AR(1) in Discrete Version of Stochastic Growth Model
I find it difficult to just say government spending follows an AR(1) process this is because you will end up with violating the &quot;No Ponzi Game Condition&quot; on most models including government.
To model changes in government spending you would simply have to concider different ways of shocking your model.
If you are thinking about optimality in your model and if there is a place for government, formulate your environment in the context of a planners problem and check how optimality looks and if in fact there is space for government.
I hope this helps