An Equation is not a Theory

A common strategy in persuasive economics is to present a Big Idea as the consequence of a single equation. For decades, the most prominent example has been the "Quantity Equation" for money

MV=PY

or

Money Supply x Velocity of Money = Price Level x Real GDP

followed by the conclusion that the the money supply and inflation are closely connected.

More recently, the equation du jour is the Present Value Relation for government debt^✸.

B/P₀ = ((1+r)/r)Σ [τ_t - g_t + s^m(π_t)]

which means

Real Government Debt = Present Value of all future fiscal surpluses and monetary seigniorages

The theory du jour that often follows is the Fiscal Theory of the Price Level (FTPL), a primary point of which is that any increase in government deficits (g_t - τ_t) is reflected in the current price P₀ , which adjusts the real debt, meaning the real value of the outstanding bonds B/P₀ .

Neither equation is controversial. The quantity equation sets equal two ways to express nominal GDP. The present value equation says governments have to pay for their debts somehow...some way...some day in the future.

Interpreting the equations is where things get messy. Old school monetarists use the quantity equation to argue for a tight connection between money supply growth and inflation. Of course the focus on M and P, means you have to explain away V and Y. Friedman and company typically say that velocity is stable and real GDP fluctuates around its natural rate. 

This talk about money and inflation was plausible through the 1970, but since 1980, the velocity of money has been anything but stable, and the idea that money and inflation are tied at the hip should be dead, though it rises again and again and again.....

The instability is largely due to the turbulence in the financial sector, from the Savings and Loan Crisis, to the tech bubble, to the housing bubble, which led to QE, etc.

The FTPL is even flimsier, with respect to time series data. There is no supporting estimation that I know of. The underlying story is also questionable. Think of the store owners who set prices. How many of them have any idea of the value of the real debt of their government? There are other interpretations of the present value equation that don't require such a stretch.

The problem is not the equations. The problem is appealing to these equations as if they are equivalent to a particular (rather aggressive) interpretation. Its a grand Motte and Bailey play. Make a strong statement with little actual support, then retreat to the Motte of the equation, which is an unassailable identity.

The equations are useful, and interpretations can be interesting. Brad DeLong uses a the FTPL to compare the debt situations of countries in the 1920s. Robert Lucas used the quantity theory to examine inflation in various countries with data at a frequency of decades in his Nobel lecture. Both applications are reasonable if not airtight.

My criticisms apply to using the equations to describe short run movements in prices and inflation. Folks on the FOMC are not looking solely at money supply growth or changes in the government debt.

To paraphrase Dr. Crick:  "The dangerous man is the one who only has one equation,....."

^✸ For details see Chapter 7. For a fuller discussion of the issues with the FTPL, see the Palgrave entry by Marco Bassetto.