I wish to model a function with the nl command:
Code:
nl (Y = {b1}*X2^{b2}*X3^{b3})
or
Code:
nl (lnY = {b1}*X2^{b2}*X3^{b3})
I've been trying to run this function with some simulation data for a small population of n=30, but I keep getting bizarrely massive values for Y no matter what I choose for X2 and X3. Does any one have any suggestion for how to create some data that will help improve my intuition on the inner workings of this model? Or even how to perform a Monte Carlo simulation of this type fo common function (I believe it's used for CobbDouglass Production Functions)

Here's how I tried to generated values for my non-linear function with additive error term.

Code:
set obs 30
egen X2 = seq(), from(0) to (6) block(1)
egen X3 = seq(), from(2) to(7) block(1)
sum X2 X3
set seed 98034
generate u = runiform()
list X2 X3 u

generate Y = X2*X3^(X2)*X3^(X3)+u

* not sure if i need to do this:
generate lnY = ln(Y)
Thank you as always for your support.