an empirical model of firm entry with endogenous product...

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result

Contributionand Weakness

Product

Information

Weakness

Suggestions

An empirical model of firm entry withendogenous product-type choicesSeim(2006), RAND Journal of Economics

Wooyong Lee

31 Jan 2013

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

Information

Weakness

Suggestions

Introduction

Before : entry model, identical products

In this paper : entry with simultaneous location choice

Before or some other papers : complete info game

In this paper : incomplete info game

(greatly reduces computational burden)

Results : video retail industry location data

firms differentiate to shield profit from competitionmore scope for product differentiation → more marketpower (more entry)

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

Information

Weakness

Suggestions

Outline

1 Summary of the paperModelEstimationData and Result

2 Contribution and weakness of the paperContribution: Endogenized product-quality choiceContribution: Incomplete information on profitsWeakness of the paper

3 Suggestions for further research

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

Information

Weakness

Suggestions

Section 1

Summary of the paper

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

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Weakness

Suggestions

Model Setup

market m = 1, 2, . . . ,M

let’s focus on one market m:(script m removed for ease of exposition)

location l = 0, 1, . . . ,Lfirm f = 1, 2, . . . ,Fdecision df = (dfl )Ll=0 ∈ {0, 1}L+1

Seim(2006)

Wooyong Lee

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Estimation

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Model Setup

payoff Πfl = Xlβ + ξ + h(Γ.l ,n) + εfl

X : observable market characteristics

ξ : unobservable market characteristics, known to firms

h() : effect of competition on profits; specified later

Γ.l : interaction between l and 1 through Ln = (nl )

Ll=1 : number of firms at location l

εfl : idiosyncratic profitability of firm f at location l

Πf 0 normalized to 0

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

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Weakness

Suggestions

Assumptions

Assumption (Independent symmetric private values)

ε1, . . . , εF are private information to the players and areindependently and identically distributed draws from thedistribution G (·)

Assumption (Additively separable competitors’ effects)

h(Γ.l ,n) =∑L

k=1 γkl nk

Assumption (Distance bands)

let dkl be the distance between location k and l.γkl = γk ′l = γb if Db ≤ γkl , γk ′l < Db+1, where Db and Db+1

denote cutoffs that define a distance band.

Seim(2006)

Wooyong Lee

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Model

Estimation

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Product

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Assumptions

Under distance bands b = 0, 1, . . . ,B, with correspondingcutoff points Db and Db+1 where D0 = 0, the resulting payofffunction is given by

Πfl = Xlβ + ξ +∑

b γbNbl + εfl

γb : competitive effect in distance band b

Nbl =∑

k Ibkl nk : number of firms in distance band b

Ibkl := I(dkl ∈ [Db,Db+1)), I(·) : indicator function

nk : number of firms at location k

E :=∑

b Nbl : total number of firms in the market

Seim(2006)

Wooyong Lee

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Model

Estimation

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Product

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Conjectures and equilibrium

Seim(2006)

Wooyong Lee

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Given the expected competitor distribution across marketlocations, firms calculate its expected profit at each location l :

E(Πfl ) = Xlβ + ξ +∑

b γbE(Nbl ) + εfl

:= E(Π̄fl ) + εfl

note that E(Nbl ) =∑

k IbklE(nk )

Structure of the game :

1 firms decide whether or not to enter → E determined

2 Given number of firms E , firms decide locations

→ solve backward

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

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Weakness

Suggestions


Due to the symmetry of rival’s types, firm f ’s perception offirm g ’s location strategy is the same for all competitors.

Let θ1 = (β, γ). Given ξ,X, E , θ1, the probability thatcompetitor g chooses location l is given by

pgl (ξ,X,E, θ1)

= P(E(Π̄gl ) + εgl > E(Π̄gk ) + εgk ∀k 6= l , ∀g 6= f )

Expected number of competitors at location k is

E(nk ) = (E − 1)pgk

E(Nbl ) =∑

k IbklE(nk ) =

∑k Ib

kl (E − 1)pgk + I(b = 0)

Seim(2006)

Wooyong Lee

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Model

Estimation

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Product

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Assumption

ε are i.i.d. draws from a type 1 extreme-value distribution withscale parameter normalized to one.

By this assumption, there exists a closed-form formula for pgl :

pgl =exp{E(Π̄gl )}∑L

k=1 exp{E(Π̄gk)}

Since types are symmetric, every firm has the same equilibriumconjecture of its competitors’ location choices :

pg := (pgl )Ll=1 = pf = p∗ := (p∗l )Ll=1

Seim(2006)

Wooyong Lee

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Model

Estimation

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Product

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A firm’s vector of equilibrium conjectures over all locations l isdefined by

p∗l =exp{E(Π̄l (X,p

∗, E , θ1))}∑Lk=1 exp{E(Π̄k (X,p∗, E , θ1))}

=exp{Xlβ + γ0 + (E − 1)

∑b γb

∑j Ib

jl p∗j }∑L

k=1 exp{Xkβ + γ0 + (E − 1)∑

b γb∑

j Ibjk p∗j }

for all l = 1, . . . ,L

Seim(2006)

Wooyong Lee

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Model

Estimation

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Product

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let’s analyze E :

In equilibrium, each entrant earns nonnegative profits inexpectation, while any additional entrant would sufferlosses.

The probability of entry by a firm into a market involves acomparison of a weighted average of payoffs acrosslocations to the normalized payoff of not entering.

Seim(2006)

Wooyong Lee

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Model

Estimation

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Product

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Given the assumption of i.i.d. type 1 extreme-valueprofitability types,

P(entry) =exp(ξ)

∑Ll=1 exp{E(Π̄l (X,p

∗, E , θ1))}1 + exp(ξ)

∑Ll=1 exp{E(Π̄l (X,p∗, E , θ1))}

Since the probability of entry is identical acrosscompetitors,

E = F × P(entry)

Ways to choose F : 50% enter the market, F = 50

Seim(2006)

Wooyong Lee

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Estimation

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Estimation : Econometric Specification

Assumption

The expected number of entrants predicted by the modelexactly equals the number of entrants observed in the data.

With E being the observed number of entrants, by the entryprobability equation,

ξ = ln E − ln(F − E)− ln( L∑

l=1

exp{E(Π̄l (X,p∗, E , θ1))}

)

Assumption

ξm are i.i.d. random draws from a Normal distribution withparameter θ2 = (µ, σ) and independent of ε.

Seim(2006)

Wooyong Lee

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Likelihood

Data from market m = 1, . . . ,M

Each market is treated as an independent Fm-playerlocation game

dm = (dm1 , . . . , d

mF ) : vector of actions taken by Fm

players in market m

The likelihood function is given by

L(θ1, θ2) =M∏

m=1

pθ1(dm|ξm,Xm, Em)gθ2(ξm|Xm, Em,Fm)

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

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Estimation Procedure

1 initialize (θ1, θ2)

2 given (θ1, θ2), (Xm)Mm=1, F , (Em)M

m=1, solve equilibriumconjecture equation for pm for each m separately

3 calculate ξm with pm, (θ1, θ2), (Xm)Mm=1, F , (Em)M

m=1 foreach m

4 estimate (θ1, θ2) by maximizing likelihood function

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

Information

Weakness

Suggestions

Estimation Issues

initial value : a grid search over the parameter space

likelihood maximization : Nelder-Mead optimizationalgorithm

problematic when there are multiple equilibria : appendixproves uniqueness for two distance bands with fourlocations, simulation evidence suggests further result

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

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Weakness

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Data description

video retail industry

videotapes are standardized; main differentiation by storelocation

isolated markets; no large city nearby, no metropolitan area

exclude tourist regions

locations by Census tracts

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

Information

Weakness

Suggestions

Data description

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

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Data description

d0 = 0.5 miles, d1 = 3 miles

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

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Weakness

Suggestions

Data description

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

Information

Weakness

Suggestions

Estimation Result

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

Information

Weakness

Suggestions

Simulation Result

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

Information

Weakness

Suggestions

Section 2

Contribution and weakness of the paper

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

Information

Weakness

Suggestions

Previous Works

focused on tradeoff between demand and intensity ofcompetition

Early works on product quality differentiation :Hotelling(1929), Lancaster(1966,1979)

(competition on characteristic space)

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

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Weakness

Suggestions

Model for Endogenized Product Choice

Empirically tractable model of competition oncharacteristic space (tractable for large L)

Unisolated market : locations affect each other viadistance

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

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Weakness

Suggestions

Empirical Results

Firms differentiate to shield from competition

More scope for product differentiation → more marketpower(more entry)

More disperse population → less gain fromdifferentiation(slightly more entry in total)

The two offset each other in video retail industry data

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

Information

Weakness

Suggestions

Previous Works

Complete information game → computational burden

→ Limited number of locations

Mazzeo(2002) : entry with product-quality choice,complete information game

→ uses motel industry data, computation is burdensomewith 3 locations

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

Information

Weakness

Suggestions

Incomplete Information Game

Introduce private information : idiosyncratic profitability

sources: cost, intangible assets, customer service,inventory maintenance etc.

As Rust(1994) notes : Bayesian Nash equilibriumconjectures are easy to derive

Other works under information asymmetry :

Aguirregabiria and Mira(2006), Pakes, Ostrovsky andBerry(2005), Pesendorfer and Schmidt-Dengler(2003)

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

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Product

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Cost of Assumptions

Distance band approach :

All locations with same distance band have the sameimpact

two at the north � one at the north and one at the south

ε being i.i.d. type 1 extreme value distribution :

idiosyncratic profitability uncorrelated across firms at alocation, across location for a firm

no spatial correlation

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

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Weakness

Suggestions

Possible Issues

When there are multiple equilibria :

matching location probabilities to observed locationchoices is problematic

uniqueness for general setting is only verified by simulation

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

Information

Weakness

Suggestions

Section 3

Suggestions for further research

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

Information

Weakness

Suggestions

Further research so far

entry game with multistore/multiproduct firms (Jia 2008)

dynamic entry game

timing game (Sweeting 2009)

estimation with multiple equilibria (Aguirregabiria 2012 :identical product case)

estimation in case of location heterogeneity(Aguirregabiria 2012)

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

Information

Weakness

Suggestions

Further research so far

estimation of demand system by quantity, price data ofstores : Wang(2010)

effect of other factors on entry decisions: regulation(Gowrisankaran and Krainer 2011), organizationalstructure (Takechi and Higashida 2012), managerial ability(Goldfarb and Xiao 2011)

Seim(2006)

Wooyong Lee

Summary

Model

Estimation

Result


Product

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Weakness

Suggestions

Suggestions

nonlinear effect of additional entrant

relaxing distance band assumption

investigation of conditions for unique equilibrium

an empirical model of firm entry with endogenous product...

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