Stata regression in multiplication format

[Paul Shlapa]

Dear Experts,

I was always wondering if its possible to have a regression in stata, that would give me an output in form of multiplication. Let me try to explain what i mean:

Standard Stata linear regression:

Y = b0 + b1*Variable1 + b2*Variable2


What i try to achieve is:

Y= b0 * b1*Variable1 * b2*Variable2

The reason: I would like to obtain results for Y in form of factor change instead of additive change.

Additionally, if Variable1 is categorical, how could one obtain coefficient b1 in form of percentage change.

Example:
Variable1 has three categories: Low, Medium, High

Running a regression in format Y= b0 + b1*i.Variable1 + b2*Variable2 gives me result for Variable1: 5 - Low; 20 - Medium and 40 - High. Interpretation, if Variable 1 is Medium than + 15 to final regression result, if High than + 35 in comparison to Low. Could it somehow be if medium Low*4, if High - Low*8

Is all of this even possible?

Sincerely,

Pavlo

[Nick Cox]

The model

Y= b0 * b1*Variable1 * b2*Variable2

doesn't make much sense to me. What are the units and dimensions of each variable and constant? How can you hope to estimate each parameter separately?

Perhaps you are confusing this with multiplication of power functions, which on taking logarithms reduces to

Y = b0 + b1 ln Variable1 + b2 ln Variable2

and can be an appropriate model.

Following what may be called Kolenikov's rule -- from a posting of his some years ago -- every device is named for two economists who did not invent it -- this appears in many guises, such as Cobb-Douglas functions.