Transcript Agenor Chapter 12 a

Chapter 12
Knowledge, Human Capital and
Endogenous Growth
© Pierre-Richard Agénor
The World Bank
1




The Accumulation of Knowledge
Human Capital and Returns to Scale
Human Capital, Public Policy, and Growth
Other Determinants of Growth
2
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).
3
The Accumulation of Knowledge
4


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).
5


Knowledge As a By-Product: Learning by Doing.
The Production of Knowledge.
6
Knowledge As a By-Product



Arrow (1962): Knowledge as an unintended byproduct 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.
7

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 - .
8

Growth rate of effective labor:
.
(K/K) +  + n
n: labor force growth rate.

Growth of capital-labor ratio:
k = s(1- )k - [ + n + (1- )]k,
a non-linear, first order differential equation in k.
9
Arrow Equilibrium Capital Effective Labor Ratio
~
k=


{
s(1- )
 + n + (1- )
}
1/(1 - )
k/ < 0 :    AL   k 
.
Arrow Steady-State Growth Rates (k = 0):
Capital Stock: gK = ( + n) /(1- )
Output, ALk: gY =( + n) /(1- )
Income per worker, Y/L: ( + n) /(1- )
10
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 negative
relationship.
 No role to savings and investment rates.
11
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.
12
Villanueva (1994):

Productivity,
.
A= (K/L) +  A
13

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, via implicit function theorem.
14
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.
15
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18
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.
19
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 =  .
20
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,
~
gK
=
~
gY/L
~
gY
~
~
= n + gA
~
= gK - n = gA

+

gA =
n,
1 - ( + )
~
21
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.
22
Human Capital and
Returns to Scale
23


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.
24
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
25

Dynamics of capital-output ratio, k,
.
k= sK kh - k,
where
=+n+

For h, the human capital-effective labor ratio,
.
h= sH kh - h,
26

The long run equilibrium values of physical and
~
~
human capital are given by k and h, with the
solution (see pages 458-459):
~
k=
~
h=

sH
{
sK1-
{
sK sH1- 


}
}
1/(1 -  - )
1/(1 -  - )
Figure 12.3 and 12.4.
27
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29
Implications
 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.
30
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.
31
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 - ( + )
32

In contrast to Solow-Swan and Mankiw-Romer-Weil,
increases in the savings rate permanently raise the
growth rate of output per capita.
33
Human Capital, Public Policy
and Growth
34




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,
35
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 growth if financed
through a discretionary tax.
36

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.
37
Other Determinants of Growth
38

Other Mechanisms through which government
intervention can directly or indirectly effect growth:
 Fiscal Policy
 Inflation
 Macroeconomic Stability
 Openness to Trade
 Financial Development
 Institutional Factors
39
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.
40
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.
41
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.
42
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.
43

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
44



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.
45
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46

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
47


: 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.
48

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)
49
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 price
signals and increased macroeconomic instability,
by crowding out private investment through the
buildup of domestic public debt.
50
Inflation and Macroeconomic
Stability
51


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).
52



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).
53
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
capital unknown variable. With irreversible
investments, increased uncertainty causes a delay
in investment.
54
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.
55
Larger variety of higher quality, less expensive
intermediate goods available to domestic agents-shifts economy wide productions possibility
frontier outward.
Caveats:
 Scale economies and learning-by-doing of little
importance in raw material production and lowtechnology 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.

56
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
57
investment in firms.
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;
58
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.

59
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.
60