I have a general question about the nature of government debt in a RBC model vs NK model.
Consider a simple government budget constraint in an RBC model:
R_(t-1)B_(t-1)=B_t+T_t where T is taxes. R is short-term nominal rate. T responds to past levels of gov. debt (i.e. T (B_(t-1)). It is thus clear that B_t is predetermined in period t.
The equivalent budget constraint in a NK model would look like this:
R_(t-1)B_(t-1)/pi_t=B_t+T_t where now pi_t is inflation (and thus the budget constraint is written in real terms).
Now, B_t is also a function of pi_t, which is a jump variable. Thus, technically B_t will change in period t because of inflation. Yet, B_t is still technically not a jump variable since agents don’t form expectations over debt. So, is B_t still technically considered predetermined in the NK model, even though its value will change in period t?