I have the following question:
The equation from part c:
My Solution
I'm thinking of solving this problem using the RESET test so something along the lines of:
$$yl_t = -0.027 + 0.537 kl_t + \hat{y}_t^2o$$
where $o$ is the coefficient.
That being said I know this is wrong, I have absolutely no idea on how to approach this problem.
Ok, now I see. So, in point (c), you have:
$$log(y) = \beta_{0} + \beta_{k}log(k) + \beta_{l}log(l) + \varepsilon$$
and estimate it: we will call this the $unrestricted$ model, since we aren't making any restriction on the parameters. We find that $SSE_{unrest}$ $=$ $0.085$
Let's now move to the $restricted$ model. In Economic terms, you are assuming constant returns to scale: have $\beta_{k}$ $+$ $\beta_{l}$ $=$ $1$. Working out the algebra we obtain the model you have in point (e):
$$log(\frac{y}{l}) = \beta_{0} + \beta_{kl}log(\frac{k}{l})$$.
We know that, for this model, $SSE_{rest}$ $=$ $0.115$. Considering that we have, de facto, put one only restriction, the F Test will be:
$$F = \frac{\frac{SSE_{rest} - SSE_{unrest}}{1}}{\frac{SSE_{unrest}}{n - k}} = \frac{0.115 - 0.085}{\frac{0.085}{n - 3}}$$
where $n$ is the sample size. You then have to check whether the computed F is larger or not of $F_{1, n - 3}$. If yes, Reject the hypothesis $\beta_{k}$ $+$ $\beta_{l}$ $=$ $1$.