Taking the Economic Pulse: An Improved Tool to Help Track Economic Cycles in Canada

Transcription

1 Insiu C.D. HOWE Insiue Conseils indispensables sur les poliiques July 26, 2016 BUSINESS CYCLE Taking he Economic Pulse: An Improved Tool o Help Track Economic Cycles in Canada by Jeremy Kronick Policymakers and economiss need a reliable way o measure he exen o which economic shocks, booms and buss spread hroughou an economy. Such a diffusion index is an imporan conribuor o he deerminaion of he onse, lengh and breadh of recessions and recoveries. Saisics Canada, which had produced a diffusion index for many years, sopped doing so in This paper, underaken under he aegis of he C.D. Howe Insiue s Business Cycle Council, fills his daa gap by generaing new, improved ways of measuring he diffusion of ripples, booms or buss in he Canadian economy. The firs and primary mehod uses a sandard saisical mehodology principal componens analysis ha more accuraely idenifies he underlying rend and co-movemens in he daa across indusries. The second mehod, called he median cu-off or MCO approach, includes only indusries ha are above he median size in erms of conribuion o overall GDP. Boh new measures provide useful addiional informaion. For example, he principal componens diffusion index indicaes an addiional quarer of greaer conracionary han expansionary indusries a he end of he recession. Also, all he mehodologies sugges he negaive oil price shock ha led o a conracionary economy in he firs half of 2015 was no diffuse enough o warran a recessionary call. When Canadians hink abou negaive economic shocks, such as he recen collapse in oil prices, many wan o know wheher he damage will be isolaed or widely spread. To provide an answer, economiss use a diffusion index ha conveys in a single number he exen o which he downs (or ups) of an economy are widespread in any given period. Saisics Canada produced a diffusion index for many years following Cross (2004) mehodology. Unforunaely, Saisics Canada sopped producing he diffusion index in This paper, underaken under he aegis of he C.D. The auhor would like o hank Craig Alexander, Daniel Schwanen, Ben Dachis and Colin Busby of he C.D. Howe Insiue, as well as Angelo Melino, Philip Cross, Eric Lascelles, Randall Barle, and anonymous reviewers for heir helpful suggesions. I reain full responsibiliy for any remaining errors or omissions.

2 2 Howe Insiue s Business Cycle Council, fills his daa gap by generaing new, improved ways of measuring he diffusion of ripples, booms or buss in he Canadian economy. Having robus, mehodologically sound daa on diffusion is imporan for he proper undersanding of business cycles, including he idenificaion of recessions. This paper presens wo mehodologies ha represen improvemens over he old Saisics Canada mehod for calculaing diffusion indices. The firs and primary mehod uses a sandard saisical mehodology principal componens analysis ha more accuraely idenifies he underlying rend and co-movemens in he daa across indusries. The hope is ha he firs principal componen explains he bulk of he variaion in he daa. The second mehod, which I label he median cu-off or MCO approach, includes only indusries ha are above he median size in erms of conribuion o overall GDP. Wih hese mehods providing a clearer picure of he level of diffusion in economic aciviy, a more reliable picure emerges as o when, and wha ype of, fiscal and/or moneary simulus or resrain is appropriae. Specifically, policymakers will be able o beer deermine wheher acing on a paricular economic shock is required and wheher blun insrumens ha impac mos, if no all, secors are appropriae, or wheher argeed responses are more likely o creae he desired oucomes. Over he period analyzed in his paper, he quarers idenified by he new indices as having more conracing han expanding indusries closely mached hose generaed using Cross (2004) mehodology. Ineresingly, all hree mehodologies sugges ha he negaive oil price shock ha led o a conracionary economy in he firs half of 2015 was no diffuse enough o warran a recessionary call. Tha said, in addiion o being more mehodologically sound, he new indices produced imporan differences ha will be valuable for business cycle analyss and policymakers alike. Specifically, he principal componens diffusion index suggess ha he recession lased slighly longer han previously hough, and he median cu-off diffusion index is more volaile han he ohers, implying greaer synchroniciy, or co-movemen, beween larger Canadian indusries in boh a posiive and negaive direcion. Measuring Diffusion: Pas, Presen, and Fuure This secion will firs describe he unweighed diffusion index from Cross (2004) and, nex, how I adap he mehod o produce a baseline version for he purposes of comparison. I hen presen he case for principal componens analysis being a saisical improvemen in calculaing he diffusion index. 1 The final par of his secion discusses how he poenial arbirariness of indusry daa breakdowns in he unweighed diffusion index can be avoided by coninuing o follow he Cross (2004) mehodology while looking only a he subse of all indusries measured by Saisics Canada ha are of median or larger size; i.e., he median cu-off approach. Origins of he Unweighed Mehodology Diffusion indices have been around as an analyical ool since In Canada, Cross (2004) is he seminal aemp a a comprehensive diffusion index. A he ime ha paper was wrien, he analysis wen back o Principal componens analysis akes a large se of correlaed observed variables and urns hem ino a smaller se of variables ha are linearly uncorrelaed, wih each new variable represening a principal componen. The firs principal componen is such ha i accouns for he larges variance across he daa. The second componen will accoun for he nex larges variance amongs he daa, and so on. 2 Developed as far back as Michell 1913.

3 3 and he decision on which indusries o use was based on he lengh of ime for which seasonally adjused daa a he 2 or 3 Sandard Indusrial Classificaion (SIC) digi level was available. The index was calculaed using 83 indusries. The index was buil as follows: expanding indusries over a given period received a score of 100, hose falling received a score of zero, and hose wih unchanged oupu received a score of An average was hen calculaed using he scores for each indusry. No weighs were aached o secoral changes o reflec he size of he indusry as his would simply ge closer o recalculaing changes in overall real GDP, which would defea he purpose of undersanding he diffusion of economic aciviy. An overall average of 50 indicaed an equal number of expanding and conracing indusries in a given period. A score above 50 indicaed more expanding han conracing indusries and a score below 50 he opposie. The series was calculaed monhly generaing an unsmoohed index. A five-monh moving average 4 version was also calculaed o smooh ou he daase and avoid puing oo much emphasis on a given monh. A quarerly version of he unsmoohed index (see Cross and Bergevin 2012) can be calculaed as well by averaging he values for he diffusion index across he hree monhs of he relevan quarer. The Baseline Version In his paper, I use he chain-weighed 5 secoral daa by Norh American Indusrial Classificaion Sysem (NAICS) code, a he hree-digi level. 6 One major advanage in using hese more recen daa over he daa in Cross (2004) is ha he breakdown of indusries is essenially one-hird goods and wo-hirds services, reflecing he rue size of hese secors in he overall economy. The older daa had he reverse spli beween goods and services. 7 A simple unweighed version can hen be calculaed using he 101 indusries ha arise from he hreedigi breakdown. I label his unweighed diffusion index he baseline version. The index is firs calculaed a a monhly frequency before averaging he hree monhs of a given quarer o generae he quarerly resuls. 3 The Conference Board of Canada (2012) describes unchanged as being a change ha is less han he absolue value of I run he resuls for he unweighed indices wih boh a hreshold of 0.05 and no hreshold a all, and found no difference beween hese wo calculaions, eiher regarding he quarers in which a majoriy of indusries are conracing, or in he average value of he diffusion indices. To avoid arbirary hresholds he resuls are presened wih no hreshold. 4 Cross (2004) found ha five-monh moving averages lead o lower sandard deviaions versus he more radiional hree-monh and six-monh moving averages. 5 Chain-weighed means ha he real GDP index is adjused for he fac ha produc subsiuions occur over ime in line wih associaed price changes and ha consumers change heir spending behavior accordingly, insead of relying on a fixed base-year baske of goods wih fixed prices. In 2013, Saisics Canada sared deriving monhly GDP daa by chaining a Laspeyres fixed weighed volume index o he prior period, moving away from he pure chain-weighed index. As we simply analyze change from one quarer o he nex, and provide a 100, 50, or 0 value o each change, he adopion of a new saisical echnique o measure GDP should no have a significan effec. 6 I use he four-digi level in cases where indusry breakdowns skip from he wo-digi o four-digi level. I use a wodigi figure in he one insance where only a wo-digi level indusry was available (Managemen of companies and enerprises). 7 Cross (2004) menions ha he reason he does no use he chain-weighed NAICS daa was ha here was no enough daa a he ime of he wriing as i only wen back o 1997.

4 4 A Beer Way: The Principal Componens Analysis Mehodology The unweighed version of diffusion provides a pure measure of breadh of changes in economic oupu, as i absracs compleely from boh he deph and ampliude of economic growh. However, here are saisical echniques ha can yield a ruer measure of he underlying rend in he economy by beer aking secoral comovemens ino accoun. One of hose saisical echniques is principal componens analysis. To allow comparison beween he principal componens analysis and he baseline version, I assign o expanding, neural, and conracing indusries he same 100, 50 and 0 breakdown described above. By defining indusry growh in his fashion, he principal componens diffusion index can also be hough of as represening he overall prediced percenage of expanding indusries in a given monh. The idea behind principal componens is ha he overall percenage of expanding indusries in a given period can be represened by a common componen, or a business cycle shock, and idiosyncraic shocks, which one would no expec o be diffuse, e.g., a srike or weaher-relaed even. Therefore, he principal componens diffusion index will remove he idiosyncraic shocks in order o focus exclusively on he rue business cycle shocks. Box 1 provides a more complee analysis on he comparabiliy beween he unweighed and principal componens analyses. I hen generae a quarerly version of he principal componen diffusion index by averaging he hree monhs comprising he relevan quarer. A Third Opion: The Median Cu-Off Diffusion Index The principal componens index, while more saisically sound, has by definiion lower volailiy compared wih he baseline version. 8 Therefore, as i sands, he baseline version ells us more abou how volaile co-movemen is likely o be. A key daa issue, however, arises from he baseline version. Specifically, Saisics Canada produces greaer breakdowns of sub-secors for some indusries han for ohers. There is no always economic reasoning for including hese greaer breakdowns, and doing so will unnecessarily pu more weigh in he diffusion index on paricular secors of he economy. 9 To accoun for his challenge, his paper calculaes a second unweighed version, where he firs sep is o esimae he percen share of GDP for each sub-indusry, hen calculae he median of hese shares, and finally, calculae he final diffusion index using Cross (2004) mehodology bu only including he 51 indusries ha si above ha median. I label his unweighed diffusion index he median cu-off or MCO version. I is worh noing ha he composiion of indusries making up he median version remains one-hird goods and wo-hirds services. 8 Proof is available on reques. 9 Noe ha here is one srong reason for some indusries having greaer breakdowns han ohers. Specifically, if an indusry is more cyclical i is likely, and useful, ha here be more daa on ha indusry. Goods indusries end o be more cyclical han services indusries (Saisics Canada 2009 references he increased cyclicaliy of manufacuring compared wih he overall economy.). However, as noed in he ex, he median cu-off index I presen in his paper reduces he number of indusries used, bu does no change he overall goods-services breakdown in my sample. This suggess ha he availabiliy of greaer sub-indusry daa breakdowns in cerain indusries is no enirely due o an aemp o focus more on cyclical indusries.

5 5 Box 1: The Principal Componens Index, Mehodology Define Y = ( Y1... YG )' where Y g, represens wheher he oupu of a paricular indusry g, is expanding, consan, or conracing in period. Depending on which i is, Y g, akes on values 100, 50, or 0. The Cross unweighed version is herefore: G 1 EY ( ) Y in each period, wih G being he number of indusries. g G g = 1 Principal componens analysis allows one o rewrie Y as a linear combinaion of uncorrelaed componens. Wihou geing ino complicaed proofs, Y can be rewrien as: Y = w* wy ' + e or Y = w* B + e where w is a vecor represening he weighs corresponding o he firs componen generaed by esimaing principal componens, w represening he ranspose of he vecor w, and B now represens he business cycle shock. a If we ake he expeced value of he righ hand side in period, where we assume he expeced value of he error erm is zero, we ge G G 1 1 E( Y) = Y = E( w* B ) = ( w* B ). g g G g= 1 G g= 1 Therefore, since we can inerpre he unweighed diffusion index as he percenage of indusries in a given quarer ha are expanding, we can make a similar saemen regarding he inerpreaion of he principal componens version. Specifically, he principal componens diffusion index represens he prediced percenage of indusries ha are expanding in a given quarer, given he common componen B. The preference for principal componens analysis is due o he fac ha, esimaed correcly, i filers ou idiosyncraic shocks, e, such as weaher, srikes, ec. and insead focuses on he rue business cycle shock B. a I check and confirm ha he firs componen explains he majoriy of he variaion in he daa. Comparing Resuls This secion presens he resuls for he baseline diffusion index developed for his sudy, and he indices calculaed using he wo mehodological improvemens I inroduced above. The diffusion indices are calculaed over due o he large change in available indusries afer 2007 a he hree-digi level, from he earlier period daing back o 1997 when chain-weighed secoral daa were firs made available To go back o 1997 would shrink he secors in half, which would sill make he unweighed versions possible where one simply acknowledges ha he index is calculaed differenly over he wo subsamples, bu would be impossible using principal componens analysis as he smaller sample would be forced on he enire esimaion period.

6 6 Figure 1: Comparison Baseline and Median Cu-Off Diffusion Indices 80 *Correlaion: Baseline- Median Cu-off = Median Cu-off Baseline Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Noe: Shaded area represens recessionary quarers as idenified by Cross and Bergevin (2012). Source: Auhor s calculaions. Figure 1 compares he baseline unweighed diffusion index o he MCO version. These resuls ell us ha he quarers in which here are a majoriy of conracing indusries are essenially idenical across boh unweighed diffusion indices. Q is he only addiional quarer wih greaer indusry conracions using he MCO approach. The implicaion is ha boh measures produce similar conclusions regarding he breadh of economic aciviy in a given quarer. Noe ha here is increased volailiy wih he MCO index, meaning ha large indusries in Canada are more likely o rise and fall a he same ime han poenially randomly chosen indusries. 11 For example, here was a fall in goods rade in Q led in par by decreasing auo and consumer goods expors. Given he size of hese indusries, here were large knock-on effecs, conribuing o he significan amoun of conracing indusries in his quarer. As a resul, he MCO diffusion index fell below 50, somehing we did no see in he baseline index. 11 Wih he excepion of Q and Q1 2015, he median cu-off index values are greaer han he baseline s when boh diffusion indices are above 50, indicaing a higher degree of growh indusries, and when he indices fall below 50, he median cu-off index values are smaller han he baseline s, implying a higher degree of conracing indusries.

7 7 Figure 2: Comparison Principal Componens versus Unweighed Diffusion Indices 80 *Correlaion: PC-Baseline = 0.85 PC- Median Cu-off = Median Cu-off Baseline Principal Componens Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Noe: Shaded area represens recessionary quarers as idenified by Cross and Bergevin (2012). Source: Auhor s calculaions. Inerpreing he Principal Componens Analysis Diffusion Index Figure 2 overlays he principal componens version of he index wih he wo unweighed versions. A few hings sand ou. Firs, here is high correlaion beween he principal componens version and boh unweighed versions. This is a srong resul as i implies ha he one common componen explains he bulk of he variaion of he overall economy and herefore does a good job of exracing he rue commonaliies beween secors. Furhermore, he principal componens diffusion index indicaes an addiional quarer of greaer conracionary han expansionary indusries a he end of he recession. Whereas boh unweighed versions sugges ha he bulk of indusries had become expansionary by Q3 2009, he principal componens index indicaes ha a sligh majoriy of indusries were sill in conracion. Business cycle analyss, including he C.D. Howe Insiue s Business Cycle Council, can benefi from having a clearer undersanding of exacly when Canada s economy escaped he Grea Recession and wha he imporan facors were in his respec. Undersanding Business Cycles As menioned above, he diffusion index is an imporan ool for undersanding business cycles, including recession deerminaion. Three elemens define recessions: duraion, ampliude, and breadh or scope (see

8 8 Cross and Bergevin 2012). Diffusion index daa are accompanied by daa on real GDP and employmen in order o evaluae wheher economic aciviy has all hree feaures in a given quarer. 12 Therefore, an ineresing quesion is wha each measure ells us abou poenial recessionary quarers experienced in Canada over he period under analysis. For employmen, his paper uses he employmen growh rae as in Cross and Bergevin (2012). Similarly, for economic aciviy, his paper follows Cross and Bergevin and analyzes average real GDP growh, he wo quarer average real GDP growh, as well as average per capia GDP growh for comparaive and assessmen purposes. Table 1 in Appendix A liss each diffusion measure; i.e., baseline, principal componens, and median cu-off, as well as daa on employmen and economic growh. All hree diffusion indices have Q o Q as quarers wih a majoriy of conracing indusries. Boh employmen and economic growh are conracionary as well during his ime, meaning ha hese quarers can be considered recessionary, consisen wih Cross and Bergevin (2012). The baseline diffusion index has no oher quarers where a majoriy of indusries are conracing so his measure suggess here are no oher recessionary quarers during he sample period. The principal componens diffusion index resuls, unlike he baseline index, indicae ha slighly more indusries han no coninued o conrac pas Q and ino Q Economic growh during his quarer was posiive, hough he wo-quarer growh rae was negaive. Employmen growh was fla hough he employmen rae no in he able fell. Therefore, i is possible ha we coninued o be in a recession in Q The MCO diffusion index labeled Q as having more conracing han expanding indusries. However, as his was a one-off negaively diffuse quarer, and economic growh iself was posiive boh during Q4 2012, and he preceding and subsequen quarers, his episode did no amoun o a recession. Lasly, his paper noes ha all hree diffusion indices show a key reason why many economiss hesiaed o call he onse of a possible recession during However, he daa used remain subjec o revisions. Overall, while he resuls are consisen across differen mehodologies during he period under analysis, he new measures inroduced in his paper do lend more confidence o he inerpreaion of how widespread ups and downs in he economy were one of he key indicaors of expansionary or recessionary periods. Conclusion The impeus for creaing he diffusion indices inroduced in his E-Brief, and hus he paper s conribuion, is wofold. Firs, his paper se ou o fill a clear daa gap creaed when Saisics Canada sopped producing is diffusion index. Second, policymakers need o have access o mehodologically robus daa on he diffusion of economic shocks in order o undersand how and why economic aciviy spreads across secors, and wha ha implies for blun versus argeed economic policies. This paper improved on he available mehodology by 12 Afer 1980, employmen moved much more closely wih business cycles han pre-1980, and herefore a higher weighing was placed on his variable han before. However, GDP remains he primary ouchpoin for evaluaing economic aciviy (see Cross and Bergevin 2012).

9 9 (i) employing a more accurae saisical analysis of co-movemen called principal componens, and (ii) inroducing he MCO diffusion index, an unweighed version wih a poenially more balanced se of indusries. Boh new measures idenified issues wih he baseline index and herefore provided useful addiional informaion. In he case of he principal componens diffusion index, we saw ha he recession may have lased slighly longer han he baseline index would sugges. For he MCO diffusion index we saw increased volailiy implying a greaer degree of synchroniciy across larger indusries in Canada in boh a posiive and negaive direcion. Therefore, in addiion o filling a daa gap, he resuls in his paper provide policymakers and business cycle analyss wih a more complee undersanding of he general level of indusry co-movemen, and he specifics of how his played iself ou in he recen Grea Recession.

10 10 Appendix A Table A1: Conracionary Quarers Under Differen Diffusion Indices Baseline Principal Componens Median Cu-Off Employmen Growh Rae Avg. GDP Growh 2 Quarer Avg. Growh Per Capia Avg. GDP Growh Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q

11 11 Table A1: coninued Baseline Principal Componens Median Cu-Off Employmen Growh Rae Avg. GDP Growh 2 Quarer Avg. Growh Per Capia Avg. GDP Growh Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Source: Auhor s calculaions.

12 12 References Conference Board of Canada How o Compue Diffusion Indexes. hps:// Cross, Philip A Diffusion Index for GDP. Canadian Economic Observer vol. 17, no.5. Cross, Philip, and Philippe Bergevin Turning Poins: Business Cycles in Canada since Commenary 366. Torono: C.D. Howe Insiue. Michell, Wesley Clair Business Cycles. Universiy of California Press, Berkeley. Saisics Canada The Canadian Manufacuring Secor: Adaping o Challenges. Economic Analysis Research Paper Series (11F0027M), no. 57. This E-Brief is a publicaion of he C.D. Howe Insiue. Jeremy Kronick is Senior Policy Analys a he C.D. Howe Insiue. This E-Brief is available a Permission is graned o reprin his ex if he conen is no alered and proper aribuion is provided.