Equation with variables in t +1 time only

Dear all,

I have just stumbled upon the following problem: I have a model with a banking sector where one of the equations contauns forward-looking variables only. The reason I ended up with it was because if I shift it back to contemporaneous time index (t insead of t+1), the BK conditions get violated and the model has no solution. To be more precise, here’s the equation:

rb(+1) = eta*(Rkss/Rbss)rk(+1)+(1-eta)(Rss/Rbss)*r(+1);

Now since I would like to have a Markov-switching model, I am using the code of Cho (2015) who proposes a forward-solution method to solving linear MS-DSGE models. The problem with this code (or Chris SIms algorithm) would be that the matrix containing the coefficients of all “t-time” variables would be singular if one of the equations contains purely forward-looking variables and hence the code wouldn’t work.

On the other hand, dynare solves it and wouldn’t solve it if I shift back the time. Now I understand that the timing of the abovementioned equation doesn’t make sense so I’d rather shift it back one period, but as I said then the BK conditions get violated.

So I’d like to ask two How come can dynare solve a model where one of the equations is only in t+1 time and why is there a difference between dynare’s and other methods’ algorithms?

Thanks a lot in advance,

In principle both algorithms/approaches should work in the same way. My guess is that any differences result from a different timing convention.