(Continuation from Chapter 4, Number 6)The Neoclassical Growth Model Predicts

(Continuation from Chapter 4, number 6)The neoclassical growth model predicts
that for identical savings rates and population growth rates, countries should
converge to the per capita income level.This is referred to as the convergence
hypothesis.One way to test for the presence of convergence is to compare the
growth rates over time to the initial starting level.
(a)The results of the regression for 104 countries were as follows: $$\begin{aligned}\widehat { g 6090 } = & 0.019 - 0.0006 \times \operatorname { RelProd } _ { 60 } , R ^ { 2 } = 0.00007 , S E R = 0.016 \\& ( 0.004 ) ( 0.0073 )\end{aligned}$$ where $g 6090$ is the average annual growth rate of GDP per worker for the $1960 -$ 1990 sample period, and $\operatorname { RelProd } _ { 60 }$ is GDP per worker relative to the United States in 1960. Numbers in parenthesis are heteroskedasticity robust standard errors. Using the OLS estimator with homoskedasticity-only standard errors, the results
changed as follows: $$\begin{aligned}\widehat { g 6090 } = & 0.019 - 0.0006 \times \operatorname { RelProd } _ { 60 } , R ^ { 2 } = 0.00007 , S E R = 0.016 \\& ( 0.002 ) ( 0.0068 )\end{aligned}$$ Why didn't the estimated coefficients change? Given that the standard error of the
slope is now smaller, can you reject the null hypothesis of no beta convergence?
Are the results in the second equation more reliable than the results in the first
equation? Explain.