One reason most central bankers do not set an inflation target of zero is:

Question

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Setting an inflation target of zero would hit the zero nominal-interest-rate bound, meaning that central banks would be unable to lower interest rates further during a recession to stimulate the economy. This could worsen economic conditions and make it difficult to achieve the central bank's overall goals. Additionally, some central bankers believe that a low level of inflation (around 2%) is desirable for a healthy economy, and that setting a target of zero could lead to deflationary pressures.

One Reason Most Central Bankers Do Not Set an Inflation