# How useful is the Fisher equation of exchange?

What empirical value does the Fisher equation of exchange MP=PV have given that the velocity of money, V, is measured as PY/M i.e. nominal GDP divided some preferred monetary aggregate? Surely there is an element of tautology here? We get: $$MV=PY\implies M\frac{PY}{M} =PY\implies PY=PY$$

Although it aids in our understanding, when inputting actual data it 'feels' useless. Is this a valid criticism and, if so, what better alternative models exist to 'predict' or, at least, allow us to understand inflation?

• I am guessing you mean that there's no way to measure $V$? As currently phrased, your critique also applies to, e.g., the formula for rectangle areas. How is $A = a \cdot b$ useful if this is also the definition of $A$? Jan 4 at 23:39
• Is the equation in the first line MP=PV (as you wrote) or rather MP=PY? Jan 9 at 7:50

Surely there is an element of tautology here?

It is tautology only in a way that within its logical system it is always true (i.e. following the definition of tautology from pure math). However, it is not a tautology following rhetorical definition of tautology (used in propositional logic) as a statement that refers to itself repetitively (e.g. MV=PY is not the tautology the same way as saying that cat is a cat because it is cat).

This applies to virtually any formula. For example, take the formula for distance from physics (which is probably the most used formula in physics):

$$d = rt$$

Distance is in most machines (e.g. car) calculated as $$rt$$.

$$rt=d \implies d=d$$

Distance simply by definition ends up being equal to speed $$r$$ and time traveled $$t$$.

Yet $$rt=d$$ is probably the most used formula in physics/engineering.

Also you should note that the same way how we can independently measure distance by ruler you can independently measure velocity by simply calculating average of the number of times unit of currency is used (even though it is practically nearly impossible to do it on national level - but you can easily do it in some very small economy in some experiment).

Velocity is not explicitly defined as $$\frac{PY}{M}$$, it has its own explicit definition as distance in physics, but the same way as distance happens to be time times rate, velocity happens to also be nominal GDP divided by money supply.

Although it aids in our understanding, when inputting actual data it 'feels' useless. Is this a valid criticism and, if so, what better alternative models exist to 'predict' or, at least, allow us to understand inflation?

The $$MV=PY$$ formula was always primarily used as an exposition tool, not an empirical model (this being said it is still used as an exposition tool even by Fed). However, more modern approach to describe money market equilibrium is to use the NK version $$M/P=L(Y,i)$$ (See Blanchard et al Macroeconomics a European Perspective) which is in essence the same thing but allows the relationship to not be proportional (interest rate in NK models negatively affects velocity so the mechanism there is pretty much same but you allow for the relationship to not be proportional).

Currently when it comes to forecasting of inflation the most preferred class of models are various versions of the Philips curve or just some simple autoregressive models (see Carnot Koen and Tissot Economic Forecasting and Policy 2nd ed ch 3.5 or see this Meyer and Pasaogullar Fed explainer).

For example, Gordon's (1990) triangle model (based on New Keynesian Philips Curve) given by:

$$\pi_{t+1} = \mu + \alpha^G(L)\pi_t + b(L)u_{t+1} + \gamma(L)z_t + v_{t+1}.$$

where $$\pi$$ is inflation, $$u$$ is unemployment and $$z$$ is some vector of supply shocks.

However, while model above gives better short-run forecasts its not really better for understanding inflation (for that you can have look at some models from Romer Advanced Macroeconomics).

When you want to predict future inflation (i.e. forecast) you do not care about understanding what drives inflation but just about getting as precise forecast as possible. There might be no good explanation why for example 24th lag of past inflation is relevant for todays forecast.

You could also build some DSGE model to forecast it (e.g. see Wickens Macroeconomic Theory as a reference for DSGE modelling). Such model offers more structural understanding of the economy but not necessary better forecasts.

My suggestion would be to review the entry on Inflation by Lawrence H. White in the Concise Encyclopedia of Economics, particularly the part where he gets into the dynamic form of the equation and its uses.