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