The Effectiveness of Price Discrimination
in the Airline Industry
Leonardo Rezende (PUC-Rio)
Fábio Roitman (PUC-Rio and BNDES)
This version: July 20, 2014
Abstract
We study price discrimination in the Brazilian airline market using a dataset that
contains information on consumer characteristics that are expected to correlate with
willingness to pay but are not directly observable to airlines, such as the passenger’s
income. This allows us to investigate the effectiveness of price discrimination practices
by airlines, decomposing the effect of an observable characteristic on price into a direct
and an informational effect. For instance, we find that when purchasing a ticket one
week later, consumers in our sample are willing to pay on average US$ 17 more, but
airlines charge US$ 33 more, since late purchases correlate with higher income and
traveling for business. We also perform a tentative analysis of the welfare effects of
price discrimination. Our estimates suggest that in our setting price discrimination on
average benefits consumers.
Keywords: Price discrimination; Air transportation.
Field: Applied Microeconomics.
JEL codes: L11; L93.
Preliminary. Please do not quote.
1. Introduction
Economy class tickets for flight 3909 from Rio de Janeiro to São Paulo in
August 24, 2012 had prices ranging from R$ 129 to R$ 989. This is an example of the
extreme dispersion in airline pricing (Borenstein and Rose, 1994). Since airline tickets
cannot be resold, this dispersion may reflect price discrimination strategies by the
airline companies.
In this paper, we seek to investigate the effectiveness of price discrimination by
exploring a data set that allows us to observe consumer attributes that are not directly
observable by airline companies. If there are other attributes that are visible to the
airline, such as the timing of the ticket purchase, that are correlated with unobserved
attributes, the airline may price discriminate in a way that seeks to capture both the
direct effect of the attribute and the implicit information it contains. Our hope is to
devise a method that decomposes the two effects.
We provide a stylized model of a profit-maximizing monopolist that faces a
linear demand and uncertainty about consumer willingness to pay. We show that if the
expectation of the willingness to pay is linear, then it is possible to estimate two sets of
parameters: those that describe how attributes affect the expected willingness to pay
from the point of view of the airline, and those that affect the true willingness to pay
based on the data. Comparing these two sets allows us to better understand how price
discrimination works.
As we employ a very stylized (but fully structural) model for estimation, it is
possible to perform some counterfactual exercises. We report some preliminary
calculation of what would be counterfactual pricing decisions if price discrimination
was restricted.
Since this is a very preliminary work, all our findings, and certainly the
counterfactual calculations, have to be taken with a grain of salt. For example, to
simplify our analysis, we assume each airline operates as a monopolist, such as in
Lazarev (2012). Contrary to him, however, in most of the routes in our data there are
several airlines operating, and presumably competing to some extent with each other.
This mismatch may be a problem if price dispersion increases (Borenstein and Rose,
1994) or decreases (Gerardi and Shapiro, 2009) with competition. To account for that,
we restrict attention to a sample of markets with similar degrees of concentration.
Another simplifying assumption is that we do not account for the possibility of
scarcity pricing (Dana, 1999; Gale and Holmes, 1993), either explicitly or implicitly. In
our framework, the marginal cost of a ticket in an airplane is constant, and the pricing
decision is static.
Our work at this point is silent about whether price dispersion is due to price
discrimination or scarcity pricing (Puller, Sengupta and Wiggins, 2009). Our task is to
investigate to what extent the observed price discrimination, that is, how prices correlate
with visible attributes of the trade, is effective in capturing variation in consumer
characteristics not directly visible by the airline. That connection is consistent with a
model of price discrimination, but may be consistent with other theories (Escobari and
Gan, 2007; Puller, Sengupta and Wiggins, 2009).
The paper is organized as follows. The next section describes the dataset we use
and provides some descriptive statistics. Section 3 describes the model we propose and
section 4 discusses the estimation strategy. The main findings are presented in section 5.
Section 6 presents a welfare evaluation of counterfactual restrictions on price
discrimination. We conclude in section 7 with a discussion of some extensions of the
analysis we plan to do in the future.
2. Data
2.1. Data Sources
The sample used in this paper is a survey of airline passengers in Brazil flying in
July and August, 2009. The survey has been conducted by the Fundação Instituto de
Pesquisas Econômicas (FIPE) and the data has been used previously in McKinsey &
Co. (2010) to describe airport utilization in Brazil. To our knowledge, we are the first to
use the sample to study airline ticket pricing.
The dataset contains information on flight characteristics, the price paid for the
ticket, when the ticket was purchased, and also individual characteristics of the
passenger that may affect his or her willingness to pay that are not directly observable
by the airline company. This is the unique feature of the data that we seek to exploit in
this paper.
The survey interviewed passengers in 32 Brazilian airports. The number of
interviewees in a route was proportional to the universe of air travel in the route.
Interviews were uniformly distributed over time and days of the week available for each
desired route.
The sample used is formed by passengers flying non-stop between two Brazilian
airports. For reasons explained below, we restrict attention to passengers in 43 large
routes. Here and elsewhere in the paper, we define a route as a pair of airports, and do
not distinguish between directions.
We complement this database with information obtained from Agência Nacional
de Aviação Civil (ANAC, the regulatory agency) and Instituto Tecnológico de
Aeronáutica (ITA). From ANAC we collected flight occupancy ratios, route distances
and fuel consumption. From ITA we obtained data on airport utilization.
2.2. Descriptive Statistics
Our sample contains data on 9850 passengers flying through 43 routes. We have
more observations on routes with more passenger traffic. For instance, there are 1057
observations on Brazil's busiest route, between São Paulo (Congonhas) and Rio de
Janeiro (Santos Dumont). Since interviews were distributed over time within a period of
one month, we have data on passengers flying on 4523 distinct flights. In 51% of these
flights, we observe a single passenger in our sample.
Table 1 below presents descriptive statistics of the variables we use in our
analysis. On average, tickets are bought one week in advance and price is R$ 316, or
US$ 166 at the exchange rate at that time. Average stated monthly income is R$ 4731,
or US$ 2490.
Figure 1 illustrates the dispersion of prices practiced by the same airline
company in the same route. We picked the airline-route pair over which we had most
observations, flights from Gol Linhas Aéreas between São Paulo (Congonhas) and Rio
de Janeiro (Santos Dumont).
We also computed the Gini coefficient for price dispersion within each airlineroute pair. Considering the 31 pairs with more than 100 observations in our sample, we
obtain a median Gini coefficient of 0.23, slightly higher but still similar to estimates for
the US market. Borenstein and Rose (1994) and Gerardi and Shapiro (2009) report 0.18
and 0.22, respectively.
In order to describe statistical relationships between variables in our data, table 2
presents regressions that show how (log) prices depend on consumer characteristics that
are not observable by the airline: (log) income and a dummy of whether the ticket was
Table 1: Descriptive statistics
Variable
Definition
price
income
employer
time of purchase
distance
Ticket price, in R$
Monthly per capita income, in R$
Dummy indicating the ticket is paid by the employer
Number of weeks between the purchase and the flight
Distance between the airports, in kilometres
Dummy indicating Guarulhos is one of the airports in the
Guarulhos
route
Galeão
Dummy indicating Galeão is one of the airports in the route
Dummy indicating the flight occurs on a Tuesday,
peak day
Wednesday or Thursday
Dummy indicating the flight departs between 7am and 10am
peak time
or 5pm and 8 pm
fuel
Average fuel consumption in the route, in 1000 litres
saturation
Sum of 4 dummy variables that indicate airport saturation
Note: 9850 observations.
Mean
Standard
deviation
316
4731
0.53
1.17
832
163
5821
0.50
1.43
487
0.24
0.43
0.20
0.40
0.44
0.50
0.42
0.49
4.30
1.83
1.87
1.08
Figure 1: Histogram of Gol prices in Congonhas –Santos Dumont route
.3
Fraction
.2
.1
0
0
200
Note: 584 observations.
400
600
price (R$)
800
1000
paid by the employer (employer). Both coefficients are positive and statistically
significant, and robust to controlling for various alternative sources of variation. Our
aim when we control for flight occupancy rate is to indicate that this relationship is not
due (or at least not only due) to scarcity pricing1.
Table 2: Descriptive regressions
Dependent variable: log(price)
(1)
0.036
(0.006)
0.324
(0.013)
log(income)
employer
(2)
0.036
(0.006)
0.319
(0.013)
time of purchase
occupancy rate
(3)
0.036
(0.006)
0.204
(0.013)
-0.126
(0.004)
(4)
0.035
(0.006)
0.206
(0.013)
-0.102
(0.007)
0.209
(0.045)
Yes
Yes
Yes
(5)
0.029
(0.007)
0.199
(0.016)
-0.091
(0.010)
0.276
(0.069)
Day of the week dummies (6)
Yes
Yes
Time of the day dummies (11)
Yes
Yes
Route-airline fixed effects (126)
Yes
Yes
Yes
Flight fixed effects (2059)
Yes
Constant
Yes
Yes
Yes
Yes
Yes
Observations
6970
6970
6970
6970
6970
Adjusted R²
0.297
0.297
0.383
0.385
0.407
Notes: (1) Heteroscedasticity-robust standard deviation in parentheses. (2) There are at least two
observations in each flight. (3) Each time of the day dummy indicates an interval of two hours.
3. Model
We describe demand for an airline ticket by the distribution of an unobserved
random variable
, the willingness to pay of a randomly chosen customer for that
ticket. We assume that a customer makes the binary decision between buying the ticket
or not depending on whether
≥ , where
is the price of the ticket and
is the
customer-specific willingness to pay.
The willingness to pay
variables
and
associated with flight, route, time of purchase and/or consumer
characteristics that correlate with
that determine
1
is not directly observed, but we observe two sets of
. The variables in
are the observable variables
; the objective of our analysis is to estimate
|
. Not all
Ideally, one wishes to control for occupancy rate at the time of the ticket purchase. We do not have this
information. Our occupancy rate variable is a proxy combining the time of purchase and the occupancy
rate at the time of the departure, assuming seats fill up according to the empirical distribution of purchase
times we observe within each route.
components of
are observable by the airline at the moment of pricing.
is the set of
characteristics that are observed and used by the airline company when determining
price. We assume that
are the determinants of
that is, in the presence of ,
| ,
=
∗
|
;
. However, as the airline
may be useful to predict
be the marginal cost of the flight ticket. Based on
pricing decision is to charge price
where
|
would be redundant to predict
does not directly observe , variables in
Let
in the sense that
∈
is the distribution of
−
1−
|
conditional on
and
|
∗
.
and
, the airline
is the price that maximizes
the expected profits for that particular seat. By considering the pricing decision for each
seat in isolation, we abstract away from explicitly modeling scarcity pricing or
competition across airlines in order to concentrate on price discrimination practices
based on the informational relationship between ,
and
.
To proceed, we assume the conditional expectations of
are linear:
|
and
|
with respect to
and
=
=
.
Similarly, we assume the marginal cost is a linear function of a vector of
covariates !:
−
= !". Our objective is to estimate ,
and ".
We rely on a simple distributional assumption for
| ~% − ,
, where
| . We assume that
is a dispersion parameter to be estimated. This is
equivalent to assuming that the airline faces a linear demand, conditional on the
information it has about consumer willingness to pay.
Under these assumptions, the optimal choice of pricing is
∗
− '(
+ + !" ⁄2 '( − ≤
=&
./ ' 0 1230 + '(
− !" ≥ 3 − !" ≤ 3
− !" ≤ −
For a market with intermediate values of expected willingness to pay compared
with marginal cost, the optimal price is simply the monopoly price, the average between
the marginal cost !" and the choke price
+
. When the expected willingness to
pay is too large compared with marginal cost, the airline prefers to charge a price that
guarantees the ticket is sold. Conversely, if willingness to pay does not cover cost, the
optimal price is higher than the choke price, to prevent the ticket from being bought.
4. Estimation
We estimate our model using a two-step procedure.
4.1. First Step
In the first step, we estimate a pricing equation using nonlinear least squares.
Our linear demand monopoly pricing model predicts that prices of the tickets that are
sold depend on parameters and attributes according to the following expression:
, !, , ",
∗
− '(
+ + !" ⁄2'( − ≤
=4
− !" ≥ 3
− !" ≤ 3
(recall that the ticket is not sold if the airline decides to charge a price above
We estimate , " and
that minimize prediction squared error 5 −
∗
+ ).
7
, !, , ",
6 .
4.2. Second Step
In the second step, we obtain
, the coefficients that describe the expected
willingness to pay with respect to its determinants. We use the estimates of
in the
first step,
|
and
to recover .
Recall that we are assuming that conditional expectations are linear (
|
and
|
=
. From these relationships we obtain the following proposition:
8
Proposition:
Proof: Let 9 =
9=
8
) and that an exclusion restriction is valid:
−
=
+:
8
| ,
8
+0=
8
=
−
=
, so
8
8
|
8
and : =
9| ,
+9
=
−
8
| ,
=
=
| . By the exclusion restriction,
9 = 0 . We then have
+0 □
This is a linear set of equations that must be valid in population. We employ it to
estimate
directly as follows:
If the number of parameters in
to-one linear mapping between
linear equations for
and
and
are the same, this is (generically) a one-
. In this case we simply solve the system of
, plugging in the first step estimates of
8
covariance estimates for
and
If the number of parameters in
8
and sample variance-
.
is larger (equivalently, if
has more variables
than ), this is a system of equations with more equations than unknowns. All equations
are satisfied in population by the true value of . In this case our estimate of
8
8
8 16 5 >
8
8 16
<− >
<− >
'.= 5 >
< 9
is
where our plug-in estimates in the right-hand side are as before.
5. Empirical Results
Since our model describes pricing decisions of a monopolist, ideally one would
like to circumscribe the empirical analysis to (isolated) routes with a single operating
airline, as in Lazarev (2012). Unfortunately this is not feasible, as the survey design did
not focus on monopoly routes. As a feasible alternative to control for market
concentration heterogeneity, we selected the 43 routes that meet the following criteria:
(i) presence of the two largest airline companies (Tam and Gol); (ii) at least one more
carrier. Our selection includes the 10 domestic routes with largest traffic in 2009.
We need to specify three sets of regressors:
, the attributes that determine
willingness to pay; , the attributes the airline uses to predict willingness to pay; and !,
the attributes that affect cost. Partition
that
7
=
7
. The variables in
?
and
into
=
?
,
7
and
=
?
,
7
so
are consumer attributes that affect willingness to pay
?
but the airline does not directly observe. The variables in
are used by the airline to
determine pricing; these variables do not directly affect willingness to pay.
In our sample we observe the reported income of the passenger and whether the
trip was paid by the employer. These variables are expected to have a positive impact on
willingness to pay, but are not observable by the airlines at the level of individual
customers. These are the variables included in the vector
The vector
7
, which is equal to
7
?
.
, is formed by variables observed by the
airline that directly affect both prices and willingness to pay. We included in
7
: route
distance, dummies for two particular airports2, a dummy for flight on a peak day3,
another dummy for flight on rush hour4 and time of purchase.
The variables in ! are the ones that affect cost. There are two variables in !: the
average fuel consumption in the route and airport saturation, which is defined as the
sum of four dummy variables that indicate saturation of the airports in the route.
We report results of two econometric specifications of our model that differ in
the definition of
?
. These variables, despite not directly affecting willingness to pay,
are used by the airline when determining price. In our first specification, we use two
variables in
?
: the average passenger income in the route and the proportion of trips in
the route paid by the employer. These variables are clearly correlated with the variables
in
?
, since the former are averages over routes of the latter. Therefore they would be
valid in our framework, if we assume they are observable by the airlines. This is
reasonable, since firms are likely to be well informed about the distribution of consumer
characteristics in each route, while still uninformed about which consumer is which at
the time of trade.
In our second specification, we use city dummies as the components of
?
. This
is a somewhat conservative choice: these variables are certainly within the relevant
information set of the airlines. On the other hand, the exclusion restriction that
?
should not directly affect willingness to pay is likely to be invalid, and for that reason
the first specification is our preferred one.
Our main estimates are presented in Table 3. In our preferred specification (1),
we find positive and statistically significant effects for both components of the
?
vector on the expected willingness to pay from the point of view of the airline. We also
find effects that are significant and with the expected sign for distance, undesirable
airports, rush hour flights and time of purchase. The coefficients of cost drivers have the
expected sign, but the effect of fuel expense is not significant. We suspect this is due to
collinearity with distance. Our estimate for
is R$113, around US$ 60. This means our
best fit is a model where the consumer willingness to pay, conditional on the
information of the airline company, is uniformly distributed in a range of US$ 120.
2
Guarulhos (São Paulo) and Galeão (Rio de Janeiro) are airports located far from city centers, and
presumably are less desirable than alternative airports within each city.
3
A dummy for flight departing on Tuesday, Wednesday or Thursday.
4
A dummy for flight departing between 7am and 10am or 5pm and 8pm.
Table 3: Estimated parameters - main results
Specification 1
standard
coefficient
error
Specification 2
standard
coefficient
error
Panel A: first-stage estimates
?
log(mean income by route)
employer by route
São Paulo
Campinas
Rio de Janeiro
Belo Horizonte
Curitiba
Porto Alegre
Brasília
Salvador
Recife
7 distance
Guarulhos
Galeão
peak day
peak time
time of purchase
constant
! fuel
saturation
153.49
346.95
(26.65)
(37.80)
0.214
-46.83
-23.23
6.14
9.64
-61.85
-1182.3
6.31
44.02
113.61
(0.018)
(7.03)
(7.96)
(4.07)
(4.11)
(2.20)
(201.9)
(3.72)
(4.09)
(21.52)
97.09
-87.94
-24.77
-18.99
-18.64
-12.65
59.90
-1.32
29.37
0.120
-119.91
-16.55
4.76
12.08
-50.04
343.1
11.88
-5.54
113.16
(9.21)
(17.22)
(14.69)
(10.05)
(10.73)
(11.90)
(9.57)
(10.66)
(9.34)
(0.015)
(12.42)
(20.61)
(3.72)
(4.07)
(6.30)
(21.4)
(84.56)
(71.01)
(20.59)
Panel B: second-stage estimates
?
log(income)
202.99
(40.92)
243.22
(44.12)
employer
274.99
(45.55)
248.19
(75.00)
7 distance
0.250
(0.016)
0.243
(0.016)
Guarulhos
-24.50
(8.87)
4.39
(15.21)
Galeão
-29.49
(9.15)
-55.32
(10.15)
peak day
-27.65
(7.70)
-24.65
(10.26)
peak time
-22.33
(6.40)
-23.48
(9.78)
time of purchase
-32.10
(4.40)
-20.87
(8.51)
constant
-1516.2
(304.9)
-1814.8
(355.9)
Notes: (1) 9850 observations. (2) Standard errors are bootstrap standard errors
from 100 resamplings.
Panel B presents our estimates for
, the implied effect of the variables we
observe (but the airline does not necessarily observe). All coefficients are statistically
significant. Within this framework, comparing the magnitude of
and
for the same
attribute allows us to identify two effects on willingness to pay: the direct effect of the
attribute on willingness to pay, captured by
, and the informational effect of the
attribute: the effect caused by the fact that the airline uses the attribute to make an
inference about unobserved characteristics that correlate with it. This effect corresponds
to the difference between
and .
Our estimates for time of purchase show that if a consumer buys a ticket one
week in advance, airlines infer that his or her expected willingness to pay is R$ 62
(approximately US$ 33) less than anticipated. Half of it (R$32 or US$ 17) is the direct
effect: early buyers are willing to pay less for the ticket. The other half is the
information effect: passengers that buy tickets on short notice tend to have high income
and/or have the tickets paid by the employer, and airlines use this correlation to price
discriminate across these unobserved attributes.
Similar effects are also found in the case of flights using the Guarulhos airport.
In the case of the rush hour flights, our estimates suggest that the direct and the
information effect are both present, but operate in opposite directions: the informative
effect is positive (R$ 32 or US$ 17), again reasonable because passengers during rush
hour are more likely to be traveling for business reasons. The direct effect is negative:
passengers themselves do not like to travel during rush hours, and are willing to pay R$
22 or US$ 12 less in that case.
Table 3 also reports our estimates for specification 2. While point estimates
change, the findings we discuss above hold qualitatively, with the exception of those
related to Guarulhos airport. The estimates related to cost are much less precise in this
specification, probably because of the correlation with the city dummies in
Surprisingly, our estimate for
?
.
is virtually identical in both specifications.
In specification 1 in table 3, we assume airlines do not observe income and
whether the ticket was paid by the employer at the level of individual buyers, but they
do observe the average values of these variables in each route. If this is true, airlines
would explore variation of these variables between routes to price discriminate. On the
other hand, if the airlines knew how the distribution of consumer attributes vary over
days of the week, then they would wish to price discriminate across days of the week as
well. Therefore, by varying our assumption about what firms observe, we can
investigate the types of price discrimination strategies they are using.
In table 4 we rerun specification 1 using alternative assumptions about how
informed airlines are about consumer attributes. We find that if we assume that the
information about consumer attributes is finer, estimated coefficients are similar.
Compared to the estimates in Table 3, the coefficients in
consumer attributes are smaller, as well as those in
employer.
associated with average
associated with income and
Table 4: Estimated parameters under alternative assumptions about consumer
attributes observability
Attributes by routepeak day
coeff.
?
7
!
standard
error
Attributes by routepeak time
coeff.
Attributes by routepeak day-peak time
standard
error
coeff.
standard
error
81.21
245.78
0.218
-57.54
-23.7
-24.1
-3.69
-64.53
-505.0
0.37
54.58
134.39
(16.23)
(33.55)
(0.016)
(7.30)
(9.04)
(7.29)
(5.60)
(2.11)
(129.4)
(2.93)
(4.08)
(19.56)
Panel A: first-stage estimates
log(mean income by route-day)
employer by route-day
log(mean income by route-time)
employer by route-time
log(mean income by route-day- time)
employer by route-day-time
distance
Guarulhos
Galeão
peak day
peak time
time of purchase
constant
fuel
saturation
101.99
325.02
(23.23)
(40.00)
109.22
305.39
0.213
-55.23
-24.64
-40.02
11.6
-62.66
-715.1
3.77
49.27
120.26
(0.025)
(7.68)
(9.94)
(9.13)
(5.20)
(2.30)
(254.4)
(4.24)
(4.41)
(183.32)
0.209
-48.3
-24.69
7.02
-13.76
-62.65
-772.8
3.56
49.74
119.31
(22.99)
(38.00)
(0.016)
(6.93)
(8.91)
(4.73)
(5.46)
(2.13)
(177.1)
(3.14)
(4.43)
(18.99)
Panel B: second-stage estimates
?
log(income)
145.36
(34.56)
139.16
(33.79)
110.56
employer
266.69
(38.62)
237.2
(45.28)
202.14
7 distance
0.24
(0.023)
0.232
(0.015)
0.238
Guarulhos
-34.92
(9.24)
-37.21
(7.58)
-45.25
Galeão
-30.90
(10.52)
-31.7
(9.82)
-29.11
peak day
-20.20
(8.22)
-21.02
(7.63)
-10.04
peak time
-17.05
(6.94)
-14.23
(6.11)
-7.04
time of purchase
-34.56
(3.81)
-37.53
(4.40)
-43.37
constant
-1042.7
(316.8)
-967.9
(249.0)
-731.2
Notes: (1) 9850 observations. (2) Standard errors are bootstrap standard errors from 100 resamplings.
(25.22)
(35.94)
(0.016)
(8.09)
(9.51)
(7.32)
(6.25)
(3.89)
(190.2)
6. Counterfactuals
This section presents some counterfactual calculations using our estimates. We
begin by discussing welfare assessments within the confines of our model.
6.1. Measuring welfare in our model
In our setting, once a ticket is sold at price
willingness to pay
, profits are @ =
−
and at cost
to a buyer with
and consumer surplus is AB =
− .
However, as we only directly observe tickets that are sold, our calculations must
account for selection bias as follows.
The expected consumer surplus, conditional on attributes , is
AB|
=
− | ;
≥
.D
≥ |
since when a ticket is not sold, the consumer surplus is 0. Similarly, expected profits are
@|
=
− !" . D
≥ |
We cannot empirically estimate D
≥ |
, the probability of the ticket
being sold conditional on attributes, since our data contains only information on
consumers that bought the ticket. Within our model, we imposed a distributional
assumption on
, so this probability can be calculated directly from our estimated
coefficients, as well as
and .
We wish to be able to compute consumer surplus and profit taking the route as
our market definition. For this, we partition
E
into
, attributes of the route, and
attributes of the particular flight and time of purchase. We are interested in
and
AB|
@|
@|
E
E
:
=H
J∈K
=H
E
J∈K
AB|
@|
FG
FG
where B is the support of
= I;
= I;
FG
E
E
.D
.D
FG
FG
.
= I|
FG
The conditional distribution of
= I|
|
E
AB|
FG
E
,
E
E
is outside of our model and not directly
observable in the data due to selection bias. However, we can empirically estimate
D
FG
D
FG
= I|
E
= I|
E
, 1L/ , the distribution of
FG
E
conditional on
and the event that the
ticket was bought. This a conditional distribution between variables observed in our
sample. According to Bayes Law, for any I ∈ B:
, 1L/ ∝ D 1L/|
Note that D 1L/|
FG
,
E
FG
= I,
=D
E
.D
≥ |
Thus, we are able to recover the distribution of
AB|
E
and
@|
E
.
Figure 2 shows our estimates for D 1L/|
FG
= I|
E
can be computed from the model.
FG
E
|
E
and, hence, we can calculate
using this estimation strategy for
the 5 routes with most passengers in 2009. These are demand curves within each route.
Unlike D 1L/|
, which are linear by assumption in our model, these curves are non-
linear, as they depend on the distribution of
FG
|
E
.
Figure 2: Demand curves for the 5 routes with most passengers in 2009
800
CGH-SDU
BSB-CGH
GRU-SSA
GRU-REC
GRU-POA
700
price (R$)
600
500
400
300
200
100
0
0
0.1
0.2
0.3
0.4
0.5
Prob.
0.6
0.7
0.8
0.9
1
Notes: (1) We employ the estimates obtained in specification 1. (2) In the horizontal axis, Prob. means
D 1L/| E .
6.2. Counterfactual exercises
In this section, we employ our estimates to compute the impact on (relative)
consumer surplus and profits of hypothetical policies that restrict price discrimination.
In the first exercise, the airline is restricted to charge a single (profit maximizing) price
for all flights and passengers in the route. In the second exercise, prices are allowed to
differ across flights within each route, but are not allowed to depend on the time of
purchase. We use the distribution of
each counterfactual.
FG
|
E
to obtain the profit maximizing prices in
Table 5 presents predicted price ranges for some routes in our sample in the
baseline and under the two counterfactuals, using as estimates the ones obtained in
specification 1. Our calculations predict that if restricted to charge a single price, a
monopolist facing the type of demand we estimate would elect to charge a high price,
near the top of the baseline distribution. This is true for almost all routes in our sample,
but we restrict Table 5 to the 10 routes with most passengers in 2009 to save space.
Table 6 presents the relative impact of the counterfactual policies in consumer
surplus, profits and social welfare, using our estimates in specification 1. Profits fall in
all cases, as they should for a monopolist. More interestingly, consumer surplus in most
routes also falls, as airlines react to the policy by hiking up prices. Thus, for this set of
estimates, social welfare would be reduced by around 10% if price discrimination were
restricted5.
Table 5: Predicted price ranges in counterfactual scenarios, in R$
Prices depend on
Route
route, flight and
time of purchase
route and flight
route
(model)
(counterfactual)
(counterfactual)
min max
min max
CGH-SDU
240 371
352 368
364
BSB-CGH
313 459
443 459
452
GRU-SSA
243 388
310 388
378
GRU-REC
299 532
454 470
455
GRU-POA
163 295
275 291
281
CGH-CNF
233 394
378 394
382
BSB-GIG
215 348
277 348
338
GIG-SSA
208 370
292 370
299
CGH-CWB
213 359
343 359
353
CGH-POA
237 395
327 395
379
Notes: (1) We employ the estimates obtained in specification 1. (2) We
report results for the 10 routes with most passengers in 2009.
Table 6: Changes in welfare measures in the counterfactual scenarios, relative to the
baseline
Route
Counterfactual
Prices depend on route and flight
Prices depend on route
AB|
E
@|
E
AB| E
+ @| E
AB|
E
CGH-SDU
-9%
-5%
-6%
-13%
BSB-CGH
-25%
-9%
-14%
-25%
GRU-SSA
-8%
-15%
-13%
-31%
GRU-REC
-8%
-17%
-15%
-3%
GRU-POA
-22%
-14%
-17%
-22%
CGH-CNF
-28%
-10%
-15%
-26%
BSB-GIG
-4%
-14%
-11%
-27%
GIG-SSA
-6%
-15%
-13%
+1%
CGH-CWB
-21%
-7%
-12%
-23%
CGH-POA
-24%
-13%
-17%
-29%
Notes: (1) We employ the estimates obtained in specification 1. (2) We
routes with most passengers in 2009.
5
@|
E
AB| E
+ @| E
-6%
-10%
-17%
-17%
-15%
-10%
-16%
-16%
-8%
-14%
report results
-8%
-15%
-22%
-14%
-17%
-15%
-19%
-11%
-12%
-19%
for the 10
If the airline is restricted to charge a single price in each route, the mean reduction of the social welfare,
considering all the routes in the sample, is 13%.
7. Concluding remarks
While our empirical findings in this paper are, in our opinion, reasonable, much
remains to be done. We explore the unique feature of the data set (namely that we
observe some consumer characteristics firms do not) to investigate price discrimination
practices. The strategy that we pursued was of postulating (and trusting) a stylized
linear demand monopoly pricing model. To trust our results, we need to better
understand to what extent they depend on the specificities of the model.
More specifically, we would like to know to what extent our results depend on
the linear demand/ uniform willingness to pay assumption. We would also like to
extend the analysis to an oligopoly framework where consumers make multinomial
decisions between flights and airlines within the same route.
Another extension we are considering is to introduce the possibility that the
airline may observe something about consumer willingness to pay that we do not
observe in our data. This unobserved component would provide a structural
interpretation for the residual of the pricing equation, and would allow us to deal with
selection issues in a more explicit way.
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