Dynamic Models of Entry and Exit

Dynamic Models of Entry and Exit Measuring Competition in Oligopolistic Markets A basic goal of empirical work in industrial organization is to measure the degree of competition in real world markets. Static models of competition estimate models of production and/or demand to measure markups Treat prices, quantities as endogenous, market structure is exogenous data requirements: prices, quantities, market shares, product characteristics, production costs key equation: f.o.c. for price or quantity choice Porter (Bell Journal, 1981), Appelbaum (J Econometrics, 1982), Bresnahan (J Econometrics, 1981), Berry, Levinsohn, and Pakes (Econometrica, 1995), De Loecker and Warzynski (AER, 2012) Measuring Competition in Oligopolistic Markets "Static Entry" models infer competition from relationship between the number of …rms and market size. Bresnahan and Reiss (JPE, 1991 and RES, 1990) insight: As a market grows in size it will support more …rms, but how many more depends on extent of competition after entry. Empirical approach: Use a cross-section of geographic markets with di¤erent populations 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 entrants Campbell 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). Empirical Models of Market Structure "Static Entry" Models - Market Structure: Entry Stage endogenizes the number of …rms in market Nm Short-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 explain simultaneous entry and exit No distrinction between incumbents and potential entrants. Same value functions, distribution of private shocks Cannot distinguish sunk entry costs from …xed costs Not explicitly dynamic. No role for market/…rm history to matter. 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’s decision 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 decisions sunk 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) 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 of future states the perceptions of future states are consistent with competitor’s optimal actions. Goal of the Structural Empirical Model Use data on observed states St and …rm actions At to estimate parameters of payo¤ functionsV (θ ) and distribution of private shocks G (ε) Conduct policy experiments which alter θ and simulate new paths for A and S. 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 model prediction 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 ) and transition process for states Pr (s 0 js ), compute value function as sum of future pro…ts. Estimate dynamic parameters by …nding max value function. Dunne, Klimek, Roberts and Xu – Entry, Exit, and the Determinants of Market Structure Similar to Static Entry Models Geographic Markets with populations from 2,500 to 50,000 people Dentists - 639 markets with n =1,2,....20 Chiropractors - 410 markets with n =1,2,....8 Di¤ers from Static Entry Models Endogenous variables are ‡ows of entry and exit Key market-level variables: n, e, x , π Distinguishes incumbents from potential entrants Separates entry costs from …xed costs 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 cost barriers? Subsidies for underserved dental markets Data Source: U.S. Census Bureau Longitudinal Business Database for 1977, 1982, 1987, 1992, 1997, 2002 Demand and Market Structure Statistics Pop Quart (mean) Market Structure n Revenue Practice Q1 (5.14) Q2 (7.67) Q3 (11.10) Q4 (19.93) 3.86 5.65 7.84 11.90 148.12 158.67 157.87 168.01 Q1 (5.50) Q2 (7.33) Q3 (11.24) Q4 (20.31) 3.92 4.57 5.16 8.55 129.11 148.62 151.27 171.99 Q1 (6.39) Q2 (9.74) Q3 (14.92) Q4 (28.20) 2.00 2.53 3.06 3.84 93.83 97.40 107.29 121.49 Demand Per-cap Fed Med Infant Income Bene…ts Mortality Dentist - non HPSA Markets 9.30 1.38 8.63 9.30 1.99 8.80 9.32 2.02 8.60 9.34 2.57 8.94 Dentist - HPSA Markets 9.12 1.30 9.12 9.13 1.51 9.13 9.18 1.47 9.18 9.17 2.02 9.17 Chiropractors 9.30 1.63 8.98 9.32 1.84 8.43 9.32 2.41 8.70 9.37 3.56 8.80 Dynamics Entry Exit Prop Rate .204 .206 .206 .209 .185 .176 .193 .198 .190 .243 .285 .246 .214 .212 .208 .175 .413 .482 .503 .518 .233 .246 .244 .254 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 and observed Evolution of state variables z evolves as an exogenous Markov process F (z 0 jz ) n evolves endogenously with …rm entry/exit decisions n 0 = n + e x Incumbent’s Exit/Continue Decision Each incumbent observes current market state s, payo¤s π (s ),and a private continuation cost λi , an iid draw from a common cdf G λ 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: p x (s ) = Pr(δλi > δVC (s )) = 1 G λ (VC (s )). The expectation of the next period’s realized value function for the …rms that choose to produce.is VC (s ) h = Esc0 π (s 0 ) + Eλ0 (max δVC (s 0 ) = Esc0 [π (s 0 ) + δ(1 p x (s 0 ))(VC (s 0 ) δλ0 , 0 ) i E (λ0 jλ0 VC (s 0 ))] Last term is the truncated mean of the …xed cost distribution given they continue. Simplifying Distribution of Fixed Costs Assume distribution of …xed costs λ is exponential: G λ = 1 e (1 /σ)λ . Truncated mean of λ depends on σ, truncation point VC (s 0 ), and prob of exit p x E (λ0 jλ0 VC (s 0 )) = σ VC (s 0 ) p x (s 0 )/(1 p x (s 0 )) VC (s ) can be rewritten as VC (s ) = Esc0 [π (s 0 ) + δVC (s 0 ) δσ(1 p x (s 0 ))] Potential Entrant’s Decision Each potential entrant observes a private entry cost κ i , an iid draw from a common cdf G κ . Makes a discrete decision to enter/stay out in the next period. Payo¤ to entry is VE (s ) = Ese0 [π (s 0 ) + δVC (s 0 ) δσ(1 p x (s 0 ))] which implies that the probability of entry is: p e (s ) = Pr(κ i < VE (s )) = G κ (VE (s )) 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 G λ (VC) where VC = Mc [π +δVC The entry condition is: δσ(1 px )] pe = G κ (VE) where VE = Me [π + δVC δσ(1 px )]. Empirical Strategy Need to measure π, VC, and VE for each state (n, z ) Mc , Me for each pair of states Fixed 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, z Transition matrices for the state variables Mc , Me from state variables over time, s, s 0 . Construct VC (s ), VE (s ). Entry cost and …xed cost parameters, α and σ, from the entry and exit ‡ow data. Pro…t Function Estimation z = (pop, per capita income, wage, fed med, mort ): 5 π mt = θ 0 + 2 + h(θ Z , Zmt ) + fm + εmt ∑ θ k I (nmt = k ) + θ 6 nmt + θ 7 nmt k =1 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 ẑmt = h(θ̂ Z , Zmt ) (1) Constructing VC and VE Discretize the state variable zmt into 10 categories (zd ), and fm into three categories(fd ) Mc (n0 , zd0 , fd jn, zd , fd ) = Mnc (n0 jn, zd , fd ) Mz (zd0 jzd ) Ifd The 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 to each state s 0 Constructing VC and VE ^ ^ ^ Given estimates of M c and π (s ), VC is a …xed point of the equation system: ^ ^ VC = M c π + δVC δσG λ (VC) It is a function of the …xed cost parameter σ ^ ^ ^ ^ Given M e ,π, and VC, VE is: ^ ^ ^ ^ VE = M e [π + δVC ^ δσG λ (VC)]. Likelihood Function for Entry and Exit Flows The log probability of observing xmt exits and emt entrants in a market with state s is: l (xmt , emt ; σ, α) = (nmt ^ xmt ) log(G λ (VC (s ))) + xmt log(1 ^ emt log(G κ (VE (s ))) + (pmt emt ) log(1 ^ G λ (VC (s ))) ^ G κ (VE (s ))) The log likelihood function for the observations on entry and exit ‡ows is: L(σ, α) = ∑ ∑ l (xmt , emt ; σ, α). m t Notice: need data on potential entrants pmt in each market. 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 organization External data sources to estimate other expenses as a share of o¢ ce revenue Adjust 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 (internal pool) measure number of doctors in excess of the number of practices Simultaneous entry and exit are the norm Size of Potential Entranty Pool Number Estabs n=1 n=2 n=4 n=6 n=7 n=8 n=10,11 n=12,13,14 n=15,16,17 n=18,19,20 Dentists internal pool external pool 2.31 23.55 2.74 25.22 4.04 23.05 6.03 25.45 6.58 27.83 7.81 29.09 9.66 27.13 11.74 25.89 13.83 27.15 15.95 28.21 Chiropractors internal pool external pool 3.42 1.95 3.78 2.88 5.13 5.37 6.19 7.74 6.16 9.37 8.75 10.67 In dentists, the de…nitions are very di¤erent. Entry rate will be lower (entry cost higher) with the external pool Pro…t Function Estimates (number of …rms only) Variable Intercept I(n=1) I(n=2) I(n=3) I(n=4) I(n=5) n n2 obs F(27,df) Dentist No Fixed E¤ect Fixed E¤ect -11.543 (4.184)* -2.561 (4.922) .0379 (.0240) .0519 (.0301) .0253 (.0173) .0342 (.0221) .0113 (.0134) .0179 (.0163) .0112 (.0100) .0108 (.0122) .0191 (.0087)* .0154 (.0088) -.0044 (.0045) -.0238 (.0059) * .0001 (.0002) 5.55e-4 (2.45e-4) * 2556 2556 32.03 58.94 Chiropractor No Fixed E¤ect Fixed E¤ect -1.215 (8.720) -23.96 (10.55) * .0200 (.0328) .0613 (.0373) .0211 (.0324) .0389 (.0373) .0100 (.0328) .0338 (.0361) .0046 (.0324) .0192 (.0355) .0005 (.0331) .0266 (.0360) -.0021 (.0339) .0041 (.0362) -.0277 (.0353) -.0205 (.0369) 1640 1640 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) Fixed Cost and Entry Cost Parameters Panel A. Dentist (All Markets) Entry pool internal external Panel Entry pool internal external Entry pool internal external σ α 0.373 (0.006) 2.003 (0.013) 0.375 (0.006) 3.299 (0.039) B. Dentist (HPSA vs Non-HPSA σ α (HPSA) 0.366 (0.009) 1.797 (0.069) 0.368 (0.008) 3.083 (0.169) Panel C. Chiropractor σ α 0.275 (0.005) 0.274 (0.005) 1.367 (0.015) 1.302 (0.022) Markets) α (non-HPSA) 2.019 (0.041) 3.376 (0.079) 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 Dynamic Bene…ts VC, VE (millions of 1983 $) n=1 n=2 n=4 n=8 n=12 n=20 n=1 n=2 n=3 n=4 n=6 n=8 VC for Incumbents - Dentist low(z,f) mid(z,f) high(z,f) 0.433 0.764 1.286 .0383 0.714 1.236 0.297 0.628 1.150 0.195 0.525 1.048 0.126 0.457 0.979 0.067 0.397 0.920 VC for Incumbents - Chiro 0.178 0.344 0.562 0.166 0.332 0.551 0.155 0.321 0.540 0.148 0.314 0.532 0.132 0.298 0.516 0.123 0.289 0.508 VE for Potential Entrants - Dentist low(z,f) mid(z,f) high(z,f) 0.394 0.722 1.247 0.350 0.678 1.202 0.273 0.601 1.126 0.180 0.508 1.032 0.117 0.445 0.969 0.064 0.392 0.916 VE for Potential Entrants - Chiro 0.170 0.335 0.553 0.161 0.326 0.544 0.151 0.316 0.534 0.144 0.308 0.527 0.129 0.294 0.512 0.123 0.287 0.506 VC di¤ers substantially across markets Chiropractors are less pro…table, decline less with n Probabilities of Exit and Entry n=1 n=2 n=4 n=8 n=12 n=20 Probability of Exit - Dentist low(z,f) mid(z,f) high(z,f) 0.313 0.129 0.032 0.358 0.148 0.036 0.451 0.186 0.046 0.593 0.244 0.060 0.713 0.294 0.072 0.836 0.345 0.085 Probability of Entry - Dentist low(z,f) mid(z,f) high(z,f) 0.141 0.216 0.382 0.126 0.204 0.371 0.100 0.182 0.352 0.067 0.155 0.328 0.044 0.136 0.312 0.024 0.117 0.297 n=1 n=2 n=3 n=4 n=6 n=8 Probability of Exit - Chiro 0.524 0.286 0.129 0.547 0.299 0.135 0.569 0.311 0.141 0.585 0.319 0.144 0.620 0.339 0.153 0.639 0.349 0.158 Probability of Entry - Chiro 0.133 0.245 0.371 0.127 0.239 0.367 0.119 0.233 0.362 0.114 0.228 0.358 0.103 0.219 0.350 0.098 0.215 0.346 Reduction in Entry Cost: Impact on Entrants n=1 n=2 n=4 n=8 n=12 n=20 Probability of Exit - Dentist low(z,f) mid(z,f) high(z,f) 0.313 0.129 0.032 0.358 0.148 0.036 0.451 0.186 0.046 0.593 0.244 0.060 0.713 0.294 0.072 0.836 0.345 0.085 Probability of Entry - Dentist low(z,f) mid(z,f) high(z,f) 0.141 0.216 0.382 0.126 0.204 0.371 0.100 0.182 0.352 0.067 0.155 0.328 0.044 0.136 0.312 0.024 0.117 0.297 n=1 n=2 n=3 n=4 n=6 n=8 Probability of Exit - Chiro 0.524 0.286 0.129 0.547 0.299 0.135 0.569 0.311 0.141 0.585 0.319 0.144 0.620 0.339 0.153 0.639 0.349 0.158 Probability of Entry - Chiro 0.133 0.245 0.371 0.127 0.239 0.367 0.119 0.233 0.362 0.114 0.228 0.358 0.103 0.219 0.350 0.098 0.215 0.346 Reduction in Entry Costs: Impact on Incumbents Number of Firms n=1 n=2 n=3 n=4 n=5 n=7 n=9 p x (n, z, f ) VC (n, z, f ) low(z,f) -6.50 -6.26 -6.50 -6.36 -6.62 -6.31 -6.06 mid(z,f) -4.26 -3.97 -3.91 -3.71 -3.66 -3.28 -2.97 high(z,f) -2.50 -2.26 -2.15 -1.98 -1.90 -1.63 -1.42 low(z,f) 7.85 6.64 5.93 5.20 4.73 3.69 2.92 mid(z,f) 9.11 7.89 7.18 6.44 5.97 4.91 4.13 high(z,f) 8.99 7.76 7.05 6.31 5.84 4.78 4.01 Cost-Bene…t Comparison of Subsidies Impact on Market Structure Pr (n=1) Pr (n 3) Pr (n 5) Av. Number of Entrants/Market Av. Number of Exits/Market Net Change in Firms/Market Cost/Market (million $) Cost/Additional Firm (millions $) Benchmark Non-HPSA costs 0.062 0.338 0.592 Entry Cost Reduction 0.055 0.313 0.562 Fixed Cost Reduction 0.056 0.319 0.571 1.396 1.029 0.367 1.657 1.131 0.526 0.027 0.170 1.423 0.950 0.473 0.054 0.500 Conclusions Source of competitive pressure - combination of direct e¤ect of n on toughness of competition, entry costs and …xed costs. As n increases, VC and VE fall, p x rises, p e falls. De…ne BTE (n, z, f ) = δ(VC VE ) δE (λjλ < VC ) E (κ jκ < δVE ) Dentist monopoly markets it is .032, .081, .172 million dollars depending on (z, f ).Declines with n Chiro 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: