Slide 1

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