There are several versions
CPI-U - Consumer Price Index for All Urban Consumers
C-CPI-U Chained Consumer Price Index for All Urban Consumers
The CPI frequently is called a cost-of-living index, but it differs in important ways from a complete cost-of-living measure. BLS has for some time used a cost-of-living framework in making practical decisions about questions that arise in constructing the CPI. A cost-of-living index is a conceptual measurement goal, however, and not a straightforward alternative to the CPI. A cost-of-living index would measure changes over time in the amount that consumers need to spend to reach a certain utility level or standard of living. Both the CPI and a cost-of-living index would reflect changes in the prices of goods and services, such as food and clothing, that are directly purchased in the marketplace; but a complete cost-of-living index would go beyond this role to also take into account changes in other governmental or environmental factors that affect consumers' well-being. It is very difficult to determine the proper treatment of public goods, such as safety and education, and other broad concerns, such as health, water quality, and crime, that would constitute a complete cost-of-living framework.
CPI for Urban Wage Earners and Clerical Workers (CPI-W)
Consumer Price Index Frequently Asked Questions : U.S. Bureau of Labor Statistics
Average Percent Change
Table 1. Consumer Price Index for All Urban Consumers (CPI-U): U. S. City Average, by expenditure category and commodity and service group
The Social Security (SS) Cost-of-Living Adjustment (COLA) is tied to the Consumer Price Index for Urban Wage Earners and Clerical Workers (CPI-W). For the last 20 years it has been pretty close to the regular CPI. See Social Security COLA in Retirement. and See: Consumer Price Index For Urban Wage Earners And Clerical Workers (CPI-W) | Investopedia and Social Security Benefits Rising 1.7% For 2015, Top Tax Up 1.3% - Forbes
While advocates for the elderly argue CPI-W understates the true increase in costs the elderly face, deficit hawks have pushed for linking COLAs to an even lower measure of inflation known as the chained CPI.
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