Should we remove non-significant lagged variables in ARDL?

Question

One video on youtube removes non-significant lags from the ARDL regression while others keep all the non-significants too and rely on Wald test for effects. My questions are as follows:

1. While using multiple regression analysis we use General to Specific procedure and keep dropping non-significant variables to reach at a good model with all significant coefficients. In Eviews 9 there is no such option, we have to drop the whole variable alongwith all its lags. What do you suggest ? Should I keep all the significant as well as non-significant lags?

2. If GDP(-1) is significant, GDP(-2) is not significant and GDP(-3) is again significant and theoretically only GDP(-1) should effect the Dependent Variable.Then how should I interpret the results i.e how should interpret the non-significant lags.

3. Researchers using ARDL do not report the ARDL regression results, they just report the long run normalized coefficients which are of course without lags. Why? How wold we show that lag 1 is affecting the output and not other lags suggested by AIC etc.

Answer 1

In that case I think you should keep all the variables, because at the end being non-significant means parameter of that variable has on effect on dependent variable. So if you have enough observations and do not suffer from over-parameteratizion it's ok to keep all variables.