Yes, inflation is understated
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Inflation indices do not reflect reality
Much of the inflation basket is theoretical and not based on increases in price.
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The Argument
Since 1983, the government has measured the price of homes not by looking at house prices but by computing what it calls Owner's Equivalent Rent (OER); the rental value of a house. It accounts for nearly a quarter of the entire Consumer Price Index.
When the change was made, the inflation rate diverged sharply from changes in house prices.[1] The OER was fairly subdued while house prices surged before the housing bust, and afterwards the reverse happened.[2]
If the Federal Reserve had focused on house prices, it would have tightened monetary policy to deal with house price inflation. Instead it relied on OER, which understated inflation. The mechanisms the government uses to estimate inflation are not reflective of the reality of prices.
Counter arguments
Premises
[P1] The mechanisms used to estimate inflation cause it to be understated by not being properly pinned to actual prices.