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?

Question

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?

Quizplus · Accepted Answer

The Answer of 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?

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

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