# st: RE: two-equation model with censored and binary dependent variables.

 From Ricardo Henriquez To statalist@hsphsun2.harvard.edu Subject st: RE: two-equation model with censored and binary dependent variables. Date Fri, 27 Jun 2003 12:36:05 -0400

```Before considering the third issue you mention, your model could be
described as follow:

Y1 = a1X1 + B1Y2 + e1		(1)

Y2*= a2X2 + e2			(2)

where,
Y1 is censored at zero
Y2=1 if Y2*>0
Y2=0 otherwise

1) To my knowledge this model is exactly the same as Model 5 described by
Maddala (1983 (pp. 120-121). This is a two-equation model which is estimated
using a two-stage procedure. Since your dependent variable is censored at
zero (left or right), you should use in the second stage a tobit censored
model (tobit). For the first stage estimation of your independent endogenous
binary variable (Y2* in our example) you can use probit (why not?). After
probit you just use predict to generate a new variable (Y2hat for instance),
that will be included as an extra variable in your two stage equation (the
one for your censored dependent variable).

2) The model defined by equations (1) and (2) is identified even if the
error terms (e1 and e2) are not independent and X1 includes all the
variables in X2. Also, you can use any set of variables as instruments for
Y2.

3) If I undertand right, what you refer as the third issue is actually how
to deal with simultaneity. In this case the model described by equations (1)
y (2) should be re-written as,

Y1 = a1X1 + B1Y2 + e1		(3)

Y2*= a2X2 + B2Y1 + e2		(4)

This means that additionally you need to get the predicted value for Y1,
from the second stage estimation of Y1, and use this predicted value (Y1hat
for instance)in your first stage estimation of Y2. However, here you surely
will face a problem of identification. I suggest you to check carefully
chapter 8 of Maddala (1983) to see the best way to deal with the
identification problem. Also see chapter 5 in the same book.

I hope this will be useful for you.

Ricardo Henriquez
Chile

-----Mensaje original-----
De: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu]En nombre de Jeff S.
Enviado el: Viernes, 27 de Junio de 2003 10:43
Para: statalist@hsphsun2.harvard.edu
Asunto: st: [matstata@yahoo.com: censored reg w/ binary explanatory var
that needs to be instrumented]

Matt Barens <matstata@yahoo.com> asked me to forward the following to the
list:

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

Hello Statalisters, I have the following problem(s) and I was wondering if
there was a way to deal with this in stata 7 (although if there is a way to
deal with it in stata 8 I would also be interested in finding out how).

I want to do the following analysis. The dependent variable is dollar amount
in checking account. This is censored, because about 15% of the sample has a
missing value since they do not own a checking account. The main explanatory
variable I use and am interested in is whether the person owns a credit card
or not. Nonetheless, there is some potential endogeneity here (e.g. people
who
spend more may both decide to hold a card and have more money in their
checking accounts). I have the following 3 questions:

1. First, I have some variables that I could use to instrument for credit
card
holding. However, it is a binary variable, so normally I would want to do a
probit in the first stage, but I dont think the ivreg command allows for
this.
Do I just forget about probit?

2. Second, how does one do iv analysis in a censored regression?

3. Third, there is one more issue. In order to hold a credit card, you
normally first need to have a checking account (and recall that it is
account
ownership or not that creates the censoring in the regression). So even if
one
solves the above two issues, how do I deal with this additional one?

thank you much for any ideas you might have on this,
matt

--Jeff
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