Price Adjustments and Inflation - Evidence from Norwegian Consumer Price Data 1975-2004

Wul sbe g, F ed ik Wo king Pape P ice Adjus men s and In la ion - E idence om No wegian Consume P ice Da a 1975-2004 Wo king Pape , No. 2009/11 P o ided in Coope a ion wi h: No ges Bank, Oslo Sugges ed Ci a ion: Wul sbe g, F ed ik (2009) : P ice Adjus men s and In la ion - E idence om No wegian Consume P ice Da a 1975-2004, Wo king Pape , No. 2009/11, ISBN 978-82-7553-507-6, No ges Bank, Oslo, h ps://hdl.handle.ne /11250/2577448 This Ve sion is a ailable a : h ps://hdl.handle.ne /10419/209927 S anda d-Nu zungsbedingungen: Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen Zwecken und zum P i a geb auch gespeiche und kopie we den. Sie dü en die Dokumen e nich ü ö en liche ode komme zielle Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich machen, e eiben ode ande wei ig nu zen. 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I he documen s ha e been made a ailable unde an Open Con en Licence (especially C ea i e Commons Licences), you may exe cise u he usage igh s as speci ied in he indica ed licence. h ps://c ea i ecommons.o g/licenses/by-nc-nd/4.0/deed.no 2009 | 11 P ice adjus men s and in la ion - e idence om No wegian consume p ice da a 1975-2004 by F ed ik Wul sbe g Wo king Pape Resea ch Depa men Wo king pape s a No ges Bank, a 1992/1 il 2009/2 kan bes illes o e e-pos . se icesen e @no ges-bank.no elle ed hen endelse il: No ges Bank, Abonnemen sse ice Pos boks 1179 Sen um 0107 Oslo Tele on 22 31 63 83, Tele aks 22 41 31 05 F a 1999 og emo e e publikasjonene ilgjengelig på www.no ges-bank.no Wo king pape s inneholde o skningsa beide og u edninge som anlig is ikke ha å sin endelige o m. Hensik en e blan anne a o a e en kan mo a kommen a e a kollege og and e in e esse e. Synspunk e og konklusjone i a beidene s å o o a e nes egning. Wo king pape s om No ges Bank, om 1992/1 o 2009/2 can be o de ed by e-mail: se icesen e @no ges-bank.no o om No ges Bank, Subsc ip ion se ice P.O.Box. 1179 Sen um N-0107Oslo, No way. Tel. +47 22 31 63 83, Fax. +47 22 41 31 05 Wo king pape s om 1999 onwa ds a e a ailable on www.no ges-bank.no No ges Bank’s wo king pape s p esen esea ch p ojec s and epo s (no usually in hei inal o m) and a e in ended in e alia o enable he au ho o bene i om he commen s o colleagues and o he in e es ed pa ies. Views and conclusions exp essed in wo king pape s a e he esponsibili y o he au ho s alone. ISSN 1502-8143 (online) ISBN 978-82-7553-507-6 (online) P ice Adjus men s and In la ion—E idence om No wegian Consume P ice Da a – F ed ik Wul sbe g∗ No ges Bank June ,  Abs ac I documen p ice adjus men s in bo h high and low infla ion yea s om  mil- lion mon hly p ice obse a ions o , goods and se ices. The a ia ion in he equency o p ice changes explains all he a ia ion in he infla ion a e. On a e - age, p ices inc ease mo e o en when infla ion is high, and dec ease mo e o en when infla ion is low. The e is also subs an ial a ia ion bo h in he du a ion and size o p ice changes wi hin and be ween i ems. jel: E, D, C Keywo ds: Consume p ices, p ice igidi y ∗No ges Bank, PO Box  Sen um,  Oslo, No way. email: ed ik.wul sbe g@no ges-bank. no, homepage: www.no ges-bank.no/ esea ch/wul sbe g. I wish o hank S a is ics No way o p o- iding da a and gi ing in aluable commen s. I am g a e ul o Al E ik Ballang ud and Ing il Ben e ud Gaa de o excellen esea ch assis ance, and o he Fede al Rese e Bank o Bos on, whe e I s a ed his p ojec . Ca los Ca alho, Mike Goloso , S eina Holden, Gisle Na ik, Julio Ro embe g, Asbjø n Rødse h, and Alexande Wolman ga e use ul commen s as did semina pa icipan s a No ges Bank, n nu, Uni e si y o Oslo, and bi No wegian School o Managemen . Views and conclusions exp essed in his pape a e mine alone and canno be a ibu ed o No ges Bank. I documen he equency and size o p ice adjus men s using obse a ions o mo e han  million mon hly e ail p ice quo es om –. Following Bils and Klenow () many empi ical s udies ha e ecen ly documen ed p ice adjus men s using mic o da a o a la ge numbe o indi idual goods. Klenow and K y so () and Nakamu a and S einsson () in es iga e us da a om –, and Dhyne e . al () summa izes he ipn s udy o  eu o a ea coun ies om –.One impo an issue is how p ice adjus men s a y wi h infla ion. Nakamu a and S einsson () find ha he equency o p ice inc eases co a y s ongly wi h infla ion, while he equency o dec eases and he size o he p ice adjus men s do no . In con as , Klenow and K y so () epo ha he a ia ion in infla ion is mos ly explained by a ia ion in he size o p ice adjus men s. Dhyne e . al () find ha infla ion has a posi i e effec on he equency and he size o p ice inc eases, and a nega i e effec on he equency and he size o p ice dec eases. These s udies, howe e , use da a om pe iods o ela i ely low s eady s a e infla ion: In he us a e age infla ion was . pe cen du ing –, while he a e age infla ion a e in he eu o a ea was . pe cen du ing –. The small amoun o infla ion a iabili y p e en s fi m conclusions ega ding how p ice adjus men s co a y wi h infla- ion. This pape p esen s e idence on p ice adjus men s om  yea s o bo h high and low s eady s a e infla ion. As in o he oecd coun ies cpi infla ion in No way was high and ola ile du ing he G ea Infla ion yea s in he s and s. A e peaking a . pe cen in Janua y , infla ion dec eased du ing he s only in e up ed in  when he nok was de alued by  pe cen . The sample pe iod spli s nicely in o a high-infla ion pe iod om  o  when he a e age cpi infla ion was . pe cen , and a low-infla ion pe iod om  o  when a e age infla ion was . pe cen pe yea . The low-infla ion pe iod is hus qui e simila in e ms o he sample a ia ion in infla ion in he us and Eu opean s udies . An impo an excep ion om he s udies ci ed abo e is Gagnon () who analyzes mic o cpi da a om Mexico –, whe e infla ion soa ed om . pe cen in  o mo e han  pe cen in  due o he collapse in he Mexican peso. The infla ion Bils and Klenow () in es iga e ca ego ies o consump ion goods and se ices (En y Le el I ems) o he us om –. The Infla ion Pe sis ence Ne wo k (ipn) analyzed da a om Aus ia, Belgium, Finland, F ance, Ge many, I aly, Luxembou g, he Ne he lands, Po ugal and Spain. See also s udies om o he coun ies: Hansen and Lynggå d Hansen () o Denma k (–); Gáb iel and Reiff () o Hunga y (–); and Co icelli and Ho á h () o Slo akia (–).  a e did no all below  pe cen un il . Gagnon finds ha he equency o p ice changes accoun o li le o he infla ion a iance, and ha he equency o p ice changes is only co ela ed wi h infla ion when infla ion is abo e – pe cen . E en i infla ion was high and ola ile in No way du ing he s and s, i did no fluc ua e as much as in Mexico in he s. Howe e , he shocks ha hi he Mexican economy in he s we e diffe en om hose leading o he G ea Infla ion in he oecd economies, which makes i in e es ing o s udy mic o da a also om his e a. Fu he mo e, he p esen da a co e a longe pe iod p o iding mo e in o ma ion o compa ing p ice se ing unde high infla ion wi h p ice se ing unde low infla ion. E idence o p ice adjus men unde high and low infla ion is impo an o e alua e he ele ance o diffe en models o p ice se ing. Assump ions ega ding p ice se ing beha - io may ha e impo an implica ions o op imal mone a y policy and wel a e analysis. Time and s a e dependen models ep esen wo pola cases o p ice se ing beha io . An impo an diffe ence is ha ime dependen models (Cal o, , and Taylo , ) as- sume ha he equency o p ice adjus men is exogenous, while s a e dependen models (Ba o,  and Sheshinski and Weiss, ) ea bo h he equency and magni udes o p ice adjus men as choice a iables o he fi ms. In s a e dependen models fi ms ace a fixed adminis a i e cos o changing p ices implying ha he e is a ange o inac i i y; fi ms keep hei p ices fixed i i is be ween an uppe and lowe h eshold p ice. Infla- ion e odes he ela i e p ice un il i equals he lowe h eshold, a which poin he fi m inc ease he p ice o he uppe h eshold. An inc ease in he a e o infla ion unambigu- ously inc ease he magni ude o p ice changes, bu he effec on he equency o p ice changes is ambiguous (Sheshinski and Weiss, , P oposi ion ) because a highe a e o infla ion has wo opposi e effec s on he p ofi abili y o ep icing. In sec ion  I desc ibe he a ia ion in he equency o p ice adjus men s o e ime and ac oss i ems. I find ha (i) he equency o p ice inc eases declined o e he pe iod and is s ongly co ela ed wi h infla ion; (ii) p ices changed on a e age once e e y  mon h in he high-infla ion pe iod, and e e y  mon h in he low-infla ion pe iod; and (iii) he e is subs an ial a ia ion in he equency o p ice changes be ween i ems. P ices o ene gy p oduc s and non-p ocessed ood change equen ly, while se ices change p ices An inc ease in infla ion educes bo h he benefi and cos o pos poning a p ice change.  in equen ly. In sec ion  I look a he magni ude o p ice adjus men s. I find ha (i ) he a e age size o p ice changes is nega i ely co ela ed wi h he infla ion a e; ( ) he a e age p ice change (in absolu e alue) inc eased om – pe cen in he high-infla ion pe iod –, o – pe cen in he low-infla ion pe iod –; and ( i) he e is subs an ial a ia ion in he magni ude o p ice changes be ween i ems. In sec ion  I decompose he a ia ion in he cpi infla ion a e in o he a ia ion in he equency and magni ude o p ice changes. I find ha ( ii) he a ia ion in he infla ion a e is explained by a ia ion in he equency and no he size o p ice changes. The declining equency o p ice inc eases and inc easing equency o p ice dec eases bo h con ibu ed o he a ia ion in infla ion. The inc easing magni ude o p ice inc eases and dec eases had opposi e effec s on he infla ion a e cancelling each o he ou . Sec ion  concludes ha nei he ime dependen models no s a e dependen models a e able o explain he obse ed pa e ns o p ice adjus men .  Da a E e y mon h S a is ics No way collec da a o p ice quo es on a wide ange o consume goods and se ices o p oduce he consume p ice index, cpi (see S a is ics No way (, ) o de ails). Fo example hey eco d he p ice o a bag o  buns wi hou aisins in a specific shop once a mon h. Such de ailed obse a ions p o ide in o ma ion o p ice se ing a he e ail le el. On he basis o hese collec ions o da a I ha e cons uc ed a panel da abase on p ices o , i ems co e ing he  mon hs om Janua y  o Decembe , all oge he ,, p ice obse a ions. The a e age numbe o obse a ions pe mon h is ,. Se e al p ices o he same i em a e eco ded a se e al ou le s. P ice obse a ions o an i em om he same ou le cons i u e a p ice ajec o y o which he e a e ,. On a e age he e a e . obse a ions pe ajec o y. The a e age numbe o obse a ions by i em is , and he a e age numbe o ajec o ies o each i em is . The sampled i ems change o e ime as new goods a e in oduced while o he goods disappea . The numbe o i ems in  a e  and in  he e a e  i ems. Figu e  shows examples o ypical p ice ajec o ies o ou diffe en i ems: Pe ol,  7 8 9 10 11 P ice 1998 1999 2000 2001 2002 2003 2004 Pe ol, unleaded 95 oc ., sel −se ice 10 20 30 40 50 P ice 1994 1995 1996 1997 1998 1999 2000 Toma os 120 140 160 180 200 220 P ice 1997 1998 1999 2000 2001 2002 2003 Pizza wi h bee and mush ooms 300 400 500 600 700 P ice 1997 1998 1999 2000 2001 2002 2003 Wash, clip and blow d y, ladies Figu e : Examples o p ice ajec o ies. unleaded  oc ane, sel -se ice; Toma oes; Pizza wi h bee and mush ooms; and Wash, clip and blow d y, ladies. The ajec o ies show diffe en pa e ns o a ia ion. Pe oleum and oma o p ices seem o change e e y mon h (and possibly mo e o en), a leas o his pe iod. In con as hai d esse s seem o keep p ices cons an o some ime, and a leas o hese hai d esse s, all p ice changes a e inc eases. The p ice o a pizza a e also kep cons an o long pe iods, bu some imes p ices a e inc eased and some imes educed. I ems a e defined wi h a ying deg ees o p ecision. I em  S o e, ce amic (Beha, AK) is p ecisely defined, while i em  Swea e , lamb’s wool, size g own-up is less p ecisely defined. The swea e s a e no necessa ily iden ical ac oss fi ms, bu he ou le s epo he p ice o he same b and, colo and size o he swea e as he p e ious mon h. Fo his pape i is impo an o compa e p ices o he same p oduc in wo consecu i e mon hs. Some imes he fi ms epo he p ice o a diffe en p oduc han he p e ious mon h i i does no longe exis , i he e is a change in he quali y o he good since las mon h, o i he good is subs i u ed by a new good. . pe cen o he obse a ions  a e flagged wi h ei he o hese p ope ies, which I d op om he da abase. Fo many ajec o ies he e a e missing alues. In his pape I do no eplace hese wi h impu ed p ices. When epo ing hei p ices o S a is ics No way, fi ms also epo when a p oduc is on sale. . pe cen (  obse a ions) o all p ice change obse a ions a e ela ed o sales. This ac ion is simila o eu o a ea da a, bu much lowe han in he us. When cons uc ing he cpi, S a is ics No way apply weigh s, ωi , o each i em, i, eflec ing i s impo ance in he a e age consump ion baske . The weigh s a e compu ed as he a e age o he ac ion o consume s’ expendi u e o e he las h ee yea s, hence i changes o e ime. The i ems in his da abase ep esen on a e age . pe cen o he cpi.  The F equency o P ice Changes In his sec ion I documen he a ia ion in he equency o p ice changes o e ime and how hey a e co ela ed wi h he cpi infla ion a e. I fi s compu e he a e age mon hly equency o p ice changes o each i em each yea , i , as he ac ion o he o al numbe o p ice changes o all (p ice change) obse a ions. Then I decompose i in o he equencies o p ice inc eases and dec eases; = + i + − i . The le panel o Figu e  shows how he mean equency o p ice inc eases, + , and dec eases, − , a ies o e ime. In compu ing he means I ha e weigh ed he i ems by hei cu en cpi-weigh . The equency o p ice inc eases declined ma kedly om a ound  pe cen in he ea ly s o a ound  pe cen a e . The p ice (and wage) eeze law in  had a clea on he equency o p ice inc eases, and he de alua ion o he nok explains he spike in . The a ia ion in he equency o p ice inc eases is clea ly connec ed o he a ia ion in he cpi infla ion a e as seen om he igh panel o Figu e  which plo s he equency o p ice inc eases and dec eases e sus he infla ion a e. The equency o p ice inc eases is highly co ela ed wi h cpi infla ion wi h a co ela ion coefficien o ., illus a ed by he eg ession line. P ice dec eases a e p ominen in he da a, bu less equen han p ice inc eases. While  pe cen o he p ice changes we e p ice dec eases du ing he s and s, his ac ion was  pe cen a e . The mean equency o p ice dec eases ho e s  Table : Weigh ed mean equency o p ice changes, du a ion and size o p ice changes by ypes o goods (coicop). Pe iod nI ems + −D Non-du able goods – ,,  . . 4.2 (3.2) – ,,  . . 5.9 (5.5) Du able goods – ,  . . 5.2 (3.8) – ,  . . 6.3 (4.9) Semi-du able goods – ,  . . 9.7 (4.8) – ,,  . . 9.4 (4.5) Se ices – ,  . . 10.6 (12.6) – ,  . . 25.6 (76.0) Table : Weigh ed mean equency o p ice changes, du a ion and size o p ice changes by hicp sec o s. hicp Pe iod nI ems + −D Unp ocessed ood – ,,  . . 2.1 (2.1) – ,,  . . 3.8 (4.9) P ocessed ood – ,,  . . 5.4 (3.0) – ,,  . . 7.3 (4.1) Ene gy – ,  . . 3.5 (3.3) – ,  . . 4.4 (7.1) Non ene gy indus ial goods – ,,  . . 7.1 (4.6) – ,,  . . 7.6 (5.0) Se ices – ,  . . 10.4 (12.3) – ,  . . 24.9 (74.5) he hicp ca ego ies show he same pa e n ac oss coun ies: Ene gy p ices change mos equen ly (excep o Japan and Po ugal) and Se ices leas equen ly. Fo No way, he p ices change mos equen ly o Unp ocessed ood wi h an implied du a ion o only . mon hs when infla ion is high and . mon hs when infla ion is low, see Table . Ene gy p oduc s change almos as equen ly wi h an implied du a ion o . and . mon hs. Fo he (hicp)Se ices he du a ion is abou  mon hs in he high infla ion uc s, ca s, PCs and TVs; and Se ices includes en s and epai s, as well as cul u al, ec ea ional and medical se ices.  0 5 10 15 20 1975 1980 1985 1990 1995 2000 2005 Mean inc ease Mean dec easeπ 10 12 14 16 18 Magni ude o p ice changes, pe cen 0 5 10 15 In la ion, pe cen P ice inc eases P ice dec eases Figu e : Le : The cpi in la ion a e (solid line), he mean weigh ed magni ude o p ice inc eases (dashed line) and dec eases in absolu e alues (do ed line). Righ : The mean weigh ed magni ude o p ice inc eases (do s) and dec eases in absolu e alues (×s) plo ed agains he in la ion a e wi h eg ession lines. Annual a es. Pe cen . pe iod and abou  mon hs in he low infla ion pe iod. Fo he o he g oups he inc ease in du a ion om he high o he low infla ion pe iod a e mode a e (in absolu e e ms). The equency o p ice inc eases is lowe in he low infla ion pe iod o all g oups apa om Ene gy. The equency o p ice dec eases is lowe when infla ion is low o bo h P ocessed and Unp ocessed ood, while i is highe in he low infla ion pe iod o he o he g oups, in pa icula Ene gy p oduc s.  The Size o P ices Changes To in es iga e he ime a ia ion in he magni ude o p ice changes, I compu e he weigh ed a e age magni ude o mon hly p ice inc eases and dec eases in pe cen o each i em and yea , dp+ i and dp− i . The le panel o Figu e  plo s he cpi-weigh ed mean inc ease and dec ease o each yea , dp+ and dp− , oge he wi h he infla ion a e. Bo h he mean size o p ice inc eases and he absolu e alue o p ice dec eases ha e ended upwa ds. The mean size o p ice inc eases ose om  pe cen in  o  pe cen in . Simila ly, he mean p ice dec ease ended upwa ds in absolu e alue om abou  pe cen o almos  pe cen by he end o he sample. As infla ion came down a he same ime, he absolu e alue o he size o he p ice inc eases and dec eases a e nega i ely co ela ed o he infla ion a e. The co ela ion coefficien be ween infla ion and p ice inc eases is –., while he co ela ion coefficien be ween infla ion and he absolu e alue o he size o p ice dec eases is –., see he igh panel o Figu e . As  Table : The weigh ed a e age p ice inc ease and dec ease. Pe cen . – – Full sample Excluding sales A e age size o p ice inc eases (%) Median . . . . Mean . . . . S d e o . . . . A e age size o p ice dec eases (%) Median –. –. –. –. Mean –. –. –. –. S d e o . . . . infla ion does pa o he job in educing ela i e p ices, we would expec a nega i e co - ela ion be ween p ice dec eases and infla ion. The nega i e co ela ion be ween infla ion and p ice inc eases is less in ui i e. While Gagnon () also epo a nega i e co ela ion be ween he magni ude o p ice inc eases and dec eases e sus infla ion, nei he Nakamu a and S einsson () no Dhyne e . al () epo any co ela ion be ween infla ion and he magni ude o p ice changes. The end in he magni ude o p ice changes documen ed abo e hus equi es some sc u iny. How obus is his finding? Fi s , he end inc ease in he magni ude o p ice changes is also p esen in he da a i I emo e ex eme obse a ions. Thi d, he end is obus i we look a he p oduc s which a e included in he cpi baske o e he en i e pe iod (i.e. I emo e he i ems ha en e o exi he sample o e ime). Hence, he end is no explained by changes in he composi ion o goods and se ices. Fou h, he end inc ease is significan o some bu no all o he coicop di isions and deli e y sec o s, (documen ed in sec ion on he e ogenei y below). Columns  and  o Table  epo he weigh ed momen s o he a e age size o p ice changes o he high-infla ion pe iod (–) and low-infla ion pe iod (–). The mean a e age size o p ice inc eases and dec eases we e . and –. pe cen in he low infla ion pe iod, abou – pe cen age poin s highe in absolu e alues han in he high infla ion pe iod. Because infla ion dec eases he ela i e p ice be ween p ice ad- jus men s, one would expec p ice inc eases o be la ge han p ice dec eases as obse ed, (see Ball and Mankiw, ). The es ima es o he low-infla ion pe iod a e simila o he Eu opean and us da a. Klenow and K y so () find ha he mean a e age See Figu e  in he May  e sion o his pape .  .05 .1 .15 .2 .25 .3 .35 −50 −40 −30 −20 −10 0 10 20 30 40 50 −50 −40 −30 −20 −10 0 10 20 30 40 50 High in la ion pe iod Low in la ion pe iod F ac ion Figu e : His og ams o a e age p ice dec eases (dp− i ) and inc eases (dp+ i ) by i em o he high in la ion pe iod – (le ) and low in la ion pe iod – ( igh ). The dis ibu ions a e unca ed a – and  pe cen . p ice inc ease is . pe cen and he mean a e age p ice dec ease is –. pe cen in he us. Dhyne e . al () epo ha he a e age p ice inc ease in he eu o a ea is . pe cen and he a e age p ice dec ease is –. pe cen . To help unde s and he inc ease in mean size o p ice changes o e ime, I plo he his og ams o he a e age size o p ice changes by i em o he high-infla ion and low infla ion pe iods in Figu e . No e ha he e a e wo his og ams in diffe en colo s o each pe iod, one o p ice dec eases and one o p ice inc eases. The ac ion o smalle p ice changes (below  pe cen ) a e abou he same o bo h pe iods. The ac ion o p ice changes be ween  and  pe cen (in absolu e alue) is smalle o bo h dec eases and inc eases in he low infla ion pe iod, while he ac ion o p ice changes be ween  and  pe cen is la ge . Also he a ails o he dis ibu ions a e a e , especially o p ice inc eases. No e ha he combined dis ibu ions o he a e age p ice dec eases and inc eases pe i em a e win peaked. Fo comple eness, Column  o Table  epo s he o e all weigh ed median, mean and s anda d e o o he a e age magni udes o p ice inc eases and dec eases. The median and mean a e age p ice inc ease by i em a e . and . pe cen , while he median and mean a e age p ice dec eases a e –. and –. pe cen . The ou h column o Table  epo he a e age size o p ice changes excluding sales ela ed obse a ions. Because he e a e ela i ely ew sales ela ed p ice changes, he effec o sales on he a e age size o p ice inc eases and dec eases a e a me e  pe cen age poin . Nakamu a and S einsson Figu e C in he appendix shows pe cen iles o he yea -specific dis ibu ions o he magni ude o p ice changes.  0 .05 .1 .15 .2 .25 .3 F ac ion −50 −40 −30 −20 −10 0 10 20 30 40 50 Figu e : His og am o all obse a ions o p ice changes unca ed a – and  pe cen . 0 .1 .2 .3 .4 .5 F ac ion −50 −40 −30 −20 −10 0 10 20 30 40 50 Figu e : His og ams o all p ice dec eases and inc eases unca ed a – and  pe cen . () epo a median a e age size o p ice inc eases and dec eases o . and –. pe cen excluding sales o he us. He e ogenei y The e is subs an ial he e ogenei y be ween goods also in he size o p ice changes. The s anda d e o o p ice inc eases and dec eases a e . and . pe cen o he ull sample (see Table ). While Figu e  illus a es he dispe sion in he a e age sizes o p ice inc eases and dec eases ac oss i ems, he his og am in Figu e  shows he dis ibu ion o he size o all p ice changes. The ze o obse a ions a e omi ed in o de no o o e whelm he g aph. P ice inc eases a e mo e common han dec eases and he e a e many la ge p ice changes (in absolu e alues) ep esen ed by he hick ails. Howe e ,  pe cen o he p ice changes a e less han  pe cen in absolu e alue. Figu e  plo s he sepa a e dis ibu ions o all p ice dec eases and inc eases, (i.e. escales he ac ions om Figu e ). Fo example abou  pe cen o he p ice dec eases a e la ge han – pe cen , and almos hal o he p ice inc eases a e less han  pe cen . No e ha he his og ams in Figu e  and  a e domina ed by i ems wi h many obse a ions. Table  epo s he mean absolu e p ice inc eases and dec eases o he coicop di i- sions o he high and low infla ion pe iods. The e a e sys ema ic diffe ences be ween and wi hin he di isions. We see ha he mean sizes o he p ice changes a e la ge o Clo h- ing and oo wea wi h . and . pe cen o inc eases and dec eases when infla ion is low, compa ed o he o he p oduc ca ego ies. The size o p ice changes a e smalle o  Table : The mean absolu e size o p ice inc eases and dec eases by coicop di ision and high and low in la ion pe iod. Pe cen . Inc eases Dec eases coicop Di ision – – – –  Food and non-alcoholic be e ages 11.5 13.6 10.6 11.9  Alcoholic be e ages, obacco and na co ics 4.5 6.0 3.6 6.1  Clo hing and oo wea 25.5 44.2 22.0 29.5  Housing, wa e , elec ici y, gas and o he uels 5.9 10.8 4.9 9.2  Fu nishings, household equipmen and ou ine household main enance 11.9 14.5 10.3 12.7  Heal h 7.1 9.5 5.7 7.1  T anspo 7.4 4.4 3.5 4.0  Communica ion 5.8 7.8 4.7 9.5  Rec ea ion and cul u e 9.9 13.7 8.7 11.6  Educa ion 9.6 6.2 2.8 15.5  Res au an s and ho els 3.7 13.3 2.6 12.4  Miscellaneous goods and se ices 8.3 9.9 8.7 10.1 Alcohol and obacco, Communica ion, T anspo , and Heal h a ying be ween . and . pe cen in absolu e alue. Fo all di isions he absolu e size o p ice changes a e highe in he low infla ion pe iod compa ed o he high infla ion pe iod wi h he excep ion o p ice inc eases o T anspo and Educa ion. In pa icula he absolu e size o p ice de- c eases we e highe in he low infla ion pe iod o Educa ion and Res au an s and ho els. Figu e C in he appendix plo s he dis ibu ions o he size o p ice changes wi hin he coicop di isions. I shows ha he dis ibu ions a e all singe peaked wi h many small p ice changes, bu he deg ee o peakedness diffe . The coicop di isions Clo hing and oo wea , Communica ion, and Rec ea ion and cul u e possess less peaked dis ibu ions han pa icula ly Alcoholic be e ages and obacco, T anspo , and Educa ion. Rega ding ypes o p oduc s, Table  also shows ha he absolu e size o p ice changes a e la ge in he low infla ion pe iod han in he high infla ion pe iod o all ca ego ies. Semi-du able goods change p ices by he la ges amoun s. Fo hicp p oduc ca ego ies, we see om he bo om panel o Table  ha p ices o Non-ene gy indus ial goods and Unp ocessed ood also change by la ge amoun s (– pe cen on a e age). P ices o Ene gy goods adjus by he smalles amoun wi h an a e age size o p ice inc eases o .  Table : The mean abolu e size o p ice inc eases and dec eases by ypes o goods. Inc eases Dec eases coicop – – – – Non-du able goods 8.0 8.5 9.6 10.6 Du able goods 6.1 7.1 7.9 9.4 Semi-du able goods 17.5 20.5 23.7 33.8 Se ices 5.3 9.6 8.2 8.8 hicp Unp ocessed ood 12.1 13.0 14.5 17.8 Ene gy 2.0 4.0 7.0 7.5 P ocessed ood 8.1 8.8 8.8 9.2 Non ene gy indus ial goods 11.2 12.6 14.2 18.5 Se ices 5.6 9.6 8.5 9.0 1 5 10 20 40 80 The size o p ice inc eases 5 10 20 30 50 The size o p ice dec eases Figu e : The size o p ice inc eases plo ed on he e ical axis agains he absolu e size o p ice dec eases. Log scales. 1 10 20 40 60 i eq 1 10 20 30 50 100 150 Figu e : The equency o p ice inc eases plo ed on he e ical axis agains he size o p ice inc eases. Log scales. pe cen when infla ion is high and wi h . pe cen when infla ion is low. In Figu e  we see a s ong posi i e co ela ion be ween he a e age size o p ice inc eases and dec eases o each i em, which was also de ec ed in he eu o a ea (see Dhyne e . al, , Figu e ). The co ela ion coefficien be ween he size o p ice inc eases and dec eases is .. Howe e , a ew goods ha e a la ge educ ion in p ices on a e age while he a e age p ice inc ease is close o ze o and ice e sa. Fu he mo e, Figu e  shows a weak, albei significan endency ha i ems which p ices inc ease mo e o en, adjus by a smalle size, indica ing ha he size o p ice inc eases may be posi i ely ela ed o du a ion. The co ela ion coefficien be ween he (log) equency o p ice inc eases and (log) size o p ice inc eases is –.. The e is no any simila ela ionship be ween he  0 .02 .04 .060 .02 .04 .060 .02 .04 .06 −50 −40 −30 −20 −10 0 10 20 30 40 50 −50 −40 −30 −20 −10 0 10 20 30 40 50 1 p oduc 2−5 p oduc s 6−10 p oduc s 11−50 p oduc s 51−100 p oduc s 101−200 p oduc s Figu e : His og ams o non-ze o p ice changes by he numbe o p oduc s pe i m. T unca ed a – and  pe cen . equency and size o p ice dec eases. The la ge numbe o small p ice changes a e no consis en wi h s a e dependen mod- els whe e fi ms ace a fixed cos o ep icing. Lach and Tsiddon () a gue ha many small p ice changes illus a ed by he peaked dis ibu ions o non-ze o p ice changes, in combina ion wi h a high a e age p ice change is, howe e , consis en wi h menu cos when fi ms sell many p oduc s and i he e a e economies o scope in p ice adjus men s (see also Mid igan, ). To in es iga e his hypo hesis I plo his og ams o non-ze o p ice changes o ca ego ies o mul i-p oduc fi ms in Figu e . The his og am in he op le shows he size p ice changes o fi ms epo ing only one p ice, he op igh panel shows he size p ice changes o fi ms epo ing p ices o – p oduc s and so on. We see ha small p ice changes in single p oduc fi ms a e as equen as small p ice changes in mul i-p oduc fi ms. Su p isingly, he his og ams o fi ms epo ing mo e han  p oduc s in a single mon h is no single peaked a ound ze o, exac ly wha we would expec o single p oduc fi ms i he e a e economies o scale in p ice se ing.   Con ibu ions o he in la ion a e Sec ion  and  show ha bo h he mean equency and he magni ude o p ice changes a e co ela ed wi h infla ion, in pa icula he equency o p ice inc eases. A simple way o illus a e hei pa ial con ibu ion o he a ia ion in infla ion and in pa icula he pe iod o disinfla ion om mid-s, is o decompose he infla ion a e in o he equencies and he magni udes o p ice inc eases and dec eases. I hen cons uc ou condi ional es ima es o cpi infla ion allowing only one componen o a y a a ime while holding he o he cons an a hei means, and compa e he co ela ion be ween he condi ional es ima es o cpi infla ion wi h cpi infla ion i sel . Fo mally, infla ion is a weigh ed a e age o i em specific p ice changes, ˆπ =X i ωi dpi ,() whe e ˆπ is he a e age mon hly infla ion a e in yea , and dpi is he a e age mon hly p ice change o i em iin yea .ωi is he cpi weigh o i em iin yea .dpi is equal o he equency o p ice changes ( he ex ensi e ma gin), i , imes he magni ude o non-ze o p ice changes ( he in ensi e ma gin), dp∗ i , dpi = i dp∗ i .() The a e age size o non-ze o p ice changes o i em iin yea , can be decomposed in o he he a e age size o p ice inc eases, dp+ i , and dec eases, dp− i , weigh ed by hei ela i e equencies: dp∗ i = + i i dp+ i + − i i dp− i .() Hence, om ()–() he es ima e o cpi infla ion is he weigh ed p oduc -sum o i em specific equencies and magni udes o p ice changes: ˆπ =X i ωi i dp∗ i =X i ωi  + i dp+ i + − i dp− i () Figu e  shows he mean adjus ed annualized ˆπ wi h he obse ed cpi infla ion a e,  0 5 10 15 Pe cen 1975 1980 1985 1990 1995 2000 πˆπ Figu e : cpi in la ion π (solid line) and (mean adjus ed) p edic ed in la ion a e, ˆπ (dashed line). Annual a es. Pe cen . π . We see ha ˆπ acks π ex emely well, wi h a co ela ion coefficien o .. No e ha () diffe s om he measu e in Klenow and K y so () who decompose he infla ion a e in o he mean a e age weigh ed equencies and magni udes o p ice changes: ˆπ = dp∗ = + dp+ + − dp− ( hei equa ion (.)). Compu ing hei p oposed es ima e o infla ion wi h he p esen da a yields a co ela ion coefficien wi h he cpi infla ion a e o . which is conside ably lowe . I hen cons uc ou condi ional es ima es o cpi infla ion, deno ed as ˆπ | +,ˆπ | −, ˆπ |dp+, and ˆπ |dp−, whe e I allow only one componen o a y a a ime while holding he o he h ee componen s cons an a hei means: ˆπ | +=X i ωi  + i dp+ i+ − idp− i,ˆπ |dp+=X i ωi  + idp+ i + − idp− i ˆπ | −=X i ωi  + idp+ i+ − i dp− i,ˆπ |dp−=X i ωi  + idp+ i+ − idp− i  Fo example, ˆπ | +is he p edic ed infla ion a e when he a e age equency o p ice inc eases a ies as obse ed while holding he o he h ee componen s cons an a hei means: − i, dp+ i,and dp− i. The ou panels o Figu e  displays ˆπ | +,ˆπ | −,ˆπ |dp+and ˆπ |dp−, oge he wi h π . We see ha he decline in he equency o p ice inc eases ( op le panel), he inc ease in he equency o p ice dec eases (bo om le ), and he inc eased magni ude The means o ˆπ and π a e . and . pe cen . No e ha cons uc ing he cpi om he obse a ions o indi idual p ices is a complica ed p ocedu e, which in ol es adjus ing o quali y, egional diffe ences, impu ing p ices, and weigh ing obse a ions (see S a is ics No way, ). Conside ing he simple algo i hm () and ha I do no ha e he ull se o obse a ions used o cons uc he cpi one should no expec a pe ec fi .  Appendix A Da a Today he No wegian cpi is compu ed om mon hly da a o  ep esen a i e goods and se ices om app oxima ely  fi ms. Once a yea he ep esen a i e goods and se ices a e e ised. The sample o fi ms is o a ed so ha a fi m is included o a maximum o  yea s ( mon hs). The p ice da a a e epo ed mon hly by he fi ms ei he by comple ed o ms o scanne da a. The quali y o he obse a ions a e e alua ed and e ised be o e used o cons uc he cpi. The e ision s a us, i.e. i he p ice obse a ion is impu ed o co ec ed, s a us o he i em i sel , and whe he he obse a ion is used o no in he cpi is known. The e a e missing obse a ions in he sample esul ing in b eaks in he ajec o ies. I ems ep esen ed by an index a e excluded om he da a se used in his pape . I ha e emo ed , obse a ions whe e he i em is no offe ed anymo e, has changed in quali y om he p e ious mon h, o is a new i em. The numbe o obse a ions pe mon h a ies be ween , and ,. Figu e A, le panel, shows ha he numbe o obse a ions pe mon h declines s eadily om an a e age o , in  o , in  o hen o inc ease o , in . The igh panel o Figu e A shows ha he e is no sys ema ic a ia ion be ween diffe en mon hs. Figu e A illus a es he numbe o obse a ions by coicop g oups o e ime wi h he numbe o obse a ions in  o he igh . 10,000 20,000 30,000 40,000 50,000 1975 1980 1985 1990 1995 2000 20,000 30,000 40,000 50,000 Jan Feb Ma Ap May Jun Jul Aug Sep Oc No Dec Figu e A: The a ia ion in he numbe o obse a ions by yea (le ) and by mon h ( igh ) 1 2 3 4 5 6 7 8 9 10 11 12 COICOP Di ision 1975 1980 1985 1990 1995 2000 2005 Figu e A: The dis ibu ion o obse a ions ac oss coicop g oups o e ime.  B Tables Table B: Mean equency o p ice changes and mean p ice du a ion in mon hs by coicop g oups ( h ee-digi le el) and classes ( ou -digi le el). coicop G oup/Class n +D dp+dp−  Food ,, . . 4.4 (4.2) . .  B ead and ce eals ,, . . 6.0 (1.8) . .  Mea ,, . . 2.6 (5.0) . .  Fish and sea ood , . . 3.7 (1.1) . .  Milk, cheese and eggs , . . 5.7 (2.1) . .  Oils and a s , . . 3.5 (0.9) . .  F ui , . . 2.4 (2.9) . .  Vege ables , . . 2.4 (2.5) . .  Suga , jam, honey, chocola e and con ec ione y , . . 9.0 (5.2) . .  Food p oduc s n.e.c. , . . 6.7 (2.1) . .  Non-alcoholic be e ages , . . 4.3 (2.6) . .  Coffee, ea and cocoa , . . 2.3 (1.3) . .  Mine al wa e s, so d inks, ui and ege able juices , . . 6.2 (2.0) . .  Alcoholic be e ages , . . 5.1 (1.0) . .  Spi i s , . . 4.4 (0.3) . .  Wine , . . 5.7 (0.7) . .  Bee , . . 5.4 (1.1) . .  Tobacco , . . 8.6 (1.4) . .  Clo hing , . . 8.5 (3.6) . .  Clo hing ma e ials , . . 13.8 (2.5) . .  Ga men s , . . 7.6 (3.0) . .  O he a icles o clo hing and clo hing accesso ies , . . 12.6 (3.5) . .  Cleaning, epai and hi e o clo hing , . . 7.7 (5.3) . .  Foo wea , . . 8.5 (2.6) . .  Shoes and o he oo wea , . . 8.4 (2.5) . .  Repai and hi e o oo wea , . . 14.1 (2.2) . .  Ac ual en als o housing , . . 13.0 (.). .  Main enance and epai o he dwelling , . . 5.9 (3.0) . .  Ma e ials o he main enance and epai o he dwelling , . . 5.9 (3.0) . . Table B con inues on nex page.  Table B con inued. coicop G oup/Class n +D dp+dp−  Elec ici y, gas and o he uels , . . 6.7 (8.2) . .  Elec ici y , . . 7.3 (11.6) . .  Liquid uels , . . 1.3 (0.1) . .  Solid uels , . . 12.3 (3.9) . .  Hea ene gy  . . 2.4 (0.0) . .  Fu ni u e and u nishings, ca pe s and o he floo co e ings , . . 8.5 (2.5) . .  Fu ni u e and u nishings , . . 8.4 (2.6) . .  Ca pe s and o he floo co e ings , . . 9.0 (1.7) . .  Household ex iles , . . 10.2 (2.3) . .  Household ex iles , . . 10.2 (2.3) . .  Household appliances , . . 5.3 (1.6) . .  Majo household appliances whe he elec ic o no , . . 5.2 (1.3) . .  Small elec ic household appliances , . . 7.1 (1.2) . .  Repai o household appliances  . . 2.6 (.). .  Glasswa e, ablewa e and household u ensils , . . 10.8 (7.0) . .  Tools and equipmen o house and ga den , . . 10.6 (5.1) . .  Majo ools and equipmen , . . 8.9 (0.6) . .  Majo ools and equipmen , . . 8.9 (0.6) . .  Small ools and miscellaneous accesso ies , . . 10.9 (5.5) . .  Small ools and miscellaneous accesso ies , . . 10.9 (5.5) . .  Goods and se ices o ou ine household main enance , . . 8.1 (6.7) . .  Non-du able household goods , . . 7.6 (7.6) . .  Domes ic se ices and household se ices , . . 9.5 (1.4) . .  Medical p oduc s, appliances and equipmen , . . 9.2 (5.0) . .  Pha maceu ical p oduc s , . . 6.3 (1.6) . .  O he medical p oduc s , . . 7.8 (2.2) . .  The apeu ic appliances and equipmen , . . 16.2 (4.0) . .  Ou pa ien se ices  . . 14.7 (4.0) . .  Medical se ices  . . 19.9 (.). .  Den al se ices  . . 12.0 (0.0) .  Pa amedical se ices  . . 17.1 (4.2) . . Table B con inues on nex page.  Table B con inued. coicop G oup/Class n +D dp+dp−  Pu chase o ehicles , . . 3.0 (1.7) . .  Mo o ca s , . . 2.8 (1.4) . .  Mo o cycles , . . 8.1 (0.9) . .  Bicycles , . . 7.0 (0.3) . .  Ope a ion o pe sonal anspo equipmen , . . 8.1 (30.6) . .  Spa e pa s and accesso ies o pe sonal anspo equipmen , . . 8.5 (1.6) . .  Fuels and lub ican s o pe sonal anspo equipmen , . . 1.3 (1.5) . .  Main enance and epai o pe sonal anspo equipmen , . . 9.3 (3.3) . .  O he se ices in espec o pe sonal anspo equipmen , . . 46.9 (90.7) . .  T anspo se ices , . . 12.7 (3.8) . .  Passenge anspo by ailway , . . 14.6 (4.6) . .  Passenge anspo by oad , . . 14.7 (3.0) . .  Passenge anspo by ai  . . 8.6 (0.0) . .  Passenge anspo by sea and inland wa e way , . . 11.6 (1.4) . .  Pos al se ices  . . 20.4 (3.0) .  Pos al se ices  . . 20.4 (3.0) .  Telephone and ele ax equipmen , . . 4.1 (3.1) . .  Telephone and ele ax se ices , . . 16.7 (25.6) . .  Audio- isual, pho og aphic and in o ma ion p ocessing equipmen , . . 6.4 (3.5) . .  Equipmen o he ecep ion, eco ding and ep oduc ion o sound and pic u es , . . 5.5 (1.9) . .  Pho og aphic and cinema og aphic equipmen and op ical ins umen s , . . 7.4 (4.0) . .  In o ma ion p ocessing equipmen , . . 4.1 (3.0) . .  Reco ding media , . . 11.4 (2.5) . .  Repai o audio- isual, pho og aphic and in o ma ion p ocessing equipmen  . . 2.5 (0.0) . .  O he majo du ables o ec ea ion and cul u e , . . 12.6 (2.4) . .  Majo du ables o ou doo ec ea ion , . . 12.2 (1.2) . .  Musical ins umen s and majo du ables o indoo ec ea ion , . . 14.0 (4.4) . .  O he ec ea ional i ems and equipmen , ga dens and pe s , . . 10.4 (8.6) . . Table B con inues on nex page.  Table B con inued. coicop G oup/Class n +D dp+dp−  Games, oys and hobbies , . . 12.5 (3.1) . .  Equipmen o spo , camping and open-ai ec ea ion , . . 16.2 (13.0) . .  Ga dens, plan s and flowe s , . . 4.8 (3.7) . .  Pe s and ela ed p oduc s , . . 8.4 (1.2) . .  Rec ea ional and cul u al se ices , . . 12.7 (6.2) . .  Rec ea ional and spo ing se ices  . . 9.4 (5.1) . .  Cul u al se ices , . . 14.4 (6.3) . .  Newspape s, books and s a ione y , . . 9.3 (6.3) . .  Books , . . 14.3 (3.8) . .  Newspape s and pe iodicals , . . 4.4 (2.9) . .  S a ione y and d awing ma e ials , . . 16.0 (4.8) . .  Package holidays  . . 9.2 (.). .  P e-p ima y and p ima y educa ion  . . 13.3 (.). .  Seconda y educa ion  . . 13.0 (0.8) . .  Te ia y educa ion , . . 12.3 (0.9) . .  Ca e ing se ices , . . 15.2 (4.8) . .  Res au an s, ca es and he like , . . 15.2 (5.0) . .  Can eens , . . 15.4 (2.4) . .  Accommoda ion se ices , . . 8.2 (3.6) . .  Pe sonal ca e , . . 8.6 (2.6) . .  Hai d essing salons and pe sonal g ooming es ablishmen s , . . 10.2 (1.2) . .  Elec ic appliances o pe sonal ca e , . . 8.0 (1.5) . .  O he appliances, a icles and p oduc s o pe sonal ca e , . . 7.6 (2.7) . .  Pe sonal effec s n.e.c. , . . 12.1 (5.9) . .  Jewelle y, clocks and wa ches , . . 11.7 (4.6) . .  O he pe sonal effec s , . . 12.4 (7.7) . .  Social p o ec ion  . . 20.4 (6.6) . .  Insu ance  . . 4.0 (.). .  Financial se ices n.e.c. , . . 48.2 (58.0) . . No es: n.e.c. is sho o no elsewhe e classified.  C Figu es 0 10 20 30 40 50 1975 1980 1985 1990 1995 2000 0 10 20 30 40 1975 1980 1985 1990 1995 2000 0 10 20 30 40 1975 1980 1985 1990 1995 2000 0 10 20 30 1975 1980 1985 1990 1995 2000 Figu e C: The annual dis ibu ions o he mon hly equency o p ice inc eases ( op le ), he equency o p ice dec eases ( op igh ), he a e age p ice inc ease (bo om le ), and he a e age p ice dec ease (bo om igh ). The uppe and lowe ends o he dashed lines ep esen he  h and  h pe cen iles, he do s ma king he uppe and lowe ends o he solid lines ep esen he  h and  h pe cen iles, he ho izon al lines ep esen he median, and he solid lines ep esen he means. Pe cen . 0 .05 .10 .05 .10 .05 .1 −40 −20 0 20 40 −40 −20 0 20 40 −40 −20 0 20 40 −40 −20 0 20 40 1234 5678 9 10 11 12 Densi y Figu e C: His og am o all non-ze o p ice changes in pe cen by coicop di ision. The dis ibu ions a e unca ed a – and  pe cen . The coicop di isions a e : Food and non-alcoholic be e ages; : Alcoholic be e ages, obacco and na co ics; : Clo hing and oo wea ; : Housing, wa e , elec ici y, gas and o he uels; : Fu nishings, household equipmen and ou ine household main enance; : Heal h; : T anspo ; : Communica ion; : Rec ea ion and cul u e; : Educa ion; : Res au an s and ho els; : Miscellaneous goods and se ices. 