Non-Renewable Resources and the Sustainability of the Economic Growth under Bilateral Trade

Transcription

1 Non-Renewable Resources and the Sustainability of the Economic Growth under Bilateral Trade Francisco Cabo 1 Guiomar Martín-Herrán 1 M.Pilar Martínez-García 2 1 Departamento de Economía Aplicada Universidad de Valladolid 2 Departamento de Métodos Cuantitativos para la Economía Universidad de Murcia SAE 2008

2 Motivation Sustained economic growth needs a continuous flow of technological innovations There is a small group of technological leading countries the world Developing countries are not investing in R&D. They are well endowed with natural resources Pattern of trade between developing and industrial countries developing countries export the natural resource in exchange for capital and technology intensive goods from industrial countries

3 Motivation Sustained economic growth needs a continuous flow of technological innovations There is a small group of technological leading countries the world Developing countries are not investing in R&D. They are well endowed with natural resources Pattern of trade between developing and industrial countries developing countries export the natural resource in exchange for capital and technology intensive goods from industrial countries

4 Motivation Sustained economic growth needs a continuous flow of technological innovations There is a small group of technological leading countries the world Developing countries are not investing in R&D. They are well endowed with natural resources Pattern of trade between developing and industrial countries developing countries export the natural resource in exchange for capital and technology intensive goods from industrial countries

5 Motivation Sustained economic growth needs a continuous flow of technological innovations There is a small group of technological leading countries the world Developing countries are not investing in R&D. They are well endowed with natural resources Pattern of trade between developing and industrial countries developing countries export the natural resource in exchange for capital and technology intensive goods from industrial countries

6 Research questions: Motivation If the traded resource is exhaustible and growth-essential... Can the trade of innovations from a technological leading country guarantee sustainable growth both in the leading and in the follower economies? How do the growth rates for the two trading economies compare along the balanced path? Does the existence of non-renewable resources have anything to say in relation to growth rates divergencies?

7 Research questions: Motivation If the traded resource is exhaustible and growth-essential... Can the trade of innovations from a technological leading country guarantee sustainable growth both in the leading and in the follower economies? How do the growth rates for the two trading economies compare along the balanced path? Does the existence of non-renewable resources have anything to say in relation to growth rates divergencies?

8 Research questions: Motivation If the traded resource is exhaustible and growth-essential... Can the trade of innovations from a technological leading country guarantee sustainable growth both in the leading and in the follower economies? How do the growth rates for the two trading economies compare along the balanced path? Does the existence of non-renewable resources have anything to say in relation to growth rates divergencies?

9 Research questions: Motivation If the traded resource is exhaustible and growth-essential... Can the trade of innovations from a technological leading country guarantee sustainable growth both in the leading and in the follower economies? How do the growth rates for the two trading economies compare along the balanced path? Does the existence of non-renewable resources have anything to say in relation to growth rates divergencies?

10 Literature Non-renewable natural resources and sustainable economic growth Exogenous technological change Solow (1974), Stiglitz (1974), Dasgupta and Heal (1974) among others Endogenous technological change Scholz & Ziemes (1999), Groth (2007), Groth and Schou (2007) Models where non-renewable resources are growth-essential vs. models where they are not Endogenous growth and trade of renewable natural resources Eliasson & Turnovsky (2004),López, Anríquez & Gulati (2007),Cabo, Martín-Herrán & Martínez-García (2005,2008)

11 Literature Non-renewable natural resources and sustainable economic growth Exogenous technological change Solow (1974), Stiglitz (1974), Dasgupta and Heal (1974) among others Endogenous technological change Scholz & Ziemes (1999), Groth (2007), Groth and Schou (2007) Models where non-renewable resources are growth-essential vs. models where they are not Endogenous growth and trade of renewable natural resources Eliasson & Turnovsky (2004),López, Anríquez & Gulati (2007),Cabo, Martín-Herrán & Martínez-García (2005,2008)

12 Literature Non-renewable natural resources and sustainable economic growth Exogenous technological change Solow (1974), Stiglitz (1974), Dasgupta and Heal (1974) among others Endogenous technological change Scholz & Ziemes (1999), Groth (2007), Groth and Schou (2007) Models where non-renewable resources are growth-essential vs. models where they are not Endogenous growth and trade of renewable natural resources Eliasson & Turnovsky (2004),López, Anríquez & Gulati (2007),Cabo, Martín-Herrán & Martínez-García (2005,2008)

13 Literature Non-renewable natural resources and sustainable economic growth Exogenous technological change Solow (1974), Stiglitz (1974), Dasgupta and Heal (1974) among others Endogenous technological change Scholz & Ziemes (1999), Groth (2007), Groth and Schou (2007) Models where non-renewable resources are growth-essential vs. models where they are not Endogenous growth and trade of renewable natural resources Eliasson & Turnovsky (2004),López, Anríquez & Gulati (2007),Cabo, Martín-Herrán & Martínez-García (2005,2008)

14 Literature Non-renewable natural resources and sustainable economic growth Exogenous technological change Solow (1974), Stiglitz (1974), Dasgupta and Heal (1974) among others Endogenous technological change Scholz & Ziemes (1999), Groth (2007), Groth and Schou (2007) Models where non-renewable resources are growth-essential vs. models where they are not Endogenous growth and trade of renewable natural resources Eliasson & Turnovsky (2004),López, Anríquez & Gulati (2007),Cabo, Martín-Herrán & Martínez-García (2005,2008)

15 Our model Bilateral trade between a technologically leading country and a resource endowed economy Technological progress: Expansion of the number goods (intermediate inputs) Extends Scholz & Ziemes (1999) model The economy is opened to trade The resource is an essential input in the growth-engine innovative sector, i.e. a resource growth-essential (Groth (2007)). The elasticity of the number of varieties in the R&D sector is not necessarily equal to one (knife-edge condition criticized by Jones (1995a, b)).

16 Our model Bilateral trade between a technologically leading country and a resource endowed economy Technological progress: Expansion of the number goods (intermediate inputs) Extends Scholz & Ziemes (1999) model The economy is opened to trade The resource is an essential input in the growth-engine innovative sector, i.e. a resource growth-essential (Groth (2007)). The elasticity of the number of varieties in the R&D sector is not necessarily equal to one (knife-edge condition criticized by Jones (1995a, b)).

17 Agenda 1 Introduction 2 The model The resource sector The final good sectors The intermediate goods sectors The R&D sector The households 3 Sustainable growth equilibrium Existence, uniqueness and stability of the balanced path The equilibrium growth rates

18 Agenda 1 Introduction 2 The model The resource sector The final good sectors The intermediate goods sectors The R&D sector The households 3 Sustainable growth equilibrium Existence, uniqueness and stability of the balanced path The equilibrium growth rates

19 Agenda 1 Introduction 2 The model The resource sector The final good sectors The intermediate goods sectors The R&D sector The households 3 Sustainable growth equilibrium Existence, uniqueness and stability of the balanced path The equilibrium growth rates

20 The model The resource sector (follower economy) Dynamics of the stock of the non-renewable resource, S Ṡ = R, S(0) = S 0 R: Total harvesting of the extracting companies R = R l +R f { Rl R f resource demand made by final output producers in { l f The resource is extracted without cost (Scholz & Ziemes (1999) and Groth & Schou (2007)) Benefit for the harvesting firms: 0 p R (t)r(t)e 1/t t 0 r f (s) ds dt, p R : resource market price; r f : the interest rate in f. Hotelling rule: γ pr = r f

21 The model The resource sector (follower economy) Dynamics of the stock of the non-renewable resource, S Ṡ = R, S(0) = S 0 R: Total harvesting of the extracting companies R = R l +R f { Rl R f resource demand made by final output producers in { l f The resource is extracted without cost (Scholz & Ziemes (1999) and Groth & Schou (2007)) Benefit for the harvesting firms: 0 p R (t)r(t)e 1/t t 0 r f (s) ds dt, p R : resource market price; r f : the interest rate in f. Hotelling rule: γ pr = r f

22 The final good sectors The model Y l = A Y f = Ã N 0 N 0 (X l (j)) α (ul) 1 α β R β l dj, A > 0, α, β > 0, α + β < 1 (X (j)) α L1 α βr β f f dj, Ã > 0, α, β > 0, α + β < 1 R l, R f : amounts of natural resource. X l (j), X f (j): amount of j-th durable intermediate good. N: number of varieties of intermediate goods. L, L: exogenous total labor in l and f. u: share of labor employed in the industry of final output in l. Technological progress: expanding the variety of intermediate inputs Grossman & Helpman (1997), Barro & Sala-i-Martin (2004) Perfect competition net marginal productivities factor prices

23 The model The intermediate goods sectors New intermediate goods are invented in the innovative sector in l. Firms in this sector sell the patent to produce a new intermediate good with an infinite duration, only valid within a specific country. Domestic and international protection of these patents gives the producer of each intermediate good a monopoly power within his borders. X l (j) = K I l (j), X f (j) = K f (j), j [0, N] K I l (j), K f (j): the capital used to produce the intermediate good of type j [0, N] in l and f. Households rent the capital stock in their hands at prices r l, r f. Monopolists maximize instantaneous benefits: π l (j), π f (j).

24 The model The intermediate goods sectors p RD l, p RD f : price that a monopolistic producer of an intermediate good in l and f pays for the patent to innovators. Free entry into this industry: p RD l (t) = p RD f (t) = p T t π l (j)e 1/(τ t) τ t t π f (j)e 1/(τ t) τ t r l(s) ds dτ r f (s) ds dτ p T : relative value of the follower s final output with respect to the leader s

25 The model The R&D sector (leading economy) Innovative sector: a number of symmetric research firms operating under perfect competition. Increment in the total number of varieties: Ṅ = B (K RD l ) η ((1 u)l) 1 η N ϕ, η (0, 1), ϕ > 0 B: the existing technology in the R&D sector; Kl RD : capital stock rented by households; (1 u)l: labor force. 1 The knowledge elasticity of the R&D production, ϕ, is not necessarily equal to one ( knife-edge condition, criticized by Jones (1995a, b)). 2 The resource is growth-essential (Groth (2007)). Assumption of free entry input prices marginal profits.

26 The model The R&D sector (leading economy) Innovative sector: a number of symmetric research firms operating under perfect competition. Increment in the total number of varieties: Ṅ = B (K RD l ) η ((1 u)l) 1 η N ϕ, η (0, 1), ϕ > 0 B: the existing technology in the R&D sector; Kl RD : capital stock rented by households; (1 u)l: labor force. 1 The knowledge elasticity of the R&D production, ϕ, is not necessarily equal to one ( knife-edge condition, criticized by Jones (1995a, b)). 2 The resource is growth-essential (Groth (2007)). Assumption of free entry input prices marginal profits.

27 The households The model Budget constraints for the households in each country: V l = r l V l + w l L C l, V l (0) = V l0, V f = r f V f + w f L + pr R C f, V f (0) = V f0. V l, V f : Households wealth in l and f. C l, C f : total consumption in l and f. Households maximization problems: (C l (t)) 1 σ max e ρt dt, C l 0 1 σ max C f 0 (C f (t)) 1 σ e ρt dt, 1 σ subject to their budget constraints. Ramsey rule defines the growth rates of consumption in both countries: γ Cl = 1 σ (r l ρ), γ Cf = 1 σ (r f ρ)

28 The households The model Budget constraints for the households in each country: V l = r l V l + w l L C l, V l (0) = V l0, V f = r f V f + w f L + pr R C f, V f (0) = V f0. V l, V f : Households wealth in l and f. C l, C f : total consumption in l and f. Households maximization problems: (C l (t)) 1 σ max e ρt dt, C l 0 1 σ max C f 0 (C f (t)) 1 σ e ρt dt, 1 σ subject to their budget constraints. Ramsey rule defines the growth rates of consumption in both countries: γ Cl = 1 σ (r l ρ), γ Cf = 1 σ (r f ρ)

29 The steady-state equilibrium The steady-state equilibrium The equilibrium growth rates The steady-state equilibrium: the growth rates of all variables are constant. Equilibria with a growing consumption in both countries even considering that the resource is declining. Bilateral trade between these countries is balanced: p T p R R l = p RD f Ṅ

30 The steady-state equilibrium The steady-state equilibrium The equilibrium growth rates The steady-state equilibrium: the growth rates of all variables are constant. Equilibria with a growing consumption in both countries even considering that the resource is declining. Bilateral trade between these countries is balanced: p T p R R l = p RD f Ṅ

31 The steady-state equilibrium The steady-state equilibrium The equilibrium growth rates Existence and stability of the balanced path Existence, uniqueness and stability There exists a unique balanced path and it presents the saddle-point property if σ α 2.

32 The steady-state equilibrium The equilibrium growth rates The steady-state equilibrium The equilibrium growth rates Along the balanced path in each country the output, the consumption, the wage earnings and the capital stock grow at the same constant rate. γ = γ Kl = γ K RD l = γ K I l = γ Yl = γ Cl = γ wl γ = γ Kf = γ Yf = γ Cf = γ wf Furthermore, the shares of labor in the innovative and the final output sectors and the rates of return in each country remain constant. γ u = γ 1 u = γ rl = γ rf = 0

33 The steady-state equilibrium The equilibrium growth rates The steady-state equilibrium The equilibrium growth rates Along the balanced path, the knowledge elasticity of the R&D production, ϕ, must be between the labor elasticity in this sector, 1 η and 1. Furthermore, η γ N = 1 ϕ γ > 0, γ Rl = 1 α β γ Rf = 1 α β (γ γ N ) = 1 α 1 ϕ η β ( γ γ N ) = 1 α β 1 ϕ γ < 0, ( γ η 1 ϕ γ ) < 0, γ Xl = 1 ϕ η 1 ϕ γ < 0, γ X f = γ η 1 ϕ γ < 0, γ prd = γ p RD f = γ p RD l = 1 η ϕ 1 ϕ γ < 0. γ R = γ Rl = γ Rf < 0.

34 The steady-state equilibrium The equilibrium growth rates The steady-state equilibrium The equilibrium growth rates Along the balanced path, the knowledge elasticity of the R&D production, ϕ, must be between the labor elasticity in this sector, 1 η and 1. Furthermore, η γ N = 1 ϕ γ > 0, γ Rl = 1 α β γ Rf = 1 α β (γ γ N ) = 1 α 1 ϕ η β ( γ γ N ) = 1 α β 1 ϕ γ < 0, ( γ η 1 ϕ γ ) < 0, γ Xl = 1 ϕ η 1 ϕ γ < 0, γ X f = γ η 1 ϕ γ < 0, γ prd = γ p RD f = γ p RD l = 1 η ϕ 1 ϕ γ < 0. γ R = γ Rl = γ Rf < 0.

35 The steady-state equilibrium The steady-state equilibrium The equilibrium growth rates Comparison growth rates of the leader and the follower Along the balanced path equilibrium the growth rates of the leader and the follower economies compare as follows: γ γ = 1 ϕ η 1 ϕ ( β 1 α 1 α ). 1 α β β The country with the greater ratio of the output elasticities of technology (N) and natural resource will show the faster economic growth. Growth rate of the terms of trade: γ pt = γ γ

36 The steady-state equilibrium The steady-state equilibrium The equilibrium growth rates Comparison growth rates of the leader and the follower Along the balanced path equilibrium the growth rates of the leader and the follower economies compare as follows: γ γ = 1 ϕ η 1 ϕ ( β 1 α 1 α ). 1 α β β The country with the greater ratio of the output elasticities of technology (N) and natural resource will show the faster economic growth. Growth rate of the terms of trade: γ pt = γ γ

37 The steady-state equilibrium The steady-state equilibrium The equilibrium growth rates Rates of return of the capital stock in the leader and follower countries Along the balanced path, the rates of return of the capital stock in the leader and follower countries are: r l = σ σ φ ((γ γ) σ ρ) + ρ, r f = φ ((γ γ) σ ρ). σ φ φ = η (1 ϕ η)(1 α)(1 α β) > η 1 ϕ (1 ϕ)(1 α)β 1 ϕ > 1.

38 The steady-state equilibrium The steady-state equilibrium The equilibrium growth rates Positive growth in the leader and follower economies Assuming that (1 ϕ)(1 α β + σβ) η(1 α) < 0, the leading economy attains a positive growth along the balanced path, the follower economy would also experience an unlimited growth if one of the following conditions is satisfied: i) 1 α β 1 α β ; ii) 1 α β < 1 α β and η 1 ϕ < β(1 α) β(1 α) β(1 α).

39 The steady-state equilibrium The steady-state equilibrium The equilibrium growth rates Non Growth-Essential Resource No Trade Natural Resource R&D γ SZ Trade Natural Resource Imported R&D γ T γ SZ Imported Nat. Resource R&D γ T > γ SZ Growth-Essential Resource Ω = 1 α β Natural Resource R&D γ E Natural Resource Imported R&D γ > γ E Ω < 0 1 α ; ( ) σ = σ; ρ = ρ β Imported Nat. Resource R&D ( ) γ >γ E (σ 1)Ω < 0

40 The steady-state equilibrium The steady-state equilibrium The equilibrium growth rates Non-Renewable Resources and the Sustainability of the Economic Growth under Bilateral Trade Francisco Cabo 1 Guiomar Martín-Herrán 1 M.Pilar Martínez-García 2 1 Departamento de Economía Aplicada Universidad de Valladolid 2 Departamento de Métodos Cuantitativos para la Economía Universidad de Murcia SAE 2008