A Canadian Business Sector Data Base and New Estimates of Canadian TFP Growth November 24, 2012

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1 1 A Canadian Business Secor Daa Base and New Esimaes of Canadian TFP Growh November 24, 2012 W. Erwin Diewer 1 and Emily Yu, 2 Discussion Paper 12-04, Deparmen of Economics, Universiy of Briish Columbia, Vancouver, Canada, V6T 1Z1. diewer@econ.ubc.ca Absrac Using new daa from Saisics Canada, he paper shows ha he produciviy performance of he business secor of he Canadian economy has been reasonably saisfacory over he pas 51 years. In paricular, radiional gross income Toal Facor Produciviy (TFP) growh averaged percenage poins per year over he period The focus of he sudy is on he real income generaed by he business secor of he Canadian economy. The growh of qualiy adjused labour inpu growh was he main driver of growh in real income followed by TFP growh, followed by growh in capial inpu and hen by falling real impor prices. However, in recen years, he conribuion of falling real impor prices urned ou o be more han wice as imporan as capial deepening. The sudy encounered many daa problems which should be addressed in fuure work on Canadian business secor produciviy performance. Journal of Economic Lieraure Classificaion Numbers C43, C67, C82, D24, E22, E43. Keywords Toal Facor Produciviy, Mulifacor Produciviy, real income, erms of rade effecs, measuremen of capial, measuremen of invenory change, user coss, real ineres raes. 1 Deparmen of Economics, Universiy of Briish Columbia and he School of Economics, Universiy of New Souh Wales. The financial assisance of he SSHRC is graefully acknowledged. The firs auhor also hanks Shuao Cao, Serge Coulombe, Wulong Gu, Ulrich Kohli, Sharon Kozicki, Danny Leung, Alice Nakamura, Andrew Sharpe and Jianmin Tang for helpful commens. None of he above are responsible for any views expressed in his paper. 2 Deparmen of Foreign Affairs and Inernaional Trade, Governmen of Canada

2 2 1. Inroducion Many observers have noed ha an improvemen in a counry s erms of rade has effecs ha are similar o an improvemen in a counry s produciviy growh. However, i is no sraighforward o work ou he exac magniude of each source of gain. Diewer (1983), Diewer and Morrison (1986), Diewer, Mizobuchi and Nomura (2005), Diewer and Lawrence (2006), Morrison and Diewer (1990) and Kohli (1990) (2003) (2004) (2006) developed producion heory mehodologies which enable one o obain index number esimaes of he conribuion of each ype of gain. In Appendix 1 below, we ouline he Diewer, Mizobuchi and Nomura (2005) and Diewer and Lawrence (2006) mehodology and in secions 2-4 of he main ex, we apply his mehodology o he business secor of he Canadian economy over he years Appendix 2 below describes how he Canadian business secor daa were developed from Saisics Canada sources. Secion 2 of he main ex aggregaes up he daa from Appendix 2 and develops convenional measures of Canadian business secor Toal Facor Produciviy for he years Produciviy growh, while perhaps he mos imporan source of growh in living sandards, is no he enire sory. If a counry s expor prices increase more rapidly han is impor prices, hen i is well known ha his has an effec ha is similar o a produciviy improvemen. Thus in secion 3, we measure he relaive conribuions of produciviy improvemens, changes in real expor and impor prices and he growh of labour and capial inpu o he growh of (gross) real income generaed by he business secor in Canada using he mehodology explained in Appendix 1. Secion 4 compares our esimaes of TFP growh wih he business secor Mulifacor Produciviy Growh esimaes recenly developed by he Saisics Canada KLEMS program; see Baldwin, Gu and Yan (2007) for a descripion of he mehodology used in he KLEMS program. I should be noed ha he Saisics Canada KLEMS program uses deailed indusry daa in order o consruc TFP esimaes by indusry and hen hese indusry esimaes are aggregaed up o give aggregae business secor esimaes of TFP growh, whereas our approach uses aggregae esimaes for he oupus produced and inpus used for he enire business secor. Thus our esimaes may suffer from some aggregaion bias. Secion 5 concludes. 2. Oupu and Inpu Aggregaes and Convenional Produciviy Growh for Canada In Appendix 2, we consruced price and quaniy series for 22 ne oupus, 12 ypes of labour inpu and 17 ypes of capial inpu for he business secor of he Canadian economy for he years The 22 ne oupus are: Q 1 : Domesic consumpion (excluding marke residenial rens and he services of owner occupied housing);

3 3 Q 2 : Real sales of goods and services by he business secor o he nonmarke secor less real sales of goods and services from he nonmarke secor o he business secor; Q 3 : Governmen invesmen; Q 4 : Business secor invesmen in residenial srucures; Q 5 : Business secor invesmen in machinery and equipmen; Q 6 : Business secor invesmen in nonresidenial srucures; Q 7 : Invenory change; Q 8 : Expors of agriculural and fish producs; Q 9 : Expors of energy producs; Q 10 : Expors of fores producs; Q 11 : Expors of indusrial goods and maerials (excluding energy and fores produc expors); Q 12 : Expors of machinery and equipmen (excluding auomoive producs); Q 13 : Expors of auomoive producs; Q 14 : Expors of oher consumer goods (excluding auomoive producs); Q 15 : Expors of services; Q 16 : Impors of agriculural and fish producs; Q 17 : Impors of energy producs; Q 18 : Impors of indusrial goods and maerials (including impors of fores producs bu excluding impors of energy producs); Q 19 : Impors of machinery and equipmen (excluding auomoive producs); Q 20 : Impors of auomoive producs; Q 21 : Impors of oher consumer goods and Q 22 : Impors of services. The price indexes ha correspond o he above quaniy indexes Q n are denoed as P n for n = 1,...,22 and = 1961,...,2011 and hey are lised in Appendix 2. We define he price of our consumpion aggregae as P C P 1. We form a domesic oupu aggregae Q D wih corresponding price P D by aggregaing Q 1 -Q 7. 3 Similarly, we form an expor aggregae Q X wih corresponding price P X by aggregaing Q 8 -Q 15 and an impor aggregae Q M wih corresponding price P M by aggregaing Q 16 -Q Once hese indexes have been consruced, a business secor aggregae oupu or real value added index Q Y is consruced as an aggregae of Q D, Q X and Q M. The corresponding aggregae oupu price index is P Y. 5 The price indexes P C, P D, P X, P M and P Y are lised in Table 1 below and he corresponding quaniy indexes Q D, Q X, Q M and Q Y are lised in Table 2 below. Saisics Canada has consruced deailed labour inpu daa for he Canadian business secor for 36 ypes of labour for he years in CANSIM Table which 3 P D is he Törnqvis price index of P 1 -P 7 and Q D is he corresponding implici quaniy index. 4 P X and P M are consruced as Törnqvis price indexes and Q X and Q M are he corresponding implici quaniy indexes. 5 P Y is a Törnqvis price aggregae of P D,P X,P M (wih corresponding quaniies Q D,Q X, Q M ) and Q Y is he implici quaniy index ha maches up wih P Y.

4 4 we will make use of in his sudy. Labour inpu is classified according o a four way classificaion in Table : By educaion level E. There are 3 caegories in his classificaion: E=1 corresponds o Primary or Secondary Educaion; E=2 corresponds o Some or Compleed Pos-Secondary Educaion and E=3 corresponds o Universiy Degrees or Above. By age of worker A. There are 3 caegories in his classificaion: A=1 corresponds o years old; A=2 corresponds o years old and A=3 corresponds o 55 years old and over. By sex S. There are 2 caegories in his classificaion: S=1 corresponds o a male worker and S=2 corresponds o a female worker. By ype of employmen T. There are 2 caegories in his classificaion: T=1 corresponds o a paid worker and T=2 corresponds o a self employed worker. Thus Table provides annual hours and oal compensaion daa for 3x3x2x2 or 36 ypes of worker in he Canadian business secor for he years We aggregaed over he age groups using Fisher chained indexes in order o form 12 price and quaniy series for labour, P L1 -P L12 and Q L1 -Q L12. These series were exended o 2011 using various Saisics Canada series as is explained in Appendix 2. These 12 price and quaniy series for he various ypes of labour were aggregaed ino aggregae qualiy adjused business secor labour inpu Q L wih corresponding price index P L. 6 P L is lised in Table 1 and Q L is lised in Table 2. Using informaion on business secor capial socks in CANSIM Table , In Appendix 2, we were able o form esimaes for business secor beginning of he year capial socks for he following 14 ypes of reproducible capial asse: Q K1 : Office furniure; Q K2 : Agriculural machinery; Q K3 : Indusrial machinery; Q K4 : Auomobiles; Q K5 : Trucks; Q K6 : Oher ranspor equipmen; Q K7 : Oher machinery and equipmen; Q K8 : Compuers; Q K9 : Telecommunicaions equipmen; Q K10 : Sofware; Q K11 : Indusrial buildings; Q K12 : Commercial buildings; Q K13 : Insiuional buildings; Q K14 : Engineering consrucion. 6 Q L is now a direc Törnqvis quaniy aggregae of Q L1 -Q L12 wih P L defined as he corresponding implici price index. These index number convenions are necessary in order o apply he ranslog mehodology explained in Appendix 1.

5 5 Using Saisics Canada Balance Shee informaion (and oher sources), we were able o consruc business secor beginning of he year capial sock inpus for invenories (Q K15 ), agriculural land (Q K16 ) and business nonagriculural land (Q K17 ). We also consruced esimaes for he corresponding sock prices, P Kn, for n = 1,...,17 and = ; see Appendix 2. As is explained in Appendix 2, user cos prices U n for he 17 capial sock inpus were consruced, using balancing or endogenous real raes of reurn ha made he value of ne oupu produced by he business secor equal o he value of primary inpus used by he business secor. 7 There is a problem wih our capial inpu daa in ha he sofware series sars only in Our ranslog mehodology does no work when an inpu is equal o 0 in one period and posiive in a subsequen period. Thus we aggregaed he sofware asse wih he compuer asse; i.e., we consruced a Fisher capial services aggregae 8 of (U 8,U 10 ) and (Q K8,Q K10 ) o replace he individual services for hese wo asses. We hen consruced a business secor capial services aggregae Q K by aggregaing he 16 ypes of capial services using direc Törnqvis quaniy aggregaion. The corresponding capial services aggregae price is denoed as P K and is lised in Table 1 while Q K is lised in Table 2 below. Once he labour and capial aggregaes have been consruced, we can consruc a direc Törnqvis quaniy inpu aggregae of Q L and Q K which we denoe by Q Z, which is lised in Table 2. The corresponding implici aggregae inpu price index, P Z, is lised in Table 1. Table 1: Prices of Canadian Business Secor Oupu and Inpu Aggregaes Year P C P D P X P M P L P K P Y P Z User coss for capial inpus are mean o approximae wha i would cos a business o ren or lease he services of he asse for he accouning period under consideraion. The use of user coss in mulifacor produciviy sudies daes back o he pioneering work of Jorgenson and Griliches (1967). Basically, a user cos consiss of he sum of four erms: (1) he ineres ha could be earned if he asse were simply sold a he beginning of he period,; (2) depreciaion; (3) axes ha are assessed on he use of he asse plus he appropriae business income ax rae and (4) expeced capial gains (or minus losses) ha he asse migh accrue over he accouning period. Wih respec o (1), we chose he ineres rae o be he balancing rae of reurn ha makes he value of inpus equal o he value of oupus; i.e., we chose an endogenous rae of reurn raher han an exogenous one. Wih respec o (4), we chose o value beginning and end of period capial socks a he average invesmen prices of he period, which eliminaed he capial gains erm. There are problems associaed wih he esimaion of expeced capial gains and so our sraegy avoids hese problems. Jorgenson (1989) and his coworkers esimae expeced capial gains (or losses) by acual gains (of losses). This sraegy ends o lead o negaive user coss for land asses and hugely posiive user coss for compuers (when saisical agencies assign large depreciaion raes o compuers). Saisics Canada uses he Jorgenson mehodology. For furher discussion on problems wih consrucing user coss, see Harper, Bernd and Wood (1980), Diewer (1980) (2005a), Schreyer (2009) and Inklaar (2010). 8 Fisher (1922) aggregaion can deal wih 0 quaniies; see Diewer (1980; ).

6 Noe ha we have also lised he price of our household consumpion aggregae, P C, in Table 1, which will play a role in subsequen secions. The (oal facor or mulifacor) produciviy level in year of he Canadian business secor T can be defined as he aggregae year oupu, Q Y divided by aggregae year inpu, Q Z : 9 (1) T Q Y /Q Z ; = 1961,..., Toal Facor Produciviy (TFP) growh for year, τ, is defined as he produciviy level in year divided by he previous year s produciviy level: 9 See definiion (34) in Appendix 1.

7 7 (2) τ T /T 1 ; = 1962,..., Table 2 liss he quaniies ha mach up o he prices in Table 1 and i also liss produciviy levels and growh raes. Table 2: Quaniies of Canadian Business Secor Oupu and Inpu Aggregaes, TFP Levels and TFP Growh Raes Year Q D Q X Q M Q L Q K Q Y Q Z T τ

8 Our geomeric average rae of TFP growh over he 50 years is 1.026% per year, 10 which can also be compared wih Saisics Canada s recen KLEMS program average Mulifacor Produciviy Growh over he same years of 0.276% per year, 11 which is a raher subsanial difference! In secion 4 below, we aemp o deermine why our resuls are so differen from he official Saisics Canada resuls. 12 Over he golden years , TFP growh 13 averaged 2.67% per year; over he dismal years, , TFP growh averaged on 0.20% per year bu over he remainder of he nineies, , TFP growh nicely recovered o average a very respecable 1.69% per year. During he naughs, , TFP growh again fell off o average only 0.21% per year. However, produciviy growh is no necessarily he enire sory behind he growh in living sandards: if he price of Canadian expors increases more rapidly han he price of Canadian impors, hen he real income generaed by he business secor should increase. This erms of rade effec is no aken ino accoun in he above produciviy compuaions. Thus in he following secion, we implemen he ranslog real income mehodology explained in secions 1-4 of Appendix 1 below and his approach will enable us o assess he conribuion o Canadian living sandards of improvemens in Canada s erms of rade. 3. Explaining Real Income Growh Generaed by he Canadian Business Secor: he Gross Oupu Approach The basic mehodology used in his secion can easily be explained in nonechnical erms. The business secor faces (exogenous) domesic and inernaional prices for he ne oupus i produces: domesic oupus, expors and (minus) impors. The business secor also uilizes inpus of labour and capial in order o produce is oupus. The value of oupus produced by he business secor less he value of impors used (value added) mus evenually flow back o he labour and capial primary inpus ha were used o produce 10 This rae of TFP growh can be compared o he average rae of produciviy growh for Ausralia obained by Diewer and Lawrence (2006) using a similar mehodology and over a similar period. The Diewer and Lawrence marke secor average rae of TFP growh for Ausralia over he period was 1.49% per year. However, here is an upward bias in he Diewer and Lawrence resuls due o he fac ha hey essenially used hours worked as heir measure of labour inpu insead of a qualiy adjused measure of labour inpu for Ausralia (which was no available). 11 See CANSIM Table , Series V Comparing levels of TFP wih he saring level being 1 in 1961, our TFP ended up a in 2011 whereas KLEMS Mulifacor Produciviy ended up a in Our measures of business secor oupu and capial inpu were differen from he KLEMS measures because we excluded renal housing from our measure of value added and we excluded he residenial land and residenial srucures inpus from our measure of capial services, whereas he KLEMS measures included renal housing in heir oupu and capial inpu measures. 13 All growh raes in his paragraph are average geomeric growh raes over he period under consideraion. The average growh raes in Table 4 are arihmeic ones (and hence are slighly higher).

9 9 value added. This is he (gross) income generaed by he business secor. We divide his gross income in year by he price of consumpion in year, P C, in order o urn his nominal income ino real income ρ ; his real income is he number of consumpion bundles ha could be purchased by he owners of he labour and capial inpus ha were used in year by he Canadian business secor. We also divide each of he prices P D, P X, P M, P L and P K by he price of consumpion, P C, in order o form he corresponding real oupu and inpu prices facing he Canadian business secor in each year. Our measure of he (gross) real income generaed by he business secor ρ and he corresponding real oupu and inpu prices are lised in Table 3. Table 3: Gross Real Income Generaed by he Canadian Business Secor and Real Oupu and Inpu Prices Year ρ P D /P C P X /P C P M /P C P L /P C P K /P C

10 Thus he gross real income generaed by he Canadian business secor has grown from $29,368 million dollars worh of 1961 consumpion bundles in 1961 o $182,140 million in 2011, a 6.20 fold increase. Looking a he change in real inpu and oupu prices, he real price of domesic oupu has fallen o imes he saring level (due o he fac ha machinery and equipmen prices have risen less rapidly han he price of consumpion) and he real price of expors has risen slighly o imes he saring level. However, he real price of impors has fallen subsanially o imes he saring level. The qualiy adjused real wages of business secor workers have risen o imes heir iniial 1961 levels. The real price of capial services has risen 1.69 fold, reflecing rapidly rising prices of agriculural land and nonagriculural business land as well as upward rends in machinery and equipmen depreciaion raes and in real raes of reurn; see Appendix 2 for deails. Noe ha real wages, P L /P C, peaked around 1977 a 1.75 and hen fell o 1.67 in They increased o 1.85 in 1989 and hen fell o 1.77 in 1994 and hen increased seadily o 2.10 in Real domesic prices, P D /P C, increased o 1.06 in 1974 and hen dropped o 0.97 a he end of he sample period. This drop is probably due o he adven of qualiy adjusmen of compuers in he 1980s. The real price of expors, P X /P C, flucuaes bu ends up close o uniy a he end of he sample period. The real price of impors, P M /P C, drops subsanially over he sample period, ending up a The real price of business secor capial services, P K /P C, increases o 1.52 in 1979 and hen decreases o 1.09 in I says in he range 1.00 o 1.75 for he res of he sample period, wih big drops during recession years, which were in 1982, 1991 and This is due o he falling balancing real rae of reurn for hose years. There are six quaniaive facors ha can be used o explain he real income ρ generaed by he business secor in year : The price of domesic producion (an aggregae of C+I+G) relaive o he price of consumpion in year, P D /P C ; The price of expors relaive o he price of consumpion in year, P X /P C ; The price of impors relaive o he price of consumpion in year, P M /P C ; The quaniy of labour used by he business secor in year, Q L ; The quaniy of capial used by he business secor in year, Q K and The level of echnology of he business secor in year. The formal model oulined in Appendix 1, based on he work of Diewer and Morrison (1986) and Kohli (1990), allows us o decompose he growh of real income from year 1 o, ρ /ρ 1, ino muliplicaive year o year conribuion facors α D, α X, α M, β L, β K and τ ha describe he effecs of changes in he six explanaory variables lised above going from year 1 o. The model oulined in Appendix 1 leads o he following equaion which decomposes he year o year growh in real income generaed by he

11 11 business secor, ρ /ρ 1, ino a produc of six year o year explanaory conribuion facors: 14 (3) ρ /ρ 1 = τ α D α X α M β L β K ; = 1962, 1963,...,2011. Thus if α D is greaer han one, his means ha he domesic price of oupu grew faser han he price of consumpion going from year 1 o and α D measures he conribuion of rising real domesic oupu prices o he growh in real income. Similarly, if α X is greaer han one, his means ha Canadian expor prices grew faser han he price of consumpion going from year 1 o and α X measures he conribuion of rising real expor prices o he growh in real income generaed by he Canadian business secor. However, if α M is greaer han one, his means ha Canadian impor prices did no increase as quickly as he price of consumpion going from year 1 o and α M measures he conribuion of falling real impor prices o he growh in real income generaed by he Canadian business secor. If β L is greaer han one, hen business secor labour inpu increased going from year 1 o and β L measures he conribuion of he increase in labour inpu o he growh in real income generaed by he Canadian business secor. Similarly, if β K is greaer han one, hen business secor capial services inpu increased going from year 1 o and β K measures he conribuion of he increase in capial inpu o he growh in real income generaed by he Canadian business secor. Finally, if τ is greaer han one, hen he efficiency of he Canadian business secor increased from year 1 o and τ measures he conribuion of he efficiency increase o he growh in real income generaed by he Canadian business secor. These year o year conribuion facors are lised in Table 4 along wih he (arihmeic) averages of hese conribuion facors over various ime periods in he las five rows of he Table. 15 Table 4: Business Secor Year o Year Growh in Real Income and Year o Year Conribuion Facors α X Year ρ /ρ 1 τ α D α M β L β K α XM 14 See he equaions in Appendix 1 in order o derive his equaion. All of he variables in equaion (3) can be idenified using he daa in Appendix The fifh row from he boom gives he average over he years and he remaining rows give he averages over he years , , and Noe ha he produciviy growh raes τ lised in Table 4 agree wih hose lised in Table 2.

12 A A A A A Looking a he sample (arihmeic) averages lised in he A62-11 row of Table 4, i can be seen ha he (gross) real income generaed by he Canadian business secor over he enire sample period grew a 3.82 percen per year over he 50 years The bigges conribuor o his growh was he growh of qualiy adjused labour inpu a 1.25 percenage poins per year. 16 Nex was capial services growh (1.08 percenage poins per year) followed by Toal Facor Produciviy growh, τ, which conribued on average 1.06 percenage poins per year and declines in real impor prices (0.41 percenage poins per year). Declines in real domesic oupu prices and real expor prices gave rise o negaive average conribuion facors, and percenage poins per year respecively. The las column in Table 4 gives he produc of he real expor and real impor price conribuion facors, α XM, defined as: (4) α XM α X α M. 16 This is he arihmeic average rae of produciviy growh which is greaer han he more accurae geomeric average rae of produciviy growh which was Due o he ease of compuaion, we work wih arihmeic average raes in Table 4.

13 13 Roughly speaking, α XM is a erms of rade conribuion facor; i gives he conribuion o real income growh of he combined effecs of real changes in he inernaional prices facing he Canadian business secor. 17 I can be seen ha he effecs of changing real inernaional prices are no negligible for Canada: on average, changing real expor and impor prices conribued 0.39 percenage poins per year o real income growh over he enire sample period. 18 However, for shorer periods, he effecs of changing real inernaional prices can be far more imporan in explaining changes in he real income generaed by he marke secor of an economy. Thus if we resric our aenion o he period , i can be seen by looking a he las row of Table 4 ha he effecs of improvemens in Canada s erms of rade are he mos imporan explanaory facor. Thus during his period, he average annual growh in he real income generaed by he Canadian business secor was 3.01 percen per year and he following facors explained his growh rae: decreases in he real price of impors (1.18), increases in qualiy adjused labour inpu (0.89), increases in capial services inpu (0.77) and improvemens in TFP (0.23). There were small negaive conribuors o marke secor real income growh during he naughs: decreases in he real price of domesically produced goods and services ( 0.005) and decreases in he real price of expors ( 0.113). Thus decreases in he real price of impors proved o be he mos imporan facor in explaining he growh in real income generaed by he marke secor during his period. Overall, he join effecs of changes in real expor and impor prices conribued abou 1.04 percenage poins per year on average o he growh of marke secor real income during he naughs, which was greaer han he conribuion of capial inpu growh over his period (which was 0.77 percenage poins per year on average). 19 Thus improvemens in he erms of rade largely compensaed for he poor produciviy performance during he naughs, leading o an overall reasonable rae of growh for he real income generaed by he Canadian business secor. The las four rows of Table 4 presen he various growh facors for 4 subperiods: The 12 golden years for he Canadian economy, , when he real income generaed by he business secor grew by 6.77% per year and TFP growh was a sellar 2.68% per year; The 18 dismal years for he Canadian economy, , characerized by sagflaion, oil shocks and rapidly increasing ax raes when he real income generaed by he business secor grew by 2.30% per year and TFP growh was only 0.25% per year; 17 Ulrich Kohli has poined ou ha his is a sligh abuse of erminology. Sricly speaking, he erms of rade is he price of expors over he price of impors and hence involves only wo prices. Our definiion of α XM involves hree prices: he price of expors, he price of impors and he price of domesic consumpion. Our erms of rade conribuion facor is he rae of change counerpar o Kohli s (2006; 50) rading gains facor. 18 Thus he conribuion of falling real impor prices ouweighs he effecs of falling real expor prices. 19 These resuls are very similar o he resuls obained for Ausralia using a similar framework by Diewer and Lawrence (2006); i.e., boh Ausralia and Canada have had very favourable changes in heir erms of rade in recen years which conribued grealy o real income growh during he naughs.

14 14 The 8 years in he nineies afer he recession of 1991, , when real income growh recovered o 4.04% per year and TFP growh also recovered o 1.70% per year and The 12 years in he presen cenury, , when TFP growh dropped off o 0.23% per year bu real income growh was sill reasonably srong a 3.01% per year due o he very srong conribuion made by falling real impor prices during his period, which conribued on average 1.18% per year o real income growh. The annual change informaion in Table 4 can be convered ino levels using equaions (38) in Appendix 1 (wih obvious exensions o muliple inpus and oupus). Thus le T, A D, A X, A M, B L, B K and A XM be he cumulaed producs of he annual link facors τ, α D, α X, α M, β L, β K and α XM respecively. Using hese definiions and cumulaing equaions (3) leads o he following equaion, which explains he cumulaive growh in real gross income generaed by he Canadian business secor relaive o he base year 1961: (5) ρ /ρ 1961 = T A D A X A M B L B K ; = 1962, 1963,..., The cumulaed variables ha appear in (5) above are repored in Table 5 below along wih he cumulaed erms of rade conribuion facor, A XM defined o be he produc of he wo cumulaed inernaional price facors, A X and A M. Table 5: Business Secor Cumulaed Growh in Real Income and Cumulaed Conribuion Facors Year ρ /ρ 1961 T A D A X A M B L B K A XM

15 Looking a he las row of Table 5, i can be seen ha he gross real income generaed by he business secor grew 6.20 fold over he years The main facors explaining his growh are growh of qualiy adjused labour inpu (cumulaive growh facor 1.85), growh of capial services or capial deepening (cumulaive growh facor 1.71), produciviy increases (cumulaive growh facor 1.67) and lower real impor prices (cumulaive growh facor 1.22). There were small negaive conribuions from declining real domesic oupu prices (cumulaive growh facor 0.97) and declining real expor prices (cumulaive growh facor.99). In recen years, he real prices of Canada s raw maerials expors have increased dramaically. However, hese increases do no show up in he A X column of Table 5; i.e., he overall real price of Canadian expors has remained relaively consan in recen years. This apparen conradicion can be explained by falling real prices for Canadian expors of manufacured goods. As already noed above, he effecs of falling real impor prices in recen years have been subsanial. The cumulaive conribuion facors lised in Table 5 are ploed in Char 1 below.

16 Char 1: Cumulaed Conribuion Facors ha Explain he Growh of Real Income Generaed by he Canadian Producion Secor T AD AX AM BL BK I can be seen ha labour, capial and Toal Facor Produciviy growh were he main conribuors o he generaion of real income growh over he period bu ha falls in impor prices were an imporan conribuory facor during he period Comparison wih he KLEMS Program Mulifacor Produciviy Esimaes As was menioned earlier, he Saisics Canada KLEMS program has recenly provided esimaes of he mulifacor produciviy growh for he Canadian business secor; see Baldwin, Gu and Yan (2007) and Baldwin and Gu (2007) for a descripion of he mehods used in his program. In secion 2, we explained ha our level of business secor Toal Facor Produciviy using our user cos framework ended up a in 2011 from is saring value of 1 in 1961 whereas he KLEMS Mulifacor business secor produciviy ended up a in In his secion, we will ry o deermine why our esimaes are so differen from he corresponding KLEMS program esimaes. Our measures of real business secor oupu, labour and capial services inpu are Q Y, Q L and Q K and our measure of he capial sock used by he business secor is Q KW. For convenience, hese measures are lised in Table 6 below. The KLEMS program provides index counerpars o our measures for he years in CANSIM Table , Series V , V , V and V respecively. The KLEMS program also provides nominal dollar esimaes for business secor oupu, labour inpu and capial services inpu for he years ; see CANSIM Table , Series V , V and V respecively. We use he saring 1961 values for he KLEMS value of business secor oupu, labour and capial inpu and conver he KLEMS consan dollar esimaes for oupu, labour and capial inpu ino 1961 consan dollar series and hese official KLEMS series are lised as Q YO, Q LO and Q KO in Table 6 below. The KLEMS daa base does no seem o have dollar esimaes for he value of

17 17 business secor capial socks, 20 so we use he KLEMS capial sock index Series V and conver i ino a 1961 consan dollar series using our esimae for he saring business secor capial sock, V 1961 KW. The resuling official series is lised as Q KWO in Table 6 below. Table 6: Our Esimaes of Business Secor Oupu Q Y, Labour Inpu Q L, Capial Services Q K, Capial Socks Q KW and he Corresponding Official Esimaes Q YO, Q LO, Q KO and Q KWO and Consan Dollar Paid Rens Q PR in 1961 Dollars (Millions) Year Q Y Q YO Q L Q LO Q K Q KO Q KW Q KWO Q PR Acually, his informaion is available in CANSIM Table