In my previous post, I started this 3-part series expanding on some of the key points raised in episode #116 of the InFi podcast, which was my two-hour-plus conversation with Eric Weinstein. If you didn’t catch that earlier post, you should definitely review it to understand the context. In today’s article, I’ll dive right in and explain what Eric (and Pia Malaney) end up favoring the Divisia index and why “path dependency” is a feature, not a bug. Specifically, I’ll go through an example where we’re trying to compare the “cost of living” between 1950 and 2025, and contrast how economists typically approach the problem, versus the gauge theoretic approach of Weinstein/Malaney.
The Price Index Problem
Suppose we’re trying to determine how much “the cost of living” has increased between 1950 and 2025. More specifically, we want to know how much (measured in dollars) standard household goods and services cost back in 1950, compared to today. This will give us a sense of how much purchasing power the dollar has lost, and—if we look at data on average wages or salaries—we can also get a sense of whether the economic position of workers has improved or fallen since 1950.
Normally economists would tackle the problem in the following way—and this is just how I would have proceeded, before I began corresponding with Eric Weinstein. You can either take a typical household basket of goods and services from 1950—which might include a dozen eggs, a gallon of gasoline, three pounds of hamburger, a gallon of milk, a week of a mortgage payment on a 2-bedroom house, etc.—and add up the total cost back then, and then do the same exercise with 2025 prices. Or, you could start in 2025 and construct a typical household basket—which now might include internet service and a smart phone monthly bill—add up the total cost, and estimate how much such a basket would have cost back in 1950. (The first method is the Laspeyres index, while the second is the Paasche index.)
Notice that these two procedures would give different estimates of the change in the price of “household” goods and services, because the actual basket is not the same. And this would be a problem even if it weren’t for the elephant in the room, which is that the bundle might be literally impossible to buy on both ends of the time interval. This is most obvious when we ask, “How much did internet or an Macbook cost back in 1950?” But it’s also true when it comes to things like automobiles: The type of car you can buy in 2025 isn’t the same as in 1950. And although most of us probably prefer the overall vehicle today (although the older cars looked cooler, in my opinion), that wouldn’t be true for things like milkman delivery, or doctors making house calls.
A common patch to alleviate these types of problems is to use a chained index approach. So rather than looking at a bunch of prices from 1950 and comparing them to prices from 2025, instead we break up the task in, say, 5-year chunks. So we estimate the increase in “household prices” from 1950 – 1955, from 1955 – 1960, …, and from 2020 – 2025. Once we get the percentage increase for each 5-year interval, we multiply them all together to get the cumulative increase in prices.
The Weinstein/Malaney Approach
In contrast, here’s an intuitive explanation of how Weinstein/Malaney approach this type of problem. First, we go to a household in 1950. We give the decisionmaker (say) $100, and let him spend it in the way that gives him the most satisfaction. We keep track of that “bundle” of goods and services that had a market value of $100 at the moment of purchase.
Then, we come back to the person a week later. We tell him, “Remember that bundle you bought yesterday? Well, you are allowed to trade it in the marketplace for any equivalent bundle—meaning its total market value is the same as your current bundle—if you think you can do better than what you originally purchased, given that prices may have moved, new products and services might be available, and even your underlying tastes may have evolved.”
We follow this procedure for 52 weeks in a row, to see how the preferred bundle—which is constantly being traded away for a bundle of equivalent market value—evolves over the course of a year. In principle we let this procedure play out for decades at a time, allowing for the fact that the person grows older, has kids and grandkids, and may move to a different city facing a different assortment of possible goods and services to barter for, starting with the bundle carried forward from the prior week.
It should be clear that after letting this process play out for a long time, the market value of the bundle at a particular snapshot in time will be much higher than $100. The percentage increase is the Weinstein/Malaney metric for assessing the increase in consumer prices. In other words, it is a measure of how much more money a person in the later time period would need to be given, to achieve the same increment in satisfaction that the $100 afforded to the person back in 1950.
Connection to Divisia
It just so happens that mathematically, the approach I outlined above is equivalent to a price index formula proposed back in the 1920s by Francois Divisia. However, it would be woefully inadequate to summarize the work of Weinstein/Malaney as simply: “They propose using the Divisia index to assess cost of living increases.” On the contrary—and as Eric stressed to me during our podcast discussion—his approach shows why the Divisia index is the most economically sensible.
Specifically, one of the historical drawbacks to the Divisia index was that it is “path dependent.” Since it works by integrating continuous price-and-quantity data over the entire time interval under analysis, the Divisia index can’t simply look at the snapshots of the starting and ending points, the way the Laspeyres or Paasche can. To repeat, economists for the last century have thought this was a problem for Divisia.
But Eric argues that once you see the problem through the gauge theoretic lens—which adopts a differential operator that allows the household to make utility-enhancing barter transactions over time, maintaining the market value of the bundle with each trade—it becomes obvious why the path matters. Seen in this light, it becomes clear why the Divisia is the appropriate construction for a price index, and why its path dependency is a feature, not a bug.
More Advanced Topics
When I first began researching Eric in his podcast discussions of these matters, I was intrigued by his claim that if the prices (and quantities purchased) of the various goods and services happened to be the same in one year versus a later year, then most economists would conclude that the purchasing power of money was the same. But Eric claimed that that was not necessarily the case; you needed more information.
As I say, when I first heard him say that, I thought he couldn't possibly be right. The way I was thinking about it—familiar with indices like the Laspeyres and Paasche—I thought surely if all of the price/quantity data remain the same, then the thorny issues dissolve and the cost of living is the same.
But now that I understand Eric’s framework better, I realize there are all sorts of possibilities. For example, suppose there are manic depressives, who happen to purchase the same assortment of goods and services at the same prices, but who get less enjoyment from them because their tastes have changed. Doesn’t this show that it would take more dollars for them to achieve the same level of satisfaction as in the earlier, manic period?
Or for a different wrinkle: Suppose there are dwindling endowments of coal, oil, and other natural resources, but that the amount actually brought to market happens to be the same. It’s true that—other things equal—we would expect higher unit prices for coal and oil, but there could be offsetting factors that render their spot prices identical. This example, though fanciful, shows yet again that the standard way economists think about price indices is extremely simplistic.
In the third and final installment in this series, I will explain why two popular “impossibility” theorems don’t actually rule out the claims Eric is making on behalf of his paradigm.
Dr. Robert P. Murphy is the Chief Economist at infineo, bridging together the dependability of Whole Life insurance policies with the benefits of blockchain-based finance.
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