Hello!

I want to evaluate how sales of a specific product change as its price increases (due to a totally exogenous input reason). In total, I have monthly data from a few hundred stores, spread across the country. I've used xtreg to evaluate the parameters of interest:
Code:
xtreg y  x  x^2  x^3  z  x*z  x^2*x  x^3z  i.month, re vce(cluster id)
I also test (and plot) marginal effects, using the following command:
Code:
xtreg y c.x##c.x##c.x c.z##c.x##c.x##c.x i.month, re vce(cluster id)

test c.xc.x#c.x  c.x#c.x#c.x

margins, a
Code:
t(z=1 x=(1.5(0.1)3)) dydx(x)

marginsplot


I have looked around but haven't found a good answer to the following questions:
  1. Can I run any test to find out if two patterns of marginal effects, for different level of z, are significantly different from each other? (not only at a given value of x, but for all x)
  2. Can I include two margin plots (with different levels of z) in the same graph?

Help would be greatly appreciated!

/Adam