Dear All:
I have a couple of questions about coding shocks with persistence in dynare. Any input is highly appreciated.
Dynare only allows white noise shocks in the line of "varexo", so we have to code persistent shocks as endogenous variables. Does it affect the determinacy of the model? For example, there are three variables [output, inflation, nominal rate] in a simple NK model. What we care is the determinacy of the three-variable system. If there are persistent shocks on the interest rate, the technology and the markup. The model computed by Dynare becomes a six-variable system. If the three-variable system is actually indeterminant, you can make the six-variable determinant by introducing some explosive eigenvalues in the shocks, or the other way around. I don't question there are someone actually doing it on purpose, but what if we do estimation in a large system, does rounding error cause similar problems?
My second question is about coding the expectation terms. There is no way we can replace the expectation of "true" endogenous variables before we solve the model, so we have to leave them there. I am asking about the case for persistent shocks. There are two ways to code them. The first way is just leave the expectation terms in the equations, for example, in the simple IS equation.
r(t)-inflation(t+1)=y(t+1)-y(t)+a(t+1).
a(t+1) is the expectation of technology shocks on the growth rate. Is it better to replace it with rho_a*a(t) or just leave it there.
The third question is related with the detrending scheme for permanent shocks. Suppose we have Y(t)=A(t)*N(t), where Y(t) is the output, N(t) is labor and A(t) is the level of technology. It is simple that you can either detrend Y(t) by A(t) or A(t-1). Both of them make economic senses, but the transformed equations won’t be the same. If we detrend it by A(t), the Euler quation is the following
r(t)-inflation(t+1)=y(t+1)-y(t)+a(t+1),
where a(t+1) is the expected growth rate.
The production function is y(t)=n(t).
If we detrend it with A(t-1), the two equations turns to be
r(t)-inflation(t+1)=y(t+1)-y(t)+a(t)
y(t)=a(t)+n(t).
Does the difference in the detrending scheme cause any sensible differences in the dyamics in Dynare? Based on my exercise, the detrend scheme itself cause some difference in the result. Then, which way is better?