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Steve Puller Anirban Sengupta Steve Wiggins Texas A&M

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1 Steve Puller Anirban Sengupta Steve Wiggins Texas A&M
Testing Theories of Price Dispersion and Scarcity Pricing in the Airline Industry Steve Puller Anirban Sengupta Steve Wiggins Texas A&M Borenstein & Rose – avg diff is 36% of mean

2 American: DFW-LAX All Tickets Sold in 2004Q4
$490 $429 $368 $248 Average rising, but not as discretely at windows, but does look like some lower fares are rarely sold after a 7 or 14 day window hits

3 American: DFW-LAX All Tickets Sold in 2004Q4
Can see bands; even lowest fares sold close to departure

4 Outline Overview of theory Data Tests Implications and future research
Tests turn on comparing pricing in high demand versus low demand flights Evidence supports some scarcity pricing Stronger evidence that ticket characteristics drive price dispersion Implications and future research Later: will want to see if prevalence of (1) vs (2) varies in market structure

5 Two Classes of Theories We Assess
“Scarcity pricing” Airlines have large fixed costs Airline seats are perishable (lose value at departure) Demand is uncertain Dana (1999) & Gale and Holmes (1993) Alternative Theories: Yield Management Ticket restrictions create fences Segment demand to implement second-degree price discrimination Which of these theories is the primary driver of prices? We test between these theories Later: will want to see if prevalence of (1) vs (2) varies in market structure

6 Dana’s (1999) Model with Perishable Goods and Uncertain Demand
Stadium seating example Prices set in advance 2 demand states – High/Low w/ prob=1/2 Heterogeneous consumers arrive & buy cheapest ticket available MC of capacity = $20 Competitive Eqbm: Offer X tickets at $20 Sell w/ pr=1 (in both High & Low) Offer Y tickets at $40 Sell w/ pr=1/2 (only High) Zero profit condition  Price = MC / probability(sale) 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 Dana expands upon previous work by Edward Prescott and Benjamin Eden. MC is *of capacity* He gives specific functional form assumptions, and I won’t mention Eqbm: expected revenue = MC of capacity. 6

7 Predictions of Dana (1999) Ideal setting: Analyst observes multiple realizations of flights with same expected load factor  same offered fares; different transacted fares 7

8 Predictions of Dana (1999) Ideal setting: Analyst observes multiple realizations of flights with same expected load factor  same offered fares; different transacted fares 8

9 Predictions of Dana (1999) Higher mean transacted fares
Ideal setting: Analyst observes multiple realizations of flights with same expected load factor  same offered fares; different transacted fares On flights with higher realized demand… Higher mean transacted fares More price dispersion Larger share of “high priced” tickets Flights with unusually high sales as of x days before departure, will sell more high priced tickets in last x days. 9

10 More Predictions of Dana (1999)
Low priced tickets sell out when demand is high Share of high priced tickets rises On peak flights Near departure Gini will be higher on peak flights

11 Gale & Holmes (1993) Monopoly airline (Mechanism design problem)
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) Prediction: Peak flights have fewer discounted fares, particularly 2-4 weeks before departure

12 Scarcity Pricing Theory Predictions
Off-peak flights sell fewer high-priced seats (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)

13 Yield Management Literature
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 Tickets are allocated with various restrictions, and are priced to maximize yield

14 Ex Ante Fixed Fare Schedules Common to Both Sets of Theories
Price (fare) schedules are set in advance The fare schedule is set by an “airline pricing department” Fares define price for each combination of characteristics (bucket) “Yield Management Department” allocates seats to each bucket Dana: sets of ticket prices chosen ex ante before any demand information realized Gale & Holmes: two types of tickets – advance purchase & spot Yield management: Planning (pricing) department chooses flight schedule (& fare structure). Yield management dept chooses seat allocated to each fare

15 Related Work Using Posted Prices
Examples: McAfee and Velde (2006) Escobari and Gan (2007) Borenstein & Rose Our work uses transaction prices and quantities McAfee & Velde – web scraping from AA, orbitz, etc. Escobari & Gan – Expedia, 228 flights departing 6/22/06

16 Data Use census of transactions for travel 2004Q4 from a major Computer Reservation System (CRS) Represents approx. one-third of tickets sold Includes data from airline sites, on-line sales, travel agent sales Ticket level data include: Origin-Destination Carrier Fare Flight no. Coupon level class of service Dates: Purchase, Departure, and Return Number of seats on plane (OAG) Can calculate flight-level Load Factor Scale up by CRS’s market share for that carrier-citypair. (We will deal with attenuation bias later) More detailed than DB1B Difficult to assess peak-load pricing without information on load factor This CRS serves all 3 major channels of selling tickets – travel agents, online and airlines

17 Data (continued) Also need data on ticket characteristics/restrictions
Use data from another CRS2 that includes restrictions including Refundability and advance-purchase restrictions Travel restrictions (e.g. day of week) Stay restrictions (Minimum and/or maximum) Match each observed transaction to CRS2 based on: Route Carrier Departure Date Fare Keep if fares match within 2 percent - Ensure other restrictions satisfied (e.g. days of advance purchase, days of travel, stay restrictions) Matched 36% of transactions

18 Matched versus Unmatched Sample Means

19 Matched v. Unmatched Fare Distributions

20 Final Ticket Level Data Contain
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 Fare Carrier Route Flight number Flight dates (departure and return) Calculated average load factor At departure At date of purchase Excl Wed-Sun around Thanksgiving, all travel beginning after Dec 22 Exclude first-class, open-jaws, circular trips, Holiday travel, > 4 coupons,

21 Airlines and Routes Almost exclusively HUB airports.

22 1 sd  = .045*.34 = 1.5%  1 sd  = 2.3% 


24 1 sd  = .045*.34 = 1.5% 

25 1 sd  = 2.3% 

26 Illustration of Mismeasurement of Load Factor
Consider 100 seat plane with 75 passengers Suppose our CRS has 1/3 market share Simulate observing each ticket w/ pr=1/3, and “scaling up” our observed # tickets by 3

27 Attenuation Bias in Load Factor Coefficient?
Use When IV with LF tertile, get

28 Empirical Approach to Testing for Scarcity Pricing
Test price rigidities assumption (common to all models) Data generally consistent with assumption Test Predictions of Dana and Gale & Holmes Test whether fares higher on unusually full flights

29 Testing for Price Rigidity: Motivation
Consider Dana’s “stadium pricing” Prices for two “types” of tickets ($20 & $40) Data on all tickets and ticket “type” (perhaps slightly measured with error) Farei = β0 + β1Typei + εi β’s are mean fares, R2≈1 Farei = β0 + β1Typei + β2LoadFactori + εi β2 = 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) Yield management (“type” = fences)

30 Testing for Price Rigidity
Ticket types are “Bins”, each with its owns fare For each route: Log(fare)i = f(Bin Dummiesi * Carrieri, Roundtripi, εi) 72 bin dummies  all possible combinations of Refundable x Travel and/or stay restriction Saturday night stay 9 categories of advance purchase restriction (None, 1 day, 3 day, 5 day, 7 day, 10 day, 14 day, 21 day, 30 day) Ideally would like to have the carriers’ “buckets”. We proxy and call them “bins”




34 Testing for Price Rigidity – R2
Median = 0.84 Mean = 0.78

35 Testing for Price Rigidity – Load Factor
Median = 0.028 Mean = 0.043

36 Testing for Price Rigidity: Summary
Ticket characteristics explain bulk of price variation Controlling for ticket characteristics, Load Factor is associated with slightly higher fares Results largely consistent with price rigidity assumption

37 Testing Dana and Gale/Holmes Quantity Allocation Predictions
These theories make specific predicitons regarding the allocation of ticket types: Share of low-priced tickets is lower in high demand states On-peak flights will have a smaller share discount tickets Off-peak flights will have more discounted advance purchase sales

38 Predictions on Price Dispersion
Describe verbally how we define the EXP LF!! 38

39 Predictions on Price Dispersion

40 Measuring Expected & Realized Load Factors
Expected Load Factor Define Flight No./Day-of-Week (FDOW) Measure mean load factors for 12 weeks for FDOW Sort FDOW into Empty, Medium-Empty, Medium-Full, Full Realized Load Factor Within each category of Expected LF, rank individual flight/departure dates by load factor at departure Separate into 4 groups e.g. AA76 on Mondays… Sorting into thirds is by carrier-route. Emphasize that we can include thru traffic here!! 40

41 Predictions on Price Dispersion

42 Testing Dana and Gale/Holmes: Quantity Allocation Predictions
Theories make specific predictions regarding the allocation of ticket types: Share of low-priced tickets is lower in high demand states On-peak flights will have smaller share of advance purchase/discount sales Need to define “discount” tickets So…will have to do 2 things: 1) define “discount” tickets 2) define peak and off-peak flights 42

43 Define “Discount” Tickets Using Characteristics
High Priced/Refundable Tickets (Group 1) Fully Refundable Few if any restrictions Mean fare = $631 26% of tickets Medium Price/Nonrefundable/Unrestricted Tickets (Group 2) Nonrefundable, but No travel or stay restrictions Mean fare = $440 32% of tickets Low Price/Nonrefundable/Restricted Tickets (Group 3) Nonrefundable Travel and/or stay restrictions Mean fare = $281 42% of tickets 43

44 Dana Compare row totals; then just Group 3 (0-6days) 44

45 Dana 45

46 Gale/Holmes (advance purchase)
27% 27% 32% 29% 35% 31% 46

47 Gale/Holmes (advance purchase)
36% 32% 17% 15% 44% 40% 47







54 Testing Dana, Gale/Holmes, & “Scarcity Pricing”: Price Predictions
Pricing Prediction 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) Generally— Scarcity Pricing would suggest higher average fares during peak times

55 Fare Comparisons by Group: Empty v. Full Flights

56 Dana: Predictions for Price Levels
Stadium Thought experiment 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, …) Then tickets purchased 1 hour before event (T-1) will be sold at higher prices 56

57 Are Fares Higher when a Flight is Getting Unusually Full?
Measuring Load Factor Deviations 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 departure—for all flights on a route 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 Deviation” Similar calculation for “Fare Deviation” 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? 57

58 Comparison Across Carriers (measured in % deviation)
Slopes: American ≈ .17 Others ≈ .08

59 Only Last 3 Days (measured in % deviation)

60 Dispersion in Fares As Approach Departure

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.

62 Conclusions and Ongoing Work
Some evidence consistent with Dana and Gale & Holmes Statistically significant effects on quantities Economically modest—reallocations of 3-7% of seats 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.

63 Interpretation 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.” Barry Smith, Interfaces, 1992 Subproblems: overbooking, discount allocation, traffic management Non-linear, stochastic, mixed integer mathematical problem

64 The End

65 Matching Procedure Match criterion: 2% price range
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 3: If still multiple, match on travel restrictions met Step 4: If still multiple, match on most restrictive stay restrictions met Yielded 36% match rate

66 Delta: Multiple Routes (measured in % deviation)
Slope ≈ 0.08

67 Pricing Practices in Airlines
Tickets purchased in advance typically cheaper Fares can change quickly Saturday night stay discount Minimum stay restrictions (e.g. overnight) Non-refundable tickets have lower fares Last minute “deals” / internet fares One-way tickets cost more than ½ roundtrip Others (we don’t address): Frequent flyer miles Bulk discounts to companies Intentional Overbooking

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