# [R] what do you do for 2SLS or 3SLS

Paul Johnson pauljohn at ukans.edu
Fri Sep 22 20:24:37 CEST 2000

```For 2 or 3 stage least squares, what do you R folks do?

Follow-up question. My student wants to estimate this. 2 variables are
governed by a system of difference equations.  His theory is like so.
Y_t and X_t are
state variables, we want estimates for a, g, b, and h.

X_(t+1) = 1 + a X_t + (a/K)* (X_t)^2 - g Y_t X_t

Y_(t+1) = b Y_t + h* X_t * Y_t

K is perhaps something to estimate, but it seems as though somebody has
a formula we can use to calculate it from data and people just want to
plug in that estimate (?!). I dunno. Seems to me like there should be
another equation for K, but nobody is giving it to me. So I'm willing to
act as if it is known.

He has no error terms, so the first thing I say is he needs some, and so
it becomes:

X_(t+1) = (1 + a) X_t + (a/K)* (X_t)^2 - g Y_t X_t +e1_t

Y_(t+1) = b Y_t + h* X_t * Y_t +e2_t

If he has given me what he actually intends, there is no conventional
simultaneity in the econometric sense, because there is no X_t+1 or
Y_t+1 on the right hand side. THere might be some seemingly unrelated
regression, though, since the error terms could be autocorrelated and
this would induce a correlation between X_t and e1_t, for example.

Well, I've not dug into the methods for estimating this kind of system,
maybe you have some ideas, I'm sure open to them.

--
Paul E. Johnson                       email: pauljohn at ukans.edu
Dept. of Political Science            http://lark.cc.ukans.edu/~pauljohn
University of Kansas                  Office: (785) 864-9086
Lawrence, Kansas 66045                FAX: (785) 864-5700
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