Dynamic Pricing, Advance Sales, and Aggregate Demand Learning

Transcription

1 Dynamic Pricing, Advance Sales, and Aggregate Demand Learning in Airlines Department of Economics & Finance The University of Texas-Pan American Duke University November, 2011

2 Outline 1 Introduction Motivation Contribution Preliminary evidence 2 3 equation estimates 4 Dynamic demand estimates with learning estimates Demand shocks 5 6

3 Motivation Contribution Preliminary evidence Motivation: Price dispersion in airlines Figure: Price dispersion in airlines 33 passengers paid 27 different fares, United flight from Chicago to Los Angeles (New York Times) Borenstein and Rose (JPE, 1994): 36% difference. Gerardi and Shapiro (JPE 2009).

4 Motivation Contribution Preliminary evidence Motivation: Price dispersion in airlines Carriers exploit fences such as: Saturday-night-stayover. Advance purchase discounts. Minimum- and maximum-stay. Refundable tickets. Frequent flier miles. Blackouts. Volume discounts. Fare classes (e.g. coach, first class) Three key features in the dynamics of prices and inventories: 1 Airlines offer tickets in advance and unsold tickets expire at departure. 2 Capacity is set in advance. 3 There is aggregate demand uncertainty. Airlines have the most sophisticated pricing systems in the world.

5 Motivation Contribution Preliminary evidence Motivation: Prices as the flight date nears Prices as the flight date nears 500 d Standard Deviation of Fares Average and Average Fares Standard Deviation of Fares Days Prior to Departure Figure: Average and standard deviation of fares

6 Contribution Introduction Motivation Contribution Preliminary evidence 1 Use a unique data set to empirically characterize the adjustment process between prices and sales as the fight date nears. 2 Estimates a dynamic demand and a dynamic supply considering the interaction between the two. 3 Considers agents that can behave dynamically. 4 For a given inventory, prices decrease as there is less time to sell. 5 At a given point, fares increase as inventory decreases. 6 The positive response of prices to unexpected sales is larger than the positive response to anticipated sales. Consistent with aggregate demand learning and price adjustment. 7 Explain within flights price dispersion. Borenstein and Rose (JPE 1994), Gerardi and Shapiro (JPE 2009) explain price dispersion across flights.

7 Preliminary evidence Introduction Motivation Contribution Preliminary evidence Demand learning and price adjustment Fare Fares Demand Shock Load Factor Load Factors and Deman nd Shocks Days Prior to Departure Figure: Fares, load factors, and demand shocks (Delta 1588 ATL-SJC)

8 Construction of the Expedia Least expensive ticket from expedia.com Pick a single day: Thursday, June 22, Controls for systematic peak load pricing. One-way, non-stop, economy-class. Connecting passengers / sophisticated itineraries / legs. Uncertainty in the return portion of the ticket. Saturday-night-stayover / min- and max-stay. Fare classes (e.g. coach, first class). Panel with 228 cross sectional observations (city pairs). Collected every 3 days with 35 observations in time. American, Alaska, Continental, Delta, United and US Airways.

9 equation equation estimates How do prices respond to inventories and days to departure? ln(fare) ijt = α ln(fare) ij,t 1 + γdayadv t + βload ij,t 1 + ν ij + ε ijt. Dynamic panel estimators: Controls for ν ij. Agents behave dynamically. Load ij,t 1 is predetermined: E(Load ij,s 1 ε ijt ) = 0, E(Load ij,s 1 ε ijt ) 0, s t s > t }, ij. Cumulative sales are affected by previous prices.

10 estimates equation estimates Table: Dynamic Pricing Estimates Load treated as: Strictly exogenous Weakly exogenous Estimator: Within Pooled Within Difference System Instruments: t 2 t 3 t 2 t 3 VARIABLES (1) (2) (3) (4) (5) (6) (7) (8) ln(fare) ij,t * 0.948* 0.706* 0.827* 0.788* 0.938* 0.932* (0.030) (0.004) (0.030) (0.045) (0.047) (0.008) (0.020) DayAdvt / * * * * 1.248* 1.763* 1.961* (0.115) (0.349) (0.093) (0.171) (0.257) (0.242) (0.278) (0.671) Load ij,t * 0.106* 0.300* 0.449* 0.482* 0.492* 0.527* (0.066) (0.013) (0.032) (0.052) (0.051) (0.052) (0.134) Serial correlation a (p-value) Sargan b (p-value) Difference Sargan c (p-value) Notes: The dependent variable is ln(fare) ijt. Figures in parentheses for the OLS are White heteroskedasticity-consistent estimates of the asymptotic standard errors, N. For the GMM are the Windmeijer finite-sample corrected standard errors of the GMM two-step estimates. significant at 10%; significant at 5%; significant at 1%. a For the GMM, the null hypothesis is that the errors in the first-difference regression exhibit no second-order serial correlation (valid specification). b The null hypothesis is that the instruments are not correlated with the residuals (valid specification). c The null hypothesis is that the additional instruments used in the levels equations are not correlated with the residuals (valid specification).

11 estimates equation estimates Table: Dynamic Pricing Estimates Instruments: t 2 t 3 t 2 t 3 t 2 t 3 VARIABLES (1) (2) (3) (4) (5) (6) ln(fare) ij,t * 0.938* 0.953* 0.947* 0.951* 0.946* (0.007) (0.018) (0.008) (0.019) (0.008) (0.022) DayAdvt / * 1.923* 1.461* 1.666* 1.547* 1.753* (0.274) (0.618) (0.286) (0.626) (0.294) (0.661) 1 [DayAdv<7] 0.091* 0.090* 0.073* 0.073* (0.019) (0.020) (0.020) (0.020) 1 [DayAdv<14] 0.060* 0.059* 0.037* (0.010) (0.014) (0.011) (0.015) Load ij,t * 0.469* 0.351* 0.390* 0.359* (0.052) (0.120) (0.059) (0.138) (0.061) (0.158) Serial correlation a (p-value) Sargan b (p-value) Difference Sargan c (p-value) Notes: The dependent variable is ln(fare) ijt. Figures in parentheses are the Windmeijer finite-sample corrected standard errors of the GMM two-step estimates. significant at 10%; significant at 5%; significant at 1%. a b c See notes on Table 2. Consistent with Gallego and van Ryzin (MS, 1994), Zhao and Zheng (MS, 2000).

12 Dynamic demand estimates with learning estimates Demand shocks Step 1: Estimate a dynamic demand equation: Load ijt = ρ Load ij,t 1 + φ ln(fare) ijt + δdayadv t + η ij + u ijt. To estimate pricing we do not need models for Load. Dynamic feedback follows Bun and Kiviet (2006). Load ijt = (1+ρ)Load ij,t 1 ρload ij,t 2 +φ ln(fare) ijt +δdayadv t +η ij +u ijt. Load = Expected Load + Unexpected Load: Load ijt = E[Load ijt Load ij,t 1, ln(fare) ij,t 1, DayAdv t, ρ, φ, δ, η ij ] + u ijt. Cumulative bookings = booking curve + demand shocks.

13 Dynamic demand estimates with learning estimates Demand shocks Booking curve: BC ijt = Load ijt Demand shocks: S ijt = Load ijt Load ijt Agents observe previous realizations of Fare and Load when they price or buy. Have their own beliefs: Consistent with rational expectations. Private information and arrival rates implies variance in who buys when. Individuals privately know their valuations and individual demand uncertainty.

14 Dynamic demand estimates with learning estimates Demand shocks Step 2: Estimate a pricing equation with learning: ln(fare) ijt = α ln(fare) ij,t 1 + γdayadv t + β BCBC ij,t 1 + β SS ij,t 1 + ν ij + ε ijt BC ij,t 1 and S ij,t 1 are generated regressors, bootstrap the two-stage process. Serially uncorrelated u ijt means S ij,t 1 cannot be predicted. Identification of demand shocks come the specific flight s demand pattern relative to other flights.

15 Dynamic demand estimates Dynamic demand estimates with learning estimates Demand shocks Table: Dynamic Demand Estimates ln(fare) treated as: Strictly exogenous Weakly exogenous Endogenous Estimator: Pooled Within Difference System System Instruments: t 2 t 3 t 2 t 3 t 2 t 3 VARIABLES (1) (2) (3) (4) (5) (6) (7) (8) Load ij,t * * * * * * * * (0.032) (0.027) (0.025) (0.026) (0.025) (0.025) (0.025) (0.025) ln(fare) ijt * * * * * * * * (0.001) (0.003) (0.007) (0.007) (0.005) (0.005) (0.006) (0.006) DayAdvt / * * * * * * * * (0.020) (0.023) (0.033) (0.030) (0.031) (0.029) (0.032) (0.031) Serial correlation a (p-value) Sargan b (p-value) Difference Sargan c (p-value) Notes: The dependent variable is LOAD ijt. Figures in parentheses for the OLS are White heteroskedasticity-consistent estimates of the asymptotic standard errors, N. For the GMM are the Windmeijer finite-sample corrected standard errors of the GMM two-step estimates. significant at 10%; significant at 5%; significant at 1%. a b c See notes on Table 2.

16 Dynamic demand estimates Dynamic demand estimates with learning estimates Demand shocks Table: Dynamic Demand Estimates ln(fare) treated as: Weakly exogenous Endogenous Instruments: t 2 t 3 t 4 t 2 t 3 t 4 VARIABLES (1) (2) (3) (4) (5) (6) Load ij,t * * * * * * (0.038) (0.038) (0.029) (0.038) (0.038) (0.037) Load ij,t * * * * * * (0.024) (0.023) (0.020) (0.025) (0.024) (0.022) ln(fare) ijt * * * * * * (0.005) (0.005) (0.009) (0.007) (0.006) (0.010) DayAdvt / * * * * * * (0.039) (0.037) (0.047) (0.041) (0.040) (0.052) Serial correlation a (p-value) Sargan b (p-value) Difference Sargan c (p-value) Notes: The dependent variable is LOAD ijt. Figures in parentheses for the OLS are White heteroskedasticity-consistent estimates of the asymptotic standard errors, N. For the GMM are the Windmeijer finite-sample corrected standard errors of the GMM two-step estimates. significant at 10%; significant at 5%; significant at 1%. a b c See notes on Table 2.

17 Dynamic demand estimates with learning estimates Demand shocks Table: Dynamic Pricing with Learning GMM Estimates BC and S from: Table 4, column 8 Table 4, column 6 Instruments: t 2 t 3 t 2 t 3 t 2 t 3 t 2 t 3 t 2 t 3 VARIABLES (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) ln(fare) ij,t * 0.966* 0.971* 0.965* 0.995* 0.987* 0.992* 0.985* 0.987* 0.979* (0.006) (0.010) (0.006) (0.011) (0.007) (0.011) (0.007) (0.010) (0.009) (0.013) DayAdvt / (0.254) (0.361) (0.252) (0.407) (0.266) (0.409) (0.290) (0.369) (0.366) (0.455) 1 [DayAdv<7] 0.068* 0.068* 0.065* 0.065* 0.074* 0.075* (0.020) (0.018) (0.018) (0.018) (0.018) (0.019) 1 [DayAdv<14] 0.056* 0.053* 0.056* 0.054* 0.048* 0.046* (0.010) (0.010) (0.010) (0.010) (0.009) (0.012) BC ij,t * 0.260* 0.226* 0.272* (0.043) (0.067) (0.0430) (0.076) (0.053) (0.076) (0.047) (0.068) (0.060) (0.093) S ij,t * 0.668* 0.627* 0.658* 0.537* 0.573* 0.462* 0.488* 1.074* 1.140* (0.102) (0.130) (0.102) (0.136) (0.106) (0.141) (0.150) (0.165) (0.219) (0.284) S ij,t 1 AA (0.275) (0.247) S ij,t 1 DayAdvt / (3.948) (4.868) Serial correlation a (p-value) Sargan b (p-value) Difference Sargan c (p-value) H 0 : β BC = β d S (p-value) Notes: The dependent variable is ln(fare) ijt. BC and S for the first two columns based on column 8, Table 4. For columns 3 through 8 based on column 6, Table 4. The figures in parentheses in columns 1 through 4 are the Windmeijer finite-sample corrected standard errors of the GMM two-step estimates. For columns 5 through 8 are bootstrap standard errors based on the two-step procedure, 500 replications and clustered by flight. significant at 10%; significant at 5%; significant at 1%. a b c See notes on Table 2. d The null hypothesis is that coefficients on expected and on unexpected sales (demand shocks) are the same.

18 Demand shocks Introduction Dynamic demand estimates with learning estimates Demand shocks Demand learning and price adjustment Fare Fares Demand Shock Load Factor Load Factors and Deman nd Shocks Days Prior to Departure Figure: Fares, load factors, and demand shocks (Delta 1588 ATL-SJC)

19 Introduction Effect of competition. One-way none-stop tickets. φ = Load ln(fare)rt. ln(fare) rt ln(fare) ow Load The estimation is also capturing = φ if ln(fare)rt = 1, ln(fare) rt ln(fare) ow which is the case when the round-trip price is always two times the one-way price. Intertemporal price discrimination. Other sources of price dispersion.

20 Introduction Dynamics of prices and sales as the departure date nears are jointly characterized by a dynamic supply and a dynamic demand. Consumers and sellers are allowed to behave dynamically (form expectations about sales and prices). Prices increase as there is more time to sell and as inventory decreases. Prices depend on expected demand. Prices respond differently to expected (booking curve) and unexpected bookings (demand shocks). Consistent with aggregate demand learning and price adjustment. Learning is more important close to departure.

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