Profitability of R&D main explanatory factor of Schumpeterian growth theory

• Profitability of R&D related to:• Market power of producers of innovation goods

• Distinguish between:• Pre-innovation market power• Post-innovation market power

Competition and growth

• Higher post-innovation market power → higher R&D → faster growth

Competition and growth

• Higher post-innovation market power → higher R&D → faster growth

• Higher post-innovation market power may result from:

• Lower competition between industries: lower α → lower elasticity of substitution between machines

Competition and growth

• Higher post-innovation market power may result from:

• Lower competition between industries: lower α → lower elasticity of substitution between machines

• Lower competition within industries: Higher protection from imitation → higher constrained monopoly price χ → faster growth

Within industry competition and growth

• Result of standard Schumpeterian model based of the assumption:radical innovations + no tacit knowledge (no explicit role for experience)

→ producer of inovation goods is a (possibly constrained) monopolist

Theory predictions at variance with empirical findings?

Scherer’s (1965) on ‘Fortune 500’ firms: relation between firm size and patenting : relation positive but weakening at large firm-size

Theory predictions at variance with empirical findings?

Nickell (1996) on London Stock Exch. Firms:

lower market share → higher TFP level

lower monopoly rents → higher TFP growth

Theory predictions at variance with empirical findings?

Blundell, Griffith, Van Renen on UK firms (1997):

Larger firms → have larger Knowledge stock

→ innovate to deter entry

This is at variance with standard result:

radical innovations + free entry

no R&D by incumbent monopolists

empirical findings on market-power and TFP growth need qualification

• TFP estimates assume: output elasticity of a factor = factor share in Y

• This follows from perfect competitionWhat if competition fails?

if competition fails… problem 1

• K share in Y > output elasticity of K Y = Kα (AL)(1 − α)

• underestimation of output elasticity of L• underestimation of contribution of technology (TFP

growth) to the growth of GDP per-capita

problem 2: reverse causality

• high-productivity firms grow faster and therefore… gain higher ex-post market shares

• Inaccurate econometrics may yield:• wrong interpretation of causal relation between

market share and TFP growth • over-estimate the productivity effects of a high

market share, hence of low competition

summing up:Deviation from perfect competition + Reverse causality

• positive relation between competition and TFP growth may be stronger than suggested by empirics

summing up:Deviation from perfect competition + Reverse causality

• positive relation between competition and TFP growth may be stronger than suggested by empirics

• positive relation between competition and GDP growth may be stronger than suggested by empirics

• On this ground we thake empirical results seriously and search for hypotheses that may eliminate the conflict between theory and facts

In search of different hypotheses…

• Lack of competition, separation between ownership and management

• Managers and workers buy themselves a quiet life (Hart 1983) → slack.. → satisficing (H. Simon)

• Introduce satisficing firms and sectors, beside profit maximizing firms and sectors

Product market competition (PMC) forces elimination of ‘slack’ in satisficing firms?

• 1. Higher PMC increases TFP levels in satisficing more than in profit maximizing firmscorroborated by evidence, but we are most interested in TFP growth…

Product market competition (PMC) forces elimination of ‘slack’ in satisficing firms?

• 2. Higher PMC increases TFP growth in satisficing more than in profit maximizing firms

• mixed evidence… non conclusive

In search of different hypotheses…

• incremental innovations + tacit knowledge

outsider’s innovation does not displace incumbent from market

→ possibly, more than 1 firm in the same sector

In search of different hypotheses…

• possibly, more than 1 firm in the same sector,

• if more than 1 firm with similar technology…,

profit depends on competition between incumbents

In search of different hypotheses…

• possibly, more than 1 firm in the same sector …

• if more than 1 firm with similar technology…,

profit depends on competition between incumbents

• If only 1 leader, profit constrained by advantage with respect to outsider

innovation• only two firms A and B in each sector (entry barriers)• Tacit knowledge: before improving upon frontier-

knowledge a follower must catch up with the leader(no immediate leap-frogging)

• Knowledge spillovers are such that maximum technological distance is 1 step

innovation• only two firms A and B in each sector (entry barriers)• → if A’s and B’s technology level is the same, the sector is

leveled and both A and B may invest in R&D

innovation• only two firms A and B in each sector (entry barriers)• → if A’s and B’s technology level is the same, the sector is

leveled and both A and B may invest in R&D• → if one firm is one step ahead, the sector is un-leveled:

the leader has no incentive to invest in R&D, because the maximum technology distance = 1 step.

A model of step by step innovations and knowledge spillovers

• PRODUCTION:• A continuum [0, 1] of consumer-good sectors (m=1)• Each sector j is a duopoly. firms A and B in j produce

xA = AA LA xB = AB LB

sector output = x = xA + xB

A model of step by step innovations and knowledge spillovers

• PRODUCTION:

• Firm i labour productivity = xi / Li = Ai = γk(i) i = A, B

• k(i) = i’s technology level γ > 1

A model of step by step innovations and knowledge spillovers

• PRODUCTION:

• Firm i labour productivity = xi / Li = Ai = γk(i) i = A, B

• k(i) = i’s technology level γ > 1

• 1/ Ai = γ ─ k(i) = Li / xi = labour input per unit of output

• i’s unit cost is: w γ ─ k(i)

innovation

• R&D expenditure ψ(n) = n2/2 by the leader moves technology 1 step ahead with probability n.

• R&D expenditure 0 by the laggard moves technology 1 step ahead with probability h.

• R&D expenditure ψ(n) = n2/2 by the laggard moves technology 1 step ahead with probability n+h

consumption

• A unit mass of identical consumers, each with

current utility u = ∫(log xj)dj

• ∂u / ∂xj = 1/ xj MRSj,f = xf / xj = pj /pf =

• In equilibrium, each j, f in [0, 1]: pjxj = pfxf = E = 1 (expenditure is our

numeraire)

consumption

• pjxj = E = 1 (expenditure is our numeraire)

• The representative household chooses xAj , xBj to maximize log(xAj + xBj) subject to: pAjxAj + pBjxBj = 1 = E

• She will choose the least expensive between xAj , xBj

pj = min(pAj , pBj )

Firm profit π1 in un-level sector 1

• technology distance = 1 step

• if leader’s unit cost is c,

• laggard’s unit cost is γc > c

• leader’s profit = π1 = p1x1 ─ cx1 = 1 ─ cx1

recalling: p1x1 = 1

Firm profit π1 in un-level sector 1

• Leader chooses maximum price p1 consistent with preservation of leadership (follower left outside of the market)

→ p1= follower’s unit cost γc

Firm profit π1 in un-level sector 1

• p1= follower’s unit cost γc

using: p1x1 = 1 x1 = 1 / p1

Firm profit π1 in un-level sector 1

• p1= γc

using: p1x1 = 1 x1 = 1 / p1

→ x1 = 1 / p1 = 1/γc cx1 = 1/γ

Firm profit π1 in un-level sector 1

• p1= γc x1 = 1 / p1 = 1/γc cx1 = 1/γ

• π1 = p1 x1 ─ cx1 = 1 ─ cx1 = 1 ─ 1/γ

firm profit π0 in level sector

• If Bertrand price competition → π0 = 0

firm profit π0 in level sector

• If Bertrand price competition → π0 = 0• If perfect collusion → firms A and B maximize total

profit π and then share π between them→ π0 = (1/2) π

with π = π1

Δ = degree of competition in a level sector defined

• Δ = (π1 ─ π0) / π1 ½ ≤ Δ ≤ 1

π0 = (1 ─ Δ) π1

• Perfect collusion Δ = ½ π0A = π0B = π1 / 2

• Bertrand competition Δ = 1 π0A = π0B = 0

• notice that (π1 ─ π0) = Δ π1

Innovation intensity n0 in a leveled sector increases with intensity of competition in this sector

• Planning horizon: 1 period• At most 1 innovation per period (1 firm succeeds)• Innovator’s gross profit:• π1 with probability n0

• π0 with probability 1 ─ n0

Innovation intensity n0 in a leveled sector increases with intensity of competition in this sector

• Planning horizon: 1 period• At most 1 innovation per period (1 firm succeeds)• Innovator’s gross profit:• π1 with probability n0

• π0 with probability 1 ─ n0 • Max: [π1 n0 + π0 (1 ─ n0)] ─ (n0)2 / 2

with respect to n0

• → n0 = π1 ─ π0 = Δπ1

• Escape competition effect: dn0 / dΔ > 0

Escape competition effect

• The higher the degree of competition in a sector in which firms are technologically similar (‘neck and neck’)

• the lower their profit

• the higher the profit gain from innovation, because the innovating firm becomes a monopolistic leader and monoply profit of the leader untouched by competition in leveled sector

Innovation intensity by outsider in un-leveled sector

• The laggard -1 is an outsider:• with R&D R = ψ(n ─1) = ½ (n ─1) 2

innovation probability n ─1 + h

Innovation intensity by outsider in un-leveled sector

• laggard -1 chooses n ─1 to maximize:

• (n-1 + h) π0 ─ (n-1)2 / 2

→ π0 = n-1

Innovation intensity by the outsider in un-leveled sector lowered by higher Δ

• π0 = n-1

π0 = (1 ─ Δ) π1 = n-1

• Because π1 is given and Δ = (π1 ─ π0) / π1

higher competition Δ in a leveled sector…→ lower π0

→ lower profit gain from innovation for the outsider → lower innovation intensity in un-leveled sector

Schumpeter’s effect

• After innovating, the new entrant competes with previous leader and faces a degree of competition Δ

• Post-innovation profit is now inversely related to competition in leveled sector

composition between lev. / unlev. sectors • μ1 = steady state fraction of unlevel sectors

• μ0 = 1 ─ μ1 = steady state fraction of level sectors

composition between lev. / unlev. sectors • μ1 = steady state fraction of unlevel sectors

• μ0 = 1 ─ μ1 = steady state fraction of level sectors

• (n-1 + h) = probability of transition:

unleveled → leveled

composition between lev. / unlev. sectors • μ1 = steady state fraction of unlevel sectors

• μ0 = 1 ─ μ1 = steady state fraction of level sectors

• (n-1 + h) = probability of transition:

unleveled → leveled• (n-1 + h) μ1 = expected steady state transitions

unleveled → leveled

composition between lev. / unlev. sectors

• n0 = probability that a level sector becomes unlevel

• n0 (1─ μ1) = expected steady state transitions

leveled → unleveled

Δ and the steady state composition

• steady state number of level/unlevel sectors is stationary

→ transitions in one direction = transitions in the other(n-1 + h) μ1 = n0 (1─ μ1)

Δ and the steady state composition

(n-1 + h) μ1 = n0 (1─ μ1)

μ1 = n0 / (n-1 + h + n0)

Aggregate innovation flow

• I = (n-1 + h) μ1 + n0 (1─ μ1) = 2 (n-1 + h) μ1

Aggregate innovation flow

• I = (n-1 + h) μ1 + n0 (1─ μ1) = 2 (n-1 + h) μ1

• μ1 = n0 / (n-1 + h + n0)

• I = 2 (n-1 + h) n0 / (n-1 + h + n0)

Aggregate innovation flow

• I = 2 (n-1 + h) n0 / (n-1 + h + n0)• using:

• n-1 = π0 = (1 ─ Δ) π1

• n0 = π1 ─ π0 = Δπ1

Obtain I as a function of Δ and leader’s profit π1

• I = 2 (n-1 + h) n0 / (n-1 + h + n0)

n-1 = π0 = (1 ─ Δ) π1

n0 = π1 ─ π0 = Δπ1

n-1 + n0 = π1

• I = {2[(1 ─ Δ) π1 + h] Δ π1} / (π1 + h)

competition and innovation

• I = {2[(1 ─ Δ) π1 + h] Δ π1} / (π1 + h)

• dI / dΔ = {2 π1[(1 ─ 2Δ) π1 + h]} / (π1 + h)

• Study sign of dI /dΔ at sufficiently low and high values of Δ

Relation between Δ and aggregate innovation

• dI / dΔ = {2 π1[(1 ─ 2Δ) π1 + h]} / (π1 + h)

d2I / (dΔ)2 < 0

Relation between Δ and aggregate innovation

• dI / dΔ = {2 π1[(1 ─ 2Δ) π1 + h]} / (π1 + h)

d2I / (dΔ)2 < 0

• Low competition:• At Δ = ½ dI / dΔ = (2π1h) / (π1 + h) > 0

Relation between Δ and aggregate innovation

dI / dΔ = {2 π1[(1 ─ 2Δ) π1 + h]} / (π1 + h)

• High competition:• at Δ = 1: dI / dΔ = (- π1 + h) 2 π1 / (π1 + h)

• dI / dΔ < 0 if and only if π1 > h

conclusions

• If leader’s post innovation rents are ‘large’

→ π1 > h

→ dI / dΔ > 0 at low Δ

dI / dΔ < 0 at high Δ

Predictions:

• If leader’s post innovation rents are ‘large’

→ π1 > h

→ dI / dΔ > 0 at low Δ

dI / dΔ < 0 at high Δ

• If leader’s post innovation rents are not ‘large’

→ π1 < h

→ dI / dΔ > 0 for any Δ

General intuition 1: distinguish between Δ levels and changes

• If competition Δ is low R&D incentives are higher in un-leveled sectors …

General intuition 1: distinguish between Δ levels and changes

• If competition Δ is low R&D incentives are higher in un-leveled sectors …→ high innovation by outsiders

→ low innovation by neck and neck firms

General intuition 1: distinguish between Δ levels and changes

• If competition Δ is low …

• In steady state most sectors end up being leveled because large R&D by outsiders.

• In leveled sectors greater competition promotes more R&D.

General intuition 2:

• If competition level Δ is high, R&D incentives are higher in leveled sectors

• → high innovation by neck and neck firms → low innovation by outsiders

General intuition 2:

• If competition level Δ is high, R&D incentives are higher in leveled sectors

• → high innovation by neck and neck firms → low innovation by outsiders

• in steady state most sectors end up being un-leveled.

• In un-leveled sectors greater competition promotes less R&D

empirical evidence (patent data)

Empirical evidence (patent data)

Qualification 1Max technology distance > 1 step

→ Optimal technology distance is endogenous• R&D investment by the leader targets optimal

technology distance

Qualification 1Max technology distance > 1 step

→ Optimal technology distance is endogenous• R&D investment by the leader targets optimal

technology distance• Relation between optimal technology distance and

ease of entry (size of knowledge spillovers, indivisibility of R&D…) needs investigation

• Possibly more R&D by the leader, with greater ease of entry (less market protection)

Qualification 2Foreing entry in a sector far from technology frontier

• If sector technology is far from technology frontier, grater ease of entry / less market protection may imply loss of the market to the advantage of technologically superior foreign firms

Qualification 2Foreing entry in a sector far from technology frontier

• If sector technology is far from technology frontier, grater ease of entry / less market protection may imply loss of the market to the advantage of technologically superior foreign firms

• Argument reminiscent of ‘infant industry protection’• Effects of competition and anti-regulation polices

may be different in sectors/country close to or far from the world wide technology frontier