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Re: st: joint effect of two endogenous variables

From   Maarten buis <>
Subject   Re: st: joint effect of two endogenous variables
Date   Tue, 24 Aug 2010 14:18:48 +0000 (GMT)

--- On Tue, 24/8/10, xueliansharon wrote:
> I want to estimate the following model:
> ivreg2 y z1 z2 (y1 y2= z3 z4 z5), cluster(mm)
> However, my instruments z3, z4 and z5 don't have enough
> independent variations (i.e.we don't have instruments that are
> correlated to y1 but not correlated to y2, or just correlated 
> to y2 but not correlated to y1, z3, z4 and z5 all affect both
> y1 and y2) and thus the effects of y1 and y2 on the dependent
> variable y can't be isolated, so I want to compute and test the
> significance of the joint effect of y1 and y2, i.e. the
> effect on dependent variable when both y1 and y2 increase by 1
> unit. Does anybody know how to realize this idea? 

The first thing that comes to mind is that you will need to make
sure that the unit of y1 and y2 are equal, if y1 is in seconds and
y2 is in liters, than what does a unit change mean? A common 
approach is to standardize variables, i.e. subtract the mean and
divide by the standard deviation. 

What you could do is constrain the effects to be equal. A quick 
scan of -help ivreg2- gave me the impression that it doesn't
allow for the -constraint()- option. You might be able to use 
an old trick: you can constrain the effects of two variables to
be equal by adding the sum of these two variables to your model.
You can see that as follows. Start with a regular regression:

y = b0 + b1 x1 + b2 x2 + e

we want to constrain b1 and b2 to be equal, so we can write:

y = b0 + b1 x1 + b1 x2 + e
  = b0 + b1 (x1 + x2) + e

So application of this trick to your model would been that 
you generate a new variable y_comb = y1 + y2, and use that
variable instead of y1 and y2. 

However, I don't know much about -ivreg2-, so other people 
who know more about it, will need to confirm that this trick
will have the desired properties before I would recommend 

Hope this helps,

Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen


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