“**Inflation is always and everywhere a monetary phenomenon**”

– Milton Friedman

Those of us who are concerned about the near doubling of the US dollar money supply over the last four years are sometimes asked “So where is this inflation you keep banging on about”. Good question.

The formula in classic economics proposed by Irving Fisher in 1911 is

MV = PQ

Where-

M is the quantity of money or M1

V is velocity of money, i.e. the number of times each dollar changes hands each year on average

P is the price level, and

Q is the quantity of goods and services produced (inflation adjusted GDP, defined as Real GDP is used as a proxy)

What we are interested in here is inflation, or the increase of P in the formula above. If we rearrange the formula to isolate P, we get

P = MV/Q

So let’s take each of these terms in turn and let’s see what’s been happening to them these last four years, using the official government figures from the St. Louis Federal Reserve.

M1, the money supply has risen by about 70% since 2008 from $1.4T to $2.4T as can be seen in the graph below

This is entirely due to massive Quantitative Easing by the Fed. The next term is V, velocity of money which has slumped from 1.96 to an historic low of 1.56 according to the government chart below.

Lastly let’s look at Real GDP which is what economists use as the standard proxy for Q. Real GDP is the inflation adjusted value for GDP, which is entirely sensible. This has dropped and risen to essentially the same number since 2008. Let’s call it $13.2T to $13.5T.

Since we are interested in the change of price P, i.e. inflation over this time period let’s look at figures for each of the two years 2008 and 2012.

P_{2008 }= (1.4 * 1.96) / 13.2 = 0.208

P_{2012} = (2.4 * 1.57) / 13.5 = 0.279

Percentage change in price P over 4 years (i.e. Inflation) is (0.279 – 0.208) / 0.208 * 100% = **34%**

To annualise that to an annual average inflation over four years we get the fourth root of 1.34 which is 1.076 or **7.6%** annual average inflation over the last four years.

The official Consumer Price Index (CPI) over these years has been –

2009: |
-0.34% |

2010: |
1.64% |

2011: |
3.16% |

2012: |
2.14% |

Multiply these out and we get (0.9966 * 1.0164 * 1.0316 * 1.0214) = 1.067 or a cumulative **6.7%** over the four years. We can get the average over four years by adding each of these figures and dividing by four which gives (0.9966 + 1.0164 + 1.0316 + 1.0214) / 4 = 1.0165 or **1.7%** pa

So there we have it, the classic formula predicts an annual inflation of 7.6% pa while the Fed reports an average of 1.7% pa.

If the classic Monetary Exchange Equation is correct then we have a large discrepancy to try to explain.

**Has the Fed been under-reporting inflation by about 6% per annum since the start of the crisis?**