Conditional regression

Hi all,

I am trying to run explanatory regression:

Y = alpha + Beta1*X*I{X.*Y>0}+Beta2*X*I{X.*Y<=0}

where I{} is indicator function

Since dependent variable info is used on the RHS and includes information about the response coefficient sign, all the statistics will be high: t-stats, R2.
How could I test if the coefficients are significant? That is conditioning on the sign is not what makes coefficient significant.


Ambassador to the humans
What exactly is your overall goal? Because in almost all situations it doesn't make sense at all to use the dependent variable in any way as part of your set of predictors.
The goal is not prediction, the goal is explanation. It's smth. similar to mixed regression, but with restriction that response coefficients are of different signs. Question is whether conditioning separates different regimes (both coefficients are significant), or just one regime from the noise (only one coefficient is significant), or X and Y are unrelated (both coefficients are insignificant).