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Models of Economic Growth BOutline: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)
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Endogenous growth models - topicsRecap on growth of technology
(A) in Solow model (..does allow long run growth)Endogenous growth
modelsNon-diminishing returns to capitalRole of human
capitalCreative destruction modelsCompetition and growthScale
effects on growth
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Exogenous technology growthSolow (and Swan) models show that
technological change drives growthBut 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 opportunitiesEndogenous growth models try to
make endogenous the driving force(s) of growthCan be technology or
other factors like learning by workers
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The AK modelThe AK model is sometimes termed an endogenous
growth modelThe model has Y = AKwhere K can be thought of as some
composite capital and labour inputClearly this has constant
marginal product of capital (MPk = dY/dK=A), hence long run growth
is possibleThus, 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
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The AK model in a diagram
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Endogenous technology growthSuppose that technology depends on
past investment (i.e. the process of investment generates new
ideas, knowledge and learning).If a+b = 1 then marginal product of
capital is constant (dY/dK = L1-a ).
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Assuming A=g(K) is Ken Arrows (1962) learning-by-doing
paperIntuition is that learning about technology prevents marginal
product declining
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Situation on growth diagramDistance between lines represents
growth in capital per worker
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Problem with Y = K1L1-a 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)Increasing returns to scale
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Knowledge externalitiesRomer (1986) paper formally proves such a
model has a competitive equilibriumHowever, the importance of
externalities in knowledge (R&D, technology) long
recognisedEndogenous growth theory combines IRS, knowledge
externalities and competitive behaviour in (dynamic optimising)
models
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More formal endogenous growth modelsRomer (1990), Jones (1995)
and others use a model of profit-seeking firms investing in
R&DA firms 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=Ka(ALY)1-aLabour 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 modelNote knife edge property of f=1. If f>1, growth
rate will accelerate over time; if f
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Jones model (semi-endogenous) No scale effects, no knife edge
property, but requires (exogenous) labour force growth hence
semi-endogenous (see Jones (1999) for discussion)
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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)
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Lucas model in detailThe production of output (Y) is given byY =
AK (uhN)1- ha g where 0 < a < 1 and g 0Lucas assumed that
technology (A) was constant Note the presence of the extra term hag
- 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
betterMain 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
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Creative destruction and firm-level activitymany 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 returnssuch models have three potential market
failures, which make policy implications unclear
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Market failures in R&D growth modelsAppropriability effect
(monopoly profits of a new innovation < consumer surplus) too
little R&DCreative-destruction, or business stealing, effect
(new innovation destroys profits of existing firms), which private
innovator ignores too much R&DKnowledge spillover effect (each
firms R&D helps reduce costs of others innovations; positive
externality) too little R&DThe overall outcome depends on
parameters and functional form of model
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What do we learn from such models?Growth of technology via
knowledge spillovers vital for economic growthCompetitive
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 vitalBut models
too generalised to offer specific policy guidance
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Competition and growthEndogenous 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 solutionBuild
models that have optimal competitionAghion-Howitt model describes
three sector model (escape from competition idea)Intuitive idea is
that monopolies dont innovate
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Do scale effects existRomer model implies countries that have
more labour in knowledge-sector (e.g. R&D) should grow
fasterJones 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, BUTmeasurement 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+ yearsanyhow. both models
show f (the knowledge spillover parameter) is important
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Questions for discussionWhat is the knife edge property of
endogenous growth models?Is more competition good for economic
growth?Do scale effects mean that Chinas growth rate will always be
high?
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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.
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Convergence debateFollowing slides discuss the above issue,
which is not included in detail in bookHowever, 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 convergenceBeta (b) convergenceSigma (s)
convergenceb-convergence (use regression analysis) growthi =
constant + b (initial GDP p.w.)i(i stands for a country. Test on
sample of 60+)If b
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b-convergence, 110 countries, 1965-2000 Source: PWT 6.1Estimated
b for above = 0.000. No beta convergence
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Problems and other evidenceThere are more than 110 countries (UN
191). The poorest countries often dont 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 1990Some view the 1960s-80s as good decades for
poorer countries normally divergenceConditional convergence. If
regression analysis controls for other factors (e.g. investment),
poorer countries do grow faster.Not very surprising . what are
other factors?
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sigma (s) convergenceVariance (110 countries GDP per worker)
increases over time divergence since 60sBut, 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
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Gini measure of inter-country inequalitySource: 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)
Figure 0.1a
19500.438838073548.07250.49545279
19510.448817513670.84550.50385862
0.568517990.450650732735.32570.50014492
0.562345830.447574392815.58130.50122571
0.561355770.449535822765.52730.50519401
0.562671890.446261392897.52320.50587446
0.559228060.452276792949.65210.50571513
0.556883090.448465063000.66190.50002837
0.545785330.447241833015.96680.49702784
0.546067360.448711072924.5960.49840479
0.545010780.463305653058.22440.50650848
0.561331860.475426893180.60420.50330387
0.566925450.477210573281.78560.50523245
0.564911670.478272853370.75240.50506952
0.563947960.48271993497.3930.50697891
0.55724710.468968323588.94120.50794657
0.556529460.469499533708.84080.51160783
0.559258040.468872793772.44020.51166399
0.563013290.470207143899.05760.50959488
0.558180350.474201514057.76220.50613787
0.548409970.471713194178.48050.49819376
0.547273420.468313264259.91210.49720801
0.551154320.470596064388.54540.4993393
0.551037470.474125624575.74120.49985113
0.547686070.469651154591.28810.49358778
0.541630210.466111194576.16890.49258315
0.547226750.467727254699.46190.49295148
0.545933890.467350364813.2910.49488169
0.544239670.467067584940.03810.49866217
0.545304530.471936655033.92380.49926491
0.540516260.473742285060.25390.49582888
0.539056590.473557315063.03760.49768404
0.533600530.472631885016.60640.49461672
0.531985290.476991955081.07230.49811013
0.536484720.483706435175.26220.51672981
0.534346850.486566845278.73580.51979878
0.53323650.490264225364.42480.52164842
0.531506990.495436265457.89210.52266122
0.528839570.499184315613.87990.52565795
0.529126510.503426685712.58940.52724552
0.528949480.509389875734.04490.52781345
0.524724180.512978575684.23930.52227525
0.521433190.522514865731.95360.52352819
0.516374290.528192565792.30520.52226286
0.513524960.533766535932.19090.52318208
0.508621890.534331666066.93850.52226607
0.506266160.534318186259.44920.52280286
0.50614330.536216726439.38180.52635934
0.50528250.538058666502.48580.53334586
0.502066110.541226476676.32670.54080637
0.501814880.544730136883.50.54254942
World unweighted
World population-weighted
World unweighted without China and India
Year
Gini index
Sheet1
Sheet2
Sheet3
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Twin peaks ?Some evidence that world income distribution is
moving to twin-peaks distribution but not very strong1965 real GDP
per worker1995 real GDP per worker
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What are mechanisms driving convergence?Important to understand
basic data, but real issue is mechanisms Consider some theory
initiallyopen economy growth models models of technological
catch-upNote: this convergence is not Solow-Swan convergence to
steady statecan consider country convergence in S-S model but must
assume technology common to all countries
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Weighted world inter-country inequality (role of China and
India)
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Summary (I)Sigma (s) convergenceUsing unweighted measures,
cross-country evidence suggests divergenceWeighted measures
convergence over last 30 years due to performance of ChinaHowever,
most recent world inequality measures based on within and across
country data, divergence
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Summary (II)Beta (b) convergenceNo unconditional
convergenceThere 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)
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Endnotes Inequality/ConvergenceGini 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.
Mark Rogers, Macro, Economic Growth I, Hilary 2006*