Removing the lag term as a modelling objective

I've presented some arguments and data recently on why the lagged income term in growth models is an indicator that the basic modelling might not be up to much. I would still use a lagged term in my models for the reasons that 1) it captures, badly, the effect of omitted and probably unobservable variables and 2) everyone else uses it. However, removing the lagged term whilst maintaining or improving the basic fit of the model is a good goal for modelling and variable choice.