I am working with following panel data linear regression model: y = f(x,y,z) + other control variables. Variables x,y,z have a three -way interactions. Given the literature, I have also used the level and lagged values of these variables. As such I have 2^3 =8 interaction terms. Should I run various nested models with the control terms and choose the model with minimum AIC and BIC criteria? Actually, some of these interaction terms make no theoretical sense and I fear that such terms would imply a specification bias. Kindly advise.

Thanks in advance.