Maybe. We have gotten so used to the idea that to the extent it is even meaningful it is flat at an inflation rate of 2%, nobody talks about the old textbook Phillips Curve that slopes down. But there is some evidence that out of all these pandemic upheavals it may be back, at least for a while. If this is the case then indeed there may be a tradeoff, and the higher inflation the US is experiencing may be due partly to strong fiscal and monetary stimulus, with that also bringing about higher growth and lower unemployment, the latter somehow not getting noticed by much of the media in all the moaning and wailing about inflation.
A possible simple measure of all this might be to compare the US and the EU. So as of the first Economist of the year, the US had an inflation rate of 6.8% last year while the EU had one of 4.9%. The US had a GDP growth rate of 4.3% while the EU was at 3.3%. And on unemployment, the US had a 4.2% rate versus the EU at 7.3%.
The most recent annual numbers for the US seem to push this even more, with inflation at 7.0% and the unemployment rate down further to 3.9%. I do recognize that the advantage of the US on unemployment is exaggerated in that many European nations have done better on labor force participation than has the US.
I also note that part of the higher inflation we are seeing does reflect global supply chain problems associated with the pandemic. The EU rate of inflation, higher than in the past, is a good sign of that. So maybe whatever higher inflation we see in the US is due to US policies might be that extra 2% the US has.