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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:
Chapter 12Knowledge, Human Capital and Endogenous Growth
© Pierre-Richard Agénor
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,
:exogenous rate of labor augmenting technical change.
In Solow-Swan, = 0: no endogenous element of labor productivity.
y = k .
sk/k - .
n: labor force growth rate.
(K/K)+ + n
k = s(1- )k-[ + n + (1- )]k,
a non-linear, first order differential equation in k.
1/(1 - )
+ n + (1- )
Capital Stock: gK = ( + n) /(1- )
Output, ALk: gY =( + n) /(1- )
Income per worker, Y/L: ( + n) /(1- )
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.
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.
A= (K/L) + A
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.
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.
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.
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.
A = (KK)(LL)AK, 0, 0.(15)
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,
1 - ( + )
gK = gY = n + gA
gY/L = gK - n = gA
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.
Returns to Scale
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.
Output given by
Y = KH(AL)1--,, >0, + < 1, (16)
H:Human capital stock,
h = H/AL.
Intensive form production function:
y = kh
k= sK kh- k,
= + n +
h= sH kh- h,
1/(1 - - )
1/(1 - - )
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.
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.
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- ( + )
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).
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.
Openness to Trade
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.
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.
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.
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.
G = Y, 0 < < 1,(32)
Growth rate of output per capita:
gY/L= A1/ (1- )/(1- ) - ( + ) (33)
: subjective rate of time preference
(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- .
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
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.
= ( - (1 - ))/k = (k,,,).
Equilibrium after-tax rate of return on capital, r, given by:
r = A(1 - )(q,)(1-) (42)
Increase in overall budgetary position may affect growth in three ways:
Alesina and Rodrik (1994):
Economic environment effects: