Models of Economic Growth B Outline: 1. Endogenous growth models – Slides 1-22 (these slides offer a slightly more detailed treatment of endogenous models.

Models of Economic Growth B

Outline:1. Endogenous growth models – Slides 1-22 (these slides offer a slightly more detailed treatment of endogenous models than Chapter 8)

2. The convergence debate – Slides 23 – 34 (this is additional to material covered in the book)

Endogenous growth models - topics

• Recap on growth of technology (A) in Solow model (…..does allow long run growth)

• Endogenous growth models

• Non-diminishing returns to ‘capital’

• Role of human capital

• Creative destruction models

• Competition and growth

• Scale effects on growth

Exogenous technology growth• Solow (and Swan) models show that technological change

drives growth• But growth of technology is not determined within the model

(it is exogenous)• Note that it does not show that capital investment is

unimportant ( A y and MPk, hence k)• In words …. better technology raises output, but also

creates new capital investment opportunities• Endogenous growth models try to make endogenous the

driving force(s) of growth• Can be technology or other factors like learning by workers

The AK model• The ‘AK model’ is sometimes termed an ‘endogenous

growth model’• The model has Y = AK

where K can be thought of as some composite ‘capital and labour’ input

• Clearly this has constant marginal product of capital (MPk = dY/dK=A), hence long run growth is possible

• Thus, the ‘AK model’ is a simple way of illustrating endogenous growth concept

• However, it is very simple! ‘A’ is poorly defined, yet critical to growth rate

• Also composite ‘K’ is unappealing

The AK model in a diagram

K

y

outp

ut p

er w

orke

r

Gross investment line

Depreciation line

Y=AK

Constant slope represents constant marginal product of

capital

Gap between lines represents net investment, which is always positive.

Endogenous technology growth• Suppose that technology depends on past

investment (i.e. the process of investment generates new ideas, knowledge and learning).

1 1 1

( ) where 0

Specifically, let 0

Cobb-Douglas production function

[ ]

dAA g K

dK

A K

Y AK L K K L K L

If + = 1 then marginal product of capital is constant (dY/dK = L1-

• Assuming A=g(K) is Ken Arrow’s (1962) learning-by-doing paper

• Intuition is that learning about technology prevents marginal product declining

k

y

outp

ut p

er w

orke

r

sy

dk

y=kL1-

Slope = marginal product = L1- =

constant (if labour force constant)

Gap between lines represents net

investment. Always positive, hence growth

Situation on growth diagram

k=K/L

“Gro

wth

of c

apita

l”

capital per worker

d+n

sy

Distance between lines represents growth in capital

per worker

• “Problem” with Y = K1L1- is that it exhibits increasing returns to scale (doubling K and L, more than doubles Y)

• IRS large firms dominate, no perfect competition (no P=MC, no first welfare theorem, …..)

• …. solution, assume feedback from investment to A is external to firms (note this is positive externality, or spillover, from microeconomics)

1 with 1Y K L

Increasing returns to scale

Knowledge externalities

• Romer (1986) paper formally proves such a model has a competitive equilibrium

• However, the importance of externalities in knowledge (R&D, technology) long recognised

• Endogenous growth theory combines IRS, knowledge externalities and competitive behaviour in (dynamic optimising) models

1A firm's production function is

but depends on aggregate capital

(hence firm does not 'control' increasing returns)

i i i i

i

Y AK L

A

More formal endogenous growth models

• Romer (1990), Jones (1995) and others use a model of profit-seeking firms investing in R&D

• A firm’s R&D raises its profits, but also has a positive externality on other firms’ R&D productivity (can have competitive behaviour at firm-level, but IRS overall)

• Assume Y=K(ALY)

• Labour used either to produce output (LY) or technology (LA)

• As before, A is technology (also called ‘ideas’ or ‘knowledge’)

• Note total labour supply is L = LY + LA

Romer modelAssume >0

This is differential equation. Can have constant growth rate?

Answer: depends on parameters and and growth of

A

A

dAL A

dtA

L

d d

Romer (1990) assumed: 1, 1

hence

/ (>0 if some labour allocated to research)

If A has positive growth, this will give long run growth in GDP . .

Note that t

A

A

dAL A

dtdA

A Ldt

p w

d

d

here is a 'scale effect' from AL

Note ‘knife edge’ property of =1. If >1, growth rate will accelerate over time; if <1, growth rate falls.

Jones model (semi-endogenous)

1

0, 1 (Jones, 1995)

Now / =

Can only have positive long run growth if far right term is constant

This only when (1 ) or (

A AA

A

A

L A LdA dA AL A A

dt dt A A A

L A A

L A A

d dd

1 )

In words: growth of technology = constant labour growth

A

A

L

L

• No scale effects, no ‘knife edge’ property, but requires (exogenous) labour force growth hence “semi-endogenous” (see Jones (1999) for discussion)

Human capital – the Lucas model • Lucas defines human capital as the skill

embodied in workers • Constant number of workers in economy is N • Each one has a human capital level of h • Human capital can be used either to produce

output (proportion u) • Or to accumulate new human capital

(proportion 1-u)• Human capital grows at a constant rate

dh/dt = h(1-u)

Lucas model in detail• The production of output (Y) is given by

Y = AKα (uhN)1-α ha

where 0 < < 1 and 0• Lucas assumed that technology (A) was constant • Note the presence of the extra term ha

- this is defined as the ‘average human capital level’

• This allows for external effect of human capital that can also influence other firms, e.g. higher average skills allow workers to communicate better

• Main driver of growth - As h grows the effect is to scale up the input of workers N, so raising output Y and raising marginal product of capital K

Creative destruction and firm-level activity

• many endogenous growth models assume profit-seeking firms invest in R&D (ideas, knowledge)– Incentives: expected monopoly profits on new product or

process. This depends on probability of inventing and, if successful, expected length of monopoly (strength of intellectual property rights e.g. patents)

– Cost: expected labour cost (note that ‘cost’ depends on productivity, which depends on extent of spillovers)

• models are ‘monopolistic competitive’ i.e. free entry into R&D zero profits (fixed cost of R&D=monopoly profits). ‘Creative destruction’ since new inventions destroy markets of (some) existing products.

• without ‘knowledge spillovers’ such firms run into diminishing returns

• such models have three potential market failures, which make policy implications unclear

Market failures in R&D growth models

1. Appropriability effect (monopoly profits of a new innovation < consumer surplus) too little R&D

2. Creative-destruction, or business stealing, effect (new innovation destroys profits of existing firms), which private innovator ignores too much R&D

3. Knowledge spillover effect (each firm’s R&D helps reduce costs of others innovations; positive externality) too little R&D

The overall outcome depends on parameters and functional form of model

What do we learn from such models?• Growth of technology via ‘knowledge spillovers’ vital

for economic growth• Competitive profit-seeking firms can generate

investment & growth, but can be market failures (‘social planner’ wants to invest more since spillovers not part of private optimisation)

• Spillovers, clusters, networks, business-university links all potentially vital

• But models too generalised to offer specific policy guidance

Competition and growth• Endogenous growth models imply greater competition,

lower profits, lower incentive to do R&D and lower growth (R&D line shifts down)

• But this conflicts with economists’ basic belief that competition is ‘good’!

• Theoretical solution– Build models that have optimal ‘competition’– Aghion-Howitt model describes three sector model (“escape

from competition” idea)

• Intuitive idea is that ‘monopolies’ don’t innovate

Do ‘scale effects’ exist• Romer model implies countries that have more ‘labour’

in knowledge-sector (e.g. R&D) should grow faster• Jones argues this not the case (since researchers in US

5x (1950-90) but growth still 2% p.a. • Hence, Jones claims his semi-endogenous model

better fits the ‘facts’, BUT– measurement issues (formal R&D labs increasingly used)– ‘scale effects’ occur via knowledge externalities (these may be

regional-, industry-, or network-specific)– Kremer (1993) suggests higher population (scale) does

increase growth rates over last 1000+ years

• anyhow…. both models show (the ‘knowledge spillover’ parameter) is important

Questions for discussion

1. What is the ‘knife edge’ property of endogenous growth models?

2. Is more competition good for economic growth?

3. Do scale effects mean that China’s growth rate will always be high?

ReferencesArrow, K. (1962). "The Economic Consequences of Learning by Doing." Review of Economic Studies XXIX(80): 155-173.

Jones, C. (1995). "R&D Based Models of Economic Growth." Journal of Political Economy 103(4): 759-784.

Jones, C. (1999) "Growth: With or Without Scale Effects?" American Economic Review Papers and Proceedings, 89, 139-144.

Kremer, M. (1993). "Population Growth and Technological Change: One Million B.C. to 1990." Quarterly Journal of Economics 108: 681-716.

Lucas, R. E. (1988). "On the Mechanics of Economic Development." Journal of Monetary Economics 22: 3-42.

Mankiw, N., D. Romer, et al. (1992). "A Contribution to the Empirics of Economic Growth." Quarterly Journal of Economics 107(2): 407-437.

Romer, P. (1986). "Increasing Returns and Long Run Growth." Journal of Political Economy 94(2): 1002-1037.

Romer, P. (1990). "Endogenous Technological Change." Journal of Political Economy 98(5): S71-S102.

Convergence debate• Following slides discuss the above issue, which is

not included in detail in book

• However, it may be a topic to include in a course on macroeconomics of growth, see:– Milanovic, B. (2002). "Worlds Apart: Inter-National and

World Inequality 1950-2000". World Bank, http://www.worldbank.org/research/inequality/world%20income%20distribution/world%20apart.pdf.

– Pritchett, L. (1997). "Divergence, Big Time." Journal of Economic Perspectives 11(3): 3-17.

– Stiglitz, J.-E. (2000). "Capital Market Liberalization, Economic Growth, and Instability." World Development 28(6): 1075-86.

Do poorer countries grow faster? (the ‘convergence’ debate)

Two common ways to assess convergence1. Beta () convergence2. Sigma () convergence

-convergence (use regression analysis) growthi = constant + (initial GDP p.w.)i

(i stands for a country. Test on sample of 60+)If <0, poorer countries, on average, grow faster

-convergencemeasure dispersion (variance) of GDP per worker across countries in a given year. If dispersion falls over time can say countries ‘converging’.

-convergence, 110 countries, 1965-2000 Source: PWT 6.1

Estimated for above = 0.000. No beta convergence

AGO

ARG

BWA

CHE

GRC

HKG

IRLJPN

KOR

LUX

MRT

NIC

NZL

PER

SGP

TWN

USA

VEN

ZAR

-4-2

02

46

8

0 10000 20000 30000 40000Real GDP per worker in 1965 (US$,PPP 96 prices)

Gro

wth

in G

DP

per

work

er

65-2

000

(or

95

)

Problems and other evidence• There are more than 110 countries (UN 191). The

poorest countries often don’t have data. Hence above result could be mis-leading.

• L Pritchett (1997) “Divergence, Big Time”. – 1870-1990, rich countries got much richer – 9/1 ratio in 1870; 45/1 ratio in 1990

• Some view the 1960s-80s as good decades for poorer countries – normally divergence

• “Conditional convergence”. – If regression analysis controls for other factors (e.g.

investment), poorer countries do grow faster.– Not very surprising …. what are other factors?

sigma () convergence• Variance (110 countries GDP per worker) increases

over time divergence since 60s• But, if you weight countries according to population,

evidence shows convergence (this appears entirely due to China, Milanovic, 2002, see next slide)(note: if you do not weight you give China and, say, Togo the same ‘importance’ or ‘weight’)

• Finally, researchers now working on ‘true’ world inequality data (i.e. combine within country, and across country, inequality). Initial results show ‘world’ inequality increasing since late 1980s

Gini measure of inter-country inequality

0.4

0.5

0.6

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

Year

Gin

i in

dex

World unweighted

World population-weighted

World unweighted without China and India

Source: Data direct from Branko Milanovic, see Milanovic (2002). The higher the Gini-coefficient, the more ‘unequal’ is GDP per capita across the world (see endnotes)

Twin peaks ?Some evidence that world income distribution is moving to ‘twin-

peaks’ distribution…… but not very strong

0.1

.2.3

Fra

ctio

n

0 10000 20000 30000 40000 50000 60000Real GDP per worker, US$ 1996 prices

0.1

.2.3

Fra

ctio

n

0 10000 20000 30000 40000 50000 60000Real GDP per worker, US$ 1996 prices

1965 real GDP per worker1995 real GDP per worker

What are mechanisms driving ‘convergence’?

• Important to understand basic data, but real issue is mechanisms

• Consider some ‘theory’ initially– open economy growth models – models of technological catch-up

• Note: this ‘convergence’ is not ‘Solow-Swan convergence to steady state’– can consider country convergence in S-S model but

must assume technology common to all countries

Weighted world inter-country inequality (role of China and India)

0.400

0.440

0.480

0.520

0.560

0.600

Gin

i co

eff

icie

nt

World without India and China

World without China

World

Summary (I)Sigma () convergence• Using unweighted measures, cross-country

evidence suggests ‘divergence’• Weighted measures convergence over

last 30 years due to performance of China• However, most recent ‘world inequality’

measures based on within and across country data, divergence

Summary (II)

Beta () convergence• No unconditional convergence• There is conditional convergence (poorer

countries grow faster if you control for other factors)

• Expect this (basic closed economy Solow and endogenous growth models predict this)

Endnotes Inequality/Convergence

• Gini coefficient, world income inequality. – The Gini coefficient varies from 0 (perfect equality) to

1 (perfect inequality).– The discussion related to this overlooks many

important and controversial issues. See Milanovic (2002) for a discussion, or google it.

– Milanovic, B. (2002). "Worlds Apart: Inter-National and World Inequality 1950-2000". World Bank, http://www.worldbank.org/research/inequality/world%20income%20distribution/world%20apart.pdf.