On inflation, I've been looking at this from a demographics perspective. If we look at the annual change in the prime working age population, there is one other period similar to the current situation - the early-to-mid 60s.
The first graph shows the year-over-year change in the prime working age population (25 to 54 years old).
Note: Ignore the steps up and down - the data was affected by changes in population controls.
The key is the prime working age population was declining in the early part of this decade and has only started increasing again recently.
This is very similar to what happened in the 60s.
In the early 60s, there was a slow increase in the prime working age population until the baby boomers started pouring into the labor force.
In the 1960s, inflation didn't pickup until the unemployment rate had fallen close to 4%. There could be several demographics reasons for the low inflation (in addition to policy reasons). As an example, maybe older workers were being replaced by younger workers who made less (just like today), and maybe the slow increase in the prime working age population put less pressure on resources.
Ignoring for the moment monetary and fiscal policy differences between the periods (LBJ's guns and butter and some austerity recently), maybe the unemployment rate will have to fall below 5% before inflation picks up.