In retrospect, I suppose it was somewhat timely that I wrote an article last week about the Consumer Price Index as a measure of inflation. Specifically, I wrote about how the CPI can overstate increases in a household’s cost of living:
The purpose of the Consumer Price Index makes it necessary to evaluate how well the CPI measures changes in a typical household’s cost of living. There are two main challenges to the CPI in this regard:
First, the Consumer Price Index doesn’t account perfectly for changes in product quality. For example, an average computer today might cost about the same as an an average computer cost last year, but today’s computer is better than last year’s computer in a number of ways that the CPI doesn’t account for. Similarly, the invention of new goods poses a challenge to the Consumer Price Index, since incorporating such goods into the basket while maintaining comparability over time can get quite tricky.
Second, the Consumer Price Index assumes that a household purchases the same basket of goods regardless of how the prices of those goods changes. In reality, however, households are probably smarter than this, and they likely substitute away from items that get disproportionately expensive to goods that got comparatively less expensive.
Both the inability of the CPI to incorporate technological progress and its failure to account for substitution in consumption decisions imply that, in most cases, the Consumer Price Index likely overstates increases in the cost of living that households actually feel.
What I didn’t get into in this article was the fact that in August 2002 the Bureau of Labor Statistics rolled out an index called the Chained Consumer Price Index that tries to correct for this shortcoming:
In August 2002, the U.S. Bureau of Labor Statistics began publishing a consumer price index (CPI) called the Chained Consumer Price Index for All Urban Consumers. Designated the C-CPI-U, the index employs a superlative Tornqvist formula and utilizes expenditure data in adjacent time periods in order to reflect the effect of any substitution that consumers make across item categories in response to changes in relative prices. The new measure is designed to be a closer approximation to a “cost-of- living” index than the existing BLS measures.
That document is, well, 56 pages of mostly math (And what the hell is a Tornqvist formula? And why does u not follow q?), so allow me to summarize a bit:
The Bureau of Labor Statistics defines a Cost of Living Index (COLI) as “the ratio of the minimum expenditure required to attain a particular level of satisfaction in two price situations, a comparison period and a base period.” In other words, a cost of living index answers the question “how much money do you need in order to be as happy now as you were before?” Using the traditional CPI as a cost of living index makes an implicit assumption that the way to be as well off as you were before is to buy the same stuff, but, while keeping consumption constant is in fact *a* way to be as well off as you were before, it’s not the only way, and not usually the cheapest way.
For example, to reference a popular meme, suppose I am indifferent between one horse-sized duck and 100 duck-sized horses. (For consuming, not fighting, of course.) Both groups of items would give me the same utility or happiness, and my choice between them would therefore be determined by which one is more expensive. Let’s say that, for now, the prices of both bundles are the same and I randomly decide to go with the horse-sized duck (so I could ride it like Nicholas Kristof, obviously). Now fast forward to next year, and imagine that the price of the horse-sized duck has risen by 10 percent but the price of the 100 duck-sized horses has remained constant. The CPI would imply that my cost of living has increased by 10 percent, whereas I, as a utility-maximizing consumer, would simply switch over to the 100 duck-sized horses and be just as happy with no additional expenditure required. The chained CPI, therefore, should state that my cost of living has remained constant.
Chained CPI uses only observed price and quantity behavior and doesn’t try to estimate cross-price elasticities of demand or anything like that and instead draws its estimates from combining traditional CPI data with expenditure data from the Consumer Expenditure Survey. (The general idea is that if you know how much money people spent on stuff and the price of that stuff, you can back out the quantities purchased over time and the substitutions made in response to changing prices.) In order to understand how chained CPI is constructed and analyze its shortcomings, it’s important to know a bit about how the regular CPI is constructed:
The CPI is built in two stages. In the first stage, price changes for roughly 80,000 specific items per month are averaged to yield 8,018 estimates of aggregate price change. This stage is often referred to as “lower-level aggregation” or “elementary-level aggregation” as it involves averaging the most fundamental component of the index – observed price change for specifically defined consumer goods, services, and products.19 For example, the prices of approximately ten different brands and styles of watches at various locations in Chicago are observed each month, compared to the prices observed in the previous month, and averaged together to produce an index of price change for watches in Chicago. Watches (ITEM=AG01) is one of 211 elementary items, and Chicago (AREA=A207) is one of 38 elementary areas in the current CPI market basket structure. The Chicago-watch index is one of the 8,018 (211 items x 38 areas) elementary indexes produced in the first stage of CPI construction.
In the second stage, the elementary indexes are averaged together to yield various aggregate indexes and ultimately the All-Items, U.S. City Average index of price change. See Figure 3.1.
Therefore, the chained CPI would ideally account for substitution at both of these levels- i.e. between different brands or types of item (intra-item) and across different items (inter-item). One of the problems that the BLS faces, however, is that expenditure data is only available at the higher level of aggregation. (For example, the BLS has expenditure data for watches but not for stainless-steel watches.) Further complicating this matter is the fact that the expenditure data is only available with a lag, so it’s not really possible to construct chained CPI in real time. The BLS’s solution to this problem is to compute interim values and then update them with final values once the expenditure data becomes available.
Because the data isn’t available, the method for the lower-level aggregation is the same for the chained CPI as it is for the regular CPI. (This is technically a little more complicated than how it is usually described in textbooks, and you can see the formula on page 15 of the pdf I linked to above.) The chained CPI is calculated by, not surprisingly, chaining together indexes of one-month price changes:
Consumer substitution behavior is not assumed by the Tornqvist formula, but rather implicitly accounted for by use of current and basemonth expenditures. An index of one-month price change is calculated and then multiplied by the previous month index value to obtain the current month index value.
If you want to go down a serious rabbit hole of math, you can check out the formulas on page 23 of the pdf. What is most important to know here, however, isn’t the specific math but rather the fact that the statisticians who calculate chained CPI aren’t making assumptions about the substitutability of different goods but are instead looking at how people actually behave. (I point this out because I recall some talking heads claiming that the BLS could mess around with chained CPI to produce different inflation numbers by changing the substitution assumptions, which isn’t really true.)
So what you’re really dying to know is what this has to do with Wile E. Coyote, I can tell. So here’s the thing- there are murmurs in the media and among policy makers regarding adopting the chained CPI described above as the official measure of inflation for a number of policy purposes. Theoretically, chained CPI seems like a totally reasonable way to think about changes in the cost of living in an economy, so it’s hard to object on principle to using this measure to adjust changes in government benefits, tax brackets, etc. However, there are two problems with this proposal.
First, the lag present in the final values of chained CPI as well as some of the other data limitations make the implementation of such a policy problematic and would likely make the laws that the policy affects more complicated. Second, the fact that the traditional CPI numbers tend to overstate the true increase in cost of living implies that the chained CPI figures will be lower than the traditional CPI, which means that government benefits that are indexed to inflation will not increase as quickly as they do now, the income cutoffs for tax brackets will not move up as quickly as they do now, and so on. Therefore, adopting chained CPI as the official measure of inflation for these purposes would translate to tax hikes and benefit reductions for a large number of people.
But that latter thing is good, right? We keep hearing about the fiscal cliff and the need to cut the deficit, and it seems like this could be one reasonable way to do so since it would raise taxes and cut spending. While this is true, it’s important to consider who would be most affected by this change- given that the most notable program that is indexed to inflation is Social Security, it’s likely that such changes will disproportionately impair the elderly. In addition, there is evidence that the tax-bracket changes resulting from adopting chained CPI would disproportionately impact lower-income households.
Maybe this chained CPI thing doesn’t sound so good after all- so why are so many people talking about it? Policy makers seem to be under the impression that, regardless of whether adopting chained CPI is a good policy in terms of distributional impact, it’s a politically popular one because policy makers seem to assume that people can’t complain about what they don’t understand. In addition to being at odds with empirical evidence that people complain about plenty of things that they don’t understand, it’s kind of crappy to favor confusing changes and a lack of transparency for the sake of political expediency.
That said, there is a potential efficiency argument to be made in favor of this approach. When it comes to taxes and policy changes, there are two types of costs that occur. The first is a transfer of money from households and companies to the government, and the second is a loss of economic activity that occurs (deadweight loss, in economic terms). (For example, if I value a t-shirt at $15 and you can produce it for $13, a $3 tax will prevent an otherwise value-creating transaction.) While the first cost is important from a distributional perspective, the second is important from an efficiency perspective as well. As counterintuitive as it may seem, taxes and policy changes are more efficient (not necessarily more fair, however) when people don’t change their behavior in response to them, since then there is only transfer and no loss of economic activity. And hey, people can’t change their behavior fully if they don’t understand how policy changes are affecting them, right? Which, at long last, brings me to Mr. Coyote:
(I particularly like this metaphor and image because of the cliff aspect. Also, I am totally envisioning John Boehner as Road Runner.) The difference is that, as long as Wile doesn’t realize that he is off the cliff, he will remain stable, but we can’t say the same for the budget of an elderly person or a lower-income household. We already have policies that rely on the frailties of human behavior in order to succeed, let’s not pile on others that rely on ignorance.