Transcript Slide 1

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 capital.

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):
y  k  h1

Households invest a fraction s of output to physical
capital and a fraction q to human capital:
k (t )  sy (t )
h(t )  qy (t )

The rate of growth of physical and human
capital can be expressed as:
k
 sr1
k
h

 qr
h
where, r is the ratio of
human to physical capital in the long run

In the long-run, both human and physical capital
must grow at the same rate (balanced growth).
Then, we get
q savings in human capital
r 
s savings in physical capital

The long-run balanced growth rate for the economy
is then given by
k h  1
 s q
k h

There may be diminishing returns to physical
and human capital individually, but when
combined, there could be 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 endogenous, 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: conscious diversion of current
resources to the production of new consumption
and investment goods
▪ Benefits are internalized by innovator
 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
 Positive (knowledge creation, government provision of public
goods like highways and ports, etc) and enhance productivity of
a larger group of economic agents, or
 Negative (pollution or highway congestion), and hurt overall
productivity.

Positive externalities are also sometimes referred to as
complementarities: when the actions of one agent prompt
others to take similar actions.

Consider an economy with many firms, each equipped
with a production function:
Y  E (t ) K (t ) L(t )1
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
E (t )  AK (t ) 
K (t ) denotes the average stock of capital in the economy
Then, the production function for each firm is given
by
Y (t )  AK (t )  K (t ) L(t )1
 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 underinvests in capital
 Economic growth is sub-optimal

Underinvestment by firms provides a
rationale for government intervention

To see this, consider the presence of a social
planner, who can internalize all externalities

The planner is not concerned with
productivity of an individual firm, but with
overall (or average) productivity

The planner therefore sets K (t )  K (t ) in the
production function

The planner’s (social) production function is
Y (t )  AK (t )   L(t )1
 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

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:
Y  F ( K , L, E )
 Totally differentiate both sides, assuming E is
constant:
F
F
dY 
dK 
dL  MPK .dK  MPL.dL
K
L
 The above can be expressed as:
dY MPK .K dK MPL.L dL


Y
Y
K
Y
L



This leads to
dY
dK
dL
 K
 L
Y
K
L
where,
MPK .K
K 
 share of capital income in total income
Y
MPL.L
L 
 share of labor income in total income
Y
dY
dK
dL
 K
 L
Y
K
L

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 the left-hand side, what can we
infer?

Our assumption of a constant level of
productivity, E, was wrong

If
dY
dK
dL
 K
  L , then it must be the
Y
K
L
case that the difference between the LHS and RHS
represents the growth of porductivity

Then, we can define total factor productivity (TFP)
growth as
TFPG 

dY  dK
dL 
 K
 L

Y
K
L 
TFP growth is thus calculated as a residual

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