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I have tried to find information about the actual changes to the calculation during the Reagan regime and can't find any. Apparently neither can you, because your link doesn't support your claim about that.

Further, when I search for "shadowstats accuracy bias" these are the links I get:

https://www.thestreet.com › economonitor › emerging-markets › deconstructing-shadowstats-why-is-it-so-loved-by-its-followers-but-scorned-by-economists
Deconstructing ShadowStats. Why is it so Loved by its Followers but ...
It is hard to think of a website so loved by its followers and so scorned by economists as John Williams' ShadowStats, a widely cited source of alternative economic data on inflation and other ...

https://econbrowser.com › archives › 2008 › 09 › shadowstats_deb
Shadowstats debunked | Econbrowser
Shadowstats debunked I've yet to find someone who has been able to reproduce the claims made by Shadow Government Statistics about the extent to which government agencies are grossly misreporting the U.S. inflation rate.

https://www.investing.com › analysis › deconstructing-and-debunking-shadowstats-249923
Deconstructing And Debunking Shadowstats - Investing.com
The ratio of the ShadowStats prediction to the actual price is 3.32, an overstatement of 223 percent. For tuna, both indexes overestimate inflation, the CPI by 34 percent and ShadowStats by 478 ...

https://www.fullstackeconomics.com › p › no-the-real-inflation-rate-isnt-14-percent
No, the real inflation rate isn't 15 percent - Full Stack Economics
According to Shadowstats, if you calculate the inflation rate using old methodology from the 1980s, the true inflation rate is 6 to 8 percentage points higher than the official statistics indicate—and has been for decades. This line of reasoning has become popular in some cryptocurrency circles.

https://www.brightworkresearch.com › how-accurate-is-shadowstats-on-the-understatement-of-us-inflation-with-the-new-cpi
How Accurate is ShadowStats on The Understatement of US Inflation With ...
Shadowstats is built on the belief that the Bureau of Labor Statistics changed their methodology in the 1980s and 1990s, and that if we were using their original methodology the level of inflation would be much higher. Shadowstats presents what they claim to be the original methodology. But Shadowstats is not calculating inflation any differently.