Cross-Country Income Differences

#economics #macro

Oh, Hyunzi. (email: wisdom302@naver.com)
Korea University, Graduate School of Economics.
2024 Spring, instructed by prof. Kang, Minwook.

Solow Model with Human Capital

Unlike previous models, incorporate the Human Capital
Human Capital
- is capital: 1) durable, 2) used in production, and 3) produced
- is rival, unlike the productivity, which is non-rival.
- is intangible, unlike the Physical Capital.
Dynamics of (Physical) Capital directly follows Solow Growth Model Solow Growth Model.

Assumptions

Model Setting

Cobb-Douglas production function.
growth rate of population and technology is given exogenous.
Human Capital is exponential growth by the education years.
Each individual has fixed lifespan , spends years of education and years working.

Production Function

: output, : capital, : effectiveness of labor
: total amount of productive services supplied by workers
- raw labor: skills endowed with individuals
- human capital: acquired skills
: same as Solow Model.
, : where are given exogenous.

Human Capital

: education years per worker
: function of years of education per worker
- : the more education, the more human capital.
- based on micro-economic evidence, suppose

Students and Workers

Total Population at :

: total population at , that equals to the number of people born from to .
: overall population growth rate.
: the number of people born at .

The Number of Workers at :

: years of spending in school
: years of spending to work

Ratio of the number of workers to the total population:

Analysis

Dynamics of

Let the physical capital per unit of effective labor services as then we have taking differentiation with respect to time, which is a similar result to Solow Model Solow Model.

Therefore, from we have thus, at S.S., as , we have

Impact of on Output

Since the change in does not affect

However, the Output per persons thus at S.S., we have If , then we can find the optimal education duration by thus

Empirical Application

Hall and Jones (1999), Klenow and Rodriguez-Clare (1997)

Question: Contribution of physical-capital vs. Contribution of human-capital on GDP per capita.
Regression formula:
- : country index
- : GDP per capita
- : labor's share
- : capital to output ratio
- : average human capital (rival good)
- : knowledge (non-rival good)
Deriving the formula:
- From the production function:
- by subtracting the both sides by , we have
- dividing the both sides by , we therefore have
Estimation results:
- .
- Physical Capital: .
- Human Capital: .
- Productivity: .
Interpretation: Human capital is more important than the physical capital?

Social Infrastructure: Hall and Jones (1999)

Regression formula:
- : country index
- : output per worker
- : social infrastructure
- : other influences on income
Estimation results: