# A Question on the concept of eqm. and impulse responses

Hello all.

I have a very basic question on the concept of stochastic eqm and impulse responses.
I ran a DSGE model with stochastic shocks and calculated the expected value of endogenuous values, e.g, E(Chat)=E(Ct-Css/Css) which is greater than zero. And then I looked at impulse responses of this to the shock and responses are always below zero; i.e, at earlier stage it decrease sharply and gradually increasingly converge to SS.

How could I reconsile this two results? Is it possible that even impulse responses of a variables(relative deviation from SS) is always below zero, expected value of this is positive?

I’m afraid I misunderstood the stochastic eqm and impulse responses since I also see this features in other papers.

Thanks a lot.

Glen

Dear Glen,

1. the impulse responses are computed from a base line of zero.

2. In the ergodic distribution of which you want to compute the mean, shocks are positives and negatives. In the IRF, we only study the response to a positive (1 standard deviation) shock.

Best

michel

Hello Michael;

Now I can understand it.

One more question regarding it,

Many people use impulse response when they interpret the result,i.e,
when there is a foreign interest shock, output increase first and converge to SS gradually…etc.

If I got positive 1st moment of a endo variable under a shock, but
positive impulse responses in all time horizon, Does this mean that
there is more positive shocks than negative shocks during stochastic shock process? What’s the implication of this? Regaring on shock process,
we only give persistence and standard deviation value in dynare.
What decide the dominance of two positive or negative shocks?

Thank you again

Glen

[quote=“MichelJuillard”]Dear Glen,

1. the impulse responses are computed from a base line of zero.

2. In the ergodic distribution of which you want to compute the mean, shocks are positives and negatives. In the IRF, we only study the response to a positive (1 standard deviation) shock.

Best

michel[/quote]

Not at all. The positive IRF means that in response to a positive shock, the endogenous variable increases then goes back monotonicaly to the Steady State. Therefore, the IRF appears as always positive.
This says nothing about the sign of the deterministic Steady State that is determined by the equilibrium condition of the model, in ABSENCE of shocks.

Best

Michel

Hello Michael.

I agree with you.
What I’m wondering is that in the “stochastic” (not deterministic) steady state, I saw positive impulse response and negative 1st moment of a variavle under a shock.
In this case, what determine the “negative” 1st moment relative to determnistic steady state of this variable?

Glen

[quote=“MichelJuillard”]Not at all. The positive IRF means that in response to a positive shock, the endogenous variable increases then goes back monotonicaly to the Steady State. Therefore, the IRF appears as always positive.
This says nothing about the sign of the deterministic Steady State that is determined by the equilibrium condition of the model, in ABSENCE of shocks.

Best

Michel[/quote]

You must mean that, in a second order approximation, the mean of the endogenous variable is lower than the steady state.

It is both the result from the shift in the decision rule induced by taking into account the variance of future shocks and the Jensen inequality, because now the dynamics aren’t linear anymore

Best

Michel

[quote=“MichelJuillard”]You must mean that, in a second order approximation, the mean of the endogenous variable is lower than the steady state.

It is both the result from the shift in the decision rule induced by taking into account the variance of future shocks and the Jensen inequality, because now the dynamics aren’t linear anymore

Best

Michel[/quote]