Profitability of R&D main explanatory factor of neo-schumpeterian growth

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1 Profitability of R&D main explanatory factor of neo-schumpeterian growth Profitability of R&D related to: Market power of producers of innovation goods Distinguish between: Pre-innovation market power Post-innovation market power

2 Competition and growth Higher post-innovation market power may result from: Lower competition between industries: lower α lower elasticity it of substitution between machines Lower competition within industries: Higher protection from imitation higher constrained monopoly price χ faster growth

3 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 inova on goods is a (possibly constrained) monopolist

4 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

5 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

6 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

7 empirical findings on market power and TFP growth need qualification TFP growth estimates assume: output elasticity of a factor = factor share in Y This follows from perfect competition What if competition fails?

8 if competition fails problem 1 K share in Y > output elasticity of K Y = K α (AL)(1 α) underestimation of output elasticity of L underestimation of contribution of technology (TFP growth) to the growth of GDP per capita

9 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

10 Effects on empirical assessment of competition and growth Deviation from perfect competition: Underestimated influence of TFP growth on GDP growth Reverse causality: Underestimated influence of competition on TFP growth

11 summing up: Deviation from perfect competition + Reversecausality 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

12 In search of different hypotheses incremental innovations + tacit knowledge outsider s s innovation does not displace incumbent from market possibly, more than 1 firm in the same sector

13 In search of different hypotheses 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

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

15 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

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

17 A model of step by step innovations and PRODUCTION: knowledge spillovers A continuum [0, 1] of consumer-good sectors (m=1) Each sector jis a duopoly. firms A and B in jproduce x A = A A L A x B = A B L B sector output = x = x A +x B

18 A model of step by step innovations and PRODUCTION: knowledge spillovers Firm i labour productivity = x i / L i = A i = γ k(i) i = A, B k(i) = i s technology level γ > 1

19 A model of step by step innovations and PRODUCTION: knowledge spillovers Firm i labour productivity = x i / L i = A i = γ k(i) i = A, B k(i) = i s technology level γ > 1 1/ A i = γ k(i) = L i / x i =labour input per unit of output i s unit cost is: w γ k(i)

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

21 consumption A unit mass of identical consumers consumer h current utility uh = j [0,1] (log x j )dj uh / x j = 1/ x j MRSj,f between good j and f MRSj,f = x f / x j = p j /p f In equilibrium p j x j = p f x f = E E = 1 (expenditure is our numeraire)

22 consumption The representative household chooses x Aj, x Bj to maximize log(x Aj + x Bj ) subject to: p Aj x Aj + p Bj x Bj = 1 = E p Aj Aj p Bj Bj Intuitively, because industry output is homogeneous, the consumer chooses the least expensive between x Aj, x Bj p j = min(p Aj, p Bj )

23 Firm profit π 1 in un-level sector 1 technology distance = 1step if leader s unit cost is c, laggard s unit cost is γc > c leader s profit = π 1 =px 1 1 cx 1 =1 cx 1 recall: p 1 x 1 = 1

24 Firm profit π 1 in un-level sector 1 Leader chooses maximum price p 1 consistent with preservation of leadership (follower left outside tid of fthe market) kt) p 1 = follower s unit cost p 1 = γc

25 Firm profit π 1 in un-level sector 1 p 1 = γc p 1 x 1 = 1 x 1 = 1 / p 1 = 1/γc cx 1 = 1/γ π 1 = p 1 x 1 cx 1 =1 cx 1 = 1 1/γ the leader s profit in unlevel sector is fixed

26 firm profit π 0 in level sector If Bertrand price competition π 0 = 0 If perfect collusion firms A and B maximize total profit π and then share π between them π 0 = (1/2) π with π= π1

27 Δ =degree of competition in a level sector defined Δ = (π 1 π 0 ) / π 1 ½ Δ 1 Perfect collusion Δ = ½ π 0A = π 0B = π 1 / 2 Bertrand competition Δ = 1 π 0A = π 0B = 0 notice that π 0 = (1 Δ) ) π 1 (π 1 π 0 ) = Δ π 1

28 Innovation intensity n 0 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: π 1 with probability n 0 π 0 with probability 1 n 0

29 Innovation intensity n 0 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: π 1 with probability n 0 π 0 with probability 1 n 0 Max: [π n 0 π 0 (1 n 0 )] (n 0 ) /2 with respect to n 0 n 0 = π 1 π 0 = Δπ 1 n 0 π 1 π 0 Δπ 1 Escape competition effect: dn 0 / dδ > 0

30 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

31 Innovation intensity by outsider in un leveled sector The laggard 1 is an outsider: with R&D R = ψ(n 1 1) = ½ (n 1 1) 2 innovation probability n 1 + h

32 Innovation intensity by outsider in un leveled sector laggard 1 chooses n 1 to maximize: π 1 = (n 1 + h) π 0 (n 1 ) 2 / 2-1 ( -1 ) 0 ( -1 ) n -1 = π 0

33 Innovation intensity by the outsider in un leveled sector lowered by higher Δ n -1 = π 0 = (1 Δ) π 1 higherh competition ii Δ in a leveled l sector lower π 0 lower profit gain from innovation for the outsider lower innovation intensity in un leveled sector

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

35 composition between lev. / unlev. sectors μ 1 = steady state fraction of unlevel sectors μ 0 = 1 μ 1 = steady state fraction of level sectors

36 composition between lev. / unlev. sectors μ 1 = steady state fraction of unlevel sectors μ 0 = 1 μ 1 = steady state fraction of level sectors (n h) = probability of transition: unleveled leveled

37 composition between lev. / unlev. sectors μ 1 = steady state fraction of unlevel sectors μ 0 = 1 μ 1 = steady state fraction of level sectors (n h) = probability of transition: unleveled leveled (n 1 + h) μ 1 = expected steady state transitions unleveled leveled

38 composition between lev. / unlev. sectors n 0 = probability that a level sector becomes unlevel n 0 (1 μ 1 ) = expected steady state transitions leveled unleveled

39 Δ and the steady state composition steady state number of level/unlevel l/ l lsectors is stationary transitions in one direction = transitions in the other (n 11 + h) μ 1 = n 0 (1 μ 1 )

40 Δ and the steady state composition (n 1 + h) μ 1 = n 0 (1 μ 1 ) μ 1 = n 0 / (n 1 + h + n 0 )

41 Aggregate innovation flow I = (n -1 + h) μ 1 + n 0 (1 μ 1 ) = 2 (n -1 + h) μ 1

42 Aggregate innovation flow I = (n -1 + h) μ 1 + n 0 (1 μ 1 ) = 2 (n -1 + h) μ 1 μ 1 = n 0 /(n -1 +h+n + n 0 ) I = 2 (n -1 + h) n 0 / (n -1 + h + n 0 )

43 Aggregate innovation flow I = 2 (n -1 + h) n 0 / (n -1 + h + n 0 ) using: n -1 = π 0 = (1 Δ) π 1 n 0 = π 1 π 0 = Δπ 1

44 Obtain I as a function of Δ and leader s profit π1 I = 2 (n -1 + h) n 0 / (n -1 + h + n 0 ) n -1 = π 0 = (1 Δ) π 1 n 0 = π 1 π 0 = Δπ 1 n -1 + n 0 = π 1 I = {2[(1 Δ) π 1 +h]δ Δ π 1 }/(π 1 +h)

45 General intuition 1: distinguish between Δ levels and changes If competition Δ is low R&D incentives are higher in un leveled than in level sectors

46 General intuition 1: distinguish between Δ levels and changes If competition Δ is low R&D incentives are higher in un leveled than in level sectors high innovation by outsiders low innovation by neck and neck firms

47 General intuition 1: distinguish between Δ levels and changes If competition Δ is low In steady state most sectors end up being leveled because larger&dby outsiders. In le el sectors greater competition promotes more In level sectors greater competition promotes more R&D.

48 General intuition 2: If competition level Δ is high, R&D incentives are higher in level than in un level sectors high innovation by neck and neck firms low innovation by outsiders

49 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 level. In un level sectors greater competition promotes less R&D

50 empirical evidence (patent data)

51 Empirical evidence (patent data)

52 competition and innovation I = {2[(1 Δ) π 1 + h] Δ π 1 } / (π 1 + h) di / dδ = {2 π 1 [(1 2Δ) π 1 +h]}/(π 1 +h) Study sign of di /dδ at sufficiently low and high values of Δ

53 Relation between Δ and aggregate innovation di / dδ = {2 π 1 [(1 2Δ) π 1 + h]} / (π 1 + h) d 2 I / (dδ) 2 < 0

54 Relation between Δ and aggregate innovation di / dδ = {2 π 1 [(1 2Δ) π 1 + h]} / (π 1 + h) d 2 I / (dδ) 2 < 0 Low competition: At Δ = ½ di / dδ = (2π 1 h) / (π 1 +h)>0

55 Relation between Δ and aggregate g innovation di / dδ = {2 π 1 [(1 2Δ) π 1 + h]} / (π 1 + h) High competition: at Δ =1: di / dδ =( (- π 1 +h)2π π 1 /(π 1 +h) di / dδ < 0 if and only if π 1 > h

56 conclusions If leader s post-innovation rents are large π 1 > h di / dδ > 0 at low Δ di / dδ < 0 at high Δ

57 Predictions: If leader s post innovation rents are large π 1 > h di / dδ > 0 at low Δ di / dδ < 0 at high Δ shaped rela on between compe on and growth If leader s post innovation rents are not large π 1 < h di / dδ > 0 at any Δ competitionalways good for growth

58 Qualification 1 Max technology distance > 1 step Optimal technology distance is endogenous R&D investment by the leader targets optimal technology distance

59 Qualification 1 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 sb yo of R&D ) needs investigation Possibly more R&D by the leader, with greater ease of entry (less market protection)

60 Qualification 2 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

61 Qualification 2 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 o and danti regulation a polices may be different in sectors/country close to or far from the world wide technology frontier