Headline Inflation vs. Core Inflation in Effective Demand model

In the determination of Effective Demand, both headline inflation and core inflation are used. How does each one affect effective demand?

Headline inflation...

If headline inflation rises (holding all else constant), effective demand will fall. However, there is a force to slow the fall of effective demand. As headline inflation rises, the effective demand monetary rule will want to prescribe a higher rate for the Fed rate. However, if the Fed rate does not change, then the Fed rate separates farther lower from the ED rule rate. This indirectly creates a looser monetary policy which raises effective demand.

So which dominates effective demand, headline inflation or the now looser monetary policy? The answer according to the equations I now use for effective demand say that headline inflation dominates. For example, if headline inflation rises by 10% from 0% to 10% over a one year period, then core inflation would have to rise by 6.8%, from 0% to 6.8% in order for effective demand to not change.

Core inflation...

So if a rise in core inflation will neutralize part of the rise in headline inflation, it is apparent that a rise in core inflation raises effective demand (as long as the Fed rate does not change).

Currently we see headline inflation dropping. Core inflation may rise as low oil prices allow consumers to spend more on core items. Assuming that the Fed rate will stay constant at the ZLB, then a fall in headline inflation will increase effective demand. Moreover, an increase in core inflation will also increase effective demand.

How can the difference be explained? Headline inflation affects overall purchases more directly. Core inflation reflects changes in monetary policy since core inflation is the basis of policy setting. So headline inflation is a factor for how inflation affects overall demand. Core inflation is a factor for determining the looseness or tightness of monetary policy. So both headline and core inflation affect effective demand in opposite yet complementary ways.

We can also see why central banks should not over-react to headline inflation. If headline inflation rises, a higher CB rate would decrease effective demand even further. The key is to allow core inflation to rise along with headline inflation making monetary policy indirectly looser. If core inflation was to rise more than 68% of the rise in headline inflation, then the central bank could worry about inflation enough to consider tightening policy against inflation.