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Ludwig von Mises demonstrated that there is no single scientifically accurate way to construct a price index. Money is the general medium of exchange and therefore, its purchasing power can be expressed in terms of any set of goods. Each person will assess the purchasing power of money according to his own interest (i.e., according to the goods that he is interested in buying and selling). Each such construction of a price index has the same justification and therefore, the same scientific status as a measure of price inflation.
It follows that when the government constructs a price index it will be according to the interests of government officials and of the multitude of price indices they construct there is no way to demonstrate that one is scientifically more sound than the others in measuring price inflation.
Here’s a small sample of government computed price indices:
There are a few non-government-agency computed price indices.
MIT compiles the billion prices project:
ShadowStats computes the CPI using the techniques employed by the government in 1980 and 1990.