My First Model


New Member

I am doing a Master's and I am at the dissertation stage, and have to write and test a model empirically.

However I am not sure about the functional form:

Y = A(a)^Z + B(b/c)^Y + D(d)^X

I want to estimate the effect of a on y. However I don't think the effect will have an elasticity of 1, therefore I have added a Z power. b/c is a ratio that I think also acts on y, so I have included it as a control, and again I am not sure the elasticity is 1. d is another control.

If I put it into this form:

lnY = ln(A) + Zln(a) + ln(B) + Yln(b/c) + ln(D) + Xln(d)

And then regress it in stata, I will presumably get this:

lnY = B0 + B1ln(a) + B2ln(b/c) + B3ln(d)

Will the coefficients on these be the elasticities of each term? I think so because it is the percentage change of each with the others' effects controlled for.

If this is correct, once I have found Z, Y and X, can I just power the original a, b/c, and d terms, and then run a regression on these new terms a^Z, (b/c)^Y, d^X, to find the true effects A, B and D, accounting for the elasticity?

I have not seen papers do this before so I don't think this is correct - however intuitively it seems to be right - do I need to "control" for the elasticity at all this way?
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Ambassador to the humans
I the way you got from your original model to the log version was to take the log of both sides then keep in mind that log(a+b) doesn't equal log(a) + log(b)