You Have Learned in One of Your Economics Courses That $\widehat {\text { RelPersInc }}$

question 45

Essay

You have learned in one of your economics courses that one of the determinants of per capita income (the "Wealth of Nations")is the population growth rate. Furthermore you also found out that the Penn World Tables contain income and population data for 104 countries of the world. To test this theory, you regress the GDP per worker (relative to the United States)in 1990 (RelPersInc)on the difference between the average population growth rate of that country (n)to the U.S. average population growth rate (n_us )for the years 1980 to 1990. This results in the following regression output: $\widehat {\text { RelPersInc }}$ = 0.518 - 18.831 × 18.831 × (n - n_us), R² = 0.522, SER = 0.197
(a)Interpret the results carefully. Is this relationship economically important?
(b)What would happen to the slope, intercept, and regression R² if you ran another regression where the above explanatory variable was replaced by n only, i.e., the average population growth rate of the country? (The population growth rate of the United States from 1980 to 1990 was 0.009.)Should this have any effect on the t-statistic of the slope?
(c)31 of the 104 countries have a dependent variable of less than 0.10. Does it therefore make sense to interpret the intercept?

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Definitions:

Effective Rate

The actual interest rate of an investment or loan, taking into account the compounding of interest.

Effective Rate

The real rate of interest earned or paid on an investment or loan in a specified period, considering compounding.

Monthly Compounded

Refers to the process of adding interest to the principal sum of a loan or deposit, recalculated on a monthly basis. This is a repeat of Compounded Monthly with a new definition focusing on recalculating interest increase.

Compounded Monthly

Compounded monthly refers to the process where the interest earned on an investment is added to the principal sum each month, causing the principal amount to grow at an increasing rate.