Entry Games // Empirical Models of Market structurechrisbontemps.free.fr/empiricalIO/entryI.pdf3 Game structure : payoff of being ... Importance of natural barriers to entry Can strategic

IntroductionModel of entry

Entry Games // Empirical Models of Marketstructure

Christian Bontemps

M2Toulouse School of Economics

February 2017

Christian Bontemps Entry Games // Empirical Models of Market structure


Introduction

Three main elements to have in mind when studying market entry :

1 Decision to operate or not (dependant variable for the model)

2 Sunk cost associated with being active in the market

3 Game structure : payoff of being active depends on the numberand characteristics of other active firms



Overview

Focus on the number of firms in a market (and their characteristics)

Relate the number of firms to :Cost efficiencyDemand(Mark-up)Fixed costs

Firm decisions are interdependent

Market structure is endogenous here

Structural approach: use nature of competition and its relation toentry decision



Questions of interest

How many firms can fit the market?

Importance of natural barriers to entry

Can strategic investment in R&D, advertising, and capacity deterentry?

Test contestable market theory : threat of potential entry vs. barrier toentry

Note: we specify and estimate a structural model that can be used forcounter-factual simulations



Overview

Based on Bresnahan and Reiss, 1991

Main idea : relate observed number of firms to market conditions

Market conditions :Profitability: Demand, (variable) production costFixed/sunk costsExtent of market power

Observations:Number of firmsMarkets with different demand/variable costSame fixed costsNote: we do not observe profits nor cost!

Underlying assumption: number of firms determined by zero-profitcondition



Model set-up

Observations from isolated markets m = 1,2, . . . ,M

Np potential entrants in the market

Each firm i decides whether or not being active in the market

Πm(N) is the profit of an active firm in market m when there are Nactive firms: Πm(N) is strictly decreasing in N

If N∗m is the equilibrium number of firms in the market m, then itshould satisfy the following condition:

Π(N∗m)≥ 0, and Π(N∗m + 1) < 0

Utilize this information to estimate the model



Profit function

We do not observe prices nor quantities, (nor profits nor fixed costs)

However, we observe the number of firms in each market and marketconditions

Idea: specify variable profit function and cost function

Key difference between variable profit and fixed costs (foridentification): variable profits increase with market size where fixedcosts do not



Model specification

Demand supposed to have the following form :

Q = d(Z ,P)×S

Where :d(Z ,P): the demand function of a ”representative consumer”Z : demographic variables affecting market demand (e.g. averageincome)S: the number of consumers (market size)

Cost information is given by variable cost, VC(q,X C), and fixed costs,F (X C), where:

q is the firm outputX C : exogenous variables affecting costs

Profit function for a monopolist can be expressed as

Π1(1) = P1d(Z ,P1)×S−(

VC(q1,X C) + F (X C))

=(

P1−AVC(q1,X C))

d(Z ,P1)×S−F (X C)



Profit function

Variable profit Vm(N), of an incumbent firm in market m when thereare N active firms, is specified:

Vm(N) = Smvm(N)

= Sm(X Dm β −α(N))

Where :Sm: the market sizevm : the variable profit per capitaX D

m : the vector of market characteristics that may affect thedemand of the product in market m (e.g : per capita income, agedistribution)β : a vector of parametersα(1), · · · ,α(N) : parameters capturing the degree of competition.We expect α to increase in N :

α(1)≤ α(2)≤ ·· · ≤ α(N)



Fixed costs

Fixed costs Fm(N), of an incumbent firm in market m where n firmsare active is :

Fm(N) = X Cm γ + δ (N) + εm

Where :X C

m : the vector of observed market characteristics that mayaffect the fixed cost of the product, (e.g. rental price)γ : the vector of parametersδ (1), . . . ,δ (N): parameters of fixed costs, fixed cost allowed todepend on the number of firms in the marketεm: unobserved (to the econometrician, but not to firms)characteristics



Interpretation of δ

There are several possible interpretations for why fixed costs maydepend on the number of firms in the market:

Entry deterrence : Incumbents create barriers to entryFirm heterogeneity in fixed costs : late entrants are less efficientin fixed costsEndogenous fixed costs : rental prices or other components ofthe fixed costs (which are not included in X C

m ) may increase withthe number of incumbents (e.g. demand effect on rental prices)

As a consequence, we expect that δ increases in n:

δ (1)≤ δ (2)≤ ·· · ≤ δ (N)



Parameters to estimate

Πm(N) = Sm(X Dβ −α(N))−X C

γ−δ (N) + εm

Since both α(N) and δ (N) increase in N, Πm(N) decreases with N

Thus, there is a unique N∗ such that:

Πm(N∗)≥ 0 and Πm(N∗+ 1) < 0

The model has unique solution for any value of the exogenousvariables and parameters

Parameters to estimate :

θ = {β ,γ,α(1), · · · ,α(N),δ (1), · · · ,δ (N)}



Estimation

Assume that the only endogenous variable is the number of firmsthat entered Ni

Additionally, assume that the (unobservable) profit ε isindependently distributed across markets according to thedistribution Φ(ε|x ,θ)

Then Φ(ε|x ,θ) describes not only the distribution of ε, but firmprofits Π(Ni ) as well



Estimation

The probability of observing markets with no firm equals:

Pr(Πi < 0) = 1−Φ(Π1)

Probability of observing N firms in equilibrium:

Pr(ΠN ≥ 0 and ΠN+1 < 0) = Φ(ΠN)−Φ(ΠN+1)

With :

Π̄n = V (N)S−F (N)

= (α1 + X Dβ −

N

∑i=2

αN)×S− γ1− γLX c−N

∑i=2

δN



Digression: maximum likelihood

Idea: find for the parameters that maximize the likelihood ofobserving the data we observeImplementation: compute the probability of observing (likelihood)the sample and maximize itLikelihood of the sample = product of the likelihood of theindividual observations

L(θ ,X ,Y ) = ΠNi=1li (θ ,Xi ,Yi )

Estimator: θ such that:

maxθ

L(θ ,X ,Y )

Trick: equivalent to maximize the likelihood and the log-likelihood:

maxtheta

LL(L(θ ,Y ,X ) =N

∑i=1

ln(φ(Yi −Xiθ))

Note: Assumption that X is exogenous, distribution of the errorterm specified



Digression: maximum likelihood

Example: linear regressionY = Xθ + UAssumption on the distribution of the error term: U ∼N (0,1).Individual likelihood:li = P(θ ,Yi ,Xi ) = P(U = Yi −Xiθ) = φ(Yi −Xiθ) where φ(.) is thepdf of the normal distribution.Likelihood of the sample: L(θ ,Y ,X ) = ΠN

i=1 (φ(Yi −Xiθ))



Back to our model

Construct a likelihood function for N∗ = N∗1 , . . . ,N∗m:

L(θ ,x ,N∗) = ∑i ln(P(Ni = N∗i ))= ∑i ln(P(Ni = 0)×1(Ni = 0) + P(Ni = 1)×1(Ni = 1))+...+ P(Ni = Nmax )×1(Ni = Nmax )

Remarks:It is essential that firms’ unobserved profits are i.i.d acrossmarketsThese independence assumptions are much more likely to berealistic if we are modeling a cross-section of different firms indifferent markets, and not the same firms over time or in differentmarkets (importance of isolated markets)If εm normally distributed, we have an ordered probit model (easyto estimate in stata, oprobit)



Entry Thresholds

Let S(N) be the entry threshold

S(N) is the minimum market size to sustain N firms in the market (s.tEΠ(N) = 0):

S(N) =X c

mγ + δ (N)

X Dm β −α(N)

s(N) is the per firm entry threshold:

s(N) =S(N)

N

The evolution of the ratio shows how would one additional entrantchange the competitiveness as N increases



Entry threshold ratio

The entry threshold ratio s∞/s1 measures the fall in variable profitsper customer between a monopoly and a competitive market (N→ ∞)

This measure is bounded below by unity and increases with asteepening of the monopolist’s demand curveEquivalently, the more efficient a monopolist is at surplusextraction, the greater this ratioChanges in the threshold ratio s∞/sN tell us how quicklyoligopoly variable profits approach competitive variable profits



Entry threshold ratio

If firms have the same costs and if entry does not change competitiveconduct, then sN+1/sN = 1

Thus departures of successive entry threshold ratios from onemeasure whether competitive conduct changes as the number offirms increases

Notice that this statistic does not measure the level ofcompetition. Instead, it measures how the level changes with thenumber of firmsWhen firms preserve the cartel as N increases, we observes2 = s1, s3 = s2, s4 = s3, and so on, just as in the competitivecase



Example

Suppose that we observe that it takes 2000 customers to support amonopolist (i.e., s1 = 2000)

The market becomes perfectly competitive when each firm has 4000customers (i.e., s∞ = 4000)

If, for instance, the fourth entrant expects to compete in a perfectlycompetitive market, then we should observe S4 = 4 ·4000 = 16000consumers, or s∞/s4 = 1

Say it differently, quadropolists earn the same variable profits percustomer as competitive firms

Alternatively, suppose that the fourth entrant is part of a cartel, itenters when it covers its fixed costs at the monopoly price, that is,when the market has S4 = 4 ·2000 = 8000 consumers. In this cases∞/s4 = 2.



Linear Cournot Example

Suppose, for example, that we assumed demand was linear inindustry output:

P = a−bQS

Additionally, suppose costs are quadratic in output and the samefor all firms:

F + C(q) = F + cq + kq2

Assume firms are Cournot-Nash competitiors.Price cost margin becomes:

P−C′(q) = a−c−bQS−2kq



Example from B & R



Data used by Bresnahan & Reiss

To estimate the model and the series of entry thresholds, Bresnahan& Reiss use data on market size and the number of firms in a market

Rather than time series, they use a cross-section of geographicallyisolated markets to conduct the same empirical comparative statics

Firms in these markets face different levels of demand for theirproducts

This variation is necessary to separately identify δ from α



Data

The sample contains 202 isolated local marketsA typical market in the sample is a county seat in the westernUnited States. These county seats are separated from othertowns in the county.Because most of the local population resides in or near thecentral town, its population provides a reasonable firstapproximation to S(Y ).Final sample includes the following five industries: doctors,dentists, druggists, plumbers, and tire dealers.



Estimation

Given Ni entrants in market i , each entrant earns:

ΠN = S(Y,λ )VN(Z ,X D,α,β )−FN(X C ,δ ,γ) + ε

All firms in market i have the same variable profit function and fixedcost Fi

The vector x = [Y,Z,XC] contains market i demand and cost variablesthat affect variable profits

The vector θ = [α,λ ,γ,δ ] contains the demand, cost and competitionparameters that we seek to estimate

ε summarizes profits that we do not observe. ε has a normaldistribution that is iid across markets and is independent of ourobservables

They also assume that ε has zero mean and a constant variance andthat each firm within a market has the same profit error.



Estimation

Approximation of market size :S(Y,λ ) =town population + λ1 nearby population + λ2 positive growth+ λ3 negative growth + λ4 commutes out of the country

Variable profit :

VN = α1 + X Dβ −

N

∑n=2

αn

Fixed costs:

FN = δ1 + γLX c +N

∑i=2

δn



Estimation

Assume that the only endogenous variable is the number of firmsthat entered Ni

Additionally, assume that the (unobservable) profit ε isindependently distributed across markets according to thedistribution Φ(ε|x ,θ)

Then Φ(ε|x ,θ) describes not only the distribution of ε, but firmprofits Π(Ni ) as well



Estimation

The probability of observing markets with no firms equals:

Pr(Πi < 0) = 1−Φ(Π1)

Probability of observing N firms in equilibrium:

Pr(ΠN ≥ 0 and ΠN+1 < 0) = Φ(ΠN)−Φ(ΠN+1)

With :

Π̄N = VNS−FN

= (α1 + X Dβ −

N

∑n=2

αn)×S− γ1− γLXc−N

∑n=2

γn



Estimation

Construct a likelihood function for N∗:

L(θ ,ω|{x ,N∗}) = ∑i

ln(Φ(V (N∗i ,xi ))−Φ(V (N∗i + 1,xi )))

It is essential that firms’ unobserved profits are i.i.d acrossmarketsThese independence assumptions are much more likely to berealistic if we are modeling a cross-section of different firms indifferent markets, and not the same firms over time or in differentmarkets (importance of isolated markets)



Results



Entry thresholds

SN =δ̂1 + γ̂LX

C+ ∑

Nn=2 δ̂n

α̂1 + XD

β̂ −∑Nn=2 α̂n

Interpretations :A monopoly tire dealer or druggist requires about 500 people intown to set up businessA monopoly doctor or dentist needs between 700 and 900people.Monopoly plumbers require at least twice what monopoly doctorsor dentists need to break even!



Results

Part B of the table reports ratios of successive per firm entrythresholds.These ratios decline with N. Notice, however, that the declinestops abruptly at N = 3 and that S3 approximately equals S4 andS5.

Robustness ?

Price discrimination and product differentiation also could cause entrythreshold ratios to depart from one



Robustness checks : price regressions

Assume that the doctors, dentists, tire dealers, druggists, andplumbers in their sample compete in relatively homogeneousmarkets.Assume that they use similar production technologies and havesimilar costs.Under the maintained hypothesis of homogeneous entrants, ourresults suggest that entry does not change margins and costs bymuch.However, they cannot completely rule out the possibility thatoffsetting movements in demand and costs could leave entrythresholds constant.E.g., one could challenge their maintained assumptions byarguing that product differentiation offsets competitive decreasesin margins, thereby leaving entry threshold ratios constant.



Price regressions

They collected price information from tire dealers.To adjust dealers’ prices for brand and quality differences, theyregressed the price of a tire, P

1 On a set of zero-one dummy variables for the number of firms inthe market,

2 The tire’s mileage rating (in thousands of miles),3 Dummy variables measure how much price falls with N

Include the mileage rating as a measure of product quality andthe retail wage to proxy dealer cost differences.The dummy variables for brands remove brand-specific demandand cost differences



Results



Results

These tests confirm that prices fall as N increasesDo not reject the null hypothesis that monopoly prices andduopoly prices are equal, nor do we reject the hypothesis thatprices in three-, four-, and five-firm markets are equalThe point estimates also show that prices fall as entry occurs, assuggested by our entry threshold estimates. Betweenmonopolies and quintopolies, price falls by about 8 percent




Documents

Entry Games // Empirical Models of Market structurechrisbontemps.free.fr/empiricalIO/entryI.pdf3 Game structure : payoff of being ... Importance of natural barriers to entry Can strategic