Macro-Economics and What the ‘Chained CPI’ Could Mean for Social Security?

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Definition of Chain-Weighted CPI

By Dr. David Edward Marcinko MBA

Dr David E Marcinko MBAAn alternative BLS measurement for the Consumer Price Index (CPI), removing the biases associated with new products, changes in quality and discounted prices.

The chain weighted CPI incorporates the average changes in the quantity of goods purchased, along with standard pricing effects. This allows the chain weighted CPI to reflect situations where customers shift the weight of their purchases from one area of spending to another.

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Investopedia Example:

The chain weighted CPI incorporates changes in both the quantities and prices of products. For example, let’s examine clothing purchases between two years. Last year you bought a sweater for $40 and two t-shirts at $35 each. This year, two sweaters were purchased at $35 each and one t-shirt for $45.

Standard CPI calculations would produce an inflation level of 13.64% 

((1 x 35 + 2 x 45)/ (1 x 40 + 2 x 35)) =1.1364

The chain weighted approach estimates inflation to be 4.55%

((2 x 35 + 1 x 45)/ (1 x 40 + 2 x 35)) =1.0455.

Using the chain weighted approach reveals the impact of a customer purchasing more sweaters than t-shirts.

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BLS Application

  • What is the C-CPI-U and when did the Bureau of Labor Statistics (BLS) begin publishing it?

BLS began publishing the Chained Consumer Price Index for All Urban Consumers effective with the release of July 2002 CPI data. Designated the C-CPI-U, the index supplements the existing indexes already produced by the BLS: the CPI for All Urban Consumers (CPI-U) and the CPI for Urban Wage Earners and Clerical Workers (CPI-W).

The C-CPI-U employs a formula that reflects the effect of substitution that consumers make across item categories in response to changes in relative prices.

Read more: C-CPI-U data can be found on the BLS web site at

Substitution Bias

  • What is substitution and substitution bias? And does the C-CPI-U eliminate it?

Traditionally, the CPI was considered an upper bound on a cost-of-living index in that the CPI did not reflect the changes in consumption patterns that consumers make in response to changes in relative prices.

Since January 1999, a geometric mean formula has been used to calculate most basic indexes within the CPI; this formula allows for a modest amount of substitution within item categories as relative price changes.

The geometric mean formula, though, does not account for consumer substitution taking place between CPI item categories. For example, pork and beef are two separate CPI item categories. If the price of pork increases while the price of beef does not, consumers might shift away from pork to beef. The C-CPI-U is designed to account for this type of consumer substitution between CPI item categories. In this example, the C-CPI-U would rise, but not by as much as an index that was based on fixed purchase patterns.

With the geometric mean formula in place to account for consumer substitution within item categories, and the C-CPI-U designed to account for consumer substitution between item categories, any remaining substitution bias would be quite small.


Link: What ‘chained CPI’ could mean for Social Security

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