1

Human Capital and Solow Model

Econ 4960: Economic Growth

Human Capital and Growth !   Modify the Cobb-Douglas prod func:

!   u is the time investment, and ψ is the returns-to education !   Per-person output is: !   Solve for BGP as before to get:

!   So, countries can also have different relative incomes if they have different (human capital) education levels

Econ 4960: Economic Growth

( )1 , uY K AH where H e Lαα ψ−= =

( )1y k Ah αα −=

( )( )

( )/ 1

* sy t hA tn g d

α α−⎛ ⎞

= ⎜ ⎟+ +⎝ ⎠

2

Understanding Relative Income Levels

!   Define the relative income of a country:

!   Obtain estimates of all the variables in this equation and assume that A is the same across countries (Bad assumption: will relax it later!)

Econ 4960: Economic Growth

( )/ 1**

*

ˆ ˆ ˆˆˆUS

y sy h Ay x

α α−⎛ ⎞≡ = × ×⎜ ⎟⎝ ⎠

Evaluating the Solow Model with Human capital

Econ 4960: Economic Growth

3

!   The model does well for rich countries and poorly for poor countries.

!   So accounting for differences in savings, population growth, etc., does not take us very far for understanding why poor countries are poor.

!   Let’s cheat a bit. Let’s calculate the differences in TFP that is necessary to justify the observed data.

!   That is, using the production function for each country calculate its A:

!   Using data on output, capital and education, we can do this.

Econ 4960: Economic Growth

( )/ 1y yAk h

α α−⎛ ⎞ ⎛ ⎞= ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

Relative A across Countries

Econ 4960: Economic Growth

4

Explaining World Income Distribution !   Relative A increases with GDP per person: that is poor countries

also have low A. !   Some countries have (SGP, ITA..) have extremely high A,

suggesting that we may need to be more careful in measuring variables.

!   With these caveats in mind, differences in A, especially in poor versus rich countries is astounding.

!   The difference between top and bottom is 30-fold. (s/x) explains about 2-fold, and education accounts for another 2-fold. So the remaining 8-fold is coming from A!

!   Some recent studies suggest focusing on standardized tests for measuring educational attainment instead of years of schooling. They find the role of A to be smaller.

Econ 4960: Economic Growth

Hall and Jones (1999, QJE)

Econ 4960: Economic Growth

5

Hall and Jones (1999, cont’d)

Econ 4960: Economic Growth

Human capital and the Wealth of Nations

Econ 4960: Economic Growth

6

Quantity versus Quality of Education

Econ 4960: Economic Growth

Differences in Relative Price of Capital

Econ 4960: Economic Growth