# Unrealized expectations

Dear all,

I am wondering if Dynare can be used to study the news shocks problem.

The basic idea of news shocks is that at time periods one, agents expect there will be an increase in TFP starting four periods later. However, at periods five, the expected increase in TFP do not realize. That is , there is no technology change.

IN a regular RBC model , change the technology process to :

A(t)=p*A(t-1)+a(t-4)+b(t)

a and b are two shocks. at time periods 1, let a=1, this increases agent’s expectation of TFP at periods 5. at periods 5, if b is set to -1, then people’s expectation is not realized. ( the effect of a and b cancels each other ); if b is set to 0, then expectation is fully realized.

In dynare, if I use deterministic simulation simul,
shock;
var a;
periods 1;
values 1;
var b;
periods 5;
values -1;
end;

the problem is both of the shocks a and b are foreseen by agents, so agents will do nothing. ( notice b is supposed to be unanticipated shock)

If I use stoch_simul, then both of the shocks a and b will happen at periods 1, shock b is supposed to happen at perids 5, but I cannot control it.

The following is an example. It is a regular RBC model except for the change in technology process.

// News shocks
var y, c, k, i, h, lamda,theta,e;
varexo a,b;

parameters beta, sigma, rho, alpha, delta, eta,v ;

alpha = 2/3;
rho = 0.95;
beta = 0.98;
delta = 0.05;
eta=1;
sigma=0.25;
v=1.7;

model;
y=c+i;
c^(-sigma)=lamda;
veta(1-h)^(eta-1)=lamdaalphaexp(theta)(h^(alpha-1))(k(-1)^(1-alpha));
betalamda(+1)(exp(theta(+1))(1-alpha)(h(+1)^alpha)(k^(-alpha))+(1-delta))=lamda;
y=exp(theta)
(h^alpha)*(k(-1)^(1-alpha));
k=(1-delta)k(-1)+i;
theta=rho
theta(-1)+e(-4)+b;
e=a;
end;

I know how to deal with shock a, the difficult part is how to get an
unanticipated shock b at period 5.

Regards,

Emma

Sorry for the delay in answering. I would simply model news as a moving average process. You need to define auxiliary variables for the lagged innovations to the moving average.

Best

Michel

1 Like

I share the question with Emma, and I don’t fully understand Michel’s answer.

To clarify the question: Yes, it straight fwd to model news shocks in Dynare using auxiliary variables. BUT, what both me and Emma wonders is how to model an “unrealized” news shock, i.e. the “coincidence” that a shock with the same size but opposite sign (and no lag of impact) hits in the period when the news shock is realized.

This is a popular way to model business cycles driven purely by expectations, where ther actual variable (often productivity) never changes.

The most useful solution that I have seen regarding modelling of this kind in Dynare is the code by Ippei Fujiwara, available at ideas.repec.org/c/dge/qmrbcd/163.html . It’s a nice code package that generates IRFs for news shocks and “unrealized” news shocks.
Unfortunately this code seems a bit unstable, I can only get it to work with his model of a pigoucycle (and very small permutations thereof).

Good luck with the news shock modelling!

Dear Karl,

sorry for the delay in replying, things have been a bit crazy lately!

I think that there are two issues. One is how to model news shocks, the other is how to simulate a particular story.

It seems to me that news shocks could be written is the following way. For example, let’s assume that one gets news about the productivity shock next period and then one observes the actual realization:

EA_{t} = EEA_t + EEA1_{t-1}

EEA1_t should be interpreted as the news shock about productivity shock next period and EEA_t would revise this news at the actual time of the shock.

EEA_t can be a varexo in Dynare, but, although that EEA and EEA1 have a similar role, EEA1 can’t be varexo in Dynare because it appears with a lag (varexo can only appear in a model at the current period). So we need to declare EEA1 as an endogenous variables (var) and have another exogenous variable EEEA1 and an auxiliary equation
EEA1 = EEEA1;

Then a particular scenario would be when EEA_t = -EEA1_{t-1}. when the news doesn’t realize itself and productivity turns out not to move. This can, of course, only be an isolated event, if it was to always take place, agents would learn not to trust the news and keep knowing that productivity doesn’t change.

Dynare isn’t equipped to simulate scenarios with particular draws of random variables in the stochastic context. This a feature that should be added to give a full account of the news shock story.

Best

Michel

Thanks Michel!