For a regression model:
Y = B0 + B1.X + B2.X2 + U,
B2 is the marginal effect on
Now, for a log - log regression model,
log(𝑌) = 𝐵0+ 𝐵1.log(𝑋) + 𝐵2.log(𝑋2) + 𝑈,
B2 is the elasticity Y wrt
In my case, I'd like to estimate elasticity
X2 is not constant. i.e cross elasticity effect.
In my case,
Y is units sold and
X is price and
X2 is available substitutes. The standard interpretation doesn't apply here because there is cross-elasticity effect of
X2, number of available substitutes on
How would I interpret elasticities and cross-elasticities in this case?
ps. I realize price is endogenous and need to add an instrument to deal with problem.