Is the CPI a fair measure of inflation?
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No, it overestimates inflation.
Yes.
No, it underestimates inflation.

I have heard widely different opinions on this topic and would like to sample the opinions here on manifold.

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From The Economist: "The CPI includes only what consumers spend on themselves, whereas the PCE index also includes expenditures on their behalf, such as employee health insurance. And the CPI’s basket of goods is updated every two years, whereas that for the PCE index is updated quarterly. This means it is quicker to pick up substitutions: as the price of one item (apples, say) rises, consumers seek cheaper alternatives (for example, pears). In 2000 the Federal Reserve’s rate-setting body switched from the CPI to the PCE index for its inflation target, citing this reason. Growth in the PCE index has generally been half a percentage point below the CPI. The gap, small in the short run, grows wider with each passing year." https://www.economist.com/finance-and-economics/2018/03/31/the-average-american-is-much-better-off-now-than-four-decades-ago

@SoniaAlbrecht The CPI also only includes urban spending, but the PCE includes rural spending as well.

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