I'm not an economist. I based this claim on common sense, and on the way that the Fed, and the Wall Street Journal, speak of the dangers of high labor costs and of unemployment rates that are "too low". But it appears that I, and my common sense, are not alone—we are in the company of some real economic heavyweights.
James K. Galbraith and Maureen Berner, in a study of of the American economy from 1984 to 2003, found that,
...contrary to official claims, the Federal Reserve does not target inflation or react to “inflation signals.” Rather, the Fed reacts to the very “real” signal sent by unemployment; in a way that suggests that a baseless fear of full employment is a principal force behind monetary policy. Tests of variations in the workings of a Taylor Rule, using dummy variable regressions, on data going back to 1969 suggest that after 1983 the Federal Reserve largely ceased reacting to inflation or high unemployment, but continued to react when unemployment fell “too low.” We further find that monetary policy (measured by the yield curve) has significant causal impact on pay inequality–a domain where the Federal Reserve refuses responsibility.
"The Fed’s Real Reaction Function: Monetary Policy, Inflation, Unemployment, Inequality – and Presidential Politics", published in Inequality and Industrial Change: A Global View
(Thanks to Robin Varghese at 3quarksdaily for pointing this paper out.)