Dear colleagues,

I am working on 15 years of repeated cross-sectional data. I was wondering whether it is an appropriate strategy to include all interaction terms with higher order time?

reg Y X1##c.T X1##c.Tsq X1##c.Tcub Xk##c.T Xk##c.Tsq Xk##c.Tcub ...

Some previous studies just simply used a linear specification, while others also include cubic terms. Suppose that we have 10 IVs, and I am particularly interested in the influences of X1 variables on Y over time. If we control time-varying effects of all other covariates including cubic terms, isn't it over-control? What is the recommended strategy for time specification? If you know a good reference, please share with me. Appreciate that.