Code Sharing and Alliances under Fixed Proration Rate: The US
Domestic Airlines
Tuba Toru Delibasi 1
1 Bahcesehir University
Abstract. This paper focuses on the analysis of the code sharing among U.S. domestic airlines. We find out
that the partner airlines benefit from the economies of code sharing, which reduce marginal cost and allows
airlines to price at higher markups. Moreover, prices increase after code sharing more if code sharing does
not induce the entry of new products. We also estimate the parameter of profit-splitting between partner firms
in a code sharing agreement and find that operating carrier receives 91% of profit from code sharing product.
Keywords: Code Sharing, Alliances, U.S. Domestic Airlines
1. Introduction
The cooperation between airlines in the form of code sharing and alliances was first popular in
international aviation. The former allows an airline to market and sell seats on flights operated by another
airline, and the latter can be considered as a code sharing between two or more airlines with further
agreements such as sharing frequent flyer program and airport facilities. Nowadays, these collaborations
between airlines are also very common in the U.S. domestic market. Although the impacts of domestic code
sharing on prices and welfare have been addressed in the literature, the analysis on the financial
arrangements between partner carriers have attracted little attention.
Code sharing allows airlines to extend their network beyond their capacity without additional input but a
transfer fee is paid by marketing carrier to operating carrier. The financial arrangements between an
operating carrier and its partner can take different forms. The general rule used in practice is split profit from
code shared product on the base of a predetermined proration rate. Alternatively, some airlines implement
dynamic bid price where the partners decide a transfer fee for each time a code shared seat sold and also
some partners share profit according to their respective available seat miles (ASM).
Traditionally, a product is code shared if at least one of the flight segments is operated by one carrier
(operating carrier) and marketed by another carrier (marketing carrier). For instant, a one stop flight from
Boston (Logan International Airport-BOS) to Los Angles (Los Angeles International Airport-LAX) can be
operated by two airlines. The first leg would be BOS to Philadelphia (Philadelphia International Airport-PHL)
operated by US Airways (US) and the second leg form PHL to LAX would be operated by United Airlines
(UA). Two partner carriers take part on the operations and the itinerary is marketed by both US and UA.
Besides the traditional code share, on the domestic market a significant amount of code shared products are
operated by only one carrier. Namely, a one stop flight from BOS to LAX through PHL is operated by US
but marketed by UA or by both carriers. Under these types of code sharing carriers practice Special Prorate
Agreements (SPAs) to share revenues and mostly a fixed proration rate is negotiated between partner carriers
before code sharing decision. Hence, in this paper we focus on these two types of code share. This paper
assesses the impact of domestic code sharing on price and quantifies the proration rate between the partner
airlines by assuming that code sharing airlines have decided a fixed proration rate to split profits, then each
airline maximizes its profit.
Corresponding author. Tel.: +902123810496
E-mail address: [email protected]
2014 3rd International Conference on Business, Management and Governance
IPEDR vol.82 (2014) © (2014) IACSIT Press, Singapore
DOI: 10.7763/IPEDR.2014.V82.2
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The major contributions of the paper are twofold. First, we provide a framework which explicitly models
code sharing activities in airline’s optimization problem, and quantifies the fixed proration rate negotiated by
airlines. We assume that partner airlines decide the fixed revenue sharing rate (proration rate) before code
sharing is realized, and then each airline sets its price which maximizes its profit. We estimate the proration
rate at 91% suggesting that operating carrier receives 91% of profit coming from code shared product.
Second, with the estimated parameters, we compared the prices pre- and post-code sharing under two cases:
number of products remains same and code share products are new to the market. We find that prices
increase after code sharing more if code sharing does not induce the entry of new products in the market.
The remainder of the paper is structured as follows. In Section 2, the literature review is given. In
Section 3, we explain the theoretical model in which passenger demand equation and airline pricing equation
including airline costs are introduced. These equations are to be estimated to obtain empirical results. In
Section 4, we describe model specification and estimation procedure. The Section 5 contains the empirical
results and counterfactual analysis. Finally, we conclude and suggest future lines of research in Section 6.
2. Literature Review
Several aspects of code share and alliances have been studied in the literature both theoretically and
empirically. Park [1] and Brueckner [2], both of which analyzes the extent to which fares, traffic levels,
profits and welfare are affected by alliances. The former points out that if the partner airlines’ networks are
complementary then the code-sharing agreement will be welfare enhancing through the elimination of double
marginalization. On the other hand, he states that the parallel networks code-share agreements are means of
collusion, thus generate welfare losses. Brueckner [2] demonstrates that international alliances put downward
pressure on prices of interline city-pair markets but the inter-hub market passengers are worse off due to
decline in competition depending on the number of competitors and potential economies of density and
scope of carriers in the concerned market.
Hassin and Shy [3] study code share agreements between two carriers competing on international routes.
They conclude that no passengers become worse off but some passengers, who are orient are strictly better
off with code sharing. Hence, code sharing is Pareto improving.
The results of above theoretical studies are consistent with the empirical ones of international code
sharing agreements. Brueckner and Whalen [4] present that international alliances have decreased ticket
prices by 25 percent. Park and Zhang [5] show that international alliances lead to a decrease of prices and an
increase of passenger volume.
Regarding domestic code-share practices, Ito and Lee [6] examine the impact of domestic alliances on
airfares and demonstrate that code shared tickets were significantly less expensive. Chen and Gayle [7]
analyzed theoretically under which conditions code sharing results in lower prices.
There are some theoretical papers study revenue management of alliances such as Wright et al. [8] and
Hu et al. [9] with two-stage game theory approach. They use a dynamic approach to model the output
negotiation of allied carriers who decide the fixed proration rate at the first stage of the game. Both find
some theoretical support for the implementation of fixed proration rate. To the best of our knowledge, this
paper is the first one to consider airlines code sharing agreements in their optimization problem and
quantifies the fixed proration rate.
3. Theoretical Model
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In this section we present the structural model be estimated. First, we derive the transport demand
equation of passengers under a standard discrete choice setting then the pricing equation of airlines. Airlines
offer a set of differentiated products and competes via Bertrand-Nash in each market. Then, each consumer
buys one of the products or takes the outside option of not traveling.
A market is defined as a directional origin and destination airports pair allowing us to consider that the
characteristics of the origin city may have different impacts on the demand. For instance, passenger demand
for air transportation may differ from Los Angles-Boston to Boston-Los Angles. We define the product as a
unique combination of origin/connecting/destination airports and ticketing/operating carriers. A product is a
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code-shared product when there exists at least one segment of the trip in which the operating carrier is
different from the ticketing carrier.
A passenger i , =1,...,i I , decides g , = 0,1g between travelling and “not travelling" or “using other
transport modes", which is its outside option referred by the index 0 , in a given market =1,...,m M . Under
the option of travelling, the passenger has to choose a product j among the set of available products
=1,..., mj J for this origin-destination and mJ is the number of product on the market m . To represent this
choice structure, we adopt a nested logit model.
The mean utility from the outside option is normalized to zero, i.e., 0 = 0mV . Following Berry [10], the
share of passengers using product j in a given market m is given by:
0 |ln( ) ln( ) = ( )jm m jm jm jm gm jms s X p ln s (4)
where |jm gms designates the share of product j within the nest travelling, g , on a market m and 0ms is the
share of outside option.
Each airline f , =1,...,f F , sets its price for product j , jmp , which maximizes its total profit, f ,
over all products across all markets. In this paper, we aim to explain how code sharing affects carriers’
pricing decisions. Hence, we assume that the marketing carrier decides the price of a code shared product
and retains a fixed proportion of the total product and gives the rest to the operating carrier. Finally, the
marketing carrier receives an amount of other carriers’ profits as it is an operating carrier in other code-
shared products.
The profit maximization problem of an airline f is written as:
= (1 )( ) ( ) . . 0max f jm jm jm jm hm hm hm hm f fp m j J m h Hjm fm fm
d p c q d p c q F s t
(7)
where fmJ is the total number of products sold by carrier f in market m and fmH is the set of products in
market m that carrier f operates but not markets. jmc is the marginal cost of product j in market m and
fF is the fixed cost of carrier f . Carrier f only sets the prices of products which it markets, not the ones it
operates for its code share partner. But, it takes into account the profits that it receives from the partner
carrier under the assumption that partner airlines split profit coming from code shared products under a
predetermined fixed proration rate, .
Since we do not observe the marginal cost, we specify that
=jm jm jmc W (8)
where jmW is the vector of cost shifters and jm is an error term.
We assume that prices are set according to Bertrand-Nash equilibrium with multi-product firms taking
into account the cross price effects among their products in the same market. Additionally, markets are
independent, thus there is no cross price effect among markets. Under these assumptions, any equilibrium
price must satisfy the following first-order condition
(1 ) (1 )( ) ( ) = 0km hmjm jm km km km hm hm hm
jm jmk J h Hfm fm
s sd s d p c d p c
p p
(9)
where h , =1,..., fmh H , signifies the products operated by airline f but marketed by an other airline. The
passenger demand (Equation (4)) and airline pricing equation derived Equation (9 characterize the
equilibrium in the market.
4. Theoretical Model
The empirical implementation of the theoretical model introduced in Section 3 requires simultaneous
estimation of demand equation of passengers (equation (4)) and pricing equation of airlines, which is the
solution of equation (9) including the functional specification for marginal cost (equation (8)). There are on
average 63 passengers per product, almost 1096 passengers on each route. The average ticket fare (price) is
$186.2. Market size is measured by the population at origin city divided by 40 since we are using a quarter of
10 percent sample data. 23% of products are code shared products while non-stop flights are only 13% of all
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products in our sample. Distance is in terms of miles flown between origin airport and destination airport, on
average 1577 miles. Moreover, 94% of products uses at least one hub airport of ticketing carrier. 38% of
flights end at hub airport while 64% of flights has a connection at the ticketing carrier’s Hub airport.
The demand is affected by the following attributes: ticket fare, distance, distance squared, a code sharing
dummy, nonstop dummy, hub used dummy, hub destination dummy, hub transfer dummy and dummies for
airlines. Code sharing dummy indicates whether the product is code shared or not while nonstop dummy
indicates direct flights. Moreover, we include three hub indicators in the demand equation. First, a hub used
dummy is equal to one if the product passes by at least one hub airport on itinerary. Second, hub destination
dummy is equal to one if the destination airport is a hub for ticketing carrier. Third, hub transfer dummy
indicates whether the connecting airport is a hub for the carrier. We use American Airline as baseline
dummy. For the marginal cost equation, we include the following variables: distance, distance squared, code
sharing dummy, hub used dummy and airline dummies. We expect that code-shared products may
experience some cost savings in order to measure it we use code sharing dummy in the marginal cost
function.
The econometric problem that we face is the endogeneity of market shares and prices. The classical
solution to this problem is to estimate two equations jointly by using instruments which are orthogonal to the
unobservables in both equations. So, we estimate the system of equations simultaneously using Generalized
Method of Moments (GMM).
5. Empirical Results and Counterfactual Analysis
We present the estimated price and marginal cost in Table 1. In order to assess prices without code share,
we focus on two scenarios in our analysis. First we compute model predicted prices by eliminating code
sharing products and keeping the number of products in the market unchanged. Then, we assume that code
shared products do not exist without code share, that is, there are less products in the market.
All Sample Code Shared Non Code Shared
Price 187.2 180.8 194.1
Marginal Cost 108.6 47.8 169.4
Margin (in % ) 42 73 12
Table 1: Estimated Price, Marginal Cost and Margin
In the first case, we assume that the number of products in each market does not change and we find out
that the average price is higher without code sharing agreements. Note that, interline poruducts (a product
with more than one operating carrier and without any form of cooperation between carriers) are more
expensive than online (products with single operating and marketing carrier) and code shared products due to
the double marginalization. (See Brueckner [2], Brueckner and Whalen [4] and Ito and Lee [6].) Double
marginalization is due to the fact that each airline in the interline itinerary maximizes its profit from its own
segment independently from other carriers. Therefore, code-sharing agreements are expected to decrease
airfares because of the existence of one single airline controlling prices over the entire itinerary. This
decrease in prices will benefit passengers and represents how code sharing may benefit consumers. However,
we need to measure the welfare effects of code sharing on overlapping networks. We expect that the prices
will be higher due to collusion between partner carriers.
The second case is generated under the assumption that the code sharing agreements introduce new
products to the market. Due to the creation of new products, code sharing can generate pro-competitive
effects so the prices decrease. There is a large difference, almost 30% between prices with code sharing and
without code sharing. (See Table 2.) We can conclude that code share products have lower quality and this
allows airlines to charge higher for the products without code sharing. That is, code sharing allows airlines to
implement second degree price discrimination between passenger prefers non-code shared product and the
others. Moreover, carriers can practice third degree of price discrimination between interline passengers and
the others. (See, Bilotkach [11].)
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Price with Code Sharing without Code Sharing % Change
Same no. of products 187.4 243.3 30
Code Share products do not exist 187.4 209.6 12
Table 2: Estimated Price, Marginal Cost and Margin
6. Conclusion
In this paper, we model the revenue sharing within code sharing airlines under Special Prorate
Agreements. First, we estimate the passenger demand and pricing equation of airlines. We identify the fixed
proration rate between partner airlines in the equilibrium. Then, we analyze how prices varied after code
sharing. According to our results, marginal cost is reduced after code sharing and code sharing carriers
practice price discrimination with code shared products. Moreover, we quantify the profit splitting rule for
the code shared products between partner carriers. Our results can be viewed as providing an empirical
support for the use of fixed proration rate as profit sharing rule between code sharing carriers.
Assuming that airlines using fixed proration rate, we manage to estimate the equilibrium rate under given
market conditions. But, the framework in this paper can be extended to a two-stage game where airline
decides to code share or not in the first stage then set its fare. This dynamic model allows us to predict
market conditions ex-ante and to characterize optimum proration rates. Then, we can realize further welfare
analysis in order to choose the optimum rate. However, this implementation requires private information
about code sharing agreements.
7. References
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[7] Y. Chen and P. G. Gayle, “Vertical contracting between airlines: An equilibrium analysis of codeshare alliances,”
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[9] X. Hu, R. Caldentey and G. Vulcano, “Revenue Sharing in Airline Alliances,” Management Science, vol. 59, no. 5,
pp. 1177-1195, 2013.
[10] S. T. Berry, "Estimating Discrete-Choice Models of Product Differentiation," RAND Journal of Economics, vol.
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[11] V. Bilotkach, “Price Competition between International Airline Alliances,” Journal of Transport Economics and
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