Regarding core versus headline inflation, again, I think the rationale was to remove the volatility that food and energy prices presented.

The theory is that expectations of inflation tend to be self reinforcing – that is, expecting inflation leads people to spend earlier, increasing the money velocity, which increases the money supply, creating inflation. Therefore, if people are not expecting “core” spending categories to increase in price, they will not create inflation in those categories. Therefore, since the “core” inflation was generally more stable, it reduced people’s inflation expectations and thus created less inflation.

From a simple perspective, however, excluding a category of spending doesn’t make sense, because excluding a category of spending, even a volatile one, misstates the inflation of the remainder of the categories – if a certain money supply is being increasingly directed toward rising energy costs, then the prices of the remainder of the categories ought to go down. More money spent on gas means less money available for household furnishings, so higher gas prices ought to lead to lower household furnishings prices.

Note that expectations of deflation are also self perpetuating. Expecting prices to fall discourages spending, reduces money velocity, and so shrinks the money supply.