There is a lot of conversation and controversy about the “chained consumer price index” being used to adjust social security payments instead of the traditional CPI. Without taking a position on that question, it is good to understand the difference.
Any consumer price index is calculated by measuring price changes over time in a specific basket of goods and services. This basket is supposed to represent the purchase patterns of a typical household. (The Bureau of Labor Statistics partners with the Census Bureau to conduct the Consumer Expenditure Survey to measure on a regular basis what people actually do buy.) The difference between a standard CPI and a chained CPI is that a chained CPI takes into account one specific aspect of consumer behavior: buying more of goods that rise less in price and less of goods that rise more. For example, if apples rise in price by 10 percent and oranges rise by 5 percent, people will tend to buy a larger share of oranges and a smaller share of apples (but possibly less of both overall).
The standard CPI ignores this behavior; it assumes that the purchase shares of the items in the basket are fixed. The chained CPI lets people substitute goods and services that experience smaller price increases for those that experience larger ones. Because people are substituting goods with smaller price increases, you expect the chained CPI to report a lower inflation rate than the standard CPI. Therein lies the source of the controversy.