The broad idea is you want a number low enough that people don't price inflation expectations into day-to-day pricing but not so low that a hiccup causes deflation.
The empirical evidence around inflation persistence is a bit all over the place, but broadly suggests people start daily indexing between 2 and 5%. When that starts to happen, restraining inflation without causing a depression becomes incredibly hard, because people will actively countermand policy moves.
The fed has a dual mandate to maintain full employment and keep inflation at 2%. Others have already explained why 2% and not 0%. Up to 3% is expected, 4% means significant price shocks and they should consider acting quickly. 5% means they are at risk of losing control of inflation as it's more than doubled from their mandate and the fed risks losing credibility with markets
The broad idea is you want a number low enough that people don't price inflation expectations into day-to-day pricing but not so low that a hiccup causes deflation.
The empirical evidence around inflation persistence is a bit all over the place, but broadly suggests people start daily indexing between 2 and 5%. When that starts to happen, restraining inflation without causing a depression becomes incredibly hard, because people will actively countermand policy moves.