Consumption-led Growth

Transcription

1 1 / 31 Consumption-led Growth Markus Brunnermeier markus@princeton.edu Pierre-Olivier Gourinchas pog@berkeley.edu Oleg Itskhoki itskhoki@princeton.edu University of Helsinki Helsinki, November 2018

2 Introduction

3 Motivation I Gourinchas and Jeanne GOURINCHAS (2013): the & JEANNE capital allocation THE ALLOCATION puzzle PUZZLE 1485 Capital Inflows (percent of GDP) RWA TGO MOZ COG TZA MLI SEN MWI NER MDG CIV HND BOL CRI BEN LKA PER JAM NPL CHL CYP CMR GHA ECU GTM TUN DOM JOR KEN MAR HTI ARGFJI ISR PAK MEXPHL PNGPRY UGA THA ETH BRACOL MUS PAN SLV TUR IDN BGD URY MYS EGY IND TTO AGO NGA ZAF GABSYR KOR IRN CHN VEN HKG BWA SGP TWN Productivity Growth (%) Average productivity growth and capital inflowsfigure between and 2000 for 68 non-oecd countries. Average productivity growth and average capital inflows between 1980 and non-oecd countries The allocation puzzle is illustrated by Figure 1, which plots the average growth rate of total factor productivity (TFP) against the average ratio of net capital inflows to GDPfor 68 developing 2 Downloaded from at Unive 2 / 31

4 Motivation I Gourinchas and Jeanne GOURINCHAS (2013): the & JEANNE capital allocation THE ALLOCATION puzzle PUZZLE 1485 Capital Inflows (percent of GDP) RWA TGO MOZ COG TZA MLI SEN MWI NER MDG CIV HND BOL CRI BEN LKA PER JAM NPL CHL CYP CMR GHA ECU GTM TUN DOM JOR KEN MAR HTI ARGFJI ISR PAK MEXPHL PNGPRY UGA THA ETH BRACOL MUS PAN SLV TUR IDN BGD URY MYS EGY IND TTO AGO NGA ZAF GABSYR KOR IRN CHN VEN HKG BWA SGP TWN Productivity Growth (%) Average productivity growth and capital inflowsfigure between and 2000 for 68 non-oecd countries. Average productivity growth and average capital inflows between 1980 and non-oecd countries In this paper, we swap the axes of this plot: can international capital flows alter The allocation puzzle is illustrated by Figure 1, which plots the average growth rate of total productivity growth factor productivity trajectories? (TFP) against the average ratio of net capital inflows to GDPfor 68 developing 2 Downloaded from at Unive 2 / 31

5 3 / 31 Motivation II 1. What is the relationship between openness and growth? trade openness financial openness

6 3 / 31 Motivation II 1. What is the relationship between openness and growth? trade openness financial openness 2. Is it possible to borrow like Argentina or Spain and grow like China? (i) What is wrong with Spanish-style (consumption-led) growth? (ii) What is special about Chinese-style (export-led) growth?

7 3 / 31 Motivation II 1. What is the relationship between openness and growth? trade openness financial openness 2. Is it possible to borrow like Argentina or Spain and grow like China? (i) What is wrong with Spanish-style (consumption-led) growth? (ii) What is special about Chinese-style (export-led) growth? A model of endogenous convergence growth to open the blackbox of productivity evolution under different openness regimes a neoclassical (DRS) environment with endogenous innovation decisions by entrepreneurs emphasis on the feedback from international borrowing into the pace and composition (T vs NT) of convergence

8 4 / 31 Empirical Motivation I Figure 1: CA imbalances in the Euro Zone

9 4 / 31 Empirical Motivation II Figure 1: Sectoral reallocation in the Euro Zone (Piton, 2017)

10 5 / 31 Main Insights Openness has two effects (on incentives for innovation): (i) change in relative market size (ii) increase in foreign competition and domestic cost of production, a price effect

11 5 / 31 Main Insights Openness has two effects (on incentives for innovation): (i) change in relative market size (ii) increase in foreign competition and domestic cost of production, a price effect With balanced trade, it s a wash: trade openness does not affect the pace and direction of productivity growth

12 5 / 31 Main Insights Openness has two effects (on incentives for innovation): (i) change in relative market size (ii) increase in foreign competition and domestic cost of production, a price effect With balanced trade, it s a wash: trade openness does not affect the pace and direction of productivity growth Trade deficits (a) unambiguously favor non-tradable sector and (b) tend to reduce pace of innovation reduced-form relationship between NX and sectoral growth furthermore, NX /Y is a sufficient statistic trade surpluses promote GDP growth

13 5 / 31 Main Insights Openness has two effects (on incentives for innovation): (i) change in relative market size (ii) increase in foreign competition and domestic cost of production, a price effect With balanced trade, it s a wash: trade openness does not affect the pace and direction of productivity growth Trade deficits (a) unambiguously favor non-tradable sector and (b) tend to reduce pace of innovation reduced-form relationship between NX and sectoral growth furthermore, NX /Y is a sufficient statistic trade surpluses promote GDP growth Sudden stops in financial flows followed by both recessions and fast tradable productivity growth take off

14 Main Insights Openness has two effects (on incentives for innovation): (i) change in relative market size (ii) increase in foreign competition and domestic cost of production, a price effect With balanced trade, it s a wash: trade openness does not affect the pace and direction of productivity growth Trade deficits (a) unambiguously favor non-tradable sector and (b) tend to reduce pace of innovation reduced-form relationship between NX and sectoral growth furthermore, NX /Y is a sufficient statistic trade surpluses promote GDP growth Sudden stops in financial flows followed by both recessions and fast tradable productivity growth take off Laissez-faire productivity growth is in general suboptimal capital controls may improve upon market allocation 5 / 31

15 6 / 31 Literature Neoclassical investment theory: Barro, Mankiw & Sala-i-Martin (1995) Learning-by-doing and dutch disease Corden and Neary (1982), Krugman (1987), Young (1991), Benigno and Fornaro (2012, 2014) Export-led growth: Rajan and Subramanian (2005), Rodrik (2008) Trade and growth Rivera-Batiz and Romer (1991), Grossman and Helpman (1993), Ventura (1997), Acemoglu and Ventura (2002), Parente and Prescott (2002) Empirics: Frankel and Romer (1999), Ben-David (1993), Dollar and Kraay (2003) Financial flows and growth: Aioke, Benigno and Kiyotaki (2009), Alfaro, Kalemli-Özcan, and Volosovych (2008), Gopinath et al (2017) Trade and growth with Frechet distributions and beyond Kortum (1997), EK (2001, 2002), Klette and Kortum (2004) Alvarez, Buera and Lucas (2017), Perla, Tonetti and Waugh (2015)...

16 Model Setup

17 Model Setup Real small open economy in continuous time exogenous world interest rate r in terms of world good Two sector economy: γ tradable (exportable) and 1 γ non-tradable (non-exportable) and symmetric in all other respects 7 / 31

18 Model Setup Real small open economy in continuous time exogenous world interest rate r in terms of world good Two sector economy: γ tradable (exportable) and 1 γ non-tradable (non-exportable) and symmetric in all other respects Rest of the world (ROW) in steady state: W = A T = A N = A and P F = P N = P = 1 We study convergence growth trajectories: A T (0), A N (0) < Ā A Growth results from new product creation by profit-maximizing entrepreneurs 7 / 31

19 8 / 31 Households Representative household: max {C(t),L(t)} 0 e ϑt U(t)dt, U = 1 1 σ C 1 σ 1 1+ϕ L1+ϕ s.t. Ḃ = r B + WL + Π }{{}}{{} PC =GDP =Y

20 8 / 31 Households Representative household: max {C(t),L(t)} 0 e ϑt U(t)dt, U = 1 1 σ C 1 σ 1 1+ϕ L1+ϕ s.t. Ḃ = r B + WL + Π }{{}}{{} PC =GDP =Y Static market clearing (goods and labor): WL = Y + NX, C σ L ϕ = W /P

21 9 / 31 Demand Two sectors: Y = PC = γp T C T + (1 γ)p N C N where [ C = C γ T C 1 γ N and C T = κ 1 ρ C ρ 1 ρ F + (1 κ) 1 ρ C H ρ 1 ρ ] ρ ρ 1, ρ > 1 Aggregators of individual varieties: C H = [ 1 ΛT γ 0 ] ρ C H (i) ρ 1 ρ 1 ρ di and C N = [ 1 ΛN 1 γ 0 ] ρ C N (i) ρ 1 ρ 1 ρ di

22 Exports and Imports Tradable expenditure: γp T C T = ΛT 0 P H (i)c H (i)di + γp F C F Aggregate imports: ( ) 1 ρ X PF = γp F C F = γκ Y, P F = τpf = τ P T Aggregate exports: Net exports: X = γp HC H = γκ(τp H ) 1 ρ Y NX = X X = γκτ 1 ρ [ P 1 ρ H ] Y P ρ 1 Y T 10 / 31

23 11 / 31 Technology and Revenues Technology of product i [0, Λ J ] in sector J {T, N}: Y J (i) = A J (i)l J (i)

24 11 / 31 Technology and Revenues Technology of product i [0, Λ J ] in sector J {T, N}: Y J (i) = A J (i)l J (i) Marginal cost pricing if technology is non-excludable: P H = W /A T where A T = [ 1 ΛT γ A 0 T (i) ρ 1 di ] 1 ρ 1

25 Technology and Revenues Technology of product i [0, Λ J ] in sector J {T, N}: Y J (i) = A J (i)l J (i) Marginal cost pricing if technology is non-excludable: P H = W /A T where A T = [ 1 ΛT γ A 0 T (i) ρ 1 di ] 1 ρ 1 Revenues: where R N = Y and ( ) 1 ρ PN (i) R N (i) = P N (i)c N (i) = R N, P N ( ) 1 ρ R T (i) = P H (i)c H (i) + PH(i)C H(i) PH (i) = R T R T = (1 κ) ( PH P T P H ) 1 ρ Y + κ(τp H ) 1 ρ Y = Y [ 1 + NX ] γy 11 / 31

26 12 / 31 Technology Draws An entrepreneur has n 1 possible ideas (projects): Z J(l) (l) iid Frechet(z, θ), l = 1..n, θ > ρ 1 A fraction γ of ideas are tradable, J(l) = T

27 12 / 31 Technology Draws An entrepreneur has n 1 possible ideas (projects): Z J(l) (l) iid Frechet(z, θ), l = 1..n, θ > ρ 1 A fraction γ of ideas are tradable, J(l) = T An entrepreneur can adopt only one project The technology is privately owned for one period

28 12 / 31 Technology Draws An entrepreneur has n 1 possible ideas (projects): Z J(l) (l) iid Frechet(z, θ), l = 1..n, θ > ρ 1 A fraction γ of ideas are tradable, J(l) = T An entrepreneur can adopt only one project The technology is privately owned for one period Period profits: Π T (l) = 1 ( ) 1 ρ ρ W 1 R T ρ ρ 1 Z T (l) P H Π N (l) = 1 ( ) 1 ρ ρ W 1 R N ρ ρ 1 Z N (l) P N

29 Technology Draws An entrepreneur has n 1 possible ideas (projects): Z J(l) (l) iid Frechet(z, θ), l = 1..n, θ > ρ 1 A fraction γ of ideas are tradable, J(l) = T An entrepreneur can adopt only one project The technology is privately owned for one period Period profits: Π T (l) = 1 ( ) 1 ρ ρ W 1 R T = ϱ R T ρ ρ 1 Z T (l) P H A ρ 1 Z T (l) ρ 1 T Π N (l) = 1 ( ) 1 ρ ρ W 1 R N = ϱ R N ρ ρ 1 Z N (l) P N A ρ 1 Z N (l) ρ 1 N 12 / 31

30 13 / 31 Technology Adoption Project choice: and we define (Ẑ T, Ẑ N, Ẑ) and (ˆΠ T, ˆΠ N, ˆΠ) ˆl = arg max l=1..n Π J(l)(l)

31 13 / 31 Technology Adoption Project choice: and we define (Ẑ T, Ẑ N, Ẑ) and (ˆΠ T, ˆΠ N, ˆΠ) ˆl = arg max l=1..n Π J(l)(l) Lemma 1 (i) The probability to adopt a tradable project: π T P{ˆΠ T ˆΠ N } = γ χ θ ρ 1, χ γ χ θ ρ γ ( PH P N ) ρ 1 R T R N.

32 13 / 31 Technology Adoption Project choice: and we define (Ẑ T, Ẑ N, Ẑ) and (ˆΠ T, ˆΠ N, ˆΠ) ˆl = arg max l=1..n Π J(l)(l) Lemma 1 (i) The probability to adopt a tradable project: π T P{ˆΠ T ˆΠ N } = γ χ θ ρ 1, χ γ χ θ ρ γ ( AN A T ) ρ 1 R T R N.

33 Technology Adoption Project choice: and we define (Ẑ T, Ẑ N, Ẑ) and (ˆΠ T, ˆΠ N, ˆΠ) ˆl = arg max l=1..n Π J(l)(l) Lemma 1 (i) The probability to adopt a tradable project: π T P{ˆΠ T ˆΠ N } = (ii) The productivity conditional on adoption: E γ χ θ ρ 1, χ γ χ θ ρ γ ρ 1 {Ẑ T ˆΠT ˆΠ } ( πt N = γ ( AN A T ) ν 1 A ρ 1, ) ρ 1 R T R N. where A EẐ = (nz)1/θ Γ(ν) 1 ρ 1 and ν 1 ρ 1 θ (0, 1). 13 / 31

34 14 / 31 Productivity Dynamics λ is the innovation rate and δ is the rate at which technologies become obsolete: Assume λ is country-specific and λ δ Λ T = λπ T δλ T

35 14 / 31 Productivity Dynamics λ is the innovation rate and δ is the rate at which technologies become obsolete: Assume λ is country-specific and λ δ Λ T = λπ T δλ T Lemma 2 The sectoral productivity dynamics is given by: [ A ( T = δ ) ρ 1 ( ) ν ( Ā πt λ 1] where A T ρ 1 γ Ā A δ A T ) 1 ρ 1.

36 15 / 31 Summary [ A T (t) A T (t) = 1 ( ) A ρ 1 ( ) ν πt (t) λ δ], ρ 1 A T (t) γ π T (t) 1 π T (t) = γ 1 γ χ(t) θ ρ 1, χ = B(0) + ( PH P N 0 ) ρ 1 R T R N = e rt NX (t) = 0. ( AN A T ) ρ 1 [ 1 + NX ], γy

37 Closed Economy

38 16 / 31 Closed Economy, κ 0 In closed economy R T = R N = Y, and therefore: ( ) ρ 1 PH χ = = P N ( ) ρ 1 AN A T The project choice is, thus: π T (t) 1 π T (t) = γ 1 γ ( ) θ AN (t) A T (t)

39 Closed Economy, κ 0 In closed economy R T = R N = Y, and therefore: ( ) ρ 1 PH χ = = P N ( ) ρ 1 AN A T The project choice is, thus: π T (t) 1 π T (t) = γ 1 γ ( ) θ AN (t) A T (t) Proposition 1 (i) Starting from A T (0) = A N (0), equilibrium project choice in the closed economy is π T (t) γ, A T (t) = [ e δt A T (0) ρ 1 + ( 1 e δt) Ā ρ 1] 1 ρ 1 (ii) Equilibrium allocation C = w 1+ϕ σ+ϕ, L = w 1 σ σ+ϕ, w = A. and Λ T = γ λ δ. (iii) Efficiency: / 31

40 Balanced Trade

41 17 / 31 Balanced Trade Consider open economy with κ > 0 and τ 1 Lemma 3 (i) The relative revenue shifter is given by: R T R N = (1 κ) ( PH P T ) 1 ρ + κ(τp H ) 1 ρ Y Y = 1 + NX γy. (ii) Under balanced trade, χ = (A N /A T ) ρ 1, and hence π T (t) and (A T (t), A N (t)) follow the same path as in autarky.

42 17 / 31 Balanced Trade Consider open economy with κ > 0 and τ 1 Lemma 3 (i) The relative revenue shifter is given by: R T R N = (1 κ) ( PH P T ) 1 ρ + κ(τp H ) 1 ρ Y Y = 1 + NX γy. (ii) Under balanced trade, χ = (A N /A T ) ρ 1, and hence π T (t) and (A T (t), A N (t)) follow the same path as in autarky. Equilibrium allocation is nonetheless different from autarkic: ( 1 A ) κγ 1+(2 κ)(ρ 1) w = C = A τ 2ρ 1 A T

43 17 / 31 Balanced Trade Consider open economy with κ > 0 and τ 1 Lemma 3 (i) The relative revenue shifter is given by: R T R N = (1 κ) ( PH P T ) 1 ρ + κ(τp H ) 1 ρ Y Y = 1 + NX γy. (ii) Under balanced trade, χ = (A N /A T ) ρ 1, and hence π T (t) and (A T (t), A N (t)) follow the same path as in autarky. Equilibrium allocation is nonetheless different from autarkic: ( 1 A ) κγ 1+(2 κ)(ρ 1) w = C = A τ 2ρ 1 A T Laisser-faire productivity dynamics is suboptimal. The planner would choose π T (t) < γ for all t 0.

44 Open Economy

45 Financial Openness With open current account: π T = γ 1 π T 1 γ ( AN A T ) θ [ 1 + NX ] θ ρ 1 γy 18 / 31

46 Financial Openness With open current account: π T = γ 1 π T 1 γ ( AN A T ) θ [ 1 + NX ] θ ρ 1 γy Lemma 4 NX (t)<0 and A T (t) A N (t) A T (t)< A N (t). Proposition 5 In st.st. with NX = r B > 0: Ā T > Ā > Ā N. Proposition 6 Starting from A T (0) = A N (0) < Ā, there exist two cutoffs 0 < t 1 < t 2 < : NX (t) < 0 for t [0, t 1) and NX (t) > 0 for t > t 1, and A T (t) < A N (t) for t (0, t 2) and A T (t) > A N (t) for t > t 2. At t = t 2, A T (t) = A N (t) = A(t) < A a (t). 18 / 31

47 19 / 31 Convergence Path Figure 2: Productivity convergence in closed and open economies

48 Impact of Openness Two effects of openness: 1. Relative size of the market: Y /Y 2. Competition: P T /P H < NX ( ) [ 1 ρ ( γy = PH τ (1 κ) + κ P T P H =X /X {}}{ ) 1 ρ P 1 ρ H Y P ρ 1 T Y ] 20 / 31

49 Endogenous Innovation

50 21 / 31 Endogenous Innovation Rate Entrepreneurship decision as in Lucas (1978) if EˆΠ φw : ( ) EˆΠ EˆΠ λ = Φ and W W = ϱr { N/W E max A ρ 1 N Lemma 5 EˆΠ ( A W = ϱ A A Â θ ) ρ 1 ( Ψ 1 + NX ) Y χẑ ρ 1 T }, Ẑ ρ 1 N

51 21 / 31 Endogenous Innovation Rate Entrepreneurship decision as in Lucas (1978) if EˆΠ φw : ( ) EˆΠ EˆΠ λ = Φ and W W = ϱr { N/W E max A ρ 1 N Lemma 5 EˆΠ ( A W = ϱ A A Â θ ) ρ 1 ( Ψ 1 + NX ) Y Proposition 8 (i) λ is increasing in A /A and in A/Âθ 1. (ii) λ increases with trade openness iff σ < 1 and ϕ <. [ ( ) 1 γ ] (iii) When σ = 1, Ψ 1 + AN A T ϕ NX 1+ϕ Y, and λ increases with NX when A N A T. χẑ ρ 1 T }, Ẑ ρ 1 N

52 Endogenous Innovation Rate Entrepreneurship decision as in Lucas (1978) if EˆΠ φw : ( ) EˆΠ EˆΠ λ = Φ and W W = ϱr { N/W E max A ρ 1 N Lemma 5 EˆΠ ( A W = ϱ A A Â θ ) ρ 1 ( Ψ 1 + NX ) Y Proposition 8 (i) λ is increasing in A /A and in A/Âθ 1. (ii) λ increases with trade openness iff σ < 1 and ϕ <. [ ( ) 1 γ ] (iii) When σ = 1, Ψ 1 + AN A T ϕ NX 1+ϕ Y, and λ increases with NX when A N A T. χẑ ρ 1 T }, Ẑ ρ 1 Endogenous non-tradable tilt reinforces the negative effect of trade deficits on innovation rate N Induced NX > 0 with policy if the goal is max growth rate 21 / 31

53 Empirical Implications

54 22 / 31 Empirical Implications Reduced-form relationship between NX and sectoral growth: with g 0 δ ρ 1 Ȧ T (t) A T (t) ȦN(t) [ A N (t) = g0 (ρ 1) (1 + µ) log A T (t) A N (t) + µ γ ( λ δ A A 0 ) ρ 1, which is also the base growth rate holds whether NX 0 are market outcomes or policy-induced i.e., applies equally for NX < 0 in Spain and NX > 0 in China ] NX (t), Y (0) NX /Y is a sufficient statistic for the feedback effect from equilibrium allocation to sectoral productivity growth

55 23 / 31 Preliminary empirical results KLEMS panel of sector-country productivity growth (17 OECD countries, 33 3-digit sectors, change) Empirical specification: log A ks = d k + d s + b log A 0 ks + c Λ s nx k + ε ks log A ks is productivity growth in sector s, country k Λ s is median sector-level home share across countries

56 Preliminary empirical results KLEMS panel of sector-country productivity growth (17 OECD countries, 33 3-digit sectors, change) Empirical specification: log A ks = d k + d s + b log A 0 ks + c Λ s nx k + ε ks Dep. var: VA/L RVA/L KLEMS VA/L RVA/L log A ks (1) (2) (3) (4) (5) Λ s nx k (0.10) (0.15) (0.20) (0.14) (0.14) log A 0 ks (1.76) (0.98) (0.72) (0.73) (0.56) R Observations % trade deficit reduces relative sectoral productivity growth by 1% across tradability quartiles (25th 75th) 23 / 31

57 24 / 31 Unit Labor Costs Two ULC measures: w/a and W /A T move together holding τ constant Autarky (assume σ = 1): w a (t) = C a (t) = A(t) Balanced trade: ( ) κγ A w b (t) = C b 1+(2 κ)(ρ 1) (t) = A(t) > A(t) A T (t) Open financial account: w b (0) < w(0) < C(0) ULC increase on impact and gradually fall along the convergence path

58 Applications

59 25 / 31 Application 1. Physical capital and financial frictions 2. Misallocation and growth policy 3. Rollover crisis Sudden stop in capital flows during transition triggers a reversal in trade deficits and a recession in non-tradable sector Rapid take off in tradable productivity growth, provided labor market can flexibly adjust by a sharp decline in wages

60 26 / 31 Rollover Crisis

61 Conclusion

62 27 / 31 Conclusion Standard endogenous growth forces have a robust implication for the relationship between trade deficits and: 1. non-tradable tilt of innovation 2. overall lower speed of convergence growth Countries that borrow along the convergence growth trajectory are likely to experience asymmetric and slower convergence lagging tradable productivity high unit labor costs and depressed innovation rate particularly vulnerable to rollover crisis along such trajectories Countries that are concerned with GDP growth rather than welfare might find it optimal to subsidize exports

63 Appendix

64 Price Indexes Average sectoral prices: [ 1 ΛT ] 1 [ P H = P H (i) 1 ρ 1 ρ 1 ΛN ] 1 di and PN = P N (i) 1 ρ 1 ρ di γ 0 1 γ 0 Aggregate price indexes: Equilibrium sectoral prices: P = P γ T P1 γ N where P T = [ κp 1 ρ F ] + (1 κ)p 1 ρ 1 1 ρ H P H = W A T, P N = W A N and P F = τ Real wage rate: w = W ( ) ] γ ρ 1 [1 P = A W κ + κ τa T ρ 1, A A γ T A1 γ N 28 / 31

65 29 / 31 Solution for NX Equilibrium system: [ C = w 1+ϕ σ+ϕ 1 + NX ] ϕ σ+ϕ Y where ( W w = A τa T ) κγ and NX Y = γκ ( ) ρ κγ W τa T [ τ 1+ϕ 1 2ρ A σ+ϕ C ( ) ] (1 κγ)+(2 κ)(ρ 1) A W A T τa T

66 30 / 31 Efficiency in Closed Economy Proposition (i) If A T (0) = A N (0), then πt (t) = γ and A T (t) = A N (t) for all t maximizes A(t) for all t. (ii) If A N (t) > A T (t) at some t, then πt (t) ( γ, π T (t) ), and laissez-faire dynamics with π T (t) is suboptimal. Optimal policy satisfies (for J {T, N}): ( ) π 1 ν T 1 γ 1 πt = ξ ( ) ρ 1 T AN, γ ξ N A T where and b J (t)ξ T (t) ξ J (t) = a J (t), ( ) AJ (t) η 1 ( ) ρ 1 ( ) Ā a J (t) A(t) ζ πj (t) ν, b J (t) ϑ + δ A(t) A J (t) γ J b J (t) plays the role of discount rate and a J (t) is the flow benefit ξ T /ξ N = R T /R N in the limit of ϑ (perfect impatience) Otherwise, ξ T /ξ T (1, R T /R N ) Patents with finite time-varying duration can decentralize π T (t) back to slides

67 31 / 31 Comparison with Learning-by-Doing General learning-by-doing formulation: Y T (t) = F ( A T (t), L T (t) ), A T (t) = G ( A T (t), A N (t), L T (t), L N (t) )

68 31 / 31 Comparison with Learning-by-Doing General learning-by-doing formulation: Y T (t) = F ( A T (t), L T (t) ), A T (t) = G ( A T (t), A N (t), L T (t), L N (t) ) Mapping of the baseline model into learning-by-doing: F (A T, L T ) = AL, G(A T, A N, L T, L N ) = G ( A T, π T (A T, A N, L T, L N ) ), [ ( G(A T, π T ) = δ ) ρ 1 ( ) ν Ā πt 1], ρ 1 γ A T π T 1 γ 1 π T γ = ( AN A T ) θ ( RT R N ) θ ρ 1 and R T R N = L T L N