Divisia monetary aggregates index

Based on Wikipedia: Divisia monetary aggregates index

The Problem with Counting Money

Here's a question that sounds simple but isn't: how much money exists in an economy?

You might think central banks have this figured out. They don't. Or rather, they have a method—but it's a bit like measuring a fruit salad by counting pieces of fruit without caring whether they're grapes or watermelons. A hundred-dollar bill in your wallet and a hundred dollars locked in a five-year certificate of deposit both count as "one hundred dollars of money." But are they really the same thing?

This is the central insight behind something called the Divisia monetary aggregates index, a more sophisticated way of measuring the money supply that most people have never heard of, even though it might tell us more about what's actually happening in an economy than the numbers central banks typically report.

How Central Banks Usually Count Money

The Federal Reserve and most other central banks use what economists call simple-sum aggregates. The idea is straightforward: add up all the different forms of money—cash, checking accounts, savings accounts, money market funds, certificates of deposit—and you get a total. M1, M2, M3—these famous monetary aggregates are all calculated this way.

The method treats a dollar as a dollar as a dollar. Cash in your pocket? One dollar. A dollar in a savings account earning interest? Also one dollar. A dollar in a certificate of deposit you can't touch for two years without paying a penalty? Still one dollar.

But think about this from a practical standpoint. Cash in your pocket provides immediate purchasing power. You can walk into any store and spend it right now. Money locked in a long-term certificate of deposit doesn't give you that same immediate liquidity. You might own it, but you can't easily use it to buy groceries today.

These different forms of money provide different amounts of what economists call "monetary services"—the actual usefulness of money as a medium of exchange. Simple-sum aggregates ignore this completely. They treat all forms of money as perfect substitutes for each other, even though everyone knows intuitively that they're not.

The Divisia Solution

In 1980, an economist named William Barnett proposed a different approach. Instead of just adding up all the dollars, what if we weighted each type of money according to how much monetary service it actually provides?

The core idea comes from something called index number theory, a branch of economics that deals with how to properly combine different quantities into a single meaningful number. François Divisia, a French economist working in the 1920s, developed sophisticated mathematical methods for this kind of problem. Barnett realized these methods could be applied to money.

Here's the key insight: the monetary service provided by any asset is related to its opportunity cost—what you're giving up by holding it in that form rather than in some other investment.

Think about it this way. Cash earns zero interest. If you could instead put that money in a high-yield investment—call it the "benchmark" return—you're sacrificing that potential income by keeping it as cash. But cash is extremely convenient for transactions. You're willing to give up that interest for the liquidity cash provides.

Now consider a certificate of deposit. It earns interest closer to that benchmark rate. You're giving up less potential return by holding it. This means you must be getting less monetary service from it—otherwise, why would you accept a lower return?

The Divisia approach uses these yield differentials to weight different monetary assets. Assets that earn returns far below the benchmark—like cash—get higher weights because they must be providing substantial monetary services. Assets earning returns close to the benchmark get lower weights because their monetary service value must be smaller.

The Mathematics Made Simple

Without diving too deep into equations, here's roughly how it works.

For each type of monetary asset, calculate what Barnett called the "user cost"—essentially the interest you're forgoing by holding that asset instead of the highest-yielding alternative. Then figure out what fraction of your total forgone interest comes from each asset. These fractions become the weights.

The growth rate of the Divisia monetary aggregate is then a weighted average of the growth rates of all the different components. If cash is growing quickly and certificates of deposit are shrinking, the Divisia aggregate reflects this differently than a simple sum would, because cash contributes more monetary services per dollar.

This approach has solid theoretical foundations in microeconomics and aggregation theory. W. Erwin Diewert showed in 1976 that index numbers constructed this way belong to a special class called "superlative" indexes—they're exact for certain reasonable assumptions about how people actually use money.

Why This Matters for Understanding the Economy

The difference between simple-sum and Divisia aggregates isn't just academic curiosity. The two measures can tell very different stories about what's happening in an economy.

Consider what happens during a financial crisis. People often shift money from less liquid assets into cash and checking accounts. A simple-sum aggregate might show little change—money is just moving between components. But a Divisia aggregate would show an increase, because money is moving into forms that provide more monetary services.

This could explain puzzles that have troubled monetary economists for decades. Sometimes central banks expand the money supply (as measured by simple sums) and nothing much seems to happen to the economy. Other times, smaller changes in the simple-sum aggregates coincide with major economic shifts. The Divisia approach suggests these puzzles might arise because simple sums aren't really measuring the right thing.

Research by John Keating and colleagues, published in 2019, examined data from 1960 to 2017 and found that Divisia M4—a broad Divisia aggregate—provided more consistent results than the federal funds rate when analyzing how monetary policy affects the economy. The Divisia measure seemed to work well across both crisis and non-crisis periods, while other approaches sometimes produced anomalous results.

Who Uses Divisia Aggregates?

Despite their theoretical advantages, Divisia monetary aggregates haven't replaced simple sums at most central banks. The Federal Reserve still focuses primarily on simple-sum M1 and M2. Old habits die hard in central banking.

But Divisia aggregates aren't unknown either. The Bank of England publishes Divisia money for the United Kingdom. The Federal Reserve Bank of St. Louis makes Divisia aggregates available for the United States, even if they're not the headline numbers. Poland's central bank publishes them as well.

Several major central banks calculate Divisia aggregates internally, even if they don't emphasize them publicly. The European Central Bank, the Bank of Japan, the Bank of Israel, and the International Monetary Fund all maintain Divisia monetary data for their own analysis.

The Center for Financial Stability in New York City has become a primary source for research and data using this approach, working to make Divisia aggregates more accessible and widely understood.

An Unexpected Connection to Palestinian Politics

Here's a curious footnote. One of the early researchers working with Divisia monetary aggregates was Salam Fayyad, who completed his Ph.D. dissertation on the topic at the University of Texas in 1986. Fayyad went on to a career at the International Monetary Fund and the World Bank before becoming Minister of Finance and then Prime Minister of the Palestinian Authority from 2007 to 2013.

It's a reminder that abstract economic theory and real-world governance aren't as disconnected as they might seem. The same mind that worked through the mathematics of proper monetary aggregation later grappled with building functioning financial institutions under extraordinarily difficult political circumstances.

The Deeper Question

The debate between simple-sum and Divisia aggregates points to a deeper issue in economics: measurement and theory are not independent of each other.

When we measure the money supply using simple sums, we're implicitly adopting a theory—that all forms of money are perfect substitutes. When we use Divisia aggregates, we're adopting a different theory—that different forms of money provide different levels of service, and these differences are reflected in their yields.

Neither measurement is purely neutral or "just the facts." Both embed assumptions about how money works and what we're trying to capture. The Divisia approach makes its assumptions more explicit and grounds them in established economic theory, which is arguably more intellectually honest.

This connection between measurement and theory isn't unique to monetary economics. Price indexes like the Consumer Price Index face similar challenges—how do you combine the prices of apples and automobiles into a single number that meaningfully tracks "the price level"? The same superlative index number theory that justifies Divisia monetary aggregates also underlies modern approaches to price measurement.

What We're Really Trying to Understand

At its core, the question of how to measure money is really a question about what role money plays in the economy. Is money just a stock of assets to be counted? Or is it better understood as a flow of services—the ability to make transactions easily, to hold purchasing power in convenient form, to meet unexpected needs?

Simple sums treat money as a stock. Divisia aggregates treat it as a source of services. This shift in perspective might seem subtle, but it can lead to very different conclusions about whether monetary policy is loose or tight, whether the economy has too much money or too little, and how changes in the financial system affect economic activity.

François Divisia published his foundational work in 1925, nearly a century ago. William Barnett applied it to money in 1980, over four decades back. Yet most central bank communications still focus on simple sums, and most news coverage of "the money supply" uses these cruder measures.

Perhaps this will change. As economic analysis becomes more sophisticated and as the financial system continues to evolve—with new forms of money-like assets appearing regularly—the case for more thoughtful monetary measurement may become harder to ignore. Or perhaps simple sums will continue to dominate simply because they're easier to explain and understand.

Either way, the Divisia approach stands as a reminder that in economics, how we measure things shapes what we think we know about them. The numbers aren't just neutral observations—they're products of theory, carrying assumptions about the world that deserve to be examined and understood.