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
IntroductionModel of entry
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
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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)
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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)
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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)
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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)}
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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))
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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)
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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.
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
Example from B & R
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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.
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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.
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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)
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
Results
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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!
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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.
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
Results
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
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
Christian Bontemps Entry Games // Empirical Models of Market structure
IntroductionModel of entry
Christian Bontemps Entry Games // Empirical Models of Market structure