Blanchard & Kahn conditions are not satisfied: indeterminacy/ no stable equilibrium

[LouisC]

Hi there, I know the timing matters in Dynare. I have a question about what is the correct timing of UIP. The log-linearised form of UIP is
E_tq_{t+1}-q_t=(R_t-\pi_{t+1})-(R^*_t-\pi^*_{t+1})
Which is the correct form should be put in Dynare
q(+1)-q=(R-pi(+1))-(R*-pi*(+1)); (1)
or
q-q(-1)=(R(-1)-pi)-(R*(-1)-pi*); (2)
I have two sets of parameters, each compatible with one form. I see most of codes use the second form while some of them use the first form.
Could anyone offer insights on this?

[jpfeifer]

Usually, it would be the first one. The UIP relates expected exchange rate changes and expected inflation differences.
But it may be different in a complete markets context where relation (1) would hold in every single state of the world (as opposed to just on average).

[LouisC]

Thanks Prof. Pfeifer. Could you give me more hints on why different forms of UIP can lead to different B&K conditions? I’ve looked through this post, and find if I change the UIP from the first form to the second form, the code posted is able to run, while with the first from, the B&K conditions are not satisfied. https://forum.dynare.org/t/soe-risk-premium-and-unit-root/16971

[jpfeifer]

The post

Oscilating or alternating IRFs

It means that there is a complex eigenvalue leading to oscillations. Usually, when people have this problem in the forum, it comes from them ignoring the Dynare timing convention and then torturing the timing until the BK conditions are satisfied. When doing so, the correct economic timing is ignored and oscillating IRFs result.

is relevant here. There is often another timing error that you “fix” be doing a second one.