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Sunday, January 10, 2021

The Implausibility Of The Chapwood Index

The Chapwood Index has become a popular source to cite by hard money proponents who are pushing the line that inflation is really much higher than what government statisticians suggest. It has taken over the limelight from Shadowstats, which pioneered pushing that particular line. Although it is entirely expected that individuals can face cost of living increases that rise faster than official the CPI inflation rate, the levels of inflation suggested by the Chapwood Index do not appear to offer any plausible information about the price level as the concept is used into macroeconomics.

Trust, But Verify

Equity analysts can survive being trusting (or even gullible) -- they only need to find a big winner to cancel out losers, and the winners often need to be bought when a firm is still in a early stage of development, requiring optimism about growth prospects for an unproven business. By contrast, fixed income investors only receive a relatively small amount of interest when compared to the capital at risk, so they generally cannot afford any significant credit impairments. (The exceptions would be high yield and emerging market fixed income investors, and distressed debt specialists that invest based on recovery values.) Since it is generally poor form to tell everyone that you are dealing with that you assume that they are lying thieves, one instead generally projects the attitude of "trust, but verify" (using a well known Cold War era phrase).

I have not spent a great deal of time looking at the Chapwood Index (URL: or the entity behind the calculation, but the website declares that they are a financial firm. Since the Chapwood Index is a form of advertising, it is clear that they have a financial incentive to have the most extreme results possible -- nobody would care if their index suggested that the cost of living is half a percent higher than CPI inflation. The question is: can we verify their results?

Based on what I saw of their website, there does not appear to be a way of validating their numbers. To do so, we need two things.
  1. The prices used for each city for each of the 500 items in the index.
  2. The weighting methodology.
For the latter, they declare the following:
We take the precise price for the same item quarter by quarter and calculate the increase or decrease. We tracked the prices on a quarterly basis and created a weighted index based on price. These items include basically everything that most Americans consume during the regular course of their lives. 
One possible interpretation of this is that the weight is according to price. Roughly speaking, take the price of 500 items and add them up, and see how the total changes each year. This is problematic, as was noted in a Reddit article that I ran into when doing a web search (link). For example, the price of a litre of gasoline where I live is currently just over $1. This would have a small weight on a price-weighted index, but it ignores that I buy many more litres of gasoline in a year than I buy Blackberry services (which amazingly is in the index). However, the word "based" is vague, and the rule they use could be more complex.

Although they offer some examples where certain items rose more than the aggregate CPI (an unsurprising outcome; price changes are not uniform), there does not appear to be any way of validating the numbers. You have to trust the producers of the index.

Other Price Indices are Not Transparent Either

By itself, the lack of access to underlying data is not that unusual -- we cannot see the underlying prices that are used in the CPI calculation. Historically, this would not have been technically feasible, but one could imagine such data being made available at present (probably for a fee). It would certainly be interesting if that data were made available, but doing so might pose issues around confidentiality. It would be possible to reverse engineer pricing strategies used by the retailers being polled (as well as the household expenditure data used for weightings), which might not be desired by the retailers.

Since it is unlikely that any fixed income analysts have the time to trawl through the raw data, there is no constituency pushing for its release. Although stories about governments cooking inflation numbers float around, the way to verify them is to look at them in the context of other economic and price data.

Nobody sensible would attempt to use personal experience with prices to look at global fixed income pricing. For example, I have no way to judge price changes in Toronto or Vancouver -- never mind Dallas, Sheffield, Osaka or Toulouse. Very simply I cannot pretend to know how the cost of living of Americans is evolving on a personal basis, but I can judge whether aggregate price level indices are coherent with other economic data.

Size of the Discrepancy

The Chapwood Index is not actually a single index, rather is given in terms of annual price changes for 50 American cities. The website for some reason compares the national CPI index to their city-level series, seemingly unaware that there are regional CPI series. I will use Boston as an example.

In order to stick to full year data, I will compare the Chapwood data to the Boston CPI data ( which I accessed at this webpage, series IDs: CUURS11ASA0,CUUSS11ASA0) for 2016-2019. The Chapwood data suggests annual inflation rates of 11.5%, 11.1%, 9.9%, 8.7%, whereas the BLS rates are 1.5%, 2.5%, 3.3%, 1.9%. This is an extremely large difference, dwarfing the dispersion between other recognised inflation series.

I will not attempt to aggregate the Chapwood Index, but would note that the lowest 5-year inflation rate (ending mid-2020) they report is 6.9% (Mesa), the median is 9.5%, and the highest is 13.2% (Oakland). 

It would be completely unremarkable that someone could develop a methodology that suggested inflation rates were higher than CPI, since we know that methodology changes have lowered CPI inflation rates. Meanwhile, it would certainly be possible to design an inflation index that has much more volatility than the CPI, which would allow for more divergences on a year-to-year basis. This allows higher inflation rates in some years -- balanced by deflation in other years (which is not happening in the Chapwood data, where only one city had a single inflation print below 6% in 2016-2019.) Nevertheless, I see no way of bridging the gap between the Chapwood Index and the CPI on good faith technical differences -- the compounded growth rate differentials are far too high.

Cost of Living Versus Price Indices

As the Bureau of Labor Statistics notes, the CPI is not a cost-of-living index. They write:
The CPI frequently is called a cost-of-living index, but it differs in important ways from a complete cost-of-living measure. We use a cost-of-living framework in making practical decisions about questions that arise in constructing the CPI. A cost-of-living index is a conceptual measurement goal, however, and not a straightforward alternative to the CPI. A cost-of-living index would measure changes over time in the amount that consumers need to spend to reach a certain utility level or standard of living. Both the CPI and a cost-of-living index would reflect changes in the prices of goods and services, such as food and clothing that are directly purchased in the marketplace; but a complete cost-of-living index would go beyond this role to also take into account changes in other governmental or environmental factors that affect consumers' well-being. It is very difficult to determine the proper treatment of public goods, such as safety and education, and other broad concerns, such as health, water quality, and crime, that would constitute a complete cost-of-living framework. Since the CPI does not attempt to quantify all the factors that affect the cost-of-living, it is sometimes termed a conditional cost-of-living index.
The creators of the Chapwood Index by contrast came up with an overly simple approach to calculating the "cost of living," and made decisions that would obviously increase the rate of inflation.

A key example is the inclusion of what they label as "Federal" in their list of 500 index items. Since they also include "state" and "property" in the list, this presumably refers to taxes. If we lump income taxes paid by a household as part of the "cost of living" it is clear that we should expect that the taxes will rise faster than the cost of goods and services, even in a magical world where there are no relative price shifts.
  1. Due to productivity, average wages should rise faster than the price of final output (otherwise all real income growth is captured by capital, which is not predicted by almost any economic theory, nor shows up in the data). By implication, there should be rising real consumption by households (the magnitude of the rise in the standard of living is a point of debate).
  2. The way seniority is treated in the market place, an individual's wages is expected to rise faster than the average. (If we compared "seniority cohorts" over time, each cohort should have wage growth in line with the average.)
  3. Income taxes feature rising marginal rates, and tax brackets are not indexed.
The net result of these factors is that an individual's income tax payments should rise faster than the cost of goods and services. Since the Chapwood Index providers offer no information on the details of their methodology, we have no way of knowing how they treated this effect.

On a personal basis, the "cost of living" is very much dependent upon life decisions. Income differentials are growing, and goods and services aimed at the wealthy have typically seen price rises that are faster than those consumed mainly by the poor (although there are exceptions, such as various medicines in the United States). If you pursue a lifestyle that is filled with markers of class position, your personal cost of living is likely to have risen faster than average. Based on some Chapwood Index components -- private school, cat grooming (spoiler: cats groom themselves), luxury box rental -- such items are probably overweighted, given the price-weighting scheme allegedly used.

Questionable Definitions

Another way the Chapwood Index could be constructed to give a high inflation rate is to take advantage of the vagueness of definitions. They specify "laptop computer," which provides almost no information. I looked at the website of a large American electronics store, and they list laptops that ranged in price from $169 to $4199. Unless there is a very specific criteria to ensure comparability from year-to-year (in an environment where laptop models are continuously changing), this leaves a spectacular amount of wiggle room to pick which price to use. (E.g., start at a low end laptop, then slide up the quality scale in later years.)

(This also shows up in "Play Station" [sic], which skates over the fact that normally only the latest versions of PlayStation™ consoles are for sale.)

We have to take on faith that the construction of the Chapwood Index handles the changes to index components in a fashion that does not lead to higher inflation rates.

Economic Implausibility

Now that I covered how someone could end up with a cost of living index that rises faster than CPI, we then turn to the economic implications. The results are implausible, for the exact same reason that the Shadowstats inflation numbers were implausible. There are a large number of critiques of Shadowstats that already exist that outline this argument. (The critiques of Shadowstats methodology details would not be applicable, of course.)

We need to look at how we define the price level from a macro perspective. We say that nominal GDP growth is (roughly) equal to real GDP growth plus the growth in the GDP deflator. The GDP deflator is an economy-wide price level, which can diverge from the price level of final consumption goods and services. However, we would not expect divergences between the economy-wide price level and consumer prices to be sustained indefinitely. 
Figure: GDP And The Effect Of Inflation Hypothesis
The above figure illustrates why the above decomposition matters. The top panel shows that reported nominal GDP growth has typically been in the neighbourhood of 5% during expansions. The growth of the GDP deflator (not shown) results in real GDP growth rates that bonce around 2-3% (also not shown).

What happens if the government was misrepresenting inflation? If we replace the reported GDP deflator with an index that grows at 2% a quarter (implying just over 8% a year inflation, which is probably below what the Chapwood Index implies, although it does not go back to 1995), we see that there is a massive divergence in the level of real GDP. As basic mathematics suggest, it is shrinking rapidly, falling by more than half since 1995.

Obviously, for inflation to be "really" 8%, either one or both of nominal and real GDP numbers have to be also manipulated. (If one looks at national accounts data, that implies that there has to be a lot of series being manipulated, since they all add up to GDP.)


We do not have to take these numbers purely on faith. As noted earlier, the government cannot just manipulate one CPI series -- they have to manipulate everything, since governments offer comprehensive national account data. We can validate the internal consistency of the data by a number of techniques.
  1. International comparisons. In addition to trade data, multinational corporations imply economic linkages across countries. A country that doctored its data would end up with data that is out-of-sync with international peers.
  2. Nominal GDP is equal to nominal gross domestic income (GDI). If we assume that nominal GDP is growing faster than reported, then nominal incomes have to be growing faster than reported as well. Average hourly earnings are reported, and one can compare that to local experience to see how plausible the numbers are. Meanwhile, earnings of corporations are relentlessly scoured by equity analysts that have nothing better to do with their lives. National accounting of profits follow different conventions than financial accounting, but analysts would pick up on corporations in aggregate massively outperforming nationally reported data.
  3. Real GDP is a vague concept that has theoretical issues if you think too much about it. However, it is expected to be highly correlated with real activity variables. Falling real production implies that workers are becoming far less productive, unless one starts inventing alternate employment data that suggests that unemployment is continuously rising beyond what is being reported. Many important real activity variables -- automobile production, oil production, railroad car loadings, even cardboard box production -- are reported by private sector bodies. If the real economy were shrinking, so would those reported figures. (I do not pay for such data sources, but based on my experience from when I did, all of them were coherent with officially reported GDP data.) By implication, a large number of private sector bodies have to be in on the conspiracy to cook internally consistent data.
  4. Many prices (e.g., commodity prices) are either available from market data, or are compiled by trade bodies. These can be compared to official price indices. Since CPI inflation is a traded financial product, there is a lot of interest in doing such comparisons. (For example, private data is narrower, and produced in a more timely fashion.)
All of these data are being scoured by analysts looking for an edge in macroeconomic prediction, and most of these analysts are happy to tell you how smart they are, and how much they love free market economics. Other than the handful of believers of Shadowstats/Chapwood Index, all of these analysts are allegedly being fooled by all of the available data sets.

Raw, Stinking, Misinformation

The government’s baseline CPI measure excludes items such as taxes, energy, and food. [emphasis mine] It is clearly manipulated and biased, therefore it is rarely accurate.

This is a line that is popular on fringe hard money websites, but is incorrect. The official CPI used for cost-of-living adjustments is the headline CPI, which includes food and energy. Economists strip out food and energy to calculate "core inflation," which is only used by them for analysis.

Including such a statement is a glaring red flag. 

Concluding Remarks

I will summarise my arguments into two key takeaways.
  1. It is entirely possible to define a "cost of living" index that rises faster than reported CPI (especially if one compares a regional price versus a national average). An individual's cost of living is based on their lifestyle choices; if you wish, you can have a very expensive lifestyle.
  2. The Chapwood Index numbers are too far away from published data to be chalked up to technical index construction issues. If we believed that the price level of the economy moved in line with the Chapwood Index, it would imply that government statisticians across the developed world are creating an elaborate fantasy world with thousands of internally consistent economic time series, and the private sector is in on the act, producing data that are coherent with the government's story. 
(c) Brian Romanchuk 2020


  1. I would like to confirm your view about the reliability of private and public data sources. I worked for 25 years with privately compiled data sources (oil, gas, refined products, e.g. motor fuel, forest products: pulp, paper, paperboard, corrugated products, lumber). The private sources tended to be more timely than the Stats Can data (which I also used), although not usually by very much. The data in both sources was confirmed by my own observations in the producing facilities and by conversations with many workers in them. I worked for the union but my management counterparts used this information as well. The idea that the numbers could be falsified and not noticed is not believable.

    1. Thanks. I was not an industry analyst, but periodically would look into random private industry data based on some macro angle (or to support other analysts), so I had a handle on the variety of data that are available.

  2. Trading has become easier and comfortable with online trading applications.
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  3. 2010-2020 annual cpi inflation

    USA 1.7%
    CHINA 2.7%
    INDIA 6.7%





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