Fed policy is not causing a massive increase in the money supply. The monetary base, which is the only monetary aggregate directly controlled by the Fed, represents only a relatively small fraction of the total US money supply. For example, the most recently announced QE3 program is currently only increasing the monetary base at a pace that, all things being equal, would cause a 3% annual increase the broad M2 money supply. This is not enough to cause significant inflation. Furthermore, the M2 money supply is currently growing at a rate that historically been associated with moderate rates of inflation in recent US history.
The money supply does not determine inflation. Even if Fed policy were causing a massive increase in the money supply, this would not, by itself, be expected to cause high levels of inflation. A great many other factors must be present in order for serious inflation to result.
Growth in the monetary base (controlled by the Fed) and broader measures of the money supply (not controlled by the Fed) can influence inflationary dynamics. However, these variables do not by themselves control inflation.
A little inflation would not be a bad thing if it were caused endogenously by rising demand and greater resource utilization, including declining unemployment.
However, rising inflation caused by internationally sourced cost-push pressures, in the context of high unemployment and stagnant wages, would represent a serious problem, as it would mean contracting real incomes and declining consumption.
Furthermore, rising inflation in a context of still-high unemployment would place the US Fed in an untenable predicament. On the one hand, the Fed could choose to affirm the integrity of its inflation-fighting credentials by tightening monetary policy and possibly triggering a recession. On the other hand, it could prioritize its full-employment mandate and choose to stand by as inflation accelerated. The later course would risk exacerbating inflationary expectations and concomitant inflationary momentum, as faith was lost in the faith's commitment to price stability. The former course of action would risk hurling the US back into a recession, with dangerous potential consequences for the US's already worrisome fiscal position as well as the still fragile US credit system.
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