on the mechanics of economy development lucas...
TRANSCRIPT
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On The Mechanics of Economy DevelopmentLucas 1988
Seyyed Ali Madanizadeh
Sharif University of Technology
December 6, 2016
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 1 / 24
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Overview
1 Introduction
2 Neoclassical growth model
3 Neoclassical growth model + Human capital
4 Learning-by-doing
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 2 / 24
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Introduction
Why is there so muchdifference between countriesper capita GDP?
Why can some countriesgrow so fast and some cannot?
Is growth possible for allcountries?
Countries Growth rate
India 1.4%South Korea 7.0%Japan 7.1%Egypt 3.4%USA 2.3%
”I do not see how one can look at figures like these without seeing themas representing possibilities.”
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 3 / 24
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Introduction: So why studying growth?
”The consequences for human welfare involved in questions like these aresimply staggering: Once one starts to think about them, it is hard to thinkabout anything else.”
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 4 / 24
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Introduction
So we need a theory to figure out what is necessary and what isopportunity
The term theory in here refer to an explicit dynamic system,something that can be put on a computer and run
This is why we call it mechanics
But it should be noticed that there are many mechanics and not justthis one in this paper
This is why the paper describes itself as ”On the mechanics...” not”The mechanics....”
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 5 / 24
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Neoclassical Growth Model
There are no convergence
Technology developments are exogenous
The differences between countries in model are because of theparameters in the model
Growth occurs not because of individuals decision to acquireknowledge
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 6 / 24
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Neoclassical Growth Model + Human Capital
Including the effects of human capital accumulation in neoclassicalgrowth model
Taking the population growth as given, NN = λ
No money in the model
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 7 / 24
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Neoclassical Growth Model + Human Capital
Human capital, h, is an individual’s general skill level.
According to this definition, a worker with human capital h(t) is asproductive as two workers with human capital 1
2h(t) for each or ahalf-time worker with 2h(t)
The introduction of human capital let individual to decide how toallocate their time to production and obtaining human capital
So one aspect of growth become micro-based and endogenous
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 8 / 24
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Neoclassical Growth Model + Human Capital
h(t) = h(t)ζG (1− u(t)) ⇒ h(t) = h(t)δ[1− u(t)]
People accumulate human capital rapidly early in life, then lessrapidly, then not at all.
Human accumulation is a social activity, involving groups of people ina way that has no counterpart in he accumulation of physical capital.
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 9 / 24
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Neoclassical Growth Model + Human Capital
N =
∫ ∞
0N(h)dh
Effective workforce in production:
Ne =
∫ ∞
0u(h)N(h)h dh ≡ uhN
So production becomes F (K ,Ne)
Hourly wage for a worker at skill h becomes FN(K ,Ne)h
Total earning FN(K ,Ne)hu(h)
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 10 / 24
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Neoclassical Growth Model + Human Capital
AK (t)β[u(t)h(t)N(t)]1−βha(t)γ = N(t)c(t) + K (t)
ha =∫∞0 hN(h)dh∫∞0 N(h)dh
⇐⇒ External effect
h(t) ⇐⇒ Internal effect
A is assumed to be constant
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 11 / 24
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Neoclassical Growth Model + Human Capital
max
∫ ∞
0e−ρtN(t)
1
1− σ[c(t)1−σ − 1]N(t)dt (1)
s.t. :AK (t)β[u(t)h(t)N(t)]1−βha(t)γ = N(t)c(t) + K (t) (2)
h(t) = h(t)δ[1− u(t)] (3)
The ha(t)ζ has external effect
Optimal path and equilibrium path are not coincide
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 12 / 24
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Neoclassical Growth Model + Human Capital
1 Optimal path▶ Choice of K (t), h(t), ha(t), c(t) and u(t) that
▶ Maximizing (1) subject to (2), (3) and h(t) = ha(t)
2 Equilibrium path▶ Choice of K (t), h(t), c(t) and u(t)
▶ Maximizing (1) subject to (2), (3)
▶ Households and firms take ha(t) as given, like A(t) in neoclassicalgrowth model
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 13 / 24
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Neoclassical Growth Model + Human Capital
Current-value Hamiltonian:
H(K , h, θ1, θ2, c, u)
=N
1− σ[c1−σ − 1] + θ1[AK
β(uhn)1−βhζ − Nc] + θ2[δh(1− u)]
FOCs for optimal path:
[c] : c−σ = θ1 (4)
[u] : (1− β)θ1AKβ(uhN)−βNh1+γ = θ2δh (5)
[K ] : θ1 = ρθ1 − θ1βAKβ−1(uhN)1−βhγ (6)
[h] : θ2 = ρθ2 − θ1(1− β + γ)AKβ(uN)1−βh−β+γ − θ2δ(1− u) (7)
[θ1] : Nc + K = AKβ[uhN]1−βhγ (8)
[θ2] : h = hδ(1− u) (9)
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 14 / 24
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Neoclassical Growth Model + Human Capital
FOCs for equilibrium path are exact the same as optimal path except forequation (7) which becomes:
[h] : θ2 = ρθ2 − θ1(1− β)AKβ(uN)1−βh−βhγa − θ2δ(1− u)
The market clearing condition gives h(t) = ha(t) so the above conditionbecomes:
[h] : θ2 = ρθ2 − θ1(1− β)AKβ(uN)1−βh−β+γ − θ2δ(1− u) (10)
The following solution is for the optimal path, although some part of thesolutions are the same for both paths.
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 15 / 24
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Neoclassical Growth Model + Human Capital
FOCs for equilibrium path are exact the same as optimal path except forequation (7) which becomes:
[h] : θ2 = ρθ2 − θ1(1− β)AKβ(uN)1−βh−βhγa − θ2δ(1− u)
The market clearing condition gives h(t) = ha(t) so the above conditionbecomes:
[h] : θ2 = ρθ2 − θ1(1− β)AKβ(uN)1−βh−β+γ − θ2δ(1− u) (11)
The following solution is for the optimal path, although some part of thesolution is the same for both paths.
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 16 / 24
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Neoclassical Growth Model + Human Capital
For solution, we find the balance growth paths
Consumption and both kinds of capital grow at constant percentagerates
The prices of two kinds of capital are declining at constant rates
Time allocation variable u(t) is constant
Interest rate, r, is constant
We also define:
r = βAKβ−1(uhN)1−βhγ (12)
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 17 / 24
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Neoclassical Growth Model + Human CapitalWe take growth from the FOCs and equation (12):
− σc
c=
θ1θ1
(13)
θ2θ2
+h
h=
θ1θ1
+ βK
K+ (1 + γ − β)
h
h+ (1− β)
N
N(14)
θ1θ1
= ρ− r (15)
θ2θ2
= ρ− 1− β + γ
β
θ1θ2
K
hr − δ(1− u) (16)
Nc
K+
K
K=
r
β⇒ K
K=
c
c+
N
N(17)
h
h= δ(1− u) (18)
(β − 1)K
K+ (1 + γ − β)
h
h+ (1− β)
N
N= 0 (19)
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 18 / 24
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Neoclassical Growth Model + Human Capital
By assuming that cc = κ and h
h = ν, we have:
θ1θ1
= −σκ (20)
r = ρ+ σκ (21)
ν = δ(1− u) (22)
K
K= λ+ κ (23)
κ = (1− β + ν
1− β) (24)
θ2θ2
= (β − σ)κ− (β − γ)ν + λ (25)
θ2θ2
= ρ− δ − γ
1− βδu (26)
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 19 / 24
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Neoclassical Growth Model + Human Capital
z1(t) = e(−κ+λ)tK (27)
z2(t) = e−νth (28)
Inserting these two into equation (21):
(βAN1−β0 u1−β)zβ−1
1 z1−β+γ2 = ρ+ σκ (29)
It is a fact that all pairs (z1, z2) satisfying (29) correspond to balancedpath
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 20 / 24
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Neoclassical Growth Model + Human Capital
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 21 / 24
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Neoclassical Growth Model + Human Capital
The system will converge to this curve from any initial configuration
The convergence will depend on the initial conditions
Initially poor countries will remain poor relatively
The long-run rate of income growth is the same for both poor andwealthier countries
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 22 / 24
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Learning-by-doing
Learning-by-doing is as important as schooling in the formation ofhuman capital
The model predicts wide and sustained differences in growth rates
Human capital specialized to old goods being ”inherited” in some wayby new goods
ci (t) = hi (t)ui (t)N(t), i = 1, 2 (30)
hi (t) = hi (t)δiui (t), i = 1, 2 (31)
U(c1, c2) = [α1c−ρ1 + α2c
−ρ2 ]−1/ρ (32)
Seyyed Ali Madanizadeh (SUT) Lucas 1988 December 6, 2016 23 / 24