hi, I don't think we should firstly considering of changing into another model; It may be just a problem of estimation, because of serial correlation between the above two regressors. Why not trying to use other estimation methods beyond least squres methods, such as generalized linear least squres methods, or Instrumentural methods;
If this also turns out to be non-working. I think we could then try to change variables, or go to a new model. For changing variables, we could use squared orginal variables; for new model, we may update it with a non-linear regression models. I hope these comments could help some~ Best wishes