Empirical Models of Entry - WeeblyIn the empirical study of markets, models of entry are often used to study the nature of rms' pro ts and the nature of competition between rms. The

Empirical Models of Entry

Li Zhao, SJTU

Spring, 2017

Li Zhao Entry 1 / 34

Introduction

In the empirical study of markets, models of entry are often used tostudy the nature of �rms' pro�ts and the nature of competitionbetween �rms.

The idea of these models is that �rms enter into a market only whenthey expect to operate pro�tably, and therefore entry decisions can beused as an indicator of a latent pro�t function.

The study of entry into oligopoly markets is complicated by strategicinteractions between �rms. This means that traditional ideas in theeconometric literature on discrete choice models have to be modi�edsomewhat to account for these strategic interactions.


Why Study Entry Models?

Market structureI Endogenous market structure is fundamental to understand the sources

of market power.I What is the prediction of equilibrium market structure under alternative

hypothetical scenarios?

Pro�tabilityI What are the sources of �rm pro�tability?I Identi�cation of �xed costs / entry costs parameters.

Strategic iterationI How fast do pro�ts decline in the number of �rms?I To what degree do high and low quality �rms compete?


Identi�cation Ideas in Entry Models

An entry model is a binary choice model with multiple decision makersand strategic interaction.

�Principle of Revealed Preference�. A �rm enters a market when entryis pro�table.

Given a pro�t function containing both variable and �xed pro�ts, onecan obtain information on the choice probabilities predicted by themodel.

The identi�cation question clari�es what can and cannot be learnedabout the parameters of the pro�ts functions under a set ofmaintained assumptions, some plausible and others not.

This is done by comparing the predicted choice probabilities under themaintained assumptions to the observed choice probabilities (thedata).


A Road Map

Homogeneous �rms + complete information: Bresnahan and Reiss(1990)

Heterogeneous �rmsI The econometric problem caused by multiple equilibriumI Solution 1: (Assumption on equilibrium selection): Berry (1992)I Solution 2: (Partial Identi�cation): Ciliberto and Tamer (2009)I Solution 3: (Model Selection): Bajari, Hong and Ryan (2010)

Product di�erentiation + complete information: Mazzeo (2002) motel

Product di�erentiation + incomplete information: Seim (2005)location of video retail

Correlated markets: Jia (2006), Walmart and Kmart.

Dynamic structure: Holmes (2008), Walmart


Outline

1 A Game-Theoretic Model of Entry

2 Entry with Homogeneous Firms

3 Heterogeneous FirmsModel and Econometric IssuesPartial Identi�cationEmpirical Application


An Econometric Model of A Game

Players i = 1,2, ...n and actions ai = {0,1, ...k} out of a �nite set.

Utility for i is ui (ai ,a−i ,εi ;θ) = Πi (ai ,a−i ;θ) + εi (ai ).

ai > 1 ⇐⇒ui > 0.

Unlike a standard discrete choice model, note a−i enters utility.

I Probit estimation (when k = 2) or multinomial Logit (k > 2) cannot beused here.


Static Entry Model: Example

Two �rms, simultaneous decide whether or not to enter the market.

Suppose the payo� matrix is

Firm TwoOut Enter

Firm OneOut (0,0) (0,5)Enter (5,0) (-5,-5)

Could you calculate the equilibria of this game?

We �nd two pure strategy equilibria and one mixed strategyequilibrium.


Static Entry Model: Empirical Goal

Empirically, we want to estimate

I W1 and W2: factors that in�uence pro�ts;I δ1 and δ2: competition e�ects.

Firm TwoOut Enter

Firm OneOut (0,0) (0,W2)Enter (W1,0) (W1−δ1,W2−δ2)

Suppose that we know δ1 = δ2 = 10.

Di�erent combinations of W 1,W 2 lead to di�erent patterns of entryby �rm 1 and 2.

Illustration: (W1,W2) = {5,5},{15,5},{15,15}.


Outline





Model and Data

Suppose we have data from a cross-section of M isolated markets.

Data = {nm, Xm} where Xm include exogenous market characteristicssuch as size, etc.

[Homogeneous �rm model]: All potential entrants in a market havethe same pro�t function: same costs, and same demand.

Let π(n) be the pro�t of an active �rm when there are n active �rms.I It is strictly decreasing in n.

The equilibrium number of �rms, n, satis�es

π(n)≥ 0,and π(n+1) < 0.

Active �rms are taking their best response; and inactive �rms aretaking their best response.


Pro�t Function

Bresnahan and Reiss (JPE, 1990).

Pro�t function takes form

πm(n) = Sm ·vp(n,Xm)−FC (Xm)− εm.

Typically models of competition imply variable pro�t is proportional tomarket size.

vp is the variable pro�t per capita that comes from some model ofquantity or price competition.

vp(n,Xm) = X vpm β

vp−α(n)

FC is the �xed cost.FC (Xm) = X fc

m βfc .

εm is market-level unobservable to us.


Estimation

πm(n) = Sm ·vp(n,Xm)−FC (Xm)− εm.

Suppose that εm is independent of Xm and i.i.d. N(0,σ2).

Equilibrium impliesnm = n⇐⇒

{Sm[X vpm β vp−α(n)]−X fc

m β fc

σ≤ εm

σ≤ Sm[X vp

m β vp−α(n+1)]−X fcm β fc

σ}.

We can estimate the model by MLE Pr(nm|Sm,Xm).

From an econometric point of view, the model has a very similarstructure as an Ordered Probit.

α measures competition e�ects.

How quickly vp(n+1)/vp(n) declines measures how strong thecompetition is.


Bresnaha and Reiss (1990)

Entry in monopoly market


Outline





The Econometric Framework

Entry considered in Bresnahan and Reiss (1990,1991), Berry (1992),Ciliberto and Tamer (2009).

Data on a cross section of markets. {yim,xim} for i = 1,2, ..n andm = 1,2, ..M.

x ,ε measures factors that in�uence revenue (such as population) andcost.

Πi (yi ,y−i ,X ;θ) is often a linear function

Πi (yi ,y−i ,X ;θ)] =

{xiβ + δ ∑j yj + εi if yi = 1

0 if yi = 0.

The mean utility of not entering is set equal to zero.

Complete information: ε is observed by all players.

A Nash Equilibrium is a N-tuple y such that for any player i

yi = 1(xiβ + δ ∑j

yj + εi > 0).


Econometric Issues

y1 = 1(βx1−δy2 + ε1 > 0);

y2 = 1(βx2−δy1 + ε2 > 0);

SimultaneityI The econometric model is a simultaneous equation model where the

endogenous variables are binary.I In an entry game, not considering simultaneity leads to over-estimation

of competition e�ects.

Correlated between �rms' unobservables.I Positive correlation between unobservables leads to under-estimation of

competition e�ects.

Unfortunately, IV is not consistent in binary choice models withendogenous binary explanatory variables.

What about likelihood estimation?


Two Person Entry Game

y1 = 1(βx1−δy2 + ε1 > 0);

y2 = 1(βx2−δy1 + ε2 > 0);

(0,0) is a NE if

{βx1 + ε1 < 0βx2 + ε2 < 0

, or equivalently

{ε1 <−βx1ε2 <−βx2

.

(0,1) is a NE if

{βx1−δ + ε1 < 0

βx2 + ε2 > 0, or

{ε1 <−βx1 + δ

ε2 >−βx2.

(1,0) is a NE if

{βx1 + ε1 > 0

βx2−δ + ε2 < 0, or

{ε1 >−βx1

ε2 <−βx2 + δ.

(1,1) is a NE if

{βx1−δ + ε1 > 0βx2−δ + ε2 > 0

, or

{ε1 >−βx1 + δ

ε2 >−βx2 + δ.


Deal With Multiplicity

There are a number of approaches to �x this problem of multiplicity:

Re�ning the set of equilibria.

I Assume the most pro�table �rm is always the �rst �rm to enter.

Looking at the number of �rms that enter.

I Works for symmetric entry game.

Model of equilibrium selection.

I Equal probability of being selected, equilibrium always favors one �rm,etc.

I Bajari, Hong and Ryan (2010).

Partial Identi�cation.

I Finding implications of the model that could have been generated bysome of the equilibria.


Ciliberto and Tamer (2009) - Introduction

Ciliberto, F. and Tamer, E., 2009. Market structure and multipleequilibria in airline markets. Econometrica, 77(6), pp.1791-1828.

Estimate entry model without making equilibrium selectionassumptions.

The model allows the e�ects that the entry of each individual airlinehas on the pro�ts of its competitors, its "competitive e�ects," to di�eracross airlines.

The identi�ed features of the model are sets of parameters (partialidenti�cation) such that the choice probabilities predicted by theeconometric model are consistent with the empirical choiceprobabilities estimated from the data.


Empirical Findings

The authors apply this methodology to investigate the empiricalimportance of �rm heterogeneity as a determinant of market structurein the U.S. airline industry.

They �nd evidence of heterogeneity across airlines in their pro�tfunctions. The competitive e�ects of large airlines (American, Delta,United) are di�erent from those of low cost carriers and Southwest.

The competitive e�ect of an airline is increasing in its airportpresence, which is an important measure of observable heterogeneityin the airline industry.

Then the authors develop a policy experiment to estimate the e�ect ofrepealing the Wright Amendment on competition in markets out ofthe Dallas airports.


Methodology - Partial Identi�cation

This paper uses the simple condition that �rms serve a market only ifthey make non-negative pro�ts in equilibrium to derive a set ofrestrictions on regressions.

In games with multiple equilibria, this simple condition leads to upperand lower bounds on choice probabilities.

The economic model implies a set of choice probabilities which liesbetween these lower and upper bounds.

Heuristically, the estimator then is based on minimizing the distancebetween this set and the choice probabilities that can be consistentlyestimated from the data.


Main Idea

y1m = 1(α1X1m + δ2y2m + ε1m ≥ 0];

y2m = 1(α2X2m + δ1y1m + ε2m ≥ 0].


Main Idea

Pr(1,0|X ) = Pr((ε1,ε2) ∈ R1(X ,θ))

+∫Pr((1,0)|ε1,ε2,X ) ·1[(ε1,ε2) ∈ R2(θ ,X )]dFε1,ε2 .

Because 0≤ Pr((1,0)≤ 1,

Pr((ε1,ε2) ∈ R1(X ,θ))≤ Pr(1,0|X )≤Pr((ε1,ε2) ∈ R1(X ,θ))+Pr((ε1,ε2) ∈ R2(X ,θ)).


Identi�cation: General Setup

Therefore the upper and lower bound of observing Pr(y |X ) is


Identi�cation: Vector Form

In vector format, these inequalities correspond to the upper and lowerbounds on conditional choice probabilities:

Let ΘI be such that

ΘI = {θ s.t. the above inequalities are satis�ed at θ ∀X a.s.}.

We say that ΘI is the identi�ed set.


Estimation

The estimation problem is based on the conditional moment inequalitymodel

H1(θ ,X )≤ Pr(y |X )≤ H2(θ ,X ).

Our inferential procedures uses the objective function

Q(θ) =∫

[||(P(X )−H1(X ,θ))−||+ ||(P(X )−H2(X ,θ))+||]dFx .

It is easy to see that Q(θ)≥ 0 for ∀θ .Q(θ) = 0 if and only if θ ∈ΘI , the identi�ed set.


Estimation (2)

We �rst replace Pr(y |X ) with a consistent estimator Pn(X ).

We then de�ne ΘI as

ΘI = {θ ∈Θ|nQn(θ)≤ τn},

where

Qn(θ) =1

n ∑[||(Pn(Xi )−H1(Xi ,θ))−||+ ||(Pn(X )−H2(Xi ,θ))+||].

ΘI is the set estimator of set ΘI .

The con�dence regions are

Cn(c) = {θ ∈Θ : n(Qn(θ)−mint

Qn(t))≤ τ}.


Simulate H1 and H2

Note thatH1(θ ,X )≤ Pr(y |X )≤ H2(θ ,X ).

where

H1(θ ,X ) =∫y is the unique equibirum

dF ε,

H2(θ ,X ) =∫y is an equibirum

dF ε,

We can approximate integration by simulation. When we draw ε(r), wecalculate its equilibrium set.

H1 =1

R ∑1(y is the unique equilibrium of ε(r));

H2 =1

R ∑1(y is an equilibrium of ε(r));


Data

Second quarter of the 2001 Airline Origin and Destination Survey(DB1B).

A market is the trip between two airports, may have stops

Key players: American, Delta, United, and Southwest, Medium, LLC.

πim = Smαi +Zimβi +Wimγi + ∑j 6=i δ ij yjm + ∑j 6=i Zjmφ i

j yjm + εim.

Sm: market size, per capita income, income growth rate, distance,close airport, Wright Amendment.

Zim:

I Market presence: A carrier's ratio of markets served by an airline out ofan airport over the total number of markets served out of an airport byat least one carrier.

Wim:

I Cost: connecting distance / non-stop distance.


The Wright Amendment

The Wright Amendment was passed in 1979 to stimulate the growthof the Dallas/Fort Worth airport.

Congress restricted airline service out of Dallas Love, the other majorairport in the Dallas area.

The Wright Amendment permitted air carrier service between LoveField and airports only in a few close states.

In October 2006, a bill was enacted that determined the full repeal ofthe Wright Amendment in 2014.

The authors constructed a binary variable Wright, equal to 1 if entryinto the market is regulated by the Wright Amendment.


The Wright Amendment


Di�erent Versions - Fixed Competitive E�ects

πim = Smαi +Zimβi +Wimγi + ∑j 6=i

δij yjm + ∑

j 6=i

Zjmφij yjm + εim.

Fixed Competitive E�ects Varible

Berry Heter δ Heter α Heter φ i.i.d. Unobs Var-covαi α α αi

βi β β

δ ij δ δj δ i

j

φ ij 0 φ 6= 0

εim ∼ i .i .d . �xed e�ects


Ciliberto and Tamer (Econometrica 2009)


Documents

Empirical Models of Entry - WeeblyIn the empirical study of markets, models of entry are often used to study the nature of rms' pro ts and the nature of competition between rms. The