09 advanced economic analysis negt i 2011

8/3/2019 09 Advanced Economic Analysis NEGT I 2011

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Advanced Economic Analysis

Lecture 9:

The New Endogenous GrowthTheory I


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Contents Background Basic Structure The AK models and optimal growth Two examples of AK models: Romer

1986 and Lucas 1988

Entrepreneurial efforts and innovation


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Background

Main objectives of the NEGT: Explain the Solow residual Make the economic growth rate

dependent on the saving decision ofindividual agents


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The basic structure of NEGT models

nacrawa +=

)/()('

)(''cc

cu

ccu

r

=

=

0

)]([ tCUU e nt e - t dt (1)

The Ramsey model:

(3)

))(/1()/( =

rcc

(2)

(5)


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The basic structure of NEGT modelsThe basic AK model:

Y = AK (6)

dK(t)/dt = sY(t) (equation (2) Solow model)

dK(t)/dt = sAK (7)

long term growth rate depends on saving(investment rate): scale effect


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ComparisonHarrod-Domar - Solow - AK

Harrod-Domar gw = s/c

where c = incremental capital-output ratio

dttdY

dttdK

/)(

/)( YK/

yk/

ky/

c =K/Y

Hence, also :

= 1/c.


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Solow model:= s (k) nk (equation 4 Solow model)

/k = s (k)/k nSince y = (k):

/k = s y/k n

Assuming = 0

s y/k = n, or

gw = s/c = n

gw = s/c = n +where stands for exogenous technical progress

k

k

k

k


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AKmodel,:y = Ak, (6.1)

where y = Y/L and k = K/L,= sAk (7.1)

/k = sA

gw = s/c = s/(1/A) = sA

k

k


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Comparison

Harrod-Domar - Solow - AK

Harrod-Domar Solow AK models

gw

= s/c n + sA


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Basic AK model Growth rate of consumption (per capita):

A = r +d. Therefore:

R = A - d

/k =

What is the meaning of constant returns tocapital?

k )))((/1()/( =

dAcc


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Romer 1986 One-sector model Learning-by-investment Firm knowledge is a public good If Ai denotes all knowledge controlled

by a firm, then changes in Ai correspond

to learning-by-doing across economyand this is proportional to changes incapital stock


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Romer 1986Yi = F (Ki, K(Li)) (9)

Yi = A (Ki) (KLi)

1- (10)

Yi/Ki = AL1- Therefore:

/k =

y/k = AL1-.Therefore:

/kPLANNER= (11a)

k ))(/1()/(1

=

LAcc

k ))(/1( 1 AL


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Romer 1986Actual growth rate of decentralised

economy is below optimal growth rate

due to knowledge externalities Perfect competition prevails since

producers remain unaware of positive

externality (firm-external) Space for government policies


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Lucas 1988 Two-sector model: capital accumulation and

investment in education

Constant rate of growth derived frominterpretation of growth of labour efficiencyas a combination of a given accumulation ofknowledge with an explanation of its growth

in terms of a societys preferences betweenpresent and future consumption


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Lucas 1988 (12)

where ay is a positive constant (i.e. a parameterfor technical progress) Ly is labour employed inthe process of the production of real output, Hicorresponds to individual human capital, and Hadenotes the general state of education

(13)

where aH is a positive constant, H is the givenstock of human capital, and LH is labour employedin the process of building human capital

Y = a K ( L H ) Hy y i1-

a

HH

HLa=H


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Lucas 1988 Firms face constant returns to capital and labour Overall production function characterised by

increasing returns to scale

Formation/accumulation of human capital (13)characterised by exactly constant returns

Existence of steady-state balanced growth attributedto human skills and knowledge (of human capital)

acquired through intentional learning process Equation (13) effectively transforms labour from a

scarce resource into an accumulable factor


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Entrepreneurial efforts: R&D

Microeconomic explanation forendogenisation of technical progress

Increasing returns to scale andimperfect competition

Constant returns to some type of capitalor accumulable factor of productionremain central


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Romer 1990

Product differentiation Knowledge is non-rivalrous and partially excludable IRS (research-intensive production) and imperfect competition 3-sector model: final goods, intermediate goods, research sector

Intermediate goods sector: monopolistic competition (high productvariety and each individiual good is produced by a monopolist), freeentry into the sector, returns to production of intermediate goodscan be made firm-specific

Research sector: perfect competition that determines theequilibrium number of intermediate inputs (A) and ensures zero

profit for marginal entrant; researches make free use of knowledgestock A

In the long run, general knowledge is both an input into and anoutput of the production of intermediate goods (blue-prints), i.e.positive knowledge externality in both intermediate and researchsector


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Romer 1990

Aggregate Production Function(14)

where Ly is labour employed in the production process.

The production of ideas and designs (A) is a function ofthe aggregate research effort (Li) and the rate of

discovery of new ideas () in the following form:

(15)

Y = K (ALy )1

ALAI

=


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Romer 1990

The rate of technological progress (or the growthrate of A) is:

(16)

Productivity of research is exactly proportional tothe existing stock of ideas, i.e. externality due to

past innovations exhibits constant returns

ILA

A=


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Romer 1990

The steady-state growth rate for the decentralisedeconomy is:

(17)

where = total labour supply, 1/ monopoly mark-up

Equilibrium growth rate of decentralised economy willbe less than social optimum

+

=Lgw


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Jones 1998

Adjusted R&D equation:

(15a)

where 01 and 01. denotes an additional externalityreflecting the likely duplication of research efforts.

Therefore, the rate of growth of the stock of ideas Anow is:

(16a)

I

1-

I L)L(A=A

I-1

1-

IL

A

L

A

A

b

=


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Jones 1998

Solving the model in the same way asRomer, the steady state growth rate of thestock of ideas or design becomes:

(17a)

where n denotes the population growth rate.

=

1

ng

w


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Jones 1998

A growing population rises the level oftechnology (conscious research efforts

resulting in non-rivalrous ideas)

Growth rate independent of the savingsrate: Solowian dynamics


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Schumpeterian innovationmodels

Vertical product innovation with obsolence(creative destruction)

Imperfect (monopolistic) competition and IRSin research-intensive and innovation sectors

Aghion and Howitt 1998: Constant returns to research activities arise from

the assumption that every innovation generates aproportionate increase in A and that the marginalproductivity of research is independent of thenumber of researchers in the economy


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Schumpeterian innovationmodels

Aghion and Howitt 1998 contd: IRS generate externalities so that optimal and

equilibrium growth paths differ (as in Romer 1990) In addition to positive intertemporal spillover

effect from innovation, there is a negativebusiness stealing effect and a positiveappropriability effect.

The relationship between the optimal and theequilibrium growth paths, and the design ofgovernment policies to promote innovation,depends on sizes of the two positive and thenegative externalities.

09 advanced economic analysis negt i 2011

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