Forecasting Inflation using Commodity Price Aggregates* Yu-chin Chen, Stephen J. Turnovsky, and Eric Zivot University of Washington, Seattle WA 98105

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1 Forecasng Inflaon usng Commody Prce Aggregaes* Yu-chn Chen, Sephen J. Turnovsky, and Erc Zvo Unversy of Washngon, Seale WA Revsed verson Aprl 011 Absrac Ths paper examnes he usefulness of commody prce aggregaes for forecasng and nflaon for fve major commody-exporng counres ha have adoped nflaon argeng moneary polces. We fnd ha he nformaon conaned n commody prces can be helpful n predcng nflaon, and ha dsaggregang o subndexes of commody prces provdes superor forecass han do aggregaes. We also examne he ou-of-sample forecasng performance. Whle we fnd some varaon n he ou-of-sample predcons, overall he sub-ndexes perform beer han do he aggregaes. They also mosly ouperform he random walk, whle on average hey are comparable o he AR(1) process. The MIDAS approach, usng mxed frequency daa, does no generae furher mprovemens n ou-of-sample forecass. Keywords: commody prces, and nflaon forecass, nflaon argeng JEL Codes: C53, E61, F31, F47 Deparmen of Economcs, Unversy of Washngon, Box , Seale, WA 98195; Chen: yuchn@uw.edu. Turnovsky: surn@uw.edu. Zvo: ezvo@uw.edu. *We would lke o hank hree anonymous referees for her consrucve suggesons and Erca Clower, Han Lan Chang, and Kelvn Wong for excellen research asssance. All remanng errors are our own. Turnovsky s research was suppored n par by he Casor Endowmen a he Unversy of Washngon.

2 1. Inroducon The ncrease n nflaon argeng as par of an objecve of moneary polcy, ogeher wh he volaly of asse prces and perodc sock marke bubbles, has rased he ssue of he proper response of moneary polcy o asse marke sgnals. Early smulaons by Fuhrer and Moore (199) argued agans respondng o asse marke prces, suggesng ha her wegh n he moneary polcy rule s equvalen o argeng he real neres rae and leads o a loss n conrol of nflaon. Bernanke and Gerler (1999, 001) also argued ha moneary polcy should no respond o changes n asse prces, excep nsofar as hey reflec nflaonary expecaons. Several reasons are gven for hs vew, ncludng he dffculy of deermnng wheher a change n an asse prce s reflecng fundamenals or s a speculave bubble. In conras, Cecche, Genberg, and Wadhan (00) argue ha argeng moneary polcy o msalgnmens n asse prces may mprove macroeconomc performance. 1 More recenly, aenon has focused o he more specfc role of commody prces as a sgnfcan deermnan of curren and fuure nflaon. Ths vew s arculaed by Federal Reserve Charman, Ben Bernanke, who has suggesed ha rsng prces for globally raded commodes have been a prncpal aspec of he more recen nflaonary experence. Boh he heorec bass for hs relaonshp and he emprcal evdence are mxed. Regardng he heorecal lnkage, here s he ssue of causaly and smulaney. Do commody prces affec nflaon, or are boh respondng o general demand condons, wh commody prces smply adjusng more rapdly? Overall, he emprcal evdence lnkng commody prces o nflaon forecas s ambguous, beng sascally sgnfcan for some perods and nsgnfcan n ohers; see e.g. Blomberg and Harrs (1995), Hooker (00), Sock and Wason (003). Par of he dffculy s he volaly of commody prces, makng hem dffcul o predc. More recenly Gospodnov and Ng (010) oban some success n usng he prncpal 1 Much of he debae s summarzed by Bean (003), who n dscussng he poson of he Bank of England, suggess ha he boom lne depends upon assumpons one s makng abou he underlyng sochasc srucure of asse prces and he nformaon avalable o he polcymaker. Ths vew was expressed n a Speech o he Federal Reserve Bank of Boson, June

3 componens of convenence yelds n predcng nflaon. However, hey also fnd ha usng he IMF aggregae commody ndex has lle power n predcng nflaon. Mos of he evdence employs Uned Saes, and o some exen, Uned Kngdom daa. In hs paper we re-examne hs queson from he vewpon of small commody-exporng counres. The movaon for dong so s hree-fold. Frs, commody prces have a drec lnk wh he real economy. Gven he hgh commody producon dependency n hese counres, world commody prce movemens have drec effecs on producon revenues and expor earnngs, and herefore oupu, real wages, and oher aspecs. Tha s, s no jus he pure fnancal asse channel addressed n he prevous leraure. Second, here s he commody currency phenomenon passng hrough o he consumer prce ndex (): Prevous leraure has demonsraed ha commody prces play a key role n drvng he currency value of major commody-exporng counres; see e.g. Amano and van Norden (1993), Chen and Rogoff (003). These responses end o be very fas and even conemporaneous. To he exen ha exchange raes pass hrough o consumer prces over me, world commody prce movemens may have an effec on domesc nflaon. Fnally, focusng on small economes elmnaes he smulaney ssues denfed by Gospodnov and Ng (010). Gven hese channels, world commody prce movemens may help predc fuure nflaon, of eher or boh of he or producer prce ndex (). We should emphasze ha our focus s on analyzng he emprcal relaonshps beween commodes prces and nflaon, raher han developng he heorecal lnkages. In dong so, we focus on wo aspecs. Frs, we deermne he exen o whch dsaggregaon of he commodes ndex mproves he accuracy of he predcons over hose obaned from he aggregae. Second, we nvesgae he exen o whch usng commody prce daa avalable over mxed frequences can mprove he forecass of quarerly nflaon of he wo ndexes. We consder fve counres: Ausrala, Canada, Chle, New Zealand, and Souh Afrca. These are all small open economes, heavly commody dependen, wh all havng markedeermned floang exchange raes. All fve counres are nflaon argeers, alhough hey do

4 no necessarly arge he same prce ndex. For example, Canada looks a core nflaon, whle he res end o focus on nflaon. However, hese counres specalze n dfferen ypes of commody producs, rangng from agrculural, mneral, o energy-relaed goods. The leraure so far has reaed hese counres expors as one aggregae baske, whou explc recognon of he dsnc rends and cycles he prces of dfferen broad commody caegores follow (see e.g. Cashn, McDermo, and Sco, 1999). In addon o lookng a he aggregae ndex, we also consder broad caegores of subndexes. Snce agrculural markes and energy markes are lkely o be drven by dfferen world shocks, allowng dfferen componens o have dfferenal mpacs s lkely o mprove he qualy of he predcons. Thus, we consder he basc me seres properes of seven commody sub-ndexes for hese fve counres. The ndexes nclude: Meals, Texles, Raw Indusrals, Foodsuffs, Fas & Ols, Lvesock and Energy. We frs esablsh ha n general hey are hghly correlaed, confrmng he sgnfcan co-movemen obaned n prevous sudes. 3 Ths observed co-movemen n commodes prces s ofen assumed o reflec some common underlyng rend, possbly due o reacon o he same global demand condons, and/or ha subsuons across producs end help ransm shocks across produc groups (e.g. ol and bofuels). Accepng hs vew, we examne wheher hey have predcve power for he wo economc ndcaors we consder: nflaon, and nflaon, respecvely. We should noe ha, alhough he Cenral Banks have her own counry-specfc commody prce ndexes [see e.g. he webse of he Bank of Canada and he Reserve Bank of Ausrala], we prefer o ulze marke nformaon ha s more readly avalable o he publc (CRB ndex). There are several reasons for hs. Frs, our neres n hs queson s movaed no only from he perspecve of he polcy maker, bu also from he sandpon of he publc. Specfcally, snce hese ndexes are observable on a daly bass hey can be used n real me, and enable us o examne he effecveness of usng mxed daa frequency forecass. Moreover, 3 See e.g. Pndyk and Roemberg (1980), Deb, Trved, and Varangs (1996). A, Charah, and Song, (006). However, we do no examne he ssue of excess co-movemen nvesgaed n some of hese sudes. 3

5 hese ndexes are chosen from markes ha are especally sensve o changes n global economc condons and as such may serve as early ndcaors for gaugng fuure economc condons and lkely polcy acons. We fnd ha boh he commody prce seres and he and conan un roos, and whle he commody prces do no appear o have any lnear rends, boh he and seres do. We also fnd evdence of a sngle conegrang vecor beween he commody prce seres and he or usng he mehodology of Johansen (1991). We frs examne n-sample predcably by regressng he wo nflaon ndcaors ( nflaon, and nflaon) one quarer ahead on he seven sub-commodes prce ndexes, plus he error correcon erm based on he conegrang relaonshp for he fve counres. We presen he resuls for a frs order vecor error correcon model (VECM(1)), alhough as par of our robusness check we also esmaed VECM()s. The man general fndng we oban s a srong n-sample Granger causaly effec from commody prce changes o boh and nflaon. In all cases, some sub-ndexes have predcve conen, energy beng almos unformly sgnfcan n predcng boh and nflaon. Lagged nflaon s ofen, bu no always, he mos mporan facor. The error correcon erm s also hghly sgnfcan n mos cases, alhough s coeffcen s small, mplyng a very gradual adjusmen oward he long-run rend. As par of a robusness check we do several hngs. Frs, we explore he effec of currency-denomnaon, ha s wheher commody prce movemens n he world marke prced n US dollars drecly has effec, or ranslang hem o domesc currency provdes a sronger sgnal (leavng srucural exploraon and nerpreaon o a separae sudy). Overall, he resuls reman generally unchanged. Second, we esmae he VECM(1) equaons usng wo alernave aggregae commody prce ndexes. Overall, neher aggregae ndex does well n predcng aggregae nflaon, alhough boh perform credbly n predcng nflaon, wh boh measures yeldng qualavely smlar resuls. Thus, our resuls sugges ha he gans from dsaggregaon are greaer n predcng nflaon han hey are n predcng nflaon. 4

6 Thrd, n lgh of he hgh correlaon among he commody prce sub-ndexes, we reduce he dmensonaly of he regressors n he VCM by adopng he Leas Angle Regressons (LARS) procedure poneered by Efron e al (004). Ths s a compuaonally effcen sagewse regresson procedure ha selecs he approprae regressors so as o mnmze he predcon error as measured by a C p sasc. Ths approach yelds resuls ha are generally conssen wh he full VECM(1) regressons, confrmng he general mporance of sub ndexes. Afer confrmng he n-sample predcve ably of commody prces for nflaon, we examne her ou-of-sample forecasng performance. In dong so, we compare he predcons usng he sub-ndexes o hose obaned usng wo benchmark unvarae predcng schemes, namely () a random walk process and () an AR(1) process, We exclude he Phllps Curve as one of he benchmark nflaon forecasng schemes. Ths s because evdence by Akeson and Ohanan (001), and more recenly by Sock and Wason (007), suggess ha s no parcularly successful n forecasng nflaon, beng ou-performed by sandard auoregressve models. In evaluang he ou-of-sample forecasng performance we employ wo classes of models. The frs s he convenonal ou-of-sample predcon parallel o he n-sample predcon where we use quarerly commody prces o predc quarerly nflaon. The second uses mxed-samplng daa, he so-called MIDAS approach of Ghysels e al (00). Ths procedure uses nformaon conaned n hgher frequency commody prce daa (e.g. daly) daa o help forecas nflaon observed a lower frequences (e.g. quarerly). Whle here s some varaon n he ou-of-sample predcons across he fve economes, overall he sub-ndexes perform beer han do he aggregaes. In addon, he sub-ndexes mosly ouperform he random walk, whle on average hey are generally comparable o he predcons from he AR(1) process. Fnally, overall he MIDAS approach does no generae subsanal mprovemen. The remander of he paper proceeds as follows. Secon dscusses some of he background ssues n greaer deal, ncludng a dscusson of he daa. Secon 3 descrbes he 5

7 n-sample predcve ably of he commody sub-ndexes, whle Secon 4 consders her ouof-sample forecasng performance. Secon 5 concludes.. Background and Daa Descrpons.1 The Inflaon-Commody Prce Lnkage n Commody Currency Economes As shown n Table A.1, Ausrala, Canada, Chle, New Zealand, and Souh Afrca produce a varey of prmary commody producs, rangng from agrculural and mnerals o energy-relaed goods. Togeher, hese commodes represen beween a quarer and well over a half of each of hese counres oal expor earnngs. Our sudy focuses on hese fve small commody-exporng economes because each has a relavely long hsory of operang under well-funconng open markes, wh floang exchange raes and ransparen moneary polces. These characerscs allow us o nerpre our fndngs, posve or negave, as reflecng marke ransmsson mechansm, raher han acve governmen managemen. Prevous sudes have documened he srong connecon beween global commody prce movemens and hese counres exchange raes, emphaszng srucural lnkages hrough he ncome effec and he erms of rade channel. 4 Emprcally, hese counres exchange raes exhb a srong and robus response o global commody prce flucuaons; her currences are hus referred o as commody currences. 5 Ths phenomenon movaes us o deermne furher, wheher he lnkage may help predc nflaon. 6 These earler sudes rely mosly on a pre-consruced counry-specfc ndex publshed by eher her cenral banks or oher organzaons, whch are no necessarly avalable o he publc n real me, especally a hgh frequency. 7 We use ndexes ha are observable daly, 4 See dscussons n Chen, Rogoff, and Ross, (010). 5 See Chen and Rogoff (003) and references heren. 6 If exchange rae pass-hrough s gradual, one would see predcably from commody prces o nflaon, for example. Noe, however, ha we do no formally es any specfc srucural channel. 7 For example, Ausrala, Canada and New Zealand all publsh hese ndexes on a monhly bass. 6

8 whch has he advanage of enablng us o es he exen o whch daly nformaon may provde nformaon wh respec o quarerly nflaon. Ths ssue s addressed n deal n Secon 4.. As s evden from Table A1, hese counres produce a varey of commody producs ha have very dfferen producon srucures (e.g. sheep vs. coal) and face dfferen marke condons whn he global economy. Ths suggess ha dfferen ypes of producs have dfferenal mpacs on he economy and s nflaon response. In addon, because of dfferences n he degree of co-movemens across caegores, sub-ndexes may mply dfferen weghs. We explore hs by lookng a sub-ndexes of world commody prces, whch are represenave major producs for he world commody markes, alhough no necessarly specfc o hese counres. 8. Daa Descrpons We use quarerly daa beween 1983Q1-010Q4 o es wheher he seven commody sub-ndexes dscussed below can predc -nflaon and -nflaon a quarer ahead n he fve commody currency counres. The quarerly prce level daa we use are from he IMF s Inernaonal Fnancal Sascs. These IFS seres are seasonally unadjused, and nflaon s measured as he log-dfference of he prce level, quoed a an annual rae. 9 The commody sub-ndexes we employ are colleced from wo dfferen sources and are avalable a he daly frequency. Sx are compled by he Commody Research Bureau (CRB), and n addon, we use he S&P GSCI Energy Index from Global Fnancal Daa. 10 Thus he seven sub-ndexes we use and her componens are as follows: 11 8 Over he pas few decades, all of hese counres experenced major changes n polcy regmes and marke condons. These nclude her adopon of nflaon argeng n he 1990s, he esablshmen of Inerconnenal Exchange and he passng of he Commody Fuures Modernzaon Ac of 000 n he Uned Saes, and he subsequen enrance of penson funds and oher nvesors no commody fuures ndex radng. We herefore pay specal aenon o he possbly of srucural breaks n our analyses. 9 /WPI s lne number: 63 ZF and 64...ZF, excep for Chlean where 64A..ZF s used nsead as 64...ZF s unavalable. Ausrala and New Zealand only have quarerly. 10 The S&P ndex has a.997 correlaon wh he Reuer's Energy Index, whch ended n Snce May 1981, he CRB began calculang s ndex on a daly bass. Tweny-wo commodes are combned no an 'All Commodes' groupng, wh wo major subdvsons (Raw Indusrals, and Foodsuffs) and four smaller 7

9 Foodsuffs: Hogs, seers, lard, buer, soybean ol, cocoa, corn, Kansas Cy whea, Mnneapols whea, and sugar (40.9%). Raw Indusrals: Hdes, allow, copper scrap, lead scrap, seel scrap, znc, n, burlap, coon, prn cloh, wool ops, rosn, and rubber. (59.1%) Lvesock and Producs: Hdes, hogs, lard, seers, and allow. Meals: Copper scrap, lead scrap, seel scrap, n, and znc. (On January, 003, he ndex was changed so ha Copper, elecrolyc cahodes, was replaced wh Copper, scrap # wre and Znc, prme wesern, was replaced wh Znc, specal hgh grade.) Texles and Fbers: Burlap, coon, prn cloh, and wool ops. Fas and Ols: Buer, coonseed ol, lard, and allow. S&P GSCI Energy: Crude ol (Bren and WTI), naural gas, heang ol, and gasolne, wh crude ol accounng for roughly 70% of he ndex. From hese descrpons we see ha here s some overlap n coverage across some of hese sunndexes, as a resul of whch hey are lkely o move closely ogeher..3. Summary Sascs Tables 1 and repor relevan summary sascs. Un roo ess confrm ha hese varables are I(1), so we use frs dfferenced log varables. 1 From hese ables he followng observaons can be made: Table 1A: The mean growh raes, as well as he volaly of he major commody prce sub-ndexes vary subsanally across he dfferen groups. The coeffcens of varaons (CV) range beween 18.5 for energy o jus over 7 for raw ndusral maeral and meals. groups (Meals, Texles and Fbers, Lvesock and Producs, and Fas and Ols). The groupngs are non muually exclusve. (Source: hp:// 1 The Ello, Rohenberg, and Sock (1996) modfed verson of he Dckey-Fuller es confrms ha he level varables (n logs) are I(1), whle he un roo null s srongly rejeced for he frs-dfferenced varables. 8

10 Table 1B: There s srong posve correlaon beween mos commody sub-ndex nflaon, supporng our earler observaon of co-movemen. Noe, however, ha prce movemens of exles do no seem o be sgnfcanly correlaed (a leas conemporaneously) wh hose of energy and foodsuffs. We do no explore wheher he co-movemen s jusfed by fundamenals or wheher s reflecng herdng behavor. However, he amoun of correlaon presen s suffcen o jusfy reducng he dmensonaly of he regressors, whch we do usng leas angle regresson echnques dscussed n Secon 3.3. Table A: Boh he growh rae of he and, and her respecve volales, exhb subsanal varaon across he fve economes. Table B: and are hghly correlaed, as o be expeced. The correlaon beween commody sub-ndex nflaon s no as srong wh eher or nflaon. For example, no such correlaons are sgnfcan n he case of eher Ausrala or NZ. Conemporaneous correlaons are mosly posve wh nflaon, bu can be negave, such as n he case of Chle. Ths possbly reflecs ssues such as he pass-hrough dynamcs from exchange rae, or feaures of he producon srucure. Fnally, we noe ha hese are all conemporaneous correlaons. In Secon 3 below we explore wheher elemens of hese co-movemens may be useful n forecasng nflaon..4. Conegraon A number of auhors have nvesgaed conegaon beween some measure of commody prces and levels; see e.g., Balle (1989), Kugler (1991), Pecchenno (199), Furlong and Ingeno (1996), Mahdav and Zhou (1997) and Belke e al (009). Early sudes usng resdual-based ess for conegraon ypcally dd no fnd conegraon whereas laer sudes usng he mehodology of Johansen (1991) generally found conegraon. To our 9

11 knowledge no prevous sudy has consdered conegraon beween dsaggregaed commody prce ndexes and or prces. We use Johansen s mehodology o deermne f here are any conegrang relaonshps (common rends) among our collecon of log prce seres. The exsence of conegraon beween consumer/produce prces and commody prces allows for anoher channel, hrough an error correcon model, by whch commody prces can be used o predc nflaon. Our analyss s based on he VAR(p) model Y D AY A Y 1 1 p p, (1) where Y s an 8 1 vecor wh frs elemen eher log or log for a gven counry and remanng elemens log commody prces, D conans deermnsc erms, and sasfes E[ ] 0, E[ ] 0 for s, and E[ ] for s. For all counres, a VAR() s s s seleced by he AIC as he bes fng model. Vsual nspecon of he prce seres show consumer and producer prces exhb clear upward rends whereas he commody prces do no. Accordngly, we es for conegraon mposng he resrcon ha he conegrang relaons conan a lnear rend. The resuls of he conegraon ess are summarzed n Tables 3A and 3B. For all counres, he Johansen race es fnds a leas one conegrang vecor a he 5% sgnfcance level and somemes wo 13. Gven he orderng of he varables ny, he frs conegrang vecor can be nerpreed as a long-run equlbrum relaonshp beween consumer or producer prces and commody prces. Tables 3A and 3B repor he maxmum lkelhood esmaes of he frs conegrang vecor for each counry normalzed on consumer and producer prces, respecvely. The conegrang vecors are somewha hard o nerpre, whch could be due o hgh correlaon among some of he commody prce ndexes and he presence of a lnear rend. Tables 4A and 4B gve he esmaed error correcon (EC) models for and nflaon, respecvely, based on conegraed VAR() models wh a sngle conegrang vecor. For all counres, he EC erm 13 We also esed for conegraon usng jus he commody prces and could no rejec he null of no conegrang vecors a he 1% sgnfcance level. 10

12 s sgnfcan a he 5% level. Ths resul ndcaes ha he devaon from he long-run rend defned by he esmaed conegrang vecor has some predcve power for fuure nflaon. However, because he magnudes of he esmaed speed of adjusmen coeffcens are small, he predcve power of he EC erms s no expeced o be large. In he nex secon, we summarze he n-sample predcve performance of commody prces for nflaon based on EC and oher models. 3. Can Commody Prces Predc Inflaon? In hs secon we explore n-sample predcve regressons usng nformaon conaned n he commody prce ndexes, and conrollng for lagged nflaon. We exclude oher fundamenal facors based on alernave srucural models of prce adjusmens, he mos common beng he oupu gap varable from he Phllps curve. Our objecve s o deermne wheher or no nformaon obaned from global commody markes, whch o a large exen are exogenous o hese small open economes, s n fac useful n complemenng forecas models based on real, srucural facors. 3.1 In-Sample Predcve Regressons: VECM We begn by consderng wheher nformaon conaned n he curren commody subndexes can help predc nflaon raes one quarer ahead. We do so by employng he sandard n-sample lnear predcve regresson equaon, as below, for each of he fve counres: p = c+ aec + rp + å y + e () where p denoes eher he -nflaon rae ( p ) or he nflaon rae ( p ), EC s he error-correcon erm from he conegraed VAR() wh a resrced rend, and are he changes n he logarhms of he seven prce ndexes of world commody aggregaes, all expressed as annual raes. We noe ha eq. () s based on a VECM(1) and ha we presen 11

13 resuls below based on hs specfcaon. Bu he general resuls are robus o a varey of specfcaons, ncludng VECM(), VAR(1), VAR() where he EC erm s omed, and oher predcve specfcaons wh dfferen lag lenghs (see ONLINE appendx). The basc resuls are repored n Tables 4A-B. All sandard error esmaes are correced for heeroskedascy and seral correlaon. In addon o ndvdual coeffcen esmaes, he ables repor he adjused R wh and whou he ncluson of he lagged nflaon erm. In addon, we conduced Wald ess for he jon sgnfcance of he 7 ndexes and he p-values (avalable n an Appendx avalable on lne) are conssenly below 10%. Turnng frs o he nflaon esmaes n Table 4A, a number of resuls are worh hghlghng. Frs, he dfference beween he R, wh and whou lagged nflaon, suggess ha a sgnfcan amoun of he explanaory power s comng from he auoregressve srucure, wh he one excepon beng Chle. Neverheless, he sub-ndexes are sll mporan. Indeed, each sub-ndex s sgnfcan for a leas one counry, and Energy s sgnfcan (a leas a he 10% level) for all fve. In erms of he ndvdual counres, Ausralan nflaon depends on four ndexes (Lvesock, Energy, Foodsuffs, and Fas and ols), whle n addon o hese four ndexes, Chlean nflaon also depends upon Texles. Souh Afrca also depends upon fve subndexes (Lvesock, Energy, Raw Indusrals, Texles, and Meals). In conras, he only subndex weakly sgnfcan for Canada s Energy, whle for New Zealand Texles s also sgnfcan. Wh respec o he nflaon resuls presened n Table 4B, we see some dfferences n he paerns. Frs, he adjused R are unformly lower han for, wh generally less explanaory power beng due o he auoregressve componen, he excepon o hs agan beng Chle. Agan, energy s he overall mos sgnfcan sub-ndex. In addon, nflaon s dependen upon fewer sub-ndexes han s, hs reflecng he specalzaon of producon. In he case of Chle, New Zealand, and Souh Afrca, Energy s he only sgnfcan sub-ndex, 1

14 whle n he case of Ausrala Fas and Ols s also margnally sgnfcan. Canadan nflaon, n conras, depends upon foodsuffs and Lvesock. We have also esmaed he same regressons usng a VECM() specfcaon. These resuls are avalable on reques from he auhors. The resuls are generally smlar, alhough nevably here are some dfferences. In he case of nflaon, he adjused R exhbs he same overall paern as for he VECM(1) case. Conemporaneous energy remans unformly sgnfcan across he fve economes, whle n he case of Canada, lagged energy s sgnfcan as well. All sub-ndexes are sgnfcan for a leas one counry. Souh Afrca, whch for he VECM(1) specfcaon had fve sgnfcan sub-ndexes, now has only wo (Lvesock and Energy), whle n conras, Ausrala now fnds sx sub-ndexes o be sgnfcan, and a smlar case apples o Canada. A smlar paern apples o he. In he case of Ausrala, all 7 of he sub-ndexes are sgnfcan n some form (eher conemporaneous or lag), resulng n an ncrease n he R from 0.46 o In conras, no sub-ndex s sgnfcan for Souh Afrca. Gven ha hese regressors are hghly correlaed, we vew he resuls here as showng evdence ha commody ndexes are collecvely useful for predcng nflaon. Ths dynamc connecon s conssen wh heores of prce rgdy and gradual exchange rae pass-hrough. Clearly, dfferen specfcaons are approprae for he dfferen economes. 3.. Alernave Predcors: Home-Currency-Based Sub-Indexes & Aggregae Indexes Gven he naure of he resuls summarzed n Table 4, s necessary o underake some robusness checks. Frs, we recall ha he sub-ndexes summarzed n Table 4 measure he changes expressed n US dollars. Tables 5A and 5B repor he analogous equaons n he case where he sub-ndexes for he commody prces have been convered no domesc currency. Ths has been done by usng he end-of-perod spo marke exchange rae. Comparng Tables 5 wh Tables 4, he pcure s prey much he same. There are small swches, he mos sgnfcan beng ha New Zealand has a lo more sgnfcan sub-ndexes n wh he sub-ndexes measures n he home currency han when hey are measured n US dollars. 13

15 As a second robusness check, we consder usng an aggregae ndex of commody prces o predc nflaon. To examne hs queson we modfy he basc equaon () o p = c+ aec + rp + y + e (3) Agg Agg where Agg s he change n he log aggregae ndex and Agg EC s he error correcon erm from he conegraon model for and and he aggregae ndex. We employ wo such aggregae measures. The frs s an aggregae spo seres (from CRB), whch we denoe by -. The oher s called Reuers-Jefferes/CRB ndex, whch by ncorporang some Agg Spo nformaon on fuures prces s, no pure spo. We denoe hs by -. The esmaes of Agg CRB (3) for and nflaon, correspondng o hese wo aggregae ndexes are repored n Tables 6A-D. Lookng frs a he resuls for he nflaon, we see ha he resuls are clearly nferor o hose usng he sub-ndexes. In no case s - sgnfcan, whle Agg Spo - s Agg CRB sgnfcan only n he case of Ausrala and Canada. In conras, boh aggregae ndexes perform much beer n explanng he nflaon, beng hghly sgnfcan n all cases, excep for Chle, where hey are sgnfcan a he 10% level. Overall, we vew hese resuls as confrmng ha here are subsanal gans o be made from usng sub-ndexes o forecas nflaon. Wh regard o nflaon, he gans are less dramac, bu sll worhwhle. No only are here margnal mprovemens n explanaory power, bu also some nsghs no srucural dfferences Leas Angle Regressons As saed earler, we choose o use he seven sub- ndexes ha are observable drecly by he marke, some of whch cover overlappng produc ses. As a way o selec a parsmonous and effcen se of predcors for nflaon, we nex employ he leas angle regressons (LARS) due o Efron, Hase, Johnsone, and Tbshran (004). Smlar o Lasso and forward-sagewse regressons, LARS as a model-selecon algorhm s relavely fas and easy o mplemen, 14

16 balancng goodness-of-f and parsmony; see Efron e al. (004) for a full descrpon of he algorhm and s relaon o oher alernaves. The LARS procedure provdes a naural way o judge he relave mporance of he varables for explanng nflaon ha s superor o he radonal sepwse regresson. LARS sars by seng he coeffcens on all predcors o zero, and adds n varables sep-by-sep based on her correlaon wh he resduals of he prevous model. To selec he shrnkage level (he number of varables o nclude), he LARS procedure compues an esmae of he predcon error, C p. Whle here are oher alernaves such as he cross-valdaon approach, he mnmzed C p creron s compuaonally smple, and can delver generally good properes; see Madgan and Rdgeway (004). As a robusness es, we nclude he seven subndexes no LARS, ogeher wh lagged nflaon and also he error-correcon erm, and see f any of hese sub-ndexes are seleced o be ncluded n he specfcaons producng he mnmum C p. Tables 7A and 7B show he LARS resuls for - and -nflaon. 14 We repor regresson specfcaons chosen by he mnmzed C p sascs and we repor he R ' s for he regresson afer he ncluson of he parcular varable. For example, we see ha n he regresson for Ausrala, he frs varable seleced s lagged nflaon,, snce has he smalles R (0.10) amongs he repored numbers. The nex varable enerng s EC, followed by Energy, Lvesock, and Meal, producng a fnal R of Regressons ha nclude addonal varables ha currenly have no repored coeffcens delver larger C p sascs, hence are no seleced. For nflaon, lagged nflaon s conssenly seleced frs (wh he excepon of Chle) followed by he EC erm. However, for nflaon, lagged nflaon s no he frs varable seleced (he one wh he lowes R ) for Ausrala and Canada. In all cases, a leas one, and up o sx, commody sub-ndexes are seleced n addon o lagged nflaon and he EC erm. The ncremenal R-squares from he sub-ndexes are ofen non- neglgble eher. 14 We used boh he R package lars and Saa o run he LARS regressons repored here. 15

17 Energy remans he mos mporan sub-ndex n explanng nflaon, beng sgnfcan n all counres excep for New Zealand, where exles connues o be mporan. Lkewse, several sub-ndexes connue o be mporan n explanng nflaon n Canada, Chle, and Souh Afrca. The mporance of Energy n explanng nflaon s agan confrmed n Table 7B. We ake hese resuls as addonal confrmaon ha world commody prce sub-ndexes have predcve conen for subsequen and nflaon a quarer laer. 4. Ou-of-Sample Forecass Ths secon analyzes he exen o whch he commody sub-ndexes can help forecas nflaon raes ou-of-sample. We compare he forecas performances of he varous commody prce-based models wh wo me-seres benchmarks: he random walk (RW) and he AR(1) specfcaons, boh of whch are commonly used n he leraure; see Akeson and Ohanon (001) and Sock and Wason (007). Gven he prevalence of parameer nsably found n he general nflaon forecas leraure, we adop he rollng ou-of-sample scheme (raher han a recursve one) as s more robus o he presence of me-varyng parameers and requres no explc assumpon as o he naure of he me varaon n he daa. We use a rollng wndow wh sze equal o 68 quarers o esmae he model parameers and generae one-quarer ahead forecass recursvely (wha we call "model forecass"), yeldng 40 forecass. 15 (The resuls are very smlar wh oher reasonable wndow szes). For each of - and - nflaon n he fve counres, we compare he forecas errors from he commody-prce-based models agans hose from he wo me-seres benchmark models, RW and AR(1), whch we specfy n he form 15 Gven ha he rollng forecas procedure s que sandard n he leraure, we do no descrbe here bu refer neresed readers o Clark and McCracken (001), Clark and Wes (006, 007) for a heorecal exposon, and Engel, Mark, Wes (007), and Chen, Rogoff, and Ross (010) for applcaons. There are no rgorous gudelnes for how bes o selec wndow sze and our choce of 68, whle reasonable and generally whn he convenonal sze, gven he sample sze, s neverheless arbrary. We have expermened wh dfferen wndow szes rangng from 60-8 and our resuls no very dfferen. 16

18 RW E( p 1) + p (4a) AR(1) E( p 1) c + rp (4b) In dong so, we employ wo forms of he model. The frs ype s he ou-of-sample specfcaon, parallel o he n-sample analyses we have conduced n he earler secons;.e. mached frequency predcors are used. These nclude he followng (as desgnaed n Table 8) AR + Agg Index: Agg Spo E( p 1) c rp - + y (5a) Agg Index: Agg Spo E( p 1) c - + y (5b) SubIndex: E( p 1) c + y (5c) In addon, we also explore he forecas combnaon, conssng of he smple average of he 7 unvarae forecass: E ( p + 1) = c + y for each, ogeher wh he AR. We denoe hs by FC: AR+7 SubIndexes n Table The second group of model-based forecass use mxed-samplng daa ( MIDAS of Ghysels e al, 00 and Andreaou e al, 010a). Mxed frequency samplng models am o exrac nformaon conen from hgh frequency ndcaors o help forecas arge varables observed a lower frequency. 17 We use he OLS-based generalzed auoregressve dsrbued lag (GADL) model developed n Chen and Tsay (011) o examne wheher daly nformaon n commody prce aggregaes may help forecas quarerly nflaon. 18 The basc movaon and seup of GADL merges he poneerng work on NLS-MIDAS by Ghysels e al. (00) and he classc work of Almon (1965) of approxmang dsrbued lag (ADL) coeffcens wh smple 16 Noe ha we have no ncluded he EC erms from he rollng forecass. The man reason for hs s ha he EC erm always has a ny coeffcen, ndcang very gradual adjusmen, and no lkely o play a sgnfcan role n he nex quarer forecas. 17 The chaper n Oxford Handbook on Economc Forecasng by Andreou e al. (010b) provdes a good survey on how hese models have been used exensvely o forecas varous macroeconomc ndcaors as well as fnancal seres. 18 GADL s a smpler mehod o run he so-called MIDAS regressons poneered by Ghysels e al (00). See Chen and Tsay (011) for a dealed comparsons and dscusson. 17

19 low-order polynomals. GADL nhers he ease of esmaon from he ADL leraure and delvers esmaes for he "aggregae mpac" parameers relevan n he NLS-MIDAS leraure. We run he followng GADL forecas equaons (agan, for rollng wndow sze = 68) E ( p + ) = c+å yw ( L, q ) for seleced from 7 sub-ndexes (6) 1/ m,( m) 1 K 1/ m ( k-1)/ m k= 1 where W( L, q) = å b( k; q) L Here m and,( m) denoe hgher samplng frequency (n our case daly) and observaons, whch we ndex wh k 1oK. We presen resuls based on hree choces of K 14,34,54, 1/m ndcang usng daa of a few weeks, over a monh, o almos he full quarer. L s he lag operaor n frequency-m space, and b( k; q ) s he wegh on each of he K lagged daly commody prce change. As n Chen and Tsay (011), we parameerze hese weghng coeffcens wh a (K n) Vandermonde marx, as n he radonal ADL leraure of Almon (1965), where n 1 denoes he degree of he polynomnal whch he lagged coeffcens are assumed o sasfy. The esmaon dmenson of eq (6) above s hus reduced from 1+K o 1+n. We choose n = 3 n our forecas analyses below. Gven our small sample sze n he rollng esmaon procedures (wndow sze = 68), we noe ha usng all 7 ndexes would sll srech he degrees of freedom. We hus do mul-varae GADL regressons nvolvng only he sub-ndexes for lvesock, energy, foodsuffs and fas & ols, as hese were ypcally he mos sascally sgnfcan ndexes n he VECM(1) equaons for each counry. These equaons are run wh and whou he AR and are denoed n Table 8 by AR+GADL-MIDAS and GADL- MIDAS, respecvely. We hen complemen hese resuls by dong Forecas Combnaon; ha s akng a smple average of 7 unvarae forecass E ( p ) = c + + yw ( L, q ) (7) 1/ m,( m) 1 for each and AR, whch we denoe by FC: AR +7 GADL-MIDAS. 18

20 We fnd ha n erms of RMSEs, models based on commody prce ndexes produce mosly smaller RMSEs han does he RW, he noable excepon beng n forecasng nflaon for Chle and Souh Afrca. Bu hey seldom produce sgnfcanly smaller RMSEs han does he AR(1) model, a resul ha s conssen wh forecasng nflaon n he US, for example. The fac ha s easy o forecas beer han RW, bu hard o forecas beer han AR s no surprsng, gven ha we already observe ha he addonal predcve power of he subndexes n-sample regressons are no very large. However, we should noe ha we have more han a 10% mprovemen for forecasng Ausralan over AR, and a 5% mprovemen n a couple oher cases. Overall, he nroducon of mxed-frequency daa does no lead o sgnfcan mprovemen over he convenonal approach, excep n he case of Souh Afrca, when s sll ouperformed by he AR forecass. In summary, we see ha overall, world commody markes do have dfferenal mpacs on he key prce varables n hese fve commody exporng economes. For boh and nflaon raes, however, commody ndexes, wheher he specfc seleced ndvdual ones or her collecve man prncpal componens, can help provde beer forecas for nflaon raes a quarer ahead. We ceranly could explore alernaves ha may mprove he forecas performance furher, such as by lookng more specfcally no possble srucural breaks and ncorporang hs nformaon no he forecas model, or by combnng hese forecas equaons usng marke-based ndcaors wh srucural varables such as he oupu gap or unemploymen raes from he Phllps' curve. 5. Conclusons Wh cenral banks ncreasngly basng her moneary polces on some form of Taylor rule n whch he nomnal neres rae s adjused n response o some measure of nflaonary pressures, he queson s rased o wha degree should he response ncorporae changes n asse prces. The consensus vew seems o be ha hese prces should be aken no accoun only o he exen ha hey reflec underlyng nflaonary expecaons, and herefore may be reasonable 19

21 predcors of fuure nflaon. Sarng from hs vewpon, hs paper has examned he nformaon conaned n sub-ndexes of commody prces, usng daa for fve small commodydependen economes. The movaon for hs choce s ha commody prces are asse prces, whch such economes can ake as exogenously gven, hereby avodng ssues nvolvng smulaney whch would naurally arse n large economes such as he Uned Saes. In addon, by nfluencng he choce of producon echnques and consumpon choces, commody prces have a drec lnk o he real economy. 19 The overall message of hs paper s he followng. Our emprcal esmaes do sugges ha he nformaon conaned n commody prces can be helpful n predcng boh and nflaon. We fnd hs o be encouragng, snce he objecve of moneary polcy s usually dreced oward argeng nflaon. Moreover, snce dfferen counres are specalzed n dfferen commody groups, he prces of whch alhough co-movng also follow dfferen dynamc pahs, our fndngs sugges ha dsaggregang o sub-ndexes s helpful as well. Havng esablshed ha he sub-ndexes of commody prces do ndeed conan nformaon ha may be useful n predcng nflaon and ha herefore may form an approprae componen of moneary polcy he naural nex sep s o add commody prces o he moneary polcy rule self. One can hen nroduce hs augmened polcy rule no a complee calbraed srucural model of a small open economy and examne he exen o whch hs addonal nformaon does n fac mprove he effecveness of moneary polcy n erms of enhancng macroeconomc performance and promong prce sably. 19 The mos wdely suded aspec of hs elemen nvolves he role of ol/energy as an nermedae npu, on whch an exensve leraure exss. 0

22 Table 1 A. Summary Sascs for Quarerly Changes n Commody Sub-Indexes ( ) 1983Q1-010Q4 ; Annual Rae Lvesock Energy Foodsuff Raw Ind. Texles Meal Fas& Ols Mean S. Dev B. B-varae Correlaons for Quarerly Changes n Commody Sub-Indexes ( ) = Lvesock Energy Foodsuff Raw Ind. Texles Meal Fas& Ols Lvesock Energy Foodsuff Raw Ind. Texles Meal 1.00 (---) (0.00) (---) (0.00) (0.01) (---) (0.00) (0.00) (0.00) (---) (0.01) (0.09) (0.03) (0.00) (---) (0.00) (0.00) (0.00) (0.00) (0.00) (---) (0.00) (0.00) (0.00) (0.00) (0.0) (0.00) (---) Fas& Ols Noe: Sample perod: 1983Q1-010Q4 (n = 11). Numbers n he parenheses are he p-values for he null hypohess ha he correlaon s zero. T1

23 Table A: Counry-Specfc Quarerly Inflaon Raes 1983Q1-010Q3; Annual Rae Ausrala Canada Chle New Zealand S. Afrca Mean Sd. Dev Mean Sd. Dev Table B: Correlaons b/w Inflaons, & World Commody Sub-Index Inflaon ( ) Ausrala Canada Chle New Zealand Souh Afrca (--) (--) (--) (--) (--) (0.00) (--) (0.00) (--) (0.00) (--) (0.00) (--) (0.00) (--) Lvesock Energy Foodsuff Raw Ind. Texles Meal Fas& Ols (0.49) (0.17) (0.00) (0.00) (0.11) (0.04) (0.88) (0.44) (0.55) (0.00) (0.79) (0.) (0.6) (0.06) (0.15) (0.) (0.46) (0.50) (0.) (0.55) (0.76) (0.57) (0.0) (0.01) (0.14) (0.0) (0.37) (0.55) (0.30) (0.07) (0.41) (0.55) (0.10) (0.05) (0.03) (0.00) (0.47) (0.38) (0.18) (0.6) (0.53) (0.54) (0.81) (0.99) (0.38) (0.06) (0.4) (0.50) (0.4) (0.76) (0.84) (0.65) (0.34) (0.1) (0.03) (0.00) (0.79) (0.16) (0.10) (0.69) (0.9) (0.61) (0.01) (0.00) (0.16) (0.14) (0.97) (0.81) (0.77) (0.03) Noe: Sample perod: 1983Q1-010Q3 (n = 106). Numbers n he parenheses are he p-values for he null hypohess ha he correlaon s zero T

24 Table 3A: Esmaed Conegrang Vecors Normalzed on lp = c + d + å blp + u where = 7 sub-ndexes 0 Ausrala Canada Chle New Zealand Souh Afrca Lvesock *** *** [ ] [0.0504] [.76336] [ ] [ ] Energy *** *** *** *** *** [ ] [ ] [0.1061] [ ] [0.7391] Foodsuff *** *** ** *** *** [ ] [0.0654] [3.3373] [ ] [ ] Raw & Ind ** *** [ ] [ ] [ ] [0.679] [4.5758] Texle *** *** *** [ ] [0.1403] [ ] [ ] [ ] Meal *** *** *** [0.054] [ ] [5.3373] [ ] [ ] Fas & Ols *** *** *** *** *** [ ] [0.0460] [1.3439] [0.0589] [ ] Trend *** *** *** *** *** [ ] [ ] [ ] [ ] [ ] Noe: The conegrang vecors are maxmum lkelhood esmaes normalzed on from conegraed VAR() models wh one conegrang vecor. Values n brackes represen sandard errors. Asersks ndcae sgnfcance a 1% (***), 5% (**), and 10% (*) level. A consan erm s ncluded n he esmaon (resuls no repored). T3

25 Table 3B: Esmaed Conegrang Vecors Normalzed on lp = c + d + å blp + u where = 7 sub-ndexes 0 Ausrala Canada Chle New Zealand Souh Afrca Lvesock *** *** *** [ ] [.01176] [ ] [0.0993] [0.0681] Energy *** *** *** *** *** [ ] [ ] [ ] [0.0008] [ ] Foodsuff *** *** *** *** *** [ ] [.71508] [ ] [0.0419] [ ] Raw & Ind *** ** [ ] [3.3585] [8.169] [ ] [ ] Texle *** *** [0.0780] [ ] [.04919] [ ] [ ] Meal *** *** * [ ] [3.9976] [ ] [ ] [ ] Fas & Ols *** *** *** *** *** [ ] [ ] [ ] [ ] [0.0990] Trend *** *** 0.084*** *** *** [ ] [ ] [ ] [ ] [ ] Noe: The conegrang vecors are maxmum lkelhood esmaes normalzed on from conegraed VAR() models wh one conegrang vecor. Values n brackes represen sandard errors. Asersks ndcae sgnfcance a 1% (***), 5% (**), and 10% (*) level. A consan erm s ncluded n he esmaon (resuls no repored). T4

26 Table 4A: VECM(1) Coeffcen Esmaes: -Inflaon p = c+ aec + rp + y + e + 1 å + 1 Ausrala Canada Chle New Zealand Souh Afrca EC Lvesock Energy Foodsuff Raw Ind. Texles Meal Fas& Ols Consan *** ** *** *** *** [ ] [ ] [ ] [ ] [0.0011] *** *** *** *** [0.0750] [ ] [ ] [ ] [0.0791] *** ** ** [ ] [0.0190] [ ] [0.009] [0.0033] *** * *** * *** [ ] [ ] [ ] [ ] [ ] ** * [ ] [0.0155] [ ] [0.069] [0.0369] ** [ ] [ ] [ ] [0.0686] [ ] * *** * [0.0176] [0.0033] [ ] [ ] [0.0384] ** [0.0101] [0.0195] [ ] [0.0306] [ ] *** *** [ ] [ ] [0.0507] [0.0168] [ ] *** *** * ** [ ] [ ] [0.001] [0.0011] [ ] N obs Adj. R Adj. R w/o Noe: The error-correcon erm: EC = lp -å blp -d-c0 and = 7 sub-ndexes, s compued based on he conegraon relaon repored n Table 3A. We noe ha each VECM regresson ncludes all sub-ndexes and s run usng a resrced rend, as chosen based on Johansen-Juselus (1990) es for conegraon. Values n brackes represen sandard errors. Asersks ndcae sgnfcance a 1% (***), 5% (**), and 10% (*) level. T5

27 Table 4B: VECM(1) Coeffcen Esmaes: -Inflaon p = c+ aec + rp + y + e + 1 å + 1 Ausrala Canada Chle New Zealand Souh Afrca EC Lvesock Energy Foodsuff Raw Ind. Texles Meal Fas& Ols Consan *** ** ** [0.0377] [ ] [0.0090] [ ] [ ] ** ** 0.47*** *** *** [ ] [0.1009] [ ] [0.0935] [ ] ** [0.0305] [0.0546] [ ] [0.0733] [0.0307] *** ** ** 0.03** [0.0085] [ ] [0.0193] [ ] [0.0095] *** [ ] [ ] [ ] [ ] [ ] [0.1150] [ ] [0.3853] [0.0918] [ ] [ ] [ ] [0.1094] [0.0435] [ ] [0.0481] [ ] [ ] [ ] [ ] * [0.0763] [0.0144] [ ] [0.065] [0.0705] *** *** * *** *** [ ] [0.0015] [ ] [0.0014] [0.0071] N obs Adj. R Adj. R w/o Noe: The error-correcon erm: EC = lp -å blp -d -c0 and = 7 sub-ndexes, s compued based on he conegraon relaon repored n Table 3B. We noe ha each VECM regresson ncludes all sub-ndexes and s run usng a resrced rend, as chosen based on Johansen-Juselus (1990) es for conegraon. Values n brackes represen sandard errors. Asersks ndcae sgnfcance a 1% (***), 5% (**), and 10% (*) level. T6

28 Table 5A: VECM(1) Esmaes wh Home Currency Sub-Indexes: -Inflaon p = c+ aec + rp + y + e HC, HC + 1 å + 1 Ausrala Canada Chle New Zealand Souh Afrca HC EC p Lvesock, HC Energy, HC Foodsuff, HC Raw Ind., HC Texles, HC Meal, HC Fas & Ols, HC Consan *** *** *** *** *** [0.0109] [ ] [ ] [ ] [ ] *** 0.300** *** *** [0.0779] [ ] [ ] [0.0704] [0.074] *** ** ** [0.0134] [0.0174] [0.0311] [0.0050] [0.0008] *** * *** * *** [ ] [ ] [ ] [ ] [ ] [0.0134] [0.0148] [0.0303] [0.0006] [ ] * ** ** [ ] [ ] [0.1016] [ ] [ ] *** * [0.0113] [0.0037] [0.0537] [0.03] [ ] ** ** ** [0.007] [ ] [ ] [ ] [ ] *** ** [ ] [ ] [0.039] [0.0153] [ ] *** *** * [ ] [ ] [0.004] [ ] [ ] N obs Adj. R Adj. R w/o p HC, HC Noe: The error-correcon erm: EC = lp -å blp -d -c0 and = 7 sub-ndexes, s compued based on he conegraon relaons parallel o hose repored n Table 3A bu usng subndexes n home currences. We noe ha each VECM regresson ncludes all sub-ndexes and s run usng a resrced rend, as chosen based on Johansen-Juselus (1990) es for conegraon. Values n brackes represen sandard errors. Asersks ndcae sgnfcance a 1% (***), 5% (**), and 10% (*) level. T7

29 Table 5B: VECM(1) Esmaes wh Home Currency Sub-Indexes: -Inflaon p = c+ aec + rp + y + e HC, HC + 1 å + 1 Ausrala Canada Chle New Zealand Souh Afrca HC EC p Lvesock, HC Energy, HC Foodsuff, HC Raw Ind., HC Texles, HC Meal, HC Fas & Ols, HC Consan *** ** *** [0.0377] [0.0098] [0.0010] [ ] [0.0099] ** *** *** *** [ ] [ ] [ ] [ ] [ ] ** [0.0983] [0.0549] [ ] [0.0636] [0.0303] *** * 0.047** *** *** [0.0079] [0.0070] [ ] [0.0079] [ ] ** [0.0973] [0.0897] [ ] [0.0568] [ ] [ ] [ ] [0.398] [0.0896] [ ] [ ] [ ] [0.191] [ ] [ ] [ ] [ ] [ ] [0.0408] [ ] [0.070] [0.0101] [0.0599] [ ] [0.0466] *** * ** [ ] [0.0010] [ ] [ ] [ ] N obs Adj. R Adj. R w/o p HC, HC Noe: The error-correcon erm: EC = lp -å blp -d -c0 and = 7 sub-ndexes, s compued based on he conegraon relaons parallel o hose repored n Table 3B bu usng subndexes n home currences. We noe ha each VECM regresson ncludes all sub-ndexes and s run usng a resrced rend, as chosen based on Johansen-Juselus (1990) es for conegraon. Values n brackes represen sandard errors. Asersks ndcae sgnfcance a 1% (***), 5% (**), and 10% (*) level. T8