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


From   "Millimet, Daniel" <millimet@mail.smu.edu>
To   <statalist@hsphsun2.harvard.edu>
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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