st: RE: 2 limit tobit in system of demand equations

 From "Millimet, Daniel" To Subject st: RE: 2 limit tobit in system of demand equations Date Tue, 3 Jun 2003 14:40:21 -0500

```Even if such a model exists in STATA, the model you propose, I believe, is not correct.  There is a fairly substantial literature on estimating demand systems with binding non-negativity constraints (and, in your case, apparently binding upper constraints as well).  The problem is that when an observation is at such a corner solution, the relevant RHS variable is no longer the market price, but the shadow price.  In addition, there is a statistical issue that arises in such a model referred to as coherency.  See the paper on my website (which is not published for a list of references in this area: http://faculty.smu.edu/millimet/pdf/corners.pdf).

Dann

-----Original Message-----
From: Brunetti Mike [mailto:bruno49_99@yahoo.com]
Sent: Tue 6/3/2003 2:25 PM
To: statalist@hsphsun2.harvard.edu
Cc:
Subject: st: 2 limit tobit in system of demand equations

Stata users:

I was wondering if there was a command in stata, or
possibly, an .ado file that can estimate a system of
demand equations with censoring on both sides.
Specifically, I am trying to estimate a system of 2
demand equations which are censored at 0 and 1.

I know that I can estimate a single equation using the
“tobit” command but how can I estimate two equations
simultaneously?

Here is the model I would like to estimate:
For 3 goods the observed expenditure share on each is:
C, S, H

C* and S* represent the desired expenditure share on
each good:
C*=Xb1+e1
S*=Xb2+e2
Where X is a matrix of variables, b1 and b2 are
coefficients, and e1 and e2 are errors.

The system is defined as:
C=      0       if C*<=0
C*      if 0<C*<1
1       if C*>1

S=      0       if S*<=0
S*      if 0<S*<1-C
1-C     if S*>1

H=1-C-S

The equations for C and S are each two limit tobits.
But estimating this system simultaneously is
complicated.  Any help or suggestions would be greatly
appreciated.

Thanks a lot.
Mike

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