According to the San Francisco Fed Letter “Have Long-Term Inflation Expectations Declined?”, they have mostly ‘danced’:
Median long-term inflation expectations from the Survey of Professional Forecasters have come down a bit since the Great Recession and are now close to their levels from the first quarter of 2007, near the Fed’s 2% objective. This decline appears to be primarily driven by revised expectations from specific forecasters who had overestimated long-term inflation in the aftermath of the crisis.
The range of projections across forecasters in the survey has also declined sharply, primarily driven by lower inflation estimates among those who were in the upper end of the cross-sectional distribution during the crisis.
The decline in both median forecasts and cross-sectional forecast dispersion back to 2007 levels and closer to the Fed’s objective suggests that inflation uncertainty has receded and that expectations, at least among professional forecasters, remain well anchored.
Alternative measures (from the TIPs Spread and from the Cleveland Fed´s Inflation Expectations) give different answers. The TIPs spread says they were ‘dancing’ and may now be trending down (‘unanchoring’). The Cleveland Fed estimate says it has mostly trended down!