Chapter 4. “Second Generation” growth models The role of human capital in economic growth ...
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Transcript of Chapter 4. “Second Generation” growth models The role of human capital in economic growth ...
Chapter 4
“Second Generation” growth models
The role of human capital in economic growth
Determinants of technological progress
Externalities and growth
Measuring Technological Progress: Total Factor Productivity (TFP)
Basic models of growth assume that production takes place through the use of physical capital and unskilled labor
By investing in education and training, the labor force acquires a set of skills over time. This is the idea of human human capitalcapital.
Physical capital can then be complemented by human capital (skilled labor) in the process of output creation.
Suppose households have two forms of savings: Physical capital (buying shares, stocks,
bonds, etc) Investing in education (to acquire skills)
Households decide on the composition of savings between physical and human capital
Production takes place via the use of the stocks of physical capital (k) and human capital (h):
Households invest a fraction s of output to physical capital and a fraction q to human capital:
1y k h
( ) ( )
( ) ( )
k t sy t
h t qy t
The rate of growth of physical and human capital can be expressed as:
1
where, is the ratio of
human to physical capital in the long run
ksr
kh
qrh
r
In the long-run, both human and physical capital must grow at the same rate (balanced growth). Then, we get
The long-run balanced growth rate for the economy is then given by
savings in human capitalsavings in physical capital
qrs
1k hs q
k h
There may be diminishing returns to physical and human capital individually, but when combined, there could be constant returns constant returns to the two reproducible factors of production
This makes per-capita output grow in a sustained fashion in the long-run
This growth is endogenousendogenous, since it is determined from within the model (by household choices)
Countries that have similar savings and technological parameters can grow at the same rate in the long-run, but there may not be any convergence in their per-capita incomes Weaker form of convergence: even
similar countries can have different levels of per-capita income in the long-run
This model helps explain why rates of return on physical capital may not be high in poor countries Poor countries have a shortage of skilled
labor, which drags down the return to physical capital
Barro (1991) tested for conditional convergence using school enrolment data (primary and secondary levels) as a proxy for human capital. His main findings were: There is evidence for conditional
convergence after controlling for human capital▪ Poor countries do grow faster once human capital
is accounted for▪ Countries with more human capital grow faster
once per-capita income is controlled for
Technical progress is not exogenous as in the Solow model, but an outcome of human behavior: R&D expenditures by firms Investment in higher education
(research at universities) Government investment in Science &
Technology “Learning by doing”
Technical progress can be of two types: Deliberate:Deliberate: conscious diversion of current
resources to the production of newnew consumption and investment goods ▪ Benefits are internalized by innovator
Diffusion: Diffusion: transfer of knowledge across firms or countries▪ “outsiders” can profit from new technology▪ Create foundation for future innovations and
research▪ Benefits accrue through “externalities”
Externalities refer to the unintended consequences of actions and decisions taken by individuals, firms, or the government
These consequences can be PositivePositive (knowledge creation, government provision of
public goods like highways and ports, etc) and enhance productivity of a larger group of economic agents, or
NegativeNegative (pollution or highway congestion), and hurt overall productivity.
Positive externalities are also sometimes referred to as complementaritiescomplementarities: when the actions of one agent prompt others to take similar actions.
Consider an economy with many firms, each equipped with a production function:
where, E(t) denotes the overall level of productivity
Assume that E(t) is a positive externality generated by capital accumulation by all firms in the economy
Let
1( ) ( ) ( )Y E t K t L t
( ) ( )E t AK t
( ) denotes the average stock of capital in the economyK t
Then, the production function for each firm is given by
How does this externality affect capital accumulation decisions by firms? An individual firm, being a small player, takes the
average stock of capital as exogenously given The firm then underestimates the true(social)
return to capital private return is less than social return
Each firm underinvestsunderinvests in capital Economic growth is sub-optimalsub-optimal
1( ) ( ) ( ) ( )Y t AK t K t L t
Underinvestment by firms provides a rationale for government intervention
To see this, consider the presence of a social plannersocial planner, who can internalizeinternalize all externalities
The planner is not concerned with productivity of an individual firm, but with overall (or average) productivity
The planner therefore sets in the production function
The planner’s (social) production function is
The planner sets social return on capital to its private return
Ensures optimal investment in capital Generates the “first-best” or “Pareto Optimal”
growth rate for the economy
( ) ( )K t K t
1( ) ( ) ( )Y t AK t L t
Therefore, the existence of externalities provide a rationale for government intervention in the growth process Subsidize the accumulation of capital to
increase the growth rate
Note also that production exhibits increasing returns at the level of society, even though there are diminishing returns for individual firms Per-capita economic growth tends to accelerate
over time in the presence of externalities This view was proposed by Romer (1990)
How should we measure technical progress?
Consider the production function in functional form:
Totally differentiate both sides, assuming E is constant:
The above can be expressed as:
( , , )Y F K L E
. .F F
dY dK dL MPK dK MPL dLK L
. .dY MPK K dK MPL L dLY Y K Y L
This leads to
where,
K L
dY dK dLY K L
.share of capital income in total income
.share of labor income in total income
K
L
MPK KY
MPL LY
The growth rate of output should be explained by the sum of the growth rates of capital and labor, weighted by their income shares
If we insert actual data and the right-hand side does not equal does not equal the left-hand side, what can we infer?
Our assumption of a constant level of productivity, E, was wrong
K L
dY dK dLY K L
If , then it must be the
case that the difference between the LHS and RHS represents the growth of porductivity
Then, we can define total factor total factor productivity (TFP) productivity (TFP) growth as
TFP growth is thus calculated as a residualresidual
K L
dY dK dLY K L
K L
dY dK dLTFPG
Y K L
To correctly estimate TFP growth we must Control for all changes in factors of
production▪ Labor force participation, rural-urban migration,
sectoral shifts, changes in education, etc Assume that all factors are paid their
marginal products▪ If industries are not competitive, then we
cannot measure TFP growth