conceptual question - shifting prices by a constant

[nelsonsunuwar]

Hi,

Thank you for the package, I have played around with it and it works great.

One question thinking more about the mapping to the BLP model.

My understanding is that when prices (pj) just enter linearly in your utility, we can shift prices as we please as only the differences should matter. This is e.g., why we can replace (y - pj) with (-pj), where y stands for income (let's say constant across individuals).

But this need not hold in the FRAC equation, since prices enter non-linearly (quadratic).

Do you have sense whether this is correct and if so what this implies for FRAC?

Best,
Nelson

[jamesbrandecon]

Thanks for trying the package and sorry for the delay -- not used to getting interactions with my repos.

I think the key conceptual issue here is the distinction between the model and the estimation. FRAC is not an economic model in and of itself, it's an approach to estimation which utilizes an approximation to BLP-style random coefficient models. To your example, FRAC doesn't assume that prices enter the utility function quadratically, it uses a constructed regressor (which includes a quadratic term in prices) in order to estimate the variance of random coefficients.

So, in fact, anything BLP permits is also permitted within FRAC (as long as you're ok with the approximation error!). Does that make sense?