Hi all,

I would like to solve the discretionary monetary policy of Monetary Union under ZLB (so I am experimenting with Perfect Foresight Solver).

However, according to Groll and Monacelli(2020), there is following issue:

if we let s_{t} denote log-linearized terms of trade, then it follows:

\Delta s_{t} = \pi^{*}_{F,t} - \pi_{H,t}

where \Delta is difference, \pi^{*}_{F,t} is the foreign inflation rate, while \pi_{H,t} home inflation rate.

When solving for the issue, I thought putting two structural equations s_{t} - s_{t-1} = \pi^{*}_{F,t} - \pi_{H,t}

and s_{t+1} - s_{t} = \pi^{*}_{F,t+1} - \pi_{H,t+1} and take differentiation with respect to s_{t} is enough.

However, it seems that because s_{t} is an endogenous state variable, a ‘Markov-perfect equilibrium’ must be found (by Groll and Monacelli), and that **Dennis (2007) is the right algorithm**.

According to Dynare Manual, it seems that the Discretion Policy Command is built around this algorithm.

Now, under perfect foresight model, is the differentiation method described above wrong? If so, is there anyway I can use Dynare Perfect Foresight Solver to get around this problem?

Thank you in advance!