A Stochastic Index of the Cost of Life; An Application to Recent and Historical Asset Price Fluctuations

Transcription

1 A Stochastc Index of the Cost of Lfe; An Applcaton to Recent and Hstorcal Asset Prce Fluctuatons Introducton Mchael F Bryan, Stephen G Cecchett, and Rósín O Sullvan * Ths paper consders the role of asset prces n the constructon of measures of nflaton Followng work begun n Bryan, Cecchett, and O Sullvan (2001), we examne the potental bas n aggregate prce statstcs that can arse n measures that focus solely on the prce of current consumpton If the role of the central bank s to elmnate changes n the overall prce level, then the approprate prce ndex should capture the current cost of purchasng clams to future as well as current consumpton One nterpretaton of ths s that polcymakers should be concerned wh the current cost of expected lfetme consumpton rather than the more conventonal measures that focus exclusvely on the current cost of current consumpton The smplest way to thnk about ths s that changes n the real nterest rate affect the current prce of future consumpton When the real nterest rate falls, the cost of lfetme consumpton rses, and ths s nflatonary Ignorng future consumpton n the computaton of nflaton s analogous to leavng out a good that belongs n the ndex and creates the potental for what we wll call ntertemporal substuton bas Snce asset prces measure the current cost of future consumpton, ncludng them n a measure of nflaton potentally allows for ths real nterest rate mpact and elmnates ths bas We call ths a cost-of-lfe ndex Followng the methodology n our earler work, we are able to ntroduce a number of canddate asset prces nto our cost-of-lfe ndex Ths allows us to estmate the sze of the ntertemporal substuton bas, both on a year-by-year bass and on average over decades We fnd that the bas from omtng asset prces n the measurement of nflaton s roughly the same sze as that assocated wh other well-known bases, ncludng those that arse from commody substuton and the lke We also show that ths bas s tme-varyng and over perods of several years may sgnfcantly dstort the magnude and tmng of how the central bank perceves nflaton Specfcally, ntertemporal substuton bas between current consumpton and future consumpton tended to understate the nflaton beng recorded by current-consumpton prce statstcs such as the Consumer Prce Index (CPI) durng the latter half of the 1990s Ths reversed the upward bas to the retal prce measure that exsted over much of the 1977 to 1995 perod Durng some perods ths bas can be extreme Such appears to have been the case between the two world wars of the last century when the relatvely low real nterest rate n the md-1920s suddenly rose Our measure of nflaton s between 1 and 2 percentage ponts hgher than conventonal (consumpton-based) ndcators suggested durng the 1920s and smlarly more deflatonary durng the early years of the 1930s The organzaton of ths paper s as follows Secton I descrbes how s that gnorng asset prces ntroduces a bas nto aggregate prce statstcs In secton II, we ntroduce the weghtng methodology used to ncorporate excessvely nosy asset prces so as to produce a prce ndex * Federal Reserve Bank of Cleveland, The Oho State Unversy and NBER, and the Oho State Unversy and Smh College, respectvely The vews expressed n ths paper do not necessarly reflect the vews of the Federal Reserve Bank of Cleveland, the Federal Reserve System, or the NBER

2 for the current cost of lfe that elmnates the ntertemporal substuton bas Secton III reports on the behavor of ths ndex relatve to the more common cost-of-lvng statstcs used by economsts and polcymakers In secton IV we show how such a prce measure would have changed our nterpretaton of prce movements durng the great deflaton between the two World Wars Secton V concludes Asset Prces and the Cost of Lfe: A Case of Mssng Goods Bas Whch goods should be used n the computaton of a prce statstc? Ths s one of the oldest questons n quantatve macroeconomcs, and not surprsngly, the answer depends on the queston the statstc s ntended to answer Whether or not to nclude asset prces n the computaton of aggregate nflaton depends on what relevant nformaton they contan for the queston at hand Asset prces are essental n any calculaton that ncorporates ntertemporal consumpton decsons snce they measure today s cost of future consumpton Households allocate current ncome to both current and future consumpton In fact, theory suggests that current decsons by economc agents attempt to nsure a partcular level of lfetme consumpton Ths means that the approprate prce statstc both for households decsons and polcymakers must take account of changes n the cost of current relatve to future consumpton Ignorng changes n ths relatve prce (changes n the real nterest rate) wll create a bas n prce measurement that s exactly analogous to what s commonly called omted goods bas Ths ssue s especally mportant to a central bank that has among s objectves the management of nflaton The lnk connectng central bank polcy to nflaton s often presumed to be long and varable, as changes n target nterest rates and central bank money affect prces slowly and unpredctably Snce these polces alter the real nterest rate, causng ntertemporal substuton n consumpton, the central bank may be mssng an mportant part of the nflatonary process by focusng exclusvely on the drft n current retal (consumpton) prces Followng the arguments frst set out by Alchan and Klen (1973), ths leads us to consder a prce statstc that s desgned to gauge the current (ntertemporal) cost of lfe that s a measure that takes account of the current cost of both current and future consumpton The cost of lfe s dstnct from the current cost of lvng that provdes the conceptual bass for statstcs such as the CPI or the deflator for personal consumpton expendures Those measures are desgned to capture the cost of current consumpton and ntentonally om current prces of future consumpton Therefore, there exsts a relatve prce change such that s excluson from the set of prces dstorts the aggregate so that no longer gves an accurate answer to the queston under consderaton To llustrate ths pont, we can thnk of prce changes for all goods, servces, and assets today as havng a common and dosyncratc component We wre ths as t x, (1) where ndcates the set of goods, servces, or assets, and t s tme, and so s the nflaton of ndvdual good at tme t, s the common trend n nflaton that we are tryng to measure, and t x s the devaton of good nflaton at tme t from ths trend An nflaton ndex s constructed by weghtng together these ndvdual nflaton measures That s, P t w (2) 2

3 where the weghts ( w ) can change over tme, but have the property that they sum to one That s w 1 t (3) Usng ths fact, we can now rewre the aggregate prce change as P w x (4) t t Our goal s the measurement of the common trend n all prces (nflaton), t To do ths we need to fnd a set of goods, servces, and assets where the (weghted) relatve changes, the x s, cancel out But the weghted sum of these relatve nflaton measures wll only cancel out f we have a complete set of prces If a good wh a non-zero relatve prce dsturbance (x) s left out, then the sum of the weghted prce adjustments wll not sum to zero, and so the ndex P t wll not equal πt, the common nflaton trend we are tryng to measure If asset prces are excluded from the cost-of-lfe statstc, any ntertemporal substuton between current and future consumpton orgnatng from a change n the real nterest rate wll create a bas n the resultng measure of nflaton Specfcally, durng perods when the real nterest rate s declnng, prces of current consumpton fall relatve to current clams on future consumpton, causng any aggregate prce measure based only on current consumpton prces to be too low (The oppose would be true n suatons when the real nterest rate has rsen) Estmatng Changes n the Cost of Lfe Usng consumer theory, Pollack (1975) and Shbuya (1992) derve and mplement a cost-of-lfe ndex that weghts tradonal consumer prces together wh varous asset prce measures We have argued elsewhere that such a methodology yelds prce measures that are mplausbly volatle over short horzons 1 In order to create an ndex that s potentally useful n a hghfrequency decson-makng envronment such as settng monetary polcy, we follow the methodology frst proposed n Bryan and Cecchett (1993) In that work, we utlze the jont statstcal propertes of the ndvdual prce seres n order to construct a dynamc factor ndex (DFI) The DFI explos the fact that the nformaton contaned n ndvdual s about the common trend t dffers that s the sgnal-to-nose rato vares across dfferent sets of goods, servces, and assets In partcular, asset prces tend to be que nosy, and so may not be very mportant n constructng the DFI As n Bryan and Cecchett (1993), we wre the model as t (5) p x ( L) t t (6) ( L) (7) x where p, t, and ẋ are the frst dfferences of the logs of the observed varables, the common unobserved component representng nflaton and the dosyncratc relatve prce movement n the th seres, respectvely ψ(l) and θ(l) are vectors of lag polynomals and ξt and ηt are d 1 See Bryan, Cecchett and O Sullvan (2001) 3

4 random varables Throughout, s assumed that both the common element, t, and the dosyncratc components, ẋ can be modeled as AR(2) processes The man dentfyng assumpton of the model s that the common component and the dosyncratc components are mutually uncorrelated at all leads and lags Ths s acheved by assumng that θ(l) s dagonal and that all the error terms n the model are mutually uncorrelated Ths s consstent wh the noton that the common component captures all the comovement n the observed seres, leavng ẋ to reflect only dosyncratc movements To set the scale of t, the varance of ξt s normalzed to one The parameters of the model are then estmated va maxmum lkelhood usng the Kalman flter As a by-product, the Kalman flter recursvely constructs MMSE estmates of the unobserved components t and ẋ gven observatons of ṗ The common ndex can be wrten as a lnear component of current and past values of the observed seres ^ ^ t w ( L) p (8) These are the (mplc) weghts used to construct the common nflaton component In an alternatve approach to ths sgnal-extracton problem, Wynne (2000) descrbes the mplementaton of a smple varance-weghted prce ndex where the weghts, w N are based on the varance of the rate of change n the prce of each good, A smple varance-weghtng scheme of ths type s a good ndcator of the lkely mportance of a partcular seres n the constructon of more complex (and dffcult to compute) dynamc factor ndces To see why, note that the varance of the common element n any scheme, smlar to that descrbe n equaton (9) above, wll have the property that the estmated nflaton ndex wll have varance equal to or less than the varance of the least volatle component used 2 In the analyss that follows n sectons III and IV, we also report the varance weghts for comparson to the weghts used n our dynamc factor ndex (9) 2 Ths s strctly true n the DFI model we use gven the dentfcaton assumptons employed In the varance weghtng case, certan restrctons are necessary on the covarances between the constuent seres 4

5 Comparng the Cost-of-Lvng to the Cost-of-Lfe Usng nne sub-ndces of the current consumer prce ndex, together wh prces of sx major assets, we estmate a cost of lfe ndex for 1977 to 2001 The assets nclude housng, stocks, bonds, commodes, money, and gold Table 1 dsplays the mpled weghts for the data set usng the alternatve methodologes In the frst three columns of the table we report results for the cost-of-lvng approach that s, retal prces excludng asset prces The remanng columns ncorporate asset prces and so are the weghts for smlarly constructed cost-of-lfe ndces The frst observaton we make s that even on a conceptually smlar bass, dynamc factor weghts are sgnfcantly dfferent from the expendure weghts used n the offcal CPI Ths s because the Kalman flter technology tends to reduce the weght assgned to prce seres wh a relatve hgh tme-seres varance, gvng more weght to those seres that provde a better sgnal of the common element (the DFI) These weghts are oblvous to the relatve mportance of the good n the typcal consumer market basket The result s an ndex smlar n spr to a core nflaton statstc lke the CPI excludng food and energy, where the market basket s altered to adjust for transory fluctuatons n the data that are not beleved to be part of a more generalzed nflaton process Note that the DFI cost-of-lvng weghts (those weghts based on CPI component seres only) are more closely algned wh the conceptually smlar cost-of-lvng varance weghts That s, food, transportaton, and housng are gven a substantally smaller share of the overall prce ndex compared wh the ordnary expendure-weghted CPI, whle medcal care, personal care, and educaton get larger weghts n these reduced-nose prce statstcs Usng the DFI procedure, we constructed a cost-of-lfe ndex that ncludes sx asset prce seres along wh nne retal prce seres We fnd that stocks (08 percent), bonds (04 percent), and gold (07 percent) are assgned very small weghts n the computaton of the cost-of-lfe ndex Ths reflects the extreme volatly of these seres at a monthly frequency (also evdenced by the near zero weght these assets are gven on the bass of the varance weghtng crera) Nevertheless, some assets are assgned a relatvely large share of the market basket, lke new homes (23 percent), commodes (56 percent) and the money supply (53 percent) Turnng to the estmated prce ndces themselves, Fgure 1 shows the 12-month growth rates of the three key nflaton statstcs for the recent era, the CPI, the cost-of-lvng dynamc factor ndex (DFI cost-of-lvng) and the cost-of-lfe dynamc factor ndex (DFI cost-of-lfe) Frst, as we expect, the two DFI seres are consderably smoother than the expendure-weghted CPI More mportantly for the purposes of ths paper, there are persstent dfferences between the DFI cost-of-lvng measure and the DFI cost-of-lfe measure Ths s the bas between these two conceptually dfferent approaches Specfcally, whle the prce seres ncludng asset prces tended to track below the consumpton-only prce measure durng the perod, tended to be hgher between 1995 and 2000, and only very recently have the two measures converged The sgnfcance of ths observaton s that a real nterest rate drop n the md-1990s appears to have been responsble for an ntertemporal substuton between current consumpton and future consumpton 3 Ths suggests that the CPI (or other smlarly conceptualzed retal prce 3 In fact, the dfference between the DFI cost-of-lvng and the DFI cost-of-lfe s an estmate of the change n the ex ante real nterest rate Ths s supported by the fact that ths dfference and the change n the ex post real nterest rate, computed from the three month US Treasury bll rate and headlne CPI nflaton, are sgnfcantly posvely correlated wh a correlaton coeffcent of 013 and a robust t-statstc of (21) 5

6 measures) were based downward by ¼ to ½ percentage pont per year as measures of nflaton compared wh the rse n prces recorded by current clams to current and future consumpton Snce 1995, the bas we have dentfed has worked n the oppose drecton to the more commonly dscussed bases n retal prce measures that come from other (but related) sources But n the frst half of our sample, ths bas worked to renforce the belef that measurement bases lead to the overestmaton of nflaton by conventonal ndces Furthermore, the tendency of the ntertemporal substuton bas to fluctuate suggests that measures of real nterest rates and other nomnal, ntertemporal phenomena can, at tmes, be sgnfcantly over- or under-stated f the prce deflator does not nclude the prce of current purchases of future consumpton assets A Retrospectve of the Inter-War Deflaton We have demonstrated that the falure to nclude asset prces when calculatng a cost of lfe ndex can create an ntertemporal substuton bas n the cost-of-lfe statstc and that ths excluson may nfluence one s nterpretaton of nflaton In ths secton, we ask f correctng ths bas mght lead to a renterpretaton of the events durng the 1920 s and 1930 s the perod between the two world wars and one of the great deflatons n US hstory The extreme movements n stock prces and the hstorcal fall n the prce level durng ths perod are well documented, and fgure 2 llustrates the movements n consumer and stock prces between 1920 and We computed our DFI measures, wh and whout asset prces usng data seres that closely match those used n the prevous secton 5 Consumer prces were obtaned from Sayre (1948), where seres on the prces of food, housng, clothng, fuel and house furnshngs and sundres were avalable along wh the overall CPI ndex Stock and bond prces and money stock data were taken from the NBER macrohstory database whle the commody prce ndex was avalable from the BLS Two seres used n the modern analyss could not be ncluded drectly The frst of these house prces are smply not avalable on a monthly bass As a compromse, we used an ndex of buldng materals costs nstead The second seres that presented a problem was gold prces Whle prce data are avalable, the behavor of gold prces was dctated by the central bank s gold standard and therefore s not suable for our purpose From 1920 to 1934 we were able to substute the prce of slver for the prce of gold After 1934, these data become unusable because of the Slver Purchase Act of 1934, whch resulted n sgnfcant government nterventon n the market for slver Table 2 summarzes the weghts obtaned when the DFI technque s appled to varous combnatons of the hstorcal seres Varance-based weghts and expendure weghts for the components of the CPI are ncluded for comparson purposes 6 Lookng frst at the constuent seres of the CPI, we see that the category wh the largest expendure weght - food - attracted a sgnfcantly smaller weght when both the DFI and varance-based sgnal extracton technques were used In contrast, the relatvely stable house furnshngs and sundres category, whch 4 See, for example, Fredman and Schwartz (1963) 5 Reasonable data on bond prces were not avalable for the perod between 1937 and 1940 and so only data up to January 1937 were used Results based on seres excludng bonds showed ltle dfference when the addonal four years of data were ncluded 6 When slver prces were added for the perod up to 1934, the seres attracted a small weght (337) the second smallest after stocks 6

7 ncludes costs assocated wh such ems as medcal care, personal care and transportaton, was attrbuted DFI and varance-based weghts more than double s expendure share Lookng more closely at the DFI cost-of-lfe ndex we see that the buldng costs ndex ncluded here as a proxy for house prces attracted the largest weght among the non-cpi seres Ths may overstate the strength of the common prce sgnal n house prces, as they tend to be more volatle than buldng costs n the short run It s also worth notng that the unprecedented developments n the stock market durng ths tme perod resulted n a hgher weght beng gven to bond prces than stock prces Ths s n contrast to the outcome obtaned usng the modern data Indeed, accordng to the varance-weghted approach, the stock prce seres contans vrtually no nformaton at all about the common trend n prces Stll, despe the volatly experenced n asset markets durng ths perod, the DFI approach attrbutes almost one thrd of the weght to the non-cpi component seres 7 The thrty-three percent share of DFI weghts attrbuted to asset prces s about twce the share assgned by a varance-weghtng approach In other words, these asset data, though volatle, appear to have an mportant common sgnal embedded n ther movement, suggestng that ther excluson would have based the cost-of-lfe measure compared wh the conventonal cost-of-lvng statstc Turnng to the growth rates of the varous nflaton seres, fgure 3 plots the year-to-year growth rates for the headlne CPI, the DFI seres based on CPI components only (DFI cost-of-lvng), and the DFI ncludng all ten seres (DFI cost-of-lfe) The growth n the cost-of-lvng based DFI seres s obvously smoother than the headlne CPI rate over the perod, wh ths seres recordng deflaton rates n the early 1930 s of about half those obtaned usng the headlne CPI rate When asset prces are ncluded, however, the deflaton was hgher than that calculated from the headlne rate, whle the rebound n the md-thrtes was also more pronounced That s, the DFI cost-of-lfe ndex shows more extreme movements than the conventonal cost-of-lvng ndex As noted for the modern perod, the gap between the DFI cost-of-lvng and the DFI cost-of-lfe (all assets) seres can be nterpreted as reflectng movements n the real nterest rate The correlaton between the change n the ex ante real nterest rate taken from Cecchett (1992) and the dfference between the two DFI seres s sgnfcantly posve the correlaton coeffcent s 016 wh a robust t-rato of 205 In partcular, the greater fall n the cost-of-lfe DFI seres compared wh the DFI seres whout asset prces durng the early 1930 s reflected the relatvely steep drop n stock prces at that tme Our nterpretaton s that ths fall n asset prces reflected a hgher dscount rate or real nterest rate at a tme when nomnal nterest rates were fallng que dramatcally But more fundamentally, suggests a strong ntertemporal substuton bas n the conventonal retal prce measure of a rather extreme level (peakng at around 6 percentage ponts n md-1932) that substantally alters the nflaton pattern we record for the perod compared wh what s shown by the CPI 7 To examne the robustness of the weghtng methodology durng ths turbulent tme, DFI and varance-based weghts were also calculated for rollng ten-year wndows, begnnng wh and endng wh The weghts assgned to the varous seres were relatvely stable across the tme perod wndows, wh a fall n the weght attached to the money stock reflected manly n an ncrease n the house furnshngs and sundres weght That s, the DFI weghts appear to be robust throughout ths sample 7

8 Concluson Ths paper consders a partcular problem assocated wh the falure to nclude asset prces n an aggregate prce statstc If the statstc s ntended to gauge nflaton, meanng a persstent change n the cost of lfe as dstnct from the current cost of lvng, then the falure to nclude asset prces n the aggregate prce measure can bas your nflaton estmate Usng a modfed Kalman flter a dynamc factor ndex we compute an aggregate cost-of-lfe ndex and compare wh both the CPI (an expendure-weghted cost-of-lvng measure) and a methodologcally smlar dynamc factor ndex that also measures only the cost-of-lvng Over tme, we fnd the dfferences between these statstcs to be somewhat small, often less than ¼ percentage pont per year However, over some perods, namely, perods when the real nterest rate fluctuates, we fnd that the excluson of asset prces can sgnfcantly dstort one s readng of monetary nflaton common to all goods Such appears to have been the case durng the great deflaton n the early 1930s, and also n the latter half of the last decade References Alchan, A A and B Klen, 1973, On a Correct Measure of Inflaton, Journal of Money, Cred, and Bankng, 5(1), February, part 1, pp Blank, Davd M, 1954, Relatonshp between an Index of House Prces and Buldng Costs, Journal of the Amercan Statstcal Assocaton, Vol 49, 265, March, pp Bryan, M and S Cecchett, 1993, The Consumer Prce Index as a Measure of Inflaton, Economc Revew of the Federal Reserve Bank of Cleveland, 29, 4, pp Bryan, M, S Cecchett, and R O Sullvan, 2001, Asset Prces n the Measurement of Inflaton, De Economst, Vol 149, no 4, pp Bureau of Labor Statstcs, 1997, Handbook of Methods, Chapter 17 Bureau of Labor Statstcs, Detaled Report, Varous Issues Cecchett, S, 1992, Prces Durng the Great Depresson: Was the Deflaton of Really Unantcpated? Amercan Economc Revew, 82, March, pp Fredman, M and A Schwartz, 1963, The Great Contracton, n A Monetary Hstory of the Uned States, Prnceton: Prnceton Unversy Press Fredman, M and A Schwartz, 1970, Monetary Statstcs of the Uned States, NBER Leavens, D, 1946, Bullon Prces and the Gold-Slver Rato , The Revew of Economcs and Statstcs, Volume 28, Issue 3 (Aug), pp Reed, S and K Stewart, 1999, Consumer Prce Index Research Seres usng current methods, , Monthly Labor Revew, June Pollack, Robert A, 1975, The Intertemporal Cost-of-Lvng Index, Annuals of Economc and Socal Measurement, 4(1), Wnter, pp Sayre, R, 1948, Consumers Prces , Natonal Industral Conference Board Inc, New York Shbuya, Hrosh, 1992, Dynamc Equlbrum Prce Index: Asset Prce and Inflaton, Bank of Japan, Monetary and Economc Studes Stock, J and M Watson, 1991, A Probably Model of the Concdent Economc Indcators, n K Lahr and GH Moore, ed, Leadng Economc Indcators, New Approaches and Forecastng Records, pp Cambrdge: Cambrdge Unversy Press Warren, G E and F A Pearson, 1935, Gold and Prces, New York: Wley & Sons Wynne, M, 2000, Core Inflaton: A Revew of Some Conceptual Issues, Unpublshed manuscrpt 8

9 Table 1: Alternatve Weghts for the Recent Era ( ) Cost-of-Lvng Weghts (CPI Components only) Cost-of-Lfe Weghts (CPI components wh asset prces) Expendure DFI Varance DFI Varance Food/Beverages Housng Apparel Transportaton Medcal Care Entertanment Educaton Tobacco Personal Care Houses Stocks Bonds Commodes Money Supply Gold Sum of Weghts

10 Fgure 1: The CPI, DFI Cost-of-Lvng and DFI Cost-of-Lfe 12-month percent change CPI DFI (cost of lvng) 6 4 DFI (cost of lfe) Fgure 1a: The Intertemporal Substuton Bas month growth n DFI cost-of-lvng less DFI cost-of-lfe

11 Table 2: Alternatve Weghts for the Hstorcal Seres ( ) Cost-of-Lvng Weghts (CPI Components only) Cost-of-Lfe Weghts (CPI components wh asset prces) Expendure DFI Varance DFI Varance Food Housng Clothng Fuel House Furnshngs and Sundres Buldng Costs Stock Prces Bond Prces Commody Prces Money Supply Sum of Weghts Fgure 2: Consumer Prces and Stock Prces n the Interwar Perod month percent change STOCKS CPI

12 Fgure 3: The CPI, DFI Cost-of-Lvng, and DFI Cost-of-Lfe n the Interwar Perod 12-month percent change 8 0 DFI (cost-oflvng) -8 CPI DFI (cost-of-lfe) Fgure 3a: The Intertemporal Substuton Bas month growth n DFI cost-of-lvng less DFI cost-of-lfe