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I am looking for the most famous alternative inflation metrics used by some acknowledged economists other then CPI and PCE. In my opinion energy, food, education, healthcare, housing and transport is much more important then say a cellphone or a new tv, if anyone knows of any index weighting in this manner and have a similar idea around why to weight like this, please let me know.

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    $\begingroup$ What are you looking for this metrics to do that CPI and PCE couldn't do? $\endgroup$ – Art Dec 30 '19 at 1:20
  • $\begingroup$ @Art just someone elses opinion of whats important to measure. Imo Energy, Food, School, Healthcare, Housing, Transport is much more important then say a Cellphone. $\endgroup$ – user1 Dec 30 '19 at 18:25
  • $\begingroup$ I see. Then you're asking about how to weigh items in the CPI or PCE and not about other measurements. If that's the case, please consider updating your question. $\endgroup$ – Art Dec 31 '19 at 0:19
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CPI and PCE have already taken into account the "importance" of different goods and services based on how much an average household spend for items in those categories. You could look at the weights here.

Your intuition seems to be correct. Food and beverages take up 14%, Housing 42%, Transportation 16%, and Medical care 9%. These four main categories take up more than 80% of household expenditure (Education is about 3%), while Telephone hardware accounts for only 0.072%.

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The PPI (Producer Price Index) measures the domestic output of raw goods and services.

The GDP deflator measures the changes in all goods and services produced in an economy.

For your purpose the US Bureau does release indexes that drill down further into the PPI in the form of industry level classifications and commodity classifications.

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