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In A Contribution To The Empirics of Economic Growth found here. The authors perform an econometric regression on the Solow-Swan model, they also do a restricted regression to find if the null hypothesis that the coefficient on the log of savings $\hat{\gamma}_1$ is equal and opposite to the coefficient of the log of depreciation $\hat{\gamma}_2$, that is:

$$ \hat{\gamma}_1 = - \hat{\gamma}_2 $$

Where in the Solow model this is:

$$ \hat{\gamma}_1 = \frac{\alpha}{1-\alpha} $$

I see how they calculated the implied $\alpha$, $1.43 = \alpha/(1-\alpha) \Rightarrow \alpha = 0.59 $

But why did they use $ln(s) - ln(n+g+\delta)$? Trying to solve this myself ...

$$ 1.43 = ln(s) - ln(n+g+\delta) \simeq \hat{\gamma}_1 - \hat{\gamma}_2 = 0 $$

$$ = \frac{\alpha}{1-\alpha} + \frac{\alpha}{1-\alpha} = 2 \frac{\alpha}{1-\alpha} $$

Which is too large by factor of 2. Also, and I don't know if I should post this as a separate question is that I have no idea how they calculated the implied $\alpha$ and $\beta$ in the next model which includes schooling as a proxy for measuring human capital.

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