The CPI captures a measure of inflation for earners in the urban economy of the US, the so-called CPI-U that is reported in most media outlets as the main indicator of inflation. A number of changes have been made to the index over the years, in particular, in the 1980s and 1990s, which have caused controversy. In particular, charges are often made that the newer CPI formulas underreport real inflation felt by consumers.
The BLS explains and tries to justify these changes in a publication put out specifically to address public concerns with the ability of the CPI to measure cost-of-living changes in general and accurately reflect increases in particular [1]. The price index formula used in all of the basic CPIs prior to 1999 is called the Laspeyres formula. The problem with this, BLS claims, is it “tends to overstate changes in the cost of living; specifically, the change in a Laspeyres index is an “upper bound” on the change in the cost of maintaining a standard of living.” The Laspeyres formula requires the continuing use of the same market basket of items tracked in spite of likely consumer changes in purchases. The “upper bound” condition assumes that prices are constantly inflating and that maintaining the basket mix requires the consumer to pay the full price of increases for each item rather than switch items. But, what this paper neglects to mention is that the inverse is also true, that the Laspeyres formula is a lower bound on the change in the cost of maintaining a standard of living as well when a deflationary environment persists and prices continue to fall. In this latter case, consumers are likely to substitute more expensive items for items that were previously purchased, and these changes are missed by the formula as well.
Laspeyres was replaced by a geometric mean formula, which makes some account of the changes in purchases due to the increase in price (and decrease in price) of items in the market basket. This change is the chief point of contention as the BLS states “Among all the criticisms leveled at the CPI, its use of the geometric mean formula to reflect consumer substitution behavior is undoubtedly the most frequently misunderstood and mischaracterized.” The BLS justification for switching to the geometric mean is based on others using this method, rather than first principle arguments of why it is the correct method to use for CPI purposes. Sort of a, well everyone else is doing it so we should too, kind of argument. They say “the geometric mean is widely used by statistical agencies around the world. One of two formulas recommended by the International Monetary Fund9 and approved by the Statistical Office of the European Communities (Eurostat) for use in those countries’ Harmonized Indexes of Consumer Prices (HICP), the geometric mean is used by 20 of 30 countries as a primary formula for computing the elementary indexes in their HICP’s”, which doesn’t explain why they prefer this method, only that they use it.
The BLS paper gives an example that is designed to explain and convince the reader that the switch to geometric mean formula was the correct decision. The example reads “Suppose that a person buys four candy bars each week: two chocolate bars and two peanut bars. The bars cost $1 each, so her total spending per week on candy bars is $4. Now suppose that, for some reason, the price of chocolate bars quadruples to $4, while peanut bars re-main at $1. The goal of the CPI is to measure how much the consumer needs to spend each week to consider her-self just as well off as she was before the price increase. A Laspeyres price index calculates the cost of the original purchase quantities: two candy bars of each type. There-fore, the answer according to the Laspeyres formula is that the consumer would need $10 to be as well off as before.”
The paper then goes on to describe the reasoning why the geometric mean is better and why the derived result is better. They say “The Laspeyres answer is correct, however, only if the consumer is completely unconcerned with changes in price and always chooses to purchase chocolate and pea-nut bars in equal numbers, regardless of which is cheaper. The Laspeyres answer is called an upper bound because the right answer cannot be greater than $10; the consumer certainly will be at least as well off as she was before if she can continue to purchase two bars of each type. At the other extreme, the right answer cannot be lower than $4. In the unlikely case that the consumer is entirely indifferent between types of candy bar, she could respond to the increase in the price of chocolate bars by buying four peanut bars instead of two of each type, and she would be no worse off than she was before, even if she still had only $4 to spend. Of course, neither the Laspeyres upper-bound answer of $10 nor the lower-bound answer of $4 is realistic. In the real world, people make tradeoffs on the basis of both price and their preferences, and the actual answer lies in between the two bounds. With $7, for example, our consumer could afford to buy seven peanut bars, one for every day of the week. Thus, $7 might be sufficient to make her as satisfied at the new prices of candy as she was with $4 at the old prices. Put another way, we can be confident that, for some consumers, the Laspeyres result of $10 would overstate the amount they need to maintain their original level of candy satisfaction. The geometric mean formula adopted by the BLS for use in most CPIs gives a somewhat lower answer than the Laspeyres formula, because it puts less weight on the prices that have increased the most (in this case, the price of chocolate bars) and more weight on the prices that have increased less. As it turns out, the geometric mean would say that $8 is the amount needed to keep the average consumer at the original satisfaction level. With $8, the consumer could purchase one chocolate bar and four peanut bars, offset-ting the reduced number of chocolate bars by an increase in the total number of candy bars.”
If the example is read carefully and the thinking process of the consumer is followed closely then one will realize that this is actually an argument against the geometric mean formula. Consider, the consumer wants two chocolate and two peanut bars. This combination is what makes the consumer happy. Then the chocolate bar price rises from $1 to $4 a bar. The explanation says that the consumer will switch to spending $8 to get the same satisfaction as before. How this is justified is not explained, but it doesn’t make much sense, as the consumer has to go with less of something or a proportion between the bars that were not the same, so something is lost. Furthermore, the consumer has to actually feel that increase in prices to induce a behavior to make the switch in consumption. That is, the actual price increase felt by the consumer is from $4 to $10 for the desired combination of bars. The consumer may then make a change to his/her purchasing combination but only after feeling the effect of the price inflation. A proper measure of inflation needs to contain this full measure of the price increase, as it is precisely this increase in price that prompted the change in behavior.
Let’s take this a bit further, as the BLS appears to have a crystal ball that tells them how people will change not just their purchase activities as a result of a price change, but how people’s satisfaction as a result of this change will be. BLS does recognize that our particular consumer may really likes two chocolate and two peanut bars and may be fairly affluent so that the price increase won’t trouble him/her much. In this case, the consumer will continue to buy two chocolate and two peanut bars end endure the full price increase. But, they discount the effect of the price increase on those of lesser mean. Those for which the price increase actually matters!
The change is actually worse than it is made out to be as the BLS may actually have created some kind of shopping budget estimator base on some means of estimating changes in purchases due to changes in price, rather than changes in prices themselves. This is not a measure of inflation; rather it is a measure of the ability of consumers to consume. For example, let’s say a mom goes grocery shopping for her family every week and has $100 dollars in her grocery budget. She buys $90 of various groceries and $10 for prime rib steak, so the total is $100. The next week the price of the various groceries stays the same, but the prime rib went up to $15, so the mom instead buys flank steak, which is only $10, resulting in the same $100 total. In a sense, the geometric mean formula measures the budget of how much consumers have to spend and how they allocate that budget, rather than the inflation in prices that go into the consumption decisions.
This is not to say that changes in consumption don’t happen, they do, but for the purposes of calculating inflation, these changes need to account for the price changes that drove the change. Indeed, the basket composition should actually be a bit sticky in that after a change is made from one item to another, some measure of the price of the original item should still be included in the price index for some months or years hence. For example, for the infamous case of switching from steak to hamburger, once the switch is made where the basket only contains hamburger, some measure of the price of the steak should still be included and followed for some time, as that consumer probably still desires the steak and checks the price to see if this time the steak can be on the menu for dinner tonight. After some years, the consumer may give up ever hoping for the steak as it appears permanently out of reach, so only then could the price of steak be dropped from this hypothetical index.
[1] https://www.bls.gov/opub/mlr/2008/08/art1full.pdf
