Quantitative Techniques for Competition and Antitrust Analysis_10 ppt

The reduced-form effects will tell ushow exogenous changes in demand and cost determinants affect market equilibriumoutcomes, but we will only be able to trace back the actual parameters

contrast, we will usually be able to observe the so-called “reduced-form” effect,that is, the aggregate effect of the movement of the exogenous variables on theequilibrium market outcomes (price, quantity) The reduced-form effects will tell ushow exogenous changes in demand and cost determinants affect market equilibriumoutcomes, but we will only be able to trace back the actual parameters of the demandand supply functions in particular circumstances.

Let us assume the following demand and supply equations, where aDt and aSt arethe set of shifters of the demand and supply curve respectively at time t :

Demand: Qt D aDt
a12Pt;Supply: Qt D aSt C a22Pt:Further, let us assume that there is one demand shifter Xtand one supply shifter Wt

so that

aDt D c11XtC uDt and aSt D c22WtC uSt:The supply-and-demand system can then be written in the following matrix form:

"

uD t

uS t

#:

Let yt D ŒQt; Pt0 be the vector of endogenous variables and Zt D ŒXt; Wt0the vector of exogenous variables in the form of demand and cost shifters which

are not determined by the system We can write the structural system in the form

utD

"

uDt

uS t

#:

The “reduced-form” equations relate the vector of endogenous variables to the

exogenous variables and these can be obtained by inverting the 2  2/ matrix

A and performing some basic matrix algebra:

ytD A1C ZtC A1ut:Let us define ˘  A1C and vt  A1utso that we can write the reduced formas

yt D ˘ ZtC vt:Doing so gives an equation for each of the endogenous variables on the left-handside on exogenous variables on the right-hand side Given enough data we can learnabout the parameters in ˘ In particular, we can learn about the parameters usingchanges in Z , the exogenous variables affecting either supply or demand

6.2.1.2 Conditions for Identification of Pricing Equations

The important question for identification is whether we can learn about the lying structural parameters in the structural equations of this model, namely thesupply and demand equations This is the same as saying that we want to know if,given enough data, we can in principle recover demand and supply functions fromthe data We examine the conditions necessary for this to be possible and then, in thenext section, we go on to examine when and how we can retrieve information aboutfirm conduct based on the pricing equations (supply) and the demand functions thusuncovered

under-Structural parameters of demand and supply functions are useful because we willoften want to understand the effect of one or more variables on either demand orsupply, or both For instance, to understand whether a “fat tax” will be effective inreducing chocolate consumption, we would want to know the effect of a change inprice on the quantity demanded But we would also want to understand the extent

to which any tax would be absorbed by suppliers To do so, and hence understandthe incidence and effects of the tax we must be able to separately identify demandand supply

As we saw in chapter 2, the traditional conditions to identify both demand andsupply equations are that in our structural equations there must be a shifter of demandthat does not affect supply and a shifter in supply that does not affect demand.Formally, the number of excluded exogenous variables in the equation must be atleast as high as the number of included endogenous variables in the right-hand side

of the equation Usually, exclusion restrictions are derived from economic theory.For example, in a traditional analysis cost shifters will generally affect supply but notdemand Identification also requires a normalization restriction that just rescales theparameters to be normalized to the scale of the explained variable on the left-handside of the equation

Returning to our example with the supply-and-demand system:

AytD C ZtC ut:The reduced-form estimation would produce a matrix ˘ such that

The identification question is whether we can retrieve the parametric elements of thematrices A and C from estimates of the reduced-form parameters In this examplethere are four parameters in ˘ which we can estimate and a maximum of eightparameters potentially in A and C For identification our sufficient conditions willbe

 the normalization restrictions which in our example require that a11 D

a21D 1;

 the exclusion restrictions which in our example implies c12D c21D 0.For example, we know that only cost shifters should be in the supply function andhence are excluded from the demand equation while demand shifters should only

be in the demand equation and are therefore excluded from the supply equation

In our example the normalization and exclusion restrictions apply so that we canrecover the structural parameters For instance, given estimates of the reduced-formparameters, 11; 21; 12; 22/, we can calculate

11

21D

By including variables in the regression that are present in one of the structuralequations but not in the other, we allow one of the structural functions to shift whileholding the other one fixed

6.2.2 Conduct Parameters

Bresnahan (1982)24 elegantly provides the conditions under which conduct can beidentified using a structural supply-and-demand system (where by the former wemean a pricing function) More precisely, he shows the conditions under which wecan use data to tell apart three classic economic models of firm conduct, namelyBertrand price competition, Cournot quantity competition, and collusion We begin

by following Bresnahan’s classic paper to illustrate the technique.25 We will seethat successful estimation of a structural demand-and-supply system is typically notenough to identify the nature of the conduct of firms in the market

24 The technical conditions are presented in Lau (1982).

25 We do so while noting that Perloff and Shen (2001) argue that the model has better properties if we use

a log-linear demand curve instead of the linear model we use for clarity of exposition here The extension

to the log-linear model only involves some easy algebra Those authors attribute the original model to Just and Chern (1980) In their article, Just and Chern use an exogenous shock to supply (mechanization

of tomato harvesting) to test the competitiveness of demand.

In all three of the competitive settings that Bresnahan (1982) considers, firmsthat maximize static profits do so by equating marginal revenue to marginal costs.However, under each of the three different models, the firms’ marginal revenuefunctions are different As a result, firms are predicted to respond to a change inmarket conditions that affect prices in a manner that is specific to each model Undercertain conditions, Bresnahan shows these different responses can distinguish themodels and thus identify the nature of firm conduct in an industry.

To illustrate, consider, for example, perfect competition with zero fixed costs

In that case, a firm’s pricing equation is simply its marginal cost curve and hencemovements or rotations of demand will not affect the shape of the supply (pricing)curve since it is entirely determined by costs In contrast, under oligopolistic orcollusive conduct, the markup over costs—and hence the pricing equation—willdepend on the character of the demand curve

6.2.2.1 Marginal Revenue by Market Structure

Following Bresnahan (1982), we first establish that in the homogeneous productcontext we can nest the competitive, Cournot oligopoly and the monopoly modelsinto one general structure with the marginal revenue function expressed in the generalform:

0 under price-taking competition;

1=N under symmetric Cournot;

1 under monopoly or cartel:

Consider the following market demand function:

Qt D ˛0
˛1PtC ˛2XtC uD1t;where Xtis a set of exogenous variables determining demand The inverse demandfunction can be written as

(i) TR D qiP Q.qi// for the Cournot case,

(ii) TR D QP Q/ for the monopoly or cartel case,

(iii) TR D qP Q/ for the price-taking competition case,

where Q is total market production and qiis the firm’s production with qiD Q=N

in the symmetric Cournot model Given these revenue functions marginal revenuescan respectively be calculated as

(i) MR D qiP0.Q/ C P Q/ for the Cournot case,

(ii) MR D QP0.Q/ C P Q/ for the monopoly or cartel case,

(iii) MR D P Q/ for the price-taking competition case

All these expressions are nested in the following form:

MR D QP0.Q/ C P Q/:

6.2.2.2 Pricing Equations

Profit maximization implies firms will equate marginal revenue to marginalcosts Using the marginal revenue expression we obtain the first-order conditioncharacterizing profit maximization in each of the three models:

QP0.Q/ C P Q/ D MC.Q/:

Under one interpretation, the parameter  provides an indicator of the extent towhich firms can increase prices by restricting output If so then the parameter might be interpreted as an indication of how close the price is to the perceivedmarginal revenue of the firm (see Bresnahan 1981) If so, then  is an indicator ofthe market power of the firm and a higher  would indicate a higher degree of marketpower while  D 0 would indicate that firms operate in a price-taking environmentwhere the marginal revenue is equal to the market price This interpretation waspopular in the early 1980s but has disadvantages that has led the field to viewsuch an interpretation skeptically (see Makowski 1987; Bresnahan 1989) Moreconventionally, provided we can identify the parameter , we will see that we canconsider the problem of distinguishing conduct as an entirely standard statisticaltesting problem of distinguishing between three nested models

The pricing equation or supply relation indicates the price at which the firmswill sell a given quantity of output and it is determined in each of these threemodels by the condition that firms will expand output until the relevant variant ofmarginal revenues equals the marginal costs of production The pricing equationencompassing these three models will depend on both the quantity and the costvariables Its parameters are determined by the parameters of the demand function(˛0; ˛1; ˛2), the parameters of the cost function, and the conduct parameter, .Assuming a linear inverse demand function and marginal cost curve, the (supply)pricing equation can be written in the form:

P Qt/ D ˇ0C QtC ˇ2WtC uS2t;where is a function of the cost parameters, the demand parameters, and the conductparameter, and W are the determinants of costs

Given the inverse linear demand function,

MC.Q/ D ˇ0C ˇ1Q C ˇ2WtC uS

2t;where W are the determinants of costs, then the first-order condition that encom-passes all three models, QP0.Q/ C P Q/ D MC.Q/, can be written as

P Qt/ D ˇ0C QtC ˇ2WtC uS2t;where D ˇ1
=˛1

We wish to examine the system of two linear equations consisting of (i) the inversedemand function and (ii) the pricing (supply) equation We have seen in chapter 2and the earlier discussion in this chapter that we can identify the parameters inthe pricing equation provided we have a demand shifter which is excluded from it.Similarly, we can identify the demand curve provided we have a cost shifter whichmoves the pricing equation without moving the demand equation In that case, wecan identify the parameter from the pricing equation and also the parameter ˛1from the demand curve Unfortunately, but importantly, this is not enough to learnabout the conduct parameter, , the parameter which allows us to distinguish thesethree standard models of firm conduct Given ; ˛1/ we cannot identify ˇ1and individually

In the next section we examine the conditions which will allow us to identify

conduct, 

6.2.2.3 Identifying Conduct when Cost Information Is Available

There are cases in which the analyst will be able to make assumptions about costs thatwill allow identification of the conduct parameter First note that if marginal costs areconstant in quantity (so that we know the true value of ˇ1, in this example ˇ1D 0),then if we can estimate the demand parameter ˛1and the regression parameter , wecan then identify the conduct parameter,  since D ˇ1
=˛1D
=˛1 Then wecan statistically check whether  is close to 0 indicating a price-taking environment

or closer to 1 indicating a monopoly or a cartelized industry In that special case,

the conditions for identification of both the pricing and demand equations and theconduct parameter remains that we can find (i) a supply shifter that allows us toidentify the demand curve, the parameter ˛1, and (ii) a demand shifter that identifiesthe pricing curve and hence .

Alternatively, if we are confident of our cost data, then we could estimate a costfunction, perhaps using the techniques described in chapter 3, or a marginal costfunction and then we could equally potentially estimate ˇ1directly This togetherwith estimates of ˛1and ... prices, the demand for physical CDs has dropped.Only the demand rotation will help us identify conduct Similarly, weather mayaffect both the level of demand for umbrellas and also demand may be less... explored and tested For example,one case that regulators and competition authorities should certainly like to under-stand would involve identification results for the difference between Ramsey andmonopoly... establish for identification We therefore examinethe algebra of demand rotations

Let us look at the algebra of identification using the demand rotation Formally, wecan specify a demand function