I am running heckprobit regression in stata. The outcome variable determines school choice - government=1 and private =0. The selection equation takes into account whether the child is currently attending education. I have added an exclusion restriction in the selection equation - headedu, which is a dummy variable.
headedu=1 if the household head has completed class 10
The reason I have included this is that a household with an educated head is more likely to send their child to school

On adding this, my main explanatory variable in the outcome equation is positive significant. However, the result changes when I use another exclusion restriction

bpl=1 if the children comes from the lowest consumption expenditure quantile. I justify this by saying that for very low income households, choice of attending school is a more serious concern than school choice.

It would be really helpful, if I get some clarification on what kind of restriction to use.

Thanks in advance

Sayoree Gooptu