Whether you like or dislike Federal Reserve policy, its policy record from World War II to the Bernanke Fed is generally related more to who was President rather than to who was Federal Reserve chairman.
President Harry Truman (1945-53) assigned Federal Reserve Chairman William McChesney Martin Jr. (serving as chairman from 1951 to 1970) to orchestrate an agreement to take monetary policy authority away from the U.S. Treasury. The Fed began to take money growth into consideration - "lean against the wind" - rather than just keeping interest rates at a low level, as Treasury had done during World War II to reward banks for holding large amounts of U.S. Treasury securities.
President Dwight Eisenhower (1953-1961) wanted slower money growth and the Martin Fed held the base of the money supply in December 1960 to slightly lower than it was in December 1952.
Although President Richard Nixon (1969 - 1974) introduced price controls with Federal Reserve Chairman Arthur Burns' support (chairman from 1970 to 1978), Nixon pressured Burns to stimulate the economy with low interest rates by gunning the money supply right up to and past the November 1972 presidential election (reaching over 10 percent yearly growth from March 1971 to July 1973).
Then monetary policy changed under President Gerald Ford (August 1974 - 1976). The Burns Fed slowed money growth beginning at the end of 1973 in line with President Ford's desire to control inflation. After the second quarter of 1975 the Burns Fed accelerated money growth back to the same levels during the previous administration, presumably to get Ford elected.
The Burns Fed's fast money growth apparently did not please President Jimmy Carter (1976 - 1981) who appointed G. William Miller to be Fed chairman (from 1979 to 1981). Money growth continued at an annual rate around 8 percent. Inflation caught up with previous Fed policy, rising to 14 percent in June 1977.
Carter then indicated a change in his priority to fighting inflation in a November 1, 1978 speech. Miller was transferred out of the Federal Reserve to be Secretary of the Treasury and Carter appointed Paul Volcker chairman (from 1979 to1987).
Volcker came to the rescue with tight money policies that halted the inflation at the cost of double dip recessions that lasted 22 months before a recovery began. That did not please some in the Reagan administration who reportedly made it clear that Volcker would not be reappointed in 1987.
Alan Greenspan was appointed Federal Reserve chairman (1987 to 2006). Volker had fought a rapid and sustained inflation. In 1990 and 1991 the Greenspan Fed overreacted with a slower money supply growth throwing the economy into a recession in 1990 and 1991, undermining President George H.W. Bush's (1989 -1993) reelection bid. Greenspan's policy was obviously not directed by the forthcoming presidential election.
President Bill Clinton (1993 - 2001) renominated Greenspan for another term and, apparently, did not interfere with Greenspan's policies, as indicated by a letter to Banking Chairman Henry B. Gonzalez who had asked for his help. Although Greenspan secretly told Fed officials he wanted a tight money policy to "prick the bubble" in the stock he changed in 1996. The Greenspan Fed helped to finance the stock market tech boom by switching from slower money growth to faster money growth. The stock market bubble burst in 2000 followed by a recession.
President George Bush (2001 - 2009) renominated Greenspan for another term. After the recession, Greenspan held interest rates low, falling below 1 percent from June 2003 to May 2004. That seemed to be his policy regardless of who was president.
In 2006 Bush nominated Ben Bernanke to be Federal Reserve chairman (whose term as chairman ends in January 2114). After the housing bubble began to burst, there was a massive crisis in the financial system in September 2008 before the presidential election. Continuing through the President Barak Obama administration that began in 2009, the Bernanke Fed stepped on the accelerator, exploding the base of the money supply and paying the private banks interest to hold 54 percent (as of September 2012) of the monetary base idle. Obama apparently liked this policy because he renominated Bernanke chairman in 2009.
The Bernanke Fed introduced a new expansionary policy 1/1/2 months before the November 2012 presidential election: the monetary base would be increased by $40 billion a month until some unspecified measure of lower unemployment occurred. The president's election opponent, Mitt Romney, and many Republican legislators do not like the explosion of the monetary base. This Bernanke Fed policy is clearly compatible with President Obama's campaign for reelection.
In my book, Deception and Abuse at the Fed, I have a chapter on "The Myth of Political Virginity".