# Interpreting Impulse Response Function after first differences of logarithm transformation

I created an impulse response function from a VAR model. I used data transformed by taking the first difference of logarithms. I am now in trouble with giving a substantive interpretation of the scale of the impulse response function. How can I properly interpret it?

The IRF is an Orthogonal impulse response function, and an example is below:

As said here:

An IRF indicates what is the impact of an upward unanticipated one-unit change in the "impulse" variable on the "response" variable over the next several periods (typically 10).

In this case, data are differentiated. Thus, I would say that the values at each time point on the x-axis represent the difference between that time point's value and the previous one. For instance, the value at time $$t3$$ is the difference between the values at time $$t3$$ and $$t2$$ ($$t3 - t2$$). This difference is then logged.

Therefore, I would interpret the above chart, for example, as follows, starting from the first time period on the x-axis:

A one-log-unit increase from time $$t-1$$ to time $$t0$$ in the impulse variable $$s1$$, leads to a change of about 0.002 log-units in the response variable $$s2$$ from the time period $$t-1$$ to $$t$$.

The maximum effect can be seen at time $$t3$$, where one-log-unit increase from the time $$t-1$$ to $$t0$$ in the impulse variable $$s1$$, leads to about 0.005 log-units change in the response variable $$s2$$ from period $$t2$$ to $$t3$$.

I could then transform back the logged units by taking the exponential of the values. In this case, I would say, for instance:

The increase in the response $$s2$$ at time $$t1$$ is about 1 ($$exp(0.002)$$) for each 2.718282 units increase ($$exp(1)$$) in the impulse variable $$s1$$.

Is that correct?

There are similar questions on CrossValidated, like this one and this one, but they are still without answers.