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st: creating polynomial expansion

From   "R.E. De Hoyos" <>
To   <>
Subject   st: creating polynomial expansion
Date   Mon, 22 May 2006 21:39:56 +0100

(Note: sorry if you get this twice)


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).

Rafael E. De Hoyos
Faculty of Economics
University of Cambridge
CB3 9DE, UK *
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