As the Federal Reserve ramped up its bond purchases over the last several years, those justifying the unprecedented policy move often pointed to a U.S. unemployment rate that was heading steadily in the opposite direction.

The Fed, which holds a policy meeting this week and is set to begin unwinding the purchases as soon as next month, says they were needed to rescue the U.S. economy from an even deeper recession in 2007-2009 and to put it on a steady course in the years since.

Over that time, unemployment fell from a crisis-era peak of 10 percent to a 16-year low of 4.3 percent this year, about as low as economists think it can go before inflation starts to rise, forcing the Fed to tighten policy.

Yet the U.S. central bank's $3.5-trillion of Treasury and mortgage purchases over six years has failed to light a fire under price measures. Five years of below-target inflation and yet more weakness through much of this year has flummoxed Fed officials and even prompted some to shelve plans for further interest-rate hikes any time soon.

"My best guess is that over time core inflation is going to move somewhat higher as we see more of an impact from the tightening labor market, but that is a very slow process and not a very reliable one," Jan Hatzius, chief economist at Goldman Sachs, said at the Council on Foreign Relations in New York last week.

A one percentage-point drop in the unemployment rate translates into only a 0.10 to 0.15 percentage-point rise in inflation, he added of the theoretical link between the two measures.

The most concerning piece of this puzzle is year after year of sluggish wage growth, which has not picked up despite robust job growth and employment, fueling concerns that American inequality has only risen over the course of an overall recovery that has left many behind.

Annual wage growth has been stuck at 2.5 percent this year, better than the sub-2-percent trend in 2010-2012 but worse than the roughly 3-percent growth before the recession.

For a full interactive graphic of the effects of Fed bond-buying on the economy and markets, click here.