st: creating polynomial expansion

["R.E. De Hoyos" <redeho@hotmail.com>]

(Note: sorry if you get this twice)


Statalist,

I am interested in running semi-parametric models where the variable of 
interest is regressed against a polynomial expansion of degree "d" of "k" 
variables and all its interactions. Say I want to estimate the following 
model:

   y = f(x,z)

Since I do not know the reduce form of it, as a first approximation, I 
estimate the following model with a polynomial expansion of degree 3:

   y = a + \sum_{i=0}^3 \sum_{j=0}^{3-i} \beta_{ij} x^i z^j + residual

What I am doing is to create the variables: x^2 , x^3 , z^2 and z^3 and then 
I am creating all possible interactions (without including those ones within 
the same variable, e.g. x * x^2). In a second step I regress these variables 
against "y". The procedure gets quite unmanageable with three variables and 
higher order polynomials.

I am wondering if there is a code that generates the variables of the 
polynomial expansion, or if there is a way to program this (perhaps there is 
something in Mata that I am not aware of).

Best,
Rafa
___________________________
Rafael E. De Hoyos
Faculty of Economics
University of Cambridge
CB3 9DE, UK
www.econ.cam.ac.uk/phd/red29/ 
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