Dynamic and steady state under second order approximations

[lapulacat]

Dear all,

For the dynamic under stoch_simul(order=2, irf=0) without “pruning”, is it common for simulated dynamic path (use simult_) with zero exogenous shocks to explode?

And for the dynamic under stoch_simul(order=2, irf=0, pruning) with “pruning”, I find the simulated dynamic path (use simult_) with zero exogenous shocks tend to have nominal interest rate below 1. does this imply that there is a problem with the model ?

[jpfeifer]

1. No, without shocks the simulations should not explode. But there are rare cases where the stochastic steady state does not exist.
2. Not necessarily. The stochastic steady state can differ from the deterministic one.

[lapulacat]

Dear professor jpfeifer:

To the second question, for such a counter-intuitive stochastic steady state result of a nominal interest rate below 1, would it affect the model’s simulation path in a larger way?

Is it necessary to find a way to increase the nominal interest rate in the stochastic steady state?

For example, increase the interest rate shock so that the nominal interest rate is greater than 1 and simulate the dynamics of other shocks on that basis.

[jpfeifer]

Depending on the model, precautionary savings can push the interest rate down. But what you describe sounds strange overall. Are you sure the shock scaling is correct. See e.g.

Shocks for IRFs in a third order approximation

At higher order, there is a difference between the shock volatility, which will determine the stochastic steady state and the ergodic mean, and the shock size for an IRF. For the first one you need to choose realistic values. For example log(R/R_ss)=rho_r*log(R(-1)/R_ss)+rho_p*log(pi/pi_ss)+rho_y*log((y/y(-1))*(g(-1)/g_ss))+sigma_r*epsilon_r ; with sigma_r=1 and shocks; var epsilon_r = 1; end implies that monetary policy shocks on average move the log quarterly interest rate by 1, which is a…

[lapulacat]

Thank you professor jpfeifer.

In absolute terms, the size of my shocks should be in the normal range.

These values are derived from Bayesian estimation, I don’t know if I’m doing it right, they are taken from oo_.posterior_mode.parameters and oo_.posterior_mode.shocks_std.

shocks;
    var e_z;   stderr 0.043289397482863;
    var e_cg;  stderr 0.042447431523015;
    var e_xg;  stderr 0.070808098908449;
    var e_trh; stderr 0.004620021752894;
    var e_b;   stderr 0.004646716194454;
    var e_mp;  stderr 0.049057652617625;
end;

stoch_simul(order=2, irf=0, pruning, nograph);

But it is indeed the size of the shock that leads to abnormal nominal interest rates.

Interestingly, when I set the standard deviation of all shocks to 0, I get the same simult_ results as under the setting that led to the anomalous nominal interest rate mentioned above.

By the way, does Perfect foresight have a function similar to simult_ that can be called for customization?

[jpfeifer]

I would need to see the codes.

@lapulacat

Interestingly, when I set the standard deviation of all shocks to 0, I get the same simult_ results as under the setting that led to the anomalous nominal interest rate mentioned above.

sounds strange.