Stochastic Model Solution Inversion
Posted: Sat Apr 26, 2014 11:44 am
I want to perform the following operation on a model object. Say I have an estimated non-linear model:
y1 = f(y2,x1,x2; coefs)+u1
y2 = g(y1,x1,x2; coefs)+u2
….
Assume x1 is a simple exog vble, in my case a parameter times a trend: x1=gamma*t.
But now assume I want to solve the previously estimated model so that the composite variable x1 is endogenous. It’s like inverting the (albeit non-linear) model so as to solve what x1 would look like against the actual data. In so doing I can see the plausibility for my original assumption about x1 (namely that it was a scaled trend).
Is it possible to do this? The manual doesn’t quite touch on this (I think?!). If I can do this, can I simulate the (inverted) model in such a way that I can do all the normal things I like, e.g., stochastic simulation with coefficient uncertainty so that when I derive the solved x1 I can also get confidence bounds around it?
Thanks!
y1 = f(y2,x1,x2; coefs)+u1
y2 = g(y1,x1,x2; coefs)+u2
….
Assume x1 is a simple exog vble, in my case a parameter times a trend: x1=gamma*t.
But now assume I want to solve the previously estimated model so that the composite variable x1 is endogenous. It’s like inverting the (albeit non-linear) model so as to solve what x1 would look like against the actual data. In so doing I can see the plausibility for my original assumption about x1 (namely that it was a scaled trend).
Is it possible to do this? The manual doesn’t quite touch on this (I think?!). If I can do this, can I simulate the (inverted) model in such a way that I can do all the normal things I like, e.g., stochastic simulation with coefficient uncertainty so that when I derive the solved x1 I can also get confidence bounds around it?
Thanks!