Technological Spillovers and Dynamics of Comparative Advantage

Transcription

1 Technological Spillovers and Dynamics of Comparative Advantage Yury Yatsynovich University of California, Berkeley January 21, 2015

2 MOTIVATION Comparative advantage is dynamic: Korea from rice to microchips.

3 MOTIVATION Comparative advantage is dynamic: Korea from rice to microchips. Industrial policy to establish new sectors and shape specialization: semiconductors in 1980s and the green energy sector in 2000s.

4 MOTIVATION Comparative advantage is dynamic: Korea from rice to microchips. Industrial policy to establish new sectors and shape specialization: semiconductors in 1980s and the green energy sector in 2000s. Rationale: economies of scale and technological spillovers.

5 MOTIVATION Comparative advantage is dynamic: Korea from rice to microchips. Industrial policy to establish new sectors and shape specialization: semiconductors in 1980s and the green energy sector in 2000s. Rationale: economies of scale and technological spillovers. Modeling the dynamics of comparative advantage with technological linkages a big open question. Challenge #1 is multiplicity of equilibria.

6 QUESTIONS FOR THIS PAPER How does comparative advantage evolve under the presence of intra- and inter-sector spillovers?

7 QUESTIONS FOR THIS PAPER How does comparative advantage evolve under the presence of intra- and inter-sector spillovers? What is the socially optimal balanced growth path?

8 LITERATURE Theory of trade and growth with spillovers: Young (1991), Greenwald and Stiglitz (2006), Hanlon (2013), Kucheryavyy et. al. (2014).

9 LITERATURE Theory of trade and growth with spillovers: Young (1991), Greenwald and Stiglitz (2006), Hanlon (2013), Kucheryavyy et. al. (2014). Empirical analysis of spillovers: Elisson et. al. (2010), Greenstone et. al. (2010).

10 OUTLINE OF THE PAPER 1. Dynamic trade model with inter-sector spillovers.

11 OUTLINE OF THE PAPER 1. Dynamic trade model with inter-sector spillovers. 2. Description of balanced growth paths.

12 OUTLINE OF THE PAPER 1. Dynamic trade model with inter-sector spillovers. 2. Description of balanced growth paths. 3. Industrial policy.

13 OUTLINE OF THE PAPER 1. Dynamic trade model with inter-sector spillovers. 2. Description of balanced growth paths. 3. Industrial policy. 4. Calibration of the model.

14 OUTLINE OF THE PAPER 1. Dynamic trade model with inter-sector spillovers. 2. Description of balanced growth paths. 3. Industrial policy. 4. Calibration of the model. 5. Optimal policy.

15 OUTLINE OF THE MODEL 1. Trade part: static, multi-sector EK (2002) Discrete number of sectors and countries, continuum of varieties within each sector. CES preferences at lower level, Cobb-Douglas at higher level. Perfect competition.

16 OUTLINE OF THE MODEL 1. Trade part: static, multi-sector EK (2002) Discrete number of sectors and countries, continuum of varieties within each sector. CES preferences at lower level, Cobb-Douglas at higher level. Perfect competition. 2. Evolution of technology part: dynamic Learning-by-doing. Accumulation of technologies through intra- and inter-sector spillovers. Exogenous population growth.

17 TRADE PART: DEMAND Utility: C σ 1 σ j,s = U j = 1 0 S s=1 C αs j,s c j,s (ω) σ 1 σ dω, where j country, s sector, ω variety within a sector.

18 TRADE PART: DEMAND Utility: C σ 1 σ j,s = U j = 1 0 S s=1 C αs j,s c j,s (ω) σ 1 σ dω, where j country, s sector, ω variety within a sector. Expenditures: ( ) pj,s (ω) 1 σ X j,s (ω) = α s L j w j, P j,s

19 TRADE PART: DEMAND Utility: C σ 1 σ j,s = U j = 1 0 S s=1 C αs j,s c j,s (ω) σ 1 σ dω, where j country, s sector, ω variety within a sector. Expenditures: Prices: p j,s (ω) = ( ) pj,s (ω) 1 σ X j,s (ω) = α s L j w j, P j,s min {p kj,s(ω)}, P 1 σ j,s = k 1,...,N 1 0 p 1 σ j,s (ω)dω.

20 TRADE PART: SUPPLY Prices are equal to marginal costs: p ij,s (ω) = w id ij,s z i,s (ω)

21 TRADE PART: SUPPLY Prices are equal to marginal costs: p ij,s (ω) = w id ij,s z i,s (ω) z i,s (ω) is the productivity of the best technology available for producing variety ω in sector s of country i.

22 TRADE PART: SUPPLY Prices are equal to marginal costs: p ij,s (ω) = w id ij,s z i,s (ω) z i,s (ω) is the productivity of the best technology available for producing variety ω in sector s of country i. The number of technologies available for ω in i, s is Poisson(T i, s ).

23 TRADE PART: SUPPLY Prices are equal to marginal costs: p ij,s (ω) = w id ij,s z i,s (ω) z i,s (ω) is the productivity of the best technology available for producing variety ω in sector s of country i. The number of technologies available for ω in i, s is Poisson(T i, s ). Productivity of each technology is drawn from Pareto: Pr(Q q) = 1 q θ.

24 TRADE PART: SUPPLY Prices are equal to marginal costs: p ij,s (ω) = w id ij,s z i,s (ω) z i,s (ω) is the productivity of the best technology available for producing variety ω in sector s of country i. The number of technologies available for ω in i, s is Poisson(T i, s ). Productivity of each technology is drawn from Pareto: Pr(Q q) = 1 q θ. Productivity z i,s (ω) is distributed Frechet: Pr(z i,s (ω) z) = e T i,sz θ.

25 TRADE PART: STATIC EQUILIBRIUM Given a vector of productivities {T i,s } i 1,...,N and sizes of s 1,...,S countries {L i } i 1,...,N solve the system for sector labor demand {L i,s } i 1,...,N and wages {w i } i 1,...,N : s 1,...,S

26 TRADE PART: STATIC EQUILIBRIUM Given a vector of productivities {T i,s } i 1,...,N and sizes of s 1,...,S countries {L i } i 1,...,N solve the system for sector labor demand {L i,s } i 1,...,N and wages {w i } i 1,...,N : s 1,...,S L i,s w i = N π ij,s α s w j L j i, s, j=1 where π ij,s X ij,s X j,s = T i,s (w i d ij,s ) θ N k=1 T k,s(w k d kj,s ) θ ;

27 TRADE PART: STATIC EQUILIBRIUM Given a vector of productivities {T i,s } i 1,...,N and sizes of s 1,...,S countries {L i } i 1,...,N solve the system for sector labor demand {L i,s } i 1,...,N and wages {w i } i 1,...,N : s 1,...,S L i,s w i = N π ij,s α s w j L j i, s, j=1 where π ij,s X ij,s X j,s = T i,s (w i d ij,s ) θ N k=1 T k,s(w k d kj,s ) θ ; S L i,s = L i i, s=1

28 EVOLUTION OF TECHNOLOGY PART: LEARNING-BY-DOING AND SPILLOVERS Labor L i,q generates a mass φl i,q of new technologies in i, q, share p qs [0, 1] of which can be used for any ω in i, s.

29 EVOLUTION OF TECHNOLOGY PART: LEARNING-BY-DOING AND SPILLOVERS Labor L i,q generates a mass φl i,q of new technologies in i, q, share p qs [0, 1] of which can be used for any ω in i, s. The number of technologies for any ω in i, s is distributed Poisson(T i,s (t))

30 EVOLUTION OF TECHNOLOGY PART: LEARNING-BY-DOING AND SPILLOVERS Labor L i,q generates a mass φl i,q of new technologies in i, q, share p qs [0, 1] of which can be used for any ω in i, s. The number of technologies for any ω in i, s is distributed Poisson(T i,s (t)) Over dτ a mass dt i,s (t) of new technologies arrives to i, s S dt i,s (t) = φp qs L i,q (t) dτ. q=1

31 EVOLUTION OF TECHNOLOGY PART: LEARNING-BY-DOING AND SPILLOVERS Labor L i,q generates a mass φl i,q of new technologies in i, q, share p qs [0, 1] of which can be used for any ω in i, s. The number of technologies for any ω in i, s is distributed Poisson(T i,s (t)) Over dτ a mass dt i,s (t) of new technologies arrives to i, s S dt i,s (t) = φp qs L i,q (t) dτ. q=1 Dynamics of sector productivity: T i,s (t) = t τ=0 q=1 S φp qs L i,q (τ)dτ + T i,s (0).

32 BALANCED GROWTH PATH (BGP): DEFINITIONS Dynamics of the model: {T i,s } {L i,s } {T i,s + dt i,s }...

33 BALANCED GROWTH PATH (BGP): DEFINITIONS Dynamics of the model: {T i,s } {L i,s } {T i,s + dt i,s }... Definition: Balanced growth path (BGP) is a sequence of static equilibria along which the state variables {T i,s } i 1,...,N and s 1,...,S {L i } i 1,...,N grow at constant rates.

34 BALANCED GROWTH PATH (BGP): DEFINITIONS Dynamics of the model: {T i,s } {L i,s } {T i,s + dt i,s }... Definition: Balanced growth path (BGP) is a sequence of static equilibria along which the state variables {T i,s } i 1,...,N and s 1,...,S {L i } i 1,...,N grow at constant rates. In BGP the relative productivity of sectors remains constant: T i,s = T i,s + dt i,s T i,s = dt i,s q = p qsl i,q T j,s T j,s + dt j,s T j,s dt j,s q p i, j, s qsl j,q

35 BGP IN AUTARKY Let s start with a simple case of autarky: d ij,s i j. Labor allocation remains the same in each period: L i,s = α s L i (follows from L i,s w i = N j=1 π ij,sα s w j L j ), thus, BGP is unique.

36 BGP UNDER COSTLESS TRADE Now let s consider another extreme case of zero trade costs: d ij,s = 1 i, j, s.

37 BGP UNDER COSTLESS TRADE Now let s consider another extreme case of zero trade costs: d ij,s = 1 i, j, s. Definition: Matrix of spillovers {p qs } has no stagnant sectors if q p qs > 0 s.

38 BGP UNDER COSTLESS TRADE Now let s consider another extreme case of zero trade costs: d ij,s = 1 i, j, s. Definition: Matrix of spillovers {p qs } has no stagnant sectors if q p qs > 0 s. Definition: Balanced growth path is interior if L i,s > 0 i, s and corner if at least one L i,s = 0.

39 BGP UNDER COSTLESS TRADE Now let s consider another extreme case of zero trade costs: d ij,s = 1 i, j, s. Definition: Matrix of spillovers {p qs } has no stagnant sectors if q p qs > 0 s. Definition: Balanced growth path is interior if L i,s > 0 i, s and corner if at least one L i,s = 0. Definition: Matrix of spillovers {p qs } has no isolated clusters if its digraph is connected.

40 BGP AND THE PATTERN OF SPILLOVERS x x x x x x x x

41 PROPOSITION ON THE UNIQUENESS OF BGP Proposition: Under zero trade costs, no isolated clusters and no stagnant sectors the model has a unique and stable interior balanced growth path in which labor allocation vectors are the same across countries: L i,s = α s L i i, s.

42 ILLUSTRATING THE PROPOSITION: PHASE-DIAGRAM

43 ILLUSTRATING THE PROPOSITION: PHASE-DIAGRAM

44 ILLUSTRATING THE PROPOSITION: PHASE-DIAGRAM

45 ILLUSTRATING THE PROPOSITION: PHASE-DIAGRAM

46 ILLUSTRATING THE PROPOSITION: PHASE-DIAGRAM

47 ILLUSTRATING THE PROPOSITION: PHASE-DIAGRAM

48 ILLUSTRATING THE PROPOSITION: PHASE-DIAGRAM

49 ILLUSTRATING THE PROPOSITION: PHASE-DIAGRAM

50 ILLUSTRATING THE PROPOSITION: MULTIPLICITY Isolated sectors: p AA > p BA = 0, p BB > p AB = 0

51 ILLUSTRATING THE PROPOSITION: MULTIPLICITY Isolated sectors: p AA > p BA = 0, p BB > p AB = 0

52 ILLUSTRATING THE PROPOSITION: MULTIPLICITY Isolated sectors: p AA > p BA = 0, p BB > p AB = 0

53 ILLUSTRATING THE PROPOSITION: UNIQUENESS Positive inter-sector spillovers: p AA > p AB > 0, p BB > p BA > 0

54 ILLUSTRATING THE PROPOSITION: UNIQUENESS Positive inter-sector spillovers: p AA > p AB > 0, p BB > p BA > 0

55 BGP UNDER COSTLESS TRADE: INTUITION Why no complete specialization? Unproductive sectors do not collapse because as they shrink it also becomes relatively easier to improve their productivity: productivity is proportional to T 1/θ.

56 BGP UNDER COSTLESS TRADE: INTUITION Why no complete specialization? Unproductive sectors do not collapse because as they shrink it also becomes relatively easier to improve their productivity: productivity is proportional to T 1/θ. Why inter-sector spillovers eliminate multiplicity of BGPs? Less productive sectors gain disproportionally more from inter-sector spillovers than more productive ones.

57 SUBOPTIMALITY OF BGP Competitive BGP can be a suboptimal equilibrium: labor allocation L i,s = α s L i i, s doesn t depend on {p qs } q,s 1,...,S...

58 SUBOPTIMALITY OF BGP Competitive BGP can be a suboptimal equilibrium: labor allocation L i,s = α s L i i, s doesn t depend on {p qs } q,s 1,...,S......while the condition for welfare-optimal labor allocation, for instance, in autarky is 1 L r ( α r + 1 θ s S α s L r p rs q S L qp qs ) = 1Lv ( α v + 1 θ s S α s L v p vs q S L qp qs )

59 TOOL OF INDUSTRIAL POLICY Policy tool: sector-specific taxes {τ i,s } that affect the unit cost of production, τ i,s w i z i,s (ω). Revenues are distributed as a lump-sum transfer to households.

60 TOOL OF INDUSTRIAL POLICY Policy tool: sector-specific taxes {τ i,s } that affect the unit cost of production, τ i,s w i z i,s (ω). Revenues are distributed as a lump-sum transfer to households. Same effect on the relative costs as an exogenous sector productivity shifter A i,s (e.g. climate, deposits of natural resources, etc.): w i A i,s z i,s (ω).

61 INDUSTRIAL POLICY IN AUTARKY Optimal taxes maximizing utility per capita on the BGP. Optimality criteria: 1 L r ( α r + 1 θ s S α s L r p rs q S L qp qs ) = 1Lv ( α v + 1 θ s S α s L v p vs q S L qp qs )

62 INDUSTRIAL POLICY IN AUTARKY Optimal taxes maximizing utility per capita on the BGP. Optimality criteria: 1 L r ( α r + 1 θ s S α s L r p rs q S L qp qs ) = 1Lv ( α v + 1 θ s S α s L v p vs q S L qp qs ) For a simple 2 2 case under α A = α B sector B should be taxed more than A if p AA p AB > p BB p BA

63 INDUSTRIAL POLICY IN AUTARKY: EXAMPLE Optimal tax τi B under spillovers p AA = p BB = 0.9, p AB = 0.7, p BA = 0.1 and α A = α B = 0.5, θ = 8; Ui/Li τ B

64 INDUSTRIAL POLICY IN AUTARKY: SUMMARY Subsidize the core sectors.

65 INDUSTRIAL POLICY IN AUTARKY: SUMMARY Subsidize the core sectors. Optimal policy in autarky depends on the presence of both intra- and inter-sector spillovers.

66 INDUSTRIAL POLICY IN AUTARKY: SUMMARY Subsidize the core sectors. Optimal policy in autarky depends on the presence of both intra- and inter-sector spillovers. If inter-sector spillovers are zero, the optimal tax is zero. The model is similar to the one with equal Marshallian externalities across sectors: C i,s = L i,s (T i,s ) 1/θ = L 1+1/θ i,s (φp ss /g) 1/θ

67 INDUSTRIAL POLICY IN OPEN ECONOMY: IMPACT ON COMPARATIVE ADVANTAGE 2 2 example with positive cross-sector spillovers:

68 INDUSTRIAL POLICY IN OPEN ECONOMY: IMPACT ON COMPARATIVE ADVANTAGE 2 2 example with positive cross-sector spillovers:

69 INDUSTRIAL POLICY IN OPEN ECONOMY: WELFARE 2 2 example: p AA = p BB = 0.9, p AB = 0.7, p BA = 0.1 τj,b U i /L i τ i,b

70 INDUSTRIAL POLICY IN OPEN ECONOMY: WELFARE 2 2 example: p AA = p BB = 0.9, p AB = 0.7, p BA = U i + U j τj,b τ i,b 1.55

71 EXOGENOUS COMPONENT OF PRODUCTIVITY Exogenous comparative advantage in a non-core sector can result in losses from trade. Example: symmetric 2 2, p AA = p BB = 0.9, p AB = 0.7, p BA = Ui/Li Autarky Costless trade /A i,b

72 INDUSTRIAL POLICY IN OPEN ECONOMY: SUMMARY Conditional on no response from trade partners, the optimal labor re-allocation is larger than in autarky, yet, can be attained with lower taxes.

73 INDUSTRIAL POLICY IN OPEN ECONOMY: SUMMARY Conditional on no response from trade partners, the optimal labor re-allocation is larger than in autarky, yet, can be attained with lower taxes. Strategic interaction between countries when implementing industrial policy.

74 INDUSTRIAL POLICY IN OPEN ECONOMY: SUMMARY Conditional on no response from trade partners, the optimal labor re-allocation is larger than in autarky, yet, can be attained with lower taxes. Strategic interaction between countries when implementing industrial policy. Uncoordinated industrial policy can have a Nash equilibrium that Pareto dominates the no-policy case.

75 INDUSTRIAL POLICY IN OPEN ECONOMY: SUMMARY Conditional on no response from trade partners, the optimal labor re-allocation is larger than in autarky, yet, can be attained with lower taxes. Strategic interaction between countries when implementing industrial policy. Uncoordinated industrial policy can have a Nash equilibrium that Pareto dominates the no-policy case. Possibility for welfare losses from trade openness.

76 CALIBRATION OF TECHNOLOGICAL SPILLOVERS Matrix of probabilities of spillovers {p qs } a new and crucial set of parameters.

77 CALIBRATION OF TECHNOLOGICAL SPILLOVERS Matrix of probabilities of spillovers {p qs } a new and crucial set of parameters. Using the data on patent citations to quantify {p qs }: US patent data and Japanese as a robustness check.

78 CALIBRATION OF TECHNOLOGICAL SPILLOVERS: COHORT APPROACH

79 CALIBRATION OF TECHNOLOGICAL SPILLOVERS: COHORT APPROACH Split patents for each pair (q, s) into non-overlapping cohorts: cited: patents issued within 1 calendar year citing: patents issued 2-11 years after the cited cohort

80 CALIBRATION OF TECHNOLOGICAL SPILLOVERS: SEQUENCE APPROACH

81 CALIBRATION OF TECHNOLOGICAL SPILLOVERS: SEQUENCE APPROACH Arrange patents by patent numbers into a sequence For each patent from origin sector q find N and K for each destination sector s.

82 COHORT AND SEQUENCE APPROACHES FOR THE US Sequence approach, log(p US qs ) Cohort approach, log(p US qs )

83 INTENSITY OF PATENTING, φ In the model I have φp qs ideas are generated by unit mass of labor in sector q for sector s. In reality it is more like φφ q p qs. The equivalent of φ in the model is φ = max r [φ r ] and the equivalent of p qs in the model is φq φ pqs. This normalization is innocuous since what matters for policy is the relative values of {p qs } within the matrix.

84 P-MATRIX FOR THE US: LOGS OF SPILLOVER PROBABILITIES log(p qs ) s q 14

85 P-MATRIX FOR JAPAN: LOGS OF SPILLOVER PROBABILITIES log(p qs ) s q

86 SPILLOVER PROBABILITIES ESTIMATES FOR THE US AND JAPAN log(p qs JP ) log(p qs US )

87 OPTIMAL INDUSTRIAL POLICY, AUTARKY Table: Actual (l q ), autarky-optimal BGP (l q ), free market BGP (α q ) labor allocations. Sector α q l q l q Construction 15.8% 14.4% 27.1% Wood products 1.6% 1.4% 2.1% Printing and related activities 1.4% 1.3% 2.8% Chemical manufacturing 7.6% 8.8% 3.6% Computer and electronic products 5.2% 6.3% 5.9% Medical equipment and supplies 0.8% 0.9% 1.1% Gains in productivity of 3.5% due to moving from the current labor allocation to the optimal one. Policy in open economy still work in progress.

88 CONCLUDING REMARKS 1. Suggest a framework for analyzing dynamics of comparative advantage.

89 CONCLUDING REMARKS 1. Suggest a framework for analyzing dynamics of comparative advantage. 2. Prove the importance of inter-sector spillovers for the growth path of comparative advantage.

90 CONCLUDING REMARKS 1. Suggest a framework for analyzing dynamics of comparative advantage. 2. Prove the importance of inter-sector spillovers for the growth path of comparative advantage. 3. Demonstrate the potential of industrial policy and possibility for losses from trade.

91 CONCLUDING REMARKS 1. Suggest a framework for analyzing dynamics of comparative advantage. 2. Prove the importance of inter-sector spillovers for the growth path of comparative advantage. 3. Demonstrate the potential of industrial policy and possibility for losses from trade. 4. Establish the criteria for optimal industrial policy based on strength of technological spillovers.