One fundamental problem with the consumer price index is that it is the result of what most people would consider a complex calculation. This should not be surprising, since they are tasked with converting the price change of large number of items (80,000 items in the United States) into a single monthly index percentage change. People who are mad about the price of eggs going up generally just look at the price of eggs, they do not want to hear academic jibber-jabber about 80,000 items or (oh dear) a Laspeyres formula.
In this section, I am not going to attempt to explain the formulae used by the national statistical agencies. Anyone comfortable with reading those equations either know the answer already or would be sensible enough to go to the source agency rather than rely on me not mangling the equation during the editing process. Instead, I will explain the fundamental issues that we see in the simplest possible price index: one with two types of apples. A reader might immediately ask: why use two types of apples, and not apples and oranges (which I used in the first draft)? The explanation for that choice is given later, but the short answer involves not mixing up apples and oranges.
I want to warn readers that they should not spend time attempting to find logical flaws with my “index” calculations. I have come up with examples that I believe give a good feel for the underlying economic issues, but I can think of at least one way of “breaking” a suggested calculation by playing around with the numbers. Statistical agencies use more complex formulae than I use, and if you want to nitpick, you need to look at those formulae.
But before we get to simplified index calculations, we need to address why we need consumption weights in the first place? Why not just look at the price of a fixed basket of goods?
Fixed Basket of Goods
The most intuitive price index is one that corresponds to a fixed basket of goods. (Price indices also include services. But I will just write goods in this section since I do not want to have to write “fixed basket of goods and services.”) The idea is straightforward: if you buy the same goods at different times, how much does the price change? One whimsical version of this index is “The PNC Christmas Price Index.” This is an index that tabulates the cost of buying the items listed in the song “The Twelve Days of Christmas” (with a certain amount of imagination needed to determine prices for things like “10 lords-a-leaping” in the non-aristocratic United States). One might run into indices of this type in economic history, where researchers are attempting to summarise price trends in earlier eras when the CPI was not calculated.
To give an example that will be used in the rest of this section, imagine a price index for a subset of fresh fruit that just includes Cortland Apples and Empire apples. (These are two popular varieties of apples that are grown in Quebec, I have no idea whether readers elsewhere are familiar with them.) Although not too many people would be interested in such an index (other than apple lovers), this might be a sub-index of a larger index. We then assume that a household buys 30 apples of each type each month.
If the price for these applies conveniently start $1 at each, then the starting price for the total fruit basket is $60. We could strip the dollar sign out of the quoted number and say the price level is 60.
Let us then imagine that the price of Empire apples doubles to $2, but the Cortland ones remain at $1. Then the cost of the basket is $90 ($60 for the 30 Empire, and still $30 for the 30 Cortland). This is a 50% increase, which makes sense. Previously, there was a 50/50 weighting between Empire and Cortland, and so the overall inflation rate is a 50/50 weighting of the two percentage changes (100% and 0%).
Mad About Weightings
If you wade through complaints about rising prices not being reflected by the CPI, most of what you see are effectively complaints about weightings. People mad about price increases just want to talk about those price increases, and do not want to discuss other goods and services whose prices did not rise. In the previous example where Empire prices doubles but Cortland were unchanged, one would be ensured that there will be hundreds of angry people on the internet discussing Empire apple prices, but not Cortland. Even though the price index rose by 50%, that is not good enough because that does not match the 100% Empire price rise.
Although one might feel sad for fans of Empire apples, we need to accept that macroeconomics is the study of overall behaviour. Although the fixed basket of Cortland and Empire apples is imperfect (for reasons to be discussed), it at least is supposed to reflect an economic concern of households: how much am I spending on apples?
As such, we need to have some means of weighting the different percentage price changes into an average price change. When we look at how price indices are used, we need to have the weighting set so that they reflect the overall consumption of households.
Why Not a “Fixed Basket?”
We can then return to the question of having a “fixed basket”: always have the same number of items purchased each month? If we buy the same things every month, why not just add up their cost (like in my example)?
The immediate response to that question is that my example “index” is misleading, as it consists of generic fresh fruit that appear somewhat timeless from the point of view of consumers who are not particularly concerned about the histories of apple varieties. If we jumped to things linked to technology, problems with fixed consumption baskets are obvious. For example, renting VHS video cassettes was an extremely common expenditure item in the 1980s. At the time of writing, it is extremely hard to find stores that rent even the successor technology to VHS cassettes – Digital Video Discs (DVDs). Conversely, cellular data plans are a feature of most families’ budgets, and such plans did not exist in the 1980s. Any attempt to create a fixed basket of consumption goods is eventually going to look laughable in modern industrial capitalist societies.
One might say that this is true for technology goods but is not true for non-processed foods. Why not have a fixed basket for those items? (One crank made exactly that argument on social media just before I wrote this section.) Even if we want to skate over awkward questions like how food with “organic” designations fit in with food when those designations did not exist, consumption weights change (admittedly slowly). North America consumption of quinoa was negligible in the 1970s. Coffee selection is vastly improved in North America since the 1980s, and grocery coffee purchases are increasingly weighted towards coffee pods.
Although whole foods are a convenient category that seems comparable over time – Statistics Canada has a section breaking out the prices used for selected ones as part of its CPI release – they are an increasingly small weighting in consumer budgets in developed countries. You can find other “generic” goods and services – natural gas, gasoline (sort of, blends change), hair cuts – but they are in scattered categories. To be useful, we need to make periodic surveys of consumption to get weights that reflect what people are actually spending money on.
Weightings are Tricky (And Get Some People Mad)
If government statisticians tracked every single transaction in the economy, they would know exactly the current consumption spending weighting of consumers. The problem is that they do not have access to that information. It is time consuming (and expensive) to survey consumers to get detailed breakdowns of their consumption. (By contrast, getting price data is relatively easy – just send government employees into stores to see what prices are posted.) Consumption surveys are done at a lower frequency. The U.S. Bureau of Labor Statistics describes the weighting situation as:
The CPI measures the change in the cost of goods and services purchased by consumers from one period to the next. Household spending weights are used to average the changes in component goods and services into the All-items index. In the first 50 years of producing the CPI, the BLS updated the spending weights roughly every 10 to 15 years based on spending information collected in periodic household surveys. In the 1980s the Consumer Expenditure Surveys (CE) became continuous and the BLS began updating the CPI spending weights every two years, starting in 2002, when the CE sample was increased to support more frequent weight updates.
(Taken from the 2022 CPI Weight Update information: https://www.bls.gov/cpi/tables/relative-importance/weight-update-information-2022.htm.)
An update frequency of every two years might not sound too bad, but there is a fundamental problem: consumption patterns will shift based on price changes. For readers who are fans of free market capitalism, one of the selling points of the system is that households and firms change behaviour based on price signals. If the price of Empire apples doubles, you are supposed to say to yourself “Maybe I will replace my intake of relatively expensive Empire apples by Cortland apples.” If we had monthly surveys of consumption weights that updated in line with prices, we would know how much substitution happened. But we do not, and so economists need a methodology to make a guess how much substitution occurred.
Although most of us accept that we are stuck with making an educated guess for substitution, this is a topic gets some people mad. By an amazing coincidence, the people who are most mad about assuming that consumers substitute away from goods that jumped in price are pretty much the same people who insist that free market capitalism is great because of price signals. (I will be dwelling on this point multiple times in this book, since it is shows up in a variety of complaints.)
I will now look at possible alternatives to what happens in response to the Empire apple jump.
Total Substitution
If we wanted to reduce the reported rate of inflation, we could assume that consumers substitute completely away from the relatively expensive apples. Instead of buying 30 Empire and 30 Cortland, they could just buy 60 Cortland apples. Since we assumed that Cortland prices are unchanged at $1, the total consumption is unchanged at $60. This is a 0% inflation rate (matching the inflation rate for the Cortland variety).
Of course, this outcome does not match the description of the fixed consumption basket – since the number of each item changed. Instead, we have a situation like the commonly used price indices (like the CPI): we are tracking the cost of a category of goods (apples within fresh fruits) over time. Since we no longer are buying a fixed basket of goods, we really should not put a dollar value on the index. Instead, we are looking at the percentage change in the price of buying two varieties of apples over time.
Since we are not using a fixed menu of purchase amounts, we are always working with relative prices. To calculate the percentage change on the overall basket, add up the percentage changes of each item multiplied by their assumed weight in the monthly purchase basket. In the case of total substitution, we have a 0% weight on the 100% change in Empire prices plus a 100% weight on the 0% change in Cortland prices. In the fixed basket example, there is a 50% weight on the two price changes, giving the 50% overall inflation rate.
However, assuming consumers always stop purchasing goods whose prices rose the most would be as silly as always putting a 100% weight on the fastest-rising prices. (In fact, there are some logical problems with such a situation. What happens if Empire apples were unchanged the next month, while Cortland apple prices doubled?) We need some magic way to split the difference.
Mysterious Model Weight
We then let some economists loose to come up with a model that gives us an updated consumption weight that is a function of relative price changes. (If every single item in the sub-index has the same percentage change, the weighting does not matter.) If you want to go through the literature, there will be a lot of jargon discussing the models. My expectation is that the reader is not in charge of developing new price indices, and so I see no need to delve into this jargon.
Since I am lazy, I will assume that the model output conveniently hits the midway point between the two previously discussed cases. This is purely a literary assumption – actual models used in practice will have different weighting shifts based on the data.
If we assume that consumers split the difference and buy 45 cheap Cortland apples and 15 expensive Empire ones (instead of 30/30), the total cost of the basket is now $75. This is 25% higher than the previous basket price of $60. This 25% inflation rate is determined by having a 75% weight on the Cortland price change, and a 25% weight on the Empire price change.
If we want to think in terms of the prices of baskets of goods, the inflation rate that is calculated is not the change in the price of the old basket of goods in the current period. Instead, it is the change in the price of the current basket of goods versus buying that new basket at the old prices.
This is not how people who get mad at inflation statistics want to think. They invariably present price changes based on buying the old basket of goods at current prices, rather than what being based on what it would have cost to buy the current basket at the old prices.
To the extent that price spikes represent shortages, we also have the problem that substitution must happen. If Empire apple prices spiked because there was a highly selective crop failure, there are less Empire apples to buy. The volume of Empire apple purchases must fall. That said, this is trickier to apply to globally traded goods. There might be a shortage of oil at the global level, leading to a price spike on oil markets, but a rich country might keep importing the same amount and keep consumption unchanged.
We only would know how much substitution there was if we had access to monthly consumption data (which we do not).
Let Us Mix Up Apples and Oranges!
We can then ask ourselves: if apple prices have a high relative price shift, why would consumers not get their fresh fruit fix by buying oranges? That is, we could assume that consumers will substitute spending based on relative price shifts within the wider fresh fruit category.
This is a possibility that creates a lot of complaints about CPI, based on people not paying attention to the actual calculations. The CPI calculations generally do not allow for substitution across item categories. To quote Greenlees and McClelland in “Addressing misconceptions about the Consumer Price Index”:
To begin, it must be stated unequivocally that the BLS does not assume that consumers substitute hamburger for steak. Neither the CPI-U, nor the CPI-W used for wage and benefit indexation, allows for substitution between steak and hamburger, which are in different CPI item categories. Instead, the BLS uses a formula that implicitly assumes a degree of substitution among the close substitutes within an item-area component of the index. As an example, consumers are assumed to respond to price variations among the different items found within the category “apples in Chicago.” Other examples are “ground beef in Chicago,” “beefsteaks in Chicago,” and “eggs in Boston.”
I used the non-intuitive “Empire versus Cortland apples” instead of “apples versus oranges” because the U.S. CPI calculation does not allow for substitutions across apples and oranges, only within “apples.” However, this is not going to hold for every price index, as they may allow for substitution effects within categories like fresh fruit.
At the higher level, one might ask whether people substitute across much different categories. If movies get more expensive, will they instead buy a video game? Although people always need to eat, they can do things like eat at home instead of at a restaurant.
To the extent that price indices do not allow substitution, they are going to overstate the true cost inflation experienced by households who react to price signals. This partly explains the massive disconnect between the mainstream economists that argue that the CPI overstates inflation versus the commentators who insist that CPI inflation rates understate inflation.
Non-Existent Goods
Another issue that pops up in index calculation is that we might have a price for a good or service in one month, but not in another. This could be the result of data gathering issues, outright shortages, a product coming into existence – or being pulled from the market.
Since we only have a price for the good or service for one month, we cannot give a percentage change in the price. One would need to dig into the methodology handbook to see how each statistical agency deals with this.
However, there is an interesting philosophical issue created by new product launches. In an environment of rising wages, it is easy to see how new product offerings might be “luxury” versions of existing ones.
One example that comes to mind is the evolution of take-away “coffee drinks” in North America from mainstream venues. Back in the Good Old Days (i.e., when I was a kid), North Americans mainly just bought plain coffees from restaurants/doughnut shops. By the 1980s, you had an infiltration of cappuccino and espresso and so forth in mainstream restaurants. Later on, we saw the rise of “iced coffee drinks.” Each of these evolutions had new beverages coming out at higher price points relative to the existing drinks.
Even though the prices of standard coffees might not have risen by much, switching to the new drinks meant that consumers were paying more money for the same amount of caffeine buzz. This allowed restaurants to grow their nominal sales, even though the stores might have had the same overall volume of customers.
This leads to one of my personal inflation theories. When we look at the late 1990s, the economy was buoyant, but the bears were mystified: where is the inflation? My reading of the situation was that companies were able to absorb increased nominal demand by pushing out luxury brands. This worked until the pandemic, where product innovations were not enough to absorb the nominal demand.
Concluding Remarks
It would be very easy to drown in jargon and mathematical notation when looking at conventional descriptions of price indices. Most of the internal debates among economists refer to complex assumed behaviour. But it is possible to see how price index calculations run into rather awkward questions by just looking at what happens with a basic example.
References
Detailed discussion of price index construction is best found at the methodology guides of national statistical agencies. Example references are listed in Section 1.2.
The PNC Christmas Price Index has been calculated by the PNC Financial Services group for over 40 years. It has a web page found at: https://www.pnc.com/en/about-pnc/topics/pnc-christmas-price-index.html
Greenlees, John S., and Robert B. McClelland. “Addressing misconceptions about the consumer price index.” Monthly Labor Review 131 (2008)
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