Solved – Standard deviation in impulse response function and significance of IRF

bootstrapimpulse responsestandard deviationstatistical significancevector-autoregression

  1. I have a VAR model and at this moment I'm using Gretl software. Gretl computes shock of IRF as one standard deviation and I saw that in many papers it is interpreted this way either. But I don't understand which standard deviation it is. Is it std deviation in residuals of variable, on which are we focusing? I.e. variable whose reactions on shock we are tracing. If yes, I can get size of the shock by taking the residuals and computing it's standard deviation, is it right? My point is – I want to interpret IRF and shock as a 1 % change (my variables are in log diff form).

  2. If I have a IRF with bootstrap confidence intervals, how can I know whether this IRF is statistically significant? I realize that too wide intervals implies insignificance but I don't know according to which I can know this for certain.
    I attach an example of IRF function with 90 % bootstrap confidence intervals. Can someone say whether it is statistically significant and according and how it is possible to recognize that?

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Best Answer

To 1: In #gretl (as in most software packages) the magnitude of the shock is indeed referring to the s.d. of the reduced-form residuals of the respective shock variable. Gretl doesn't offer computation of standardized IRFs at the moment even though it is not hard to compute.

To 2: You'll never be certain. Nevertheless, if both interval bounds are jointly above or below the zero line, this indicates statistical significance at the chosen significance level and at a specific horizon. The chosen width of the interval usually depends on sample size

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