# The Odd Couple: QE and Inflation

By: Ben Proos

Economic theory predicts that the quantity of money in circulation is directly proportional to general price levels. This makes intuitive sense: If the supply of money increases, the ‘price’ (value) of money will fall, and thus it takes more money to purchase the same quantity of goods whose value has remained constant. Economist Irving Fisher originally expressed this concept as the Quantity equation: MV=PT where V and T can be held roughly constant, thus making P (price) directly proportional to M (money supply). It should follow then that when M increases, such as when central banks initiated Quantitative Easing (QE) during the 2008-2009 financial crisis, P should also increase. However, reality didn’t follow the model. Why not?

To understand this conundrum, we need to look deeper into M. As an example, consider the US –often described as ‘QE enthusiasts’. The US uses two money aggregates, narrow money supply M1 (mostly cash held by the non-bank sector and checkable deposits) and M2, which is equal to M1 plus other types of deposits. An equation illustrates money aggregate M1.

(Where k tells us how much cash non-banks wish to hold relative to deposits, and r tells us how much reserves banks wish to hold with the central bank relative to checkable deposits. B is the monetary base that is equal to cash plus bank reserves held in the central bank; m is the money multiplier.)

The equation shows that if M1 is to increase, either B or m or both must increase. What about the constants k and r, and their relevance to the financial crisis? The behaviour of the non-bank sector (k) indicates the confidence that the non-bank sector has towards the banking sector; if there is a fear of banks becoming insolvent or illiquid, they will convert their deposits into cash, and the cash coefficient k will rise. On the other hand, the reserve coefficient r describes the confidence of banks with regard to other banks. After the collapse of Lehman Brothers, banks became dubious of other banks and interbank lending slowed. Banks chose to hold more reserves with central banks rather than lend with each other, leading to a rise in the reserve coefficient. A rise in both k andr implies a fall in the money multiplier m. This equation thus connects the monetary interaction of the non-bank sector, the banking sector, and the central bank.

If m contracts as we would predict from falling confidence, we would also expect the money supply M1 to contract and thus, via the Quantity equation, prices to fall. Indeed, this is exactly what occurred in the US during the Great Depression. To avoid the contraction in money supply that Milton Friedman argued underlay the Great Depression, during the 08-09 crisis, central banks around the world initiated QE instead. While QE led to a rise in B, the effect of the rise in B was offset by the fall in m, hence the money aggregate M1 remained stable and with it, prices.

Thus remains the question: what is the future for the relationship between QE and inflation? Only time, or new economic theories, will tell.