The COLI’s inability to reflect reality

Difference in Laspeyres (traditional CPI) and Törnqvist (COLI) annual percent change: December 2003 — December 2019 (Klick & Stockburger; 2021).

1. Introduction

The way inflation ought to be measured is strongly debated due to several conceptual challenges in constructing an appropriate indicator. In this essay, I argue that the most prevalent indicator for inflation, the consumer price index (CPI), should not approximate a cost-of-living-index (COLI). This is because social security benefits (SSB) tied to a CPI approximating a COLI fail to properly insulate social security recipients from increases in the cost-of-living, which is one of the main purposes of the CPI. I argue this in the context of the current convention of measuring inflation with a single indicator representing changes in the aggregate expenditure of the general population.

I will begin by providing historical background surrounding the debate around measuring inflation in the United States (US) and I will briefly explain two contentious assumptions within the COLI framework. I will then challenge these assumptions by providing two premises in support of my conclusion that the CPI should not approximate a COLI. Lastly, I will respond to an objection that fails considering current conventions for measuring inflation.

2. Background

In this section I will provide historical background to shed light on the problems of measuring inflation. Inflation is commonly understood as the increase in prices over a certain period (Oner, 2022). In the US and most other regions the CPI is the most widely used measure of inflation (BLS, 2020). The importance of the CPI for SSB indexation is attributable to the introduction of legislative measures in 1969 by the Nixon administration. Since then, SSB are pegged to changes in the CPI. The aim is to insulate recipients (over 64 million Americans in 2021) from “rises in the cost-of-living” (Reiss, 2008; SSA, 2022). The CPI has been measured by the Bureau of Labor Statistics (BLS) using a version of the Laspeyres price index formula. This formula compares the changes in the cost of purchasing a fixed basket of goods in the base period with the current period. The quantity weights of this index are given by the share of a good in the total expenditure of all households in the base period (Reiss, 2008).

In 1996, a group of economists called the Boskin Commission reviewed whether the CPI accurately measured changes in the cost-of-living. The Commission estimated an overall upward bias in the CPI of 1.1% due to unaccounted quality changes and substitution bias (Reiss, 2008). Quality change refers to the observation that goods captured in the fixed base period basket of goods change over time, whether marginally (i.e. new version of a good) or significantly (i.e. a discontinued good is replaced by a new one). It is easy to see how the quality of, e.g., consumer electronics changes dramatically within a decade (a decade was the frequency with which quantity weights were updated before the commission’s report). The traditional CPI (Laspeyres) could only inadequately account for quality changes (by “linking”, see Nordhaus, 1998). Nordhaus (1998) detailed how the real price of light, measured in lumen-hours, dramatically decreased over a 200-year period even though the traditional light index, which tracked prices of lighting devices, increased. Furthermore, the traditional CPI could not account for the phenomenon that consumers substitute base period goods for cheaper alternatives in the current period when prices of the initial goods increase (substitution bias). If, for instance, prices for beef in the US increase due to an export ban from Argentina (FAS USDA, 2021), people in the US might substitute beef for, say, chicken. To sum up, the traditional CPI overstates increases in the cost-of-living due to quality changes and substitution bias.

To remedy this shortcoming, the Boskin Commission proposed to approximate a COLI using a superlative index formula (i.e. Törnqvist index). It’s worth noting that the Boskin Commission simply applied the COLI standard without arguing for it even though that is “[...] a contentious proposition that requires serious argument” (Deaton, 1998). The Törnqvist index is obtained by weighting the growth rates of prices by their shares within the budget. The shares of the prices within the budget are averaged over the base and current period. Thus, unlike the Laspeyres price index, the Törnqvist index also considers current period quantities. Subsequently, the commission argued, a Törnqvist index could account for both quality change and substitution bias since in theory, it only relies on price and quantity data of both the base and the current period to approximate the true cost-of-living. It does so by holding a given level of utility constant, and not a certain basket of goods. Therefore, a COLI answers the question of how much more/less one needs to spend to maintain the base period utility level (Reiss, 2008).

However, to infer the level of utility certain assumptions are needed. First, consumers must be utility maximising since the consensus among economists is that we can only attribute utility functions to such consumers. Second, a COLI-approximating CPI formula (i.e. Törnqvist index) is accurate for a single utility maximising consumer (Deaton, 1998). Thus, to represent the utility of many agents in an approximation of a COLI presupposes stable, homogenous consumer preferences within the group considered (Reiss, 2008). As Reiss (2008) noted, these presuppositions are neither necessarily nor universally true, and, as I aim to show in the next section, pose serious challenges to the practicability of approximating the true cost-of- living increases of social security recipients.

3. Practical difficulties in maximising utility and diverging preferences

In this section I will provide two premises for my argument and respond to one objection. The first premise states that it is unlikely that social security recipients can effectively maximise their utility. Within the framework of a COLI, it is assumed that consumers can maximise their utility rather instantaneously without taking a long time to adapt to price changes. If they took a long time to adapt to price changes, they wouldn’t be able to substitute away from the relatively more expensive beef to the less expensive chicken like the aggregate COLI approximation requires them to do. In practice, this requires consumers (i) to have accurate information at every point in time about price and quality changes of goods and services and (ii) to be able to act on this information. For indexing SSB, it is particularly important that social security recipients can switch to cheaper alternatives when prices of goods and services increase. This is because they are, in theory, compensated for exactly the amount that allows them to reach the same level of utility as in the base period provided they switch to cheaper alternatives. However, it is unreasonable to expect consumers to gather quasi-real-time information on price and quality changes. Even econometricians are restricted by limited information and must approximate the state of the economy (Branch, 2004). Even when we assume that consumers had perfect information, they would also need to be able to purchase the cheaper goods. As Cartwright and Runhardt (2014) point out, the gain in market share of discount stores in recent years led the BLS to adjust the CPI accordingly. However, discounters are often located outside the town centres. Social security recipients who live on such a limited budget that they cannot afford the transportation costs to go there cannot buy these cheaper goods (BBC, 2022). Thus, neither condition (i) (gathering accurate information about prices) nor (ii) (acting on this information) are likely to be met by social security recipients.

The second premise states that a COLI insufficiently accounts for possibly diverging preferences of social security recipients, which might force them to substitute regardless of whether they can maintain their level of utility. Reiss (2008, p. 41) notes that changes in the market share of a good, which a Törnqvist index takes into account, often fail to be indicative of consumer preferences. In a recent interview (BBC, 2022), food blogger Jack Monroe detailed how she noticed that at the beginning of 2022 in the United Kingdom (UK), price increases of relatively cheaper goods within a product category (e.g. conventional rice) that are disproportionally consumed by low-income households fast outpaced price increases of relatively more expensive goods (e.g. premium rice). Since social security recipients are at the lower end of the income distribution and for many, SSB make up most of their total income (CBPP, 2020), they face extraordinary challenges when trying to avoid these price increases. If they wanted to keep their base period level of utility constant, they would have to spend more than what their COLI adjusted SSB allow them to spend. If that is not possible, they are forced to consume a different basket of goods in the current period. If low-income consumers are then able to maintain their level of utility depends on whether suitable substitutes exist. If substitutes exist, consumers might be able to maintain their level of utility contingent on their ability to overcome the previously mentioned practical challenges of maximising utility. However, adequate substitutes for the most basic but necessary goods rarely exist (BBC, 2022). Thus, it seems that a CPI approximating a COLI representative of the overall population insufficiently accounts for price increases in the basic items typically chosen by social security recipients. Therefore, in the case of diverging preferences social security recipients might be forced to substitute away from their base period choices. As shown, this leaves them with little chance of maintaining their base period level of utility, particularly when most of their income depends on SBB.

One objection to the argument is that a CPI approximating a COLI would be more accurate in measuring the true cost-of-living increases of social security recipients if it were adjusted to reflect the choices of this subset of the population. By doing so, the inadequacies stemming from preference differences between the general population and social security recipients can be mitigated. Monroe currently develops a new CPI (“Vimes Boots Index”) that is composed of precisely those most basic but necessary items typically chosen by low-income households (Flood, 2022). While this is an option worth exploring, it confronts us with one of two scenarios. First, the convention of a single CPI would be maintained, with the CPI reflecting only the cost-of-living increases of social security recipients. This scenario would mean that 4/5 of the US population would be inadequately represented by the CPI, making the CPI rather impractical. Second, the social security administration would tie adjustments to a CPI for social security recipients that would coexist next to the current CPI. An example could be a CPI for the elderly (CPI-E, Klick & Stockburger, 2021), or a version of a “Vimes Boots Index”. Such a scenario would raise multiple issues like general confusion about the usefulness and applications of the CPI, which was initially intended to capture the single phenomenon of “rising prices”, and the danger of “index rate shopping” by employers and politicians (see David, 2019). Therefore, it is rather uncertain whether adapting a CPI that approximates a COLI to the subgroup of the population would really address the concerns raised.

4. Conclusion

The Boskin Commission intended to provide a framework for calculating the CPI that measures increases in the costs to maintain a certain level of utility. However, as shown, it is unlikely that social security recipients can effectively track prices and act on this information in practice. Moreover, preference differences between the general population and social security recipients might force social security recipients to substitute away from their initial choices leaving them with little chance of maintaining utility levels. Given current conventions of measuring inflation with a single indicator representative of the aggregate expenditure of the general population, SSB tied to a COLI fail to properly insulate recipients from increases in the cost-of-living. Since indexing SSB to the CPI is a major use of the CPI, I conclude that the CPI should not be a COLI.


BBC. (2022, January 26). Should you follow the 5 second rule? And does inflation hit the poorest harder? BBC Radio: More or Less: Behind the Stats. Retrieved January 29, 2022, from does/id267300884?i=1000549039264

BLS (2020, November 24). Handbook of methods: U.S. bureau of labor statistics. Bls.Gov. Retrieved January 19, 2022, from

Branch, W. A. (2004). The theory of rationally heterogeneous expectations: evidence from survey data on inflation expectations. The Economic Journal, 114(497), 592–621.

Cartwright, N., & Runhardt, R. (2014). Measurement. In Cartwright, N., & Montuschi, E., Philosophy of social science: A new introduction. (p. 265–287). Oxford University Press

CBPP. (2020, August 13). Policy basics: Top ten facts about social security. Center on Budget and Policy Priorities. Retrieved January 19, 2022, from ten-facts-about-social-security

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Deaton, A. (1998). Getting prices right: what should be done?. Journal of Economic Perspectives, 12(1), 37–46.

FAS USDA. (2021, May 27). Argentina: 30-day Beef Export Ban. USDA Foreign Agricultural Service. Retrieved March 20, 2022, from day-beef-export-ban

Flood, A. (2022, January 26). Terry Pratchett estate backs Jack Monroe’s idea for ‘Vimes Boots’ poverty index. The Guardian. Retrieved March 19, 2022, from
https://www poverty-index

Klick, J., & Stockburger, A. (2021, March). Experimental CPI for lower and higher income households (№537). U.S. Department of Labor, U.S. Bureau of Labor Statistics, Office of Prices and Living Conditions. Retrieved January 29, 2022, from

Nordhaus, W. D. (1998). Quality change in price indexes. Journal ofEconomic Perspectives, 12(1), 59–68.

Oner, C. (2022). Inflation: Prices on the Rise. Https://Www.Imf.Org/External/Pubs/Ft/Fandd/Basics/30-Inflation.Htm. Retrieved January 19, 2022, from

Reiss, J. (2008). Methodology and expert judgement in evidence-based economics: lessons from the CPI controversy. In Error in Economics (1st ed.). Routledge.

SSA. (2022). Cost-of-Living adjustment (COLA) information. Retrieved January 19, 2022, from




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