I want to change a parameter in my model and then compare the impulse response functions. However, the parameter that I want to change will change the steady state values and I was told that the impulse response functions are no longer comparable since the steady state values are different. Any suggestion on the best way to do the sensitive analysis? Thank you.

What is the economic purpose of your parameter? Typically you should calibrate the parameter. I guess sensitivity of the steady-state can always be studied if you do not want to calibrate it or do not have appropriate data. Unfortunately, as you mentioned, comparing IRFs would be wrong in this case.

I have seen some papers that compare IRFs under different values of a parameter (hence, different steady-state values). The last one I reviewed was a gender paper called “The Effects of Gender Discrimination in DSGE Models”, where they model a scenario where there is gender discrimination, (in that scenario one parameter is positive), and compare it with the scenario where there is no gender discrimination (the parameter mentioned above is zero), finding different responses in the IRFs.

In my model, I have a calibrated parameter that will set the steady state value of external debt (% of GDP), and I want to see the IRFs of output, inflation, etc when I shock the model. From my conversation with my friends, they said the more accurate ways are either to do a transitional dynamic or static analysis, which I am unsure how to do it. I also read somewhere the better way is to compare the IRFs in levels instead of % of deviation from steady state. But I am not so sure.

It seems your interest is in the variable in levels, not in the deviations from steady state. For that reason, you should compare IRFs in levels, i.e. including the steady state value.