i am running instrumental variables estimations. y=f(X,W), and W is
endogenours, so stage one becomes W=f(Z), and stage 2 becomes y=f
(X, Predicted W). My function is aproduction function with
conventional inputs such as fertiliser, seeds, labour and then credit
which is the (W). Must the number of RHS variables in stage one be
the same number as RHS ones in stage two.
George should heed the Statalist FAQ and use informative subject
headings on his postings.
He should read any textbook discussion of instrumental variables /
two stage least squares. He might also find the Baum/Schaffer/
Stillman Stata Journal article useful; a working paper version can be
accessed from http://ideas.repec.org/a/tsj/stataj/v3y2003i1p1-31.html
One does not run the first stage and second stage as separate
regressions. The number of included endogenous variables (one in his
example, W) must be less than or equal to the number of excluded
instruments. His mention of Z does not make clear whether that is a
variable or a matrix of variables. If Z is a single variable, the
equation would be exactly identified via the order condition. It
would be preferable if the equation were overidentified---if Z
contained more than one column---for then Sargan/Hansen tests for
overidentifying restrictions could shed some light on the adequacy of
the instruments.