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We all know that the government's calculation of inflation using the CPI is flawed as it understates inflation. Right?

Well the Fed agrees - the CPI is flawed. However, while most assert that the government's calculation of the CPI understates inflation, the Fed contends in a new paper that it actually overstates inflation. In short, the paper claims that government bookkeepers do not accurately adjust the price of new cars (5.2% of the overall CPI) for all the different types of incentives manufacturers offer. The end result is that while the CPI asserts that auto prices have been falling at one rate, the true rate of decline is even greater.

Source: Does the CPI Understate Inflation?