The Federal Reserve is putting some of its post-crisis actions under a magnifying glass and not liking everything it sees. In a white paper dissecting the U.S. central bank's actions to stem the financial crisis in 2008 and 2009, Stephen D. Williamson, vice president of the St. Louis Fed, finds fault with three key policy tenets. Specifically, he believes the zero interest rates in place since 2008 that were designed to spark good inflation actually have resulted in just the opposite. And he believes the "forward guidance" the Fed has used to communicate its intentions has instead been a muddle of broken vows that has served only to confuse investors. Finally, he asserts that quantitative easing, or the monthly debt purchases that swelled the central bank's balance sheet past the $4.5 trillion mark, have at best a tenuous link to actual economic improvements. Williamson is quick to acknowledge that then-Chairman Ben Bernanke's Fed, through liquidity programs like the Term Auction Facility that injected cash into banks, "helped to assure that the Fed's Great Depression errors were not repeated."

There is no work, to my knowledge, that establishes a link from QE to the ultimate goals of the Fed—inflation and real economic activity Stephen D. Williamson St. Louis Fed vice president

But as for spurring inflation, reducing employment or otherwise generating sustained economic activity, the results, particularly for QE, are "at best best mixed." In addition to muted inflation, gross domestic product has yet to eclipse 2.5 percent for any calendar year during the recovery, while wage gains, and consequently living standards, have been mired around 2 percent or less. Read MoreThis is 'more damaging...than the Great Recession'

"There is no work, to my knowledge, that establishes a link from QE to the ultimate goals of the Fed—inflation and real economic activity. Indeed, casual evidence suggests that QE has been ineffective in increasing inflation," Williamson wrote.

"For example, in spite of massive central bank asset purchases in the U.S., the Fed is currently falling short of its 2 percent inflation target," he added. "Further, Switzerland and Japan, which have balance sheets that are much larger than that of the U.S., relative to GDP, have been experiencing very low inflation or deflation."

The primary place where QE seems to have worked is in the stock market, where the has soared by 215 percent since the recession lows in March 2009. Elsewhere, though, deflation fears have permeated and interest rates have remained low. Interestingly, one of the biggest fears Fed critics have espoused about its activities has been that the bloated balance sheet would drive inflation by releasing that "high-powered" money into the economy and driving up prices. However, the inflation rate for the U.S., and for much of the other developed world where central bank activism is high, has remain muted, at least by conventional measures. Read MoreFed's trillions haven't helped worker paychecks

In Williamson's view, that's a product of policymakers wed to the Taylor rule, which dictates the level of interest rates in regard to economic conditions. The thinking essentially is that low rates beget low inflation, trapping central banks in zero interest rate policies (or ZIRP). "With the nominal interest rate at zero for a long period of time, inflation is low, and the central banker reasons that maintaining ZIRP will eventually increase the inflation rate. But this never happens and, as long as the central banker adheres to a sufficiently aggressive Taylor rule, ZIRP will continue forever, and the central bank will fall short of its inflation target indefinitely," Williamson said. "This idea seems to fit nicely with the recent observed behavior of the world's central banks."

Steven Williamson Source: Federal Reserve Bank of St. Louis