Question

You have collected data for 104 countries to address the difficult questions of the determinants for differences in the standard of living among the countries of the world. Your model has the relative personal income (RelPersInc) determined by the saving rate (SK) and population growth rate (n). To test the predictions of this growth model, you run the following regression:

= 0.339 – 12.894 × n + 1.397 × SK,      R2=0.621

                  (0.068) (3.177)     (0.229)

Numbers in parentheses are the standard errors.

1. Calculate the t-statistics and test whether or not each of the population parameters are significantly different from zero.

2. Calculate the overall F-statistic for the regression. Test the null hypothesis that that all the slope coefficients are equal to zero at the 5% level.

You remember that human capital in addition to physical capital also plays a role in determining the standard of living of a country. You therefore collect additional data on the average educational attainment and add this variable (Educ) to the above regression. This results in the modified regression output:

= 0.046 – 5.869 × n + 0.738 × SK + 0.055 × Educ,    R2=0.775,

                      (0.079)   (2.238)      (0.294)           (0.010)

3. How has the inclusion of Educ affected your previous results?

4. Perform a test to find out if it is worth keeping Educ in the model at the 5% level.

Answer 1

Que.1

Test statistic for growth rate:

Test statistic for saving rate :

Degrees of freedom for t = n-3 = 104 - 3 = 101

Critical value = 1.984 (This value is obtained by using R software using command qt(0.975,101))

Since t value for both the variables are greater than critical value,hence we reject null hypothesis in both the cases and conclude that both variables are statistically significant.

Que.2

Critical value = 3.086

This value is obtained by using R software using command qf(0.95,2,101)

Since cal .F is greater than critical value hence we reject null hypothesis and conclude that all slope coefficient are statistically significant at 5% level of significance.

Que.3

i . Adding education variable increase R2 by ( 0.775 - 0.621 =) 0.154. It means this variable will explain 15.4% more variation in the personal variable.

ii.

Degrees of freedom = 100

Critical value= 1.984

Since cal. t is greater than critical value we reject null hypothesis and conclude that variable education is statistically significant.