Changes in the Terms of Trade and Canada s Productivity Performance Revised April 14, 2008

Transcription

1 1 Changes in he Terms of Trade and Canada s Produciviy Performance Revised April 14, 2008 W. Erwin Diewer 1 Discussion Paper 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 46 years. In paricular, radiional gross income Toal Facor Produciviy (TFP) growh averaged 1.14 percenage poins per year over he period and when a ne income framework was used, TFP growh averaged 1.26 percenage poins per year. The focus of he sudy is on he real income generaed by he business secor of he Canadian economy. Two conceps of income are used: a gross concep ha includes depreciaion as a par of income and a more appropriae ne concep where depreciaion is excluded from income. In boh he gross and ne income frameworks, he 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, real income, erms of rade effecs, measuremen of capial, measuremen of invenory change, user coss, real ineres raes. 1 The financial assisance of Indusry Canada is graefully acknowledged. The auhor also hanks John Baldwin, Serge Coulombe, Wulong Gu, Ulrich Kohli, 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 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), Morrison and Diewer (1990) and Kohli (1990) (1991) (2003) (2004a) (2004b) (2006) (2007) 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 adap his mehodology and show how i can be used o measure he deerminans of growh in an economy s gross and ne real income. 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 was 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 However, 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. 2 Thus in secion 3, we measure he relaive conribuions of produciviy improvemens, changes in real expor and impor prices and 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 secions 1-4 of Appendix 1. However, his is no he end of he sory. GDP is an (imperfec) measure of producive poenial, no welfare. 3 For welfare measuremen purposes, i is generally conceded ha Ne Domesic Produc (NDP) is a beer measure of oupu, since invesmen ha jus mees depreciaion means ha sociey is no made any beer off from he viewpoin of susainable final consumpion possibiliies. Hence, in he second par of he paper, we subrac depreciaion off from gross invesmen and use consumpion plus sales o he nonbusiness secor plus ne invesmen plus he rade balance as our business secor oupu concep. Thus depreciaion will be reaed as an inermediae inpu in his model of producion. Secion 5 of Appendix 1 explains his real ne produc approach and adaps a ranslog model of producion based on he work of Diewer and Morrison (1986) and Kohli (1990) o his new model of marke secor real ne income generaion. 4 This 2 See for example Diewer and Morrison (1986). 3 For a more exensive discussion of he meris of GDP versus ne income, see Diewer (2006a). 4 For previous implemenaions of his model of real ne income o Japan and Ausralia, see Diewer, Mizobuchi and Nomura (2005) and Diewer and Lawrence (2006).

3 3 approach is implemened for he Canadian business secor in secion 4 of he main ex. The main deerminans of growh in real ne income generaed by he business or marke secor of he economy are: Technical progress or improvemens in Toal Facor Produciviy; Growh in domesic oupu prices or he prices of inernaionally raded goods and services relaive o he price of consumpion; and Growh in primary inpus. I urns ou ha produciviy growh becomes a more imporan facor for explaining real ne income growh compared o explaining real gross income growh. Also he imporance of capial deepening is grealy reduced in he ne income framework compared o he gross income framework. Somewha surprisingly, for he years , improvemens in he erms of rade made almos he same conribuion o real income growh as capial deepening in he gross income framework and in he ne income framework, he effecs of falling real impor prices conribued subsanially more o real income growh han capial deepening over he period Appendix 3 compares our mehodology for deermining he effecs of improvemens in he erms of rade on real income growh wih he mehodology worked ou by Kohli (2006). Appendix 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. Secion 5 concludes Oupu and Inpu Aggregaes and Convenional Produciviy Growh for Canada In Appendix 2, we consruced price and quaniy series for 11 ne oupus and 8 primary inpus for he business secor of he Canadian economy for he years The 11 ne oupus are: Domesic consumpion (excluding marke residenial rens and he services of owner occupied housing); Governmen invesmen; 5 The final secion of Appendix 1 has some new maerial on how he real ne income model used in he presen paper can be exended from a single producion secor o he case of many indusries. Also he final secion of Appendix 4 has some suggesions for improving he measuremen of produciviy by Saisics Canada bu hese recommendaions may be useful for oher official produciviy programs. The nex revision of he Sysem of Naional Accouns 1993 will inroduce capial services ino he accouns so ha price and quaniy decomposiions of primary inpus will be possible, which will grealy faciliae he measuremen of produciviy by secor. However, he inroducion of capial services ino he main producion accouns will no be easy and i will be necessary for saisical agencies o do a considerable amoun of preparaory work.

4 4 Business secor invesmen in residenial srucures; Business secor invesmen in nonresidenial srucures; Business secor invesmen in machinery and equipmen; Invenory change; Sales of goods and services by he business secor o he nonmarke secor less sales of goods and services from he nonmarke secor o he business secor; Expors of goods; Expors of services; Impors of goods (he quaniies are indexed wih a minus sign) and Impors of services (he quaniies are indexed wih a minus sign). The eigh primary inpus ino he business secor are: The labour services of workers wih primary or secondary educaion The labour services of workers wih some or compleed pos secondary cerificae or diploma; The labour services of workers wih a universiy degree or above; 6 The sock of machinery and equipmen available o he business secor a he sar of each year; The saring sock of business secor nonresidenial srucures; The sock of nonagriculural, nonresidenial land used by he business secor; The sock of agriculural land used by he business secor and The saring socks of invenories used by he business secor. As is explained in Appendix 2, user cos prices for he las five primary 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. All of he price and quaniy series for he above 19 oupus produced and inpus used by he Canadian business secor are lised in Appendix 2. In his secion, we will aggregae he above ne oupus and primary inpus ino D, domesic oupu, equal o an aggregae of he firs seven ne oupus lised above; X, expors equal o an aggregae of expors of goods and services; M, impors equal o an aggregae of impors of goods and services; L, labour services equal o an aggregae of he hree ypes of labour and K, capial services equal o an aggregae of he five ypes of capial services. Once hese aggregaes have been consruced, we furher aggregae he hree ne oupus, D+X M, ino real gross domesic produc Y and aggregae he wo inpus, L and K, ino domesic inpu Z and finally consruc a convenional measure of produciviy Y/Z. The aggregaions were performed using chained Törnqvis price indexes. 7 The resuls are lised in Tables 1 and 2 below. Table 1: Prices of Canadian Business Secor Oupu and Inpu Aggregaes 6 These hree ypes of labour inpu are aken direcly from Saisics Canada recen KLEMS program; see Baldwin, Gu and Yan (2007; 26-27) for a descripion of hese daa. 7 More specifically, he chained Divisia opion in Shazam was used o do he aggregaions.

5 5 Year P C P D P X P M P L P K P Y P Z

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 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 : 8 (1) T Q Y /Q Z ; = 1961,..., Produciviy growh for year, τ, is defined as he produciviy level in year divided by he previous year s produciviy level: (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 This is also known as Mulifacor Produciviy or Toal Facor Produciviy.

7 The average rae of TFP growh over he 45 years is 1.14% per year, 9 which is much higher han he 0.5 o 0.7% per year range ha Diewer and Lawrence (2000) found over he period The presen 1.14% average rae of TFP growh can also be compared wih Saisics Canada s recen KLEMS program average Mulifacor Produciviy Growh over he same years of 0.43% per year, 10 which is a raher subsanial difference! In Appendix 4 below, we aemp o deermine why our resuls are so differen from he official Saisics Canada resuls. 11 Over he golden years , TFP growh averaged 2.73% per year; over he dismal years, , TFP growh averaged only 0.25% per year bu over he remainder of 9 This rae of TFP growh is reasonably close 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). 10 See CANSIM II series V , Canada, Mulifacor Produciviy, Business Secor, able , Mulifacor Produciviy, Value Added, Capial Inpu and Labour Inpu in he Aggregae Business Secor and Major Sub-Secors. Comparing levels of TFP wih he saring level being 1 in 1961, our TFP ended up a 1.65 in 2006 whereas KLEMS Mulifacor Produciviy ended up a 1.20 in This is a very subsanial difference. 11 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 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. Our measures of labour inpu were idenical and i urned ou ha he average rae of growh of our business secor value added measure was very close o he corresponding KLEMS average growh rae. The capial services growh raes differed subsanially.

8 8 he nineies, , TFP growh nicely recovered o average a very respecable 1.46% per year. During he naughs, , TFP growh again fell off o average only 0.34% per year. There were wo recen poor produciviy growh years, 2001 and 2003, where drops of 1.09% and 3.68% occurred and if hese years are excluded, he average TFP growh rae during he remaining years of he naughs is 1.43% per year. Hopefully he Canadian produciviy recovery since he recession of 1991 is no a saisical mirage and i will coninue ino he fuure. 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 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

9 Thus he gross real income generaed by he Canadian business secor has grown from $27,683 million dollars worh of 1961 consumpion bundles in 1961 o $163,864 million in 2006, a 5.92 fold increase. Looking a he change in real inpu and oupu prices, he real price of domesic oupu has fallen o.969 imes he saring level (due o he fac ha machinery and equipmen prices have risen less rapidly han he price of consumpion)

10 10 and he real price of expors has fallen slighly o.997 imes he saring level. However, he real price of impors has fallen subsanially o.790 imes he saring level. This probably reflecs he China facor ; i.e., he growh of lower priced impors from Asia in recen years. The qualiy adjused real wages of business secor workers have risen o 1.74 imes heir iniial 1961 levels. The real price of capial services has risen 1.78 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. 12 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 business secor, ρ /ρ 1, ino a produc of six year o year explanaory conribuion facors: 13 (3) ρ /ρ 1 = τ α D α X α M β L β K ; = 1962, 1963,...,2006. 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 if α M is greaer han one, his means ha Canadian impor prices did no 12 The volailiy of he real price of capial services reflecs he fac ha we have used balancing real raes of reurn in our user coss and hese real raes are subjec o a considerable amoun of measuremen error. One would expec he aggregae real price of capial services o decline, reflecing he decline in he real price of machinery and equipmen, bu his decline is offse by a large increase in he real price of land services. 13 See equaions (42), (51) and (56) in Appendix 1 in order o derive his equaion. All of he variables in equaion (3) can be idenified using he daa in Appendix 2.

11 11 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 averages of hese conribuion facors in he las wo rows of he Table. 14 Table 4: Business Secor Year o Year Growh in Real Income and Year o Year Conribuion Facors Year ρ /ρ 1 τ α D α X α M β L β K α XM The fifh row from he boom gives he average over he years and he remaining rows give he averages over he years , , and The careful reader will noice ha he produciviy growh raes τ lised in Table 4 do no quie agree wih hose lised in Table 2. The reason for hese small differences is ha when calculaing τ in Table 4, he inpu aggregae is a direc Törnqvis quaniy index whereas in Table 2, he inpu aggregae was an implici quaniy index; i.e., he value of inpus was deflaed by he Törnqvis inpu price index.

12 A A A A A Looking a he sample averages lised in he fifh las 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 4.10 percen per year over he 46 years The bigges conribuor o his growh was he growh of qualiy adjused labour inpu a 1.6 percenage poins per year. Nex was Toal Facor Produciviy growh, τ, which conribued on average 1.14 percenage poins per year, followed by capial services growh (1.11 percenage poins per year) and declines in real impor prices (0.28 percenage poins per year). Declines in real domesic oupu prices and real expor prices gave rise o negaive average conribuion facors, 0.07 and 0.03 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. 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

13 13 facing he Canadian business secor. 15 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 0.23 percenage poins per year o real income growh over he enire sample period. 16 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 become almos as imporan as he effecs of capial deepening; i.e., during his period, he average annual growh in he real income generaed by he Canadian business secor was 4.07 percen per year and he following facors explained his growh rae: decreases in he real price of impors (1.58), increases in qualiy adjused labour inpu (1.38), increases in capial services inpu, 1.19) and improvemens in TFP (0.34). 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 ( 0.05) and decreases in he real price of expors ( 0.42). 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 1.14 percenage poins per year on average o he growh of marke secor real income during he naughs, which was very close o he conribuion of capial deepening over his period (which was 1.19 percenage poins per year on average). 17 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 6.60% per year and TFP growh was a sellar 2.73% 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 2.53% per year and TFP growh was a disappoining 0.25% per year; The 8 years in he nineies afer he recession of 1991, , when real income growh recovered o 3.94% per year and TFP growh also recovered o 1.46% per year and The 7 years in he presen cenury, , when TFP growh dropped off o 0.34% per year bu real income growh was sill srong a 4.07% per year due o he very srong conribuion made by falling real impor prices during his period, which conribued on average 1.58% per year o real income growh. 15 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. See Appendix 3 for a discussion of he differences beween our approach and ha of Kohli. 16 Thus he conribuion of falling real impor prices ouweighs he effecs of falling real expor prices. 17 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 annual change informaion in Table 4 can be convered ino levels using equaions (46) 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 5.92 fold over he years The main facors explaining his growh are growh of qualiy adjused labour inpu (cumulaive growh facor 2.04), produciviy increases (cumulaive growh facor 1.65), growh of capial services (cumulaive growh facor 1.65) and lower real impor prices (cumulaive growh facor 1.13). There were negaive conribuions from declining real domesic oupu prices (cumulaive growh facor 0.97) and declining real expor prices (cumulaive growh facor.98). 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. As is noed in secion 5 of Appendix 1, he income concep used in his secion is biased upwards. The problem is ha depreciaion paymens are par of he user cos of capial for each asse bu depreciaion does no provide households wih any susainable purchasing power. Hence he measure of real income ρ ha is used in his secion is oversaed. In he following secion, we implemen he ne real income model ha is described in more deail in secion 5 of Appendix Explaining Real Income Growh Generaed by he Canadian Business Secor: he Ne Oupu Approach

16 16 The oversaemen of income problem ha is implici in he approach used in he previous secion can readily be remedied: all we need o do is o ake he user cos formula for an asse ha has invesmen price P I in year and decompose i ino wo pars: One par ha represens depreciaion and foreseen obsolescence, δp I K, and The remaining par ha is he reward for posponing consumpion, r P I K. The depreciaion par δp I K, will be removed from he user cos and reaed as an inermediae inpu as an offse o gross invesmen. We now explain his raher simple idea in more deail below. In our empirical work hus far (described in deail in Appendix 2), our user coss ook he following form: (6) U = (r + δ + τ B )P I where r is he balancing period real rae of ineres, δ is a geomeric depreciaion rae for period, τ B is an appropriae business axaion rae on he asse (including propery axes if applicable) and P I is he period invesmen price for he asse. However, in he ne produc approach o he measuremen of income, 18 we spli up each (gross produc) user cos imes he beginning of he period sock K ino he depreciaion componen δ P I K and he remaining erm (r +τ B )P I K and we regard he second erm as a genuine income componen bu we rea he firs erm as an inermediae inpu cos for he business secor and rea i as an offse o gross invesmen made by he business secor during he year under consideraion. Thus in he presen secion, our new aggregae for domesic oupu will aggregae he same C+I+G componens as before, bu now we add he depreciaion series for business srucures and for machinery and equipmen as negaive oupus of he business secor. As noed above, he machinery and equipmen and nonresidenial srucures user coss are also changed since he depreciaion erms are now omied. Thus he new invesmen aggregae I is a ne invesmen aggregae (gross invesmen componens were indexed wih a posiive sign in he aggregae and depreciaion componens were indexed wih a negaive sign in he aggregae) and he new capial services aggregae is now a reward for waiing capial services aggregae. 19 The above changes mean ha our aggregae daa series have changed somewha. The new ne produc counerpars o he old gross produc Tables 1-3 are presened below as Tables See Diewer (2006a) for a more deailed discussion of he ne income approach o income measuremen. 19 This approach seems o be broadly consisen wih an approach advocaed by Rymes (1968) (1983), who sressed he role of waiing services: Second, one can consider he waiing or absinence associaed wih he ne reurns o capial as he nonlabour primary inpu. T.K. Rymes (1968; 362). Denison (1974) also advocaed a ne produc approach o produciviy measuremen. 20 The TFP growh raes τ in Tables 7 and 9 differ slighly because when calculaing τ in Table 9, he inpu aggregae is a direc Törnqvis quaniy index whereas in Table 7, he inpu aggregae was an implici quaniy index; i.e., he value of inpus was deflaed by he Törnqvis inpu price index. Boh he direc and implici Törnqvis indexes are superlaive and hence will generally approximae each oher very closely; see Diewer (1978).

17 17 Table 6: Prices of Canadian Business Secor (Ne) Oupu and Inpu Aggregaes Year P C P D P X P M P L P K P Y P Z

18 Comparing Table 6 wih Table 1, we see ha he 2006 price of domesic absorpion, P D, has increased o 6.07 from is earlier 2006 gross approach level of This is due o he fac ha ne invesmen is considerably smaller han gross invesmen and so he relaively low inflaion price of machinery and equipmen ges a much smaller weigh in ne domesic absorpion compared o is weigh in gross domesic absorpion. The oher sriking difference beween Tables 1 and 6 is ha he price of waiing services, P K, in Table 6 grew 17.4 fold over he sample period whereas he price of radiional capial services, P K, in Table 1, grew only 10.5 fold. This difference in growh raes is explained by he fac ha he price of machinery and equipmen services ges a much lower weigh in he Table 6 capial services aggregae compared o is weigh in he Table 1 capial services aggregae because he corresponding user cos for he ne concep of capial services now excludes he very large depreciaion erm in he ne user cos. Thus he price of agriculural land and business nonagriculural land ges a much higher weigh in he ne user cos compared o he gross concep user cos. 21 However, even hough he land componens now ge a much higher weigh in weighing services compared o machinery and equipmen, he overall price increase in inpu prices has only increased o 11.8 fold (compared o he gross oupu model 10.4 fold increase in inpu prices) over he sample period due o he fac ha he imporance of capial services dramaically shrinks relaive o labour services in he ne oupu framework. Table 7: Quaniies of Canadian Business Secor Ne 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 21 From Table 10 in Appendix 2, we esimae ha he price of agriculural land increased 18.6 fold and he price of business nonagriculural land increased 48.5 fold over he period For comparison purposes, he price of residenial land increased 78.1 fold over his period.