anticipated shocks

[alipinska]

Dear all,

I am trying to write in Dynare a model in which I could study the anticipated shocks. I have succeeded doing it in REDS&SOLDS but Dynare gives me an error message by saying that : the matrix is singular and so on...the variables cannot be determined uniquely.
Here it is a simple example (which works in REDS&SOLDS):

y = y(+1)-sigma*r+sigma*pi(+1);
r = roy*y+ropi*pi+ro*r(-1)+er;
pi = k*y-k*yn+beta*pi(+1);
yn=z1+roy*z2+eyn;
z1(+1)=exps;
z2(+1)=yn;

z1 and z2 stand for the lead and lagged natural output (yn(+1), yn(-1)). EXPS is the anticipated productivity shock which will occur in two periods time.
So the predetermined variables in my setting are: z1, z2 and also r(-1).
I will be grateful for any suggestion.

Ania

[MichelJuillard]

Please, can you write the maths with explicit expectation operators. I don't understand what you want to do.

Best

Michel

[alipinska]

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:
- IS equation:

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

[MichelJuillard]

I'm attaching mod1.mod that does what you want I believe.

Note that you could simplify your model as
Et(yne(t=1)) is simply ea_yn(t-1)

But I'm not sure to understand the economics behind it

Best wishes

Michel

[alipinska]

Hi,

Thanks a lot. The code that you posted exactly reproduces my code in REDS&SOLDS.
My main interest are the effects of anticipated fiscal shocks (and this was rather treated as an exercise): so announcement of a tax change which takes place in some specific future and how this affects the other variables.
Once again thanks.

Ania