st: Reverse Causation Solutions?

[Mai Anh Ngo <maianh.ngo@gmail.com>]

I have a problem of reverse causation in my regression model for a
panel data set with unobserved heterogeneity. My regression equation
is as follows:

Y1it = a + b*Y2it + c*Xit + ui + eit

where Y1it and Y2it are binary and it is suspected that there is
possibly reverse causation from Y2it to Y1it or from Y2i,t-1 to Y1it

I could not find a good instrument to use the instrumental variable
method and I am thinking of estimating a bivariate model:

Y1it = a + b*Y2it + c*Xit + ui + eit

Y2it= d +e*Y1it  +  f*Zit + vi +  rit

where the error term eit and rit are allowed to be correlated.
However, I was told that in general, a bivariate model would not solve
reverse causation/simultaneity problem. Is that true?

What are the methods that can be used to solve reverse causation or
simultaneity problem?  Thank you for your consideration.

Mai Ngo
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