More General Dynamic Model:

An alternative derivation of the lagged dependent variable model, which allows for the system dynamics and disturbance dynamics to differ, is given  below. Let us consider, as earlier, a simple model with a lagged dependent variable on  the right hand side and on other explanatory variable. Assume that the disturbances follow a first-order autoregressive  process.  Then, there are two equations to be considered.  

This is similar to the representation of  the  lagged  dependent variable model  in equation but allows for the parameters of  the disturbance dynamics to  be different from the parameters of the system dynamics.