Sumner, Krugman, Williamson, and My Two Cents

There's been a recent row in the economics blogosphere over the nature of quantitative easing, and its long-term effects on the price level. FOMC member John Williamson recently implied that quantitative easing, instead of causing inflation, instead will exert deflationary pressures on the economy in the long-run. Here's a quote: "The Fed is stuck. It is committed to a future path for policy, and going back on that policy would require that people at the top absorb some new ideas, and maybe eat some crow. Not likely to happen. The observation of continued low, or falling, inflation will only confirm the Fed's belief that it is not doing enough, not committed to doing that for a long enough time, or not being convincing enough."

Paul Krugman, Scott Sumner, and Nick Rowe, among others, have already jumped into the fray, with predictably intriguing discourse ensuing. 

Here's my two cents: Williamson mixed up the difference between real and nominal. Its really as simple as that. Quantitative easing, i.e. dramatically increasing the supply of base money in an economy, doesn't by definition induce asset owners to increase their real holdings of money, i.e. a great amount of purchasing power over goods and services in the form of currency or demand deposits; it by definition induces them to increase holdings of nominal balances.

Lets investigate this using some preliminary algebra. The real money supply is equal to the nominal money supply divided by the price level so that we write:

mD = MS/P

This means the real purchasing power of the money supply is equal to total amount of base dollars in the economy, i.e. paper money plus bank reserves at the Fed, divided by the price level, which is the "average" price of all output in the economy. Quantitative easing means an increase in the nominal money supply, the MS term in the above equation. Williamson has in effect postulated that for an increase in MS, mD must rise by the same amount, which implies that P must correspondingly fall to maintain the equality. What he overlooked is that just because a central bank decides to increase the supply of nominal money, asset holders do not necessarily want to hold more purchasing power in the form of money base. Instead, it is the level of prices that rises via inflation so that the newly issued money is held as real balances to keep purchasing power constant.