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Human Capital and Solow Model

Econ 4960: Economic Growth

Human Capital and GrowthModify the Cobb-Douglas prod func:

u is the time investment, and ψ is the returns-to educationPer-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 Laa y-= =

( )1y k Ah aa -=

( )( )

( )/ 1

* sy t hA tn g d

a a-æ ö

= ç ÷+ +è ø

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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

a a-æ öº = ´ ´ç ÷è ø

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

a a-æ ö æ ö= ç ÷ ç ÷è ø è ø

Relative A across Countries

Econ 4960: Economic Growth

4

Explaining World Income DistributionRelative 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