2nd order linearized models: 2 questions on IRFs: SOLVED

Dynare help (legacy posts)
1

Hi,

I have 2 questions on IRFs for models linearized to the second order:

  1. In DYNARE User Guide, it is written "if you instead linearize to a second order, impulse response functions will be the result of actual Monte Carlo simulations of future shocks."
    I was wondering how many times the model is simulated. Can one change (increase/decrease) the number of simulations?

  2. One of my equations has the following form: y_t=ax_t+bz_t . When t=0, x_t=0 and z_t=0, this would imply that y_t also should be equal to 0. But for 2nd order approximation, according to IRFs, y_t>0. Is this due to the shift effect of the variance of future shocks?
    However, if model is linearized up to order 1, then y_t=0 if t=0, x_t=0 and z_t=0. This would suggest that 1st order approximation is able to produce more accurate results, wouldn’t it?

Sigitas

2

  1. Set the option “replic” to the number of periods you desire (See page 34 of the Reference Manual, version 4.2.2, the default value is 50 for higher order approximations).

  2. Part one: Yes. The correction to the constant in second order is indeed the “shift effect of the variance of future shocks”. Part two: No. The IRFs in Dynare set the state variables in the policy functions to their nonstochastic steady state values (in your case x and z both equal to zero), but once the correction for the “variance of future shocks” has been implemented, your original linear equation should hold only when all variables are set to this new, stochastic steady state. Try setting your x_t and z_t each to their steady state values plus the corresponding elements of 0.5oo_.dr.ghs2 and then inserting them into your equation. Is y_t now equal to its steady state value plus its corresponding element of 0.5oo_.dr.ghs2? In some sense (i.e. w.r.t. the uncertainty of future shocks up to second order), this new, stochastic steady state is more accurate.

3

Thank you very much for answering both questions!