“Real-Feel” Inflation: Quantitative Estimation of Inflation Perceptions

MICHAEL J. ASHTONn

Inflation expectations are believed to influence actualinflation and therefore policymaker actions. How-ever, methods usually employed to evaluate inflationexpectations are insufficient. Survey methods eitherrecord economists’ forecasts of the official ConsumerPrice Index (CPI) (which isn’t what policymakersneed to know) or consumers’ attempts to calculatetheir own inflation experience. Consumers havelittle chance to perform the calculations needed toaccurately compute inflation. I propose functionalforms to substitute for the heuristics consumersactually use to form inflation perceptions. I alsopropose adjustments to reconcile official pricemeasurements with consumers’ perceptions. Theseadjustments are corrections for cognitive biasesrelated to loss aversion and mental accounting.Business Economics (2012) 47, 14–26.

doi:10.1057/be.2011.35

Keywords: inflation perceptions, inflation expecta-tions, inflation

Modern monetary policy considers inflationexpectations a metric of signal importance

in the formulation of monetary policy. While theTaylor Rule [Taylor 1993] provides a well-knownheuristic for monetary policymakers that relies onactual, not expected inflation, policy discussionsrely heavily on the question of whether inflationexpectations are, and will continue to be,“contained.” (See, for example, selected statementsof the Federal Reserve Open Market Committee(FOMC) [Board of Governors 2006, 2008, and2010].) Current Federal Reserve Chairman BenBernanke [2007] himself described the importance

and significance of inflation expectations in aspeech by saying “Undoubtedly, the state of infla-tion expectations greatly influences actual inflationand thus the central bank’s ability to achieve pricestability” [Bernanke 2007].

In that speech, Bernanke highlights threeimportant questions that remain to be addressedabout inflation expectations:

(1) How should the central bank best monitor thepublic’s inflation expectations?

(2) How do changes in various measures ofinflation expectations feed through to actualpricing behavior?

(3) What factors affect the level of inflationexpectations and the degree to which they areanchored?

According to Bernanke, the staff at the FederalReserve struggle with even the first of these ques-tions, although this has not deterred them fromtackling the second and third questions.

Frederic Mishkin [2007] described recentchanges in the persistence of inflation, the tradeoffbetween inflation and unemployment, and theresponsiveness of inflation to other shocks as afunction of well-grounded inflation expectations.To proxy inflation expectations he used theLivingston Survey of the Federal Reserve Bank ofPhiladelphia and the measure used in the FederalReserve’s FRB/US macroeconometric model ofthe United States, which itself consists of theHoey survey1 and the Survey of Professional

nMichael Ashton is Managing Principal at Enduring Investments LLC, a boutique consulting and investment managementcompany that offers focused inflation-market expertise. Prior to founding Enduring Investments, Ashton worked as a trader,strategist, and salesman for several sell-side financial institutions, including Deutsche Bank, Bankers Trust, Barclays Capital, andJ.P. Morgan. Since 2003 he has played an integral role in developing the U.S. inflation derivatives markets and is widely viewed asan expert on inflation products and inflation trading. Ashton has written extensively about the use of inflation-indexed productsfor hedging real exposures. He runs the Inflation-Indexed Investing Association. He received a B.A. in Economics from TrinityUniversity in 1990 and was awarded his Chartered Financial Analyst charter in 2001.

1Richard B. Hoey in “Decision Makers Poll” conductedoccasional surveys of inflation expectations. The number ofrespondents varied between 175 and 500 and included chiefinvestment officers, corporate financial officers, bond and

Business EconomicsVol. 47, No. 1r National Association for Business Economics

Forecasters (SPF). He also referred to theMichigan Survey of Consumer Attitudes andBehavior (Michigan survey). Levin, Natalucci, andPiger [2004] also examined the response of surveymeasures of the inflation expectations of profes-sional forecasters to near-term changes in actualinflation rates, begging the question of whether theexpectations of forecasters, much less a survey ofsuch expectations, are valuable measures them-selves.

Mankiw, Reis, and Wolfers [2003] comparedsurvey measures of inflation, including the afore-mentioned Livingston survey, the SPF, and theMichigan survey. They illustrated that both con-sumers and economists tend to be broadly correctabout near-term future inflation, on average, butthat economists tend to have tightly groupedestimates, while consumers have very dispersedviews; in the year to December 2003 (their Chart 2),economist estimates generally fell between 1½ and3 percent while the interquartile range of consumerexpectations lay between 0 and 5 percent.

We should be careful not to dismiss the widerrange of consumer expectations as representing alack of forecasting sophistication. The wider rangepartly represents the fact that the economists areresponding to a question about a well-defined dataseries – for example, the Consumer Price Index(CPI) for the Livingston survey and the GDP de-flator for the SPF—while consumers are expressingtheir views about “the expected change in prices,”which will in fact be different for each respondent.It ought also be observed that the tight grouping ofeconomists, especially in the context of the cross-currents of 2002-2003, suggests herding.2 This isone reason that relying on economist expectationsof inflation to help inform policy may be danger-ous.

Many authors, such as Gurkaynak, Sack, andSwanson [2005], have used the spread betweenthe yield on nominal bonds and the yield oninflation-indexed bonds (such as Treasury Infla-tion-Protected Securities) as a market-based proxyfor inflation expectations. This is a conceptually

sound method for tracking short-term responsesof inflation expectations to changes in policy andnonpolicy variables, since the participants inthose markets face pecuniary consequences if theirinflation forecasts prove incorrect, althoughAshton [2008] demonstrated that inflation swapsare a theoretically purer measure of inflationexpectations, due to the presence of differentfinancing conditions for inflation-indexed bondsand nominal bonds. This paper deals, however,with consumer inflation expectations, which aredistinct from longer-term investor inflation ex-pectations as embodied in the market for inflation-indexed financial products.

In setting monetary policy, the FOMC refersto all of these measures in forming its view of whatis the current state of “inflation expectations.” Butthe fundamental problems identified by Bernankeremain.

Policymakers rely on economists to forecastinflation; relying on economists’ estimates to alsorepresent the state of inflation expectations seemsto be putting a different saddle on the same horseand expecting to win the race twice.

Clearly, the FOMC would like to sample theperceptions of the people who are involved in price-setting and wage-setting behavior.3 But consumersurveys are not ideal instruments for at least tworeasons. First, as Mankiw, Reis, and Wolfers[2003] point out, taking the “median” expectationobscures a lot of information, and it isn’t exactlyclear what role the variation in expectations shouldplay. Second, and more importantly, surveys ofinflation don’t work well because consumers do notdiscern inflation properly. Perceptions of inflationare muddied by a myriad of practical problems andbehavioral biases that tend to impair a consumer’saccurate assessment of price changes. For example:

(1) Quality change and substitution adjustmentsmay not be recognized viscerally by con-sumers, although they are a necessary part ofa cost-of-living index. It might also be the casethat people notice downward quality adjust-ments (“my insurance coverage is shrinking”)more than upward quality adjustments.

stock portfolio managers, industry analysts, and economists.The survey began in 1978, was discontinued in March 1991,resumed in March 1993, and ended in August 1993 [Darin andHetzel 1995, p. 33].

2Spencer and Huston [1993] presented econometric evi-dence that suggests economic forecasters do in fact use theprevious inflation forecasts of others as one input into theirown forecasts.

3In 1998, Canetti and others [1998] conducted a survey of200 corporate price setters to find what factors are importantto them in setting prices. While the study was not meant toprovide an ongoing survey of expectations, some of theirinsights may be useful to consider in designing a betterinflation-expectations gauge.

“REAL-FEEL” INFLATION

15

(2) Consumers seem to have an asymmetric per-ception of inflation as a whole, as well, so thatthey tend to notice goods whose prices areinflating faster than the overall market basket,but to notice less the goods whose prices arenot inflating as fast. This sense is enhancedby classic attribution bias: higher prices areinflation, lower prices are “good shopping.”

(3) Items whose prices are volatile tend to drawmore attention, and give more opportunitiesfor these asymmetries to compound, so theytend to factor more heavily into our sensationof inflation.

(4) People have a tendency to notice price chan-ges of small, frequently purchased items morethan they notice large, infrequently purchaseditems even though the latter can be a biggerpart of the consumption basket. Gasoline ishugely important in the mind of the con-sumer, even though it’s not a huge part of thebasket, because it is purchased frequently andits price is volatile, which means attributionbias acts constantly.4

(5) Consumers do not viscerally record imputedcosts, such as owners’-equivalent rent as dis-tinct from what they see as their costs (prin-cipal plus interest, taxes, and insurance). Eventhough the former is better for a CPI, thelatter (which the pre-1983 method attemptedto measure) probably affects perception moredirectly.

(6) People often perceive increases in incometaxes as inflation.

Respondents who reply to questions about whatthey perceive inflation to be with an answer that issomewhat near the current rate of inflation areprobably basing that response on their recollectionof what inflation rate has actually been reported,rather than on their own consumption. It would bea daunting mental task indeed for a consumer to

catalog all of the year’s purchases and to calculatethe differences from the same basket from the yearbefore. Clearly, this is not what a survey is meant todo. But it is almost as challenging for a consumerto distinguish 1 percent inflation from 2 percentinflation—that fine of a gradation in perceptionwould be extremely unusual to find.

However, if we can model the behavioral biasesthen we might identify not only changes in inflationperceptions but also better understand the driversof those changes in any particular episode. Themonetary policy prescription might vary if, forexample, elevated perceptions of inflation weredriven because of an increase in taxes than becauseof an increase in the volatility of price changes inthe consumption basket.5

In this paper, I will describe methodologies toquantify, and thus to correct for, each of theseperceptual biases.

1. Correcting For Misperceived Quality andSubstitution Adjustments

A complaint that noneconomists frequently raiseabout the CPI is that the practice of adjustingprice changes for changes in the quality of thesurveyed item—in particular when the method usedis hedonic adjustment—doesn’t mesh with thereal-life experience of inflation. A consumer mightcomplain, “I paid $150 for a digital camera threeyears ago; I just paid $200 for a new one – there issurely no deflation in digital photography!” Thefact that the new digital camera has 14.1 megapixelsof resolution while the old one had 5.1 megapixelsis often considered significant by the consumer,but it doesn’t get mentally accounted for as a pricedecrease, even though the consumer is getting muchmore for the money.

Another gripe concerns the adjustments madeto correct for substitution bias. Consumers willtend to change their consumption patterns as rela-tive prices change, even if the absolute level ofprices does not change. For example, if a consumerwho consumes 50 percent chicken and 50 percent4Ranyard and others [2008] tied several of these phe-

nomena to Tversky and Kahneman’s [1974] “availability”heuristic. According to Ranyard and others, “For judgementsof inflation, four aspects may affect the availability of pricechanges: recency of purchase, frequency of purchase, size ofprice change, and direction of change. Price changes of morerecently and more frequently purchased items may be moreactivated in memory, while larger price changes as well aslosses (price increases) may be more salient, all of which wouldincrease the availability of instances of price changes.” Thereader will soon see how the volatility and direction of pricechanges can be incorporated into a quantitative model of thesebiases.

5A better understanding of the drivers of inflationexpectations may also be useful in solving other economicconundrums. As one example, Akerloff and Shiller [2009] haveproposed that worker resistance to nominal wage decreasesmay not be due just to money illusion but also to a sense thatnominal decreases are unfair in some sense. But if consumersperceive some inflation even when the measurement of CPIindicates that there is none, we must also consider that theyperceive not only a nominal, but a real wage cut even if thewage cut equals the drop in prices.

Michael J. Ashton

16

beef sees the price of beef fall 10 percent while theprice of chicken rises 10 percent, he is likely toconsume less chicken and more beef even thoughthe price index consisting of equally weighted

chicken and beef has not changed.6 This would be

an example of an “upper-level” substitution ofitems that are significantly different. A more subtle,and less controversial, adjustment is made for“lower-level” substitution of very similar items,such as two different brands of orange juice.7

Because the CPI is intended to track the costof a static standard of living,8 real-life consumerswho tend to drift gradually to higher standardsof living will experience price changes associatedwith quality improvements and opportunisticsubstitution, as well as those due to inflation as weunderstand it. All three types of price increasewill tend to be recorded mentally as inflation, eventhough from the standpoint of the index two ofthem are not.9

Adjusting for substitution

Our goal here, however, is not to improve on theCPI but to converge on the consumer’s perceptionof inflation. It is conceptually fairly easy to deductthe adjustments made for substitution andhedonics. Johnson, Reed, and Stewart [2006]

demonstrate how to use other BLS indices toestimate the effects of lower- and upper-levelsubstitution. To estimate the lower-level substitu-tion effect, the authors compared the regularCPI—which includes a geometric-means adjust-ment—to the CPI-U-XL, an experimental indexthat used the pre-1999 method for computinglower-level substitution effects.10 To estimate theupper-level substitution effect, the authorscompared the regular CPI to the chained CPI(C-CPI-U). The BLS began producing the C-CPI-Uin 2002; it uses actual consumer behavior, ratherthan a model of it, to determine expenditureweights. Therefore, the difference between the CPI-U-XL and the C-CPI-U represents a reasonableestimate of the total of the substitution effects.11

For our purposes we can ignore the upper-levelsubstitution effect, because the “official” CPI(CPI-U) does not incorporate the inflation-lowering adjustment made in the C-CPI-U.

The CPI-U-XL is not readily available, but itcan be obtained on request from the BLS. For theyear ended September 2010, the difference betweenthe CPI-U-XL and the CPI-U was 0.247 percent.The effect has been reasonably stable, rangingbetween 0.2 and 0.4 percent over the last decadeor so. Johnson, Reed, and Stewart’s [2006] estimatefor the 1999-2004 period was 0.28 percent, andGreenlees and McClelland [2008] noted thatunpublished results for the longer period fromDecember 1998 to December 2007 resulted in a0.27 percent effect. I will use that estimate as aconstant, in the absence of a convenient way toaccess the CPI-U-XL.

Adjusting for quality change

Adjusting for the misperception of quality adjust-ments is more difficult, partly because this oneconcept affects many different parts of the CPI indifferent ways and because different adjustmentsare made depending on the type of quality change.Johnson, Reed, and Stewart [2006] state, “the neteffect of hedonics from 1999 onwardy on the All

6An important point is that consumers will buy more ofthe item whose price relative to other goods has declined (beefin this case) even if the consumer is compensated for thatchange. Suppose a consumer pays $10 per week for soda, $5each for Coke and Pepsi (which he considers interchangeable).Now suppose the price of Pepsi doubles, but the AmericanSociety for the Promotion of Cola Products sends the con-sumer $5. With the additional $5 he could continue to buyequal amounts of Coke and Pepsi, but will he? Of course not;the consumer will spend his $10 all on the cheaper brand andkeep the extra $5, or buy more total cola by spending the entire$15—but all on the cheaper brand. The consumer’s utility/dollar is now much higher with one (formerly interchangeable)brand.

7For an excellent explanation of lower-level substitutionand why the effect is small and not particularly controversial,see the section on Substitution in Greenlees and McClelland[2008].

8The Bureau of Labor Statistics on its website points outthat this is not precisely true because a true cost-of-living indexwould consider other factors that affect quality-of-life, such aspublic goods like safety or other concerns, such as waterquality [U.S. Bureau of Labor Statistics 2010], but in thecontext of our problem it is.

9Some academic work has suggested that the qualityadjustments may in fact over-adjust, perhaps giving someammunition to the people who complain about theseadjustments. See for example Gordon [2004] and Gordon andVanGoethem [2005].

10Technically, a modified Laspeyres or “Lowe” index.11From December 1999 to December 2004, Johnson,

Reed, and Stewart [2006] estimate that the total of the twosubstitution effects amounted to approximately 0.68 percent,although some 0.1 percent of this was due to a “functionalform” effect. The authors note, however, that this was due toan “anomalously high 0.80 percent effect in 2000” and observethat from 2001 to 2004 the aggregate effect was a modest 0.3percent.

“REAL-FEEL” INFLATION

17

Items index is estimated to be less than 1-hundredthof 1 percent per year, specifically þ 0.005 percent.”This result, however, obtains from the fact thathedonic adjustment lowers the CPI for a numberof categories whose weights total to around 0.7percent of the index, but increases the CPI some-what for Rent, Owners’ Equivalent Rent (OER),and Apparel, in addition to several smaller cate-gories. Rent, OER, and Apparel have a combinedweight of around 31.5 percent of the CPI. So, thelarge downward adjustments to the lightweightcategories are finely balanced by very small upwardadjustments to the heavyweight categories.

It seems reasonable to suppose that consumerswould object to thinking of the quality improve-ments in computers as deflation, while not beingparticularly opposed to the idea that their homestend to deteriorate over time. As a coarse adjust-ment, I would suggest simply removing the qualityadjustments that tend to depress the index.12

However, as a practical matter, the unadjusted CPIfor the various categories is not available outsidethe BLS. Moreover, as discussed above, the effectof the quality adjustments on the overall index isquite small. Johnson, Reed, and Stewart [2006]estimate the aggregate impact of quality adjust-ment as around þ 0.005 percent. This implies thatall of the categories where quality adjustments tendto lower CPI must sum to around �0.095 percent,so as a fair approximation I will use an adjustmentfor quality, ADJQual¼ þ 0.1 percent.

Thus, the corrections for misperceived qualityand substitution would be:

AdjSubs ¼ ½ðCPIU�XLÞ � ðCPIUÞ� � 0:27%; (1Þ

AdjQual ¼Xi

weighti �MAX;

½0%CategoryCPIunadj � CategoryCPIadj� � 0:1% ð2Þ

Note that, because I am subtracting the adjustedinflation rate for the category from the unadjustedrate, quality adjustments that tend to depressmeasured inflation rates will be positive in the

MAX operator—we are extracting theadjustment to add back to the rate, but only foradjustments that pull down the rate. Given presentBLS methodologies, the main effect here is to addback the OER age bias adjustment, which is thesingle most significant quality adjustment in thatdirection (by a wide margin).

2. Correcting for Asymmetric Perception(Selective Memory) of Price Changes

A far more important effect than the mechanicaladjustments that have been made to the index is thedifference between the cold precision of the BLS’scalculation and the hot imprecision of our percep-tion of price changes. Daniel Kahneman andAmos Tversky demonstrated [1979] that humans(as opposed to Homo economicus) exhibit a ten-dency toward loss aversion; that is, a gain of acertain size is less valuable to the economic actorthan is a loss of the same size.

In the context of the perception of inflation,this tendency manifests in the greater attentiona consumer pays to price increases—which areeconomic losses to a consumer—than to pricedecreases. This tendency is compounded by attri-bution bias, in which the consumer perceivesprice gains as inflation and price declines as “goodshopping.” David Leonhardt [2008] gets the visc-eral sense right: “You hate that ground chuck nowcosts $2.83 a pound, but you didn’t notice thatoranges are 31 percent cheaper than they were ayear ago.” He also perceptively observes, in a re-lated but distinct problem (the confusion of nom-inal and real values), that

There is also something particular toinflation that aggravates loss aversion. Priceincreases are obvious. But price declines areoften hidden. The cost of an item stays aboutthe same for years, while everything else getsmore expensive and nominal incomes rise.

This is known as reference dependence, anotherbehavioral phenomenon first discussed (anddemonstrated) by Tversky and Kahneman [1991],who introduced a functional form for the simplecase of constant loss aversion as

RiðxiÞ ¼uiðxiÞ � uiðriÞ if xiXri;½uiðxiÞ � uiðriÞ�=li if xiori:

�

Here R is called a “reference function” expressingthe perceived gain or loss in utility (ui(xi) is a utilityfunction describing the total utility experienced

12Having a similar effect, but seeming a bit less biased,would be to eliminate only the hedonic adjustments that ex-ceed a certain threshold. Deducting only those adjustmentsthat exceeded 0.50 percent (in either direction) in a category’sinflation rate would tend to remove the large negative adjust-ments on small-weight categories while retaining the smallpositive adjustments on high-weight categories, resulting in ahigher perceived inflation. While this sounds less biased, it isno less arbitrary in the choice of a hurdle.

Michael J. Ashton

18

when x units of good i are possessed/consumed) ina movement from the reference amount ri to theamount xi. You can see that for increases in thegood, the simple difference in the utility functiondescribes the net change in utility, whereas for de-creases, the change in utility is scaled by li. Ifli¼ 1, there is no loss aversion. Tversky andKahneman imply that this coefficient of loss aver-sion should be between 0 and 1.

This is a good form for our correcting forasymmetric perception of price changes. Instead ofutility functions, we will substitute inflation rates(with a “loss” occurring when inflation goes up,so the inequalities are reversed).13 For each goodi in the consumption basket, the perceived pricechange compared with the actual price changelooks like Figure 1 if l¼ 0.6.

Let us assume that the tendency to downplaydisinflation or deflation is consistent across goods,and further assume that the “reference level” is thegeneral degree of inflation.14 If wi is the weight inthe basket of good i, CPIi is the inflation rate ofgood i, and CPIU is the headline inflation rate, thenthe aggregate adjustment we need to make to thereported CPI is given by formula (3).

AdjSelMem

¼Xi

wi

CPIi � CPIU if CPIioCPIU;

½CPIi � CPIU�=l if CPIiXCPIU:

�ð3Þ

If l¼ 1, or if all goods inflate at a rate equal to theheadline rate, this adjustment will be equalto zero; in all other cases (assuming l is boundedby [0,1]) this will be a positive adjustment, tendingto increase the perceived rate of inflation over thecoldly rational measurement thereof.

This measure is clearly related to the dispersionof the inflation rates. As I just noted, if all rates ofinflation for the various goods and services in the

consumption basket are the same, the adjustmentwill be zero. As the degree of dispersion rises, thesense of inflation will also increase for any given l.Figure 2 illustrates this effect. I generated “inflationrates” for five equally weighted hypothetical“goods” and combined them into an aggregateindex. I then computed the standard deviation ofthe five rates, and figured the adjustment impliedby equation (3). I ran multiple trials with variousrandomization for each of two ls, and the effectis reasonable and expected. The size of theadjustment is positively related to the standarddeviation of the sample, and inversely related tothe l.

In practice, the dispersion of actual inflationrates is much higher than a 5 percent standard

Figure 1. Selective Deflation Memory

Figure 2. AdjSelMem vs. inter-item Std Dev

13Essentially, I am assuming that utility varies negativelywith quality-adjusted real price change. This seems fairlyreasonable.

14There is a case to be made that the correct frame may bepersonal income rather than the general level of price in-creases. Fischer [1986] argued that because the salience of aprice increase is related to how well the individual can meet it,the “decrease in economic well-being” is tied to the incidenceof inflation relative to income rather than the level of inflationitself. Since incomes and inflation generally rise at similarrates, I suspect this is likely to be a fairly small effect onaggregate measures of perceived inflation, but it does raise thequestion of whether the volatility of personal incomes relativeto the volatility of inflation might be an additional factor toconsider in future research.

“REAL-FEEL” INFLATION

19

deviation. Applying formula (3) to the actual timeseries of CPI item strata produces the time seriesfor this adjustment that is shown in Figure 3.

3. Correcting for the Perception of Volatility asInflation

The prior correction is based on a static observa-tion of the dispersion of inflation rates among thevarious groups of goods and services in the con-sumption basket, which gives rise to an error due toselective memory of price increases compared withdecreases (relative to a reference point). Considerwhat happens over time, however, as the rates ofchange oscillate.

As the inflation rate applicable to a certaingood rises, a consumer records this as, sensiblyenough, inflation. As the rate declines, the con-sumer tends to discount it because the lower infla-tion rate is less salient, as noted above, and may bementally accounted for as “good shopping.” Whenprice changes for a particular good are volatile,then not only is that good more likely to end upwidely dispersed, but the very volatility itself willtend to create an impression of inflation.

This happens because the frame of reference forthe price of a particular good will tend to be theprevious price observed by a consumer, adjustedfor an expected drift. Winer [1986], studying theimplications for price-related sales promotionstrategy of the way consumers form fair-price re-ferences, found considerable evidence supportingthe notion that the relative price of an item com-pared with that seen at the prior purchase, adjustedfor the drift trend, has a statistically significant

effect on the brand-purchase decision. That is,“consumer brand choice decisions for two out ofthree major brands of coffee were strongly affectedby discrepancies between expected and observedprices at the point of purchase” [Winer 1986, p.55].For our purposes, predicting which brand aconsumer will buy is unimportant. However, theauthor’s further conclusion is relevant to us:

The important managerial implication ofthe results is that manufacturers may bepenalized in the long run by frequent short-term price-related deals since consumersmake forecasting errors about the point-of-purchase prices. An opposite strategy ofinfrequent price adjustments may allow priceto become less important in the householdbrand choice process relative to advertisingand product quality since observed prices atthe point of purchase will be fully antici-pated. [Winer 1986, p.55]

In other words, artificial point-of-purchaseprice volatility induced by marketing hurtsmanufacturer’s long-run sales. Price volatility is anegative.

Tversky and Kahneman [1991, p. 1055], furtherciting both Winer [1986] and Kahneman, Knetsch,and Thaler [1986], imply that this effect operatesdue to repeated application of loss aversionphenomena, saying “asymmetric evaluations ofgains and losses will affect the responses of bothbuyers and sellers to changes of price and profit,relative to the reference levels established in priortransactions.”15

Suppose that period-to-period percentage pricechanges are lognormally distributed with no drift.16

Then what we would like to do is to adjust inflationby the expected value of the “loss aversion” for aparticular item category, given the category’sstandard deviation and the loss-aversion constant, l.

If the distribution of percentage price changesis distributed as N(m,s2)—but we are abstractingfrom the trend price change m—then for randompercentage changes drawn from this distribution

Figure 3. AdjSelMem, 2000–2010

15But see also footnote 12 for an alternative hypothesisabout the reference frame.

16This may or may not be true, and certainly is unlikely tobe true for every surveyed price if only because of granularityeffects and non-stochastic adjustment methodologies, but itseems a defensible approximation for our purposes. The no-drift assumption is clearly false—the regular price drift iscalled inflation—but as noted earlier consumers tend to takeprior drift trends into account when ascertaining whether theprice has changed relative to their expectations [Winer 1986].

Michael J. Ashton

20

we want to know the expected value of the change,conditional on the change being positive, andthe expected value of the change, conditional onthe change being negative.

AdjVolatility

¼Xi

wi

E½Nð0;s2i Þ� if DCPIio0;

E½Nð0;s2i Þ�=l if DCPIiX0:

(ð4Þ

This reduces nicely. The first line of equation (4)expands, if we take x¼DCPIi, to:

Z0�1

x1

2ps2e�x2

2s2 dx

66647775=0:5;

which evaluates to

�sffiffiffi2

pffiffiffip

p � �0:8s

This is a well-known result describing theexpected future value of a one-period, at-the-moneyput option (a put option’s value, obviously, isdefined as the absolute value of this quantity).

The call option, described in the second line ofequation (4), is analogously priced at 0.8s, but thevalue of this “option” is amplified by 1/l sinceupwards volatility is more keenly felt than down-wards volatility. Accordingly, the adjustment forvolatility is simply:

AdjVolatility ¼Xi

wi0:8sil

� 0:8si

� �;

or simply

AdjVolatility ¼ 0:81� ll

� �Xi

wisi ð5Þ

It isn’t a guarantee that the l in equation (5) isthe same as the l in equation (3), but since both arecoefficients of loss aversion, one would at leastexpect them to be closely related. In this exercise,they are taken to be the same scalar.

Figure 4 shows the result of applying equation (5)to the actual time series of CPI item strata. Thisadjustment is much more stable, because individualitem volatilities change slowly over time. The largejumps in late 2001 and late 2008 are those asso-ciated with crisis levels of economic volatility.

5. Other Biases

Some other biases are worth discussion and furtherresearch but are difficult to quantify. I brieflydiscuss a few of them below.

Primacy/recency bias

Psychologists recognize that people tend to have abetter recollection, in a sequence of observations,of both the earliest observations and the laterobservations compared with the ones in the middle.These are called the “primacy” and “recency”effects, respectively. More interestingly, theseobservations are perceived to have more salience tothe observer merely as a result of their temporalposition.

This effect, I believe, is one reason that peopletend to remember inflation when it involves theprice of eggs (an item which has likely been pur-chased recently) more than they remember inflationin the price of cable television, even though thelatter has roughly a dozen times the weight of theformer in the average consumption basket.

Large purchases, even though infrequent, aremade salient by their size. Accordingly, we mightexpect that consumers will tend to sense greaterinflation when large and small items are inflatingthan when the median items (size-wise) are inflat-ing. This hypothesis, however, must be subject to afuture test, since the literature on quantifying theprimacy/recency effects is decidedly thin.

Failure to disentangle bundled costs

Bundled costs, where some of the cost of an itemrepresents current consumption and some representsinvestment or deferred consumption, are difficult tointernalize correctly. This is unfortunate, becausea very important part (about 25 percent) of the CPIinvolves the imputed cost for the consumption partof a capital good: owner-occupied housing.

Figure 4. Adjvolatility, 2000–2010

“REAL-FEEL” INFLATION

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The goal of the CPI is to measure the cost ofmaintaining a given standard of living, and forthat reason it is necessary to separate the cost ofconsuming housing from the value of a house asa financial asset. Prior to 1983, the cost of owner-occupied housing was recorded using the “assetprice method.” This method treated shelter costsas consisting of five elements: (1) home purchase,(2) mortgage interest costs, (3) property taxes,(4) homeowner insurance charges, and (5) main-tenance and repair costs [Poole, Ptacek, andVerbrugge 2005, p. 11]. This is, viscerally, howhomeowners tend to think about their cost ofhomeownership: principal plus interest plus taxesplus insurance plus maintenance.

Unfortunately, this is a cognitive error: home-owners are blending housing consumption costswith investment carry costs. This can be seen bynoting that a homeowner can achieve essentiallythe same financial outcome by renting a housetoday and contracting to buy a different house, at aprice fixed today but adjusted for inflation, in fiveyears. Rental is clearly consumption; the contractto buy is clearly investment. The seller of the housewill include in the forward price all the costs ofcarrying the house for five years: interest, taxes,insurance, maintenance, and the expected after-inflation change in the house’s market price overthat time.

The CPI, as a cost-of-living index, considersonly the first part of that transaction, but thehomeowner, of course, cares about both parts.When mortgage costs and taxes are rising, hisstandard of living is deteriorating; the fact thatthis is due to investment considerations and notconsumption is a subtle point lost on him.

It is clear that this bias is upward (the consumerfeels more inflation than is included in the CPI)when property taxes are rising, when mortgagerates are rising, and probably when real propertyvalues are rising (which causes new homeowners totake out larger mortgages and therefore pay moreinterest), and is biased lower when the opposite istrue. But it is challenging to disentangle theseeffects, and I will leave it as a future improvementon the model.

Another case where entangled costs causeissues, also in shelter, is in the difference between“pure rent” and “economic rent.” The BLSrecognizes that rent paid to a landlord includes notonly a payment for consumption of shelter but alsoin many cases a payment for ancillary servicesprovided by the landlord. For example, the land-

lord may not meter separately for utilities but somepart of the tenant’s rent in a “utilities included”rental represents the cost of those utilities. Thismeans that when the cost of utilities rises whilethe rent stays the same, it means the implied costof the housing itself declined. The renter, of course,is paying a constant rent and so will not realize thatthe true cost of his apartment has declined due tothe rise in natural gas prices, and vice-versa.17

Accordingly, shelter costs will be mentally recordedas higher than the CPI reading when energy pricesare rising and lower when energy prices are falling.This, too, is difficult to disentangle from thegeneral effect of rising or falling energy prices.

Internalizing tax increases as inflation

The computation of the CPI excludes taxes thatdon’t have anything to do with consumption, sinceCPI is only supposed to measure changes in thecosts of consumption items. There is no questionthat rising (or, less commonly, declining) taxesaffect our standard of living, but the question theCPI is meant to answer is not “what is the cost, inpre-tax dollars, of achieving the standard of livingactually achieved in the base period.” If incometaxes are rising, it causes a decline in living stan-dards that are achievable for someone receiving agiven nominal wage; equivalently, that person willhave to earn more money to purchase the sameliving standard. That sounds, and feels, like infla-tion to an ordinary person, but it is not.

In principle, this should be an easy adjustmentto make. Total federal income taxes, dividedby nominal GDP, gives the average tax burden asa percentage of income; using that ratio (we canrefine it further with state and local levies, ifdesired) we can convert inflation into “effectivepre-tax inflation rates.”

The problem is that tax rates, and even thechanges in tax rates, are not remotely close toevenly distributed. A large proportion of the citi-zenry pays effectively no taxes while a minoritypays high rates. As a result, this particular effectis extremely heterogeneous. It is not even clear

17One reader of an earlier draft argued that since thispractice artificially reduces the volatility of expenditure, it maytend to lower the sense of inflation. But in the context of theadjustments we are making, this is not the case, since volatilityof prices produces an illusion of inflation. Removing thevolatility removes the illusion induced by volatility, but doesnot actually induce a negative illusion. I am grateful for theopportunity to clarify that point.

Michael J. Ashton

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that we can get the direction of the effect correct,because total receipts may rise—implying that thegeneral perception of inflation should be rising—even while the majority of consumers experienceeither a tax cut, or no change in taxes. Accordingly,I have not attempted to include this effect in themodel.

There are doubtless other effects we can in-clude, although many will be subject to debate.I believe the most important of the omissions to besome adjustment for the perception of housingcosts relative to the recorded inflation in shelterconsumption for owner-occupied housing, and Ilook forward to refinements of the model.

6. Synthesis and Discussion

The sum of the adjustments discussed above—in-cluding two widely discussed but economicallyunimportant ones and two rarely discussed buteconomically important ones—is:

AdjSubs þ AdjQual þ AdjSelMem þ AdjVolatility

¼ 0:27%þ 0:1%þ AdjSelMem þ AdjVolatility ð6Þ

The latter two terms of equation (6) are theresults of equation (3) and equation (5), respec-tively. Both of those equations involve calculationsbased on readily available data but also rely oncalibration of the l term.

There are at least two ways to determine whatvalue of l is appropriate. The first is to take anexisting survey measure and try to find what valueof l is broadly consistent with the differencebetween the survey measure and the reported CPI.

Comparing the Michigan survey with the actualreported CPI (Figure 5), you can see an interestingphenomenon. The respondents to the Michigansurvey sometimes see more inflation than isactually measured, but sometimes actually see less.Apart from the fact that this doesn’t mesh at allwith anecdotal evidence, the difference is smallenough that it is easier to suspect it is merely noise.That is, the respondents to the Michigan surveyare extremely efficient at assessing actual inflation,so that the actual difference between theirresponses and current inflation is merely chance.

From January 2000 to July 2010, the averageabsolute difference was 0.8 percent, but this washighly influenced by wide deviations around thetime of the financial crisis. From January 2000 toSeptember 2008, the average absolute differencebetween trailing one-year inflation and the Michigansurvey’s one-year (forward) inflation expectations

was only 0.5 percent. But more surprisingly, theaverage difference (retaining relative values) wasonly 0.1 percent over the shorter time period. Thisstrongly suggests that respondents are eitheradvanced econometric robots, or are in fact recal-ling what they have seen as the latest reportedCPI figure and informing their responses with thisinformation. Interestingly, Bryan and Venkatu[2001] found that in a study of multiple years ofresults from an inflation survey of Ohioans, re-spondents who said they had “heard of CPI” wereable to quite accurately indicate by how muchit had increased over the last year, and yetwhen asked about their own inflation experienceresponded on average that their experience of priceincreases ran 4 percent faster than the measuredCPI (6.7 percent versus 2.7 percent over thesurvey period). Other studies have found similarlydiscouraging results about the perceptions ofconsumers: a 1986 survey in the United Kingdom[Bates and Gabor 1986] found that respondentsoverestimated the inflation of general groceryprices dramatically, at 16.8 percent per annumcompared with an official rate of 4 percent! Giventhese results, it is hard to understand how theMichigan survey can be so close to reportedCPI—either the Michigan respondents are simplylots more observant than the English andOhioan respondents, or they are somehow an-choring on the CPI measure when they offer theirresponses.

Calibrating the model described in equation (6)to the Michigan survey results thus turns out to beimpossible. The tracking error is so small that itimplies essentially no loss aversion at all, which

Figure 5. Michigan survey vs. reported CPI

“REAL-FEEL” INFLATION

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makes sense only if behavioral biases play no rolein inflation perceptions.

In any event, calibrating a model to such asurvey is not likely to be fully satisfactory for thesame reasons, cited in the introduction and ex-panded on above, that the survey measure itself isunsatisfactory. Why calibrate a model to a surveymeasure that is not likely to accurately reflect whatconsumers really think is happening to prices?

The second approach is to experimentallyevaluate consumer perceptions of inflation undertest conditions designed to calibrate the behavioraleffects discussed here. I have not attempted to dothat, due to resource constraints, but I hope thatother researchers will.

However, for illustrative purposes I havecomputed the aggregate upwards adjustment toheadline inflation that would result from settingl¼ 0.7. The result of that exercise is shown inFigures 6 and 7.

There are several interesting implications ofthis analysis. One is that the aggregate adjustmentseems to be slightly procyclical. The correlationbetween the level of headline inflation and thesize of the aggregate adjustment, from 2000 toJun-2008, is 0.14. But in the crisis, it becamesharply anticyclical; the correlation run from Jul-2008 to Aug-2010 is �0.62 and as a consequencethe standard deviation of the “perceived” index was18 percent lower than the standard deviation of thereported headline CPI over that time frame.

That is, during the financial crisis the largedispersion of price changes and the great volatilityin prices generally served to blunt consumers’perception of the price declines, so that although

the country actually experienced deflation, consu-mers didn’t perceive it as such. There are of coursecompeting explanations for the fact that the sharpcompression in activity did not affect inflation asdramatically as some expected, but this analysissuggests (and quantifies!) a behavioral reason thatmay also have been in play.

7. Conclusion

It may seem strange, to purists, that I am arguingin favor a model that is clearly mis-measuring theunderlying phenomenon of price inflation. Indeed,I think we can state unequivocally that thosewho claim that the inflation rate as reported issubstantially understating the true rate of inflationare simply wrong. One particular, somewhat pop-ular website claims that CPI understates actualinflation by some 7 percent per annum. This isabsurd, and rudimentary arithmetic illustrates theabsurdity:

Using government statistics (specifically, theEmployment Cost Index), we can figure thatsomeone earning $20,000 in after-tax wages in 1980should be now making roughly $59,300.18 Theoriginal $20,000 standard of living now shouldcost, according to CPI, some $52,800, so thisperson is somewhat better-off. However, if we usea 7 percent higher rate of inflation, the $20,000standard-of-living in 1980 now should cost$353,000. I would hope that consumers generally

Figure 6. Aggregate adjustment for l¼0.7

Figure 7. Perceived inflation vs. reported CPI

18This assumes, improbably, that taxes were unchangedbut we will see this imprecision is small enough to be irrelevantfor the illustration.

Michael J. Ashton

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would notice a seven-fold decline in their livingstandards.19

I don’t intend for the methodology cited inthis paper to be used to support the conspiracymythology that the government is trying to “stick itto us” by falsifying CPI. So I want to say veryclearly that even as we seek to measure consumerperceptions of inflation, we should recognize thatconsumers are wrong. Inflation is certainly not ashigh as they think it is.

That doesn’t mean, however, that this is apointless exercise. After all, while no one wouldargue that the thermometer is falsifying the actualtemperature, we nevertheless calculate “windchill” or “real feel” temperatures to express a senseof how the temperature outside will feel on exposedskin. Even though this number is “wrong” in thesense that it doesn’t measure the true temperature,it is more predictive of the risks of exposure. Thus,it matters more to people who may be venturingout-of-doors.

In the case of inflation, although consumersare wrong about the actual pace of changes inprices, their perceptions matter. Their perceptionsof inflation will affect their perceptions of realyields and, therefore, investment opportunities.20

Their perceptions may also feed more efficientlyinto price pressures via a cost-push inflationmechanism. For example, workers who perceive ahigher inflation rate may hold out for higher wageincreases. If true, this will matter to policymakers.

The existence of such biases helps to explainseveral puzzles in the literature. For example,Bryan and Venkatu [2001] found in their surveyof Ohioan inflation expectations that even afteradjusting for income, marital status, ethnic andage group affiliations, and market basket, womenstill had higher inflation perceptions than did men.One possible explanation is that since women(still) tend to do more of the household’s shopping

than do men, these cognitive biases have moreopportunities to affect their perceptions.

Mankiw, Reis, and Wolfers [2003] found thatdisagreement among survey respondents aboutthe future path of inflation tends to (a) rise withinflation, (b) rise when inflation changes sharply,(c) rise in concert with dispersion in rates of infla-tion across commodity groups, and (d) show noclear relationship with measures of real activity.The model developed in this paper clearly explains(b) and (c), and confirms—at least, in noncrisisperiods—that (a) should be expected.

It makes sense to pursue research along thelines of inquiry that have been laid out here for thevalue such research can have in illuminating suchfindings. This model and discussion can be viewedas a starting point on the path. The implicationsfor our understanding of how consumers interactin the economy to produce real outcomes are sig-nificant. But also, of course, it is important forpolicymakers looking at inflation perceptions asan anchoring influence to understand that theremay be such an influence, but the anchor isn’tnecessarily set where they think it is.

Acknowledgments

The author would like to thank Luca Vidozzi,Robert McClelland, John Huston, Thomas Jacobs,Henry Willmore, Marty McGuire, and twoanonymous referees for their comments on earlierdrafts of this paper.

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