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From |
Kit Baum <baum@bc.edu> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: identification status of a linear simultaneous equations system |

Date |
Sun, 7 Oct 2007 12:14:09 -0400 |

Thomas said

Kit, thanks a lot for your reply!

Isn't the question of identification independent from the question of

whether I chose a system estimator or an equation-by-equation estimator?

When I use the option 3sls with that model,

reg3 (w tenure schooling male) (tenure w) (schooling pubsec male expft)

if welle==2000, 3sls

it's the same, Stata estimates the model and doesn't complain.

I understand that in the first equation there are 2 endogenous variables

on the right hand side (tenure and schooling), and that there are 2

exogenous variables

excluded from the first equation. But should the 2 instruments really be

used as instruments for the tenure variable in that particular model? I

am wondering, because they are explicitly excluded from the tenure

equation. And that exclusion from the tenure equation causes zeros in

the (A3, A5) matrix in Greene 2003, page 393, which make the matrix not

full rank and make the rank condition analyzed by Greene fail. If I

recall right, in Greene there is also a rule of thumb for

identification: "Each equation should have its own exogenous variable

excluded from the other equations." And this is violated for the first

and second equation in this model.

As I understand it, failing the rank condition analyzed by Greene means

that there are different sets of structural parameters consistent with

the same reduced form.

Does that mean that I should worry about whether the structural

estimates of the above model are unique? And does it imply that before

estimating a system of equations by 3sls, one should always check

identification of the model, maybe at least by Greene's rule of thumb

mentioned above?

Yes, you are absolutely right, working with a simultaneous system without checking this condition is

dangerous. The issue does not arise in limited-information (single equation) estimation, for there the

only concern is that the rank of the instrument matrix is sufficient. But in that context we don't know where

else in the system the instruments do (or do not) appear.

Stata's -reg3- should check this condition and warn the user if the condition is not satisfied. As -reg3- does not (yet) do that (perhaps StataCorp developers will consider it!) I have written -checkreg3-, which I believe is capable of determining whether the conditions laid out in Greene's and Wooldridge's examples are satisfied:

TITLE

'CHECKREG3': module to check identification status of simultaneous equations system

DESCRIPTION/AUTHOR(S)

checkreg3 checks whether the coefficients of a linear

simultaneous equations system to be estimated by reg3 are

identified.

KW: simultaneous system

KW: reg3

KW: identification

Requires: Stata version 9.2

Distribution-Date: 20071007

Author: Christopher F Baum, Boston College

Support: email baum@bc.edu

INSTALLATION FILES (type net install checkreg3)

checkreg3.ado

checkreg3.hlp

------------------------------------------------------------------------ ---------

(type -ssc install checkreg3- to install)

The routine requires Mata, thus the requirement for Stata 9.2.

Thanks to Thomas for cogently explaining this issue and citing the relevant literature.

Kit Baum, Boston College Economics and DIW Berlin

http://ideas.repec.org/e/pba1.html

An Introduction to Modern Econometrics Using Stata:

http://www.stata-press.com/books/imeus.html

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