Testing Theories of Price Dispersion and Scarcity Pricing in the
Airline Industry Steve Puller Anirban Sengupta Steve Wiggins Texas
A&M Slide 2 American: DFW-LAX All Tickets Sold in 2004Q4
$490$429 $368 $248 Slide 3 American: DFW-LAX All Tickets Sold in
2004Q4 Slide 4 Outline 1) Overview of theory 2) Data 3) Tests Tests
turn on comparing pricing in high demand versus low demand flights
Tests turn on comparing pricing in high demand versus low demand
flights Evidence supports some scarcity pricing Evidence supports
some scarcity pricing Stronger evidence that ticket characteristics
drive price dispersion Stronger evidence that ticket
characteristics drive price dispersion 4) Implications and future
research Slide 5 Two Classes of Theories We Assess 1) Scarcity
pricing Airlines have large fixed costs Airlines have large fixed
costs Airline seats are perishable (lose value at departure)
Airline seats are perishable (lose value at departure) Demand is
uncertain Demand is uncertain Dana (1999) & Gale and Holmes
(1993) Dana (1999) & Gale and Holmes (1993) 2) Alternative
Theories: Yield Management Ticket restrictions create fences Ticket
restrictions create fences Segment demand to implement
second-degree price discrimination Segment demand to implement
second-degree price discrimination Which of these theories is the
primary driver of prices? Which of these theories is the primary
driver of prices? We test between these theories We test between
these theories Slide 6 Danas (1999) Model with Perishable Goods and
Uncertain Demand Stadium seating example Stadium seating example
Prices set in advance Prices set in advance 2 demand states
High/Low w/ prob=1/2 2 demand states High/Low w/ prob=1/2
Heterogeneous consumers arrive & buy cheapest ticket available
Heterogeneous consumers arrive & buy cheapest ticket available
MC of capacity = $20 MC of capacity = $20 Competitive Eqbm:
Competitive Eqbm: Offer X tickets at $20 Offer X tickets at $20
Sell w/ pr=1 (in both High & Low) Sell w/ pr=1 (in both High
& Low) Offer Y tickets at $40 Offer Y tickets at $40 Sell w/
pr=1/2 (only High) Sell w/ pr=1/2 (only High) Zero profit condition
Price = MC / probability(sale) Zero profit condition Price = MC /
probability(sale) Yields intrafirm price dispersion as a pure
strategy eqbm in a perfectly competitive environment (and monopoly,
oligopoly) Yields intrafirm price dispersion as a pure strategy
eqbm in a perfectly competitive environment (and monopoly,
oligopoly) Do NOT need fences to get price dispersion Do NOT need
fences to get price dispersion Slide 7 Predictions of Dana (1999)
Ideal setting: Analyst observes multiple realizations of flights
with same expected load factor same offered fares; different
transacted fares same offered fares; different transacted fares
Slide 8 Predictions of Dana (1999) Ideal setting: Analyst observes
multiple realizations of flights with same expected load factor
same offered fares; different transacted fares same offered fares;
different transacted fares Slide 9 Predictions of Dana (1999) Ideal
setting: Analyst observes multiple realizations of flights with
same expected load factor same offered fares; different transacted
fares same offered fares; different transacted fares On flights
with higher realized demand 1) Higher mean transacted fares 2) More
price dispersion 3) Larger share of high priced tickets 4) Flights
with unusually high sales as of x days before departure, will sell
more high priced tickets in last x days. Slide 10 More Predictions
of Dana (1999) 1) Low priced tickets sell out when demand is high
2) Share of high priced tickets rises On peak flights On peak
flights Near departure Near departure 4) Gini will be higher on
peak flights Slide 11 Gale & Holmes (1993) Contract on prices
Consumers learn if prefer peak flight Flights Occur Monopoly
airline (Mechanism design problem) 2 flights peak and off-peak
Consumers: Consumers prefer peak or off-peak flight Learn preferred
time just before departure. Vary in time cost of waiting.
Equilibrium: Airline offers discounted advance purchase tickets on
off-peak flight. No advance purchase sales on peak flight.
Consumers self-select (low value of time consumers buy discounted
off-peak tickets) eak flights have fewer discounted fares,
particularly 2-4 weeks before departure Prediction: Peak flights
have fewer discounted fares, particularly 2-4 weeks before
departure Slide 12 Scarcity Pricing Theory Predictions Off-peak
flights sell fewer high-priced seats (both theories) Off-peak
flights sell fewer high-priced seats (both theories) A greater
proportion of seats sold off-peak will be discounted fares (both
theories) A greater proportion of seats sold off-peak will be
discounted fares (both theories) There will be more dispersion in
fares for peak flights (Only Dana) There will be more dispersion in
fares for peak flights (Only Dana) Slide 13 Yield Management
Literature Airline prices are set to charge different prices to
different groups of customers Airline prices are set to charge
different prices to different groups of customers Airline customers
vary in terms of their willingness to pay to avoid restrictions
Airline customers vary in terms of their willingness to pay to
avoid restrictions Tickets are allocated with various restrictions,
and are priced to maximize yield Tickets are allocated with various
restrictions, and are priced to maximize yield Slide 14 Ex Ante
Fixed Fare Schedules Common to Both Sets of Theories Price (fare)
schedules are set in advance Price (fare) schedules are set in
advance The fare schedule is set by an airline pricing department
The fare schedule is set by an airline pricing department Fares
define price for each combination of characteristics (bucket) Fares
define price for each combination of characteristics (bucket) Yield
Management Department allocates seats to each bucket Yield
Management Department allocates seats to each bucket Dana: sets of
ticket prices chosen ex ante before any demand information realized
Dana: sets of ticket prices chosen ex ante before any demand
information realized Gale & Holmes: two types of tickets
advance purchase & spot Gale & Holmes: two types of tickets
advance purchase & spot Yield management: Yield management:
Planning (pricing) department chooses flight schedule (& fare
structure). Planning (pricing) department chooses flight schedule
(& fare structure). Yield management dept chooses seat
allocated to each fare Yield management dept chooses seat allocated
to each fare Slide 15 Related Work Using Posted Prices Examples:
Examples: McAfee and Velde (2006) McAfee and Velde (2006) Escobari
and Gan (2007) Escobari and Gan (2007) Borenstein & Rose
Borenstein & Rose Our work uses transaction prices and
quantities Our work uses transaction prices and quantities Slide 16
Data Use census of transactions for travel 2004Q4 from a major
Computer Reservation System (CRS) Use census of transactions for
travel 2004Q4 from a major Computer Reservation System (CRS)
Represents approx. one-third of tickets sold Represents approx.
one-third of tickets sold Includes data from airline sites, on-line
sales, travel agent sales Includes data from airline sites, on-line
sales, travel agent sales Ticket level data include: Ticket level
data include: Origin-Destination Origin-Destination Carrier Carrier
Fare Fare Flight no. Flight no. Coupon level class of service
Coupon level class of service Dates: Purchase, Departure, and
Return Dates: Purchase, Departure, and Return Number of seats on
plane (OAG) Number of seats on plane (OAG) Can calculate
flight-level Load Factor Can calculate flight-level Load Factor
Scale up by CRSs market share for that carrier-citypair. (We will
deal with attenuation bias later) Scale up by CRSs market share for
that carrier-citypair. (We will deal with attenuation bias later)
More detailed than DB1B More detailed than DB1B Difficult to assess
peak-load pricing without information on load factor Difficult to
assess peak-load pricing without information on load factor Slide
17 Data (continued) Also need data on ticket
characteristics/restrictions Also need data on ticket
characteristics/restrictions Use data from another CRS 2 that
includes restrictions including Use data from another CRS 2 that
includes restrictions including Refundability and advance-purchase
restrictions Refundability and advance-purchase restrictions Travel
restrictions (e.g. day of week) Travel restrictions (e.g. day of
week) Stay restrictions (Minimum and/or maximum) Stay restrictions
(Minimum and/or maximum) Match each observed transaction to CRS 2
based on: Match each observed transaction to CRS 2 based on: Route
Route Carrier Carrier Departure Date Departure Date Fare Fare Keep
if fares match within 2 percent Keep if fares match within 2
percent - E nsure other restrictions satisfied (e.g. days of
advance purchase, days of travel, stay restrictions) - E nsure
other restrictions satisfied (e.g. days of advance purchase, days
of travel, stay restrictions) Matched 36% of transactions Slide 18
Matched versus Unmatched Sample Means Slide 19 Matched v. Unmatched
Fare Distributions Slide 20 Final Ticket Level Data Contain Fare
Fare Carrier Carrier Route Route Flight number Flight number Flight
dates (departure and return) Flight dates (departure and return)
Calculated average load factor Calculated average load factor At
departure At departure At date of purchase At date of purchase
Ticket characteristics Refundability Travel restrictions (e.g. day
of week, length of stay) Stay restrictions (e.g. minimum or max
stay) Booking class Saturday stay-over Round trip and direct
Exclude first-class, open-jaws, circular trips, Holiday travel,
> 4 coupons, Slide 21 Airlines and Routes Slide 22 1 sd
=.045*.34 = 1.5% 1 sd = 2.3% Slide 23 Slide 24 1 sd =.045*.34 =
1.5% Slide 25 1 sd = 2.3% Slide 26 Illustration of Mismeasurement
of Load Factor Consider 100 seat plane with 75 passengers Consider
100 seat plane with 75 passengers Suppose our CRS has 1/3 market
share Suppose our CRS has 1/3 market share Simulate observing each
ticket w/ pr=1/3, and scaling up our observed # tickets by 3
Simulate observing each ticket w/ pr=1/3, and scaling up our
observed # tickets by 3 Slide 27 Attenuation Bias in Load Factor
Coefficient? Use Use Slide 28 Empirical Approach to Testing for
Scarcity Pricing 1)Test price rigidities assumption (common to all
models) Data generally consistent with assumption Data generally
consistent with assumption 2)Test Predictions of Dana and Gale
& Holmes 3)Test whether fares higher on unusually full flights
Slide 29 Testing for Price Rigidity: Motivation Consider Danas
stadium pricing Consider Danas stadium pricing Prices for two types
of tickets ($20 & $40) Prices for two types of tickets ($20
& $40) Data on all tickets and ticket type (perhaps slightly
measured with error) Data on all tickets and ticket type (perhaps
slightly measured with error) Fare i = 0 + 1 Type i + i s are mean
fares, R 2 1 Fare i = 0 + 1 Type i + 2 LoadFactor i + i Fare i = 0
+ 1 Type i + 2 LoadFactor i + i 2 = 0 fare not adjusted to LF
Greater share of $40 seats sold when demand/LF are high Gale &
Holmes (type=advance purchase/not advance purchase) Gale &
Holmes (type=advance purchase/not advance purchase) Yield
management (type = fences) Yield management (type = fences) Slide
30 Testing for Price Rigidity Ticket types are Bins, each with its
owns fare Ticket types are Bins, each with its owns fare For each
route: For each route: Log(fare) i = f(Bin Dummies i * Carrier i,
Roundtrip i, i ) 72 bin dummies all possible combinations of
Refundable x Travel and/or stay restriction x Saturday night stay x
9 categories of advance purchase restriction (None, 1 day, 3 day, 5
day, 7 day, 10 day, 14 day, 21 day, 30 day) Slide 31 Slide 32 Slide
33 Slide 34 Testing for Price Rigidity R 2 Median = 0.84 Mean =
0.78 Slide 35 Testing for Price Rigidity Load Factor Median = 0.028
Mean = 0.043 Slide 36 Testing for Price Rigidity: Summary Ticket
characteristics explain bulk of price variation Ticket
characteristics explain bulk of price variation Controlling for
ticket characteristics, Load Factor is associated with slightly
higher fares Controlling for ticket characteristics, Load Factor is
associated with slightly higher fares Results largely consistent
with price rigidity assumption Results largely consistent with
price rigidity assumption Slide 37 Testing Dana and Gale/Holmes
Quantity Allocation Predictions These theories make specific
predicitons regarding the allocation of ticket types: These
theories make specific predicitons regarding the allocation of
ticket types: 1)Share of low-priced tickets is lower in high demand
states 2)On-peak flights will have a smaller share discount tickets
3)Off-peak flights will have more discounted advance purchase sales
Slide 38 Predictions on Price Dispersion Slide 39 Slide 40
Measuring Expected & Realized Load Factors Expected Load Factor
Expected Load Factor Define Flight No./Day-of-Week (FDOW) Define
Flight No./Day-of-Week (FDOW) Measure mean load factors for 12
weeks for FDOW Measure mean load factors for 12 weeks for FDOW Sort
FDOW into Empty, Medium-Empty, Medium- Full, Full Sort FDOW into
Empty, Medium-Empty, Medium- Full, Full Realized Load Factor
Realized Load Factor Within each category of Expected LF, rank
individual flight/departure dates by load factor at departure
Within each category of Expected LF, rank individual
flight/departure dates by load factor at departure Separate into 4
groups Separate into 4 groups Slide 41 Predictions on Price
Dispersion Slide 42 Testing Dana and Gale/Holmes: Quantity
Allocation Predictions Theories make specific predictions regarding
the allocation of ticket types: Theories make specific predictions
regarding the allocation of ticket types: 1)Share of low-priced
tickets is lower in high demand states 2)On-peak flights will have
smaller share of advance purchase/discount sales Need to define
discount tickets Need to define discount tickets Slide 43 Define
Discount Tickets Using Characteristics High Priced/Refundable
Tickets (Group 1) High Priced/Refundable Tickets (Group 1) Fully
Refundable Fully Refundable Few if any restrictions Few if any
restrictions Mean fare = $631 Mean fare = $631 26% of tickets 26%
of tickets Medium Price/Nonrefundable/Unrestricted Tickets (Group
2) Medium Price/Nonrefundable/Unrestricted Tickets (Group 2)
Nonrefundable, but Nonrefundable, but No travel or stay
restrictions No travel or stay restrictions Mean fare = $440 Mean
fare = $440 32% of tickets 32% of tickets Low
Price/Nonrefundable/Restricted Tickets (Group 3) Low
Price/Nonrefundable/Restricted Tickets (Group 3) Nonrefundable
Nonrefundable Travel and/or stay restrictions Travel and/or stay
restrictions Mean fare = $281 Mean fare = $281 42% of tickets 42%
of tickets Slide 44 Dana Slide 45 Slide 46 Gale/Holmes (advance
purchase) 27% 32% 29% 35% 31% Slide 47 Gale/Holmes (advance
purchase) 36%32% 17% 15% 44%40% Slide 48 Slide 49 Slide 50 Slide 51
Slide 52 Slide 53 Slide 54 Testing Dana, Gale/Holmes, &
Scarcity Pricing: Price Predictions Pricing Prediction Pricing
Prediction Average prices will be higher when flights are full,
particularly near departure (Dana) Average prices will be higher
when flights are full, particularly near departure (Dana) More
advance purchase tickets sold on off- peak flights, and so higher
average fares on peak flights (Gale & Holmes) More advance
purchase tickets sold on off- peak flights, and so higher average
fares on peak flights (Gale & Holmes) Generally Generally
Scarcity Pricing would suggest higher average fares during peak
times Scarcity Pricing would suggest higher average fares during
peak times Slide 55 Fare Comparisons by Group: Empty v. Full
Flights Slide 56 Dana: Predictions for Price Levels Stadium Thought
experiment Stadium Thought experiment Suppose consumers arrive at
different periods before event Suppose consumers arrive at
different periods before event Suppose an unusually higher number
of seats sold 2 or more hours before event (T-2, T-3, ) Suppose an
unusually higher number of seats sold 2 or more hours before event
(T-2, T-3, ) Then tickets purchased 1 hour before event (T-1) will
be sold at higher prices Then tickets purchased 1 hour before event
(T-1) will be sold at higher prices Slide 57 Measuring Load Factor
Deviations Measuring Load Factor Deviations Measure mean load
factor for particular days in advance at the carrier/route/day
prior level Measure mean load factor for particular days in advance
at the carrier/route/day prior level E.g., mean share of seats sold
7 days before departurefor all flights on a route E.g., mean share
of seats sold 7 days before departurefor all flights on a route For
each flight/route/date/day prior, calculate load factor, and
determine % deviation from mean For each flight/route/date/day
prior, calculate load factor, and determine % deviation from mean
(Load factor for flight/date/day prior mean) / mean = (Load factor
for flight/date/day prior mean) / mean = % Load Factor Deviation %
Load Factor Deviation Similar calculation for Fare Deviation
Similar calculation for Fare Deviation Are Fares Higher when a
Flight is Getting Unusually Full? For a ticket bought 7 days before
departure, if the plane is 10% fuller than normal (for a plane 7
days before departure), what % more expensive is the fare? Slide 58
Comparison Across Carriers (measured in % deviation) Slopes:
American.17 Others.08 Slide 59 Only Last 3 Days (measured in %
deviation) Slide 60 Dispersion in Fares As Approach Departure Slide
61 Dispersion vs. Load Factor Note: Kernel regression of
coefficient of variation vs. actual load factor using one-way
tickets on each flight. Obs = carrier-route-flightNo-departure
date. Slide 62 Conclusions and Ongoing Work Some evidence
consistent with Dana and Gale & Holmes Some evidence consistent
with Dana and Gale & Holmes Statistically significant effects
on quantities Statistically significant effects on quantities
Economically modestreallocations of 3-7% of seats Economically
modestreallocations of 3-7% of seats Much stronger evidence that
ticket characteristics drive variation in pricing Much stronger
evidence that ticket characteristics drive variation in pricing
While not ruling out pricing model based on perishable good &
demand uncertainty, suggests that ticket characteristics that
segment consumers play a larger role. While not ruling out pricing
model based on perishable good & demand uncertainty, suggests
that ticket characteristics that segment consumers play a larger
role. Slide 63 Interpretation Actual airline decision is a complex
OR problem Actual airline decision is a complex OR problem To solve
the system-wide yield-management problem would require
approximately 250 million decision variables. Because this
mathematical programming formulation is intractable, American
Airlines Decision Technologies has developed a series of operations
research models. These models effectively reduce the large problem
to three much smaller and far more manageable subproblems while
still realistically modeling the real-world situation. To solve the
system-wide yield-management problem would require approximately
250 million decision variables. Because this mathematical
programming formulation is intractable, American Airlines Decision
Technologies has developed a series of operations research models.
These models effectively reduce the large problem to three much
smaller and far more manageable subproblems while still
realistically modeling the real-world situation. Barry Smith,
Interfaces, 1992 Barry Smith, Interfaces, 1992 Slide 64 The End
Slide 65 Matching Procedure Match criterion: 2% price range Match
criterion: 2% price range Step 1: Match on Carrier, Date of
Departure (not return), Cabin Class, Price Step 1: Match on
Carrier, Date of Departure (not return), Cabin Class, Price Step 2:
If multiple matches, match on most restrictive advance purchase
requirement met Step 2: If multiple matches, match on most
restrictive advance purchase requirement met Step 3: If still
multiple, match on travel restrictions met Step 3: If still
multiple, match on travel restrictions met Step 4: If still
multiple, match on most restrictive stay restrictions met Step 4:
If still multiple, match on most restrictive stay restrictions met
Yielded 36% match rate Yielded 36% match rate Slide 66 Delta:
Multiple Routes (measured in % deviation) Slope 0.08 Slide 67
Pricing Practices in Airlines 1) Tickets purchased in advance
typically cheaper 2) Fares can change quickly 3) Saturday night
stay discount 4) Minimum stay restrictions (e.g. overnight) 5)
Non-refundable tickets have lower fares 6) Last minute deals /
internet fares 7) One-way tickets cost more than roundtrip Others
(we dont address): 7) Frequent flyer miles 8) Bulk discounts to
companies 9) Intentional Overbooking