Quantitative Techniques for Competition and Antitrust Analysis_11 pptx

Theimportant lesson from MNL and the property of independence of irrelevant alterna-tives IIA is not that the MNL is a hopeless model though that is probably true,but rather that we can

and cross-price elasticities In practice, therefore, MNL models are quite good forlearning about the characteristics which tend to be associated with high or low levels

of market shares, but we recommend strongly against using MNL models in tions where we must learn about substitution patterns (e.g., for merger simulation).There have been a number of responses to the problems the literature has identifiedwith MNL and we explore some of those responses in the rest of this section Theimportant lesson from MNL and the property of independence of irrelevant alterna-tives (IIA) is not that the MNL is a hopeless model (though that is probably true),but rather that we can use the IIA property to our advantage; since the MNL makesunreasonable predictions about what will happen to market shares following entry,

situa-if we observe what happens to market shares following entry, we will be able to usedata to reject MNL models and identify parameters in richer discrete choice models.Furthermore, the literature has grown from MNL models and many of its tools aremost simply explained in that context For example, in the next section we explorethe introduction of unobserved product characteristics in the context of the MNLmodels but we shall see later that the basic techniques for analyzing models withunobserved product characteristics can be used in far richer discrete choice models

9.2.4.3 Introducing Unobserved Product Characteristics in MNL Models

A famous, possibly true, marketing story is that the first car which introduced acupholder experienced dramatically high sales—customers thought it was a greatnovel idea Economists working with data from the time period, however, probablywould not have had a variable in their data set called “cupholder”—it would havebeen a product characteristic driving sales, differentiating the product, which would

be observed by customers but unobserved by our analyst Such a situation must

be common As a result Bultez and Naert (1975), Nakanishi and Cooper (1974),Berry (1994), and Berry et al (1995) have each argued that we should introduce anunobserved product characteristic into our econometric demand models Following

jso that the conditionalindirect utility function that an individual gets from a given product j is

vij D NvjC "ij D xj0ˇ
˛pj j C "ij;

product characteristic (known to the consumer but not to the economist), and sumer types are represented by "i D "i 0; "i1; : : : ; "iJ/ In general, there may be

con-j but the class of models which have been developedall aggregate unobserved product characteristics into one

The parameters of the model which we must estimate are ˛ and ˇ The basicMNL model attempts to force observed product characteristics to explain all ofthe variation in observed market shares, which they generally cannot Instead of

estimating a model

sj D sj.p; xI ˛; ˇ/ C Errorj; j D 0; : : : ; J;

where an error term is “tagged on” to each equation in the demand system, the newmodel gives an explicit interpretation to the error term and integrates it fully intothe consumer’s behavioral model, sj D sj

Of course, just introducing an unobserved product characteristic does not get youvery far In particular, there is a clear potential problem with introducing unobservedproduct characteristics in that the term enters in a nonlinear way—it is not obvioushow to run a regression in such cases Fortunately, Nakanishi and Cooper (1974) andBerry (1994) have shown that we can recover the unobserved product characteristicsfrom every product in the MNL model Berry et al (1995) then extend the “we canrecover the error terms” result to a far wider set of models

To see how, define the vector of common (across individuals) utilities with thecommon utility of the outside good normalized to zero Nv D 0; Nv1; : : : ; NvJ/ Suppose

we choose Nv to make the MNL model’s predicted market shares exactly match theactual market shares so that

sj.p; Nv/ D sj for j D 1; : : : ; J:

Since Nv D 0; Nv1; : : : ; NvJ/, we have J equations like the one specified above with

J unknowns If the J equations match the predicted and actual market share of allmarkets, then the market share of the outside good will also match s0.p; y; Nv/ D s0since the actual and predicted market shares must add to one.40Taking logs of themarket share equations gives us an equivalent system with J equations of the form:

So that our J equations become

us to write and estimate the linear equation with now “observed” level of utility asthe dependent variable:

ln sj
ln s0D xjˇ
˛pj j:Note that this formulation of the model provides a simple linear-in-the-parametersregression model to estimate, a familiar activity The prices pj and product char-acteristics xj are observed, the parameters to be estimated are ˛ and ˇ and the

j Since this is a simple linearequation we can use all of our familiar techniques upon it, including instrumentalvariable techniques

For the avoidance of doubt, note that the market shares in this equation are volumemarket shares (or equivalently here number of purchasers, since in this model onlyone inside good can be chosen per person) In addition, the market shares must becalculated as a proportion of the total potential market S including the set of peoplewho choose the outside good The appropriate way to calculate the total potentialmarket can be a matter of controversy, depending on the setting In the new carmarket it may be reasonable to assume that the largest potential market is for eachperson of driving age to buy a new car In breakfast cereals it may be reasonable toassume that at most all people in the country will eat one portion of cereal a day,

so, for example, no one eats bacon and eggs for breakfast if the price of cereal issufficiently low and the quality sufficiently high Obviously, such propositions arenot uncontroversial: some people own two cars and some people eat two bowls ofcereal a day It may sometimes be possible to estimate the market size S , thoughfew academic articles have managed to More frequently, it is a very good idea totest the sensitivity of estimation results to whatever assumption has been made.Table 9.5 presents results from Berry et al (1995) Specifically, in the first columnthey report an OLS estimation of the logit demand specification and in the second

Table 9.5. Estimation of the demand for cars.

Notes: The standard errors are reported in parentheses.

a The continuous product characteristics—horsepower/weight, size, and fuel efficiency (miles per dollar

or miles per gallon)—enter the demand equations in levels but enter the column 3 price regression in natural logs.

Source: Table III from Berry et al (1995).

Columns 1 and 2 report MNL demand estimates obtained using (1) OLS and (2) IV Column 3 reports

a regression of the price of car j on the characteristics of car j , sometimes called a “hedonic” pricing

regression If a market were perfectly competitive, then price would equal marginal cost and the final

regression would tell us about the determinants of cost in this market.

column the instrumental variable (IV) estimation Note in particular that the movefrom OLS to IV estimation moves the price coefficient downward This is exactly

as we would expect if price were “endogenous”—if it is positively correlated withthe error term in the regression Such a situation will arise when firms know moreabout their product than we have data about and price the product accordingly Interms of our opening example, a car which introduces the feature of cupholder willsee high sales and the firm selling it may wish to increase its price to take advantage

of high or inelastic demand If so, then the unobserved product characteristic (ourerror term) and price will be correlated

We have mentioned previously that the multinomial logit model, even with theintroduction of an unobserved product characteristic, imposes severe and unde-sirable structure on own- and cross-price elasticities To see that result, recall

This means that all own- and cross-price elasticities between any pair of products

j and k are entirely determined by one parameter ˛, the market share of the goodwhose price changed and also the price of that good Most strikingly, substitutionpatterns do not depend on how good substitutes goods j and k really are, for example,whether they have similar product characteristics Because of the inflexible andunrealistic structure that the MNL model imposes on the preferences, they probablyshould never be used in merger simulation exercises or in any other exercise wherethe pattern of substitution plays a central role in informing decision makers aboutappropriate policy

Despite all of the comments above, the MNL model does remain tremendouslyuseful in allowing analysts a simple way of exploring which product characteristicsplay an important role in determining the levels of market shares However, it isoften the departures from the simple MNL model that are most informative Forexample, it can be informative to include rival characteristics in product j ’s payoffsince that may inform us when close rival products drive down each individualproduct’s market share because each product cannibalizes the demand for the other.Indeed, it is precisely such patterns in the data that richer models will use to generatemore realistic substitution patterns than those implied by models such as MNL withIIA The observation is useful generally, but it also provides the basis of the formalspecification tests for the MNL proposed by Hausman and McFadden (1984)

9.2.5 Extending the Multinomial Logit Model

In this section we follow the literature in extending the MNL model to allow foradditional dimensions of consumer heterogeneity To illustrate the process, we bringtogether the MNL model with the Hotelling model and also the vertical productdifferentiation model

Specifically, suppose that the conditional indirect utility function can be defined as

vj.zj; Lj; pj j; i; Li; "ij/ D izj
tg.d.Li; Lj//
˛pj j C "ij;where the term zj is a quality characteristic where all consumers agree that allelse equal more is better than less—a vertical source of product differentiation.Additionally, products are available in different locations Lj and depending on theconsumer’s location Lithe travel cost may be small or large—a horizontal source

of product differentiation Finally, we suppose that consumers have an intrinsicpreference for particular products as in the multinomial logit The consumer type inthis model is  D "i 0; "i1; : : : ; "iJ; Li; i/, where "i krepresents the idiosyncraticpreference of consumer i for product k, Li indicates the individual’s taste for thehorizontal product characteristic, and irepresents his or her willingness to pay forthe vertical product characteristic

As usual, aggregate demand is simply the sum of individual demands,

xj i; Li; "i 0; : : : ; "iJ/;

over the set of all consumer types In the first instance, that sum involves a J C dimensional integral involving (J C 1) dimensions for the epsilons plus 1 each forthe location and vertical tastes Li, i Thus aggregate demand is

kD1expf zk
tg.d.Lk; Li//
˛pkgfL;.Li; / dLid :For any given Li, i, the model is exactly an MNL model Thus we can use the MNLformula to perform the integration over the J C 1/ dimensions of consumer het-erogeneity arising from the epsilons Doing so means that the resulting integrationproblem becomes in this instance just two dimensional, which is a relatively straight-forward activity that can be accomplished using numerical integration techniquessuch as simulation.41

Berry et al (1995) show that even in this kind of context we can follow an approachsimilar to that taken to analyze the MNL model We discuss their model below, butbefore doing so we describe the nested logit specification, which is a less flexiblebut more tractable alternative popular among some antitrust practitioners

41 For an introductory discussion in this context, see Davis (2000) For computer programs and a good technical discussion, see Press et al (2007) For a classic text, see Silverman (1989) For the econometric theory underlying estimation when using simulation estimators, see Pakes and Pollard (1989), McFadden (1989), and Andrews (1994).

Rigids Tractors Outside good

Truck models Truck models

Figure 9.5. A model for the demand for trucks Source: Ivaldi and Verboven (2005).

9.2.6 The Nested Multinomial Logit Model

The nested multinomial logit (NMNL) model is a somewhat more flexible structurethan the MNL model and yet retains its tractability.42It is based on the assumptionthat consumers each choose a product in stages The concept is very similar to thenested model we studied by Hausman et al (1994) for the demand for beer In eachcase, consumers first choose a broad category of products and then a specific productwithin that category Hausman et al estimated their model using different regressionsfor each stage In contrast, the NMNL model allows us to estimate the demand forthe final products in a single estimation Ivaldi and Verboven (2005) apply thismethodology in their analysis of a case from the European merger jurisdiction, theproposed Volvo–Scania merger.43The product overlap of concern involved the sale

of trucks generally and heavy trucks in particular since the commission found thatheavy trucks constituted a relevant market The authors suggest that the heavy trucksmarket can be segmented into two groups involving (1) rigid trucks (“integrated”trucks, from which no semi-trailer can be detached) and (2) tractor trucks, whichare detachable A third group is specified for the outside good Figure 9.5 describesthe nesting structure they adopt

The NMNL model itself can be motivated in a number of ways

Motivation method 1 McFadden (1978) initially motivated the NMNL model

by assuming that consumers undertook a two-stage decision-making process Atthe first stage he suggested they decide which broad category (group) of goods

g D 1; : : : ; G to buy from and then, at the second stage, they choose between goodswithin that group Each of the groups consists of a set of products and all productsare in only one group The groups are mutually exclusive and exhaustive collections

Motivation method 2 Cardell (1997) (see also Berry 1994) provide an alternative

way to motivate the NMNL model as a random coefficient model with a conditionalindirect utility function defined as

vij D

K

X

lD1

xj lˇi l j C &igC 1
 /"ij for product j in group g;

vi 0D &i 0C 1
 /"i 0 for the outside good;

unob-served product characteristics, &ig is the consumer preference for product group g,and "ij is the idiosyncratic preference of the individual for product j For reasons

we describe below, since for every individual any products in group g get the samevalue of &ig, which in turn depends on  , the parameter  introduces a correlation

in all consumers’ tastes across products within a group Consumers with a high tastefor group g, a large &ig, will tend to substitute for other products in that groupwhen the price of a good in group g goes up The consumer type in a model with Gpre-specified groups is

i D &i1; : : : ; &iG; "i 0; "i1; : : : ; "iJ/:

Cardell (1997) showed that for given  , if &ig are independent with "ij having atype I extreme value distribution, then the expression &igC 1
 /"ijwill also have

a type I extreme value distribution if and only if &ighas a particular type I extremevalue distribution.44 Cardell (1997) also showed that the required distribution of

&ig depends on the parameter  so that some authors prefer to write &ig. / and

&ig. / C 1
 /"ij The parameter  is restricted to be between zero and one As

 approaches zero the model approaches the usual MNL model and the correlationbetween goods in a given group becomes zero On the other hand, as  increases

to one, so does the relative weight on &igand hence correlation between tastes forgoods within a group

Motivation method 3: the MEV class of models A third way to motivate the

NMNL model is to consider it a special case of McFadden’s (1978) generalizedextreme-value (GEV) class of models (which is probably more appropriately calledthe multivariate extreme-value (MEV) class of models since the statistics com-munity use GEV to mean a generalization of the univariate extreme value distri-bution) That model effectively relaxes the independence assumptions across thetastes "i 0; : : : ; "iJ/ embodied in the MNL model The basic bottom line is that theMEV class of models assumes that the joint distribution of consumer types can beexpressed as

F "i 0; : : : ; "iJI / D exp.
H.e"i 0; : : : ; e"iJI //;

44 As Cardell describes, his result is analogous to the more familiar result that if "  N.0; 2/ and " and v are independent, then " C v  N.0; 2C  2 / if and only if v  N.0;  2 /.

where H.r0; : : : ; rJI / is a possibly parametric function (hence the inclusion ofparameters ) with some well-defined properties (e.g., homogeneity of some pos-itive degree in the vector of arguments) We have already mentioned that the stan-dard MNL model has distribution function F "ij/ D exp.e"ij/ so that underindependence the multivariate distribution of consumer types is

F "i 0; : : : ; "iJI / D F "i 0/F "i1/    F "iJ/

D exp

JX

j D0

e"ij

:

In that case the MNL corresponds to the simple summation function

H.r0; : : : ; rJI / D

JX

Whichever method is used to motivate the NMNL model, specifying the groupsappropriately is absolutely vital for the results one will obtain The groups must bespecified before proceeding to estimate the model, and the choice of groups will haveimplications for which goods the model predicts will be better substitutes for oneanother Recall that the parameter  controls the correlation in tastes between goodswithin a group Company information on market segments or consumer surveysmay be helpful in establishing which products are likely to be “closer” substitutesand therefore form distinct market segments that can be associated with a particulargroup

Following the earlier literature, Berry (1994) shows that in a manner very similar

to that used for the MNL model the NMNL model can also be estimated using aregression equation linear in the parameters that can be estimated with instrumentalvariables (see Bultez and Naert 1975; Nakanishi and Cooper 1974) In particular,

we have

ln sj
ln s0D

KX

xj lˇlC  ln sj jg j;

where sj jgis the market share of product j among those purchased in group g If

qj denotes the volume of sales of product j , then sj jgD qj=P

j 2= gqj The use ofinstrumental variables is likely to be essential when using this regression equation

j and the conditionalmarket shares sj jg Verboven and Brenkers (2006) suggest allowing the parameter

of the model controlling the within-group taste correlation to be group-specific sothat

H.r1; : : : ; rJI / D

GXgD1

XJ

j 2= g

r1=.1g / j

1g:

In that case, they show that Berry’s regression can be estimated similarly byestimating G group-specific taste parameters,

ln sj
ln s0D

KXlD1

xj lˇlC gln sj jg j:The additional taste parameters will help free-up substitution patterns across goodswithin each group since they are no longer constrained to be the same acrossgroups However, even this model will suffer from similar problems as MNL whenexamining substitution across groups

9.2.7 Random Coefficient Models

Economists studying discrete choice demand systems have used consumer geneity to generate models with better properties than either pure MNL or evenNMNL models These approaches have been taken with both aggregate data andalso consumer-level data We focus primarily on approaches with aggregate-leveldata but note that the models are identical, although their method of estimation typi-cally is not.45In the aggregate demand literature, the first random coefficient modelswere estimated by Boyd and Mellman (1980) and Cardell and Dunbar (1980) usingdata from the U.S car industry Those authors did not incorporate an unobservedproduct characteristic into their model The modern variant of the random coeffi-cient model for aggregate data was developed in Berry et al (1995) and throughtheir initials (Berry, Levinsohn, and Pakes) is often referred to as the “BLP” model

hetero-In principle, random coefficients can provide us with very flexible models that putfew constraints on the substitution patterns in demand If the models place few con-straints on substitution patterns, then in an ideal world with enough data we will beable to use that data to learn about the true substitution patterns

Because the utility is expressed in terms of product characteristics and not interms of products, the number of parameters to be estimated does not increaseexponentially with the number of products in the market as in the case of the AIDS

45 See Davis (2000) and the references therein for more on the connections between the two types of discrete choice models.

model It is richer but also substantially harder to program and compute than eitherthe AIDS or the nested logit models.

The model allows for individual tastes for product characteristics FollowingBLP, suppose the individuals’ conditional indirect utility functions are expressed

as follows:

vij D

KXlD1

xj lˇi l C ˛ ln.yi
pj j C "ij; vi 0D "i 0;

where as before the variable xj l represents the characteristic l of product j Forexample, a product characteristic might be horsepower in the case of a car Thecoefficient ˇi l is the taste parameter of individual i for characteristic l There is a

j and there is the usual MNLrandom component "ijcapturing an individual’s idiosyncratic taste for a given prod-uct As in previous cases, the valuation of the outside good is assumed to consistonly of an individual random component

In this model, the consumer’s type can be summarized by the vector of individualspecific taste parameters and the individual’s income:

.yi; ˇi1; : : : ; ˇiK; "i 0; "i1; : : : ; "iJ/:

As always, in an aggregate data discrete choice demand model we have to make

an assumption about how these types are distributed across the population, and weassume the MNL elements are independent of the other tastes:

f yi; ˇi1; : : : ; ˇiK; "i 0; "i1; : : : ; "iJ/

D f ˇi1; : : : ; ˇiK j yi/f yi/f "i 0; "i1; : : : ; "iJ/:Furthermore, BLP assume the distribution of the individual idiosyncratic terms

f "i 0; "i1; : : : ; "iJ/ is made up of independent standard type I extreme value terms(i.e., the multinomial logit assumption) For f yi/, one can use the empirical distri-bution of income, perhaps observed from survey data One needs only to assume adistribution for the random taste coefficients The taste parameters may or may not

be independent of income, f ˇi1; : : : ; ˇiK j yi/ BLP assume they are while Nevo(2000) allows the taste parameters to vary with consumer characteristics includingincome

As always, the market demands are just the aggregated individual demands Let

 D y; ˇ1; : : : ; ˇK; "0; "1; : : : ; "J/;

the vector of 1 C K C J C 1 elements determining the consumer type The demand

for product j will be

In their paper, BLP assume that the tastes for characteristics f ˇi1; : : : ; ˇiK/are normally distributed in the population and independent of income Let.!i1; : : : ; !iK/ be a set of standard normal N.0; 1/ random variables DefineN

ˇ1; : : : ; NˇK to be the mean consumer’s taste parameters And define 1; : : : ; K/

as variance parameters in the distribution of tastes Then we can write

ˇi l D NˇlC l!i l for l D 1; : : : ; K;

which implies that the distribution of tastes in the population is normal:

0B

@

ˇ1::

:ˇK

1C

A  N

0B

@

0B

@

Nˇ1::

:NˇK

1C

A ;

0B

1C

A :

Given these distributional assumptions for tastes, we can equivalently write therandom coefficient conditional indirect utilities by decomposing the individual tastefor a given characteristic into a component which depends on the individual tasteand one which does not We get

vij D

KXlD1

xj lˇlN j C

KXlD1

lxj l!i lC ˛ ln.yi
pj/ C "ij;

where the first two terms do not contain individual-specific elements (they are stant across individuals) while the last three terms do contain individual-specificelements For example, the third term involves expressions lxj l!i l which puts a

con-46 See Nevo (2000) and also, in particular, the appendix of Davis (2006a), which provides practical notes on the econometrics including how to calculate standard errors.

parameter from the distribution of tastes in the population (which is to be estimated)

l on an interaction between product characteristic xj land consumer taste for thatcharacteristic, !i l

The individual conditional indirect utility function can be rewritten as

vij D Nvj C ij;where

xj ll!i lC ˛ ln.yi
pj/ C "ij:

As always, market demands are just the aggregate of individual demands which is,

in this case, an integral In terms of market shares,

sj.p; x; Nv/ D

Zy;ˇsij Nvj; yi; ˇ1i; : : : ; ˇiK; : : : /f y; ˇ/ dy dˇ1   dˇK;where Nvj  PJ

j D1xj lˇlN j is common across individuals The BLP papershows that for given values of the prices p, observed product characteristics x,and parameters 1; : : : ; K; ˛/, the J nonlinear equations

sj Nv; p; xI 1; : : : ; K; ˛/ D sj; j D 1; : : : ; J;

can be considered as J equations in the J unknowns Nvj and furthermore that there

is a unique solution to these equations under fairly general conditions Furthermore,BLP provide a remarkably useful technique for calculating the solution to thesenonlinear equations rapidly Specifically, they show that all we need to do is to pick

an initial guess, perhaps a vector of zeros, and then use the following very simpleiteration:

N

vjNew guessD NvjOld guessC ln so
ln sj.p; x; NvOld guess/ for j D 1; : : : ; J;where sois the observed market share and sj.p; x; NvOld guess/ is the predicted marketshare at this iteration’s values of the variables

The BLP technique means that for fixed values of a subset of the models’ eters, namely 1; : : : ; K; ˛/, we can solve for the J common components of theconditional indirect utilities Nv1; : : : ; NvJ/ and so we can run the instrumental variablelinear regression exactly as we did in the MNL case

param-N

vj D

KXlD1

xj lˇNl j

in order to estimate the remaining taste parameters Nˇ1; : : : ; NˇK and also

evalu-j We will get different residuals from this regression for eachvalue of the taste distribution parameters 1; : : : ; K; ˛/ Hence, we will write.1; : : : ; K; ˛/ These taste distribution parameters need to be estimated BLP

Table 9.6. BLP model: estimated parameters of demand equations.

Source: Table IV in Berry et al (1995).

use the general method of moments (GMM), but one might initially simply choosethem by minimizing the sum of squared errors in the model:47

min. 1 ;:::; K ;˛/

KXlD1

j.1; : : : ; K; ˛/2:

BLP apply their method to estimate the demand for cars Their estimation resultsare shown in table 9.6 while the resulting own-characteristic elasticities of demandare shown in table 9.7

Their results48show the own-price elasticity of a Mazda 323 to be 6.4 at a price of

$5,049 while the own-price elasticity of a BMW 735i is 3.5 evaluated at the price of

$37,490 Overall, the results predict that markups will be much higher for high-endBMWs and Lexuses than for low-end Mazdas and Fords

9.3 Demand Estimation in Merger Analysis

The above introduction to the common models used for demand system estimationhas hopefully served at least to illustrate that estimating demands, although anessential part of many quantification exercises, is quite a complex and even optimistictask An analyst is faced with a trade-off between imposing structure from themodel that may not fully reflect reality and developing a model that is flexible

47 For technical details on the econometrics, see also Berry et al (2004).

48 Note that table 9.7 describes the value of the attribute for that car as the first entry in each cell in the table and the elasticity with respect to the characteristic as the second entry in each cell in the table.

Table 9.7. The own-characteristic elasticity of demand.

Value of attribute/priceElasticity of demand with respect to:

Notes: The value of the attribute or, in the case of the last column, price, is the top number and the

number below it is the elasticity of demand with respect to the attribute (or, in the last column, price).

Source: Table V in Berry et al (1995).

but computationally complex (or at least difficult) If the simpler option is chosen,perhaps because of lack of resources one must be extremely cautious and probablytreat the answers obtained as at most indicative Using models which impose theanswer is not learning about the world, it is learning only about the property ofyour model, and obviously we should not, for example, be making merger decisionsbecause of properties of econometric models Although the use of the simpler modelssuch as NMNL and its variants may be appropriate in many cases, in some instancesestimating such an “off-the-shelf” model can be useless at best and in fact activelymisleading As in any quantitative exercise, demand estimation must be undertaken

by knowledgeable economists and the assumptions and results must be confronted

with the facts of the case As a rule of thumb, if all the documents and the industryand consumer testimony in a case points in one direction while the econometricresults point in another, then treat the econometric results with extreme caution Itmay be that the econometrics is right and able to tell you more than the anecdotesbut it may also be that the econometric analysis is based on invalid assumptions, apoor model specification, or the data are not good enough In this section we pointout some practical issues relating to model specification and the data needed forestimation.49

9.3.1 Specification Issues

The purpose of demand estimation is often to retrieve price elasticities and to late their effect on optimal pricing In the merger context, for example, we usuallywant to evaluate the impact of a change in ownership on pricing and we saw in chap-ter 8 that the impact depends on the own- and cross-price elasticities at least betweenthe merging parties’ products Demand estimation can be very useful, particularly ifother more straightforward sources such as company estimates are unavailable Forexample, sometimes companies choose to measure price sensitivity and run exper-iments to evaluate particularly their own-price elasticity of demand We discussedone such marketing experiment in chapter 4, where we also discussed approaches tomeasuring diversion ratios using survey data Demand estimation is another tool inthe economists’ toolbox—but one that is sometimes easy to physically implementand yet difficult to use well

calcu-If demand estimation produces unrealistic demand elasticities, one must revisethe specification of the demand model Assuming that the demand estimation is cor-rectly specified and that proper instruments are being used, one must check for othersources of error It could be that the time frame used is incorrect so that quantityvariation is not being correctly matched to the appropriate price variation; contracts,for example, can mean price variation occurs annually while you might have quar-terly data It could also be that other factors explaining variation in sales such aspromotions, advertising campaigns, rival product entry, or changes in tastes are notbeing appropriately accounted for Those simple checks should be undertaken first.Ultimately, it may be that the model is misspecified, particularly if a lot of structuralassumptions on the shape of preferences have been imposed In this case, other moreflexible demand specifications may be more appropriate Always remember that ouraim is to write down an approximation to the data-generating process (DGP) and thatthe DGP will incorporate both the underlying economic process and the samplingprocess being used to physically generate the data that end up on your computer

49 The discussion draws partly on Hosken et al (2002).

9.3.1.1 The Functional Specification of the Demand System

Merger simulation results are sensitive to the assumed demand specification andthis has been elegantly demonstrated in Crooke et al (1999) In simulation exercisesevaluating mergers in differentiated markets with price competition, they found thatsimulations based on a log-linear specification predicted price increases three timeslarger than simulations using linear demands Using AIDS models produced priceincreases twice as big as the linear demand model and the logit model showed anincrease in price 50% higher than the linear demand model These results reflect thefact that the greater the curvature of the demand curve, the lower the price elasticity

of demand as prices increase (think about moving upward and leftward along aninverse demand curve that is either steeply or shallowly curved) and the greater theincentives to increase prices after a merger

On the one hand, such sensitivity is theoretically a highly admirable feature ofmerger simulation models: the predicted price increases for a given merger willdepend on the form of the demand curve, an important input to the model Onthe other hand, it can often be difficult to have an a priori idea of which demandspecification is more adequate, particularly if there have not been large historicalvariations in prices With enough data we will be able to tell which type of demandcurve best fits the data, but we do not always (or even often) have large enough datasets to be able to perform such checking systematically.50

One response is to consider running merger simulations using several demandspecifications in order to assess the robustness and sensitivity of the estimates.Crooke et al.’s experience suggests that estimation using a log-linear or an AIDSmodel is likely to produce higher-end estimates of price effects while linear spec-ification will produce lower-end estimates It is not uninteresting to examine thebracket of outcomes generated by the different models If the sensitivity to the modelspecification is very large, the merger simulation exercise may not be informative

9.3.1.2 Accuracy of the Estimate of Demand Elasticity

Using evidence presented in court in merger proceedings, Walker (2005) also trates that small changes in the demand elasticity estimates at current prices can havesignificant effects on the results of merger simulations Even variation within theconfidence interval of very precisely estimated coefficients can significantly alterpredicted price increases from mergers One should therefore be wary when slightchanges within realistic ranges of the elasticity estimate produce sharp changes in

illus-50 On some occasions it would be possible to nest the models and use statistical tests to examine which

is preferred by the data; for example, linear and log-linear models can be tested using the Box–Cox test.

On the other hand, models such as linear demands and AIDS may need to be tested against each other using nonnested model tests.

9.3 Demand Estimation in Merger Analysis

The above introduction to the common models used for demand... is not.45In the aggregate demand literature, the first random coefficient modelswere estimated by Boyd and Mellman (1980) and Cardell and Dunbar (1980) usingdata from the U.S car... be useless at best and in fact activelymisleading As in any quantitative exercise, demand estimation must be undertaken

by knowledgeable economists and the assumptions and results must be