313

PERCEPTIOti OF CHANGES IN THE COST OF LIVING

Received Xl+ 1 I. 1984. ~~crpted July 30. lYX4

.A rcccnt scrics of cxpcrinicnts undcrtakcn by Wagcnaar and his co-

\sxxkcrs hax dtx~onstratcd that exponential growth i5 systematically

mispcrccivd (Wagcnx~r and Sagaria 1975: Wagcnaar and Timmcrs

197X. 1970: Wagcnaar 1982). In these cxpcrinicnts. suhjccts wcrc prc-

sc~itctl Lvith short series of cxponcntially increasing numhcrs. gcncxatcd

from the gcncral equation j’ = UC>“’ + C, II = I, 2.. . . They wart’ in-

formd that the scrics rcprcsentcd observations of some real-life proctxs

and dxd to cstimatc the next numhcr in the scrics. The results of the

expcrinicnt.\ diowccl ;l consistent iln~erestimation of the number, rcla-

tivc to that cxptxtcd from nunicricnl knowleclgc of ai txponcntial

stxcs. This unciercstimation. according to Wngcnaar, has been char-

xtcriscd by. and is the conscqucncc of, uncl~rc.\timation of the expo-

I) I674x70/XJ,‘S? 00 1 IYXJ. 1:lw.w Sc~cncc Puhll4kzr\ B.V (Norrh-I I~~ll,m~l)

nent. h. in the generating equation. The underestim~tinn ~%a found to occur for numeric. graphical. and pictorial series (U’agenaar and Sqaria 1975: Wagen;jtar and Timmers 1979). and \\as not reduced by increa- ing the length of the presented series (Wagenaar and Timmers 1978). The phenomenon thus appears to be fairly robust.

Probably the mat obvious example of a process that approximates exponential gro\s th in everyday life is the rise in the cost of living. If the

inflation rate in a country kens to remain constant. exponential gwvth in the average prices of goods and seri,ices uould be realised. Over the period 1967-1933 the long-term inflation rate in New Zealand has been approximately constant (see figs. 1 and 2 and table 1). the major exceptions occurring prior to 1970. \\hen there IV;IS a generally Imvcr

inflation rate. and in 1982-1983 when a national price and wage freeze ~~3s in force. This economic circumstance provided the opportunity for

n studv which ww~ld investigate the retrospective perception of. or

nieniory for. cxponaitial gro\vth in the cost 0f living.

Studica of inflation and inflationary espcctations ha\12 hwn fre-

qucntly undcrt;iken (see. e.g.. Chnn-Lee 19SO). Typically these studica

have atteniptcd to prctlict inflatiomiry c\pcctations in tcrnis of past and

prcxcnt actual inflation rata (e.g. I3lomqvist 19S3). but .Icmitng (1951)

found ;i gc)od relationship hct\vccn the indi\~idii:rla’ t‘stimatcx of future

inflation and their chtimatcs c>f the actual inflation rate over ;i pcricd 01

;i year. At firat it might appear that their estiniatc5 of the actual inflation rate should rcflcct diffcrcnt individual cspcricnccs (i.c. Lvith

diffcrcnt good5 and scrvica kvhich \vcwld of court 5hou Jiffc‘rcnt price

rich). but it is also poasiblc that the atinlata rcflcct diffcrcnt intlivitl-

vial pcrccption5. Such dlffcrcnt pcrccption5 might occur. for cuamplc, il

an individual \v;~s simply un;tblc to rcmcmbcr accurately l\,hat an item

h:ltl cost ;I year bcforc.

The possibility that pcrccption of. or mcnwry for. past prices might

not bc accurate and might, for example. show the sanw sort of unclcr-

estimation found by Wagtmaar in an experimental contt’xt suggcstccl

the present study. It was felt that asking subjects to estimate costs in

previous years shouIcl provide information of both psychological and

ccononiic significance. and in the process provide a \vorth\\,hilc test of

the gcneralisability of the phenomenon of misperception of exponential

growth.

315

Alethod

122 subjects were interviwed in their wvn homes in the third quarter of

1983. Subjects Lvert: obtained by random sampling methods in three

urban electorates in the Christchurch area that \vere believed to provide

a reasonable range of age and class groupings. Subjects were chosen

subject to the requirement of bein, 0 over thirty wars of age at the time _ _ of the interview and ha\ing continuously resided in New Zealand

(excluding short trips abroad) for sixteen years or more.

The personal information collected suggests that the sample was

fairly representative of the Christchurch population aged over 30. The

sample contained 53 males and 69 females varving in age from 30 to

over 80. 96 of the 127 subjects were married. Information on the

rtxpondents‘ incomes, occuputions, education and political party sup-

ported show no marked deviation from NW Zealand norms, and the

differences kvhich appcnr (e.g. 19% of the sample rcceivcd their highest

cducationnl qualification at primary school; 43 x of the sampk vntlxi

for t tic major oppk tion party, 36Y for the governing party) arc

consistait with the age group and xc;I sampled.

All suhjccts bvcrc intcrvkvcd cx-ally from an intcrvicw sclied~~lc.

Sub_jccts iicrc not pcrmittcd to view the quchtionnairc while king

intcrvic\vcd; rc.4ponscb wwc rccordcd by the intcrvictvcr at the time.

Intcrviws. all of which wcrc: conducted by the s;~nic intcrviavcr.

typically I;i~tccl thirty minutes.

Ail inkrvicws followed ;I wt format \.chich was cltltwiiined by the

structurt’ of the schedule. The major part of the schcdulc consisted ol

questions dcsignctd to asses.\ the subject’s pcrccption of inflation and

the rising cost of living. Thcsc questions \vcrc of four types:

(I) Suppose you ivish to buy something that cost.4 $1000 today. How

rn~~cli cl0 ycu think it ww_~lcl hve cost . . . year(b) ago. that is in

19...

(7) As for 1. but the amount was $10.

(3) Imagine that this is . . . year(s) ago. that is, in 19.. . Imagine you

bought something for $100 then. How much do you think. you

would pay for the same thing toduv?

(4) What do you think the aterage annual rate of inflation has been

over the past . . . year(s)?

Eight variations of each question type were asked with responses to

time periods of one. t\vo, four. six. eight. ten. thirteen, and sixteen >ears

requested. (Longer time periods were not used because New Zealand

had a different currency prior to 1967.) All variants of each question

type were asked in one block in randomised orders that were different

for each question type and subject.

In the interests of brevity the four different question types are

referred to below as $1000 questions. $10 questions. $100 questions and

inflation rate questions. The first three types of questions are also

referred to as costs questions.

Before any of the inflation perception questions were asked subjects

were instructed to give their ‘general view of costs and prices’ and not

to try to remember \vhat they paid for specific things. They were told

that the study was not a test of their accuracy but rather they were to

rn:tke ‘rough. quick estimates’. Requests for personal information (e.g.

age, marital status, household income) were interspcrscd between ques-

(ions of tliffcrcnt types. so as to try to mininiisc the influence of the

previous block of questions. Before hcginning each block subjects Lvert’

reminded of lhc instructions.

In addition to the perso~~al information and the four types of

inflation pcrccption questions. subjects wet-c further asked t\vo qucs-

Lion5 relating to inflation. The first a&cd subject:, to rate the impact of

inflation and rising prices on them personally on a seven-point scale

ranging from ’ very unfavourablc’ to ’ very favourahlc’. The second (and

the la.4t question) asked ‘If ~‘e say the annual rate of inflation is 108

what do you interpret this as meaning?’ I<~spo~xes were scored from 1 _ reasonably accurate answer - to 3 - irrelevant or incorrect ans\\‘er.

Figs. 1 and 2 show the median answers to the $1000, $10. and SlOO

questions as a function of year. Owing to occasional missing and ‘don’t

kno\v’ rcsponscs, points are not generally based on the same number of

respondents: the number of missing cxes hourver ih small and ranges from a minimum of zero to a maximum of 17. The figures also show the actual increase in costs based on movements in the New Zealand

Cnnmmer Price Index (all group.41 in that periad and rcfcrrai 1~3 the

Septenitxr 19S3 quarter (Snurct:: Ktw Zealand hl~~nth~) Abstract of

Statistic). It is dear from the figures that there is ;I general undc’rexti-

rnation of the extent to u hich coats have risen o\w the period. one

which increases as the time period lengthens.

Fig. 3 shws the same median data as figs. 1 and 2 plotted on a

lngprd scale apainat the (also lagptxi) real chmipex in cmts. The figure

also shwvs t\vo of the lines of hot fit. that relating to $10 quot~ons

ha\ing been nmittsci since it ia \w-> similar to the $1000 clueticmh line.

Lines of bat fit were calculated mitti Ieast squart’s methods using nine

point5 for txch question type. Cc~rrelation wefficicnta (r ) and line

slopes (II) fnr the three sets of data art’: SlOOO questinns. I’ = 0.9s.

II = 0.59: $10 questionk r = 0.98. II = 0.60; SlOO quc5tinn5. I’ = 0.9s.

II = 0.46. Theac results sugpt that the data arc reaaonahly ~cell dc-

scribed b! ;I po\\cr Iaw of the form:

Perceived Coat = :I ( Actual Coat)“.

100 200 500 1000 Real Costs (from NZCPI)($)

u hose exponent. II. is provided by the line slopes on log-axes and .-l is a

constant. It should be remarked that the form of analysis carried out

here is that commonly used in magnitude estimation experiments in

perceptual and social psychology suggested by Stevens (1957. 1975).

In order to examine the effects of demographic and attitudinal

variables on the perception of inflation and to examine the relationship

between the question types. power law exponents kvere calculated for

each subject and costs question type. Correlations het\veen the expo-

nents obtained for each question type kvere: btavettn the $1000 and $10

questions (based on 100 subjects \\ith valid responses on all of the

questions) r = 0.71; brtaeen the $1000 and $100 questions (based on 98

subjects). r = 0.40: betwwn the $100 and ($10 questions (based on 105

subjects). r = 0.44. These results confirm on the individual level \vhat is

apparent from the median data: responses to the $1000 and $10

questions Lvert: very similar, kvhile responses to the $100 questions.

Lvhich are essentially the inverse of the other questions. were some\vhat

different.

In order to obtain one summary measure for each of the 97 subjects

Lvith no missing data on any of these questions, the thrw expo~~ents for

that individual were averaged. The significance of effects exerted by the

demographic and attitudinal variables on this avrragc exponent was

then assrsscd for each of these tariablcs. The results of iln;llysis of

variance shokvcd ii0 significant ( p = 0.05) effects of the rtapondent’s

SCX. age. ~l~ctori~tc. marital status. cducation:~l kvel attained. or ;tbilitl

to ascribe meaning to ;i 10% :lIlnllill rate of inflatic~n. Party voted for in

the previous clcction had ;i significant effect ( F(2. 86) = 3.537, IJ c 0.05).

tvith .\upportcrs of the ni;ljor opposition party having ;i higher average

cuponcnt (0.67) than supporters of the governing party (0.55) or niinc>r

opposition party (0.46). No significant corrcI;Itions u’crc c>btainccl bc-

town the avcragc cxponc‘nt and houwhold inconic. respondent’s ;ISS~‘S+

mcnt of the pcrsonal impact of inflation on them, or sociocconc,niic

ii&x (Ellcy and Irving 1976). None of the non-.\ignific;rnt results

rxamincd \vas suggestive (1’ < 0.10). Thus ovcr;~ll it appears that indi-

viduals’ perception of price rises art’ conipar~~tivcly tiii~~ffccttxl b)

attitudinal ilnd demographic variables.

T:lhlc 1 summ;lrises the rcsponws to the inflation rate questions.

While the $1000, $10 and $100 questions all clicitcd unclcrcstiniates of

the real extent to \vhich prices have risen in the period. median

estimates of the inflation raw at-t’ fairly accurate. tending if anything to

Ma.h~ axf upper .tnJ lower quatde estrmatr$ of the acragr dnnwl mfI.~twn rate snd ,~tu.d

a~erdgt! ~nnudi mfldtwn raks for perwd\ ending September IYX?. The number of SU~JCCI~

respondmp vahdl~ IO the questmn for that period IS gl\en under ‘n’. Acrud InflJtwn rdtr flgurrb

are baaed on the offlcd ftgurrb (N.Z. hionthly Abstract of Stattstlch).

Estlmatrs

Lowr quart& Me&al Upper quxttlr

n Actud

1 55 80 12.0 8X 5.3

2 10.0 12.0 16.5 86 11.0

4 100 140 170 86 13.45

6 10.5 14.0 17.3 84 13.35

x 10.0 140 17.0 79 1396

10 100 13.5 17 5 7x 13.79

13 100 14.0 1’) 5 80 12.65 16 9.0 12.5 25.0 7x 11.21

The major rault, that tlierc was systcm~tic ilncl~rcstimaticln of the

actual rise in costs ovt’r the ptzriods surveyed, shows lhal fhc unckr-

estimation of rxponentinl grttwth found by W~lg~Ii~~~lr gencrdises hc-

yard the laboratory. Further. the irniicrestint~rtion ha5 gcnmtiiscd from

a task in which subjects extrapolated a short series of numbers to a tush

in which subjects wrrt: askrd to mak estimatrb based on uhat the)

could remember or reconstruct of past costs.

According to Wagenaar. misperception of exponential gro\vth can bt:

charactrrised by an underrstimatt: of the exponent. h. in the equation

J* = ueh-’ + C responsible for gttnerclting tht: series. If Wagenaar’s account

is correct for tht: results of this investigation then a power ia\v rtllation-

ship of the form: Pwxived Cost = A (Actual Cost)” should hold

assuming that costs have actually increased in an e?cponrntial fashion

[l]. As the results shown in fig. 3 show an approximately linear trend.

thus indicating a po\ver law relationship to hold. Wagenaar’s account of

tht: underttstimation is correspondingly upheld. A problem in interpret-

ing this result too rigorously arises because: tht: actual inflation rate for

tht: period ~YIS not constant and hence tht: actunl bchuviour of prices

over time did not strictly follow an txponaitial stxies. It is thus possihlc

that the small deviations from linwrity stun in fig. 3 are thr consc-

quencc of this actual price Miaviour rather than the perception of it. It

is noteworthy. in this rcspcct. that the estrcnic Icft-hand point in fig. 3

for thr: $1000 and $10 questions (right hand for the $100 questions)

Lvhich is furthcst from the lint of hcst fit is bxcd on the time period

\vhich includes 1967-70, ;I period of substantiallv lower inflation.

A further parallcl \vith the results of Wagcnnar’~ c?cperinlents Jcscrvcs

nicntion. 7‘hc results prcswtcci lwrc shv that L1IiClL’rL’~tiIii;itio[i of the

rise in costs ~;IS greater when subjects \vcrc nskcd to respond bq

cstiniating incrcmxl prices (as for the $100 questions) than Lvhcn

subjects u’crc ashcti to respond by c~timatin g dccrcxcd pricch (as for

$10 and $1000 questions). IIicsc diffcrcnt hinds of rcsponsc corre.4poncl

to incrcxsing and dccrcasing cxponcnti;~l xrich Ivliicli follonal the mfnc

pattern.

Thus o\srall the results of this In\estigatian are similar to those

obtained by b’agenax. and appear to have arisen becaue of the

exponential nuture of cost increases. An implication of these results.

which has not been explored here. is that both rupectations regarding

price changes and the perception of, or memory for. actual price

changes are constructed, probably in the same way. Certainly expecta-

tions regarding price changes are also subject to the general process of

underestimation (Keren 1983).

Figs. 1 and 2 show that substantial individual differences exist in the

extent to tvhich changes in costs are underestimated. but. as ~~1s

described above. the individual differences are not strongly related to

the demographic and attitudinal variables measured here. Such ;I result

may suggest that the cause of the individual differences may be of ;1

cognitive rather than an economic or nttitudinal nature.

The subjects in this study revealed ~1 fairly low Iwel of understanding

of inflation. Only half the subjects provided estimates for all the

inflation rate and all the costs qutxtions. and thoxc that did apparently

did not rclatc their rt’sponscs on one type of question kvith those on the

other. Thcsc findinga arc capable of mow than WC intcrprctation: one

could argue. for txamplc. that h~io~vltxlgc of the inflation rate is gained

through the media, lvhilcl co.\ts of actual goods end scrvices arc rclattxl

to cvcryclay c?cpcricnce. Altcrnativcly one could argue that rcmcmbcring

cobts ova ;I period of ycarh ih the more artificial task.

Not yet considcrcd is the question of prcciscly \vhat cognitive

procosxs Lvcrc uwd by the suh~ccts 10 cxtimatc past costs. I’robahiy the

simplest possibility hcrc i5 that suhjcct5 in effect “rcmcmbcr” only an

uncl~rc~ti~iiatc~l cxpc~icnt, h, L\ hich i5 then uwtl to construct the c\ti-

matc.4 of past co.\t5. A,. ll,linst thi3. howxvcr. might lx argual the fact Illat

subjects’ c5tirnate5 of inflation rate arc not only on avcragc accurate but

aI50 do not corrclatc ivith cxpnncnts obt:tincd from the cost.4 clucstion5.

‘I‘hi~s. if SLI~JCC~~ did niahc: i15c of an iln~l~r~.4ti~i~;it~~l cxponcnt. h. they

did ho indcpcndcntlv of their 0timatc of the inflation rate. Of courx.

such indcpcndcnce is quite poshiblc. hoawcr unp~lrsimonious. Ancjthcr

possibility i5 that wbjwt5 L’ktimatccl the past costs from compcwitcs 01

item5 Lvhow past price5 Lvcrc. on avcragc. ovcrc~tim~~tcd. Such over-

cxtimation might occur through confusion of pa.41 \vith prcxcnt or. at

any rate, more recent prices. On the other hand. it i\ not easy 10 xc

~vhy, in this c;ix. lhc: rcsult5 obtained ~houIcl 50 cloaly rcwmblc thaw

obtained from pcrccptual cxpcrimcnt>.

It is clear that an amaver lo the question of precisely how subjects estimate past costs. and thus why the! overestimate them. must a[ rhis stage be speculative. It should be noted, ho\vever. that the apparentI> related phenomenon of misperception of exponential growth is also not completely explained. It is possible that both phenomena are examples of the compression commonly found in perceptual scaling and char- acterised by exponents of less than one in po~ver law functions relating perceived to actual stimuli (Wagenaar 1982: Stevens 1975).

One last issue should be mentioned. The results of this investigation suggest that a general perceptual phenomenon - misperception of exponential growth - affects estimates of the cost of living. Some recent research sugges& lha1 ;I 1ask in visual perception - estimating the sizes of notes and coins - may be influenced by inflation (Lea 1981: Furnham 1983). Findings of this kind indicate ;I complex relationship between traditional psychotogicnt and economic variabtcs.

Rcfcrenccs