Question

Examine the models in set A and set B. For which set of models is the comparison "straightforward"?

Set A

Y=b1+b2X+u

log (Y) =b1+b2X+u

Set B

Y=b1+b2X+u

Y=b1+b2logX+u

Answer 1

Both these models compare two different specifications to estimate Y. In model A,  the comparison between the two specifications can only be made when the second equation is determined in terms of Y and not logY. For this, we take the antilog on both sides of equation two in model A. We get,

Y = e^{(b1 + b2X + u)}

So, in model 1, the first equation has linear specification while the second equation has exponential specification. This is evident only after making certain changes. So, the comparison is not straightforward.

In model B, we can straightaway say that the first equation has linear specification while second has logarithmic specification. So the comparison is straightforward.