## Eighth-Grade Math vs ShadowStats

I spend a large amount of my time, when talking about inflation, addressing the quality of the Consumer Price Index and other measures of inflation. This is understandable because internalizing the effects of inflation so that “2.2% increase in my market basket” seems intuitive is, to put it mildly, challenging. But what is a little surprising is how much time I spend answering questions about the website ShadowStats. For many years, I assumed the website was a hoax since the claims made on it are patently ridiculous, but finally realized that the site’s owner *actually believes* that inflation has run at something like 5-7% higher than the “official” measures since the early 1980s, if you “use the method before the government made all the changes designed to lower the measure.” The basic claim is false – lots of people have looked at the impact of those changes on the future path of the index, and none of them has concluded that the methodological alterations make any more than a fractional difference over time. And there are lots of ways to illustrate that the substance of the claim is nonsense (see for example some of my arguments here). But the disturbing thing is that you don’t need to be an inflation nerd or mathematician to be able to prove that the claims are false. You just need eighth-grade math.

I’m assuming that they teach exponents in 8^{th} grade, but I know in some venues they get taught earlier than that. I think I’m being conservative here. We are just going to focus on one formula:

(1 + annual growth rate)^{number of years} = how many times as large something is at the end, vs the start

For example, if my bank account has $1 in it, and grows at 10% per year for 5 years, it is worth (1+10%)^{5} = 1.61x as much, or $1.61. I only walk through this in case the reader hasn’t been through 8^{th} grade, or is too many years removed from the 8^{th} grade, or works for ShadowStats.

Now let’s use real numbers. Since April 1981, roughly when the Bureau of Labor Statistics (BLS) started changing these methods in a sinister way (but chosen because it means it was exactly 40 years ago, which is nice and clean), the BLS says that prices have risen an average of 2.78% per year. This means that the general level of prices, according to the BLS, has almost exactly tripled. What cost $1 in 1981 costs about $3 now. Meanwhile, if instead we use an annual inflation figure that is (only) 5% higher, so that inflation averaged 7.78% per year, then the general level of prices has risen 20x.

(1 + .0278)^{40}=3.00

(1 + .0778)^{40}=20.02

What does that mean practically? Let’s look at the 1981 prices of various goods and services, then at the approximate 2021 price that would be implied by a tripling in the price level (BLS-based estimate) or by a 20x multiplication (ShadowStats-based estimate). Obviously, neither the BLS nor ShadowStats claims that all prices move the same amount as the average, but we’re talking an order of magnitude here so let’s just see who is closer. See the first footnote[1] for sourcing of 1981 prices and the second footnote[2] for current prices.

You don’t need to have a PhD in Mathematics to see that the implications of ShadowStats’ claim about “real” inflation being 5% or more higher than the CPI makes the claim **obviously ridiculous on its face**. (Note that I assumed a 5% spread above CPI – if you use a 7% spread then you can double the numbers again over what ShadowStats implies at a 5% spread.) A dozen eggs in 1981 cost $0.90. If that grew at 2.78% per annum, it would be $2.70 today; ShadowStats thinks you’re probably paying around $19. They also think a gallon of milk should be $34, a loaf of bread $11, and the median home price a cool $1.3mm. Your average new car? $115k, but that’s not nearly as bad as $6,300 per month for rent. By the way, note that my “actual” prices do not have “hedonic adjustments” in them, which is one of ShadowStats’ complaints they “correct” for. Those are actual prices for what you’d actually buy today, not the 1981 version.

I included Tuition on here because I wanted to have a line-item for the biggest inflator I could think of that we could all agree on. Clearly, tuition has increased by more than the 2.78%/yr of the whole basket. But even if it was an **average** item, ShadowStats would have tuition at double the current rates (four times the current level, if you use a 7% spread, and more, if you apply that spread to what the BLS estimated).

So I think we can be definitive here: the BLS may not be right about the exact price level or the exact change of the mythical consumption basket. But CPI is not, cannot be, dramatically wrong the way that ShadowStats claims that it is. Eighth grade math proves it.

[1] Sources for 1981 prices: car, gallon of milk, bread from http://www.inthe80s.com/prices.shtml. Rent, dishwasher, gallon of gas, median home price from http://www.thepeoplehistory.com/1981.html. McDonald’s hamburger from https://www.insider.com/fast-food-burgers-cost-every-year-2018-9#in-2018-your-burger-costs-an-average-of-264-25. Private 4y college tuition from https://research.collegeboard.org/trends/college-pricing/resource-library. First-class stamp, dozen eggs from http://www.1980sflashback.com/1981/economy.asp.

[2] Sources for 2021 prices: cars: https://www.kbb.com/car-news/new-car-and-suv-buyers-guides/. Rent: https://www.rentable.co/blog/annual-rent-report/. Dishwasher (installed): https://www.homeadvisor.com/cost/kitchens/install-dishwasher/. Burger (delivered!): I checked UberEats in NJ. Stamp: USPS. Gallon of gas: https://gasprices.aaa.com/state-gas-price-averages/. Eggs, milk, and bread: Wal-mart online. Median home price: https://fred.stlouisfed.org/series/MSPUS. Tuition (2020-21 school year): https://research.collegeboard.org/trends/college-pricing/resource-library.