Interpreting VAR Impulse Responses in Log Differences

Summary

The document asks how to read a vector autoregression impulse response when the variables are log differences, using exchange-rate volatility and interest rates as an example. It focuses on the vertical-axis value and whether a plotted response should be read as an absolute change, a percentage change, or a change scaled by the shock. The response gives the basic interpretation: an impulse response traces how another variable changes over time after a one-standard-deviation shock to the shocked variable.

For a response value of 0.001 in a log-difference variable, the answer describes this as approximately a 0.1% change. That reading depends on the variables’ transformations and units, as well as the impulse-response normalization and model setup. The short exchange does not discuss confidence intervals, identification choices, or whether the shock is structural or orthogonalized, so it offers an introductory interpretation rather than a complete guide to VAR inference.

Key ideas

• An impulse response traces the dynamic effect of a shock to one variable on another variable.
• The example concerns interest rates and exchange-rate volatility expressed in log differences.
• A response of 0.001 in a log-difference series is interpreted as approximately a 0.1% change.
• Interpretation depends on variable transformations, units, shock scaling, and model specification.
• The document does not address uncertainty bands or the identification of shocks.

Tags

# Impulse response function interpretation


# Impulse response function interpretation












I would need a quick help with Impulse response function interpretation which I have done after Vector autoregression model in stata.

I need to understand how to interpret IRF graph or table values correctly. What does the value on y axis mean?

In am trying to understand response of Exchange rate volatility to Interest rate (both values are in log differences). Possible interpretations when there is 0.001 spike visible:

- 1 standard deviation shock in IR cause 0.001 change to ER volatility value

- 1 standard deviation shock in IR cause 0.1% change to ER volatility

- 1 standard deviation shock in IR cause change to ER volatility of 0.001 of shock size

- any other explation...

## Answer by doncharles005 (score 0, accepted)

https://quant.stackexchange.com/a/31277

An impulse response shows after a variable A has been shocked by 1 standard deviation, how the other variables respond to the shock.

Eg. when there is 0.001 spike visible for variable B 1 standard deviation shock to variable A cause 0.1% change to variable B

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.