Dynamic Models of Entry and ExitBoston University

Mark J. RobertsPennsylvania State University and NBER

December 2015

M. Roberts () Dynamic Models of Entry and Exit December 2015 1 / 30

Measuring Competition in Oligopolistic Markets

A basic goal of empirical work in industrial organization is to measure the degreeof competition in real world markets.

Static models of competition estimate models of production and/or demandto measure markups

Treat prices, quantities as endogenous, market structure is exogenousdata requirements: prices, quantities, market shares, product characteristics,production costskey equation: f.o.c. for price or quantity choicePorter (Bell Journal, 1981), Appelbaum (J Econometrics, 1982), Bresnahan (JEconometrics, 1981), Berry, Levinsohn, and Pakes (Econometrica, 1995), DeLoecker and Warzynski (AER, 2012)

M. Roberts () Dynamic Models of Entry and Exit December 2015 2 / 30

Measuring Competition in Oligopolistic Markets

"Static Entry" models infer competition from relationship between thenumber of �rms and market size.

Bresnahan and Reiss (JPE, 1991 and RES, 1990) insight: As a market growsin size it will support more �rms, but how many more depends on extent ofcompetition after entry.

Empirical approach: Use a cross-section of geographic markets with di¤erentpopulations and measure how the number of �rms varies with market size.

long-run market structure (number of �rms) is endogenous.key equation: zero pro�t condition for entrantsCampbell and Hopenhayn (JIE, 2005), Berry (Econometrica, 1992), Mazzeo(Rand, 2002), Seim (Rand, 2007), Syverson (JPE, 2004), Berry and Reiss(Handbook of IO, 2007), Verboven (Rand, 2008).

M. Roberts () Dynamic Models of Entry and Exit December 2015 3 / 30

Empirical Models of Market Structure

"Static Entry" Models - Market Structure:

Entry Stage endogenizes the number of �rms in market NmShort-Run Competition determines payo¤s to �rm i as Vim(Nm ,Zim)

Empirical model uses zero-pro�t condition:

observe Nm �rms if Vim(Nm ,Zim) � Fim > Vim(Nm + 1,Zim)leads to ordered probit models for the number of �rms

Limitations of the Static Entry Framework

Di¢ cult to separate competition from entry costs (Berry and Reiss, 2007)Not empirical models of entry (E ) and exit (X ) �ows. Cannot explainsimultaneous entry and exitNo distrinction between incumbents and potential entrants. Same valuefunctions, distribution of private shocksCannot distinguish sunk entry costs from �xed costsNot explicitly dynamic. No role for market/�rm history to matter.

M. Roberts () Dynamic Models of Entry and Exit December 2015 4 / 30

Dynamic Models of Entry, Exit, and Market Equilibrium

Fully dynamic models of entry, exit, and market equilibrium

Distinguish incumbent�s decision to remain/exit from potential entrant�sdecision to enter/stay out.

Goal: Quantify three determinants of market structure

"toughness of competition" - e¤ect of N on V .�xed costs/scrap values that drive exit decisionssunk entry costs

Methodological papers on estimation of dynamic games:

Aguirregabiria and Mira (Econometrica, 2007)Bajari, Benkard, and Levin (Econometrica, 2007)Pakes, Ostrovsky, and Berry (Rand Journal, 2007)Pesendorfer and Schmidt-Dengler (Review of Economic Studies, 2003)

Empirical applications to entry/exit and investment:

Collard-Wexler (Econometrica, 2012)Ryan (Econometrica, 2011)Dunne, Klimek, Roberts, and Xu (Rand Journal, 2013)

M. Roberts () Dynamic Models of Entry and Exit December 2015 5 / 30

Common Elements of a Dynamic Entry/Exit Model

Market with N �rms (incumbents and potential entrants)

St = (s1t , s2t , ...sNt )�observed state variables (in/out, capital stock,productivity)

At = (a1t , a2t , ...aNt )�observed action (in/out, invest)εt = (ε1t , ε2t , ...εNt )� private payo¤ shock for each �rm (cost or demand)

Markov transition process for each �rm�s state variable P(sit+1 jsit , ait )Long-run payo¤ function for �rm i : Vit = V (St , εit )

includes entry costs, �xed costs, scrap values related to entry, exit

Equilibrium Description (Markov Perfect Equilibrium)

Given state St , each �rm�s actions max long-run payo¤s given perceptions offuture statesthe perceptions of future states are consistent with competitor�s optimalactions.

M. Roberts () Dynamic Models of Entry and Exit December 2015 6 / 30

Goal of the Structural Empirical Model

Use data on observed states St and �rm actions At to estimate parameters ofpayo¤ functionsV (θ) and distribution of private shocks G (ε)

Conduct policy experiments which alter θ and simulate new paths for A andS .

Approaches to estimation

Given initial θ and S , compute �rm�s optimal action A(S , ε; θ) and payo¤V (S , ε; θ). Iterate until equilibrium conditions are satis�ed. Match modelprediction on optimal actions to data on observed actions to estimate θ.Ericson and Pakes (RES, 1995), Pakes and McGuire (Rand, 2001)Two step estimators that avoid solving for the equilibrium strategies.Empirically estimate static pro�t function, policy functions A(S) andtransition process for states Pr(s 0js), compute value function as sum of futurepro�ts. Estimate dynamic parameters by �nding max value function.

M. Roberts () Dynamic Models of Entry and Exit December 2015 7 / 30

Dunne, Klimek, Roberts and Xu �Entry, Exit, and theDeterminants of Market Structure

Similar to Static Entry Models

Geographic Markets with populations from 2,500 to 50,000 peopleDentists - 639 markets with n =1,2,....20Chiropractors - 410 markets with n =1,2,....8

Di¤ers from Static Entry Models

Endogenous variables are �ows of entry and exitKey market-level variables: n, e, x ,πDistinguishes incumbents from potential entrantsSeparates entry costs from �xed costs

M. Roberts () Dynamic Models of Entry and Exit December 2015 8 / 30

DKRX - Entry, Exit, and Determinants of Market Structure

Dentists and Chiropractors are good industries to contrast

similar technology, market demand is closely tied to population, income.di¤er in per �rm pro�ts and turnover rates

Are the di¤erences due to di¤erences in toughness of competition or entry costbarriers?

Subsidies for underserved dental markets

Data Source: U.S. Census Bureau Longitudinal Business Database for 1977,1982, 1987, 1992, 1997, 2002

M. Roberts () Dynamic Models of Entry and Exit December 2015 9 / 30

Demand and Market Structure Statistics

Market Structure Demand DynamicsPop Quart n Revenue Per-cap Fed Med Infant Entry Exit(mean) Practice Income Bene�ts Mortality Prop Rate

Dentist - non HPSA MarketsQ1 (5.14) 3.86 148.12 9.30 1.38 8.63 .204 .185Q2 (7.67) 5.65 158.67 9.30 1.99 8.80 .206 .176Q3 (11.10) 7.84 157.87 9.32 2.02 8.60 .206 .193Q4 (19.93) 11.90 168.01 9.34 2.57 8.94 .209 .198

Dentist - HPSA MarketsQ1 (5.50) 3.92 129.11 9.12 1.30 9.12 .190 .214Q2 (7.33) 4.57 148.62 9.13 1.51 9.13 .243 .212Q3 (11.24) 5.16 151.27 9.18 1.47 9.18 .285 .208Q4 (20.31) 8.55 171.99 9.17 2.02 9.17 .246 .175

ChiropractorsQ1 (6.39) 2.00 93.83 9.30 1.63 8.98 .413 .233Q2 (9.74) 2.53 97.40 9.32 1.84 8.43 .482 .246Q3 (14.92) 3.06 107.29 9.32 2.41 8.70 .503 .244Q4 (28.20) 3.84 121.49 9.37 3.56 8.80 .518 .254

M. Roberts () Dynamic Models of Entry and Exit December 2015 10 / 30

Theoretical Model: Pakes, Ostrovsky, and Berry (2007)

Goal: Empirically tractable model to explain market-level entry and exit �ows.

A market is characterized by a pair of state variables s = (n, z)

z are exogenous market demand and cost shifters (population, input prices)n is the number of �rms

Firm pro�t in the market is π(n, z ; θ) = π(s), identical for all �rms andobserved

Evolution of state variables

z evolves as an exogenous Markov process F (z 0jz)n evolves endogenously with �rm entry/exit decisions n0 = n+ e � x

M. Roberts () Dynamic Models of Entry and Exit December 2015 11 / 30

Incumbent�s Exit/Continue Decision

Each incumbent observes current market state s, payo¤s π(s),and a privatecontinuation cost λi , an iid draw from a common cdf Gλ

Make a discrete continue/exit decision. Payo¤ is

V (s,λi ) = π(s) +max fδVC (s)� δλi , 0g

which implies that probability of exit is:

px (s) = Pr(δλi > δVC (s)) = 1� Gλ(VC (s)).

The expectation of the next period�s realized value function for the �rms thatchoose to produce.is

VC (s) = E cs 0hπ(s 0) + E

λ0 (max

�δVC (s 0)� δλ0, 0

)i

= E cs 0 [π(s0) + δ(1� px (s 0))(VC (s 0)� E (λ0jλ0 � VC (s 0))]

Last term is the truncated mean of the �xed cost distribution given they continue.

M. Roberts () Dynamic Models of Entry and Exit December 2015 12 / 30

Simplifying Distribution of Fixed Costs

Assume distribution of �xed costs λ is exponential: Gλ = 1� e�(1/σ)λ .

Truncated mean of λ depends on σ, truncation point VC (s 0), and prob of exit px

E (λ0jλ0 � VC (s 0)) = σ� VC (s 0)�px (s 0)/(1� px (s 0))

�VC (s) can be rewritten as

VC (s) = E cs 0 [π(s0) + δVC (s 0)� δσ(1� px (s 0))]

M. Roberts () Dynamic Models of Entry and Exit December 2015 13 / 30

Potential Entrant�s Decision

Each potential entrant observes a private entry cost κi , an iid draw from acommon cdf G κ.

Makes a discrete decision to enter/stay out in the next period. Payo¤ to entry is

VE (s) = E es 0 [π(s0) + δVC (s 0)� δσ(1� px (s 0))]

which implies that the probability of entry is:

pe (s) = Pr(κi < VE (s)) = Gκ(VE (s))

M. Roberts () Dynamic Models of Entry and Exit December 2015 14 / 30

Exit and Entry Conditions

Let π,VC, and VE be the vector of payo¤s in each state.Let Mc ,Me be transition matrices from s to s 0.

The exit condition is:px = 1� Gλ(VC)

whereVC =Mc [π+δVC� δσ(1� px )]

The entry condition is:pe = G κ(VE)

whereVE =Me [π + δVC� δσ(1� px )].

M. Roberts () Dynamic Models of Entry and Exit December 2015 15 / 30

Empirical Strategy

Need to measure

π,VC, and VE for each state (n, z)Mc ,Me for each pair of statesFixed cost and sunk cost distributions G λ(σ) and G κ(α)

Three step estimator

Pro�t function parameters θ from data on π, n, zTransition matrices for the state variables Mc ,Me from state variables overtime, s , s 0. Construct VC (s),VE (s).Entry cost and �xed cost parameters, α and σ, from the entry and exit �owdata.

M. Roberts () Dynamic Models of Entry and Exit December 2015 16 / 30

Pro�t Function Estimation

z = (pop, per capita income,wage, fed med , mort):

πmt = θ0 +5

∑k=1

θk I (nmt = k) + θ6nmt + θ7n2mt + h(θZ ,Zmt ) + fm + εmt

fm controls for omitted market factors that will bias coe¢ cient on n toward zero.Introduces a new state variable for each market.Create a single, exogenous state variable

zmt = h(θZ ,Zmt ) (1)

M. Roberts () Dynamic Models of Entry and Exit December 2015 17 / 30

Constructing VC and VE

Discretize the state variable zmt into 10 categories (zd ), and fm into threecategories(fd )

Mc (n0, z 0d , fd jn, zd , fd ) = Mnc (n0jn, zd , fd ) �Mz (z 0d jzd ) � IfdThe pieces can be estimated nonparametrically from the market-level data, i.e.fraction of surviving plants in state s that move to each state s 0

Similar calculation for Me - fraction of entering plants in state s that move toeach state s 0

M. Roberts () Dynamic Models of Entry and Exit December 2015 18 / 30

Constructing VC and VE

Given estimates of^Mc and

^π(s),

^VC is a �xed point of the equation system:

VC =^Mc

�^π + δVC� δσGλ(VC)

�It is a function of the �xed cost parameter σ

Given^Me ,

^π, and

^VC,

^VE is:

^VE =

^Me [

^π + δ

^VC� δσGλ(

^VC)].

M. Roberts () Dynamic Models of Entry and Exit December 2015 19 / 30

Likelihood Function for Entry and Exit Flows

The log probability of observing xmt exits and emt entrants in a market with states is:

l(xmt , emt ; σ, α) =

(nmt � xmt ) log(Gλ(^VC (s))) + xmt log(1� Gλ(

^VC (s)))

emt log(G κ(^VE (s))) + (pmt � emt ) log(1� G κ(

^VE (s)))

The log likelihood function for the observations on entry and exit �ows is:

L(σ, α) = ∑m

∑tl(xmt , emt ; σ, α).

Notice: need data on potential entrants pmt in each market.

M. Roberts () Dynamic Models of Entry and Exit December 2015 20 / 30

Measurement of Key Variables

Entry and exit change the number of �rms (practices) between census years.Sales are not entry/exit.

Average pro�t per owner-practitioner

Census data on revenue, payroll and legal form of organizationExternal data sources to estimate other expenses as a share of o¢ ce revenueAdjust payroll for di¤erent legal forms (corporation vs proprietor)

Potential Entrants - two de�nitions

maximum number of di¤erent practices ever observed in the market (internalpool)measure number of doctors in excess of the number of practices

Simultaneous entry and exit are the norm

M. Roberts () Dynamic Models of Entry and Exit December 2015 21 / 30

Size of Potential Entranty Pool

Dentists ChiropractorsNumber Estabs internal pool external pool internal pool external pool

n=1 2.31 23.55 3.42 1.95n=2 2.74 25.22 3.78 2.88n=4 4.04 23.05 5.13 5.37n=6 6.03 25.45 6.19 7.74n=7 6.58 27.83 6.16 9.37n=8 7.81 29.09 8.75 10.67

n=10,11 9.66 27.13n=12,13,14 11.74 25.89n=15,16,17 13.83 27.15n=18,19,20 15.95 28.21

In dentists, the de�nitions are very di¤erent. Entry rate will be lower (entry costhigher) with the external pool

M. Roberts () Dynamic Models of Entry and Exit December 2015 22 / 30

Pro�t Function Estimates (number of �rms only)

Dentist ChiropractorVariable No Fixed E¤ect Fixed E¤ect No Fixed E¤ect Fixed E¤ectIntercept -11.543 (4.184)* -2.561 (4.922) -1.215 (8.720) -23.96 (10.55) *I(n=1) .0379 (.0240) .0519 (.0301) .0200 (.0328) .0613 (.0373)I(n=2) .0253 (.0173) .0342 (.0221) .0211 (.0324) .0389 (.0373)I(n=3) .0113 (.0134) .0179 (.0163) .0100 (.0328) .0338 (.0361)I(n=4) .0112 (.0100) .0108 (.0122) .0046 (.0324) .0192 (.0355)I(n=5) .0191 (.0087)* .0154 (.0088) .0005 (.0331) .0266 (.0360)n -.0044 (.0045) -.0238 (.0059) * -.0021 (.0339) .0041 (.0362)n2 .0001 (.0002) 5.55e-4 (2.45e-4) * -.0277 (.0353) -.0205 (.0369)obs 2556 2556 1640 1640

F(27,df) 32.03 58.94 13.47 5.51

Fixed e¤ect estimates - Negative e¤ect of n on π. Larger decline for dentists

OLS estimates of n biased toward zero (no e¤ect)

M. Roberts () Dynamic Models of Entry and Exit December 2015 23 / 30

Fixed Cost and Entry Cost Parameters

Panel A. Dentist (All Markets)Entry pool σ αinternal 0.373 (0.006) 2.003 (0.013)external 0.375 (0.006) 3.299 (0.039)

Panel B. Dentist (HPSA vs Non-HPSA Markets)Entry pool σ α (HPSA) α (non-HPSA)internal 0.366 (0.009) 1.797 (0.069) 2.019 (0.041)external 0.368 (0.008) 3.083 (0.169) 3.376 (0.079)

Panel C. ChiropractorEntry pool σ αinternal 0.275 (0.005) 1.367 (0.015)external 0.274 (0.005) 1.302 (0.022)

Entry Costs > Fixed Costs

Fixed Costs are not sensitive to entry pool/distribution

Entry pool does a¤ects entry cost for dentists

Comparing industries: �xed cost and entry cost are higher for dentists

M. Roberts () Dynamic Models of Entry and Exit December 2015 24 / 30

Dynamic Bene�ts VC, VE (millions of 1983 $)

VC for Incumbents - Dentist VE for Potential Entrants - Dentistlow(z,f) mid(z,f) high(z,f) low(z,f) mid(z,f) high(z,f)

n=1 0.433 0.764 1.286 0.394 0.722 1.247n=2 .0383 0.714 1.236 0.350 0.678 1.202n=4 0.297 0.628 1.150 0.273 0.601 1.126n=8 0.195 0.525 1.048 0.180 0.508 1.032n=12 0.126 0.457 0.979 0.117 0.445 0.969n=20 0.067 0.397 0.920 0.064 0.392 0.916

VC for Incumbents - Chiro VE for Potential Entrants - Chiron=1 0.178 0.344 0.562 0.170 0.335 0.553n=2 0.166 0.332 0.551 0.161 0.326 0.544n=3 0.155 0.321 0.540 0.151 0.316 0.534n=4 0.148 0.314 0.532 0.144 0.308 0.527n=6 0.132 0.298 0.516 0.129 0.294 0.512n=8 0.123 0.289 0.508 0.123 0.287 0.506

VC di¤ers substantially across marketsChiropractors are less pro�table, decline less with n

M. Roberts () Dynamic Models of Entry and Exit December 2015 25 / 30

Probabilities of Exit and Entry

Probability of Exit - Dentist Probability of Entry - Dentistlow(z,f) mid(z,f) high(z,f) low(z,f) mid(z,f) high(z,f)

n=1 0.313 0.129 0.032 0.141 0.216 0.382n=2 0.358 0.148 0.036 0.126 0.204 0.371n=4 0.451 0.186 0.046 0.100 0.182 0.352n=8 0.593 0.244 0.060 0.067 0.155 0.328n=12 0.713 0.294 0.072 0.044 0.136 0.312n=20 0.836 0.345 0.085 0.024 0.117 0.297

Probability of Exit - Chiro Probability of Entry - Chiron=1 0.524 0.286 0.129 0.133 0.245 0.371n=2 0.547 0.299 0.135 0.127 0.239 0.367n=3 0.569 0.311 0.141 0.119 0.233 0.362n=4 0.585 0.319 0.144 0.114 0.228 0.358n=6 0.620 0.339 0.153 0.103 0.219 0.350n=8 0.639 0.349 0.158 0.098 0.215 0.346

M. Roberts () Dynamic Models of Entry and Exit December 2015 26 / 30

Reduction in Entry Cost: Impact on Entrants

Probability of Exit - Dentist Probability of Entry - Dentistlow(z,f) mid(z,f) high(z,f) low(z,f) mid(z,f) high(z,f)

n=1 0.313 0.129 0.032 0.141 0.216 0.382n=2 0.358 0.148 0.036 0.126 0.204 0.371n=4 0.451 0.186 0.046 0.100 0.182 0.352n=8 0.593 0.244 0.060 0.067 0.155 0.328n=12 0.713 0.294 0.072 0.044 0.136 0.312n=20 0.836 0.345 0.085 0.024 0.117 0.297

Probability of Exit - Chiro Probability of Entry - Chiron=1 0.524 0.286 0.129 0.133 0.245 0.371n=2 0.547 0.299 0.135 0.127 0.239 0.367n=3 0.569 0.311 0.141 0.119 0.233 0.362n=4 0.585 0.319 0.144 0.114 0.228 0.358n=6 0.620 0.339 0.153 0.103 0.219 0.350n=8 0.639 0.349 0.158 0.098 0.215 0.346

M. Roberts () Dynamic Models of Entry and Exit December 2015 27 / 30

Reduction in Entry Costs: Impact on Incumbents

Number VC (n, z , f ) px (n, z , f )of Firms low(z,f) mid(z,f) high(z,f) low(z,f) mid(z,f) high(z,f)n=1 -6.50 -4.26 -2.50 7.85 9.11 8.99n=2 -6.26 -3.97 -2.26 6.64 7.89 7.76n=3 -6.50 -3.91 -2.15 5.93 7.18 7.05n=4 -6.36 -3.71 -1.98 5.20 6.44 6.31n=5 -6.62 -3.66 -1.90 4.73 5.97 5.84n=7 -6.31 -3.28 -1.63 3.69 4.91 4.78n=9 -6.06 -2.97 -1.42 2.92 4.13 4.01

M. Roberts () Dynamic Models of Entry and Exit December 2015 28 / 30

Cost-Bene�t Comparison of Subsidies

Benchmark Entry Cost Fixed CostImpact on Market Structure Non-HPSA costs Reduction Reduction

Pr (n=1) 0.062 0.055 0.056Pr (n�3) 0.338 0.313 0.319Pr (n�5) 0.592 0.562 0.571

Av. Number of Entrants/Market 1.396 1.657 1.423Av. Number of Exits/Market 1.029 1.131 0.950Net Change in Firms/Market 0.367 0.526 0.473Cost/Market (million $) 0.027 0.054

Cost/Additional Firm (millions $) 0.170 0.500

M. Roberts () Dynamic Models of Entry and Exit December 2015 29 / 30

Conclusions

Source of competitive pressure - combination of direct e¤ect of n ontoughness of competition, entry costs and �xed costs.

As n increases, VC and VE fall, px rises, pe falls.

De�ne BTE (n, z , f ) = δ(VC � VE )� δE (λjλ < VC )� E (κjκ < δVE )

Dentist monopoly markets it is .032, .081, .172 million dollars depending on(z , f ).Declines with nChiro monopoly markets it is smaller, .069 in high (z , f ) state

Comparing long-run e¤ect on VC for dentist

7% reduction in entry cost ($100,000) has same e¤ect as shift from n = 1 to 2:

M. Roberts () Dynamic Models of Entry and Exit December 2015 30 / 30