Question

6) 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. You recall from your macroeconomics lectures that the neoclassical growth model suggests that output per worker (per capita income) levels are determined by, among others, the saving rate and population growth rate. To test the predictions of this growth model, you run the following regression: RelPersinc = 0.339 - 12.894 x n +1.397 x SK, R2 = 0.621, SER -0.177 (0.068) (3.177) (0.229) where RelPers Inc is GDP per worker relative to the United States, n is the average population growth rate, 1980-1990, and SK is the average investment share of GDP from 1960 to 1990 (remember investment equals saving). Numbers in parentheses are for heteroskedasticity-robust standard errors. (a) Calculate the t-statistics and test whether or not each of the population parameters are significantly different from zero. (b) The overall F-statistic for the regression is 79.11. What is your decision on the null hypothesis? (C) 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 in years for 1985, and add this variable (Educ) to the above regression. This results in the modified regression output: RelPersinc =0.046 - 5.869 x n +0.738 SK + 0.055 Educ, R2 = 0.775, SER=0.1377 (0.079) (2.238) (0.294) (0.010)

Answer 1

a)

n = 104

k = 3

df = n-k = 104-3 = 101

For Intercept

t = β0 / Sb0 = 0.339/0.068 = 4.9853

The p-value is < .00001, the result is significant at p < .05.(Use t table or calculator)

For β1

t = β1 / Sb1 = -12.894/3.177 = -4.0585

The p-value is .000098, the result is significant at p < .05.(Use t table or calculator)

For β2

t = β2 / Sb2 = 1.397/0.229 = 6.1004

The p-value is < .00001, the result is significant at p < .05.(Use t table or calculator)

b)

Hypothesis:

H0 : β1 = β2 = 0

Ha : at least one β is not equal to 0

F stat = 79.11

The p-value is < .00001, (Use F table or calculator)

The result is significant at p < .05, Reject H0

There is a significant relationship between dependent and independent variables

c)

Before : R^2 = 0.621 and Standard error = 0.177

After : R^2 = 0.775 and Standard error = 0.1377

R^2 increased and Standard error decreased

R^2 = % of variation in Y variable is explained by Regression

Low standard error gives better regression ("Distance of observed values fall from regression line on average")