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Transcript of Profitability of R&D main explanatory factor of Schumpeterian growth theory Profitability of R&D...
![Page 1: Profitability of R&D main explanatory factor of Schumpeterian growth theory Profitability of R&D related to: Market power of producers of innovation goods.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649d015503460f949d3941/html5/thumbnails/1.jpg)
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
![Page 2: Profitability of R&D main explanatory factor of Schumpeterian growth theory Profitability of R&D related to: Market power of producers of innovation goods.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649d015503460f949d3941/html5/thumbnails/2.jpg)
Competition and growth
• Higher post-innovation market power → higher R&D → faster growth
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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
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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
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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
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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
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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
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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
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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?
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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
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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
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summing up:Deviation from perfect competition + Reverse causality
• positive relation between competition and TFP growth may be stronger than suggested by empirics
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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
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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
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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…
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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
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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
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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
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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
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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
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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
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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.
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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
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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
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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)
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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
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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)
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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 )
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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
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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
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Firm profit π1 in un-level sector 1
• p1= follower’s unit cost γc
using: p1x1 = 1 x1 = 1 / p1
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Firm profit π1 in un-level sector 1
• p1= γc
using: p1x1 = 1 x1 = 1 / p1
→ x1 = 1 / p1 = 1/γc cx1 = 1/γ
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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
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firm profit π0 in level sector
• If Bertrand price competition → π0 = 0
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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
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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
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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
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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
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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
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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
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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
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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
![Page 43: Profitability of R&D main explanatory factor of Schumpeterian growth theory Profitability of R&D related to: Market power of producers of innovation goods.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649d015503460f949d3941/html5/thumbnails/43.jpg)
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
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composition between lev. / unlev. sectors • μ1 = steady state fraction of unlevel sectors
• μ0 = 1 ─ μ1 = steady state fraction of level sectors
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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
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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
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composition between lev. / unlev. sectors
• n0 = probability that a level sector becomes unlevel
• n0 (1─ μ1) = expected steady state transitions
leveled → unleveled
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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)
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Δ and the steady state composition
(n-1 + h) μ1 = n0 (1─ μ1)
μ1 = n0 / (n-1 + h + n0)
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Aggregate innovation flow
• I = (n-1 + h) μ1 + n0 (1─ μ1) = 2 (n-1 + h) μ1
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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)
![Page 52: Profitability of R&D main explanatory factor of Schumpeterian growth theory Profitability of R&D related to: Market power of producers of innovation goods.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649d015503460f949d3941/html5/thumbnails/52.jpg)
Aggregate innovation flow
• I = 2 (n-1 + h) n0 / (n-1 + h + n0)• using:
• n-1 = π0 = (1 ─ Δ) π1
• n0 = π1 ─ π0 = Δπ1
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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)
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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
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Relation between Δ and aggregate innovation
• dI / dΔ = {2 π1[(1 ─ 2Δ) π1 + h]} / (π1 + h)
d2I / (dΔ)2 < 0
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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
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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
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conclusions
• If leader’s post innovation rents are ‘large’
→ π1 > h
→ dI / dΔ > 0 at low Δ
dI / dΔ < 0 at high Δ
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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
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General intuition 1: distinguish between Δ levels and changes
• If competition Δ is low R&D incentives are higher in un-leveled sectors …
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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
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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.
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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
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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
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empirical evidence (patent data)
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Empirical evidence (patent data)
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Qualification 1Max technology distance > 1 step
→ Optimal technology distance is endogenous• R&D investment by the leader targets optimal
technology distance
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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)
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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
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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