Demand-Driven Innovation and Spatial Competition Over Time

Transcription

1 Demand-Driven Innovation and Spatial Competition Over Time Boyan Jovanovic and Rafael Rob Presented by Román Fossati Universidad Carlos III September 2010 Fossati Román (Universidad Carlos III) Demand-Driven Innovation and Spatial Competition Over Time September / 13

2 Introduction Relevant Question Why do di erences in rm size tend to be more persistent over time in industries with more product di erentiation? Motivation Empirical evidence (Singh and Whittington, 1957) shows that across industries persistence is positively correlated with an index of product heterogeneity (i.e. chemicals and allied industries, and clothing and footwear). However, there seem to be no model on competition in product space and the dynamic behavior of industry structure. Fossati Román (Universidad Carlos III) Demand-Driven Innovation and Spatial Competition Over Time September / 13

3 Introduction The insight Demand-pull hypotesis: in the course of doing business, a rm gets information from its customers (improvements they would like to see in the future) in addition rms can gather information directly )the rm decides the direction of innovation activity (product to market in future). Fossati Román (Universidad Carlos III) Demand-Driven Innovation and Spatial Competition Over Time September / 13

4 Introduction The insight Demand-pull hypotesis: in the course of doing business, a rm gets information from its customers (improvements they would like to see in the future) in addition rms can gather information directly )the rm decides the direction of innovation activity (product to market in future). the larger its volume of business the greater the amount of information it gets)better chances in coming up with a superior product )successful rms learn more) success feed on itself (persistence) Across industries the degree of persistence should be positively related to product-heterogeneity Fossati Román (Universidad Carlos III) Demand-Driven Innovation and Spatial Competition Over Time September / 13

5 Model Competition in 3 dimensions: price (p x ), location (x) and information investment (z) Consumers market for a di erentiated good: u 2 R 1 type consumer s utility: u p x ρ(x, θ) each consumer demands only 1 unit perfect information about all price-quality pairs o ered in equilibrium: p x + ρ(x, θ) = p 8x 2 X B(u) population distribution of u (total demand: 1 B(u)) Fossati Román (Universidad Carlos III) Demand-Driven Innovation and Spatial Competition Over Time September / 13

6 Model Firms Each period a rm receives a signal s on θ iid over t Ψ(θ) choose a product design x before knowing θ (commitment is costless and irreversible) θ is observed each rm is of measure 0 (price taker): p x = p ρ(x, θ) choose output y ) c(y) and invest in direct information z on θ 0 ) k(z) (convex) Fossati Román (Universidad Carlos III) Demand-Driven Innovation and Spatial Competition Over Time September / 13

7 Model Information Acquisition s F (s/θ, y + z) a higher y + z leads to a more informative s: i.e. the rm observes a sample (a 1, a 2,...a n ), where ai 0 s are iid r.v. n φ(n/y + z) )size of the sample is ramdom but depends on (y + z) s n (a 1, a 2,...a n ) is a su cient statistic F (s/θ, y + z) = F 1 (s/θ, n)φ(n/y + z) n=0 Fossati Román (Universidad Carlos III) Demand-Driven Innovation and Spatial Competition Over Time September / 13

8 Model Firm s problem: Let F (θ/s) distribution of θ ven s v t distribution of decisions (y, z): v t = α(θ t, v t 1 ) p(θ t, v t 1 ) equilibrium price p x =p(θ t, v t 1 ) ρ(x, θ) Value Function Z V (s, v 1 ) = max max 1) x y,z ρ(x, θ)] c(y) k(z) Z +β V (s 0, α(θ t, v t 1 )) df (s 0 /θ, y + z) df (θ/s) Fossati Román (Universidad Carlos III) Demand-Driven Innovation and Spatial Competition Over Time September / 13

9 Model: Policy functions (1) x(s, v 1 ) = arg min x (2) y(p x, θ, v 1 ) = arg max y yp x c(y) + β (3) z(p x, θ, v 1 ) = Z arg max k(z) + β z Z Z ρ(x, θ)df (θ/s) V (s 0, α(θ t, v t 1 )) df (s 0 /θ, y + z) V (s 0, α(θ t, v t 1 )) df (s 0 /θ, y + z) at the beginnig of each period 9 some distrib.of s over rms (1))dispersion of optimal locations) θ observed)dispersion on p x (2))dispersion of optimal y 0 s, then by (3))dispersion of optimal z 0 s cross rms di erences in (y + z) and θ 0 )new rms distribution of s 0 luck may persist for several periods: (x θ)- rms)higher p x 0s )" y )If (y + z) is higher) +informed)larger next period. Fossati Román (Universidad Carlos III) Demand-Driven Innovation and Spatial Competition Over Time September / 13

10 Equilibrium Is a set of functions V (s, v 1 ), x(s, v 1 ), y(p x, θ, v 1 ), z(p x, θ, v 1 ), α(θ t, v t 1 ) and P(ρ/θ, y + z) (CDF of ρ(x(s), θ) conditional on θ) satistying i) the rm s Bellman Equation, ii) the law of motion for aggregate states v t = α(θ t, v t 1 ), and iii) Market clearing condition: Z y(p ρ, θ, v 1 )dp(ρ/θ, y + z)dv 1 (y, z) = 1 B(p) Fossati Román (Universidad Carlos III) Demand-Driven Innovation and Spatial Competition Over Time September / 13

11 Results Proposition 1. Equilibrium has a dominant strategy property with respect to rm s choice of x. Proposition 2. If φ is such that n is stochastically increasing in y + z )for rms with higher y + z this period will face a higher expected price p x next period. Propositions 3 and 4: (y +z ) p x > 0 and z y > 0 Proposition 5. If F (s/θ, ) depended only on z and not on y, there would be no persisting size di erences. Each rm s rank would be a serially uncorrelated random variable. Fossati Román (Universidad Carlos III) Demand-Driven Innovation and Spatial Competition Over Time September / 13

12 Results Aggregate dynamics Even though θ is a shock to relative demands (not to the scale of demand), it has aggregate e ects which, in spite of the serial independence of θ, persist over time. Aggregate output is an increasing function of aggregate location-quality, and this in turn is an increasing function of aggregate information. Fossati Román (Universidad Carlos III) Demand-Driven Innovation and Spatial Competition Over Time September / 13

13 Final Remarks This paper explores a model of innovation and spatial competition over time. A key implication of the paper: rms size is positively autocorrelated across time. The mechanism that generates this persistence works only in heterogenous-product markets: larger rms get better information about the design of future products. Fossati Román (Universidad Carlos III) Demand-Driven Innovation and Spatial Competition Over Time September / 13