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The World Bank. Chapter 12 Knowledge, Human Capital and Endogenous Growth. © Pierre-Richard Agénor. The Accumulation of Knowledge Human Capital and Returns to Scale Human Capital, Public Policy, and Growth Other Determinants of Growth. Interest in endogenous mechanisms resulting from:

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The World Bank

Chapter 12Knowledge, Human Capital and Endogenous Growth

© Pierre-Richard Agénor


The Accumulation of Knowledge

  • Human Capital and Returns to Scale
  • Human Capital, Public Policy, and Growth
  • Other Determinants of Growth

Interest in endogenous mechanisms resulting from:

  • Recognition that Solow-Swan model does not fully explain some basic facts about economic growth in developing countries.
  • Technological progress as prime determinant of changes in steady state growth rate, an exogenous and unexplainable variable in Solow-Swan.
  • Recent focus on endogenous mechanisms that foster economic growth (Lucas, 1998, Grossman and Helpman, 1991, and Romer, 1986).
Technological innovation; involves creation of new knowledge, captured in two types of endogenous growth models.
  • Solow Skepticism…
    • There is probably an irreducibly exogenous element in the research and development (R&D) process…an internal logic--or sometimes non-logic--to the advance of knowledge that may be orthogonal to the economic logic. This is not at all to deny the partially endogenous character of innovation but only to suggest that the “production” of new technology may not be a simple matter of inputs and output. (Solow, 1994, pp. 51-52).
Knowledge As a By-Product

Arrow (1962): Knowledge as an unintended by-product of production or investment.

Experience raises labor productivity over time; Learning by Doing.

Productivity determined by endogenous element, (K/K), and exogenous element, ,by,

A/A = (K/K) + , 0< < 1,



:learning coefficient.

:exogenous rate of labor augmenting technical change.


In Solow-Swan,  = 0: no endogenous element of labor productivity.

Arrow Equations:

  • Start with Cobb-Douglas in intensive form,

y = k .

  • Growth rate of the capital stock,

sk/k - .

Growth rate of effective labor:

n: labor force growth rate.

(K/K)+ + n


  • Growth of capital-labor ratio:

k = s(1- )k-[ + n + (1- )]k,

a non-linear, first order differential equation in k.

Arrow Equilibrium Capital Effective Labor Ratio


1/(1 - )


s(1- )


k =

 + n + (1- )

  • Arrow Steady-State Growth Rates (k = 0):
  • k/ < 0 :  AL   k 

Capital Stock: gK = ( + n) /(1- )

Output, ALk: gY =( + n) /(1- )

Income per worker, Y/L: ( + n) /(1- )


Arrow Implications

Learning Coefficient, , raises level of effective labor, reducing steady state capital to effective labor ratio and increasing steady state growth rate of output per worker.

Positive relationship between population growth rate, n, and steady-state growth rate of output per work. Solow-Swan predicts no relationship. Empirical evidence suggests a negativerelationship.

No role to savings and investment rates.

Villanueva (1994): Modified Arrow Model

Three Main Attractions:

Equilibrium growth rate becomes endogenous and may be influenced by government policies.

Faster speed of adjustment to equilibrium growth path than in the Solow-Swan model. Enhanced learning reduces adjustment time.

Equilibrium rate of output growth exceeds the sum of the exogenous rates of technical change and population growth.


Villanueva (1994):

  • Productivity,

A= (K/L) +  A



To determine the steady-states, use Cobb-Douglas,

A/A + L/L = k +  + n

k/k = sk-1 - k + ( + n + ),

setting k = 0, equilibrium capital-effective ratio given

by, sk-1 - k + ( + n + ) = 0,

k/ < 0,viaimplicit function theorem.







Villanueva (1994): Model Implications (See Figure 12.1, 12.2):

Balanced growth path higher than in Solow-Swan by a factor of k .

Increase in savings rate increases steady-state growth rate.

Increases in the capital-effective labor ratio raise the rate of labor-augmenting technical change and with it the rate of growth of effective labor.

Process continues until the growth rates of capital stock and effective labor are equal.

The Production of Knowledge

Romer (1990);

Economy with two production sectors:

Goods-producing sector: employs physical capital, knowledge and labor in production process.

Knowledge-producing sector: uses same inputs in the production of knowledge.

Nonrivalry:The use of knowledge in one sector does not preclude its use in another sector.

Using Cobb-Douglas,

Output in goods producing sector, Y,

Y = [(1-K)K][A(1-LL)]1- ,0 <  < 1, (14)

1-K: Capital used in goods producing sector.

1-L: Labor used in goods producing sector.

  • Production of knowledge, A,

A = (KK)(LL)AK,  0,   0.(15)

  • In (15), setting  =  = K = L = 0, and  = 1, A/A =  .



The Steady-States:

K and A: Endogenous variables

Using (3) for capital accumulation and labor force growth rate, steady states for capital, output per worker and knowledge are given by,

 + 

gA =



1 - ( + )

gK = gY = n + gA

gY/L = gK - n = gA







Romer Model Implications

Steady-state growth rate: increasing function of population growth.

Retains many of Solow-Swan Limitations: s, K , and L all have zero effect on steady-state growth rate.


Human Capital and

Returns to Scale

Human capital: abilities, skill, and knowledge of individual workers.

Human capital is

rival:use of human capital in one sector does preclude its use in another sector;

excludable:it is possible to exclude others from use.

The Mankiw-Romer-Weil Model

Output given by

Y = KH(AL)1--,, >0,  +  < 1, (16)

H:Human capital stock,

h = H/AL.

Intensive form production function:

y = kh


Dynamics of capital-output ratio, k,

k= sK kh- k,


 =  + n + 


  • For h, the human capital-effective labor ratio,

h= sH kh- h,







1/(1 -  - )

1/(1 -  - )


sKsH1- 



k =

h =

  • The long run equilibrium values of physical and human capital are given by k and h, with the solution (see pages 458-459):



  • Figure 12.3 and 12.4.

Steady-state still determined by exogenous term, A.

Savings rate increases growth only temporarily.

Elasticity of output to underlying variables, e.g. savings and population growth, far higher than in Solow-Swan.

The AK Model

Possibility of constant or increasing returns under:

internal economies of scale once output reaches a certain threshold;

positive externalities vis-à-vis learning by doing;

external economies of scale when increased industry size increases efficiency and the return to each input.

Rebelo (1991)

Production function is given by the linear form,

Y = AK

K: reproducible capital, both human and physical.

A: technology parameter.

Steady state growth rate of capital stock per worker and output per worker given by,

gK/L = g Y/L = sA- ( + )

In contrast to Solow-Swan and Mankiw-Romer-Weil, increases in the savings rate permanently raise the growth rate of output per capita.
Educational attainment: crucial determinant of earnings capacity and county’s stock of human capital.

Low-education, low-skill, and low-income trap: poor families unable to forego current income and invest in education.

Higher inequalities in income and asset distributions lead to a larger probability of a self-perpetuating poverty trap.

Endogenous growth theories have emphasized that in the absence of adequate collateral and other forms of credit market imperfections, (poor) individuals may find it impossible to borrow on capital markets and finance human capital accumulation (De Gregorio, 1996).

Restrictions on the ability to borrow may act as a constraint on the rate of economic growth in the long run.

Free basic education public credit schemes may be welfare enhancing (Stern, 1989) as it creates positive externalities, raises the steady-state rate of economic growth, and reduces income disparities.

Zhang (1996): direct provision of education, by the public sector, rather than government subsidies to private education may reduce growthif financed through a discretionary tax.

Upadhyay: Subsidies can produce excess education. Subsidy raises demand for higher education at the cost of physical capital. Leads to inefficient substitution, with output constrained by lack of unskilled labor.
Other Mechanisms through which government intervention can directly or indirectly effect growth:

Fiscal Policy


Macroeconomic Stability

Openness to Trade

Financial Development

Institutional Factors

Fiscal Policy

Government Spending

Tanzi and Zee (1997)

Government spending, G, effects growth in two ways:

Public investment: increases the economy’s capital stock.

Indirectly: Raises marginal productivity of private factors of production via public spending on education, health and other human capital enhancing activities.

G effectiveness:

Subject to diminishing marginal returns, e.g. excessive G relative to private savings may be inefficient.

Contingent on form of taxation used to finance public investment at the expense of private investment.

The Dual Effects of Taxation

Distortionary versus lump-sum taxes: Most taxes distort allocation of resources through their impact on saving and investment and are therefore distortionary.

Distortionary tax effect on net growth: contingent on the growth benefits of the expenditures financed.

Net effect depends on whether the tax considered is used as an instrument to correct for negative externalities or other related distortions.

Barro (1990) Model: Dual Effects of Taxation

Government activity complements private capital.

Production function for firm h, with h = 1,…n:

Yh = AG1-Lh1-Kh, 0 <  < 1 (31)

Kh: Capital stock held by h,

Lh: labor used by h,

G: flow of government spending.

Government balanced budget given by:

G = Y, 0 <  < 1,(32)

Growth rate of output per capita:

gY/L= A1/  (1- )/(1- ) - ( + ) (33)

: subjective rate of time preference


By (33), G has a dual effect,

(1- ):drag effect of taxation on after-tax marginal product of capital;

 (1- )/:positive effect of public services on after tax marginal product of capital.

* : gY/L/ = 0, represents most efficient tax rate, the solution of which is found at * = 1- .

Figure 12.5.

Loazya Model (1996): provision of public goods in an economy with both a formal and informal sector.

Firms in formal sector generate net of tax income at,

YhF = (1- ) A(G/Y)Kh. 0 <  < 1

For firms operating in informal sector,

YhI = (1- )A((G)/Y)Kh, 0 < ,  < 1

:fraction of public services firms in informal sector still have access to.

Ratio of public services to output can be written as,

G/Y = (q,)(1-), (39)

: fraction of government revenues utilized in public services used in the production process.

: relative size of the informal sector, YI /Y.

Given unrestricted mobility, rates of return between YI and YF must be equal, therefore,  will equal:

 = ( - (1 - ))/k =  (k,,,).

Equilibrium after-tax rate of return on capital, r, given by:

r = A(1 - )(q,)(1-) (42)

budget deficits and growth
Budget Deficits and Growth

Increase in overall budgetary position may affect growth in three ways:

  • by lowering aggregate saving,
  • by contributing to higher inflation by monetizing deficits, leading to a distortion of relative pricesignals and increased macroeconomic instability,
  • by crowding out private investment through the buildup of domestic public debt.
Endogenous models identify various mechanisms whereby inflation negatively effects steady-state growth:
  • inflation reduces the rate of investment and lowers the efficiency of investment (De Gregorio, 1993);
  • inflation raises nominal interest rates, reduces real money balances, increases transactions costs to private agents, lowers the return on physical and human capital and reduces investment and long run growth rates (Palokangas, 1997).
Causes of inflation: high fiscal deficit with high degree of monetization.
  • Roubini and Sala-i-Martin (1995): inflation as a proxy for government imposed restrictions on financial markets.
  • Inflation as an alternative to conventional taxation, set to maximize seigniorage revenues. Thus inflation caused by an inefficient tax system, subject to rising marginal collection costs (De Gregorio, 1993).
Macroeconomic Instability:
  • Increases in overall uncertainty and distorting information hampers private investment and savings and leads to an inefficient allocation of resources.
  • Aizenman-Marion Model: policy uncertainty is endogenous to the model, future tax rate on capitalunknown variable. With irreversible investments, increased uncertainty causes a delay in investment.
trade and openness
Trade and Openness
  • Static gains to free trade: productive resources reallocated towards more efficient activities to the expense of less efficient activities.
  • Dynamic gains to free trade:
    • improved allocation--less rent-seeking;
    • enhance overall productivity of the economy--knowledge spillovers;
    • reduce risk premium on world capital markets. if marginal productivity of domestic investment is higher than world interest rate, trade openness will also increase the supply of foreign capital and may improve domestic welfare.
Larger variety of higher quality, less expensive intermediate goods available to domestic agents--shifts economy wide productions possibility frontier outward.


  • Scale economies and learning-by-doing of little importance in raw material production and low-technology manufactured goods.
  • Specialization may discourage domestic R&D activity by soaking limited supply of skilled labor into low level manufacturing sector.
  • Transmission of new inputs may not be enough: transmission of ideas is vital.
financial development
Financial Development
  • Government policies that restrain process of financial intermediation impede economic growth.
  • Links between economic growth and financial markets development:
    • financial intermediaries raise average return to capital by facilitating the allocation of capital to its highest valued use by pooling funds and acquiring information (Greenwood and Jovanovich, 1990);
    • banks engage in maturity intermediation:induce savers to switch from unproductive investment in tangible assets to productive investment in firms.
political factors and income inequality
Political Factors and Income Inequality
  • Analytical literature is somewhat limited and inconclusive.
  • Fertility lower in countries with higher civil and political liberties (Dasgupta, 1995).
  • Political instability:
    • negative effect on growth.
    • limits the availability and quality of public policy choices.
    • has adverse effects on investment.
  • Income inequality:
    • viscous cycle of increasing inequality and low growth;
reduction in average skill level of labor force. low income education financing trap.

Alesina and Rodrik (1994):

  • Income inequality causes the tax rate to rise above its optimal level, because the median voter gains from the re-distributive effects of a higher tax rate if the degree of inequality is large.
  • Higher than optimal tax rate reduces the propensity to invest.
institutions and the allocation of talent
Institutions and the Allocation of Talent

Economic environment effects:

  • Pro-growth environment: protection for property rights, gives agents incentive to produce, invest and accumulate skills.
  • Anti-growth-discourages production and effort, corrupt bureaucracy operates as a tax on production activities.
  • Would be entrepreneurs go down the dirty road of rent-seeking.
  • Olson (1996): poor countries waste more resources than richer countries; don’t accumulate more resources to increase growth, rather waste less of what already exists.