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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
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