OK, so the immediate reaction of many to this title might be to laugh, but I challenge anybody reading this to name another Fed Chair who was clearly better than she is. I do not think you can. However, one reason why one may not think much about her is that things have been so inconsequential since she has been Chair. Nothing much has happened. She continued the Quantitative Easing for awhile started by Bernanke and then stopped it. Inflation has remained below 2% mostly. Growth has not been dramatic, but it has been steady and higher than in most other advanced market capitalist economies. There has not been a recession since 2009. There have been no bubbles and no crashes. Nothing dramatic has happened and certainly nothing bad, even if lots of deep problems of the US economy such as inequality remain. But that one is not the Fed's responsibility anyway. So, bottom line, she has been doing a great job even if everybody is quite certain Trump will replace her, with all kinds of candidate names being thrown around. But none of these will be better than she has been.
So, going backwards her most serious rival might be her immediate predecessor, who looks to have played a substantial role in the save of September, 2008 that involved buying a lot of eurojunk from the ECB, only to roll it off over the next six months or so. Of course some of the more innovative things done then were coming out of the NY Fed, but Bernanke did an excellent job when the crisis hit. At the same time, Janet was around during that period, initially as San Fran Fed president, and then later as Vice Chair. But where Bernanke looks not so good is the runup to that crisis, where he seems really not to have seen it coming. Who saw it coming and as far back as 2005 sounding the alarm about the housing bubble? Oh, right. Janet Yellen.
Frankly the records look worse as one goes back further in time. Of course Alan Greenspan got lots of praise during the "Great Moderation," but then many later decided that he laid the groundwork for the housing bubble and crash that came later, and even he himself has admitted that he may have contributed to it. I give him credit for a great save at the time of the 1987 crash, but it does seem that he stayed in too long and deserves some of the blame for what came later.
Volcker gets lots of praise for breaking the inflation that came out of the 1970s, but then this was done in connection with the deepest recession since the Great Depression, even if it did not last long. His legacy is certainly a mixed bag. G. William Miller before him was viewed as pretty much of a disaster with inflation taking off under him, and with his predecessor, Arthur Burns getting blamed for stagflation, even if it was not all his fault. Earlier Fed chairs in the 40s, 50s, and 60s had a generally strong economy to deal with, but they had this tendency to "take away the pumchbowl just as the party got going," leading to stop and go policies that marked that period.
Arguably earlier chairs had greater challenges with the Great Depression and World War II, but in much of that either they engaged in disastrous policies or were subordinate to others, and behavior of the Fed chairs early in its history seems to have bee mostly awful, with the recession of the early 20s and then the reatlly total botches of 1929 and 1931, with Bernanke struggling to avoid the mistakes made in that latter year, which turned what had been a bad recession into the Great Depression.
So, really, Janet Yellen looks about as good as they get when you think about it. We are now in a situation where Donald Trump has three openings on the Board of Governors to appoint. I have no idea who he will pick, but I lay odds that they will not improve what goes on there, especially if he decides to go for some gold bug nuts or whomever. However, for all the talk now that assumes it is a done deal that she will be replaced, if things go downhill for Trump, it may come to pass that he may be betting Yellen to stay on next January, although I shall not bet on that. In the meantime, she and Obama and others have handed him a pretty well functioning economy that will probably continue to do well at least for awhile to come and that he will take credit for. We shall see.