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A Canadian Business Sector Data Base and New Estimates of Canadian TFP Growth November 24, 2012 W. Erwin Diewert1 and Emily Yu,2 Discussion Paper 12-04, Department of Economics, University of British Columbia, Vancouver, Canada, V6T 1Z1. Email: diewert@econ.ubc.ca Abstract Using new data from Statistics Canada, the paper shows that the productivity performance of the business sector of the Canadian economy has been reasonably satisfactory over the past 51 years. In particular, traditional gross income Total Factor Productivity (TFP) growth averaged 1.026 percentage points per year over the period 1961-2011. The focus of the study is on the real income generated by the business sector of the Canadian economy. The growth of quality adjusted labour input growth was the main driver of growth in real income followed by TFP growth, followed by growth in capital input and then by falling real import prices. However, in recent years, the contribution of falling real import prices turned out to be more than twice as important as capital deepening. The study encountered many data problems which should be addressed in future work on Canadian business sector productivity performance. Journal of Economic Literature Classification Numbers C43, C67, C82, D24, E22, E43. Keywords Total Factor Productivity, Multifactor Productivity, real income, terms of trade effects, measurement of capital, measurement of inventory change, user costs, real interest rates.

1 Department of Economics, University of British Columbia and the School of Economics, University of New South Wales. The financial assistance of the SSHRC is gratefully acknowledged. The first author also thanks Shutao Cao, Serge Coulombe, Wulong Gu, Ulrich Kohli, Sharon Kozicki, Danny Leung, Alice Nakamura, Andrew Sharpe and Jianmin Tang for helpful comments. None of the above are responsible for any views expressed in this paper. 2 Department of Foreign Affairs and International Trade, Government of Canada

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1. Introduction Many observers have noted that an improvement in a country’s terms of trade has effects that are similar to an improvement in a country’s productivity growth. However, it is not straightforward to work out the exact magnitude of each source of gain. Diewert (1983), Diewert and Morrison (1986), Diewert, Mizobuchi and Nomura (2005), Diewert and Lawrence (2006), Morrison and Diewert (1990) and Kohli (1990) (2003) (2004) (2006) developed production theory methodologies which enable one to obtain index number estimates of the contribution of each type of gain. In Appendix 1 below, we outline the Diewert, Mizobuchi and Nomura (2005) and Diewert and Lawrence (2006) methodology and in sections 2-4 of the main text, we apply this methodology to the business sector of the Canadian economy over the years 1961-2011. Appendix 2 below describes how the Canadian business sector data were developed from Statistics Canada sources. Section 2 of the main text aggregates up the data from Appendix 2 and develops conventional measures of Canadian business sector Total Factor Productivity for the years 1961-2011. Productivity growth, while perhaps the most important source of growth in living standards, is not the entire story. If a country’s export prices increase more rapidly than its import prices, then it is well known that this has an effect that is similar to a productivity improvement. Thus in section 3, we measure the relative contributions of productivity improvements, changes in real export and import prices and the growth of labour and capital input to the growth of (gross) real income generated by the business sector in Canada using the methodology explained in Appendix 1. Section 4 compares our estimates of TFP growth with the business sector Multifactor Productivity Growth estimates recently developed by the Statistics Canada KLEMS program; see Baldwin, Gu and Yan (2007) for a description of the methodology used in the KLEMS program. It should be noted that the Statistics Canada KLEMS program uses detailed industry data in order to construct TFP estimates by industry and then these industry estimates are aggregated up to give aggregate business sector estimates of TFP growth, whereas our approach uses aggregate estimates for the outputs produced and inputs used for the entire business sector. Thus our estimates may suffer from some aggregation bias. Section 5 concludes. 2. Output and Input Aggregates and Conventional Productivity Growth for Canada In Appendix 2, we constructed price and quantity series for 22 net outputs, 12 types of labour input and 17 types of capital input for the business sector of the Canadian economy for the years 1961-2011. The 22 net outputs are:

• Q1: Domestic consumption (excluding market residential rents and the services of owner occupied housing);

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• Q2: Real sales of goods and services by the business sector to the nonmarket sector less real sales of goods and services from the nonmarket sector to the business sector;

• Q3: Government investment; • Q4: Business sector investment in residential structures; • Q5: Business sector investment in machinery and equipment; • Q6: Business sector investment in nonresidential structures; • Q7: Inventory change; • Q8: Exports of agricultural and fish products; • Q9: Exports of energy products; • Q10: Exports of forest products; • Q11: Exports of industrial goods and materials (excluding energy and forest

product exports); • Q12: Exports of machinery and equipment (excluding automotive products); • Q13: Exports of automotive products; • Q14: Exports of other consumer goods (excluding automotive products); • Q15: Exports of services; • Q16: Imports of agricultural and fish products; • Q17: Imports of energy products; • Q18: Imports of industrial goods and materials (including imports of forest

products but excluding imports of energy products); • Q19: Imports of machinery and equipment (excluding automotive products); • Q20: Imports of automotive products; • Q21: Imports of other consumer goods and • Q22: Imports of services.

The price indexes that correspond to the above quantity indexes Qn

t are denoted as Pnt for

n = 1,...,22 and t = 1961,...,2011 and they are listed in Appendix 2. We define the price of our consumption aggregate as PC

t ≡ P1t. We form a domestic output aggregate QD

t with corresponding price PD

t by aggregating Q1t-Q7

t.3 Similarly, we form an export aggregate QX

t with corresponding price PXt by aggregating Q8

t-Q15t and an import aggregate QM

t with corresponding price PM

t by aggregating Q16t-Q22

t.4 Once these indexes have been constructed, a business sector aggregate output or real value added index QY

t is constructed as an aggregate of QD

t, QXt and −QM

t. The corresponding aggregate output price index is PY

t.5 The price indexes PCt, PD

t, PXt, PM

t and PYt are listed in Table 1 below

and the corresponding quantity indexes QDt, QX

t, QMt and QY

t are listed in Table 2 below. Statistics Canada has constructed detailed labour input data for the Canadian business sector for 36 types of labour for the years 1961-2010 in CANSIM Table 3830024 which

3 PD

t is the Törnqvist price index of P1t-P7

t and QDt is the corresponding implicit quantity index.

4 PXt and PM

t are constructed as Törnqvist price indexes and QXt and QM

t are the corresponding implicit quantity indexes. 5 PY

t is a Törnqvist price aggregate of PDt,PX

t,PMt (with corresponding quantities QD

t,QXt,−QM

t) and QYt is

the implicit quantity index that matches up with PYt.

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we will make use of in this study. Labour input is classified according to a four way classification in Table 3830024:

• By education level E. There are 3 categories in this classification: E=1 corresponds to Primary or Secondary Education; E=2 corresponds to Some or Completed Post-Secondary Education and E=3 corresponds to University Degrees or Above.

• By age of worker A. There are 3 categories in this classification: A=1 corresponds to 15-34 years old; A=2 corresponds to 35-54 years old and A=3 corresponds to 55 years old and over.

• By sex S. There are 2 categories in this classification: S=1 corresponds to a male worker and S=2 corresponds to a female worker.

• By type of employment T. There are 2 categories in this classification: T=1 corresponds to a paid worker and T=2 corresponds to a self employed worker.

Thus Table 3830024 provides annual hours and total compensation data for 3x3x2x2 or 36 types of worker in the Canadian business sector for the years 1961-2010. We aggregated over the age groups using Fisher chained indexes in order to form 12 price and quantity series for labour, PL1-PL12 and QL1-QL12. These series were extended to 2011 using various Statistics Canada series as is explained in Appendix 2. These 12 price and quantity series for the various types of labour were aggregated into aggregate quality adjusted business sector labour input QL

t with corresponding price index PLt.6 PL

t is listed in Table 1 and QL

t is listed in Table 2. Using information on business sector capital stocks in CANSIM Table 310003, In Appendix 2, we were able to form estimates for business sector beginning of the year capital stocks for the following 14 types of reproducible capital asset:

• QK1: Office furniture; • QK2 : Agricultural machinery; • QK3 : Industrial machinery; • QK4 : Automobiles; • QK5 : Trucks; • QK6 : Other transport equipment; • QK7 : Other machinery and equipment; • QK8 : Computers; • QK9 : Telecommunications equipment; • QK10 : Software; • QK11 : Industrial buildings; • QK12 : Commercial buildings; • QK13 : Institutional buildings; • QK14 : Engineering construction.

6 QL

t is now a direct Törnqvist quantity aggregate of QL1t-QL12

t with PLt defined as the corresponding

implicit price index. These index number conventions are necessary in order to apply the translog methodology explained in Appendix 1.

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Using Statistics Canada Balance Sheet information (and other sources), we were able to construct business sector beginning of the year capital stock inputs for inventories (QK15), agricultural land (QK16) and business nonagricultural land (QK17). We also constructed estimates for the corresponding stock prices, PKn

t, for n = 1,...,17 and t = 1961-2011; see Appendix 2. As is explained in Appendix 2, user cost prices Un

t for the 17 capital stock inputs were constructed, using balancing or endogenous real rates of return that made the value of net output produced by the business sector equal to the value of primary inputs used by the business sector.7 There is a problem with our capital input data in that the software series starts only in 1981. Our translog methodology does not work when an input is equal to 0 in one period and positive in a subsequent period. Thus we aggregated the software asset with the computer asset; i.e., we constructed a Fisher capital services aggregate8 of (U8

t,U10t) and

(QK8t,QK10

t) to replace the individual services for these two assets. We then constructed a business sector capital services aggregate QK

t by aggregating the 16 types of capital services using direct Törnqvist quantity aggregation. The corresponding capital services aggregate price is denoted as PK

t and is listed in Table 1 while QKt is listed in Table 2

below. Once the labour and capital aggregates have been constructed, we can construct a direct Törnqvist quantity input aggregate of QL

t and QKt which we denote by QZ

t, which is listed in Table 2. The corresponding implicit aggregate input price index, PZ

t, is listed in Table 1. Table 1: Prices of Canadian Business Sector Output and Input Aggregates Year t PC

t PDt PX

t PMt PL

t PKt PY

t PZt

1961 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1962 1.00617 1.00659 1.02992 1.05787 1.03794 1.03913 0.99856 1.03835

7 User costs for capital inputs are meant to approximate what it would cost a business to rent or lease the services of the asset for the accounting period under consideration. The use of user costs in multifactor productivity studies dates back to the pioneering work of Jorgenson and Griliches (1967). Basically, a user cost consists of the sum of four terms: (1) the interest that could be earned if the asset were simply sold at the beginning of the period,; (2) depreciation; (3) taxes that are assessed on the use of the asset plus the appropriate business income tax rate and (4) expected capital gains (or minus losses) that the asset might accrue over the accounting period. With respect to (1), we chose the interest rate to be the balancing rate of return that makes the value of inputs equal to the value of outputs; i.e., we chose an endogenous rate of return rather than an exogenous one. With respect to (4), we chose to value beginning and end of period capital stocks at the average investment prices of the period, which eliminated the capital gains term. There are problems associated with the estimation of expected capital gains and so our strategy avoids these problems. Jorgenson (1989) and his coworkers estimate expected capital gains (or losses) by actual gains (of losses). This strategy tends to lead to negative user costs for land assets and hugely positive user costs for computers (when statistical agencies assign large depreciation rates to computers). Statistics Canada uses the Jorgenson methodology. For further discussion on problems with constructing user costs, see Harper, Berndt and Wood (1980), Diewert (1980) (2005a) , Schreyer (2009) and Inklaar (2010). 8 Fisher (1922) aggregation can deal with 0 quantities; see Diewert (1980; 498-501).

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1963 1.01956 1.02135 1.04054 1.09648 1.07171 1.15465 1.00652 1.09996 1964 1.02317 1.03169 1.05692 1.10526 1.11443 1.21329 1.01867 1.14810 1965 1.03598 1.05587 1.07980 1.10214 1.18778 1.26095 1.04940 1.21265 1966 1.07430 1.09618 1.12451 1.11930 1.26637 1.34035 1.09696 1.29150 1967 1.10738 1.12882 1.15421 1.14426 1.34823 1.26412 1.13097 1.31788 1968 1.14786 1.16368 1.20119 1.16726 1.43529 1.33957 1.17273 1.40076 1969 1.18479 1.20467 1.23088 1.19648 1.54823 1.36588 1.21411 1.48226 1970 1.21483 1.24199 1.26710 1.21965 1.64546 1.40943 1.25562 1.55976 1971 1.24210 1.28773 1.28552 1.24798 1.76322 1.45186 1.29829 1.64947 1972 1.29301 1.34785 1.33325 1.27498 1.91504 1.53498 1.36563 1.77569 1973 1.38394 1.45887 1.51489 1.35954 2.09632 2.01445 1.50883 2.06965 1974 1.58215 1.67355 1.91283 1.64641 2.42435 2.40403 1.75214 2.42165 1975 1.81969 1.89101 2.16694 1.89029 2.80455 2.20560 1.96977 2.57725 1976 1.90416 1.99827 2.29702 1.92853 3.22888 2.38963 2.11056 2.90675 1977 2.02765 2.12535 2.50231 2.17241 3.54148 2.71724 2.21606 3.22786 1978 2.19006 2.29116 2.73837 2.41667 3.71108 3.05188 2.37354 3.46737 1979 2.40319 2.51056 3.20786 2.73027 3.97716 3.65969 2.63294 3.87685 1980 2.69102 2.79419 3.73464 2.97957 4.38358 3.79070 3.00323 4.17210 1981 2.89817 3.05927 3.99821 3.26618 4.92831 3.71089 3.25853 4.45740 1982 3.16581 3.31615 4.08926 3.43918 5.46977 3.46038 3.49392 4.65741 1983 3.40715 3.50995 4.15051 3.42324 5.67612 4.30538 3.72144 5.15751 1984 3.56365 3.64735 4.29656 3.58225 5.97769 4.82321 3.85122 5.56225 1985 3.67559 3.75645 4.38071 3.67711 6.29468 5.09990 3.95557 5.86656 1986 3.75577 3.84444 4.37060 3.74437 6.48667 4.99177 4.01524 5.92882 1987 3.85242 3.95329 4.45792 3.69150 6.72738 5.59267 4.18608 6.33075 1988 3.95781 4.06089 4.47080 3.60108 7.19929 5.58832 4.34753 6.60219 1989 4.07115 4.17642 4.56005 3.59364 7.54058 5.46841 4.51068 6.74673 1990 4.30215 4.33491 4.52868 3.64367 7.85340 5.34227 4.64745 6.86966 1991 4.53970 4.45950 4.37107 3.57992 8.22512 4.63500 4.75245 6.75605 1992 4.59854 4.50278 4.49573 3.72567 8.41018 5.11800 4.77305 7.08515 1993 4.68858 4.58490 4.69389 3.92460 8.40036 5.29335 4.83888 7.16161 1994 4.71799 4.65944 4.97322 4.16089 8.33127 6.11925 4.91530 7.50346 1995 4.73527 4.69157 5.29132 4.27688 8.49758 6.54938 5.04377 7.79354 1996 4.83325 4.74750 5.32097 4.22185 8.61170 6.88983 5.15196 8.01251 1997 4.91285 4.80627 5.32718 4.23677 8.91603 6.78040 5.20713 8.13610 1998 4.97834 4.87196 5.31558 4.37960 9.19622 6.68674 5.17039 8.25245 1999 5.06934 4.93553 5.3787 4.36044 9.43856 7.13227 5.28780 8.59284 2000 5.20684 5.04961 5.71039 4.44227 9.91534 8.06215 5.55310 9.28700 2001 5.36470 5.16717 5.80311 4.58416 10.20478 7.97327 5.63050 9.40991 2002 5.43364 5.24828 5.68895 4.61494 10.37528 8.59389 5.62481 9.78947 2003 5.57127 5.32455 5.64768 4.31493 10.58453 8.39331 5.88407 9.81693 2004 5.65242 5.41524 5.78629 4.20643 10.89676 9.24512 6.13937 10.38008 2005 5.77665 5.53128 5.95233 4.15583 11.37321 9.79203 6.40068 10.89866 2006 5.87995 5.66176 5.97500 4.11704 11.91346 9.77832 6.59048 11.19634 2007 5.98858 5.79781 6.03062 4.01439 12.30606 10.05555 6.86085 11.54442 2008 6.15649 5.97473 6.64397 4.24350 12.62162 10.72831 7.21870 12.03461 2009 6.18318 6.04400 5.99089 4.28278 12.84741 8.71005 6.93473 11.19818 2010 6.25491 6.09382 6.12294 4.10323 13.03350 9.76371 7.20209 11.80370 2011 6.39168 6.21545 6.55859 4.17485 13.43103 10.82140 7.51572 12.52343

Note that we have also listed the price of our household consumption aggregate, PC

t, in Table 1, which will play a role in subsequent sections. The (total factor or multifactor) productivity level in year t of the Canadian business sector Tt can be defined as the aggregate year t output, QY

t divided by aggregate year t input, QZt:9

(1) Tt ≡ QY

t/QZt ; t = 1961, ..., 2011.

Total Factor Productivity (TFP) growth for year t, τt, is defined as the productivity level in year t divided by the previous year’s productivity level:

9 See definition (34) in Appendix 1.

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(2) τt ≡ Tt/Tt−1 ; t = 1962, ..., 2011. Table 2 lists the quantities that match up to the prices in Table 1 and it also lists productivity levels and growth rates. Table 2: Quantities of Canadian Business Sector Output and Input Aggregates, TFP Levels and TFP Growth Rates Year t QD

t QXt QM

t QLt QK

t QYt QZ

t Tt τ t

1961 30398 6867 −7897 19240 10128 29368 29368 1.00000 0 1962 32414 7195 −8033 20049 10326 31585 30375 1.03984 1.03984 1963 34157 7832 −8031 20506 10613 34008 31120 1.09283 1.05096 1964 36431 9105 −8989 21372 11091 36591 32466 1.12706 1.03132 1965 40024 9418 −10180 22321 11655 39269 33983 1.15556 1.02529 1966 43167 10696 −11579 23452 12450 42286 35917 1.17734 1.01885 1967 43510 11827 −12306 23822 13105 43046 36941 1.16526 0.98974 1968 45235 12910 −13527 23864 13515 44645 37378 1.19445 1.02504 1969 48343 13802 −15377 24366 13986 46806 38338 1.22087 1.02212 1970 48289 15211 −15293 24395 14513 48260 38850 1.24222 1.01749 1971 50936 15929 −16480 24836 14953 50452 39711 1.27050 1.02276 1972 54541 17257 −18892 25469 15415 53041 40792 1.30027 1.02343 1973 61382 19008 −21754 26868 16106 58832 42891 1.37169 1.05492 1974 67244 18347 −23977 27717 17037 61727 44662 1.38211 1.00760 1975 65767 16951 −23228 27534 18122 59494 45471 1.30840 0.94667 1976 69516 18390 −24774 27417 18769 63195 45885 1.37724 1.05262 1977 72993 19678 −24836 27616 19366 67878 46601 1.45657 1.05760 1978 74955 21544 −26197 28636 20037 70536 48284 1.46085 1.00293 1979 80182 22467 −28092 30208 20912 74698 50730 1.47244 1.00794 1980 79002 22548 −28715 31015 22012 73053 52586 1.38920 0.94347 1981 82000 23012 −30716 31669 23302 74433 54414 1.36792 0.98468 1982 72384 22882 −25710 29737 23850 70175 52644 1.33300 0.97448 1983 76539 24326 −28444 29747 24016 73155 52786 1.38589 1.03967 1984 81657 28444 −33270 30714 24312 78122 54090 1.44428 1.04213 1985 87008 29938 −35548 31892 24809 82738 55787 1.48311 1.02689 1986 90012 31456 −37965 33124 25343 85019 57578 1.47658 0.99559 1987 96002 32933 −39889 34682 26064 90559 59880 1.51234 1.02422 1988 102460 35371 −45163 36105 27136 94670 62340 1.51861 1.00415 1989 106238 35434 −47820 36972 28278 96089 64243 1.49572 0.98493 1990 104078 37556 −48551 36814 29056 95610 64682 1.47816 0.98826 1991 98192 38167 −49281 35445 29504 90121 63394 1.42159 0.96173 1992 100685 40921 −51473 35000 29544 93349 62887 1.48441 1.04418 1993 100614 45382 −55461 35683 29642 94373 63765 1.48001 0.99704 1994 105514 51076 −60606 37145 30070 100395 65766 1.52655 1.03145 1995 107894 55452 −64385 38163 30529 103938 67266 1.54518 1.01220 1996 110521 58646 −67340 39243 31132 107231 68949 1.55523 1.00651 1997 118530 63457 −77378 40501 32269 111367 71275 1.56249 1.00467 1998 122860 69086 −81755 41680 33566 117544 73645 1.59610 1.02151 1999 127598 76337 −88261 43103 34865 123965 76284 1.62503 1.01813 2000 134789 83350 −95661 44563 35944 131753 78781 1.67240 1.02915 2001 135351 80654 −90649 45096 36583 133537 79903 1.67124 0.99931 2002 143444 81599 −92347 45811 36720 140604 80788 1.74041 1.04139 2003 145573 79268 −96341 46610 37380 137165 82214 1.66839 0.95862 2004 154248 83281 −104558 48181 38111 142907 84524 1.69074 1.01339 2005 163288 84847 −112552 48777 39392 146935 86293 1.70274 1.00710 2006 171384 85213 −118273 49653 41010 150603 88649 1.69887 0.99773 2007 178411 86367 −125533 50817 42360 153232 91066 1.68265 0.99046 2008 184343 82650 −126364 51240 43583 154363 92591 1.66714 0.99078 2009 172892 71414 −108643 49049 43323 145283 89970 1.61480 0.96860

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2010 183521 76559 −123691 50315 43405 149898 91461 1.63893 1.01494 2011 191904 80232 −132890 51312 43896 154899 92960 1.66630 1.01670

Our geometric average rate of TFP growth over the 50 years 1962-2011 is 1.026% per year,10 which can also be compared with Statistics Canada’s recent KLEMS program average Multifactor Productivity Growth over the same years of 0.276% per year,11 which is a rather substantial difference! In section 4 below, we attempt to determine why our results are so different from the official Statistics Canada results.12 Over the golden years 1962-1973, TFP growth13 averaged 2.67% per year; over the dismal years, 1974-1991, TFP growth averaged on 0.20% per year but over the remainder of the nineties, 1992-1999, TFP growth nicely recovered to average a very respectable 1.69% per year. During the naughts, 2000-2011, TFP growth again fell off to average only 0.21% per year. However, productivity growth is not necessarily the entire story behind the growth in living standards: if the price of Canadian exports increases more rapidly than the price of Canadian imports, then the real income generated by the business sector should increase. This terms of trade effect is not taken into account in the above productivity computations. Thus in the following section, we implement the translog real income methodology explained in sections 1- 4 of Appendix 1 below and this approach will enable us to assess the contribution to Canadian living standards of improvements in Canada’s terms of trade. 3. Explaining Real Income Growth Generated by the Canadian Business Sector: the Gross Output Approach The basic methodology used in this section can easily be explained in nontechnical terms. The business sector faces (exogenous) domestic and international prices for the net outputs it produces: domestic outputs, exports and (minus) imports. The business sector also utilizes inputs of labour and capital in order to produce its outputs. The value of outputs produced by the business sector less the value of imports used (value added) must eventually flow back to the labour and capital primary inputs that were used to produce

10 This rate of TFP growth can be compared to the average rate of productivity growth for Australia obtained by Diewert and Lawrence (2006) using a similar methodology and over a similar period. The Diewert and Lawrence market sector average rate of TFP growth for Australia over the period 1961-2004 was 1.49% per year. However, there is an upward bias in the Diewert and Lawrence results due to the fact that they essentially used hours worked as their measure of labour input instead of a quality adjusted measure of labour input for Australia (which was not available). 11 See CANSIM Table 3830021, Series V41712881. Comparing levels of TFP with the starting level being 1 in 1961, our TFP ended up at 1.6663 in 2011 whereas KLEMS Multifactor Productivity ended up at 1.1477 in 2011. 12 Our measures of business sector output and capital input were different from the KLEMS measures because we excluded rental housing from our measure of value added and we excluded the residential land and residential structures inputs from our measure of capital services, whereas the KLEMS measures included rental housing in their output and capital input measures. 13 All growth rates in this paragraph are average geometric growth rates over the period under consideration. The average growth rates in Table 4 are arithmetic ones (and hence are slightly higher).

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value added. This is the (gross) income generated by the business sector. We divide this gross income in year t by the price of consumption in year t, PC

t, in order to turn this nominal income into real income ρt; this real income is the number of consumption bundles that could be purchased by the owners of the labour and capital inputs that were used in year t by the Canadian business sector. We also divide each of the prices PD

t, PXt,

PMt, PL

t and PKt by the price of consumption, PC

t, in order to form the corresponding real output and input prices facing the Canadian business sector in each year. Our measure of the (gross) real income generated by the business sector ρt and the corresponding real output and input prices are listed in Table 3. Table 3: Gross Real Income Generated by the Canadian Business Sector and Real Output and Input Prices Year t ρ t PD

t/PCt PX

t/PCt PM

t/PCt PL

t/PCt PK

t/PCt

1961 29368 1.00000 1.00000 1.00000 1.00000 1.00000 1962 31346 1.00042 1.02360 1.05138 1.03157 1.03276 1963 33574 1.00176 1.02058 1.07544 1.05115 1.13250 1964 36430 1.00833 1.03299 1.08023 1.08919 1.18581 1965 39778 1.01920 1.04230 1.06386 1.14653 1.21715 1966 43178 1.02036 1.04674 1.04189 1.17879 1.24765 1967 43963 1.01936 1.04229 1.03330 1.21750 1.14154 1968 45613 1.01378 1.04646 1.01690 1.25040 1.16701 1969 47964 1.01678 1.03890 1.00987 1.30676 1.15285 1970 49880 1.02235 1.04303 1.00397 1.35448 1.16019 1971 52734 1.03673 1.03496 1.00473 1.41955 1.16888 1972 56020 1.04241 1.03112 0.98606 1.48107 1.18714 1973 64142 1.05415 1.09462 0.98237 1.51475 1.45559 1974 68360 1.05777 1.20901 1.04062 1.53231 1.51947 1975 64401 1.03919 1.19083 1.03880 1.54122 1.21208 1976 70045 1.04943 1.20632 1.01280 1.69570 1.25495 1977 74186 1.04818 1.23409 1.07139 1.74659 1.34009 1978 76445 1.04616 1.25036 1.10347 1.69451 1.39352 1979 81839 1.04468 1.33483 1.13610 1.65495 1.52285 1980 81529 1.03834 1.38782 1.10723 1.62897 1.40865 1981 83688 1.05559 1.37956 1.12698 1.70049 1.28043 1982 77448 1.04749 1.29169 1.08635 1.72776 1.09305 1983 79904 1.03017 1.21818 1.00472 1.66594 1.26363 1984 84425 1.02349 1.20566 1.00522 1.67741 1.35345 1985 89040 1.02200 1.19184 1.00041 1.71256 1.38750 1986 90893 1.02361 1.16370 0.99696 1.72712 1.32909 1987 98402 1.02618 1.15717 0.95823 1.74627 1.45173 1988 103992 1.02604 1.12961 0.90987 1.81901 1.41197 1989 106463 1.02586 1.12009 0.88271 1.85220 1.34321 1990 103284 1.00761 1.05266 0.84694 1.82546 1.24177 1991 94344 0.98233 0.96285 0.78858 1.81182 1.02099 1992 96892 0.97918 0.97764 0.81019 1.82888 1.11296 1993 97398 0.97789 1.00113 0.83706 1.79166 1.12899 1994 104594 0.98759 1.05410 0.88192 1.76585 1.29700 1995 110709 0.99077 1.11743 0.90320 1.79453 1.38311 1996 114302 0.98226 1.10091 0.87350 1.78176 1.42551 1997 118038 0.97831 1.08434 0.86239 1.81484 1.38014 1998 122079 0.97863 1.06774 0.87973 1.84725 1.34317 1999 129307 0.97360 1.06103 0.86016 1.86189 1.40694 2000 140515 0.96980 1.09671 0.85316 1.90429 1.54838 2001 140153 0.96318 1.08172 0.85450 1.90221 1.48625 2002 145551 0.96589 1.04699 0.84933 1.90945 1.58161 2003 144866 0.95572 1.01372 0.77450 1.89984 1.50654 2004 155219 0.95804 1.02368 0.74418 1.92780 1.63560 2005 162807 0.95752 1.03041 0.71942 1.96882 1.69510 2006 168802 0.96289 1.01617 0.70018 2.02612 1.66299 2007 175551 0.96815 1.00702 0.67034 2.05492 1.67912

10

2008 180996 0.97048 1.07918 0.68927 2.05013 1.74260 2009 162942 0.97749 0.96890 0.69265 2.07780 1.40867 2010 172597 0.97425 0.97890 0.65600 2.08372 1.56097 2011 182140 0.97243 1.02611 0.65317 2.10133 1.69304

Thus the gross real income generated by the Canadian business sector has grown from $29,368 million dollars worth of 1961 consumption bundles in 1961 to $182,140 million in 2011, a 6.20 fold increase. Looking at the change in real input and output prices, the real price of domestic output has fallen to 0.972 times the starting level (due to the fact that machinery and equipment prices have risen less rapidly than the price of consumption) and the real price of exports has risen slightly to 1.026 times the starting level. However, the real price of imports has fallen substantially to 0.653 times the starting level. The quality adjusted real wages of business sector workers have risen to 2.101 times their initial 1961 levels. The real price of capital services has risen 1.69 fold, reflecting rapidly rising prices of agricultural land and nonagricultural business land as well as upward trends in machinery and equipment depreciation rates and in real rates of return; see Appendix 2 for details. Note that real wages, PL

t/PCt, peaked around 1977 at 1.75 and then fell to 1.67 in 1983.

They increased to 1.85 in 1989 and then fell to 1.77 in 1994 and then increased steadily to 2.10 in 2011. Real domestic prices, PD

t/PCt, increased to 1.06 in 1974 and then dropped

to 0.97 at the end of the sample period. This drop is probably due to the advent of quality adjustment of computers in the 1980s. The real price of exports, PX

t/PCt, fluctuates but

ends up close to unity at the end of the sample period. The real price of imports, PMt/PC

t, drops substantially over the sample period, ending up at 0.63. The real price of business sector capital services, PK

t/PCt, increases to 1.52 in 1979 and then decreases to 1.09 in

1982. It stays in the range 1.00 to 1.75 for the rest of the sample period, with big drops during recession years, which were in 1982, 1991 and 2009. This is due to the falling balancing real rate of return for those years. There are six quantitative factors that can be used to explain the real income ρt generated by the business sector in year t:

• The price of domestic production (an aggregate of C+I+G) relative to the price of consumption in year t, PD

t/PCt;

• The price of exports relative to the price of consumption in year t, PXt/PC

t; • The price of imports relative to the price of consumption in year t, PM

t/PCt;

• The quantity of labour used by the business sector in year t, QLt;

• The quantity of capital used by the business sector in year t, QKt and

• The level of technology of the business sector in year t. The formal model outlined in Appendix 1, based on the work of Diewert and Morrison (1986) and Kohli (1990), allows us to decompose the growth of real income from year t−1 to t, ρt/ρt−1, into multiplicative year to year contribution factors αD

t, αXt, αM

t, βLt, βK

t and τt that describe the effects of changes in the six explanatory variables listed above going from year t−1 to t. The model outlined in Appendix 1 leads to the following equation which decomposes the year to year growth in real income generated by the

11

business sector, ρt/ρt−1, into a product of six year to year explanatory contribution factors:14 (3) ρt/ρt−1 = τt αD

t αXt αM

t βLt βK

t ; t = 1962, 1963,...,2011. Thus if αD

t is greater than one, this means that the domestic price of output grew faster than the price of consumption going from year t−1 to t and αD

t measures the contribution of rising real domestic output prices to the growth in real income. Similarly, if αX

t is greater than one, this means that Canadian export prices grew faster than the price of consumption going from year t−1 to t and αX

t measures the contribution of rising real export prices to the growth in real income generated by the Canadian business sector. However, if αM

t is greater than one, this means that Canadian import prices did not increase as quickly as the price of consumption going from year t−1 to t and αM

t measures the contribution of falling real import prices to the growth in real income generated by the Canadian business sector. If βL

t is greater than one, then business sector labour input increased going from year t−1 to t and βL

t measures the contribution of the increase in labour input to the growth in real income generated by the Canadian business sector. Similarly, if βK

t is greater than one, then business sector capital services input increased going from year t−1 to t and βK

t measures the contribution of the increase in capital input to the growth in real income generated by the Canadian business sector. Finally, if τt is greater than one, then the efficiency of the Canadian business sector increased from year t−1 to t and τt measures the contribution of the efficiency increase to the growth in real income generated by the Canadian business sector. These year to year contribution factors are listed in Table 4 along with the (arithmetic) averages of these contribution factors over various time periods in the last five rows of the Table.15 Table 4: Business Sector Year to Year Growth in Real Income and Year to Year Contribution Factors Year t ρ t/ρ t−1 τ t αD

t αXt αM

t βLt βK

t αXMt

1962 1.06736 1.03984 1.00043 1.00548 0.9866 1.02745 1.00666 0.99201 1963 1.07105 1.05096 1.00138 0.99930 0.99406 1.01476 1.00961 0.99336 1964 1.08508 1.03132 1.00665 1.00300 0.99884 1.02686 1.01597 1.00184 1965 1.09191 1.02529 1.01096 1.00227 1.00412 1.02826 1.01797 1.00640 1966 1.08547 1.01885 1.00117 1.00108 1.00577 1.03221 1.02393 1.00686 1967 1.01818 0.98974 0.99900 0.99885 1.00235 1.01023 1.01810 1.00120 1968 1.03752 1.02504 0.99449 1.00115 1.00474 1.00118 1.01062 1.00590 1969 1.05155 1.02212 1.00300 0.99785 1.00217 1.01381 1.01173 1.00001 1970 1.03995 1.01749 1.00552 1.00122 1.00185 1.00078 1.01254 1.00308 1971 1.05722 1.02276 1.01400 0.99755 0.99976 1.01200 1.01004 0.99732 1972 1.06231 1.02343 1.00552 0.99883 1.00608 1.01701 1.01006 1.00491 1973 1.14497 1.05492 1.01139 1.01937 1.00125 1.03560 1.01529 1.02064 1974 1.06576 1.00760 1.00352 1.03277 0.98009 1.01973 1.02114 1.01221 1975 0.94209 0.94667 0.98156 0.99518 1.00065 0.99575 1.02246 0.99582 1976 1.08764 1.05262 1.01035 1.00408 1.00933 0.99720 1.01194 1.01345

14 See the equations in Appendix 1 in order to derive this equation. All of the variables in equation (3) can be identified using the data in Appendix 2. 15 The fifth row from the bottom gives the average over the years 1962-2011 and the remaining rows give the averages over the years 1962-1973, 1974-1991, 1992-1999 and 2000-2011. Note that the productivity growth rates τt listed in Table 4 agree with those listed in Table 2.

12

1977 1.05911 1.05760 0.99877 1.00736 0.98004 1.00475 1.01081 0.98725 1978 1.03046 1.00293 0.99802 1.00446 0.98919 1.02357 1.01225 0.99360 1979 1.07055 1.00794 0.99855 1.02377 0.98887 1.03386 1.01625 1.01238 1980 0.99621 0.94347 0.99384 1.01471 1.01009 1.01634 1.01992 1.02495 1981 1.02649 0.98468 1.01695 0.99773 0.99292 1.01327 1.02120 0.99066 1982 0.92544 0.97448 0.99228 0.97527 1.01432 0.95971 1.00810 0.98923 1983 1.03170 1.03967 0.98375 0.97819 1.02845 1.00020 1.00248 1.00602 1984 1.05659 1.04213 0.99359 0.99600 0.99981 1.01989 1.00472 0.99581 1985 1.05466 1.02689 0.99855 0.99536 1.00191 1.02329 1.00789 0.99726 1986 1.02080 0.99559 1.00158 0.99045 1.00141 1.02383 1.00810 0.99184 1987 1.08262 1.02422 1.00254 0.99778 1.01608 1.02902 1.01064 1.01382 1988 1.05681 1.00415 0.99986 0.99074 1.02050 1.02540 1.01530 1.01105 1989 1.02377 0.98493 0.99982 0.99680 1.01207 1.01523 1.01506 1.00883 1990 0.97014 0.98826 0.98187 0.97682 1.01657 0.99724 1.00963 0.99300 1991 0.91344 0.96173 0.97444 0.96615 1.02934 0.97509 1.00513 0.99450 1992 1.02700 1.04418 0.99672 1.00613 0.98868 0.99155 1.00045 0.99475 1993 1.00522 0.99704 0.99867 1.01049 0.98531 1.01282 1.00113 0.99565 1994 1.07388 1.03145 1.00996 1.02561 0.97455 1.02610 1.00515 0.99951 1995 1.05846 1.01220 1.00316 1.03184 0.98772 1.01698 1.00572 1.01917 1996 1.03245 1.00651 0.99177 0.99166 1.01753 1.01733 1.00756 1.00905 1997 1.03269 1.00467 0.99611 0.99133 1.00694 1.01966 1.01382 0.99821 1998 1.03423 1.02151 1.00033 0.99089 0.98857 1.01815 1.01482 0.97956 1999 1.05921 1.01813 0.99500 0.99613 1.01332 1.02123 1.01431 1.00939 2000 1.08668 1.02915 0.99631 1.02134 1.00478 1.02060 1.01189 1.02623 2001 0.99742 0.99931 0.99365 0.99128 0.99911 1.00725 1.00693 0.99040 2002 1.03852 1.04139 1.00264 0.98046 1.00332 1.00959 1.00148 0.98371 2003 0.99529 0.95862 0.98993 0.98173 1.04980 1.01054 1.00703 1.03063 2004 1.07147 1.01339 1.00232 1.00542 1.02050 1.02025 1.00769 1.02602 2005 1.04889 1.00710 0.99949 1.00356 1.01704 1.00733 1.01351 1.02067 2006 1.03682 0.99773 1.00543 0.99272 1.01348 1.01061 1.01651 1.00610 2007 1.03998 0.99046 1.00535 0.99545 1.02135 1.01389 1.01319 1.01670 2008 1.03101 0.99078 1.00237 1.03479 0.98671 1.00488 1.01181 1.02104 2009 0.90025 0.96860 1.00732 0.95175 0.99770 0.97400 0.99763 0.94956 2010 1.05925 1.01494 0.99656 1.00442 1.02565 1.01583 1.00073 1.03019 2011 1.05529 1.01670 0.99808 1.02109 1.00205 1.01183 1.00451 1.02318

A62-11 1.03820 1.01060 0.99949 0.99995 1.00410 1.01250 1.01080 1.00390 A62-73 1.06770 1.02680 1.00450 1.00220 1.00060 1.01830 1.01350 1.00280 A74-91 1.02300 1.00250 0.99610 0.99687 1.00510 1.00960 1.01240 1.00180 A92-99 1.04040 1.01700 0.99896 1.00550 0.99533 1.01550 1.00790 1.00070 A00-11 1.03010 1.00230 0.99995 0.99867 1.01180 1.00890 1.00770 1.01040

Looking at the sample (arithmetic) averages listed in the A62-11 row of Table 4, it can be seen that the (gross) real income generated by the Canadian business sector over the entire sample period grew at 3.82 percent per year over the 50 years 1961-2011. The biggest contributor to this growth was the growth of quality adjusted labour input at 1.25 percentage points per year.16 Next was capital services growth (1.08 percentage points per year) followed by Total Factor Productivity growth, τt, which contributed on average 1.06 percentage points per year and declines in real import prices (0.41 percentage points per year). Declines in real domestic output prices and real export prices gave rise to negative average contribution factors, − 0.051 and −0.005 percentage points per year respectively. The last column in Table 4 gives the product of the real export and real import price contribution factors, αXM

t , defined as: (4) αXM

t ≡ αXt αM

t . 16 This is the arithmetic average rate of productivity growth which is greater than the more accurate geometric average rate of productivity growth which was 1.026. Due to the ease of computation, we work with arithmetic average rates in Table 4.

13

Roughly speaking, αXMt is a terms of trade contribution factor; it gives the contribution to

real income growth of the combined effects of real changes in the international prices facing the Canadian business sector.17 It can be seen that the effects of changing real international prices are not negligible for Canada: on average, changing real export and import prices contributed 0.39 percentage points per year to real income growth over the entire sample period.18 However, for shorter periods, the effects of changing real international prices can be far more important in explaining changes in the real income generated by the market sector of an economy. Thus if we restrict our attention to the period 2000-2011, it can be seen by looking at the last row of Table 4 that the effects of improvements in Canada’s terms of trade are the most important explanatory factor. Thus during this period, the average annual growth in the real income generated by the Canadian business sector was 3.01 percent per year and the following factors explained this growth rate: decreases in the real price of imports (1.18), increases in quality adjusted labour input (0.89), increases in capital services input (0.77) and improvements in TFP (0.23). There were small negative contributors to market sector real income growth during the naughts: decreases in the real price of domestically produced goods and services (−0.005) and decreases in the real price of exports (−0.113). Thus decreases in the real price of imports proved to be the most important factor in explaining the growth in real income generated by the market sector during this period. Overall, the joint effects of changes in real export and import prices contributed about 1.04 percentage points per year on average to the growth of market sector real income during the naughts, which was greater than the contribution of capital input growth over this period (which was 0.77 percentage points per year on average).19 Thus improvements in the terms of trade largely compensated for the poor productivity performance during the naughts, leading to an overall reasonable rate of growth for the real income generated by the Canadian business sector. The last four rows of Table 4 present the various growth factors for 4 subperiods:

• The 12 golden years for the Canadian economy, 1962-1973, when the real income generated by the business sector grew by 6.77% per year and TFP growth was a stellar 2.68% per year;

• The 18 dismal years for the Canadian economy, 1974-1991, characterized by stagflation, oil shocks and rapidly increasing tax rates when the real income generated by the business sector grew by 2.30% per year and TFP growth was only 0.25% per year;

17 Ulrich Kohli has pointed out that this is a slight abuse of terminology. Strictly speaking, the terms of trade is the price of exports over the price of imports and hence involves only two prices. Our definition of αXM

t involves three prices: the price of exports, the price of imports and the price of domestic consumption. Our terms of trade contribution factor is the rate of change counterpart to Kohli’s (2006; 50) trading gains factor. 18 Thus the contribution of falling real import prices outweighs the effects of falling real export prices. 19 These results are very similar to the results obtained for Australia using a similar framework by Diewert and Lawrence (2006); i.e., both Australia and Canada have had very favourable changes in their terms of trade in recent years which contributed greatly to real income growth during the naughts.

14

• The 8 years in the nineties after the recession of 1991, 1992-1999, when real income growth recovered to 4.04% per year and TFP growth also recovered to 1.70% per year and

• The 12 years in the present century, 2000-2011, when TFP growth dropped off to 0.23% per year but real income growth was still reasonably strong at 3.01% per year due to the very strong contribution made by falling real import prices during this period, which contributed on average 1.18% per year to real income growth.

The annual change information in Table 4 can be converted into levels using equations (38) in Appendix 1 (with obvious extensions to multiple inputs and outputs). Thus let Tt, AD

t, AXt, AM

t, BLt, BK

t and AXMt be the cumulated products of the annual link factors τt,

αDt, αX

t, αMt, βL

t, βKt and αXM

t respectively. Using these definitions and cumulating equations (3) leads to the following equation, which explains the cumulative growth in real gross income generated by the Canadian business sector relative to the base year 1961: (5) ρt/ρ1961 = Tt AD

t AXt AM

t BLt BK

t ; t = 1962, 1963, ... , 2011. The cumulated variables that appear in (5) above are reported in Table 5 below along with the cumulated terms of trade contribution factor, AXM

t defined to be the product of the two cumulated international price factors, AX

t and AMt.

Table 5: Business Sector Cumulated Growth in Real Income and Cumulated Contribution Factors Year t ρ t/ρ1961 Tt AD

t AXt AM

t BLt BK

t AXMt

1961 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1962 1.06736 1.03984 1.00043 1.00548 0.98660 1.02745 1.00666 0.99201 1963 1.14320 1.09283 1.00181 1.00478 0.98074 1.04262 1.01633 0.98543 1964 1.24046 1.12706 1.00847 1.00780 0.97960 1.07062 1.03256 0.98724 1965 1.35447 1.15556 1.01952 1.01008 0.98364 1.10087 1.05111 0.99356 1966 1.47025 1.17734 1.02072 1.01117 0.98932 1.13633 1.07626 1.00037 1967 1.49697 1.16526 1.01970 1.01001 0.99165 1.14796 1.09575 1.00157 1968 1.55314 1.19445 1.01408 1.01117 0.99635 1.14931 1.10739 1.00748 1969 1.63321 1.22087 1.01713 1.00899 0.99851 1.16518 1.12038 1.00749 1970 1.69845 1.24222 1.02274 1.01023 1.00036 1.16609 1.13443 1.01059 1971 1.79564 1.27050 1.03706 1.00776 1.00012 1.18008 1.14583 1.00788 1972 1.90753 1.30027 1.04279 1.00658 1.00621 1.20016 1.15735 1.01283 1973 2.18407 1.37169 1.05467 1.02607 1.00746 1.24288 1.17505 1.03373 1974 2.32769 1.38211 1.05838 1.05970 0.98741 1.26741 1.19990 1.04636 1975 2.19290 1.30840 1.03886 1.05459 0.98805 1.26203 1.22685 1.04199 1976 2.38508 1.37724 1.04962 1.05889 0.99727 1.25850 1.24150 1.05600 1977 2.52608 1.45657 1.04833 1.06669 0.97736 1.26447 1.25492 1.04254 1978 2.60302 1.46085 1.04625 1.07144 0.96680 1.29428 1.27030 1.03587 1979 2.78667 1.47244 1.04473 1.09692 0.95604 1.33810 1.29094 1.04869 1980 2.77611 1.38920 1.03830 1.11305 0.96569 1.35997 1.31665 1.07486 1981 2.84965 1.36792 1.05589 1.11052 0.95885 1.37801 1.34456 1.06482 1982 2.63717 1.33300 1.04774 1.08306 0.97258 1.32249 1.35545 1.05336 1983 2.72078 1.38589 1.03071 1.05944 1.00025 1.32277 1.35882 1.05970 1984 2.87474 1.44428 1.02410 1.05520 1.00006 1.34908 1.36523 1.05526 1985 3.03188 1.48311 1.02262 1.05030 1.00197 1.38049 1.37601 1.05237 1986 3.09495 1.47658 1.02424 1.04027 1.00338 1.41339 1.38715 1.04378 1987 3.35065 1.51234 1.02684 1.03796 1.01951 1.45441 1.40191 1.05821 1988 3.54099 1.51861 1.02670 1.02835 1.04041 1.49135 1.42335 1.06991 1989 3.62515 1.49572 1.02651 1.02506 1.05296 1.51407 1.44479 1.07935

15

1990 3.51690 1.47816 1.00790 1.00130 1.07041 1.50988 1.45870 1.07180 1991 3.21248 1.42159 0.98214 0.96741 1.10181 1.47227 1.46618 1.06590 1992 3.29923 1.48441 0.97892 0.97334 1.08934 1.45983 1.46684 1.06030 1993 3.31647 1.48001 0.97761 0.98355 1.07334 1.47855 1.46849 1.05569 1994 3.56150 1.52655 0.98735 1.00875 1.04602 1.51713 1.47606 1.05517 1995 3.76972 1.54518 0.99046 1.04087 1.03318 1.54290 1.48451 1.07540 1996 3.89206 1.55523 0.98231 1.03219 1.05130 1.56963 1.49573 1.08514 1997 4.01928 1.56249 0.97849 1.02324 1.05859 1.60048 1.51640 1.08319 1998 4.15686 1.59610 0.97881 1.01392 1.04649 1.62953 1.53888 1.06106 1999 4.40298 1.62503 0.97392 1.00999 1.06043 1.66413 1.56090 1.07102 2000 4.78464 1.67240 0.97033 1.03154 1.06550 1.69840 1.57945 1.09911 2001 4.77230 1.67124 0.96416 1.02255 1.06455 1.71072 1.59041 1.08856 2002 4.95612 1.74041 0.96671 1.00256 1.06809 1.72713 1.59275 1.07083 2003 4.93277 1.66839 0.95698 0.98425 1.12129 1.74533 1.60396 1.10363 2004 5.28530 1.69074 0.95920 0.98958 1.14427 1.78068 1.61629 1.13235 2005 5.54370 1.70274 0.95871 0.99311 1.16377 1.79372 1.63813 1.15575 2006 5.74783 1.69887 0.96392 0.98588 1.17945 1.81276 1.66518 1.16280 2007 5.97765 1.68265 0.96907 0.98139 1.20463 1.83793 1.68714 1.18222 2008 6.16302 1.66714 0.97137 1.01553 1.18863 1.84691 1.70706 1.20709 2009 5.54828 1.61480 0.97848 0.96654 1.18589 1.79889 1.70301 1.14621 2010 5.87703 1.63893 0.97512 0.97081 1.21631 1.82737 1.70425 1.18081 2011 6.20199 1.66630 0.97324 0.99129 1.21881 1.84900 1.71193 1.20819

Looking at the last row of Table 5, it can be seen that the gross real income generated by the business sector grew 6.20 fold over the years 1961-2011. The main factors explaining this growth are growth of quality adjusted labour input (cumulative growth factor 1.85), growth of capital services or capital deepening (cumulative growth factor 1.71), productivity increases (cumulative growth factor 1.67) and lower real import prices (cumulative growth factor 1.22). There were small negative contributions from declining real domestic output prices (cumulative growth factor 0.97) and declining real export prices (cumulative growth factor .99). In recent years, the real prices of Canada’s raw materials exports have increased dramatically. However, these increases do not show up in the AX

t column of Table 5; i.e., the overall real price of Canadian exports has remained relatively constant in recent years. This apparent contradiction can be explained by falling real prices for Canadian exports of manufactured goods. As already noted above, the effects of falling real import prices in recent years have been substantial. The cumulative contribution factors listed in Table 5 are plotted in Chart 1 below.

16

Chart 1: Cumulated Contribution Factors that Explain the Growth of Real Income Generated by the Canadian

Production Sector

0.9

1.1

1.31.5

1.7

1.9

19611964196719701973197619791982198519881991199419972000200320062009

T AD AX AM BL BK

It can be seen that labour, capital and Total Factor Productivity growth were the main contributors to the generation of real income growth over the period 1961-2011 but that falls in import prices were an important contributory factor during the period 2002-2007. 4. Comparison with the KLEMS Program Multifactor Productivity Estimates As was mentioned earlier, the Statistics Canada KLEMS program has recently provided estimates of the multifactor productivity growth for the Canadian business sector; see Baldwin, Gu and Yan (2007) and Baldwin and Gu (2007) for a description of the methods used in this program. In section 2, we explained that our level of business sector Total Factor Productivity using our user cost framework ended up at 1.6663 in 2011 from its starting value of 1 in 1961 whereas the KLEMS Multifactor business sector productivity ended up at 1.1477 in 2011. In this section, we will try to determine why our estimates are so different from the corresponding KLEMS program estimates. Our measures of real business sector output, labour and capital services input are QY

t, QLt

and QKt and our measure of the capital stock used by the business sector is QKW

t. For convenience, these measures are listed in Table 6 below. The KLEMS program provides index counterparts to our measures for the years 1961-2011 in CANSIM Table 3830021, Series V41712932, V41712949, V41713051 and V41713068 respectively. The KLEMS program also provides nominal dollar estimates for business sector output, labour input and capital services input for the years 1961-2008; see CANSIM Table 3830021, Series V41713153, V41713170 and V41713228 respectively. We use the starting 1961 values for the KLEMS value of business sector output, labour and capital input and convert the KLEMS constant dollar estimates for output, labour and capital input into 1961 constant dollar series and these official KLEMS series are listed as QYO

t, QLOt and QKO

t in Table 6 below. The KLEMS data base does not seem to have dollar estimates for the value of

17

business sector capital stocks,20 so we use the KLEMS capital stock index Series V41713068 and convert it into a 1961 constant dollar series using our estimate for the starting business sector capital stock, VKW

1961. The resulting “official” series is listed as QKWO

t in Table 6 below. Table 6: Our Estimates of Business Sector Output QY, Labour Input QL, Capital Services QK, Capital Stocks QKW and the Corresponding Official Estimates QYO, QLO, QKO and QKWO and Constant Dollar Paid Rents QPR in 1961 Dollars (Millions)

Year t QYt QYO

t QLt QLO

t QKt QKO

t QKWt QKWO

t QPRt

1961 29368 30805 19240 19201 10128 11604 65074 65074 1107 1962 31585 33059 20049 20025 10326 12054 66186 66820 1149 1963 34008 35013 20506 20540 10613 12593 67985 68814 1170 1964 36591 37567 21372 21466 11091 13493 70874 72554 1221 1965 39269 40122 22321 22444 11655 14752 73925 76793 1278 1966 42286 42827 23452 23577 12450 16281 78410 82029 1337 1967 43046 43728 23822 24040 13105 17451 82234 86766 1390 1968 44645 46133 23864 24143 13515 18350 84583 90256 1420 1969 46806 48537 24366 24658 13986 19430 87164 94495 1476 1970 48260 49889 24395 24761 14513 20599 90627 98733 1530 1971 50452 51843 24836 25276 14953 21588 92937 102723 1551 1972 53041 54998 25469 26048 15415 23028 94972 107460 1584 1973 58832 59206 26868 27541 16106 25007 98134 112945 1566 1974 61727 61310 27717 28519 17037 26986 103385 119677 1558 1975 59494 62061 27534 28467 18122 28785 110211 126159 1544 1976 63195 66118 27417 28467 18769 30764 112964 132642 1482 1977 67878 68823 27616 28776 19366 32383 115949 138127 1384 1978 70536 71979 28636 29960 20037 34092 119537 143363 1322 1979 74698 75134 30208 31710 20912 36341 123921 149845 1295 1980 73053 76938 31015 32740 22012 38949 130218 156079 1313 1981 74433 80244 31669 33615 23302 41828 135275 163309 1359 1982 70175 77088 29737 31968 23850 42817 138323 165802 1410 1983 73155 79192 29747 32174 24016 43897 136998 167298 1444 1984 78122 84752 30714 33358 24312 45246 137639 169044 1471 1985 82738 89260 31892 34748 24809 47045 140493 172285 1500 1986 85019 91514 33124 36241 25343 48844 142988 176523 1539 1987 90559 96022 34682 38042 26064 51453 145848 182258 1599 1988 94670 100981 36105 39793 27136 54331 150432 189738 1662 1989 96089 103685 36972 40874 28278 57389 155302 197218 1726 1990 95610 103235 36814 40874 29056 59368 158744 202703 1798 1991 90121 99027 35445 39587 29504 60538 160238 205445 1853 1992 93349 99628 35000 39123 29544 61527 158327 205695 1899 1993 94373 102483 35683 39998 29642 62517 157980 206443 1943 1994 100395 108795 37145 41543 30070 64496 158425 208437 1982 1995 103938 112401 38163 42727 30529 66834 159699 210681 2016 1996 107231 114956 39243 43962 31132 69353 162378 213673 2049 1997 111367 121417 40501 45404 32269 73401 166742 220904 2097 1998 117544 127127 41680 46845 33566 77269 170681 227386 2139 1999 123965 135542 43103 48389 34865 81676 174830 234118 2187 2000 131753 144108 44563 50088 35944 85454 178130 241598 2231 2001 133537 146362 45096 50706 36583 87793 181277 245338 2279 2002 140604 150269 45811 51478 36720 89952 180822 249327 2341 2003 137165 153124 46610 52405 37380 92830 183931 254812 2413 2004 142907 158383 48181 54206 38111 96698 185502 261544 2487 2005 146935 163492 48777 54927 39392 101646 189852 270021 2560 2006 150603 167850 49653 55905 41010 107223 195631 279994 2638 2007 153232 171306 50817 57295 42360 111990 200440 288720 2715 2008 154363 171306 51240 57758 43583 116398 205062 295702 2797

20 Actually, this information is available in CANSIM Table 3830025.

18

2009 145283 163042 49049 55493 43323 115948 205338 294455 2881 2010 149898 169203 50315 56935 43405 117477 204637 295452 2966 2011 154899 173861 51312 58119 43896 121435 205655 300439 3054

Geo Growth 1.03382 1.03522 1.01981 1.02240 1.02977 1.04808 1.02328 1.03107 1.02050

The geometric average rate of growth for each series over the 51 years is listed in the last row of Table 6. Our average rate of output growth, 3.38% per year, is a bit smaller than the KLEMS average rate of output growth, which was 3.52% per year. This relatively small difference in output growth rates does not explain the large difference in rates of productivity growth (and the difference goes in the wrong direction). As was mentioned in section 2 of the main text, our business sector output concept differs from the corresponding KLEMS concept in two ways:

• We exclude the services of both owned and rented residential housing from our output concept whereas the KLEMS program excludes only owned residential housing services and

• We measure real inventory change as a difference in real inventory stocks whereas the KLEMS program follows national income accounting conventions and measures inventory change in a different manner.

However, the effect of the above two differences on output growth rates is obviously not large21 since our average output growth rate is fairly close to the corresponding official rate. In order to see more clearly where the differences between our productivity estimates and the official estimates are coming from, we plot our productivity level estimates (PROD) and the corresponding official ones normalized to equal one in 1961 (PRODO) in Chart 2 below. It can be seen that the official estimates have been essentially flat since 1972, which does not seem very likely. The top two series in Chart 2 are the output series, QY and QYO, and they are not too different. The next highest series is the official aggregate input series normalized to equal one in 1961, QZO, and it can be seen that it lies far above our counterpart series, QZ.

21 See the last column in Table 6 which lists real paid rents for the Canadian economy. They are small relative to the size of the business sector.

19

Chart 2: Normalized Business Sector Output, Input and Productivity Levels; New and Official (O)

0.9

1.9

2.9

3.9

4.9

5.9

19611964196719701973197619791982198519881991199419972000200320062009

QY QYO QZ QZO PROD PRODO

In order to see what causes the differences in estimates of aggregate input, our labour and capital services series (normalized to equal one in 1961), QL and QK, are plotted in Chart 3 along with the official (normalized) series, QLO and QKO. We also plot our normalized wealth (real) capital stock, QKW, along with the counterpart official normalized wealth stock, QKWO. It can be seen that QL and QLO are reasonably close, but the official capital services series, QKO, is far above our normalized capital services series QK. We have also plotted our normalized capital stock series, QKW, in Chart 3 along with the counterpart (normalized) KLEMS series, QKWO. It can be seen that the KLEMS wealth series, QKWO, is also above our series QKW, but the differences in the wealth series are far smaller than the differences in the capital services series.

20

Chart 3: Normalized Labour, Capital Services and Capital Stock Levels; New and Official Estimates

0.9

2.9

4.9

6.9

8.9

10.9

1961

1964

1967

1970

1973

1976

1979

1982

1985

1988

1991

1994

1997

2000

2003

2006

2009

QL QLO QK QKO QKW QKWO

Our measure of quality adjusted labour grew on average at 1.98% per year, which is somewhat slower than the corresponding KLEMS rate, which was 2.24% per year. This difference does help to explain the difference in productivity growth rates. We believe that our estimates for quality adjusted labour growth are just as credible as the KLEMS program estimates due to the difficulties in measuring the experience variable in an objective manner (which the KLEMS program uses and we do not). However, the big explanatory factor lies in the differences in the growth of capital services: our capital services aggregate grew at the geometric rate of 2.98% per year whereas the KLEMS capital services aggregate grew at 4.81% per year, a whopping difference of 1.83% per year! Our capital stock aggregate grew at 2.33% per year and the KLEMS capital stock grew at 3.11% per year, a difference of 0.78% per year. It is understandable why our capital stock aggregate grew more slowly than the corresponding KLEMS capital stock aggregate since our estimates for the price of business land are likely much higher than the KLEMS estimates and since we assumed no business land growth, our assumptions will lead to a much lower rate of growth of the aggregate capital stock. It is possible to explain why the average growth rate of capital services should be bigger than the average growth rate of capital stock components: basically, the faster growing components of the capital stock (ICT and other M&E) have bigger user costs relative to the slower growing components of the capital stock (agricultural land and nonagricultural land) compared to their stock prices. Thus aggregate capital services will tend to grow

21

faster than the corresponding aggregate capital stock.22 In order to obtain a rough estimate for how much of a difference in growth rates between capital stocks and services should be expected, we calculated average rates of growth over our sample period for each of our 17 capital stock components. We also calculated sample average shares for each type of capital service and for each component of the wealth stock. We calculated a share weighted average of the average rates of asset growth using average capital service shares and found that the resulting average rate of growth of capital services was 3.028% per year. We then calculated a share weighted average of the average rates of asset growth using average capital stock shares and found that the resulting average rate of growth of capital stocks was 2.377% per year. Thus we expect the difference between the average services rates of growth and the corresponding stock rates of growth to be 3.028% − 2.377% or 0.651 percentage points per year. Recall that our average geometric rate of growth of capital services was 2.98% and our average geometric rate of growth of the capital stock was 2.33% per year for a difference of 0.65 percentage points per year. Thus we think that our difference between the rates of growth in the capital stock and the corresponding capital services is very reasonable whereas we find the differences in the KLEMS estimates to be far too big to be credible. Part of the problem is that the KLEMS program does not provide enough detailed data for us to determine the exact source of the differences. Some of the differences may be due to the following factors:

• The inclusion of ex post capital gains terms in the KLEMS user cost formula. This will give high tech assets an enormous user cost (due to their rapidly declining prices) as compared to our weights.23

• We are using a sector wide balancing rate of return whereas the KLEMS program uses sector specific rates that could be very variable and volatile.

• The KLEMS program has access to more detailed data and so our estimates may be subject to some aggregation bias.

5. Conclusion There are three major conclusions that we can draw from the above results. First, using recent Statistics Canada data sources and a top down approach, we have shown that the productivity performance of the business sector of the Canadian economy has been reasonably satisfactory over the past 51 years. In particular, traditional gross income Total Factor Productivity growth averaged 1.026 percent per year over the period 1962-2011.24 However, there was a long period (1974-1991) where the productivity performance of the Canadian business sector was decidedly unsatisfactory.

22 This observation dates back to Jorgenson and Griliches (1967) at least. 23 The Statistics Canada depreciation rates are not necessarily incorrect. This is a topic that requires further research. 24 The corresponding Statistics Canada average Multifactor Productivity growth rate over this period was only 0.28 percent per year.

22

Second, the results presented here show that over short periods of time, changes in the external price environment facing an economy can have substantial effects on living standards. Thus during the years 2000-2011, the real income generated by the Canadian business sector grew at an average rate of 3.01 percent per year and declines in real import prices contributed 1.18 percentage points to this increase, which was greater than the effects of quality adjusted labour input growth (0.89 percentage points per year), capital deepening (0.77 percentage points per year) and TFP growth (0.23 percentage points per year). Finally, the study uncovered many data problems which should be addressed in future work on Canadian productivity performance. In particular, the treatment of capital services need additional documentation and experimentation, particularly with respect to the measurement of land services, the form of the user cost formula, the treatment of taxes, the determination of depreciation rates and the choice of a reference rate of return. Appendix 1: Explaining Real Income Growth: The Translog Approach 1. The Production Theory Framework In this Appendix, we present the production theory framework which will be used in the main text of the paper.25 The main reference is Diewert and Morrison (1986)26 but we also draw on the theory of the output price index, which was developed by Fisher and Shell (1972) and Archibald (1977). This theory is the producer theory counterpart to the theory of the cost of living index for a single consumer (or household) that was first developed by the Russian economist, A. A. Konüs (1924). These economic approaches to price indexes rely on the assumption of (competitive) optimizing behavior on the part of economic agents (consumers or producers). Thus we consider only the market sector of the economy in what follows; i.e., that part of the economy that is motivated by profit maximizing behavior. In our empirical work, we define the market sector to be the Canadian business sector of the economy less the rental and owner occupied housing sectors.27 Initially, we assume that the market sector of the economy produces quantities of M (net)28 outputs, y ≡ [y1,...,yM], which are sold at the positive producer prices P ≡ 25 This material is drawn from Diewert, Mizobuchi and Nomura (2005) and Diewert and Lawrence (2006). 26 The theory also draws on Diewert (1983; 1077-1100), Kohli (1990) (2003) (2004) (2006), Morrison and Diewert (1990), Fox and Kohli (1998) and Chapter 24 in the IMF, ILO, OECD, Eurostat, UNECE and the World Bank (2009). 27 The Canadian business sector excludes all of the general government sectors such as schools, hospitals, universities, defence and public administration where no independent measures of output can be obtained. For owner occupied housing, output is equal to input and hence no productivity improvements can be generated by this sector according to SNA conventions. Due to the difficulties involved in splitting up the residential housing stock into the rental and owner occupied portions, we omit the entire residential housing stock and the consumption of residential housing services in our data. However, we do include investment in residential housing, since that investment is part of the output of the market production sector. 28 If the mth commodity is an import (or other produced input) into the market sector of the economy, then the corresponding quantity ym is indexed with a negative sign. We will follow Kohli (1978) (1991) and Woodland (1982) in assuming that imports flow through the domestic production sector and are

23

[P1,...,PM]. We further assume that the market sector of the economy uses positive quantities of N primary inputs, x ≡ [x1,...,xN] which are purchased at the positive primary input prices W ≡ [W1,...,WN]. In period t, we assume that there is a feasible set of output vectors y that can be produced by the market sector if the vector of primary inputs x is utilized by the market sector of the economy; denote this period t production possibilities set by St. We assume that St is a closed convex cone that exhibits a free disposal property.29 Given a vector of output prices P and a vector of available primary inputs x, we define the period t market sector GDP function, gt(P,x), as follows:30 (1) gt(P,x) ≡ max y {P⋅y : (y,x) belongs to St} ; t = 0,1,2, ... . Thus market sector GDP depends on t (which represents the period t technology set St), on the vector of output prices P that the market sector faces and on x, the vector of primary inputs that is available to the market sector. If Pt is the period t output price vector and xt is the vector of inputs used by the market sector during period t and if the GDP function is differentiable with respect to the components of P at the point Pt,xt, then the period t vector of market sector outputs yt will be equal to the vector of first order partial derivatives of gt(Pt,xt) with respect to the components of P; i.e., we will have the following equations for each period t:31 (2) yt = ∇P gt(Pt,xt) ; t = 0,1,2, ... . Thus the period t market sector supply vector yt can be obtained by differentiating the period t market sector GDP function with respect to the components of the period t output price vector Pt. If the GDP function is differentiable with respect to the components of x at the point Pt,xt, then the period t vector of input prices Wt will be equal to the vector of first order partial

“transformed” (perhaps only by adding transportation, wholesaling and retailing margins) by the domestic production sector. The recent textbook by Feenstra (2004; 76) also uses this approach. 29 For a more explanation for the meaning of these properties, see Diewert (1974; 134). The assumption that St is a cone means that the technology is subject to constant returns to scale. This is an important assumption since it implies that the value of outputs should equal the value of inputs in equilibrium. In our empirical work, we use an ex post rate of return in our user costs of capital, which forces the value of inputs to equal the value of outputs for each period. The function gt is known as the GDP function or the national product function in the international trade literature; see Kohli (1978) (1991), Woodland (1982) and Feenstra (2004; 76). It was introduced into the economics literature by Samuelson (1953). 30 The function gt(P,x) will be linearly homogeneous and convex in the components of P and linearly homogeneous and concave in the components of x; see Diewert (1974; 136). Notation: P⋅y ≡ ∑m=1

M Pmym. 31 These relationships are due to Hotelling (1932; 594). Note that ∇P gt(Pt,xt) ≡ [∂gt(Pt,xt)/∂P1, ...,∂gt(Pt,xt)/∂PM].

24

derivatives of gt(Pt,xt) with respect to the components of x; i.e., we will have the following equations for each period t:32 (3) Wt = ∇x gt(Pt,xt) ; t = 0,1,2, ... . Thus the period t market sector input prices Wt paid to primary inputs can be obtained by differentiating the period t market sector GDP function with respect to the components of the period t input quantity vector xt. The constant returns to scale assumption on the technology sets St implies that the value of outputs will equal the value of inputs in period t; i.e., we have the following relationships: (4) gt(Pt,xt) = Pt⋅yt = Wt⋅xt ; t = 0,1,2, ... . The above material will be useful in what follows but of course, our focus is not on GDP; instead our focus is on the income generated by the market sector or more precisely, on the real income generated by the market sector. However, since market sector GDP (the value of market sector production) is distributed to the factors of production used by the market sector, nominal market sector GDP will be equal to nominal market sector income; i.e., from (4), we have gt(Pt,xt) = Pt⋅yt = Wt⋅xt. As an approximate welfare measure that can be associated with market sector production,33 we will choose to measure the real income generated by the market sector in period t, ρt, in terms of the number of consumption bundles that the nominal income could purchase in period t; i.e., define ρt as follows: (5) ρt ≡ Wt⋅xt/PC

t ; t = 0,1,2, ... = wt⋅xt = pt⋅yt = gt(pt,xt) where PC

t > 0 is the period t consumption expenditures deflator and the market sector period t real output price pt and real input price wt vectors are defined as the corresponding nominal price vectors deflated by the consumption expenditures price index; i.e., we have the following definitions:34 32 These relationships are due to Samuelson (1953) and Diewert (1974; 140). Note that ∇x gt(Pt,xt) ≡ [∂gt(Pt,xt)/∂x1, ...,∂gt(Pt,xt)/∂xN]. 33 Since some of the primary inputs used by the market sector can be owned by foreigners, our measure of domestic welfare generated by the market production sector is only an approximate one. Moreover, our suggested welfare measure is not sensitive to the distribution of the income that is generated by the market sector. 34 Our approach is similar to the approach advocated by Kohli (2004; 92), except he essentially deflates nominal GDP by the domestic expenditures deflator rather than just the domestic (household) expenditures deflator; i.e., he deflates by the deflator for C+G+I, whereas we suggest deflating by the deflator for C. Another difference in his approach compared to the present approach is that we restrict our analysis to the market sector GDP, whereas Kohli deflates all of GDP. Our treatment of the balance of trade surplus or deficit is also different.

25

(6) pt ≡ Pt/PCt ; wt ≡ Wt/PC

t ; t = 0,1,2, ... . The first and last equality in (5) imply that period t real income, ρt, is equal to the period t GDP function, evaluated at the period t real output price vector pt and the period t input vector xt, gt(pt,xt). Thus the growth in real income over time can be explained by three main factors: t (Technical Progress or Total Factor Productivity growth), growth in real output prices and the growth of primary inputs. We will shortly give formal definitions for these three growth factors. Using the linear homogeneity properties of the GDP functions gt(P,x) in P and x separately, we can show that the following counterparts to the relations (2) and (3) hold using the deflated prices p and w:35 (7) yt = ∇p gt(pt,xt) ; t = 0,1,2, ... ; (8) wt = ∇x gt(pt,xt) ; t = 0,1,2, ... . Now we are ready to define a family of period t productivity growth factors or technical progress shift factors τ(p,x,t):36 (9) τ(p,x,t) ≡ gt(p,x)/gt−1(p,x) ; t = 1,2, ... . Thus τ(p,x,t) measures the proportional change in the real income produced by the market sector at the reference real output prices p and reference input quantities used by the market sector x where the numerator in (9) uses the period t technology and the denominator in (9) uses the period t−1 technology. Thus each choice of reference vectors p and x will generate a possibly different measure of the shift in technology going from period t−1 to period t. It is natural to choose special reference vectors for the measure of technical progress defined by (9): a Laspeyres type measure τL

t that chooses the period t−1 reference vectors pt−1 and xt−1 and a Paasche type measure τP

t that chooses the period t reference vectors pt and xt: (10) τL

t ≡ τ(pt−1,xt−1,t) = gt(pt−1,xt−1)/gt−1(pt−1,xt−1) ; t = 1,2, ... ; (11) τP

t ≡ τ(pt,xt,t) = gt(pt,xt)/gt−1(pt,xt) ; t = 1,2, ... . Since both measures of technical progress are equally valid, it is natural to average them to obtain an overall measure of technical change. If we want to treat the two measures in a symmetric manner and we want the measure to satisfy the time reversal property from

35 If producers in the market sector of the economy are solving the profit maximization problem that is associated with gt(P,x), which uses the original output prices P, then they will also solve the profit maximization problem that uses the normalized output prices p ≡P/PC; i.e., they will also solve the problem defined by gt(p,x). 36 This measure of technical progress is due to Diewert and Morrison (1986; 662). A special case of it was defined earlier by Diewert (1983; 1063).

26

index number theory37 (so that the estimate going backwards is equal to the reciprocal of the estimate going forwards), then the geometric mean will be the best simple average to take.38 Thus we define the geometric mean of (10) and (11) as follows:39 (12) τt ≡ [τL

t τPt]1/2 ; t = 1,2, ... .

At this point, it is not clear how we will obtain empirical estimates for the theoretical productivity growth indexes defined by (10)-(12). One obvious way would be to assume a functional form for the GDP function gt(p,x), collect data on output and input prices and quantities for the market sector for a number of years (and for the consumption expenditures deflator), add error terms to equations (7) and (8) and use econometric techniques to estimate the unknown parameters in the assumed functional form. However, econometric techniques are generally not completely straightforward: different econometricians will make different stochastic specifications and will choose different functional forms. Moreover, as the number of outputs and inputs grows, it will be impossible to estimate a flexible functional form. Thus we will suggest methods for implementing measures like (12) in this Appendix that are based on exact index number techniques. We turn now to the problem of defining theoretical indexes for the effects on real income due to changes in real output prices. Define a family of period t real output price growth factors α(pt−1,pt,x,s):40 (13) α(pt−1,pt,x,s) ≡ gs(pt,x)/gs(pt−1,x) ; s = 1,2, ... . Thus α(pt−1,pt,x,s) measures the proportional change in the real income produced by the market sector that is induced by the change in real output prices going from period t−1 to t, using the technology that is available during period s and using the reference input quantities x. Each choice of the reference technology s and the reference input vector x will generate a possibly different measure of the effect on real income of a change in real output prices going from period t−1 to period t. Again, it is natural to choose special reference vectors for the measures defined by (13): a Laspeyres type measure αL

t that chooses the period t−1 reference technology and reference input vector xt−1 and a Paasche type measure αP

t that chooses the period t reference technology and reference input vector xt: 37 See Fisher (1922; 64). 38 See the discussion in Diewert (1997) on choosing the “best” symmetric average of Laspeyres and Paasche indexes that will lead to the satisfaction of the time reversal test by the resulting average index. 39 The theoretical productivity change indexes defined by (10)-(12) were first defined by Diewert and Morrison (1986; 662-663) in the nominal GDP context. 40 This measure of real output price change was essentially defined by Fisher and Shell (1972; 56-58), Samuelson and Swamy (1974; 588-592), Archibald (1977; 60-61), Diewert (1980; 460-461) (1983; 1055) and Balk (1998; 83-89). Readers who are familiar with the theory of the true cost of living index will note that the real output price index defined by (13) is analogous to the Konüs (1924) true cost of living index which is a ratio of cost functions, say C(u,pt)/C(u,pt−1) where u is a reference utility level: gs replaces C and the reference utility level u is replaced by the vector of reference variables x.

27

(14) αL

t ≡ α(pt−1,pt,xt−1,t−1) = gt−1(pt,xt−1)/gt−1(pt−1,xt−1) ; t = 1,2, ... ; (15) αP

t ≡ α(pt−1,pt,xt,t) = gt(pt,xt)/gt(pt−1,xt) ; t = 1,2, ... . Since both measures of real output price change are equally valid, it is natural to average them to obtain an overall measure of the effects on real income of the change in real output prices:41 (16) αt ≡ [αL

t αPt]1/2 ; t = 1,2, ... .

Finally, we look at the problem of defining theoretical indexes for the effects on real income due to changes in input quantities. Define a family of period t real input quantity growth factors β(xt−1,xt,p,s):42 (17) β(xt−1,xt,p,s) ≡ gs(p,xt)/gs(p,xt−1) ; s = 1,2, ... . Thus β(xt−1,xt,p,s) measures the proportional change in the real income produced by the market sector that is induced by the change in input quantities used by the market sector going from period t−1 to t, using the technology that is available during period s and using the reference real output prices p. Each choice of the reference technology s and the reference real output price vector p will generate a possibly different measure of the effect on real income of a change in input quantities going from period t−1 to period t. As usual, it is natural to choose special reference vectors for the measures defined by (17): a Laspeyres type measure βL

t that chooses the period t−1 reference technology and reference real output price vector pt−1 and a Paasche type measure βP

t that chooses the period t reference technology and reference real output price vector pt: (18) βL

t ≡ β(xt−1,xt,pt−1,t−1) = gt−1(pt−1,xt)/gt−1(pt−1,xt−1) ; t = 1,2, ... ; (19) βP

t ≡ β(xt−1,xt,pt,t) = gt(pt,xt)/gt(pt,xt−1) ; t = 1,2, ... . Since both measures of real input growth are equally valid, it is natural to average them to obtain an overall measure of the effects of input growth on real income:43 (20) βt ≡ [βL

t βPt]1/2 ; t = 1,2, ... .

Recall that market sector real income for period t was defined by (5) as ρt equal to nominal period t factor payments Wt⋅xt deflated by the household consumption price

41 The indexes defined by (13)-(16) were defined by Diewert and Morrison (1986; 664) in the nominal GDP function context. 42 This type of index was defined as a true index of value added by Sato (1976; 438) and as a real input index by Diewert (1980; 456). 43 The theoretical indexes defined by (17)-(20) were defined in Diewert and Morrison (1986; 665) in the nominal GDP context.

28

deflator PCt. It is convenient to define γt as the period t chain rate of growth factor for

real income: (21) γt ≡ ρt/ρt−1 ; t = 1,2, ... . 3. The Translog GDP Function Approach We now follow the example of Diewert and Morrison (1986; 663) and assume that the log of the period t (deflated) GDP function, gt(p,x), has the following translog functional form:44 (22) lngt(p,x) ≡ a0

t + ∑m=1M am

t lnpmt + (1/2) ∑m=1

M∑k=1M amk lnpm

t lnpkt

+ ∑n=1N bn

t lnxnt + (1/2)∑n=1

N∑j=1N bnj lnxn

t lnxjt + ∑m=1

M∑n=1M cmn lnpm

t lnxnt ;

t = 0,1,2, ... . Note that the coefficients for the quadratic terms are assumed to be constant over time. The coefficients must satisfy the following restrictions in order for gt to satisfy the linear homogeneity properties that we have assumed in section 2 above:45 (23) ∑m=1

M amt = 1 for t = 0,1,2, ...;

(24) ∑n=1N bn

t = 1 for t = 0,1,2, ...; (25) amk = akm for all k,m ; (26) bnj = bjn for all n,j ; (27) ∑k=1

M amk = 0 for m = 1,...,M ; (28) ∑j=1

N bnj = 0 for n = 1,...,N ; (29) ∑n=1

N cmn = 0 for m = 1,...,M ; (30) ∑m=1

M cmn = 0 for n = 1,...,N . Diewert and Morrison (1986; 663) showed that46 if gt−1 and gt are defined by (22)-(30) above and there is competitive profit maximizing behavior on the part of all market sector producers for all periods t, then (31) γt = τt αt βt ; t = 1,2, ... where γt, τt, αt and βt are defined above by (21), (12), (16) and (20) respectively. In addition, Diewert and Morrison (1986; 663-665) showed that τt, αt and βt could be

44 This functional form was first suggested by Diewert (1974; 139) as a generalization of the translog functional form introduced by Christensen, Jorgenson and Lau (1971). Diewert (1974; 139) indicated that this functional form was flexible. 45 There are additional restrictions on the parameters which are necessary to ensure that gt(p,x) is convex in p and concave in x. Note that when we divide the original prices by one of the prices, then one of the scaled prices will be identically equal to one and hence its logarithm will be identically equal to zero. 46 Diewert and Morrison established their proof using the nominal GDP function gt(P,x). However, it is easy to rework their proof using the deflated GDP function gt(p,x) using the fact that gt(p,x) = gt(P/PC,x) = gt(P,x)/PC using the linear homogeneity property of gt(P,x) in P.

29

calculated using empirically observable price and quantity data for periods t−1 and t as follows: (32) lnαt = ∑m=1

M (1/2)[(pmt−1ym

t−1/pt−1⋅yt−1) + (pmtym

t/pt⋅yt)] ln(pmt/pm

t−1) = ln PT(pt−1,pt,yt−1,yt); (33) lnβt = ∑n=1

N (1/2)[(wnt−1xn

t−1/wt−1⋅xt−1) + (wntxn

t/wt⋅xt)] ln(xnt/xn

t−1) = ln QT(wt−1,wt,xt−1,xt); (34) τt = γt/αt βt where PT(pt−1,pt,yt−1,yt) is the Törnqvist (1936) and Törnqvist and Törnqvist (1937) output price index and QT(wt−1,wt,xt−1,xt) is the Törnqvist input quantity index. Equations (31) are in rates of growth. It is possible to obtain counterparts to these equations in a levels form as follows. Thus we can express the level of real income in period t in terms of an index of the technology level or of Total Factor Productivity in period t Tt, of the level of real output prices in period t At, and of the level of primary input quantities in period t, Bt.47 Thus we use the growth factors τt, αt and βt as follows to define the levels Tt, At and Bt: (35) T0 ≡ 1 ; Tt ≡ Tt−1 τt ; t = 1,2, ... ; (36) A0 ≡ 1 ; At ≡ At−1αt ; t = 1,2, ... ; (37) B0 ≡ 1 ; Bt ≡ Bt−1βt ; t = 1,2, ... . Using the above definitions and the exact equations (31), we can establish the following exact relationship for the level of real income in period t, ρt, and the period t levels for technology, real output prices and input quantities: (38) ρt/ρ0 = Tt At Bt ; t = 1,2, ... . 4. The Translog GDP Function Approach and Changes in the Terms of Trade For some purposes, it is convenient to decompose the aggregate period t contribution factor due to changes in all deflated output prices αt into separate effects for each change in each output price. Similarly, it can sometimes be useful to decompose the aggregate period t contribution factor due to changes in all market sector primary input quantities βt into separate effects for each change in each input quantity. In this section, we indicate how this can be done, making the same assumptions on the technology that were made in the previous section. We first model the effects of a change in a single (deflated) output price, say pm, going from period t−1 to t. Counterparts to the theoretical Laspeyres and Paasche type price indexes defined by (14) and (15) above for changes in all (deflated) output prices are the 47 This type of levels presentation of the data is quite instructive when presented in graphical form. It was suggested by Kohli (1990) and used extensively by him; see Kohli (2003) (2004) and Fox and Kohli (1998).

30

following Laspeyres type measure αLmt that chooses the period t−1 reference technology

and holds constant other output prices at their period t−1 levels and holds inputs constant at their period t−1 levels xt−1 and a Paasche type measure αPm

t that chooses the period t reference technology and reference input vector xt and holds constant other output prices at their period t levels: (39) αLm

t ≡ gt−1(p1t−1,...,pm−1

t−1,pmt,pm+1

t−1,..., pMt−1,xt−1)/gt−1(pt−1,xt−1); m = 1,...,M; t = 1,...;

(40) αPmt ≡ gt(pt,xt)/gt(p1

t ,...,pm−1t,pm

t−1,pm+1t,..., pM

t,xt) ; m = 1,...,M; t = 1,2, ... . Since both measures of real output price change are equally valid, it is natural to average them to obtain an overall measure of the effects on real income of the change in the real price of output m:48 (41) αm

t ≡ [αLmt αPm

t]1/2 ; m = 1,...,M ; t = 1,2, ... . Under the assumption that the deflated GDP functions gt(p,x) have the translog functional forms as defined by (22)-(30) in the previous section, the arguments of Diewert and Morrison (1986; 666) can be adapted to give us the following result: (42) lnαm

t = (1/2)[(pmt−1ym

t−1/pt−1⋅yt−1) + (pmtym

t/pt⋅yt)] ln(pmt/pm

t−1) ; m = 1,...,M ; t = 1,2, ... . Note that lnαm

t is equal to the mth term in the summation of the terms on the right hand side of (32). This observation means that we have the following exact decomposition of the period t aggregate real output price contribution factor αt into a product of separate price contribution factors; i.e., we have under present assumptions: (43) αt = α1

tα2t... αM

t ; t = 1,2, ... . The above decomposition is useful for analyzing how real changes in the price of exports (i.e., a change in the price of exports relative to the price of domestic consumption) and in the price of imports impact on the real income generated by the market sector. In the empirical illustration which follows later, we let M equal three. The three net outputs are:

• Domestic sales (C+I+G); • Exports (X) and • Imports (M).

Since commodities 1 and 2 are outputs, y1 and y2 will be positive but since commodity 3 is an input into the market sector, y3 will be negative. Hence an increase in the real price of exports will increase real income but an increase in the real price of imports will decrease the real income generated by the market sector, as is evident by looking at the

48 The indexes defined by (39)-(41) were defined by Diewert and Morrison (1986; 666) in the nominal GDP function context.

31

contribution terms defined by (42) for m = 2 (where ymt > 0) and for m = 3 (where ym

t < 0). As mentioned above, it is also useful to have a decomposition of the aggregate contribution of input growth to the growth of real income into separate contributions for each important class of primary input that is used by the market sector. We now model the effects of a change in a single input quantity, say xn, going from period t−1 to t. Counterparts to the theoretical Laspeyres and Paasche type quantity indexes defined by (18) and (19) above for changes in input n are the following Laspeyres type measure βLn

t that chooses the period t−1 reference technology and holds constant other input quantities at their period t−1 levels and holds real output prices at their period t−1 levels pt−1 and a Paasche type measure βPn

t that chooses the period t reference technology and reference real output price vector pt and holds constant other input quantities at their period t levels: (44) βLn

t ≡ gt−1(pt−1,x1t−1,...,xn−1

t−1,xnt,xn+1

t−1,..., xNt−1)/gt−1(pt−1,xt−1) ; n = 1,...,N; t = 1,2, ... ;

(45) βPnt ≡ gt(pt,xt)/gt(pt,x1

t ,...,xn−1t,xn

t−1,xn+1t,..., pN

t) ; n = 1,...,N; t = 1,2, ... . Since both measures of input change are equally valid, as usual, we average them to obtain an overall measure of the effects on real income of the change in the quantity of input n:49 (46) βn

t ≡ [βPnt βPn

t]1/2 ; n = 1,...,N ; t = 1,2, ... . Under the assumption that the deflated GDP functions gt(p,x) have the translog functional forms as defined by (22)-(30) in the previous section, the arguments of Diewert and Morrison (1986; 667) can be adapted to give us the following result: (47) lnβn

t = (1/2)[(wnt−1xn

t−1/wt−1⋅xt−1) + (wnt xn

t/wt⋅xt)] ln(xnt/xn

t−1); n = 1,...,N ; t = 1,2, ... . Note that lnβn

t is equal to the nth term in the summation of the terms on the right hand side of (33). This observation means that we have the following exact decomposition of the period t aggregate input growth contribution factor βt into a product of separate input quantity contribution factors; i.e., we have under present assumptions: (48) βt = β1

tβ2t... βN

t ; t = 1,2, ... . Appendix 2: Business Sector Data on Outputs and Inputs for Canada 1961-2011 1. Introduction The basic approach to measuring productivity growth in this paper is to use Statistics Canada information on the outputs produced by the Canadian business sector from the national accounts along with Statistics Canada information on labour and capital inputs

49 The indexes defined by (52)-(54) were defined by Diewert and Morrison (1986; 667) in the nominal GDP function context.

32

used by the business in order to construct “top down” measures of the productivity performance of the Canadian business sector.50 We also make extensive use of Statistics Canada’s National Balance Sheet estimates for information on various capital inputs used by the business sector along with the more disaggregated information on business sector investment and capital stocks that is listed in CANSIM Table 310003. Our business sector labour information for 36 types of labour for the years 1961-2011 comes from CANSIM Table 3830024. The present approach to productivity measurement is an aggregate “top down” approach as opposed to the usual industry “bottom up” approach which makes use of detailed data on inputs used and outputs produced by industrial sectors and aggregates up sectoral productivity growth rates in order to obtain national business sector estimates.51 With reliable data, the two approaches should give very similar answers.52 Unfortunately, data on industry inputs and outputs are not likely to be as reliable as the corresponding national data for a variety of reasons53 so it is useful to provide a check on the industry approach to productivity measurement by using the national aggregate approach. There is another reason for undertaking a productivity study using final demand data and this reason is that the effects of changes in a country’s terms of trade can be measured in this framework whereas these effects cannot be measured in the industry accounts framework using the System of National Accounts 1993 (SNA 1993); see Chapter 15 in Eurostat, IMF, OECD, UN and World Bank (1993). In particular, the Input Output accounts as outlined in Table 15.1 in the SNA 1993 do not show the role of international trade in goods and services by industry. Exports and imports enter the main supply and use tables (Table 15.1) as additions (or subtractions) to total net supply or to total domestic final demand in the familiar C+I+G+X−M setup. This means that Table 15.1 in the main production accounts of SNA 1993 does not elaborate on which industries are actually using the imports or on which industries are actually doing the exporting by commodity.54 Thus at present, data difficulties prevent us from looking at the effects of changes in the terms of trade using the bottom up industry aggregation approach.

50 The present data base was constructed national accounts information that was available prior the recently released revised national accounts data. Our reason for not using the newly revised data is that the trade data were extensively revised but the new data only extended back to 1981 whereas our present data base extends back to 1961. 51 The bottom up approach is used by the Statistics Canada KLEMS program; see Baldwin, Wu and Yan (2007) for an overview and Baldwin and Yu (2007) for additional information on the construction of the Statistics Canada KLEMS capital services aggregates. 52 In fact, if indirect tax effects could be ignored and if nominal and real input output tables were perfectly consistent, the two approaches should give exactly the same answer; see Chapter 19 in the IMF, ILO, OECD, Eurostat, UNECE and the World Bank (2004), Diewert (2005c) (2006) and Moyer, Reinsdorf and Yuskavage (2006). 53 For a detailed discussion of these reasons, see Diewert (2001). 54 It should be noted that SNA 1993 does have a recommended optional Table 15.5 which is exactly suited to our present needs; i.e., this table provides the detail for imports by commodity and by industry. However, SNA 1993 does not provide a recommendation for a corresponding commodity by industry table for exports. The situation is remedied in SNA 2008 but statistical agencies generally do not have the data base to construct these detailed export and import matrices by industry and commodity. Thus for Canada, the necessary detailed trade data by industry and commodity are not publically available.

33

Diewert and Lawrence (2000) undertook a study of Canada’s business sector productivity using the national approach for the years 1962-1996 and Diewert (2002) extended their data to cover the years 1962-1998. Diewert (2008) updated these early studies that used the top down approach, noting that there were some differences in his study compared to the earlier studies:

• Statistics Canada provided new data on national expenditure aggregates back to 1961 using annual chained index numbers and so it was no longer necessary to work with the old fixed base data on the most disaggregated level possible and then use chain indexes to aggregate up these data.

• Statistics Canada also provided new data on the outputs produced and inputs used by the Canadian business sector back to 1961 using chained Fisher indexes as part of their KLEMS productivity measurement program. In particular, Statistics Canada provided new estimates of labour input, which were a big improvement over the estimates of labour input used by Diewert and Lawrence.

• Diewert and Lawrence (2000) worked with a rather narrow definition of the government sector; their definition included only the public administration industry. In Diewert (2008), the Statistics Canada definition of the nonbusiness sector was used (except that Diewert also added the residential rental housing industry to the nonbusiness sector). The Statistics Canada definition of the nonbusiness sector includes the general government sector and the publicly funded defence, hospital and education sectors in the nonbusiness sector.55 Since output in the nonbusiness sector is measured by input, the use of the broader definition of the government sector should lead to higher estimates of productivity growth in the business sector compared to the estimates tabled in Diewert and Lawrence (2000) and Diewert (2002).

• Statistics Canada reorganized its information on indirect taxes (less subsidies) into two categories: taxes that fall primarily on outputs and taxes that fall primarily on inputs. This new information was very useful in making adjustments to output prices for indirect tax effects.56

However, since Diewert (2008) appeared, there has been a substantial revision of the Statistics Canada data used in his study. Thus the present paper uses more recent published Statistics Canada data57 as well as some unpublished disaggregated capital data made available to us from the Statistics Canada KLEMS database. Note that the business 55 The nonbusiness sector consists of the following industries: (1) Government funding of hospitals; (2) Government funding of residential care; (3) Government funding of universities; (4) Government funding of other education; (5) Defence services; (6) Other municipal government services; (7) Other provincial government services and (8) Other federal government services. 56 In early studies of the Total Factor Productivity of an economy like those done by Solow (1957) and Jorgenson and Griliches (1967), outputs were priced at final demand prices, which include indirect taxes. However, Jorgenson and Griliches (1972; 85) noted that this treatment was not consistent with competitive price taking behavior on the part of producers, since producers do not derive any benefit from indirect taxes that fall on their outputs and thus these taxes should be removed. 57 These data were downloaded on October 1, 2012.

34

sector used here differs from the Statistics Canada business sector in that we have excluded all residential housing services (Owner Occupied Housing services plus Rental Housing services) from our business aggregate whereas Statistics Canada includes the services of rental housing in its business aggregate.58 The main conceptual changes in our present data base from the data tabled in Diewert (2008) are as follows:

• The trade data were disaggregated; • Machinery and equipment investment in Diewert (2008) has been disaggregated

into 10 types of machinery and equipment and 4 types of structure using the information in CANSIM Table 310003;

• We used the Statistics Canada KLEMS data on the price of inventory stocks in the present study whereas before, we used another Statistics Canada price series to value inventory stocks;

• The depreciation rates for the 10 types of machinery and equipment and the 4 types of structure were reestimated using information on capital stocks and investments contained in CANSIM Table 310003;

• We were able to construct disaggregated estimates for the price and quantity of 36 types of labour for the years 1961-2011 using information from CANSIM Table 3830024. These 36 types of labour were aggregated to form quality adjusted aggregate labour price and quantity series. The resulting business sector labour aggregate should be comparable to the KLEMS program labour aggregate.

In section 2 of this Appendix, we will list the basic final demand expenditure series that were used in this study. Section 3 lists the prices and quantities for the 36 types of business sector labour input that are available in three published business sector measures of quality adjusted labour input for the Canadian business sector that are available on CANSIM Table 3830024. Section 4 studies the problems associated with forming estimates for capital inputs. Section 5 concludes by forming estimates of tax rates on primary inputs. This information is used to calculate estimates of balancing after tax real rates of return. Then this information is used along with the information developed in previous sections in order to calculate user costs for 17 classes of capital input: 10 types of machinery and equipment, 4 types of nonresidential structures, agricultural land, nonagricultural and nonresidential business land and inventories. Section 6 concludes with some observations on the weak points in the data and recommendations for further work on developing a set of productivity accounts for Canada. 58 Our reason for excluding the services of rental housing from our business sector aggregate is due to the lack of accurate data on residential structures investment on rental housing and the lack of information on the quantity and value of land that is occupied by rental housing. Our measure of business sector labour input is the conceptually the same as that used by the Statistics Canada KLEMS program since we ignore the labour inputs used by the residential rental market. In practice, our labour estimates for the business sector (which are based on CANSIM Table 3830024) turn out to be substantially different from the KLEMS estimates. Our output measures and capital services input measures also differ from the corresponding KLEMS estimates because we have dropped rental housing inputs and outputs from our definition of the business sector.

35

2. Estimates of Canadian Final Demand Expenditures Much of the information tabled in this section was downloaded from CANSIM Table 3800002, Gross Domestic Product; Expenditure Based. The July 17, 2012 version of these data were used, using the Statistics Canada online data service CANSIM, which were listed as quarterly data. If the quarterly data were seasonally adjusted, then the data for a year were summed and divided by 4 in order to obtain annual data. If the quarterly data were not seasonally adjusted, then they were simply summed in order to obtain annual data. In what follows, we will use the CANSIM individual series label to identify the exact series used. The first two series are Personal Expenditures on Goods and Services in current and constant chained 2002 dollars, CANSIM Series V498087 and V1992044 respectively. Dividing the current dollar series VCT by the constant dollar series QCT gives us an implicit price series PCT for (total) personal consumption. We would like to exclude the imputed expenditures on Owner Occupied Housing (OOH) from the above series since there is no possibility of productivity gains occurring in this sector. However, if we exclude imputed rent from the business sector output series, we also need to exclude the services of the owner occupied housing capital stock as an input into the business sector. Unfortunately, we are not able to construct a reliable measure of the Owner Occupied Housing capital stock from available data; we can only construct a more reliable residential housing capital stock which includes the housing capital stock that is rented. We also were not able to split residential land input into reliable owner occupied and rental components.59 Hence we excluded both imputed and paid rents from our list of business sector outputs and we excluded the entire residential housing stock and the associated land as an inputs into the business sector.60 Information on current dollar expenditures on imputed rents and paid rents (VIMR

t and VPRt) for the years 1961-

2011 is available from CANSIM Series V498532 and V498533 respectively. The corresponding information on chained 2002 constant dollar expenditures on imputed rents and paid rents (QIMR and QPR) is available from CANSIM Series V1992078 and V1992079 only for the years 1981-2011. We divide VIMR by QIMR and VPR by QPR in order to form price index series for imputed and paid rents, PIMR and PPR for the years 1981-2011.

59 The determination of the structures and land inputs into the production of rented residential housing is a difficult task since the investment data on residential housing is not decomposed into owned and rented investments. This lack of information was also a problem for the Statistics Canada KLEMS program: “Data on investment in rental residential buildings are not available. For the annual MFP programs, we divide the total investment in residential building into rental building and owner-occupied dwelling using paid rents for rental buildings and imputed rents for owner occupied dwelling as the split ratios. The investment in residential buildings and paid and imputed rents are available from the Income and Expenditure Accounts. On average, we find that about 30% of total rents are paid rents and the remaining 70% are imputed rents.” Baldwin, Wu and Yan (2007; 43). 60 This means our productivity estimates will be biased downward slightly since the labour inputs that are used in the rental housing market are incorrectly included in our estimates of labour input.

36

From the Input-Output accounts, we can obtain alternative estimates for the value of imputed rents for owner occupied dwellings, VOOH

t, for the years 1961-2008 from CANSIM Series V3859926. We can also obtain alternative series for the value of imputed rents for owner occupied dwellings, VOOH1

t, from CANSIM Series V334072 and we can obtain the corresponding constant 1992 dollar estimates QOOH1

t from CANSIM Series V328857 for the years 1961-1997. We used these two series to form a price series for owner occupied housing rents, POOH

t, for the years 1961-1997. We divided the earlier more accurate value series VOOH by POOH to form QOOH for the years 1961-1997. The QOOH series was extended from 1997 to 2006 using CANSIM Series V14183160 from CANSIM Table 3790018 which had estimates in chained 1997 dollars for owner occupied housing. The QOOH series was further extended from 2006 to 2011 using the chained 2002 dollar estimates from Series V41881435 using CANSIM Table 3790027. Using this QOOH series, we were able to construct the implicit price index for imputed owner occupied housing rents, POOH, for 1961-2008 by dividing VOOH by QOOH. POOH was extended to cover the years 2009-2011 by using the movements in PIMR. Finally, VOOH was extended to cover the years 2009-2011 by multiplying together POOH

t times QOOHt.

We decided to use the industry oriented VOOHt series rather than the final demand

oriented series VIMRt so that our business sector output concept would better align with

the Statistics Canada KLEMS output aggregate. Recall that we had a paid rent value series VPR

t that covered the years 1961-2011 but the corresponding price series PPR

t covered only the years 1981-2011. We linked PPR to POOHt

at 1981 to obtain continuous price series for paid rents for the years 1961-2011.61 The resulting imputed and paid rent series are listed in Table 1 below. Table 1: Housing Value, Quantity and Price Series for Imputed and Paid Rents62

Year t VOOHt QOOH

t VPRt QPR

t POOHt PPR

t

1961 2292 2292 1107 1107 1.00000 1.00000 1962 2436 2380 1176 1149 1.02350 1.02350 1963 2660 2412 1290 1170 1.10275 1.10275 1964 2832 2477 1396 1221 1.14316 1.14316 1965 2976 2531 1503 1278 1.17565 1.17565 1966 3249 2620 1658 1337 1.23992 1.23992 1967 3585 2678 1860 1390 1.33856 1.33856 1968 3985 2707 2091 1420 1.47212 1.47212 1969 4416 2784 2342 1476 1.58633 1.58633 1970 4897 2833 2645 1530 1.72855 1.72855 1971 5388 2864 2918 1551 1.88118 1.88118 1972 5757 2866 3183 1584 2.00889 2.00889 1973 6307 2862 3451 1566 2.20366 2.20366 1974 7107 2923 3787 1558 2.43126 2.43126 1975 8313 2992 4290 1544 2.77854 2.77854 1976 10038 3072 4842 1482 3.26746 3.26746

61 Thus we are assuming that the price movements in paid rents for the years 1961-1981 followed the movements in imputed rents for those years. 62 The units for all value and quantity series in this Appendix are millions of current dollars for the V series and millions of 1961 dollars for the Q series.

37

1977 12126 3084 5443 1384 3.93199 3.93199 1978 14090 3051 6106 1322 4.61807 4.61807 1979 15797 2996 6829 1295 5.27283 5.27283 1980 17869 3053 7686 1313 5.85278 5.85278 1981 20512 3159 8822 1359 6.49322 6.49322 1982 23489 3213 10082 1410 7.31046 7.15154 1983 26285 3256 11295 1444 8.07270 7.82159 1984 28446 3294 12181 1471 8.63567 8.28079 1985 30694 3360 12967 1500 9.13517 8.64482 1986 33386 3463 13955 1539 9.64089 9.06928 1987 36117 3573 15090 1599 10.10837 9.43653 1988 39587 3801 16419 1662 10.41493 9.87670 1989 44078 4011 18201 1726 10.98935 10.54481 1990 48016 4221 19786 1798 11.37552 11.00446 1991 51779 4469 21133 1853 11.58636 11.40566 1992 54872 4627 22269 1899 11.85900 11.72872 1993 57263 4770 23108 1943 12.00486 11.89235 1994 60557 4887 24056 1982 12.39142 12.13540 1995 63613 5001 24869 2016 12.72013 12.33820 1996 65418 5116 25632 2049 12.78691 12.51068 1997 67405 5245 26425 2097 12.85127 12.59838 1998 69835 5389 27223 2139 12.95872 12.72809 1999 72144 5557 28173 2187 12.98263 12.87911 2000 74582 5704 29059 2231 13.07545 13.02515 2001 77093 5843 30092 2279 13.19410 13.20509 2002 80895 6074 31491 2341 13.31831 13.44940 2003 83916 6250 32829 2413 13.42651 13.60407 2004 87609 6482 34133 2487 13.51571 13.72279 2005 91542 6730 35435 2560 13.60208 13.84028 2006 96748 6985 37137 2638 13.85079 14.07831 2007 103305 7249 39263 2715 14.25093 14.45908 2008 109860 7528 41381 2797 14.59357 14.79683 2009 115263 7786 43243 2881 14.80390 15.01058 2010 120256 8049 44955 2966 14.94045 15.15466 2011 125685 8322 46819 3054 15.10268 15.33019

Recall the price and quantity series, PCT and QCT, for a consumption aggregate (which includes all rents, paid and imputed) along with the two price and quantity series for imputed and paid rents in Table 1 above. We changed the sign of the rent quantity series from plus to minus and then calculated a chained Fisher net consumption aggregate by aggregating all consumption (plus sign for these quantities) and rents (negative signs for these quantities). The resulting price and quantity series should closely approximate the price and quantity of consumption excluding housing services. However, the price series includes indirect taxes (less subsidies) on outputs but for productivity measurement purposes, as mentioned earlier, these tax wedges should be excluded. Statistics Canada has a series for indirect taxes less subsidies on products VIT

t, CANSIM II series V1997473, for the years 1961-2011. We subtracted two other tax series from this indirect tax series because these other tax series will be taken into account separately in the price of exports of goods (this is the Oil Export Tax series, CANSIM series V499746) and in

38

the price of imports of goods (this is the Customs Import Duties series, CANSIM series V499741). The resulting indirect taxes less subsidies on products (less trade taxes) series was used to remove the tax wedges on the price of consumption series. The resulting prices and quantities of consumption, PC

t and QCt, are listed in Tables 2 and 3 below.

We turn our attention to the investment components of final demand. Current dollar government gross fixed capital formation is available as CANSIM series V498093 for the years 1961-2011. The corresponding chained 2002 dollar series is CANSIM II series V1992050 and we use these two series to form price and quantity series for general government sector investment, PIG

t and QIGt, which are listed in Tables 2 and 3 below.63

The current and constant chained dollar series for the years 1961-2011 for residential structures investment can be obtained as CANSIM series V498096 and V1992053 respectively, the current and constant 2002 chained dollar series for nonresidential structures investment can be obtained as CANSIM series V498098 and V1992053 respectively and the current and constant chained dollar series for machinery and equipment investment can be obtained as CANSIM series V498099 and V1992056 respectively. The resulting price and quantity series are denoted by PIR

t, PINt, QIR

t, QINt

and are listed in Tables 2 and 3 below. These Tables also include the price and quantity of inventory change, PII

t and QIIt, the price and quantity of business sector net deliveries

to the nonbusiness sector, PGNt and QQN

t, the export and import price indexes PXt and PM

t

and the corresponding quantity indexes QXt and QM

t but the description of how these series were constructed is deferred until later. Table 2: Price Indexes for Business Sector Net Outputs: Consumption, Investment and Trade Year t PC

t PGNt PIG

t PIRt PIN

t PIMt PII

t PXt PM

t 1961 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1962 1.00617 0.99388 1.00855 1.00504 1.00592 1.01973 1.00240 1.02992 1.05787 1963 1.01956 0.97566 1.03939 1.02769 1.03251 1.03352 1.01346 1.04054 1.09648 1964 1.02317 0.92683 1.06231 1.07312 1.06158 1.06837 1.03169 1.05692 1.10526 1965 1.03598 0.91239 1.13926 1.13368 1.12281 1.09293 1.05486 1.07980 1.10214 1966 1.07430 0.88328 1.21007 1.20765 1.19323 1.11917 1.07231 1.12451 1.11930 1967 1.10738 0.89087 1.23160 1.28518 1.24188 1.13235 1.08449 1.15421 1.14426 1968 1.14786 0.96139 1.23844 1.31431 1.25227 1.14980 1.10971 1.20119 1.16726 1969 1.18479 0.96769 1.28464 1.38118 1.32495 1.19542 1.13490 1.23088 1.19648 1970 1.21483 1.00582 1.33877 1.42615 1.39058 1.24395 1.15046 1.26710 1.21965 1971 1.24210 1.10291 1.40873 1.53179 1.46812 1.28144 1.20264 1.28552 1.24798 1972 1.29301 1.14412 1.48528 1.67349 1.55098 1.32335 1.31611 1.33325 1.27498 1973 1.38394 1.22092 1.64838 1.97123 1.71873 1.37155 1.42683 1.51489 1.35954 1974 1.58215 1.35752 2.01078 2.36134 2.03419 1.52083 1.54691 1.91283 1.64641 1975 1.81969 1.48446 2.23421 2.56072 2.27337 1.70347 1.65112 2.16694 1.89029 1976 1.90416 1.64265 2.34499 2.76853 2.40093 1.82172 1.77007 2.29702 1.92853 1977 2.02765 1.78697 2.48990 2.87768 2.52980 1.95440 1.92666 2.50231 2.17241 1978 2.19006 1.92861 2.66206 3.04069 2.71145 2.13274 2.13561 2.73837 2.41667 1979 2.40319 2.18540 2.88522 3.28046 2.96312 2.31511 2.34120 3.20786 2.73027 1980 2.69102 2.48896 3.19858 3.55455 3.32520 2.49752 2.55883 3.73464 2.97957 1981 2.89817 2.79431 3.68313 3.99273 3.68676 2.79726 2.75849 3.99821 3.26618 1982 3.16581 3.10614 3.92658 4.08226 3.96113 3.01411 2.91040 4.08926 3.43918

63 The price series for investment should be adjusted for indirect taxes that fall on investment outputs. Since these taxes are relatively small and it is difficult to collect consistent information on these taxes over our sample period, we neglect these indirect tax wedges on investment components of final expenditure.

39

1983 3.40715 3.37412 4.01498 4.25350 3.93090 3.08751 3.04428 4.15051 3.42324 1984 3.56365 3.48567 4.17063 4.41785 4.08142 3.09060 3.12590 4.29656 3.58225 1985 3.67559 3.67204 4.20827 4.55564 4.21351 3.12859 3.15838 4.38071 3.67711 1986 3.75577 3.74218 4.20267 4.90827 4.27520 3.16319 3.20668 4.37060 3.74437 1987 3.85242 3.79747 4.22375 5.40819 4.47320 3.11015 3.26271 4.45792 3.69150 1988 3.95781 3.78607 4.33769 5.78293 4.72840 3.06780 3.31521 4.47080 3.60108 1989 4.07115 3.82606 4.43728 6.13195 4.92520 3.07778 3.36284 4.56005 3.59364 1990 4.30215 3.86395 4.53066 6.11231 5.08853 3.09245 3.36458 4.52868 3.64367 1991 4.53970 3.92576 4.31837 6.32257 5.00311 2.93829 3.51938 4.37107 3.57992 1992 4.59854 3.94383 4.31896 6.39710 4.97541 2.95425 3.52557 4.49573 3.72567 1993 4.68858 3.96988 4.34342 6.58445 5.03758 3.01578 3.70024 4.69389 3.92460 1994 4.71799 4.17941 4.42033 6.76485 5.20497 3.11452 3.83041 4.97322 4.16089 1995 4.73527 4.29853 4.51572 6.76717 5.27332 3.12739 3.91857 5.29132 4.27688 1996 4.83325 4.20205 4.53812 6.75581 5.43035 3.10234 3.78206 5.32097 4.22185 1997 4.91285 4.10280 4.57906 6.87512 5.56694 3.10301 3.80677 5.32718 4.23677 1998 4.97834 4.13974 4.59706 6.95993 5.71450 3.14384 3.86651 5.31558 4.37960 1999 5.06934 4.29033 4.57201 7.13210 5.82995 3.04811 3.95640 5.37870 4.36044 2000 5.20684 4.43225 4.68967 7.29782 6.02775 3.02212 4.04039 5.71039 4.44227 2001 5.36470 4.45850 4.68012 7.48766 6.07934 3.06002 4.10861 5.80311 4.58416 2002 5.43364 4.56662 4.72977 7.81242 6.18175 3.08815 3.87128 5.68895 4.61494 2003 5.57127 4.56905 4.72659 8.21290 6.30506 2.88779 3.91048 5.64768 4.31493 2004 5.65242 4.65063 4.79882 8.71618 6.70389 2.77547 3.95736 5.78629 4.20643 2005 5.77665 4.74909 4.91404 9.12487 7.12456 2.67650 4.02157 5.95233 4.15583 2006 5.87995 4.80962 5.10654 9.79903 7.63305 2.60268 4.13713 5.97500 4.11704 2007 5.98858 4.95398 5.28215 10.51028 8.10047 2.52615 4.14869 6.03062 4.01439 2008 6.15649 5.11078 5.64290 10.79847 8.55985 2.54541 4.18721 6.64397 4.24350 2009 6.18318 5.27294 5.68597 10.81072 8.71321 2.68320 4.19106 5.99089 4.28278 2010 6.25491 5.38816 5.68001 11.13668 8.99324 2.50320 4.32588 6.12294 4.10323 2011 6.39168 5.55785 5.83989 11.44031 9.28560 2.42539 4.42989 6.55859 4.17485

Table 3: Quantity Indexes for Business Sector Net Outputs: Consumption, Investment and Trade Year t QC

t QGNt QIG

t QIRt QIN

t QIMt QII

t QXt QM

t 1961 20117 1420 1887 2211 2618 2144 1 6867 7897 1962 21175 1447 2094 2271 2545 2322 560 7195 8033 1963 22127 1446 2101 2354 2637 2556 936 7832 8031 1964 23357 1596 2141 2715 3050 3027 532 9105 8989 1965 24791 1798 2426 2825 3320 3611 1228 9418 10180 1966 26048 2320 2668 2699 3802 4337 1313 10696 11579 1967 27029 2684 2718 2754 3613 4350 454 11827 12306 1968 28317 2950 2758 3132 3593 3984 619 12910 13527 1969 29705 3068 2700 3551 3592 4307 1580 13802 15377 1970 30227 3858 2645 3254 3946 4419 180 15211 15293 1971 32085 3885 2985 3728 4089 4537 −232 15929 16480 1972 34636 3942 2938 4066 4074 4940 148 17257 18892 1973 37401 4247 2781 4371 4396 5993 2542 19008 21754 1974 39498 4819 2845 4464 4675 6737 4839 18347 23977 1975 41166 5397 2962 4386 5286 7121 −334 16951 23228 1976 43591 5254 2855 5172 5168 7363 250 18390 24774 1977 45148 5963 2916 5242 5479 7260 1319 19678 24836 1978 46909 5833 2875 5291 5626 7492 1300 21544 26197 1979 48338 5796 2803 5251 6337 8526 3691 22467 28092 1980 49160 6062 2869 4977 7055 9054 167 22548 28715 1981 49549 5845 2967 5279 7620 10142 891 23012 30716 1982 47858 6019 3095 4340 6929 8597 −4603 22882 25710 1983 49205 5998 2991 5079 6361 8207 −1049 24326 28444 1984 51575 5838 3124 5131 6288 8696 1744 28444 33270 1985 54441 6539 3497 5578 6590 9652 1467 29938 35548 1986 56557 6635 3485 6267 6210 10605 1029 31456 37965 1987 58999 6789 3621 7190 6454 12171 1701 32933 39889 1988 61384 7814 3789 7340 7110 14394 2078 35371 45163 1989 63294 8423 4184 7640 7345 15424 1406 35434 47820

40

1990 63534 9043 4463 6835 7346 14706 −583 37556 48551 1991 61649 9508 4692 5824 7075 14271 −3899 38167 49281 1992 62362 9458 4621 6238 5960 14120 −551 40921 51473 1993 63317 9223 4560 6024 5993 13731 −878 45382 55461 1994 65342 8537 4894 6271 6533 15058 709 51076 60606 1995 66670 8165 4740 5340 6574 16239 3164 55452 64385 1996 68463 8263 4536 5852 6696 17230 2417 58646 67340 1997 71965 8414 4390 6330 7881 21703 1780 63457 77378 1998 73991 9511 4361 6106 7906 23575 2329 69086 81755 1999 76954 9380 5039 6324 8101 25951 1249 76337 88261 2000 80310 10022 5229 6656 8266 27580 2915 83350 95661 2001 82116 11040 5830 7363 8712 26758 −1856 80654 90649 2002 85095 11443 6044 8403 8195 25995 3367 81599 92347 2003 87666 12088 6370 8854 8651 27991 −1722 79268 96341 2004 90491 12331 6773 9519 9257 30529 1058 83281 104558 2005 93826 12483 7543 9820 10211 34837 2299 84847 112552 2006 97845 13197 8058 10023 11167 38396 1693 85213 118273 2007 102531 13469 8580 10303 11423 40009 1554 86367 125533 2008 105442 14353 9237 9977 12322 39824 2911 82650 126364 2009 105202 15394 10049 9181 9593 32063 −3031 71414 108643 2010 108742 15922 11852 10119 9863 35861 −1410 76559 123691 2011 111173 15718 11482 10355 11210 40330 1671 80232 132890

With the exceptions of QGN and QM, all of the quantities listed in Table 3 can be regarded as outputs produced by the business sector and sold to final demanders. However, the business sector also sells goods and services to the nonbusiness sector and it also purchases smaller amounts of goods and services from the nonbusiness sector. We now describe how we formed price and quantity estimates for the net sales of the business sector to the nonbusiness sector, QGN. For the years 1961-2011 from the National Income and Expenditure Accounts, CANSIM II series V498092; Government Current Expenditure on Goods and Services, Table 3800002, we have estimates of total government gross current expenditures on goods and services (less sales of goods and services to the business sector) in current dollars. From the same Table and for the same years, CANSIM II series V1992049; Government Current Expenditure on Goods and Services, Table 3800002, we have estimates of total government gross current expenditure on goods and services (less sales of goods and services to the business sector) in chained 2002 dollars. We use these two series to form price and quantity series for final demand government sector net expenditures on goods and services, PG

t and QGt, which are listed in Table 4.

Recall that the Statistics Canada KLEMS productivity program business sector value added aggregate includes rental residential housing but excludes the services of owned residential housing (whereas our business sector value added aggregate excludes all forms of residential rents). The Industry Division of Statistics Canada produces yet another business sector estimate of nominal and real value added (at factor cost) which includes all residential rents, both imputed and paid. We will denote this value added aggregate by VB

t in year t. Statistics Canada also produces a companion nonbusiness sector value added aggregate (at factor cost) which we will denote by VN

t in year t. If the value of indirect taxes less subsidies on products for year t, VIT

t, is added to the sum of these two industry value added aggregates, we get an estimate of the value of GDP at final demand prices in year t; i.e., we have the following identity:

41

(1) VBt + VN

t + VITt = VGDP

t . We will now describe how we formed estimates for VB

t and VNt along with the

corresponding price and quantity decompositions. From Table 3790024, Gross Domestic Product (GDP) at Basic Prices in Current Dollars, SNA, Benchmark Values, Special Industry Aggregations Based on the North American Industry Classification System (NAICS), we can obtain the VB

t series (series title is Canada: Business Sector Industries) for the years 1961-2008 from CANSIM II Series V3860037. From the same Table 3790024, we can obtain the VN

t series (series title is Canada: Non-Business Sector Industries) for the years 1961-2008 from CANSIM II Series V3860040. We can obtain price indexes PB

t, PNt and quantity indexes QB

t, QNt for VB

t and VNt for the years 1961-

1997 by using the series V334562, V335071, V334565 and V335074 from CANSIM Table 3790002, Gross Domestic Product (GDP) at Factor Cost, System of National Accounts Benchmark Values by Industry (Special Aggregations). These series give business and nonbusiness sector value added at basic prices in current dollars and in constant 1992 dollars. Using CANSIM Table 3790020, we can find estimates for QB

t (Series V14182646) and for QN

t (Series V14182651) in chained 1997 dollars for the years 1997-2006. The QB series can be extended to 2011 by aggregating the monthly data in CANSIM Table 3790027, Series V41881176, which has the title: Gross Domestic Product at Basic Prices, by North American Industry Classification System, Canada, Seasonally Adjusted at Annual Rates, Chained 2002 Dollars, Business Sector Industries. The QN series can be extended to 2011 by aggregating the monthly data in CANSIM Table 3790027, Series V41881179. Thus we now have enough information to define the PB

t and PNt series through to 2008. We extend the price series PN

t from 2008 using an implicit price index for government goods and services, PG

t, which was constructed using CANSIM Table 3800002, Series V498092 in current dollars and Series V1992049 for chained 2002 dollars, QG

t, which are listed in Table 4. It turns out that the total of VBt and

VNt is available in CANSIM Series V3860274. Canada, Gross Domestic Product (GDP)

at Basic Prices in Table 3800030: GDP and GNP at Market Prices and Net National Income at Basic Prices. Thus we have enough information to deduce the price PB

t and the value of business sector output VB

t for the years 2009-2011.The business and nonbusiness sector price and quantity series, PB

t, PNt and QB

t, QNt are listed in Table 4

below. Table 4: Business Sector, Nonbusiness Sector, Government Final Demand and Net Sales of the Business Sector to the Nonbusiness Sector Price and Quantity Aggregates

Year t QBt QN

t QGt

QGN

t PBt PN

t PGt

PGN

t 1961 33097 5204 6624 1420.0 1.00000 1.00000 1.00000 1.00000 1962 35338 5480 6928 1447.2 1.00919 1.03863 1.02916 0.99388 1963 37217 5713 7164 1446.5 1.02992 1.08205 1.05990 0.97566 1964 39810 5952 7542 1596.0 1.04877 1.14227 1.09761 0.92683 1965 42658 6120 7883 1798.1 1.07554 1.21527 1.15160 0.91239 1966 45529 6409 8581 2320.4 1.12248 1.34490 1.24333 0.88328 1967 46616 6870 9334 2684.3 1.16053 1.45671 1.32836 0.89087 1968 49335 7263 9944 2950.2 1.19304 1.54780 1.41575 0.96139

42

1969 51965 7585 10376 3067.7 1.23452 1.71317 1.53846 0.96769 1970 52968 7962 11287 3857.9 1.29437 1.84146 1.64279 1.00582 1971 55844 8255 11631 3885.3 1.33615 1.95964 1.75921 1.10291 1972 59086 8549 11995 3941.8 1.40300 2.12810 1.89268 1.14412 1973 63467 8887 12559 4247.0 1.54872 2.31234 2.04912 1.22092 1974 65346 9295 13357 4819.0 1.79635 2.65779 2.33927 1.35752 1975 65545 9790 14251 5397.0 2.03754 3.05325 2.65962 1.48446 1976 70082 10097 14525 5253.9 2.17572 3.45337 2.99471 1.64265 1977 72425 10348 15205 5963.5 2.32657 3.73913 3.24567 1.78697 1978 74875 10644 15473 5833.4 2.51505 3.96850 3.45708 1.92861 1979 77878 10805 15635 5795.8 2.80145 4.29236 3.77635 2.18540 1980 79169 11138 16169 6061.5 3.12982 4.66836 4.14895 2.48896 1981 81847 11496 16441 5845.2 3.40152 5.22919 4.64970 2.79431 1982 78970 11693 16767 6018.8 3.65996 5.83630 5.18504 3.10614 1983 81077 11952 17045 5997.9 3.89493 6.12278 5.48059 3.37412 1984 86041 12198 17222 5837.5 4.03944 6.37296 5.69544 3.48567 1985 90944 12471 17959 6538.6 4.13895 6.57967 5.90593 3.67204 1986 93580 12708 18283 6635.1 4.19906 6.81314 6.09362 3.74218 1987 97824 12840 18525 6789.3 4.38354 7.17180 6.36273 3.79747 1988 102723 13057 19370 7814.3 4.58086 7.53056 6.60377 3.78607 1989 105427 13224 19903 8422.7 4.75619 8.03351 6.95695 3.82606 1990 106128 13541 20605 9043.3 4.85194 8.60166 7.34874 3.86395 1991 104194 13849 21208 9508.3 4.90597 9.01919 7.64969 3.92576 1992 105171 14045 21414 9457.7 4.92162 9.36188 7.88200 3.94383 1993 108151 14150 21422 9223.4 4.97722 9.50865 7.98997 3.96988 1994 113766 14218 21156 8536.8 5.08269 9.55910 8.11082 4.17941 1995 117124 14279 21034 8165.1 5.23638 9.61980 8.19895 4.29853 1996 119744 14025 20786 8263.1 5.33957 9.72826 8.23447 4.20205 1997 125797 13787 20579 8413.8 5.40168 9.95401 8.34626 4.10280 1998 131475 13890 21240 9511.2 5.37429 10.0751 8.44225 4.13974 1999 139515 14320 21687 9379.8 5.47529 10.18237 8.57899 4.29033 2000 147808 14614 22356 10021.8 5.71191 10.65177 8.94989 4.43225 2001 149733 14926 23229 11040.4 5.80825 10.88586 9.11375 4.45850 2002 153895 15241 23802 11443.2 5.82601 11.29659 9.42889 4.56662 2003 156933 15608 24551 12087.9 6.02555 11.73665 9.71085 4.56905 2004 162130 15921 25044 12330.9 6.23729 11.93710 9.87845 4.65063 2005 167081 16154 25398 12483.5 6.46382 12.41623 10.23156 4.74909 2006 171718 16519 26169 13197.2 6.64006 12.96292 10.60811 4.80962 2007 175499 17001 26882 13469.3 6.85982 13.34517 10.92219 4.95398 2008 176113 17640 28064 14353.2 7.19205 13.75401 11.25935 5.11078 2009 169030 18080 29074 15394.2 6.97843 14.19040 11.61659 5.27294 2010 175238 18467 29786 15921.7 7.17976 14.50048 11.87043 5.38816 2011 180295 18735 30020 15717.7 7.41730 14.95717 12.24428 5.55785

Recall the GDP identity defined by (1) above, which expressed the nominal value of GPD, VGDP

t, at final demand prices as being equal to the value added of the Industry Division business sector value added at basic prices, VB

t, plus nonbusiness sector value added, VN

t, plus the value of indirect taxes less subsidies on products, VITt. We can also

express the value of GDP at final demand prices as the familiar sum of final demand values; i.e., as the following sum of final demand expenditures on consumption plus

43

investment plus government expenditures on goods and services plus exports less imports: (2) VGDP

t = VCTt + VI

t + VGt + VX

t − VMt.

Define a new consumption aggregate at basic prices VCN

t as the value of consumption at final demand prices, VCT

t, less indirect taxes less subsidies on products, VITt:

(3) VCN

t ≡ VCTt − VIT

t . Now equate the two expressions for the value of GDP given by (1) and (2) and use the resulting equation to express business sector value added VB

t in terms of final demand components and the value of nonbusiness sector value added VN

t. Making use of (3), the resulting equation is the following one:64 (4) VB

t = VCNt + VI

t + VXt − VM

t + (VGt − VN

t). Conceptually, the aggregate VG

t − VNt should be equal to the sales of the business sector

of goods and services to the nonbusiness sector less the purchases of intermediate inputs of the business sector from the nonbusiness sector. Put another way, the business sector’s net sales of goods and services should equal its net deliveries to final demand sectors (VC

t + VI

t + VXt − VM

t) plus its net deliveries to the nonbusiness sector (VGt − VN

t). Recall that we did not use the Industry Division’s concept of Business Sector value added; we subtracted the value of imputed and paid residential rent from our business sector aggregate. Let VR

t be equal to the sum of imputed residential rent VOOHt and paid

residential rent VPRt (see Table 1 for these series). Conceptually, if we subtract rents VR

t from VCN

t, we should get VCt, the consumption aggregate whose price and quantity is

listed in Tables 2 and 3 above. Thus subtracting VRt from both sides of (4) leads to the

following identity: (5) VB

t − VRt = VC

t + VIt + VX

t − VMt + (VG

t − VNt).

Thus our business sector value added aggregate can be formed using either the left or right hand sides of the identity (5). We will use the right hand side of (5) to form our value measure of business sector net output since we want to focus on the effects of changing international prices on the performance of the business sector. How should the corresponding real quantities that correspond to the value aggregates on either side of (5) be calculated? Obviously, each cell in the supply and use tables that correspond to the value aggregate on the left hand side of (5) could be aggregated up using a chained superlative index number formula provided that an appropriate price 64 The identity (4) is not quite consistent with our treatment of indirect taxes less subsidies since we also made some indirect tax adjustments to the prices of exports and imports as explained above; i.e., since we used a slight modification of (3) to adjust final demand consumption prices for indirect tax wedges, we used a corresponding slight modification of the identity (4).

44

deflator were available for each cell.65 On the other hand, the value cells that are components on the right hand side of (5) that correspond to final demand components (at basic prices) could be aggregated up using a chained superlative index number formula. We can then ask: under what conditions would the corresponding quantity aggregates be equal? This question is addressed by Moyer, Reinsdorf and Yuskavage (2006) and in more detail by Diewert (2005c) (2006). The answer to this question is that if the detailed data are constructed in an appropriate manner and the Fisher formula is used, then the direct industry aggregation and the aggregation of final demand component approaches are perfectly consistent.66 In addition, if two stage aggregation procedures are used and a superlative index number formula is used at each stage of aggregation, then the theoretical and empirical results in Diewert (1978) show that the commonly used single stage superlative indexes will approximate their two or more stage counterparts to a high degree of approximation if the chain principle is used.67 Using the above results, we will construct our measure of business sector real value added by aggregating up the value components on the right hand side of (5). Rather than work with both VG

t and VNt as final demand components, we will aggregate over these

two components to form the value aggregate VGNt equal to (VG

t − VNt), and conceptually,

this value aggregate should be equal to the net deliveries of goods and services of our business sector to the nonbusiness sector less the purchases of intermediate inputs by our business sector from the nonbusiness sector. The year t price and quantity aggregates, PGN

t and QGNt, that correspond to these value aggregates VGN

t are calculated using chained Fisher indexes with QN

t getting a negative weight in the index number formula. PGN

t and QGNt are listed in Table 4 above.

We now turn our attention to the export and import components of final demand. Current dollar exports of goods are available as CANSIM Series V498104 for the years 1961-2011. The corresponding chained 2002 dollar series is CANSIM Series V1992061 and these two series could be used to form price and quantity series for the exports of goods. However, in this study, we will form series for more detailed components of the exports and imports of goods. Current dollar exports of services are available as CANSIM Series V498105 for the years 1961-2011. The corresponding chained 2002 dollar series is CANSIM Series V1992062 and we use these two series to form price and quantity series for the exports of services, P15

t and Q15t, which are listed in Tables 5 and 6 below.

Our starting point for obtaining disaggregated data on the exports and imports of goods is CANSIM Table 3800012, Exports and Imports of Goods and Services, Canada, Current Prices. It is possible to obtain disaggregated information on the value of exports for the following 7 classes for the years 1971-2011:

65 Quantities in the Make matrix would have a positive sign while quantities in the Use matrix would have a negative sign. 66 See Diewert (2005c) (2006) and the numerical examples in Chapters 19 and 20 of the IMF, ILO, OECD, Eurostat, UNECE and the World Bank (2004) (2009). 67 The results of Hill (2006) show that these approximation results will not necessarily hold for mean of order r superlative indexes if r is large in magnitude.

45

• Q8: Exports of agricultural and fish products; • Q9: Exports of energy products; • Q10: Exports of forest products; • Q11: Exports of industrial goods and materials (excluding energy and forest

product exports); • Q12: Exports of machinery and equipment (excluding automotive products); • Q13: Exports of automotive products; • Q14: Exports of other consumer goods (excluding automotive products);

The CANSIM Series numbers for the first 7 classes of exports are V498730-V498736. It is also possible to find corresponding constant dollar series in 1992 constant dollars over the period 1971-1997 in CANSIM Table 3800012 and the CANSIM Series numbers are V498767-V498773. Finally, constant dollar chained estimates for these export categories (in 2002 chained dollars) can be found for the years 1981-2011 in CANSIM Table 3800012 and the Series numbers are V1992162- V1992168. We used these series to form chained price and quantity series for these 7 export categories for the years 1981-2011. The constant dollar price series were linked to each chained price series at the year 1981 in order to extend the chained series back to 1971.68 There remains the problem of obtaining price series for the above 7 classes of exports to cover the years 1961-1971. From Leacy (1983), Series G415-428 Foreign trade, domestic exports, excluding coin and bullion, by main commodity sections, current values, we can obtain value series covering exports for the years 1946-1975 for the following 5 commodity classes:

• Live animals (G415); • Food, feed, beverages and tobacco (G417); • Crude materials (inedible) (G419); • Fabricated materials (inedible) (G421); • End products (inedible) (G423).

From the same source, price indexes for each of the above 5 classes of exports are available as Series K57-K61 in the Table with the title: Export price indexes, trade of Canada commodity classification, 1926-1975. Thus we can find price and quantity series for these 5 classes of exports that cover the years 1961-1971. Unfortunately, these price indexes are of the fixed base variety with a base year of 1948 so they are likely to differ substantially from the corresponding chain indexes (which are not publicly available). However, Leacy (1983) also lists as part of export price Series K57-K61 (Panel A) for the above 5 classes of exports some indexes that have a 1971 base year but these price indexes cover only the years 1968-1975. We use these latter price indexes to construct export price indexes for the years 1968-1971 and then we use the 1948 based indexes to further extend these 5 series back to 1961.

68 There were two other categories in the export and import classifications: Special transactions and Other balance of payments adjustments. These categories were small and were omitted in our analysis.

46

The above operations give us 5 disaggregated export price and quantity series for the period 1961-1971 but we have 7 classes of exports of goods for the years 1971-2011. We generated Fisher chained price and quantity indexes for exports of Live animals and for exports of Food, feed, beverages and tobacco for the years 1961-1971 and linked these series to our earlier series, P8 and Q8, exports of agricultural and fish products. But we need some additional series so that we can match the export and import series for the 1960s to the series that cover the post 1971 period. We will create separate export series for energy, forest products, automotive products and other consumer goods. Our sources for these extra series are the input output tables for the Canadian economy that cover the years 1961-1981; see Statistics Canada (1987a) (1987b). In order to create a price and quantity series for aggregate Energy exports for the years 1961-1971, we aggregated data for 6 classes of energy exports using the M level of aggregation: Coal, Crude mineral oils, Natural gas, Gasoline and fuel oil, Other petroleum and coal products and Electric power. These components were aggregated using Fisher (1922) chained indexes. The resulting price and quantity series were linked to our earlier price and quantity series, P9 and Q9, for energy at the year 1971. In order to create aggregate Forestry exports for the years 1961-1971, we aggregated data for 7 classes of forest product exports using the M level of aggregation: Lumber and timber, Veneer and plywood, Other wood fabricated materials, Furniture and fixtures, Pulp, Newsprint and other paper stock, and Paper products. These components were aggregated using Fisher (1922) chained indexes. The resulting price and quantity series were linked to our earlier price and quantity series, P10 and Q10, for forest product exports at the year 1971. We aggregated the input output data for 2 classes of automotive product exports using the M level of aggregation: Motor vehicles and Motor vehicle parts. These components were aggregated using Fisher (1922) chained indexes. The resulting price and quantity series were linked to our earlier price and quantity series, P13 and Q13, for automotive product exports at the year 1971. In order to create an aggregate for Exports of other consumer goods (excluding automotive products) for the years 1961-1971, we aggregated data for 8 classes of consumer goods type exports using the M level of aggregation: Leather and leather products, Other textile products, Hosiery and knitted wear, clothing and accessories, appliances and receivers (households), Pharmaceuticals, Other chemical products and Other manufactured products. These components were aggregated using Fisher (1922) chained indexes. The resulting price and quantity series were linked to our earlier price and quantity series, P14 and Q14, for exports of other consumer goods at the year 1971. We generate price and quantity series over the years 1961-1971 for Exports of industrial goods and materials (excluding energy and forest product exports), P11 and Q11, as a chained Fisher aggregate of our price and quantity series for Crude materials (inedible) (G419) and Fabricated materials (inedible) (G421) less our series for Exports of energy

47

products P9 and Q9) and Exports of forest products (P10 and Q10).69 The resulting export price and quantity series for the years 1961-1971 are linked to our earlier series for P11 and Q11 at the year 1971. Finally, we generate price and quantity series over the years 1961-1971 for Exports of machinery and equipment (excluding automotive products), P12 and Q12, as a chained Fisher aggregate of our price and quantity series for Exports of end products (inedible) (G423) less our series for Exports of automotive products P13 and Q13) and less Exports of other consumer goods (P14 and Q14).70 The resulting export price and quantity series for the years 1961-1971 are linked to our earlier series for P12 and Q12 at the year 1971. There is one additional adjustment which affects the price of energy exports. During the years 1974-1985, Canada imposed an export tax on its energy exports, which is included in the price of exports. However, producers do not receive this export tax revenue and so it must be subtracted from the export price. This adjustment of the export price index for exports of goods can be accomplished using the Oil Export Tax series, CANSIM Series V499746 from the National Income and Expenditure Accounts. After making this adjustment, the resulting price and quantity series are P9

t and Q9t, which are listed in

Tables 5 and 6 below along with the other price and quantity series for the 8 classes of exports. Aggregate price and quantity indexes for exports, PX

t and QXt, were formed as

chained Fisher aggregates of the 8 classes of exports listed in Tables 5 and 6 and the resulting PX

t and QXt are listed in Tables 2 and 3 above.

Table 5: Price Indexes for Eight Commodity Classes of Exports, 1961-2011

Year t P8t P9

t P10t P11

t P12t P13

t P14t P15

t 1961 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1962 1.05659 0.98534 1.03706 1.01977 1.03488 1.01167 0.9988 1.01858 1963 1.05292 1.01104 1.04975 1.02746 1.04642 1.02781 1.00853 1.04402 1964 1.06146 0.99854 1.06857 1.04333 1.06452 1.03785 1.02909 1.07736 1965 1.07552 1.01886 1.08666 1.06777 1.09035 1.03617 1.03692 1.12159 1966 1.13905 1.02441 1.10752 1.12360 1.12856 1.05032 1.05855 1.18364 1967 1.15369 0.96541 1.12890 1.15308 1.17596 1.06607 1.07630 1.26762 1968 1.14873 1.00454 1.15804 1.22731 1.25191 1.08830 1.10360 1.34554 1969 1.11043 1.05284 1.21103 1.26468 1.28144 1.09898 1.14735 1.41327 1970 1.07460 1.06679 1.20448 1.33958 1.36481 1.12160 1.14015 1.50120 1971 1.10272 1.12301 1.24675 1.28936 1.37181 1.15193 1.15590 1.57903 1972 1.16574 1.15550 1.34600 1.30236 1.41712 1.17423 1.18547 1.66505 1973 1.65562 1.39072 1.61655 1.49521 1.46833 1.18656 1.25988 1.79018 1974 2.47603 3.44477 1.97968 1.94140 1.65047 1.27902 1.42184 2.02338 1975 2.44172 4.39214 2.31660 2.10541 1.86186 1.40313 1.56638 2.29526 1976 2.27544 5.07944 2.39386 2.22651 1.90587 1.48840 1.66746 2.51896 1977 2.13627 5.88992 2.62455 2.50906 2.02758 1.61582 1.76846 2.72893 1978 2.37658 6.28301 2.90165 2.77108 2.11566 1.78223 1.88273 2.90258

69 All four prices are entered as positive numbers in the index number formula while the first two quantities are entered positively and the last two quantities are entered negatively. 70 All three prices are entered as positive numbers in the index number formula while the first quantity is indexed with a positive sign and the last two quantities are indexed with negative signs.

48

1979 2.88982 8.05282 3.47704 3.53655 2.27395 1.96622 2.00068 3.14587 1980 3.28365 11.2874 3.73797 4.45064 2.41362 2.17714 2.24946 3.49696 1981 3.56932 12.19745 3.96546 4.55036 2.55522 2.41373 2.49659 3.94719 1982 3.46707 12.36200 3.85284 4.31903 2.72280 2.63304 2.66992 4.34103 1983 3.39310 11.85517 3.83642 4.35230 2.75291 2.73815 2.80369 4.66353 1984 3.53005 11.84249 4.26336 4.45480 2.69323 2.90539 2.88654 4.87299 1985 3.51503 11.15158 4.32498 4.41174 2.68327 3.12972 3.00305 5.13320 1986 3.43645 7.75428 4.78008 4.59745 2.97757 3.01503 3.28669 5.40392 1987 3.32350 7.55588 5.20316 4.73208 3.02031 3.02347 3.40733 5.59379 1988 3.49449 6.35623 5.36339 5.05742 3.04258 2.91102 3.52049 5.72724 1989 3.73084 6.87199 5.59564 5.03255 3.06798 2.86952 3.71759 5.93246 1990 3.47655 7.84685 5.24427 4.74911 3.11615 2.87959 3.73982 6.08151 1991 3.14681 6.82156 4.69849 4.45427 3.07176 2.96769 3.82601 6.29162 1992 3.48817 7.07296 4.84492 4.47367 3.06279 3.15213 3.82959 6.33223 1993 3.71935 7.47530 5.37177 4.53039 3.09777 3.35449 3.89234 6.51684 1994 3.96389 7.25372 6.18573 5.11913 3.17302 3.52359 3.99910 6.66734 1995 4.40988 7.11026 7.36498 5.72144 3.21973 3.65787 4.09757 6.88429 1996 4.71556 8.77046 6.80562 5.32837 3.18323 3.74681 4.16933 7.03680 1997 4.46079 9.00830 6.77946 5.28875 3.12343 3.83816 4.19780 7.22032 1998 4.38396 7.35245 7.02909 5.13339 3.13173 4.05650 4.25986 7.34563 1999 4.31935 9.26009 7.12821 5.03383 3.08837 4.03743 4.31663 7.46192 2000 4.37477 15.28916 7.16500 5.39152 3.06944 4.02821 4.36260 7.72519 2001 4.62634 15.71996 7.30172 5.31976 3.09180 4.17233 4.43899 7.74816 2002 4.63446 13.37888 6.82281 5.26906 3.10623 4.21091 4.46478 7.87210 2003 4.53195 16.64222 6.33572 5.24802 2.97965 3.84484 4.47389 7.93621 2004 4.46913 18.36274 6.82304 5.79875 2.92001 3.66998 4.48713 8.09962 2005 4.14804 23.47336 6.44686 6.11849 2.87534 3.46175 4.51188 8.29493 2006 4.09413 22.97607 6.08570 6.85702 2.82677 3.31229 4.54024 8.44827 2007 4.37717 23.07177 5.71782 7.40791 2.79211 3.16579 4.54902 8.58932 2008 5.17612 31.12435 5.83859 7.88371 2.81519 3.24480 4.56323 9.00024 2009 4.74562 20.28049 5.49139 7.07909 2.94270 3.45964 4.65313 9.04693 2010 4.51778 22.39633 5.67721 7.76360 2.84243 3.23149 4.65108 9.11352 2011 5.11599 25.91659 5.66559 8.77593 2.83876 3.18988 4.67970 9.39743

Table 6: Quantity Indexes for Eight Commodity Classes of Exports, 1961-2011

Year t Q8t Q9

t Q10t Q11

t Q12t Q13

t Q14t Q15

t 1961 1432.1 252.3 1573.6 2057.2 402.1 50.1 63.7 1036.0 1962 1328.6 363.9 1593.1 2130.2 511.5 62.5 77.7 1132.0 1963 1571.9 364.1 1684.6 2242.7 581.5 93.7 90.9 1204.0 1964 1963.5 408.9 1834.5 2531.7 792.8 187.7 102.2 1285.6 1965 1798.9 425.8 1869.5 2721.2 791.3 347.5 112.1 1359.7 1966 1954.0 484.2 1964.9 2809.4 910.9 985.6 135.7 1492.0 1967 1613.2 578.7 1927.6 2997.6 1147.4 1620.4 146.5 1864.9 1968 1589.7 657.2 2127.4 3282.7 1239.5 2533.5 183.3 1499.0 1969 1492.5 757.0 2290.6 3091.0 1378.2 3181.6 214.8 1657.1 1970 1967.9 951.2 2339.2 3675.8 1437.1 3137.5 236.2 1767.3 1971 2168.3 1154.0 2374.2 3611.1 1436.8 3613.9 243.1 1747.3 1972 2268.9 1479.9 2662.0 3707.9 1662.5 4001.8 270.8 1720.7 1973 2217.2 1789.7 2825.7 4085.7 1950.5 4539.2 319.8 1893.1

49

1974 1778.2 1508.4 2809.5 3986.3 2088.5 4430.7 323.6 2094.5 1975 1879.8 1216.3 2185.5 3513.3 2165.0 4554.8 289.8 1997.6 1976 2047.5 977.6 2718.2 3824.4 2325.5 5499.2 311.3 2048.5 1977 2445.0 919.8 3001.2 3955.3 2345.1 6388.1 338.2 2052.1 1978 2524.7 937.6 3313.3 4281.0 2914.9 6954.2 404.7 2272.8 1979 2538.2 1101.5 3369.6 4292.6 3880.9 6004.4 506.8 2556.4 1980 2785.9 951.8 3286.8 4633.9 4469.2 5002.0 570.8 2658.0 1981 2923.8 950.1 3126.5 4529.3 4810.1 5585.9 548.3 2738.1 1982 3142.7 1009.7 2962.3 4133.5 4586.9 6387.7 525.1 2508.2 1983 3256.3 1079.1 3284.3 4169.5 4413.1 7748.3 546.8 2534.8 1984 3299.9 1210.3 3501.3 4965.2 5761.5 10115.0 652.0 2685.2 1985 2979.2 1461.0 3544.7 5178.9 6360.5 10539.3 666.0 2839.4 1986 3178.0 1416.6 3708.8 5606.6 6826.0 10494.1 767.4 3254.1 1987 3565.5 1701.0 4031.4 5790.7 6884.4 10540.5 775.7 3294.5 1988 3527.3 2009.2 4025.0 6316.1 7120.6 11928.4 798.8 3546.0 1989 3101.7 1997.4 3836.1 6412.9 7810.3 11838.6 709.3 3704.0 1990 3830.8 1779.1 3877.8 6765.1 9259.5 12042.3 895.2 3857.1 1991 4169.0 2068.3 3958.3 7016.2 9536.5 10949.5 908.0 3892.6 1992 4397.4 2184.7 4131.5 7237.9 10413.1 12087.4 1167.0 4156.5 1993 4342.7 2374.6 4352.4 7773.7 11895.0 14490.7 1440.8 4519.2 1994 4746.4 2646.9 4708.9 8301.8 14402.7 16349.5 1775.9 5093.3 1995 4754.3 2868.3 4989.3 8896.4 17402.0 17200.2 2029.5 5395.8 1996 4913.1 2970.5 5073.4 9821.5 19457.0 16912.7 2278.7 5850.5 1997 5553.7 3016.9 5178.1 10708.6 22070.0 18099.8 2555.4 6263.6 1998 5711.7 3238.6 5042.1 11525.7 25770.1 19342.2 2949.8 7084.9 1999 5929.8 3226.3 5623.2 11889.3 28713.2 24097.5 3239.8 7400.4 2000 6309.4 3476.8 5969.8 12608.7 35853.8 24300.2 3484.0 7936.8 2001 6717.8 3547.7 5517.3 12744.0 33169.5 22176.3 3673.6 7967.1 2002 6661.8 3687.1 5458.9 13317.5 31256.9 22958.2 3959.7 8276.2 2003 6450.4 3636.6 5448.2 12730.0 29760.9 22727.9 3841.6 7982.5 2004 6863.6 3708.9 5777.2 13443.3 31200.7 24629.3 3848.1 8268.8 2005 7256.0 3703.0 5653.4 13761.7 32346.1 25419.3 3800.7 8345.0 2006 7696.9 3778.0 5495.3 13738.8 32989.3 24755.9 3922.9 8300.2 2007 7936.6 3956.9 5118.6 14143.9 33462.8 24324.7 4119.1 8335.4 2008 7893.8 4039.5 4342.5 14120.8 32756.3 18847.1 3982.1 8257.4 2009 7846.8 3936.6 3556.1 11180.3 27239.6 12663.7 3854.4 7757.6 2010 8176.1 4058.1 3849.0 12428.8 26771.4 17571.8 3532.1 8042.2 2011 8021.7 4327.3 3951.1 13321.9 28392.4 18592.3 3494.4 8243.0

We now turn our attention to imports. Current dollar information on imports of services can be found as CANSIM Series V498108 for the years 1961-2011 and the corresponding constant 2002 chained dollar series is CANSIM Series V1992065. We use these two series to form price and quantity series for the imports of services, P22

t and Q22t, which are listed in Tables 7 and 8. Note

that since imported goods and services are inputs into the business sector, when we form a value added aggregate, we need to append a minus sign to any quantity series pertaining to imports.

50

As was the case for our treatment of exports, the starting point for obtaining disaggregated data on imports of goods is CANSIM Table 3800012, Exports and Imports of Goods and Services, Canada, Current Prices. Using this Table, it is possible to obtain disaggregated information on the value of imports for the same 7 classes of imported good that was used for exports for the years 1971-2011. However, imports of forest products was small throughout the sample period and so this import component was aggregated with imports of industrial goods and materials (excluding forest and energy imports).71 Thus we used CANSIM Table 38000012 in order to generate prices and quantities for the following 7 classes of imports for the years 1971-2011:72

• Q16: Imports of agricultural and fish products; • Q17: Imports of energy products; • Q18: Imports of industrial goods and materials (including imports of forest

products but excluding imports of energy products); • Q19: Imports of machinery and equipment (excluding automotive products); • Q20: Imports of automotive products; • Q21: Imports of other consumer goods and • Q22: Imports of services.

There remains the problem of obtaining price series for the above 6 classes of imports to cover the years 1961-1971. From Leacy (1983), Series G429-442: Foreign trade, imports, excluding coin and bullion, by main commodity sections, current values, 1946-1975, millions of dollars (all countries), we can obtain value series covering imports for the years 1946-1975 for the following 5 commodity classes:

• Live animals (G429); • Food, feed, beverages and tobacco (G431); • Crude materials (inedible) (G433); • Fabricated materials (inedible) (G435); • End products (inedible) (G437).

From the same source, price indexes for each of the above 5 classes of imports are available as Series K62-K67 in the Table with the title: Import price indexes, trade of Canada commodity classification, 1926-1975. Thus we can find price and quantity series for these 5 classes of exports that cover the years 1961-1971. Unfortunately, these price indexes are of the fixed base variety with a base year of 1948 so they are likely to differ substantially from the corresponding chain indexes. However, as was the case for export price indexes, Leacy (1983) also lists as part of import price Series K62-K67 (Panel A) for the above 5 classes of imports counterpart indexes that have a 1971 base year but these price indexes cover only the years 1968-1975. We used these latter price indexes to construct import price indexes for the years 1968-1971 and then we used the 1948 based indexes to further extend these 5 series back to 1961.

71 Chained Fisher indexes were used in order to do the aggregation. 72 As in the case of export indexes, we used chained indexes whenever they were available.

51

The above operations give us 5 disaggregated export price and quantity series for the period 1961-1971 but we have 6 classes of imports of goods for the years 1971-2011. We generated Fisher chained price and quantity indexes for imports of Live animals and for exports of Food, feed, beverages and tobacco for the years 1961-1971 and linked these series to our earlier series, P16 and Q16, imports of agricultural and fish products. As was the case for extending our export series back to the 1960s, we need some additional series so that we can match the import series for the 1960s to the series that cover the post 1971 period. We created separate import series for energy, automotive products and other consumer goods using the input output tables for the Canadian economy that cover the years 1961-1981; see Statistics Canada (1987a) (1987b). The rest of our import series computations paralleled our export series computations, except that we did not generate a separate series for forest product imports due to their small size throughout the sample period. The price of imports does not include import duties that are added to the international cost of these imported goods. Hence we must add these import duties to the price of imports. We assumed that energy, automotive and service imports were exempt from import duties and we assumed a uniform rate for the remaining import categories.73 The series on customs import duties is CANSIM Series V499741 and after adjusting the price of imports using this series, the resulting price and quantity series for the imports of goods and services are listed in Tables 7 and 8 below. Aggregate price and quantity indexes for imports, PM

t and QMt, were formed as chained Fisher aggregates of the 7

classes of imports listed in Tables 7 and 8 and the resulting PMt and QM

t are listed in Tables 2 and 3 above. Table 7: Price Indexes for Seven Commodity Classes of Imports, 1961-2011

Year t P16t P17

t P18t P19

t P20t P21

t P22t

1961 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1962 1.03679 1.02856 1.04366 1.08555 1.05195 1.00091 1.05228 1963 1.30001 1.00981 1.08215 1.09317 1.06958 1.01035 1.07921 1964 1.28444 1.00471 1.10864 1.09893 1.09414 1.02505 1.09777 1965 1.07953 1.02524 1.13667 1.13146 1.07648 1.03046 1.13619 1966 1.06040 1.05430 1.14101 1.16121 1.09270 1.04532 1.17024 1967 1.03086 0.98958 1.17032 1.19545 1.12302 1.06167 1.22610 1968 1.06736 1.04752 1.16131 1.21251 1.16016 1.08044 1.28761 1969 1.07876 1.00624 1.19393 1.23657 1.18860 1.10386 1.36902 1970 1.14162 1.01555 1.20586 1.23682 1.20108 1.10884 1.42900 1971 1.17185 1.11732 1.17348 1.26723 1.24031 1.11507 1.49900 1972 1.25938 1.20329 1.16895 1.27976 1.26989 1.15774 1.53952 1973 1.55812 1.43514 1.30847 1.33031 1.29640 1.21598 1.63282 1974 1.93210 4.22172 1.71221 1.46612 1.40659 1.33756 1.75102 1975 2.03201 5.43394 1.88856 1.72092 1.63529 1.49190 1.98130 1976 1.89812 5.63358 1.90383 1.71902 1.71458 1.55837 2.04366 1977 2.29882 6.42113 2.13976 1.85394 1.93225 1.75401 2.34119 1978 2.57793 7.14772 2.49948 1.89328 2.20965 2.01280 2.69834

73 This is only a very rough approximation to the “truth”.

52

1979 2.91552 9.22856 3.05479 2.02173 2.44387 2.23857 3.04229 1980 3.20471 14.04487 3.56934 1.79771 2.71841 2.56582 3.39335 1981 3.37015 16.89476 3.72305 1.68542 3.26363 2.81296 3.81611 1982 3.24924 16.65354 3.76051 1.80849 3.52543 2.91341 4.10352 1983 3.19476 15.35401 3.78803 1.75020 3.62370 2.95831 4.30819 1984 3.44566 15.57686 3.97534 1.81775 3.82410 3.22426 4.63802 1985 3.36833 16.05971 3.93340 1.85207 4.02632 3.34781 4.98855 1986 3.61452 10.45556 4.04659 1.87982 4.20229 3.59926 5.29276 1987 3.54040 10.91648 4.06052 1.79479 4.15738 3.63097 5.28864 1988 3.63036 9.09050 4.20864 1.73566 4.03524 3.63769 5.09254 1989 3.59686 9.69611 4.23220 1.70224 4.08857 3.67097 5.09401 1990 3.59654 11.94481 4.17415 1.68326 4.16440 3.72491 5.24914 1991 3.58709 10.19284 4.03594 1.65311 4.12731 3.75249 5.31731 1992 3.59244 10.16216 4.12468 1.71222 4.39452 3.96906 5.63381 1993 3.66587 9.84044 4.31220 1.81784 4.68083 4.27953 6.19826 1994 3.97780 9.83576 4.63802 1.91168 4.99133 4.58008 6.68231 1995 4.25257 10.17736 5.09236 1.89156 5.15679 4.75625 6.90224 1996 4.21246 11.94335 4.91330 1.80535 5.19805 4.73478 7.01253 1997 4.36570 11.84732 4.94351 1.77995 5.26105 4.78921 7.26074 1998 4.35559 9.76539 5.09294 1.83126 5.51748 5.11888 7.80221 1999 4.24238 11.43514 5.01393 1.79281 5.52100 5.13696 7.97505 2000 4.24712 16.95310 5.21160 1.76324 5.52428 5.17855 8.18543 2001 4.39529 16.32263 5.39399 1.79583 5.67016 5.40894 8.64576 2002 4.45329 16.80830 5.33330 1.79374 5.73431 5.42202 8.84642 2003 4.28964 18.58307 5.01857 1.60033 5.39577 4.92399 8.39644 2004 4.18959 21.35868 5.20935 1.48039 5.21353 4.58968 8.24087 2005 4.09424 27.04231 5.29607 1.39025 5.00304 4.40869 8.15836 2006 3.98553 30.13522 5.50808 1.32194 4.84946 4.22727 8.13200 2007 4.09461 30.84683 5.39832 1.26023 4.63140 4.03590 8.09839 2008 4.48367 40.53568 5.90236 1.27627 4.59101 4.14295 8.40782 2009 4.65392 27.56948 5.70383 1.38886 4.84188 4.52760 8.65967 2010 4.39014 32.83824 5.63361 1.25722 4.64455 4.19990 8.19974 2011 4.50083 40.35358 5.97449 1.20917 4.56046 4.18015 8.21143

Table 8: Quantity Indexes for Seven Commodity Classes of Imports, 1961-2011

Year t Q16t Q17

t Q18t Q19

t Q20t Q21

t Q22t

1961 720.4 478.0 1617.4 1609.1 615.1 659.1 1535.0 1962 734.6 480.7 1684.1 1571.7 699.1 709.5 1479.6 1963 687.1 541.8 1706.5 1563.1 707.1 699.0 1466.8 1964 708.8 547.7 1954.5 1828.8 857.4 736.2 1618.7 1965 816.9 583.4 2169.8 2098.6 1157.2 829.3 1692.5 1966 897.5 592.8 2331.0 2471.0 1573.4 932.6 1850.0 1967 949.9 638.9 2210.4 2689.8 1963.9 969.7 1934.6 1968 986.0 685.5 2383.7 2741.2 2649.7 1084.2 2013.8 1969 1128.5 737.9 2668.1 3079.3 3030.9 1277.2 2336.7 1970 1118.6 766.3 2659.0 3102.2 2758.7 1275.8 2471.7 1971 1130.7 817.1 2936.6 3245.7 3249.2 1443.0 2476.3 1972 1245.0 895.9 3370.6 3890.5 3819.2 1757.7 2585.9 1973 1420.9 928.1 3656.2 4694.4 4619.0 2032.9 2888.3

53

1974 1463.7 788.6 4146.1 5557.6 4931.1 2310.2 3277.5 1975 1464.5 766.1 3558.8 5272.2 4954.5 2258.2 3550.2 1976 1695.9 719.6 3652.1 5410.6 5417.1 2621.4 3971.3 1977 1613.9 654.2 3636.9 5517.9 5864.7 2572.9 3883.1 1978 1637.0 625.7 3933.2 6688.4 5918.6 2612.3 3824.2 1979 1621.7 624.7 4442.9 8152.0 6096.9 2752.2 3637.1 1980 1679.7 598.8 4298.8 10725.8 4900.3 2636.6 3760.0 1981 1743.6 573.7 4514.0 13412.1 4799.6 2721.7 3860.0 1982 1673.9 404.5 3624.3 10469.5 4128.6 2526.6 3594.5 1983 1736.0 336.2 4178.2 11847.2 5142.3 2821.9 3689.7 1984 1896.3 393.7 4781.2 14574.1 6668.0 3158.5 3774.9 1985 1914.6 395.2 5291.1 15289.3 7684.4 3109.5 3904.9 1986 2000.0 486.3 5568.1 16642.5 7845.2 3327.3 4267.7 1987 2087.6 541.7 5616.3 18559.9 7844.3 3489.5 4536.3 1988 2081.9 569.4 6379.7 23461.4 8225.8 3729.8 5184.6 1989 2295.3 641.6 6683.8 25438.9 7812.7 4092.4 5792.5 1990 2429.8 686.3 6623.9 25497.0 7319.2 4256.0 6405.6 1991 2510.1 650.4 6418.9 25941.9 7501.5 4427.7 6664.1 1992 2710.2 637.4 6949.7 27259.5 7664.1 4772.7 6738.8 1993 3004.5 708.1 7821.8 29208.2 8533.4 4992.9 6865.2 1994 3162.0 707.6 8839.3 34377.2 9583.4 5118.2 6755.0 1995 3145.1 711.1 9348.9 40019.9 9712.7 5371.2 6763.0 1996 3356.2 804.2 9850.6 42310.3 9832.0 5457.3 7110.7 1997 3585.4 897.0 11519.6 51315.3 11561.6 6215.2 7374.5 1998 3961.3 884.1 12329.7 55221.2 12105.0 6754.4 7366.6 1999 4161.8 936.4 12946.7 60378.6 13753.7 7202.9 7683.6 2000 4369.3 1053.1 13875.2 69708.8 14016.8 7746.6 8114.0 2001 4634.5 1087.2 13220.8 62337.1 12799.3 7930.6 7954.1 2002 4890.3 985.7 13505.5 59065.6 14207.5 8571.6 8090.6 2003 5014.0 1066.2 13605.4 61664.8 14176.3 9404.2 8830.5 2004 5107.2 1160.3 14719.9 70313.0 14839.8 10397.2 9363.0 2005 5383.9 1244.7 15422.8 79791.9 15666.9 11224.7 9858.2 2006 5887.8 1152.8 15839.6 86789.6 16464.9 12303.4 10246.8 2007 6235.5 1209.1 16364.7 92507.8 17263.7 13574.4 11035.8 2008 6359.3 1311.8 16085.6 96094.1 15673.7 13905.0 11284.3 2009 6306.1 1231.4 13579.1 77688.7 11425.5 12704.0 10536.9 2010 6737.8 1234.8 15900.0 90578.9 14794.3 13754.8 11563.8 2011 7249.7 1289.2 16827.0 103132.2 15630.9 14262.9 12283.4

We turn our attention to forming estimates of business sector labour input. 3. Business Sector Labour Input Estimates Statistics Canada has constructed detailed labour input data for the Canadian business sector for 36 types of labour for the years 1961-2010 in CANSIM Table 3830024 which we will make use of in this study. Labour input is classified according to a four way classification:

54

• By education level E. There are 3 categories in this classification: E=1 corresponds to Primary or Secondary Education; E=2 corresponds to Some or Completed Post-Secondary Education and E=3 corresponds to University Degrees or Above.

• By age of worker A. There are 3 categories in this classification: A=1 corresponds to 15-34 years old; A=2 corresponds to 35-54 years old and A=3 corresponds to 55 years old and over.

• By sex S. There are 2 categories in this classification: S=1 corresponds to a male worker and S=2 corresponds to a female worker.

• By type of employment T. There are 2 categories in this classification: T=1 corresponds to a paid worker and T=2 corresponds to a self employed worker.

Thus Table 3830024 provides annual hours and total compensation data for 3x3x2x2 or 36 types of worker in the Canadian business sector for the years 1961-2010. We aggregated over the age groups using Fisher chained indexes in order to form 12 price and quantity series for labour, PL1-PL12 and QL1-QL12. These series are listed below in Tables 9 and 10. The characteristics of the 12 types of labour are as follows:

• QL1 : E=1; S=1; T=1; • QL2 : E=1; S=2; T=1; • QL3 : E=1; S=1; T=2; • QL4 : E=1; S=2; T=2; • QL5 : E=2; S=1; T=1; • QL6 : E=2; S=2; T=1; • QL7 : E=2; S=1; T=2; • QL8 : E=2; S=2; T=2; • QL9 : E=3; S=1; T=1; • QL10 : E=3; S=2; T=1; • QL11 : E=3; S=1; T=2; • QL12 : E=3; S=2; T=2.

Table 9: Price Indexes for 12 Types of Business Sector Labour Year PL1

t PL2t PL3

t PL4t PL5

t PL6t PL7

t PL8t PL9

t PL10t PL11

t PL12t

1961 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1962 1.00892 1.01455 1.21991 1.16068 1.19233 1.26194 1.30719 1.39658 1.02363 1.06699 1.00477 1.22412 1963 1.04264 1.03970 1.25378 1.18648 1.25073 1.29879 1.37026 1.41025 1.06714 1.10416 1.02752 1.26888 1964 1.08945 1.07346 1.30325 1.21999 1.28027 1.30968 1.40299 1.37233 1.11706 1.16637 1.06166 1.23793 1965 1.16254 1.13566 1.45365 1.31285 1.32331 1.35055 1.51703 1.40319 1.19240 1.21746 1.13374 1.23855 1966 1.25026 1.20997 1.53201 1.36570 1.37082 1.40049 1.52855 1.38945 1.29155 1.26907 1.20684 1.23729 1967 1.35150 1.26873 1.60491 1.42038 1.41803 1.42662 1.56447 1.40490 1.37165 1.32996 1.28035 1.25711 1968 1.45022 1.34049 1.74830 1.50327 1.46103 1.46579 1.62298 1.43270 1.47387 1.47070 1.36531 1.27888 1969 1.57997 1.44527 1.86424 1.59480 1.52944 1.54311 1.67441 1.49441 1.59586 1.54996 1.52120 1.38363 1970 1.69922 1.52368 1.98493 1.66675 1.58072 1.59231 1.69821 1.53146 1.69716 1.58329 1.64305 1.47921 1971 1.81458 1.65846 2.04716 2.20797 1.76001 1.77571 1.88843 1.91012 1.62977 1.67459 1.65929 1.61716 1972 1.97498 1.83786 2.23181 2.88387 1.91462 1.95321 2.08248 2.34448 1.61826 1.71971 1.72431 1.80710 1973 2.18289 2.02236 2.53124 3.76221 2.07248 2.09983 2.32451 2.87345 1.63231 1.69693 1.82105 2.05132 1974 2.56040 2.34947 2.96801 4.93500 2.35615 2.37590 2.61007 3.51935 1.78640 1.82396 2.02758 2.36199 1975 3.02395 2.69355 3.38973 6.16168 2.67729 2.66559 2.83316 4.17743 1.97428 1.96806 2.37472 2.81102 1976 3.54879 3.10959 4.10306 7.94199 3.00220 2.97026 3.17392 5.06019 2.14395 2.08332 2.57787 3.23376 1977 3.93053 3.49257 4.57325 9.74508 3.22786 3.24024 3.41229 5.92600 2.16195 2.12505 2.83500 3.72869

55

1978 4.08207 3.73081 4.80660 11.02464 3.34780 3.47183 3.48544 6.54152 2.35996 2.37977 2.95325 4.16126 1979 4.35203 4.06912 4.97968 12.54042 3.56981 3.80902 3.51574 7.22990 2.60870 2.69372 3.05538 4.60019 1980 4.77142 4.46771 5.51890 15.10441 3.94289 4.35655 3.86209 9.05132 2.79991 3.03936 3.39126 5.64786 1981 5.37760 4.96816 5.72454 15.28663 4.39555 4.86467 3.97020 9.41607 3.50017 3.81336 3.87238 6.75922 1982 6.13162 5.43140 5.53867 14.44997 4.94259 5.26712 3.94249 9.76053 3.71139 3.76980 4.36105 7.16442 1983 6.10898 5.78498 5.25140 14.69121 5.22653 5.92367 3.97942 10.76563 4.03609 4.32476 4.41561 8.13672 1984 6.49576 6.27899 5.70639 16.81662 5.32382 6.14421 4.00334 11.98680 4.26749 4.59334 4.70816 8.74881 1985 6.84242 6.43132 5.96946 17.75200 5.71231 6.37800 4.11822 12.40413 4.58490 4.62989 5.02829 9.13351 1986 6.87750 6.75393 6.99521 22.09708 5.75948 6.77628 4.64316 14.5667 4.84219 5.25402 5.10481 10.41693 1987 7.28338 7.12360 6.25983 20.24931 5.91773 7.06768 4.32448 13.69955 4.87347 5.37623 5.32750 10.41412 1988 7.80967 7.51959 7.81912 25.53517 6.32827 7.46734 5.07353 16.15506 5.08809 5.55036 5.58359 10.91049 1989 8.01131 7.89165 7.00415 23.63192 6.54400 7.89553 4.77222 15.50560 6.09402 6.81955 5.95806 12.04049 1990 8.00963 7.84162 7.24642 24.70847 7.29189 8.27337 5.30477 17.18560 6.39511 7.38267 5.93031 13.33156 1991 8.16262 8.30053 6.89314 26.89143 7.54668 8.89027 5.10772 18.39741 7.28480 8.50450 5.95581 14.57506 1992 8.25704 8.75147 6.80263 31.14830 7.63241 9.54512 5.03471 20.70240 7.23284 9.00169 5.59743 16.12764 1993 8.44473 8.81499 7.02311 31.95103 7.55074 9.48799 4.82717 20.49813 7.14082 8.51906 5.30861 14.64884 1994 8.39840 8.85269 6.57734 32.81800 7.56278 9.51634 4.63688 20.03522 6.88566 8.25042 5.03182 14.51999 1995 8.58442 8.66676 8.09676 36.59026 7.74285 9.71738 5.29667 22.46062 7.08554 7.78346 5.00227 14.27076 1996 8.66847 8.79603 8.80087 36.73066 7.68300 9.76200 5.36059 21.29428 7.19747 9.35692 4.79635 15.72222 1997 8.92519 9.04197 8.23664 33.22780 7.93034 10.01868 5.48724 20.19812 8.16801 9.70109 4.35626 13.63632 1998 9.19607 9.22066 8.65018 32.61557 8.18084 10.28508 5.60551 19.54420 8.56293 10.13196 4.49204 13.41471 1999 9.34401 9.39912 9.54466 35.03364 8.38211 10.41028 5.98870 20.54213 8.94527 10.48379 4.66822 13.88940 2000 9.83159 9.85829 10.14056 36.74486 8.75334 10.98708 6.56431 22.64575 9.32373 10.99704 5.11842 15.16402 2001 10.02149 10.04042 9.55383 36.52866 9.02695 11.34553 6.42198 23.05921 9.71431 11.51098 5.57743 17.25972 2002 10.13824 10.18629 9.53290 36.98813 9.14670 11.47733 6.49564 23.96382 9.97487 11.77011 6.06408 17.78047 2003 10.38985 10.45671 9.46881 37.82576 9.36676 11.77714 6.53074 24.56537 9.99751 11.98959 6.03752 18.52500 2004 10.72483 10.82166 9.89673 38.53207 9.56673 12.28590 6.68915 24.62262 10.29495 12.36352 6.16181 18.08819 2005 11.33524 11.48687 10.34997 43.42255 9.98342 12.70816 7.02723 27.60046 10.56816 12.68156 6.35149 19.49023 2006 11.92688 11.87140 11.18877 40.92914 10.46599 13.33853 7.30903 25.30442 11.21138 13.40464 6.14100 18.43612 2007 12.23543 12.24787 12.14166 42.61140 10.87018 13.90235 7.93833 26.41743 11.45676 13.74147 6.38591 18.34237 2008 12.60978 12.59008 12.47479 43.63268 11.20373 14.11439 8.26287 26.35143 11.78102 13.82406 6.50058 18.42252 2009 12.68637 13.01534 12.78503 44.92175 11.31574 14.62592 8.32693 27.47910 11.88060 14.40573 6.73748 19.01061 2010 12.99135 13.56518 13.34321 46.13085 11.43671 14.91555 8.43530 27.28155 11.87580 14.50795 6.52947 19.09764 2011 13.26899 14.16025 14.35475 48.38655 11.68113 15.56985 9.07477 28.61556 12.12960 15.14437 7.02446 20.03147

Table 10: Quantity Indexes for 12 Types of Business Sector Labour Year QL1

t QL2t QL3

t QL4t QL5

t QL6t QL7

t QL8t QL9

t QL10t QL11

t QL12t

1961 12607.7 2758.3 1737.8 46.4 554.2 65.6 91.2 2.3 768.1 55.4 550.3 3.0 1962 12795.8 2834.6 1677.9 47.7 933.9 143.6 114.2 4.5 809.3 64.7 566.5 4.0 1963 12687.0 2884.9 1617.3 49.4 1295.5 219.8 135.7 6.6 833.3 74.6 568.1 4.9 1964 12847.4 2985.3 1577.7 49.8 1683.4 299.3 161.1 8.7 876.6 83.2 594.4 5.8 1965 13189.2 3095.2 1443.3 47.9 2102.9 380.7 177.4 10.4 930.2 93.1 611.0 6.5 1966 13433.1 3203.2 1469.4 48.8 2543.6 463.2 212.1 12.6 990.6 103.5 673.3 7.7 1967 13218.0 3308.0 1412.8 52.1 2901.9 545.8 231.7 15.0 1030.2 113.4 673.9 8.7 1968 12944.2 3358.6 1287.4 51.7 3227.9 621.0 239.0 16.6 1052.9 117.5 641.3 9.1 1969 12859.8 3440.0 1260.0 52.0 3590.5 702.6 265.4 18.4 1095.0 124.9 658.0 9.8 1970 12573.2 3458.4 1158.7 51.2 3889.1 770.6 280.0 19.9 1119.1 133.1 678.9 10.6 1971 12353.1 3493.9 1124.4 52.9 4283.1 868.1 305.9 22.4 1226.9 162.3 705.4 13.1 1972 12267.6 3595.1 1046.6 50.2 4728.7 982.2 325.6 23.1 1362.4 194.0 689.2 14.7 1973 12605.9 3795.0 1001.9 47.1 5349.1 1124.2 345.4 23.4 1538.1 232.6 639.7 15.5 1974 12550.2 3892.3 1005.6 49.1 5832.4 1240.8 388.6 26.3 1675.8 265.0 677.7 18.5 1975 11964.1 3936.2 966.5 48.6 6072.9 1337.6 418.3 28.2 1760.8 292.7 684.2 20.9 1976 11574.7 3947.4 901.6 47.0 6366.7 1414.7 433.6 29.5 1839.3 315.6 618.0 21.1 1977 11383.9 3919.5 830.6 46.5 6742.1 1488.6 440.6 30.7 1946.7 333.8 647.1 24.4 1978 11429.7 4090.8 804.7 49.5 7296.9 1617.9 486.1 35.2 2089.7 364.7 694.5 27.9 1979 11653.1 4339.6 792.6 50.5 8030.8 1791.9 538.5 37.9 2321.6 409.0 729.3 31.1 1980 11511.4 4591.0 724.2 47.3 8557.4 1955.4 540.0 38.6 2502.3 447.7 751.6 34.8 1981 11494.2 4662.0 756.5 48.3 8772.6 2132.4 566.0 38.9 2688.7 524.0 728.8 37.4 1982 10532.6 4404.3 740.5 48.3 8161.9 2144.0 546.6 40.9 2543.7 535.1 779.6 42.9 1983 10446.2 4329.0 747.7 49.1 8189.5 2219.1 550.4 43.6 2535.2 556.0 834.1 50.6 1984 10596.7 4384.6 755.5 50.1 8472.6 2388.6 567.7 48.2 2701.2 626.8 945.1 67.9 1985 10820.1 4437.1 847.5 52.6 8834.5 2543.2 633.6 54.7 2857.7 692.6 1035.4 76.3 1986 11039.1 4633.7 793.6 48.1 9253.1 2760.7 620.3 50.8 3110.8 810.9 1042.2 73.7 1987 11435.0 4777.5 789.7 48.8 9819.9 2940.4 642.7 53.7 3375.6 895.3 1045.5 79.3

56

1988 11662.7 4942.0 791.9 49.4 10314.5 3132.2 663.6 57.0 3650.4 995.4 1111.7 89.9 1989 11738.8 5018.5 795.2 52.8 10625.7 3273.2 692.5 61.6 3850.6 1084.9 1123.6 93.8 1990 11383.1 4984.0 797.9 57.0 10577.9 3402.1 695.0 64.2 4044.8 1110.3 1079.5 85.1 1991 10602.5 4714.9 787.3 55.7 10150.1 3391.1 718.1 63.7 4072.6 1121.4 1134.7 95.2 1992 10216.3 4498.1 778.5 58.8 10019.1 3398.5 702.8 68.4 4183.7 1244.0 1199.4 91.1 1993 10011.8 4309.6 751.2 62.4 10392.1 3502.5 757.0 72.2 4604.7 1369.2 1296.3 115.1 1994 10133.3 4194.2 766.9 60.6 11236.5 3719.1 774.6 87.5 4870.1 1504.4 1334.9 125.3 1995 10070.2 4179.9 735.9 57.0 11928.6 3968.6 821.5 90.8 5052.9 1604.2 1240.8 123.5 1996 10206.9 4145.1 729.5 61.5 12258.5 4152.5 915.4 103.4 5218.4 1715.5 1402.5 138.0 1997 9887.9 4049.2 722.1 57.5 13261.7 4426.8 1024.9 113.3 5511.4 1834.5 1391.7 152.2 1998 9747.6 4183.1 758.2 59.7 13562.9 4664.5 1028.6 118.8 5864.0 1983.5 1539.9 174.2 1999 10128.4 4369.1 719.4 58.7 13999.7 4809.3 1047.0 120.9 6008.3 2189.0 1521.5 161.4 2000 10229.2 4536.3 690.2 55.4 14539.4 4996.1 982.3 115.2 6405.2 2392.6 1478.9 178.9 2001 10137.6 4452.1 628.0 48.0 14729.5 5182.7 945.4 114.9 6721.8 2514.2 1525.2 168.9 2002 10220.9 4519.0 589.0 49.3 15090.4 5258.7 940.0 116.1 6930.7 2538.3 1470.4 169.5 2003 9930.4 4470.7 579.5 47.3 15637.4 5476.2 979.8 116.4 7072.3 2721.3 1562.5 170.4 2004 10119.3 4547.1 587.9 46.6 16144.2 5655.6 990.8 117.3 7537.8 2882.2 1580.8 179.5 2005 10193.9 4454.9 589.2 47.2 16145.0 5581.7 927.3 118.1 7984.3 3194.0 1489.2 187.0 2006 10285.7 4573.2 565.0 45.0 16264.6 5614.5 900.6 114.8 8398.5 3293.6 1603.0 198.4 2007 10255.7 4454.5 567.3 46.0 16712.7 5835.5 967.0 123.2 8772.5 3499.6 1605.7 211.9 2008 10221.8 4448.2 554.0 44.2 16933.2 5905.5 933.0 119.9 8880.5 3640.9 1597.2 201.8 2009 9391.6 4109.4 535.2 44.4 16059.3 5778.9 887.5 122.5 8817.4 3639.6 1538.9 217.4 2010 9507.2 4085.5 509.3 40.5 16812.2 5763.3 890.0 121.8 9143.1 3855.3 1573.2 226.7 2011 9776.2 4110.6 503.1 41.0 17287.9 5798.6 879.2 123.4 9401.8 3878.9 1554.2 229.7

We have not explained how our estimates for the 12 types of labour input were constructed for 2011. From CANSIM Table 2820022, it is possible to estimate the total employment for the business sector for the years 2010 and 2011 by 4 types of labour: by employees and the self employed and by sex. From Table 3830010 and Series V15901071, the annual number of hours worked in the business sector over all jobs dropped from 1702 in 2010 to 1700 in 2011 so it appears that hours of work did not change much over the two years. Thus we estimated QL1

2011, QL52011 and QL9

2011 by the growth in employment of male business sector employees from 2010 to 2011, QL2

2011, QL6

2011 and QL102011 by the growth in employment of female business sector employees

from 2010 to 2011, QL32011, QL7

2011 and QL112011 by the growth in male self employment

from 2010 to 2011 and we estimated QL42011, QL8

2011 and QL122011 by the growth in female

self employment from 2010 to 2011. Our estimates for the prices of the 12 types of labour for 2011 were constructed in a very approximate manner. Define VLn

2010 as PLn2010×QLn

2010 for n = 1,...,12. Estimates for aggregate employee wages and salaries and supplementary labour income from business are available in CANSIM Table 3800004, Series V498167. We used the ratio of the 2011 entry for this series to the 2011 series times VLn

2010 to form estimates for VLn2011 for n =

1,2,5,6,9,10. From CANSIM Table 3800004, Series V498170, we obtained estimates for unincorporated business net income for 2010 and 2011. We used the ratio of the 2011 entry for this series to the 2010 series times VLn

2010 to form estimates for VLn2011 for n =

2,3,7,8,11,12. Finally, we defined PLn2011 ≡ VLn

2011/QLn2011 for n = 1,...,12.

The 12 labour price and quantity series listed above in Tables 9 and 10 can be regarded as quality adjusted labour input series for the Canadian business sector. It should be noted that the KLEMS program has provided data for 3 types of quality adjusted labour; see CANSIM Table 3830021, Series V41713187, V41713204 and V41713221 for values for the years 1961-2008 and Series V41713000, V41713017 and V41713034 for the

57

corresponding quantity indexes for the years 1961-2011.74 The quantity series have the following titles: Canada: Labour Input of Workers with Primary or Secondary Education; Business Sector, Labour Input of workers with Some or Completed Post-Secondary Certificate or Diploma; Business Sector and Labour Input of Workers with University Degree or Above, Business Sector. When we aggregated our 12 types of labour input into the 3 categories used by the KLEMS program, we found that our value aggregates were very close to the corresponding KLEMS value aggregates for the 3 types of labour. However, our aggregated (Fisher chained) indexes of the 3 types of labour grew more slowly than the corresponding KLEMS 3 labour quantity indexes.75 The Statistics Canada productivity program aggregate labour input measure is described as follows: “The labour input is an aggregate of the hours worked of all persons classified by their education, work experience and class of employment (paid versus self-employed workers). This aggregate labour input measure is constructed by aggregating hours at work data for each of 56 types of workers classified by their educational attainment (4), work experience (7) and class of workers (2) using an annual chained-Fisher index. The effect of Fisher aggregation is to produce a measure of labour input that reflects both changes in total hours of work and changes in the composition of workers.” John R. Baldwin, Wulong Gu and Beiling Yan (2007; 37). Baldwin, Gu and Yan (2007; 26) describe their more disaggregated measures of labour input as follows: “Labour input for MFP measures reflects the compositional shifts of workers by education, experience and class of workers (paid versus self-employed). The growth of labour input (labour services) is an aggregate of the growth of hours worked by different classes of workers, weighted by the hourly wages of each class.” Thus each of the three types of labour classified by educational attainment QL1

t, QL2t and

QL3t is a Fisher quantity aggregate over the other characteristics, holding constant the

relevant educational levels. Baldwin, Gu and Yan (2007; 26) also comment on the difficulties associated with breaking up the net operating surplus generated by the self employed into labour and capital compensation components: “We have modified the assumptions about the share of labour going to the self-employed workers to reflect changes that occurred during the 1990s. In the past, it had been assumed that the self employed essentially earned incomes similar to the employed. The Census of Population up to 1990 showed that this was a reasonable assumption; however, during the 1990s, self-employed income fell behind that of production workers. The new measure of self-employed for calculating labour input assumes that the hourly earning of self-employed workers is proportional to that of paid workers with the same level of education and

74 It is not apparent to us why the KLEMS program posts quantity data for the years 1961-2011 but only posts the corresponding value data for the years 1961-2008. 75 The differences between the 3 KLEMS labour quantity indexes and our counterpart indexes are substantial. The KLEMS program probably uses the same data base but on a more disaggregated basis that takes into account work experience; i.e., the KLEMS program distinguishes 56 types of labour whereas our data base distinguishes on 36 types of labour. The KLEMS method for aggregating over sectors may also be different. We prefer to use our labour estimates rather than the KLEMS estimates for two reasons: (i) the data base that we use is published (by Statistics Canada) and is readily available for researchers to check and (ii) the experience variable is a difficult one to quantify in a reproducible way.

58

experience. The proportional or scaling factor for each level of education and experience is based on the relative hourly earnings of paid versus self-employed workers derived from the Census of Population.” We now turn our attention to the problems associated with the estimation of beginning of the year capital stocks for the business sector. 4. Business Sector Capital Stock Estimates Our main source of information on beginning of the period capital stocks used by the Canadian business sector is CANSIM Table 310003, which has the title: Flows and stocks of fixed non-residential capital, by sector of North American Industry Classification System (NAICS) and asset, Canada, annually. This Table has a wealth of information on the reproducible capital stocks used by the business sector along with the corresponding annual investment and depreciation information by type of asset and by sector. This source of information on reproducible assets will be supplemented by the use of estimates from the Statistics Canada National Balance Sheets to obtain estimates of inventory and land stocks used by the business sector; see Statistics Canada (1997). Table 310003 has estimates of current VIn

t and chained dollar QInt business sector

investment in the following 14 types of reproducible asset:

• QI1: Office furniture; • QI2 : Agricultural machinery; • QI3 : Industrial machinery; • QI4 : Automobiles; • QI5 : Trucks; • QI6 : Other transport equipment; • QI7 : Other machinery and equipment; • QI8 : Computers; • QI9 : Telecommunications equipment; • QI10 : Software; • QI11 : Industrial buildings; • QI12 : Commercial buildings; • QI13 : Institutional buildings; • QI14 : Engineering construction.

The annual current dollar investment that was used by the business sector for the years 1961-2011 for the above 14 assets, VIn

t for n = 1,...,14 can be found in CANSIM Table 310003. The Series numbers are: V43985602, V43985603, V43985604, V43985607, V43985608, V43985609, V43985611, V43985606, V43985610, V43985612,76 V43985613, V43985614, V43985615 and V43985616. The corresponding chained 2002 dollar series, QIn

t, can also be found in Table 310003. The Series numbers are: V43993266, V43993267, V43993268, V43993271, V43993272, V43993273,

76 The software investment series (VI10

t and QI10t) start in 1981 and the corresponding beginning of the year

capital stock series (QK10t) starts in 1982.

59

V43993275, V43993270, V43993274, V43993276, V43993277, V43993278, V43993279 and V43993280. Implicit price indexes PIn

t for the 14 types of investment can be obtained by dividing the current dollar series by the corresponding chained dollar series; i.e., define PIn

t as follows:77 (6) PIn

t ≡ VInt/QIn

t ; n = 1,...,14; t = 1961,....,2011. CANSIM Table 31003 also has chained 2002 dollar information on year end capital stocks for the Canadian business sector constructed using geometric depreciation rates for each of the above asset classes. We use these year end stocks as beginning of the next year capital stocks by asset class and denote these year t starting stocks as QKn

t for n = 1,...,14 and t = 1962-2012. The Series numbers for these 14 stocks are as follows: V43993448, V43993449, V43993450, V43993453, V43993454, V43993455, V43993457, V43993452, V43993456, V43993458, V43993459, V43993460, V43993461 and V43993462. Define the amount of depreciation for asset n in year t by QDn

t. Using the geometric model of depreciation, the beginning of year t+1 capital stock for asset n, QKn

t+1, should be related to the corresponding beginning of year t capital stock, QKn

t, plus year t investment, QIn

t, less year t depreciation, QDnt; i.e., the following equations should hold:

(7) QKn

t+1 = QKnt + QIn

t − QDnt ; n = 1,...,14; t = 1962,....,2011.78

Equations (7) can be solved for the depreciation amounts QDn

t and then these depreciation estimates can be divided by the corresponding year t starting stocks QKn

t to give us estimates for the year t geometric depreciation rates δn

t: (8) δn

t ≡ QDnt/QKn

t ; n = 1,...,14; t = 1962,....,2011. The resulting depreciation rates were somewhat volatile and many asset depreciation rates had substantial trends.79 We do not expect geometric depreciation rates to change much from year to year so we decided to smooth the rates which were generated by (8). The trends in the depreciation rates were not linear or even piecewise linear so we used a nonparametric smoothing method in order to reduce the volatility in the rates. We used the Lowess locally weighted nonparametric method due to Cleveland (1979) as implemented by White (2004) in the econometrics program Shazam.

77 For n = 10 (software), t starts at 1981. After we estimate depreciation rates for the 14 classes of asset, the prices defined by (6) were normalized to equal 1 in 1961 (except the software price was normalized to equal 1 in 1981) and the units for the QIn

t were adjusted accordingly. The price of software investment was artificially set equal to 1 for the years 1961-1980. 78 For n = 10, t = 1982,...,2011. The same years t also apply to equations (8) for n = 10. 79 The sample average depreciation rates were as follows: δ1 = 0.19583; δ2 = 0.32578; δ3 = 0.19064; δ4 = 0.39929; δ5 = 0.31457; δ6 = 0.18500; δ7 = 0.12853; δ8 = 0.45736; δ9 = 0.20666; δ10 = 0.37454; δ11 = 0.08088 ; δ12 = 0.06641 ; δ13 = 0.04787; δ14 = 0.08308.

60

We used the cross validation criterion to pick the best smoothing parameter.80 We set the depreciation rates δn

1961 for 1961 equal to the corresponding smoothed rates for 1962.81 The resulting smoothed depreciation rates δn

t are listed in Table 11. Table 11: Smoothed Depreciation Rates for 14 Business Sector Reproducible Assets Year δ1

t δ2t δ3

t δ4t δ5

t δ6t δ7

t δ8t δ9

t δ10t δ11

t δ12t δ13

t δ14t

1961 0.1322 0.2777 0.1627 0.3072 0.2296 0.1349 0.1017 0.2788 0.1453 0.2839 0.0735 0.0611 0.0446 0.0656 1962 0.1322 0.2777 0.1627 0.3072 0.2296 0.1349 0.1017 0.2788 0.1453 0.2839 0.0735 0.0611 0.0446 0.0656 1963 0.1312 0.2880 0.1661 0.3137 0.2351 0.1358 0.1019 0.2861 0.1472 0.2839 0.0744 0.0613 0.0446 0.0661 1964 0.1303 0.2966 0.1696 0.3207 0.2406 0.1381 0.1021 0.2924 0.1491 0.2839 0.0753 0.0615 0.0445 0.0665 1965 0.1294 0.3025 0.1740 0.3323 0.2460 0.1419 0.1016 0.2989 0.1514 0.2839 0.0768 0.0616 0.0445 0.0671 1966 0.1299 0.3049 0.1758 0.3451 0.2513 0.1455 0.1010 0.3004 0.1532 0.2839 0.0774 0.0618 0.0445 0.0677 1967 0.1323 0.3028 0.1748 0.3520 0.2565 0.1472 0.1011 0.3014 0.1533 0.2839 0.0768 0.0619 0.0445 0.0684 1968 0.1350 0.2981 0.1734 0.3584 0.2610 0.1476 0.1021 0.3051 0.1527 0.2839 0.0761 0.0619 0.0446 0.0691 1969 0.1369 0.2934 0.1741 0.3637 0.2656 0.1483 0.1024 0.3092 0.1523 0.2839 0.0764 0.0619 0.0446 0.0698 1970 0.1385 0.2937 0.1753 0.3672 0.2709 0.1496 0.1025 0.3159 0.1527 0.2839 0.0768 0.0621 0.0446 0.0707 1971 0.1389 0.3012 0.1756 0.3740 0.2767 0.1518 0.1028 0.3230 0.1537 0.2839 0.0765 0.0624 0.0446 0.0713 1972 0.1369 0.3153 0.1764 0.3937 0.2828 0.1561 0.1023 0.3308 0.1553 0.2839 0.0762 0.0629 0.0446 0.0717 1973 0.1349 0.3308 0.1786 0.4149 0.2887 0.1630 0.1014 0.3389 0.1579 0.2839 0.0765 0.0632 0.0446 0.0721 1974 0.1364 0.3423 0.1804 0.4305 0.2939 0.1694 0.1013 0.3477 0.1610 0.2839 0.0770 0.0635 0.0446 0.0728 1975 0.1404 0.3488 0.1803 0.4354 0.2979 0.1715 0.1013 0.3575 0.1625 0.2839 0.0770 0.0636 0.0447 0.0732 1976 0.1449 0.3485 0.1794 0.4339 0.3005 0.1712 0.1015 0.3717 0.1618 0.2839 0.0769 0.0636 0.0448 0.0735 1977 0.1483 0.3449 0.1785 0.4339 0.3014 0.1719 0.1025 0.3912 0.1600 0.2839 0.0770 0.0636 0.0449 0.0738 1978 0.1520 0.3427 0.1783 0.4418 0.3012 0.1758 0.1049 0.4146 0.1586 0.2839 0.0772 0.0636 0.0451 0.0745 1979 0.1570 0.3432 0.1790 0.4479 0.3001 0.1799 0.1073 0.4425 0.1587 0.2839 0.0779 0.0634 0.0453 0.0756 1980 0.1631 0.3431 0.1814 0.4556 0.2993 0.1825 0.1100 0.4593 0.1603 0.2839 0.0791 0.0633 0.0455 0.0769 1981 0.1691 0.3399 0.1827 0.4570 0.2996 0.1795 0.1125 0.4622 0.1613 0.2839 0.0795 0.0632 0.0457 0.0781 1982 0.1755 0.3377 0.1816 0.4650 0.3010 0.1750 0.1145 0.4629 0.1607 0.2839 0.0786 0.0632 0.0459 0.0787 1983 0.1830 0.3401 0.1796 0.4858 0.3037 0.1725 0.1164 0.4607 0.1601 0.2937 0.0777 0.0633 0.0462 0.0792 1984 0.1921 0.3476 0.1794 0.5084 0.3082 0.1755 0.1193 0.4687 0.1607 0.3029 0.0779 0.0635 0.0464 0.0799 1985 0.2020 0.3542 0.1811 0.5200 0.3141 0.1782 0.1231 0.4819 0.1621 0.3115 0.0783 0.0639 0.0466 0.0808 1986 0.2122 0.3579 0.1836 0.5296 0.3200 0.1785 0.1277 0.4899 0.1643 0.3192 0.0784 0.0643 0.0467 0.0814 1987 0.2198 0.3612 0.1866 0.5522 0.3248 0.1813 0.1325 0.4899 0.1677 0.3262 0.0785 0.0647 0.0469 0.0819 1988 0.2231 0.3641 0.1899 0.5690 0.3284 0.1871 0.1365 0.4860 0.1720 0.3326 0.0791 0.0649 0.0471 0.0824 1989 0.2208 0.3654 0.1917 0.5663 0.3312 0.1896 0.1382 0.4746 0.1769 0.3395 0.0797 0.0649 0.0473 0.0829 1990 0.2172 0.3615 0.1905 0.5305 0.3334 0.1887 0.1377 0.4731 0.1822 0.3445 0.0799 0.0647 0.0475 0.0832 1991 0.2157 0.3544 0.1876 0.4899 0.3351 0.1929 0.1355 0.4824 0.1889 0.3468 0.0798 0.0646 0.0476 0.0832 1992 0.2191 0.3550 0.1855 0.4631 0.3368 0.1928 0.1327 0.4974 0.1960 0.3507 0.0797 0.0644 0.0478 0.0831 1993 0.2231 0.3583 0.1859 0.4500 0.3383 0.1880 0.1308 0.5199 0.2026 0.3592 0.0801 0.0643 0.0480 0.0836 1994 0.2247 0.3546 0.1885 0.4327 0.3402 0.1853 0.1309 0.5405 0.2097 0.3670 0.0810 0.0644 0.0482 0.0850 1995 0.2245 0.3434 0.1916 0.4101 0.3429 0.1898 0.1321 0.5600 0.2190 0.3716 0.0824 0.0646 0.0485 0.0865 1996 0.2293 0.3372 0.1954 0.3842 0.3461 0.1953 0.1341 0.5792 0.2325 0.3767 0.0837 0.0650 0.0488 0.0881 1997 0.2353 0.3381 0.1989 0.3648 0.3486 0.2027 0.1365 0.5959 0.2473 0.3842 0.0847 0.0655 0.0492 0.0900 1998 0.2383 0.3348 0.2015 0.3556 0.3497 0.2100 0.1400 0.6043 0.2625 0.3904 0.0857 0.0660 0.0497 0.0910 1999 0.2380 0.3220 0.2032 0.3515 0.3513 0.2146 0.1441 0.6002 0.2778 0.3941 0.0868 0.0669 0.0502 0.0922 2000 0.2408 0.3084 0.2043 0.3400 0.3529 0.2192 0.1496 0.5811 0.2913 0.3993 0.0875 0.0684 0.0508 0.0942 2001 0.2433 0.3008 0.2044 0.3275 0.3537 0.2194 0.1552 0.5614 0.2973 0.4080 0.0876 0.0705 0.0513 0.0966 2002 0.2467 0.2975 0.2053 0.3222 0.3548 0.2150 0.1593 0.5522 0.2979 0.4167 0.0875 0.0726 0.0519 0.0978 2003 0.2522 0.2974 0.2080 0.3212 0.3572 0.2106 0.1618 0.5566 0.2996 0.4214 0.0877 0.0750 0.0524 0.0991 2004 0.2581 0.3002 0.2131 0.3166 0.3594 0.2142 0.1649 0.5661 0.3032 0.4250 0.0878 0.0770 0.0530 0.1008 2005 0.2626 0.3031 0.2191 0.3140 0.3602 0.2210 0.1689 0.5714 0.3070 0.4273 0.0882 0.0777 0.0536 0.1023 2006 0.2649 0.3069 0.2241 0.3142 0.3590 0.2297 0.1725 0.5676 0.3089 0.4304 0.0884 0.0776 0.0542 0.1035 2007 0.2650 0.3111 0.2268 0.3114 0.3570 0.2372 0.1741 0.5559 0.3110 0.4310 0.0884 0.0776 0.0547 0.1044

80 In case of a tie in the criterion between two smoothing parameters, we chose the higher parameter, which led to slightly smoother depreciation rates. The smoothing parameter choices varied between 0.09 and 0.23 except that the best smoothing parameter for institutional buildings turned out to be 0.55. The sample averages for the smoothed depreciation rates turned out to be as follows: 0.19584; 0.32574; 0.19063; 0.39927; 0.31429; 0.18502; 0.12854; 0.45733; 0.20668; 0.37445; 0.08088; 0.06640; 0.04802; 0.008307. These smoothed average rates are very close to the raw average depreciation rates listed earlier. 81 The depreciation rates for software for the years 1961-1981 were set equal to the smoothed rate for 1982.

61

2008 0.2623 0.3087 0.2267 0.3020 0.3552 0.2359 0.1733 0.5409 0.3119 0.4268 0.0884 0.0776 0.0553 0.1048 2009 0.2612 0.3037 0.2260 0.2948 0.3530 0.2294 0.1724 0.5345 0.3141 0.4196 0.0886 0.0774 0.0559 0.1046 2010 0.2615 0.3005 0.2271 0.2952 0.3507 0.2275 0.1734 0.5388 0.3178 0.4165 0.0887 0.0772 0.0566 0.1040 2011 0.2620 0.3028 0.2287 0.2964 0.3484 0.2324 0.1745 0.5452 0.3222 0.4168 0.0888 0.0771 0.0572 0.1037

We can use our estimated depreciation rates for 1961, the Statistics Canada estimated starting capital stocks for 1962 and the investment information for 1961 in chained 2002 dollars in order to generate estimated starting capital stocks for our 14 types of asset for 1961; i.e., consider the following equation: (9) QKn

t+1 = (1−δnt)QKn

t + QInt .

Rearrange the above equation for t = 1961 to solve for QKn

1961 for n = 1,2,...,9,11,...,14. A similar equation can be used to generate the starting stock for asset 10 for 1981, QK10

1981. Now use equations (9), the smoothed depreciation rates listed in Table 11 and the investment information QIn

t along with the starting capital stocks QKn1961 in order to

generate capital stock series QKnt for the 14 reproducible assets.82 We will value the

starting capital stocks for year t at the average investment prices for year t, PInt, that were

described earlier. We renormalized these prices to equal 1 in 1961 (instead of in 2002) and we changed the capital stock units to match these normalized investment prices.83 These normalized prices for investment and the corresponding starting capital stocks, PKn

t, are listed in Table 12 below. The corresponding normalized capital stocks, QKnt, are

listed in Table 13 below.84 We turn our attention to the problems associated with the construction of business inventory change and inventory stock. From CANSIM Table 3800002, we can obtain current dollar estimates for business sector investment in inventories from Series V498100 and in chained 2002 dollars from Series V1992057. However, division of the current value series by the constant dollar series produces nonsensical implicit price estimates for many years.85 Thus a different method for constructing estimates of real inventory change must be used.

82 The capital stock series for software start at 1981 rather than 1961. 83 Define the constants Cn = PIn

1961 and define new investment and capital stock prices for period t as PInt/Cn

and the corresponding beginning of year t capital stocks are rescaled to equal QKnt×Cn for n =

1,...,9,11,...14. The rescaling is of course a bit different for asset 10 which only starts in 1981. We denote the rescaled capital stock (and investment) prices as PIn

t and quantities QKnt in an abuse of notation.

84 Note that our investment series for the 14 assets, QInt, can be recovered from Tables 12 and 13 using

equations (9). Thus we did not table the QInt.

85 Diewert (2005b) showed that traditional index number theory breaks down when the value aggregate can take both positive and negative signs and he suggested that indexes of inventory stocks be constructed (in place of indexes of inventory change) and then the stock estimates should be differenced in order to obtain estimates of inventory change. It is interesting to note that SNA 2008 suggested this solution to the problem: “Index number formulae are generally not applicable to time series that can take positive, negative and zero values. Nevertheless, there are ways of deriving pseudo chain volume series expressed in terms of monetary values in such cases. The most commonly used approach is to identify two associated time series that take only positive values and are such that when differenced yield the target series.” Eurostat, IMF, OECD, UN and the World Bank (2008; 302).

62

End of the year current market value86 starting stocks of inventories for persons and unincorporated business and for corporations the entire economy and for the government sector are available from the National Balance Sheet Accounts; see CANSIM Table 3780051, Series V52229234 and Table 3780052, Series V52229291) for the years 1961-2011. Adding these two series will give us estimates for the value of the business sector beginning of the year inventory stocks for the years 1962-2012, VK15

t. We can subtract the value of inventory change for 1961 (see CANSIM Series V498100) from the starting stock of inventories in 1962 in order to extend the value of inventory stock series back to 1961. Statistics Canada87 provided us with a price index for business sector inventory stocks for the years 1961-2006, PK15

t. We extended this price series to the years 2007-2011 by using the January indexes for the Industrial Product Price Index for Canada and for All Commodities, CANSIM Series V53384722, Table 3290056. The inventory value series VK15

t can be divided by the inventory stock price series PK15t, in order to obtain a

real beginning of the year business sector stock of inventories, QK15t. The resulting price

and quantity series (after normalization so that the price is unity in 1961) are listed in Table 12 for PK15

t and Table 13 for QK15t.

It is possible to generate an alternative value of inventory stock series by cumulating information on the value of inventory change from the System of National Accounts. Thus the CANSIM series V498100 estimates the current value of business investment in inventories, which conceptually, should equal the value of inventory change over the year. Using the balance sheet estimates of the starting stock of inventories for 1962 (which was $13,698 million) and the above series, we can cumulate inventory changes and obtain an alternative SNA based estimated value of inventory change, which ended up at $108,049 million at the start of 2012. However, using the balance sheet estimates for the beginning of 2012 value of business inventories, we obtain the estimate $242,049 million, which is 2.42 times as big as the implied SNA estimate. Thus the SNA based estimates basically give us an inventory to output ratio that is implausibly low at the end of the sample period. It is true that inventory to output ratios have been falling due to just in time delivery and other inventory management techniques but the number of goods that are being produced has also been growing, which implies an increasing need for inventories. In any case, we will take the balance sheet estimates of inventory stocks as the “truth”.88 A preliminary price series for inventory change PII

t in year t is set equal to PK15t+1 listed in

Table 12.89 A preliminary series for the quantity of inventory change in year t listed in Table 13, QII

t, is set equal to the stock at the beginning of year t+1, QK15t+1, less the stock

at the beginning of year t, QK15t. These preliminary series, PII

t and QIIt are then

86 These series are labelled as book value series but we believe that they are market value series. 87 Our thanks to Wulong Gu. 88 This choice will lead to an increase in measured Total Factor Productivity compared to estimates that rely on the SNA estimates of inventory change. See Diewert and Smith (1994) for a detailed accounting framework for inventories that is consistent with the Hicks (1961) and Edwards and Bell (1961) model of production and Diewert (2005b) for a critical review of SNA conventions for measuring inventory change. 89 Diewert (2005b) showed that in order to obtain a user cost of inventories that is consistent with other user costs and the measurement of output, inventory changes should be valued at end of year prices.

63

renormalized so that PIIt equals unity in 1961 and QII

t is adjusted accordingly to offset this change in units and these renormalized series are the series which appear in Tables 2 and 3 above. We need estimates for the price and quantity of agricultural land and other land that is used by the Canadian business sector. We will also construct estimates for the stock of residential housing and the stock of residential land. The National Balance Sheets have annual values for 5 classes of nonfinancial assets:90

• Residential structures; • Nonresidential structures; • Machinery and Equipment; • Inventories and • Land.

There are estimates for the above 5 components for 3 sectors:

• Persons and unincorporated businesses; • Corporate and government businesses and • The nonbusiness government sector.

It can be seen that the Balance Sheet Sectors do not correspond exactly to our business sector. We have already formed estimates for business sector structures, machinery and equipment and inventories, which leaves agricultural land, other business land, residential land and residential structures to be estimated. We first form estimates for the quantity and value of agricultural land. For the years 1981-2011, we can obtain end of year estimates for the value of agricultural land from CANSIM Table 20020 (Balance Sheet of the Agricultural Sector), Series V157699. This series will give us beginning of the year values for agricultural land VK16

t for the years t = 1982-2012. For census years, we can obtain direct estimates for the quantity of agricultural land from CANSIM Table 1530038, Series V32166910, which provides estimates for the agricultural land area for Canada.91 To obtain estimates for noncensus years, we interpolated between census years using an annualized geometric rate of growth.92 The resulting preliminary quantity series is QK16

t. For the years 1982-2011, we can obtain a preliminary price series for agricultural land, PK16

t, by dividing VK16t by

90 The CANSIM National Balance Sheet value estimates that we will use are labelled as book values but we note that these book value series which start in 1961 coincide with market value series that start in 1971. Thus we will interpret these “book value” series as market value series. 91 These estimates for the census years 1971-2006 (at 5 year intervals) were as follows: 622426.1, 619900.4, 597154.8, 611111.6, 613317.0, 616541.4, 610788.8, 674007.5. The 10% jump in land area going from 2001 to 2006 does not seem possible. Hence we will use earlier data from this source (downloaded in 2008) augmented by information from Leacy (1983), Series M-23, Area of Land in Farm Holdings, Census Data, Canada (thousands of acres). The estimates for 1961 and 1966 were converted into hectares at 1 hectare = 2.471 acres. 92 We used the annualized 2001-2006 geometric growth rate to extrapolate our agricultural land estimates from 2006 to 2011.

64

QK16t. We linked PK16

t to a value of farmland per acre series at 1982. This series was Series V381831 in CANSIM Table 2003. The resulting price series PK16

t was normalized to equal 1 in 1961 (and QK16

t was renormalized as well); see Table 12 for a listing of PK16t

and Table 13 for a listing of QK16t.

From the National Balance Sheets, we can obtain estimates for the market value of land held by corporations and government business enterprises at the end of the year for the years 1961-2011; see CANSIM Table 3780052, Series V52229292.93 We will convert these estimates into beginning of the year stocks of business land for the years 1962-2012 and label the resulting series VK17

t for t = 1962,...,2012. We assume that the stock of nonagricultural business land is fixed over the sample period. This is a very rough approximation to the actual situation but it is likely that land used for manufacturing has declined while land used for office space and warehousing has increased over time and so the assumption that the aggregate amount of nonagricultural land is fixed may be satisfactory.94 Thus a preliminary price series for business nonagricultural land PK17

t can be obtained for t = 1962,...,2012 by dividing the year t value VK17

t by VK171962, which

equals QK17t. We use the rate of change of an average land cost series over the years

1961-1962 to extrapolate our price series PK17t back to 1961.95 The resulting PK17

t series is normalized to equal 1 in 1961 (and the units of QK17

t are adjusted to offset the change in the units of measurement for PK17

t). PK17t is listed in Table 12 and QK17

t is listed in Table 13. From the National Balance Sheets, we can obtain estimates for the market value of land held by persons and unincorporated business at the end of the year for the years 1961-2011; see CANSIM Table 3780051, Series V52229235. We will convert these estimates into beginning of the year stocks of personal and unincorporated business land for the years 1962-2012 and label the resulting series VLP

t for t = 1962,...,2012. We will form an estimate of the value of residential land held by households, VK18

t by subtracting the value of agricultural land VK16

t from VLPt; i.e., define VK18

t as follows: (10) VK18

t ≡ VLPt − VK16

t ; t = 1962,...,2012. We estimate the value of household residential land for 1961 by multiplying VK18

1962 by the same rate of change of an average land cost series over the years 1961-1962 that we used to extrapolate our price series PK17

t back to 1961. We make the assumption that the quantity of household residential land QK18

t has remained fixed throughout the sample period so that QK18

t ≡ VK181961 and PK18

t ≡ VK18t/QK18

t for t = 1961-2012. Finally, we normalize the price and quantity series so that PK18

1961 = 1. The resulting price and 93 Unfortunately, the household sector owns a considerable amount of land that is used for business purposes; i.e., unincorporated persons own land used for business purposes and the land used in these enterprises should appear as inputs into the business sector. The corporate business sector also owns some land associated with residential rental properties but we are trying to exclude these inputs from our measure of business sector input. Thus our estimates for the value of business sector land are only approximate ones. 94 We know of no accurate published source of information on the quantity of business land. The National Balance Sheets may have this information but it is not publically available. 95 The series is the series S317 in Leacy (1983): NHA average land cost per dwelling unit, single detached dwelling units. This series matches up well with PK17

t for the early 1960s.

65

quantity series are listed in Tables 12 and 13. Note that we do not include this asset (and the following one) as inputs into our definition of the Canadian Business Sector; we include information on the price and quantity of housing assets in this data Appendix mainly for comparison purposes.96 From the National Balance Sheets, we can obtain estimates for the market value of residential structures held by all sectors at the end of the year for the years 1961-2011; see CANSIM Table 3780049, Series V52229098. We will convert these estimates into beginning of the year stocks of residential structures for the years 1962-2012 and label the resulting (preliminary) series VK19

t for t = 1962,...,2012. From Table 2 above, we have a price series for residential investment, PIR

t, for the years 1961-2011. We set the stock price equal to this flow price; i.e., define PK19

t ≡ PIRt for t = 1961,...,2011. We can

obtain a preliminary quantity series for residential housing stocks by setting QK19t ≡

VK19t/PK19

t for t = 1962-2011. Recall that estimates of annual investment in residential structures, QIR

t, are available in Table 3 above. Thus we can solve the following equations to produce annual estimates for the residential housing depreciation rates, δ19

t: (11) QK19

t+1 = (1−δ19t)QK19

t + QIRt ; t = 1962,....,2010.

We found that (12) δ19

t = 0.04 fit the data very well; i.e., the geometric model of depreciation and a residential housing annual depreciation rate of 4% fits the Balance Sheet and SNA information on residential structure stocks and flows very well. Thus we used equations (11) with δ19

t defined by (12) to generate new estimates for QK19

t for t = 1963-2012, starting with our initial estimate for QK19

1962.97 The price and quantity series PK19t and QK19

t are listed in Tables 12 and 13. Table 12: Price Indexes for 19 Beginning of the Year Capital Stock Components

Year t PK1t PK2

t PK3t PK4

t PK5t PK6

t PK7t PK8

t PK9t

1961 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1962 1.01137 1.05740 1.00113 0.97324 1.02038 1.00615 1.02898 0.96354 0.99806 1963 1.06806 1.07996 1.04047 0.96994 1.02078 1.00645 1.08707 1.01749 0.98263 1964 1.02381 1.08338 1.09732 0.97278 1.04130 1.07556 1.05941 0.99721 0.98891 1965 1.05075 1.09966 1.15339 0.96659 1.04664 1.09366 1.10754 1.05390 1.00360 1966 1.05018 1.13146 1.17819 0.96359 1.05823 1.11560 1.12872 1.02490 1.02479 1967 1.09264 1.17977 1.16282 0.97557 1.07306 1.13414 1.12377 1.05175 1.08257 1968 1.09879 1.22245 1.16269 1.00199 1.11088 1.17024 1.10695 1.05929 1.13927 1969 1.11761 1.28120 1.20288 1.00466 1.13732 1.22880 1.11334 1.05960 1.19422 1970 1.15443 1.30675 1.29237 1.02439 1.16312 1.27389 1.17338 1.08151 1.26897 1971 1.22861 1.31818 1.32178 1.04236 1.19444 1.34283 1.24500 1.09954 1.30351 1972 1.22357 1.36632 1.37009 1.06063 1.22881 1.40326 1.24382 1.10132 1.37394 1973 1.21221 1.41521 1.45972 1.05513 1.26635 1.40600 1.26447 1.11202 1.43225 1974 1.28130 1.59136 1.69131 1.12335 1.41044 1.54433 1.43841 1.08798 1.54785

96 However, this residential housing information will prove to be useful in allocating property taxes to households and businesses. 97 We also used equation (11) for t = 1961 to generate QK19

1961.

66

1975 1.38326 1.84802 2.01676 1.19462 1.50690 1.74331 1.68135 1.12790 1.69758 1976 1.39815 1.95575 2.16731 1.24240 1.60922 1.88471 1.72575 1.00642 1.81061 1977 1.39296 2.07919 2.40430 1.34913 1.78596 2.13016 1.83303 0.87721 1.94505 1978 1.32407 2.36104 2.72273 1.46803 1.99582 2.37471 1.96439 0.62628 2.32966 1979 1.40302 2.68065 3.06840 1.62655 2.24490 2.64614 2.13660 0.54810 2.47951 1980 1.40777 3.03363 3.46024 1.78610 2.48954 2.92389 2.28656 0.39077 2.50626 1981 1.48352 3.27532 3.88176 2.00006 2.75787 3.28385 2.53117 0.32430 2.51086 1982 1.55444 3.42949 4.20365 2.06901 2.91878 3.55360 2.72246 0.31423 2.77445 1983 1.48959 3.57802 4.29091 2.12851 3.03895 3.79390 2.71550 0.21880 2.95432 1984 1.47416 3.68604 4.52775 2.20129 3.21889 4.06867 2.78977 0.18735 3.07119 1985 1.50081 3.72044 4.77971 2.30097 3.44011 4.37413 2.90008 0.15354 3.15055 1986 1.51389 3.81671 4.98417 2.47250 3.63963 4.50238 2.95874 0.12732 3.24551 1987 1.51574 3.79651 4.97729 2.49291 3.68843 4.50965 2.93865 0.10448 3.28044 1988 1.52322 3.81818 4.91862 2.52330 3.77979 4.43663 2.91099 0.09391 3.25547 1989 1.54349 3.88082 5.06505 2.64768 3.95045 4.48751 2.96917 0.07721 3.16149 1990 1.58096 3.93327 5.15746 2.67951 4.08369 4.61281 3.03857 0.06877 3.17528 1991 1.41407 3.99896 5.10975 2.40750 4.06793 4.58257 2.92008 0.05109 3.00177 1992 1.43464 4.16202 5.35656 2.43376 4.26652 4.88918 2.98946 0.04488 3.02568 1993 1.46428 4.39606 5.64167 2.48274 4.45729 5.19908 3.07587 0.04291 3.04357 1994 1.49919 4.70444 5.95830 2.58874 4.72753 5.50579 3.20771 0.03934 2.98295 1995 1.55593 4.93813 6.21333 2.74150 5.07428 5.86279 3.35640 0.03406 2.86384 1996 1.56508 5.11723 6.38381 2.90523 5.20258 5.96886 3.41910 0.02663 2.98413 1997 1.56414 5.32937 6.59795 2.95349 5.32276 6.11654 3.55781 0.02348 3.07353 1998 1.58318 5.66773 7.05546 2.94295 5.53270 6.42328 3.71816 0.01978 3.19248 1999 1.57667 5.81141 7.17665 2.88543 5.64746 6.52884 3.73623 0.01579 3.16260 2000 1.58588 5.87946 7.26683 2.92371 5.73134 6.72690 3.79080 0.01376 3.13046 2001 1.60658 6.13482 7.54231 2.92648 5.75421 6.97438 3.91737 0.01234 3.22725 2002 1.64072 6.37435 7.75505 2.92764 5.81061 7.20856 4.15430 0.01107 3.23343 2003 1.56471 5.88828 7.17821 2.86451 5.66628 6.84374 3.78666 0.00972 2.87898 2004 1.54173 5.74325 6.94005 2.81064 5.04410 6.55533 3.66071 0.00817 2.58985 2005 1.52893 5.66743 6.79384 2.78114 4.76832 6.46206 3.56390 0.00697 2.42055 2006 1.49286 5.44049 6.68246 2.78306 4.52203 6.32149 3.47244 0.00615 2.29796 2007 1.47546 5.41808 6.58960 2.72652 4.40738 6.21833 3.41083 0.00560 2.16953 2008 1.50786 5.61826 6.83242 2.66622 4.44467 6.36765 3.49734 0.00519 2.15092 2009 1.57350 6.08854 7.38066 2.71667 4.80255 6.79368 3.74390 0.00534 2.26037 2010 1.49541 5.70031 6.83808 2.60605 4.49149 6.36145 3.49382 0.00465 2.07804 2011 1.46646 5.62986 6.65434 2.50397 4.33844 6.17248 3.41098 0.00390 1.98147

Year t PK10

t PK11t PK12

t PK13t PK14

t PK15t PK16

t PK17t PK18

t PK19t

1961 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1962 1.00000 0.99608 0.99460 0.99392 1.01575 1.00758 1.04000 1.06956 1.06956 1.00504 1963 1.00000 1.01320 1.01217 1.00954 1.04878 1.01000 1.10000 1.14186 1.13138 1.02769 1964 1.00000 1.02701 1.02799 1.02792 1.08754 1.02114 1.22000 1.22953 1.17489 1.07312 1965 1.00000 1.07668 1.07303 1.07230 1.15834 1.03951 1.36000 1.33883 1.28108 1.13368 1966 1.00000 1.14637 1.14633 1.14271 1.22039 1.06286 1.52000 1.50884 1.40204 1.20765 1967 1.00000 1.19421 1.18943 1.18623 1.27431 1.08044 1.72000 1.72055 1.53236 1.28518 1968 1.00000 1.19457 1.18660 1.18014 1.29594 1.09271 1.90000 1.90357 1.65913 1.31431 1969 1.00000 1.24911 1.24269 1.24678 1.36883 1.11812 1.94000 2.06400 1.85677 1.38118 1970 1.00000 1.31097 1.30737 1.30589 1.44017 1.14350 1.96000 2.30803 2.07210 1.42615 1971 1.00000 1.37628 1.37575 1.38556 1.53340 1.15918 2.00000 2.57526 2.29359 1.53179 1972 1.00000 1.43938 1.48457 1.42652 1.62592 1.21176 2.16000 2.91981 2.62666 1.67349 1973 1.00000 1.67138 1.63218 1.70557 1.76318 1.32609 2.62000 3.37790 3.07434 1.97123 1974 1.00000 2.01596 1.97824 2.00075 2.08006 1.43765 3.42000 4.09743 3.74775 2.36134 1975 1.00000 2.15089 2.23056 2.14258 2.39908 1.55864 4.34000 5.14001 4.45256 2.56072 1976 1.00000 2.25171 2.28171 2.21538 2.62725 1.66364 5.14000 6.11266 5.00058 2.76853 1977 1.00000 2.33723 2.33639 2.33707 2.82966 1.78349 5.92000 6.86747 5.54137 2.87768 1978 1.00000 2.48283 2.44204 2.45389 3.07450 1.94126 7.02000 7.73958 6.22057 3.04069 1979 1.00000 2.72726 2.62735 2.70399 3.37288 2.15180 8.68000 8.75269 6.89425 3.28046 1980 1.00000 3.05028 2.92066 2.98077 3.72927 2.35895 10.94000 10.13151 7.82788 3.55455 1981 1.00000 3.34986 3.37340 3.26366 4.17375 2.57823 12.30000 11.80501 9.46235 3.99273 1982 1.04668 3.60647 3.64903 3.53304 4.57405 2.77940 12.28000 13.59583 11.1252 4.08226 1983 1.04158 3.70109 3.63211 3.55784 4.73954 2.93246 12.00746 14.67903 10.97657 4.25350 1984 1.03509 3.72530 3.58418 3.54937 4.92451 3.06736 11.47452 15.06937 11.89405 4.41785 1985 1.04110 3.86573 3.67106 3.61473 5.07752 3.14959 10.77083 15.91875 13.04512 4.55564 1986 0.99762 4.07351 3.82303 3.75332 5.16941 3.18232 9.98330 16.60220 13.36892 4.90827 1987 0.98632 4.30996 4.04672 3.92222 5.24581 3.23099 9.38642 17.78782 15.51504 5.40819

67

1988 0.95560 4.54914 4.28021 4.13983 5.46324 3.28744 9.22342 19.23126 18.32986 5.78293 1989 0.90493 4.83669 4.58493 4.46342 5.60941 3.34034 9.82631 21.05861 20.90959 6.13195 1990 0.86944 4.98129 4.73149 4.64393 5.81539 3.38833 10.62426 22.80582 24.58675 6.11231 1991 0.84938 4.85493 4.57374 4.52112 5.80948 3.39008 10.91042 24.32908 24.22111 6.32257 1992 0.78550 4.90011 4.57571 4.53163 5.69966 3.54606 10.69755 24.94996 26.88125 6.39710 1993 0.77630 4.99264 4.59136 4.54853 5.74033 3.55229 10.75269 25.42013 28.75011 6.58445 1994 0.76296 5.15658 4.67721 4.66114 5.95345 3.72829 11.17139 26.61217 30.94243 6.76485 1995 0.74869 5.29164 4.89424 4.81102 6.00867 3.85944 12.03048 28.07898 33.02674 6.76717 1996 0.73898 5.42507 4.98452 4.89972 6.23529 3.94827 13.01832 29.02794 32.17431 6.75581 1997 0.72378 5.56044 5.08641 5.00667 6.43924 3.81073 14.07653 30.40692 33.04791 6.87512 1998 0.70786 5.62718 5.18595 5.11441 6.61189 3.83563 15.65784 31.72819 34.68720 6.95993 1999 0.70234 5.79023 5.30161 5.21495 6.65698 3.89582 16.57088 33.12003 36.34749 7.13210 2000 0.72074 6.01999 5.58007 5.46397 6.83468 3.98639 17.36315 34.73818 39.07382 7.29782 2001 0.72951 6.17581 5.73544 5.61734 6.93482 4.07102 18.10348 36.73098 41.53887 7.48766 2002 0.71574 6.30878 5.83813 5.72697 7.01826 4.13975 19.15359 38.19277 45.85210 7.81242 2003 0.67374 6.55451 6.04697 5.89756 7.07896 3.90062 20.51253 39.90438 52.02609 8.21290 2004 0.65255 6.95679 6.43910 6.27399 7.49242 3.94012 21.92495 42.36014 57.04940 8.71618 2005 0.63392 7.39366 6.83092 6.61162 8.03111 3.98736 23.44333 45.97595 65.83547 9.12487 2006 0.61349 7.91121 7.37042 7.21658 8.71238 4.05205 25.14717 49.63661 75.28426 9.79903 2007 0.60917 8.56620 8.08661 7.83753 9.20799 4.16849 26.98601 54.78682 85.69017 10.51028 2008 0.62557 9.41887 8.74072 8.47363 9.63875 4.18013 29.51155 60.39559 96.37451 10.79847 2009 0.64807 8.87153 8.37817 8.26826 9.91446 4.21894 31.56851 66.28022 101.98280 10.81072 2010 0.63975 8.90035 8.44794 8.35579 10.36743 4.22283 33.02810 68.25891 106.26550 11.13668 2011 0.63687 9.25009 8.73135 8.64498 10.79124 4.35867 34.74666 71.88240 111.73700 11.44031

Table 13: Quantity Indexes for 19 Beginning of the Year Capital Stock Components

Year t QK1t QK2

t QK3t QK4

t QK5t QK6

t QK7t QK8

t QK9t

1961 974.6 1147.0 4325.6 535.0 934.0 1909.3 2655.6 313.2 1359.9 1962 977.2 1125.9 4391.6 560.1 898.9 1872.8 2719.0 370.5 1405.5 1963 981.0 1152.7 4477.9 597.7 897.7 1865.7 2780.2 409.0 1464.5 1964 1013.2 1212.6 4818.6 642.5 916.6 1860.6 2907.8 461.1 1530.0 1965 1062.5 1293.4 5294.3 698.3 953.6 1949.7 3071.2 522.1 1628.9 1966 1132.2 1389.1 5959.3 769.4 1004.7 2069.9 3383.4 618.3 1771.7 1967 1208.2 1451.0 6354.5 823.0 1047.4 2227.5 3728.0 703.0 1899.0 1968 1259.7 1432.8 6514.9 833.1 1082.8 2331.6 4015.6 741.5 1985.4 1969 1325.5 1378.7 6785.5 928.4 1134.7 2401.8 4359.3 828.5 2075.4 1970 1386.5 1278.0 7136.3 955.1 1148.9 2443.1 4693.8 892.1 2147.1 1971 1427.0 1238.5 7397.6 1003.5 1209.7 2447.1 4986.9 938.2 2262.8 1972 1532.8 1250.1 7582.2 1103.3 1370.0 2489.0 5311.5 998.4 2387.8 1973 1690.1 1338.5 7981.1 1242.0 1617.5 2718.5 5739.1 1093.7 2530.3 1974 1877.7 1496.7 8515.8 1351.3 1783.0 2974.9 6221.9 1273.6 2786.6 1975 2049.8 1652.7 8910.0 1508.1 1953.6 3090.9 6704.7 1450.8 3068.8 1976 2182.4 1851.1 9238.0 1543.6 2059.9 3040.5 7366.4 1634.4 3296.0 1977 2316.1 1917.6 9474.7 1547.3 2142.5 2971.0 7920.9 1889.6 3442.3 1978 2526.2 1964.2 9545.9 1646.5 2204.7 2984.1 8475.4 2579.0 3475.7 1979 2814.3 2076.0 9760.6 1805.9 2359.8 3165.6 9008.0 3470.7 3522.4 1980 3119.6 2109.4 10108.2 1899.9 2307.6 3299.1 9555.6 5563.3 3638.9 1981 3471.1 2179.8 10917.9 2281.9 2232.7 3467.0 10028.4 9732.4 3829.5 1982 3502.7 2042.0 11166.9 2149.2 2054.2 3355.4 10582.9 11479.8 3928.8 1983 3725.7 1854.1 10985.8 2233.1 1962.2 3322.6 10844.9 16736.0 3882.3 1984 4100.2 1739.6 10702.0 2440.6 1930.5 3279.2 10893.6 22210.0 3871.8 1985 4627.9 1617.3 10659.5 2292.0 1850.4 3415.6 11068.6 28441.0 3858.1 1986 5232.5 1502.0 11020.5 2437.1 1756.9 3436.8 11091.5 35833.1 3886.3 1987 6125.0 1385.3 11478.1 2503.6 1720.8 3298.9 11379.9 54456.7 4059.9 1988 6863.1 1288.6 12235.7 3024.2 1722.3 3567.2 11820.6 61763.7 4341.6 1989 7450.8 1200.6 13161.0 3477.3 1675.4 3688.7 12133.4 77685.6 4688.3 1990 7422.1 1134.0 13652.3 3790.8 1625.4 3632.3 12451.4 86679.7 5032.6 1991 7464.5 1050.5 13754.6 3749.6 1538.7 3704.8 12901.3 102616.8 5283.0 1992 7572.4 984.1 13420.8 3805.5 1494.5 3730.3 13081.6 132747.5 5569.1 1993 8078.3 1090.4 12986.3 4101.8 1438.1 3426.9 12835.3 144592.1 5658.0 1994 8335.7 1130.9 12801.3 4882.9 1428.7 3260.9 12594.4 176603.4 5638.6 1995 8353.7 1151.6 12817.0 5421.3 1481.4 3124.9 12429.6 222673.6 5613.9 1996 8320.8 1206.2 12782.1 6061.8 1391.0 3076.8 12192.3 284098.0 5564.6 1997 9081.5 1336.3 13294.2 6480.4 1410.5 3265.4 12159.6 365548.8 5846.7

68

1998 9195.9 1638.7 13441.6 7290.8 1529.3 3552.1 11958.2 548271.2 5882.0 1999 9019.5 1741.4 13453.4 8795.9 1683.4 3838.5 11832.9 755556.8 6155.2 2000 8826.3 1707.9 13546.0 10059.2 1784.5 4054.1 11781.4 978557.3 6786.9 2001 9016.1 1712.7 13151.9 10145.9 1577.0 4454.9 12228.5 1055585.0 7229.9 2002 8755.7 1561.5 12719.3 10703.1 1905.8 4258.5 12728.8 1187980.0 7302.9 2003 9128.4 1518.7 12763.9 11201.8 1857.7 4055.3 13408.9 1375561.0 7326.2 2004 9943.9 1492.1 12919.3 11436.5 1985.1 3994.3 14112.1 1732471.0 7470.1 2005 10488.4 1468.1 13823.5 11112.5 2318.4 4156.8 14801.4 2156580.0 7617.0 2006 11654.5 1537.7 14699.0 11364.1 2761.4 4292.6 15533.6 2737726.0 7881.4 2007 12325.7 1604.9 15400.8 11480.1 2838.5 4669.6 16071.0 3144545.0 7915.5 2008 12760.6 1754.9 16121.9 10600.4 2949.0 5060.4 15936.8 3570520.0 8275.2 2009 12919.9 1691.5 15628.5 8983.4 2871.0 4766.5 15462.1 3448026.0 8278.6 2010 13259.3 1675.4 15592.4 7932.5 3016.8 4621.7 15425.0 3782510.0 8714.2 2011 13572.3 1681.8 15694.8 7146.1 3179.0 4517.7 15686.7 4497614.0 9330.9

Year t QK10

t QK11t QK12

t QK13t QK14

t QK15t QK16

t QK17t QK18

t QK19t

1961 0 4365.0 5135.9 535.6 14959.3 13594.0 5953.9 6376.4 10679.8 28710.3 1962 0 4481.0 5460.2 566.3 15429.6 13595.0 5964.7 6376.4 10679.8 29772.9 1963 0 4599.4 5770.1 589.2 15934.1 14150.5 5975.5 6376.4 10679.8 30852.5 1964 0 4801.5 6158.7 605.2 16615.7 15079.2 5986.4 6376.4 10679.8 31972.2 1965 0 5072.5 6636.8 623.9 17350.1 15607.4 5997.3 6376.4 10679.8 33408.8 1966 0 5462.7 7244.7 640.9 18213.6 16826.3 6008.2 6376.4 10679.8 34897.8 1967 0 5675.4 7685.6 651.0 19086.3 18129.7 5977.1 6376.4 10679.8 36201.3 1968 0 5792.2 8040.6 655.4 19988.1 18580.4 5946.2 6376.4 10679.8 37507.0 1969 0 5979.2 8367.0 648.1 20772.8 19194.7 5915.5 6376.4 10679.8 39139.1 1970 0 6209.6 8710.1 639.3 21740.9 20762.6 5884.9 6376.4 10679.8 41124.2 1971 0 6352.6 9119.0 623.7 22735.1 20941.5 5854.4 6376.4 10679.8 42733.4 1972 0 6422.5 9590.4 610.3 23594.9 20711.2 5806.3 6376.4 10679.8 44751.7 1973 0 6521.3 10279.5 595.8 24466.6 20858.3 5758.6 6376.4 10679.8 47028.0 1974 0 6701.9 11025.7 584.1 25327.8 23381.2 5711.3 6376.4 10679.8 49518.3 1975 0 6855.7 11910.3 582.9 26459.7 28183.5 5664.4 6376.4 10679.8 52001.1 1976 0 6940.1 12662.4 584.6 27475.9 27852.2 5617.8 6376.4 10679.8 54306.9 1977 0 7113.1 13332.1 584.3 28631.6 28100.5 5634.1 6376.4 10679.8 57306.7 1978 0 7190.1 14071.5 585.3 29807.1 29409.2 5650.5 6376.4 10679.8 60256.5 1979 0 7368.3 15104.4 592.9 31128.7 30699.9 5666.9 6376.4 10679.8 63137.5 1980 0 7734.6 16155.1 608.1 32775.9 34363.6 5683.3 6376.4 10679.8 65863.1 1981 796.8 8176.9 17102.8 623.7 34514.1 34529.1 5699.8 6376.4 10679.8 68205.3 1982 1526.9 8409.0 17457.4 632.8 36004.2 35413.4 5716.4 6376.4 10679.8 70755.9 1983 2216.7 8403.6 17907.9 647.2 36761.6 30844.8 5732.9 6376.4 10679.8 72265.9 1984 2967.8 8443.4 18486.2 660.1 37316.8 29803.2 5749.6 6376.4 10679.8 74454.6 1985 3710.4 8600.5 19289.6 677.4 37836.1 31533.6 5766.3 6376.4 10679.8 76607.0 1986 4659.3 8643.6 20362.7 695.8 37654.3 32989.5 5783.0 6376.4 10679.8 79120.6 1987 5660.4 8707.0 21647.3 709.2 37450.9 34010.9 5781.8 6376.4 10679.8 82223.0 1988 7023.3 8834.7 23078.6 733.0 37609.6 35698.9 5780.5 6376.4 10679.8 86123.7 1989 8500.7 9028.6 24560.9 745.9 37762.1 37761.1 5779.3 6376.4 10679.8 90018.8 1990 10131.4 9125.5 25813.5 753.2 38084.4 39156.5 5778.1 6376.4 10679.8 94058.0 1991 11473.7 9079.5 26545.2 748.1 38622.1 38577.6 5776.9 6376.4 10679.8 97130.4 1992 12822.5 8894.2 26768.0 742.4 38622.0 34708.1 5782.0 6376.4 10679.8 99069.0 1993 14902.0 8717.0 26961.8 724.9 38707.7 34161.6 5787.1 6376.4 10679.8 101343.9 1994 17361.5 8686.2 26877.9 756.6 39265.9 33290.6 5792.2 6376.4 10679.8 103314.3 1995 18979.1 8684.1 26727.8 752.8 39692.4 33994.1 5797.4 6376.4 10679.8 105452.7 1996 21101.4 8843.3 26613.1 763.1 39873.6 37134.0 5802.5 6376.4 10679.8 106574.5 1997 23824.2 8999.0 27057.5 773.5 40542.1 39532.6 5793.1 6376.4 10679.8 108164.0 1998 27181.5 9059.5 27430.2 755.7 41268.3 41299.3 5783.6 6376.4 10679.8 110167.3 1999 29843.2 9157.4 27899.8 723.0 41871.8 43611.1 5774.2 6376.4 10679.8 111866.6 2000 31779.3 9325.5 27784.7 708.3 42819.5 44851.1 5764.8 6376.4 10679.8 113715.4 2001 33827.0 9290.3 27761.3 710.3 43880.0 47743.8 5755.4 6376.4 10679.8 115822.5 2002 34473.7 9126.8 27703.5 714.3 44406.8 45902.0 5756.8 6376.4 10679.8 118552.8 2003 35644.2 8909.1 27605.8 701.5 45330.3 49243.5 5758.3 6376.4 10679.8 122214.1 2004 38259.1 8680.1 27685.3 709.1 46540.0 47534.3 5759.7 6376.4 10679.8 126179.2 2005 42475.4 8406.3 27645.7 707.6 48566.4 48584.3 5761.2 6376.4 10679.8 130650.5 2006 45812.7 8282.3 27958.8 706.0 50681.1 50865.9 5762.6 6376.4 10679.8 135244.2 2007 51424.7 8168.2 28086.5 700.8 52815.3 52546.4 5764.1 6376.4 10679.8 139857.3 2008 54804.4 8028.6 28421.7 700.5 55348.8 54089.0 5765.5 6376.4 10679.8 144566.2 2009 55870.3 7839.5 28624.8 697.1 55605.4 56978.0 5767.0 6376.4 10679.8 148760.4 2010 57608.3 7653.3 28614.6 691.4 56263 53969.5 5768.4 6376.4 10679.8 151990.6

69

2011 59617.0 7510.4 28642.3 682.1 57383.1 52570.4 5769.9 6376.4 10679.8 156030.0

The units for the quantities in Table 13 are in millions of 1961 constant (mostly chained) dollars. 5. Primary Input Tax Rates, Balancing Real Rates of Return and User Costs Nonresidential structures (office buildings, factories, etc.) and business land have to pay property taxes on these inputs whereas machinery and equipment and inventory stocks are generally exempt from paying these taxes. Thus it is necessary to take into account property taxes when constructing user costs of capital for business nonresidential structures and business land. Information on property taxes for the years 1961-2011 is available from Statistics Canada; see CANSIM Series V499942, Table 3800035 (Real Property Taxes of Local Governments) and CANSIM Series V499841, Table 3800033 (Real Property Taxes of Provincial Governments). We approximate the asset base on which these taxes fall as the total beginning of the year national value of land, residential structures and nonresidential structures. Data on these values are available for the years 1962-2012 from the National Balance Sheets: Series V52229098 for residential structures, Series V52229099 for nonresidential structures and Series V52229103 for land. These series were summed and the sum was used as the tax base for the sum of the two property tax series, V499942 plus V499841. The resulting property tax rates are reported as the series τP

t in Table 14 below98 and it will be used in the construction of the user costs of business sector land and nonresidential structures.99 Our estimated property tax rate starts at 1.5% and trends down to 1%.100 We will apply this property tax rate to assets 11-14 and 16 and 17. Thus define the asset specific property tax rates for year t and asset n, τPn

t, as follows: (13) τPn

t ≡ 0 for n = 1-10 and 15 and τPnt ≡ τP

t for n = 11-14 and 16-17. It is of some interest to calculate the average business tax rate for taxes that apply to the use of financial capital in the business sector so we provide estimates for this tax rate by year. These business taxes that fall on the return to capital are defined to be the sum of the following taxes:

• Taxes less subsidies on factors of production (CANSIM Series V1992216, Table 3800001) less local government and Provincial government property taxes;

• Total government taxes on income from corporations and government business enterprises (CANSIM Series V499131, Table 3800007);

98 The tax rate for 1961 was set equal to the corresponding rate for 1962. 99 This is a very rough approximation to the actual property tax rates on business sector land and nonresidential structures since actual property tax rates are different across different sectors and assets. For example, business sector property assets are generally taxed more heavily than household property assets. 100 This property tax rate is probably too high for residential property and too low for business property, which is generally taxed at higher rates than corresponding residential properties.

70

• Total government taxes on income from nonresidents (CANSIM Series V499132, Table 3800007).

The sum of the above three sources of general business taxes that fall on capital stock components for year t was divided by the corresponding sum of the beginning of the year t value of assets for our 17 types of business sector asset, VKn

t ≡ PKntQKn

t for n = 1,...,17. We denote the resulting business tax rate for year t as τB

t and it is listed in Table 14. Using the asset specific property tax rates τPn

t, the general business tax rates τBt, the

depreciation rates δnt for n = 1-14 that are listed in Table 11101 and the asset prices PKn

t that are listed in Table 12, we can define user costs Un

t for our 17 asset classes as follows:102 (14) Un

t ≡ [rt + τBt + τPn

t + δnt]PKn

t ; n = 1,...,17 ; t = 1961,...,2011 where rt is suitable after tax cost of capital that applies to the business sector in year t. In the present study, we will follow national income accounting conventions and will take rt to be the balancing real rate of return;103 i.e., it is the rate of return that is consistent with the year t value of business sector net output being equal to the value of primary inputs used by the business sector in year t, where the user costs defined by (14) are used as prices for the beginning of the year capital inputs. Thus rt can be determined as the solution to the following linear in rt equation for t = 1961,...,2011: (15) PC

tQCt + PGN

tQGNt + PIG

tQIGt + PIR

tQIRt + PIN

tQINt + PIM

tQIMt + PII

tQIIt + ∑n=8

15 PntQn

t + ∑n=16

22 PntQn

t = ∑n=112 PLn

tQLnt + ∑n=1

12 [rt + τBt + τPn

t + δnt]PKn

tQKnt

where the various price and quantity series are defined in the above Appendix 2 tables.104 The resulting series of balancing real rates of return are listed in Table 14 below. It should be noted that rt can be interpreted as a real interest rate; i.e., it is the income earned by the business sector in year t relative to the starting capital stock, valued at the average investment prices for the period. This explains why we have not included a capital gains term in the user cost formulae defined by (14).105

101 The depreciation rates δn

t for assets n = 15-17 are defined to be zero; i.e., we assume that inventories, agricultural land and non-agricultural business land does not depreciate. 102 For additional material on user costs and many historical references, see Hall and Jorgenson (1967), Christensen and Jorgenson (1969), Harper, Berndt and Wood (1980), Jorgenson (1989) (1996a) (1996b), Diewert (1980) (2005a) and Schreyer (2009). 103 For most purposes, it is probably preferable to use an exogenous real rate of return in the user costs (14) since the resulting prices will probably approximate market rental prices better. However, when we used the sample average real rate of return in the user costs defined by (14), our results were basically unchanged. 104 PXG

t and QXGt are chained Fisher aggregates of our 7 classes of exports of goods, PXS

t and QXSt are the

price and quantity of exports of services, PMGt and QMG

t are chained Fisher aggregates of our 6 classes of imports of goods and PMS

t and QMSt are the price and quantity of imports of services.

105 We have essentially absorbed the capital gains (or losses) term into rt.

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Table 14: Business Sector Property Tax Rates, Business Income Tax Rates, Balancing Real After Tax Rates of Return, Output Price and Quantity Indexes, Wealth Stock Price and Quantity Indexes and Nominal and Real Capital-Output Ratios Year t τP

t τBt rt PY

t PKWt QY

t QKWt VKW

t/VYt QKW

t/QYt

1961 0.01523 0.03321 0.05249 1.00000 1.00000 29368 65074 2.21582 2.21582 1962 0.01583 0.03397 0.05515 0.99856 1.01729 31585 66186 2.13478 2.09549 1963 0.01591 0.03456 0.06656 1.00652 1.04665 34008 67985 2.07874 1.99905 1964 0.01604 0.03577 0.06765 1.01867 1.08317 36591 70874 2.05957 1.93692 1965 0.01625 0.03448 0.06610 1.04940 1.14039 39269 73925 2.04574 1.88251 1966 0.01628 0.03327 0.06909 1.09696 1.20301 42286 78410 2.03354 1.85428 1967 0.01608 0.03161 0.05413 1.13097 1.26118 43046 82234 2.13031 1.91037 1968 0.01651 0.03449 0.05643 1.17273 1.29867 44645 84583 2.09799 1.89454 1969 0.01706 0.03601 0.05072 1.21411 1.35379 46806 87164 2.07649 1.86225 1970 0.01675 0.03309 0.05049 1.25561 1.42103 48260 90627 2.12529 1.87789 1971 0.01628 0.03369 0.04699 1.29828 1.49080 50453 92937 2.11522 1.84206 1972 0.01572 0.03551 0.04524 1.36563 1.58234 53041 94972 2.07466 1.79052 1973 0.01472 0.03931 0.07376 1.50882 1.74242 58833 98134 1.92626 1.66801 1974 0.01369 0.04264 0.07498 1.75211 2.04007 61729 103385 1.95010 1.67484 1975 0.01293 0.03756 0.04134 1.96979 2.35402 59494 110211 2.21382 1.85247 1976 0.01341 0.03425 0.04494 2.11057 2.56869 63195 112964 2.17556 1.78756 1977 0.01379 0.03232 0.05507 2.21607 2.78161 67878 115949 2.14413 1.70820 1978 0.01370 0.03218 0.05921 2.37355 3.05881 70536 119537 2.18396 1.69469 1979 0.01263 0.03319 0.07172 2.63295 3.41664 74697 123921 2.15276 1.65897 1980 0.01265 0.03361 0.05810 3.00323 3.84243 73053 130218 2.28060 1.78251 1981 0.01284 0.03219 0.03896 3.25854 4.29723 74433 135275 2.39672 1.81740 1982 0.01266 0.02878 0.02220 3.49379 4.64812 70178 138323 2.62225 1.97104 1983 0.01293 0.02982 0.04906 3.72131 4.78184 73158 136998 2.40631 1.87263 1984 0.01291 0.03350 0.05951 3.85108 4.88711 78124 137639 2.23576 1.76179 1985 0.01298 0.03328 0.06376 3.95543 5.01468 82741 140493 2.15271 1.69799 1986 0.01323 0.03220 0.05644 4.01511 5.10543 85022 142988 2.13847 1.68178 1987 0.01323 0.03484 0.07100 4.18593 5.20489 90562 145848 2.00251 1.61048 1988 0.01316 0.03499 0.06524 4.34738 5.36693 94673 150432 1.96160 1.58896 1989 0.01328 0.03510 0.05478 4.51052 5.59149 96093 155302 2.00349 1.61617 1990 0.01344 0.03458 0.04658 4.64727 5.80048 95614 158744 2.07224 1.66025 1991 0.01392 0.03274 0.02901 4.75227 5.79147 90124 160238 2.16676 1.77796 1992 0.01441 0.03299 0.04309 4.77287 5.85051 93353 158327 2.07894 1.69601 1993 0.01449 0.03555 0.04305 4.83870 5.93265 94376 157980 2.05239 1.67394 1994 0.01421 0.03816 0.05980 4.91510 6.15537 100399 158425 1.97612 1.57795 1995 0.01381 0.04015 0.06486 5.04356 6.37125 103942 159699 1.94088 1.53643 1996 0.01385 0.04396 0.06544 5.15174 6.56306 107236 162378 1.92903 1.51422 1997 0.01381 0.04711 0.05355 5.20691 6.72535 111372 166742 1.93377 1.49716 1998 0.01398 0.04268 0.04900 5.17017 6.94852 117549 170681 1.95143 1.45200 1999 0.01406 0.04860 0.05328 5.28758 7.07901 123970 174830 1.88806 1.41027 2000 0.01328 0.05433 0.06836 5.55287 7.29671 131759 178130 1.77651 1.35194 2001 0.01297 0.04388 0.07092 5.63026 7.50574 133542 181277 1.80963 1.35745 2002 0.01260 0.04278 0.08428 5.62453 7.68304 140612 180822 1.75662 1.28597 2003 0.01246 0.04509 0.07926 5.88377 7.66301 137172 183931 1.74636 1.34088 2004 0.01230 0.04868 0.09290 6.13906 7.91101 142915 185502 1.67264 1.29799 2005 0.01186 0.04811 0.09927 6.40036 8.25856 146942 189852 1.66713 1.29202 2006 0.01138 0.05080 0.08666 6.59016 8.67958 150611 195631 1.71075 1.29892 2007 0.01080 0.04651 0.08824 6.86052 9.15476 153240 200440 1.74543 1.30802 2008 0.01040 0.04330 0.09625 7.21836 9.67526 154370 205062 1.78052 1.32838 2009 0.01017 0.03930 0.05044 6.93438 10.02875 145290 205338 2.04395 1.41329 2010 0.01036 0.04011 0.07177 7.20173 10.15786 149905 204637 1.92545 1.36511 2011 0.01027 0.03884 0.09084 7.51534 10.47166 154907 205655 1.84984 1.32760

The sample average property tax rate was τP ≡ 0.01368, the sample average business income tax rate was τB ≡ 0.03780 and the sample average real after tax rate of return was r ≡ 0.06133. Once rt has been determined, then the 17 series of user costs defined by (14) can also be calculated; these series are listed in Table 15. Note that rt is a real after tax

72

rate of return because we do not include a capital gains term in our user costs and all user costs are evaluated at the average prices for the corresponding investment good for year t. Table 15: Business Sector User Costs for 17 Asset Classes. Year t U1

t U2t U3

t U4t U5

t U6t U7

t U8t

1961 0.21788 0.36335 0.2484 0.39288 0.31527 0.22065 0.18744 0.36447 1962 0.22381 0.38782 0.2521 0.38569 0.32518 0.22545 0.19639 0.35447 1963 0.24816 0.42021 0.27800 0.40237 0.34325 0.23844 0.22067 0.39402 1964 0.23925 0.43337 0.29957 0.41255 0.35825 0.25976 0.21774 0.39467 1965 0.24163 0.44325 0.31666 0.41845 0.36275 0.26524 0.22396 0.42102 1966 0.24395 0.46078 0.32770 0.43115 0.37425 0.27654 0.22951 0.41273 1967 0.23825 0.45836 0.30292 0.42705 0.36728 0.26413 0.20992 0.40718 1968 0.24824 0.47554 0.30730 0.45027 0.39090 0.27912 0.21362 0.41947 1969 0.24993 0.48709 0.31372 0.45257 0.40069 0.28874 0.21061 0.41948 1970 0.25641 0.49302 0.33462 0.46183 0.41230 0.29711 0.21839 0.43205 1971 0.26972 0.50336 0.33879 0.47391 0.42692 0.31214 0.22842 0.44391 1972 0.26628 0.54119 0.35238 0.50318 0.44674 0.33237 0.22771 0.45323 1973 0.30057 0.62811 0.42571 0.55704 0.50874 0.38814 0.27125 0.50263 1974 0.32548 0.73192 0.50400 0.61569 0.58046 0.44318 0.31497 0.50629 1975 0.30341 0.79039 0.52274 0.61444 0.56782 0.43659 0.30289 0.49221 1976 0.31325 0.83651 0.56040 0.63747 0.61095 0.47191 0.31184 0.45377 1977 0.32829 0.89871 0.63925 0.70331 0.69441 0.55224 0.34814 0.41981 1978 0.32227 1.02501 0.73419 0.78276 0.78349 0.63446 0.38556 0.31690 1979 0.36753 1.20113 0.87126 0.89915 0.90920 0.75377 0.45329 0.30006 1980 0.35865 1.31903 0.94514 0.97756 0.97352 0.80174 0.46128 0.21530 1981 0.35645 1.34637 0.98536 1.05640 1.02258 0.82311 0.46481 0.17298 1982 0.35214 1.33307 0.97789 1.06769 1.02752 0.80321 0.45045 0.16149 1983 0.39017 1.49919 1.10891 1.20189 1.16280 0.95360 0.53026 0.11806 1984 0.42032 1.62413 1.23352 1.32394 1.29154 1.09242 0.59231 0.10524 1985 0.44875 1.67862 1.32937 1.41985 1.41419 1.20405 0.63853 0.08888 1986 0.45535 1.70433 1.35676 1.52861 1.48720 1.20269 0.64010 0.07365 1987 0.49360 1.77298 1.45542 1.64051 1.58850 1.29500 0.70049 0.06225 1988 0.49254 1.77271 1.42705 1.68875 1.62021 1.27487 0.68898 0.05506 1989 0.47955 1.76670 1.42596 1.73727 1.66365 1.25430 0.67730 0.04358 1990 0.47168 1.74107 1.40099 1.63890 1.69282 1.24455 0.66491 0.03812 1991 0.39226 1.66427 1.27383 1.32821 1.61438 1.16707 0.57588 0.02780 1992 0.42349 1.79401 1.40134 1.31214 1.76161 1.31481 0.62409 0.02574 1993 0.44172 1.92074 1.49207 1.31226 1.85839 1.38625 0.64422 0.02568 1994 0.48365 2.12922 1.70686 1.37374 2.07122 1.55945 0.73408 0.02512 1995 0.51266 2.21439 1.84292 1.41228 2.27260 1.72839 0.79596 0.02265 1996 0.53011 2.28512 1.94568 1.43392 2.37005 1.81891 0.83256 0.01834 1997 0.52549 2.33849 1.97631 1.37483 2.39132 1.85541 0.84385 0.01635 1998 0.52243 2.41737 2.06848 1.31640 2.44216 1.93774 0.86144 0.01377 1999 0.53589 2.46363 2.18924 1.30828 2.55943 2.06605 0.91896 0.01109 2000 0.57640 2.53450 2.37616 1.35268 2.72558 2.29978 1.03230 0.00968 2001 0.57534 2.54947 2.40776 1.29422 2.69581 2.33100 1.05774 0.00834 2002 0.61328 2.70658 2.57774 1.31520 2.79987 2.46536 1.18944 0.00752 2003 0.58923 2.48322 2.38584 1.27626 2.72844 2.29253 1.08349 0.00662 2004 0.61624 2.53701 2.46127 1.28780 2.52713 2.33231 1.12189 0.00578 2005 0.62684 2.55327 2.48958 1.28329 2.42024 2.38066 1.12725 0.00501 2006 0.60064 2.41754 2.41605 1.25689 2.24505 2.32132 1.07639 0.00434 2007 0.58988 2.41560 2.38221 1.21652 2.16733 2.31273 1.05354 0.00387 2008 0.60590 2.51826 2.50236 1.17735 2.19890 2.39053 1.09414 0.00353 2009 0.55223 2.39551 2.33063 1.04460 2.12645 2.16824 0.98160 0.00333 2010 0.55840 2.35051 2.31795 1.06073 2.07775 2.15887 0.99653 0.00303 2011 0.57443 2.43488 2.38461 1.06703 2.07401 2.23508 1.03746 0.00263

Year t U9

t U10t U11

t U12t U13

t U14t U15

t U16t U17

t 1961 0.23103 0.36964 0.17439 0.16200 0.14550 0.16654 0.08570 0.10093 0.10093 1962 0.23399 0.37306 0.17771 0.16512 0.14861 0.17324 0.08979 0.10915 0.11225 1963 0.24399 0.38506 0.19392 0.18048 0.16312 0.19203 0.10213 0.12873 0.13363 1964 0.24971 0.38736 0.20005 0.18599 0.16859 0.20230 0.10561 0.14575 0.14688 1965 0.25289 0.38452 0.20848 0.19149 0.17304 0.21306 0.10456 0.15889 0.15642

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1966 0.26188 0.38630 0.22471 0.20680 0.18646 0.22743 0.10879 0.18033 0.17900 1967 0.25881 0.36967 0.21329 0.19475 0.17361 0.21694 0.09263 0.17512 0.17517 1968 0.27752 0.37486 0.21923 0.20095 0.17936 0.22876 0.09935 0.20412 0.20451 1969 0.28541 0.37067 0.22510 0.20594 0.18496 0.23768 0.09698 0.20135 0.21422 1970 0.29982 0.36753 0.23223 0.21234 0.18925 0.24632 0.09558 0.19666 0.23158 1971 0.30548 0.36462 0.23880 0.21928 0.19614 0.25807 0.09352 0.19392 0.24970 1972 0.32432 0.36469 0.24856 0.23654 0.20126 0.27350 0.09785 0.20838 0.28168 1973 0.38812 0.39701 0.34143 0.31176 0.29407 0.35251 0.14994 0.33481 0.43166 1974 0.43122 0.40156 0.41991 0.38531 0.35206 0.42446 0.16910 0.44909 0.53804 1975 0.40987 0.36284 0.36315 0.34667 0.29248 0.39586 0.12297 0.39853 0.47199 1976 0.43642 0.36314 0.38179 0.35653 0.30439 0.43641 0.13176 0.47600 0.56608 1977 0.48114 0.37133 0.41637 0.38508 0.34147 0.49519 0.15586 0.59898 0.69484 1978 0.58238 0.37533 0.45265 0.41188 0.36856 0.55213 0.17742 0.73775 0.81338 1979 0.65369 0.38884 0.53314 0.47543 0.44030 0.65132 0.22573 1.02020 1.02875 1980 0.63159 0.37564 0.55971 0.48960 0.44671 0.67609 0.21632 1.14163 1.05726 1981 0.58361 0.35509 0.54758 0.49655 0.42338 0.67654 0.18345 1.03313 0.99156 1982 0.58740 0.35056 0.51294 0.46287 0.38718 0.65124 0.14172 0.78160 0.86535 1983 0.70609 0.38810 0.62745 0.56331 0.49084 0.81047 0.23132 1.10242 1.34770 1984 0.77912 0.40984 0.68473 0.60725 0.54045 0.91515 0.28528 1.21534 1.59609 1985 0.81658 0.42531 0.72810 0.63842 0.56595 0.96883 0.30563 1.18498 1.75134 1986 0.82103 0.40686 0.73426 0.63540 0.55775 0.94741 0.28206 1.01693 1.69115 1987 0.89737 0.42611 0.85136 0.74368 0.65110 1.05421 0.34198 1.11766 2.11804 1988 0.88631 0.41362 0.87553 0.76300 0.66449 1.06977 0.32951 1.04586 2.18066 1989 0.84345 0.38860 0.88424 0.77036 0.67156 1.04357 0.30023 1.01368 2.17239 1990 0.83635 0.37010 0.8693 0.75388 0.65968 1.03399 0.27497 1.00498 2.15727 1991 0.75229 0.34703 0.75477 0.64149 0.55734 0.92298 0.20932 0.82553 1.84086 1992 0.82311 0.33521 0.83411 0.70897 0.62655 0.98947 0.26979 0.96804 2.25777 1993 0.85586 0.33987 0.86474 0.72274 0.64150 1.01439 0.27919 1.00090 2.36619 1994 0.91764 0.35473 0.99619 0.82561 0.74736 1.17389 0.36522 1.25307 2.98504 1995 0.92785 0.35686 1.06456 0.89764 0.80477 1.23374 0.40527 1.42943 3.33626 1996 1.02029 0.35925 1.12274 0.93835 0.84316 1.31785 0.43196 1.60456 3.57780 1997 1.06960 0.35091 1.10777 0.91517 0.81966 1.31646 0.38360 1.61139 3.48080 1998 1.13082 0.34126 1.07690 0.89004 0.79450 1.29999 0.35167 1.65448 3.35255 1999 1.20090 0.34831 1.17385 0.96913 0.86667 1.38525 0.39691 1.92123 3.83994 2000 1.29613 0.37622 1.34515 1.14066 1.02049 1.57339 0.48908 2.36082 4.72326 2001 1.32990 0.38135 1.32980 1.13684 1.00609 1.55572 0.46733 2.31297 4.69289 2002 1.37403 0.38918 1.43319 1.23946 1.09691 1.66638 0.52597 2.67489 5.33379 2003 1.22046 0.36771 1.47131 1.28064 1.11613 1.66980 0.48505 2.80637 5.45941 2004 1.15183 0.36974 1.68144 1.48645 1.29795 1.90785 0.55783 3.37377 6.51829 2005 1.09994 0.36428 1.82916 1.61856 1.40699 2.10083 0.58764 3.73303 7.32104 2006 1.02576 0.34838 1.87718 1.66911 1.46490 2.19875 0.55700 3.74292 7.38794 2007 0.96714 0.34464 2.00442 1.80462 1.56987 2.30173 0.56171 3.92785 7.97429 2008 0.97105 0.35431 2.24479 1.98868 1.73971 2.45594 0.58337 4.42551 9.05683 2009 0.91289 0.33007 1.67216 1.48525 1.28866 2.02737 0.37859 3.15388 6.62177 2010 0.89299 0.33804 1.87751 1.68483 1.49399 2.34571 0.47244 4.03727 8.34379 2011 0.89532 0.34802 2.11590 1.89544 1.70413 2.62965 0.56525 4.86294 10.06024

Tables 13 and 15 provide estimates for the prices and quantities of business sector capital services for the 17 assets in our data base for the years 1961-2011. As noted earlier, the sample average of the balancing after tax real rates of return rt was a rather large 6.133% per year. The average property tax rate τP

t was 1.368% while the average business tax rate on assets was 3.780%. The before business tax real rate of return averaged 9.913%. Thus it appears that governments are taking about 38.1% of the before tax return to capital assets on average.106 However, it must be kept in mind that these balancing rates of return may not be very reliable; they contain the net effect of all the measurement errors that were made in constructing this data set. 106 This relatively high rate of business taxation has two negative effects: (i) it raises the user cost of capital and hence lessens the beneficial effects of capital deepening and (ii) the high rates lead to a relatively large loss of productive efficiency; i.e., the deadweight losses of such large tax rates are likely to be large.

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The high average after tax rates of return for the business sector are a source of concern. The corresponding balancing real rate of returns for Australia averaged around 3 percent; see Diewert and Lawrence (2006). Normally, after tax real rates of return are in the 1 to 3 percent rate whereas our estimated average rate is over 6 percent. This suggests that our estimates of the value of output may be too high107 or that the value of labour input is too low or that our estimated asset values for business sector capital inputs are too small. We think that the last possibility is the most probable one. Using the data tabled in this Appendix, we calculated a business sector nominal and real value of business sector output, VY

t and QYt,108 and we also calculated the corresponding business sector nominal

and real capital stock inputs, VKWt and QKW

t. Nominal and real business sector capital-output ratios were computed, VKW

t/VYt and QKW

t/QYt respectively. These capital-output

ratios are listed in Table 14 above. We found that the nominal business sector capital output ratio fell from 2.22 in 1961 to 1.85 in 2011 while the real capital output ratio fell from 2.22 in 1961 to 1.33 in 2011. These falls in the capital output ratio seem unlikely. It is very likely that the Statistics Canada depreciation rates for reproducible assets are too high. However, for the purposes of this study, we will accept these high depreciation rates. 6. Sources of Error There are many problems with the data constructed in this Appendix. Some of the more important possible sources of error are listed as follows:

• Our adjustments for converting final demand prices (those facing the final demanders of the goods and services produced by the business sector) into basic prices (prices facing the producers of the goods and services) were rather crude and some aggregation error will be associated with our procedures. In particular, only crude adjustments for the effects of indirect taxes on the components of consumption were made. Also our method for estimating the net supplies of the business sector to the nonbusiness sector are rather indirect and subject to some error.109

• Our tax adjustments for the price of imports and exports were also not completely satisfactory due to various aggregation errors; i.e., we were not able to assign taxes accurately to the various components of imports and exports.

• Our measure of labour input relies on CANSIM Table 3830024, which provides price and quantity information for 36 separate types of labour. However, the KLEMS program makes use of even more disaggregated data and obtains significantly different rates of growth of quality adjusted labour input for the

107 See Diewert and Fox (2001) for a discussion of output mismeasurement problems. 108 PY

t was computed as a chained Törnqvist price index of the 9 net output aggregates listed in Tables 2 and 3 above (the sign of import quantities QM

t was changed from a positive sign to a negative sign) and QYt

is the corresponding implicit quantity index of business sector value added at producer prices. PKWt and

QKWt are the chained Fisher index price and quantity of wealth stocks that are used as inputs into the

business sector; see Tables 12 and 13 for a listing of the 17 components that were used in constructing these indexes. These price and quantity indexes are listed in Table 14. 109 In particular, we did not have access to chained price indexes for the nonbusiness sector for the years prior to 1997 and this will lead to some aggregation errors.

75

Canadian business sector and so our estimates may be subject to some aggregation error.

• Our estimates for 14 capital stock components relied on CANSIM Table 310003 and the estimates of business sector capital stocks and investment flows implied very high depreciation rates for these assets. These high depreciation rates are not really plausible since they essentially lead to a declining real capital-output ratio for the Canadian business sector, which seems unlikely.

• We also relied heavily on the Statistics Canada Balance Sheet estimates for the value of business land but the Balance Sheet estimates are highly aggregated in particular, there is not enough detail on the allocation of land. Moreover, there is a lack of accurate information on the quantity of land used by the business sector.

• Our treatment of property taxes and business income taxes is very approximate. • Our user costs of capital were constructed using a particular set of assumptions

(no capital gains and endogenous real rates of return) and these assumptions are not universally accepted.

• The roles of infrastructure capital and R&D investments were not taken into account.

• The role of resource depletion was also not taken into account. • We did not take into account the business sector’s holdings of working capital

including bank deposits and currency. The latest international version of the System of National Accounts, SNA 2008, recognized the role of capital services in the production accounts. This is a big step forward since it allows inputs in the SNA production accounts to be decomposed into price and quantity components and hence the revised SNA will facilitate the development of productivity accounts for each country that implements the revised SNA. However, just introducing capital services into the SNA will not be sufficient in order to develop accurate sectoral productivity accounts. Some of the problems associated with the introduction of capital services into the SNA are as follows:

• More attention needs to be given to the development of basic prices by industry and by commodity; i.e., we need accurate information on the exact location of indirect taxes (and commodity subsidies) by commodity and industry on both outputs and intermediate inputs.

• In order to deal adequately with the complications introduced by international trade, the existing Input Output production accounts need to be reworked so that the role of traded goods and services can be tracked by industry.110

• The treatment of inventory change in the present SNA seems inadequate for the needs of productivity accounts. Inventory change should be integrated with the balance sheet accounts and the user cost accounts.111

• The investment accounts need to be integrated with the corresponding balance sheet accounts, both in nominal and real terms.

110 In principle, this problem is recognized in SNA 2008. However, implementation by national statistical agencies will be difficult. 111 Again, in principle, these problems are recognized in SNA 2008.

76

• The treatment of land in the balance sheets requires additional work; i.e., there are problems in obtaining information on the quantity of land used by each industry and sector and valuing the land appropriately.112

• Difficult decisions must be made on the exact form of the user cost formula to be used when measuring capital services; i.e., the revised SNA should make specific recommendations on how user costs should be constructed so that some measure of international comparability can be achieved in the accounts.

• The problems involved in making imputations for the labour input of the self employed (and unpaid family workers) should also be addressed.

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