MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES

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1 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 performance. 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 accuracy in predicting the post-merger outcomes. In addition, the paper considers the consumer 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 characteristics, airline mergers. 1. INTRODUCTION AND LITERATURE REVIEW Understanding how firms make production decisions is of fundamental importance in economics. The classic approach considers firms optimal choices of prices to maximize profits[1, 3, 4, 25, 30]. While the literature considers endogenous prices, the product characteristics are usually held exogenous. The assumption 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 reconsideration 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 E. 59th Street, Chicago, IL ziyiqiu@uchicago.edu. 1

2 2 Z. QIU consider the endogeneity of prices and product characteristics as we study firms competition behavior. Therefore, a re-evaluation of the pricing and product repositioning incentives is of an important and timely research topic. Realizing the importance and necessity of endogenous product qualities, the current guidelines for merger analysis shall be reconsidered for improvement. The current benchmark merger guidelines issued by the U.S. Department of Justice and the Federal Trade Commission mainly focus on firms changes of prices post mergers. The product characteristics are usually assumed to be exogenous and remain constant pre- and post-mergers [6, 7, 13, 18, 26]. However, constant and exogenous product characteristics are unduly demanding assumptions and are generally not supported by the real data, as we observe in many merger cases that firms change their product characteristics post-merger [2, 12, 24, 20, 23, 27]. While it becomes a more realistic concern when conducting merger analysis, the frontier literature has started to consider changes in firms product characteristics in the process of merger evaluation. A series of recent papers [5, 10, 17, 19, 21, 23, 28, 31] has considered firms optimal product characteristics in a variety of merger applications. Among them, Mazzeo (2003) [23] studied the U.S. airline industry and found that carriers are likely to deteriorate the on-time performance when markets become less competitive. His later paper (2012) [24] found that this observation could have substantial effects by allowing for repositioning, particularly in cases where the merging parties offered relatively similar products prior to the merger. Peters (2006) [27] showed that a merged airline tends to reduce flight frequency on segments where the merging carriers were competing with each other. Watson(2008) [33] focused on the product variety decision in terms of the number of product offerings sold by eyewear retailers. It is found therein that per-firm product variety has a nonmonotonic relationship with competition. When facing a closer rival in geographic space, firms tend to offer more options but the number of product varieties does eventually decline with more competition. This finding again suggests that the optimal response following a merger could be either to increase or to decrease product 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 vehicles. In their model, firms provide more or less fuel efficiency depending on the stochastically changing gas price. Lee (2013) [20] studied the merger of Delta and Northwest Airlines and found that: 1) the merged firm tends to increase product differentiation post-merger, 2) the higher product differentiation reduces the firm s incentive to raise prices, and 3) the changes in characteristics and prices increase not only the merged firm s profit but also the consumer s welfare. He also argued that endogenizing characteristics are essential to better predict the actual outcome as the simulated results become closer to actual post-merger data. The results from these papers indicate that firms make distinct changes to their product characteristics, in addition to changes in prices post-merger.

3 MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES 3 However, there are some limitations of the existing work. Since the existing works are all case-by-case studies, there is a lack of generalized framework to serve as a merger guideline. Moreover, the often inconsistent conclusions among researchers make the generalized theorem a challenge. For example, a series of papers including Berry and Waldfoger (2001) [5], Gandhi et al (2008) [14] and Sweeting (2010) [31] showed that the merged firms tend to increase product differentiation to avoid market cannibalization. On the other hand, Gotz and Gugler (2006) [16] found that higher concentration in retail gasoline market reduces product variety. Secondly, the current literature imposes strong assumptions of firms homogenous production technology in order to recover the marginal cost function. The assumption rules out the possibility that firms can endow with different production technologies, which is actually one of the key reasons that firms have different incentive to merger and induce different post-merger outcomes. This paper uses disaggregate level data and studies firms product repositioning and pricing incentives post mergers. The paper studies how the inclusion of endogenous product attributes could affect firms post-merger prices, qualities and market shares. Motivated by the limitations of the current merger guidelines and the existing literature, this paper has two main contributions: 1) allowing firms to be differentiated in their production technologies and study how the heterogenous productivities shall affect the post-merger outcomes; 3) generalizing conditions to predict different post-merger outcomes under different market conditions, including changes in post-merger market shares, prices and product characteristics for both merged and non-merging firms. The paper finds that firms adjustments of their post-merger market shares, prices and product attributes are determined by the cross elasticity of demand (Definition 2.1), the net benefit of improving product quality by one unit, (Definition 2.2), the threshold market share of each firm that makes dpj ds j = 0, i.e. Sj c and the pre-merger market share of each firm (Definition 2.3). The generalized theorem (our main Theorem 3.1) is presented to predict the post-merger outcomes for both the merged and non-merging firms under different market conditions. The generalized theorem is then applied to study the 2010 merger of the United and the Continental Airlines. The paper finds that the Theorem 3.1 has a high prediction accuracy power of post-merger outcomes in market shares, flight frequencies, and airfares for both merged and non-merging firms. The paper also considers the changes in the consumer s preferences and airlines cost efficiencies post-merger and decomposes the changes in market outcomes into the four effects: (1) the merger effect; (2) the consumer s preference effect; (3) the firms cost efficiency effect; (4) the other effect. The rest of the paper is organized as follows. Section 2 proposes the model with endogenous prices and product characteristics and generalizes conditions to predict the post-merger outcomes. Section 3 characterizes the generalized theorem for the post-merger prediction. Section 4 describes the data and the

4 4 Z. QIU basic features of the U.S. airline industry. Section 5 discusses the identification strategy 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 the estimated values of model parameters. Comparison between the predicted postmerger changes of prices and product qualities with the actual observed post merger outcomes are also shown in Section 6. Section 7 estimates the airline industry using post-merger data to understand the changes of the consumer s preference and airlines cost efficiencies post-merger. Section 8 decomposes the effects on changes of post-merger market outcomes into four effects. The paper concludes in Section MODEL In this section, we propose a model for the merger of two firms within an industry. The proposed model is based on the discrete choice framework as each consumer purchases the product with the highest utility. The paper allows the endogeneity of product characteristics and prices pre- and post-merger. We consider the market with three major firms before the merger. Firm 1 and 2 will merge and stay under the same name after the merger. When the two firms merge, firm 2 will rename to firm 1 and adopt the same operation, technology and reputation as of firm 1. After the merger, there are two firms existing in the industry, i.e firm 1 and firm Demand Side Let i, j and t be the consumer, firm and time index, respectively. The utility of the consumer i choosing the product j at time t is (1) U ijt = βz jt αp jt + ξ j + ξ jt + ε ijt, where P jt is the price for product j, Z jt is the major product characteristic that affects the consumer s utility. Z jt can be extended to a vector of product characteristics. Here we consider one key feature that measures the product quality. ξ j is the product fixed effect of firm j. ξ jt contains the unobserved product quality term that affects the consumer s utility. ε ijt is the idiosyncratic shock and follows the type 1 extreme value distribution. To simplify the model, we do not consider the interaction of individual demographics with product attributes. By the property of type 1 extreme value (T1EV) distribution, the market share of firm j at time t is characterized by (2) S jt = exp(βz jt αp jt + ξ j + ξ jt ) c j =1 exp(βz j t αp j t + ξ j + ξ j t).

5 MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES 5 where we assume the mean utility of purchasing the outside option is c 0 and there is a fraction µ of people shall choose to purchase from the outside option Supply Side Next, we describe each firm s profit maximization by simultaneously choosing its optimal product price and quality. The profit of firm j is (3) π jt = S jt (P jt mc jt ) F ixed jt, where F ixed jt is firm j s fixed cost of production and mc jt is firm j s marginal cost of production. A firm s decision on product characteristics affects both its marginal 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 for the firm s fixed cost. Then, the marginal cost and the marginal fixed cost are characterized by (4) mc jt = γ j Z jt + ω jt, and (5) df ixed jt dz jt = δ j Z jt + θ jt, where ω jt and θ jt are the marginal and fixed cost shocks respectively, both unobserved. To use consistent notations through this paper, we denote the derivative df ixedjt of the fixed cost with respect to the product quality, i.e. dz jt, the marginal fixed cost term Necessary Conditions In this section, necessary equilibrium conditions for product characteristics and prices shall be derived for each firm. From those conditions, we may recover the marginal cost and the fixed cost for each firm. For firm j, the first order conditions for the optimal price P j and the product characteristic Z j are (6) (7) [P jt ] : (P jt mc jt ) dp jt + S jt = 0, [Z jt ] : (P jt mc jt ) dz jt dmc jt dz jt S jt df ixed jt dz jt = 0, where dmcjt dz jt = γ j and df ixedjt dz jt = δ j Z jt + θ jt. 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

6 6 Z. QIU 1 and 2 merge, firm 2 will rename to firm 1 by adopting the same technology and brand reputation. Hence, there are two firms, i.e. firm 1 and firm 3, existing in the industry after the merger. The necessary conditions remain the same for firm 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 conditions for firm 1 and firm 3 after the merger. Simplifying the necessary conditions for firm 1 and 3 implies that (8) (9) [P jt ] : S jt ( α)(1 S jt )(P jt γ j Z jt ω jt ) + S jt = 0, [Z jt ] : S jt β(1 S jt )(P jt γ j Z jt ω jt ) S jt γ j δ j Z jt θ jt = 0. Recall that the first order conditions for firm 1 and 3 remain the same preand post-merger but the market share equations change. To understand how the equilibrium outcomes change post-merger, we may rewrite the equilibrium prices and product characteristics for firm 1 and 3 as functions of their equilibrium market shares respectively (10) Z jt = S jt ( α 1 β γ j δ j ) θ jt, δ j ) θ jtγ j ( α 1 (11) β γ j 1 P jt = γ j S jt + ω jt + δ j δ j α(1 S jt ). Equations (10) and (11) jointly characterize the firm j s equilibrium price and product characteristic as a function of its equilibrium market share. Knowing the changes of firms market shares post-merger, we can apply the equations above to predict the changes of firms prices and product characteristics post-merger Prediction of Post-merger Market Shares In order to predict changes in post merger prices and product characteristics, we need to first predict changes in firms post-merger market shares. We first relate the market share of firm 1 and 2 as a function of firm 3 by the property of T1EV distribution. Observe that for j = {1, 2}, we have (12) S jt exp (βz jt αp jt + ξ j + ξ jt ) = S 3t exp (βz 3t αp 3t + ξ 3 + ξ 3t ). We then apply equations (10) and (11) to substitute each firm s price P jt and product characteristic Z jt as a function of its market share S jt, i.e. S jt exp (S jt ( β α γj δ j )(β αγ j ) 1 1 S jt ) exp ( θjt δ j (αγ j β) ω jt α + ξ j + ξ jt ) S 3t. exp (S 3t ( β α γ3 δ 3 )(β αγ 3 ) 1 1 S 3t ) exp ( θ3t δ 3 (αγ 3 β) ω 3t α + ξ 3 + ξ 3t ) =

7 MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES 7 To simplify the notation, we let F j (S jt ) = M kjt = Then we can write (13) F 1 (t ) = F 3 (S 3t )M 31t, S jt β, α exp (S γj jt δ j (β αγ j ) 1 1 S jt ) θjt exp ( δ j (αγ j β) ω jt α + ξ j + ξ jt ) exp ( θ kt δ k (αγ k β) ω kt α + ξ k + ξ kt ). (14) F 2 (S 2t ) = F 3 (S 3t )M 32t. Taking the inverse function to write t and S 2t as a function of S 3t, we obtain that (15) t = F1 1 (F 3 (S 3t )M 31t ), (16) S 2t = F2 1 (F 3 (S 3t )M 32t ). Recall that a fraction µ of people shall choose the outside option. In the premerger period, we have that t + S 2t + S 3t = 1 µ. We then apply equations (15) and (16) to write the market shares of firm 1 and firm 2 as a function of firm 3 (17) F 1 1 (F 3 (S 3t )M 31t ) + F 1 2 (F 3 (S 3t )M 32t ) + S 3t = 1 µ. Equation (17) determines the equilibrium market share of firm 3 pre-merger. Combining it with equations (15) and (16) shall fully characterizes the equillibrium market share of each firm pre-merger. We denote the sum of t and S 3t as L 3 (S 3t ) = F1 1 (F 3 (S 3t )M 31t ) + S 3t. Since the market share of firm 2 is positive pre-merger, the sum of t and S 3t shall increase in the post-merger period. We then take the derivative of L 3 (S 3t ) with respect to S 3t, i.e. dl(s3t). The post merger market share of firm 3 shall increase if dl(s3t) > 0 and shall decrease if dl(s 3t) < 0 (18) dl 3 (S 3t ) = 1 3t(µ 3 exp(µ 3 S 3t 1 (1 S 3t) 2 ) 1 S 3t ) exp(µ 1 t 1 1 t ) 1 1 t (µ 1 (1 t) ) M 31t where µ j = (β αγ j )( β α γj δ j ) 2. We notice that (19) = 1 3t(µ 3 exp(µ 3 S 3t 1 (1 S 3t) 2 ) 1 S 3t ) exp(µ 1 t 1 1 t ) 1 1 t (µ 1 (1 t) ) M 31t. 2 When ds1t > 1, one unit increase in S 3t is corresponding with less than 1 unit decrease in t, therefore dl3(s3t) > 0 and the market share of firm 3 shall

8 8 Z. QIU increase post-merger. On the other hand, when ds1t < 1, the increase in S 3t is too small to offset the decrease in t and hence dl3(s3t) < 0 and the market share of firm 3 shall decrease post-merger. Given the formula for ds1t and the pre-merger market shares of t and S 3t, we shall define the cross elasticity of demand of firm 1 relative to firm 3 Definition 2.1 The cross elasticity of demand of firm 1 relative to firm 3 is defined as ɛ(t, S 3t ) = S 3t (20) t = 1 3t(µ 3 (1 S 3t) ) exp(µ 2 1 t 1 1 t ) exp(µ 3 S 3t S 3t ) 1 t (µ 1 (1 t) ) M S 3t (21) 31t. S 2 1t When ɛ(t, S 3t ) > S3t t, dl 3(S 3t) > 0 and the market share of firm 3 shall increase post-merger. On the other hand, when ɛ(t, S 3t ) < S3t < 0 and the market share of firm 3 shall decrease post-merger. Similarly, we can relate the market share of firm 2 and firm 3 with firm 1 by the parallel analysis (22) F 2 (S 2t ) = F 1 (t )M 12t, t, dl3(s3t) (23) F 3 (S 3t ) = F 1 (t )M 13t. Note that M 13t = M31t 1. We can then write the pre-merger market share of each firm as a function of t, i.e. (24) t + F 1 2 (F 1 (t )M 12t ) + F 1 3 (F 1 (t )M 13t ) = 1 µ. We denote L 1 (t ) = t + F3 1 (F 1 (t )M 13t ). t shall increase post-merger if dl 1(t) > 0 and t shall decrease post-merger if dl1s1t < 0. The derivative term dl1(s1t) can be derived as (25) dl 1 t = ( ds1t ) 1 + 1, where ds1t is shown in equation (19) above. When 1 < ds1t < 0, dl1(s1t) < 0 and the market share of firm 1 shall decrease post-merger. On the other hand, when ds1t > 0 or ds1t < 1, dl1(s1t) > 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 t < ɛ(t, S 3t ) < 0, dl1(s1t) < 0 and the market share of firm 1 shall decrease post-merger. On the other hand, when ɛ(t, S 3t ) > 0 or ɛ(t, S 3t ) < S3t t, dl1(s1t) > 0 and the market share of firm 1 shall increase post-merger.

9 MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES 9 To summarize, we define the cross elasticity of demand term ɛ(t, S 3t ) in Definition 2.1, which measures the percentage change of firm 1 s market share relative to the percentage change of firm 3 s market share. When ɛ(t, S 3t ) > 0, both t and S 3t shall increase post-merger. When S3t < ɛ(t, S 3t ) < 0, then t shall decrease and S 3t shall increase post-merger. When ɛ(t, S 3t ) < S3t t, t shall increase and S 3t shall decrease post-merger. The cross elasticity of demand can be expressed as a function of the demand and supply side parameters and the pre-merger equilibrium market shares 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 characteristics based on equations (10) and (11). We see a linear relation of the firm s product quality Z jt with its market share S jt. Thus knowing the demand and supply side parameters and the changes of post-merger market shares enables the prediction of post-merger product characteristic for each firm. The derivative of firm j s product characteristic with respect to its market share is thus (26) dz jt = α 1 β γ j δ j. For each firm j, the derivative implies the direction of change for the firm j s postmerger product characteristic together with its market share. If α 1 β γ j δ j > 0, then dzjt > 0, and the post-merger product quality and market share shall move in the same direction. On the other hand, if α 1 β γ j δ j < 0, then dzjt < 0, and the post-merger product quality and market share shall move in the opposite direction. It is reasonable to assume that the marginal fixed cost coefficient δ j is positive, thus the change of direction for firm j s post-merger product characteristic is determined by the term of α 1 β γ j. In essence, the term α 1 β quantifies the relative benefit of improving the product quality compared to improving the product price. The term γ j indicates the marginal cost of improving the product quality for one unit. Therefore, the term α 1 β γ j measures the net benefit of firm j to increase its product quality for one unit. Definition 2.2 unit is defined as The net benefit of firm j to increase its product quality for one (27) b j = α 1 β γ j. Clearly, if b j > 0, the firm would like to increase its product quality when its post-merger market share becomes larger. Otherwise, the firm would like to decrease its product quality when the post-merger market share becomes larger.

10 10 Z. QIU For the firm with a better production technology, i.e. γ j is smaller, and the net benefit to increase its product quality is more likely to be positive. Thus the firm is more likely to increase its product quality when it expands its market share. For the firm with inefficient production technology, it may be too costly for the firm to improve its product quality and thus we would expect the postmerger 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 of the product quality or less sensitive to the price, then b j is more likely to be positive and the post-merger product quality is more likely to improve with the post-merger market share. Once the direction of changes for firm j s post-merger market share and product quality are known, we could then predict the change of direction for firm j s product price by the necessary conditions. Equation (11) characterizes a nonlinear relation of the firm j s product price with its market share. We shall denote the marginal cost and the markup term as (28) mc jt = γ j S jt ( β α γ j δ j ) θ jtγ j δ j + ω jt, (29) 1 σ jt = α(1 S jt ). Thus the price of firm j consists of two terms: the marginal cost and the markup term (30) P jt = mc jt + σ jt. When b j > 0, the equilibrium market share and the product characteristic are positive correlated, i.e. dzjt > 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 share shall also give the firm a higher market power and increase its markup. In that case, both the marginal cost and the markup effects work in the same direction. The derivative dpjt is positive and the price shall increase with a higher market share of firm j. On the other hand, when b j < 0, the equilibrium market share and the product characteristic are negative correlated. Therefore, to increase the market share shall decrease the marginal cost by lowering the product quality of the firm. The markup effect is positive regardless of the value of b j. In that case, the marginal cost effect and the markup effect work in the opposite way and whether the price increases or not depends on which effect dominates. To tell which effect dominates, we shall derive the slope of change in firm j s price as a function of its market share (31) dp jt = γ j ( α 1 β γ j δ j ) 1 + α(1 S jt ) 2.

11 MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES11 dp jt If the marginal cost effect dominates, < 0 and the post-merger product price moves in the opposite direction with the market share. If the markup effect dominates, dpjt > 0 and the post-merger product price moves in the same direction with the market share. From the equation (31) above, whether dpjt is positive or negative depends on the net benefit of improving product quality b j and the pre-merger equilibrium market share S jt. We then calculate the threshold market share Sj c dpjt that makes = 0 and hence propose the following definition. Definition 2.3 defined as [ (32) Sj c = 1 The threshold market share of firm j such that dpjt δ j αγ j b j ] 1 2. = 0 is When b j < 0, and S jt > Sj c, the post-merger price shall increase with the market share and the markup effect dominates. When b j < 0 and S jt < Sj c, the postmerger price shall decrease with the market share and the markup effect is too weak to offset the marginal cost effect. In addition, when b j > 0, both effects work in the same direction and the price shall increase with the market share regardless of the pre-merger market share. To summarize, we can predict the changes of directions for the post-merger market shares, prices and product qualities by knowing the cross elasticity of demand, i.e. ɛ(t, S 3t ), the net benefit for adjusting product quality b j and the threshold market share Sj c that balances off the marginal cost and the markup effect. The generalized conditions and predictions shall be rigorously presented in the main theorem; c.f. Theorem 3.1 in Section GENERALIZED THEOREM FOR THE POST-MERGER PREDICTION Now, we present our main theorem by generalizing the conditions for the postmerger prediction under the assumptions that there is no consumer s preference changes and cost efficiency gains post merger. Theorem 3.1 Let ɛ(t, S 3t ) be the cross elasticity of demand defined by Definition 2.1, b j be the firm j s net benefit of improving its product quality defined by Definition 2.2, and Sj c dpjt be the threshold market share of firm j such that = 0 defined by Definition If ɛ(t, S 3t ) > 0, the post-merger market shares increase for both firm 1 and firm If S3t t < ɛ(t, S 3t ) < 0, the post-merger market share decreases for firm 1 and increases for firm 3.

12 12 Z. QIU 3. If ɛ(t, S 3t ) < S3t t, 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 can then predict the changes of firms post-merger prices and product qualities. 1. If b j > 0, firm j s post-merger price and product quality move in the same direction with the post-merger market share. dz jt > 0, dp jt > If b j < 0, and S jt > Sj c, firm j s post-merger price moves in the same direction and the product quality moves in the opposite direction with the post-merger market share. dz jt < 0, dp jt > If b j < 0, and S jt < Sj c, firm j s post-merger price and product quality move in the opposite direction with the post-merger market share. dz jt < 0, dp jt < 0. There are a number of implications of Theorem 3.1 we shall discuss. Remark 1 The theorem addresses firms endogenous choices of prices and product qualities pre- and post-merger. When the cross elasticity of demand is positive, the one unit increase in S 3t shall increase the market share for firm 1, i.e. ds1t > 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 market share shall increase for both firm 1 and firm 3. When the cross elasticity of demand is negative but is not too small, i.e S3t t < ɛ(t, S 3t ) < 0, the one unit increase in firm 3 s market share shall correspond to a less than one unit decrease in firm 1 s market share, i.e. 1 < ds1t < 0. The post merger market share shall increase for firm 3 and decrease for firm 1. When the cross elasticity of demand is negative and small, i.e. ɛ(t, S 3t ) < S3t t, we have that ds1t < 1. Hence an one unit increase in S 3t corresponds to a more than one unit decrease in t. Therefore, the post merger market share of firm 1 shall increase and of firm 3 shall decrease. Note that in the later two cases, the two products of firm 1 and firm 3 are substitutes of each other. Remark 2 Knowing the direction of changes for firms market shares post merger, we can then predict the changes in firms product qualities and prices by knowing the signs of the derivative terms, i.e dzjt and dpjt. For product

13 MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES13 qualities, the sign of changes in product qualities to market shares, i.e. dzjt, is the same as the sign of the net benefit b j = α 1 β γ j. When firm j is sufficiently efficient with its production, the term b j is positive and hence firm j chooses to increase its product quality when the post merger market share increases. The product quality and the market share shall move in the same direction post merger. When firm j is not sufficiently good with its production technology, increasing product quality would be too costly and hence the firm would like to decrease its product quality when the market share increases post merger. In that case the product quality and market share shall move in the opposite direction after the merger. Moreover, when the merger involves consumers who value the product quality a lot and/or are less sensitive to product price, the b j is more likely to be positive and the post-merger product quality is more likely to 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. b j > 0, both the marginal cost and the markup effects are positive, and the post-merger price moves in the same direction with the post merger market share. In that case, the positive correlation holds regardless of firm j s pre-merger market share level. The post-merger price shall move in the opposite direction with the market share if the net benefit b j is negative and firm j has a small market share pre-merger, i.e. S jt < Sj c. In that case, the firm has a small market power. The positive markup effect is too small to offset the negative marginal cost effect and hence the overall effect is negative, i.e dpjt dz jt < 0. On the other hand, when the net benefit is negative b j < 0 but the firm j s pre-merger market share is sufficient, i.e. S jt > Sj c, the firm j has a big market power to induce a higher markup effect. Therefore, even though the marginal cost effect is negative, the post-merger price and market share can still have a positive correlation, in the sense that the loss in marginal cost effect is cancelled out by the gain in the markup effect 1/[α(1 S jt )]. We can tell that even a negative net benefit b j can still induce an increase in post-merger price with the market share. The production efficiency is more restrictive for obtaining a positive correlation of product qualities than of product prices together with market shares. To summarize, the post merger market shares, prices and product qualities are endogenously determined by the cross elasticity of demand, i.e. ɛ(t, S 3t ), the net benefit of increasing the product quality, i.e. b j and the threshold market share that balances off the marginal cost and markup effect, i.e. Sj c. The theorem above can be extended with more than three major firms existing pre-merger. Besides, we assumed one major product characteristic which measures the product quality for each firm. The theorem can be extended to study a vector of product characteristics for each product.

14 14 Z. QIU 3.1. Predictions of Post-merger Outcomes Applying the theorem above, we can predict the post-merger outcomes for the merged and non-merging firms. We list the conditions required for different postmerger outcomes. The conditions are based on the pre-merger equilibrium market shares, and the demand and supply side parameters, in particular, ɛ(t, S 3t ), b j and Sj c. Table I summarizes the prediction of post-merger outcomes, in particular, the changes of market shares, prices and product qualities for firm 1 and 3 post-merger. From Table I, the post merger market share shall increase for both or at least one firm, depending on the cross elasticity of demand. The more complementary of the two products, the more likely for the market shares to increase for both firms post merger. If the two products are substitutable, then the merger shall increase the market share of one firm and decrease the market share of the other firm, depending on the magnitude of the cross elasticity of firm 1 relative to firm 3, i.e. ɛ(t, S 3t ). A more negative cross elasticity implies that a one unit increase in S 3t shall cause a more than one unit decrease in t. Given the post merger market shares add up to a fixed fraction, we can predict an increase of the market share for firm 1 and a decrease of the market share for firm 3 post merger. Similarly, the less negative cross elasticity implies that one unit increase in market share of firm 3 would correspond to a less than one unit decrease in firm 1 s market share. Hence, the post-merger market share shall increase for firm 3 and decrease for firm 1. The changes in post merger price and product quality can go either way, depending on the firm s net benefit of improving product quality relative to price, i.e. b j and the pre-merger market share S j. The more productive a firm is, the more likely for b j to be positive and hence the product price and quality are more likely to move in the same direction with the market share. When b j is negative, the post-merger product quality shall change in the opposite direction with the market share. The price shall move in the same direction with the market share if the pre-merger market share is big enough, S j > Sj c so that the positive markup effect dominates the negative marginal cost effect. For the firm with a small premerger market share, the merger may cause a decrease of the post merger price with 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 of the U.S. airline industry. There are a number of reasons to choose the U.S. airline industry. First, there are several mergers happened in the U.S. airline industry in the past few years, with the well-known ones including the merger of

15 MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES15 TABLE I Prediction of post-merger market shares, prices and product characteristics Conditions Post-merger Outcomes ɛ(t, S 3t ) b 1, b 3 S1, c S3 c S 3 P 1 P 3 Z 1 Z 3 > 0 b 1 > 0, b 3 > 0 > 0 b 1 > 0, b 3 < 0 S 3 > S3 c > 0 b 1 > 0, b 3 < 0 S 3 < S3 c > 0 b 1 < 0, b 3 > 0 > S1 c > 0 b 1 < 0, b 3 > 0 < S1 c > 0 b 1 < 0, b 3 < 0 > S1, c S 3 > S3 c > 0 b 1 < 0, b 3 < 0 > S1, c S 3 < S3 c > 0 b 1 < 0, b 3 < 0 < S1, c S 3 > S3 c > 0 b 1 < 0, b 3 < 0 < S1, c S 3 < S3 c ( S3, 0) b 1 > 0, b 3 > 0 ( S3, 0) b 1 > 0, b 3 < 0 S 3 > S3 c ( S3, 0) b 1 > 0, b 3 < 0 S 3 < S3 c ( S3, 0) b 1 < 0, b 3 > 0 > S1 c ( S3, 0) b 1 < 0, b 3 > 0 < S1 c ( S3, 0) b 1 < 0, b 3 < 0 > S1, c S 3 > S3 c ( S3, 0) b 1 < 0, b 3 < 0 > S1, c S 3 < S3 c ( S3, 0) b 1 < 0, b 3 < 0 < S1, c S 3 > S3 c ( S3, 0) b 1 < 0, b 3 < 0 < S1, c S 3 < S3 c < S3 b 1 > 0, b 3 > 0 < S3 b 1 > 0, b 3 < 0 S 3 > S3 c < S3 b 1 > 0, b 3 < 0 S 3 < S3 c < S3 b 1 < 0, b 3 > 0 > S1 c < S3 b 1 < 0, b 3 > 0 < S1 c < S3 b 1 < 0, b 3 < 0 > S1, c S 3 > S3 c < S3 b 1 < 0, b 3 < 0 > S1, c S 3 < S3 c < S3 b 1 < 0, b 3 < 0 < S1, c S 3 > S3 c < S3 b 1 < 0, b 3 < 0 < S1, c S 3 < S3 c 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 industry from the Bureau of Transportation Statistics. The availability of both pre- and post-merger data allows me to predict the post-merger outcomes applying the

16 16 Z. QIU pre-merger estimation and to compare the theorem prediction with the actual observed post-merger outcomes. Finally, the airline industry serves as a critical component of domestic, overseas, commercial and social functions. It counts for around 5% of the U.S. GDP and has created 10 million job opportunities, which is an influential industry to study. In this paper, we shall study the merger of the United and the Continental airlines in October The merger makes the United airline superseded the Delta airline as the world s largest carrier at that time. The merger was approved in October After the approval, however, the United and the Continental airlines still operate separately until March 2012 when the Continental airline changed its name to the United and completely merged the operation system and the technology with the United. Given the longer timespan needed for product characteristics to adjust, we shall look at four quarters after Q as the post merger period. Although we may aware that the complete adjustment of product characteristics may take longer, it would be a good time to look at given that the merger of the American airline and U.S. airway in Dec 9th, 2013 would make the whole picture complicated. We use the four quarters from Q to Q as the pre-merger period being aware that it may include some merger effect from the 2008 merger of the Delta and the Northwest airlines and the 2010 merger of Air Tran airways and the Southwest airlines. For the merger of the United and the Continental airlines in 2010, we shall focus our study on the routes that overlap the two merged airlines with the total number of passengers exceeding ten thousand. We look at the pre-merger periods and find there are 8 overlapping airport pairs/16 origin-dest one-way routes that have both the United and the Continental airlines under operation. We summarize the pre-merger number of passengers and the conditional market shares for those 16 overlapping routes in Table II. For those 16 overlapping routes, both the United and the Continental airlines have 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 two operation carriers and hence obtain the monopoly power on those routes. We expect the merger may have an effect on the non-overlapping routes as well and we shall leave this concern to the future work 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 the U.S. airline industry. The primary datasets for our empirical study include the Airline Origin and Destination Survey, T-100 Domestic Segment Data, and the Airline Fuel Cost and Consumption Data. We construct the average airfare per mile using the Airline Origin and Destination Survey, the flight frequency using

17 MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES17 TABLE II Passengers on overlapping routes between UA and CO Q Airport Pair Passengers Conditional Shares UA CO Others UA CO Others LAX-OGG OGG-LAX SFO-IAH IAH-SFO EWR-SFO SFO-EWR LAX-HNL HNL-LAX EWR-ORD ORD-EWR ORD-IAH IAH-ORD EWR-DEN DEN-EWR DEN-IAH IAH-DEN Datasource: T100 Domestic Segment. the T-100 Domestic Segment Data. Besides, we use the Airline Fuel Cost and Consumption data to calculate the fuel cost per gallon for each airline. The datasets are summarized in Table III. 5. IDENTIFICATION STRATEGY This section addresses the identification strategy for estimating the demand and supply sides of the U.S. airline industry. We shall use the estimation results to predict the post-merger outcomes applying Theorem 3.1. The estimation results and the comparison of the prediction with the real data are shown in the later sections Demand Estimation In our estimation, both product prices and characteristics are allowed to be endogenous pre- and post-merger. The flight frequency and the average airfare per mile are generally important features for the consumer to make airline-route decision. We define each airport pair (origin-destination) as one submarket and each airline-airport pair as the product in the submarket. Hence, the consumer i s utility of choosing airline j on the airport pair r at time t is

18 18 Z. QIU TABLE III Data Sources. Dataset Variables Sample Periods T-100 Domestic Market Share, Frequencies 2009 Q Q3 Segment Airlines 2012 Q Q1 Origin and Destination Airfare, Distance 2009 Q Q3 Survey 2012 Q Q1 Airline Fuel Cost Fuel Cost 2009 Q Q3 and Consumption 2012 Q Q1 (33) U ijrt = βz jrt αp jrt + ξ j + ξ jrt + ε ijrt, where P jrt is the average airfare per mile for one airline-airport pair combination and Z jrt is the flight frequency which measures the product quality in the airline industry. We consider three airlines existing pre-merger, the United, the Continental 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 the other airlines as firm 3. ξ j is the airline s brand effect. ξ jrt is the unobserved product quality that affects the consumer utility. ε ijrt is the idiosyncratic shock and is assumed to follow the T1EV distribution. To estimate the demand, we consider four quarters from Q to Q as the pre-merger period. We assume there is a fixed fraction of people that shall choose the outside option, i.e. S ort = µ. The value of µ shall be estimated from the data. By the property of type one extreme value distribution (34) ln( S jrt S ort ) = βz jrt αp jrt + ξ j + ξ jrt. We shall estimate the consumer s utility function by the log regression. Since the flight frequency and airfare are endogenous variables, they are potentially correlated with the unobserved product quality term, ξ jrt. Instrumental variables (IV) are required for each of them to obtain consistent estimation. We use the fuel cost per gallon of each airline as the instrument variable for average airfare per mile. We expect the higher the fuel cost, the higher the average airfare level P jrt is. For flight frequency, we use the hub status and the population of the origin and destination cities as the instruments. If the origin or destination airport has the airline hub or has a big population size, then we would expect the flight frequency to be higher for that airline-route.

19 MERGER ANALYSIS WITH ENDOGENOUS PRICES AND PRODUCT QUALITIES Supply Estimation After estimating the demand side of the airline industry, we can then recover the marginal cost for each airline-route pair by the necessary condition (35) mc jrt = P jrt 1 α(1 S jrt ). Observing the pre-merger price and the market share for each airline-route pair and having estimated the consumer s utility function, we can then recover the marginal cost for each firm by equation (36) above. Different from the classical approach, we consider the heterogeneity in firms production technologies. The heterogenous production technology shall play an important role in explaining firms different merger incentives and post-merger outcomes. To estimate the airlines marginal cost of production, we adopt a linear marginal cost functional form from the existing literature. Therefore the marginal cost for each airline shall depend on the flight frequency and the unobserved shock (36) mc jrt = γ j Z jrt + ω jrt, where we expect a higher flight frequency implies a higher marginal cost, i.e. γ j > 0. Here ω jrt is the unobserved marginal cost shock and is allowed to be correlated with the observed product quality. Hence instrument variables are required to obtain consistent estimation. We shall use the airlines hub status and the population at the origin- and destination cities as the instruments for flight frequencies. After recovering the firm s specific productivity, i.e. γ j, we then recover the value of marginal fixed cost for each airline-route pair from the necessary conditions (37) df ixed jrt dz jrt = ( β α γ j)s jrt. Observing the pre-merger market share, and having estimated the demand and supply sides of the airline industry, we can then calculate the marginal fixed cost for each airport-route pair. We then estimate the airlines marginal fixed costs as a function of the flight frequencies. We adopt a quadratic form of firms fixed costs from the existing literature (38) df ixed jrt dz jrt = δ j Z jrt + θ jrt, where we would expect a higher flight frequency implies a higher marginal fixed cost, i.e. δ j > 0. Here θ jrt is the unobserved fixed cost shock and is allowed to be correlated with the observed product quality Z jrt. Hence we apply the same set of instruments for flight frequencies. Once the estimates of the consumer s utility and the firms marginal costs and fixed costs are obtained, we can then apply Theorem 3.1 to predict changes in firms post-merger market shares, prices and flight frequencies. The empirical results are shown in Section 6.

20 20 Z. QIU TABLE IV Estimation Results on Parameters for Utilities Pre-merger. Mean Utilities Coeff St. Error Z p-value 95% Conf. Interval Frequency [1.571, 3.985] Airfare [0.348, 2.236] UA [-5.646, ] CO [-6.411, ] Firm [-8.934, ] 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 United and the Continental Airlines. We first estimate the demand side of the airline industry by estimating the consumer s utility function. We then recover the marginal costs and fixed costs for each airline from the conditions shown in equations (35) and (37). Finally, the pre-merger estimation results are used to predict the post-merger outcomes according to Theorem 3.1. For the pre-merger period, we use the airline data that covers Q to Q In particular, we focus on the changes of market shares, average airfares and flight frequencies for the United and the other airlines pre- and post-mergers. We use the airline hub status and the population at the origin- and end-point airports as the instruments for flight frequencies. We use the fuel cost per gallon of each airline as the instrument for flight airfare per mile. The pre-merger estimation results are shown in Table IV, V, and VI. Table IV shows the estimation results of the consumer s utility function. We shall denote β to be the coefficient of flight frequency and α to be the coefficient of average airfare. From the estimation, a consumer values the flight frequency and more likely to purchase from the airline with frequent flights. A higher airfare shall decrease a consumer s utility. The airline fixed effect is the highest for the United airline, and the Continental airline has the second highest. Other airlines, on average, have the lowest fixed effect. From Table IV, we calculate the marginal benefit of improving flight frequency relative to airfare, i.e. β/α. We then compare the marginal benefit with the marginal cost estimated in table V to predict changes in flight frequencies and airfares post merger. Table V shows the estimation results of firms marginal cost functions. We denote the marginal cost coefficient of firm j s flight frequency as γ j, which measures how costly to improve the flight frequency by one unit. The estimation results in Table V imply that the Continental airline has a better production technology in terms of marginal cost compared to the United airline, i.e. γ 2 < γ 1. The other

21 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. Interval UA frequency [1.018, 1.363] CO frequency [0.782, 0.984] Others frequency [0.445, 0.616] Instrumented: UA frequency CO frequency Others frequency Instruments: ua-hub-origin ua-hub-dest co-hub-origin co-hub-dest others-hub-origin others-hub-dest ua-pop-origin ua-pop-dest co-pop-origin co-pop-dest others-pop-origin others-pop-dest TABLE VI Estimation Results on Parameters for the Fixed Costs Pre-merger. Fixed Costs Coeff St. Error Z p-value 95% Conf. Interval UA frequency [0.009, 0.014] CO frequency [0.017, 0.020] Others frequency [0.010, 0.013] Instrumented: UA frequency CO frequency Others frequency Instruments: ua-hub-origin ua-hub-dest co-hub-origin co-hub-dest others-hub-origin others-hub-dest ua-pop-origin ua-pop-dest co-pop-origin co-pop-dest others-pop-origin others-pop-dest airlines, on average, have the best production technology in terms of marginal cost compared to the United and the Continental airlines. Combining these with Table IV, we form the measure of firm j s net benefit of improving flight frequency, i.e. b j = β/α γ j > 0. We then estimate the marginal fixed cost for each airline 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 δ j. A positive coefficient shows that a higher flight frequency shall cause a higher marginal fixed cost of production. From the estimation results, the United airline and the other airlines have a comparable level of marginal fixed cost coefficient, while the Continental airline has a higher marginal fixed cost coefficient. After estimating the demand and supply sides of the airline industry, we can then combine the estimation results together with the pre-merger market shares to predict the post-merger outcomes. Using the parameter estimation from Table IV, 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. ɛ(, S 3 ), the net benefit of improving product quality, i.e. b j, and the threshold market share of each firm Sj c dpj such that ds j = 0. The conditions of the three measures together with the pre-merger levels of market shares shall be shown in Table VII below. Based on the Table, we can then apply Theorem 3.1 to predict the post

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