Testing Theories of Price Dispersion and Scarcity Pricing in the Airline Industry

1. Testing Theories of Price Dispersion and Scarcity Pricing in the Airline Industry Steve Puller Anirban Sengupta Steve Wiggins Texas A&M

2. American: DFW-LAX All Tickets Sold in 2004Q4 $490 $429 $248 $368

3. American: DFW-LAX All Tickets Sold in 2004Q4

4. Outline • Overview of theory • Data • Tests • 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

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

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

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

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

9. Predictions of Dana (1999) 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.

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. Contract on prices Flights Occur Consumers learn if prefer peak flight Gale & Holmes (1993) 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 SchedulesCommon 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 pricesand quantities

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

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. Fare Carrier Route Flight number Flight dates (departure and return) Calculated average load factor At departure 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 Final Ticket Level Data Contain Exclude first-class, open-jaws, circular trips, Holiday travel, > 4 coupons,

21. Airlines and Routes

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

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 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)

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

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

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

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

44. Dana

45. Dana

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

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