Using the Energy Data given in Table 3.4, corrected as in problem 16 part (d), is it legitimate to reverse the form of the equation?

log(RDGP) = γ + δlog(En) + 

(a) Economically, does this change the interpretation of the equation? Explain.

(b) Estimate this equation and compare R2 of this equation with that of the previous problem.

Also, check ifδ = 1/β. Why are they different?

(c) Statistically, by reversing the equation, which assumptions do we violate?

(d) Show thatδ β = R2.

(e) Effects of changing units in which variables are measured. Suppose you measured energy in BTU’s instead of kilograms of coal equivalents so that the original series was multiplied by 60. How does it change α and β in the following equations?
log(En) = α + βlog(RDGP) +u En= α
∗ + β
∗
RGDP + ν
Can you explain why α changed, but not β for the log-log model, whereas both α
∗and β
∗
changed for the linear model?

(f) For the log-log specification and the linear specification, compare the GDP elasticity for Malta and W. Germany. Are both equally plausible?
(g) Plot the residuals from both linear and log-log models. What do you observe?
(h) Can you compare the R2 and standard errors from both models in part (g)? Hint: Retrieve log(En) and log(En) in the log-log equation, exponentiate, then compute the residuals and s. These are comparable to those obtained from the linear model.