Hi,

My objective is to analyze the anticipated shocks, e.g. a productivity shocks that occurs in two periods time from now and is known for the agents.

The simplest possible model that I consider includes:

y(t)=Et(y(t+1))-sigma*(r(t)-Et(pi(t+1))

-Phillips curve:

pi(t)=k(y(t)-yn(t))+beta*Et(pi(t+1))

-Monetary policy rule

r(t)=ro*r(t-1)+ropi*pi(t)+roy*y(t)

where:

y - output

yn - natural level of output

pi - inflation

r - nominal interest rate

Et-stands for expectation symbol.

Now I define the anticipated productivity shocks as the shock to ‘natural’ level of output which will occur at period (t+2).

I define the process for ‘natural’ level of output (it is like AR(1) but also includes the expectations concerning the natural level of output):

yn(t)=Et(yne(t+1))+royn*yn(t-1)+e_yn(t)

Et(yne(t+2))=ea_yn(t)

moreover:

where:

e_yn(t) - unanticipated productivity shock

ea_yn(t) - anticipated productivity shock

Et(yne(t+1)) - expectations at time t about natural level of output at (t+1)

(it is a predetermined variable)

similarly:

Et(yne(t+2)) - expectations at time t about natural level of output at (t+2)

(it is also predeterminate variable).

This is the way I introduce the equations into the REDS&SOLDS framework. The variables considered were:

y(t), pi(t), r(t), yn(t), yne(t+1), yne(t+2), r(t-1), yn(t-1) (where the last 4 variables are predeterminate - one has to add to complete the system in the REDS&SOLDS framework: Et(r(t-1+1)=r(t), Et(yn(t-1+1)=yn(t)).

So observing impulse response of the anticipated productivity shock (ea_yn(t)) what we see is that natural level of output changes only at period (t+2).

I tried to input this model into Dynare but it states that the model does not solve the variables uniquely…

I hope that this exposition is clearer. (if not I can also add the corresponding codes)

Ania