Hello,

We are running the following regression:

Y = aX1 + bX2 + cX1#X2 + `XVars' + error

Our dependent variable is a dummy and X1 is endogenous. Hence we are running an IV-probit model using Z as an excluded instrument for X1 . We believe that X2 is exogenous. Our issue arises in the treatment of the interaction of X1 and X2. After having read multiple statalist threads and other help articles we are down to two basic questions that I am listing below:

1. Do we necessarily have to treat X1#X2 (interaction) as endogenous, after having controlled for X1 separately and instrumenting it?

2. We believed the answer to (1) was yes..so we did the following: since X2 is exogenous, we instrumented our interaction term X1#X2 with Z#X2. This is something we came across as a commonly used technique to treat endogenous interactions. So our final regression command looks as follows:

ivprobit Y (X1 X1#X2 = Z Z#X2) `Xvars', vce(cluster district) Note: `Xvars' also includes X2.

When we run this, our model does not converge at all, even after almost 100 iterations. However, as soon as we put the either the interaction term X1#X2 or X1 out of the bracket and not treat it as endogenous, the model converges and gives us statistically significant results and the IVs also perform well. So, all four of the specs below work fine:

a) ivprobit Y (X1= Z Z#X2) X1#X2 `Xvars', vce(cluster district)...............this is overidentified but Converges
b) ivprobit Y (X1= Z) X1#X2 `Xvars', vce(cluster district)...............this also Converges
c) ivprobit Y (X1#X2= Z Z#X2) X1 `Xvars', vce(cluster district)...............this is overidentified but Converges
d) ivprobit Y (X1#X2= Z) X1 `Xvars', vce(cluster district)...............this also Converges

We are at a complete loss as to why the model does not converge the moment we treat both X1 and the interaction as endogenous. Any help or guidance to fix this issue will be very very helpful. We have tried all possible fixes but to no avail. Looking forward to some guidance. Thanks a lot!!