Monetary policy as White Noise

Dear every one
I have a question that I often see in literature that people model the moneteray policy shock in the Taylor rule as the White Noise process rather than the AR(1) process

My question is that why they do that, for example,


Thank you so much indeed

My understanding is that the monetary policy shock is often interpreted as “a mistake” committed by the central bank. As such, it should not be predictable over time. Otherwise, today’s mistake could be used to forecast the mistake you do next period.

Dear Prof. Pfeifer

Your answer is very intuitive for me

Thank you a lot

Best wishes

Perhaps, the answer to the question should start from the problem of endogeneity in macroeconomics whereby in the estimation of monetary policy effects, you want to make a distinction between the systematic (predictable) actions and the unsystematic actions (shocks) of monetary policy. So, the endogeneity problem is taken care of by the systematic component of monetary policy and the independent action (or ‘‘mistake’’) must be captured by the shock. But should it be random, independent, or ‘mistake’? Yes, I think so because, it is an intervention by a policymaker to change a course/direction/path of a variable(s) which is dependent, or endogenous.

Big thank Reinh for your detailed explanation