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Konowledge spillovers and convergence

Konowledge spillovers and convergence. Introduce sector specific knowledge spillovers across countries Study sectoral dynamic behavior of: Expected distance of country productivity from world frontier productivity Expected growth rate of productivity. Technology transfer in sector i.

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Konowledge spillovers and convergence

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  1. Konowledge spillovers and convergence • Introduce sector specific knowledge spillovers across countries • Study sectoral dynamic behavior of: • Expected distance of country productivity from world frontier productivity • Expected growth rate of productivity

  2. Technology transfer in sector i • h countries • m sectors in each country • Cross country sector-specific spillovers • A*t1 cross country maximum sector i productivity (subscript i omitted) at the beginnining of period t. • If 1 innovation arrives in country j at t: Aj,t = γ A*t  1γ > 1 sector productivity in country j reaches and improves upon frontier productivity, however large the distance A*t  1/ Aj,t  1

  3. Sector specific knowledge spillovers • knowledge spillovers induce technology catch up • At = γ A* t  1 with probability μ • At = At  1 with probability 1  μ • μ = λn* • n* = n(χ, λ) = optimal R&D effort • μ = country innovation rate in the given sector (sectors are ex ante identical, but differ in realized productivity At )

  4. Sector technology frontier • h countries • A* t  1 world-wide sector technology frontier at t − 1 • logA*t = logγ +logA* t  1 with probability μ* • logA*t = logA*t  1 with probability 1  μ* • μ* = ∑hj = 1λj n*j = probability that some innovation occurs in some country in sector i

  5. Expected sector growth in 1 country gt = E[logAt]  logA t  1 = • = μlogA*t  1 + μlogγ + (1μ)logAt  1 logAt  1 • = μ[logA*t  1 + logγ logAt  1] gt = μ[logγ + log(A*t  1 /A t  1)] = μ[logγ + dt  1]

  6. Distance to frontier may favor growth gt = μ[logγ + log(A*t  1 /A t  1)] = μ[logγ + dt  1] • dt  1 = distance to frontier = log(A*t  1 /A t  1) • If μ = λ n* > 0 … expected sector growth increases with dt  1 If μ = λ n* = 0 gt = 0

  7. Convergence of sector productivity in country j • expected country j distance from frontier z j, t = E(d j , t) • If μj= λ nj* > 0 …z j, t converges to: • z j * = [(μ*  μ j) / μ]logγ if μ > 0 • z j * = +∞ if μ = 0 • zj* is a decreasing function of nj* • The higher R&D effort nj*, the lower steady state distance from frontier productivity

  8. Convergence/divergence of sector growth in country j • Long-run expected country j growth in sector i: • gj* = g* = μ*logγif μ > 0 • gj* = 0 if μ = 0 • g* = μ*logγ • μ* = ∑hj = 1λj n*j = probability that some innovation occurs in some country in sector i

  9. Divergence… • If research productivity λ and/or monopoly profit π is too low, then → no R&D • Expected distance to frontier grows to infinity

  10. Competition and growth • Implicity assuming high indivisibility of R&D investment and/or high replicability of innovation prototypes standard Schumpeterian growth model predicts: • Higher post-innovation market power of innovator → 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 • Lower competition within industries: Higher protection from imitation → higher constrained monopoly price χ → faster growth

  11. Within industry competition and growth • Result of standard Schumpeterian model based of the assumption: radicalinnovations + no tacit knowledge (no explicit role for experience) → producer of inovation goods is a (possibly constrained) monopolist

  12. 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 sizes Nickell (1996) on London Stock Exch. Firms: lower market share → higher TFP level lower monopoly rents → higher TFP growth Blundell Grittith Van Renen on UK firms (1997): Larger firms → have larger Knowledge stock → innovate to deter entry

  13. empirical findings on relation between market-power and productivity need qualification • TFP estimates assume: • output elasticity of a factor = factor share in Y • This follows from perfect competition • What if competition fails? • K share in Y > output elasticity of K • underestimation of output elasticity of L • Distortion of the contribution of technology to growth

  14. Reverse causality: • high-productivity firms grow faster and gain higher ex-post market shares • The data may over-estimate the productivity effects of a high market share • The positive relation between competition and TFP growth may be stronger than suggested by empirics • On this ground we thake empirical results seriously and search for better hypotheses…

  15. 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

  16. 3 predicted effects of product market competition PMC • 1. Higher PMC increases productivity (including TFP) levels in satisficing more than in profit maximizing firms corroborated by evidence, but we are most interested in TFP growth… • 2. Higher PMC increases productivity (including TFP) growth in satisficing more than in profit maximizing firms • mixed evidence…possibly affected by failure to consider debt • 3. Debt repayment obligation → discipline on satisficing → higher debt financing → more positive effect of PMC on productivity growth (‘complementarity effect’) no evidence: financial pressure and PMC are substitutes, not complements

  17. In search of different hypotheses… • 1. incremental innovations + tacit knowledge→ possibly, more than 1 firm in the same sector, because outsider’s innovation does not displace the incumbent leader from market. • 2. if more than 1 firm with similar technology level, profit depends on competition between incumbents • 3. If only 1 leader, profit constrained by advantage with respect to outsider

  18. innovation • Assume 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 • Knowledge spillovers are such that maximum technological distance is 1 step • → 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 and the leader has no incentive to invest in R&D. R&D by the leader would require max. tech. distance > 1 step

  19. 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 x = xA + xB • Firm i labour productivity = Ai = γk(i) i = A, B • k(i) = i’s technology level γ > 1 • γ─ k(i) = Li / xi = labour input per unit of output • i’s unit cost is w γ─ k(i)

  20. 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

  21. consumption • A unit mass of identical consumers, each with current utility u = ∫(log xj)dj • In equilibrium, for each j in [0, 1]: 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

  22. Firm profit π1 in un-level sector 1 • technology distance = 1 step • If the leader’s unit cost is c, the laggard’s unit cost is γc > c • leader’s profit = π1 = p1x1 ─ cx1 = 1 ─ cx1 • Leader chooses maximum price p1 consistent with p1x1 = 1 • → p1= γc x1= 1/γc cx1= 1/γ • π1 = γc x1 ─ cx1 = 1 ─ cx1 = 1 ─ 1/γ

  23. firm profit π0 in level sector • Bertrand price competition → π0 = 0 • Perfect collusion: firms A and B maximize total profit π and then share π between them →π0 = (1/2) π • With degree of competition Δ in a level sector: • → π0 = (1 ─ Δ)π1 ½ ≤ Δ ≤ 1 • Δ = (π1 ─ π0) / π1 • Perfect collusion Δ = ½ • Bertrand competition Δ = 1

  24. 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

  25. 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 untouched by competition in leveled sector

  26. Innovation intensity by the outsider in un-leveled sector lowered by higher Δ • The laggard -1 chooses n ─1 to maximize: • (n-1 + h) π0 ─ (n-1)2 / 2 • → n-1 = π0 = (1 ─ Δ) π1 • Lower competition Δ in a leveled sector… • increases innovation intensity in un-leveled sector

  27. 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

  28. composition between lev. / unlev. sectors • μ1 = steady state fraction of unlevel sectors • μ0 = 1 ─ μ1 = steady st. fraction of level sect.s • (n-1 + h) = prob. that a unlevel sector becomes level • (n-1 + h) μ1 = steady state expected number of sectors moving from un-level to level • n0 = prob. that a level sector becomes unlevel • n0 (1─ μ1) = steady state expected number of sectors moving from level to unlevel

  29. Δ and the steady state composition • the steady state number of level/unlevel sectors is stationary • (n-1 + h) μ1 = n0 (1─ μ1) • μ1 = n0 / (n-1 + h + n0) • The aggregate innovation flow is: • I = (n-1 + h) μ1 + n0 (1─ μ1) = 2 (n-1 + h) μ1 =

  30. General intuition 1: distinguish between Δlevels and changes • If competition Δ is low R&D incentives are higher in un-leveled sectors → high innovation by outsiders and low innovation by neck and neck firms. • In steady state most sectors end up being leveled. • In leveled sectors greater competition promotes more R&D.

  31. 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

  32. empirical evidence (patent data)

  33. Empirical evidence (patent data)

  34. Aggregate innovation flow and competition in level sectors • 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) • using: • n-1 = π0 = (1 ─ Δ) π1 • n0 = π1 ─π0 = Δπ1

  35. Obtain I as a function of Δ and leader’s profit π1 • I = {2[(1 ─ Δ) π1 + h] Δπ1} / (π1 + h) • dI / dΔ = {2 π1[(1 ─ 2Δ) π1 + h]} / (π1 + h) • Study sign of dI /dΔat sufficiently low and high values of Δ

  36. Relation between Δ and aggregate innovation • dI / dΔ = {2 π1[(1 ─ 2Δ) π1 + h]} / (π1 + h) • Low competition: • At Δ = ½ dI / dΔ = (2π1h) / (π1 + h) > 0 • d2I / (dΔ)2 < 0

  37. Relation between Δ and aggregate innovation • High competition: • at Δ = 1: dI / dΔ = (- π1 + h) 2 π1 / (π1 + h) • dI / dΔ < 0 if and only ifπ1 > h

  38. conclusions • If leader’s post innovation rents are ‘large’ • →π1 > h • → dI / dΔ > 0 at low Δ and dI / dΔ < 0 at high Δ • If leader’s post innovation rents are not ‘large’ • → π1 < h dI / dΔ > 0 for any Δ • On the assumption that leader’s post innovation rents are ‘large’ the model is consistent with the evidence…

  39. Max 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)

  40. Foreing 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

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