Inflation is reported by the government in the US as the inflation derived from CPI, not the GDP Deflator. It is calculated by the Bureau of Labor Statistics.
Problems:
- Heterogeneity error
- This effects GDP Deflator as well
- Geography
- Age
- Many other factors
- Your personal inflation depends on the price behaviors of the goods you consume.
- A non-subjective, market-wide estimate depends on non-selective averages.
- Substitution bias
- Quality changes (up or down)
- Goods no longer bought, new goods on the market
- Selection bias for the basket of goods
- Political determination of the basket of goods
- Confirmation bias on the size on inflation
- Calculation problem from a restricted set of minds estimating the market effects
- Representative of the “average consumer.”
- This consumer doesn’t exist.
- This consumer doesn’t represent a real measure of economic growth. The full distribution of consumption better predicts market behavior. Market calculations are based on full distribution calculations. This is another form of a calculation problem. The GDP Deflator better accounts for this and many of the other errors.
- The “average consumer” is selectively determined and as a result selection bias occurs once again. The “average consumer” is constructed by taking various averages of various selected behaviors and consumptions.
In conclusion, a more proper estimate of inflation would be based on GDP, as GDP is far less selectively determined and biased than the CPI, although GDP is a simplification as well. The secondary goods market matters for the economy as well, for example.