AR(1) in Discrete Version of Stochastic Growth Model If I assume a stochastic growth model in discrete time and the production function is defined as $F(K_{t}(s^{t-1}), L_{t}(z^{t}))$ where $z^{t}$ is history of the technological shock up to time $t$. A government also exists in the economy and the government spending at period $t$ is $g_{t}(z^{t})$. Can I assume that the government spending follows an AR(1) process given the setting in a stochastical process? If not, do you have any suggestions on modeling the change in government spending? Thank you!
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