The problem with an inflation targeting central bank is that it has a hard time ignoring supply shocks because they move inflation. The central bank should only respond to inflation caused by demand shocks, but it is hard to distinguish the source of inflation movements in real time.
One way to get around this problem is to directly target demand itself. That is, the Federal Reserve could aim to stabilize the growth of total dollar spending. This way the Federal Reserve would not have to worry about divining the sources of movements in inflation.
Note that the price level times real GDP is equal to total dollar spending. That is, the dollar price of everything produced and sold equals, by definition, the total number of times money is spent.
This relationship implies, then, that if the Federal Reserve directly targeted the growth of total dollar spending it would by default be allowing the price level to move inversely with productivity-driven changes in real GDP. This would amount to a monetary-policy regime that ignores supply shocks.
To be clear, ignoring supply shocks means allowing such shocks to be reflected in relative price changes. No attempt is made to offset them or their effect on the price level. Ignoring supply shocks also means allowing market interest rates to more closely track the market-clearing or natural-interest-rate level. Doing so reduces financial instability.
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