I'm very confused about if it's legitimate to include a lagged dependent variable into a regression model. Basically I think if this model focuses on the relationship between the change in Y and other independent variables, then adding a lagged dependent variable in the right hand side can guarantee that the coefficient before other IVs are independent of the previous value of Y.
Some say that the inclusion of LDV will biase downward the coefficient of other IVs. Some others say that one can include LDV which can reduce the serial correlation.
I know this question is pretty general in terms of which kind of regression. But my statistical knowledge is limited and I really have a hard time figuring out if I should include a lagged dependent variable into a regression model when the focus is the change of Y over time.
Are there other approaches to deal with the influence of Xs on the change of Y over time? I tried different change scores as DV as well, but the R squared in that situation is very low.