At the height of the financial crisis's QE program, the Fed held ~ 4.25T of bonds on their balance sheet. This was up from the ~ 800B held prior to the crisis. Four-point-two-five trillion seems like a lot, but it is small compared to the total amount of bonds outstanding. The Fed then tapered down to ~ 3.8T. In March of 2019, the fed announced they would further reduce by selling ~50B per month down to ~3.25T. That phase would have ended ~ early Fall 2019. By no later than Dec 2019, however, the then president was aware that a serious Pandemic was on the way. Further tapering was interrupted, and the Fed responded by March 2020 with further QE in an attempt to aid an economy that was becoming increasingly hard hit by what was by then a raging pandemic. There was still little coordination of pandemic responses among the States. This was the big mistake the U.S. made. The U.S. Administration refused to recognize the need for a massive covid response well coordinated among the States. Instead, the federal administration's position, as announced by the president, was that the pandemic would "just go away on its own". The States were essentially left on their own to deal with Covid infections and ask as needed for Federal assistance.. What was clearly needed instead was a pro-active Federal program. There was none. Finally, by late January the incoming administration had developed a unified, nationally coordinated plan for vaccination and for proactive assistance to States coping with a shortage of medical personnel and supplies. By ~mid April, the first Covid stimulus checks arrived in private sector bank accounts.
The fed, since being transformed into a thoroughly federal agency by the Banking Acts of the 1930s, had no experience with recessions brought on by pandemics. When the fed first responded to the developing pandemic in March of 2020, they were responding to the Pandemic in the way they would have responded to an anticipated, severe recession. They had no power to respond fiscally, of course. Their response made sense in the context of what was happening and known at the time.
When the Congress finally acted to provide a massive fiscal response starting in April of 2021, the U.S. suddenly had in place a dual response to financial disruption caused by the worsening pandemic. The fiscal response was just was "just what the doctor ordered" and far more effective in ameliorating the non-health aspects of the pandemic crisis than anything the Fed could have provided.
In my opinion, but this is admittedly Monday morning quarterbacking, as soon as the 2021, 2nd quarter's data was available, the fed should have began to taper. That would have been by August 2021. I believe they are now at least one quarter late in starting to taper. As a result, we may expect to have to wait longer for the inflation rate to come down to tolerable levels.
The present inflation is mostly supply driven in the face of stimulus preserved demand. Had the Fed began to taper by late summer, 2021, that would would have helped to cool the equity markets, reducing their "wealth effect" on consumers, raising the cost of credit and might have had, by now, some dampening affect on demand and inflation. The generous Federal, fiscal stimulus was enough to save the economy almost by itself. Delayed Fed tapering has been unnecessary icing on top of the rescue cake. This will result in a little too much of a good thing. Because the fed was late to respond to the effect of fiscal stimulus laid on top of an already generous monetary policy, we are going to have to put up with troublesome inflation for a little longer than we would have otherwise had to.
The overall result we've experienced, despite too much inflation, is clearly somewhat better than had the government continued to do virtually nothing. But it could have been better still had the Fed started to taper QE back in August, and especially had the administration began to coordinate anti-Covid measures beginning in December 2019, well before a full blown viral onslaught was underway. Humans will happily substitute perception for reality, and therefore are easy marks for demagogues. Viruses however are deaf, dumb and blind to manufactured perception. They only respond to reality.