Peter Ireland 2020 paper issue with BK conditions

Hey Dynare community :slight_smile:

Has anyone had a go at modelling Peter Irelands latest paper titled ‘A reconsideration of money growth rules’?

I am having trouble with the BK conditions for the (second) simulation under which the interest rate is at the lower zero bound. It states there are 4 eigenvalues for 5 forward looking variables. When I remove the forward looking variables in Eqn 20 (namely lambda(+1) and pihat(+1) ) and change them to contemporaneous variables, I get 4 eigenvalues for 4 forward looking variables, and BK conditions are met. These two variables lambda(+1) and pihat(+1) both have expectation terms in front of them in the log linearized version of Eqn 20. So my question is, is there perhaps something pertaining to habit formation that falls away or something along those lines than would enable changing these two effects to be contemporaneous being a valid restriction?

Or perhaps someone has other thoughts, I’d be happy to hear them!

Please find attached mod files (MGR32 - zero interest rate specification, MGR31O - altering Eqn 20, MGR31 - taylor rule specification, MGR33 - money growth rule)
MGR31.mod (3.7 KB) MGR33.mod (3.7 KB) .
MGR31O.mod (3.7 KB) MGR32.mod (3.7 KB)

I haven’t read the paper. But the ZLB, i.e. a permanent interest rate peg, usually violates the Taylor principle. So there is usually some auxiliary assumption if stochastic simulations are conducted.