Paying More for a Shorter Flight? - Hidden City
Ticketing
Quanquan Liu
Department of Economics, University of Pittsburgh, Pittsburgh, PA 15260, USA
Hidden city ticketing occurs when an indirect flight from city A to city C through connection node city
B is cheaper than the direct flight from city A to city B. Then passengers traveling from A to B have an
incentive to purchase the ticket from A to C but get off the plane at B. In this paper, I build a structural
model to explain the cause and impact of hidden city ticketing. I collect empirical data from the Skiplagged
webpage and apply global optimization algorithms to estimate the parameters of my model. I also conduct
counterfactual analysis to shed some light on policy implications. I find that hidden city opportunity occurs
only when airlines are applying a hub-and-spoke network structure, under which they intend to lower their
flying costs compared to a fully connected network. I find that in the short run, hidden city ticketing does
not necessarily decrease airlines’ expected profits. Consumer welfare and total surplus always increase. In
the long run, the welfare outcomes become more complicated. For some routes airlines have the incentive
to switch from hub-and-spoke network to a fully connected one when there are more and more passengers
informed of hidden city ticketing. During this process, firms always result in lower expected profits, while
consumers and the whole society are not necessarily better off.
Keywords: hidden city ticketing, network structure, second-degree price discrimination, informed con-
sumers.
1. Introduction
Hidden city ticketing is an interesting pricing phenomenon occurring after the deregulation of the
airline industry in 1978 (Wang & Ye (2016)). It is an airline booking strategy passengers use to
reduce their flying costs. Hidden city ticketing occurs when an indirect flight from city A to city
C, using city B as the connection node, turns out to be cheaper than the direct flight from city
A to city B. In which case passengers who wish to fly from A to B have an incentive to purchase
the indirect flight ticket, pretend to fly to city C, while disembark at the connection node B, and
discard the remaining segment B to C. When this happens, city B is called the “hidden city”, and
this behavior is then called “hidden city ticketing”.
The following real world example (Figure 1) illustrates hidden city ticketing. On November 19,
2018, a direct flight operated by Delta Air Lines flying from Pittsburgh to New York city cost $218.
On the same day, for the same departure and landing time, another indirect flight also operated
1
Liu: Hidden City Ticketing 2
Figure 1 An example of hidden city ticketing.
by Delta Air Lines flying from Pittsburgh to Boston, with one stop at New York city, cost only
$67.
These two flights share exactly the same first segment: they are operated by the same airline
company, they departure at the same date, same airports and same time. However, the price of
the indirect flight accounted for only 30% of that of the direct one. That is, you are able to fly
more than 200 miles further but pay $151 less! The New York city is then called a “hidden city”
in this case. It is “hidden” because literally, if we use Google Flights, Orbitz, Priceline, Kayak, or
any other “normal” travel search tools to look for a flight from Pittsburgh to NYC, we will not be
able to see the indirect flight above showing up in our search results.
Although technically legal, hidden city ticketing actually violates the airfare rules of most airline
companies in United States. For example, according to the Contract of Carriage of United Airlines
(revised by December 31, 2015):
“Fares apply for travel only between the points for which they are published. Tickets may not
be purchased and used at fare(s) from an initial departure point on the Ticket which is before the
Passenger’s actual point of origin of travel, or to a more distant point(s) than the Passenger’s
actual destination being traveled even when the purchase and use of such Tickets would produce a
lower fare. This practice is known as “Hidden Cities Ticketing” or “Point Beyond Ticketing” and
is prohibited by UA.”
Similarly, American Airlines also claim that conducting hidden city ticketing is “unethical” and
doing so “is tantamount to switching price tags to obtain a lower price on goods sold at department
stores”. Passengers might be penalized when conducting hidden city ticketing. Airlines are able to
“confiscate any unused Flight Coupons”, “delete miles in the passenger’s frequent flyer account”,
“assess the passenger for the actual value of the ticket”, or even “take legal action with respect to
the passenger”.
Liu: Hidden City Ticketing 3
Meanwhile, members of Congress have proposed several bills, including “H.R. 700, H.R. 2200,
H.R. 5347 and S. 2891, H.R. 332, H.R. 384, H.R. 907 and H.R. 1074”, trying to prohibit airlines
from penalizing passengers for conducting hidden city ticketing (GAO (2001)). Furthermore, the
European Union has passed a passenger bill of rights since around 2005, in which the European
Commission has specifically ruled that “airlines must honor any part of an airline ticket” and
hidden city ticketing then becomes perfectly legal. After the ruling EU find that “fares have become
more fair, hidden city bargains are difficult to find, and the airlines have not suffered drastic losses
due to this”.
Therefore, whether hidden city ticketing should be legally prohibited or not, and what policy
does the best for consumers, airline companies, and social welfare, still remain to be open questions.
The fact is, although being “threatened” by airline companies, there have been more and more
consumers coming to realize the existence of hidden city opportunities, and may try to exploit
them to lower their flying costs. In December 2014, United Airlines and Orbitz (an airline booking
platform) sued the founder of Skiplagged (a travel search tool) for his website of “helping travelers
find cheap tickets through hidden city ticketing”. According to CNNMoney, Orbitz eventually
settled out of court one year later, and a Chicago judge threw out United’s lawsuit using the excuse
that the founder “did not live or do business in that city”. In contrast to the willingness of United,
this lawsuit brought the search of key words “hidden city ticketing” to a peak (Figure 2).
Corresponding to this higher demand, nowadays there are more travel search tools specifically
designed to achieve this task (Skiplagged, Tripdelta, Fly Shortcut, AirFareIQ, ITA Matrix, etc).
And finding hidden city opportunies and exploiting them become much easier today.
This paper aims at providing some plausible explanations for the cause of hidden city ticketing,
and estimating its possible impact on welfare outcomes for airlines, consumers, and society as a
whole. I build a structural model in which airlines can choose both prices and network structures as
their strategic variables following Shy (2001), and derive several propositions based on that. Then
I collect daily flights information by scraping the Skiplagged website to build my own empirical
dataset. I apply global optimization algorithms to estimate the parameters of my model, and then
conduct counterfactual analysis to evaluate the possible impact of hidden city ticketing on airlines’
expected profits, consumers’ welfare, and total surplus, based on which I could help shed some
light on policy implications.
In this paper, I find that 1) hidden city ticketing only occurs when airline companies are applying
a hub-and-spoke network structure; 2) under some conditions, hub-and-spoke network is more cost-
saving compared to fully connected network; 3) in the short run, hidden city ticketing does not
Liu: Hidden City Ticketing 4
Figure 2 Average monthly web search data of hidden city ticketing. Data source for the relative value is
Google Trends. Numbers represent search interest relative to the highest point on the chart for the given region
and time. A value of 100 is the peak popularity for the term. Data source for the absolute value is Google
AdWords, unit is number of times.
necessarily decrease airlines’ expected profits, while consumers’ surplus and total welfare always
increase; 4) in the long run, i.e., when airlines can change their choices of prices and networks freely,
the impact of hidden city ticketing differs for different routes. For some routes airlines have the
incentive to switch from hub-and-spoke network to a fully connected one when there are more and
more passengers informed of hidden city ticketing, during which process firms always result in lower
expected revenue, while consumers and the whole society are not necessarily better off. Therefore,
whether hidden city ticketing should be permitted or forbidden depends on the characteristics of
different routes, and this problem cannot be solved by one simple policy.
The remainder of this paper is organized as follows: Related works are summarized in Section 2.
The structural model is introduced in Section 3, together with the propositions of short run impacts
derived from it. Section 4 describes the data in details. Section 5 shows the estimation strategy
and the MLE results. In Section 6 I conduct counterfactual analysis to shed some light on long run
impacts and policy implications. The limitation and future questions of this paper are discussed
in Section 7 and Section 8 concludes.
Liu: Hidden City Ticketing 5
2. Literature Review
To the best of my knowledge, this is the first paper to quantitatively study the cause and impact
of hidden city ticketing on welfare outcomes using real empirical data. In fact, there are only a
few papers paying attention to this phenomenon. One government report from the Government
Accountability Office (GAO (2001)) conducted some correlation analysis based on their selected
data, and found that the possibility of hidden city ticketing is significantly affected by the size of the
markets and the degree of competition in the hub markets and the spoke markets. Another report
from Hopper Research (Surry (2005)) also provides some summary statistics of this phenomenon.
Based on four weeks of airfare search data from Hopper, the analyst found that 26% of domestic
routes could be substituted by some cheaper options through hidden city ticketing, and the price
discount could be nearly 60%. The most quantitative study is Wang & Ye (2016), which applied
a network revenue management model to look at the cause and impact of hidden city ticketing.
They base all their findings on simulated data rather than real world data. Therefore, their model
is quite different from an economic model. They find that hidden city opportunity may arise when
the price elasticity of demand on different routes differ a lot. In order to eliminate any hidden
city opportunities, airlines will rise the prices of certain itineraries and hurt consumers. But even
airlines optimally react, they will still suffer from a loss in revenue.
There have been a lot of literature focusing on the airline industry ever since its deregulation
in 1978. A bunch of them have confirmed significant difference of price elasticity lying between
tourists and business travelers. For example, Berry & Jia (2010) has estimated a price elasticity of
demand for tourists as −6.55, while that for business travelers is only −0.63. Robert S & Daniel L
(2001) find a large difference between price elasticity of demand for business travelers (−0.9 to
−0.3) and that for leisure travelers (about −1.5). And Gerardi & Shapiro (2009) also confirm that
the demand for business travelers is less price elastic than that of tourists, and through applying
certain ticket restrictions, airline companies are able to distinguish between these two types. Based
on these findings, researchers have further found that airlines are exploiting these differences and
engaging in second-degree price discrimination through many different methods, such as advanced-
purchase discounts (Dana (1998)), ticket restrictions such as Saturday-night stayover requirements
(Stavins (2001); Giaume & Guillou (2004)), refundable and non-refundable tickets (Escobari &
Jindapon (2014)), intertemporal price discrimination (Liu (2015); Lazarev (2013)), and even the
day-of-the-week that a ticket is purchased (Puller & Taylor (2012)). This paper follows previous
findings and assumes that airline companies are price discriminating between leisure travelers and
business travelers, with the latter being less price sensitive and valuing time more. My model also
follows Shy (2001) book about economics of network industries, assuming that airlines can choose
Liu: Hidden City Ticketing 6
Figure 3 Left: Fully-Connected (FC) Network. Right: Hub-and-Spoke (HS) Network.
both airfares and network structures. Finally, I find that while informed passengers could possibly
enjoy some benefits of hidden city ticketing, uninformed passengers are always bearing the costs,
if any. This is similar to the finding of Varian (1980) where the author shows some “detrimental
externalities” that uninformed consumers suffer from due to the behavior of informed consumers.
3. The Model
Following Shy (2001), I assume that airlines are choosing from two different network structures:
fully-connected network or hub-and-spoke network (Figure 3). Under fully-connected network,
passengers fly nonstop from one city to the other. While under hub-and-spoke network, everyone
who wishes to fly from city A to city C needs to stop at the hub city B. To simplify my analysis
below, I will apply an one-way traveling pattern instead of the two-way traveling pattern showed
in Figure 3. After the 1978 Airline Deregulation Act, the absence of price and entry controls
led to increased use of the hub-and-spoke structure (Shy (2001)). Responding to the increased
competition and to reduce flying costs, airlines started to cut the number of direct flights and
reroute the passengers through a hub city. While in recent years, especially since late 1990s, with
the expansion of low-cost carriers (LCCs), passengers started to show a higher aversion toward
connecting flights, and fully-connected structure becomes more popular again (Berry & Jia (2010)).
Assume that there is only one airline serving the three cities, thus the firm charges monopoly
airfares. Aircrafts are further assumed to have an unlimited capacity, thus there is only one flight
on each route. C
2
denote the airline’s cost per mile on any route j. This simplified cost pattern
is referred as ACM cost (AirCraft Movement cost) in Shy (2001), and it is widely used in airline
related literature. Cost pattern can be simplified because in airline industry, large percentage of
costs are fixed before flights taking off, such as capital costs (renting gates for departure and
arrival, landing fees), labor costs (hiring local staff), etc. (GAO (2001)) The costs of fuel account
for approximately 15% of the total operation costs (Berry & Jia (2010)), while the marginal cost
of airline seats is nearly negligible (Rao (2009)).
Liu: Hidden City Ticketing 7
Assume that direct flight has a quality of q
h
per mile and indirect flight has a quality of q
l
per
mile, with 0 < q
l
< q
h
< 1. Each individual i has a time preference parameter of λ
i
, obtaining utility
u
i
= C
1
·e
λ
i
qd −p
from consuming a good of quality q. Under the assumption of free disposal, he/she will get 0 utility
if chooses not to fly. Utility decreases when price increases. And if a passenger values time more
(i.e., with a larger λ), he/she will acquire a larger utility increase when switching from an indirect
flight (with quality q
l
) to a direct flight (with quality q
h
). Furthermore, for a longer itinerary
(larger d), the utility improvement from indirect flight to direct flight is also larger. C
1
is a scaling
parameter to make the utility comparable to dollar value p.
On each route j, the distribution of consumers’ time preferences satisfies λ
ij
∼ N (θ
j
, σ
2
1
). For
passengers flying from A to B, the fraction of passengers being aware of hidden city opportunities
is δ, and the fraction of uninformed passengers is 1 −δ. When hidden city opportunities exist (i.e.,
p
AB
> p
ABC
), informed passengers will pay p
ABC
instead, while uninformed passengers will still
pay p
AB
. The amount of passengers on each route j are normalized to 1. p
j
denote the airfare on
route j, and d
j
denote the distance of route j.
Airline chooses both network structures (fully-connected or hub-and-spoke) and prices
(p
AB
, p
BC
, p
AC
, p
ABC
) to maximize expected profits, as shown in the figure below.
Airline
Π
F C
(p
F C
)
p
F C
= (p
AB
, p
BC
, p
AC
)
Fully-Connected
Π
HS
(p
HS
)
p
HS
= (p
AB
, p
BC
, p
ABC
)
Hub-and-Spoke
I will show later in this section that there exists an optimal choice set for the airline, and the
choice set is unique. According to the assumptions above, on each route j, for each individual i,
u
ij
= C
1
·e
λ
ij
qd −p, λ
ij
∼N(θ
j
, σ
2
1
).
Therefore, on each route j, the proportion of consumers choosing to fly is equal to:
P r
[
u
ij
≥0
]
= P r
C
1
·e
λ
ij
qd ≥p
Liu: Hidden City Ticketing 8
= P r
λ
ij
≥ln
p
C
1
·qd
= 1 −Φ
θ
j
,σ
2
1
ln
p
C
1
·qd
.
3.1. Fully-Connected Network
Under fully-connected network, airline’s expected profits (producer surplus) are equal to the rev-
enue it collects minus the costs:
Π
F C
= Π
AB
+ Π
BC
+ Π
AC
= p
AB
·
1 −Φ
θ
AB
,σ
2
1
ln
p
AB
C
1
·q
h
d
AB
−C
2
·d
AB
+ p
BC
·
1 −Φ
θ
BC
,σ
2
1
ln
p
BC
C
1
·q
h
d
BC
−C
2
·d
BC
+ p
AC
·
1 −Φ
θ
AC
,σ
2
1
ln
p
AC
C
1
·q
h
d
AC
−C
2
·d
AC
.
Under fully-connected network structure, the only way to fly “indirectly” from A to C is to take
the two direct flights A to B and B to C together. Obviously, with p
AB
< p
AB
+ p
BC
, we can easily
derive the following proposition:
Proposition 1 Hidden city opportunity does not exist under fully-connected network structure.
Consumer surplus is the difference between our willingness to pay and the price we actually
being charged, which equals:
CS
F C
= CS
AB
+ CS
BC
+ CS
AC
=
Z
∞
ln
p
AB
C
1
·q
h
d
AB
!
C
1
·e
λ
i
q
h
d
AB
−p
AB
dF (λ
i
)
+
Z
∞
ln
p
BC
C
1
·q
h
d
BC
!
C
1
·e
λ
i
q
h
d
BC
−p
BC
dF (λ
i
)
+
Z
∞
ln
p
AC
C
1
·q
h
d
AC
!
C
1
·e
λ
i
q
h
d
AC
−p
AC
dF (λ
i
).
Adding them together, our total surplus under fully-connected network is:
T S
F C
= P S
F C
+ CS
F C
=
Z
∞
ln
p
AB
C
1
·q
h
d
AB
!
C
1
·e
λ
i
q
h
d
AB
dF (λ
i
) −C
2
·d
AB
Liu: Hidden City Ticketing 9
+
Z
∞
ln
p
BC
C
1
·q
h
d
BC
!
C
1
·e
λ
i
q
h
d
BC
dF (λ
i
) −C
2
·d
BC
+
Z
∞
ln
p
AC
C
1
·q
h
d
AC
!
C
1
·e
λ
i
q
h
d
AC
dF (λ
i
) −C
2
·d
AC
.
No transaction fee is assumed under the setting, thus the prices we pay are equal to the prices
airline receives, and both cancel out.
3.2. Hub-and-Spoke Network (without Hidden City Ticketing)
Given hub-and-spoke network structure, first consider the simple case when hidden city opportu-
nities do not exist (i.e., p
AB
≤p
ABC
). Under this circumstances, airline’s expected profits are equal
to:
Π
HS
= Π
AB
+ Π
BC
+ Π
ABC
= p
AB
·
1 −Φ
θ
AB
,σ
2
1
ln
p
AB
C
1
·q
h
d
AB
−C
2
·d
AB
+ p
BC
·
1 −Φ
θ
BC
,σ
2
1
ln
p
BC
C
1
·q
h
d
BC
−C
2
·d
BC
+ p
ABC
·
1 −Φ
θ
ABC
,σ
2
1
ln
p
ABC
C
1
·q
l
d
ABC
.
Proposition 2 If the cost associated with maintaining route AC is sufficiently large, then the hub-
and-spoke network is more profitable to operate than the fully-connected network for the monopoly
airline.
Proof of Proposition 2. Compare airline’s expected profits under these two different networks:
Π
HS
−Π
F C
= p
ABC
·
1 −Φ
θ
ABC
,σ
2
1
ln
p
ABC
C
1
·q
l
d
ABC
− p
AC
·
1 −Φ
θ
AC
,σ
2
1
ln
p
AC
C
1
·q
h
d
AC
+ C
2
·d
AC
.
Therefore, if the last term (C
2
·d
AC
, refers to the cost associated with maintaining route AC) is
sufficiently large, hub-and-spoke network is more profitable.
This is in accordance with the findings of previous literatures. Caves et al. (1984), Brueckner
et al. (1992), Brueckner & Spiller (1994), and Berry et al. (2006) all confirm the cost economies
of hubbing. Under a different framework, Shy (2001) also find that hub-and-spoke network is cost-
saving if the fixed cost is large enough.
Liu: Hidden City Ticketing 10
Similarly, consumer surplus equals:
CS
HS
= CS
AB
+ CS
BC
+ CS
ABC
=
Z
∞
ln
p
AB
C
1
·q
h
d
AB
!
C
1
·e
λ
i
q
h
d
AB
−p
AB
dF (λ
i
)
+
Z
∞
ln
p
BC
C
1
·q
h
d
BC
!
C
1
·e
λ
i
q
h
d
BC
−p
BC
dF (λ
i
)
+
Z
∞
ln
p
ABC
C
1
·q
l
d
ABC
!
C
1
·e
λ
i
q
l
d
ABC
−p
ABC
dF (λ
i
).
Adding them together, total surplus is equal to:
T S
HS
= P S
HS
+ CS
HS
=
Z
∞
ln
p
AB
C
1
·q
h
d
AB
!
C
1
·e
λ
i
q
h
d
AB
dF (λ
i
) −C
2
·d
AB
+
Z
∞
ln
p
BC
C
1
·q
h
d
BC
!
C
1
·e
λ
i
q
h
d
BC
dF (λ
i
) −C
2
·d
BC
+
Z
∞
ln
p
ABC
C
1
·q
l
d
ABC
!
C
1
·e
λ
i
q
l
d
ABC
dF (λ
i
).
3.3. Hub-and-Spoke Network (with Hidden City Ticketing)
Now consider the scenario when hidden city opportunities exist (i.e., p
AB
> p
ABC
). Firstly, is there
a possibility that p
AB
> p
ABC
, in other words, are we paying more for a shorter flight sometimes?
The answer is yes. To see why this might occur, recall that
p
AB
= arg max
p
p ·
1 −Φ
θ
AB
,σ
2
1
ln(
p
C
1
q
h
d
AB
)
,
p
ABC
= arg max
p
p ·
1 −Φ
θ
ABC
,σ
2
1
ln(
p
C
1
q
l
d
ABC
)
,
where q
h
> q
l
and d
AB
< d
ABC
. For simplification, let q
h
d
AB
= q
l
d
ABC
and σ
1
= 1, rewrite the
problem as
p = arg max
p
p ·
h
1 −Φ
θ
ln(
p
C
)
i
= arg max
p
p ·
h
1 −Φ
ln(
p
C
) −θ
i
,
where C is a constant.
Liu: Hidden City Ticketing 11
Let f(p, θ) = p ·
h
1 −Φ
ln(
p
C
) −θ
i
, to find out the maximizer p
∗
, take derivative of f(p, θ) with
respect to p and make it equal 0:
f
p
(p, θ) = 1 −Φ
ln(
p
C
) −θ
−φ
ln(
p
C
) −θ
= 0.
Let g(p, θ) = 1 −Φ
ln(
p
C
) −θ
−φ
ln(
p
C
) −θ
, and take derivative of g(p, θ) with respect to θ,
we get
g
θ
(p, θ) = φ
ln(
p
C
) −θ
+ φ
θ
ln(
p
C
) −θ
= φ
ln(
p
C
) −θ
1 −ln(
p
C
) + θ
.
Since φ
ln(
p
C
) −θ
> 0, if θ > ln(
p
C
) − 1, we would have g
θ
(p, θ) > 0, hence as long as θ
AB
>
θ
ABC
, the optimal prices would be p
AB
> p
ABC
. Therefore, under some conditions, there is a pos-
sibility that p
AB
> p
ABC
, in other words, we are paying more for a shorter flight sometimes and
hidden city opportunities exist. The underlying explanation is that airlines are pricing based on
demand, rather than costs.
Comparing to Section 3.2 where there is no hidden city ticketing, the difference lies in the
informed passengers who wish to fly directly from A to B. Under this circumstances, airline’s
expected profits are equal to:
Π
HCT
= Π
AB
+ Π
BC
+ Π
ABC
= (1 −δ) ·p
AB
·
1 −Φ
θ
AB
,σ
2
1
ln
p
AB
C
1
·q
h
d
AB
−C
2
·d
AB
+ p
BC
·
1 −Φ
θ
BC
,σ
2
1
ln
p
BC
C
1
·q
h
d
BC
−C
2
·d
BC
+ p
ABC
·
1 −Φ
θ
ABC
,σ
2
1
ln
p
ABC
C
1
·q
l
d
ABC
+ δ ·p
ABC
·
1 −Φ
θ
AB
,σ
2
1
ln
p
ABC
C
1
·q
h
d
AB
.
Proposition 3 When airlines do not alter their choices of prices and network structures, hidden
city ticketing does not necessarily decrease airline’s expected profits.
Proof of Proposition 3. Compare airline’s expected profits with and without hidden city tick-
eting respectively, and compute the difference:
Π
HCT
−Π
HS
= δ ·
p
ABC
·
1 −Φ
θ
AB
,σ
2
1
ln
p
ABC
C
1
·q
h
d
AB
Liu: Hidden City Ticketing 12
− p
AB
·
1 −Φ
θ
AB
,σ
2
1
ln
p
AB
C
1
·q
h
d
AB
.
Note that p
ABC
< p
AB
while
1 −Φ
θ
AB
,σ
2
1
ln
p
ABC
C
1
·q
h
d
AB
>
1 −Φ
θ
AB
,σ
2
1
ln
p
AB
C
1
·q
h
d
AB
.
We find that although airline suffers from a loss when informed passengers are paying a lower price,
it also obtains some gain when this lower price attracts more consumers to take the flight. How
hidden city ticketing will affect airline’s expected profits actually depends on the relative dominance
of these two inequalities, and this conduct does not necessarily decrease airline’s expected revenue.
Consumer surplus equals:
CS
HCT
= CS
AB
+ CS
BC
+ CS
ABC
= (1 −δ)
Z
∞
ln
p
AB
C
1
·q
h
d
AB
!
C
1
·e
λ
i
q
h
d
AB
−p
AB
dF (λ
i
)
+
Z
∞
ln
p
BC
C
1
·q
h
d
BC
!
C
1
·e
λ
i
q
h
d
BC
−p
BC
dF (λ
i
)
+
Z
∞
ln
p
ABC
C
1
·q
l
d
ABC
!
C
1
·e
λ
i
q
l
d
ABC
−p
ABC
dF (λ
i
).
+ δ
Z
∞
ln
p
ABC
C
1
·q
h
d
AB
!
C
1
·e
λ
i
q
h
d
AB
−p
ABC
dF (λ
i
).
Proposition 4 When airlines do not alter their choices of prices and network structures, con-
sumers are always better off when hidden city ticketing is allowed.
Proof of Proposition 4. Compute the difference of consumer surplus with and without hidden
city ticketing, we have
CS
HCT
−CS
HS
= δ
Z
∞
ln
p
ABC
C
1
·q
h
d
AB
!
C
1
·e
λ
i
q
h
d
AB
−p
ABC
dF (λ
i
)
− δ
Z
∞
ln
p
AB
C
1
·q
h
d
AB
!
C
1
·e
λ
i
q
h
d
AB
−p
AB
dF (λ
i
)
= δ
Z
ln
p
AB
C
1
·q
h
d
AB
!
ln
p
ABC
C
1
·q
h
d
AB
!
C
1
·e
λ
i
q
h
d
AB
−p
ABC
dF (λ
i
)
+ δ
Z
∞
ln
p
AB
C
1
·q
h
d
AB
!
(
p
AB
−p
ABC
)
dF (λ
i
) > 0.
The increase in consumer surplus is composed of two different parts. Firstly, the existing informed
passengers are now paying a lower price, which provides them extra utility gain. Secondly, some
Liu: Hidden City Ticketing 13
travelers who will not fly with the original price p
AB
are now participating in this market activity,
because they are informed of the lower price p
ABC
. These new passengers also obtain utility gain,
increasing the total consumer surplus.
Adding the producer surplus and consumer surplus together, we have the total surplus under
the scenario of hub-and-spoke network structure with hidden city ticketing being equal to:
T S
HCT
= (1 −δ)
Z
∞
ln
p
AB
C
1
·q
h
d
AB
!
C
1
·e
λ
i
q
h
d
AB
dF (λ
i
) −C
2
·d
AB
+
Z
∞
ln
p
BC
C
1
·q
h
d
BC
!
C
1
·e
λ
i
q
h
d
BC
dF (λ
i
) −C
2
·d
BC
+
Z
∞
ln
p
ABC
C
1
·q
l
d
ABC
!
C
1
·e
λ
i
q
l
d
ABC
dF (λ
i
)
+ δ
Z
∞
ln
p
ABC
C
1
·q
h
d
AB
!
C
1
·e
λ
i
q
h
d
AB
dF (λ
i
).
Proposition 5 When airlines do not alter their choices of prices and network structures, total
social welfare always increase when hidden city ticketing is allowed.
Proof of Proposition 5. Compute the difference of total surplus with and without hidden city
ticketing, we have
T S
HCT
−T S
HS
= δ
Z
∞
ln
p
ABC
C
1
·q
h
d
AB
!
C
1
·e
λ
i
q
h
d
AB
dF (λ
i
)
− δ
Z
∞
ln
p
AB
C
1
·q
h
d
AB
!
C
1
·e
λ
i
q
h
d
AB
dF (λ
i
)
= δ
Z
ln
p
AB
C
1
·q
h
d
AB
!
ln
p
ABC
C
1
·q
h
d
AB
!
C
1
·e
λ
i
q
h
d
AB
dF (λ
i
) > 0.
Total surplus increase because compared to the original price p
AB
, there are more travelers
choosing to take the flight with the lower price p
ABC
. Extra passengers obtain extra utility gain.
Since I have assumed unlimited capacity for the aircrafts, the whole society benefit from this
change.
With a full analysis of airline’s expected profits under fully-connected network and hub-and-
spoke network, with and without hidden city ticketing, we can now show that there exists an
optimal choice set for the airline to maximize its producer surplus, and the solution is unique.
Liu: Hidden City Ticketing 14
Proposition 6 Under the assumptions listed at the beginning of this section, there exists an opti-
mal choice set (network, p
AB
, p
BC
, p
AC
, p
ABC
) for the airline to maximize its expected profits, and
the solution is unique.
Proof of Proposition 6. According to our previous analysis,
Π
F C
= p
AB
·
1 −Φ
θ
AB
,σ
2
1
ln
p
AB
C
1
·q
h
d
AB
−C
2
·d
AB
+ p
BC
·
1 −Φ
θ
BC
,σ
2
1
ln
p
BC
C
1
·q
h
d
BC
−C
2
·d
BC
+ p
AC
·
1 −Φ
θ
AC
,σ
2
1
ln
p
AC
C
1
·q
h
d
AC
−C
2
·d
AC
.
Π
HS
= p
AB
·
1 −Φ
θ
AB
,σ
2
1
ln
p
AB
C
1
·q
h
d
AB
−C
2
·d
AB
+ p
BC
·
1 −Φ
θ
BC
,σ
2
1
ln
p
BC
C
1
·q
h
d
BC
−C
2
·d
BC
+ p
ABC
·
1 −Φ
θ
ABC
,σ
2
1
ln
p
ABC
C
1
·q
l
d
ABC
if p
AB
≤p
ABC
, and
Π
HS
= (1 −δ) ·p
AB
·
1 −Φ
θ
AB
,σ
2
1
ln
p
AB
C
1
·q
h
d
AB
−C
2
·d
AB
+ p
BC
·
1 −Φ
θ
BC
,σ
2
1
ln
p
BC
C
1
·q
h
d
BC
−C
2
·d
BC
+ p
ABC
·
1 −Φ
θ
ABC
,σ
2
1
ln
p
ABC
C
1
·q
l
d
ABC
+ δ ·p
ABC
·
1 −Φ
θ
AB
,σ
2
1
ln
p
ABC
C
1
·q
h
d
AB
if p
AB
> p
ABC
.
Note that solving for the optimal choice set (network, p
AB
, p
BC
, p
AC
, p
ABC
) is equivalent to firstly
solving for the optimal price bundles (p
AB
, p
BC
, p
AC
, p
ABC
) under fully-connected network and hub-
and-spoke network respectively, and further compare Π
F C
(p
AB
, p
BC
, p
AC
) and Π
HS
(p
AB
, p
BC
, p
ABC
)
to determine which joint choices of network structure and prices are optimal.
Solving for the optimal price bundle (p
AB
, p
BC
, p
AC
, p
ABC
) to maximize expected profits Π
F C
and Π
HS
, when there is no hidden city ticketing, is equivalent to solving the following problem:
max
p
p ·
h
1 −Φ
θ,σ
2
ln(
p
C
)
i
where C is a constant.
Take derivative of the objective function and make it equal 0:
1 −Φ
θ,σ
2
ln(
p
C
)
+ p ·
−φ
θ,σ
2
ln(
p
C
)
·
C
p
·
1
C
= 0
Liu: Hidden City Ticketing 15
1 −Φ
θ,σ
2
ln(
p
C
)
−φ
θ,σ
2
ln(
p
C
)
= 0.
Let x = ln(
p
C
), y = Φ
θ,σ
2
(x), the equation above becomes a typical ODE:
1 −y =
dy
dx
dx =
dy
1 −y
x = −ln(1 −y) + C
1
ln(
p
C
) = −ln(1 −y) + C
1
p
C
= e
−ln(1−y)
·e
C
1
=
e
C
1
1 −y
p =
C ·e
C
1
1 −y
p −p ·
1
2
1 + erf
ln(
p
C
) −θ
σ
√
2
= C ·e
C
1
where
erf(z) =
1
√
π
Z
z
−z
e
−t
2
dt
=
2
√
π
z −
z
3
3
+
z
5
10
−
z
7
42
+
z
9
216
−···
by Taylor expansion.
Therefore, the optimal price bundle is solvable. To further confirm that function f(p) = p ·
1 −Φ
θ,σ
2
ln
p
C ·q ·d
is unimodal, I depict function f(p) with parameters θ = 0.5, σ =
0.3, C = 10, q = 0.8, d = 30, as shown in Figure 4 below.
When there is hidden city ticketing, the difference lies in the optimal value of p
ABC
. Instead of
looking for a p
ABC
that maximizes p
ABC
·
1 −Φ
θ
ABC
,σ
2
1
ln
p
ABC
C
1
·q
l
d
ABC
, we are now solving
the following problem instead:
max
p
p ·
1 −Φ
θ
1
,σ
2
ln(
p
C
1
)
+ δ ·p ·
1 −Φ
θ
2
,σ
2
ln(
p
C
2
)
where C
1
and C
2
are constants.
Take derivative of the objective function and make it equal 0:
1 −Φ
θ
1
,σ
2
ln(
p
C
1
)
−φ
θ
1
,σ
2
ln(
p
C
1
)
+ δ
1 −Φ
θ
2
,σ
2
ln(
p
C
2
)
−φ
θ
2
,σ
2
ln(
p
C
2
)
= 0.
Left-hand side is a function of p, f(p) with p ∈ [0, +∞). It is continuous because it is a lin-
ear combination of probability density function and cumulative distribution function of normal
distribution, which are all continuous functions.
Liu: Hidden City Ticketing 16
Figure 4 Illustration of function f (p) with parameters θ = 0.5, σ = 0.3, C = 10, q = 0.8, d = 30.
When p → 0, Φ
θ,σ
2
ln(
p
C
)
→ 0, φ
θ,σ
2
ln(
p
C
)
∈ (0, 1). Therefore, f (p) > 0. When p → +∞,
Φ
θ,σ
2
ln(
p
C
)
→1, φ
θ,σ
2
ln(
p
C
)
∈(0, 1). Therefore, f(p) < 0. According to Mean Value Theorem,
there exists at least one p that makes f(p) = 0. Therefore, the solution of the model still exists.
Note that Propositions 3, 4 and 5 are derived under the assumption that airlines are not aware
of hidden city ticketing, thus they do not alter their choices of prices and network structures in
reaction to this booking strategy. This might be valid in the short run, while during a longer period,
airlines should be able to realize the conduct of hidden city ticketing and adjust their optimal
choices of prices and networks in response to the behavior. In such a scenario, obtaining a closed-
form solution is challenging, and to reveal what would be the airline’s optimal choice set with a
changing proportion of informed passengers (changing δ) is even more difficult. Therefore, in the
rest of the paper I will use numerical approach instead to solve for the optimal choices of airline
with changing δ, and estimate the possible impacts of hidden city ticketing on welfare outcomes in
the counterfactual analysis below.
4. Data
I have collected daily flights data by scraping the tickets information on Skiplagged webpage on
February 6, 2016 with all quotes of April 6, 2016. This date was chosen because it was neither
a weekend nor a holiday, and it was 60 days before the departure date, which should not be
severely affected by seat sales. Information being collected include the origin, connecting (if any)
and destination airports, time of departure, connection and landing, operation airlines and airfares.
Liu: Hidden City Ticketing 17
Figure 5 Distribution of busy commercial service airports around United States.
According to the Passenger Boardings at Commercial Service Airports of Year 2014 released in
September 2015 by Federal Aviation Administration (FAA), there are more than 500 commercial
service airports around United States. To reduce the computational burden of collecting data, I
have restricted my sample to the 133 busy commercial service airports identified by FAA. Only
focusing on those 133 airports is reasonable because those airports actually accounted for 96.34%
of total passenger enplanements in 2014. The distribution of the busy commercial service airports
around United States is shown in Figure 5. From the graph we can see that my data has covered
airports in Alaska, Hawaii and Puerto Rico, while no airport in Wyoming has been identified as
busy commercial service airport in my analysis.
Overall, my sample includes 16,142 routes (airport A to airport B) and 2,822,086 itineraries
(flight from A to B with specific information of time, connection node, operation airline(s) and
airfare(s)). Flights are operated by 45 different airline companies, among which 11 companies show
some hidden city opportunities lying in the itineraries they operate.
To the best of my knowledge, there is no official definition of hidden city opportunity in existing
literatures. GAO (2001) define that “a hidden-city ticketing opportunity exists for business travelers
if the difference in airfares between the hub market and the spoke airport was $100 or more, and for
Liu: Hidden City Ticketing 18
leisure passengers if the difference in airfares was $50 or more”. In this paper, I have constructed
two intuitive definitions of hidden city opportunity myself and listed below.
Definition 1 Hidden city opportunity exists if the cheapest non-stop ticket of that itinerary is still
more expensive than some indirect flight ticket with the direct destination as a connection node.
Definition 2 Hidden city opportunity exists if the non-stop ticket is more expensive than some
indirect flight ticket which shares exactly the same first segment of that itinerary.
The example being illustrated at the beginning of this paper belongs to the second scenario.
And the second definition is also the one being defined in Wang & Ye (2016).
According to the daily flights data I have collected, these two definitions show similar magnitude
with respect to hidden city opportunities. For example, among all the itineraries, the first definition
indicates a total of 366,754 (13.00%) flights and 1,095 (6.78%) routes that exhibit possible hidden
city opportunities. Those amounts of Definition 2 are 394,544 (13.98%) flights and 1,316 (8.15%)
routes respectively. This magnitude is slightly smaller compared to the findings in GAO (2001),
in which the authors find that among the selected markets for six major U.S. passenger airlines
in their data, 17% provided such opportunities. Table 1 shows the top 10 origin-destination pairs
with most hidden city opportunities, which are the same under both definitions.
Table 1 Top 10 Origin-Destination pairs with most hidden city itineraries
Popularity Origin Destination # of Itineraries % under Def.1 % under Def.2
1 ISP PHL 11105 3.03% 2.81%
2 SRQ CLT 8590 2.34% 2.18%
3 CAK CLT 5948 1.62% 1.51%
4 GRR ORD 5733 1.56% 1.45%
5 MSN ORD 5640 1.54% 1.43%
6 XNA ORD 5529 1.51% 1.40%
7 COS DEN 4000 1.09% 1.01%
8 FSD ORD 3665 1.00% 0.93%
9 CAE CLT 3659 1.00% 0.93%
10 ORF CLT 3540 0.97% 0.90%
Furthermore, the maximum payment reduction would be as large as 89.57% if hidden city tick-
eting is allowed. Table 2 shows the top 10 origin-destination pairs with the largest price differences,
which are slightly different under both definitions. These statistics help reveal the fact that hidden
city ticketing might no longer be negligible nowadays and related research becomes necessary and
valuable.
Liu: Hidden City Ticketing 19
Table 2 Top 10 Origin-Destination pairs with largest price differences
Definition 1 Definition 2
Origin Destination % Saving Origin Destination % Saving
LGA IAH 89.57% LGA IAH 89.57%
CLE IAH 88.49% CLE IAH 88.49%
PHL DTW 87.54% PHL DTW 87.54%
IAH EWR 86.61% MKE MSP 86.65%
IAH IAD 86.36% IAH EWR 86.61%
DTW PHL 86.20% IAH IAD 86.36%
KOA SFO 85.87% DTW PHL 86.20%
SNA SLC 85.46% KOA SFO 85.87%
ICT MSP 85.38% SNA SLC 85.46%
CLE EWR 85.03% ICT MSP 85.38%
Recall that my primary data contains flights operated by 45 different airline companies, among
which 11 companies shown some hidden city opportunities lying in the itineraries they operated.
Table 3 exhibits the amounts of hidden city itineraries of these airlines unber both definitions.
We can see that the three largest airlines: American Airlines, Delta Air Lines and United Airlines
operated more than 99% of those itineraries. This is similar to the findings of Surry (2005), in
which he found that 96% of those hidden city discounts came from American Airlines, Delta Air
Lines, United Airlines and Alaska Airlines. All of them are major hub-and-spoke carriers and apply
a hub-and-spoke network business model.
Table 3 Number of hidden city itineraries of different airlines
Airline IATA Code Def.1: # of Itineraries (%) Def.2: # of Itineraries (%)
American Airlines AA 203096 (55.38%) 210287 (53.30%)
Delta Air Lines DL 93062 (25.38%) 106867 (27.09%)
United Airlines UA 69587 (18.98%) 76175 (19.31%)
Alaska Airlines AS 598 (0.16%) 666 (0.17%)
Hawaiian Airlines HA 221 (0.06%) 221 (0.06%)
Frontier Airlines F9 56 (0.02%) 157 (0.04%)
JetBlue Airways B6 48 (0.01%) 106 (0.03%)
Virgin America VX 29 (0.01%) 36 (0.01%)
Silver Airways 3M 11 (0.00%) 11 (0.00%)
Spirit Airlines NK 8 (0.00%) 11 (0.00%)
Sun Country Airlines SY 7 (0.00%) 7 (0.00%)
A notable exception is Southwest Airlines, where no hidden city opportunity is found in the
itineraries operated by it, and whose fare rules actually do not specifically prohibit the practice of
hidden city ticketing. Since Southwest Airlines is a typical operator of fully-connected network, this
Liu: Hidden City Ticketing 20
finding in the real data is in accordance with my previous proposition that hidden city opportunity
does not exist under fully-connected network structure.
5. Estimation
To estimate the parameters of my model, firstly I retrieve all the ordered triplets (A-B-C) from
my primary dataset. Then, with all the observed information of prices, distances and consumers’
preferences, I choose the parameters of my model to maximize the likelihood of observed airlines’
choices of network structures. In order to deal with this implicit maximum likelihood function, I
have applied global optimization algorithms, more specifically, Pattern Search to solve the MLE
and estimate the parameters.
5.1. Sample Build-up
To build my own sample, the first step is to retrieve ordered triplets (A-B-C) from the 133 busy
commercial service airports of my primary dataset. The triplet needs to satisfy the following three
conditions: 1) it must include direct flight from A to B; 2) it must include direct flight from B to
C; 3) it must include either direct or one-stop indirect flight from A to C using B as the connection
node.
In total, I have obtained 114,635 ordered triplets from my dataset that satisfy the conditions
listed above. Based on the differences in condition 3), I divide them into three different types.
Type I includes only direct flight from A to C with a subsample size of 26,198. To estimate p
ABC
of Type I, I add observed p
AB
and p
BC
up manually. Type II includes only indirect flight from A
to C through B with a subsample size of 61,092. To estimate p
AC
of Type II, I use the observed
p
AB
and assume flights from A to B and A to C share the same price per mile: p
AC
=
p
AB
d
AB
·d
AC
.
Type III includes both direct flight from A to C and indirect flight from A to C through B, with
a subsample size of 27,345. d represents geodesic distance computed based on the longitude and
latitude of the pair-airports provided by Google Maps.
On each route j, assume that θ
j
∼N(µ
j
, σ
2
2
). Recall that each individual i has a time preference
parameter of λ
i
and on each route j, the distribution of consumers’ time preferences satisfies
λ
ij
∼N(θ
j
, σ
2
1
). Therefore, µ
j
measures the dependency of the destination city on business travelers.
Previous literature have constructed several indexes to capture this characteristic. For example,
Borenstein (1989) and Borenstein & Rose (1994) built a tourism index at the MSA level based
on the ratio of hotel income to total personal income. Brueckner et al. (1992) and Stavins (2001)
assumed that the difference in January temperature between origin and destination cities could
Liu: Hidden City Ticketing 21
Figure 6 Business travel index for each airport as the destination city.
serve as a proxy for tourism. Gerardi & Shapiro (2009) segmented their data into “leisure routes”
and “big-city routes” based on the ratio of accommodation earnings to total nonfarm earnings.
In this paper, I have constructed my own index based on Borenstein (2010) and data provided
by TripAdvisor. Borenstein (2010) provides an index of the share of commercial airline travel to
and from cities that is for business purposes, which is based on the 1995 American Travel Survey.
This index was also used as one of the measures in Puller & Taylor (2012) to distinguish between
“leisure” and “mixed” routes. The shortage for this index is that it only includes data for each
state and metropolitan statistical area, while city level data might be a better fit corresponding
to the location of an airport. To solve this problem, I have also collected data from TripAdvisor
(the largest travel site in the world) for each city, and compute the average number of the reviews
of hotels/lodging, vocation rentals, things to do, restaurants, and posts of forum, standardized
by the city population from 2010 census. The underlying assumption is that a larger number of
reviews on TripAdvisor might be an indicator of being more popular among leisure travelers, and
this city-level data together with the indices constructed by Borenstein (2010) should be able to
provide more complete information of the city’s characteristics. After taking exponential of the
opposite of the average number from TripAdvisor’s review data, I compute the mean of that and
the indices from Borenstein (2010) (both state-level and MSA-level) and get µ.
From Figure 6 we can see that the largest µ = 0.7450 belongs to Dallas Fort Worth International
Airport (DFW) in Texas, while Ellison Onizuka Kona International Airport (KOA) on the Island
Liu: Hidden City Ticketing 22
of Hawaii has the smallest µ = 0.0773. In general, places that are more popular among tourists,
such as Orlando, Puerto Rico and Hawaii, get the smaller µ(s). While places such as Dallas, Austin
and Chicago that are more attractive to business travelers have larger µ(s).
5.2. Maximum Likelihood Estimation
Overall, I have a set of 7 parameters: ζ = (δ, C
1
, C
2
, σ
1
, σ
2
, q
h
, q
l
), with δ ∈ [0, 1] as my
parameter of interest, and the others are nuisance parameters. Observed attributes in my
dataset include the prices, distances, and time preference indices on each route: x
i
=
(p
AB,BC,AC,ABC
, d
AB,BC,AC,ABC
, µ
AB,BC,AC,ABC
). And observed decision variable is the airline’s net-
work choices: y
i
∈{F C, HS}.
The maximum likelihood estimation needs to be processed in 2 steps. Firstly, I sample
θ
AB,BC,AC,ABC
from the normal distribution N|
x
i
,σ
2
. Then airline makes a decision to maximize
expected profits:
y
i
= arg max
y∈{F C,HS}
Π(x
i
, y, ζ).
The maximum likelihood estimation problem is therefore:
b
ζ = arg max
ζ
1
n
n
X
i=1
log p(y
i
|x
i
; ζ),
with the probabilistic model as
P r[y
i
= y|x
i
, ζ] = P r
θ∼N |
x
i
,σ
2
[
Π(x
i
, y, ζ, θ) ≥Π(x
i
, ¬y, ζ, θ)
]
.
5.3. Pattern Search
This maximum likelihood estimation is challenging because the likelihood is implicit with a random
sampling in the first step, and the gradient is also difficult to evaluate with respect to ζ. Here I
apply global optimization algorithms to solve this MLE problem. That is, for each ζ
t
, obtain an
estimation of likelihood function:
log p(y
i
|x
i
; ζ
t
) = log P r
θ∼N|
x
i
,σ
2
[
Π(x
i
, y
i
, ζ
t
, θ) ≥ Π(x
i
, ¬y
i
, ζ
t
, θ)
]
≈ log
(
1
M
M
X
m=1
1
[
Π(x
i
, y
i
, ζ
t
, θ
m
) ≥Π(x
i
, ¬y
i
, ζ
t
, θ
m
)
]
)
.
I have tried several global optimization techniques including Pattern Search, Genetic Algorithm,
Simulated Annealing, etc., to get the optimal set of parameters ζ = (δ, C
1
, C
2
, σ
1
, σ
2
, q
h
, q
l
) that
Liu: Hidden City Ticketing 23
maximizes my log likelihood function. It turns out that Pattern Search works best in this case. It
costs the shortest time; It achieves the maximum log likelihood; And it obtains quite similar and
robust results when I change the starting point from δ = 0.1, 0.5 to 0.9.
Pattern Search algorithm fits this problem quite well because firstly, it does not require the
calculation of gradients of the objective function, which are quite difficult to compute in this case.
Secondly, it lends itself to constraints and boundaries. For example, it could deal with the constraint
that 0 < q
l
< q
h
< 1 quite well in this case.
How does the Pattern Search algorithm operate? Pattern search applies polling method (Math-
Works (2018)) to find out the minimum of the objective function. Starting from an initial point,
it firstly generates a pattern of points, typically plus and minus the coordinate directions, times
a mesh size, and center this pattern on the current point. Then, for each point in this pattern,
evaluate the objective function and compare to the evaluation of the current point. If the minimum
objective in the pattern is smaller than the value at the current point, the poll is successful, and
the minimum point found becomes the current point. The mesh size is then doubled in order to
escape from a local minimum. If the poll is not successful, the current point is retained, and the
mesh size is then halved until it falls below a threshold when the iterations stop. Multiple starting
points could be used to insure that a robust minimum point has been reached regardless of the
choice of the initial point.
This algorithm is simple but powerful, provides a robust and straightforward method for global
optimization. It works well for the maximum likelihood function in this paper, which is derivative-
free with constraints and boundaries.
5.4. Estimation Results
The estimation results from Pattern Search are shown in Table 4 below.
Table 4 Results of MLE
log likelihood -0.3023
δ 0.0373
C
1
10.0935
C
2
0.3125
σ
1
0.2094
σ
2
0.7406
q
h
0.7010
q
l
0.1125
Liu: Hidden City Ticketing 24
According to the estimation results, the informed passengers account for around 3.73% of the
whole population. This proportion appeals to be trivial at first glance, but it is not surprising
because those are the travelers who are not only informed of hidden city ticketing, but also exploit-
ing those opportunities, and whose behavior in fact result in affecting the choices made by airlines.
And in the counterfactual analysis section below, I will further show that even a small fraction of
informed passengers will affect airline’s choices of network structures and prices significantly.
In order to derive the confidence interval of my parameter of interest δ, again I apply numerical
approach using bootstrap to find out the standard errors. I run the MLE for 1,000 times, and for
each run, sample the entire data with replacement and construct a data set of equal size. The
sample mean of the 1,000 estimates of the MLE is 0.0296, and the standard error is the sample
standard deviation as 0.0093. We can see that δ is significantly different from zero at 99% confidence
interval.
In Figure 7, I have plotted the log likelihood as a function of δ with all other parameters being
constant at their optimal values. From the figure it is clear that δ = 3.73% is the global maximizer.
Recall that in my theoretical model, I have assumed that there is only one airline serving the three
cities, thus the firm charges monopoly airfares. Liu (2015) also made similar monopoly assumption
in the paper, and corresponding to this assumption, the author refined the data and only paid
attention to the routes with a single carrier operating one or two flights per day. Following this idea,
I also define route AB, BC, AC, or ABC as monopoly if there is only one single carrier providing
services on that route. Refining my sample of ordered triplets according to this condition results in
a subsample size of 36,645, comparing to the total sample size of 114,635 before. Applying the same
estimation algorithm, I have solved the MLE problem again based on the monopoly subsample,
and get an estimation of δ being equal to 0.0303. The result is not significantly different from the
0.0373 we obtain above from the whole sample.
Furthermore, on September 17, 2019, I collected daily flights data again by scraping the tickets
information on Skiplagged webpage with all quotes of October 1, 2019, which was neither a weekend
nor a holiday, and was two weeks (rather than two months) before the departure date. This different
dataset provides a slightly larger estimation of δ being equal to 0.0407, which is still not significantly
different from our previous result. These two analysis provide robustness of my empirical data and
my estimation methodology.
6. Counterfactual Analysis
Based on our previous analysis, given a longer horizon, airlines should be able to adjust their
prices and networks in response to hidden city ticketing, in order to maximize their expected
Liu: Hidden City Ticketing 25
Figure 7 Up: Plot of log likelihood when δ varies from 0 to 1. Below: Plot of log likelihood when δ varies from
0 to 0.1 (zoom in).
profits. To reveal what would be the airline’s optimal joint choices of prices and network structures
when δ changes, and further estimate the possible impacts of hidden city ticketing on welfare
outcomes, I have conducted several counterfactual analysis using numerical approach below. Will
airline companies always suffer from revenue loss with hidden city ticketing? Will hidden city
ticketing always benifit consumers and social welfare? Should government enact regulations to
clearly prohibit or permit this booking ploy? My counterfactual experiments will help shed some
light on those important policy implications.
Basically, assume that the proportion of informed passengers (δ) increases from 0 to 100%, and
airline companies always choose optimal prices under different network structures to maximize
Liu: Hidden City Ticketing 26
their expected profits when δ changes. After obtaining the optimal price bundle p
∗
under different
networks, I compute the surplus of producer, consumer, and society according to our previous
analysis in Section 3. Then I plot producer surplus (blue), consumer surplus (red) and total sur-
plus (black) under fully-connected network (dotted line) and hub-and-spoke network (solid line)
respectively, when δ varies.
6.1. Fully-Connected Network Outperforms Hub-and-Spoke Network
Findings 1 Among all the 114,635 data points (i.e., ordered triplets A-B-C), 75,995 (66.29%) have
expected profits under fully-connected network being always higher than that under hub-and-spoke
network, regardless of the value of δ.
My first finding is that under major cases, fully-connected network creates higher expected
profits for airlines comparing to hub-and-spoke network, regardless of the proportion of informed
passengers. One example would be the ordered triplets MIA→SEA→COS (Miami International
Airport to Seattle-Tacoma International Airport to Colorado Springs Airport). Figure 8 shows the
surplus of producer, consumer, and society with different δ(s). The dotted lines are always horizonal
because according to my model, hidden city ticketing will not affect the welfare outcomes under
fully-connected network structure. It is clear that in this example, the dotted blue line is always
above the solid blue one, regardless of the value of δ, which means that for airlines operating from
Miami International Airport to Colorado Springs Airport, a direct flight always outperforms an
indirect one through Seattle-Tacoma International Airport. This is not surprising because flying
from Miami to Colorado through Seattle is counter intuitive.
When we plot the surplus in Figure 8, there is a pattern of kink, which is not uncommon and also
found in other examples. Digging deep I find what happens at the kink is that airlines keep raising
the price p
ABC
in response to the increasing proportion of informed passengers, δ. Consumers
benefit at first because more and more informed travelers are able to exploit the hidden city
opportunities, pay lower prices and obtain extra utility. However, when the kink point is reached,
p
ABC
hits the magnitude of p
AB
and hidden city opportunities disappear. The informed passengers
can no longer obtain extra utility, while since the new p
ABC
turns out to be higher than the original
price without hidden city ticketing, those passengers flying from A to C through B also get hurt.
This is similar to what is called “detrimental externalities” in Varian (1980), in which the author
also found that sometimes more informed consumers would cause the price paid by uninformed
consumers to increase. This finding also helps confirm the concern mentioned in GAO (2001) that
allowing hidden city ticketing might lead to unintended consequences, including higher prices.
Liu: Hidden City Ticketing 27
10 20 30 40 50 60 70 80 90 100
proportion of informed passengers (%)
200
300
400
500
600
700
800
900
1000
1100
surplus
Producer surplus, FC
Producer surplus, HS
Consumer surplus, FC
Consumer surplus, HS
Total surplus, FC
Total surplus, HS
Figure 8 Surplus for MIA→SEA→COS when δ changes.
6.2. Hub-and-Spoke Network Outperforms Fully-Connected Network
Findings 2 22,551 (19.67%) data points have expected profits under hub-and-spoke network being
always higher than that under fully-connected network, regardless of the value of δ.
Contradict to the previous finding, sometimes the hub-and-spoke network structure always does
a better job achieving higher revenue compared to fully-connected network. One example would
be the ordered triplets CID→DTW→MSN (The Eastern Iowa Airport to Detroit Metropolitan
Airport to Dane County Regional Airport in Madison). Figure 9 shows the surplus of producer,
consumer, and society in this case when δ varies.
We can see that the solid blue line is always above the dotted blue one, regardless of the value
of δ, which means that for airlines flying from The Eastern Iowa Airport to Dane County Regional
Airport in Madison, an indirect flight through Detroit Metropolitan Airport always outperforms a
direct flight. This usually happens when both airports A and C are small, which is exactly what
occurs when you are flying from CID to MSN. In this case, it might be costly for airlines to provide
a direct flight service, especially when compared to the relatively low demand.
Liu: Hidden City Ticketing 28
10 20 30 40 50 60 70 80 90 100
proportion of informed passengers (%)
80
100
120
140
160
180
200
220
240
260
surplus
Producer surplus, FC
Producer surplus, HS
Consumer surplus, FC
Consumer surplus, HS
Total surplus, FC
Total surplus, HS
Figure 9 Surplus for CID→DTW→MSN when δ changes.
6.3. Switch from Hub-and-Spoke Network to Fully-Connected Network
Findings 3 16,089 (14.03%) data points have crossings, which means that airline’s expected prof-
its are higher under hub-and-spoke network when there are less informed passengers, while fully-
connected network becomes more profitable when δ gets large.
A more interesting story lies in the cases remained: hub-and-spoke network structure is more
profitable when δ is small, but becomes gradually outperformed by fully-connected network when
there are more and more informed passengers. In other words, for some specific routes, airlines
have the incentive to switch from one network structure to another, and δ will affect companies’
network choices. This finding could be supported by what we called “dehubbing” phenomenon in
recent years (Berry et al. (2006)). For example, Delta closed its Dallas-Fort Worth International
Airport (DFW) hub in year 2005 and reduced the number of flights at its Cincinnati hub by 26%
in the same year. And Pittsburgh was also downgraded from a hub to a “focus city” by US Airways
in 2004.
One example would be the ordered triplets AUS→JFK→RDU (Austin–Bergstrom International
Airport to JFK to Raleigh–Durham International Airport). Figure 10 shows the surplus of pro-
ducer, consumer, and society in this case when δ varies.
Liu: Hidden City Ticketing 29
10 20 30 40 50 60 70 80 90 100
proportion of informed passengers (%)
150
200
250
300
350
400
450
500
550
600
650
surplus
Producer surplus, FC
Producer surplus, HS
Consumer surplus, FC
Consumer surplus, HS
Total surplus, FC
Total surplus, HS
Figure 10 Surplus for AUS→JFK→RDU when δ changes.
We can see that the solid blue line crosses the dotted blue one at the point when δ is around
6%, which means that when δ is smaller than the threshhold, airline would pursue hub-and-spoke
network structure. While when there are more and more informed passengers and δ crosses the
threshhold, airline has the incentive to switch from the hub-and-spoke network to fully-connected
network, and this decision will also affect both consumer surplus and total surplus dramatically.
In this example, after the airline company making the change, both consumer surplus and total
surplus increase a lot, which refer to the increase from the solid red, black lines to the dotted red,
black lines respectively. But this is not always the case, and we will see more details later in this
paper.
The crossing point varies for different ordered triplets. This is because different routes have differ-
ent characteristics and attract different types of travelers. Some routes would be quite “sensitive”
to hidden city ticketing and airlines operating on those routes would switch from hub-and-spoke
network to fully-connected network when δ is relatively small. Some routes would have operat-
ing airlines changing their network choices only when the amount of informed passengers are
large enough. And we have already known that sometimes airlines will never change to the fully-
connected network (Findings 2), while in other cases they will stick to the fully-connected network
from the very beginning (Findings 1). To have a more complete idea about the impact of different
δ(s) on airlines’ network choices, I can always depict the graph of surplus for every ordered triplet
Liu: Hidden City Ticketing 30
Figure 11 Distribution of crossings when δ changes (pmf)
in my data. However, it is impossible to display all those figures here (recall that I have as many
as 114,635 data points in total). Therefore, in Figure 11 I have plotted the distribution of all the
crossing points when δ changes.
We can see that even a small δ matters. Airlines’ choices can be affected significantly even with
a quite small proportion of informed passengers. For example, airlines would switch from hub-
and-spoke network to fully-connected network on nearly 1,000 routes with only 1% of informed
passengers, and further change their choices on another 900 routes if the proportion increases to
2%. Recall that we have obtained an estimation of δ = 3.73% in Section 5, which appeals to be
trivial at first glance, but in fact, 3% of informed passengers could affect airlines’ choices of network
structures on approximately 2,700 routes (out of 16,089 in my whole sample), and this amount of
routes being affected would increase to around 3,600 when the proportion of informed passengers
increase to 4%. To make this illustration clearer, I have also drawn the cumulative distribution
function of the crossing points when δ varies from 0 to 1, and obtain my next finding from the
following Figure 12.
Findings 4 Airlines have the incentive to switch from hub-and-spoke network to fully-connected
network for half of the routes when there are approximately 10% of informed passengers, and for
75% of the routes when δ is only around 19%.
Recall that after airlines changing their choices of network structures, consumers and the whole
society are not always better off. After comparing the consumer surplus and total surplus before
and after the change for all those 16,089 routes, I am able to further conclude that:
Liu: Hidden City Ticketing 31
Figure 12 Distribution of crossings when δ changes (cdf)
Findings 5 If airlines switch from hub-and-spoke network to fully-connected network, under
11,458 cases (71.22%) consumer surplus is going to increase, and under 11,128 (69.17%) cases
total surplus is going to increase.
In other words, unlike what could be derived from the theoretical model when airlines do not
alter their choices of network structures and airfares in the short run, during a longer horizon,
firms would actively react to the conduct of hidden city ticketing and change their optimal choices.
This will result in different welfare outcomes for producer, consumer, and whole society compared
to the propositions in Section 3. What I have found in my counterfactual analysis is that, during
this process, firms always result in lower expected profits, while consumers and the whole society
are not necessarily better off. Therefore, enacting a simple regulation for prohibiting or permitting
the conduct of hidden city ticketing would be difficult.
7. Discussion
There are some limitations and future questions remained in this paper. Firstly, I have made a
critical assumption in my model that there is only one airline serving the three cities, thus the
firm charges monopoly airfares. The monopoly assumption is not uncommon in airline related
literatures, but some researchers believe that after the deregulation, the US airline industry should
be characterized as being hightly oligopolistic (Shy (2001)). And in GAO (2001), the authors also
find that “hidden city opportunities may arise when a greater amount of competition exists for
travel between spoke communities than on routes to and from hub communities, and where airfares
Liu: Hidden City Ticketing 32
in those markets reflect such competition”. In other words, besides the factors I have raised in my
propositions, competition might be another possible cause of hidden city ticketing, which does not
enter my model under the monopoly assumption. And given competition, besides the cost-saving
effect, another advantage of hub-and-spoke network compared to fully-connected network would
be that airlines could have stronger market power in the hub, which helps them increase the entry
barrier and drive up the prices for the origin-hub passengers. Since there are business travelers
who favor the origin-hub route and appeal to be price-inelastic, this market power of raising prices
could result in higher profits for the hubbing airlines. (Borenstein (1989), Borenstein (1991))
Another interesting question raised by Varian (1980) is that does it pay to be informed? If
this is true, a better way to take this into consideration might be assuming that it is possible to
become fully informed by paying a fixed cost C. Conducting hidden city tickeing is definitely costly.
Passengers are “threatened” by the airline companies and need to “bear some risk” to conduct this
behavior. As I have quoted from the contract of carriage in Section 1, consumers will be penalized if
being caught. And hidden city ticketing might be treated as “unethical” and a breach of the contract
between passengers and the airlines. There are also possible negative externalities such as causing
delays of the other passengers because of waiting and double checking baggages. Furthermore, the
condition of conducting hidden city ticketing is also highly restrictive. For example, if you have
luggage that is not carry-on, you are not able to leave the flight earlier without picking up your
bag. Normally, your checked baggage will be delivered to your final destination directly rather than
to your connection city. Also, you cannot conduct hidden city ticketing for the first segment of
your round-trip. Your second trip will be cancelled if you missed the connection of the first one.
Besides, you might need to bear the risk that you are switched to another flight because of initial
flight being cancelled or overbooked, with the same origin and destination airports, but bypass the
connection city. Therefore, cost will incur to be informed might be a reasonable assumption when
studying hidden city ticketing in the future, while measuring this cost would still be challenging.
Furthermore, airlines claim in the news that in reaction to the booking ploy of hidden city
ticketing, they might choose to charge more on flights, stop offering some flights, and re-calibrate
their no show algorithms. My analysis successfully predicts the increase in airfares of some flights.
But since I have assumed that airline companies are choosing between fully-connected network and
hub-and-spoke network, I do not provide an outside option for airlines to stop offering the flights
for certain routes. Instead of raising the prices of flights to eliminate hidden city ticketing, another
possibility is that the airlines could stop serving those defective routes. This is also another major
concern in GAO (2001) that allowing hidden city ticketing might result in unintended decreasing
service. Including this outside option could help make the analysis more complete, although the
Liu: Hidden City Ticketing 33
Figure 13 Percentage of Passengers Denied Boarding by the U.S. Air Carriers, 1990 to 2019.
magnitude might be difficult to evaluate without a good measure of the costs. Another concern
raised by purchasing hidden city tickets is related to logistics and public-safety. When hidden
city ticketing becomes more popular, airlines might need to re-calibrate their no show algorithms.
They might have the incentive to oversell more, which is an act that could turn problematic
and expensive if the estimates are wrong. Unfortunately, I did not find the dataset of airlines’
oversales. Related statistics provided by United States Department of Transportation are numbers
of passengers boarded and denied boarding by the U.S. Air Carriers. Figure 13 shows the percentage
of passengers being denied boarding by the U.S. Air Carriers because of oversales, both voluntarily
and involuntarily, from year 1990 to 2019.
From Figure 13 we can see a declining trend of percentage of passengers being denied boarding
because of oversales in recent years, which indicates that the concern of possible oversales raised
by hidden city ticketing might be subtle.
8. Conclusion
To conclude, this paper aims at analyzing the possible cause and impact of hidden city ticketing. To
achieve this goal, I have constructed a structural model, collected innovative data, applied global
optimization algorithm to solve the MLE, and conducted counterfactual analysis. I find that hidden
city ticketing occurs only when airline companies are applying a hub-and-spoke network structure.
Liu: Hidden City Ticketing 34
And airlines apply hub-and-spoke network rather than fully-connected network in order to reduce
their operation costs. When airlines are not aware of hidden city ticketing, hence do not alter their
choices of prices and network structures in the short run, we can derive from the theoretical model
that, 1) hidden city ticketing does not necessarily decrease airline’s expected profits, since the lower
price also attracts more passengers to take the flight; 2) consumers are always better off when
hidden city ticketing is allowed; 3) total social welfare always increase when hidden city ticketing
is allowed.
During a longer horizon, firms would actively react to the conduct of hidden city ticketing and
freely change their optimal choices of network structures and airfares. Under this circumstances,
based on the counterfactual analysis I have conducted, I find that 1) to maximize expected profits,
fully-connected network is always better than hub-and-spoke network for some routes (66.29%),
while hub-and-spoke network outperforms fully-connected network for some other routes (19.67%),
regardless of the proportion of informed passengers; 2) for the rest (14.03%) of the cases, airlines’
expected profits are larger under hub-and-spoke network when there are less informed passengers,
while fully-connected network becomes more profitable when more and more passengers starting
to exploit hidden city opportunities; 3) airlines have the incentive to switch from hub-and-spoke
network to fully-connected network for half of the routes when there are approximately 10% of
informed passengers, and for 75% of the routes when informed passengers increase to around 19%;
4) if airlines change their network choices because of hidden city ticketing, firms are suffering from
revenue loss, while consumers are not always better off (28.78% of the cases consumer surplus will
decrease), and total social welfare is not always larger neither (30.83% of the cases total surplus
will decrease). Therefore, enacting a simple regulation for prohibiting or permitting the conduct
of hidden city ticketing would be difficult, because welfare outcome varies route by route.
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