An extension of the Solow growth model that includes human capital in addition t

Question

An extension of the Solow growth model that includes human capital in addition to physical capital, suggests that investment in human capital (education) will increase the wealth of a nation (per capita income). To test this hypothesis, you collect data for 104 countries and perform the following regression: RelPersInc= 0.046-5.869 x gpop + 0.738 × SK + 0.055 × Educ (0.079) (2.238) (0.294) (0.010) R2-0.775, SER 0.1377 where RelPersInc is GDP per worker relative to the United States, gpop is the average population growth rate, 1980 to 1990, SK is the average investment share of GDP from 1960 to 1990, and Educ-is the average educational attainment in years for 1985. Numbers in parentheses are for heteroskedasticity-robust standard errors.

Explanation / Answer

Given that the regression equation is,

RelPersinc = 0.046 – 5.869*gpop + 0.738*SK + 0.055*Educ

SE(intercept) = 0.079

SE(gpop) = 2.238

SE(SK) = 0.294

SE(Educ) = 0.010

R2 = 0.775

SER = 0.1377

Number of countries (n) = 104

Interpretation of intercept and slope :

Intercept = 0.046

Slope = -5.869 , 0.738 and 0.055

If we take gpop, SK and Educ are 0 then RelPersinc = 0.046

If we fix SK and educ then one unit change in gpop will be 5.869 unit decrease in RelPersinc.

If we fix gpop and educ then one unit change in SK will be 0.738 unit increase in RelPersinc.

If we fix gpop and Sk then one unit change in Educ will be 0.055 unit increase in RelPersinc.

Now her e we have to test the hypothesis that,

H0 : B = 0     Vs       H1 : B not= 0

Where B is population slope for independent variable.

Assume alpha = level of significance = 0.05

Test statistic follows t-distribution with n-2 degrees of freedoms.

The test statistic is,

   T = b / SE

Where b is sample slope

And SE is standard error of the estimate.

And we have to find P-value for taking decision.

P-value we can find in excel.

Syntax :

=TDIST(x, deg_freedom, tails)

Where x is absolute value of test statistic.

Deg_freedoms = n-2 = 104 – 2 = 102

Tails = 2

Here we can see that all the three variables have P-value less that 0.05 (alpha).

Reject H0 at 5% level of significance.

COnclusion: ALl the variables are significant.

Here we have to test ,

H0 : Bj = 0       Vs         H1 : Bj not= 0

Where Bj is population slope.

Here Test statistic (F) = 6.76

And P-value = 0.000

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : Atleast one of the slope is differ than zero.

coefficients SE t P-value 0.046 0.079 0.58 0.5617 -5.869 2.238 -2.62 0.0101 0.738 0.294 2.51 0.0136 0.055 0.01 5.50 0.0000

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