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I and others have been critical of the Fed because they failed to timely adjust their monetary policy to adequately take into account what would be the affect on demand for goods and services of the extraordinary fiscal measures put in place to deal with massive unemployment resulting from Covid-driven shutdown of the economy...
Therefore, it's not about what the Fed did to be a major cause of inflation, but what they DID NOT do to abate it beforee it got out of control.
Either way, the Fed played the most major role in this, and still is, and by now starting to go overboard with their hawkishness.