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An Empirical Model of Dynamic Limit Pricing: The Airline Industry

U(ɛ ijm , p jm , x jm , ξ jm ; θ) = x jm β − αp jm + ξ jm + ɛ ijm = δ jm + ɛ ijmwhere θ = (α, β) is the parameters **of** the system to be estimated.For convenience **of**notation the subscript m will be dropped except where its inclusion aids understanding.As is standard in the literature p j is the fare for product j, ξ j is a common (to allconsumers) vector **of** unobserved product attributes that acts to vertically differentiateairline-product pairs, e.g. upholstery quality, cabin attendant friendliness, and x j willinclude all observed product attributes, e.g. seat size, number **of** connections, distance,etc. Consumer i chooses product j if and only if,U(ɛ ij , p j , ξ j , x j ; θ) ≥ U(ɛ ik , p k , ξ k , x k ; θ) ∀ k = 0, 1, ....J (1)where product 0 is the outside option, to be thought **of** as taking an alternative mode **of**transport.Heterogeneity in tastes will enter the model through ɛ, which is assumed to be independentlydistributed multivariate extreme value across consumers and products. Fromequation (1) these ɛ define the set **of** consumers who purchase product j. Formally, thisset is given by A j (δ) = {ɛ i : δ j + ɛ i,j ≥ δ k + ɛ i,k , ∀k ≠ j}. **The** market share **of** airline j isgiven by the probability that ɛ i is contained in A j ,∫s j (δ(x, p, ξ), x, θ) =A j (δ)f(ɛ, x, σ ɛ )dɛ =exp(δ j )∑k∈J exp(δ k)(2)where the second equality follows from the assumptions on the distribution **of** ɛ.**The** measure **of** consumers in market m is given by M.As with elsewhere in theliterature (e.g. Borenstein and Rose [1995], Ciliberto and Tamer [2009]) this is taken to bethe average **of** the population in the two endpoints **of** the route 3 . **The** observed output **of**3 **The** other popular definition (e.g. Berry and Jia [2008], Ciliberto and Williams [2010]) is to use thegeometric mean **of** the endpoints.8

firm j is thus,q j = Ms j (x, ξ, p; θ) (3)with q m = (q 1m , q 2m , ...q Jm ) denoting the vector **of** quantities on market m.3.2 Firm BehaviorWhilst the consumer side **of** the model is familiar the supply side will require more attention.As an overview, on each independent market there exists a monopolist incumbent anda potential entrant. At time t the incumbent has a private marginal cost **of** serving passengers,c I,t , and sets prices so as to maximize the flow **of** future pr**of**its. Importantly, priceis used as a strategic variable for two purposes. **The** first is as a mark-up over marginalcosts so as to choose the point on the demand curve that maximizes static pr**of**its as inmodels **of** complete information. **The** second is as a mechanism to deter entry, the ideabeing that the firm can set its price so as to signal its marginal cost. This second objectivemay well operate in conflict with the first so that price deviates from that **of** a staticpr**of**it maximizing monopolist. **The** intuition is simple: by setting a price below that **of** amonopolist the entrant may infer that the marginal cost **of** the incumbent is sufficientlylow so as to make entry unattractive. If the signaled cost is insufficient to deter entry thenthe potential entrant can pay an entry cost κ t . Once the entrant is in the market the firmscompete as complete information price setting duopolists for the remainder **of** the game.**The** setup thus far described is similar to that **of** Milgrom and Roberts [1982]. Whereit will differ is that the marginal cost **of** the incumbent is assumed to be time varying andthat it will evolve according to a Markov process defined on continuous support. This generatesa repeated incentive to signal (Roddie [2012a,b]). Additionally, the entry cost willbe independently time varying and identically distributed. **The** advantage **of** this approachis that it can rationalize entry at different periods **of** the game, in contrast to the all ornothing outcome **of** the existing literature.9

- Page 1 and 2: An Empirical Model of Dynamic Limit
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- Page 13 and 14: Figure 1: Entry Regionsbe non-zero
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- Page 21 and 22: Table 2: Linear Demand: Welfare Eva
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- Page 25 and 26: Figure 4: Histogram of Southwest’
- Page 27 and 28: same reason there are more monopoly
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- Page 31 and 32: third of fourth entrant. It would a
- Page 33 and 34: Table 7 reports the results for thi
- Page 35 and 36: 5.2 Welfare ImplicationsThe above r
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- Page 39 and 40: I.K. Cho and D.M. Kreps. Signaling
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- Page 45 and 46: where φ I is given an explicit for
- Page 47 and 48: Collecting these results we have th
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