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Global Environment

Long Run

Francesco Franco

Nova SBE

November 26, 2014

Francesco Franco Global Environment 1/29

The question of growth

Cross-coutry

Figure :Francesco Franco Global Environment 2/29


Cross-coutry



Time-series



Link

http://press.princeton.edu/chapters/s8764.pdf• unconditional convergence• conditional convergence: schooling/life expectancy• correlates: human capital/physical capital/technology


Growth

Theories

1 Exogenous growth. The Solow model principal conclusion isthat accumulation of physical capital cannot account foreither the vast growth over time in output per person ot thevast geographic di�erences in output per person

2 Endogenous growth. Allocation of resources to the creation ofnew technologies. Important for global growth phenomenon.(imperfect competition/Schumpeter)

3 Linkages across societies: adoption.4 Structural transformations5 Policy, political economy


The Solow Model

The aggregate neoclassical production function

The Solow model focuses on the aggregate produciton function.We need four variables:

1 output Y

2 capital K

3 labor L

4 knowledge, e�ectiveness of labor A

Y (t) = F (K (t), A(t)L(t)),

where t denotes time. Remarks: F , Harrod-neutral.


The Solow Model


F is assumed to have CRS

F (cK , cAL) = cF (K , AL) for all c Ø 0.

Discuss (Large, Natural resources). Allows to write the productionin intensive form

y = f (k)

where y = YAL , k = K

AL , f (k) = F (k, 1). Intuition.


The Solow Model


f is assumed to satisfy

f (0) = 0, f

Õ(k) > 0, f

ÕÕ(k) < 0,

and the Inada conditions:

limkæ0

f

Õ(k) = Œ, limkæŒf

Õ(k) = 0.

Example: Cobb-Douglas.


The Solow Model

Input dynamics

Initial conditions are given and Labor and Knowledge grow atexogenous rates n and g

L(t) = nL(t)

A(t) = gA(t)

Remark: natural logs and growth rates.Exponential gorwth

L(t) = L(0)ent ,

A(t) = A(0)egt .


The Solow Model

Capital dynamics

Output is divided between saving and consumption. Saving isconstant at a rate s and one unit of output invested yields one unitof capital. Existing capital depreciates at a rate ”.

K (t) = sY (t) ≠ ”K (t).

Comments: one good, simplifications...


The Solow Model

Capital dynamics

Let us derive the key equation of the model (di�erential equation)

k(t) = sf (k(t)) ≠ (” + n + g)k(t)


The Solow Model

Capital dynamics

Figure : Solow Model


The Solow Model

Capital dynamics



The Solow Model

The balanced Growth Path

k converges to k

ú. What about the other variables of interest?The Solow model implies that regardless of the starting point theeconomy converges to a Balanced Growth Path: each variable ofthe model grows at a constant rate. Furthermore the gorwth ofoutput per capita is equal to the growth rate of technologicalprogress.


The Solow Model

Comparative Statics: the saving rate

An interesting question is what changes when we change thesaving rate (taxes, government, ...). To study this question weproceed in a laboratory type of exercise. Start with an economy onthe BGP and chang permanently the saving rate.


The Solow Model




The Solow Model


The evolution of each variable on the whiteboard.The main lesson is that a permanent increase in s produces atemporary increase in the growth rate of output per worker and apermanent increase in the level of output per capita.


The Solow Model


Welfare, consumption.

c(t) = (1 ≠ s)f (k(t))

and on the BGP

c

ú = f (kú) ≠ (n + ” + g)kú.

The Golden Rule.


The Solow Model

quantitative questions

How fast do we expect an economy to converge to the BGP? Orhow long is the transition towards the BGP? How long/short istemporary? How strong are the e�ects?A technique to evaluate quantitatively a model is to take anapproximation around the BGP.


The Solow Model


Long Run impact:

s

yúˆyúˆs

=k

úf

Õ(kú)/f (kú)

1 ≠ k

úf

Õ(kú)/f (kú)=

–K1 ≠ –K

.

if –K = 0.3, the elasticity is 1/2.


The Solow Model


Speed of convergence around the BGP

k(t) ƒ ≠⁄ [k(t) ≠ k

ú]

where ⁄ = [1 ≠ –K (kú)] (n + ” + g). Calibration suggests⁄ = 0.04. Slow.


The Solow Model

Extensions: natural resources

Conside Land, T , and Resources R

Y (t) = K (t)–R(t)—

T (t)“ [A(t)L(t)]1≠–≠“≠—

with – < 1, “ < 1, — < 1 and – + — + “ < 1.Assume

T = 0

andR(t) = ≠bR(t)

with b > 0.


The Solow Model

Extensions

• Human capital: now two capital acumulation equations.• Optimal decisions


Take-o�

Scale

population-inventions

Y (t) = L(t)– (A(t)Z )1≠–

A(t) = ⁄L(t)

L(t) = „Y (t)


Causes of growth

Luck

• multiple equilibria: high investment/low investment game• multiple steady states: history dependence• stochastic: leaders?


Causes of growth

Geography

• climate• climate -> tecnhologies• climate -> diseases


Causes of growth

Institutions

• rules of the game that structure incentives• economic institutions (rule of law, private property,...):

experiments 2 Koreas, 2 Germany• political economy, conflict of interests


Causes of growth

Culture

• Weber: protestant revolution• ...Italy,Japan,China,...


Solow Robert, “A contribution to the theory of EconomicGrowth”, Quarterly Journal of Economics 70 (February 1956):65-94.Solow Robert, “Technical Change and the AggregateProduction Function”, Review of Economics and Statistics 39(1957): 312-320.

Swan, T.W, “Economic Growth and Capital Accumulation”,Economic Record 32 (November 1956): 334-361.

Acemoglu Daron, Modern Economic Theory, PrincetonUniversity Press 2009, chpater 1.


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