Generalized Theorem and Application to the U.S. Airline Industry MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES Ziyi Qiu * University of Chicago This paper studies firms’ endogenous choices of prices and product characteristics pre- and post-mergers. Different from the current merger guidelines which focus on the merger effect on prices with exogenous product qualities, this paper allows firms to use product characteristics as another instrument to control their market perfor- mance. The paper finds that firms’ adjustment of post merger prices and product qualities depends on the cross elasticity of demand, the net benefit of improving the product quality, and the threshold market share. A generalized theorem is proved to characterize the conditions to predict post-merger outcomes, in particular the changes of post-merger market shares, product qualities and prices for both the merged and non-merging firms. A real application to study the 2010 merger of the United and Continental Airlines demonstrates that the theorem achieves high prediction accu- racy in predicting the post-merger outcomes. In addition, the paper considers the con- sumer’s preference changes and firms’ cost efficiency gains post-merger. The changes in post-merger market outcomes are decomposed into four effects: (1) the merger effect; (2) the consumer’s preference effect; (3) the firms’ cost efficiency effect; and (4) other effects. Keywords: Antitrust analysis, merger and acquisition, endogenous product char- acteristics, airline mergers. 1. INTRODUCTION AND LITERATURE REVIEW Understanding how firms make production decisions is of fundamental impor- tance in economics. The classic approach considers firms’ optimal choices of prices to maximize profits[1, 3, 4, 25, 30]. While the literature considers en- dogenous prices, the product characteristics are usually held exogenous. The as- sumption of exogenous product characteristics does bring concerns. Firstly, since product characteristics affect consumers’ purchasing decisions and the costs of production, it is reasonable that firms could gain a higher profit by adjusting product characteristics. Allowing both prices and product characteristics to be endogenous could potentially improve firms’ profits and necessitate the recon- sideration of the classical pricing theory with exogenous product characteristics. Secondly, the endogenous product characteristics are generally supported by real data. Firms’ adjustment over their product qualities is widely observed in real applications [22, 29, 9, 15, 32, 33, 14, 11, 8]. Both concerns suggest that we should * Department of Economics, the University of Chicago. 1126 E. 59th Street, Chicago, IL 60637. Email: [email protected]. 1
Transcript
Generalized Theorem and Application to the U.S. Airline Industry
MERGER ANALYSIS WITH ENDOGENOUS PRICES ANDPRODUCT QUALITIES
Ziyi Qiu∗
University of Chicago
This paper studies firms’ endogenous choices of prices and product characteristicspre- and post-mergers. Different from the current merger guidelines which focus onthe merger effect on prices with exogenous product qualities, this paper allows firmsto use product characteristics as another instrument to control their market perfor-mance. The paper finds that firms’ adjustment of post merger prices and productqualities depends on the cross elasticity of demand, the net benefit of improving theproduct quality, and the threshold market share. A generalized theorem is proved tocharacterize the conditions to predict post-merger outcomes, in particular the changesof post-merger market shares, product qualities and prices for both the merged andnon-merging firms. A real application to study the 2010 merger of the United andContinental Airlines demonstrates that the theorem achieves high prediction accu-racy in predicting the post-merger outcomes. In addition, the paper considers the con-sumer’s preference changes and firms’ cost efficiency gains post-merger. The changesin post-merger market outcomes are decomposed into four effects: (1) the mergereffect; (2) the consumer’s preference effect; (3) the firms’ cost efficiency effect; and(4) other effects.
Understanding how firms make production decisions is of fundamental impor-tance in economics. The classic approach considers firms’ optimal choices ofprices to maximize profits[1, 3, 4, 25, 30]. While the literature considers en-dogenous prices, the product characteristics are usually held exogenous. The as-sumption of exogenous product characteristics does bring concerns. Firstly, sinceproduct characteristics affect consumers’ purchasing decisions and the costs ofproduction, it is reasonable that firms could gain a higher profit by adjustingproduct characteristics. Allowing both prices and product characteristics to beendogenous could potentially improve firms’ profits and necessitate the recon-sideration of the classical pricing theory with exogenous product characteristics.Secondly, the endogenous product characteristics are generally supported by realdata. Firms’ adjustment over their product qualities is widely observed in realapplications [22, 29, 9, 15, 32, 33, 14, 11, 8]. Both concerns suggest that we should
∗Department of Economics, the University of Chicago. 1126 E. 59th Street, Chicago, IL60637. Email: [email protected].
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consider the endogeneity of prices and product characteristics as we study firms’competition behavior. Therefore, a re-evaluation of the pricing and product repo-sitioning incentives is of an important and timely research topic.
Realizing the importance and necessity of endogenous product qualities, thecurrent guidelines for merger analysis shall be reconsidered for improvement.The current benchmark merger guidelines issued by the U.S. Department ofJustice and the Federal Trade Commission mainly focus on firms’ changes ofprices post mergers. The product characteristics are usually assumed to be ex-ogenous and remain constant pre- and post-mergers [6, 7, 13, 18, 26]. How-ever, constant and exogenous product characteristics are unduly demanding as-sumptions and are generally not supported by the real data, as we observe inmany merger cases that firms change their product characteristics post-merger[2, 12, 24, 20, 23, 27]. While it becomes a more realistic concern when conductingmerger analysis, the frontier literature has started to consider changes in firms’product characteristics in the process of merger evaluation. A series of recentpapers [5, 10, 17, 19, 21, 23, 28, 31] has considered firms’ optimal product char-acteristics in a variety of merger applications. Among them, Mazzeo (2003) [23]studied the U.S. airline industry and found that carriers are likely to deterio-rate the on-time performance when markets become less competitive. His laterpaper (2012) [24] found that this observation could have substantial effects byallowing for repositioning, particularly in cases where the merging parties offeredrelatively similar products prior to the merger. Peters (2006) [27] showed that amerged airline tends to reduce flight frequency on segments where the mergingcarriers were competing with each other. Watson(2008) [33] focused on the prod-uct variety decision in terms of the number of product offerings sold by eyewearretailers. It is found therein that per-firm product variety has a nonmonotonicrelationship with competition. When facing a closer rival in geographic space,firms tend to offer more options but the number of product varieties does eventu-ally decline with more competition. This finding again suggests that the optimalresponse following a merger could be either to increase or to decrease prod-uct variety. Gramlich (2009) [17] developed and estimated a model of the U.S.automobile industry in which firms choose the fuel efficiency of their new vehi-cles. In their model, firms provide more or less fuel efficiency depending on thestochastically changing gas price. Lee (2013) [20] studied the merger of Delta andNorthwest Airlines and found that: 1) the merged firm tends to increase prod-uct differentiation post-merger, 2) the higher product differentiation reduces thefirm’s incentive to raise prices, and 3) the changes in characteristics and pricesincrease not only the merged firm’s profit but also the consumer’s welfare. Healso argued that endogenizing characteristics are essential to better predict theactual outcome as the simulated results become closer to actual post-mergerdata. The results from these papers indicate that firms make distinct changes totheir product characteristics, in addition to changes in prices post-merger.
MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES 3
However, there are some limitations of the existing work. Since the existing worksare all case-by-case studies, there is a lack of generalized framework to serve as amerger guideline. Moreover, the often inconsistent conclusions among researchersmake the generalized theorem a challenge. For example, a series of papers in-cluding Berry and Waldfoger (2001) [5], Gandhi et al (2008) [14] and Sweeting(2010) [31] showed that the merged firms tend to increase product differentia-tion to avoid market cannibalization. On the other hand, Gotz and Gugler (2006)[16] found that higher concentration in retail gasoline market reduces productvariety. Secondly, the current literature imposes strong assumptions of firms’ ho-mogenous production technology in order to recover the marginal cost function.The assumption rules out the possibility that firms can endow with differentproduction technologies, which is actually one of the key reasons that firms havedifferent incentive to merger and induce different post-merger outcomes.
This paper uses disaggregate level data and studies firms’ product repositioningand pricing incentives post mergers. The paper studies how the inclusion of en-dogenous product attributes could affect firms’ post-merger prices, qualities andmarket shares. Motivated by the limitations of the current merger guidelines andthe existing literature, this paper has two main contributions: 1) allowing firms tobe differentiated in their production technologies and study how the heterogenousproductivities shall affect the post-merger outcomes; 3) generalizing conditionsto predict different post-merger outcomes under different market conditions, in-cluding changes in post-merger market shares, prices and product characteristicsfor both merged and non-merging firms. The paper finds that firms’ adjustmentsof their post-merger market shares, prices and product attributes are determinedby the cross elasticity of demand (Definition 2.1), the net benefit of improvingproduct quality by one unit, (Definition 2.2), the threshold market share of each
firm that makesdPjdSj
= 0, i.e. Scj and the pre-merger market share of each firm
(Definition 2.3). The generalized theorem (our main Theorem 3.1) is presentedto predict the post-merger outcomes for both the merged and non-merging firmsunder different market conditions. The generalized theorem is then applied tostudy the 2010 merger of the United and the Continental Airlines. The paperfinds that the Theorem 3.1 has a high prediction accuracy power of post-mergeroutcomes in market shares, flight frequencies, and airfares for both merged andnon-merging firms. The paper also considers the changes in the consumer’s pref-erences and airlines’ cost efficiencies post-merger and decomposes the changes inmarket outcomes into the four effects: (1) the merger effect; (2) the consumer’spreference effect; (3) the firms’ cost efficiency effect; (4) the other effect.
The rest of the paper is organized as follows. Section 2 proposes the modelwith endogenous prices and product characteristics and generalizes conditionsto predict the post-merger outcomes. Section 3 characterizes the generalizedtheorem for the post-merger prediction. Section 4 describes the data and the
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basic features of the U.S. airline industry. Section 5 discusses the identificationstrategy for estimating the demand and supply sides of the U.S. airline industry.Section 6 presents the estimation results and the merger prediction based on theestimated values of model parameters. Comparison between the predicted post-merger changes of prices and product qualities with the actual observed postmerger outcomes are also shown in Section 6. Section 7 estimates the airlineindustry using post-merger data to understand the changes of the consumer’spreference and airlines’ cost efficiencies post-merger. Section 8 decomposes theeffects on changes of post-merger market outcomes into four effects. The paperconcludes in Section 9.
2. MODEL
In this section, we propose a model for the merger of two firms within an in-dustry. The proposed model is based on the discrete choice framework as eachconsumer purchases the product with the highest utility. The paper allows theendogeneity of product characteristics and prices pre- and post-merger.
We consider the market with three major firms before the merger. Firm 1 and 2will merge and stay under the same name after the merger. When the two firmsmerge, firm 2 will rename to firm 1 and adopt the same operation, technologyand reputation as of firm 1. After the merger, there are two firms existing in theindustry, i.e firm 1 and firm 3.
2.1. Demand Side
Let i, j and t be the consumer, firm and time index, respectively. The utility ofthe consumer i choosing the product j at time t is
(1) Uijt = βZjt − αPjt + ξj + ξjt + εijt,
where Pjt is the price for product j, Zjt is the major product characteristic thataffects the consumer’s utility. Zjt can be extended to a vector of product charac-teristics. Here we consider one key feature that measures the product quality. ξjis the product fixed effect of firm j. ξjt contains the unobserved product qualityterm that affects the consumer’s utility. εijt is the idiosyncratic shock and followsthe type 1 extreme value distribution. To simplify the model, we do not considerthe interaction of individual demographics with product attributes.
By the property of type 1 extreme value (T1EV) distribution, the market shareof firm j at time t is characterized by
(2) Sjt =exp(βZjt − αPjt + ξj + ξjt)
c0 +∑3j′=1 exp(βZj′t − αPj′t + ξj′ + ξj′t)
.
MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES 5
where we assume the mean utility of purchasing the outside option is c0 andthere is a fraction µ of people shall choose to purchase from the outside option.
2.2. Supply Side
Next, we describe each firm’s profit maximization by simultaneously choosing itsoptimal product price and quality. The profit of firm j is
(3) πjt = Sjt(Pjt −mcjt)− Fixedjt,
where Fixedjt is firm j’s fixed cost of production and mcjt is firm j’s marginalcost of production. A firm’s decision on product characteristics affects both itsmarginal cost and fixed cost. Following Lee (2013) [20] and Fan (2013) [12],we adopt a linear form for the firm’s marginal cost and a quadratic form forthe firm’s fixed cost. Then, the marginal cost and the marginal fixed cost arecharacterized by
(4) mcjt = γjZjt + ωjt,
and
(5)dF ixedjtdZjt
= δjZjt + θjt,
where ωjt and θjt are the marginal and fixed cost shocks respectively, both unob-served. To use consistent notations through this paper, we denote the derivativeof the fixed cost with respect to the product quality, i.e.
dFixedjtdZjt
, the marginal
fixed cost term.
2.3. Necessary Conditions
In this section, necessary equilibrium conditions for product characteristics andprices shall be derived for each firm. From those conditions, we may recoverthe marginal cost and the fixed cost for each firm. For firm j, the first orderconditions for the optimal price Pj and the product characteristic Zj are
[Pjt] : (Pjt −mcjt)dSjtdPjt
+ Sjt = 0,(6)
[Zjt] : (Pjt −mcjt)dSjtdZjt
− dmcjtdZjt
Sjt −dF ixedjtdZjt
= 0,(7)
wheredmcjtdZjt
= γj anddFixedjtdZjt
= δjZjt + θjt.1
Given each firm chooses the optimal product quality and price to maximize profit,we shall have six first order conditions for the three firms pre-merger. When firm
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1 and 2 merge, firm 2 will rename to firm 1 by adopting the same technologyand brand reputation. Hence, there are two firms, i.e. firm 1 and firm 3, existingin the industry after the merger. The necessary conditions remain the same forfirm 1 and firm 3 post merger, except that the denominator of the market share(2) now contains two firms instead of three. There are four first order conditionsfor firm 1 and firm 3 after the merger. Simplifying the necessary conditions forfirm 1 and 3 implies that
Recall that the first order conditions for firm 1 and 3 remain the same pre-and post-merger but the market share equations change. To understand how theequilibrium outcomes change post-merger, we may rewrite the equilibrium pricesand product characteristics for firm 1 and 3 as functions of their equilibriummarket shares respectively
Zjt = Sjt
(α−1β − γj
δj
)− θjtδj,(10)
Pjt = γjSjt
(α−1β − γj
δj
)− θjtγj
δj+ ωjt +
1
α(1− Sjt).(11)
Equations (10) and (11) jointly characterize the firm j’s equilibrium price andproduct characteristic as a function of its equilibrium market share. Knowing thechanges of firms’ market shares post-merger, we can apply the equations aboveto predict the changes of firms’ prices and product characteristics post-merger.
2.4. Prediction of Post-merger Market Shares
In order to predict changes in post merger prices and product characteristics, weneed to first predict changes in firms’ post-merger market shares. We first relatethe market share of firm 1 and 2 as a function of firm 3 by the property of T1EVdistribution. Observe that for j = {1, 2}, we have
(12)Sjt
exp (βZjt − αPjt + ξj + ξjt)=
S3t
exp (βZ3t − αP3t + ξ3 + ξ3t).
We then apply equations (10) and (11) to substitute each firm’s price Pjt andproduct characteristic Zjt as a function of its market share Sjt, i.e.
Sjt
exp (Sjt(βα−γjδj
)(β − αγj)− 11−Sjt ) exp (
θjtδj
(αγj − β)− ωjtα+ ξj + ξjt)=
S3t
exp (S3t(βα−γ3δ3
)(β − αγ3)− 11−S3t
) exp ( θ3tδ3 (αγ3 − β)− ω3tα+ ξ3 + ξ3t).
MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES 7
To simplify the notation, we let
Fj(Sjt) =Sjt
exp (Sjtβα−γjδj
(β − αγj)− 11−Sjt )
,
Mkjt =exp (
θjtδj
(αγj − β)− ωjtα+ ξj + ξjt)
exp ( θktδk (αγk − β)− ωktα+ ξk + ξkt).
Then we can write
F1(S1t) = F3(S3t)M31t,(13)
F2(S2t) = F3(S3t)M32t.(14)Taking the inverse function to write S1t and S2t as a function of S3t, we obtainthat
S1t = F−11 (F3(S3t)M31t),(15)
S2t = F−12 (F3(S3t)M32t).(16)Recall that a fraction µ of people shall choose the outside option. In the pre-merger period, we have that S1t + S2t + S3t = 1 − µ. We then apply equations(15) and (16) to write the market shares of firm 1 and firm 2 as a function offirm 3
Equation (17) determines the equilibrium market share of firm 3 pre-merger.Combining it with equations (15) and (16) shall fully characterizes the equillib-rium market share of each firm pre-merger. We denote the sum of S1t and S3t asL3(S3t) = F−11 (F3(S3t)M31t) + S3t. Since the market share of firm 2 is positivepre-merger, the sum of S1t and S3t shall increase in the post-merger period. We
then take the derivative of L3(S3t) with respect to S3t, i.e. dL(S3t)dS3t
. The post
merger market share of firm 3 shall increase if dL(S3t)dS3t
> 0 and shall decrease ifdL(S3t)dS3t
< 0
(18)dL3(S3t)
dS3t=
1− S3t(µ3 − 1(1−S3t)2
)
exp(µ3S3t − 11−S3t
)
exp(µ1S1t − 11−S1t
)
1− S1t(µ1 − 1(1−S1t)2
)M31t + 1
where µj = (β − αγj)(βα−γjδj
) 2. We notice that
(19)dS1t
dS3t=
1− S3t(µ3 − 1(1−S3t)2
)
exp(µ3S3t − 11−S3t
)
exp(µ1S1t − 11−S1t
)
1− S1t(µ1 − 1(1−S1t)2
)M31t.
When dS1t
dS3t> −1, one unit increase in S3t is corresponding with less than 1
unit decrease in S1t, therefore dL3(S3t)dS3t
> 0 and the market share of firm 3 shall
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increase post-merger. On the other hand, when dS1t
dS3t< −1, the increase in S3t
is too small to offset the decrease in S1t and hence dL3(S3t)dS3t
< 0 and the market
share of firm 3 shall decrease post-merger. Given the formula for dS1t
dS3tand the
pre-merger market shares of S1t and S3t, we shall define the cross elasticity ofdemand of firm 1 relative to firm 3
Definition 2.1 The cross elasticity of demand of firm 1 relative to firm 3 isdefined as
ε(S1t, S3t) =dS1t
dS3t
S3t
S1t(20)
=1− S3t(µ3 − 1
(1−S3t)2)
exp(µ3S3t − 11−S3t
)
exp(µ1S1t − 11−S1t
)
1− S1t(µ1 − 1(1−S1t)2
)M31t
S3t
S1t.(21)
When ε(S1t, S3t) > −S3t
S1t, dL3(S3t)
dS3t> 0 and the market share of firm 3 shall
increase post-merger. On the other hand, when ε(S1t, S3t) < −S3t
S1t, dL3(S3t)
dS3t< 0
and the market share of firm 3 shall decrease post-merger. Similarly, we canrelate the market share of firm 2 and firm 3 with firm 1 by the parallel analysis
F2(S2t) = F1(S1t)M12t,(22)
F3(S3t) = F1(S1t)M13t.(23)Note that M13t = M−131t. We can then write the pre-merger market share of eachfirm as a function of S1t, i.e.
dS3tis shown in equation (19) above. When −1 < dS1t
dS3t< 0, dL1(S1t)
dS1t< 0
and the market share of firm 1 shall decrease post-merger. On the other hand,
when dS1t
dS3t> 0 or dS1t
dS3t< −1,dL1(S1t)
dS1t> 0 and the market share of firm 1 shall
increase post-merger. Given the proposed definition of cross elasticity of demand,
we can show that when −S3t
S1t< ε(S1t, S3t) < 0, dL1(S1t)
dS1t< 0 and the market share
of firm 1 shall decrease post-merger. On the other hand, when ε(S1t, S3t) > 0
or ε(S1t, S3t) < −S3t
S1t,dL1(S1t)
dS1t> 0 and the market share of firm 1 shall increase
post-merger.
MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES 9
To summarize, we define the cross elasticity of demand term ε(S1t, S3t) in Defini-tion 2.1, which measures the percentage change of firm 1’s market share relativeto the percentage change of firm 3’s market share. When ε(S1t, S3t) > 0, bothS1t and S3t shall increase post-merger. When − S3t
dS1t< ε(S1t, S3t) < 0, then S1t
shall decrease and S3t shall increase post-merger. When ε(S1t, S3t) < −S3t
S1t, S1t
shall increase and S3t shall decrease post-merger. The cross elasticity of demandcan be expressed as a function of the demand and supply side parameters andthe pre-merger equilibrium market shares.
2.5. Prediction of Post-merger Prices and Product Characteristics
Knowing the changes of direction for firm 1 and 3’ market shares post-merger,we can then predict the changes of the post-merger prices and product charac-teristics based on equations (10) and (11). We see a linear relation of the firm’sproduct quality Zjt with its market share Sjt. Thus knowing the demand andsupply side parameters and the changes of post-merger market shares enablesthe prediction of post-merger product characteristic for each firm. The derivativeof firm j’s product characteristic with respect to its market share is thus
(26)dZjtdSjt
=α−1β − γj
δj.
For each firm j, the derivative implies the direction of change for the firm j’s post-
merger product characteristic together with its market share. Ifα−1β−γj
δj> 0,
thendZjtdSjt
> 0, and the post-merger product quality and market share shall move
in the same direction. On the other hand, ifα−1β−γj
δj< 0, then
dZjtdSjt
< 0, and
the post-merger product quality and market share shall move in the oppositedirection. It is reasonable to assume that the marginal fixed cost coefficient δj ispositive, thus the change of direction for firm j’s post-merger product character-istic is determined by the term of α−1β−γj . In essence, the term α−1β quantifiesthe relative benefit of improving the product quality compared to improving theproduct price. The term γj indicates the marginal cost of improving the productquality for one unit. Therefore, the term α−1β − γj measures the net benefit offirm j to increase its product quality for one unit.
Definition 2.2 The net benefit of firm j to increase its product quality for oneunit is defined as
(27) bj = α−1β − γj .
Clearly, if bj > 0, the firm would like to increase its product quality when itspost-merger market share becomes larger. Otherwise, the firm would like to de-crease its product quality when the post-merger market share becomes larger.
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For the firm with a better production technology, i.e. γj is smaller, and the netbenefit to increase its product quality is more likely to be positive. Thus thefirm is more likely to increase its product quality when it expands its marketshare. For the firm with inefficient production technology, it may be too costlyfor the firm to improve its product quality and thus we would expect the post-merger product quality to move in the opposite direction with the market share.Moreover, if the merger happens in the market with consumers valuing a lot ofthe product quality or less sensitive to the price, then bj is more likely to bepositive and the post-merger product quality is more likely to improve with thepost-merger market share.
Once the direction of changes for firm j’s post-merger market share and productquality are known, we could then predict the change of direction for firm j’sproduct price by the necessary conditions. Equation (11) characterizes a non-linear relation of the firm j’s product price with its market share. We shalldenote the marginal cost and the markup term as
mcjt = γjSjt(βα − γjδj
)− θjtγjδj
+ ωjt,(28)
σjt =1
α(1− Sjt).(29)
Thus the price of firm j consists of two terms: the marginal cost and the markupterm
(30) Pjt = mcjt + σjt.
When bj > 0, the equilibrium market share and the product characteristic are
positive correlated, i.e.dZjtdSjt
> 0. Hence, to increase firm j’s market share shall
increase the marginal cost for the firm. The increase in the firm j’s market shareshall also give the firm a higher market power and increase its markup. In thatcase, both the marginal cost and the markup effects work in the same direction.The derivative
dPjtdSjt
is positive and the price shall increase with a higher market
share of firm j. On the other hand, when bj < 0, the equilibrium market shareand the product characteristic are negative correlated. Therefore, to increase themarket share shall decrease the marginal cost by lowering the product qualityof the firm. The markup effect is positive regardless of the value of bj . In thatcase, the marginal cost effect and the markup effect work in the opposite wayand whether the price increases or not depends on which effect dominates. Totell which effect dominates, we shall derive the slope of change in firm j’s priceas a function of its market share
(31)dPjtdSjt
= γj
(α−1β − γj
δj
)+
1
α(1− Sjt)2.
MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES11
If the marginal cost effect dominates,dPjtdSjt
< 0 and the post-merger product
price moves in the opposite direction with the market share. If the markupeffect dominates,
dPjtdSjt
> 0 and the post-merger product price moves in the same
direction with the market share. From the equation (31) above, whetherdPjtdSjt
is
positive or negative depends on the net benefit of improving product quality bjand the pre-merger equilibrium market share Sjt. We then calculate the threshold
market share Scj that makesdPjtdSjt
= 0 and hence propose the following definition.
Definition 2.3 The threshold market share of firm j such thatdPjtdSjt
= 0 is
defined as
(32) Scj = 1−[
δj−αγjbj
] 12
.
When bj < 0, and Sjt > Scj , the post-merger price shall increase with the marketshare and the markup effect dominates. When bj < 0 and Sjt < Scj , the post-merger price shall decrease with the market share and the markup effect is tooweak to offset the marginal cost effect. In addition, when bj > 0, both effectswork in the same direction and the price shall increase with the market shareregardless of the pre-merger market share.
To summarize, we can predict the changes of directions for the post-mergermarket shares, prices and product qualities by knowing the cross elasticity ofdemand, i.e. ε(S1t, S3t), the net benefit for adjusting product quality bj and thethreshold market share Scj that balances off the marginal cost and the markupeffect. The generalized conditions and predictions shall be rigorously presentedin the main theorem; c.f. Theorem 3.1 in Section 3.
3. GENERALIZED THEOREM FOR THE POST-MERGER PREDICTION
Now, we present our main theorem by generalizing the conditions for the post-merger prediction under the assumptions that there is no consumer’s preferencechanges and cost efficiency gains post merger.
Theorem 3.1 Let ε(S1t, S3t) be the cross elasticity of demand defined by Defi-nition 2.1, bj be the firm j’s net benefit of improving its product quality defined by
Definition 2.2, and Scj be the threshold market share of firm j such thatdPjtdSjt
= 0
defined by Definition 2.3.1. If ε(S1t, S3t) > 0, the post-merger market shares increase for both firm 1
and firm 3.2. If −S3t
S1t< ε(S1t, S3t) < 0, the post-merger market share decreases for firm
1 and increases for firm 3.
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3. If ε(S1t, S3t) < −S3t
S1t, the post-merger market share increases for firm 1
and decreases for firm 3.Knowing the changes of direction of firms’ post-merger market shares, we canthen predict the changes of firms’ post-merger prices and product qualities.
1. If bj > 0, firm j’s post-merger price and product quality move in the samedirection with the post-merger market share.
dZjtdSjt
> 0,dPjtdSjt
> 0.
2. If bj < 0, and Sjt > Scj , firm j’s post-merger price moves in the samedirection and the product quality moves in the opposite direction with thepost-merger market share.
dZjtdSjt
< 0,dPjtdSjt
> 0.
3. If bj < 0, and Sjt < Scj , firm j’s post-merger price and product qualitymove in the opposite direction with the post-merger market share.
dZjtdSjt
< 0,dPjtdSjt
< 0.
There are a number of implications of Theorem 3.1 we shall discuss.
Remark 1 The theorem addresses firms’ endogenous choices of prices andproduct qualities pre- and post-merger. When the cross elasticity of demandis positive, the one unit increase in S3t shall increase the market share for firm1, i.e. dS1t
dS3t> 0. In this case, two products are complementary of each other and
the market shares of firm 1 and 3 shall move in the same direction post-merger.Given that two firms exist in the market post-merger, the post-merger marketshare shall increase for both firm 1 and firm 3. When the cross elasticity of de-mand is negative but is not too small, i.e −S3t
S1t< ε(S1t, S3t) < 0, the one unit
increase in firm 3’s market share shall correspond to a less than one unit decreasein firm 1’s market share, i.e. −1 < dS1t
dS3t< 0. The post merger market share shall
increase for firm 3 and decrease for firm 1. When the cross elasticity of demandis negative and small, i.e. ε(S1t, S3t) < −S3t
S1t, we have that dS1t
dS3t< −1. Hence
an one unit increase in S3t corresponds to a more than one unit decrease in S1t.Therefore, the post merger market share of firm 1 shall increase and of firm 3shall decrease. Note that in the later two cases, the two products of firm 1 andfirm 3 are substitutes of each other.
Remark 2 Knowing the direction of changes for firms’ market shares postmerger, we can then predict the changes in firms’ product qualities and pricesby knowing the signs of the derivative terms, i.e
dZjtdSjt
anddPjtdSjt
. For product
MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES13
qualities, the sign of changes in product qualities to market shares, i.e.dZjtdSjt
, is
the same as the sign of the net benefit bj = α−1β−γj . When firm j is sufficientlyefficient with its production, the term bj is positive and hence firm j chooses toincrease its product quality when the post merger market share increases. Theproduct quality and the market share shall move in the same direction postmerger. When firm j is not sufficiently good with its production technology,increasing product quality would be too costly and hence the firm would liketo decrease its product quality when the market share increases post merger.In that case the product quality and market share shall move in the oppositedirection after the merger. Moreover, when the merger involves consumers whovalue the product quality a lot and/or are less sensitive to product price, the bjis more likely to be positive and the post-merger product quality is more likelyto improve with the post-merger market share.
Remark 3 The conditions get slightly more complicated for post-merger prices.When the net benefit is positive, i.e. bj > 0, both the marginal cost and themarkup effects are positive, and the post-merger price moves in the same direc-tion with the post merger market share. In that case, the positive correlationholds regardless of firm j’s pre-merger market share level. The post-merger priceshall move in the opposite direction with the market share if the net benefit bjis negative and firm j has a small market share pre-merger, i.e. Sjt < Scj . In thatcase, the firm has a small market power. The positive markup effect is too smallto offset the negative marginal cost effect and hence the overall effect is negative,i.e
dPjtdZjt
< 0. On the other hand, when the net benefit is negative bj < 0 but
the firm j’s pre-merger market share is sufficient, i.e. Sjt > Scj , the firm j has abig market power to induce a higher markup effect. Therefore, even though themarginal cost effect is negative, the post-merger price and market share can stillhave a positive correlation, in the sense that the loss in marginal cost effect iscancelled out by the gain in the markup effect 1/[α(1 − Sjt)]. We can tell thateven a negative net benefit bj can still induce an increase in post-merger pricewith the market share. The production efficiency is more restrictive for obtaininga positive correlation of product qualities than of product prices together withmarket shares.
To summarize, the post merger market shares, prices and product qualities areendogenously determined by the cross elasticity of demand, i.e. ε(S1t, S3t), thenet benefit of increasing the product quality, i.e. bj and the threshold marketshare that balances off the marginal cost and markup effect, i.e. Scj . The theoremabove can be extended with more than three major firms existing pre-merger.Besides, we assumed one major product characteristic which measures the prod-uct quality for each firm. The theorem can be extended to study a vector ofproduct characteristics for each product.
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3.1. Predictions of Post-merger Outcomes
Applying the theorem above, we can predict the post-merger outcomes for themerged and non-merging firms. We list the conditions required for different post-merger outcomes. The conditions are based on the pre-merger equilibrium marketshares, and the demand and supply side parameters, in particular, ε(S1t, S3t), bjand Scj . Table I summarizes the prediction of post-merger outcomes, in particu-lar, the changes of market shares, prices and product qualities for firm 1 and 3post-merger.
From Table I, the post merger market share shall increase for both or at leastone firm, depending on the cross elasticity of demand. The more complementaryof the two products, the more likely for the market shares to increase for bothfirms post merger. If the two products are substitutable, then the merger shallincrease the market share of one firm and decrease the market share of the otherfirm, depending on the magnitude of the cross elasticity of firm 1 relative tofirm 3, i.e. ε(S1t, S3t). A more negative cross elasticity implies that a one unitincrease in S3t shall cause a more than one unit decrease in S1t. Given the postmerger market shares add up to a fixed fraction, we can predict an increase ofthe market share for firm 1 and a decrease of the market share for firm 3 postmerger. Similarly, the less negative cross elasticity implies that one unit increasein market share of firm 3 would correspond to a less than one unit decrease infirm 1’s market share. Hence, the post-merger market share shall increase forfirm 3 and decrease for firm 1.
The changes in post merger price and product quality can go either way, depend-ing on the firm’s net benefit of improving product quality relative to price, i.e.bj and the pre-merger market share Sj . The more productive a firm is, the morelikely for bj to be positive and hence the product price and quality are morelikely to move in the same direction with the market share. When bj is negative,the post-merger product quality shall change in the opposite direction with themarket share. The price shall move in the same direction with the market share ifthe pre-merger market share is big enough, Sj > Scj so that the positive markupeffect dominates the negative marginal cost effect. For the firm with a small pre-merger market share, the merger may cause a decrease of the post merger pricewith the market share, as the marginal cost effect dominates the markup effect.
4. DATA DESCRIPTION AND THE U.S. AIRLINE INDUSTRY
4.1. The U.S. Airline Industry
To test the proposed theorem, we shall apply the theorem to the application ofthe U.S. airline industry. There are a number of reasons to choose the U.S. airlineindustry. First, there are several mergers happened in the U.S. airline industryin the past few years, with the well-known ones including the merger of
MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES15
TABLE I
Prediction of post-merger market shares, prices and product characteristics
Conditions Post-merger Outcomesε(S1t, S3t) b1, b3 Sc1, S
• Delta and Northwest Airlines in 2008;• United and Continental Airlines in 2010;• Air Tran Airways and Southwest Airlines in 2010;• American Airlines and U.S. Airways in 2013 (most recent).
Second, there are publicly available data sources of the U.S. airline industryfrom the Bureau of Transportation Statistics. The availability of both pre- andpost-merger data allows me to predict the post-merger outcomes applying the
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pre-merger estimation and to compare the theorem prediction with the actualobserved post-merger outcomes. Finally, the airline industry serves as a criticalcomponent of domestic, overseas, commercial and social functions. It counts foraround 5% of the U.S. GDP and has created 10 million job opportunities, whichis an influential industry to study.
In this paper, we shall study the merger of the United and the Continentalairlines in October 2010. The merger makes the United airline superseded theDelta airline as the world’s largest carrier at that time. The merger was approvedin October 2010. After the approval, however, the United and the Continentalairlines still operate separately until March 2012 when the Continental airlinechanged its name to the United and completely merged the operation systemand the technology with the United. Given the longer timespan needed for prod-uct characteristics to adjust, we shall look at four quarters after Q1 2012 as thepost merger period. Although we may aware that the complete adjustment ofproduct characteristics may take longer, it would be a good time to look at giventhat the merger of the American airline and U.S. airway in Dec 9th, 2013 wouldmake the whole picture complicated. We use the four quarters from Q4 2009 toQ3 2010 as the pre-merger period being aware that it may include some mergereffect from the 2008 merger of the Delta and the Northwest airlines and the 2010merger of Air Tran airways and the Southwest airlines.
For the merger of the United and the Continental airlines in 2010, we shallfocus our study on the routes that overlap the two merged airlines with thetotal number of passengers exceeding ten thousand. We look at the pre-mergerperiods and find there are 8 overlapping airport pairs/16 origin-dest one-wayroutes that have both the United and the Continental airlines under operation.We summarize the pre-merger number of passengers and the conditional marketshares for those 16 overlapping routes in Table II.For those 16 overlapping routes, both the United and the Continental airlineshave significant market shares. And for the two-way routes of SFO-IAH, EWR-SFO and EWR-DEN, the United and the Continental airlines are the only twooperation carriers and hence obtain the monopoly power on those routes. Weexpect the merger may have an effect on the non-overlapping routes as well andwe shall leave this concern to the future work.
4.2. Data Description
In this paper we use the data from the Bureau of Transportation Statistics,which contains disaggregated level data from demand and supply sides of theU.S. airline industry. The primary datasets for our empirical study include theAirline Origin and Destination Survey, T-100 Domestic Segment Data, and theAirline Fuel Cost and Consumption Data. We construct the average airfare permile using the Airline Origin and Destination Survey, the flight frequency using
MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES17
TABLE II
Passengers on overlapping routes between UA and CO Q3 2010.
Airport Pair Passengers Conditional SharesUA CO Others UA CO Others
the T-100 Domestic Segment Data. Besides, we use the Airline Fuel Cost andConsumption data to calculate the fuel cost per gallon for each airline. Thedatasets are summarized in Table III.
5. IDENTIFICATION STRATEGY
This section addresses the identification strategy for estimating the demand andsupply sides of the U.S. airline industry. We shall use the estimation results topredict the post-merger outcomes applying Theorem 3.1. The estimation resultsand the comparison of the prediction with the real data are shown in the latersections.
5.1. Demand Estimation
In our estimation, both product prices and characteristics are allowed to beendogenous pre- and post-merger. The flight frequency and the average airfareper mile are generally important features for the consumer to make airline-routedecision. We define each airport pair (origin-destination) as one submarket andeach airline-airport pair as the product in the submarket. Hence, the consumeri’s utility of choosing airline j on the airport pair r at time t is
where Pjrt is the average airfare per mile for one airline-airport pair combina-tion and Zjrt is the flight frequency which measures the product quality in theairline industry. We consider three airlines existing pre-merger, the United, theContinental and the other airlines. To use consistent notation with Theorem 3.1,we denote the United airline as firm 1, the Continental airline as firm 2 and theother airlines as firm 3. ξj is the airline’s brand effect. ξjrt is the unobservedproduct quality that affects the consumer’ utility. εijrt is the idiosyncratic shockand is assumed to follow the T1EV distribution. To estimate the demand, weconsider four quarters from Q4 2009 to Q3 2010 as the pre-merger period. Weassume there is a fixed fraction of people that shall choose the outside option,i.e. Sort = µ. The value of µ shall be estimated from the data. By the propertyof type one extreme value distribution
(34) ln(SjrtSort
) = βZjrt − αPjrt + ξj + ξjrt.
We shall estimate the consumer’s utility function by the log regression. Sincethe flight frequency and airfare are endogenous variables, they are potentiallycorrelated with the unobserved product quality term, ξjrt. Instrumental variables(IV) are required for each of them to obtain consistent estimation. We use the fuelcost per gallon of each airline as the instrument variable for average airfare permile. We expect the higher the fuel cost, the higher the average airfare level Pjrtis. For flight frequency, we use the hub status and the population of the originand destination cities as the instruments. If the origin or destination airport hasthe airline hub or has a big population size, then we would expect the flightfrequency to be higher for that airline-route.
MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES19
5.2. Supply Estimation
After estimating the demand side of the airline industry, we can then recover themarginal cost for each airline-route pair by the necessary condition
(35) mcjrt = Pjrt −1
α(1− Sjrt).
Observing the pre-merger price and the market share for each airline-route pairand having estimated the consumer’s utility function, we can then recover themarginal cost for each firm by equation (36) above. Different from the classicalapproach, we consider the heterogeneity in firms’ production technologies. Theheterogenous production technology shall play an important role in explainingfirms’ different merger incentives and post-merger outcomes. To estimate theairlines’ marginal cost of production, we adopt a linear marginal cost functionalform from the existing literature. Therefore the marginal cost for each airlineshall depend on the flight frequency and the unobserved shock
(36) mcjrt = γjZjrt + ωjrt,
where we expect a higher flight frequency implies a higher marginal cost, i.e.γj > 0. Here ωjrt is the unobserved marginal cost shock and is allowed to becorrelated with the observed product quality. Hence instrument variables arerequired to obtain consistent estimation. We shall use the airlines’ hub statusand the population at the origin- and destination cities as the instruments forflight frequencies. After recovering the firm’s specific productivity, i.e. γj , wethen recover the value of marginal fixed cost for each airline-route pair from thenecessary conditions
(37)dF ixedjrtdZjrt
= (β
α− γj)Sjrt.
Observing the pre-merger market share, and having estimated the demand andsupply sides of the airline industry, we can then calculate the marginal fixed costfor each airport-route pair. We then estimate the airlines’ marginal fixed costsas a function of the flight frequencies. We adopt a quadratic form of firms’ fixedcosts from the existing literature
(38)dF ixedjrtdZjrt
= δjZjrt + θjrt,
where we would expect a higher flight frequency implies a higher marginal fixedcost, i.e. δj > 0. Here θjrt is the unobserved fixed cost shock and is allowed to becorrelated with the observed product quality Zjrt. Hence we apply the same setof instruments for flight frequencies. Once the estimates of the consumer’s utilityand the firms’ marginal costs and fixed costs are obtained, we can then applyTheorem 3.1 to predict changes in firms’ post-merger market shares, prices andflight frequencies. The empirical results are shown in Section 6.
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TABLE IV
Estimation Results on Parameters for Utilities Pre-merger.
Mean Utilities Coeff St. Error Z p-value 95% Conf. IntervalFrequency 2.778 0.616 4.51 0.000 [1.571, 3.985]
Firm3 -7.622 0.669 -11.38 0.000 [-8.934, -6.310]†Instrumented: Airfare Frequency
†Instrumentals: ua co cost-per-gallon pop-origin pop-dest hub-origin hub-dest
6. PRELIMINARY RESULTS
This section describes the estimation results for the 2010 merger of the Unitedand the Continental Airlines. We first estimate the demand side of the airlineindustry by estimating the consumer’s utility function. We then recover themarginal costs and fixed costs for each airline from the conditions shown inequations (35) and (37). Finally, the pre-merger estimation results are used topredict the post-merger outcomes according to Theorem 3.1. For the pre-mergerperiod, we use the airline data that covers Q4 2009 to Q3 2010. In particular,we focus on the changes of market shares, average airfares and flight frequenciesfor the United and the other airlines pre- and post-mergers. We use the airlinehub status and the population at the origin- and end-point airports as the in-struments for flight frequencies. We use the fuel cost per gallon of each airlineas the instrument for flight airfare per mile. The pre-merger estimation resultsare shown in Table IV, V, and VI.
Table IV shows the estimation results of the consumer’s utility function. We shalldenote β to be the coefficient of flight frequency and α to be the coefficient ofaverage airfare. From the estimation, a consumer values the flight frequency andmore likely to purchase from the airline with frequent flights. A higher airfareshall decrease a consumer’s utility. The airline fixed effect is the highest for theUnited airline, and the Continental airline has the second highest. Other air-lines, on average, have the lowest fixed effect. From Table IV, we calculate themarginal benefit of improving flight frequency relative to airfare, i.e. β/α. Wethen compare the marginal benefit with the marginal cost estimated in table Vto predict changes in flight frequencies and airfares post merger.
Table V shows the estimation results of firms’ marginal cost functions. We denotethe marginal cost coefficient of firm j’s flight frequency as γj , which measureshow costly to improve the flight frequency by one unit. The estimation results inTable V imply that the Continental airline has a better production technologyin terms of marginal cost compared to the United airline, i.e. γ2 < γ1. The other
MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES21
TABLE V
Estimation Results on Parameters for the Marginal Costs Pre-merger.
Marginal Costs Coeff St. Error Z p-value 95% Conf. IntervalUA frequency 1.191 0.088 13.55 0.000 [1.018, 1.363]CO frequency 0.883 0.051 17.17 0.000 [0.782, 0.984]
Others frequency 0.531 0.044 12.18 0.000 [0.445, 0.616]†Instrumented: UA frequency CO frequency Others frequency
airlines, on average, have the best production technology in terms of marginalcost compared to the United and the Continental airlines. Combining these withTable IV, we form the measure of firm j’s net benefit of improving flight fre-quency, i.e. bj = β/α−γj > 0. We then estimate the marginal fixed cost for eachairline and the results are shown in Table VI below.
Table VI shows the estimation results of airlines’ marginal fixed cost functions.We denote the coefficient with respect to firm j’s flight frequency as δj . A posi-tive coefficient shows that a higher flight frequency shall cause a higher marginalfixed cost of production. From the estimation results, the United airline and theother airlines have a comparable level of marginal fixed cost coefficient, whilethe Continental airline has a higher marginal fixed cost coefficient.
After estimating the demand and supply sides of the airline industry, we canthen combine the estimation results together with the pre-merger market sharesto predict the post-merger outcomes. Using the parameter estimation from TableIV, V, and VI and combining them with the pre-merger observed market shares,we can then form the measures of the cross elasticity of demand, i.e. ε(S1, S3),the net benefit of improving product quality, i.e. bj , and the threshold market
share of each firm Scj such thatdPjdSj
= 0. The conditions of the three measures
together with the pre-merger levels of market shares shall be shown in Table VIIbelow. Based on the Table, we can then apply Theorem 3.1 to predict the post
merger changes of market shares, flight frequencies and airfares for the Unitedand the other airlines.
From the Table VII, the net benefit of improving the product quality term bj ispositive on all routes for both the United and the other airlines. Given bj > 0,
we know from the theorem thatdPjtdSjt
> 0 on all routes regardless of the pre-
merger market shares. The cross elasticity of demand term ε(S1t, S3t) is positiveon the two-way routes of LAX-OGG, LAX-HNL and on the one-way route ofEWR-ORD. On the two-way routes of SFO-IAH, EWR-SFO, and EWR-DEN,there are only the United and the Continental Airlines under operation. Thusthe cross elasticity of demand term is not well defined on those routes. The crosselasticity of demand is negative on the one-way route of ORD-EWR and on thetwo-way routes of ORD-IAH and DEN-IAH. After forming the measures of thecross elasticity of demand, i.e. ε(S1t, S3t), the net benefit of improving flight fre-
quency, i.e. bj anddPjtdSjt
, we can then predict for the post-merger outcomes based
on Theorem 3.1. In particular, we predict the changes of market shares, flightfrequencies and airfares for the United and the other airlines post-merger. Theprediction outcomes for the United and the other airlines are shown in TableVIII and IX respectively. We also compare the predicted outcomes with the ac-tual observed post merger outcomes in those tables.
MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES23
TABLE VIII
Pre- and post-merger comparison for the United Airline.
Pre- Post- ComparisonAirport pair P Fr S P Fr S Actual PredictedLAX-OGG 1.32 0.81 0.413 1.54 0.82 0.393 S ↓, P ↑, Fr ↑ S ↑, P ↑, Fr ↑OGG-LAX 1.43 0.81 0.398 1.55 0.81 0.391 S ↓, P ↑, Fr ↑ S ↑ P ↑ , Fr ↑SFO-IAH 1.49 3.00 0.095 2.36 3.05 1 S ↑, P ↑, Fr ↑ S ↑, P ↑, Fr ↑IAH-SFO 1.21 3.00 0.078 2.28 3.05 1 S ↑, P ↑, Fr ↑ S ↑, P ↑, Fr ↑
EWR-SFO 1.38 0.60 0.181 1.74 2.88 1 S ↑, P ↑, Fr ↑ S ↑, P ↑, Fr ↑SFO-EWR 1.26 0.89 0.263 1.66 2.89 1 S ↑, P ↑, Fr ↑ S ↑, P ↑, Fr ↑LAX-HNL 1.17 0.90 0.258 1.25 1.40 0.280 S ↑, P ↑, Fr ↑ S ↑, P ↑ , Fr ↑HNL-LAX 1.20 0.90 0.256 1.29 1.41 0.288 S ↑, P ↑, Fr ↑ S ↑, P ↑ , Fr ↑EWR-ORD 3.74 0.15 0.252 4.04 3.63 0.744 S ↑, P ↑, Fr ↑ S ↑, P ↑, Fr ↑ORD-EWR 3.66 0.12 0.222 4.17 3.85 0.789 S ↑, P ↑, Fr ↑ S ↑, P ↑, Fr ↑ORD-IAH 2.64 0.84 0.148 3.88 3.13 0.878 S ↑, P ↑, Fr ↑ S ↑, P ↑ , Fr ↑IAH-ORD 2.72 0.63 0.115 3.80 3.37 0.880 S ↑, P ↑, Fr ↑ S ↑, P ↑ , Fr ↑EWR-DEN 1.80 0.82 0.435 1.73 2.02 0.759 S ↑, P ↓, Fr ↑ S ↑, P ↑, Fr ↑DEN-EWR 1.86 0.83 0.443 1.72 1.94 0.752 S ↑, P ↓, Fr ↑ S ↑, P ↑, Fr ↑DEN-IAH 2.13 0.89 0.216 3.27 2.77 0.869 S ↑, P ↑, Fr ↑ S ↑, P ↑, Fr ↑IAH-DEN 2.15 0.11 0.275 3.16 2.87 0.897 S ↑, P ↑, Fr ↑ S ↑, P ↑, Fr ↑
†S:share; F: frequency; P: price.
Table VIII compares the actual observed changes in post-merger market shares,airfares and flight frequencies for the United airline with the predicted changesin those dimensions. To conduct the comparison, we use the 2010 Q3 as thepre-merger period and 2012 Q3 as the post-merger period. The last columnshows the theorem predicted post-merger outcomes. Theorem 3.1 predicts thatafter the merger of the United and the Continental airlines, the market shares,the flight frequencies and the average airfares shall increase on all routes of theUnited airline. The second last column shows the actual observed changes ofpost-merger market shares, flight frequencies and airfares of the United airline.From the table, the observed post-merger outcomes match with the predictedpost-merger outcomes with few exceptions.
Table IX compares the actual observed changes in post-merger market shares,airfares and flight frequencies for the other airline with the predicted changes inthose dimensions. The last column shows the theorem predicted post-merger out-comes. Theorem 3.1 predicts that the post-merger market shares, flight frequen-cies and average airfares shall increase on the routes of LAX-OGG, OGG-LAX,LAX-HNL, HNL-LAX and EWR-ORD for the other airlines, while it predictsdecreases of post-merger market shares, flight frequencies and airfares on theroutes of ORD-EWR, ORD-IAH and IAH-ORD for the other airlines. The sec-ond last column shows the actual observed changes in the post-merger outcomes.We find that the observed post-merger outcomes in Table IX match with the pre-dicted outcomes with few exceptions. The few exceptions could potentially be
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TABLE IX
Pre- and post-merger comparison for other airlines.
Pre- Post- ComparisonAirport pair P Fr S P Fr S Actual PredictedLAX-OGG 1.37 1.21 0.534 1.47 1.32 0.607 S ↑, P ↑, Fr ↑ S ↑, P ↑, Fr ↑OGG-LAX 1.38 1.20 0.531 1.49 1.32 0.609 S ↑, P ↑, Fr ↑ S ↑, P ↑, Fr ↑LAX-HNL 1.16 2.69 0.663 1.31 3.00 0.721 S ↑, P ↑, Fr ↑ S ↑, P ↑, Fr ↑HNL-LAX 1.18 2.67 0.654 1.32 2.98 0.712 S ↑, P ↑, Fr ↑ S ↑, P ↑, Fr ↑EWR-ORD 3.20 3.35 0.360 3.67 2.53 0.257 S ↓, P ↑, Fr ↓ S ↑, P ↑, Fr ↑ORD-EWR 3.18 3.38 0.393 3.56 2.12 0.211 S ↓, P ↑, Fr ↓ S ↓, P ↓, Fr ↓ORD-IAH 2.56 1.53 0.163 2.96 1.09 0.122 S ↓, P ↑, Fr ↓ S ↓, P ↓, Fr ↓IAH-ORD 2.51 1.74 0.185 3.08 1.09 0.120 S ↓, P ↑, Fr ↓ S ↓, P ↓, Fr ↓
†S:share; F: frequency; P: price.
explained by realizing that there could be a lot of events besides merger activityhappened during that period. Those events could include changes of firms’ pro-ductivities, consumer’s preferences and so on. Overall, the comparison in TableVIII and IX suggests that Theorem 3.1 has a prediction accuracy rate of 87.5%for the United and the other airlines. Hence the theorem prediction is stronglysupported by the airline merger application, with the high prediction accuracyfor the post-merger outcomes for the merged and non-merging firms.
7. ESTIMATION RESULTS USING POST-MERGER DATA
In the previous section, we predict the post merger outcomes applying Theorem3.1. In particular, we estimate the demand and supply sides of the airline industryusing the pre-merger data. We then combine the estimation with the pre-mergermarket shares to predict the post-merger outcomes, i.e. the market shares, air-fares, and flight frequencies for both the United and other airlines. We assumethat the consumer’s preferences and the airlines’ productivities of marginal costsand fixed costs stay constant pre- and post-merger. The recent availability ofpost-merger airline data allows us to also consider the changes in the consumer’sutility and the airlines’ production technologies in the post-merger period. Byestimating the changes of the consumer’s preferences and firms’ production tech-nologies in the post-merger period, we can then consider the effects of those twofactors on the post-merger outcomes in addition to the merger effect that wepresent earlier. We shall then decompose the changes in airlines’ post-mergermarket shares, flight frequencies and airfares to the following four effect: (1) themerger effect, (2) the consumer’s preference effect, (3) the firms’ cost efficiencyeffect, and (4) the other effect.
To proceed, we shall first re-estimate the demand and supply sides of the airlineindustry using the post-merger data. The estimation results are shown in Table
MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES25
TABLE X
Estimation Results on Parameters for Utilities Post-merger.
Mean Utilities Coeff St. Error Z p-value 95% Conf. IntervalFrequency 1.033 0.112 9.23 0.000 [0.814, 1.252]
X, XI and XII below. We then compare the estimated results using pre- andpost-merger data. The comparison allows us to understand how the consumer’spreferences and the airlines’ cost efficiencies change post-merger. In the later sec-tion, we show the results of decomposing the changes of airlines’ market shares,flight frequencies and airfares to the four effects described below.
Table X shows the estimation of the consumer’s utility using the post-mergerdata. We calculate the term β/α to measure the consumer’s preference of flightfrequency relative to airfare. Comparing it with the pre-merger estimation inTable IV, we find that the consumer values less of flight frequency and more ofairfare in the post-merger period, i.e. βpost/αpost < βpre/αpre. Similarly, we ob-serve that while the consumer’s preference over the United airline stays relativelythe same post-merger, the consumer prefers a lot more of the other airlines post-merger. By calculating the consumer’s relative preference of the United airlineto the other airline, i.e. ξ1ξ3 , we find that the consumer prefers less of the Unitedairline relative to the other airlines in the post-merger period.
We then estimate the airlines’ marginal costs using the post-merger data andthe estimation results are shown in Table XI below. Comparing it with the pre-merger estimation in Table V, we find that the United airline gets relatively moreefficient in terms of its marginal cost compared to the other airlines post merger,i.e γpost1 /γpost3 < γpre1 /γpre3 .
Similarly, we conduct estimation of the airlines’ marginal fixed costs using the
26 Z. QIU
TABLE XII
Estimation results on parameters for the fixed costs post-merger.
Fixed Costs Coeff St. Error Z p-value 95% Conf. IntervalUA frequency 0.016 0.001 30.95 0.000 [0.015, 0.017]
Others frequency 0.013 0.001 13.47 0.000 [0.011, 0.015]†Instrumented: UA frequency Others frequency
post-merger data. The estimation results are shown in Table XII below. Compar-ing it with Table VI in the previous section, we find that the United airline getsrelatively less efficient of its margianl fixed cost compared to the other airlinespost merger, i.e. δpost1 /δpost3 > δpre1 /δpre3 .
To summarize, we estimate the consumer’s utility function and the airlines’marginal cost and marginal fixed cost functions using both pre- and post-mergerdata. The comparison of pre- and post-merger estimation suggests that the con-sumer values more of flight frequency relative to airfare post-merger. The con-sumer prefers less of the United airline relative to the other airfares post-merger.The United airline gets relatively more productive compared to the other air-lines in terms of marginal cost post-merger. The United airline gets relativelyless productive compared to the other airlines in terms of fixed cost post-merger.After we estimate the changes in the consumer’s preferences and the airlines’costs of production, we shall then decompose the changes of post-merger marketshares, flight frequencies and airfares of the United and the other airlines intothe four effects shown in the later section.
8. DECOMPOSITION OF CHANGES IN THE POST-MERGER OUTCOMES
Estimating the demand and supply sides of the airline industry using the pre-and post-merger data enables the decomposition of changes in the post-mergermarket outcomes into different effects. From the estimation above, we know thatthe consumer’s preferences and the airlines’ marginal costs and marginal fixedcosts change post merger. To take into consideration those effects in additionto the merger effect on the post-merger outcomes, we hence decompose the ob-served changes of post-market market outcomes into the four effects: (1) mergereffect; (2) consumer preference effect; (3) firms’ cost efficiency effect; and (4) theother effect. The decomposition shall consist of the following five steps.
Step 1. We first estimate the consumer’s utility and the firms’ cost functionsusing the pre-merger airline data. We then conduct the merger simulationto predict the post-merger market outcomes for both the United and theother airlines. We call the difference of the predicted post-merger marketoutcomes and the pre-merger observed market outcomes the merger effect.
MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES27
Instead of using the absolute value, we measure the percentage changes asthe differences divided by the observed pre-market market outcomes. Themerger effects of changes in the airlines’ market shares, flight frequenciesand airfares are shown in the first column in the six tables below.
Step 2. We then estimate the consumer’s utility using the post-merger airlinedata to get the new estimates of α, β, ξ1, and ξ3. We then conduct themerger simulation using the post-merger estimates of the consumer’s pref-erences while holding the airlines’ marginal costs and marginal fixed costsat the pre-merger level. The difference between the new predicted post-merger market outcomes and the predicted post-merger market outcomesin Step 1 measures the effect of the consumer’s preference change. We shallcall it the consumer’s preference effect. The consumer’s preference effectsof changes in the airlines’ market shares, flight frequencies, and airfares areshown in column 2 of the six tables below.
Step 3. We then estimate the airlines’ marginal costs and marginal fixed costsusing the post-merger data to get the new estimates of γ1, γ3, δ1, δ3. Weconduct the merger simulation using the post-merger estimates of the con-sumer’s utility and the post-merger estimates of the firms’ marginal costsand marginal fixed costs. The difference between the new predicted marketoutcomes and the predicted market outcomes from Step 2 measures howmuch of the changes in market outcomes are caused by firms’ observed pro-duction technology change. We shall call it the firms’ cost efficiency effect.The firms’ cost efficiency effects of changes in the airlines’ market shares,flight frequencies and airfares are shown in column 3 of the six tables below.
Step 4. Besides the three effects described above, there are some other un-observed changes that shall also affect the post-merger market outcomes.Those factors could potentially include unobserved shocks on the demandand supply sides, inflation and so on. We shall call the difference betweenthe actual observed post-merger market outcomes with the predicted post-merger market outcomes in Step 3 the effect of all others. We calculate thepercentage changes of the other effects on the airlines’ post-merger marketshares, flight frequencies and airfares in column 4 of the six tables below.
Step 5. We then calculate the actual observed percentage changes in the post-merger market outcomes by using the observed pre- and post-merger data.The actual observed percentage changes are shown in column 5 of the sixtables below.
The decomposition tables are presented in the following. Table XIII and XIVcontain the decomposition of changes in the post-merger market shares for theUnited and the other airlines respectively. Table XV and XVI contain the de-
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TABLE XIII
Effect Decomposition of Market Share for United Airlines in Percentage Term.
composition of changes in the post-merger flight frequencies for the United andthe other airlines respectively. Table XVII and XVIII contain the decompositionof changes in the post-merger airfares for the United and the other airlines re-spectively.
Table XIII and XIV decompose the changes of post-merger market shares for theUnited and the other airlines into the four effects described above. The first col-umn shows the merger effect on the post-merger market shares. For the Unitedairline, the merger effect is positive and significant on all the routes. While forthe other airlines, the merger effect is positive on the routes of LAX-OGG, OGG-LAX and LAX-HNL, HNL-LAX and is negative on the routes of EWR-ORD,ORD-EWR and ORD-IAH, IAH-ORD. The decomposition of the merger effectson the post-merger market shares is consistent with the theorem prediction forboth the United and the other airlines. Column 2 in Table XIII and XIV mea-sures the effect of the consumer’s preference change on the post-merger marketshares. The consumer’s preference change effect is negative on all routes for theUnited airline and is positive on all routes for the other airlines. This resultmatches with the comparison of the consumer’s utility using both the pre- and
MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES29
TABLE XV
Effect Decomposition of Flight Frequency for United Airlines in PercentageTerm.
post-merger data. We find that the consumer prefers less of the United airlinerelative to the other airlines post-merger. The relatively lower brand fixed effectfor the United airline shall lead to a negative effect on its market share post-merger. The relatively higher brand fixed effect for the other airlines shall leadto a positive merger effect on the post-merger market shares. Column 3 in TableXIII and XIV measures the effect of firms’ observed cost efficiency change onthe post-merger market shares. We find that the cost efficiency has a positiveeffect on the post-merger market shares of the United airline and a negative ef-fect on the post-merger market shares of the other airlines. This finding suggeststhat overall the United airline gets relatively more productive compared to theother airlines post-merger so that its post-merger market share expands due tothe better technology. Moreover, Column 4 in Table XIII and XIV includes theeffect of all other factors such as the unobserved demand and supply shocks andinflation. Column 5 shows the actual observed changes in the post-merger mar-ket shares for the United and the other airlines.
After we obtain the decomposition of the post-merger market shares into differenteffects, we can then decompose the changes of post-merger flight frequencies andairfares accordingly. Table XV and XVI contain the decomposition effects for thepost-merger flight frequencies of the United and the other airlines respectively.Table XVII and XVIII contain the decomposition effects for the post-mergerairfares of the United and the other airlines respectively.
Table XV and XVI show the decomposition effects of the post-merger flight fre-quencies for the United and the other airlines respectively. Column 1 of thosetables shows the merger effect on changes of the post-merger flight frequencies.Given that we have estimated bj > 0 for both the United and the other airlines,we know from Theorem 3.1 that the change of directions of the flight frequenciesis the same as that of the market shares. The theorem prediction is consistent
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TABLE XVI
Effect Decomposition of Flight Frequency for other airlines in Percentage Term.
with what we find in Table XV and XVI above. The merger effect is postiveon all routes of the United airline. For the other airlines, the merger effect ispositive on the routes of LAX-OGG, OGG-LAX and LAX-HNL, HNL-LAX andis negative on the routes of EWR-ORD, ORD-EWR and ORD-IAH, IAH-ORD,which shows highly consistency with the theorem prediction. Column 2 measuresthe consumer’s preference effect on the airlines’ post-merger flight frequencies.The consumer’s preference effect is negative on all routes for the United airlineand is positive on all routes for the other airlines. This result is also consistentwith the pre- and post-merger estimation that the consumer prefers less of theUnited airline relative to the other airlines post-merger. Column 3 measures theairlines’ cost efficiency effect on the post-merger flight frequencies. The cost ef-ficiency effects are positive on all routes of the United airline and are negativeon all routes of the other airlines. As we find in the previous tables, the Unitedairline gets relatively more efficient in its production technology and thus itsmarket share expands post-merger. The higher market share and the positive bjfor both airlines imply that the cost efficiency effect follows the same directionas the market share effect. Column 4 in Table XV and XVI measures all theother effects which could potentially include the changes in unobserved supplyand demand shocks and inflation. The actual observed percentage changes in thepost-merger flight frequencies are shown in Column 5. Overall, the decomposi-tion effects of the post-merger flight frequencies are in consistent pattern withthe decomposition effects of the post-merger market shares. The flight frequencyhas a positive linear relation with the market share.
We then present the decomposition of the post-merger airfares for the Unitedand the other airlines in Table XVII and XVIII respectively. Column 1 showsthe merger effect on the airlines’ post-merger airfares. We know that bj > 0and therefore the direction of changes for the post-merger airfares should bethe same as that of the post-merger market shares. Column 1 shows that themerger effects are positive on all routes of the United airline. The merger effects
MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES31
TABLE XVII
Effect Decomposition of Airfare for United Airlines in Percentage Term.
are positive on the routes of LAX-OGG, OGG-LAX, LAX-HNL and HNL-LAXand are negative on the routes of EWR-ORD, ORD-EWR and ORD-IAH, IAH-ORD for the other airlines. The decomposition results of post-merger airfaresshow consistent pattern with the merger effect on post-merger market shares.Column 2 measures the effect of the consumer’s preference change on the air-lines’ post-merger airfares. The consumer’s preference effects are positive on halfroutes for the United airline and on all routes for the other airlines. Column 3measures the effect of firms’ cost efficiency changes on the post-merger airfares.The decomposition shows that the cost efficiency effects are negative on half theroutes of the United airline and on all routes of the other airlines. Given that theflight airfare has a non-linear relation with the market share, it is likely that thechanges of the post-merger airfares do not necessarily follow the same patternwith the changes of the post-merger market shares. In addition, column 4 in Ta-ble XVII and XVIII measures all the other effects which could potentially includethe changes in unobserved supply and demand shocks and inflation. The actualobserved percentage changes in the post-merger airfares are shown in Column 5.Overall, the decomposition effects of the airlines’ post-merger market shares,flight frequencies and airfares are consistent with the prediction of Theorem 3.1and the estimation using both the pre- and post-merger data.
9. CONCLUSION
Different from the current merger guidelines which predict an increase in post-merger prices under the restrictive assumption that product qualities are exoge-nous, this paper allows the simultaneous endogeneity of both prices and prod-uct characteristics. The paper performs the merger analysis by providing thegeneralized theorem to predict post-merger outcomes of market shares, prod-uct characteristics and prices for both the merged and non-merging firms. Thepaper also makes major contributions by allowing firms to be differentiated intheir production technologies and study how differentiated production technolo-
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TABLE XVIII
Effect Decomposition of Airfare for other in Percentage Term.
gies change firms’ pricing and product repositioning incentives post-merger. Thepaper finds that the changes of firms’ post-merger market outcomes depend onthe consumer’s utility and the firms’ marginal and fixed costs. In particular, thefirms’ endogenous choices of post-merger market shares, product qualities andprices depend on the pre-merger market share Sjt, the cross elasticity of demandε(S1t, S3t), the net benefit of improving the product quality bj and the threshold
market share such thatdPjtdSjt
= 0, i.e. Scj . By generalizing the conditions required
for different post-merger predictions, the paper provides a generalized frame-work that can predict the post-merger outcomes in a variety of dimensions. Inaddition, it helps solve some puzzles from the observed merger cases and theliterature and provides some new insights regarding to: 1) why we do not alwaysobserve an increase in firms’ post-merger prices, and 2) why the existing litera-ture with different merger applications arrives at opposite conclusions regardingto how firms change their product characteristics post mergers.
The generalized theorem is then applied to study the 2010 merger of the Unitedand Continental Airlines. The theorem predicts changes of the post-merger flightfrequencies and airfares for the United and the other airlines. In summary, thetheorem has a very good prediction power for the post-merger outcomes for boththe merged and non-merging firms. The paper then estimates the U.S. airlineindustry using both the pre- and post-merger data. The comparison of the pre-and post-merger estimation implies that the consumer prefers less of the Unitedairline compared to the other airlines post-merger. The consumer also valuesless of the flight frequency relative to the airfare post-merger. The United airlinegets relatively more efficient in its production compared to the other airlinespost-merger. The paper then decomposes the changes of post-merger outcomesin the four effects: (1) the merger effect; (2) the consumer’s preference effect;(3) the firms’ cost efficiency effect; and (4) other effects. The decompositionsuggests consistency with the theorem prediction and the pre- and post-mergerestimation.
MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES33
NOTES
1Derivation of the expressions fordSjtdPjt
,dSjtdZjt
,dSjtdPkt
anddSjtdZkt
gives that
dSj
dPjt= Sjt(−α)(1 − Sjt),(39)
dSjt
dZjt= Sjtβ(1 − Sjt),(40)
dSjt
dPkt= αSjtSkt,(41)
dSjt
dZkt= −SjtβSkt.(42)
2Recall that we denote
Fj(Sjt) =Sjt
exp (Sjtβα−γjδj
(β − αγj) − 11−Sjt
)
.
Take derivative to get
dFj
dSjt=
exp (Sjtβα−γjδj
(β − αγj) − 11−Sjt
) − Sjt exp (Sjtβα−γjδj
(β − αγj) − 11−Sjt
)((β − αγj)(βα−γjδj
) − 1(1−Sjt)2
)
(exp (Sjtβα−γjδj
(β − αγj) − 11−Sjt
))2.
dS1t
dS3t=
dF3(S3t)dS3t
dF1(S1t)dS1t
M31t
=1 − S3t(µ3 − 1
(1−S3t)2)
exp(µ3S3t − 11−S3t
)
exp(µ1S1t − 11−S1t
)
1 − S1t(µ1 − 1(1−S1t)2
)M31t.
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