\VLV RI WKH HVWLPDWHG VWDWH FDWFK HTXDWLRQV 7KH IROORZLQJ VHFWLRQ SUHVHQWV D VLPLODU DQDO\VLV IRU WKH HVWLPDWHG VWDWH SULFH HTXDWLRQV 7KH WKLUG VHFWLRQ GHYHORSV WKH FRPn SOHWH UHHI ILVKHU\ PRGHO XVHG WR GHWHUPLQH PD[LPXP HFRQRPLF \LHOG )XUWKHU WKH UHVXOWV RI SURILW PD[LPL]DWLRQ LQ WKH ILVKHU\ DUH SUHVHQWHG DQG GLVFXVVHG LQ GHWDLO 7KH ILQDO VHFWLRQ RI WKLV FKDSWHU FRPSDUHV WKH UHVXOWV RI WKLV DQDO\VLV ZLWK WKRVH REWDLQHG E\ WKH *XOI RI 0H[LFR )LVKHU\ 0DQDJHPHQW &RXQFLO $QDO\VLV RI 3URGXFWLRQ LQ WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ 7KH VWDWH FDWFK HTXDWLRQV ZHUH FKDUDFWHUL]HG LQ HTXDWLRQ f DV D V\VWHP RI VHHPLQJO\ XQUHODWHG UHJUHVVLRQ HTXDWLRQV ZLWK DXWRUHJUHVVLYH GLVWXUEDQFHV DQG FURVV HTXDWLRQ SDUDPHWHU UHVWULFWLRQV $V VXFK D IRXU VWDJH $LWNHQnV HVWLPDWRU )6$(f ZDV XWLOL]HG LQ HVWLPDWLQJ WKH FDWFK HTXDWLRQ SDUDPHWHUV 7R D FHUWDLQ H[WHQW WKH YDOLGLW\ RI WKH D SULRUL VSHFLILFDWLRQ RI WKH FDWFK HTXDWLRQV FDQ EH PHDVXUHG E\ WKH JDLQV LQ
PAGE 89
HIILFLHQF\ REWDLQHG E\ XVLQJ WKH )6$( DV RSSRVHG WR WKH RUGLQDU\ OHDVW VTXDUHV ZLWK GXPP\ YDULDEOHV 2/6'9f HVWLPDWRU $Q H[DPLQDWLRQ RI WKH SDUDPHWHU HVWLPDWHV REWDLQHG IURP WKH WZR HVWLPDWRUV LQGLFDWHV WKDW ERWK HVWLPDWRUV \LHOG SDUDPHWHU YDOXHV RI VLPLODU PDJQLWXGH ZLWK WKH H[FHSWLRQ RI WKH SDUDPHWHU HVWLPDWH IRU YHVVHO VL]H 7DEOHV DQG f )XUWKHUPRUH ERWK HVWLPDWRUV \LHOG SDUDPHWHU HVWLPDWHV RI UHDVRQDEOH PDJQLWXGH DQG WKH H[SHFWHG VLJQ 7KH JDLQV IURP XVLQJ WKH V\VWHPV HVWLPDWRU EHFRPH DSSDUHQW ZKHQ WKH VWDQGDUG HUURUV RI WKH SDUDPHWHU HVWLPDWHV DUH H[DPLQHG $OO VWDQGDUG HUURUV REWDLQHG XWLOL]LQJ WKH )6$( DUH VXEVWDQWLDOO\ ORZHU WKDQ WKH FRUUHVSRQGn LQJ HVWLPDWHG VWDQGDUG HUURUV REWDLQHG IURP WKH 2/6'9 HVWLPDWRU ZLWK WKH H[FHSWLRQ RI WKH VWDQGDUG HUURU RI WKH YHVVHO VL]H SDUDPHWHU)LQDOO\ H[DPLQDWLRQ RI WKH HVWLPDWHG DXWRUHJUHVVLYH SDUDPHWHUV LOOXVWUDWHV WKDW WKH HVWLPDWHG HTXDWLRQV IRU DOO VWDWHV H[FHSW /RXLVLDQD DUH FKDUDFn WHUL]HG E\ VLJQLILFDQW ILUVW RUGHU DXWRUHJUHVVLRQ 7DEOH f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
PAGE 90
7DEOH 2UGLQDU\ OHDVW VTXDUHV ZLWK GXPP\ YDULDEOHV SDUDPHWHU HVWLPDWHV IRU WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ FDWFK HTXDWLRQV 'HSHQGHQW YDULDEOH ,QWHUFHSW eQ YHVVHOV eQ FUHZ VL]H eQ YHVVHO VL]Hr eQ )ORULGD FDWFK 5 f f f f eQ $ODEDPD FDWFK f f f f eQ 0LVVLVVLSSL FDWFK f f f f eQ /RXLVLDQD FDWFK f f f f eQ 7H[DV FDWFK f f f f D&DWFK LV PHDVXUHG LQ WKRXVDQGV RI SRXQGV A9HVVHO VL]H LV PHDVXUHG LQ JURVV UHJLVWHUHG WRQV
PAGE 91
7DEOH )RXU VWDWH $LWNHQnV SDUDPHWHU HVWLPDWHV IRU WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ FDWFK HTXDWLRQV 'HSHQGHQW YDULDEOH ,QWHUFHSW $Q YHVVHOV $Q FUHZ VL]H $Q YHVVHO VL]Hr DQ )ORULGD FDWFK f f f f f ÂQ $ODEDPD FDWFK f f f f f $Q 0LVVLVVLSSL FDWFK f f f f f $Q /RXLVLDQD FDWFK f f f f f $Q 7H[DV FDWFK f f f f f U? &DWFK LV PHDVXUHG LQ WKRXVDQGV RI SRXQGV A9HVVHO VL]H LV PHDVXUHG LQ JURVV UHJLVWHUHG WRQV
PAGE 92
)LVKLQJ 3RZHU 7KH HVWLPDWHG FDWFK HTXDWLRQV UHSUHVHQW UHGXFHG IRUP H[SUHVVLRQV ,W FDQ EH UHFDOOHG IURP HTXDWLRQ f WKDW WRWDO HIIRUW ZDV FRPSRVHG RI QRPLQDO HIIRUW DQG ILVKLQJ SRZHU DQG WKDW WKH HVWLPDWHG ILVKLQJ SRZHU IXQFWLRQ FDQ EH GHULYHG IURP WKH HVWLPDWHG UHGXFHG IRUP FDWFK HTXDWLRQV 7KH HVWLPDWHG ILVKLQJ SRZHU IXQFWLRQ FRUUHVSRQGLQJ WR HTXDWLRQ f IRU DQ DUELWUDU\ VWDWH LQ WKH *05)) LV JLYHQ E\ B \ Y 3L $OL ;L f ZKHUH ;A DQG DUH DYHUDJH FUHZ VL]H DQG DYHUDJH YHVVHO VL]H LQ WKH WK L Q VWDWH UHVSHFWLYHO\ ([DPLQDWLRQ RI HTXDWLRQ f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nV FRQVWDQW WHUP ZDV VXEVXPHG LQ WKH LQWHUFHSW RI WKH FDWFK IXQFWLRQ ,Q WKDW WKH HQVXLQJ GLVFXVVLRQ SURFHHGV LQ UHODWLYH WHUPV WKH FRQVWDQW LQ HTXDWLRQ f KDV EHHQ VHW HTXDO WR RQH ZLWK QR ORVV RI JHQHUDOLW\
PAGE 93
LV UHDVRQDEOH VLQFH IDFWRUV VXFK DV ZHDWKHU DQG VHD FRQGLWLRQV FDQ LPSDLU RU SUHYHQW ILVKLQJ 7KH VFDOH HODVWLFLW\ IRU WKH ILVKLQJ SRZHU IXQFWLRQ LQ HTXDWLRQ f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n WLRQ UHVWHG PDLQO\ RQ WKH GHILQLWLRQDO QDWXUH RI WKH ILVKLQJ SRZHU 3URSRUWLRQDWH ,QFUHDVH LQ $YHUDJH &UHZ DQG 9HVVHO 6L]H )LJXUH (VWLPDWHG UHODWLYH ILVKLQJ SRZHU IRU SURSRUWLRQDWH LQFUHDVHV LQ DYHUDJH FUHZ VL]H DQG YHVVHO VL]HA ,Q )LJXUH DYHUDJH FUHZ VL]H DQG YHVVHO VL]H DUH DVVXPHG WR WDNH DQ LQLWLDO YDOXH RI :KLOH QR DFWXDO YHVVHOV H[KLELW VXFK LQSXW SURSRUWLRQV FKRRVLQJ VXFK OHYHOV DOWHUV RQO\ WKH VFDOH RI WKH ILJXUH
PAGE 94
H[SUHVVLRQ 7KH LQWHUSUHWDWLRQ RI WKH RXWSXW HODVWLFLWLHV KRZHYHU VHUYH WR PDNH WKH DSSHDUDQFH RI LQFUHDVLQJ UHWXUQV D UHDVRQDEOH UHVXOW 7KH SULPDU\ UROH RI WKH ILVKLQJ SRZHU IXQFWLRQ LQ UHODWLRQ WR WKH HPSLULFDO FDWFK HTXDWLRQV LQYROYHV ZHLJKWLQJ WKH QRPLQDO HIIRUW FRPSRn QHQW YHVVHOVf 7KH EDVLF QRWLRQ KHUH LV WKDW D VWDQGDUGL]HG PHDVXUH RI ILVKLQJ HIIRUW FDQ EH GHULYHG E\ ZHLJKWLQJ YHVVHOV LQ WKH ILVKHU\ E\ FHUWDLQ LQSXW FKDUDFWHULVWLFV 6XFK D VWDQGDUGL]HG PHDVXUH RI ILVKLQJ HIIRUW LV H[WUHPHO\ LPSRUWDQW QRW RQO\ LQ DQDO\VHV VXFK DV WKH FXUUHQW VWXG\ EXW DOVR LQ HVWLPDWLQJ 6FKDHIHU f W\SH VXVWDLQDEOH \LHOG IXQFWLRQV %\ ZHLJKWLQJ YHVVHOV DFFRUGLQJ WR WKHLU UHODWLYH ILVKLQJ SRZHU ZLWK UHVSHFW WR VRPH EDVH SHULRG D VWDQGDUGL]HG PHDVXUH RI ILVKn LQJ HIIRUW VXFK DV VWDQGDUGL]HG YHVVHOV FDQ EH REWDLQHG 7KH HVWLPDWHG ILVKLQJ SRZHU LQGLFHV IRU HDFK VWDWH SDUWLFLSDWLQJ LQ WKH *05)) IRU WKH \HDUV WR DUH VKRZQ LQ 7DEOH 7KH ILVKLQJ SRZHU LQGH[ LV GHILQHG E\ LW YOLW ;OE ;LW } ;E r f ZKHUH DQG DUH DYHUDJH FUHZ DQG YHVVHO VL]H LQ WKH EDVH \HDU DQG VWDWH ,Q 7DEOH )ORULGDnV LQSXW FRPSRVLWLRQ VHUYHV DV WKH EDVH ([DPLQDWLRQ RI WKH ILVKLQJ SRZHU LQGLFHV LOOXVWUDWHV WKDW )ORULGD YHVVHOV LQ DUH FKDUDFWHUL]HG E\ WKH ORZHVW DYHUDJH ILVKLQJ SRZHU SHU YHVVHO LQ WKH ILVKHU\ 3HUKDSV PRUH VXUSULVLQJ LV WKH IDFW WKDW LQ )ORULGD YHVVHOV SRVVHVVHG RQO\ DERXW SHUFHQW RI WKH ILVKLQJ SRZHU RI YHVVHOV LQ WKH EDVH SHULRG 6LQFH 0LVVLVVLSSL YHVVHOV RQ DYHUDJH KDYH KDG WKH JUHDWHVW ILVKLQJ SRZHU 0LVVLVVLSSL YHVVHOV LQ KDG VOLJKWO\ RYHU IRXU WLPHV WKH ILVKLQJ SRZHU RI )ORULGD YHVVHOV
PAGE 95
7DEOH (VWLPDWHG UHODWLYH ILVKLQJ SRZHU LQGLFHV E\ VWDWH
PAGE 99
LQ YHVVHO VL]H RI JURVV UHJLVWHUHG WRQV WR PDLQWDLQ ILVKLQJ SRZHU DW WKH VDPH OHYHO SRLQW %f 7KHVH DVSHFWV RI WKH VXEVWLWXWDELOLW\ EHWYHHQ FUHZ VL]H DQG YHVVHO VL]H DUH VLJQLILFDQW LQ UHJDUGV WR PDQDJLQJ WKH *05)) 0DQDJHPHQW PHDn VXUHV PXVW IRFXV RQ UHJXODWLQJ QRPLQDO ILVKLQJ HIIRUW YHVVHOVf ILVKLQJ SRZHU RU ERWK )LJXUH GHPRQVWUDWHV WKDW VLJQLILFDQW FKDQJHV LQ WKH DYHUDJH LQSXW FRPSRVLWLRQ LQ HDFK VWDWH PD\ EH UHTXLUHG WR PDLQWDLQ ILVKLQJ SRZHU DW FRQVWDQW OHYHOV )XUWKHUPRUH JLYHQ WKH VXEVWDQWLDO GLIIHUHQFHV LQ WKH DYHUDJH ILVKLQJ SRZHU RI YHVVHOV DFURVV VWDWHV LQ WKH *05)) LW FDQ EH VHHQ WKDW PDQDJHPHQW PHDVXUHV DLPHG DW PDLQWDLQLQJ ILVKLQJ SRZHU DW FRQVWDQW OHYHOV PXVW EH IRUPXODWHG RQ DQ LQGLYLGXDO VWDWH EDVLV &DWFK (TXDWLRQV 7KH FDWFK HTXDWLRQV GHULYHG LQ HTXDWLRQ f H[SUHVVHG FDWFK DV D IXQFWLRQ RI HIIHFWLYH ILVKLQJ HIIRUW ZLWK HIIHFWLYH ILVKLQJ HIIRUW GHILQHG WR EH WKH SURGXFW RI QRPLQDO HIIRUW YHVVHOVf DQG ILVKLQJ SRZHU 7KLV VHFWLRQ FHQWHUV RQ FDWFK HTXDWLRQV FRQGLWLRQHG E\ IL[HG OHYHOV RI ILVKLQJ SRZHU 7KXV HDFK VWDWHnV FDWFK EHFRPHV D IXQFWLRQ RI WKH QXPEHU RI YHVVHOV ILVKLQJ SRZHU EHLQJ IL[HG 7KH RXWSXW HODVWLFLW\ RI YHVVHOV ZLWK JLYHQ ILVKLQJ SRZHU LV HVWLn PDWHG WR EH 7DEOH f 5HFDOOLQJ WKDW WKLV SDUDPHWHU LV FRQn VWUDLQHG WR EH FRQVWDQW DFURVV VWDWHV LW PD\ EH LQWHUSUHWHG WR HVWLPDWH D SHUFHQW LQFUHDVH LQ FDWFK LQ HDFK VWDWH JLYHQ D SHUFHQW LQFUHDVH LQ YHVVHOV KROGLQJ ILVKLQJ SRZHU LQ HDFK VWDWH DW D IL[HG OHYHO *LYHQ WKH PDQQHU LQ ZKLFK ILVKLQJ SRZHU KDV EHHQ GHILQHG WKLV RXWSXW HODVn WLFLW\ LV V\QRPRXV ZLWK UHWXUQV WR VFDOH LQ WKH ILVKHU\ 7KH QRWLRQ RI
PAGE 100
UHWXUQV WR VFDOH PXVW EH XVHG ZLWK FDXWLRQ ZLWKLQ WKH FRQWH[W RI ILVKHU\ SURGXFWLRQ KRZHYHU 6FDOH HODVWLFLWLHV PHDVXUH WKH SHUFHQWDJH FKDQJH LQ RXWSXW JLYHQ D SHUFHQW FKDQJH LQ DOO LQSXWV :LWKLQ WKH FRQWH[W RI ILVKHU\ SURGXFn WLRQ WKH UHVRXUFH VWRFN FRQVWLWXWHV DQ XQREVHUYDEOH LQSXW $ VLPXOWDn QHRXV LQFUHDVH LQ DOO SK\VLFDO LQSXWV ZKLFK VHUYHV WR LQFUHDVH FDWFK PXVW QHFHVVDULO\ DOWHU WKH UHVRXUFH VWRFN VL]H 7KXV DQ\ WUXH PHDVXUH RI UHWXUQV WR VFDOH LQ WHUPV RI RQO\ PHDVXUHG SK\VLFDO LQSXWV LV FRQn IRXQGHG E\ XQREVHUYHG VWRFN VL]H FKDQJHV *LYHQ WKH LQFRUSRUDWLRQ RI WKH DXWRUHJUHVVLYH SURFHVV WR DFFRXQW IRU VXFK XQREVHUYHG FKDQJHV WKH HVWLPDWHG VFDOH HODVWLFLW\ RI FDQ EH FRQVLGHUHG DV D UHDVRQDEOH DSSUR[LPDWLRQ 7KH FDWFK HTXDWLRQV XQGHUO\LQJ DOO VWRFN SURGXFWLRQ PRGHOV KDYH DVVXPHG FRQVWDQW UHWXUQV WR ILVKLQJ HIIRUW DV SRLQWHG RXW LQ &KDSWHU ,, ,I RQH LV ZLOOLQJ WR DFFHSW WKDW WKH DXWRUHJUHVVLYH SURFHVVHV LQ WKH HVWLPDWHG FDWFK HTXDWLRQV DGHTXDWHO\ DFFRXQW IRU FKDQJHV LQ WKH UHVRXUFH VWRFN WKH HVWLPDWHG VFDOH HODVWLFLW\ IRU YHVVHOV PD\ EH XVHG WR FRQGXFW DQ DSSUR[LPDWH WHVW RI WKH FRQVWDQW UHWXUQV K\SRWKHVLV $ WWHVW RI WKH QXOO K\SRWKHVLV RI HTXDO WR RQH YHUVXV WKH DOWHUQDWLYH RI OHVV WKDQ RQH FDQ EH UHMHFWHG DW WKH OHYHO RI VLJQLILFDQFH *LYHQ WKH UHMHFWLRQ RI WKLV K\SRWKHVLV DQG WKH ODUJH DEVROXWH GLIIHUHQFH EHWZHHQ WKH HVWLPDWHG SDUDPHWHU DQG XQLW\ LW LV DSSDUHQW WKDW WKH *05)) LV FKDUDFWHUL]HG E\ GLPLQLVKLQJ UHWXUQV WR VFDOH 'HULYHG (TXLOLEULXP &DWFK (TXDWLRQV 7KH HVWLPDWHG FDWFK HTXDWLRQV LQ WKH IRUP SUHVHQWHG LQ 7DEOH FRUUHVSRQG WR QRQHTXLOLEULXP HTXDWLRQV 1RQHTXLOLEULXP IXQFWLRQV
PAGE 101
FRQWDLQ QR H[SOLFLW FRQVWUDLQWV ZLWK UHVSHFW WR HTXDWLQJ FDWFK ZLWK VXVWDLQDEOH \LHOG +RZHYHU DSSUR[LPDWH HTXLOLEULXP FDWFK IXQFWLRQV FDQ EH GHULYHG IURP WKRVH SUHVHQWHG LQ 7DEOH JLYHQ WKDW WKH DXWRUHJUHVVLYH SURFHVVHV LQ WKH HVWLPDWHG FDWFK HTXDWLRQV DFFRXQW IRU D SRUWLRQ RI WKH GLIIHUHQFH EHWZHHQ SUHGLFWHG FDWFK DQG VXVWDLQDEOH \LHOG 7KH GHULYDWLRQ RI VXFK GHULYHG HTXLOLEULXP FDWFK HTXDWLRQV UHVWV WR D ODUJH GHJUHH RQ WKH IDFW WKDW IL[LQJ HIIRUW DW D JLYHQ OHYHO IRU D VXIILFLHQW SHULRG RI WLPH ZLOO FDXVH WKH UHVRXUFH VWRFN WR DGMXVW WR WKH SRLQW ZKHUH FDWFK FRUUHVSRQGLQJ WR WKH IL[HG OHYHO RI HIIRUW DQG VXVWDLQDEOH \LHOG DUH HTXDWHG $SSHQGL[ *f :LWKLQ WKH FRQWH[W RI WKH HVWLPDWHG FDWFK HTXDWLRQV WKLV VWRFN DGMXVWPHQW LV FDSWXUHG E\ WKH HVWLPDWHG UHVLGXDO FRPSRQHQW RI WKH DXWRUHJUHVVLYH SURFHVV 7R VHH KRZ WKLV SURFHVV LV FDUULHG RXW LQ WKH FRQWH[W RI WKH SUHVHQW PRGHO FRQn VLGHU WKH HVWLPDWHG FDWFK HTXDWLRQ IRU )ORULGD &WN H[S 8WBf 9M f < < $OW rW $ $ ZKHUH &A LV SUHGLFWHG FDWFK LQ WLPH W 8ABM LV WKH HVWLPDWHG UHVLGXDO FRPSRQHQW LV QXPEHU RI YHVVHOV DQG W L DUH GHILQHG DV DERYH ,I HIIRUW LV IL[HG DW WLPH W WKH H[SUHVVLRQ IRU FDWFK LQ WLPH WN FDQ EH JLYHQ E\ &WN H[S > fN 84 @ 7 f ZKHUH ( GHQRWHV WKH IL[HG OHYHO RI YHVVHOV DYHUDJH FUHZ DQG YHVVHO VL]H DQG 8T UHSUHVHQWV WKH HVWLPDWHG GLIIHUHQFH EHWZHHQ FDWFK DQG VXVWDLQDEOH \LHOG DW WKH WLPH ZKHQ HIIRUW EHFRPHV IL[HG %\ OHWWLQJ N DSSURDFK
PAGE 102
LQILQLW\ WKH GHULYHG HTXLOLEULXP \LHOG IXQFWLRQ & H f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n YHVVHOV 7KXV WKH ILJXUH GRHV QRW DFFRPRGDWH D GLUHFW FRPSDULVRQ RI WKH UHODWLYH SURGXFWLYLWLHV RI YHVVHOV LQ GLIn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f 0RUH VSHFLILFDOO\ LW ZDV DUJXHG WKDW SURGXFWLYH LQWHUGHSHQGHQFH DQG WKH DEVHQFH RI SURSHUW\ ULJKWV ZRXOG OHDG WR D VLWXDWLRQ ZKHUH ILVKLQJ (TXDWLRQ f LOOXVWUDWHV WKH IDFW WKDW DQ\ OHYHO RI HIIRUW FDQ EH FKRVHQ DV ORQJ DV LW UHPDLQV IL[HG IRU D VXIILFLHQW DPRXQW RI WLPH WR HQDEOH WKH DXWRUHJUHVVLYH SURFHVV WR FRQYHUJH WR ]HUR
PAGE 103
)LJXUH 'HULYHG HTXLOLEULXP FDWFK HTXDWLRQV IRU WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\
PAGE 104
HIIRUW ZRXOG EH DOORFDWHG VXFK WKDW DYHUDJH SURGXFWLYLW\ RQ DOO JURXQGV DUH HTXDO *LYHQ WKH FURVV HTXDWLRQ SDUDPHWHU UHVWULFWLRQV RQ WKH VWDWH J FDWFK IXQFWLRQV WKLV K\SRWKHVLV PD\ EH WHVWHG XWLOL]LQJ WKH HVWLPDWHG LQWHUFHSW SDUDPHWHUV 7KHVH SDUDPHWHUV DUH XQFRQVWUDLQHG DFURVV VWDWHV DQG KHQFH VHUYH WR HVWLPDWH WKH UHODWLYH DYHUDJH SURGXFWLYLWLHV RI YHVVHOV ILVKLQJ RXW RI GLIIHUHQW VWDWHV (VWLPDWHG GLIIHUHQFHV LQ WKH LQWHUFHSW WHUPV IRU DOO RI WKH HVWLn PDWHG VWDWH FDWFK HTXDWLRQV DQG WKH FRUUHVSRQGLQJ HVWLPDWHG WYDOXHV DUH VKRZQ LQ 7DEOH 7DEOH (VWLPDWHG GLIIHUHQFHV LQ LQWHUFHSWV IRU WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ VWDWH FDWFK HTXDWLRQV 6WDWH )ORULGD $ODEDPD 0LVVLVVLSSL /RXLVLDQD 7H[DV )ORULGD f§ f§ f§ f§ f§ $ODEDPD f f§ f§ f§ f§ 0LVVLVVLSSL f f f§ f§ f§ /RXLVLDQD f f f f§ f§ 7H[DV f f f f f§ D 1XPEHU LQ SDUHQWKHVHV DUH HVWLPDWHG WYDOXHV J PHVH FURVV HTXDWLRQ SDUDPHWHU UHVWULFWLRQV ZHUH GLVFXVVHG LQ WKH SUHFHGLQJ FKDSWHU
PAGE 105
7KH FULWLFDO YDOXH RI WKH QXOO K\SRWKHVLV RI WKH GLIIHUHQFH EHWZHHQ WKH LQWHUFHSWV EHWZHHQ VWDWH L DQG M L M HTXDO WR ]HUR DJDLQVW WKH DOWHUQDWLYH RI QRW HTXDO WR ]HUR LV *LYHQ WKLV LW LV DSSDUHQW WKDW WKH QXOO K\SRWKHVLV RI HTXDO DYHUDJH SURGXFWLYLW\ FDQ EH UHMHFWHG LQ QHDUO\ DOO FDVHV 7KH UHVXOWV RI WKHVH WHVWV VXJJHVWV WKDW SURGXFWLYHLQWHUGHSHQGHQFH DFURVV VWDWH FDWFK HTXDWLRQV LV QRW RI VXIILFLHQW PDJQLWXGH WR YHULI\ *RUGRQnV f HTXDO DYHUDJH SURGXFWLYLW\ K\SRWKHVLV $ IXUWKHU LPSOLFDWLRQ RI WKHVH WHVWV LV WR JLYH VXSSRUW WR WKH VSHFLILFDWLRQ RI WKH UHHI ILVKHU\ FDWFK HTXDWLRQV RQ D VWDWH E\ VWDWH EDVLV 7KH VWDWLVWLFDO GLIIHUHQFH LQ WKH LQWHUFHSW WHUPV DFURVV VWDWHV VXJJHVWV WKDW WKH HVWLPDWHG FDWFK HTXDWLRQV SURYLGH D UHDVRQDEOH FKDUDFWHUL]DWLRQ RI WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\nV SURGXFWLYH VWUXFWXUH $QDO\VLV RI WKH 3ULFH (TXDWLRQV (VWLPDWLRQ RI D V\VWHP RI SULFH HTXDWLRQV ZKHUHLQ WKH GHSHQGHQW YDULDEOH FRUUHVSRQGV WR DQ DJJUHJDWH SULFH RI UHHI ILVK DV PHQWLRQHG SUHYLRXVO\ LV DQ XQIRUWXQDWH UHVXOW RI VHYHUH GDWD OLPLWDWLRQV 7KH SULFH YDULDEOH PHDVXUHV WKH ZHLJKWHG DYHUDJH YDOXH SHU SRXQG DW GRFN VLGH UHFHLYHG IRU WKH FRPELQHG FDWFK RI JURXSHU DQG UHG VQDSSHU 7R GUDZ LQIHUHQFHV IURP VXFK HVWLPDWHG HTXDWLRQV LW LV FUXFLDO WR XQGHUn VWDQG WKH LPSOLFLW XQGHUO\LQJ DVVXPSWLRQV RI VXFK D IRUPXODWLRQ 7KH EDVLF DVVXPSWLRQ LPSOLFLW LQ IRUPXODWLQJ WKH SULFH HTXDWLRQV LQ WHUPV RI SULFH RI UHHI ILVK LV WKDW ILVKLQJ LV QRQVHOHFWLYH EHWZHHQ VSHFLHV JURXSV 7KDW LV YHVVHOV LQ WKH ILVKHU\ GLUHFW ILVKLQJ WRZDUG QR SDUWLFXODU VSHFLHV JURXS ,QVWHDG RI ILVKLQJ VSHFLILFDOO\ IRU UHG VQDSSHU RU JURXSHU UHHI ILVK YHVVHOV PHUHO\ ILVK IRU UHHI ILVK ZLWK
PAGE 106
WKH VSHFLHV FRPSRVLWLRQ RI FDWFK XQNQRZQ H[ DQWH 6XFK DQ DVVXPSWLRQ DW WKH ILUP OHYHO LV PRVW SUREDEO\ SRRU DW EHVW )ORULGD IRU H[DPSOH KDV UHDVRQDEO\ GLVWLQFW JURXSHU DQG UHG VQDSSHU ILVKHULHV &DWR DQG 3URFKDVND f 7KH PDLQ XVH RI WKH HVWLPDWHG SULFH HTXDWLRQV KRZHYHU LV GLUHFWHG WRZDUGV DQDO\]LQJ WKH ILVKHU\ LQ DJJUHJDWH 7KXV WKH YDOLGLW\ RI WKH XVH RI WKH HVWLPDWHG SULFH HTXDWLRQV LQ DSSO\LQJ HFRQRPLF RSWLPL]DWLRQ FULWHULD WR WKH HVWLPDWHG FDWFK HTXDWLRQV GHSHQGV RQ WKH GHJUHH WR ZKLFK WKH ILVKHU\ LQ DJJUHJDWH EHKDYHV DÂ LI QRQ VHOHFWLYH ILVKLQJ RFFXUV 7KH HVWLPDWHG SULFH HTXDWLRQV DUH SUHVHQWHG LQ 7DEOHV DQG 7DEOH FRQWDLQV WKH VLQJOH HTXDWLRQ RUGLQDU\ OHDVW VTXDUHV SDUDPHWHU HVWLPDWHV RI WKH SULFH HTXDWLRQV ZKLFK ZHUH VSHFLILHG LQ HTXDWLRQV f DQG f ,W PD\ EH UHFDOOHG WKDW VXEVWDQWLDO FRQWHPSRUDQHRXV FRUUHODn WLRQ LQ WKH GLVWXUEDQFHV RI WKHVH HTXDWLRQV ZDV DQWLFLSDWHG 7KLV D SULRUL H[SHFWDWLRQ LPSOLHG WKDW D WZR VWDJH $LWNHQnV HVWLPDWRU ZDV DSSURSULDWH IRU HVWLPDWLQJ WKH SULFH HTXDWLRQV 7KH SDUDPHWHU HVWLPDWHV UHVXOWLQJ IURP WKLV HVWLPDWRU DUH SUHVHQWHG LQ 7DEOH $ SULRUL DOO RI WKH HVWLPDWHG SDUDPHWHUV FRUUHVSRQGLQJ WR WKH FDWFK YDULDEOHV ZHUH K\SRWKHVL]HG WR EH QHJDWLYH ([DPLQDWLRQ RI WKH SDUDPHWHU HVWLPDWHV LQ 7DEOH GHPRQVWUDWHV WKDW WKH VLQJOH HTXDWLRQ RUGLQDU\ OHDVW VTXDUHV HVWLPDWRU UHVXOWHG LQ VHYHUDO ZURQJ VLJQV +RZHYHU DOO RI WKH WLPH WUHQG YDULDEOHV KDG WKH H[SHFWHG SRVLWLYHf VLJQ ,Q FRQWUDVW HVWLPDWLRQ XVLQJ WKH $LWNHQnV WZR VWDJH HVWLPDWRU UHVXOWHG LQ RQO\ RQH SDUDPHWHU HVWLPDWH RI WKH ZURQJ VLJQ $V ZLWK WKH RUGLQDU\ OHDVW VTXDUH HVWLPDWHV DOO RI WKH HVWLPDWHG WLPH WUHQG SDUDPHn WHUV WDNH RQ WKH H[SHFWHG VLJQ
PAGE 107
7DEOH 2UGLQDU\ OHDVW VTXDUHV SDUDPHWHU HVWLPDWHV IRU WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ SULFH HTXDWLRQV 'HSHQGHQW YDULDEOHX ,QWHUFHSW )ORULGD FDWFK $ODEDPD FDWFK 0LVVLVVLSSL FDWFK /RXLVLDQD FDWFK 7H[DV FDWFK 7LPH 5L )ORULGD SULFH f f f§ f§ f§ f§ f $ODEDPD SULFH f f f f§ f§ f§ f 0LVVLVVLSSL SULFH f f f§ f f§ f§ f /RXLVLDQD SULFH f f f§ f§ f f§ f 7H[DV SULFH f f f§ f§ f f D1XPEHUV LQ SDUHQWKHVHV DUH HVWLPDWHG VWDQGDUG HUURUV NSULFH LV PHDVXUHG LQ GROODUV SHU SRXQG U &DWFK LV PHDVXUHG LQ WKRXVDQGV RI SRXQGV
PAGE 108
7DEOH 7ZR VWDJH $LWNHQnV SDUDPHWHU HVWLPDWHV IRU WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ SULFH HTXDWLRQVn 'HSHQGHQW YDULDEOHr ,QWHUFHSW )ORULGD FDWFK $ODEDPD FDWFK 0LVVLVVLSSL FDWFKF /RXLVLDQD FDWFK 7H[DV FDWFK 7LPH )ORULGD SULFH f f§ f§ f§ f§ f $ODEDPD SULFH f f f f§ f§ f§ 0LVVLVVLSSL SULFH f f f§ f f§ f§ f /RXLVLDQD SULFH f f f§ f§ f f§ f 7H[DV SULFH f f f§ f§ f§ f D1XPEHUV LQ SDUHQWKHVHV DUH HVWLPDWHG VWDQGDUG HUURUV E3ULFH LV PHDVXUHG LQ GROODUV SHU SRXQG F&DWFK LV PHDVXUHG LQ WKRXVDQGV RI SRXQGV
PAGE 109
([DPLQDWLRQ RI WKH HVWLPDWHG VWDQGDUG HUURUV IRU ERWK WKH RUGLQDU\ OHDVW VTXDUHV DQG WZR VWDJH $LWNHQnV HVWLPDWRUV GHPRQVWUDWHV WKDW D FRQVLGHUDEOH JDLQ LQ HIILFLHQF\ ZDV UHDOL]HG E\ LQFRUSRUDWLQJ WKH DGGLn WLRQDO LQIRUPDWLRQ RI FRQWHPSRUDQHRXV FRUUHODWLRQ DFURVV VWDWHV LQ WKH HVWLPDWLRQ SURFHGXUH ,Q DOO FDVHV WKH HVWLPDWHG VWDQGDUG HUURUV REWDLQHG YLD WKH WZR VWDJH HVWLPDWRU DUH OHVV WKDQ RU HTXDO WR WKH FRUn UHVSRQGLQJ VWDQGDUG HUURU HVWLPDWHV REWDLQHG XVLQJ RUGLQDU\ OHDVW VTXDUHV 7KHVH JDLQV LQ HIILFLHQF\ DUH HVSHFLDOO\ VLJQLILFDQW JLYHQ WKH VPDOO VDPSOH VL]H HPSOR\HG LQ WKH HVWLPDWLRQ SURFHGXUH 7KH DERYH UHVXOWV JLYH FRQVLGHUDEOH VXSSRUW WR WKH VSHFLILFDWLRQ RI WKH V\VWHP RI SULFH HTXDWLRQV DQG WKH FKRLFH RI HVWLPDWRU ZKHQ WDNHQ DV D ZKROH 7KH LQFRUSRUDWLRQ RI FRQWHPSRUDQHRXV FRUUHODWLRQ DFURVV HTXDn WLRQV QRW RQO\ \LHOG WKH H[SHFWHG VLJQV RQ DOO EXW RQH SDUDPHWHU HVWLn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n PDWHG WR GHFUHDVH SULFH E\ DQG SHUFHQW UHVSHFWLYHO\ &KDQJHV LQ
PAGE 110
7DEOH (VWLPDWHG ZLWKLQ DQG DFURVV VWDWH SULFH IOH[LELOLWLHV IRU VWDWHV SDUWLFLSDWLQJ LQ WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ 6WDWH )ORULGD $ODEDPD 0LVVLVVLSSL /RXLVLDQD 7H[DV )ORULGD f§ f§ f§ f§ $ODEDPD f§ f§ f§ 0LVVLVVLSSL f§ f§ f§ /RXLVLDQD f§ f§ f§ 7H[DV f§ f§ f§ $ODEDPD DQG /RXLVLDQD ODQGLQJV KDYH YLUWXDOO\ QR HIIHFW RQ WKHLU SULFH )ORULGDnV GRPLQDQFH ZLWK UHVSHFW WR SULFH GHWHUPLQDWLRQ LQ WKH *05)) LV FRQILUPHG E\ WKH HVWLPDWHG FURVV VWDWH SULFH IOH[LELOLWLHV :LWK WKH H[FHSWLRQ RI 0LVVLVVLSSL TXDQWLW\ ODQGHG LQ )ORULGD KDV D PXFK ODUJHU HIIHFW RQ HDFK VWDWHnV SULFH WKDQ GRHV WKH FRUUHVSRQGLQJ ZLWKLQ VWDWH FDWFK )RU $ODEDPD DQG /RXLVLDQD ZKLFK KDYH DOPRVW QR HIIHFW RQ WKHLU RZQ SULFH D SHUFHQW LQFUHDVH LQ )ORULGD UHHI ILVK FDWFK LV HVWLPDWHG WR FDXVH SULFH GHFUHDVHV RI DQG SHUFHQW UHVSHFWLYHO\ 7KH WLPH WUHQG YDULDEOHV LQ WKH HVWLPDWHG SULFH HTXDWLRQV ZHUH LQFOXGHG DV SUR[\ YDULDEOHV IRU GHPDQG VKLIWHUV VXFK DV LQFRPH DQG SRSXODWLRQ 7KH UHODWLYH PDJQLWXGH RI WKH HVWLPDWHG SDUDPHWHUV FRUn UHVSRQGLQJ WR WKHVH YDULDEOHV LQ UHODWLRQ WR WKH HVWLPDWHG FDWFK SDUDPHn WHUV VXJJHVW WKDW GHPDQG VKLIWV RYHU WKH VDPSOH SHULRG KDYH VHUYHG WR FUHDWH D VWHDG\ LQFUHDVH LQ WKH GRFNVLGH SULFH RI UHHI ILVK ,W VKRXOG EH QRWHG KRZHYHU WKDW SULFH LV PHDVXUHG LQ QRPLQDO WHUPV +HQFH WKH WLPH WUHQG YDULDEOHV DUH LQ DOO SUREDELOLW\ PHDVXULQJ VRPH SULFH LQn FUHDVHV GXH WR LQIODWLRQ DV ZHOO DV RWKHU GHPDQG HIIHFWV 7KXV WKH
PAGE 111
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nV HVWLn PDWRU VHUYH WR VXSSRUW WKH H[SHFWDWLRQ WKDW VLJQLILFDQW FRQWHPSRUDQHRXV FRUUHODWLRQ DFURVV VWDWHV ZRXOG EH SUHVHQW )XUWKHUPRUH WKH HVWLPDWHG ZLWKLQ DQG DFURVV VWDWH SULFH IOH[LELOLWLHV FRQILUP WKH D SULRUL QRWLRQ RI )ORULGDnV GRPLQDQFH LQ WKH ILVKHU\ ZLWK UHJDUGV WR SULFH GHWHUPLQDWLRQ *XOI RI 0H[LFR 5HHI )LVK 2SWLPL]DWLRQ 0RGHO 7KH FRQFHSW RI PD[LPXP HFRQRPLF \LHOG 0(
PAGE 112
FURVV VWDWH SULFH HIIHFWV H[LVW 7KH LPSOLFDWLRQ KHUH LV WKDW PD[LPL]Dn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n WLRQ WR OHYHOV W ZDV VHW DW FRUUHVSRQGLQJ WR 7KH UHVXOWn LQJ FRQVWDQW ZDV WKHQ VXEVXPHG LQWR WKH LQWHUFHSW RI WKH SULFH HTXDWLRQ
PAGE 113
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n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
PAGE 114
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n PDWHV IRU UHHI ILVK YHVVHOV &RVW GDWD E\ YHVVHO VL]H ZHUH REWDLQHG IURP VXUYH\ GDWD RQ *XOI RI 0H[LFR JURXSHUUHG VQDSSHU YHVVHOV &DWR DQG 3URFKDVND Ef &RVW LWHPV LQFOXGHG LQ FDOFXODWLQJ WKH DQQXDO FRVW RI RSHUDWLQJ DQG PDLQWDLQLQJ D UHHI ILVK YHVVHO ZHUH IXHO DQG RLO UHSDLUV DQG PDLQWHQDQFH GHSUHFLDWLRQ OLFHQVH LQWHUHVW LQVXUDQFH DQG PLVFHOODQHRXV FRVWV &RVW LWHPV GLUHFWO\ DVVRFLDWHG ZLWK FUHZ VKDUHV ZHUH H[FOXGHG $OO FRVW LWHPV ZHUH UHSRUWHG LQ QRPLQDO WHUPV IRU DQG 7KHVH FRVW ILJXUHV ZHUH WKHQ LQIODWHG WR OHYHOV XVLQJ ZKROHVDOH SULFH LQGLFHV IRU VSHFLILF LWHPV %XUHDX RI /DERU 6WDWLVWLFV f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n XWDEOH WR WKH SVXHGR FDSWDLQ FUHZPHQ SDUWQHUVKLS
PAGE 115
PHDVXUHG LQ WHUPV RI JURVV UHJLVWHUHG WRQQDJH 7R GHULYH DQ H[SUHVVLRQ IRU FRVW DV D IXQFWLRQ RI JURVV UHJLVWHUHG WRQQDJH D FRQYHUVLRQ UHODn WLRQ EHWZHHQ WRQQDJH DQG OHQJWK ZDV GHYHORSHG $Q HTXDWLRQ H[SUHVVLQJ JURVV UHJLVWHUHG WRQQDJH DV D IXQFWLRQ RI YHVVHO OHQJWK YDV HVWLPDWHG XVLQJ RSHUDWLQJ XQLWV JHDU GDWD REWDLQHG IURP WKH 86 1DWLRQDO 0DULQH )LVKHULHV 6HUYLFH f 7KHVH GDWD SURn YLGHG LQIRUPDWLRQ RQ OHQJWK DQG JURVV UHJLVWHUHG WRQQDJH RI YHVVHOV VLPLODU WR WKRVH LQ WKH UHHI ILVK ILVKHU\ 7KXV WKH FRQYHUVLRQ UHODn WLRQ REWDLQHG LV VSHFLILF WR YHVVHOV VLPLODU LQ QDWXUH WR UHHI ILVK YHVVHOV 6HYHUDO GLIIHUHQW FRQYHUVLRQ HTXDWLRQV ZHUH HVWLPDWHG 7KH EHVW HVWLPDWHG HTXDWLRQ LQ WHUPV RI JRRGQHVV RI ILW LV JLYHQ E\ *57 /7 5 f f f ZKHUH *57 LV JURVV UHJLVWHUHG WRQQDJH DQG /7 LV YHVVHO OHQJWK LQ IHHW (VWLPDWHG VWDQGDUG HUURUV DUH JLYHQ LQ SDUHQWKHVHV %\ VXEVWLWXWLQJ WKH YHVVHO OHQJWKV FRQWDLQHG LQ WKH VXUYH\ GDWD LQWR HTXDWLRQ f D VHULHV RI REVHUYDWLRQV IRU FRVW DQG YHVVHO VL]H PHDVXUHG LQ WHUPV RI HVWLPDWHG JURVV UHJLVWHUHG WRQV YDV REWDLQHG $Q HTXDWLRQ UHODWLQJ FRVW WR YHVVHO VL]H ZDV WKHQ HVWLPDWHG E\ DSSO\LQJ RUGLQDU\ OHDVW VTXDUHV WR WKHVH GDWD 7KH UHVXOWLQJ HVWLPDWHG FRVW HTXDWLRQ LV JLYHQ E\ & *57 5 f f f ZKHUH & LV DQQXDO RSHUDWLQJ DQG PDLQWHQDQFH FRVW DQG *57 LV JURVV UHJLVWHUHG WRQQDJH (VWLPDWHG VWDQGDUG HUURUV DUH JLYHQ LQ SDUHQWKHVHV &RVW ZDV PHDVXUHG LQ WKRXVDQGV RI GROODUV ,W FDQ EH VHHQ IURP HTXDWLRQ
PAGE 116
f WKDW WKH PDUJLQDO LQFUHPHQW LQ FRVW RI DQ DGGLWLRQDO JURVV UHJLVn WHUHG WRQ LV HVWLPDWHG WR EH DSSUR[LPDWHO\ (TXDWLRQ f GHILQHV WKH DQQXDO RSHUDWLQJ DQG PDLQWHQDQFH FRVW HVWLPDWHV XVHG LQ WKH 0(< RSWLPL]DWLRQ PRGHO &RUUHVSRQGLQJ WR HDFK SUHGHWHUPLQHG OHYHO RI ILVKLQJ SRZHU DQG KHQFH YHVVHO VL]H LV DQ DQQXDO YHVVHO FRVW GHILQHG E\ DSSURSULDWH VXEVWLWXWLRQ LQ HTXDWLRQ f )LVKLQJ SRZHU IRU WKH 0(< VROXWLRQ ZDV H[RJHQRXVO\ VHW DW OHYHOV 8WLOL]LQJ WKH DYHUDJH YHVVHO VL]H IRU HDFK VWDWH LQ 7DEOH SUHVHQWV WKH HVWLPDWHG DQQXDO YHVVHO RSHUDWLQJ DQG PDLQWHQDQFH FRVWV IRU HDFK VWDWH 7KHVH FRVW HVWLPDWHV FRPSDUH IDYRUDEO\ ZLWK WKRVH UHSRUWHG E\ &DWR DQG 3URFKDVND Df 7KH HIIHFW RI WKH YHVVHO VL]H FRPSRQHQW RI ILVKLQJ SRZHU RQ WKH HVWLPDWHG DQQXDO WRWDO FRVW RI D UHHI ILVK YHVVHO LV VXEVWDQWLDO 7KH HODVWLFLW\ RI WRWDO FRVW HVWLPDWHG DW PHDQ OHYHOV RI FRVW DQG YHVVHO VL]H LV 7KXV D SHUFHQW LQFUHDVH LQ YHVVHO VL]H LQFUHDVHV HVWLPDWHG FRVW E\ SHUFHQW 7DEOH (VWLPDWHG DQQXDO RSHUDWLQJ DQG PDLQWHQDQFH FRVWV IRU UHHI ILVK YHVVHOV E\ VWDWH 6WDWH 9HVVHO VL]H JURVV UHJLVWHUHG WRQVf (VWLPDWHG FRVW GROODUVf )ORULGD $ODEDPD 0LVVLVVLSSL /RXLVLDQD 7H[DV
PAGE 117
&DWFK (TXDWLRQ &RQVWUDLQWV 7KH DERYH GLVFXVVLRQV FRQFHUQLQJ WKH WRWDO UHYHQXH DQG WRWDO FRVW FRPSRQHQWV RI WKH UHHI ILVKHU\ SURILW IXQFWLRQ VHUYH WR GHILQH WKH EDVLF HFRQRPLF UHODWLRQV QHFHVVDU\ WR GHULYH 0(< 7R FRPSOHWH WKH PRGHO WHFKQLFDO FRQVWUDLQWV LQ WKH IRUP RI WKH HVWLPDWHG VWDWH FDWFK HTXDWLRQV DUH QHFHVVDU\ 7KH HVWLPDWHG VWDWH FDWFK HTXDWLRQV ZHUH GLVFXVVHG LQ GHWDLO LQ SUHFHHGLQJ VHFWLRQV ZKHUH LW ZDV VKRZQ WKDW WKH HVWLPDWHG FDWFK HTXDn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n WLRQ REWDLQHG WR EH D FRQGLWLRQDO RSWLPXP 7KH RSWLPXP LV FRQGLWLRQDO LQ WKH VHQVH WKDW QR HFRQRPLF HIILFLHQF\ FULWHULD VXFK DV PDUJLQDO FRQGLWLRQV RQ WKH ILVKLQJ SRZHU FRPSRQHQWV DUH FRQVLGHUHG )DLOXUH WR FRQVLGHU VXFK FULWHULD LV QRW XQUHDVRQDEOH KRZHYHU 7KH PHDVXUHV ZKLFK GHILQH FUHZ VL]H DQG YHVVHO VL]H DUH DJJUHJDWH DYHUDJHV FRUUHVSRQGLQJ WR YHVVHOV LQ HDFK VWDWH :LWKLQ WKH FDWFK HTXDWLRQV WKHVH IDFWRUV VHUYH WR PHDVXUH WKH DJJUHJDWH DYHUDJH LQSXW FRPSRVLWLRQ RI YHVVHOV LQ
PAGE 118
HDFK VWDWH $Q\ DWWHPSW WR GHULYH DQ RSWLPXP LQSXW FRPSRVLWLRQ IRU D VWDWH EDVHG RQ ILUP OHYHO GHFLVLRQ FULWHULD ZRXOG EH PHDQLQJOHVV 7KH H[RJHQRXV OHYHOV RI ILVKLQJ SRZHU XVHG LQ REWDLQLQJ WKH FDWFK FRQVWUDLQWV DUH JLYHQ E\ WKH OHYHOV RI DYHUDJH FUHZ VL]H DQG DYHUDJH YHVVHO VL]H LQ HDFK VWDWH $SSHQGL[ % 7DEOHV % DQG %f )L[LQJ WKH ILVKLQJ SRZHU FRPSRQHQWV VHUYHV WR ORFDWH WKH FDWFK HTXDWLRQV LQ HDFK VWDWH VLQFH WKHVH FRPSRQHQWV DUH LQFRUSRUDWHG LQWR WKH LQWHUFHSW WHUP 7KH DGMXVWHG FDWFK FRQVWUDLQW LQWHUFHSWV ZLWK IL[HG ILVKLQJ SRZHU DUH JLYHQ LQ 7DEOH 7KH IRUP WKHVH DGMXVWHG LQWHUFHSW HVWLPDWHV WDNH LQ WKH DFWXDO PRGHO DUH WKH DQWLORJV RI WKRVH SUHVHQWHG LQ WKH WDEOH 7KH HIIHFW WKDW ILVKLQJ SRZHU KDV RQ WKH FDWFK FRQVWUDLQWV FDQ EH VHHQ E\ FRPSDULQJ WKH DGMXVWHG LQWHUFHSWV WR WKH XQDGMXVWHG LQWHUFHSWV ,W FDQ LPPHGLDWHO\ EH VHHQ WKDW WKH DGMXVWHG LQWHUFHSWV IRU $ODEDPD DQG 0LVVLVVLSSL DUH ODUJHU WKDQ )ORULGDnV ZKHUHDV )ORULGDnV XQDGMXVWHG LQWHUFHSW GRPLQDWHV DOO RWKHU VWDWHVn LQWHUFHSWV 7KLV RFFXUUHQFH UHIOHFWV WKH JUHDWHU ILVKLQJ SRZHU RI YHVVHOV LQ $ODEDPD DQG 0LVVLVVLSSL UHODWLYH WR )ORULGD YHVVHOV )ORULGD YHVVHOV LQ IDFW KDYH WKH VPDOOHVW DYHUDJH ILVKLQJ SRZHU SHU YHVVHO RI DOO RI WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ VWDWHV 0D[LPXP (FRQRPLF
PAGE 119
7DEOH $GMXVWHG DQG XQDGMXVWHG LQWHUFHSWV IRU WKH HVWLPDWHG *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ FDWFK HTXDWLRQV E\ VWDWH 6WDWH $GMXVWHG LQWHUFHSW 8QDGMXVWHG LQWHUFHSW )ORULGD $ODEDPD 0LVVLVVLSSL /RXLVLDQD 7H[DV D,QFOXGHV ILVKLQJ SRZHU GHWHUPLQDQWV IL[HG DW OHYHOV RSWLPL]DWLRQ PRGHO DQG FRUUHVSRQGLQJ ILUVW RUGHU FRQGLWLRQV DUH JLYHQ LQ $SSHQGL[ + 7KH RSWLPL]DWLRQ SUREOHP GHILQHG DERYH LV FKDUDFWHUL]HG DV D QRQn OLQHDU RSWLPL]DWLRQ SUREOHP ZKLFK UHTXLUHV WKH XVH RI QXPHULFDO RSWLPLn ]DWLRQ WHFKQLTXHV IRU VROXWLRQ 7KH PHWKRG RI VROXWLRQ HPSOR\HG ZDV D TXDGUDWLFDOO\ FRQYHUJHQW 1HZWRQOLNH PHWKRG %URZQ f DYDLODEOH LQ WKH ,QVWLWXWH RI 0DWKHPDWLFV DQG 6WDWLVWLFV /LEUDU\ ,06/f VRIWZDUH SDFNDJH ,06/ f 7KH UHVXOWV RI WKH RSWLPL]DWLRQ SURFHGXUH DUH SUHVHQWHG LQ 7DEOH 7KH PD[LPXP HFRQRPLF \LHOG HVWLPDWHG IRU WKH *05)) FRQGLWLRQHG E\ OHYHOV RI ILVKLQJ SRZHU LV DSSUR[LPDWHO\ PLOOLRQ SRXQGV 7RWDO SURILW LQ WKH ILVKHU\ LV HVWLPDWHG DW DSSUR[LPDWHO\ PLOOLRQ GROODUV ([DPLQDWLRQ RI WKH DYHUDJH SURILW SHU YHVVHO VKRZV FRQVLGHUn DEOH YDULDWLRQ DFURVV VWDWHV 0LVVLVVLSSL YHVVHOV GHPRQVWUDWH WKH
PAGE 120
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n IHUHQW VWDWHV KDYH GLIIHUHQW ILVKLQJ SRZHU UHVXOWLQJ IURP GLIIHUHQW FUHZ VL]HV DQG WRQQDJHV 7KHVH GLIIHUHQFHV VKRXOG UHVXOW LQ GLIIHUHQFHV LQ DYHUDJH SURILW SHU YHVVHO ,Q FRQMXQFWLRQ ZLWK WKLV LV WKH IDFW WKDW WKH FDSWDLQ DQG FUHZ DUH FRQVLGHUHG WR UHSUHVHQW D SVXHGR SDUWQHUVKLS YLD WKH FUHZ VKDUH V\VWHP 7KXV GLIIHUHQFHV LQ VKDUH DUUDQJHPHQWV DFURVV VWDWHV DQG YDULDWLRQV LQ DYHUDJH FUHZ VL]HV DOVR OHDG WR GLIIHUn LQJ SURILW OHYHOV DFURVV VWDWHV )LQDOO\ WKH FDWFK FRPSRVLWLRQ RI UHG VQDSSHU DQG JURXSHU YDULHV DFURVV VWDWHV 7KXV YHVVHOV LQ VWDWHV ZKLFK
PAGE 121
QR FDWFK ODUJHU SURSRUWLRQV RI WKH ORZHU SULFHG JURXSHU ZLOO WHQG WR KDYH ORZHU SURILW OHYHOV 7KH WRWDO QXPEHU RI YHVVHOV LQ WKH UHHI ILVKHU\ QHFHVVDU\ WR SURn GXFH 0(< LV HVWLPDWHG DW DSSUR[LPDWHO\ $ FRPSDULVRQ ZLWK WKH QXPEHU RI YHVVHOV LQ WKH ILVKHU\ LQGLFDWHV WKDW D SHUFHQW UHGXFWLRQ LQ WKH WRWDO QXPEHU RI YHVVHOV RSHUDWLQJ LQ WKH ILVKHU\ LV UHTXLUHG WR PD[LPL]H SURILW LQ WKH ILVKHU\ 7KH LPSOLHG FKDQJHV LQ YHVVHOV QHFHVn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
PAGE 122
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f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n WDWH IXUWKHU GLVFXVVLRQ LW LV FRQYHQLHQW WR H[SUHVV WKLV QRPLQDO PHDn VXUH RI ILVKLQJ HIIRUW LQ VWDQGDUGL]HG WHUPV 'RLQJ VR QRW RQO\ HQDEOHV HIIRUW OHYHOV WR EH GLUHFWO\ FRPSDUHG DFURVV VWDWHV DQG RYHU WLPH EXW DOVR HQDEOHV D FRPSDULVRQ WR EH PDGH EHWZHHQ WKH 0(< OHYHOV RI ILVKLQJ HIIRUW DQG WKRVH XWLOL]HG LQ HVWLPDWLQJ WUDGLWLRQDO VXVWDLQDEOH \LHOG FXUYHV %\ PXOWLSO\LQJ WKH QXPEHU RI YHVVHOV LQ HDFK VWDWH QHFHVVDU\ WR
PAGE 123
FDSWXUH 0(< E\ WKH FRUUHVSRQGLQJ HVWLPDWHG ILVKLQJ SRZHU LQGH[ GHILQHG E\ HTXDWLRQ f D VWDQGDUGL]HG PHDVXUH RI ILVKLQJ HIIRUW VWDQGDUGL]HG YHVVHOV FDQ EH REWDLQHG ,Q WHUPV RI VWDQGDUGL]HG YHVVHOV WKH 0(< FDWFK RI PLOOLRQ SRXQGV ZRXOG EH REWDLQHG E\ DSSUR[LPDWHO\ VWDQGDUGL]HG YHVVHOV 7DEOH f 7KH UHHI ILVKHU\ DV D ZKROH LQ UHSRUWHG D FDWFK RI PLOOLRQ SRXQGV UHVXOWLQJ IURP WKH RSHUDWLRQ RI VWDQGDUGL]HG YHVVHOV 7KXV D SHUFHQW UHGXFWLRQ LQ HIIHFWLYH ILVKLQJ HIIRUW LV HVWLPDWHG WR EULQJ DERXW RQO\ D SHUFHQW UHGXFWLRQ LQ FDWFK 7KH UHDVRQDEO\ VPDOO GHFOLQH LQ FDWFK LQ VSLWH RI D UHGXFWLRQ LQ ILVKLQJ HIIRUW RI PRUH WKDQ SHUFHQW VXJJHVWV WKDW WKH FRPPHUFLDO UHHI ILVKHU\ PD\ LQ IDFW EH RSHUDWLQJ ZLWK HIIRUW OHYHOV JUHDWHU WKDQ WKRVH QHFHVn VDU\ WR FDWFK PD[LPXP VXVWDLQDEOH \LHOG *LYHQ WKDW WKH UHHI ILVKHU\ KDV EHHQ XQUHJXODWHG ZLWK UHVSHFW WR HIIRUW UHVWULFWLRQV VXFK D UHVXOW LV KDUPRQLRXV ZLWK WKH WKHRU\ RI DQ RSHQ DFFHVV FRPPRQ SURSHUW\ UHVRXUFH :LWKLQ WKH FRQILQHV RI WKH SUHVHQW PRGHO WKH LPSOLFDWLRQ RI RYHUn ILVKLQJ LV GLIILFXOW WR GLUHFWO\ YHULI\ EHFDXVH WKH GHULYHG HTXLOLEULXP FDWFK IXQFWLRQV DSSUR[LPDWH RQO\ WKH OHIW KDQG VLGH RI WKH WUDGLWLRQDO 6FKDHIHU f VXVWDLQDEOH \LHOG FXUYH VHH )LJXUH f )URP DQ HFRQRPLF VWDQGSRLQW WKLV UHVXOW GRHV QRW OLPLW WKH XVHIXOQHVV RI WKH SUHVHQW PRGHO VLQFH WKH SRUWLRQ RI WKH VXVWDLQDEOH \LHOG IXQFWLRQ WR WKH OHIW RI 06< UHSUHVHQWV WKH HFRQRPLF UHJLRQ RI SURGXFWLRQ +RZHYHU WR YHULI\ WKDW RYHUILVKLQJ LV SUHVHQW UHTXLUHG WKDW D FRPSOHWH 6FKDHIHU W\SH VXVWDLQDEOH \LHOG IXQFWLRQ HTXDWLRQ f EH HVWLPDWHG 6HYHUDO GDWD DGMXVWPHQWV ZHUH SHUIRUPHG EHIRUH WKLV VXVWDLQDEOH \LHOG IXQFWLRQ ZDV HVWLPDWHG ,Q WKDW RQO\ ILVKLQJ JURXQGV ZLWKLQ WKH PLOH OLPLW ZHUH RI LQWHUHVW WKH FDWFK RI UHHI ILVK RII IRUHLJQ
PAGE 124
VKRUHV ZDV HOLPLQDWHG IURP WKH WRWDO FDWFK RI UHHI ILVK FDXJKW E\ J GRPHVWLF UHHI ILVK YHVVHOV 7RWDO HIIRUW H[SUHVVHG LQ WHUPV RI VWDQGDUGL]HG YHVVHOV ZDV DOVR DGMXVWHG WR UHIOHFW ILVKLQJ HIIRUW H[SHQGHG LQ IRUHLJQ ZDWHUV 7KLV DGMXVWPHQW ZDV DFFRPSOLVKHG E\ UHGXFn LQJ HIIRUW LQ SURSRUWLRQ WR WKH FDWFK RI UHHI ILVK LQ IRUHLJQ ZDWHUV 7KXV DGMXVWHG FDWFK DQG HIIRUW VHULHV IRU WKH GRPHVWLF UHHI ILVK ILVKHU\ IRU WKH \HDUV WR ZHUH REWDLQHG DQG XVHG IRU HVWLPDWLRQ 7KH UHVXOWLQJ HVWLPDWHG VXVWDLQDEOH \LHOG IXQFWLRQ ZDV & ( ( f f f ZKHUH & LV GRPHVWLF UHHI ILVK FDWFK PHDVXUHG LQ WKRXVDQGV RI SRXQGV ( GHQRWHV HIIRUW DV PHDVXUHG E\ WKH QXPEHU RI VWDQGDUGL]HG YHVVHOV DQG WKH HVWLPDWHG VWDQGDUG HUURUV DUH LQ SDUHQWKHVHV 7KH PD[LPXP VXVWDLQDEOH \LHOG REWDLQHG IRU HTXDWLRQ f ZDV HVWLn PDWHG WR EH DSSUR[LPDWHO\ PLOOLRQ SRXQGV REWDLQHG IURP VWDQn GDUGL]HG YHVVHOV *LYHQ HTXDWLRQ f DQG WKH IDFW WKDW VWDQGDUGL]HG UHHI ILVK YHVVHOV ZHUH UHSRUWHG LQ WKH ILVKHU\ LQ LW LV DSSDUHQW WKDW FXUUHQW HIIRUW OHYHOV DUH JUHDWHU WKDQ WKRVH QHFHVVDU\ WR FDWFK PD[LPXP VXVWDLQDEOH \LHOG 7KH VXVWDLQDEOH \LHOG HVWLPDWH REWDLQHG IURP HTXDWLRQ f FRUUHVSRQGLQJ WR VWDQGDUGL]HG YHVVHOV ZDV DERXW PLOOLRQ SRXQGV ZKLFK LV DERXW PLOOLRQ SRXQGV OHVV WKDQ WKH UHSRUWHG FDWFK 7KXV FDWFK OHYHOV H[FHHGHG VXVWDLQDEOH \LHOG E\ D FRQVLGHUn DEOH DPRXQW 6XVWDLQDEOH \LHOG IRU WKH 0(< HIIRUW OHYHO RI J 7KH DGMXVWPHQW RI ILVKLQJ HIIRUW DQG FDWFK ZDV RQ DQ DJJUHJDWH EDVLV UDWKHU WKDQ LQGLYLGXDOO\ IRU HDFK VWDWH 7KLV UHVXOWHG IURP WKH DEVHQFH RI VSHFLILF LQIRUPDWLRQ RQ FDWFK DQG HIIRUW RII IRUHLJQ FRDVWV RQ D VWDWH E\ VWDWH EDVLV
PAGE 125
VWDQGDUGL]HG YHVVHOV ZDV HVWLPDWHG WR EH PLOOLRQ SRXQGV 7KLV HVWLPDWH OHQGV VRPH VWUHQJWK WR WKH HTXLOLEULXP LQWHUSUHWDWLRQ RI WKH FDWFK HTXDWLRQV XVHG LQ REWDLQLQJ 0(< 7KH GHULYHG HTXLOLEULXP FDWFK REWDLQHG IURP WKH 0(< VROXWLRQ ZDV PLOOLRQ SRXQGV ZKLFK LV H[WUHPHO\ FORVH WR WKH VXVWDLQDEOH \LHOG HVWLPDWH REWDLQHG IURP HTXDWLRQ f 7KH PLOOLRQ SRXQG HVWLPDWH IRU 0(< LV FRXFKHG LQ WHUPV RI DOO UHHI ILVK 6LQFH WKH VSHFLHV FRPSRVLWLRQ RI UHHI ILVK ZLWKLQ HDFK VWDWH KDV EHHQ UHPDUNDEO\ FRQVWDQW RYHU WLPH WKH 0(< FDWFK HVWLPDWH FDQ EH GLVDJJUHJDWHG LQWR UHG VQDSSHU DQG JURXSHU FDWFK FRPSRQHQWV 7KH WRWDO FDWFK RI UHHI ILVK LV HVWLPDWHG WR EH FRPSRVHG RI DSSUR[LPDWHO\ PLOOLRQ SRXQGV RI UHG VQDSSHU DQG PLOOLRQ SRXQGV RI JURXSHU 7DEOH f 7KH HVWLPDWHG FDWFK SURSRUWLRQV LQGLFDWH WKH )ORULGD UHHI ILVK FDWFK KDV WKH ODUJHVW JURXSHU FRPSRVLWLRQ 2Q DYHUDJH DSSUR[LPDWHO\ SHUFHQW RI WRWDO UHHI ILVK ODQGLQJV E\ ZHLJKW LQ )ORULGD DUH DWWULEXWn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f )ORULGD YHVVHOV ZLWK D FDSLWDOODERU UDWLR RI UHSUHVHQW WKH OHDVW FDSLWDO LQWHQVLYH
PAGE 126
7DEOH (VWLPDWHG VSHFLHV FRPSRVLWLRQ RI 0(< FDWFK RI UHHI ILVK 6WDWH 5HG 6QDSSHU &DWFK SURSRUWLRQ *URXSHU &DWFK SURSRUWLRQ )ORULGD $DEDPD 0LVVLVVLSSL 7H[DV 727$/ D&DWFK LV PHDVXUHG LQ WKRXVDQGV RI SRXQGV DYHUDJH ILVKLQJ SRZHU SHU YHVVHO ZKLOH $ODEDPD YHVVHOV ZLWK KDYH WKH PRVW FDSLWDO LQWHQVLYH DYHUDJH ILVKLQJ SRZHU 7DEOH f 7KH UHODn WLYHO\ FDSLWDO LQWHQVLYH QDWXUH RI YHVVHOV LQ $ODEDPD DQG 7H[DV PD\ SDUWLDOO\ H[SODLQ ZK\ WKH SURILW SHU YHVVHO LQ WKHVH VWDWHV UHVXOWLQJ IURP KDUYHVW RI 0(< LQ WKH ILVKHU\ ZRXOG EH ORZ FRPSDUHG WR YHVVHOV LQ 0LVVLVVLSSL 7KH QXPEHU RI YHVVHOV LQ WKH *05)) QHFHVVDU\ WR KDUYHVW PD[LPXP HFRQRPLF \LHOG GHFUHDVHV DV WKH DYHUDJH ILVKLQJ SRZHU SHU YHVVHO LQFUHDVHV )LJXUH f 7KH UDWH RI GHFUHDVH LQ WKH RSWLPXP QXPEHU RI YHVVHOV RFFXUV DW D UDWH RI DERXW QLQH YHVVHOV IRU HDFK SHUFHQW LQFUHDVH LQ ILVKLQJ SRZHUA +RZHYHU WRWDO ILVKLQJ HIIRUW DV PHDVXUHG LQ WHUPV RI VWDQGDUGL]HG YHVVHOV FRUUHVSRQGLQJ WR 0(< LQFUHDVHV DV A$SSHQGL[ + FRQWDLQV D FRPSOHWH SUHVHQWDWLRQ RI WKHVH UHVXOWV RQ D VWDWH E\ VWDWH EDVLV
PAGE 127
7DEOH )LVKLQJ SRZHU FRPSRQHQWV IRU SURSRUWLRQDO LQFUHDVHV DORQJ UD\V GHILQHG E\ FRQVWDQW YHVVHO VL]H FUHZ VL]H UDWLRV 3HUFHQWDJH )ORULGD $ODEDPD 0LVVLVVLSSL 7H[DV LQFUHDVH &UHZ 9HVVHO &UHZ 9HVVHO &UHZ 9HVVHO &UHZ 9HVVHO 1R 7RQV 1R 7RQV 1R 7RQV 1R 7RQV 9HVVHO VL]Hr &UHZ VL]H D 9HVVHO VL]H PHDVXUHG LQ JURVV UHJLVWHUHG WRQV A &DSLWDOODERU UDWLR
PAGE 128
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n DEOH WR YHVVHO VL]H LQFUHDVH 7KXV WKH LQFUHDVHG ILVKLQJ SRZHU RI YHVVHOV UHVXOWLQJ IURP LQFUHDVLQJ WKHVH WZR IDFWRUV PRUH WKDQ RIIVHWV WKH LQFUHDVH LQ FRVW DULVLQJ IURP ILVKLQJ ZLWK ODUJHU YHVVHOV 7KH LQFUHDVH LQ VWDQGDUGL]HG YHVVHOV LV VLJQLILFDQW LQ PDJQLWXGH $W OHYHOV RI ILVKLQJ SRZHU 0(< LV DWWDLQHG ZLWK YHVVHOV RU VWDQn GDUGL]HG YHVVHOV $ SHUFHQW LQFUHDVH LQ FUHZ VL]H DQG YHVVHO VL]H UHGXFHV WKH QRPLQDO QXPEHU RI YHVVHOV QHFHVVDU\ WR FDWFK PD[LPXP
PAGE 129
3URSRUWLRQDWH ,QFUHDVH LQ )LVKLQJ 3RZHU &RPSRQHQWV )LJXUH 2SWLPXP QXPEHU RI VWDQGDUGL]HG YHVVHOV FRUUHVSRQGn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
PAGE 130
WKRXJK WKH QRPLQDO QXPEHU RI YHVVHOV KDV UHPDLQHG IL[HG 7KXV ILVKHU\ PDQDJHUV DWWHPSWLQJ WR OLPLW ILVKLQJ HIIRUW ZLOO KDYH WR SODFH UHVWULFn WLRQV RQ ILVKLQJ SRZHU LQ DGGLWLRQ WR WKH QRPLQDO QXPEHU RI YHVVHOV WR DFKLHYH D JLYHQ FDWFK OHYHO $OWHUQDWLYHO\ PDQDJHUV FDQ FRQWLQXDOO\ UHGXFH WKH QRPLQDO QXPEHU RI YHVVHOV WR RIIVHW LQFUHDVHV LQ ILVKLQJ SRZHU ,W VKRXOG EH QRWHG KRZHYHU WKDW WKHUH LV VRPH OLPLW WR ZKLFK DYHUDJH ILVKLQJ SRZHU SHU YHVVHO FDQ H[SDQG $OVR WKH FRVWV RI PDQDJn LQJ ILVKLQJ SRZHU FRXOG EH SURKLELWLYH $Q DGGLWLRQDO HIIHFW RI WKH LQFUHDVH LQ HIIHFWLYH ILVKLQJ HIIRUW WKURXJK LQFUHDVHV LQ ILVKLQJ SRZHU LV WKDW WKH OHYHO RI FDWFK FRUUHVSRQGn LQJ WR PD[LPXP HFRQRPLF \LHOG DOVR LQFUHDVHV )LJXUH f )RU H[DPSOH SHUFHQW LQFUHDVHV LQ DYHUDJH YHVVHO VL]H DQG DYHUDJH FUHZ VL]H IURP OHYHOV LQFUHDVHV PD[LPXP HFRQRPLF \LHOG IURP PLOOLRQ SRXQGV WR PLOOLRQ SRXQGV 7KH 0(< HVWLPDWH IRU WKH SHUFHQW LQFUHDVH LQ FUHZ DQG YHVVHO VL]H LV HVSHFLDOO\ LQWHUHVWLQJ LQ WKDW LW LV YHU\ QHDU WKH PD[LPXP VXVWDLQDEOH \LHOG RI PLOOLRQ SRXQGV HVWLPDWHG IURP HTXDWLRQ f &RPSDULVRQ ZLWK 3UHYLRXV 6WXGLHV 7KH RQO\ DJJUHJDWH DQDO\VLV SHUIRUPHG RQ DOO VWDWHV LQYROYHG LQ WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ RWKHU WKDQ WKH FXUUHQW VWXG\ ZDV WKDW SHUIRUPHG E\ WKH *XOI RI 0H[LFR )LVKHU\ 0DQDJHPHQW &RXQFLO f $ FRPSDULVRQ RI WKH &RXQFLOnV ILQGLQJV ZLWK WKRVH SUHVHQWHG DERYH SURYLGH DQ HQOLJKWHQLQJ FRQFOXVLRQ WR WKLV FKDSWHU $ GLUHFW FRPSDULVRQ RI WKH PDQDJHPHQW FRQFOXVLRQV UHDFKHG E\ WKH *XOI RI 0H[LFR )LVKHU\ 0DQDJHPHQW &RXQFLO f ZLWK WKRVH RI WKH SUHVHQW VWXG\ PXVW EH GRQH ZLWK FDXWLRQ 7KH PD[LPXP VXVWDLQDEOH \LHOG
PAGE 131
3URSRUWLRQDWH ,QFUHDVH LQ )LVKLQJ 3RZHU &RPSRQHQWV )LJXUH (VWLPDWHG PD[LPXP HFRQRPLF \LHOG IRU LQFUHDVLQJ OHYHOV RI DYHUDJH ILVKLQJ SRZHU HVWLPDWH IRU WKH *05)) REWDLQHG E\ WKH PDQDJHPHQW FRXQFLO KDV EHHQ VHW DW PLOOLRQ SRXQGV RI VQDSSHU DQG JURXSHU 7KLV HVWLPDWH KRZHYHU LV EDVHG RQ KLVWRULFDO &XEDQ DQG UHFUHDWLRQDO FDWFK DV ZHOO DV FRPPHUn FLDO FDWFKA )XUWKHUPRUH DOO UHHI ILVK VWRFNV DUH WUHDWHG DV D VLQJOH XQLW VWRFN 7KH PDQDJHPHQW FRXQFLO IXUWKHU HVWLPDWHV WKDW DW FXUUHQW OHYHOV RI FRPPHUFLDO ILVKLQJ HIIRUW DV PHDVXUHG E\ PDQGD\V ILVKHG H[SHFWHG FRPn PHUFLDO KDUYHVW RI JURXSHU DQG UHG VQDSSHU ZLOO EH DSSUR[LPDWHO\ PLOOLRQ SRXQGV )XUWKHU WKH HVWLPDWHG FDWFK E\ UHFUHDWLRQDO ILVKHUPHQ 7KLV HVWLPDWH RI 06< KDV EHHQ TXHVWLRQHG DV EHLQJ ORZ GXH WR HUURUV LQ WKH GDWD XVHG IRU HVWLPDWLRQ $ UHYLVHG HVWLPDWH RI PLOOLRQ SRXQGV KDV EHHQ VXJJHVWHG %RWK HVWLPDWHV DUH FRQVLGHUHG SUHn OLPLQDU\ E\ WKH PDQDJHPHQW FRXQFLO DW WKH WLPH RI ZULWLQJ WKLV GLVVHUWDWLRQ 7KH FRXQFLOnV SODQ KDV EHHQ UHWXUQHG WR FRPPLWWHH IRU UHYLVLRQ *)0)& f
PAGE 132
KDV EHHQ VHW DW DSSUR[LPDWHO\ PLOOLRQ SRXQGV 7KH WRWDO RI WKHVH HVWLPDWHV PLOOLRQ SRXQGV RULJLQDOO\ OHG WKH 0DQDJHPHQW &RXQFLO WR FRQFOXGH WKDW WKH ILVKHU\ EDVHG RQ GDWD WKURXJK LV FXUUHQWO\ RSHUDWLQJ YHU\ QHDU PD[LPXP VXVWDLQDEOH \LHOG LQ DJJUHJDWH ,Q WHUPV RI WKH UHFUHDWLRQDO DQG FRPPHUFLDO VHFWRUV KRZHYHU WKH FRXQFLO KDV FRQn FOXGHG WKH RYHUILVKLQJ PD\ EH SUHVHQW LQ WKH DUHDV IUHTXHQWHG E\ UHFUHDWLRQLVWV DQG FRQYHUVHO\ WKH VWRFNV VXEMHFW WR FRPPHUFLDO ILVKLQJ PD\ EH XQGHUILVKHG *05)) f 7KH DQDO\VLV RI WKH FXUUHQW VWXG\ ZDV UHVWULFWHG VROHO\ WR WKH GRPHVWLF FRPPHUFLDO UHHI ILVK ILVKHU\ 7KH H[FOXVLRQ RI WKH UHFUHDn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n PHUFLDO UHHI ILVK VWRFNV 7KLV LV FRQWUDU\ WR WKH ILQGLQJV RI WKH *XOI 0DQDJHPHQW &RXQFLO ZKLFK VXJJHVW WKDW D FDWFK RI DERXW PLOOLRQ SRXQGV E\ FRPPHUFLDO ILVKHUPHQ LV VXVWDLQDEOH 7KH PD[LPXP VXVWDLQDEOH \LHOG HVWLPDWH GHULYHG IRU WKH FRPPHUFLDO UHHI LQ WKLV VWXG\ ZDV VHW DW PLOOLRQ SRXQGV %DVHG RQ WKLV HVWLPDWH D FRPPHUFLDO FDWFK RI PLOOLRQ SRXQGV LV QRW VXVWDLQDEOH DQG ZRXOG UHVXOW LQ D GHFOLQH LQ
PAGE 133
WKH UHHI ILVK VWRFNV DQG KHQFH D GHFOLQH LQ FDWFK 3UHOLPLQDU\ GDWD RQ UHHI ILVK ODQGLQJV IRU WKURXJK VKRZ D VLJQLILFDQW GHFOLQH LQ FDWFK ZHOO EHORZ WKH 06< HVWLPDWH REWDLQHG IURP HTXDWLRQ f &DWFK RI UHG VQDSSHU DQG JURXSHU ZDV UHSRUWHG WR EH PLOOLRQ SRXQGV LQ 6LQFH WKDW WLPH ODQGLQJV KDYH LQFUHDVHG VOLJKWO\ WR DSSUR[Ln PDWHO\ PLOOLRQ SRXQGV LQ 7KHVH GDWD OHQG FRQVLGHUDEOH VXSSRUW WR WKH LPSOLFDWLRQ RI RYHUILVKLQJ LQ WKH FRPPHUFLDO UHHI ILVKHU\ DV ZHOO DV WKH PD[LPXP VXVWDLQDEOH \LHOG HVWLPDWH RI PLOOLRQ SRXQGV REWDLQHG IURP HTXDWLRQ f 7KH RSWLPXP \LHOG IRU WKH UHHI ILVKHU\ DV VHW E\ WKH *0)0& ZDV GHILQHG WR EH HTXDO WR WKH HVWLPDWHG 0<6 RI DSSUR[LPDWHO\ PLOOLRQ SRXQGV *0)0& f 2SWLPXP \LHOG LV GHILQHG WR EH WKDW \LHOG RI ILVK ZKLFK SURYLGHV WKH JUHDWHVW RYHUDOO VRFLDO DQG HFRQRPLF EHQHILWV ZKLOH HQVXULQJ FRQVHUYDWLRQ RI WKH UHVRXUFH VWRFN 7KH FRXQFLO LQ VHWWLQJ RSWLPXP \LHOG
PAGE 134
&+$37(5 9 6800$5< $1' &21&/86,216 7KH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ *05))f LV RQH RI WKH PRVW LPSRUWDQW *XOI ILVKHULHV LQ WHUPV RI ERWK TXDQWLW\ ODQGHG DQG WRWDO YDOXH 7KH ILVKHU\ LQFOXGHV DOO RI WKH *XOI FRDVWDO VWDWHV DQG HQFRPn SDVVHV D ZLGH YDULHW\ RI VSHFLHV 7KH PRVW DEXQGDQW RI WKHVH VSHFLHV LQ FRPPHUFLDO FDWFK DUH UHG VQDSSHU /XWMDQXV FDPSHFKDQXVf UHG JURXSHU (SLQHSKHOXV PRULRf DQG EODFN JURXSHU 0\FWHURSHUFD ERQDFLf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nV ZHVW FRDVW LQ ,Q WHUPV RI LQGLYLGXDO VSHFLHV )ORULGDnV ZHVW FRDVW DFFRXQWHG IRU DSSUR[LPDWHO\ SHUFHQW RI DOO UHG VQDSSHU FDXJKW DQG SHUFHQW RI DOO JURXSHU WDNHQ LQ WKH ILVKHU\ LQ ,Q RI WKH YHVVHOV UHSRUWHG LQ WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ ILVKHG RXW RI )ORULGD :HVW &RDVW SRUWV
PAGE 135
9HVVHO VL]HV DQG FUHZ VL]HV YDU\ JUHDWO\ DFURVV VWDWHV LQ WKH ILVKHU\ 9HVVHOV ILVKLQJ IURP )ORULGD SRUWV KDYH W\SLFDOO\ EHHQ WKH VPDOOHVW )ORULGD YHVVHOV DYHUDJHG JURVV UHJLVWHUHG WRQV LQ ZHLJKW ZLWK DQ DYHUDJH RI WKUHH FUHZPHQ SHU YHVVHO LQ ,Q FRQWUDVW 0LVVLVVLSSL YHVVHOV KDYH JHQHUDOO\ EHHQ WKH ODUJHVW DYHUDJLQJ JURVV UHJLVWHUHG WRQV ZLWK DYHUDJH FUHZ VL]HV RI QLQH PHQ 7RWDO ODQGLQJV RI UHHI ILVK LQ WKH *XOI RI 0H[LFR GHFOLQHG IDLUO\ FRQVLVWHQWO\ VLQFH WKH PLGVL[WLHV &RPELQHG FRPPHUFLDO ODQGLQJV RI UHG VQDSSHU DQG JURXSHU DPRXQWHG WR DSSUR[LPDWHO\ PLOOLRQ SRXQGV LQ 3UHOLPLQDU\ ODQGLQJV GDWD IRU UHSRUW FRPELQHG ODQGLQJV RI JURXSHU DQG VQDSSHU RI RQO\ PLOOLRQ SRXQGV 7KLV GHFOLQH LQ FDWFK RI RYHU SHUFHQW RFFXUUHG LQ VSLWH RI LQFUHDVHG QXPEHUV RI YHVVHOV RSHUDWLQJ LQ WKH ILVKHU\ 7KLV VWXG\ UHSUHVHQWV WKH ILUVW DWWHPSW WR GHULYH GHILQLWLYH FRQn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n PDWLQJ D V\VWHP RI FDWFK HTXDWLRQV ZKHUHLQ IDFWRUV VXFK DV UHVRXUFH VWRFN HIIHFWV DQG SURGXFWLYH LQWHUGHSHQGHQFH ZHUH LQFRUSRUDWHG E\ PHDQV RI VWRFKDVWLF VSHFLILFDWLRQV DQG WKH HVWLPDWLRQ RI DQ LQWHUUHODWHG
PAGE 136
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n WLRQ LQ FRQVWUXFWLQJ WKH HPSLULFDO PRGHOV 7KHRUHWLFDO &RQFOXVLRQV 7KH ELRORJLFDO WKHRU\ RI SRSXODWLRQ G\QDPLFV KDV WUDGLWLRQDOO\ VHUYHG DV WKH ELRORJLFDO IRXQGDWLRQ IRU ELRHFRQRPLF PRGHOV RI RFHDQ ILVKHULHV *HQHUDOO\ WKHVH ELRHFRQRPLF PRGHOV KDYH XWLOL]HG VXUSOXV VWRFN SURGXFWLRQ PRGHOV WR DSSUR[LPDWH WHFKQLFDO SURGXFWLRQ UHODWLRQVKLSV &RVWV DQG SULFHV KDYH EHHQ DGGHG WR DQDO\]H TXHVWLRQV RI HFRQRPLF HIILFLHQF\ 7KH DOPRVW XQLYHUVDO FRQFOXVLRQ UHDFKHG ZLWK VXFK PRGHOV KDV EHHQ WKDW WKH FRPPRQ SURSHUW\ QDWXUH RI WKH UHVRXUFH LQ FRPELQDWLRQ ZLWK XQUHJXODWHG FRPSHWLWLRQ ZRXOG OHDG WR HFRQRPLFDOO\ LQHIILFLHQW OHYHOV RI ILVKLQJ HIIRUW 0D[LPL]DWLRQ RI UHWXUQV WR WKH UHVRXUFH KDV EHHQ DVVXPHG WR UHVXOW LQ HFRQRPLFDOO\ HIILFLHQW FDWFK DQG HIIRUW OHYHOV 7KLV UHVXOW KDV QRW JRQH XQTXHVWLRQHG KRZHYHU )URP D VRFLDO VWDQGSRLQW PDQ\ KDYH DUJXHG WKDW PD[LPXP VXVWDLQDEOH \LHOG
PAGE 137
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n FRVWV DQG UHYHQXHV KDG WR EH FRQVLGHUHG VLPXOWDQHRXVO\ 7KH DWWDLQPHQW RI PD[LPXP HFRQRPLF \LHOG UHTXLUHG WKDW WKH PDUJLQDO FRVW LQ HDFK VWDWH EH HTXDWHG WR WKH PDUJLQDO FKDQJH LQ WRWDO LQGXVWU\ UHYHQXH DWWULEXWDEOH WR FKDQJHV LQ FDWFK LQ HDFK VWDWH 6LPXOWDQHRXV WUHDWPHQW RI DOO VHFWRUV LQ REWDLQLQJ WKH PDUJLQDO FRQGLWLRQV IRU PD[LPXP HFRQRPLF \LHOG WKXV LQWHUQDOL]HG WKH SHFXQLDU\ H[WHUQDOLWLHV SUHVHQW 7R DSSO\ WKLV WKHRU\ WR WKH *05)) D VWDWLVWLFDO PRGHO ZDV VSHFLn ILHG DQG HVWLPDWHG 7KH PRGHO LQFOXGHG D V\VWHP RI VWDWH FDWFK HTXDn WLRQV DQG D V\VWHP RI VWDWH SULFH HTXDWLRQV ,Q DGGLWLRQ D FRVW HTXDWLRQ IRU HDFK VWDWH ZDV GHYHORSHG
PAGE 138
(PSLULFDO FDWFK HTXDWLRQV IRU WKH *05)) VWDWHV ZHUH FKDUDFWHUL]HG DV D V\VWHP RI VHHPLQJO\ XQUHODWHG UHJUHVVLRQ HTXDWLRQV ZLWK ILUVW RUGHU DXWRUHJUHVVLYH GLVWXUEDQFHV DQG FURVVHTXDWLRQ SDUDPHWHU UHVWULFWLRQV 7KH SUHVHQFH RI FRQWHPSRUDQHRXV FRUUHODWLRQ DFURVV VWDWHV ZDV H[SHFWHG GXH WR WKH SURGXFWLYH LQWHUGHSHQGHQFH RI YHVVHOV RSHUDWLQJ RXW RI GLIn IHUHQW VWDWHV 7KH DXWRUHJUHVVLYH SRUWLRQ RI WKH GLVWXUEDQFHV ZDV DQWLFLSDWHG WR UHVXOW IURP WKH RPLVVLRQ RI H[SOLFLW LQIRUPDWLRQ RQ FKDQJHV LQ WKH UHVRXUFH VWRFN 7KH HVWLPDWRU FKRVHQ WR HVWLPDWH WKH V\VWHP RI FDWFK HTXDWLRQV ZDV D IRXU VWDWH IHDVLEOH $LWNHQnV HVWLPDWRU $OO SDUDPHWHU HVWLPDWHV ZHUH RI WKH DSSURSULDWH VLJQ UHDVRQDEOH PDJQLn WXGH DQG GHPRQVWUDWHG DFFHSWDEOH VWDWLVWLFDO VLJQLILFDQFH (VWLPDWHG 3DUDPHWHUV 7KH FDWFK HTXDWLRQV HVWLPDWHG ZHUH UHGXFHG IURP H[SUHVVLRQV ZKLFK UHVXOWHG IURP WKH VSHFLDO WUHDWPHQW RI ILVKLQJ HIIRUW )LVKLQJ HIIRUW ZDV GHILQHG WR EH WKH SURGXFW RI QRPLQDO HIIRUW YHVVHOVf DQG ILVKLQJ SRZHU )LVKLQJ SRZHU ZDV H[SUHVVHG DV D IXQFWLRQ RI DYHUDJH FUHZ VL]H DQG DYHUDJH YHVVHO VL]H 7KH DPRXQW RI ILVKLQJ HIIRUW DWWULEXWHG WR YHVVHOV LQ DQ\ JLYHQ VWDWH DQG WLPH SHULRG ZDV WKHQ GHWHUPLQHG E\ WKH FRUUHVSRQGLQJ DYHUDJH FUHZ DQG YHVVHO VL]H 3DUDPHWHUV RI WKH GRXEOH ORJ ILVKLQJ SRZHU IXQFWLRQ ZHUH FRQn VWUDLQHG WR EH HTXDO DFURVV VWDWHV GXH WR WKH H[WUHPH VLPLODULW\ RI SURGXFWLRQ SUDFWLFHV LQ DOO VWDWHV SDUWLFLSDWLQJ LQ WKH *05)) 7KH ILVKLQJ SRZHU IXQFWLRQ SDUDPHWHUV FRXOG QRW EH HVWLPDWHG LQGHSHQGHQWO\ RI FDWFK GXH WR WKH GHILQLWLRQDO QDWXUH RI WKH ILVKLQJ SRZHU IXQFWLRQ 7KXV DQ H[SUHVVLRQ UHODWLQJ FDWFK LQ HDFK VWDWH WR ILVKLQJ HIIRUW DV GHILQHG DERYH ZDV GHYHORSHG 7KH UHVXOW ZDV D VHW RI UHGXFHG IRUP
PAGE 139
HTXDWLRQV LQ GRXEOH ORJ IRUP H[SUHVVLQJ FDWFK LQ HDFK VWDWH DV D IXQFn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n QHRXVO\ ZRXOG EULQJ DERXW D SHUFHQW LQFUHDVH LQ DYHUDJH ILVKLQJ SRZHU SHU YHVVHO *LYHQ WKH LQWHUSUHWDWLRQV RI WKH SDUWLDO HODVWLFLWLHV WKH DSSHDUDQFH RI LQFUHDVLQJ UHWXUQV LQ WKH ILVKLQJ SRZHU IXQFWLRQ DSSHDUV UHDVRQDEOH ,W VKRXOG EH HPSKDVL]HG WKDW WKLV VFDOH HODVWLFLW\ UHODWHV WR ILVKLQJ SRZHU DQG QRW FDWFK 7KH HVWLPDWHG ILVKLQJ SRZHU IXQFWLRQ ZDV XVHG WR GHILQH D ILVKLQJ SRZHU LQGH[ 7KH LQGH[ ZDV XVHG WR REWDLQ D VWDQGDUGL]HG PHDVXUH RI ILVKLQJ HIIRUW VWDQGDUGL]HG YHVVHOVf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
PAGE 140
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n WLFLW\ HTXDO WR RQH DJDLQVW WKH DOWHUQDWLYH RI OHVV WKDQ RQH ZDV UHMHFWHG DW WKH D OHYHO RI VLJQLILFDQFH *LYHQ WKDW FRQVWDQW UHWXUQV WR ILVKLQJ HIIRUW KDV EHHQ RQH RI WKH PDLQ DVVXPSWLRQV XQGHUO\n LQJ VXUSOXV VWRFN SURGXFWLRQ PRGHOV WKH UHVXOW RI WKLV WHVW LV VLJQLILn FDQW LQ UHODWLRQ WR WKH XVH RI VXFK PRGHOV LQ DGGUHVVLQJ ILVKHU\ PDQDJHPHQW TXHVWLRQV FRQFHUQLQJ WKH *05)) 7KH HVWLPDWHG FDWFK HTXDWLRQV ZHUH QRQHTXLOLEULXP H[SUHVVLRQV 0RQHTXLOLEULXP DV XVHG KHUH LPSOLHV WKDW WKH HVWLPDWHG FDWFK UHVXOWn LQJ IURP D JLYHQ OHYHO RI ILVKLQJ HIIRUW LV QRW FRQVWUDLQHG WR EH HTXDO WR VXVWDLQDEOH \LHOG 'HULYHG HTXLOLEULXP FDWFK HTXDWLRQV FDQ KRZHYHU EH REWDLQHG JLYHQ FHUWDLQ DVVXPSWLRQV 7KH PDLQ DVVXPSWLRQ QHFHVVDU\ IRU VXFK D GHULYDWLRQ ZDV WKDW WKH UHVLGXDO FRPSRQHQWV RI WKH DXWRn UHJUHVVLYH SURFHVV FRQWDLQHG LQ WKH FDWFK HTXDWLRQV EH SURSRUWLRQDO WR WKH GLIIHUHQFH EHWZHHQ FDWFK DQG VXVWDLQDEOH \LHOG IRU DQ\ JLYHQ OHYHO RI ILVKLQJ HIIRUW *LYHQ WKLV DVVXPSWLRQ DQG WKH IDFW WKDW WKH UHVRXUFH
PAGE 141
VWRFN ZLOO DGMXVW VXFK WKDW FDWFK DQG VXVWDLQDEOH \LHOG DUH HTXDWHG LI ILVKLQJ HIIRUW LV KHOG FRQVWDQW IRU D VXIILFLHQW SHULRG RI WLPH WKH OLPLW RI WKH HVWLPDWHG FDWFK HTXDWLRQV RYHU WLPH ZDV VKRZQ WR FRUUHVSRQG WR DQ HTXLOLEULXP UHODWLRQVKLS EHWZHHQ FDWFK DQG ILVKLQJ HIIRUW 7KLV RFFXUV EHFDXVH WKH DXWRUHJUHVVLYH FRPSRQHQW RI WKH FDWFK HTXDWLRQ DSSURDFKHV ]HUR RYHU WLPH IRU DQ\ IL[HG OHYHO RI ILVKLQJ HIIRUW 7KH GHULYHG HTXLOLEULXP UHODWLRQVKLS EHWZHHQ FDWFK DQG ILVKLQJ HIIRUW LV RQO\ YDOLG LQ WKH HFRQRPLF UHJLRQ RI SURGXFWLRQ 7KDW LV WKH HTXLOLEULXP FDWFK HTXDWLRQV GHULYHG IURP WKH HVWLPDWHG HTXDWLRQV DSSUR[Ln PDWH RQO\ WKH OHIW KDQG VLGH RI WKH VXVWDLQDEOH \LHOG FXUYH +RZHYHU LQ UHODWLRQ WR ILVKHU\ PDQDJHPHQW TXHVWLRQV LW LV SUHFLVHO\ WKLV SRUn WLRQ RI WKH VXVWDLQDEOH \LHOG IXQFWLRQ WKDW LV RI LQWHUHVW IURP DQ HFRQRPLF HIILFLHQF\ VWDQGSRLQW 7KH V\VWHP RI SULFH HTXDWLRQV ZDV VSHFLILHG LQ WHUPV RI D QRPLQDO ZHLJKWHG DYHUDJH GRFNVLGH SULFH RI UHHI ILVK 3ULFH HTXDWLRQV ZHUH VSHFLILHG VXFK WKDW SULFH RI UHHI ILVK LQ HDFK VWDWH ZDV H[SUHVVHG DV D IXQFWLRQ RI ZLWKLQ VWDWH FDWFK )ORULGD FDWFK DQG D WLPH WUHQG YDULDEOH 7KH SUHVHQFH RI )ORULGDnV FDWFK LQ HDFK VWDWHnV SULFH HTXDWLRQ SURYLGHG D PHDQV WR PHDVXUH WKH GHJUHH WR ZKLFK SHFXQLDU\ H[WHUQDOLWLHV H[LVW LQ WKH ILVKHU\ 7KH WLPH WUHQG YDULDEOH SURYLGHG D SUR[\ PHDVXUH RI GHPDQG VKLIWV UHODWHG WR LQFRPH DQG SRSXODWLRQ FKDQJHV DV ZHOO DV LQIODWLRQDU\ WUHQGV LQ SULFH (VWLPDWLRQ RI WKH SULFH HTXDWLRQV ZDV DFFRPSOLVKHG E\ XWLOL]LQJ D WZR VWDJH $LWNHQnV HVWLPDWRU 7KLV HVWLPDWRU ZDV FKRVHQ EHFDXVH VXEn VWDQWLDO FRQWHPSRUDQHRXV FRUUHODWLRQ LQ WKH GLVWXUEDQFHV DFURVV HTXDn WLRQV ZDV H[SHFWHG $OO SDUDPHWHU HVWLPDWHV H[FHSW RQH KDG WKH DSSURSULDWH VLJQ DQG UHDVRQDEOH PDJQLWXGH )XUWKHU WKH VXEVWDQWLDO
PAGE 142
GURS LQ WKH HVWLPDWHG VWDQGDUG HUURUV REWDLQHG IURP XWLOL]LQJ WKH V\VWHPV HVWLPDWRU DV FRPSDUHG WR WKRVH UHVXOWLQJ IURP VLQJOH HTXDWLRQ RUGLQDU\ OHDVW VTXDUHV FRQILUPHG WKH SUHVHQFH RI VLJQLILFDQW FRQWHPSRUDn QHRXV FRUUHODWLRQ 7KH HVWLPDWHG RZQ VWDWH SULFH IOH[LELOLWLHV LQGLFDWHG WKDW )ORULGD ODQGLQJV KDG WKH ODUJHVW ZLWKLQ VWDWH HIIHFW RQ SULFH $ SHUFHQW LQFUHDVH LQ )ORULGD UHHI ILVK FDWFK ZDV HVWLPDWHG WR GHFUHDVH SULFH LQ )ORULGD E\ DSSUR[LPDWHO\ SHUFHQW (VWLPDWHG RZQ VWDWH SULFH IOH[Ln ELOLWLHV IRU 0LVVLVVLSSL DQG 7H[DV LQGLFDWHG D SHUFHQW LQFUHDVH LQ ODQGLQJV LQ WKHVH VWDWHV ZRXOG GHFUHDVH SULFH E\ DQG SHUFHQW UHVSHFWLYHO\ $ODEDPD DQG /RXLVLDQD SULFH IOH[LELOLW\ HVWLPDWHV LQGLn FDWHG WKDW WKHVH VWDWHV KDG YLUWXDOO\ QR HIIHFW RQ SULFH 7KH HIIHFW RI )ORULGDnV FDWFK RQ UHHI ILVK SULFHV LQ HDFK VWDWH ZDV JUHDWHU WKDQ WKH FRUUHVSRQGLQJ ZLWKLQ VWDWH FDWFK ZLWK WKH H[FHSn WLRQ RI 0LVVLVVLSSL (VWLPDWHG FURVV VWDWH SULFH IOH[LELOLWLHV LQGLn FDWHG WKDW D SHUFHQW LQFUHDVH LQ )ORULGD FDWFK ZRXOG GHFUHDVH UHHI ILVK SULFHV E\ DERXW SHUFHQW LQ 7H[DV DQG SHUFHQW LQ /RXLVLDQD 7KH FURVV SULFH IOH[LELOLW\ HVWLPDWHV IRU $ODEDPD DQG 0LVVLVVLSSL LQGLFDWHG D VLPLODU LQFUHDVH LQ )ORULGDnV FDWFK ZRXOG GHFUHDVH UHVSHFn WLYH SULFHV E\ DQG SHUFHQW 7KHVH HVWLPDWHG FURVV VWDWH SULFH IOH[LELOLWLHV VHUYHG WR FRQILUP )ORULGDnV GRPLQDQFH LQ WKH UHHI ILVKHU\ LQ UHODWLRQ WR GRFNVLGH SULFH GHWHUPLQDWLRQ 7KH HVWLPDWHG HIIHFWV RQ UHHI ILVK SULFH LQ HDFK VWDWH DWWULEXWDEOH WR GHPDQG VKLIWV DQG LQIODWLRQ DV PHDVXUHG E\ WKH WLPH WUHQG YDULDEOH ZHUH VLPLODU IRU DOO VWDWHV )ORULGD SULFH RI UHHI ILVK GHPRQVWUDWHG WKH JUHDWHVW DQQXDO SULFH FKDQJH RYHU WLPH LQFUHDVLQJ DQ DYHUDJH RI
PAGE 143
FHQWV SHU \HDU /RXLVLDQD KDG WKH VPDOOHVW HVWLPDWHG DQQXDO SULFH LQFUHDVH DYHUDJLQJ DERXW FHQWV SHU \HDU 7KH HVWLPDWHG FDWFK DQG SULFH HTXDWLRQV ZHUH SODFHG LQWR WKH WKHRn UHWLFDO IUDPHZRUN GHYHORSHG LQ WKLV VWXG\ WR HVWLPDWH PD[LPXP HFRQRPLF \LHOG IRU WKH *05)) 7R XSGDWH WKH PRGHO WKH SULFH HTXDWLRQV ZHUH LQIODWHG WR OHYHOV E\ XVLQJ WKH WLPH WUHQG YDULDEOHV ,Q DGGLWLRQ WKH GHULYHG HTXLOLEULXP IRUP RI WKH FDWFK HTXDWLRQV ZHUH XWLOL]HG WR HQVXUH D ELRORJLFDO HTXLOLEULXP ZRXOG EH SUHVHQW LQ WKH ILQDO VROXWLRQ )LVKLQJ SRZHU ZDV H[RJHQRXVO\ IL[HG IRU YHVVHOV LQ HDFK VWDWH DW OHYHOV RI DYHUDJH FUHZ VL]H DQG DYHUDJH YHVVHO VL]H 7KXV WKH PDLQ GHFLVLRQ YDULDEOHV LQ WKH PRGHO ZHUH WKH FDWFK RI UHHI ILVK LQ HDFK VWDWH DQG WKH FRUUHVSRQGLQJ QXPEHU RI YHVVHOV LQ HDFK VWDWH &RVWV UHODWLQJ WR YHVVHOV LQ WKH PRGHO ZHUH HVWLPDWHG IURP VXUYH\ GDWD 7KH FRVWV XWLOL]HG FRUUHVSRQGHG WR WKH DQQXDO WRWDO RSHUDWLQJ DQG PDLQWHQDQFH FRVW RI D YHVVHO RI JLYHQ VL]H PLQXV FUHZ VKDUHV DQG JURFHU\ H[SHQVHV 7KH VXEWUDFWLRQ RI FUHZ VKDUHV IURP WRWDO FRVW ZDV EDVHG RQ WKH DVVXPSWLRQ WKDW WKH FDSWDLQ DQG FUHZ RQ HDFK ERDW FRQVWLn WXWH D SVXHGR SDUWQHUVKLS ZLWK WKH WHUPV RI WKH SDUWQHUVKLS EHLQJ GHWHUPLQHG E\ WKH VKDUH DJUHHPHQW 7KXV SURILW LQ WKH ILVKHU\ FRUn UHVSRQGHG WR WKH DJJUHJDWH UHWXUQV RYHU FRVW DWWULEXWDEOH WR WKHVH SDUWQHUVKLSV $OO FRVWV ZHUH H[SUHVVHG LQ WHUPV RI GROODUV 7KH *05)) PRGHO ZDV VROYHG IRU PD[LPXP HFRQRPLF \LHOG XVLQJ D TXDGUDWLFDOO\ FRQYHUJHQW 1HZWRQOLNH QXPHULFDO RSWLPL]DWLRQ DOJRULWKP 0D[LPXP HFRQRPLF \LHOG LQ WKH UHHI ILVKHU\ ZDV HVWLPDWHG WR EH DSSUR[Ln PDWHO\ PLOOLRQ SRXQGV 7KH RSWLPXP QXPEHU RI YHVVHOV QHFHVVDU\ WR SURGXFH WKLV FDWFK ZDV HVWLPDWHG WR EH VWDQGDUGL]HG YDULDEOHVf
PAGE 144
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n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
PAGE 145
7KXV SULFH UHFHLYHG E\ SURGXFHUV YDULHV DFURVV VWDWHV RQ WKH EDVLV RI GLIIHULQJ VSHFLHV FRPSRVLWLRQV RI FDWFK &RQGLWLRQ DQG 0DQDJHPHQW RI WKH )LVKHU\ ,Q WHUPV RI D VWDQGDUGL]HG PHDVXUH RI ILVKLQJ HIIRUW WKH HVWLPDWHG PD[LPXP HFRQRPLF \LHOG RI PLOOLRQ SRXQGV ZDV REWDLQHG IURP DSSUR[Ln PDWHO\ VWDQGDUGL]HG YHVVHOV 7KH FDWFK UHVXOWLQJ IURP WKH VWDQGDUGL]HG YHVVHOV RSHUDWLQJ LQ WKH ILVKHU\ LQ ZDV UHSRUWHG DW PLOOLRQ SRXQGV 7KXV D PRUH WKDQ SHUFHQW UHGXFWLRQ LQ ILVKLQJ HIIRUW ZDV HVWLPDWHG WR GHFUHDVH FDWFK E\ RQO\ SHUFHQW $Q LPSOLFDn WLRQ RI WKLV UHVXOW LV WKDW WKH UHHI ILVKHU\ LQ HPSOR\HG HIIRUW OHYHOV LQ H[FHVV RI WKRVH QHFHVVDU\ WR FDSWXUH PD[LPXP VXVWDLQDEOH \LHOG *LYHQ WKH ILVKHULHV ORQJ H[LVWHQFH DQG WKH DEVHQFH RI HIIRUW UHVWULFWLRQV VXFK DQ RFFXUUHQFH LV LQ KDUPRQ\ ZLWK FXUUHQW ELRHFRQRPLF WKHRULHV RI XQUHJXODWHG ILVKHULHV 7R WHVW WKLV LPSOLFDWLRQ RI RYHUILVKLQJ D 6FKDHIHU W\SH VXVWDLQn DEOH \LHOG IXQFWLRQ ZDV HVWLPDWHG IRU WKH GRPHVWLF FRPPHUFLDO *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ 7KH ODQGLQJV GDWD XVHG ZDV DGMXVWHG E\ UHPRYn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
PAGE 146
RI ILVKLQJ HIIRUW VWDQGDUGL]HG YHVVHOVf ZDV HVWLPDWHG WR EH PLOOLRQ SRXQGV 7KH DFWXDO FDWFK RI PLOOLRQ SRXQGV LQGLFDWHG WKDW FDWFK OHYHOV LQ H[FHHGHG VXVWDLQDEOH \LHOG 7KH HVWLPDWHG VXVWDLQDEOH \LHOG IXQFWLRQ ZDV DOVR XWLOL]HG WR FKHFN WKH YDOLGLW\ RI WKH GHULYHG HTXLOLEULXP LQWHUSUHWDWLRQ RI WKH FDWFK HTXDWLRQV XWLOL]HG LQ WKH *05)) PRGHO 7KH VXVWDLQDEOH \LHOG FRUUHVSRQGn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n LQJ SRZHU 7KH RSWLPXP QXPEHU RI QRPLQDO YHVVHOV QHFHVVDU\ WR FDWFK PD[LPXP HFRQRPLF \LHOG GHFOLQHG DV ILVKLQJ SRZHU LQFUHDVHG 7KH RSWLPXP QXPEHU RI YHVVHOV UDQJHG IURP JLYHQ D SHUFHQW LQFUHDVH LQ ILVKn LQJ SRZHU WR FRUUHVSRQGLQJ WR D SHUFHQW LQFUHDVH LQ DYHUDJH ILVKLQJ SRZHU SHU YHVVHO (IIHFWLYH ILVKLQJ HIIRUW VWDQGDUGL]HG YHVVHOVf LQ WKH ILVKHU\ LQFUHDVHG KRZHYHU 7KXV WKH LQFUHDVHV LQ ILVKLQJ SRZHU SHU YHVVHO PRUH WKDQ RIIVHW WKH GHFOLQH LQ QRPLQDO
PAGE 147
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n VLGHUDEOH VLPSOLILFDWLRQ LQ WKH HPSLULFDO PRGHOLQJ RI WKH *05)) $ SOHD IRU PRUH DQG EHWWHU GDWD LV UHJLVWHUHG 7KH PRGHO GHYHORSHG LV DOVR
PAGE 148
FRQGLWLRQDO ZLWK UHVSHFW WR WKH GHWHUPLQDQWV RI ILVKLQJ SRZHU 7KH OHYHOV RI WKHVH IDFWRUV DULVH DV D UHVXOW RI ILUP OHYHO GHFLVLRQV $QDO\VLV RI UHHI ILVK SURGXFWLRQ DW WKH ILUP OHYHO LQ VXFK DV PDQQHU DV WR LQWHUIDFH ZLWK WKH SUHVHQW PRGHO ZRXOG JUHDWO\ HQKDQFH LWV XVHIXOQHVV WR GHFLVLRQ PDNHUV FKDUJHG ZLWK WKH UHVSRQVLELOLW\ RI PDQDJLQJ WKH ILVKHU\ )LQDOO\ WKH PRGHO GHYHORSHG KDV SURYLGHG D PHWKRGRORJ\ IRU DQDO\]LQJ WKH ELRORJLFDO DQG HFRQRPLF IDFWRUV ZKLFK LQWHUDFW LQ DQ RFHDQ ILVKHU\ ZLWK OLPLWHG HFRQRPLF DQG ELRORJLFDO LQIRUPDWLRQ +RZHYHU WKH HIIHFWV RI RWKHU FRPPHUFLDO ILVKHULHV DQG WKRVH RI WKH UHFUHDWLRQDO ILVKHU\ KDYH EHHQ LJQRUHG ,W LV KRSHG WKDW WKH PHWKRGRORJ\ GHYHORSHG KHUH ZLOO EH H[WHQGHG WR HQFRPSDVV WKH DQDO\VLV RI PDQ\ GLIIHUHQW ILVKHULHV VLPXOWDQHRXVO\
PAGE 149
$33(1',&(6
PAGE 150
$33(1',; $ 63(&,(6 &20326,7,21 2) 7+( ),6+(5< $1' 7+( ',675,%87,21 2) ),6+,1* $&7,9,7<
PAGE 151
7DEOH $O 6SHFLHV LQ WKH PDQDJHPHQW XQLW 6QDSSHUV/XWMDQLGDH )DPLO\ 4XHHQ VQDSSHU 0XWWRQ VQDSSHU 6FKRROPDVWHU *XOI UHG VQDSSHU &XEHUD VQDSSHU *UD\ VQDSSHU 'RJ VQDSSHU 0DKRJDQ\ VQDSSHU /DQH VQDSSHU 6LON VQDSSHU
PAGE 152
7DEOH $ 6SHFLHV LQFOXGHG LQ WKH ILVKHU\ EXW QRW LQ WKH PDQDJHPHQW XQLW 7LOHILVKHV%UDQFKLRVWHJLGDH )DPLO\ *UHDW QRUWKHUQ WLOHILVK /RSKRODWLOXV FKDPDHOHRQWLFHSV 7LOHILVK &DXORODWLOXV VSS -DFNV&DUDQJLGDH )DPLO\ $PEHUMDFNV 6HULOD VSS 7ULJJHUILVK&DUDQJLGDH )DPLO\ *UD\ WULJJHUILVK %DOLVWHV FDSULVFXV :UDVVHV/DEULGDH )DPLO\ +RJILVK /DFKQRODLPXV PD[LPXV 7RPWDWH :KLWH JUXQW 3LJILVK *UXQWV3RPDGDV\LGDH )DPLO\ +DHPXORQ DXUROLQHDWXP +DHPXORQ SOXPLHUL 2UWKRSULVWLV FKU\VRSWHUD 3RUJLHVf§6SDULGDH )DPLO\ 5HG SRUJ\ .QREEHG SRUJ\ -ROWKHDG SRUJ\ /LWWOHKHDG SRUJ\ 3LQILVK *UDVV SRUJ\ 3DJUXV VHGHFLP &DODPXV QRGRVXV &DODPXV EDMRQDGR &DODPXV SURULGHQV /DJDGRQ UKRPERLGHV &DODPXV DUFWLIURQV 6DQG 3HUFKHV6HUUDQLGDH )DPLO\ 'ZDUI VDQG SHUFK 3L SOHFWUXP ELYLWWDWXP 6DQG SHUFK 3L SOHFWUXP IRUPRVXP 6285&( *XOI RI 0H[LFR )LVKHU\ 0DQDJHPHQW &RXQFLO f
PAGE 153
)LJXUH $ *HRJUDSKLF GLVWULEXWLRQ RI ILVKLQJ LQ WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ 6285&( $OOHQ DQG 7DVKLUR f
PAGE 154
$33(1',; % '$7$ 87,/,=(' ,1 $1$/<=,1* 7+( *8/) 2) 0(;,&2 &200(5&,$/ 5(() ),6+ ),6+(5<
PAGE 155
7DEOH %O 5HG 6QDSSHU FDWFK E\ FRXQWULHV &RXQWU\ 4XDQWLW\D 3HUFHQW 4XDQWLW\ 3HUFHQW 4XDQWLW\ 3HUFHQW 4XDQWLW\ 3HUFHQW &XED 0H[LFR 86 727$/ D&DWFK LV UHSRUWHG LQ WKRXVDQG PHWULF WRQV 6285&( .OLPD f
PAGE 156
7DEOH % *URXSHU FDWFK E\ FRXQWULHV &RXQWU\ 4XDQWLW\ 3HUFHQW 4XDQWLW\ 3HUFHQW 4XDQWLW\ 3HUFHQW 4XDQWLW\ 3HUFHQW &XED 0H[LFR 86 9HQH]XHOD 727$/ D&DWFK LV UHSRUWHG LQ WKRXVDQG PHWULF WRQV 6285&( .OLPD f
PAGE 157
7DEOH % (VWLPDWHG FDWFK DQG HIIRUW LQ *XOI RI 0H[LFR UHFUHDWLRQDO UHHI ILVKHU\ IRU VHOHFWHG \HDUV 6SHFLHV JURXS 1XPEHU RI ILVK 3RXQGV RI ILVK 3HUFHQW RI WRWDO SRXQGV 1XPEHU RI DQJOHUV 1XPEHU RI ILVK 3RXQGV RI ILVK 3HUFHQW RI WRWDO SRXQGV 1XPEHU RI DQJOHUV 1XPEHU RI ILVK 3RXQGV RI ILVK 3HUFHQW RI WRWDO SRXQGV 1XPEHU RI DQJOHUV WKRXVDQGV WKRXVDQGV WKRXVDQGV WKRXVDQGV *URXSHUV *UXQWV QR -DFNV 3RUJLHV 6HD EDVV 6QDSSHUV 6QDSSHUV 5HG D f§D D D 6QDSSHUV
PAGE 158
7DEOH % (VWLPDWHG QXPEHU DQG ZHLJKW RI UHHI ILVK FDXJKW E\ UHFUHDWLRQDO ILVKHUPHQ LQ WKH *XOI RI 0H[LFR D 6SHFLHV JURXS 1XPEHU RI ILVK WKRXVDQGVf 3RXQGV RI ILVK WKRXVDQGVf 3HUFHQW RI WRWDO SRXQGV *URXSHUV *UXQWV -DFNV 3RUJLHV 6HD EDVV f§ f§ f§ 6QDSSHU UHG 6QDSSHUV 7ULJJHUILVK f§ f§ f§ 727$/ D([WUHPHO\ KLJK VWDQGDUG HUURUV IRU WKHVH HVWLPDWHV VHULRXVO\ OLPLW WKH DFFXUDF\ RI WKHVH QXPEHUV 6285&( 86 1DWLRQDO 0DULQH )LVKHULHV 6HUYLFH f
PAGE 159
7DEOH % (VWLPDWHG FDWFK RI UHHI ILVK SHU KDQGOLQH YHVVHO LQ WKH *XOI RI 0H[LFR}
PAGE 160
7DEOH % &DWFK RI UHHI ILVK E\ KDQGOLQH YHVVHOV LQ WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ 6WDWH
PAGE 161
7DEOH % $YHUDJH FUHZ VL]H RI UHHI ILVK YHVVHOV E\ VWDWH 6WDWH
PAGE 162
7DEOH % $YHUDJH VL]H RI UHHI ILVK YHVVHOV E\ VWDWH $YHUDJH YHVVHO VL]H JURVV UHJLVWHUHG WRQVf
PAGE 163
7DEOH % 1XPEHU RI UHHI ILVK YHVVHOV E\ VWDWH 9HVVHOV
PAGE 164
$33(1',; & '(5,9$7,21 2) ())257 /(9(/6 )25 0$;,080 6867$,1$%/( <,(/' $1' 0$;,080 (&2120,& <,(/'
PAGE 165
7KH 6FKDHIHU f VXVWDLQDEOH \LHOG IXQFWLRQ JLYHQ LQ HTXDWLRQ f LV UHVWDWHG EHORZ DV F D( E (f &Of ZKHUH F GHQRWHV FDWFK DQG ( LV GHILQHG DV ILVKLQJ HIIRUW DQG D DQG E DUH FRQVWDQWV 0D[LPXP VXVWDLQDEOH \LHOG FRUUHVSRQGV WR WKH PD[LPXP RI HTXDWLRQ &Of 7KH HIIRUW OHYHO FRUUHVSRQGLQJ WR PD[LPXP VXVWDLQDEOH \LHOG LV REWDLQHG E\ VROYLQJ WKH ILUVW RUGHU FRQGLWLRQ IRU WKH PD[LPXP RI HTXDWLRQ &Of IRU ( 6HWWLQJ a DE D( &f HTXDO WR ]HUR DQG VROYLQJ IRU ( \LHOGV (r &f fN ZKHUH ( GHQRWHV WKH OHYHO RI ILVKLQJ HIIRUW ZKLFK SURGXFHV PD[LPXP VXVWDLQDEOH \LHOG 7R REWDLQ WKH HIIRUW OHYHO FRUUHVSRQGLQJ WR PD[LPXP HFRQRPLF \LHOG DQ LQGXVWU\ SURILW IXQFWLRQ LV UHTXLUHG 7KLV IXQFWLRQ ZLWKLQ WKH FRQWH[W RI WKH 6FKDHIHU PRGHO LV JLYHQ E\ WW 3D (E (f U( &f ZKHUH LU GHQRWHV SURILW 3 LV WKH FRQVWDQW SURGXFW SULFH U LV WKH XQLW FRVW RI HIIRUW DVVXPHG FRQVWDQW DQG DOO RWKHU WHUPV DUH GHILQHG DV DERYH 7KH HIIRUW OHYHO ZKLFK UHVXOWV LQ PD[LPXP HFRQRPLF \LHOG LV REWDLQHG E\ VROYLQJ WKH ILUVW RUGHU FRQGLWLRQ IRU WKH PD[LPXP RI HTXDWLRQ &f LQ WHUPV RI ( %\ VHWWLQJ
PAGE 166
A_ 3DE 3D( &f HTXDO WR ]HUR DQG VROYLQJ IRU ( WKH HIIRUW OHYHO FRUUHVSRQGLQJ WR PD[LPXP HFRQRPLF \LHOG (n ? E f aN ` &ff LV REWDLQHG 6LQFH U 3 DQG D DUH DOO SRVLWLYH FRQVWDQWV D FRPSDULVRQ RI HTXDWLRQV &f DQG &f LOOXVWUDWHV WKDW WKH HIIRUW OHYHO FRUUHVSRQGn LQJ WR PD[LPXP HFRQRPLF \LHOG LV DOZD\V OHVV WKDQ WKDW FRUUHVSRQGLQJ WR PD[LPXP VXVWDLQDEOH \LHOG
PAGE 167
$33(1',; *5$3+,&$/ '(5,9$7,21 2) 7+( '28%/( +803(' 6867$,1$%/( 5(9(18( &859(
PAGE 168
7RWDO 5HYHQXH )LJXUH 'O *UDSKLFDO GHULYDWLRQ RI WKH GRXEOH KXPSHG VXVWDLQDEOH UHYHQXH FXUYH 7KH GHULYDWLRQ SUHVHQWHG DERYH LV EDVHG RQ WKDW JLYHQ E\ $QGHUVRQ f 7KH GRXEOH KXPSHG UHYHQXH FXUYH LV GHULYHG E\ FKRRVLQJ D OHYHO RI HIIRUW DQG WUDFLQJ WKURXJK WKH YDULRXV TXDGUDQWV LQ D FRXQWHUn FORFNZLVH IDVKLRQ 7KUHH VXFK HIIRUW OHYHOV DUH GHSLFWHG LQ WKH ILJXUH
PAGE 169
$33(1',; ( ,'(17,),&$7,21 2) 7+( 25'(5 2) 7+( $8725(*5(66,9( 352&(66(6 ,1 7+( &$7&+ (48$7,216
PAGE 170
7KH HVWLPDWHG UHVLGXDO VHTXHQFHV XVHG LQ LGHQWLI\LQJ WKH RUGHU RI WKH DXWRUHJUHVVLYH FRPSRQHQWV LQ WKH FDWFK HTXDWLRQV ZHUH JHQHUDWHG E\ HTXDWLRQ f (DFK HVWLPDWHG UHVLGXDO VHTXHQFH FRQVWLWXWHG D VWDn WLRQDU\ WLPH VHULHV ZLWK 7 REVHUYDWLRQV 'XH WR WKH VPDOO VDPSOH VL]H LGHQWLILFDWLRQ RI WKH RUGHU RI WKH DXWRUHJUHVVLYH SURFHVVHV ZDV H[WUHPHO\ GLIILFXOW 7KH GLIILFXOW\ LQ LGHQWLILFDWLRQ DURVH IRU WZR UHDVRQV )LUVW HVWLPDWLRQ RI WKH DXWRFRUUHODWLRQ FRHIILFLHQWV LQFXUV ELDVHG HVWLPDWHV ZLWK WKH ELDV RI PDJQLWXGH 7aAf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f 7KLV WHVW LV VRPHZKDW DG KRF LQ QDWXUH %DVLFDOO\ WKLV SURFHGXUH LQYROYHV FRPSDULQJ WKH HVWLPDWHG DXWRFRUUHODn WLRQ DQG SDUWLDO DXWRFRUUHODWLRQ IXQFWLRQ ZLWK WKRVH JHQHUDWHG E\ D WKHRUHWLFDO WLPH VHULHV SURFHVV )RU H[DPSOH JLYHQ DQ DXWRUHJUHVVLYH SURFHVV RI RUGHU 3 WKH DXWRFRUUHODWLRQ IXQFWLRQ WDLOV RI DFFRUGLQJ WR
PAGE 171
D PL[WXUH RI GDPSHG H[SRQHQWLDOV DQGRU VLQH ZDYHV ZKLOH WKH SDUWLDO DXWRFRUUHODWLRQV FXW RII IRU ODJV JUHDWHU WKDQ 3 7KXV LI WKH HVWLn PDWHG DXWRFRUUHODWLRQ DQG SDUWLDO DXWRFRUUHODWLRQ IXQFWLRQV H[KLELW WKLV EHKDYLRU WKH SURFHVV LV LGHQWLILHG DV 3Ar RUGHU DXWRUHJUHVVLYH 0D[ [ 7HVW 2 7KH 0D[ [ WHVW ZDV GHYHORSHG E\ 0F&ODYH f 7KLV SURFHGXUH LQYROYHV VWHSXS VHTXHQWLDO K\SRWKHVLV WHVWLQJ RI HVWLPDWHG DXWRUHJUHVn VLYH SURFHVVHV RI LQFUHDVLQJ RUGHUV 7KH WKHRUHWLFDO GLVWULEXWLRQ RI WKH WHVW VWDWLVWLF FRUUHVSRQGV WR WKDW RI WKH PD[LPXP RUGHU VWDWLVWLF RI D VHTXHQFH RI N LQGHSHQGHQW [_ UDQGRP YDULDEOHV ZKHUH N LV WKH RUGHU RI WKH DXWRUHJUHVVLYH SURFHVV EHLQJ WHVWHG 7KLV WHVW LV EDVHG PDLQO\ RQ DV\PSWRWLF UHVXOWV DQG DV VXFK LV RI OLPLWHG YDOXH ZKHQ VDPSOH VL]H LV VPDOO $NDLNHnV )LQDO 3UHGLFWLRQ (UURU )3(f 7HVW 7KH $NDLNHnV )3( WHVW LV EDVHG XSRQ WKH IDFW WKDW WKH YDULDQFHV RI DXWRUHJUHVVLYH SURFHVVHV RI LQFUHDVLQJ RUGHUV JHQHUDWH D PRQRWRQLF GHFUHDVLQJ VHTXHQFH $NDLNH f %\ DGMXVWLQJ WKLV VHTXHQFH RI YDULDQFH HVWLPDWHV IRU GHJUHHV RI IUHHGRP D PRQRWRQLF LQFUHDVLQJ DGMXVWPHQWf D 8VKDSHG IXQFWLRQ RI DGMXVWHG YDULDQFHV )3(f DV SORWWHG DJDLQVW WKH RUGHU SDUDPHWHUV UHVXOWV 7KH RUGHU SDUDPHWHU FRUUHVSRQGLQJ WR WKH PLQLPXP RI WKLV IXQFWLRQ LV WKHQ FKRVHQ DV WKH RUGHU RI WKH DXWRUHJUHVVLYH SURFHVV LQ TXHVWLRQ
PAGE 172
'XUELQ:DWVRQ 7HVW 7KH 'XUELQ:DWVRQ WHVW LV PDLQO\ FRQFHUQHG ZLWK WHVWLQJ IRU RQO\ ILUVW RUGHU DXWRUHJUHVVLRQ 0DGGDOD f 7KH PDLQ DGYDQWDJH RI WKLV WHVW LV WKDW WKH WHVW VWDWLVWLF KDV DQ H[DFW ILQLWH GLVWULEXWLRQ +RZHYHU WKH WHVW LV QRW YHU\ SRZHUIXO DV HYLGHQFHG E\ WKH SUHVHQFH RI DQ LQFRQFOXVLYH UHJLRQ
PAGE 173
$33(1',; ) 0$5.(7,1* $1' 35,&( ,1)250$7,21 &21&(51,1* *8/) 2) 0(;,&2 5(' 61$33(5 $1' *5283(5
PAGE 174
7DEOH )O 'RPHVWLF PDUNHWLQJ RI JURXSHU DQG VQDSSHU E\ *XOI RI 0H[LFR FRPPHULFDO ILVK GHDOHUV ,WHP *URXSHU 6QDSSHU 3HUFHQW 0DUNHW /RFDWLRQ 1RUWKHDVWrr 6RXWKHDVW 0LG 6RXWKF 5HVW RI 86 3URGXFW )RUP )UHVK LFHG )UR]HQ ZKROH )LOHWV 7\SH RI %X\HU 5HWDLO PDUNHW RU UHVWDXUDQW 2WKHU ZKROHVDOHU 1HZ
PAGE 175
7DEOH ) 7ZR VWDJH $LWNHQnV SDUDPHWHU HVWLPDWHV IRU 5HG 6QDSSHU DQG *URXSHU SULFH HTXDWLRQV 'HSHQGHQW YDULDEOHV ,QWHUFHSW )ORULGD FDWFKF $ODEDPD FDWFK 0LVVLVVLSSL FDWFKF /RXLVLDQD FDWFK 7H[DV FDWFKF ,QFRPHG )ORULGD SULFH RI 5HG 6QDSSHU f f f§ f§ f§ f§ f $ODEDPD SULFH RI 5HG 6QDSSHU f f f f f§ f§ f§ f 0LVVLVVLSSL SULFH RI 5HG 6QDSSHU f f f§ f f§ f§ f /RXLVLDQD SULFH RI 5HG 6QDSSHU f f f§ f§ f f§ f 7H[DV SULFH RI 5HG 6QDSSHU f f f§ f§ f§ f f )ORULGD SULFH RI *URXSHU f f f§ f§ f§ f§ f D*URXSHU SULFH HTXDWLRQV IRU VWDWHV RWKHU WKDQ )ORULGD ZHUH QRW HVWLPDWHG GXH WR WKH VPDOO SURSRUWLRQ RI WRWDO *URXSHU FDWFK DWWULEXWDEOH WR WKRVH VWDWHV ESULFH IRU DOO VSHFLHV FRUUHVSRQGV WR QRPLQDO GRFNVLGH SULFH PHDVXUHG LQ GROODUV SHU SRXQG F&DWFK LV PHDVXUHG LQ WKRXVDQGV RI SRXQGV A,QFRPH LV GHILQHG DV QRPLQDO SHU FDSLWD LQFRPH LQ WKRXVDQGV RI GROODUV
PAGE 176
$33(1',; 5(6285&( 672&. $'-8670(17 )25 ),;(' /(9(/6 2) ())257
PAGE 177
&DWFK )LJXUH *O 5HVRXUFH VWRFN DGMXVWPHQW IRU IL[HG HIIRUW OHYHOV 7KH DGMXVWPHQW RI WKH UHVRXUFH VWRFN WR WKH SRLQW ZKHUH FDWFK HTXDOV VXVWDLQDEOH \LHOG LV EHVW GHVFULEHG E\ PHDQV RI JUDSKLF LOOXVWUDWLRQ 7KH ILJXUH DERYH FRQWDLQV D W\SLFDO 6FKDHIHU W\SH VXVn WDLQDEOH \LHOG IXQFWLRQ DQG D VHULHV RI VKRUW UXQ FDWFK IXQFWLRQ (DFK VKRUW UXQ FDWFK HTXDWLRQ LV LQGH[HG E\ D UHVRXUFH VWRFN OHYHO )RU H[DPSOH WKH FDWFK IXQFWLRQ &SA FRUUHVSRQGV WR D VWRFN VL]H RI 3c $VVXPH WKDW WKH UHVRXUFH VWRFN VL]H LV 3M DQG WKDW HIIRUW LQ WKH ILVKHU\ LV JLYHQ E\ (M 7KH FRUUHVSRQGLQJ FDWFK &M UHSUHVHQWV DQ HTXLOLEULXP FDWFK LQ WKDW &SA LQWHUVHFWV WKH VXVWDLQDEOH \LHOG IXQFWLRQ DW (_ XQLWV RI HIIRUW 1RZ VXSSRVH HIIRUW LV GHFUHDVHG WR ( DQG UHPDLQV IL[HG DW WKDW OHYHO ,QLWLDOO\ FDWFK ZLOO GHFOLQH DORQJ &SA WR D OHYHO GHQRWHG LQ WKH ILJXUH E\ & 7KLV OHYHO RI FDWFK KRZHYHU LV EHORZ VXVWDLQDEOH \LHOG UHVXOWLQJ LQ DQ LQFUHDVH LQ WKH UHVRXUFH
PAGE 178
VWRFN VL]H $VVXPH WKDW WKH UHVRXUFH VWRFN LQFUHDVHV LQ VL]H WR 3 7KH VKRUW UXQ FDWFK HTXDWLRQ ZLOO VKLIW XSZDUG WR &SA UHVXOWLQJ LQ D FDWFK RI &M :LWK HIIRUW IL[HG DW (}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
PAGE 179
$33(1',; + 7+( *8/) 2) 0(;,&2 237,0,=$7,21 02'(/ $1' 5(68/76 2) (;2*(1286 &+$1*(6 ,1 ),6+,1* 32:(5
PAGE 180
7! & &U 2242& & &IW &IW &I & & &f &+ &S & 6 &7 &7 &U &" 9F 9 9 0 7 7 ) L ) $ 0 97 [ S&S 9ff ;$&$ 9Âf ;0^&-c 9Âf ;U&U 9f )LUVW 2UGHU &RQGLWLRQV f &S &$ &0 &7 ;S r &U & ; 6 ) $ $ &S &0 [f 0 AU ‘ &S ;S a 6 9S ;S 9Sf A 9$ ;$66 9Df : f f 9f r ;P&6 9f Q m 9S ;7 9Mf &S 9S MO ‘ &$ 9 A n &f r 9$ r &M 9I r 2 2 r 2 r R r R r R m 2 r 2 r 2 r 2 r 2 } R D)LVKLQJ SRZHU FRPSRQHQWV IRU HDFK VWDWH DUH IL[HG DW OHYHOV 'HILQLWLRQ RI 9DULDEOHV Y r 7RWDO *XOI RI 0H[LFR 5HHI )LVK )LVKHU\ SURILW &S r )ORULGD FDWFK RI UHHI ILVK WKRXVDQGV RI SRXQGVf &$ r $ODEDPD FDWFK RI UHHI ILVK WKRXVDQGV RI SRXQGVf &I r 0LVVLVVLSSL FDWFK RI UHHI ILVK WKRXVDQGV RI SRXQGVf &M ‘ 7H[DV FDWFK RI UHHI ILVK WKRXVDQGV RI SRXQGVf 9S r 1XPEHU RI )ORULGD YHVVHOV 9$ r 1XPEHU RI $ODEDPD YHVVHOV r 1XPEHU RI 0LVVLVVLSSL YHVVHOV 9M f +XPEHU RI 7H[DV YHVVHOV ;S r /DJUDQJH PXOWLSOLHU IRU )ORULGD FDWFK FRQVWUDLQW r$ r /DJUDQJH PXOWLSOLHU IRU $ODEDPD FDWFK FRQVWUDLQW r /DJUDQJH PXOWLSOLHU IRU 0LVVLVVLSSL FDWFK FRQVWUDLQW DQG r /DJUDQJH PXOWLSOLHU IRU 7H[DV FDWFK FRQVWUDLQW )LJXUH +O (TXDWLRQ IRU REWDLQLQJ PD[LPXP HFRQRPLF \LHOG IRU WKH *XOI RI 0H[LFR 5HHI )LVK )LVKHU\
PAGE 181
7DEOH +O 0D[LPXP HFRQRPLF \LHOG LQ WKH UHHI ILVKHU\ JLYHQ D SHUFHQW LQFUHDVH LQ DYHUDJH ILVKLQJ SRZHU SHU YHVVHO 6WDWH &DWFK 7RWDO SURILWr 3URILW SHU YHVVHOr 9HVVHOV 6WDQGDUGL]HG YHVVHOV )ORULGD $ODEDPD 0LVVLVVLSSL 7H[DV 727$/ D&DWFK LV PHDVXUHG LQ WKRXVDQGV RI SRXQGV A3URILW LV PHDVXUHG LQ WKRXVDQGV RI GROODUV 7DEOH + 0D[LPXP HFRQRPLF \LHOG LQ WKH UHHI ILVKHU\ JLYHQ D SHUFHQW LQFUHDVH LQ DYHUDJH ILVKLQJ SRZHU SHU YHVVHO 6WDWH &DWFK 7RWDO SURILWr 3URILW SHU YHVVHOr 9HVVHOV 6WDQGDUGL]HG YHVVHOV )ORULGD $ODEDPD 0LVVLVVLSSL 7H[DV 727$/ D&DWFK LV PHDVXUHG LQ WKRXVDQGV RI SRXQGV A3URILW LV PHDVXUHG LQ WKRXVDQGV RI GROODUV
PAGE 182
7DEOH + 0D[LPXP HFRQRPLF \LHOG LQ WKH UHHI ILVKHU\ JLYHQ D SHUFHQW LQFUHDVH LQ DYHUDJH ILVKLQJ SRZHU SHU YHVVHO 6WDWH &DWFKD 7RWDO SURILWr 3URILW SHU YHVVHOr 9HVVHOV 6WDQGDUGL]HG YHVVHOV ),RULGD $ODEDPD 0LVVLVVLSSL 7H[DV 727$/ D&DWFK LV PHDVXUHG LQ WKRXVDQGV RI SRXQGV A3URILW LV PHDVXUHG LQ WKRXVDQGV RI GROODUV 7DEOH + 0D[LPXP HFRQRPLF \LHOG LQ WKH UHHI SHUFHQW LQFUHDVH LQ DYHUDJH ILVKLQJ ILVKHU JLYHQ D SRZHU SHU YHVVHO 6WDWH &DWFK 7RWDO SURILWr 3URILW SHU YHVVHOr 9HVVHOV 6WDQGDUGL]HG YHVVHOV )ORULGD $ODEDPD 0LVVLVVLSSL 7H[DV 727$/ D&DWFK LV PHDVXUHG LQ WKRXVDQGV RI SRXQGV A3URILW LV PHDVXUHG LQ WKRXVDQGV RI GROODUV
PAGE 183
%,%/,2*5$3+< $NDLNH + )LWWLQJ $XWRUHJUHVVLYH 0RGHOV IRU 3UHGLFWLRQ $QQDOV RI WKH ,QVWLWXWH RI 6WDWLVWLFDO 0DWKHPDWLFV $NDLNH + 6WDWLVWLFDO 3UHGLFWRU ,GHQWLILFDWLRQ $QQDOV RI WKH ,QVWLWXWH RI 6WDWLVWLFDO 0DWKHPDWLFV $OOHQ 'RQDOG 0 DQG -RVHSK ( 7DVKLUR 6WDWXV RI WKH 86 &RPPHUFLDO 6DQSSHU*URXSHU )LVKHU\ /Q +DUYH\ 5 %XO OLV DQG $OEHUW & -RQHV (GVf 3URFHHGLQJV &ROORTXLXP RQ 6QDSSHU *URXSHU )LVKHU\ 5HVRXUFHV RI WKH :HVWHUQ &HQWUDO $WODQWLF 2FHDQ *DLQHVYLOOH )ORULGD 6HD *UDQW &ROOHJH $QGHUVRQ /HH 2SWLPXP (FRQRPLF
PAGE 184
&DWR -DPHV & 'RFNVLGH 3ULFH $QDO\VLV LQ WKH )ORULGD 0XOOHW )LVKHU\ 0DULQH )LVKHULHV 5HYLHZ -XQHf &DWR -DPHV & DQG )UHG 3URFKDVND D 7KH *XOI RI 0H[LFR &RPPHUFLDO DQG 5HFUHDWLRQDO 5HG 6DQSSHU*URXSHU )LVKHU\ $Q (FRQRPLF $QDO\VLV RI 3URGXFWLRQ 0DUNHWLQJ DQG 3ULFHV -ML +DUYH\ 5 %XOO LV DQG $OEHUW & -RQHV (GVf 3URFHHGLQJV &ROORTXLXP RQ 6QDSSHU*URXSHU )LVKHU\ 5HVRXUFHV RI WKH :HVWHUQ &HQWUDO $WODQWLF 2FHDQ *DLQHVYLOOH )ORULGD 6HD *UDQW &ROOHJH &DWR -DPHV & DQG )UHG 3URFKDVND E 8QSXEOLVKHG VXUYH\ GDWD IRU VQDSSHUJURXSHU YHVVHOV LQ WKH *XOI RI 0H[LFR 5HHI )LVKHU\ &DWR -DPHV & DQG )UHG 3URFKDVND $ 6WDWLVWLFDO DQG %XGJHWDU\ (FRQRPLF $QDO\VLV RI )ORULGD %DVHG *XOI RI 0H[LFR 5HG 6QDSSHU*URXSHU 9HVVHOV E\ 6L]H DQG /RFDWLRQ DQG 0DULQH )LVKHULHV 5HYLHZ 1RYHPEHUf &ODUN &ROLQ 0DWKHPDWLFDO %LRHFRQRPLFV 1HZ
PAGE 185
*XOODQG $ 0DQXDO RI 0HWKRGV IRU 6WRFN $VVHVVPHQW 3DUW )LVK 3RSXODWLRQ $QDO\VLV )$2 )LVKHU\ 7HFKQLFDO 3DSHU ,06/ 7KH ,QVWLWXWH RI 0DWKHPDWLFV DQG 6WDWLVWLFV /LEUDU\ +RXVWRQ 7H[DV ,QWULOOLJDWRU 0LFKDHO 0DWKHPDWLFDO 2SWLPL]DWLRQ DQG (FRQRPLF 7KHRU\ (QJOHZRRG &OLIIV 3UHQWLFH +DOO ,QF .OLPD (GZDUG ) 6QDSSHU DQG *URXSHU 5HVRXUFHV RI WKH :HVWHUQ &HQWUDO $WODQWLF ,M[ 3URFHHGLQJV &ROORTXLXP RQ 6QDSSHU*URXSHU )LVKHU\ 5HVRXUFHV RI WKH :HVWHUQ &HQWUDO $WODQWLF 2FHDQ 6WDWH 8QLYHUVLW\ 6\VWHP RI )ORULGD 6HD *UDQW 5HSRUW *DLQHVYLOOH 8QLYHUVLW\ RI )ORULGD .UQHQWD -DQ (OHPHQWV RI (FRQRPHWULFV 1HZ
PAGE 186
5RWKFKL,G %ULDQ )LVKLQJ (IIRUW /Q *XOODQG (Gf )LVK 3RSXODWLRQ '\QDPLFV 1HZ
PAGE 187
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
PAGE 188
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nKQ ( 5H\QROGV 3URIHVVRU RI )RRG DQG 5HVRXUFH (FRQRPLFV FHUWLI\ WKDW KDYH UHDG WKLV VWXG\ DQG WKDW LQ LU?\ RSLQLRQ LW FRQIRUPV WR DFFHSWDEOH VWDQGDUGV RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHTXDWH LQ VFRSH DQG TXDOLW\ DV D GLVVHUWDWLRQ IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ 7KRPDV + 6SUHHQ $VVLVWDQW 3URIHVVRU RI )RRG DQG 5HVRXUFH (FRQRPLFV
PAGE 189
, FHUWLI\ WKDW KDYH UHDG WKLV VWXG\ DQG WKDW LQ QW\ RSLQLRQ LW FRQIRUPV WR DFFHSWDEOH VWDQGDUGV RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHTXDWH LQ VFRSH DQG TXDOLW\ DV D GLVVHUWDWLRQ IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ :LOOLDP 6HDPDQ $VVLVWDQW 3URIHVVRU RI )RUHVW 5HVRXUFHV DQG &RQVHUYDWLRQ 7KLV GLVVHUWDWLRQ ZDV VXEPLWWHG WR WKH *UDGXDWH )DFXOW\ RI WKH &ROOHJH RI $JULFXOWXUH DQG WR WKH *UDGXDWH &RXQFLO DQG ZDV DFFHSWHG DV SDUWLDO IXOILOOPHQW RI WKH UHTXULHPHQWV IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ 'HFHPEHU :U W t X 'HDQ&R+ HJH RI $JULFXOWX 'HDQ *UDGXDWH 6FKRRO
PAGE 190
$XJXVW ,QWHUQHW 'LVWULEXWLRQ &RQVHQW $JUHHPHQW ,Q UHIHUHQFH WR WKH IROORZLQJ GLVVHUWDWLRQ ÂLD 8\OR/ $XWKRU Q 08. I: *MI n ILLR D Af3n6 RU NL: UHHI ILV$ K6InFU\ 3XEOLFDWLRQ 'DWH PR 7LWOH L R\ DV FRS\ULJKW KROGHU IRU WKH DIRUHPHQWLRQHG GLVVHUWDWLRQ KHn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f DV ZHOO DV WR WKH PDLQWHQDQFH DQG SUHVHUYDWLRQ RI D GLJLWDO DUFKLYH FRS\ 'LJLWL]DWLRQ DOORZV WKH 8QLYHUVLW\ RI )ORULGD WR JHQHUDWH LPDJH DQG WH[WEDVHG YHUVLRQV DV DSSURSULDWH DQG WR SURYLGH DQG HQKDQFH DFFHVV XVLQJ VHDUFK VRIWZDUH 7KLV JUDQW eISHUPLVVMMU"VaSURKLELWV XVH RI WKH GLJLWL]HG YHUVLRQV IRU FRPPHUFLDO XVH RU SURILW IQWUHRI &RS\ULJKW +ROGHU ILK ^$YORL QR QI UQQYULQKL +ROGHL [f§ f§ Wr0RPR +ROGHU/LFHQVHH 3HUVRQDOO ,QIRUPDWLRQ %OXUUHG Â0 'DWH RI 6LJQDWXUH 5HWXUQ WKLV IRUP WR &DWK\ 0DUW\QODN 3UHVHUYDWLRQ 'HSW 8QLYHUVLW\ RI )ORULGD /LEUDULHV 32 %R[ *DLQHVYLOOH )/
|