# [Limdep Nlogit List] Use of Other Dependent Variables in Multivariate Probit Equations

William Greene wgreene at stern.nyu.edu
Fri Oct 8 09:17:35 EST 2010

```Professor Savolainen:  The result in Greene (text, 2008) for a recursive bivariate
probit model generalizes to more than two equations. You can fit the model
consistently by MLE if it can be written in the form

y1 = f1(X1)
y2 = f2(X2,y1)
y3 = f3(X3,y1,y2)
etc.

Not all of the preceding ys need appear in every equation. But, the model must
be expressed in a recursive form such as above.  A simultaneous equations model
in which the binary variables are simply mixed in the equations is not identified.
Such a model is "estimable" in that the computer can compute something. But, the
something that it computes is meaningless.

/B. Greene

----- Original Message -----
From: "Peter Tarmo Savolainen" <bb2725 at wayne.edu>
To: limdep at limdep.itls.usyd.edu.au
Sent: Thursday, October 7, 2010 4:21:20 PM GMT -05:00 US/Canada Eastern
Subject: [Limdep Nlogit List] Use of Other Dependent Variables in Multivariate Probit Equations

Hello all,

I am in the process of estimating a multivariate probit model, which includes separate probit models for each of a series of variables that are endogenous in relation to my primary variable of interest.

My question is whether these dependent variables can be included as regressors in the other probit models (i.e., those aside from my primary variable of interest).  For example, say y1 is my primary variable of interest and I am estimating separate equations for y2, y3, and y4 (as each is endogenous with y1).  Can y2 be included in the equations for y3 and y4 without violating any assumptions or compromising the validity of my results (y2, y3, and y4 are exogenous)?

Any insight would be very much appreciated.

Sincerely,

Peter T. Savolainen, Ph.D., P.E.
Assistant Professor
Department of Civil and Environmental Engineering
Wayne State University-Transportation Research Group
5050 Anthony Wayne Drive, EDC 0504.01
Detroit, MI 48202
Phone: (313) 577-9950
Fax: (313) 577-8126
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