RDP 2018-08: Econometric Perspectives on Economic Measurement Appendix D: Some Choices of f (x), {U_tv}, and {quality_tv} are Always Equivalent

In

let g(·) = A + Bf (·), where A and B are scalars.

Then

So choosing any function f (·) is always equivalent to choosing any of its affine transformations A + B(f (·)).

Now let , where C and D are strictly positive scalars.

The identity in Equation (11) becomes

So for {U_tv}, changes to the relativities across t do not matter.