<p>Let's consider a baseline regression equation,
<span class="math-container">$$y=\beta_0 +\beta_1 x+u$$</span>
<span class="math-container">$\beta_1$</span> is &quot;the average change in <span class="math-container">$y$</span> that is associated with <span class="math-container">$x$</span> increasing by 1&quot;.</p>
<p>Thus, <span class="math-container">$\sigma_x\cdot \beta_1$</span> is &quot;the average change in <span class="math-container">$y$</span> that is associted with <span class="math-container">$x$</span> increasing by <span class="math-container">$\sigma_x$</span>.</p>
<p>I believe this logic applies to IRF of VARX, so I think the answer to your question is &quot;yes&quot;. However, I am not a macro guy and don't use those tools at all, so if someone else has a contradictory answer, they are probably correct.</p>

CC BY-SA 4.0
2023-07-07T10:01:56.237Z
2023-07-07T10:01:56.237Z
Michael Gmeiner
<p>One way to estimate the effect of a one-standard deviation shock is to standardize your shock variable. I don't know which program you are currently using, however in R the function standardize() in the package datawizard produce the correct standardization ! I also think that Michael answer is true !</p>

CC BY-SA 4.0
2023-12-04T12:22:36.927Z
2023-12-04T12:22:36.927Z
justaneconomist
<p>I'm manually calculating the IRF of a VARX. I calculated the IRF to a unit-shock to the independent variable. Now I want to switch to a one-standard-deviation shock.</p>
<p>Do I multiply the resulting one-unit shock IRFs by the standard deviation of the shocked (independent) variable?</p>

<econometrics>
Switching from one-unit IRF to one-standard-deviation
user44548
# Switching from one-unit IRF to one-standard-deviation

(Asked by: username_0 on 2023-07-06)

I'm manually calculating the IRF of a VARX. I calculated the IRF to a unit-shock to the independent variable. Now I want to switch to a one-standard-deviation shock.

Do I multiply the resulting one-unit shock IRFs by the standard deviation of the shocked (independent) variable?

**Tags:** econometrics

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## 2 answers

### Answer by username_1 on 2023-07-07. Score: 1

Let's consider a baseline regression equation,
$$y=\beta\_0 +\beta\_1 x+u$$
$\beta\_1$ is "the average change in $y$ that is associated with $x$ increasing by 1".

Thus, $\sigma\_x\cdot \beta\_1$ is "the average change in $y$ that is associted with $x$ increasing by $\sigma\_x$.

I believe this logic applies to IRF of VARX, so I think the answer to your question is "yes". However, I am not a macro guy and don't use those tools at all, so if someone else has a contradictory answer, they are probably correct.


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### Answer by username_2 on 2023-12-04. Score: 0

One way to estimate the effect of a one-standard deviation shock is to standardize your shock variable. I don't know which program you are currently using, however in R the function standardize() in the package datawizard produce the correct standardization ! I also think that Michael answer is true !


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