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The Allocation of Aircraft Between Markets
under Regulation and Deregulation

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THE ALLOCATION OF AIRCRAFT BETWEEN MARKETS UNDER
REGULATION AND DEREGULATION

BY

John Howard Brown

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Economics

1989

A/V’III‘) lg)"

7

ABSTRACT

THE ALLOCATION OF AIRCRAFT BETWEEN MARKETS UNDER

REGULATION AND DEREGULATION

BY

John Howard Brown

The work of Douglas and Miller prior to deregulation
suggested that competition in flight frequency led the
airlines to acquire larger stocks of aircraft,and
particularly smaller aircraft, than were necessary in a
deregulated environment. Stocks of aircraft acquired when
regulation held fares above minimum levels of average cost
were too large, since frequent flights require more
aircraft. In addition, airline fleets contained too many
smaller aircraft because the economies of aircraft size
were not realized under regulation.

The relationship between airline route structures and
the fleets of aircraft possessed by airlines both before

and after regulation is investigated here. The chief

theoretical assertation of this dissertation is that
airline behavior since deregulation is best understood in
terms of the unique characteristics of aircraft as capital
goods. It is asserted here that the major consequence of
regulation of the airlines was they were not able to adopt
efficient route structures, i.e. hubbing-and-spoking.
(Hubbing-and-spoking is a method of increasing flight
frequency which is treated as a problem of joint
production.) Airline stocks of aircraft chosen to maximize
profits under regulation were efficient in a deregulated
environment since flight frequency remains a competitive
variable.

Several distinct strands of evidence are brought to
bear on this question. First, analysis of route level data
shows that the pattern of aircraft allocation subsequent to
deregulation did not vary in a manner consistent with
prederegulation prediction. Regression analysis is also
performed using gross fleet composition data and route
structure variables. These regressions indicate that,
although the relationship between the numbers of aircraft
in airline fleets and route structure variables changed
with deregulation, the relative shares of each type of
aircraft in relation to route structure was unchanged. The
evidence is thus consistent with the hypothesis advanced in

this dissertation.

Copyright by
JOHN HOWARD BROWN

1989

DEDICATED TO THE MEMORY OF
HOWARD GRAHAM BROWN (1907-1987)

HUSBAND, FATHER, GRANDFATHER, BUILDER

ACKNOWLEDGEMENTS

Any modern work of scholarship is in reality a

collaboration. Most of the contributors are acknowledged
in the bibliography. However, two groups deserve special
recognition.

The first of these is the members of my guidance
committee who, individually and collectively, have provided
the assistance and constructive criticism necessary to
transform a vague notion into an acceptable work of
scholarship. As is usual, they cannot be held responsible
for the shortcomings of this work.

The other group is my family. My mother and my late
father gave me much encouragement and material support
throughout my academic career. My brother and my in-laws
have also helped me through the rigors of my academic
program. Most of all, my wife and son have been crucial to
this achievement: my son, by being understanding when
"Daddy can’t come out to play, he’s got a dissertation to
write": and even more importantly my wife, who swore she
would never put a husband through school. My thanks are

owed to everyone for their assistance.

vi

TABLE OF CONTENTS

LIST OF TABLES ix
LIST OF FIGURES X
INTRODUCTION 1
CHAPTER 1 -

THE STRUCTURE OF THE PROBLEM 4

The Structure of Demand

The Structure of Supply:
The Capital Constraints

CHAPTER 2 -
AIRLINES IN THE ECONOMIC LITERATURE 12
CHAPTER 3 - THEORETICAL TREATMENT -
AIRLINE DEMAND FOR AIRCRAFT 24

Differentiated Products Treatment of
Airline Flights and Aircraft Demand

A Model of Flight Scheduling
Airline Response to Regulation

Airline Response to Varying Aircraft
Capacities

Effects and Mechanisms of Price
Discrimination

Joint Products, and Rubbing and Spoking
as Explanations of Airline Behavior

Joint Products and Rubbing and Spoking
From Theory to Empirical Specification

Empirical Specification of the Relationship
of Flights per Day to Route Characteristics

vii

Empirical Specification of the Relationship
of Equipment Choice to Route Characteristics

Empirical Specification of the Relationship
of Fleet Composition to Route Characteristics

Summary of Theoretical Results
CHAPTER 4 - EMPIRICAL TESTS 76

The Relationship of Number of Flights to Route
Characteristics

Specific Aircraft Types and Route Characteristics
Econometric Procedure
Theoretical Expectations
Analysis of Empirical Results

The Effects of Route Structure on Fleet Selection
Econometric Procedure
Theoretical Expectations
Analysis of Empirical Results
Summary of Empirical Results
CHAPTER 5 -
CONCLUSIONS AND SUGGESTIONS FOR FURTHER
RESEARCH 143
The Structure of the Industry
Previous Economic Analysis of Airlines
A Theory of Airline Behavior
Empirical Models of Airline Behavior

Welfare Implications and Suggestions
for Additional Research

APPENDIX 153
- Data Types and Sources

BIBLIOGRAPHY 157
- LIST OF REFERENCES
- GENERAL REFERENCES

viii

LIST OF TABLES

TABLE 1 ALTERNATIVE SPECIFICATIONS OF THE
RELATIONSHIPS BETWEEN MARKET PARAMETERS
AND NUMBER OF FLIGHTS

TABLE 2 THE RELATIONSHIP OF NUMBER OF FLIGHTS
PER DAY TO ROUTE CHARACTERISTICS

TABLE 3 THE RELATIONSHIP OF AVERAGE SEATS PER
FLIGHT AND ROUTE CHARACTERISTICS

TABLE 4 COMPARISONS OF THEORETICAL PREDICTIONS
AND EMPIRICAL RESULTS: ROUTE LEVEL DATA

TABLE 5 FLIGHTS PER DAY -INDEPENDENT VARIABLES
IN NATURAL FORM

TABLE 6 ROUTE LEVEL DATA RESULTS 1974 & 1984
TABLE 7 THE RELATIONSHIP OF AVERAGE SEATS PER
FLIGHT AND ROUTE CHARACTERISTICS - FLEET
DATA
TABLE 8 EQUATIONS RELATING ROUTE STRUCTURE AND
NUMBERS OF AIRCRAFT
PART A - ABSOLUTE VARIABLES
PART B - RELATIVE VARIABLES
TABLE 9 PANEL DATA RESULTS 1970-1984

TABLE 10 COMPARISON OF THEORETICAL PREDICTIONS
AND EMPIRICAL RESULTS

ix

65

81

84

90

98

107

111

112

125

128

LIST OF FIGURES

FIGURE 1 AIRLINE FLIGHTS AS DIFFERENTIATED
PRODUCTS IN A CIRCULAR MODEL

FIGURE 2 POSSIBLE EQUILIBRIA -
FULLY AND PARTIALLY SERVED MARKETS

FIGURE 3 COMPARISON OF REGULATED AND
COMPETITIVE EQUILIBRIA

FIGURE 4 THE RELATIONSHIP OF AVERAGE COST
PER MILE AND PER PERSON FOR A SINGLE
VARIETY OF AIRCRAFT

FIGURE 5 AVERAGE COST PER PASSENGER WITH
THREE AIRCRAFT VARIETIES

FIGURE 6 EQUILIBRIA WITH TWO AIRCRAFT
VARIETIES

FIGURE 7 THE RELATIONSHIP BETWEEN FLIGHT
FREQUENCY, FARES, AND NUMBER OF
PASSENGERS PER FLIGHT

FIGURE 8 SERVING SEVERAL MARKETS ON A SINGLE
FLIGHT

28

34

37

40

42

44

53

59

INTRODUCTION

The process of deregulation of domestic air
transport in the United States has attracted considerable
attention. There are several reasons for this. First,
the domestic air transport industry in the United States,
as in most countries, was "born regulated"; government
policy has determined the structure and conduct of the
industry from its very beginnings. Thus, the
adjustments which the industry experiences as it moves
towards a more competitive structure will indicate what
the resource misallocation costs of regulatory
intervention were. A second reason is that the
deregulatory process is among the most advanced of the
attempts at deregulation in this country in the past
decade. In addition, the airline industry has been
proposed as an industry closely fulfilling the
requirements of contestability (Baumol and Bailey 1984).

Although a great deal of attention has been paid to
the process of deregulation, most of the literature has

analyzed the effects of deregulation on the product

2
markets. Thus, pricing policy, route structure, and

quality of service effects of deregulation have been
analyzed intensively. Likewise, the effects on the
labor force of the various carriers have been examined.
However, little or no attention has been given to the
changes which deregulation has or is likely to bring
about in the airlines’ usage of aircraft types. This
dissertation begins by analyzing the manner in which
airlines can be expected to adjust their deployment of
aircraft in deregulated markets. Previous treatments of
the effects of airline regulation have not yielded
accurate predictions about the nature of airline
responses to deregulation.

It is demonstrated below that this failure is the
result of three flaws in previous treatments of airline
industry behavior. The first flaw is that aircraft have
been treated as homogeneous units of capacity. However,
aircraft provide capacity which varies in quality from the
point of view of both consumers and airlines. Second, it
has been assumed that airlines would not vary their route
structures after deregulation. In fact, previous
treatments viewed routes in isolation rather than
treating an airlines' route structure as a form of joint
product. In addition, they have uniformly assumed that
airlines will only charge a single fare to their
customers, or at least only charge differential fares to

the extent that such fares can be justified by differences

3
in service class. As demonstrated below, airlines have

utilized a unique form of price discrimination as a part
of their response to deregulation.

This dissertation consists of five chapters. The first
defines the problem. The second chapter is a
literature review discussing in detail the relevant
theoretical and empirical results which have been produced
about the effects of airline deregulation on the
deployment of capital equipment (i.e. aircraft). The
third chapter outlines the model which is used to
analyze these effects. The fourth chapter is devoted to
empirical tests of this model. The fifth chapter
summarizes the findings of this dissertation, analyzes the
welfare effects of airline deregulation, and suggests some
possible extensions of the theoretical and empirical work

discussed herein.

CHAPTER I

THE STRUCTURE OF THE PROBLEM

The airline industry exists to provide transportation
services to consumers and businesses. These services can
take the form of passenger or freight transportation,
separately or jointly provided. Firms provide these
services by combining labor, materials, and capital.
Airline capital is largely embodied in the form of
vehicles, the aircraft. These vehicles differ
significantly from the form capital is usually conceived
of in economic theory. Airline capital is "lumpy", that
is, it is available only in discrete units. In addition,
the vehicles are of different capacities in terms of both
the number of passengers they are capable of carrying and
their range. This has important effects on the cost
structures of individual flights.

The lumpiness of capital has important implications

for the conduct of airlines. It implies airlines should

5
offer scheduled service. This permits potential passengers

to plan their trips effectively (De Vany 1975). However,
since flights are not continuously available, some
passengers must accept departure times that are not their
preferred times. This fact of life for air passengers is
acceptable only because scheduled service can be supplied
at a much lower cost than individualized but unscheduled
service.

When regulation was established in the 19305, the
existing (trunk) airlines were granted authority to operate
on the routes which they operated at the start of
regulation (grandfathered). All other attempts to begin
operations in city-pair markets were subject to approval by
the Civil Aeronautics Board (CAB). Likewise, the fares
which airlines were permitted to charge were brought under
CAB regulation.1

The demand for aircraft, like that for all factors of
production is a derived demand. Consequently, the price
and incentive distortions imposed by regulation of the
product markets are expected to distort the airline's
investment decisions also.

When the process of deregulation began, the airlines
possessed stocks of aircraft suited to maximize profits
under the regulatory constraint. Since the lead time for

new aircraft orders is from three to five years, the

1 There are many excellent discussions of the regulatory
process as it existed prior to deregulation, such as Levine
1987. For this reason I do not discuss the process in any
detail here.

6
airlines were forced in the short run to change their

patterns of equipment utilization rather than discard
obsolescent aircraft and replace them with technically
appropriate types. The process of adaption to the newly
deregulated environment is the object of this study. In
the following subsections, we consider more formally the
elements of the markets for air transport which define the

nature of the problem.

The Structure of Demand

In general, there are two major dimensions in the
demand for airline services. The first dimension is, of
course, price. The second major dimension is quality.
This variable, or more properly, this set of variables, is
of considerable importance in determining the overall level
of demand for air transport. The complexity of quality as
a variable has discouraged a complete treatment of it as an
element in demand. Thus, such important aspects of air
travel quality as passenger comfort (including, e.g. seat
width, aisle arrangements, and in-flight service) have
received scant attention (cf. Bennett 1984).

In fact, the only element of quality to receive
extensive treatment--flight frequency--is really another
element of the opportunity cost of travel. Under the usual
assumptions of utility maximization and full information,

consumers choose those goods which are lowest priced. The

7
money price is not the only important variable in

determining the opportunity cost of travel.2 Indeed, if it
were, there would be little or no demand for air transport,
since it almost always suffers a price disadvantage
relative to other modes of transportation. The other and
more important element in determining the opportunity costs
of air transport is the time savings that air travel
confers relative to other modes of transportation. This
time element in the opportunity costs of air travel is
affected by the necessity of scheduling mentioned above.
In brief, since airline capacity is lumpy, carriers must
offer scheduled service in order to allow their customers
to plan their itineraries.
To quote DeVany,

"There are two significant consequences of the
discreteness of airline capacity. First, it makes
scheduling the most efficient means of offering
capacity by allowing the passenger to preplan his
activities. Second, the discreteness of capacity
means that there will always be intervals between
flights, and, therefore, an interval between a
passenger's desired departure time (a stochastic
variable) and the time he actually departs on a
flight." (1975,328)

The fact of scheduling a departure at a particular
2 The literature on airline demand frequently refers to
the combination of fare and time costs as the "full" costs

of flying. Here, except when specifically citing previous
literature, I will use the term opportunity cost.,

8
time means that some potential passengers will not be able

to depart at their preferred time. Thus, convenience of
service is important to the demand for air transport,
particularly where the time savings it offers is not
great relative to alternative modes.

Another important aspect of this demand structure is
that preferred departure times are not uniformly
distributed over the course of any period. Instead,
demand is subject to regular "peaking." This gives rise
to one of the important characteristics of the airline
industry. The industry produces an almost endlessly
varied offering of differentiated products.3 Each city
pair between which air transport is offered defines a
product class. Each departure time between any given city
pair defines a distinct product. While the airline
products in any city pair product class (i.e. differing
departure times) are good substitutes they are not the same
product.4 This imperfect substitutability coupled with the
temporal variation in demand gives rise to some interesting

strategic problems for airlines in their scheduling of

flights.
T uctur ° ' a 'n s
3 It nonetheless remains an industry on the criterion

of Boyer (1984) i.e. all suppliers of air transportation
services must be members of the producer cartel for
cartelization to be effective.

4 Winston argues for a similarly disaggregate approach to
transportation in the treatment of both costs and demand
(1985, particularly 64-65).

9
The second blade of the Marshallian scissors, the

supply of air transport services, is largely dictated by
the capital available to provide them. The first major

limitation imposed by the capital is that it is available

only in discrete units. Some of the implications of this
have already been touched upon, for example, that
optimizing behavior implies scheduling of services. Yet

another implication is that the costs of providing airline
services consist of three distinct types. These are
overhead costs; direct passenger, or traffic, costs; and
what are commonly called capacity, or flight, costs
(Douglas and Miller 1974, particularly 18-26).

Capacity costs arise because a large proportion of the
costs of employing a particular aircraft on any given route
are not affected by the actual number of passengers carried
on the flight. This distinction is made by the airlines as
the difference between Available Seat: Miles, or capacity,
and Revenue Seat: Miles, or actual transportation services
provided. Capacity costs are fixed with respect to any
given flight (i.e., once the aircraft and route are
chosen). Thus airline markets are served with declining
average costs when the number of passengers rises, at least
up to the capacity of the largest available aircraft.
Since the airline product was defined above as
transportation between city pairs at a particular time, the
individual flight has the cost characteristics of a natural

monopoly. Many airline markets (city pairs) may be natural

10
monopolies if traffic density is so thin that competing

flights can only be offered at increased average cost per
Revenue Passenger Mile. This is, however, determined by
the interaction of supply and demand.

Another important effect of capital on the provision
of airline services arises because of the specific forms
in which the capital is embodied. There are economies of
aircraft size. All other things equal, the average cost
of an Available Seat Mile falls as the size of aircraft on
a given route rises. In addition, the average cost per
mile of an Available Seat Mile declines as the distance
covered on a route increases.

The nature of airline capital also contributes to
another supply-side aspect of airline service. Airlines
produce a product which is necessarily differentiated.
However, the capital used to provide it is not specialized
to the provision of any particular product or product
class, as these concepts are described above. Aircraft can
be freely transferred between markets. This, coupled with
the necessity of providing gate and ground services in any
market served, means that the provision of airline services
is marked by substantial economies of scope.5 Thus,
substantial competitive advantages accrue to firms which
offer air transport services in a network. _ This tendency
is reinforced by the peculiarity of demand that travelers
not able to make direct connections between their origin

and destination prefer to make all stages of their journey

11
with a single firm.6 (Johnson, 1985)

Airline markets possess many features which make them
differ from the sorts of markets which are usually subject
to theoretical analysis in economics. Regulation added yet
another layer of complexity. Both price charges and
service entry on routes were regulated. The analysis of
the effects of the combination of the industry's unique
characteristics and of its regulation which has developed

in the literature is the subject of the next chapter.

5 These economies of scope arise most clearly because of
the existence of indivisibilities in the provision of gate
and ground service. This in itself should not necessarily
result in competitive disadvantage to firms offering only
single city-pair service since time-sharing arrangements

should be possible. In practice, however, most airlines
seem to treat these services as indivisible.
6 Note: This peculiarity, so—called, in demand is

probably a result of rational decision making on the part
of the consumers of airline trips--minimizing connections
also minimizes the wedge for "Murphy’s law."

CHAPTER 2

AIRCRAFT UTILIZATION IN THE ECONOMIC LITERATURE

As mentioned in the introduction, the airline industry
has been the subject of a considerable amount of economic
analysis. Interest in the airline industry preceded the
process of deregulation. Indeed, the analysis of
economists was instrumental in providing the rationale for
deregulation. In contrast, there has been far less
economic analysis of the employment of aircraft by
airlines. This chapter surveys and critiques the available
literature.

There are two distinct strands to be considered in the
literature. First, aircraft are chosen by airlines to
provide certain performance characteristics in light of the
airlines existing route system. In addition, the existing
fleets of aircraft must be redeployed properly as the
conditions in markets and the structure of an airlines
routes change.

When regulated, both price and route structure are

12

13
fixed. Thus, the airline planner has only two interrelated

decision variables--flight frequency, and vehicle type to be
employed. Since the route structure is known, the choice
of airline fleets is based on choosing a fleet which
offers optimum performance on the existing routes.
Peyrelevade (1969) was the first to consider the
problem. He produced a method for computing the optimal

structure of an airline fleet given the set of routes to be

served. Unfortunately, his method is limited by two
factors. First, the quantity of flights demanded is
parametric. The effects of price and flight frequency on

demand are not even considered. In addition, there is no
treatment of rivalrous behavior on the part of airlines.

The failures of the work discussed above are addressed
in the work of Douglas and Miller (1974). They
hypothesize that firms respond to regulatory constraints on
price by offering greater flight frequency. Flight
frequency is a competitive tool since greater flight
frequency reduces the opportunity cost of flying.

Given their model, Douglas and Miller explicitly
discuss the rules for optimal allocation of aircraft among
markets. Their model implies the following behavior with
respect to allocation of aircraft. When all other things
are equal:
1)Larger aircraft should serve more dense routes

(density is in this case measured in emplanements per

unit of time).

14
2)Larger aircraft should serve longer haul markets

(Those where the time savings air travel confers are
greatest).

3)Larger aircraft should serve markets where passenger
value of time is low.

Douglas and Miller verify that these guidelines for
efficient allocation of aircraft are violated by airlines
in the regulated environment. They found, in particular,
that load factors were the lowest, and average costs
therefore the highest, on the most dense of the
transcontinental routes. This was a result of the
mechanism for fare computation developed by the CAB, the
Standard Industry Fare Level (SIFL). The SIFL formula did
not fully reflect the lower costs incurred by airlines when
serving transcontinental routes. This encouraged excessive
flight frequency, both absolutely and relative to shorter
haul routes.

Pollack (1977) offers a critique of the existing
methods of fleet planning, describing those elements which
he asserts have been insufficiently considered in
developing fleet planning models. There is no specific
technique or conclusion cited: instead, there is a general
discussion of the elements needed to construct an adequate
fleet plan.

Baumol et a1. (1982, 7) suggest that the
contestability of airline city-pair markets leads to

efficient allocations of aircraft on routes. Since

15
aircraft are "...virtually 'capital on wings’...," firms

which do not use the most efficient type of aircraft for a
route will suffer entry by entrepreneurs seeking economic
profits. Ironically, since their book largely deals with
the topic, this argument ignores the economies of joint
production which airlines can enjoy by restructuring their
routes as hub-and-spoke systems.

Graham et al, discuss the evolution of the airline
industry since deregulation. They offer a test of the
Douglas and Miller excess-capacity hypothesis. They assert
that the hypothesis "... implies that if there were
economies of scale at the market level, load factors should
have risen most in denser markets, ceteris paribus, as the
result of deregulation"(1983 126-7). Their reported
empirical results indicate that the effects of density on
load factors did not change in the expected direction with
deregulation.

The papers discussed above were mostly completed
before the process of deregulation was well begun and
assume that airlines view their route structures as fixed
and beyond their control. After deregulation, planners
must take into account a much wider range of variables.
Thus, in place of a single price (or small set of prices)
on a given route and a fixed route network, planners must
choose routes served, schedules offered, and the pricing
formula used. Aircraft choice remains an important problem

for the airlines.

16
The extent to which airlines wish to alter their

stock of vehicles depends in large part on environmental
factors beyond the airlines direct control. For instance,
the rapid increases in fuel costs in the late 19705 made
fuel economy a primary consideration in fleet planning.
These fuel-cost considerations interact with other costs of
operation of a particular type of aircraft in determining
the actual composition of an airlines fleet.
"In 1978 aviation fuel cost $1.50 a gallon in
America and interest rates were at 6%. Then it
was easy to persuade airlines to buy efficient new
aircraft (hence the peak in deliveries in 1981).
After all, on McDonnell Douglas's calculations
fuel accounted for 46% of the cost of flying 2,000
nautical miles: operating costs such as wages and
landing fees another 30%: and ownership-paying off
the price of the aircraft-only 24%. By last year,
things had changed. Fuel was down to 88 cents a
gallon and interest rates were up to 12%. The
result was that fuel accounted for only 31% of a
route’s cost and ownership a daunting 36%.
...United Airlines, the world’s biggest carrier,
is still operating its first Boeing 727, bought
more than 20 years ago. When interest rates are
high and fuel prices low, economic obsolesence
recedes to the horizon." (Economist 818)

Of course, airlines may also purchase used equipment.

17
Used airliners are usually cheaper. "A used aircraft's

price tracked 15 to 20 percent below the price of a new
model of the same aircraft" (F1 in , March 1984, 64-66).
Thus the capital costs for used aircraft can be
significantly lower. This possibility can carry much
weight in airline decision making, thus, "A 757 covers the
route from La Guardia to Houston in about the same time and
carries about the same number of passengers as a 727-
200....But the public doesn’t care whether the machine
costs $35 million or $7 million” (Flying, cc, cic.).

In either case, the same factors are important in
making decisions regarding fleet composition. First of
all, "...airlines tailor their fleets to their routes"
(Eccnomist, 1985). In doing so, they trade off among
factors like trip costs and seat-mile costs, specific fuel
consumption and fuel burn, over a set distance, payload and
range, and "price per seat". In an application of these
principles, Thayer notes,

"...for Braniff’s domestic route system and for

some of our Latin American routes, the advanced

727-200 fills the needs well. This aircraft meets

the requirements of markets with low density and

heavy business travel: it meets schedule
requirements of multiple frequencies and limited
capacity per trip: and it meets equipment
requirements of low operating cost and appropriate

capacity.” (James, 279-280)

18
As the preceding discussion indicates, airline choice

of aircraft is centered on profit maximization. Profit
maximization is also the central concern when determining
what sort of route structure to serve.

The exact nature of the adjustments of route structure
to deregulation is the concern of Morrison and Winston
(1985). They provide a simple model of the behavior of
intercity route structures after deregulation. They
suggest that profit-maximizing firms alter their route
structures according to a simple principle. If the cost
savings of serving a route jointly with some other route
are great enough to offset the revenue lost because demand
falls on the jointly served route due to decreased
convenience of service, the new joint route should be
adopted. Thus, economies of scope are the crucial
determinant of the routes adopted. In particular, when
there exist economies of vehicle size, economies of scope
are likely to exist. Such economies may lead to joint
provision of service (hubbing and spoking). However, if the
economies realized are insufficient to offset the decreased
convenience of service, route structures are likely to
remain linear. Their discussion does not consider any
strategic elements that exist in firm decisions on route
structures and their ultimate configuration.

Bailey and Baumol (1984) also note the presence of
economies of scope in the provision of airline services.

They assert that contestability in airline markets results

19
in the restructuring of airline route systems as hub and

spoke systems.

They note that the drastic increases in fuel prices
experienced between 1978 and 1981 rendered many multi—
engine jets technologically obsolete. This created excess
capacity, which they expect to result in substantial price
warfare. Such price warfare is not in accord with the
theory of contestablility but is seen as a transitional
phase in the evolution of the airline industry to its
ultimate deregulated structure.

Crandell suggests that stage length, trends in
emplanements, and interdependence of routes are important
factors in the process of deciding the routes to be served
(James 1982, 231-232). In addition, he suggests that size,
cost, fuel economy and environmental restrictions all play
a role both in the short and longer term capital decisions
of airlines. Also stressed is the importance of maximizing
stage length in scheduling, since short hauls. are more
expensive per mile and imply that a larger proportion of
the aircraft’s day is spent on the ground.

Thayer also stresses the importance of long stage
lengths. In addition, he stresses the importance of high
density for profitable operation on a route (James, 265).
Aircraft selection is, in his words,"...the fulcrum of this
scheduling concept." Selection is made with the end of
achieving low cost per seat-mile through high utilization

of equipment and productivity, frequent service, and the

20
capture of flow-through traffic. Particular stress is laid

on the necessity of providing passengers with convenient
connections on the carrier's own flights.

The logical outcome of the concern with establishing
on-line connections is the hub-and-spoke pattern of routing
that emerged with deregulation. As Bailey et a1, note,
”The hubbing carrier serves more passengers on its flights
so it can use larger aircraft at higher load factors. Its
greater traffic may also enable it to offer more frequent
flights" (1985, 74). They present evidence showing that
flights have increased (p. 84). Flight frequencies are
shown to have risen substantially for large hubs connecting
to other large hubs, also for both other size classes of
hubs and for non-hubs connecting to large hubs. 0n the
other hand small hubs and non-hubs have lost
interconnections both among themselves and with medium
hubs. This suggests a decline in the ability, in general,
to complete direct connections which were previously
achievable. The increased overall flight frequency
reported appears contrary to the beliefs held before
deregulation that carriers offer too large an amount of
flight frequency while regulated. In fact, it is not,
since those predictions assume an unchanged route
structure. Freedom of exit and entry makes that assumption
invalid.

Thomchick (1978) attempts to determine the

characteristics which make existing airline routes

21
profitable or unprofitable. These route characteristics

and a model of firm behavior are employed to determine
which of a sample of routes are likely to be served after
deregulation. 0n the basis of these techniques, she
offers a series of hypotheses about the evolution of
airline route structures after deregulation.

First, small communities close to hub airports lose
the services they previously received, as do routes which
are less than 200 miles long. A second prediction is that
quality of airline service will vary in certain predictable
ways. For instance, she infers that airlines will offer
more one-stop flights in place of multi stop flights.
However, she also asserts that more non-stop flights will
be offered, which does not appear to be the case. She also
asserts that smaller aircraft will be employed to increase
the frequency of flight service. Finally, in discussing how
the industry as a whole will change, she predicts that
airlines will include large numbers of small- and medium-
sized aircraft in their fleets and commuter airlines will
become more important providers of service. Thus, the
behavior which she predicts is almost exactly opposite the
predictions of Douglas and Miller.

Bailey, Graham, and Kaplan, in their evaluation of the
effects of deregulation, note that part of the reason for
the low fares experienced by airlines after deregulation
"...was the excess supply of equipment, and most notably

wide-bodied equipment during the recession" (1985, 62).

22
They contend that

"...regulation encouraged service competition, [thus]
carriers faced incentives to purchase a larger stock
of equipment than they needed. The freedom to exit
and enter markets allowed carriers to more
efficiently employ their narrow-bodied equipment,
further exacerbating the excess supply of wide
bodies....Three- and four-engine wide-bodied
equipment was especially in excess supply. The
Board’s regulatory policy set fares in dense long-
haul markets well above costs. Yet this equipment
can only be efficiently deployed in these markets."
(13-62)

To summarize the preceding discussion, it was
generally recognized before deregulation that airlines had
adopted inefficient patterns of aircraft utilization.
However, the predictions of airline behavior after
deregulation gave insufficient recognition to the
efficiencies which airlines could achieve through changing
their route structures. The key factor is that vehicles
are capable of providing low average costs on routes given
the densities attained on those routes.

The general status of belief about the relationship
between regulation and aircraft size is that plane sizes
would rise following deregulation, that is, that regulation
encouraged aircraft that were too small. But these

theories were all based on the assumptions of a fixed-route

23
structure. Once the possibility of varying routes is

admitted, the predictions of the effect of deregulation
should have been much different. In the next chapter
theoretical models will be presented which seek to explain
the changes in airline utilization of their aircraft

subsequent to deregulation in terms of these principles.

CHAPTER 3

THEORETICAL TREATMENT -

AIRLINE DEMAND FOR CAPITAL

Previous treatments of airline deregulation have been
flawed because they assumed that, upon deregulation, firms
would only vary the number of flights offered on a fixed
set of routes. Such treatments imply that, with
deregulation, firms would abandon their dependence upon
flight frequency as a competitive weapon, substituting
price competition. They also predict that smaller
communities might lose service because competition on
profitable routes would eliminate the cross-subsidies that
existed under regulation. In addition they assume that,
under deregulation, airlines would charge a single fare, or
would differentiate fares only according to class of
service.

These adjustments to deregulation imply that, under
regulation, airlines respond to regulatory constraints by
making inappropriate decisions about their aircraft stocks.

24

25
In particular, airlines forced by regulation to compete

with flight frequency tend to use smaller aircraft than
those competing on price and maximizing without constraint.
They also have stocks of aircraft that are too large for
markets where price and entry are not regulated. In
addition, airlines under regulation faced a fare structure
intended to cross-subsidize by permitting fares well above
costs on long-haul routes. Since rents were available on
long-haul service, these were exactly the routes most
likely to experience frequency competition. Thus, the
changed environment created by deregulation was expected to
induce airlines to replace their smaller craft with larger
aircraft capable of flying longer stages.

This chapter establishes a theoretical framework to
analyze the developments in the airline industry subsequent
to deregulation. This framework permits a comprehensive
approach to the problems of airline capital allocation,
including a useful approach to empirical specification.

This chapter contains three major sections. The first
presents a simple method of characterizing the demand faced
by airline firms in a competitive market. The analysis is
based on a model developed by Salop (1984). However, only
the first section is directly based on Salop's model: the
balance of the chapter is entirely new. The results
derived from this model allow inferences about the nature
of airline capital demand. The second section extends the

model to treat the supply response of airlines where they

26
are permitted to hub and spoke. The third section develops

the empirical specifications which will be employed in the
next chapter. A fourth section summarizes the results

derived in the chapter.

Differentiated Products Treatment of Airline

Flights and Aircraft Demand

A Model of Flight Scheduling

We begin with a consideration of the demand for air
service on a particular route. We suppose that a consumer
makes a choice between an outside good (for present

purposes this may be . considered an alternative

transportation mode) and a differentiated good.l In
addition, the consumer chooses the exact variety of the
good to purchase. Because there are fixed costs of
providing any variety of a good, "custom made" types of the
good cannot be produced. The customer will purchase the
commodity only if the cash price plus the opportunity cost
of not getting precisely the desired variety of the
commodity is less than his or her reservation price. In
the case of airline service this opportunity cost can be

quantified much more exactly than with other varieties of a

1 The original inspiration for this model is Stephen
Salop’s "Monopolistic Competition with Outside
Goods"(1978). However, Salop specifically denies the
realism of the product characterization that he employs.

27
differentiated product. The displacement from the preferred

good is a departure time different than the preferred time,
the cost of which is the wage of the individual displaced
times the time differential.

In developing this model, we make the simplifying
assumption that all consumers have identical preferences
for the competing goods. Additionally, the consumers are
assumed to be uniformly distributed on the circumference of
a circle where each point on the circle represents a
possible variety of the differentiated good. Different
positions on the circumference of the circle are considered
to represent the times of departure available throughout
the course of a day. (This situation is represented in
Figure 1.) All consumers have identical costs of being
displaced from their preferred product.

Using these assumptions, we can develop two distinct

demand equations for varieties of the differentiated good

in this market.2 Each variety of the good will have an

identical demand equation because customers are distributed
uniformly throughout the market. In the analysis which
follows, each flight (i.e., variety of the good) is
considered to be supplied by an individual profit-
maximizing firm. Each variety’s demand curve is thus a
firm-demand curve. This assumption has the virtue of

considerably simplifying the analysis which follows,

2 Salop characterizes these as the "monopoly" and
"competitive" demands.

28‘

DUE E) mu III]?

GE]

IND

meow

anomms fl
sasssms sszamvs as
sssmvssrss assesses
a censuses HEDEE

IBFF

29
although it is clearly not very realistic.

The first demand equation arises when not all
customers in the market are served. In this case, there
would be some times of day when customers would resort to
alternative modes of transportation. Another way of
describing this situation is that, when the price of a
flight in an incompletely served market changes,‘ only the
quantity demanded for that flight changes. Other flights
in the market are not affected. This demand function

takes the form:
2L
(1) = —(R-P)
0‘» T
where qp is quantity demanded if not all customers in the

market are served, L is total number of consumers in the
market, and T is the opportunity cost per unit of
displacement from a preferred product (in this case, it is
the value of time wasted by the consumer because a flight
at the preferred time is not available). In addition, R is
the consumer's reservation price. Its value is determined
by the opportunity cost, again in terms of the consumer's
time used for travel, of the best alternative mode of
transportation. Finally, p is the price paid for the
transportation service. When all customers are served,the

demand function becomes:

(2) q,=i’(p'--E-p)

30
where, L,T,and p are defined as before, qI is the

quantity demanded when all preferred times of departure are
served by a flight, p‘ is the price charged on competing
flights, that is, flights whose departure times are closest

to the time of the flight in question, and n is the number

of flights per day in the market.3 In this model, a
fully served market is one in which no potential customer
chooses to buy the alternative good. The notion of a fully
served market arises because the condition of identical
costs of displacement from the preferred variety of the
differentiated good is imposed on consumers. The identical
cost assumption has considerable merit in simplifying the
theory which follows but no appreciable merit as a
characterization of any real market.

These two types of demand must be combined in a single
demand curve faced by a flight serving this market and
characterized by a "kink" where the two segments join.
This occurs in spite of the Nash conjectures employed by
the flights in the market, itself a remarkable result.

Given these demand characterizations and the
assumptions about the nature of flight costs presented
below, it is possible to determine a Symmetric Zero Profit
Equilibrium (SZPE) for this market. In other words, in
equilibrium there are no economic profits earned, thus no

entry, and each firm will produce the same output, that is,

3 For a development of these demand characterizations from
first principles, consult Salop op. cit.

31
carry the same number of passengers on a flight.

Each flight, which acts as a profit maximizing firm,

is assumed to have total costs of the form:
(3) C = mg + F

where C is total costs of the flight and m is marginal cost
per unit of realized demand, that is, per passenger
carried, assumed to be constant at all levels of demand.
In this case, these are the costs associated with
transporting one more passenger, for example, ticketing,
baggage handling, and in—flight meals. F is the fixed
cost of providing service, characterized in the airline
literature as flight costs. It depends on the route flown,
or, distance, and the type of aircraft employed on the
route.

The conditions for a SZPE are:

d
(4) p+q<—p)sm

dq

and:

(5) p=m+E
q

In other words, marginal revenue must not exceed
marginal cost and price must be equal to average cost so
that no economic profits are earned. This is so because
individual flights are thought of in this analysis as
monopolistic competitors whose zero profit equilibrium will
pct be achieved at the minimum of average

total cost. Since the equilibrium must be symmetric, and

32
assuming it has no gaps (i.e., unserved customers) it will

be true that:

(5) q =

3"."

The derivative of each segment of the demand
function, where the number of flights is fixed at the
equilibrium number of flights on the route, can be

calculated as:

dqb T

and:
(7b) 2?. = II.
dqf I.

for the incompletely- and completely-served segments of a
flight’s demand curve, respectively.

Combining these derivatives with the equilibrium
conditions and equation (6), it is possible to solve for
the equilibrium price and number of products offered (here
flights per day) for both completely and incompletely

served markets. These are:

(8a) pp=m+—I—
an

and

(8b) ‘5 = m +

PM

33
for the equilibrium prices and:

(9a) nP= IL
25

and

(9b) n‘= T—L-
F

for the number of flights offered in equilibrium.4

In addition to equilibria where the markets are either
completely or incompletely served, there exists the
possibility of an equilibrium at the "kink" where the two
demand segments join. Since no tangency is possible at
the "kink," a range of parameter values will be consistent
with an equilibrium at the kink. The upper bound of these
values is the partially served equilibrium where the demand

and average cost curves are just tangent, or:

(10) R-2m= :

\L

The lower bound is the upper limit for tangency in

r11

 

fully served equilibrium, or:

1112
2L

(11) R-m=

The three possible equilibrium outcomes of the model

are illustrated in Figure 2. Considering the choice by an

4 In this expression, n9 is in fact only the upper

limit of the number of products which may be offered in the
market. This reservation will be true of all the
incompletely served markets considered below.

P1
P2

P3

34

 

 

 

 

 

 

 

 

RC 1.
'C 2
0.1. oz _
FIGURE 3

POSSIBLE EQUILIBRIQ"
FOR AN INDIVIDUAL FLIGHT

35
airline of aircraft to fly a particular route, the number

of aircraft used is obviously a direct function of the

number of flights (np,n')which a market will support.
Airline Responses to Regulation

In this section, the model is altered to consider the
case of an exogenous price. This alteration reflects the
situation faced by airlines during the regulatory period
when the CAB controlled both the price of the airlines
services and the routes on which the airlines were able to
offer service. Thus the model also holds route structure
constant, and only the number of flights which can be

offered will be varied. Price is set at the level p“

which the firms accept as a given in their maximization
process. As a result the zero profit equilibrium condition

is altered to:
(12) Prqr=mqr+ F
Here qr is the equilibrium quantity demanded realized at

the fixed price pr. Rearranging this expression yields:

(13) <1r = F/ (Pr - 111)
Remembering that if the entire market is served, q =

L/n and q = qr, then the number of flights offered is :

(14) n=L/<lr

So that the equilibrium number of flights under regulation

36
is :
(15) n,=(pr-m)L/F
where nr is the number of flights offered under regulated

price pr The equilibrium for an individual flight is

illustrated in Figure 3. In Figure 3, average cost is not
minimized, since to do so would result in economic profits.
Instead, entry occurs until economic profits have
disappeared.

Consulting equation 9b, we see that in fully served
markets the number of flights offered without regulation of
price is:

IL
F

(16) If =

So that relative to unregulated competition, the number of

flights offered under regulation is :

(17) nr = (pr - m )J—f- n‘
TF

From the conditions of equilibrium it is possible to
calculate the value of T as a function of equilibrium price

and the parameters of the model :
(18) T = < p, - m )2(—L-)
F

The relationship between the number of flights offered
when the price is exogenous and the number offered when

price is market-determined is :

(p,-m)

 

(19) n
(pr-m)

37

FARE
RES
PRICE

MIN
FARE

  
 

AVERAG

0:226 0 COMP Passsueens

lfiulimlflalg :3
companrson or REGULATED
AND comparzrzvs EQUILIBRIA

38
Thus, the number of flights offered under regulated

prices is proportional to the relative price cost margins
under regulation and competition. Since there is no
competition to insure that prices will be driven to minimum
average total cost, prices and number of flights must be
higher under regulation. This implies that the number of
aircraft held by firms under regulation must be excessive.
This result depends crucially on the fact that regulated
airlines are not able to alter the routes which they
serve.

So far, this result is not novel; it depends on the
model used by most economists before deregulation. But
this result has been contradicted by airline experience
since deregulation. This dissertation provides an
alternative framework, one which explains the experience of

deregulation in a more satisfactory fashion.

Airline response to varying aircraft capacity

Airlines do not choose only the number of flights to
offer in either the regulated or deregulated state. They
must also determine which of the several different
varieties of aircraft to employ on any given route. They
face this problem because different aircraft types will
offer superior cost performance for different routes.

There are two distinct variables which determine the

behavior of aircraft costs on a route. One is economies of

39
aircraft size. Economies of aircraft size result in

decreasing average costs on a per passenger basis as
progressively larger aircraft are employed on a particular
route. This is the case since the marginal costs of
providing service on a route are not strongly dependent on
choice of aircraft and the flight costs of a route increase
less than proportionately as aircraft size increases. This
phenomenon leads to the economies of density reported by
Caves et al.(1984), since increases in the

density of a route will permit an airline to employ larger
aircraft on any given route without decreases in flight

frequency.

The second variable which determines the behavior of
flight costs is the distance covered on a route. Flight
costs increase less than proportionately with the distance
covered by the route for all aircraft types. In addition,
the rate of increase in flight costs with distance is
slower for large aircraft varieties than for smaller
aircraft types. As a result, average costs per mile decline
with distance and decline more than proportionately as
aircraft capacity increases. The relationship of average
costs to both distance and aircraft capacity is illustrated
in Figure 4.

In the model presented below, aircraft assignment to
an already selected route is considered. Thus the distance

of the route is fixed and the variables controlled by a

40

 

AVERAGE COSTS

AC PER MILE

  

 

 

AC

DISTANCE

 

E'EIIIIIIB 6

ATIONSHIP O

M
N

COST
CRAFT

E
N
R

F AVERAG
PER PERSO
ETY OF AI

ILE AND
GLE VARI

REL
PER
A SI

THE
FOR

41
firm are the number of flights to offer and the type of

aircraft to assign.

As a simplifying assumption, suppose that the per
passenger marginal costs on a route are identical for all
varieties of capital. This assumption may not be too
unrealistic. The marginal cost of handling another
passenger is related to such items as ticketing, baggage
handling, and in-flight meals, which are not necessarily
specific to any given route or aircraft. Thus the firm may
choose to bear fixed (flight) costs:

(20) F1 < F2 < F3
The relationship between these costs is such that for

some q“ the average cost per flight using technology 1

is equal to the average cost per flight of technology 2.

For demands less the q” technology 1 is lowest cost, and
for demands greater than q1 but less than qr

technology 2 is least cost. At demand levels greater than

(H’ technology 3 dominates the alternative technologies

with respect to cost. The relationship between the three
technologies' average cost curves is illustrated in Figure
5.

As a result of this modification in technology,
equilibrium condition (5) is modified. It now becomes:

(21) min(p=m+F‘/q) i=lt03

Any higher price will result in entry by firms employing
the more appropriate technology, assuming that competitive

entry is permitted. This relationship yields an

42

AVER
COST

 

 

I
I
I
I
I
I
I
I
I
I
1
Q

I
I
I
I
.1. 02 PASSENGERS

E'EIEJEJE 5

AVERAGE COST PER PASSENGER
WITH THREE AIRCRAFT VARIETIES

43
equilibrium when the slope of the demand curve (either -L/T

or —2L/T) is equal to the slope of the average cost curve.
The relationship of the family of average cost curves
generated by the different varieties of aircraft and the
demand curves for an individual flight on a route is
illustrated in Figure 6. As is illustrated in Figure 6,
each different size of aircraft, since it supports a
different level of flights on a route, yields a slightly
different demand curve. All demands share a common origin,
since the reservation price is determined by the
opportunity cost of alternative modes. Aircraft varieties
with higher flight costs will support a smaller number of
flights. Thus, such aircraft varieties are only chosen
when their lower average costs more than offset the
increased opportunity cost to the consumer of reduced
flight frequency.

Referring to the previous section where price is set
by some outside agency, Figure 6 makes it clear that, when
price is not market-determined, smaller than optimal
aircraft will be employed.

At the same time, this modification of the model leads
to the prediction that a single type of aircraft will be
employed on a route. Exactly which variety of aircraft
will be employed on a particular route depends on which
variety of aircraft fulfills condition 21.

This prediction is at variance with observation (see,

for instance, the Official Airline Guide,

 

PASS

EEIIIIEJE (5

EQUILIBRIA WITH THREE
AIRCRAFT VARIETIES

45
which lists aircraft assignments on each route). Two

plausible explanations can be supplied for this. First,
the deviation between the model’s prediction and
observation is largely the result of an unrealistic
simplifying assumption used in creating the model. The
parameter values T,R and D = L/c are not, as assumed,

constant, but vary along the circumference of the circle or

over the course of a day.5 In Figure l, the period
between midnight and 6 A.M. was assumed to have as many
potential customers as the equally long period between 6
A.M. and noon. Of course this is not the case. The
variation of these parameters destroys the symmetry
properties of the equilibrium. Different times of day have
different demands for flights and so different types of
aircraft could be appropriate.

This pervasive asymmetry creates some interesting
strategic problems for airlines considering the structure
of their flight schedules. However, these strategic
problems will not be further considered here.

In addition, even if the market were symmetric, the
equilibrium number of cost-minimizing flights of a single
aircraft variety in a market is unlikely to be an integer.
If only a single scale of operation is possible (i.e. if
only one variety of aircraft is employed) in a market and

5 T is the opportunity cost of passengers' time, R is the
reservation price for a flight, and D is the density of
customers per unit of the circle,c, the circumference of
the circle.

46
the equilibrium number of flights is noninteger, economic

profits can be earned in the long run. The use of other
varieties of aircraft, permitting entry on another scale,

could erode these economic profits.
Effects and Mechanisms of Price Discrimination

We complete the analysis by considering a variant of
the model where there are two distinct and equal—sized,
classes of consumers distributed around the circle. Both
of these consumer groups are assumed to be uniformly
distributed around the circumference of the circular
product space. In other words, there are equal numbers of
consumers for each hour of the day. These consumer groups
differ only in the costs they bear when displaced from
their preferred product (time of departure). Each set of

consumers has demand:

(22) qp = 2L(R-p)
I

T
when not all of the customers of type i in the market are

served and :

TI
(23) Q,=T—(P“;"P)
i

when all customers of type i in the market are served.
These demand functions are minor modifications of equations

1 and 2 above.

47
If the firm can charge only one price in the market,

the demand curve a firm faces will consist of three
segments. In the first segment, demand will consist of the
sum of the demands for each class of consumers when not all
consumers in the market are served or:

Tl+ T2
(24) qp=2L(R-p)(———

T35

)

Let T‘<: T3 ; then the second segment of the demand
curve faced by the firm will equal the sum of consumer type
1's fully served demand and consumer type 2's incompletely
served demand over the appropriate range of prices and

outputs, or :

T
(25) qt=%‘R'P’+(f”P"fi’P)
2 l

Finally, for price sufficiently low, firm demand will
equal the sum of competitive demands for both consumer

types :

L THE
(25) CI, = —((T2 + T1)( P' "P) + — )
2T1 n

This segmented demand curve could be subjected to
analysis similar to our earlier treatment for a market with
only two demand segments. However, the real interest in
this variant lies in analyzing supply responses when the

different classes of consumers can be charged different

48
prices. In this we can follow our previous procedure quite

closely. In other words, we will seek a Symmetric Zero
Profit Equilibrium, where each supplier charges two prices.

As is apparent from the characterization of product
demands above, three distinct cases may be distinguished.
The first is the analog of the earlier case, where not all
customers in each class are served. A second case is where
customers of the class with the lowest displacement costs
are fully served and customers with higher displacement
costs are not. Finally, there is the case where all
customers of both classes are served.

The starting point of this analysis is a modification
of condition (3), that marginal revenue be less than or
equal to marginal cost. In this case, the condition must

hold for both classes of consumers:

dpl
(27a) p1+'q!(-——) s m
6%
dp2
and (27b) p2 + q2 (— ) s m

6‘1.

All customers are assumed to give rise to the same
incremental costs of service, m. The zero profit condition
must also be rewritten to reflect the fact that the revenue
contribution of one class of consumers affects the
contribution the other class must make. The zero profit

condition thus becomes:

(28) (plq,I+<p2q2)=m(q1+q2)+F

49

Condition (5), q‘==I/n, is still fulfilled and the

value of the derivative of price with respect to quantity

is either:

 

dp dP

(29a) -—4 = - —ZL or -——L= - L
dql T1 dql 'E
dp dp

and (2913) —-g = - A or 2: - _L
dqz T2 dqz T2

depending on whether or not all customers of a given
service class are served in the market.

Combining all these equations and solving for p“ 15

and n in the completely, mixed, and incompletely served

markets respectively yields: 5

 

(L(Tl + '13))
\ 2F

 

(30a) n

 

6 The algebra involved in deriving these equilibrium
values is tedious and will not be reproduced here. Details
can be supplied upon request.

50

 

 

 

 

 

Tl T2
p = m + — and p2 = m + —
1 n 2n
(30b) n = (L(2Tl + T2))
\ 2F
_ fl _ 12.
pl - m + and p2 -— m +
2n 2n
(30c) n = L(Tl+ T»
N F

 

This analysis raises two points of interest for the
topic of this dissertation. The first is how the number of
flights offered in a market changes when the airline is
able to practice a form of price discrimination such as the
one outlined above. The second is the method by which an
airline might be able to achieve segregation of its
customers according to their different demand elasticities.

The ratio of equation 31c to equation 9b is:

(Tl+-TE)

(31)
\ 2T

...5 LP

 

Rearranging this equation yields:

 

where n1 is the number of flights offered when price

51
discrimination is practiced in a fully served market, nf

is the number of flights offered where price discrimination
is not practiced, T1 and T2 are the unit displacement
costs of the price discriminating markets, and T is the
cost per unit of displacement from ones preferred product
in the non discriminating market.

Condition 32 means the number of flights offered will
be greater with price discrimination than without. This is
only true if the average of the displacement costs of the
consumer classes in price-discriminating markets is greater
than the displacement cost of markets without price
discrimination. In other words, the average value of time
must be higher in a market for the number of flights to be
increased by the practice of price discrimination.

The price-discriminating airline will charge a lower
price to individuals who place a lower value upon their
time. This raises the problem: What mechanism permits the
airline to segregate customers according to their differing
elasticities with respect to displacement from desired time
of departure? One possibility is purchase and length-of-
stay restrictions on tickets.

The price discrimination practiced by airlines since
deregulation is unique. It hinges upon the elasticity of
Vdemand with respect to flight frequency. It has long been
observed in the airline industry that flight frequency
serves as a competitive variable, since the traveler's

opportunity cost of air travel is minimized by flights

52
departing frequently from any given origin (i.e., a

departure will occur close to the desired time of
departure). This resulted in a competitive strategy under
regulation involving increasing flight frequency until the
price fixed by regulators just covered average costs.
Average costs, of course, increased since load factors
declined with increasing flight frequency.

The mechanism through which the airlines are able to
achieve segregation is the tactic of fares subject to
significant restrictions upon the flexibility with which
the tickets can be employed. The requirement of advance
purchase effectively reduces the implicit flight frequency
from an origin available to the consumer to one flight per
week, month, or other relevant time period. The same
reasoning applies to restrictions on length of stay. In
return for this lowered flight frequency, the customer will
only be willing to pay a lower fare. The lower fare in
turn increases the quantity demanded for transport at the
relevant flight frequency. In effect, the airline is
combining consumers off of several distinct demand curves,
one for each flight frequency implicit in the restrictions
imposed in the fares.

This concept is illustrated in Figure 7. In Figure 7,
the vertical axis represents fare: the horizontal axis
extending out of the page, the quantity demanded of a
particular flight: and the horizontal axis in the plane of

the page, the reciprocal of flight frequency. The

53

   
  

;; :5. $55" . . 1/ F L I G H Ts
g? " PER DAY

 
 

PASSENGERS
PER FLIGHT

fi'flIL'JElI ‘6’
THE RELATIONSHIP BETWEEN
FLIGHT FREQUENCY. FARES. AND
QUANTITY OF FLIGHTS DENANDED

54
reciprocal is used to dimension this second horizontal axis

since the amount of time spent waiting for a flight, and
with it the opportunity cost of flying, decreases as flight
frequency increases.

As illustrated in Figure 7, each flight frequency has
a demand curve associated with it. Airlines are able to
maximize profits by choosing output levels where the
marginal revenue of each class of passenger is equal to the

marginal costs of flying the passengers in that class.

Joint Products and Hubbing and Spoking

as Explanations of Airline Behavior

The theoretical framework outlined in this section has
implications distinctly different than the theories
advanced before deregulation whose content has been
outlined above. Previous theoretical treatments of
deregulation implicitly assumed that airlines would change
their deployment of aircraft within an essentially fixed
set of routes.

The early literature anticipated that there would be a
significant decrease in flight frequency in deregulated
markets as carriers switched to competition based on price,
since less frequent flights would permit the airlines to
utilize more economically sized aircraft. What was not
anticipated was the extent to which airlines would be able

to achieve the higher densities necessary for successful

55
operation through the restructuring of their networks into

so-called hub-and-spoke route systems.

In fact, the major effect of deregulation has been a
restructuring of airline route networks as hub-and-spoke
systems. Hub-and-spoke networks make possible higher
levels of frequency than could be achieved in the linear
networks that prevailed before deregulation. These
increased flight frequencies can be achieved in two ways-—
either by increasing the stock of aircraft or by utilizing
existing stocks of aircraft more efficiently. Both appear
to have occurred subsequent to deregulation.

Hub-and-spoke restructuring of airline routes implies
that airlines should maintain relatively larger stocks of
aircraft subsequent to deregulation than suggested by
earlier theories such as that of Douglas and Miller (1974).
This contradicts the results of previous sections which
imply that stocks of aircraft under price and entry
regulation should have been too large. An additional
implication is that airlines should make few changes in the
relative holdings of aircraft types in their fleets.
Flight frequency still plays an important competitive role
and smaller aircraft are necessary to provide high levels
of flight frequency.

It is the contention of this dissertation that airline
behavior since deregulation has been directed towards
achieving economies of density.7 Two distinct strands

have constituted the industry response to the challenge of

56
attaining economies of density. The first consists of the

hub-and-spoke restructuring of airline routes. The second
is the unique form of price discrimination discussed in the
previous section. The interaction of these two strategies
has resulted in the achievement of notable economies on the
part of airlines since deregulation.

The basic principle of the hub-and-spoke routing is
simple. Passengers from a single origin, proceeding to
diverse destinations, are brought to a central point.
There they change planes to proceed to their final
destinations, along with other passengers who have been
similarly concentrated at the hub. The advantages of this
type of routing for achieving economies of density are
obvious. Passengers for many destinations use a single
aircraft, permitting a larger aircraft to service the
airport, At the same time the airline can maintain, or even
expand, the number of flights offered. Likewise, flights
outbound from the hub combine passengers from many origins,

which also permits larger, and more economical, aircraft to

be used.8
The efficiency of hub-and-spoke routings from the

point of view of an individual air carrier is enhanced by

7 See Caves, Christensen, and Tretheway (1986) for
evidence that economies of density exist for airlines and
are of substantial importance.

8 This argument depends on the economies of aircraft
size, i.e. on the assumption that larger aircraft with
equal load factors will have lower average costs. This is
generally accepted in the literature (Bailey and Panzar
1981).

57
the known reluctance of passengers to accept interline

routings. Thus, airlines need not fear that the passengers
which they deliver to the hub will be lured_ to other
carriers to reach their destination. In fact, there exists
some evidence that airlines are using the reluctance of
passengers to accept interline routings as a marketing tool
( Oster and Pickrell 1986). Consequently, hubbing and
spoking guarantees the high load factors and high passenger
densities necessary to achieve economies of density.

So far, no mention has been made of possible economies
of scope in the provision of airline services through a
network. It is possible that the pursuit of economies of
density has been the sole motive for the restructuring of
airline route networks subsequent to deregulation.
However, substantial economies of scope would, if
available, strengthen the tendencies implicit in the
pursuit of economies of density. In particular, the
reported economies of scale in baggage handling could be a
source of economies of scope for individual airlines
operating hub-and-spoke networks, since the volume of
baggage to be handled at the hub will be substantially
greater than in non hub-and-spoke systems (Bailey et al.
1986).

In the following subsection, a simple method of

treating demand in hub and spoke routings will be

presented.

58
Joint Products and Hubbing and Spoking

In treating the profit maximization problem of an
airline which hubs and spokes, the key element is the fixed
(flight) cost each flight incurs. The so-called flight
costs of an aircraft flying a spoke are fixed and can be
spread over the passengers for many origins or
destinations. As presented above, the demand for airline
transportation on a particular route can be considered as
distributed along the circumference of a circle. Different
points on a circle are considered to represent different
times of departure throughout the day. Flights offered at
particular times of day are then seen as monopolistic
competitors with other flights on the same route.

Routes sharing a point of origin were previously
treated as unrelated. In terms of the theory, the demands
for flights on routes sharing an origin are treated as
distinct products. Each route, in our clock face analogy
presented in Figure 1, lies on a non-intersecting circle.

The novelty of the treatment of hubbing in this
section is the manner in which different routes are seen as
relating to each other. The central element of the hub-
and-spoke concept is that customers proceeding from a
single origin to diverse destinations are served by a
single aircraft. Thus, each flight is located at a point
where a number of distinct product spaces intersect. Each

route has its own distinctive demand characteristics.

59

ORIGIN
NEW YORK
SERVICE

THROUGH
CHICAGO

(HUB)

I
nssmsamm
NEW YORK/L A

 
  
  

 
 
  
  

NEW YORK/DENVER

 

6 Pl
new YORK/DES MOINES

momma EB

SERVING SEVERAL,MARKETS
ON A SINGLE FLIGHT

60
These include the population of potential customers on the

route, the value of time of that population, and the
reservation price for the route.

Each flight is then imagined as occupying a point on
the circumference of many distinct circles simultaneously.
This situation is illustrated in Figure 8, where each
circle is labeled as a distinct route. (An infinite number
of distinct circles can, of course, share a single common
point.) In each of these distinct markets, the demand for

the product qiis.represented by a demand curve with two

segments, as previously described. When demand is
insufficient to insure that all passengers on all routes

will be served, the flight faces demand such that:

n n21.
(33) Q=Zq,=Z—'-(R.-p)
: i=1 Tl

_
p—o

If, on the other hand, all passengers on all routes are

served then:

(34) Q =

b4:
.0

II
b4:
E?

I

I
'3

_-
II
.—
no
I

Id TI

In this analysis, neither the incomplete service case
nor the intermediate case (i.e., where some markets are
fully served and others not) will be considered, since it
appears that hubbing and spoking will insure that all

markets are fully served.

61
The firm then must maximize the profit function:

n
(35) H = gm- mm, - Fr.

Here, Fh is the per-flight cost of flying from the origin
to the hub.
Since we are still seeking Symmetric Zero Profit

Equilibria, the zero profit condition still holds, or:
n n
(36) ‘Z-lp‘qugq‘ + Fh

If the demand on each route is independent of the
demand on any other route, then differentiation with

respect to quields n identical first-order conditions

62
of the form:

T 2Tq
(37).§il=p-+_I_- ‘1

5‘!t n LI

 

-m

Solving these n equations and the zero-profit

restriction for q“ 1%, and nh, the number of

flights offered from an origin yields:

(38a) q1 = L,/ nh

(38b) pi Ti/nh +m

(38c) nh==‘~\

The expressions for price and quantity are identical

 

 

 

1
ZTILI
i=1

Fh

to the expressions derived when the problem of price
discrimination was considered previously. Thus hubbing and
spoking is one of the class of problems where different
classes of customer share the fixed costs of a product with
a joint production technology. Hubbing and spoking in
effect means that a flight from an origin provides a set of
joint products, that is, one for each unique passenger
destination on the flight. This result can be extended to
multiple classes of consumers on a particular route as was
done in a previous section.

The relative number of flights in a market when route
structures are fixed in proportion to the number of flights

in a hub-and-spoke route system cannot be determined

63
analytically from these results. However, in general,

products offered under conditions of joint production are
produced in greater quantity than if joint production were
not possible. This is the case, since an airline flight is
an example of a public input in the sense of Baumolet al.;
that is, once a spoke flight is provided, it is capable of
providing a variety of different products (1982, 75-77).
Thus the lower costs of production permit a firm to offer a
larger supply at any particular price. The fixed costs of
production can be allocated to the consumers most willing
to bear the burden of the fixed cost, that is, those with
the least elastic demand for the product. Other classes of
consumers will benefit from lower prices for the jointly
produced good.

In addition, two crucial assumptions underlie the
preceding analysis. First, the number of routes served per
point of origin do not vary when airline markets are
deregulated. Second, the number of points of origin served
by an airline is unchanged after deregulation. Both of
these assumptions are invalid for the American experience
of deregulation. Thus, as airline flights became joint
products because of hubbing and spoking and the number of
points served as origins increased, the airlines’ demand

for aircraft should have increased with deregulation.

64
From Theory to Empirical Specification

Empirical Specification of the Relationship of Flights per

Day to Route Characteristics

The first section of this chapter investigated
theories of airline response to various constraints where
route structure was accepted as given. This is the
situation which airlines faced while regulated. The
subsequent section presented an alternative theory whereby
airlines alter their route structures into hub-and-spoke
systems. In this section, we develop an empirical
specification of the relationship between route
characteristics and number of flights offered per day on
the route which is intended to permit a test of the nature
of the relationship.

Each of the previous subsections developed a different
relationship between route characteristics and flights per
day. ( The different results are summarized in table 1.)
All employed the same variables to explain the
relationship, differing only in functional form.
Prederegulation predictions offer the expectation that the
number of flights on a route per day will decline with
deregulation. In contrast, the theory of hubbing and
spoking offered here suggests that the number of flights
offered per day should remain constant or increase upon the

removal of regulation.

65
Table 1

Alternative Specifications of the Relationship Between
Market Parameters and Number of Flights Offered

1. Completely Served Markets with Free Entry and
Unregulated Pricing

 

 

‘ 1°” “I = x F...

2. Completely Served Markets with Price Regulation

_ (p,-m)
n"(pr-m)“

 

(19)

3. Serving Two Classes of Consumers in One Market

 

 

 

(T + T)
(32) n‘ = \ in 2
4. Hub and Spoke Networks

(i.e. multiple routes served on one flight)

 

(38c) nh==

 

 

n is number of flights per day on a route except for
equation 4, where it is number of flights per day to and
from origin. Subscripts indicate differing assumptions
used to derive the formulae.

T is the opportunity cost of an air traveler’s time,

measured in dollars.
L is the population of potential air travelers.

F is the cost of providing a flight on a given route.

66
As exemplified in table 1, all specifications require

number of flights per day to be determined by the
population of potential travelers (L), the opportunity
costs of the travelers' time (T), and the fixed costs of
providing the services (F). Theoretically reasonable
proxies must be developed for each of these variables.

The populations of the route terminals are employed as
a proxy for L. This is a general practice in making
estimates of airline demand (Brueckner 1985). As a proxy
for T, the per capita income of the respective route
terminals is employed. In addition, the percentage of
families with high incomes (more than $15,000 [1974] or
$35,000 [1984]) was employed as an opportunity cost
variable. Finally, the distance of the route is used as a
proxy for the flight costs of serving the route, F.

Two further additions to the model are necessary
before it can be estimated econometrically. The first,
mandated by theoretical considerations, is the addition of
a variable identifying routes that have as a terminal
popular vacation destinations. This variable is added to
allow for the differences in opportunity cost of pleasure
travelers as opposed to business travelers. Use of a dummy
variable is a common practice in empirical estimation of
airline demand (Ippolito 1981). Alternatively, variables
measuring the per capita expenditures at a route terminal
on hotels or on both hotels and amusement facilities are

used to show the extent of vacation travel on the route.

67
The other addition to the model to be estimated is a

dummy variable for flights which serve as connecting
flights. According to the theories presented above, where
airlines are able to establish hub-and-spoke route
structures, their response will be to increase the number
of flights offered from an origin per day. Accordingly, a
dummy variable was constructed, taking the value of one (1)
when the flight is one providing connections through a
third city and zero otherwise.

A final consideration is the functional form in which
the relationship should be estimated. The multiplicative
nature of the relationships illustrated in table 1,
indicates that the independent variables should enter the
estimating equations in logarithmic form.

The model to be estimated then is :

(39) n=c+oz,lnPOP+a21nINC+a31nDIS+

a, HUBDUM + a5 VACDUM + e

n is number of flights per day on a route, POP is
population of the route terminals, INC is per capita income
of the route terminals, DIS is the distance of the route,
HUBDUM is the dummy variable for connecting as opposed to
direct flights described above, and VACDUM is the dummy
variable for preferred vacation spots. Population and per
capita income enter this equation both separately and

combined in different estimates.

68
Empirical Specification of the Relationship of Equipment

Choice to Route Characteristics

The model of the demand for flights in the previous
sections is effectively a model of the demand for aircraft,
since every flight must have an aircraft assigned to it.
However, this model must be extended to provide estimable
forms for the relationship between choice of aircraft type
and route characteristics.

The choice of aircraft on a particular route is
determined by which type is able to provide lowest cost
service. However, since realizable demand is different
at different times of day, differing aircraft may exhibit
least-cost characteristics over the course of the day.
The number of flights per day must equal the number of
aircraft of all types used to provide flights on the route

during the day, or :

(40) n1 = g K1

The right hand side of this expression is substituted
directly into the left hand side of the estimating form

developed in the previous section, which yields:

(41) 2K1=c+allnPOP+a2 ln INC+cII3 1n DIS
I

+ anHUBDUM + ag‘VACDUM + e

To derive the estimating relationship between any

particular aircraft type and route characteristics, the

69
expression must be rearranged, yielding:

(42) K1=c+a,lnPOP+ozzlnINC+a31nDIS
m

+ 01., HUBDUM + 0:5 VACDUM -Z[Ill(l + 6
1:2

where K1 is the quantity of aircraft variety one and

m
21:29:19 is the total of all other varieties of aircraft

employed on the route. There is a system of m such
equations. The relationship of each aircraft variety to
the characteristics of a route can be determined by
applying the principle of cost minimization. In other
words, given the cost performance of each aircraft type as
relevant variables change, the model developed above can
make detailed predictions about the manner in which

aircraft deployments will alter with deregulation.

Empirical Specification of the Relationship of Fleet

Composition to Route Characteristics

The analysis of the preceding subsection has
illustrated how the number of airline flights ( and thus
the number of aircraft employed) on a given route depends
on market characteristics such as density (i.e., the
number of passengers in the market), value of time of
passengers in the market and the cost of offering a flight
(chiefly determined by aircraft choice). In this section,
the analysis will be extended to the choice of number of
aircraft when an airline serves many different routes from

many different points of origin.

70
The number of flights offered on any particular route

is determined by the theory outlined above. When an
airline offers flights on many different routes from a
single point of origin, the number of flights the airline

is able to offer from that point of origin is :

(43) 1% = ; nU

where N’is total flights from point j, and nU is the

number of flights per day on route i from point j. It is
assumed that each aircraft is able to provide only one
flight per day on a route from any point of origin,
although an aircraft may serve several different routes,
each with a different point of origin, in one day. Thus the

minimum number of aircraft required by the airline is:

(44) 2 K1 2 max 2 nU
i I

where K1 is the number of aircraft of type 1 in the
airlines fleet, and the total of all aircraft in the fleet
must be greater than or equal to the number of flights
offered per day from the the point of origin with the
largest number of originations per day.

If this constraint is not binding, the total number of

flights offered by the airline will be:
(45) NT 3 I; 1"II

where NT is total number of flights offered over a
network of j points of origin and i routes served per
origin.

In addition, since an aircraft must be assigned to

71
every flight, total flights will also be :

(46) NT 2 ; c:1 Kl

where 01 is the average number of flights per day for

aircraft of type 1. This relationship must be expressed as
an inequality, because aircraft characteristics may be such
that some types of aircraft are not usable on some routes.
Thus, aircraft may be used at less than full capacity in an
airline’s fleet. Assuming profit-maximizing behavior on
the part of airlines, however, the relationship expressed
in equation 16 should tend towards equality. Thus an

airline’s total capital should approximate:
(47) ; c,1g = g§2rm
Substituting for nU from equation 10b and
rearranging yields:
1 TU LU nrl
(48) K5;- ( Z Z ‘— “261 K1)

n I I \ Fmi In

In this equation, K5 is the number of aircraft of type

 

n held by an airline, cn the average number of flights per
day by an aircraft of type n. TU is the opportunity

cost per unit of deviation for a passenger on the ith route
from origin j taking a flight departing at a time other
than the passenger's preferred time. LU is the population
of potential passengers on route 1 from origin j. These

passengers are making the choice between some alternative

mode of transport and flying. Fm‘is the cost of a~flight

72
on the ith route from the jth origin when aircraft of type

n is used.3 There is a simultaneous system of n such
equations which can be solved for unique values of each
1g.

In the econometric analysis which follows, a different
set of proxies is employed for the independent variables in
the regression. The classification of airline origins and
destinations as large, medium, and small hubs is assumed to
be related to the demand characteristics of hubs. The
inner summation in the equation above (representing the
product of the potential passengers and the opportunity
cost of those passengers' time) is proxied for each airline
by the average number of passengers per day served in each
hub classification. The number of each type of hub served
then enters as a significant variable for characterizing
the total scope of the airline's operations. This is
similar to the procedure followed by Gillen et al.(1985).
In other words, the total number of hubs served is the
index of summation of the outer summation, j. Each class
of hub enters the estimating equation separately. Average

stage length here serves as a proxy for Fwfl

the fixed costs of providing a flight. The estimating form
then becomes:

n-l
(49)Kn=C+BlL+BZM+038+B4RPE+BSASL+l§qu+E

where K; is the number of aircraft of type n in an

9 Fm, under the assumptions of this model, always

achieves the smallest attainable value on the route for the
type of aircraft actually employed.

73
airlines fleet, L is the number of large hubs an airline

serves, M is the number of medium hubs served, S is the
number of small hubs served, RPE is revenue passenger
emplanements, or, the number of passengers served annually,
and ASL is the airlines average stage length.

There is a system of these equations, one for each
type of aircraft. In addition, the relative percentages of
different types of aircraft are employed as a dependent

variable.

Summary of Results

 

Let us summarize what our theory leads us to expect.
The analysis began with a stylized model of the demand for
airline flights. This model permits prediction of the
number of flights per day that a market could support. The
number of flights was related to the population of
potential customers, the opportunity costs of not having a
flight depart at the desired time, and the costs of
providing a flight which do not vary with the number of
passengers per flight. These results are presented as the
first entry in table 1. The capital (i.e., aircraft)
requirements of an airline, in terms of the number of
flights per day that an airline offers from all of the
origins it serves, were then determined.

A series of extensions to the model were developed.

First to be investigated was the response of airlines to

74
the regime of price and entry regulation. As illustrated

in the second entry of table I, the number of flights per
day should be increased by the imposition of price
regulation.

Next, the problem of fleet composition was considered.
When load factor (i.e., percentage of aircraft capacity
actually used) is held constant, average costs decline as
larger aircraft are used. Thus, the largest aircraft
capable of minimizing average costs will be employed on a
route.

Where airline competition is limited to competition
over flight frequency, smaller aircraft will actually be
employed. This occurs because higher frequency, given a
fixed population of potential customers, means fewer
passengers per flight. Average costs of a flight can then
only be minimized by high-load factors on smaller aircraft.

Results to this point merely duplicated predictions
which were made prior to deregulation. They imply that
airlines entered deregulation with aircraft fleets which
contained too many aircraft for efficient operations.
Additionally, they possessed relatively too many smaller
aircraft.

The results of subsequent sections yielded the
opposite conclusion. The ability of airlines to use demand
for flight frequency as a method of segregating passengers
in order to practice price discrimination was investigated.

Then, hubbing and spoking was analyzed as a problem of

75
joint production. The results indicate that airline

responses to deregulation were more sophisticated than
economists had predicted. In particular, route
restructuring into hub-and—spoke systems coupled with price
discrimination meant increased flight frequencies. Thus,
smaller aircraft types remained in use to provide high-
flight frequencies on lower- density spokes. Larger
aircraft were used on both high density spokes and interhub
flights. Route restructuring permitted airlines to realize
economies with their existing fleets.

Prederegulation predictions about airline fleet
composition imply a different set of empirical outcomes
than the theory developed here. In particular, they
predicted that flight frequencies should fall on most
individual routes and that the average size of aircraft
employed should increase. Finally, the theoretical models
developed previously were used to develop the empirical
specifications needed to test the performance of airlines
when deregulation occurred. In the next chapter, the

results of the empirical investigations are reported.

CHAPTER IV

EMPIRICAL TESTS

In this chapter the hypotheses developed in the
previous chapter are subjected to empirical test. Two
distinct sets of tests will be conducted. In the first set
reported, tests of the relationship of market
characteristics to aircraft assignments and routings are
conducted. In the second, the relationship of airline
route structures and the gross composition of their fleets
is tested.

As discussed in the previous chapter , an airline's
demand for aircraft can be explained in terms of the demand
characteristics of the markets served and the economic
and regulatory environment. The variables presented in the
theory are not represented exactly by any data sources
readily available. In order to perform econometric
estimates, proxies must be found for four distinct varieties
of variables.

76

77
The first is aircraft types. Two distinct sources of

data were consulted to develop models of aircraft
utilization. The aircraft data for the route level
estimates presented in chapter 3 comes from the July 1974

and July 1984 editions of The Official Airline Guide,

 

North American Edition.
The demographic and other market demand-related data

are derived from supplements to The Statistical Abstract

 

of the United States and other U.S. government publications.

 

These were supplemented as necessary by commercially

available data sources. ‘

For the second set of regressions the primary source

of data was The Handbook of Airline Statistics, published

 

biennially between 1963 and 1973, with a supplement
published for the years 1974 and 1975. This data source

was supplemented for years after 1976 by The Inventory and

 

Age of Aircraft Trunks and Locals, prepared by the Office

 

of Economic Analysis of the CAB and the Air Transport

Association's Annual Report for 1983 and 1984. In these

 

data sources, different models of aircraft were classified
according to their body style (i.e., either narrow bodied
or wide bodied.) In addition, aircraft are classified by
type and number of engines. These data were collected
for the period 1963-1984 and consisted of the
inventory of each of the CAB-defined types of aircraft in
carriers fleets as of December 31 of a given year.

1 The nature and sources of the data are described in
greater detail in Appendix A.

78
The descriptive statistics used to characterize the

route structure of the carriers were constructed from

Airport Activity Statistics of Certificated Route Carriers

 

reported annually for the years 1963-1984. In using this
data, the conventions of the FAA in classifying
airports as large,medium, small hubs, and non-hubs,
depending on the percentage of U.S. airline passenger
emplanements, was adopted. Airline route structures were
characterized by the numbers of each hub classification
that they served and the total number of revenue passenger
emplanements each airline experienced.2

The chapter consists of three sections. First, the
results of tests of the model relating route
characteristics to number of flights offered per day are
reported. Second, the results for aircraft assignment on
individual routes are reported. Finally, the empirical

results related to gross fleet composition are reported.

The Relationship of Number of Flights to Route

Characteristics

In this section of the chapter, data drawn from
The Official Airline Guide are used to test the theoretical

results derived in the previous chapter. The validity of

2 Large hubs have more than 1% of US passenger
emplanements. Medium hubs have between 0.99% and 0.50% of
US passenger emplanements. Small hubs have between 0.49%
and 0.25% of emplanements. Non—hubs emplane fewer than
0.25% of U.S. airline passengers.

79
the general model is tested by a simple regression of the

number of flights per day on a specific route against the
population, real income, and distance of the route for both
of the years 1974 and 1984. In the second set of tests,
the utilization of specific varieties of aircraft on a
route is regressed against the same demographic and
technical variables using two stage least squares
techniques.

In chapter 3 the result was derived that indicated the
number of flights offered in a particular airline market
(i.e., on a specific route) would depend on three factors.
These are, first, the density of potential purchasers of
the transportation service. The second is the cost to
passengers of not receiving the precise variety of the
product (i.e., time of departure) which they prefer. These
costs depend both on the availability of alternative modes
of transportation and the distance of the route. The final
independent variable is the cost of providing service on
the route, known in the context of the airline industry as
the flight costs.

In the text of chapter 3, a number of variants of a
basic formula are developed dependent upon market
structure, regulatory environment and carrier strategies.
(See table 1 above for a summary of the theoretical results
derived in chapter 3.) The purpose of this chapter is to
determine which of the different theoretical treatments in

chapter 3 correctly describes the airline response to

8O
deregulation. The maintained hypothesis of this

dissertation is that aircraft choice was not distorted by
regulation but that airline utilization patterns were.

The basic estimating equation is equation (40) of
chapter 3, reproduced below .
(40) n=c+allnPOP+a21nINC+a3lnDIS

+ a, HUBDUM + as VACDUM + e

The results of these regressions for both 1974 and 1984 are
reported in table 2.

All estimates using the basic functional form outlined
above are highly significant with F-statistics greater than
ten. This implies, with a sample size of 657, that there

is less than one chance in one thousand that the

relationship is one arising from chance. The R2
associated with these estimates are quite modest--
approximately 0.1. The coefficients for the population
proxies are uniformly significantly different from zero at
the 5% level, as are the constant terms.

Average income per capita is significant in only one
equation. Route distance has a significant negative
coefficient of approximately -0.5. All of the coefficients
of route distance are not significantly different from the
value of -0.5. This is of particular interest, since all
of the theoretical models specified above imply a

coefficient of precisely this value when the equation is

81

TABLE 2

THE RELATIONSHIP OF NUMBER OF FLIGHTS PER DAY TO
ROUTE CHARACTERISTICS

 

DEPENDENT NUMBER OF
VARIABLE FLIGHTS ’74

CONSTANT

ORIGIN
POPULATION

DESTINATION
POPULATION

COMBINED
POPULATION

AVERAGE OF
ORIGIN AND
DESTINATION
PER CAPITA
INCOME

ROUTE
DISTANCE

HUB
DUMMY

VACATION
SPOT DUMMY

R-SQUARED
ADJ R-SQ
F-STATISTIC

-27.711

15.407

0.858*
0.141

0.701*
0.135

1.472
1.974

-0.532*
0.173

-1.575*
0.435

-0.237
0.358

0.100
0.092
12.083*

NUMBER OF

-35.649*

15.377

1.305*
0.219

2.559
1.979

-0.431*
0.172

-1.144*
0.424

-0.272
0.361

0.082
0.075
11.570*

NUMBER OF
FLIGHTS ’74 FLIGHTS ’84 FLIGHTS ’84

-38.062*

13.644

0.261
0.143

0.890*
0.243

2.859
1.596

-0.519*
0.159

0.305
0.389

-0.762*
0.327

0.099
0.091
11.964*

NUMBER OF

-41.002*

13.573

1.094*
0.216

3.218*
1.587

-0.503*
0.159

0.358
0.389

-0.740*
0.327

0.095
0.088
13.645*

 

ALL EQUATIONS ESTIMATED WITH 657 OBSERVATIONS AND ARE
SIGNIFICANT AT THE 99% LEVEL.
SIGNIFICANTLY DIFFERENT FROM ZERO AT THE 5% LEVEL.

STANDARD ERRORS OF THE COEFFICIENTS ARE REPORTED BELOW

THE COEFFICIENT.

STARRED COEFFICIENTS ARE

82
estimated in log-linear form.

An interesting pattern develops in the case of the two
dummy variables. The dummy for connecting flights is
significantly different from zero only for the regressions
on 1974 data. The vacation dummy, introduced to allow for
the lower value of time of vacationers as opposed to
business travelers, is only significantly different from
zero for regressions run on 1984 data.

Each of these results presents no problem of
interpretation for our theoretical framework. In the case
of the hub dummy, the 1974 (i.e., pre-deregulation)
coefficient values are negative. This represents the fact
that before deregulation, airlines were not able to
systematically provide connecting flights through "hubs" as
they can today. During the regulatory period, airlines
were not able to improve connections, since regulatory
approval was required for scheduling additional connections
on new routes.

In the case of the vacation dummy, the significant
negative coefficients are precisely of the sign predicted.
A lower value of time on a particular route, all other
things being equal, indicates that fewer flights should be
scheduled. The fact that this variable is statistically
significant only in 1984 indicates that airlines were able
to employ the greater pricing freedom enjoyed under
deregulation. 1

In the era before deregulation, airlines were

83
constrained by the presence of competition in the form of

charter flights to pOpular vacation destinations. Thus,
since they were unable to compete on price, they competed
for vacation travelers in the same manner as all other
travelers--with flight frequency. Deregulation permitted
airlines to use price to compete for the vacation traveler,
which in turn allowed them to decrease flight frequencies

on routes connecting with popular vacation spots.

Specific Aircraft Types and Route Characteristics

Econometric Procedure

In the preceding section it was established that the
model developed in chapter 3 was a good predictor of the
number of flights scheduled on a particular route. In this
section the model as extended is applied to allocation of
specific types of aircraft to particular markets. The
basic model to be utilized was presented in equation 40
above. Two distinct sets of equations are estimated. In
the first set, the dependent variable is the average number
of seats flown on a route per day. This is computed by
taking the maximum number of seats for each type of
aircraft actually flown on the route and multiplying it by
the number of flights using that variety of aircraft. This
number is then divided by total flights per day on the

route. These results are reported in table 3. They will

84

TABLE 3
THE RELATIONSHIP OF AVERAGE SEATS PER FLIGHT
AND ROUTE CHARACTERISTICS
(VARIABLES IN NATURAL FORM)

 

 

 

DEPENDENT AVERAGE SEATS AVERAGE SEATS
VARIABLE '74 ’84
CONSTANT -68.713* -113.578
33.140 23.017
ORIGIN
POPULATION 5.358x10'6* 1.119X10'6
1.272X10-6 1.322X10'6
DESTINATION
POPULATION 5.444x10'6* 2.558X10-6*
1.052X10-6 9.570x10'7
ROUTE
DISTANCE 4.731 10.779*
2.887 2.397
HUB
DUMMY 13.680* 40.097*
7.102 5.817
ORIGIN
PER CAPITA
INCOME 0.0103* 0.00294*
0.0050 0.00126
DESTINATION
PER CAPITA
INCOME 0.00313 0.00264*
0.00475 0.00132
R-SQUARED 0.133 0.211
ADJ R-SQ 0.125 0.204
F-STATISTIC 16.668* 28.948

ALL EQUATIONS ESTIMATED WITH 657 OBSERVATIONS AND
SIGNIFICANT AT THE 99% LEVEL. STARRED COEFFICIENTS ARE
SIGNIFICANTLY DIFFERENT FROM ZERO AT THE 5% LEVEL.
UNDERLINED COEFFICIENTS ARE SIGNIFICANTLY DIFFERENT FROM
ZERO. STANDARD ERRORS OF THE COEFFICENTS ARE REPORTED
BELOW THE COEFFICIENT.

85
be discussed in the following section with the results

reported for individual aircraft types.

In the second set of equations, the dependent variable
is the number of each variety of aircraft flown on the
route. The form of the estimating equation actually
appropriate to relating specific types of aircraft to
particular routes is equation (43), reproduced below.

(43) K1 = c + 0:, ln POPi + (:2 ln INC1+ «3 1n DIS, 4» 0:4 HUBDUM!

m

In order to estimate this set of equations, both the
natural logarithms of the proxies for T“ L“ F,n and
untransformed values of the data were employed. The same
proxies are employed as were used in estimating the general
model. In determining the varieties of capital to be

utilized as K5, the same classifications used were the

classifications employed by the CAB and the FAA.3 These
were chosen for two reasons. First, this permits
comparisons with the panel data results reported later.
Second, more detailed breakdown of types of aircraft would
require treatment of the idiosyncrasies of individual
airlines’ fleets. (e.g., for many years only United and
Western among the majors flew Boeing 7375). In other
words, both the type of route served and the type of
aircraft are related to a third (unobserved) variable, the

3 Aircraft were classified by the CAB and FAA, according
to their body style (i.e., either narrow or wide bodied)
and the number and type of their engines. It is an
important assumption of these econometric results that the
categories employed by the FAA and CAB for aircraft make
economically meaningful distinctions.

86
airline holding the route franchise, when aircraft types

are treated at too high a level of detail.

Theoretical Expectations

Before analyzing the regression results, the a
priori predictions of the theoretical model should
be reviewed. Increased density of potential customers

should cause an increase in the number of flights offered

in the market, ceteris paribus. Thus we

 

expect this parameter to have a positive coefficient.
However, this result is strictly true only when the
supplier of airline flights is limited to a single type of
aircraft. Typically the scheduler has several types of
aircraft which will have lowest average cost at different
levels of usage. The aircraft with lowest average cost at
low volumes of traffic is usually the smallest. As volume
of traffic rises, larger aircraft become the lowest cost
variety of aircraft in roughly increasing order of
capacity. Assuming cost minimization, smaller aircraft
would be expected to have smaller coefficients with respect
to population, while larger aircraft will have larger
coefficients.

Since prior treatments of regulation maintain that it
causes too many flights to be scheduled, previous

treatments of deregulation implied that smaller aircraft

87
types would experience decreases in relation to route

density relative to larger aircraft. The alternative
theoretical model of this dissertation implies that this
not need be the case.

The theoretical model indicates that increases in the
opportunity cost of a flight not leaving at the preferred
time will lead to an increase in the number of flights
offered. A cost minimization assumption leads to the
expectation that as the number of flights is increased the
size of aircraft employed will decrease. Thus the proxy
employed in these regressions, per capita income, is
expected to have a positive sign for smaller aircraft and a
negative sign for larger aircraft.

An increase in flight costs, all other things equal,
should result in a decreased number of flights offered. It
is expected that the costs of a flight increase with
distance, thus the number of flights should decrease as
distance increases. Another reason for this expectation is
that as distance increases, the opportunity cost of
alternative means of transportation also increases. In
fact, alternative transportation modes experience
relatively greater increases in opportunity cost than air
travel. Thus the opportunity cost of air travel, in terms
of waiting for a flight, can rise significantly without a
loss of customers to alternative modes. A final
consideration, cost minimization, also comes into play: the

largest aircraft have the lowest average cost per passenger

88
on longer flights. Thus the expectation is that smaller

aircraft have negative parameters in route distance while
larger aircraft possess positive coefficients.

The treatment of the response of airlines to price
regulation of the sort to which they were subjected prior
to 1976 indicated that airlines did not minimize costs.
This was true because airlines responded to regulation of
their prices by reducing the opportunity cost of the air
traveler through increased flight frequency. Thus smaller
aircraft should be expected to be more heavily utilized in
the earlier sample period (1974). In the later, post-
deregulation period, larger aircraft should be more heavily
utilized.

However, as previously asserted, earlier arguments
about the effects of deregulation ignore airlines’ ability
to achieve better aircraft utilization by changing the
structure of their route networks. As the theoretical
treatment of hub-and-spoke networks in the previous chapter
suggests, hubbing and spoking is a means for airlines to
spread the flight costs over several classes of customer.
It is thus an example of the problem of pricing a joint
product. Hub-and-spoke route structures should result in a
larger number of flights offered than linear route
structures, common before deregulation.

The general principles outlined above can be used to
make specific predictions about the relationships of the

number of a given aircraft employed on a route and the

89
characteristics of that route. In addition, it is possible

to make predictions about the how the parameter values will
change subsequent to deregulation. As an example of the
process of deriving such predictions from the theory of
hubbing and spoking, the behavior of three-engined regular
bodied jets is analyzed below. Detailed predictions of the
sign and post-deregulation behavior of all parameters for
each dependent variable are provided in table 4.

Three-engine regular bodied aircraft are among the
most versatile of the aircraft types available to the
airlines during the sample period. Their most important
limitation is their limited capacity of only about 120-150
seats, depending on the configuration adopted. As is
expected for all aircraft types, increased market size will
cause an increase in the number of aircraft employed on a
route. The effect of deregulation in the hub-and-spoke
model presented here is to increase the effective demand
for a flight, since any flight serves many different
routes. Thus the value of this parameter should increase
with deregulation.

Distance, as an independent variable, is expected to
have a negative sign for two reasons. First, it is the
expectation of the theory in general that increased
distance will cause a decrease in the number of flights.
In addition, theory leads to the expectation that increased
route distance will result in a movement towards larger

aircraft. In the environment after deregulation, the

90

TABLE 4
COMPARISONS OF THEORETICAL PREDICTIONS AND EMPIRICAL RESULTS:
ROUTE LEVEL DATA

PART I
Dependent variable is number of flights
by all types of aircraft per day

 

INDEPENDENT EXPECTED OBSERVED EXPECTED OBSERVED

 

VARIABLE SIGN 74 SIGN 74 CHANGE 84 CHANGE
POPULATION + + ? NO CHANGE
FLIGHT COSTS - - DECREASED NO CHANGE

(DISTANCE) ABSOLUTE VALUE
HUB DUMMY - - INCREASED YES

MAGNITUDE
INCOME + + DECREASED ?
MAGNITUDE
VACATION - - DECREASED YES

ABSOLUTE VALUE

+ means the parameter is expected to be or measured as
positive, - means the parameter is expected to be or measured
as positive, ? means sign is ambiguous.

Dependent variable is
average number of seats per flight

i
.-

INDEPENDENT EXPECTED OBSERVED EXPECTED OBSERVED

 

VARIABLE SIGN 74 SIGN 74 CHANGE 84 CHANGE
POPULATION + + ? DECREASED
MAGNITUDE
FLIGHT COSTS + + INCREASED YES
(DISTANCE) MAGNITUDE
HUB DUMMY + + INCREASED YES
MAGNITUDE
INCOME - + DECREASED YES
MAGNITUDE

VACATION + N.A. N.A. N.A.

91

PART II
Dependent variable is number of flights
by a type of aircraft per day
PROPELLER

INDEPENDENT EXPECTED OBSERVED EXPECTED OBSERVED

 

VARIABLE SIGN 74 SIGN 74 CHANGE 84 CHANGE

POPULATION + + DECREASED ?
MAGNITUDE

FLIGHT COSTS - - INCREASED YES

(DISTANCE) ABSOLUTE VALUE

HUB DUMMY + - DECREASED YES
MAGNITUDE

INCOME + + DECREASED NONE
MAGNITUDE

VACATION - - INCREASED ?

ABSOLUTE VALUE

+ means the parameter is expected to be or measured as
positive, - means the parameter is expected to be or measured
as positive, ? means sign is ambiguous.

Two-engine NARROW-BODY

 

INDEPENDENT EXPECTED OBSERVED EXPECTED OBSERVED

 

VARIABLE SIGN 74 SIGN 74 CHANGE 84 CHANGE
POPULATION + + ? NONE
FLIGHT COSTS - - INCREASED NO

(DISTANCE) ABSOLUTE VALUE
HUB DUMMY + - INCREASED YES

MAGNITUDE
INCOME + ? DECREASED

MAGNITUDE ?
VACATION - ? INCREASED YES

ABSOLUTE VALUE

92

Three-engine NARROW-BODY

 

 

INDEPENDENT EXPECTED OBSERVED EXPECTED OBSERVED

VARIABLE SIGN 74 SIGN 74 CHANGE 84 CHANGE

POPULATION + + INCREASED INCREASED
MAGNITUDE MAGNITUDE

FLIGHT COSTS - ? DECREASED YES

(DISTANCE) ABSOLUTE VALUE

HUB DUMMY + + INCREASED ?
MAGNITUDE

INCOME + + DECREASED INCREASED
MAGNITUDE MAGNITUDE

VACATION - ? DECREASED NO

ABSOLUTE VALUE

 

+ means the parameter is expected to be or measured as

positive, - means the parameter is expected to be or measured
means sign is ambiguous.

as positive,

four-engine NARROW-BODY

 

 

VACATION

'0

INDEPENDENT EXPECTED OBSERVED EXPECTED OBSERVED
VARIABLE SIGN 74 SIGN 74 CHANGE 84 CHANGE
POPULATION + +
AIRCRAFT
TYPE
FLIGHT COSTS + + BECAME
(DISTANCE) OBSOLETE
HUB DUMMY - ?
INCOME - ?

 

93

THREE-ENGINE WIDE-BODY

 

 

 

INDEPENDENT EXPECTED OBSERVED EXPECTED OBSERVED
VARIABLE SIGN 74 SIGN 74 CHANGE 84 CHANGE
POPULATION + + DECREASED DECREASED
MAGNITUDE MAGNITUDE
FLIGHT COSTS + + DECREASED DECREASED
MAGNITUDE MAGNITUDE
(DISTANCE)
HUB DUMMY - ? DECREASED ?
ABSOLUTE VALUE
INCOME - ? DECREASED ?
ABSOLUTE VALUE
VACATION + ? INCREASED ?
MAGNITUDE

+ means the parameter is expected to be or measured as
positive, - means the parameter is expected to be or measured

as positive,

means sign is ambiguous.

four-engine WIDE-BODY

 

 

INDEPENDENT EXPECTED OBSERVED EXPECTED OBSERVED
VARIABLE SIGN 74 SIGN 74 CHANGE 84 CHANGE
POPULATION + + DECREASED NONE
MAGNITUDE
FLIGHT COSTS + + DECREASED YES
(DISTANCE) MAGNITUDE
HUB DUMMY - -(?) INCREASED NO
ABSOLUTE VALUE CHANGE
INCOME - ? DECREASED MAYBE
ABSOLUTE VALUE
VACATION + ? INCREASED ?

MAGNITUDE

94
continued use of frequency as a competitive variable leads

to the prediction that distance will be less negative.
This prediction arises because the three-engine wide-body
jet can be employed on both the dense spokes of a hub-and-
spoke system and the thin inter-hub routes.

The dummy used to denote connecting flights is
expected to have a positive value before deregulation.
These aircraft are especially suited to short-haul routes
which means that they will be useful to fly spokes.

Income as a variable is expected to be positively
related to the number of small aircraft of all types, since
an increased opportunity cost of time will lead to more
flights being scheduled which, when a firm attempts to
minimize costs, implies use of smaller aircraft. In the
new environment, where airlines have the flexibility both
to hub and to practice price discrimination based on the
demand for flight frequency, income should not affect
flight frequency as strongly, since high opportunity cost
passengers will share flights with other lower opportunity
cost passengers.

The variables intended to measure the effect of
vacation travel on a route are expected to result in a
negative parameter estimate. Since vacationers are
presumed to have lower opportunity cost of time, they are
assumed to be less sensitive to displacement from
desired time of departure. Thus they can be accomodated on

larger aircraft. Subsequent to deregulation, the

95
mechanisms of hubbing and spoking and price discrimination,

described above in relation to the effects of income on
aircraft scheduling, have the opposite effects. In other
words, after deregulation, vacationers can be accommodated
on the same aircraft as high-value-of-time business
travelers, and the effect of a route leading to a popular

vacation spot is diminished.

Analysis of Empirical Results

Before addressing the values of the various
coefficients reported below, a few general statements can
be made about the equations. First, all equations possess

a high degree of statistical significance. A second point

is that the R2 achieved are quite modest, ranging from
about .035 to .166. With the exception of the equations
estimated for the smallest types of aircraft (i.e.,
propeller-driven and two-engine narrow-bodied jet
aircraft), higher correlations and levels of significance
are achieved when explanatory variables are entered in
their natural rather than logarithmic forms. This may
indicate that the relationship of utilization to route
characteristics for the smaller aircraft is non-linear.

All of the estimates made using the various
combinations of variables yielded significant F-statistics.
The various coefficient values of the equations tended to

maintain the patterns of significance reported below.

96
The behavior of variables as shown in table 5 is

discussed below. These variables are treated in the same
order as the previous section to facilitate comparisons.
Population is discussed first. Coefficients for all
aircraft types have the expected positive sign for the
population variable. For the propeller driven aircraft,
the coefficient is significant only for the 1974 data in
log form. For the smallest classes of aircraft,
coefficients are significantly smaller than those for
three-engine regular bodied jets. (The most important type
of aircraft in this category is the Boeing 727, long a
workhorse of airline fleets.) This is in accord with the
predictions made above. However, the coefficients on
population decrease for the larger varieties of aircraft.
The other important aspect of the relationship of
aircraft scheduling to population is whether and how much
it has changed since the advent of deregulation. The
manner in which these relationships changed with
deregulation is not, in fact, simple. It was expected that
larger aircraft would become more heavily utilized relative
to the population of the routes they served. Here the
nature of the changes subsequent to deregulation is
ambiguous. For the very largest aircraft types (four-
engine wide bodies, i.e., the Boeing 747), there is no
evidence of any change. For the next smaller size class,
there is limited evidence for an actual decrease in the

coefficient of population. On the other hand, the

97
relationship of population to the utilization of three-

engine regular-bodied aircraft shows an unambiguous
increase. In other words, increases in population on a
route lead to heavier utilization of these aircraft. Two-
engine jets show some evidence of also experiencing
increased utilization in more populous markets after
deregulation. Propeller-driven aircraft give slight
evidence of a decline in this relationship. Overall, the
evidence disconfirms the naive prederegulation predictions
about aircraft utilization patterns subsequent to
deregulation, but is consistent with the predictions of the
theory, including hubbing.

The income coefficients are almost all statistically
insignificant. Two factors probably serve to explain this.
First, per capita income is a very weak proxy for the
opportunity cost of an air traveler’s time. About the only
thing which can be said in favor of it is that the data is
readily available. Second, some of the effects of the
opportunity costs of time may be captured in the variable
measuring route distance.

For the only aircraft type where the coefficients on
income are generally significant (three-engine narrow-
bodied aircraft), they are uniformly greater than zero.
There is also strong evidence that these coefficients
increased with deregulation, approximately doubling. For

other aircraft types, the only other statistically

98
TABLE 5
FLIGHTS PER DAY - INDEPENDENT VARIABLES IN NATURAL FORM

ALL EQUATIONS ESTIMATED WITH 657 OBSERVATIONS AND ARE
SIGNIFICANT AT THE 99% LEVEL.
SIGNIFICANTLY DIFFERENT FROM ZERO AT THE 5% LEVEL.
STANDARD ERRORS ARE REPORTED BENEATH COEFFICIENTS.

PART A: PROPELLOR-DRIVEN AIRCRAFT

DEPENDENT NUMBER OF
VARIABLE FLIGHTS ’74

NUMBER OF
FLIGHTS ’74 FLIGHTS

NUMBER OF

STARRED COEFFICIENTS ARE

NUMBER OF
'84 FLIGHTS ’84

 

CONSTANT 0.338 0.328 1.220* 1.250*
0.310 0.310 0.480 0.480

ORIGIN 1.059D-08 -5.4llD-09

POPULATION 1.253D-08 2.254D-08

DESTINATION 1.622D-08 1.564D-08

POPULATION 1.042D-08 2.1620-08

COMBINED 1.419D-08 5.2220-09

POPULATION 8.387D-09 1.639D-08

ORIGIN

PER CAPITA 5.356D-05 4.915D-05

INCOME 4.9380-05 5.996D-05

DESTINATION

PER CAPITA 5.086D-06 -8.46SD-05

INCOME 4.69OD-05 6.250D-05

AVERAGE OF

ORIGIN AND

DESTINATION 5.5810-05 -2.971D-05

PER CAPITA 6.7500-05 8.797D-05

INCOME

ROUTE -0.000278* -0.000278* -0.000520* -0.000517*

DISTANCE 4.318D-05 4.3200-05 8.136D-05 8.130D-05

HUB -0.396* -0.396* -0.432* -0.426*

DUMMY 0.071 0.071 0.132 0.132

VACATION -0.0135 -0.0271

SPOT DUMMY 0.061 0.111

R-SQUARED 0.0853 0.0859 0.0802 0.0836

ADJ R-SQ 0.0783 0.0775 0.0732 0.0752

F-STATISTIC 12.141 10.184 11.355 9.884

99

 

 

TABLE 5
PART B: TWO-ENGINE REGULAR-BODIED AIRCRAFT

DEPENDENT NUMBER OF NUMBER OF NUMBER OF NUMBER OF
VARIABLE FLIGHTS '74 FLIGHTS '74 FLIGHTS ’84 FLIGHTS
CONSTANT 0.813 0.872 1.018 0.926

0.584 0.582 0.670 0.673
ORIGIN 4.498D—08 4.786D—08
POPULATION 2.3510—08 3.162D-08
DESTINATION 2.277D-08 4.9770-08
POPULATION 1.955D-08 3.033D-08
COMBINED 3.4520-08* 4.496D-08*
POPULATION 1.581D-08 2.286D-08
ORIGIN
PER CAPITA -0.0001045 -1.930D-05
INCOME 8.8030—05 8.4llD-05
DESTINATION
PER CAPITA 0.0001140 1.6500—05
INCOME 9.268D—05 8.768D—05
AVERAGE OF
ORIGIN AND
DESTINATION 1.927D-05 -5.576D-06
PER CAPITA 0.0001273 0.0001227
INCOME
ROUTE -0.000561* -0.000557* -0.000422* -0.000428*
DISTANCE 8.142D-05 8.1080-05 0.000114 0.000114
HUB -0.158 -0.150 0.304 0.294
DUMMY 0.133 0.133 0.185 0.185
VACATION 0.0163 -0.343*
SPOT DUMMY 0.114 0.155
R-SQUARED 0.0713 0.0803 0.0428 0.0358
ADJ R-SQ 0.0642 0.0718 0.0354 0.0269
F-STATISTIC 9.996 9.463 5.821 4.025

100
TABLE 5

PART C: THREE-ENGINE REGULAR-BODIED AIRCRAFT

DEPENDENT NUMBER OF
VARIABLE FLIGHTS '74

CONSTANT -1.195
0.726
ORIGIN
POPULATION
DESTINATION
POPULATION

COMBINED 1.055D-07*

POPULATION 1.966D-08

ORIGIN
PER CAPITA
INCOME

DESTINATION
PER CAPITA
INCOME

AVERAGE OF

ORIGIN AND
DESTINATION 0.000357*
PER CAPITA 0.000158
INCOME

ROUTE -0.000283*
DISTANCE 0.000101
HUB -0.120
DUMMY 0.166

VACATION -0.0836
SPOT DUMMY 0.142

R-SQUARED 0.0742
ADJ R-SQ 0.0671

F-STATISTIC 10.430

NUMBER OF
FLIGHTS ’74

-1.191
0.727

1.211D-07*
2.937D-08

9.802D-08*
2.442D-08

0.000107
0.000116

0.000241*
0.000110

-0.000284*
0.000101

-0.123
0.166

0.0748
0.0662

8.753

NUMBER OF

NUMBER OF

FLIGHTS '84 FLIGHTS ’84

-4.212*
0.848

1.514D-07*

2.892D-08

0.000765*
0.000155

-0.000138
0.000144

0.449
0.233

-0.373
0.197

0.147
0.141

22.484

-4.305*
0.850

1.395D-07*
3.994D-08

1.703D-07*
3.831D-08

0.000392*
0.000106

0.000376*
0.000111

-0.000145
0.000144

0.438
0.234

0.143

0.135

18.0827

101

TABLE 5
PART D: FOUR-ENGINE REGULAR-BODIED AIRCRAFT
DEPENDENT NUMBER OF NUMBER OF NUMBER OF NUMBER OF
VARIABLE FLIGHTS '74 FLIGHTS ’74 FLIGHTS ’84 FLIGHTS ’84

 

CONSTANT -0.155 -0.1786001
0.457 0.460
ORIGIN 6.727D-08*
POPULATION '1.850D-08
DESTINATION 7.038D-08*
POPULATION 1.538D-08

COMBINED 6.901D-08*
POPULATION 1.238D-08

ORIGIN

PER CAPITA 4.642D-05
INCOME 7.291D-05
DESTINATION

PER CAPITA -2.405D-05
INCOME 6.926D-05
AVERAGE OF

ORIGIN AND

DESTINATION 1.921D-05
PER CAPITA 9.964D-05

INCOME

ROUTE 0.000199* 0.000198*
DISTANCE 6.374D-05 6.379D-05
HUB -0.153 -0.153
DUMMY 0.104 0.104

VACATION -0.0725
SPOT DUMMY 0.0894

R-SQUARED 0.0971 0.0970
ADJ R-SQ 0.0902 0.0886
F-STATISTIC 14.006 11.634

 

Note: There were not sufficient observations available to
run regression for four-engined regular-bodied aircraft
in 1984, due to the technological obsolescence of the class.

102
TABLE 5

PART E: THREE-ENGINE WIDE-BODIED AIRCRAFT

DEPENDENT NUMBER OF

VARIABLE FLIGHTS ’74

CONSTANT -0.292
0.536

ORIGIN
POPULATION

DESTINATION
POPULATION

COMBINED 9.049D-08*
POPULATION 1.451D-08

ORIGIN
PER CAPITA
INCOME

DESTINATION
PER CAPITA
INCOME

AVERAGE OF

ORIGIN AND
DESTINATION -2.1OSD-05
PER CAPITA 0.0001168
INCOME

ROUTE 0.000371*
DISTANCE 7.471D-05
HUB -0.0580
DUMMY 0.122

VACATION -0.0176
SPOT DUMMY 0.105

R-SQUARED 0.137
ADJ R-SQ 0.130

F-STATISTIC 20.583

NUMBER OF NUMBER OF NUMBER OF
FLIGHTS '74 FLIGHTS '84 FLIGHTS ’84

-0.277 -0.475 —0.470
0.537 0.273 0.273
9.7580-08* 5.775D-08*
2.167D—08 1.284D-08
8.557D-08* 6.414D-08*
1.8020-08 1.232D-08

6.1030-08*
9.325D-09

-1.068D-05 3.389D-05
8.544D-05 3.417D-05

-1.518D-05 9.7130—06
8.116D—05 3.562D-05

4.440D-05
5.006D-05

0.000372* 0.000102* 0.000102*
7.475D-05 4.630D-05 4.634D-05

-0.0572 -0.0226 -0.0219
0.122 0.0753 0.0753
-0.00500
0.0634
0.137 0.115 0.115
0.129 0.108 0.107

17.178 16.872 14.089

103
TABLE 5
PART F: FOUR-ENGINE WIDE-BODIED AIRCRAFT
DEPENDENT NUMBER OF NUMBER OF NUMBER OF NUMBER OF
VARIABLE FLIGHTS ’74 FLIGHTS ’74 FLIGHTS ’84 FLIGHTS ’84

 

CONSTANT 0.141 0.141 0.0402 0.0458
0.131 0.132 0.0939 0.0940

ORIGIN 2.187D-08* 1.905D-08*

POPULATION 5.321D-09 4.413D-09

DESTINATION 2.181D-08* 2.296D-08*

POPULATION 4.425D-09 4.233D-09

COMBINED 2.179D-08* 2.127D-08*

POPULATION 3.562D-09 3.203D-09

ORIGIN

PER CAPITA -2.711D-05 -3.884D-06

INCOME 2.0980-05 1.174D-05

DESTINATION

PER CAPITA -2.260D-05 -1.417D-05

INCOME 1.993D-05 1.224D-05

AVERAGE OF

ORIGIN AND

DESTINATION -4.968D-05 -1.780D-05

PER CAPITA 2.867D-05 1.719D-05

INCOME

ROUTE 8.799D-05* 8.795D-05* 2.679D-05 2.714D-05

DISTANCE 1.834D-05 1.835D-05 1.590D-05 1.5920-05

HUB -0.0449 -0.0450 -0.0389 -0.0383

DUMMY 0.0301 0.0301 0.0259 0.0259

VACATION 0.000158 0.0160

SPOT DUMMY 0.0257 0.0218

R-SQUARED 0.117 0.117 0.0884 0.0884

ADJ R-SQ 0.117 0.109 0.0814 0.0800

F-STATISTIC 17.245 14.355 12.619 10.504

104
significant coefficient is negative (two-engine regular-

bodied jet).

As usual, the vacation dummy variable is included to
allow for the lower value of time that vacationers are
likely to have relative to business travelers. Generally
this dummy is not statistically significant at a 5% level.
For two-engine jets it is significant in 1984. For four—
engine regular-bodied jets it is significant in 1974, while
it is significant at the 10% level for three-engine regular
bodied jets in 1984. The sign on all of these is negative.
This is in accord with the expectation that lower value of
time results in fewer scheduled flights on a route.

The coefficients associated with route distance
usually differ significantly from zero at the 5% level.
For smaller aircraft varieties (i.e., prop and two-engine
jets), the parameter values are uniformly negative, as was
predicted a priori. Wide-bodied aircraft have positive
values, as was also predicted. A more interesting case is
three-engine regular bodied jets. Here the sign of the
parameter differs between the pre and post deregulation
periods. For 1974 data, the parameter was significantly
negative, with a value in the log form of about —O.1. In
1984, the parameter value in the logarithmic form was about
+0.2. For the variables in natural form, the indicated
coefficient value is always negative but apparently rises
significantly with deregulation.

The effects of deregulation on these parameters are

105
dramatic. For propeller aircraft, the value of the

parameter on route distance doubles in absolute value (i.e.
becomes significantly more negative) for both log and
natural forms. For two-engine jets, in log form, the value
of the parameter increases (i.e., becomes less negative) by
about 60%. As mentioned above the parameter value for 3
engine regular bodied aircraft changes dramatically with
deregulation. In addition, the parameter values for wide
bodied aircraft diminish notably in the later period,
falling in absolute value by 40% to 60%. All of these
changes are consistent with the reorganization of airline
route structures on hub-and-spoke principles. For
instance, before deregulation a 2.5% increase in route
distance would cause the number of two—engine regular-
bodied aircraft employed on a route to fall by one. After
deregulation, a 5 % increase in route distance caused the
same change. This reflects the greater flight frequencies
used as a competitive variable after deregulation, with
smaller aircraft employed on the spokes to provide the high
frequency.

The final variable to be discussed is the hub dummy.
This variable is given a value of one on routes which
provide a connecting flight for a route from the original
sample. The variable is assigned a value of zero for

flights listed as direct in the Official Airline Guide.

 

Only for propeller aircraft is this variable significantly

different from zero. Here the value is consistently

106
negative and in the range of 0.4. No other types of

aircraft have significant values of this coefficient for
all years. For 1974, in the log form, four-engine wide-
bodies have a negative and significant coefficient for the
hub dummy. In 1984, the log form of the equation for three-
engine regular-bodied jets has a significant and positive
coefficient, equal to approximately 0.6.

Further evidence regarding the effects of deregulation
is shown in table 6. This table reports the results of
Chow tests performed on the estimating equations reported
here. The null hypothesis tested is that the estimated
coefficients were jointly identical for both 1974 and 1984.

These tests produce several interesting results.
First, combining 1974 and 1984 observations for the general
model--that is, where the dependent variable is the number
of flights per day on a particular route--yields a lower
residual sum of squares than does estimating each year
separately. This is exactly what would be expected when
additional observations generated by the same process are
added to a regression. The number of flights offered on a
route is apparently unaffected by the elimination of
regulation.

In addition, it is not possible to reject the null
hypothesis of the equality of coefficients for 1974 and
1984 for both three and four-engined wide bodied aircraft.
Since such aircraft have been and can only be employed on

longer routes with more passengers per day, it is not

107
TABLE 6
ROUTE LEVEL DATA RESULTS 1974 & 1984

The statistics reported here are calculated as Chow
statistics and are distributed as F, with degrees of
freedom as reported. They were calculated by combining the
data from the 1974 and 1984 samples and running the same
regressions as for the separated samples. The null
hypothesis is that the coefficients are jointly identical
for both 1974 and 1984.

 

Natural form variables

Aircraft type Chow - statistic
All Fs have 10 & 1292 d.f.

Number of Flights 1.820
Average Seats Per 5.897*
Flight
Two-engine 3.924*
Narrow-body
Three-engine 2.648*

Narrow-body

Four-engine 7.822*
Narrow-body

Three-engine 2.732*
Wide-body

Four-engine 1.124
Wide-body

Propeller 2.475

 

108
Logaritmic form variables

Aircraft type Chow - statistic
All F's have 10 & 1292 d.f.

Number of flights 2.422
Average seats 6.934*
per flight
Two-engine 6.968*
Narrow-body
Three-engine 3.912*
Narrow-body
Four-engine 6.900*
Narrow-body
Three-engine 1.407
Wide-body
Four-engine 0.219
Wide-body
Propeller 4.132*

 

Starred F-statistics indicate that the differences between
the coefficients of the equations for the sample years are

significantly different from zero at the 5% level.

109
unreasonable that their patterns of deployment did not

change with deregulation.

In other words, even before deregulation wide bodied
aircraft were chiefly employed connecting major hubs.
Deregulation resulted in no change in this pattern of
deployment.

Most of the other Chow statistics indicate a
significant change in the relationship of aircraft types
and route characteristics. The case where the Chow
statistic is not significant at the 5% level-—for propeller
driven aircraft-~the relationship is insignificant at the

5% level for variables estimated in natural form.

The Effects of Route Structure on Fleet Selection

Econometric Procedure

The analysis of chapter 3 demonstrated a relationship
between certain demand characteristics of a route and the
number of flights that would be offered on that route in a
given time period. Tests of this basic relationship
derived were presented previously. In this section the
composition of an airline’s fleet is analyzed as it is
affected by the characteristics of the airline's routes.

The hypothesis of this analysis is that an airline’s
route characteristics determine the numbers and relative

frequency of different varieties of aircraft in the fleet.

110
In addition, the average number of seats on the airline's

flights is employed as a dependent for one set of
regressions. This analysis uses the number of hubs of each
size class defined by the CAB and the number of revenue
passenger emplanements of each airline as characterizations
of the route structure. The estimating equation presented
in chapter 3 as equation (50) is reproduced below.

(50) Kn=C+|3lL-+-l32M-i>[538+134 RPE+BSASL

n-1
+ Z c,l§ + 8
1:1

Since these are panel data each year was identified by
a unique dummy variable. Each of these was assigned a value
of one for that year and zero for all other years. These
dummies control for such unobserved common effects on
industry behavior as business cycle effects and industry
growth trends (Fomby, Hill, and Johnson 1984).

The results of the regressions using average number of
seats is shown in table 7. Selected regression results for
specific aircraft types are shown in table 8. This table
is divided into two sections. In the first, the dependent
variable is the number of aircraft of each type present in
an airline's fleet. In the table these are referred to as
absolute variables, since the absolute number of a type of
aircraft in an airline’s fleet is the dependent variable.
Five types of aircraft were present in significant
quantities in airlines’ fleets during the sample period.
These are two-, three-, and four-engine regular-bodied jet

aircraft, and three- and four-engine wide-bodied jet

111
TABLE 7

THE RELATIONSHIP OF AVERAGE SEATS PER FLIGHT

AND ROUTE CHARACTERISTICS-
(VARIABLES IN NATURAL FORM)

FLEET DATA

 

 

DEPENDENT AVERAGE NO. AVERAGE NO. AVERAGE NO.
VARIABLE SEATS 63-84 SEATS 63-75 SEATS 76-84
CONSTANT 67.047* 68.076* 75.230*

7.651 7.515 12.408
NO. LARGE 1.331* 1.383* 1.272*
HUBS 0.428 0.492 0.643
NO. MEDIUM -2.913* -2.057* -3.864*
HUBS 0.377 0.475 0.531
NO. SMALL -0.211 -0.418 -0.119
HUBS 0.233 0.250 0.409
STAGE 0.0950* 0.0696* 0.133*
LENGTH 0.0084 0.0106 0.0119
REVENUE
PASSENGER 0.00139* 0.00128* 0.00160*
EMPLANEMENTS 0.00028 0.00046 0.000354
R-SQUARED 0.836 0.765 0.862
ADJ R-SQ 0.819 0.737 0.841
F-STATISTIC 47.907* 27.506* 42.225*
NUMBER OF
OBSERVATIONS 281 185 96
NUMBER OF
REGRESSORS 27 19 13

 

ALL EQUATIONS SIGNIFICANT AT THE 99% LEVEL.
COEFFICIENTS ARE SIGNIFICANTLY DIFFERENT FROM ZERO
AT THE 5% LEVEL. UNDERLINED COEFFICIENTS ARE

SIGNIFICANTLY DIFFERENT FROM ZERO. STANDARD ERRORS
OF THE COEFFICENTS ARE REPORTED BELOW THE COEFFICIENT.

STARRED

112

TABLE 8
EQUATIONS RELATING ROUTE STRUCTURE AND NUMBERS OF AIRCRAFT
IN AN AIRLINES FLEET

PART A

TABLE 8-PART A ABSOLUTE VARIABLES
SECTION 1 - TWO-ENGINE REGULAR BODIED JETS

 

DEPENDENT NUMBER OF PLANES NUMBER OF PLANES NUMBER OF PLANES

 

VARIABLE 1963-1984 1963-1977 1978-1984

CONSTANT -1.733 2.642 50.796*
7.705 3.365 15.891

NUMBER OF -0.836* -1.143* -1.603*

LARGE HUBS 0.431 0.424 0.825

SERVED

NUMBER OF -0.0662 -1.028 -0.256

MEDIUM HUBS 0.367 0.408 0.640

SERVED

NUMBER OF 1.173* 0.939* 2.204*

SMALL HUBS 0.221 0.195 0.529

SERVED

AVERAGE

STAGE -0.0278* -0.0135* -0.0506*

LENGTH 0.0058 0.0058 0.0110

REVENUE

PASSENGERS 0.00112* 0.00255* 0.000391

EMPLANEMENTS 0.00028 0.00037 0.000440

R-SQUARED 0.572 0.642 0.624

ADJ R-SQUARED 0.528 0.603 0.569

F-STATISTIC 13.041* 16.509* 11.460*

NUMBER OF

OBSERVATIONS 281 185 96

NUMBER OF

REGRESSORS 27 19 13

 

STARRED COEFFICIENTS ARE SIGNIFICANTLY DIFFERENT FROM ZERO

AT THE 5% LEVEL.
REPORTED BELOW COEFFICIENT.
SIGNIFICANT AT 5% OR BETTER.

VARIABLES NOT REPORTED.

STANDARD ERRORS OF THE COEFFICIENTS ARE

STARRED F-STATISTIC INDICATES

COEFFICIENTS OF ANNUAL DUMMY

TABLE 8-PART A

113

ABSOLUTE VARIABLES
SECTION 2 - THREE-ENGINE REGULAR BODIED JETS

 

DEPENDENT NUMBER OF PLANES NUMBER OF PLANES NUMBER OF PLANES

 

VARIABLE 1963-1984 1963-1977 1978-1984

CONSTANT -5.080 -0.764 -33.0760*
6.617 5.118 15.395

NUMBER OF

LARGE HUBS 1.302* 1.195* 2.396*

SERVED 0.370 0.341 0.799

NUMBER OF

MEDIUM HUBS -1.075* -l.467* 0.250

SERVED 0.315 0.328 0.620

NUMBER OF

SMALL HUBS -0.799* -0.485* -l.585*

SERVED 0.190 0.157 0.512

AVERAGE

STAGE -0.00355 -0.00391 0.00690

LENGTH 0.00495 0.00463 0.01064

REVENUE

PASSENGERS 0.00299* 0.00267* 0.00296*

EMPLANEMENTS 0.00024 0.00030 0.00043

R-SQUARED 0.754 0.706 0.696

ADJ R-SQUARED 0.728 0.674 0.655

F—STATISTIC 29.889* 22.169* 16.027*

NUMBER OF

OBSERVATIONS 281 185 96

NUMBER OF

REGRESSORS 27 19 13

STARRED COEFFICIENTS ARE SIGNIFICANTLY DIFFERENT FROM ZERO
AT THE 5% LEVEL. STANDARD ERRORS OF THE COEFFICIENTS ARE
REPORTED BELOW COEFFICIENT. STARRED F-STATISTIC INDICATES
SIGNIFICANT AT 5% OR BETTER. COEFFICIENTS OF ANNUAL DUMMY
VARIABLES NOT REPORTED.

TABLE 8-PART A
SECTION 3 - FOUR-ENGINE REGULAR BODIED JETS

114

ABSOLUTE VARIABLES

DEPENDENT NUMBER OF PLANES NUMBER OF PLANES NUMBER OF PLANES

 

 

VARIABLE 1963-1984 1963-1977 1978-1984

CONSTANT -29.579* -25.828* -33.913*
7.478 8.0726 10.601

NUMBER OF

LARGE HUBS 0.740 0.523 -0.142

SERVED 0.418 0.538 0.550

NUMBER OF 2.111* 1.133* 1.626*

MEDIUM HUBS 0.356 0.517 0.427

SERVED

NUMBER OF -0.393 -0.533* 0.0872

SMALL HUBS 0.215 0.247 0.353

SERVED

AVERAGE

STAGE -0.0639* -0.0689* -0.0455*

LENGTH 0.0056 0.0073 0.0073

REVENUE

PASSENGERS 0.000591* 0.00220* 9.801x10'5

EMPLANEMENTS 0.000275 0.00047 0.000293

R-SQUARED 0.668 0.729 0.550

ADJ R-SQUARED 0.634 0.700 0.485

F-STATISTIC 19.655* 24.828* 8.457*

NUMBER OF

OBSERVATIONS 281 185 96

NUMBER OF

REGRESSORS 27 19 13

STARRED COEFFICIENTS ARE SIGNIFICANTLY DIFFERENT FROM ZERO
AT THE 5% LEVEL. STANDARD ERRORS OF THE COEFFICIENTS ARE
REPORTED BELOW COEFFICIENT. STARRED F-STATISTIC INDICATES
SIGNIFICANT AT 5% OR BETTER. COEFFICIENTS OF ANNUAL DUMMY
VARIABLES NOT REPORTED.

TABLE 8-PART A

SECTION

4 -

115

ABSOLUTE VARIABLES

THREE-ENGINE WIDE BODIED

JETS

 

DEPENDENT NUMBER OF

PLANES NUMBER OF PLANES NUMBER OF

 

 

PLANES VARIABLE 1970-1984 1970-1977

1978-1984

CONSTANT 1.602 -0.980 -l6.822*
2.722 4.272 5.765

NUMBER OF -0.212 -0.0254 0.235

LARGE HUBS 0.152 0.259 -0.299

SERVED

NUMBER OF

MEDIUM HUBS -0.419* -0.0644 -0.0818

SERVED 0.139 0.298 0.232

NUMBER OF

SMALL HUBS -0.130 -0.423* 0.0413

SERVED 0.078 0.128 0.192

AVERAGE

STAGE 0.00481* -0.00163 0.0200*

LENGTH 0.00204 0.00298 0.0040

REVENUE

PASSENGERS 0.00119* 0.00109* 0.00105*

EMPLANEMENTS 9.992x10’5 0.00026 0.00016

R-SQUARED 0.722 0.626 0.713

ADJ R-SQUARED 0.694 0.575 0.672

F-STATISTIC 25.431* 12.331* 17.217*

NUMBER OF

OBSERVATIONS 281 185 96

NUMBER OF

REGRESSORS 27 19 13

STARRED COEFFICIENTS ARE SIGNIFICANTLY DIFFERENT FROM ZERO

AT THE 5% LEVEL.
REPORTED BELOW COEFFICIENT.
SIGNIFICANT AT 5% OR BETTER.

VARIABLES NOT REPORTED.

STANDARD ERRORS OF THE COEFFICIENTS ARE

STARRED F-STATISTIC INDICATES

COEFFICIENTS OF ANNUAL DUMMY

TABLE 8-PART A

116

ABSOLUTE VARIABLES
SECTION 5 - four-engine WIDE BODIED JETS

 

DEPENDENT NUMBER OF PLANES NUMBER OF PLANES NUMBER OF PLANES

 

VARIABLE 1963-1984 1970-1977 1978-1984

CONSTANT -8.022* -10.971* -23.254*
2.288 3.323 4.727

NUMBER OF

LARGE HUBS 0.334* 0.542* 0.795*

SERVED 0.128 0.201 0.255

NUMBER OF

MEDIUM HUBS -0.606* -0.430 -0.804*

SERVED 0.109 0.232 0.198

NUMBER OF

SMALL HUBS 0.190* -0.0653 0.398*

SERVED 0.066 0.0993 0.164

AVERAGE

STAGE 0.0258* 0.0189* 0.0376*

LENGTH 0.0017 0.0023 0.0034

REVENUE

PASSENGERS 0.000105 0.000296 -3.676x10'S

EMPLANEMENTS 8.4002(10”5 0.000199 0.000136

R-SQUARED 0.653 0.689 0.723

ADJ R-SQUARED 0.618 0.647 0.683

F-STATISTIC 18.396* 16.309* 18.903*

NUMBER OF

OBSERVATIONS 281 185 96

NUMBER OF

REGRESSORS 27 19 13

 

STARRED COEFFICIENTS ARE SIGNIFICANTLY DIFFERENT FROM ZERO
AT THE 5% LEVEL. STANDARD ERRORS OF THE COEFFICIENTS ARE
REPORTED BELOW COEFFICIENT. STARRED F-STATISTIC INDICATES
SIGNIFICANT AT 5% OR BETTER. COEFFICIENTS OF ANNUAL DUMMY
VARIABLES NOT REPORTED.

117

PART B

TABLE 8-PART B

RELATIVE VARIABLES

 

 

SECTION 1 - Two-ENGINE REGULAR BODIED JETS
DEPENDENT PERCENTAGE PERCENTAGE PERCENTAGE
OF PLANES OF PLANES OF PLANES
VARIABLE 1963-1984 1963-1977 1978-1984
CONSTANT 0.520* 0.518* 0.683*
0.015 0.014 0.028
NUMBER OF
LARGE HUBS -0.00349* -0.00406* -0.00485*
SERVED 0.00082 0.00090 0.00148
NUMBER OF
MEDIUM HUBS 0.00294* 0.00273* 0.00137
SERVED 0.00070 0.00087 0.00115
NUMBER OF
SMALL HUBS 0.00124* 0.000931* 0.00259*
SERVED 0.00042 0.000417 0.00095
AVERAGE
STAGE -7.485x10** -4.164x10** -0.000129*
IENGTH 1.100x10‘5 1.230x10’S 1.970x10'5
REVENUE
PASSENGERS -1.384x10** -2.816x10‘7 -1.655x10**
EMPLANEMENTS -5.397x10’7 --7.981xIO'7 1.970x10’7
R-SQUARED 0.490 0.484 0.619
ADJ R-SQUARED 0.437 0.428 0.563
F-STATISTIC 9.284* 8.554* 11.111*
NUMBER OF
OBSERVATIONS 281 185 96
NUMBER OF
REGRESSORS 27 19 _13

STARRED COEFFICIENTS ARE SIGNIFICANTLY DIFFERENT FROM ZERO

AT THE 5% LEVEL.

REPORTED BELOW COEFFICIENT.

SIGNIFICANT AT 5% OR BETTER.

VARIABLES NOT REPORTED.

STANDARD ERRORS OF THE COEFFICIENTS ARE

STARRED F-STATISTIC INDICATES

COEFFICIENTS OF ANNUAL DUMMY

TABLE 8-PART B

118
RELATIVE VARIABLES

 

 

SECTION 2 - THREE-ENGINE REGULAR BODIED JETS
DEPENDENT PERCENTAGE PERCENTAGE PERCENTAGE
OF PLANES OF PLANES OF PLANES

VARIABLE 1963-1984 1963-1977 1978-1984

CONSTANT 0.486* 0.495* 0.554*
0.0182 0.019 0.034

NUMBER OF

LARGE HUBS 0.00464* 0.00570* 0.00342

SERVED 0.00101 0.00130 0.00178

NUMBER OF

MEDIUM HUBS -0.00136 -0.00243* 0.000310

SERVED 0.00087 0.00125 0.00138

NUMBER OF

SMALL HUBS -0.00162* -0.00155* -0.00278*

SERVED 0.00052 0.00060 0.00114

AVERAGE

STAGE -2.806x10'6 -1.962x10’5 1.6743(10’5

LENGTH 1.364x10'S 1.762x10‘5 2.366x10*

REVENUE

PASSENGERS 9.917x10"7 1.517x10‘6 1.136x10'E

EMPLANEMENTS 6.690x10’6 1.143x10* 9.475x10’7

R-SQUARED 0.408 0.375 0.1807

ADJ R-SQUARED 0.347 0.307 0.0608

F-STATISTIC 6.653* 5.472* 1.507

NUMBER OF

OBSERVATIONS 281 185 96

NUMBER OF

REGRESSORS 27 19 13

 

STARRED COEFFICIENTS ARE SIGNIFICANTLY DIFFERENT FROM ZERO

AT THE 5% LEVEL.
REPORTED BELOW COEFFICIENT.

STANDARD ERRORS OF THE COEFFICIENTS ARE

STARRED F-STATISTIC INDICATES

SIGNIFICANT AT 5% OR BETTER. COEFFICIENTS OF ANNUAL DUMMY
VARIABLES NOT REPORTED.

TABLE 8-PART B

119

RELATIVE VARIABLES
SECTION 3 - four-engine REGULAR BODIED JETS

 

DEPENDENT PERCENTAGE PERCENTAGE PERCENTAGE
OF PLANES OF PLANES OF PLANES
VARIABLE 1963-1984 1963-1977 1976-1984
CONSTANT 0.474* 0.469* 0.466*
0.009 0.009 0.013

NUMBER OF

LARGE HUBS 0.00244* 0.00358* 0.000210
SERVED 0.00048 0.00062 0.000665
NUMBER OF

MEDIUM HUBS 0.00075 -0.00036 0.00143*
SERVED 0.00041 0.00060 0.00052
NUMBER OF

SMALL HUBS -0.000693* -0.00075* -0.000207
SERVED 0.000245 0.00029 0.000427
AVERAGE

STAGE 7.592x10** 8.390x10** 6.086x10**
LENGTH 6.3971(10'5 8.472x10‘ 8.8611(10’E
REVENUE

PASSENGERS 2.748x104’ 6.9321(10'7 5.438x10’a
EMPLANEMENTS 3 . 139x10'7 5 . 497x10‘7 3 . 548x10'7
R-SQUARED 0.643 0.681 0.549
ADJ R-SQUARED 0.606 0.646 0.483
F-STATISTIC 17.356* 19.485* 8.305*
NUMBER OF

OBSERVATIONS 281 185 96
NUMBER OF

REGRESSORS 27 19 13

 

STARRED COEFFICIENTS ARE SIGNIFICANTLY DIFFERENT FROM ZERO

AT THE 5% LEVEL.
REPORTED BELOW COEFFICIENT.
SIGNIFICANT AT 5% OR BETTER.

VARIABLES NOT REPORTED.

STARRED

STANDARD ERRORS OF THE COEFFICIENTS ARE
F-STATISTIC INDICATES
COEFFICIENTS OF ANNUAL DUMMY

TABLE 8-PART B

120

RELATIVE VARIABLES

 

 

SECTION 4 - THREE-ENGINE WIDE BODIED JETS
DEPENDENT PERCENTAGE PERCENTAGE PERCENTAGE
OF PLANES OF PLANES OF PLANES
VARIABLE 1970-1984 1970-1976 1977-1984
CONSTANT 0.520* 0.529* 0.529*
0.009 0.011 0.013

NUMBER OF

LARGE HUBS -0.000360 -0.000731 5.960x10*
SERVED 0.000469 0.000671 0.00068
NUMBER OF
MEDIUM HUBS -0.00109* -0.000891 -0.00117*
SERVED 0.00041 0.000782 0.00053
NUMBER OF
SMALL HUBS -0.000539* -0.000712* -0.000456
SERVED 0.000266 0.000335 0.000434
AVERAGE
STAGE -3.062x10“7 -1.027x10'5 1.285x10'5
LENGTH 5.820x10‘ 7.839x10’6 9.0173410”E
REVENUE

PASSENGERS 1.135x10** 1.356x10‘t 1.035x10**

EMPLANEMENTS 3.039x104'
R-SQUARED 0.289

ADJ R-SQUARED 0.208

F-STATISTIC 3.550*
NUMBER OF
OBSERVATIONS 281
NUMBER OF
REGRESSORS 27

6.722x10‘7
0.249
0.144
2.375

185

19

3.611xIO’7
0.208
0.092
1.797

96

13

STARRED COEFFICIENTS ARE SIGNIFICANTLY DIFFERENT FROM ZERO

AT THE 5% LEVEL.

SIGNIFICANT AT 5% OR BETTER.

VARIABLES NOT REPORTED.

STANDARD ERRORS OF THE COEFFICIENTS ARE
REPORTED BELOW COEFFICIENT.

STARRED F-STATISTIC INDICATES

COEFFICIENTS OF ANNUAL DUMMY

121

TABLE 8-PART B RELATIVE VARIABLES
SECTION 5 - FOUR-ENGINE WIDE BODIED JETS

 

 

DEPENDENT PERCENTAGE PERCENTAGE PERCENTAGE
OF PLANES OF PLANES OF PLANES
VARIABLE 1970-1984 1970-1976 1977-1984
CONSTANT 0.485* 0.505* 0.472*
0.009 0.012 0.011

NUMBER OF

LARGE HUBS 0.00124* 0.000343 0.00195*
SERVED 0.00045 0.000698 0.00056
NUMBER OF
MEDIUM HUBS -0.00241* -0.00307* -0.00247*
SERVED 0.00040 0.00081 0.00044
NUMBER OF

SMALL HUBS 4.431x10‘5 -0.000302 0.000287
SERVED 2.563):10'4 0.000348 0.000361
AVERAGE
STAGE 4.571x10** 2.858x10** 6.381x10**
LENGTH 5.602x104 8.151x10* 7.4883(10'E
REVENUE

PASSENGERS 5.167x10‘7 1.781x10** 1.523x10'7
EMPLANEMENTS 2.922x10’7 6.9893(10‘7 2.9963(10'7
R-SQUARED 0.585 0.496 0.717
ADJ R-SQUARED 0.538 0.426 0.677
F-STATISTIC 12.404* 7.073* 17.560*
NUMBER OF
OBSERVATIONS 281 185 96
NUMBER OF
REGRESSORS 27 19 13

 

STARRED COEFFICIENTS ARE SIGNIFICANTLY DIFFERENT FROM ZERO
AT THE 5% LEVEL. STANDARD ERRORS OF THE COEFFICIENTS ARE
REPORTED BELOW COEFFICIENT. STARRED F-STATISTIC INDICATES
SIGNIFICANT AT 5% OR BETTER. COEFFICIENTS OF ANNUAL DUMMY
VARIABLES NOT REPORTED.

122
aircraft.

In the second section of this table, the dependent
variable represented is the percentage of each of the
aircraft types listed above in the various airline fleets.
For this reason these tables are referred to as relative
variables. These dependent variables were subjected to a
logit transformation before the estimating equations were
run. The coefficients of the annual dummies are not
reported in table 8.

In addition to the results reported for the entire
sample period, estimates were made of the relationship
between route characteristics and the number and type of
aircraft employed for two sub-periods within the sample
period. These sample periods were chosen on the basis of
historical events which might have affected the
relationships studied. The advent of airline deregulation
in 1978 represents an obvious change in the operating
environment of the airlines. The regression results
reported in table 8 include full-period results for 1963-
1984 or 1970-1984, depending on the variety of aircraft,
and 1963-1977 or 1970-1977 and 1978-1984 are the sub-
periods.

Of major interest in dealing with the sub-periods is
the stability of the parameter values of the dependent
variables. In order to determine this we perform the
following test on the regressions. The null hypothesis is

that there is no structural change over the full sample

 

123
period. In the test, the regression is run with and

without an interacted variable, which takes the value of
zero for the prederegulation period and the value of the
independent variables for the period subsequent to
deregulation. The test of the null hypothesis is an F test
of the equality of the coefficients of the interacted
variables and zero. The results of these test are reported
in table 9.

Theoretical Expectations

The maintained hypothesis of this dissertation is that
the effects of airline regulation were felt most strongly
in the inefficient allocation of aircraft among markets and
not in the initial choice of aircraft. Thus deregulation
should witness an alteration in the relationship between
route structure and the number of aircraft in airline
fleets. However, if efficient mixes of aircraft for
serving diverse markets were chosen by airlines prior to
deregulation, these relationships should not have been
altered subsequent to deregulation. The results reported
above support this hypothesis.

In the theoretical analysis of chapter 3, the number
of aircraft an airline needs to serve its route network is
a direct function of the number of flights per day
scheduled on the network. The number of flights scheduled
will in turn depend on the demand characteristics (i.e.,

passenger density or value of time) of each route served.

124
In the regressions conducted here, the average number of

passengers per day emplaned at each of the three hub
classes ( small, medium, and large ) are employed as
proxies for the magnitude of the demand characteristics.
The number of each class served also enters the
regressions.

The numbers of each of the five varieties of aircraft
respond differently to changes in the numbers of passengers
emplaned. In the case of the smallest varieties of
aircraft, cost minimization considerations should result in

fewer aircraft in the fleet, ceteris paribus, as the number

 

of large hubs served increases. For small hubs the
opposite should hold. Also, as the number of passengers
served by an airline increases, fewer small aircraft should
be used. The coefficients for these independent variables
should be negative for two- and three-engine narrow-body
jets. In other words, the same cost minimization
considerations should lead to greater representation of
these aircraft in fleets.

Three- and four-engine wide-body jets, according to
the same logic, will be the cost minimizing types for
airlines which serve predominantly large hubs. Thus, for
these aircraft, the expected sign of these independent
variables is positive. Again, the reciprocal logic holds
for small hubs for both average numbers of passengers and
number served. The coefficients for these variables are

expected to be negative.

125
TABLE 9
PANEL DATA RESULTS 1970-1984

The statistics reported here, distributed as F with
the indicated degrees of freedom, were calculated from the
data panel used in these regressions for the time period
1970-1984. The functional form estimated in the
unrestricted regressions was:

Dependent variable = Intercept +q Dependent
variable + q Dependent variable * Dummy (=0 for
observations before 1978, =1 for observations there after)

'+'H dummy variables (=1 in year of the observation,
=0 otherwise)

The null hypothesis is m = 0 for all i.

RELATIVE VARIABLES

AIRCRAFT TYPE F-statistic
(all Fs have 6&159 d.f)

two-engine 2.6017465626*
narrow-body

three-engine 1.2991934175
narrow-body

four-engine 5.6073423858*
narrow-body

three-engine 1.5800478791
wide-body

four-engine 3.2185994789*

wide-body

 

 

126

TABLE 9 (CONT)
ABSOLUTE VARIABLES

 

AIRCRAFT TYPE F-statistic
(all Fs have 6&162 d.f)

 

two-engine 5.5421539469*
narrow-body

three-engine 6.0238452157*
narrow-body

four-engine 4.3664467113*
narrow-body

three-engine 5.6120964069*
wide-body

four-engine 3.8286429632*
wide-body

STARRED F-STATISTICS INDICATE THE COMPUTED F EXCEEDS THE
FIVE PERCENT LEVEL OF SIGNIFICANCE.

127
The intermediate cases ( i.e., four-engine narrow-body

jets and number of passengers and number of medium hubs
served ) have not yet been discussed. As might be
expected, the signs for these variables cannot readily be
predicted.

The predictions made above apply equally to the
absolute variables and to the relative variables estimated
as dependent variables in the regressions. One further
prediction can be ventured, based on the hypothesis
discussed in the first paragraph of this section. The
maintained hypothesis is that aircraft choices, but not
utilization, are efficient. In the post-deregulation
environment, the relationship between route structure and
the relative shares of different aircraft in an airline’s
fleet should not have changed significantly. On the other
hand, given the joint product nature of airline flights
where hubbing and spoking is employed, the number of
flights and thus airline fleet requirements should have
increased. Therefore, statistical tests of changes in the
relationship of route characteristics to fleet composition
should show a change for absolute variables and no such
change for relative variables.

The theoretical predictions and the signs resulting

from the empirical estimates are reported in table 10.

128

TABLE 10

COMPARISONS OF THEORY AND EMPIRICAL RESULTS

PART I

Dependent variable is the average number of seats per
flight for an airline in a year.

INDEPENDENT PREDICTED OBSERVED

VARIABLE SIGN

SIGN

EXPECTED OBSERVED

CHANGE

CHANGE

(FULL PERIOD) (FULL PERIOD) (’76-'84) ('76—'84)

 

LARGE HUB +

MEDIUM HUB -

SMALL HUB -

PASSENGERS +
(REVENUE
PASSENGER
EMPLANEMENTS)

AVERAGE STAGE +
LENGTH

ANNUAL <0 before 1970
DUMMIES >0 after 1970

INCREASED
MAGNITUDE

?

DECREASED
ABSOLUTE VALUE

INCREASED
MAGNITUDE

DECREASED
MAGNITUDE

NEGATIVE
VALUES

NONE

INCREASED

YES

NOT
SIGNIFICANT

INCREASED

129

PART II
Dependent variable is the number of aircraft of the
given type in an airline fleet in a year.

two-engine narrow-body
(DC-9, B-737, MD-80)
INDEPENDENT PREDICTED OBSERVED EXPECTED OBSERVED
VARIABLE SIGN SIGN CHANGE CHANGE
(FULL PERIOD) (FULL PERIOD) (’76-’84) (’76-’84)

LARGE HUB - - INCREASED YES
ABSOLUTE VALUE

MEDIUM HUB ? ? ? ?

SMALL HUB + + INCREASED YES
MAGNITUDE

PASSENGERS - + INCREASED NO

(REVENUE ABSOLUTE VALUE

PASSENGER

EMPLANEMENTS)

AVERAGE - - INCREASED YES

STAGE ABSOLUTE VALUE

LENGTH

ANNUAL ? ACHIEVE

DUMMIES POSITIVE

SIGNIFICANCE

130

three-engine narrow-body
(BOEING 727)

 

INDEPENDENT PREDICTED OBSERVED EXPECTED OBSERVED
VARIABLE SIGN SIGN CHANGE CHANGE
(FULL PERIOD) (FULL PERIOD) (’76-’84) (’76-’84)

 

LARGE HUB - + INCREASED YES
ABSOLUTE VALUE

MEDIUM HUB ? - ? ?

SMALL HUB + - DECREASED YES

MAGNITUDE

PASSENGERS + + INCREASED YES

(REVENUE MAGNITUDE

PASSENGER

EMPLANEMENTS)

AVERAGE - ? DECREASED ?

STAGE ABSOLUTE VALUE

LENGTH

ANNUAL ? ACHIEVE

DUMMIES POSITIVE

SIGNIFICANCE

131

four-engine narrow-body

INDEPENDENT PREDICTED OBSERVED EXPECTED OBSERVED
VARIABLE SIGN SIGN CHANGE CHANGE
(FULL PERIOD) (FULL PERIOD) ('76-’84) (’76-’84)

 

 

LARGE HUB + +(?)

ALL SIGNS
MEDIUM HUB ? +

AMBIGUOUS
SMALL HUB - -(?)

BECAUSE OF
PASSENGERS + +
(REVENUE OBSOLESCENCE
PASSENGER
EMPLANEMENTS)

AVERAGE - -
STAGE
LENGTH

ANNUAL POSITIVE
DUMMIES BUT
DECLINING

132

three-engine wide-body

 

INDEPENDENT PREDICTED OBSERVED EXPECTED OBSERVED
VARIABLE SIGN SIGN CHANGE CHANGE
(FULL PERIOD) (FULL PERIOD) (’76-’84) (’76-’84)

 

LARGE HUB + ? INCREASED YES
MAGNITUDE
MEDIUM HUB (-)? -(?) INCREASED NO

ABSOLUTE VALUE

SMALL HUB - - INCREASED ?
ABSOLUTE VALUE

PASSENGERS + + INCREASED NO
(REVENUE MAGNITUDE
PASSENGER

EMPLANEMENTS)

AVERAGE STAGE + + INCREASED NO
LENGTH MAGNITUDE
ANNUAL =0 1963-1971 DECREASED

DUMMIES >0 1971-1984 MAGNITUDE

133

four-engine wide-body
INDEPENDENT PREDICTED OBSERVED EXPECTED OBSERVED
VARIABLE SIGN SIGN CHANGE CHANGE
(FULL PERIOD) (FULL PERIOD) (’76-’84) (’76-’84)

LARGE HUB + + INCREASED YES
MAGNITUDE
MEDIUM HUB - INCREASED YES

ABSOLUTE VALUE

SMALL HUB -(?) + INCREASED YES
ABSOLUTE VALUE

PASSENGERS + ? INCREASED ?

(REVENUE MAGNITUDE

PASSENGER

EMPLANEMENTS)

AVERAGE + + INCREASED YES

STAGE MAGNITUDE

LENGTH

ANNUAL =0 BEFORE 1970 NO SIGNIFICANT

DUMMIES >0 AFTER 1970 DIFFERENCE

PART III

Dependent variable is the percentage of aircraft of the
given type in an airline fleet in a year.

 

two-engine narrow-body

 

INDEPENDENT PREDICTED

VARIABLE

(FULL PERIOD)

LARGE HUB

MEDIUM HUB

SMALL HUB

PASSENGERS
(REVENUE
PASSENGER
EMPLANEMENTS)

AVERAGE
STAGE
LENGTH

ANNUAL
DUMMIES

OBSERVED EXPECTED OBSERVED

CHANGE CHANGE

(FULL PERIOD) (’76-'84) ('76-’84)

INCREASED YES
ABSOLUTE VALUE

? ?
INCREASED YES
MAGNITUDE
INCREASED YES

ABSOLUTE VALUE

INCREASED YES
ABSOLUTE VALUE

SIGNIFICANTLY
POSITIVE

135

three-engine narrow-body
INDEPENDENT PREDICTED OBSERVED EXPECTED OBSERVED
VARIABLE SIGN SIGN CHANGE CHANGE
(FULL PERIOD) (FULL PERIOD) (’76-’84) (’76-’84)

LARGE HUB + + INCREASED ?
MAGNITUDE

MEDIUM HUB + ? INCREASED +(?)
MAGNITUDE

SMALL HUB - - INCREASED YES

ABSOLUTE VALUE

PASSENGERS + 2 INCREASED ?

(REVENUE MAGNITUDE

PASSENGER

EMPLANEMENTS)

AVERAGE - ? DECREASED ?

STAGE ABSOLUTE VALUE

LENGTH

ANNUAL + SIGNIFICANTLY

DUMMIES POSITIVE

136

four-engine narrow-body

INDEPENDENT PREDICTED OBSERVED EXPECTED OBSERVED
VARIABLE SIGN SIGN CHANGE CHANGE
(FULL PERIOD) (FULL PERIOD) (’76-’84) (’76-’84)

 

 

LARGE HUB -

AIRCRAFT TYPE
MEDIUM HUB -

OBSOLETE IN
SMALL HUB —

LATE 19703
PASSENGERS +
(REVENUE
PASSENGER
EMPLANEMENTS)

AVERAGE +
STAGE
LENGTH

ANNUAL POSITIVE
DUMMIES BUT
DIMINISHING

137

three-engine wide-body
INDEPENDENT PREDICTED OBSERVED EXPECTED OBSERVED
VARIABLE SIGN SIGN CHANGE CHANGE
(FULL PERIOD) (FULL PERIOD) ('76-'84) (’76-'84)

 

LARGE HUB + ? INCREASED ?

MAGNITUDE
MEDIUM HUB - - INCREASED ?

ABSOLUTE VALUE

SMALL HUB - - INCREASED ?
ABSOLUTE VALUE

PASSENGERS + + INCREASED NONE
(REVENUE MAGNITUDE
PASSENGER

EMPLANEMENTS)

AVERAGE + ? INCREASED ?
STAGE MAGNITUDE

LENGTH

ANNUAL =0 BEFORE 1971 SIGNIFICANTLY
DUMMIES >0 AFTER 1971 DIFFERENT FROM

REGULATION

138

four-engine wide-body

 

 

INDEPENDENT PREDICTED OBSERVED EXPECTED OBSERVED
VARIABLE SIGN SIGN CHANGE CHANGE
(FULL PERIOD) (FULL PERIOD) (’76-'84) (’76-'84)

 

LARGE HUB + + INCREASED YES
MAGNITUDE
MEDIUM HUB - - INCREASED NO

ABSOLUTE VALUE

SMALL HUB - ? INCREASED ?
ABSOLUTE VALUE

PASSENGERS + ? INCREASED ?
(REVENUE MAGNITUDE
PASSENGER

EMPLANEMENTS)

AVERAGE + + INCREASED YES
STAGE MAGNITUDE

LENGTH

ANNUAL =0 BEFORE 1970 SIGNIFICANTLY

DUMMIES >0 AFTER 1970 DIFFERENT

139

Analysis of Empirical Results

The predictions ventured in the previous section were
only partly correct, as can be established by consulting
table 10. For two-engine narrow-body aircraft, the signs
of the coefficients for large and small hubs and passengers
per day emplaned at each are as predicted for both the
full sample and the sub-periods. They are also
significantly different from zero in almost all equations,
whether the dependent variable is number of aircraft or of
an aircraft type in a fleet. The coefficients for medium
hubs are seldom significant and, as predicted, of varying
sign.

The predictions regarding the signs of the
coefficients in the equations for three-engine narrow-body
jets are almost completely wrong. The number of large hubs
and the average number of passengers per day at large hubs
have significant,' positive coefficients. The coefficient
of the average number of passengers per day served at small
hubs is insignificantly different from zero in all
equations. The coefficient of the number of small hubs is
negative where significantly different from zero.

Four-engine narrow-body jets, for which no prediction
was ventured, have the same pattern of sign and

significance as was predicted for larger jets.

140
For wide-bodied aircraft, the predictions are largely

confirmed. The coefficients on the large hub variables are
uniformly positive and generally significant. The
coefficients of the small hub variables are negative but
seldom significant. The medium-hub variables are negative
and usually significant. These results are quite striking.

Finally, the change of regimes test reported in table
9 yields some striking results. For the regressions where
the dependent variable is the numbers of aircraft of each
type employed by the carriers during the period, the tests
indicate that the relationship between route
characteristics and number of aircraft selected of a given
type changed in a statistically significant fashion.

In those regressions where the dependent variable is
the percentage of aircraft of a given type in the airlines
fleet, application of the same structural tests yields
results that are different. In fact, these tests indicate
that the relationship of the relative composition of
airlines' fleets to their routes did not change for three-
engine narrow-body and three-engine wide-body jets
subsequent to deregulation. In other words, airline
fleets tended to contain about the same proportions of
three-engine jets after deregulation. This finding is at
variance with predictions that would have been made about
the airline fleets on the basis of the economic analysis of
airlines prior to deregulation. However, three varieties

of aircraft show changed relationships between aircraft

141
fleet proportions and route characteristics. In the case

of four-engine narrow-body aircraft this finding can be
explained by the technological obsolescence of the class.
In the case of two-engine narrow-body aircraft, the
utilization of these craft on lower density spokes may in
fact mean that they are needed in increased proportions
since deregulation.

Since flight frequency was identified as the prime
competitive weapon under regulatory constraint, airlines
would have been expected to have fleets with small aircraft
over-represented relative to large aircraft. This is not
reflected in the empirical results. In fact, these results
support the thesis of this dissertation that the major
effects of airline deregulation on airline allocation of
capital have not been upon the choice of aircraft in
general but on the route structures within which the
aircraft are employed.

Summary of Empirical Results

In summary, these regressions indicate that the model
presented in chapter 3 has significant explanatory power.
The changes in aircraft utilization patterns in the period
from 1974 to 1984 clearly reflects the effects of
deregulation. In particular the restructuring of airline
networks into hub-and-spoke systems is reflected.

In the post-deregulation scheme of things, wide-bodied

aircraft are used predominantly for long-haul, inter-hub

142
transfers. The smaller aircraft are used to carry

passengers on the spokes where passenger densities are
lowest. All other things equal, as passenger densities
and/or route distance increase, three-engine jets (i.e.
Boeing 727) displace smaller varieties of aircraft on the
spokes. Such aircraft are also employed on the less dense

inter-hub flights (e.g., Chicago to Charlotte, N.C.).

CHAPTER 5

CONCLUSION AND SUGGESTIONS FOR FURTHER RESEARCH

This dissertation has been concerned with some
elements of the structure of the airline industry which
make it unique. These idiosyncratic features result in
industry conduct and performance not easily explained
within the framework of conventional models of economic
behavior. An alternative analytical framework was provided
above. This framework was then tested empirically using
two distinct data sets. These empirical results were
largely consistent with the predictions of the model
developed here.

This chapter reviews the unique elements of the
airline industry’ s structure, the predictions of
deregulated industry performance, and the specific
shortcomings of these a priori models. These models are
then compared with the superior predictive performance of
the alternative model developed here. Finally, the

empirical tests of the model are reviewed and conclusions

143

144
drawn from the results advanced. In addition, some possible

empirical and theoretical extensions of this investigation

are suggested.

The srrgcture of the Industry

As outlined in chapter I, the passenger airline
industry has a number of unique structural elements which
make it both rewarding and difficult to analyze
economically. An important feature throughout the first
half century of the industry's history was pervasive
regulation. of’ price and route entry. Since the late
1970s, much of the behavior of airlines has taken the form
of adjustment to the changes caused by elimination of the
price and entry regulation of the industry.

Two related elements of the industry structure also
help to make it unique. The first is the nature of its
product. The "product" of the airline industry consists
of point-to-point transportation offered at a particular
time of day. Any product is one of a class of related
products, each consisting of a flight between the same two
points but originating at a different time of day.

This is true Ibecause the. opportunity cost of air
transport is not merely the cash price paid for such
transport but also the opportunity cost of time of travel.

Travel time itself includes several elements including the

145
actual point-to-point time, the delay occasioned by flights

not departing at the preferred time, and delays caused by
not being able to take a preferred flight because it is
full.

Of these, only the first--the point-to-point transit
time-~is truly exogenous in the short run. It is
determined by the the technological characteristics of the
aircraft available. Aircraft availability is the second
element of the structure of airline transportation that
makes the airline industry unique. Because of the
lumpiness of airline capital-—that is, aircraft--airlines
are faced with a choice of several varieties of aircraft.
The lumpiness of airline capital makes it impossible for
airlines to offer custom-tailored "products." Instead
airlines :must offer' products ‘which. provide lowest
opportunity cost of air travel.

The combination of these three elements before
deregulation resulted in a voluminous literature about the
industry structure. This body of theoretical and empirical

literature will be discussed next.

co O ' 'n 5

Two empirical observations were seminal in the

analysis of airline performance under CAB regulation.

First, it was recognized that, despite fares set above

146
competitive levels and the protection from competitive

pressures provided by CAB entry restrictions, airlines did
not earn economic profits. Indeed, they frequently earned
no 'profits at all. In addition, observation of less
regulated intrastate carriers in California and Texas
revealed that these carriers were able to earn profits with
lower fares than CAB-regulated carriers. This was caused
by the substantially lower costs of the intrastate
carriers.

Providing an explanation of these observations
consistent with profit maximizing behavior was an important
challenge of the economic literature of the early 19705.
The key element in the explanation eventually adopted was
the nature of the opportunity costs faced by air travelers
and the absence of price competition in the airline
industry. Since airlines could not freely compete in price
of service, they competed on the other element of air
travelers' cost of air travel: travel time. Specifically,
competition took the form of offering increased flight
frequency, a competitive variable not subject to
regulation. This had the effect of increasing airline
average costs, since fewer passengers were carried on each
individual flight, thereby increasing the per-passenger
share of flight costs which are fixed once the route and
type of aircraft employed are determined.

This theory provided the basis for a series of

147
predictions regarding airline behavior subsequent to

removal of regulation. With airlines free to compete on
price of service, it was predicted that flight frequency
would fall and airlines would increase their utilization of
larger aircraft. There were two hidden weaknesses of this
theory, however. First, it was generally assumed that
airlines would not substantially alter their route
structures except to expand them. A second assumption was
that airlines would charge a single fare for any particular
class of service after receiving pricing freedom. Both of
these assumptions proved false after deregulation. The

consequences of this are considered in the next section.

W

The third chapter presents a theoretical framework for
understanding the responses of airlines to deregulation.
Its basis is a model of how airlines might determine flight
frequency in particular markets, and is an extension of
work by Steven Salop (1984). The model forms the building
block upon which an understanding of the principles of
airline fleet selection can be constructed.

An important extension of Salop's model is one
utilized to explain the practice of hub-and-spoke networks.
In this framework, hub-and-spoke networking can be

interpreted as a problem of joint production. In addition,

148
a form of price discrimination, where customers are

distinguished by both their differing destinations and
differing opportunity cost of time, is illustrated. As is
common in joint production and price discrimination models,
the result is higher levels of provision of the good. The
ability to spread the fixed costs of production across
several different classes of consumers yields these
increases in production. This leads to the conclusion that
the effect of the adoption of hubbing and spoking on
airline flight frequencies is to increase flight frequency
from an origin, ggrgr1§__pgribg§. This conclusion is
contrary to the expectations held before deregulation but
is a natural consequence of the model employed.

This result is a generalization of the result of
Morrison and Winston discussed above(1984). In this model,
the decision to hub and spoke involves balancing revenue
losses caused by decreased convenience of service with the
lowered costs of joint production. Airlines are the only
passenger transportation mode where the cost savings in
both cash and time are generally enough to offset the
increased time cost of not proceeding directly to a
destination. There is some evidence that for surface
freight transportation, particularly less than truckload
shipment, can enjoy economies with a network of the hub-
and-spoke variety.

In general, the theoretical results derived in the

149
third chapter point to a very different interpretation of

the consequences of deregulation than was previously held.
In particular, the model of this dissertation indicates
that a) deregulation should lead to increased flight
frequencies as airlines adjust their networks to the more
efficient hub-and-spoke structure, and b) the requirements
of frequency of service imply that smaller aircraft will
not be displaced by larger aircraft as was predicted in
previous models.

m 1 cal od 5 ' avio

The fourth chapter of this dissertation presented
tests of its theoretical framework. Two distinct sets of
data are used. In the first set, the airlines behavior at
the level of individual routes is investigated. The number
of aircraft of different types employed is the dependent
variable regressed against the route characteristics of a
randomly chosen set of American airline routes for two
years, 1974 and 1984. In another set of regressions the
average number of seats per flight on a route is employed
as the dependent variable. The results tend to provide
confirmation for the theory constructed here. There was a
clear movement towards employing aircraft whose
characteristics make them especially suitable for the

"spokes" of a hub-and-spoke network.

150
In the second set of regressions, the gross fleet

composition of major airlines is regressed against the
route characteristics of those airlines. This is done in
three ways. The first utilizes the absolute numbers of
each of several aircraft types. In the second the relative
frequency of different aircraft varieties is the dependent
variable in the regressions. Additionally, the average
number seats in the airline's fleet is employed as the
dependent variable.

These regressions confirm some of the theoretical
predictions about airline fleet composition. The
regression employing absolute fleet numbers as dependent
variable indicates both that the relationship between route
characteristics and fleet composition changed with
deregulation and that the direction of the change is toward
larger numbers of aircraft in fleets. In the regressions
employing relative fleet composition, there is less
indication of a changed relationship between the route
structures of airlines and the relative proportions of
different types of aircraft in their fleets. In
particular, the early prediction that smaller jets would
disappear with service competition in terms of flight

frequency was never borne out.

151

-re _m‘, 1 "'1‘ '11.. -°"_: ’I O 13!. .133

What implications may be drawn from the results of
this research? One is that regulation did not necessarily
induce airlines to make inefficient choices of aircraft.
Instead, the inefficiencies were generated through the
airline's inability to create efficient route structures
while subject to entry regulation.

Thus far this dissertation has not directly discussed
the welfare implications of airline deregulation.
Implicitly, the argument of the previous paragraph is that
the welfare consequences of regulation were less
significant than previously believed. A further statement
about the welfare consequences of deregulation can in fact
be made. Salop's model (1978), which forms the basis for
the theoretical model of this dissertation, also permits
the evaluation. of social welfare in. a :monopolistically
competitive industry. This welfare evaluation indicates
that the number of varieties of the good offered will be
excessive from a social point of view. The model of Panzar
(1979) is specifically intended to evaluate the behavior of
the deregulated airline industry. It also suggests that
airlines will offer more than the socially optimal number

of flights. The theory of hubbing and spoking developed

152
here implies that an even greater number of flights will be

offered than is indicated by the simple, monopolistically
competitive models. Thus, it is a likely consequence of
deregulation that an excessive number of flights will be
offered. The relatively weak welfare results presented by
the authors cited can be considered strengthened.

In addition, the mathematical similarity of the hub-
and-spoke model presented here to the price discrimination
results also presented in chapter 3 indicates that the
distributional consequences of deregulation have been
insufficiently considered. In fact, this model provides an
alternative to Levine’s (1987) explanation of how the
incumbent airlines with significantly higher costs were
able to prevail in competition with lower cost, new
entrants. Their ability to earn rents through the hub—and-
spoke system and the advantages conferred by their more
extensive route systems in hubbing and spoking surely
contribute to their succeSs. Thus, despite the significant
benefits of deregulation, the picture is perhaps not so
rosy as its proponents would have it. Air carriers
continue to earn some rents in the deregulated environment.

At least three possibilities for building on this work
present themselves. In the case of the empirical results
reported here, two useful extensions might be made. First,
the route level results reported here might be duplicated

with another sample to confirm the results reported. A

153
second step would be to find a superior proxy for the

opportunity cost of air traveler's time. Per capita income
was seldom statistically significant, despite strong
theoretical expectations, regarding' income's role in
determining' the cost. of time and its implications for
flight scheduling.

On a theoretical level, the assumption that the
population of potential airline travelers is uniformly
distributed throughout the course of a day is used here and
elsewhere for want of an alternative. The problem of
rivalrous airline scheduling where demand assymetries exist
is worthy of attention, on both theoretical and empirical

grounds.

Appendix A

Data Types and Sources

As discussed in chapter 3, an airline’s demand for
aircraft can be explained in terms of the demand
characteristics of the markets served and the economic
and regulatory environment. The variables presented in the
theory (are not represented exactly by any data sources
readily available. In order to perform econometric
estimates proxies must be found for four distinct varieties
of variables.

The first is aircraft types. Two distinct sources of
data were consulted to develop models of aircraft
utilization. The aircraft data for the route level
estimates presented in chapter 3 comes from the July 1974
and July 1984 editions of The Offigial Airline Guidel North
American Edition. A random sample of domestic airlines'
routes was constructed from these editions of the guide and
utilized to construct statistics on the utilization of
various types of aircraft on those routes. In addition,
the hubbing variable was constructed by assigning a value
of one to all routes listed as providing connecting flights

on the sampled route.

154

155
Population and per capita income variables were

constructed by using either The Stare and Metropolitan Data
@3433, 1986 edition, The Citvfiand Countv Data Book, 1977
edition, or the Rand-McNallv Commercial Atlae, 1986
edition. For“ route terminals (i.e. either’ origins or
destinations) which were elements of Standard Metropolitan
Statistical areas, the population and per capita income of
the SMSA was utilized. For terminals which were not so
classified, the population and per capita income of the
surrounding county was employed.

The route distance variable was also derived form
multiple sources. For many major cities, the 1974 edition
of the OAG provided a table of domestic airline mileages,
routes not listed in this source were taken from either
foieel Table ef Distances, Continental U.S.ll Alaska,
Hawaii, and Puerto Rico, Direct Line Distances, U.S.
Editiog, or as a last resort nd-McNall Standard Hi
Mileage Guide.

The final variable in the route level regressions was
the vacation variable. The vacation spot dummy was created
by assigning a value of one to all routes with a terminal
in Florida, Hawaii, coastal California, or the desert
Southwest (i.e., Nevada, Arizona, and. New’ Mexico.) A
continuous vacation variable was the per capita
expenditures on lodging at either the origin or

destination. The source of these continuous variables was

156
either The Statistical Abetracr or gounty Business Patterne

both published by the U.S. Census Bureau.

For the second set of regressions the primary source
of data was The Handbook of Airline Statietice, published
biannually between 1963 and 1973, with a supplement
published for the years 1974 and 1975. This data source
was supplemented for years after 1976 by The Inventory and
Age of Aircraft Trunks d Loc ls, prepared by the Office of
Economic Analysis of the CAB and the Air Transport
Association’s Annual Reporr for 1983 and 1984. In these data
sources different models of aircraft were classified
according to their body style (i.e., either narrow-bodied
or wide-bodied.) In addition, aircraft are classified by
type and number of engines. These data were collected for
the period 1963-1984 and consisted of the inventory of each
of the CAB-defined types of aircraft in carrier fleets as
Of December 31 of a given year. The initial year chosen
was 1963 to minimize the disturbance to airline fleet
composition consequent to the introduction of jet aircraft
in the late 19503 (c.f. Yance, QRE_£il)- Nineteen eighty—
four 'was chosen as an upper' bound by limits in data
availability and the necessity to have sufficient sample
years subsequent to deregulation. Since no single data
source reported all years, the carrier fleet series were
constructed only for carriers still existing and defined as

"majors" in 1984. Where a merger had resulted in the

157
creation of a new "major ," the fleets and other statistics

were combined for the entire sample period.

The descriptive statistics used to characterize the
route structure of the carriers were constructed from
Airport Activity Statistics of Certificated Route Carriers
reported annually for the years 1963-1984. In using this
data, the conventions of the FAA in classifying airports as
large,medium, and small hubs and as non-hubs depending on
the percentage of U.S. airline passenger emplanements, was
adopted.1 Adrline route structures were characterized by
the numbers of each hub classification that they served and
the average number of passengers served per day in each of
these classifications.

An additional variable used in the two stage least
squares estimates of chapter 4 was the average stage length
of airlines. This was reported in The Handbook of Airline
Steeristics before 1976 and in Air Carrier Traffic
firerieriee, also published by the CAB beginning in 1976.

Each set of regressions reported below has a distinct
source of data. Thus two independent tests of the

hypothesis are provided by these results.

 

1 Large hubs have more than 1% of US passenger
emplanements. Medium hubs have between 0.99% and 0.50% of
U.S. passenger emplanements. Small hubs have between 0.49%
and 0.25% of emplanements. Non-hubs emplane fewer than
0.25% of U.S. airline passengers.

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