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)

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

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

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

The AK model in a diagram

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 ).

Assuming A=g(K) is Ken Arrows (1962) learning-by-doing paperIntuition is that learning about technology prevents marginal product declining

Situation on growth diagramDistance between lines represents growth in capital per worker

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

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

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

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)

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 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

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

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

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

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

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

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?

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 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

b-convergence, 110 countries, 1965-2000 Source: PWT 6.1Estimated b for above = 0.000. No beta convergence

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?

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

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

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World unweighted

World population-weighted

World unweighted without China and India

Year

Gini index

Sheet1

Sheet2

Sheet3

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

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

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

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

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)

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*