# Recursive System

Considering a two equation model:

Equation 1

Trunk=f(Headroom)


In the first step I regress the first equation to get predicted values of Trunk.

Equation 2

Price=f(Trunk_hat, Displacement)


I have performed this in Stata, however I also want a mathematical derivation of this procedure. What is the method to go about it?

• These sorts of things come up a lot in econometrics -- Simultaneous_equations model – Glen_b Mar 12 '14 at 7:36
• The manual entry for a command in Stata (the .pdf or the book, not the help-file, i.e. what you get when you type help something) usually contains a "methods and formulas" section. – Maarten Buis Mar 12 '14 at 11:01

Start with the matrix algebra performed for OLS. The beta estimates in OLS are: $(X'X)^{-1} X'Y$; that multiplied by your $X$ vector will get you the first stage fitted values.