Quantitative Techniques for Competition and Antitrust Analysis_13 docx

Thepricing equation of given goods will also depend on the demand and cost parameters of other goods which are produced by the same firm.. A merger will result in a change in the pricing

Static ‘‘Nash equilibrium’’ prices where each firm is doing the bestthey can given the price charged

Figure 8.6. A two-to-one merger in a differentiated product pricing game.the demand model For example, the linear model could involve D2.p/ D a2C

b21p1C b22p22so that @D2.p/=@p1D b21and, analogously, @D1.p/=@p2D b12.Note that if the two products are substitutes and @Di.p/=@pj > 0, then the equi-librium price for a firm maximizing joint profits will be higher, absent countervailingefficiencies This is because the monopolist, unlike the single-product firm in theduopoly, gains the profits from the customers who switch to the competing productafter a price increase We illustrated this fact for the two-product game in chapter 2.The effect of a merger in a two-to-one merger in a market with two differentiatedsingle-product firms is illustrated in figure 8.6 Because Bertrand price competitionwith differentiated products is a model where products are strategic complements,the reaction functions are increasing in the price of the other good The intersection

of the two pricing functions gives the optimal price for the Bertrand duopoly Afterthe merger, the firm will price differently since it internalizes the effect of changingthe price of a product on the other product’s profits This will result in higher pricesfor both products In this case, the post-merger price is also that which would beassociated with a perfect cartel’s prices

8.3.2.2 Multiproduct Firms

Let us now consider the case of a firm producing several products pre-merger If amarket is initially composed of firms producing several products, this means thatfirms’ profit maximization already involves optimization across many products Thepricing equation of given goods will also depend on the demand and cost parameters

of other goods which are produced by the same firm A merger will result in a change

in the pricing equation of certain goods as the parameters of the cost and demand

of the products newly acquired by the firm will now enter the pricing equations of

all previously produced goods This is because the number of products over whichthe post-merger firm is maximizing profits has changed relative to the pre-mergersituation.

Suppose firm f produces a set of products which we denote =f  = D f1; : : : ; J gand which is unique to this firm The set of products produced by the firm does nottypically include all J products in the market but only a subset of those The profit-maximization problem for this firm involves maximization of the profits on all thegoods produced by the firm:

To these equations, we must add the first-order conditions of the remaining firms

so that in the end we will, as before in the single-product-firms case, end up with atotal of J first-order conditions, one for each product being sold Solving these Jequations for the J  1 vector of unknown prices pwill provide us with the Nashequilibrium in prices for the game

In comparison with the case where firms produced only a single product, thefirst-order conditions for multiproduct firms have extra terms This reflects the factthat the firms internalize the effect of a change in prices on the revenues of thesubstitute goods that they also produce Because of differences in ownership, first-order conditions may well not have the same number of terms across firms

To simplify analysis of this game, we follow the literature and introduce a J  Jownership matrix
with the j kth element (i.e., j th row, kth column) defined by

j D1

j k.pj
mcj/@Dj.p/

@pk D 0 for all k 2 =f;where the
j kterms allow the summation to be across all products in the market

in all first-order conditions for all firms The matrix
acts to select the terms thatinvolve the products produced by firm f and changes with the ownership pattern

of products in the market At the end of the day, performing the actual mergersimulations will only involve changing elements of this matrix from zero to one andtracing through the effects of this change on equilibrium prices Once again, we will

have a set of equations for every firm resulting in a total of J pricing equations, onefirst-order condition for each product being sold.

In order to estimate demand parameters, we need to specify demand equations.For simplicity, let us assume a system of linear demands of the form,

qk D Dk.p1; p2; : : : ; pJ/ D akC

JX

j k.pj
mcj/bj kD 0 for all j; k D 1; : : : ; J

but one must then remember that the vector of quantities is endogenous and dent on prices Writing the system of equations this way and adding it togetherwith the demand system provide the 2J equations which we could solve for the2J endogenous variables: J prices and J quantities Doing so provides the directanalogue to the standard supply-and-demand system estimation that is familiar forthe homogeneous product case Sometimes we will find it easier to work with only

depen-J equations and to do so we need only substitute the demand function for eachproduct into the corresponding first-order condition Doing so allows us to write a

J -dimensional system of equations which can be solved for the J unknown prices.Large systems of equations are more tractable if expressed in matrix form Fol-lowing the treatment in Davis (2006d) to express the demand system in matrix form,

we need to define the matrix of demand parameters B0as

B0D

26666

b11    b1j    b1J::

bk1    bkj    bkJ::

b    b    b

37777

;

where bkj D @Dk.p/=@pj, and also define

a D

266664

a1::

:

ak::

:

aJ

37777

a1::

:

ak::

:

aJ

377775C

266664

b11    b1j    b1J::

bk1    bkj    bkJ::

bJ1    bJj    bJJ

377775

266664

p1::

:

pj::

:

pJ

377775

;

or, far more compactly in matrix form, as q D a C B0p

In order to express the system of pricing equations in matrix format, we need tospecify the J  J matrix
 B, which is the element-by-element product of
and

B, sometimes called the Hadamard product.15 Note that B is the transpose of B0.Specifically, define

 B D

266664

11b11   
j1bj1   
J1bJ1::

1kb1k
j kbj k
J kbJ k::

1Jb1J   
jJbjJ   
JJbJJ

377775

;

where bj k D @Dj.p/=@pk The rows will include the parameters of the pricingequation of a given product k The term
j k will take the value of either 1 or 0depending on whether the firm produces goods j and k or not and
jj D 1 for all

j since the producer of good j produces good j

Recall the analytic expression for the pricing equations:

c D

26

mc1::

:

mcJ

37

5 and a D

26

a1::

:

aJ

37

5 :

Alternatively, as we have already mentioned we may sometimes choose to workwith the J pricing equations without substituting the demand equations: q C
B/.p
c/ D 0 We will then need to work with a system of equations comprisingthese J equations and also the J demand equations

Written in matrix form, the equations that we need to solve simultaneously canthen compactly be written as

q C
 B/.p
c/ D 0 and q D a C B0p:

Using a structural form specification with all endogenous variables on the left side

of the equations and the exogenous ones on the right side we have

#D

#D

#:

This expression gives an analytic solution for all prices and all quantities for anyownership structure that can be represented in
since we may arbitrarily changethe values of
j k from 0s to 1s to change the ownership structure provided onlythat we always respect the symmetry condition that
j k D
kj

With this system in place, once the parameters in B, c, and a are known, we cancalculate equilibrium prices after a merger by setting the corresponding elements of

j kto 1 Indeed, we can calculate the equilibrium prices and quantities (and henceprofits) for any ownership structure

8.3.2.3 Example of Merger Simulation

To illustrate the method, consider the example presented in Davis (2006f), a marketconsisting of six products that are initially produced by six different firms Supposethe demand for product 1 is approximated by a linear demand and its parametershave been estimated as follows:

q1D 10
2p1C 0:3p2C 0:3p3C 0:3p4C 0:3p5C 0:3p6:

By a remarkably happy coincidence, the demands for other products have also beenestimated and conveniently turned out to have a similar form so that we can write

the full system of demand equations in the form

#D

2 0:3 0:3 0:3 0:3 0:30:3
2 0:3 0:3 0:3 0:30:3 0:3
2 0:3 0:3 0:30:3 0:3 0:3
2 0:3 0:30:3 0:3 0:3 0:3
2 0:30:3 0:3 0:3 0:3 0:3
2

377775

;

.
Pre B/ D

26666

;

c D

266664

111111

377775

266664

101010101010

377775:

We can solve for prices and quantities:

#:

If the firm that produced product 1 merges with the firm that produced product 5 theownership matrix will change so that

.
Post-merger B/ D

26666

This is because the new pricing equation for product 1 will be derived from thefollowing first-order condition:

#:

These kinds of matrix equations are trivial to compute in programs such as lab or Gauss They may also be programmed easily into Microsoft Excel, makingmerger simulation using the linear model a readily available method The predictedequilibrium prices for each product under different ownership structure are repre-sented in table 8.1 The market structure is represented by n1; : : : ; nF/, where thelength of the vector F indicates the total number of active firms in the market andeach of the values of nf represents the number of products produced by the f thfirm in the market The largest firm is represented by n1 Tables 8.1 and 8.2 showequilibrium prices and profits respectively for a variety of ownership structures Theresults show, for example, that a merger between a firm that produces five productsand one firm that produces one product, i.e., we move from market structure 5; 1/

Mat-to the market structure with one firm producing six products (6), increases the prices

by more than 33% Table 8.2 shows that the merger is profitable

Table 8.1. Prices under different ownership structures.

8.3.2.4 Inferring Marginal Costs

In cases where estimates of marginal costs cannot be obtained from industry mation, appropriate company documents, or management accounts, there is analternative approach available Specifically, it is possible to infer the whole vec-tor of marginal costs directly from the pricing equations provided we are willing

infor-to assume that observed prices are equilibrium prices Recall the expression for thepricing equation in our linear demand example:

a C B0p C
 B/.p
c/ D 0:

In merger simulations, we usually use this equation to solve for the vector of prices

p However, the pricing equation can also be used to solve for the marginal costs c

in the pre-merger market, where prices are known Rearranging the pricing equation

we have

c D p C
 B/1.a C B0p/:

More specifically, if we assumer pre-merger prices are equilibrium prices, then giventhe demand parameters in a; B/ and the pre-merger ownership structure embodied

in
Pre, we can infer pre-merger marginal cost products for every product using theequation:

cPreD pPreC
Pre B/1.a C B0pPre/:

One needs to be very careful with this calculation since its accuracy greatly depends

on having estimated the correct demand parameters and also having assumed thecorrect firm behavior Remember that the assumptions made about the nature ofcompetition determine the form of the pricing equation What we will obtain when

we solve for the marginal costs are the marginal costs implied by the existing prices,the demand parameters which have been estimated and also the assumption aboutthe nature of competition taking place, in this case differentiated product Bertrandprice competition

Given the strong reliance on the assumptions, it is necessary to be appropriatelyconfident that the assumptions are at least a reasonable approximation to reality Tothat end, it is vital to proceed to undertake appropriate reality checks of the results,including at least checking that estimated marginal costs are actually positive andideally are within a reasonable distance of whatever accounting or approximatemeasures of marginal cost are available This kind of inference involving marginalcosts can be a useful method to check for the plausibility of the demand estimates andthe pricing equation If the demand parameters are wrong, you may well find that theinferred marginal costs come out either negative or implausibly large at the observedprices If the marginal costs inferred using the estimated demand parameters areunrealistic, then this is a signal that there is often a problem with our estimates ofthe price elasticities Alternatively, there could also be problems with the way wehave assumed price setting works in that particular market

8.3.3 General Linear Quantity Games

In this section we suppose that the model that best fits the market involves petition in quantities Further, suppose that firm f chooses the quantities of theproducts it produces to maximize profits and marginal costs are constant, then thefirm’s problem can be written as

In that case, the quantity setting equations become

#D

#:

As usual, the expression that will allow us to calculate equilibrium quantities andprices for an arbitrary ownership structure will then be

"

pq

#D

#:

8.3.4 Nonlinear Demand Functions

In each of the examples discussed above, the demand system of equations had aconvenient linear form In some cases, more complex preferences may require thespecification of nonlinear demand functions The process for merger simulation inthis case is essentially unaltered One needs to calibrate or estimate the demandfunctions, solve for the pre-merger marginal costs if needed and then solve for thepost-merger predicted equilibrium prices That said, solving for the post-mergerequilibrium prices is harder with nonlinear demands because it may involve solving

a J  1 system of nonlinear equations Generally, and fortunately, simple iterativemethods such as the method of iterated best responses seem to converge fairlyrobustly to equilibrium prices (see, for example, Milgrom and Roberts 1990).Iterated best responses is a method whereby given a starting set of prices, thebest responses of firms are calculated in sequence One continues to recalculatebest responses until they converge to a stable set of prices, the prices at which allfirst-order conditions are satisfied At that point, provided second-order conditionsare also satisfied, we will know we will have found a Nash equilibrium set of prices.The process is familiar to most students used to working with reaction curves asthe method is often used to indicate convergence to Nash equilibrium in simpletwo-product pricing games that can be graphed

In practice, iterated best responses work as follows:

1 Define the best response for firm f given the rival’s prices as the price thatmaximizes its profits under those market conditions:

3 Pick a starting firm f =1 and a starting value for the prices of all products

second-In pricing games we do not need to use iterated best responses and typically alarge range of updating equations will result in convergence of prices to an equilib-rium price vector In the empirical literature, it has been common to use a simplyrearranged version of the pricing equation to find equilibrium prices To ease presen-tation of this result we will change notation slightly Specifically, we denote demandcurves as q.p/ in order for Dpq.p/ to denote the differential operator with respect

to p applied to q.p/ Specifically, denote the J  J matrix of slopes of the demandcurves as Dpq.p/ which has j; k/th element, @qj.p/=@pk Using the general form

of the first-order conditions for nonlinear demand curves, we can write our pricingequations as

q.p/ C Œ
 Dpq.p/.p
c/ D 0;

where as before the “dot” denotes the Hadamard product As a result the empiricalliterature has often used the iteration

pkC1D c
Œ
 Dpq.pk/1q.pk/

to define a sequence of prices beginning from some initial value p0, often set equal

to c In practice, for most demand systems used for empirical work, this iterationappears to converge to a Nash equilibrium in prices The closely related equation

c D p
Œ
 Dpq.p/1q.p/

can be used to define the value of marginal costs that are consistent with Nash pricesfor a given ownership structure in a manner analogous to that used for the lineardemand curves case in section 8.3.2.4

Iterated best responses do not generally work for quantity-setting games becauseconvergence is not always achieved due to the form of the reaction functions Thereare other methods of solving systems of nonlinear equations, but in general there aregood reasons to expect iterated best responses to work and converge to equilibriumwhen best response functions are increasing.16

As in most games, one should in theory check for multiple equilibria Once wehave more than two products with nonlinear demands, the possible existence ofmultiple equilibria may become a problem and, depending on the starting values

of prices, it is possible that we may converge to different equilibrium solutions.That said, if there are multiple equilibria, supermodular game theory tells us that

in general pricing games among substitutes we will have “square” equilibrium sets.One equilibrium will be the bottom corner, another will be the top corner, and if

we take the values of the other corners they will also be equilibria This result isreferred to as the fact that equilibria in pricing games are “complete lattices” (i.e.,squares).17If we think firms are good at coordinating, one may argue that the highprice equilibrium will be more likely In that case, it may make sense to start theprocess of iterating on best responses from a particularly high prices levels sincesuch sequences will tend to converge down to the high price and therefore high profitequilibrium

Even though it is good practice, it is by no means common practice to report

in great detail on the issue of multiple equilibria beyond trying the convergence toequilibrium prices from a few initial prices and verifying that each time the algorithmfinds the same equilibrium.18

8.3.5 Merger Simulation Applied

In this section, we describe two merger exercises that were executed in the context ofmerger investigations by the European Commission The discussion of these mergersimulations includes a brief description of the demand estimation that underlies thesimulation model, but we also refer the reader to chapter 9 for a more detailedexploration of the myriad of interesting issues that may need to be addressed in thatimportant step of a merger simulation The examples we present below illustrate

16 The reason is to do with the properties of supermodular games See, for example, the literature cited in Topkis (1998) In general, in any setting where we can construct a sequence of monotonically increasing prices with prices constrained within a finite range, we will achieve convergence of equilibrium For those who remember graduate school real analysis, the underlying mathematical reason is that monotonic sequences in compact spaces converge Although, in general, quantity games cannot be solved in this way, many such games can be (see Amir 1996).

17 See Topkis (1998) and, in particular, the results due to Vives (1990) and Zhou (1994).

18 Industrial economists are by no means unique in such an approach since the same potential for multiplicity was, for example, present in most computational general equilibrium models and various authors subsequently warned of the dangers of ignoring multiplicity in policy analysis The computation

of general equilibrium models became commonplace following the important contribution by Scarf (1973) The issue of multiplicity has arisen in applications See, for example, the discussion in Mercenier (1995) and Kehoe (1985).

what actual merger simulations look like and also provide examples of the type ofscrutiny and criticisms that such a simulation will face and hence the analyst needs

to address

8.3.5.1 The Volvo–Scania Case

The European Commission used a merger simulation model for the first time in theinvestigation of its Volvo–Scania merger during 1999 and 2000 Although the Com-mission did not base its prohibition decision on the merger simulation, it mentionedthe fact that the results of the simulation confirmed the conclusions of the morequalitative investigation.19 The merger involved two truck manufacturers and theinvestigation centered on five markets where the merger seemed to create a dom-inant firm with a market share of more than or close to 50% in Sweden, Norway,Finland, Denmark, and Ireland Ivaldi and Verboven (2005) details the simulationmodel developed for the case The focus of the analysis was on heavy trucks, whichcan be of two types known as “rigid” and “tractor,” the latter carrying a detachablecontainer

The demand for heavy trucks was modeled as a sequence of choices by theconsumer, who in this case was a freight transportation company Those companieschose the category of truck they wanted and then the specific model within thechosen category

A model commonly used to represent this kind of nested choice behavior is thenested logit model In this case, because the data available were aggregate data, asimple nested logit model was estimated using the three-stage least-squares (3SLS)estimation technique (a description of this method can be found in general economet-ric books such as, for example, Greene (2007), but see also the remarks below) Thenested logit model is worthy of discussion in and of itself and, while we introducethe model briefly below for completeness, the reader is directed to chapter 9 and inparticular section 9.2.6 for a more extensive discussion Here, we will just illustratehow assumptions about customer choices underpin the demand specifications wechoose to estimate

The nested logit model supposes that the payoff to individual i from choosingproduct j is given by the “conditional indirect utility” function:20

uij D ıj C igC 1
 /"ij;where ıj is the mean valuation for product j which is assumed to be in nest, orgroup, g We denote the set of products in group g as Gg A diagram describing

19 Commission Decision of 14.03.2000 declaring a concentration to be incompatible with the common market and the functioning of the EEA Agreement (Case no COMP/M 1672 Volvo/Scania) Council Regulation (EEC) no 4064/89.

20 This is termed the conditional indirect utility model because it is “conditional” on product j , while

it depends on prices (through ı j D ˛pjC ˇ xj C j as explained further below) Direct utility functions depend only on consumption bundles.

the nesting structure in this example is provided in figure 9.5 Note that "ij isproduct-specific while ig is common to all products within group g for a givenindividual The individual’s total idiosyncratic taste for product j is given by thesum, igC 1
 /"ij The parameter  takes a value between 0 and 1 and note that itcontrols the extent to which a consumer’s idiosyncratic tastes are product- or group-specific If  D 1, the individual consumer’s idiosyncratic valuations for all theproducts in a group are exactly the same and their preferences for each good in thegroup g are perfectly correlated That means, for example, that a consumer who buys

a good from group g will tend to be a consumer with a high idiosyncratic taste for allproducts in group g In the face of a price rise by the currently preferred good j , such

a consumer will tend to substitute toward another product in the same group sinceshe tends to prefer goods in that group In Volvo–Scania the purchasers of truckswere freight companies and if  is close to 1 it captures the taste that some freightcompanies will prefer trucks to be rigid while others will prefer tractors, and in eachcase freight companies will not easily shop outside their preferred group of products

In contrast, if  D 0 and we make a judicious choice for the assumed distribution of

ig, then the valuation of products within a group is not correlated and consumerswho buy a truck in a particular group will not have any systematic tendency toswitch to another product in that group.21 They will compare models across allproduct groups without exhibiting a particular preference for a particular group.The average valuation ıj is assumed to depend on the price of the product p, theobserved characteristics of the product xj, and the unobserved characteristics of the

j that will play the role of product specific demand shocks In particular,

a common assumption is that

ıj D
˛pj C ˇxj j:

In this case, the observed product characteristics are horsepower, a dummy for

“nationally produced,” as well as country- and firm-specific dummies

Normalizing the average utility of the outside good to 0, ı0D 0, and making usualconvenient assumptions about the distribution of the random terms, in particular,that they are type 1 extreme value (see, for example, chapter 9, Berry (1994), or, forthe technically minded, the important contribution by McFadden (1981)), the nestedlogit model produces the following expression for market shares, or more preciselythe probability sj that a potential consumer chooses the product j :

21 This is by no means obvious We have omitted some admittedly technical details in the formulation

of this model and this footnote is designed to provide at least an indication of them As noted in the text, for this group-specific effect formulation to correspond to the nested logit model, we must assume a particular distribution for ig and moreover one that depends on the value of  so that it is more accurate

to write ig  / In fact, Cardell (1997) shows that there is a unique choice of distribution for ig such that if " ij is an independent type I extreme value random variable, then ig  / C 1   /"ijis also

an extreme value random variable provided 0 6  < 1.

In particular, we need ˛ > 0 and 0 6  6 1 We discuss this model at greaterlength in chapter 9 For now we note one potentially problematic feature of thenested logit model: the resulting product demand functions satisfy the assumption

of “independence of irrelevant alternatives” (IIA) within a nest IIA means that if

an alternative is added or subtracted in a group, the relative probability of choosingbetween two other choices in the group is unchanged This assumption was heavilycriticized by the opposing experts in the case

The data needed for the estimation are the prices for all products, the teristics of the products, and the probability that a particular good is chosen Thisprobability is approximated by the product market share so that

charac-sj D qj

M;where qj is the quantity sold of good j and M is the total number of potentialconsumers The market share needs to be computed taking into account the outsidegood, which is why the total number of potential consumers and not the total number

of actual buyers is in the denominator Ivaldi and Verboven assume that the potentialmarket is either 50% or 300% larger than the actual sales A potential market that is50% larger than market sales can be described as M D 1:5.PJ

wj and an error term The observed cost shifters included horsepower, a dummyvariable for “tractor truck,” a set of country-specific fixed effects, and a set of firm-specific fixed effects The marginal cost function is assumed to be of the form,

f D X

j 2=

.pj
cj/qj.p/
F;

where =f is the subset of product produced by firm f , cj is the marginal cost ofproduct j , which is assumed to be constant, and F are the fixed costs The Nashequilibrium for a multiproduct firm in a price competition game is represented bythe set of j pricing equations:

qjC Xk2= f

D 0 for j 2 =f and also for each firm f:

These J equations, together with the J demand equations, provide us with thestructural form for this model Note that the structural model involves a demandcurve and a “supply” or pricing equation for each product available in the market,

a total of 2J equations The only substantive difference between the linear and thisnonlinear demand curve case is that these supply (pricing) and demand equationsmust be solved numerically in order to calculate equilibrium prices for given values

of the demand- and cost-side parameters and data

The data used to estimate the model covered two years of sales from truck panies in sixteen European countries To estimate the model, we use identificationconditions based on the two error terms of the model Specifically, we assume that

com-j.ˇ; / j z1j D 0 and EŒ!j.ˇ; / j z2j D 0(where z1jand z2jare sets of instrumental variables) in order to identify the demandand supply equations These moment conditions are exactly analogous to the momentconditions imposed on demand and supply shocks in the homogeneous product con-text.22Ivaldi and Verboven undertake a simultaneous estimation of the demand andpricing equations using a nonlinear 3SLS procedure While in principle at least thedemand side could be estimated separately, the authors use the structure to imposeall the cross-equation parameter restrictions during estimation The sum of horse-power of all competing products in a country per year and the sum of horsepower

of all competing products in a group per year are used as instruments to account forthe endogeneity of prices and quantities in both the demand and pricing equationfollowing the approach suggested initially by Berry et al (1995) The techniquethey use, 3SLS, is a well-known technique for estimation of simultaneous equation

22 The analyst may on occasion find it appropriate to estimate such a model using 2J moment ditions, one for each supply (pricing) and demand equation Doing so requires us to have multiple observations on each product’s demand and pricing intersection, perhaps using data variation over time from each product (demand and supply equation intersection) Alternatively, it may be appropriate to estimate the model using only these two moment conditions and use the cross-product data variation directly in estimation This approach may be appropriate when unobserved product and cost shocks are largely independent across products or else the covariance structure can be appropriately approximated.

con-Table 8.3. Estimates of the parameters of interest.

Potential market factor

Source: Table 2 from Ivaldi and Verboven (2005).

models The first two stages of 3SLS are very similar to 2SLS while in the Ivaldi–Verboven formulation the third stage attempts to account for the possible correlationbetween the random terms across demand and pricing equations

Estimation produces results consistent with the theory such as the fact that specific effects that are associated with higher marginal costs produce higher valua-tions for consumers Horsepower also increases costs On the other hand, the authorsfind that horsepower has a negative albeit insignificant effect on customer valuation.The authors explain this by arguing that the higher maintenance costs associated withhigher horsepower may lower the demand but the result is nevertheless somewhattroubling The authors also report that they obtain positive and reasonable estimatesfor marginal costs and mean product valuations The estimated marginal costs implymargins which were higher than those obtained in reality, although this observationwas a criticism rejected by the authors on the grounds that accounting data do notnecessarily reflect economic costs

firm-Table 8.3 shows the results for a subset of the demand parameters, namely ˛ and

 , for two scenarios regarding the size of the total potential market Specifically,

r D 0:5 corresponds to M D 1:5.PJ

j D1qj/ while r D 3:0 describes a potentialmarket size 300% greater than the actual market size The parameter  is positiveand less than 1 but insignificantly different from 0, which means that the hypothesisthat rigid and tractor trucks form a single group of products cannot be rejected Sincethe hypothesis that  D 1 can be rejected, the hypothesis of perfect correlations

in idiosyncratic consumer tastes across the various trucks within a group can berejected

Ivaldi and Verboven (2005) calculate the implied market demand elasticities forthe two different potential market size scenarios The larger the potential marketsize, the larger is the estimated share of the outside good and the higher is theimplied elasticity The reason is that the outside option has a higher likelihood—byconstruction Estimating a large outside option produces a large market demandelasticity and therefore a smaller estimate of the effect of the merger The higherelasticity was therefore chosen to predict the merger effect Analysts using merger

of all competing products in a group per year are used as instruments to account forthe endogeneity of prices and quantities in both the demand and pricing... and demand equation Doing so requires us to have multiple observations on each product’s demand and pricing intersection, perhaps using data variation over time from each product (demand and supply... demandand supply equations These moment conditions are exactly analogous to the momentconditions imposed on demand and supply shocks in the homogeneous product con-text.22Ivaldi and