I ended a recent MoneyIllusion post with this amusing equation, as a sort of throwaway:

M*V = C + I + G + (X-M)

The comment section convinced me to say a bit more about the equation. How should we think about it?

Start with a barter economy and look at the exchange of apples and oranges. If the price of apples in terms of oranges moves over time, how should we think of that change? Obviously it might reflect a shock in the apple industry, the orange industry, or both. Therefore it might be useful to compare each good against many other goods, to see if one of the two goods was clearly moving in price against almost all other goods.

A more familiar example is exchange rates. If the yen price of euros goes up, that might mean a stronger euro, a weaker yen, or both. Here again you might look at each currency in terms of all other currencies, to get a better read as to where the “shock” was concentrated.  If the euro appreciated against all other currencies, then that would be suggestive that the move didn’t just reflect events in Japan.

Of course most transactions involve money for goods.  My general view is that in a microeconomic context it makes more sense to focus on the good in question, whereas in macro I focus on the money side of the transaction.

Consider a case where global oil output suddenly falls by 2%, and oil prices shoot up by 20% in the short run.  (Oil demand is highly inelastic in the short run.)  In that case, money expenditures on oil rise by about 18%.  And yes, that expenditure is a part of NGDP.  So why do I focus on the OPEC output shock and not the money side when explaining why 18% more is spent on oil?  Because the oil market is just one of many uses of money.  If people spend more on oil, it’s pretty easy to move money over from other sectors, or from savings.

In macro it’s almost exactly the opposite.  When we spend more at a macro level, we have more money being exchanged for thousands of different types of goods, services, and assets, in a wide variety of markets.  Now it’s simpler to focus on the money side of the transaction.  It’s easier to figure out why M times V goes up, rather than explain spending on many different types of goods.

In my book on the gold standard I looked at changes in the price level, although I would have used NGDP if better high frequency data were available.  I found that the easiest way to explain the big fall in global prices (and NGDP) during the early 1930s was to look at changes in the supply and demand for gold, rather than C + I + G in dozens of countries.

That’s not to say it’s impossible to tell a “Keynesian” story.  You could claim that reduced animal spirits led to less investment demand and a lower equilibrium global interest rate.  A lower interest rate boosted gold demand (or reduced gold velocity.)  But in practice, animal spirits don’t typically change that dramatically for no reason, especially in the aggregate.  In the early 1930s, it was increased demand for gold by central banks that first triggered the Great Depression, and this is what later reduced “animal spirits”, leading to additional feedback effects that further boosted gold demand and further reduced NGDP and prices.

Overall, I believe that NGDP during the gold standard can be best explained by focusing on the global gold market, but it’s not the only option.  It’s when we turn to fiat money regimes that the argument for a monetary explanation for NGDP becomes completely overwhelming, for two reasons:

1. Central banks have almost infinite ability to impact M (and great ability to impact V as well—via IOER)

2. Central banks often have mandates to target things that are closely related to NGDP, like prices and employment.

Perhaps the following analogy would help explain why the money focus is even more desirable with fiat money than with gold.

With old-fashioned sailing ships, you might want to focus on the captain’s decisions when explaining the path of the ship, but wind and waves would also play a non-trivial role.

With modern oil tankers, you’d be crazy to not focus on the captain’s decisions when explaining the path of the ship; the role of wind and waves would be trivial.

Now let’s return to M*V = C + I + G + (X-M)

It’s an identity, so it tells us nothing about causation.  One can think of this equation as a sort of argument, a debate.  It reflects two ways of describing NGDP, and it can be viewed as a dispute as to which approach is more useful in explaining what causes changes in NGDP.  Should we focus on the goods sold, or the money spent on those goods?

When inflation is extremely high, it’s pretty obvious that the monetary approach is the most useful.  You can’t explain hyperinflation by looking at what causes prices rises in 13,000 individual markets, and then adding them up.  There’s obviously a common factor. In most cases, close to 99% of hyperinflation is due to money growth, and the rest is higher velocity.  When inflation is very low, it’s more debatable as to which approach is the most useful for explaining changes in P and NGDP.

I happen to believe the monetary approach continues to be the most useful framework at lower rates of NGDP growth and inflation, because even though M and P (or M and NGDP) are no longer closely correlated, the central bank can and should move M to offset changes in V.  When if fails to do so, we can think about monetary reform proposals to make that failure less likely in the future.  Such reforms were enacted after both the Great Depression and the Great Inflation, which is why we now freak out about 1.5% inflation when there’s a 2% target, instead of minus 12% inflation or plus 13% inflation, which used to happen before we fixed the Fed.

If the monetary approach were not the most useful, then it’s unlikely that Fed reforms would have eliminated the wild price level swings we used to see, from double digit inflation to double-digit deflation.  Perhaps fiscal reforms could be said to have fixed the deflation problem (I doubt it), but obviously fiscal didn’t fix the high inflation episodes.

So what does M*V = NGDP actually mean?  One definition is, “The person who wrote down this equation believes that one should explain movements in NGDP by looking at the market for money.”  It’s a sort of exhortation:  Look at money!

And what does C + I + G + (X-M) = NGDP actually mean?  One definition is, “The person who wrote down this equation believes that one should explain movements in NGDP by looking at the factors that determine each type of spending.”  It’s a sort of exhortation:  Look at the major expenditure categories!

Me:  Look at money!