This article is taken directly from pages 3.3-3.5 of the 2018 COLI Manual.
Why Are the Weights Identical Everywhere?
In published Cost of Living Index reports, the numbers above the index data at the top of each column show the weight each component index carries in the Composite Index: 13.36% for grocery items, 28.64% for housing, 10.46% for utilities, 10.46% for transportation, 4.44% for health care, and 32.44% for miscellaneous goods and services.
These figures reflect the typical distribution, for the entire nation, of spending for the specified kind of household. It’s not uncommon for someone to object that it’s unreasonable to weight housing at 28.64% for, say, a booming metropolitan area where housing prices are extremely high and a depressed metropolitan area that suffers from a housing glut and has exceptionally low prices. Clearly, housing is going to demand a larger share of the consumer dollar in the rapidly expanding economy. Remember that the Composite Index for an area is the sum of six products, each of the six component indexes multiplied by the weight for that index. Each of those six products is the ratio of local cost for that category to nationwide total living costs. Let’s demonstrate this, using housing as our example:
• First, consider the weight used for housing. Where does it come from? The weight housing carries in the Composite Index is the ratio of nationwide housing costs to nationwide total living costs: Housing Index Weight = 0.2864 = (U.S. Housing Costs/U.S. Total Living Costs) And the housing index for an area is the ratio of its housing costs to nationwide housing costs: Local Housing Index = (Local Housing Costs/U.S. Housing Costs) When we multiply 0.2864 by the local housing index to obtain housing’s contribution to the local composite index, U.S. housing costs in the two ratios cancel: 0.2864*(Local Housing Index) = (Local Housing Costs)/(U.S. Total Living Costs) Clearly, if we didn’t use the same weights for housing everywhere, we wouldn’t wind up with the ratio of local housing costs to total living costs nationwide.
We go through this process for each of the six component indexes and then sum the results. What we get is the ratio of total local costs to total nationwide costs. We multiply that figure by 100 to obtain the Composite Index.
What Can the Index Tell Us About Dollar Amounts?
The Cost of Living Index can be mined for more data than many users realize. By using the six products (local component index times index weight), we can find out how we’d expect expenditures to be distributed in different areas; and by assuming a given dollar amount for total spending in one place, we can determine what amount of money would be required and how it would be spent anywhere. Let’s work through an example. For simplicity, assume that annual spending by professional and managerial households on consumer goods and services averages $80,000 per year nationwide. Let’s look at data for two MSAs and determine not only how much the same standard of living would cost in those areas, but also how spending would be distributed by category. In the table on the following page, the first lines for U.S., Area A, and Area B show how the data would appear in the published report. Now we’ll go through a series of steps:
• Multiply each component index by its weight (the second line in each listing).
• Calculate each of these six products (the third line) as a percentage of the sum of products (that is, of the Composite Index) for each area. This figure is shown on the fourth line of each listing.
• Multiply the local Composite Index by $80,000 to determine total spending (the first cell in the last line of each entry).
• Multiply each category’s share of total local spending by total local spending to determine spending by category.
If our professional/managerial standard of living costs an average of $80,000 per year nationwide (after taxes), then such a household moving from Area B to Area A could expect to spend about $18,080 per year more for consumer goods and services. Its housing costs would rise by about $19,790 per year, its health care costs would grow by about $656, and its spending for miscellaneous goods and services
would increase by roughly $1,596. Lower costs for grocery items, utilities, and transportation wouldn’t offset the increases in other categories