Understanding the Conditional Forecast

[houwang]

Hi, I have been using the conditional forecast command in Dynare. However, I have a question on the reference manual of that subject. It says that "A few things need to be noted. ... Third, although controlled exogenous variables are taken as instruments perfectly under the control of the policy-maker, they are nevertheless random and unforeseen shocks from the perspective of the households. That is, households are in each period surprised by the realization of a shock that keeps the controlled endogenous variables at their respective level. " How do we understand it? Is there any reference that I can read on this subject?

Thanks a lot!

[jpfeifer]

This is a simple consequence of the state space system of the solution. Take the monetary policy shock in the Taylor rule as the instrument. In each period the central bank sets this shock to keep the controlled endogenous variable at the prespecified level. Thus the instrument is perfectly under the control of the policy-maker. But this does not change the fact that the monetary policy shock is a shock from the perspective of the households and that its realization comes as a surprise in each period.

There is no reference on this, but the statement directly follows from using an unanticipated, stochastic shock in the model to keep an endogenous variable at a prespecified level.

[houwang]

Thanks for the clarification and prompt response! The Taylor rule example is a good one, however, I still have some trouble understanding it. I am using a much simpler model to illustrate my questions and I hope that you can help me...

Code: Select all


var y c k i;
varexo e s;
parameters a d;

a=0.5;
d=0.9;

model;
y=k^a+e;
y=c+i;
i=s*y;
k=(1-d)*k(-1)+i;
end;

initval;
k=0.308641975308642;
y=0.555555555555556;
i=0.277777777777778;
c=0.277777777777778;
e=0;
s=0.5;
end;

shocks;
var e; stderr 0.01;
var s; stderr 0.01;
end;

stoch_simul(order=1, periods=1000);

conditional_forecast_paths;
var y;
periods 1,2;
values 0.6,0.7;
end;
conditional_forecast(parameter_set = calibration, controlled_varexo = (e), replic = 3000);
plot_conditional_forecast(periods = 10) y i;



I don't know how to attach graphs here, but basically I get forecast for 'y' and 'i'. Both have an upper and a lower band around their mean.
My questions are:
1) Are the bands due to both the shocks in 's' and 'e'?
2) How exactly do we get the bands? I thought that the value of 's' would affect the steady state values of all the endogenous variables. Does that explain why both the mean and the bands converge to constant levels and stay there after some periods?

Thanks a million!

Holly

[jpfeifer]

See the description in mcforecast3.m

% Algorithm:
% Relies on state-space form:
% y_t=T*y_{t-1}+R*shocks(:,t)
% Shocks are split up into shocks_uncontrolled and shockscontrolled while
% the endogenous variables are also split up into controlled and
% uncontrolled ones to get:
% y_t(controlled_vars_index)=T*y_{t-1}(controlled_vars_index)+R(controlled_vars_index,uncontrolled_shocks_index)*shocks_uncontrolled_t
% + R(controlled_vars_index,controlled_shocks_index)*shocks_controlled_t
%
% This is then solved to get:
% shocks_controlled_t=(y_t(controlled_vars_index)-(T*y_{t-1}(controlled_vars_index)+R(controlled_vars_index,uncontrolled_shocks_index)*shocks_uncontrolled_t)/R(controlled_vars_index,controlled_shocks_index)
%
% After obtaining the shocks, and for uncontrolled periods, the state-space representation
% y_t=T*y_{t-1}+R*shocks(:,t)
% is used for forecasting

The bands come from the fact that there are also other uncontrolled shocks that create uncertainty about the value of tomorrow's uncontrolled variables. For example GDP might be high or low for the same value of the nominal interest rate, depending on whether a positive or negative cost-push shock hits. The bands on y will reflect this. They are created by simulating the controlled system for different series for the uncontrolled shocks.

[houwang]

Thanks! Just to clarify, you mean that the bands come from the uncontrolled shocks, and the controlled shocks will be assumed to be zero forever after the controlling period, is that correct?

[jpfeifer]

Yes, exactly. Controlled shocks in uncontrolled periods are 0 and do not add to uncertainty.

[houwang]

Thanks!!!

Another question , I see no difference between 'shocks' and 'parameter uncertainty' in a calibrated model... Like in my very simple model example above, I model 's' as an exogenous shock that follows a normal distribution, but it was really a parameter of the model (in the absence of that distribution thing), and I can also interpret it as an uncertain parameter following that distribution... What do you think??

H.

[jpfeifer]

I would not agree. The object s has a time index and is not time-invariant. That would be the definition of a variable, not a parameter.

[houwang]

I agree that s has a time subscript. But can we interpret it as a parameter that has a distribution with different realizations in different periods? (Sorry for so many questions!)

H.

[jpfeifer]

You can interpret it as you like. The s is a random variable and it can represent anything that is random.
That being said, you might have a hard time persuading other people that somthing that is time-variant should be seen as a parameter.

[houwang]

Thanks! It's not that I must interpret it that way... I am just trying to think about ways to incorporate parameter uncertainty in a calibrate model.

[jpfeifer]

But isn't parameter uncertainty that a parameter is time invariant (and agents know it), but the econometrician does not know this fixed value? What you are simulating is that parameters change over time, agents learn the parameter fully when its new value is realized and the econometrician also does not know its value and has to use least squares learning using the Kalman filter to infer the value.

[houwang]

I see what you mean. This is very helpful!!! Thanks a million.