Firm Turnover in Imperfectly Competitive Markets

Transcription

1 Firm Turnover in Imperfectly Competitive Markets Marcus Asplund and Volker Nocke Review of Economic Studies, 2006 Presented by Román Fossati Universidad Carlos III January 2011 Fossati Román (Universidad Carlos III) Firm Turnover in Imperfectly Competitive Markets January / 17

2 Introduction Relevant Question What are the e ects of market size and xed costs on rm turnover and age distributions of rms within industries? Motivation Empirical literature on turnover and mobility of rms (Dunne, Roberts and Samuelson 1988, Caves 1998, Cabral 1997 and Sutton 1997): simultaneous rm entry and exit at industry level, and considerable variation in rm turnover across industries To explain these cross-industry di erences in rm turnover is one of the important research agendas Fossati Román (Universidad Carlos III) Firm Turnover in Imperfectly Competitive Markets January / 17

3 Introduction This paper Considers observable ind. characteristics (FC and market size) as determinants of E/X rates in an imperfectly competitive industry Develops a stochastic dynamic model of a monopolistic industry and test its empirical implications Main results The rate of rm turnover is increasing in market size, and the expected lifespan of rms is decreasing in market size An increase in FC leads to higher rm turnover and shorter expected lifespan of rms Fossati Román (Universidad Carlos III) Firm Turnover in Imperfectly Competitive Markets January / 17

4 Introduction Mechanism: price e ect of competition " market size)under free-entry "population of active rms) two opposing e ects on rms pro ts: larger sales (bc " in market size) lower price-cost margins (bc endogenous " intensity of competition) in equilibrium, the net e ect is positive for more e cient rms, but negative for less e cient rms the expected lifespan of rms is shorter, and the rate of rm turnover larger Fossati Román (Universidad Carlos III) Firm Turnover in Imperfectly Competitive Markets January / 17

5 Model Environment Discrete time, in nite horizon model, δ discount factor Continuum of consumers and potential rms Each rm produces a unique di erentiated product and hence faces a downward-sloping D curve Firms di er in their e ciency levels which evolves over time: c t 2 [0, 1] ct c t = 1 with Pr: α G () with Pr: 1 α φ xed cost of production entrants pay ɛ sunk cost of entry)draw c t G () µ is the state of the ind. (measure on [0, 1]) Fossati Román (Universidad Carlos III) Firm Turnover in Imperfectly Competitive Markets January / 17

6 Model Timing Entry stage: potential entrants decide whether to enter the market or take up the outside option (=0). Learning stage: entrants and incumbents observe c t Exit stage: entrants and incumbents decide whether to leave the market forever Output stage: active rms pay the FC, decide production, and receive pro ts They make assumptions directly on rms reduced-form eqlm. pro t function: Sπ(c, µ) where S is a measure of market size (i.e. mass of consumers) Fossati Román (Universidad Carlos III) Firm Turnover in Imperfectly Competitive Markets January / 17

7 Adding more active rms (c < c(µ)) reduces rms gross pro ts (# c(µ)) Key result: if 9µ to µ 0 which induces more intense competition, c(µ 0 ) < c(µ) )#gross pro t of more e cient rms by a larger total amount, but by a smaller fraction, than that of less e cient rms Fossati Román (Universidad Carlos III) Firm Turnover in Imperfectly Competitive Markets January / 17 Model Example 1 (linear demand model with a cont. of rms) Cont. (of mass S) of identical consumers with 0 1 nz nz U x 2 (i) 2σ x(j)x(i)dja di + H 0 where H is a composite alternative good Linear D system)in eqlm. each rm faces the same residual D curve) Sπ(c, µ) = ( S [c(µ) c] 2 8 if c c(µ) 0 otherwise σ c(µ) Z where c(µ) = 1 + σµ([0, c(µ)]) 0 zµ(dz)

8 Model Assumptions (MON) π(c, µ) is strictly decreasing in c on [0,c(µ)) and π = 0 8c 2 [c(µ), 1], and de ne partial order of measures as: µ 0 µ () f8c 2 [0, 1], π(c, µ 0 ) π(c, µ)g µ 0 µ () f8c 2 [0, c(µ)], π(c, µ 0 ) < π(c, µ)g µ 0 µ () same degree of competition Intuition: an " in the population of rms should " intensity of price competition)# pro ts (DOM) If µ 0 ([0, z]) µ([0, z]) 8z 2 (0, 1) ) µ 0 µ ( if some z >) Intuition: any shift in the population towards more e cient rms " competition intensity, #value of rms and)entrants value (ORD) The set of measures (M,) is completely ordered (CON) π(c, µ) is continuous Fossati Román (Universidad Carlos III) Firm Turnover in Imperfectly Competitive Markets January / 17

9 Model Main Assumptions (properties of a class of het. rms oligopoly models) Ass. 1: For µ 0 µ the pro t di erence π(c, µ) decreasing in c on [0, c(µ)) Ass. 2: For µ 0 µ the pro t ratio π(c,µ0 ) π(c,µ) [0, c(µ)) π(c, µ 0 ) is strictly is strictly decreasing in c on Prop. 1: Suppose c is the MC and rms compete either in P or Q: Sπ(c, µ) = (P(q(c, µ, S)/S, µ) c)q(c, µ, S) i) Ass. 1 holds i eqlm output q(c, µ, S) is decreasing in µ ii) Ass. 2 holds i eqlm price P(q(c, µ, S)/S, µ) is decreasing in µ Ass 1 holds in many models, but Ass 2 does not hold in the D-S monopolistic competition model. Fossati Román (Universidad Carlos III) Firm Turnover in Imperfectly Competitive Markets January / 17

10 Stationary Equilibrium (focus on M>0,c*<1) Value of an incumbent rm of type c : V (c) = maxf0, V (c)g 2 V (c) = [Sπ(c, µ) φ] + δ 4αV (c) + (1 α) Z V (z)g (dz) 5 De ne the threshold c as c supfc 2 [0, 1] j V (c) > 0 if V (1) = 0 = 1 if V (1) > 0 as V (c) is str # on [0, minfc, c(µ)g] ) 9 a threshold exit rule Value of an entrant: V e = Z 1 0 V (c)g (dc) ɛ Fossati Román (Universidad Carlos III) Firm Turnover in Imperfectly Competitive Markets January / 17

11 Stationary Equilibrium (focus on M>0,c*<1) Under Free Entry) V e = 0 ) V (c) = Sπ(c, µ) φ + δ(1 α)ɛ 1 αδ if c c in c = c Sπ(c, µ) φ + δ(1 α)ɛ = 0 Let V e (x,µ) be the value of a new entrant who uses exit policy x : xz V e (x, µ) = V (c)g (dc) ɛ )the free entry condition can be rewritten as and the condition for optimal exit as: 0 V e (c, µ) = 0 V e (c, µ) x = 0 Fossati Román (Universidad Carlos III) Firm Turnover in Imperfectly Competitive Markets January / 17

12 Stationary Equilibrium Fossati Román (Universidad Carlos III) Firm Turnover in Imperfectly Competitive Markets January / 17

13 Stationary Equilibrium (focus on M>0,c*<1) Invariant measures of rms e ciencies at stage 4: µ[c, M]([0, z]) = M (1 α)(1 G (c )) G (minfz, c g) has the shape of dist. G (), is truncated at equilibrium exit policy c, and is scaled by a factor Turnover: θ = M µ([0, 1]) = (1 α)(1 G (c )) G (c ) decreasing in c Share of active rms whose age is less than a: A(a/c ) 1 (1 G (c )θ) a str # in c Prop. 4: " ɛ )" c )# θ (shift of the age dist. of rms towards older rms, and total mass of active rms µ and entrants M decrease) Fossati Román (Universidad Carlos III) Firm Turnover in Imperfectly Competitive Markets January / 17

14 Model Prop. 5: If Ass. 1 holds) an " φ )# c )" θ (shift of the age dist. of rms towards younger rms, and µ and # M) Impact of market size changes on turnover and age dist. of rms: Prop. 6: If Ass. 2 holds) an " S )# c )" θ (shift of the age dist. of rms towards younger rms, and " µ and # M) : Empirical Application :Hairdressers salons in Sweden Test the comparative dynamics properties of the model: Impact of observables FC, entry costs and S on age distribution of rms Idea: examine the age distribution of rms that compete in the same sector but in di erent geographical markets. Fossati Román (Universidad Carlos III) Firm Turnover in Imperfectly Competitive Markets January / 17

15 Empirical Application Hairdressers salons in Sweden Take: land rents (proxy of FC) and population (proxy of market size) Fossati Román (Universidad Carlos III) Firm Turnover in Imperfectly Competitive Markets January / 17

16 Empirical Application Hairdressers salons in Sweden Fossati Román (Universidad Carlos III) Firm Turnover in Imperfectly Competitive Markets January / 17

17 Final Remarks Develops a stochastic dynamic model of a monopolistic industry to analyze the connection between market size and xed costs and rm turnover and age distribution of rms Test some empirical implications of the model Fossati Román (Universidad Carlos III) Firm Turnover in Imperfectly Competitive Markets January / 17