Bank of Japan Review. Performance of Core Indicators of Japan s Consumer Price Index. November Introduction 2015-E-7

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1 Bank of Japan Review 5-E-7 Performance of Core Indicaors of Japan s Consumer Price Index Moneary Affairs Deparmen Shigenori Shirasuka November 5 The Bank of Japan (BOJ), in conducing moneary policy, employs he core indicaors of he consumer price index (CPI) o idenify he underlying rend of inflaion by excluding various idiosyncraic disurbances from he overall CPI. Considering ha sources of such idiosyncraic disurbances are no always consan over ime, his aricle examines he performance of he core indicaors by focusing on he sabiliy over he esimaion period. Empirical evidence reveals ha he CPI excluding fresh food and rimmed mean generally show beer performance han oher indicaors. I also shows ha he performance of he CPI excluding fresh food is deerioraing currenly, even hough such deerioraion, affeced by large swings in crude oil prices, is likely o be emporary. In examining he underlying rend of inflaion and explaining i o he public, i is hus imporan o consider various indicaors, such as rimmed mean, and he CPI excluding fresh food and energy, even hough he CPI excluding fresh food remains a main indicaor, considering is high public awareness. Inroducion The Bank of Japan (BOJ) defines Price Sabiliy Targe a percen by using he overall index in he consumer price index (CPI). While he CPI is influenced by various idiosyncraic disurbances in he shor erm, such effecs diminish in he medium o long erm. I is hus appropriae o use he overall index wih he broades coverage when considering he price sabiliy in he medium o long erm. However, in conducing moneary policy, he BOJ needs o idenify he underlying rend of inflaion from he monhly publicaion of he CPI daa. To ha end, i employs he core indicaors of he CPI ha exclude various idiosyncraic disurbances when idenifying he underlying rend of inflaion and explaining i o he public. I should be noed ha sources of such idiosyncraic disurbances are no always consan over ime. I is raher he case ha iems ha should be excluded from he overall index vary over ime in accordance wih economic and price developmens. In addiion o fresh food wih volaile price flucuaions due o weaher condiions, energy is producing significan disurbances currenly, reflecing large swings in crude oil prices since he collapse of Lehman Brohers. I is hus highly possible ha he performance of he core indicaors varies over ime. This aricle comprehensively examines he performance of he core indicaors by focusing on he sabiliy of heir performance over he esimaion period. Following he empirical framework of Shirasuka (6) and updaing daa for en years, he performance of he core indicaors is examined in wo respecs: one is he racabiliy of he curren underlying rend of inflaion, and he oher is he predicing power of he underlying inflaion rend in he fuure. In doing so, he performance of he core indicaors is examined by paying aenion o he sabiliy over ime. The six core indicaors considered in his sudy are caegorized ino wo groups (Char ). The firs group includes he CPI excluding fresh food, he CPI excluding fresh food and energy, and he CPI excluding food and energy. These always exclude pre-specified iems wih high shor-erm volailiy. The second group includes rimmed mean, weighed median, and mode. These adjus he disored impacs from oulier iems wih exreme increases/decreases by mechanically excluding such oulier iems. Thus, he iems excluded are no specified in advance. Bank of Japan November 5

2 5 [Char ] CPI Core Indicaors Ex. fresh food Ex. fresh food and energy Ex. food and energy [Char ] Exracion of Underlying Trend (Toal) (Underlying changes) = (Disurbances) + 5 Trimmed mean (Insiuional changes) + Weighed median Source: Minisry of Inernal Affairs and Communicaions, "Consumer Price Index." Noe: CPI excluding fresh food and energy, rimmed mean, weighed median, and mode are calculaed by he Research and Saisics Deparmen, Bank of Japan. Figures are adjused o exclude he esimaed effec of changes in he consumpion ax rae. Effecs of Idiosyncraic Disurbances Basic concep Char gives a hypoheical example of how o exrac he underlying rend of inflaion by excluding he effecs of idiosyncraic disurbances. changes in inflaion (op panel) correspond o he sum of: (i) he underlying componen ha moves on a cyclical rend (second panel), (ii) he idiosyncraic componen ha flucuaes from ime o ime (hird panel), and (iii) he one-ime componen, including insiuional changes, ha rises/declines for a cerain period of ime and hen vanishes (boom panel). Therefore, overall changes in inflaion end o move up and down in he shor erm due o he effecs of various disurbances, hereby making i difficul o idenify is underlying rend. Focusing on he period surrounded by he doed lines, overall changes firs pick up, and hen drop sharply. However, his movemen is influenced by changes in he insiuional componen and he underlying rend sars o decline when overall inflaion rises. As shown in he hypoheical example above, i is crucially imporan o exclude he effecs of idiosyncraic disurbances appropriaely when idenifying he underlying rend of inflaion. Effecs of idiosyncraic disurbances Which iems produce idiosyncraic disurbances, hereby making i difficul o exrac he underlying rend of inflaion in Japan s CPI? Char plos he conribuions of possible idiosyncraic facors on he deviaions beween he overall CPI and is Hodrick-Presco (HP) filered rend. HP-filering is a saisical mehod o exrac smooh componens from ime-series daa as an underlying rend. Looking a Char, deviaions beween year-on-year changes in he overall CPI and hose in he HP-filered rend move up and down wih shor inervals. These flucuaions are mainly aribuable o fresh food, confirming ha fresh food, wih high shor-erm volailiy due o weaher condiions, is he mos significan source of idiosyncraic disurbances in he CPI. The char also shows ha he conribuions of energy become larger during he periods from 986 o 987 as well as he period afer s. In he firs period, energy relaed prices, including elecriciy, declined significanly, reflecing he yen appreciaion afer he Plaza Accord and he crude oil price plunge due o he reverse oil-shock. In he second period, crude oil prices showed large swings several imes afer he collapse of Lehman Brohers, making he conribuions of energy larger as well as more persisen. Bank of Japan November 5

3 [Char ] Deviaions beween Inflaion and Is Trend HP-filered rend Fresh food - Conribuions - Deviaions b/w overall and HP-filered rend Food excluding fresh food Energy Source: Minisry of Inernal Affairs and Communicaions, "Consumer Price Index." Noe: The rend is compued by applying he Hodrick- Presco filer o he overall index wih he smoohing parameer of,, which is he defaul for monhly daa. I is hus confirmed ha fresh food coninues o be he mos significan source of idiosyncraic disurbances in Japan s CPI. In addiion, energy someimes becomes an addiional major source of disurbances. I should be noed ha sources oher han fresh food are no always significan, suggesing ha he performance of he core indicaors are likely o vary over ime. In he following, saisical mehods are applied o examine he performance of he core indicaors by focusing on he sabiliy of he performance over ime. movemens in he medium o long erm, as he effecs of idiosyncraic disurbances are smoohed ou. This also corresponds o he idea ha he numerical definiion of price sabiliy uses he overall CPI, whereas he curren underlying rend of inflaion is moniored mainly by he core indicaors. More precisely, differences in he year-on-year changes in he core indicaors and hose in he overall CPI are regressed on a consan erm, hereby esing he hypohesis wheher he esimaes are differen from zero a a cerain significance level. In doing so, esimaions are repeaedly carried ou using subsamples of en years while paying aenion o changes in esimaes and heir saisical significance over ime (rolling regression). Looking a he esimaion resuls in Char, he CPI excluding fresh food shows he highes performance in a fairly sable manner: confidence inervals are exremely narrow and include zero over he whole period. Trimmed mean, he CPI excluding fresh food and energy, and weighed median come nex: confidence inervals are generally narrow and mosly include zero. In conras, he CPI excluding food and energy, and mode show relaively poor performance. The empirical evidence confirms ha he CPI excluding fresh food neiher overesimaes nor underesimaes he level of he CPI inflaion over en years. This suggess ha excluded iems, even hough - [Char ] Deviaions from Index Ex. Fresh Food Ex. Fresh Food and Energy - Trimmed Mean Weighed Median Tracabiliy of Curren Underlying Trend Firs, he racabiliy of he curren underlying rend of inflaion is esed by applying wo approaches Ex. Food and Energy Deviaions from overall CPI The firs approach examines wheher year-on-year changes in he core indicaors and hose in he overall CPI are equalized over he medium o long erm. This implies ha boh indexes are supposed o show similar Noe: Figures in he chars show esimaes of he consan erm ha are esimaed repeaedly using subsamples of monhs ending a each monh on he horizonal axis. The doed lines show 95-percen confidence inervals, compued from auocorrelaion robus sandard errors based on Newey-Wes s mehod. - Bank of Japan November 5

4 having he smalles weigh among all he core indicaors, have fairly symmeric effecs on he CPI inflaion. Trimmed mean, he CPI excluding fresh food and energy, and weighed median also deliver saisfacory performance. However, he CPI excluding food and energy, and mode show significan and persisen deviaions, indicaing he exisence of biases in esimaing he level of he CPI inflaion. Deviaions from rend inflaion The second approach examines o wha exen he core indicaors race he HP-filered rend, as a proxy for he underlying rend, on a real ime basis. Roo mean squared errors (RMSEs) are used as a yardsick o examine he deviaions, and compued repeaedly from subsamples of en years. Looking a he esimaion resuls in Char 5, rimmed mean generally shows he smalles RMSEs, and weighed median and he CPI excluding food and energy follow. In conras, he CPI excluding food and energy, and mode show significan deviaions, especially unil he second half of he 99s. Meanwhile, he CPI excluding fresh food shows raher limied deviaions unil he mid s, while i significanly increases he deviaions hereafer. To sum up, rimmed mean shows he highes and he mos sable performance over he whole period. I exhibis high racabiliy of he underlying rend of inflaion on a real ime basis by properly excluding ime-varying sources of idiosyncraic disurbances. The CPI excluding fresh food worsens is performance in racing he underlying rend of inflaion, as disurbing effecs of energy become significan afer he second half of he s [Char 5] Deviaions from Trend Inflaion Less fresh food Less fresh food and energy Less food and energy Noe: Roo mean squared errors, which are he square roo of he mean squared deviaions, are used for quaniaive assessmen of he degree of deviaions from he rend inflaion. Figures in he chars are compued repeaedly using subsamples of monhs ending a each monh on he horizonal axis Trimmed mean Weighed median Assessmen on racabiliy of curren underlying rend Two ypes of saisical analysis show ha rimmed mean and he CPI excluding fresh food have generally high and sable performance in racking he curren underlying rend of inflaion. I should be noed ha he performance of he CPI excluding fresh food is deerioraing currenly, even hough such deerioraion, affeced by large swings in crude oil prices, is likely o be emporary. Predicive Power on Fuure Underlying Trend Nex, he predicive power of he core indicaors regarding he fuure direcion of he underlying rend of inflaion is examined. Rolling esimaions are again employed o examine he sabiliy of he predicive power over ime. Saisical es on predicive power The firs esimaion exercise employs he specificaion below: Esimaion Equaion CORE h ) (, where denoes he year-on-year changes of he overall CPI and core refers o he year-on-year changes in he core indicaors. The parameer h akes he value of (monhs). and are esimaed coefficiens. Esimaion equaion examines wheher he deviaions beween he overall CPI and he core indicaors are jus emporary, and he overall CPI ends o converge o he core indicaors, as he idiosyncraic disurbances diminish. If = and = in esimaion equaion, he core indicaor will be an unbiased predicor of he overall CPI unil one-year ahead. Char 6 summarizes he es resuls on he join hypohesis of = and =. In erms of he duraion for no rejecing he join hypohesis even a he -percen confidence level, i.e. p-values exceed., he CPI excluding fresh food is he longes and rimmed mean comes nex. The CPI excluding fresh food and energy, weighed median, and mode are slighly shorer, and he CPI excluding food and energy is he shores. Bank of Japan November 5

5 [Char 6] Join Hypoheses Tes on Equaion % level Noe: Figures in he chars show p-values for join hypoheses esing on = and = in esimaion equaion, based on he rolling esimaion resuls using subsamples of monhs ending a each monh on he horizonal axis. Focusing furher on he esimaes of he slope coefficien,, which are expeced o be posiive and no o be differen from one a a cerain significance level, Char 7 plos he esimaes for all he six core indicaors. The CPI excluding fresh food and energy is posiive and no differen from one over he whole period. Trimmed mean shows generally he same resuls excep for he shor period in he early s. The CPI excluding fresh food becomes less credible afer he mid-s, as he confidence inervals ge wider and include zero, even hough hey are no saisically significanly differen from one over he whole period. Weighed median is also no differen... Ex. fresh food Ex. fresh food and energy Ex. food and energy Trimmed mean Weighed median [Char 7] Esimaes for in Equaion Ex. Fresh Food Ex. Fresh Food and Energy Ex. Food and Energy Noe: Figures shown in he chars show esimaes for in esimaion equaion, based on he rolling regression resuls using subsamples of monhs ending a each monh on he horizonal axis. The doed lines show 95-percen confidence inervals, compued from auocorrelaion robus sandard errors based on Newey-Wes s mehod.... Trimmed Mean Weighed Median from one hroughou mos of he period, bu is no saisically significanly posiive in he second half of he 99s when confidence inervals become wider. The CPI excluding food and energy, and mode show relaively weak predicive power, especially in he 99s. Nex, he second esimaion exercise employs an alernaive specificaion of esimaion equaion below, replacing he explained variable from he overall CPI o he core indicaors: Esimaion Equaion CORE CORE CORE h ) (, CORE where and are esimaed coefficiens. Esimaion equaion examines wheher he deviaions beween he overall CPI and he core indicaors are jus emporary, bu he core indicaors do no end o converge o he overall CPI, as he idiosyncraic disurbances diminish. In his case, he slope esimaes of are expeced no o be differen from zero a a cerain significance level. Looking a Char 8 for he esimaion resuls, he esimaes of for all he core indicaors are generally close o zero. Among hem, rimmed mean shows he mos sable performance, as evidenced by he resuls ha esimaes are no significanly differen from zero over almos he enire period. Focusing on he recen [Char 8] Esimaes for in Equaion Ex. Fresh Food Ex. Fresh Food and Energy Ex. Food and Energy Trimmed Mean Weighed Median Noe: Figures shown in he chars show esimaes for in esimaion equaion, based on he rolling regression resuls using subsamples of monhs ending a each monh on he horizonal axis. The doed lines show 95-percen confidence inervals, compued from auocorrelaion robus sandard errors based on Newey-Wes s mehod. 5 Bank of Japan November 5

6 period, he esimaes for weighed median and mode are close o zero wih very narrow confidence inervals. In conras, he performance of he CPI excluding fresh food is deerioraing currenly, as clearly seen in he widening of he confidence inervals. Summary of es resuls To sum up he es resuls for predicive power, rimmed mean and he CPI excluding fresh food are judged as showing relaively high performance. However, i should be noed ha, jus he same as he racabiliy of he underlying rend of inflaion, he performance of he CPI excluding fresh food is deerioraing currenly, due o large swings in crude oil prices. indicaors. For deails, see Yoshihiko Hogen, Takuji Kawamoo, and Moe Nakahama, Core Inflaion and he Business Cycle (Bank of Japan Review, 5-E-6, 5). See Shigenori Shirasuka, Core Indicaors of Japan s Consumer Price Index (Bank of Japan Review 6-E-7, 6). The deails of he core indicaors in he second group, which are less familiar o he public, compared wih hose in he firs group, are summarized below. Trimmed mean mechanically discards a cerain percenage from each ail of he price flucuaion disribuion (-percen). Weighed median is he weighed average of price changes of he iem a around he 5 percenile poin of he disribuion (5-percen in he cener of he disribuion). corresponds o he highes frequency (densiy) in he disribuion. As explained in he main ex, hose indicaors are called limied influence indicaors, which imply ha he effecs of oulier iems are excluded. The sample period sars in 98, when he adverse effecs of he oil-shock were generally subdued, and ends in Augus 5, which is he end of daa readily available when preparing his aricle. Concluding Remarks This aricle examined he six core indicaors used in Japan by applying saisical mehods o compare heir performance in wo respecs: (i) racabiliy of he curren underlying rend of inflaion, and (ii) predicive power on he fuure underlying rend of inflaion. Given ha idiosyncraic disurbances, which make i difficul o idenify he underlying rend, possess a ime-varying naure boh in sources and magniude of impacs, he performance of he core indicaors was examined paying aenion o he sabiliy over ime. To sum up he overall es resuls, i is confirmed ha he CPI excluding fresh food and rimmed mean show relaively high performance. A he same ime, i should be noed ha he performance of he CPI excluding fresh food is deerioraing currenly, alhough such deerioraion is likely o be emporary due o large swings in crude oil prices. Thus, i is imporan o monior a wide range of indicaors in properly assessing he underlying rend of inflaion and explaining i o he public. Alhough he CPI excluding fresh food, given is high public awareness, remains a main core indicaor, oher indicaors, such as rimmed mean and he CPI excluding food and energy, also need o play an imporan role. I is also necessary o examine he performance of he core indicaors coninuously, considering heir ime-varying naure. Bank of Japan Review is published by he Bank of Japan o explain recen economic and financial opics for a wide range of readers. This repor, 5-E-7, is a ranslaion of he original Japanese version, 5-J-, published in November 5. The views expressed in he Review are hose of he auhor and do no necessarily represen hose of he Bank of Japan. If you have commens or quesions, please conac he Policy Sudies Division, Moneary Affairs Deparmen (Tel ). Bank of Japan Review and Bank of Japan Working Paper can be obained hrough he Bank of Japan s websie (hp:// The Bank of Japan sared employing some new core 6 Bank of Japan November 5