Monetary Velocity, an oft-misunderstood metric that quantifies the pace at which money is spent, has recently shown signs of rising after trending lower for the better part of the last decade. Since increasing velocity is frequently associated with inflation, it comes as no surprise the Federal Reserve (Fed) has upped their vigilance towards inflation. While one would think higher interest rates and a reduced balance sheet both currently being employed by the Fed, would hamper inflation, there exists a well-known financial identity that argues otherwise.
In this article, we closely examine the Monetary Exchange Equation with a focus on monetary velocity. Decomposing this simple formula and extracting the inflation identity shows precisely how the level of economic activity and the Fed's monetary actions come together to affect price levels. This analysis demonstrates that the broadly held and seemingly logical conclusions are incorrect.
Might it be possible the Fed is stoking the embers of inflation while the world thinks they are being extinguished?
Monetary Exchange Equation
To understand how the Fed's commitment to continued interest rate hikes and balance sheet reduction (Quantitative Tightening – QT) affect inflation or deflation, the Monetary Exchange Equation should be analyzed closely. The equation is not a theory, like most economic frameworks based on assumptions and probabilities. The equation is a mathematical identity, meaning the result will always be true no matter the values of its variables. The monetary exchange equation is as follows:
PQ = MV
The equation states that the amount of nominal output purchased during any period is equal to the money spent. Said differently, the price level (P) times real output (Q) is equal to the monetary base (M) times the rate of turnover or velocity of the monetary base (V). The monetary base – currency plus bank reserves, is the only part of the equation that the Federal Reserve can directly control. Therefore, we believe to form future price expectations, an analysis of the Monetary Exchange Equation using the forecasted monetary base is imperative.
The Inflation Identity
Through simple algebra, we can alter the Monetary Exchange Equation and solve for prices. Once the formula is rearranged, the change in prices (%P) can be solved for, as shown below. In doing so, what is left is called the Inflation Identity.
%P = %M + %V – %Q
Before moving on, we urge you to study the equation above. The logic of this seemingly modest formula is often misunderstood. It is not until one contemplates how M, V, and Q interact with each other to derive price changes that the power of the formula is fully appreciated.
Per the inflation identity, the rate of inflation or deflation (%P) is equal to the rate of money growth (%M), plus the change in velocity (%V), less the rate of output growth (%Q). The word “less” is highlighted because in isolation, assuming no changes in the monetary factors (%M and %V), inflation and economic growth should have a near perfect negative relationship. In other words, stronger economic growth leads to lower prices and vice versa. While that relationship may seem contradictory, consider that more output increases the supply of goods, therefore all other things being equal, prices should decline. Alternatively, less output results in less supply and higher prices.
It is important to note that the inflation identity solves for the GDP deflator, which is one of the price indices on which the Fed relies heavily. While the equation does not solve for the more popular consumer price index (CPI), the deflator is highly correlated with it. The graph below highlights the perfect (correlation = 1.00) relationship between the deflator and the price identity as well as the durable, but not perfect (correlation = 0.93), relationship of CPI to the deflator and price identity.
Data Courtesy: Federal Reserve
Let us now discuss %M, %V and %Q so we can consider how %P may change in the current environment.
%M – As noted earlier, the change in the monetary base is a direct function of the Fed's monetary policy actions. To increase or decrease the monetary base the Fed buys and sells securities, typically U.S. Treasuries and more recently mortgage-Backed Securities (MBS). For example, when they want to increase the money supply, they create (print) money and distribute it via the purchase of securities in the financial markets. Conversely, to reduce the monetary base they sell securities, pulling money back out of the system. The Fed does not set the Fed Funds rate by decree. To target a certain interest rate they use open market transactions to increase or decrease money available in the Fed Funds market.
