An Extension of the Solow Growth Model That Includes Human

question 2

Essay

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: $\begin{aligned}\widehat { \text { RelPersInc } } = & 0.046 - 5.869 \times \text { gpop } + 0.738 \times S _ { K } + 0.055 \times \text { Educ, } R 2 = 0.775 , \text { SER } = 0.1377 \\& ( 0.079 ) ( 2.238 ) \quad\quad\quad\quad\quad( 0.294 ) \quad\quad\quad( 0.010 )\end{aligned}$
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.
(a)Interpret the results and indicate whether or not the coefficients are significantly different from zero. Do the coefficients have the expected sign?
(b)To test for equality of the coefficients between the OECD and other countries, you introduce a binary variable (DOECD), which takes on the value of one for the OECD countries and is zero otherwise. To conduct the test for equality of the coefficients, you estimate the following regression: $\begin{array} { l } \overline { \text { RelPersInc } } = - 0.068 - 0.063 \times \text { gpop } + 0.719 \times S _ { K } + 0.044 \times E d u c \text {, } \\\begin{array} { l l l } \quad\quad\quad\quad\quad\quad( 0.072 ) ( 2.271 ) \quad \quad\quad\quad\quad\quad( 0.365 ) \quad\quad\quad ( 0.012 )\end{array} \\\\0.381 \times D O E C D - 8.038 \times ( D O E C D \times g p o p ) - 0.430 \times \left( D O E C D \times S _ { K } \right) \\( 0.184 ) \quad\quad\quad\quad\quad (5.366) \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad ( 0.768 ) \\\\+ 0.003 \times ( D O E C D \times E d u c ) , R ^ { 2 } = 0.845 , S E R = 0.116 \\\quad\quad\quad\quad\quad( 0.018 ) \\\end{array}$
Write down the two regression functions, one for the OECD countries, the other for the non-OECD countries. The F- statistic that all coefficients involving DOECD are zero, is 6.76. Find the corresponding critical value from the F table and decide whether or not the coefficients are equal across the two sets of countries.
(c)Given your answer in the previous question, you want to investigate further. You first force the same slopes across all countries, but allow the intercept to differ. That is, you reestimate the above regression but set ?_{DOECD × gpop} = ?_{DOECD ×}
$S _ { K }$ = ?_{DOECD × Educ} = 0. The t-statistic for DOECD is 4.39. Is the coefficient, which was 0.241, statistically significant?
(d)Your final regression allows the slopes to differ in addition to the intercept. The F-statistic for ?_{DOECD × gpop} = ?_{DOECD ×}
$S _ { K }$ = ?_{DOECD × Educ} = 0 is 1.05. What is your decision? Each one of the t-statistics is also smaller than the critical value from the standard normal table. Which test should you use?
(e)Looking at the tests in the two previous questions, what is your conclusion?

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