The February issue of the Cleveland Fed's Economic Trends has the following, on page 3, related to the discussion in this post and this post:

Clearly, as the trend rate of inflation has moderated over time, so too has inflation’s year-to-year volatility. Indeed, the trend’s volatility, which decreased dramatically with the great disinflation of the early 1980s, has been reduced further as inflation has moved even lower in the current decade. The more stable inflation environment has been accompanied by reduced volatility in household inflation expectations. That is, households’ inflation sentiment appears to be more firmly “anchored” than in the past.

Here's the picture that goes along with that thought.

Mikes_inflation_expectations_volatility_
Here's more:

A crude way to gauge that steadiness is to consider what impact a change in the inflation trend has on household predictions for future inflation—are they likely to perceive a change in the inflation trend as a passing event or a persistent phenomenon?

Here's a look at that experiment, calculated by my colleague Mike Bryan. 

Mikes_inflation_expectations_chart_ii
Each point in the figure represents the average effect over a moving ten-year window of changes in inflation on year-ahead expectations.  For example, the data point for December 1995 represents the average effect over the period from January 1986. 

One way to interpret the pattern in this picture is that Fed credibility dissipated between about 1988 and 1992, and has recovered since.  Is that enough to support the low inflation-risk premium story?  Good question.