Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
An empirical model of firm entry with
endogenous product-type choices
Seim(2006), RAND Journal of Economics
Suggestions
Wooyong Lee
31 Jan 2013
Introduction
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
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 competition
more scope for product differentiation → more market
power (more entry)
Outline
Seim(2006)
Wooyong Lee
1
Summary of the paper
Model
Estimation
Data and Result
2
Contribution and weakness of the paper
Contribution: Endogenized product-quality choice
Contribution: Incomplete information on profits
Weakness of the paper
3
Suggestions for further research
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
Section 1
Summary of the paper
Model Setup
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
market m = 1, 2, . . . , M
let’s focus on one market m:
(script m removed for ease of exposition)
location l = 0, 1, . . . , L
firm f = 1, 2, . . . , F
L+1
decision df = (dfl )L
l=0 ∈ {0, 1}
Model Setup
Seim(2006)
Wooyong Lee
Summary
payoff Πfl = Xl β + ξ + h(Γ.l , n) + εfl
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
X : observable market characteristics
ξ : unobservable market characteristics, known to firms
h() : effect of competition on profits; specified later
Suggestions
Γ.l : interaction between l and 1 through L
n = (nl )L
l=1 : number of firms at location l
εfl : idiosyncratic profitability of firm f at location l
Πf 0 normalized to 0
Assumptions
Seim(2006)
Wooyong Lee
Assumption (Independent symmetric private values)
Summary
ε1 , . . . , εF are private information to the players and are
independently and identically distributed draws from the
distribution G (·)
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
Assumption (Additively separable competitors’ effects)
P
h(Γ.l , n) = L
k=1 γkl nk
Assumption (Distance bands)
let dkl be the distance between location k and l.
γkl = γk 0 l = γb if Db ≤ γkl , γk 0 l < Db+1 , where Db and Db+1
denote cutoffs that define a distance band.
Assumptions
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
Under distance bands b = 0, 1, . . . , B, with corresponding
cutoff points Db and Db+1 where D0 = 0, the resulting payoff
function is given by
P
Πfl = Xl β + ξ + b γb Nbl + εfl
γb : competitive effect in distance band b
P
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
P
E := b Nbl : total number of firms in the market
Conjectures and equilibrium
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
Conjectures and equilibrium
Seim(2006)
Wooyong Lee
Given the expected competitor distribution across market
locations, firms calculate its expected profit at each location l :
Summary
Model
Estimation
Result
E(Πfl ) = Xl β + ξ +
Contribution
and Weakness
P
b
γb E(Nbl ) + εfl
:= E(Π̄fl ) + εfl
P
note that E(Nbl ) = k Ibkl E(nk )
Product
Information
Weakness
Suggestions
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
Conjectures and equilibrium
Seim(2006)
Wooyong Lee
Summary
Due to the symmetry of rival’s types, firm f ’s perception of
firm g ’s location strategy is the same for all competitors.
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
Let θ1 = (β, γ). Given ξ, X, E, θ1 , the probability that
competitor 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
P
P
E(Nbl ) = k Ibkl E(nk ) = k Ibkl (E − 1)pgk + I(b = 0)
Conjectures and equilibrium
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
Assumption
ε are i.i.d. draws from a type 1 extreme-value distribution with
scale parameter normalized to one.
By this assumption, there exists a closed-form formula for pgl :
exp{E(Π̄gl )}
pgl = PL
k=1 exp{E(Π̄gk )}
Since types are symmetric, every firm has the same equilibrium
conjecture of its competitors’ location choices :
∗
∗ L
pg := (pgl )L
l=1 = pf = p := (pl )l=1
Conjectures and equilibrium
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
A firm’s vector of equilibrium conjectures over all locations l is
defined by
pl∗ =
Suggestions
=
exp{E(Π̄l (X, p∗ , E, θ1 ))}
PL
∗
k=1 exp{E(Π̄k (X, p , E, θ1 ))}
P
P
exp{Xl β + γ0 + (E − 1) b γb j Ibjl pj∗ }
PL
P
P b ∗
k=1 exp{Xk β + γ0 + (E − 1)
b γb
j Ijk pj }
for all l = 1, . . . , L
Conjectures and equilibrium
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
let’s analyze E :
In equilibrium, each entrant earns nonnegative profits in
expectation, while any additional entrant would suffer
losses.
The probability of entry by a firm into a market involves a
comparison of a weighted average of payoffs across
locations to the normalized payoff of not entering.
Conjectures and equilibrium
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
Given the assumption of i.i.d. type 1 extreme-value
profitability types,
P
∗
exp(ξ) L
l=1 exp{E(Π̄l (X, p , E, θ1 ))}
P(entry ) =
P
∗
1 + exp(ξ) L
l=1 exp{E(Π̄l (X, p , E, θ1 ))}
Since the probability of entry is identical across
competitors,
E = F × P(entry )
Ways to choose F : 50% enter the market, F = 50
Estimation : Econometric Specification
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
Assumption
The expected number of entrants predicted by the model
exactly equals the number of entrants observed in the data.
With E being the observed number of entrants, by the entry
probability equation,
ξ = ln E − ln(F − E) − ln
L
X
exp{E(Π̄l (X, p∗ , E, θ1 ))}
l=1
Assumption
ξ m are i.i.d. random draws from a Normal distribution with
parameter θ2 = (µ, σ) and independent of ε.
Likelihood
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Data from market m = 1, . . . , M
Each market is treated as an independent F m -player
location game
dm = (d1m , . . . , dFm ) : vector of actions taken by F m
players in market m
Suggestions
The likelihood function is given by
L(θ1 , θ2 ) =
M
Y
m=1
pθ1 (dm |ξ m , Xm , E m )gθ2 (ξ m |Xm , E m , F m )
Estimation Procedure
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
1
2
3
Suggestions
4
initialize (θ1 , θ2 )
m M
given (θ1 , θ2 ), (Xm )M
m=1 , F, (E )m=1 , solve equilibrium
m
conjecture equation for p for each m separately
m M
calculate ξ m with pm , (θ1 , θ2 ), (Xm )M
m=1 , F, (E )m=1 for
each m
estimate (θ1 , θ2 ) by maximizing likelihood function
Estimation Issues
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
initial value : a grid search over the parameter space
likelihood maximization : Nelder-Mead optimization
algorithm
problematic when there are multiple equilibria : appendix
proves uniqueness for two distance bands with four
locations, simulation evidence suggests further result
Data description
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
video retail industry
videotapes are standardized; main differentiation by store
location
isolated markets; no large city nearby, no metropolitan area
exclude tourist regions
locations by Census tracts
Data description
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
Data description
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
Data description
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
d 0 = 0.5 miles, d 1 = 3 miles
Data description
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
Estimation Result
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
Estimation Result
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
Simulation Result
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
Simulation Result
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
Section 2
Contribution and weakness of the paper
Previous Works
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
focused on tradeoff between demand and intensity of
competition
Early works on product quality differentiation :
Hotelling(1929), Lancaster(1966,1979)
(competition on characteristic space)
Model for Endogenized Product Choice
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
Empirically tractable model of competition on
characteristic space (tractable for large L)
Unisolated market : locations affect each other via
distance
Empirical Results
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
Firms differentiate to shield from competition
More scope for product differentiation → more market
power(more entry)
More disperse population → less gain from
differentiation(slightly more entry in total)
The two offset each other in video retail industry data
Previous Works
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
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 burdensome
with 3 locations
Incomplete Information Game
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
Introduce private information : idiosyncratic profitability
sources: cost, intangible assets, customer service,
inventory maintenance etc.
As Rust(1994) notes : Bayesian Nash equilibrium
conjectures are easy to derive
Other works under information asymmetry :
Aguirregabiria and Mira(2006), Pakes, Ostrovsky and
Berry(2005), Pesendorfer and Schmidt-Dengler(2003)
Cost of Assumptions
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
Distance band approach :
All locations with same distance band have the same
impact
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 a
location, across location for a firm
no spatial correlation
Possible Issues
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
When there are multiple equilibria :
matching location probabilities to observed location
choices is problematic
uniqueness for general setting is only verified by simulation
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
Section 3
Suggestions for further research
Further research so far
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
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)
Further research so far
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
estimation of demand system by quantity, price data of
stores : Wang(2010)
effect of other factors on entry decisions: regulation
(Gowrisankaran and Krainer 2011), organizational
structure (Takechi and Higashida 2012), managerial ability
(Goldfarb and Xiao 2011)
Suggestions
Seim(2006)
Wooyong Lee
Summary
Model
Estimation
Result
Contribution
and Weakness
Product
Information
Weakness
Suggestions
nonlinear effect of additional entrant
relaxing distance band assumption
investigation of conditions for unique equilibrium