Humped IRF graphs？

1

Dear all ,
I have a question whether IRFs have to start at zero？ When my code include the cost of investment adjustment, why there is no humped impulse response graphs? Does the calculation of steady state affect impulse response pattern?
The attachment is my code. Is there any mistake in my code?
bankH1.mod (4.5 KB)

2

Hi
In your code, the investment adjustment cost is set high, but it appears in the numerator. It should be in the denominator of the coefficient on Tobin’s Q.

phiI = 5.9 ;

//3. investment equation;
ii = 1/(1+beta)* ii(-1) + beta/(1+beta)* ii(+1) + phiI /(1+beta)* Q ;

So the elasticity of investment to the price of capital is more than 1 to 1. (5.9/(1+0.99)).

With regard to your question, if the model is linearised, the IRFs will start from zero. However, in the period of impact of the shock, many endogenous variables will react contemporaneously, and that is not surprising.
In the presence of investment adjustment costs (correctly specified), the peak impact on investment will usually (also depends on source of the shock) will be delayed.

Reuben

4

Reuben，Thank you for your advice. I should change to the following form, right?

ii = 1/(1+beta)* ii(-1) + beta/(1+beta)* ii(+1) + 1 /(phiI*(1+beta))* Q ;

But I still can’t get humped IRFs. Is my code correct? I want the impulse response figture to start at 0. can I set it up?

5

Did you try investment shocks?

6

Maybe there is a misunderstanding here about the vocabulary. Even if you append the steady state (zero in your case) to the IRFs as a first point, you will not get a true humped shape pattern… Or I do not understand what you mean by humped IRFs. Usually it is an endogenous mechanism in the model that forces a variable to grow for a number of periods and then decay to the steady state. If you append the steady state in period one (or I would say zero) you will have a jump in period two (I would say one) caused by the impulse. But this is not an endogenous humped shape pattern (which is the effect we are usually looking for) but rather something mechanical (that you would observe even with an first order autoregressive process).

In the IRF plots Dynare draws a red horizontal line (in your case it should be on the abscissa) which represents the steady state. So you already have the information about the steady state or initial condition in these plots.

The IRFs data are stored in oo_ (see the reference manual) so you can do the plots yourself with matlab commands if you want to add the initial condition (steady state) in period zero.

Best,
Stéphane.