Shocks for IRFs in a third order approximation

Stochastic simulations
5

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 about 100 percent! That makes no sense. Scaling by 100 is not allowed for models solved at higher order.

The way to proceed is to

  1. fully calibrate the model using the correct shock standard deviations.
  2. compute the stochastic steady state based on these values.
  3. compute IRFs at the stochastic steady state for a chosen shock size. For that, you can set the shock matrix entering the simult_-function.
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