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Essays of Canadian productivity and international trade Yu, Emily 2010

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Essays in Canadian Productivity and International Trade by Emily Yu B.A., The University of British Columbia, 2000 M.A., The University of British Columbia, 2001 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Doctor of Philosophy in The Faculty of Graduate Studies (Economics) The University of British Columbia (Vancouver) April, 2010 c© Emily Yu 2010 Abstract This thesis is a collection of three empirical papers that made use of recent Canadian trade and production data. The first chapter “Productivity Performance of Canada” examines Canada’s productivity and changes in terms of trade 1961-2007. These changes have been mostly favourable and have had the same effect on real income growth as Total Factor Productivity improvements of the business sector of the econ- omy. The framework applied is developed by Diewert, Kohli and Morrison and is based on production theory. We utilised published and unpublished data from the Statistics Canada Multifactor Productivity program, which develops “bottom up” estimates of business sector productivity from indus- try estimates. However, we use in this chapter a “top down” approach which utilises (adjusted) final demand data to form a business sector output ag- gregate and thus leads to much higher estimates of TFP growth for Canada than the corresponding Statistics Canada estimates. Finally, the new ex- port and import time series are used to determine the contributions to real income growth of changes in these disaggregated export and import prices over the 47 year period. The second chapter “Business Sector Data on Outputs and Inputs for Canada 1961-2007” details the business sector data used in the first chapter and explains the construction of estimates of Canadian final demand expen- ditures, business sector labour input, business sector capital stock, primary input tax rates, balancing real rates of return and user costs. We also make some recommendations for possible improvements that Statistics Canada could make to its productivity program. ii Abstract The third chapter “Does Lobbying Affect Antidumping Case Determina- tions in Canada?” examines whether the mandate of antidumping legislation in Canada was independent of influences other than those allowed. The re- lation between antidumping case determinations and various determinants is examined, in particular, whether lobbying activities can influence case determinations. Unlike previous studies that constructed political variable with data that have limited information on policy influence targets, this chapter constructs the variable using the Canadian Lobbyists Registration data with detailed information on lobbyists who had indicated they lobbied for administered protection. The current empirical evidence suggests that the antidumping mandate is not apolitical. iii Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . x Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii 1 Productivity Performance of Canada . . . . . . . . . . . . . 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Output and Input Aggregates and Conventional Productivity Growth in Canada . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Explaining Real Income Growth Generated by the Canadian Business Sector: the Gross Output Approach . . . . . . . . . 14 1.4 Explaining Real Income Growth Generated by the Canadian Business Sector: the Net Output Approach . . . . . . . . . . 29 1.5 Productivity Performance Comparison with Other Countries 50 1.6 The Effects of Changing Real Export and Import Prices on Real Income Growth . . . . . . . . . . . . . . . . . . . . . . . 53 1.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 1.8 Explaining Real Income Growth with The Translog Approach 76 1.8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 76 1.8.2 The Production Theory Framework . . . . . . . . . . 77 iv Table of Contents 1.8.3 The Translog GDP Function Approach . . . . . . . . 88 1.8.4 The Translog GDP Function Approach and Changes in the Terms of Trade . . . . . . . . . . . . . . . . . . 91 1.8.5 The Deflated NDP Translog Approach . . . . . . . . 95 1.8.6 Sectoral Contributions to Real Income Growth . . . . 101 2 Business Sector Data on Outputs and Inputs for Canada 1961-2007 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 2.2 Estimates of Canadian Final Demand Expenditures . . . . . 113 2.3 Business Sector Labour Input Estimates . . . . . . . . . . . 152 2.4 Business Sector Capital Stock Estimates . . . . . . . . . . . 158 2.5 Primary Input Tax Rates, Balancing Real Rates of Return and User Costs . . . . . . . . . . . . . . . . . . . . . . . . . . 174 2.6 Sources of Error . . . . . . . . . . . . . . . . . . . . . . . . . 182 2.7 Recommendations for the Statistics Canada Productivity Pro- gram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 3 Does Lobbying Affect Antidumping Case Determinations in Canada? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 3.2 Antidumping and Lobbying . . . . . . . . . . . . . . . . . . . 191 3.3 Empirical Analysis . . . . . . . . . . . . . . . . . . . . . . . . 199 3.3.1 Economic and Political Determinants . . . . . . . . . 200 3.3.2 Econometric Analysis . . . . . . . . . . . . . . . . . . 208 3.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . 217 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 v List of Tables 1.1 Prices of Canadian Business Sector Output and Input Aggre- gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Quantities of Canadian Business Sector Output and Input Aggregates, TFP Levels and TFP Growth Rates . . . . . . . 11 1.3 Gross Real Income Generated by the Canadian Business Sec- tor and Real Output and Input Prices . . . . . . . . . . . . . 16 1.4 Business Sector Year to Year Growth in Real Income and Year to Year Contribution Factors . . . . . . . . . . . . . . . 22 1.5 Business Sector Cumulated Growth in Real Income and Cu- mulated Contribution Factors . . . . . . . . . . . . . . . . . . 27 1.6 Prices of Canadian Business Sector Net Output and Input Aggregates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 1.7 Quantities of Canadian Business Sector Net Output and In- put Aggregates, TFP Levels and TFP Growth Rates . . . . . 33 1.8 Net Real Income Generated by the Canadian Business Sector and Real Output and Input Prices . . . . . . . . . . . . . . . 38 1.9 Business Sector Year to Year Growth in Net Real Income and Net Year to Year Contribution Factors . . . . . . . . . . . . . 40 1.10 Business Sector Cumulated Growth in Net Real Income and Cumulated Contribution Factors . . . . . . . . . . . . . . . . 48 1.11 Average Productivity Growth in Canada and the United States, 1961-2008 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 1.12 Real Income and TFP Growth of Canada, Japan and Australia 52 1.13 Year to Year Export Contribution Factors Using the Gross Output Approach . . . . . . . . . . . . . . . . . . . . . . . . 62 vi List of Tables 1.14 Year to Year Import Contribution Factors Using the Gross Output Approach . . . . . . . . . . . . . . . . . . . . . . . . 65 1.15 Year to Year Export Contribution Factors Using the Net Out- put Approach . . . . . . . . . . . . . . . . . . . . . . . . . . 68 1.16 Year to Year Import Contribution Factors Using the Net Out- put Approach . . . . . . . . . . . . . . . . . . . . . . . . . . 71 2.1 Housing Value, Quantity and Price Series for Imputed and Paid Rents . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 2.2 Prices Indexes for Business Sector Outputs: Consumption and Investment . . . . . . . . . . . . . . . . . . . . . . . . . . 120 2.3 Quantity Indexes for Business Sector Outputs: Consumption and Investment . . . . . . . . . . . . . . . . . . . . . . . . . . 122 2.4 Business Sector, Non-business Sector, Government Final De- mand and KLEMS Business Sector Price and Quantity Ag- gregates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 2.5 Price Indexes for Business Sector Outputs: Net Sales to the Non-business Sector . . . . . . . . . . . . . . . . . . . . . . . 134 2.6 Price Indexes for Eight Commodity Classes of Exports, 1961- 2007 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 2.7 Quantity Indexes for Eight Commodity Classes of Exports, 1961-2007 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 2.8 Price Indexes for Seven Commodity Classes of Imports, 1961- 2007 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 2.9 Quantity Indexes for Seven Commodity Classes of Imports, 1961-2007 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 2.10 Price and Quantity Indexes for Three Types of Business Sec- tor Labour . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 2.11 Beginning of Year Asset Values for Residential Structures and Land and Six Business Sector Capital Stocks . . . . . . . . . 162 vii List of Tables 2.12 Smoothed Geometric Depreciation Rates for ICT, Non-ICT Machinery and Equipment, Non-residential Structures and Residential Structures Capital Stocks Implied by the Balance Sheets and Investment Flow Data . . . . . . . . . . . . . . . 167 2.13 Prices for Residential Structures and Land and Six Business Sector Capital Stocks . . . . . . . . . . . . . . . . . . . . . . 169 2.14 Quantities of Residential Structures and Land and Six Busi- ness Sector Capital Stocks . . . . . . . . . . . . . . . . . . . . 171 2.15 Business Sector Tax Rates, Balancing Real Rates of Return and User Costs . . . . . . . . . . . . . . . . . . . . . . . . . . 179 3.1 Antidumping Cases in Canada 1990-2006 . . . . . . . . . . . 194 3.2 Antidumping Cases in Canada by the Named Country’s Eco- nomic Status 1990-2004 . . . . . . . . . . . . . . . . . . . . . 195 3.3 Active Lobbyist Registrations in Canada 1996-2005 . . . . . . 197 3.4 Percentage of Lobbyists that Lobbied Canadian International Trade Tribunal 1996-2003 . . . . . . . . . . . . . . . . . . . . 198 3.5 Regression of Lobbying Efforts . . . . . . . . . . . . . . . . . 206 3.6 Expected Signs of Determinants . . . . . . . . . . . . . . . . . 209 3.7 Negative Binomial Regression on Antidumping Case Deter- minations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 3.8 Negative Binomial Regression on Antidumping Case Deter- minations (Cont’d) . . . . . . . . . . . . . . . . . . . . . . . . 212 3.9 Negative Binomial Regression on Antidumping Petitions . . . 216 viii List of Figures 1.1 Real Income Change and Terms of Trade Contribution 1962- 2007 (Gross Output Approach) . . . . . . . . . . . . . . . . . 24 1.2 Level of Total Factor Productivity in Canada 1961-2007 . . . 36 1.3 Rate of Productivity Growth in Canada 1962-2007 . . . . . . 37 1.4 Real Income Generated by the Business Sector in Canada 1961-2007 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 1.5 Real Income Change and Terms of Trade Contribution 1962- 2007 (Net Output Approach) . . . . . . . . . . . . . . . . . . 44 1.6 Canadian Export Values 1961-2007 . . . . . . . . . . . . . . . 55 1.7 Canadian Export Prices 1961-2007 . . . . . . . . . . . . . . . 56 1.8 Canadian Export Quantities 1961-2007 . . . . . . . . . . . . . 57 1.9 Canadian Import Values 1961-2007 . . . . . . . . . . . . . . . 58 1.10 Canadian Import Prices 1961-2007 . . . . . . . . . . . . . . . 59 1.11 Canadian Import Quantities 1961-2007 . . . . . . . . . . . . . 60 3.1 Antidumping Cases in Canada by the Named Countries 1990- 2006 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 ix Acknowledgements First and foremost I owe my sincerest gratitude to my thesis supervisor, Professor Brian Copeland, who has supported me throughout my thesis with his advices, guidance and patience. I am extremely grateful to his incredible patience with me, without which this thesis could not have happened. He was also the reason I have chosen my field to be International Trade. I thank him for giving me a direction to the very interesting field of Economics. I would also like to thank my other thesis supervisor, Professor Erwin W. Diewert who constantly assisted me on my research, who gave me plenty of useful suggestions and not to mention the enormous amount of encour- agements when I was feeling stressful. He has taught me many many things that I would not have learnt if not for him. The first and second chapters of this thesis are inspired by his earlier work and the results of a joint research with him. I am indebted to Dr Werner Antweiler who served on my thesis com- mittee and gave me many sound advices during the early formation stage of this thesis. I like to thank my first year advisor in the doctoral program, Professor Margaret Slade, who told me there is no limit to what I can do if I dare to dream. Many thanks also to the librarian at Koerner’s Library, Mary Luebbe who assisted me in data search for more than two years. I also like to acknowledge the KLEMS program of Statistics Canada for providing the data used in this thesis. I am grateful to many of the fellow schoolmates who lent me their ears when I needed someone to discuss my work with. I also have been blessed with many wonderful friends, Dr. Edmond Ng, Kenneth Mak, Iris Yeung, Jasmine Poon, Steve (Chubby) Xu, Steve Yong and Markus von Wartburg, to name a few, thanks for the occasional amateur therapy sessions, supports x Acknowledgements and kind (sometimes harsh) words. Their existences remarkably brightened my life as a graduate student. I wholeheartedly thank my best friend at UBC, Carl Ruest, for spending a lot of his precious time to help me improve the thesis. He was undoubtedly my best lunch companion during all those rainy days at school. Lastly, and most importantly, I wish to thank my parents, Wing Chow Yu and Tsang Dor Sin. They sacrificed a lot to give me the best. Without their sacrifices, I will not be who I am today. xi Dedication To my parents and my family, I dedicate this thesis. xii Chapter 1 Productivity Performance of Canada 1.1 Introduction Gains in productivity are an important factor in leading higher living standards. However, the calculation of productivity is not a straightforward matter. Statistics Canada calculates business sector Multifactor Produc- tivity (MFP) growth or Total Factor Productivity (TFP) growth using a “bottom up” approach; i.e., separate TFP growth estimates are made for each major industrial sector in the Canadian business sector and then these sector estimates are aggregated to provide an estimate of total business sec- tor TFP growth. But aggregate TFP growth can also be calculated using a “top down” approach; i.e., instead of aggregating over business sector industry outputs and intermediate inputs, it is possible to use estimates of deliveries to final demand as the measure of aggregate output growth and this aggregate output information can be combined with information on aggregate primary input usage to give an alternative approach to the measurement of aggregate TFP growth. In this chapter, using the “top down” approach and using new data from Statistics Canada, we show that the productivity performance of the Canadian business sector appears to be much better than the lacklustre official Statistics Canada estimates of TFP growth, which are based on the “bottom up” approach.1 This indicates the “productivity gap” between the official estimates by Statistics Canada and 1However, we will show later that the main source of difference between the two meth- ods for computing TFP growth appears to be in the aggregation of capital services rather than in differences in the aggregation of outputs. 1 Chapter 1. Productivity Performance of Canada the U.S. may not be as wide as we have come to believe. Diewert (2006b) (2007c) had shown that if effects of indirect tax can be ignored and that data from the input output tables are consistent then the “top down” approach used in this chapter and the “bottom up” approach used by Statistics Canada should give similar measures of productivity. The “top down” approach can provide a comparison to the official estimates. Furthermore, it also allows us to estimate individual contribution of export and import commodity classes which is not possible using the “bottom up” approach. Thus, the “top down” approach makes it possible to carry out the calculation of terms of trade contribution to real income growth. In addition to developing new estimates of TFP growth for the Canadian business sector for the years 1962-2007, this chapter will provide new es- timates for the growth in real income generated by the Canadian business sector and provide estimates of how various growth factors contributed to this overall real income growth. There are three main factors which explain the growth in real income: • TFP growth; • Growth in primary inputs used by the business sector and • Changes in real output prices. Included in the last explanatory factor are changes in real export and real import prices. We have developed some new time series for disaggregated components of Canadian exports and imports so that the gains in real income generated by increasing real export prices or decreasing real import prices can be traced back to particular classes of exports and imports. Note that this type of analysis cannot be done using the “bottom up” approach to TFP measurement because the industry input output tables do not have an accurate breakdown of industrial outputs into exports and deliveries to domestic demanders or a breakdown of intermediate inputs into imports and domestically produced intermediates. 2 Chapter 1. Productivity Performance of Canada When economists measure TFP growth, the output concept is almost al- ways the gross product produced by the sector or economy and a traditional Jorgenson and Griliches (1967) user cost of capital is used to measure the contribution of capital inputs. The traditional user cost of capital has three main components: • A nominal interest rate component; • A depreciation component and • A (negative) price appreciation term. Sometimes the first and third components listed above are combined into a single real interest rate component. The important points to note are that (i) depreciation appears in the user cost of capital and (ii) a gross out- put concept is used in the traditional approach to the measurement of TFP growth. However, depreciation is not a source of income; households cannot consume depreciation. Depreciation should be treated as a charge against income instead of a component of income. Thus instead of using a gross output approach to the measurement of output and a user cost of capital that includes depreciation, when attempting to measure the income gener- ated by the private production sector, the depreciation component in the user cost should be removed and treated as an (intertemporal) intermediate input, leading to a net output approach to the measurement of output and a waiting services approach to the user cost of capital. We will implement both the traditional approach to TFP measurement as well as the net output approach and compare the two approaches using Canadian business sector data over the period 1961-2007. As noted above, it is not easy to measure the exact magnitude of pro- ductivity gains or of terms of trade. Diewert (1983), Diewert and Morri- son (1986), Diewert, Mizobuchi and Nomura (2005), Diewert and Lawrence (2006), Morrison and Diewert (1990) and Kohli (1990, 1991, 2003, 2004a, 2004b, 2006, 2008) have developed methodologies based on production the- ory that allow the contribution of each type of gain be represented by an 3 Chapter 1. Productivity Performance of Canada index number estimate. In Section 1.8, we outline the Diewert, Mizobuchi and Nomura (2005) and Diewert and Lawrence (2006) methodology and show how it can be used to measure the determinants of growth of an econ- omy’s gross and net real income. In Sections 1.2-1.4, we apply this same methodology to the business sector of the Canadian economy over the years 1962-2007. The details of how the Canadian business sector data was developed from Statistics Canada sources are described in Chapter 2 “Business Sector Data on Outputs and Inputs for Canada 1961-2007”. Section 1.2 aggregates up the data from Chapter 2 and develops conventional measures of Canadian business sector Total Factor Productivity (TFP) for the years 1961-2007. However, 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.2 Thus in Section 1.3, we measure the relative contributions of productivity improvements, changes in real export and import prices and growth of labour and capital inputs to the growth of (gross) real income generated by the business sector in Canada using the methodology explained in Subsections 1.8.2-1.8.5. This is still not the end of the story; GDP is an imperfect measure of productive potential, not welfare.3 For welfare measurement purposes, it is generally conceded that Net Domestic Product (NDP) is a better measure of output, since investment that just equals depreciation means that society is not made any better off from the viewpoint of sustainable final consumption possibilities. Hence in Section 1.4, we subtract depreciation off from gross investment and use consumption plus sales to the non-business sector plus net investment plus the trade balance as our business sector output concept. Thus depreciation will be treated as an intermediate input in this production model. 2See for example Diewert and Morrison (1986). 3For a more extensive discussion of the merits of GDP versus net income, see Diewert (2006a). 4 Chapter 1. Productivity Performance of Canada Subsection 1.8.6 explains this real net output approach and adapts a translog model of production based on the work of Diewert and Morrison (1986) and Kohli (1990) to this new model of market sector real net income generation.4 This approach is implemented for the Canadian business sec- tor in Section 1.4. The main determinants of growth in real net income generated by the business or market sector of the economy are: • Technical progress or improvements in Total Factor Productivity; • Growth in domestic output prices or the prices of internationally traded goods and services relative to the price of consumption and • Growth in primary inputs. It turns out that productivity growth becomes a more important factor for explaining real net income growth compared to explaining real gross income growth. Also the importance of capital deepening is greatly reduced in the net output framework compared to the gross output framework. Somewhat surprisingly, for the years 2000-2007, improvements in the terms of trade made almost the same contribution to real income growth as capital deep- ening in the gross output framework and in the net output framework, the effects of falling real import prices contributed substantially more to real income growth than capital deepening over the period 2000-2007. Section 1.5 discusses how our estimates compare to the productivity estimates of other countries. We compare our Canadian real income growth estimates using the “top down” approach with the estimations that were done for Aus- tralia and Japan. It can be seen that the overall average income growth of the three countries are similar, but the productivity performances are very different. Canada had benefited from terms of trade improvement and thus even without a stellar productivity performance, the real income growth was as much as the two other countries that have relatively higher productivity growths. Then in Section 1.6, we look at changes in real export and import 4For previous implementations of this model of real net income to Japan and Australia, see Diewert, Mizobuchi and Nomura (2005) and Diewert and Lawrence (2006). 5 Chapter 1. Productivity Performance of Canada prices by commodity class and their effects on real income growth in both the gross output and the net output frameworks. These new results are somewhat surprising. Finally Section 1.7 concludes.5 1.2 Output and Input Aggregates and Conventional Productivity Growth in Canada In Chapter 2, we constructed price and quantity series for 23 net outputs and 9 primary inputs for the business sector of the Canadian economy for the years 1961-2007. The 23 net outputs are, • Q1, Domestic consumption (excluding market residential rents and the services of owner occupied housing); • Q2, Real sales of goods and services by the business sector to the non- market sector less real sales of goods and services from the non-market sector to the business sector; • Q3, Government investment; • Q4, Business sector investment in residential structures; • Q5, Business sector investment in information and communication technology (ICT) machinery and equipment; • Q6, Business sector investment in non-ICT machinery and equipment; • Q7, Business sector investment in non-residential structures; • Q8, Inventory change; • Q9, Exports of agricultural and fish products; • Q10, Exports of energy products; 5The final part of Section 1.8 has some new material on how the real net output model used in the present paper can be extended from a single production sector to the case of many industries. 6 Chapter 1. Productivity Performance of Canada • Q11, Exports of forest products; • Q12, Exports of industrial goods and materials (excluding energy and forest product exports); • Q13, Exports of machinery and equipment (excluding automotive prod- ucts); • Q14, Exports of automotive products; • Q15, Exports of other consumer goods (excluding automotive prod- ucts); • Q16, Exports of services; • Q17, Imports of agricultural and fish products; • Q18, Imports of energy products; • Q19, Imports of industrial goods and materials (including imports of forest products but excluding imports of energy products); • Q20, Imports of machinery and equipment (excluding automotive prod- ucts); • Q21, Imports of automotive products; • Q22, Imports of other consumer goods and • Q23, Import of services. The nine primary inputs into the business sector are, • Q24, The labour services of workers with primary or secondary educa- tion; • Q25, The labour services of workers with some or completed secondary certificate or diploma; 7 Chapter 1. Productivity Performance of Canada • Q26, The labour services of workers with a university degree or above;6 • Q27, The stock of ICT machinery and equipment available to the busi- ness sector at the start of each year; • Q28, The stock of non-ICT machinery and equipment available to the business sector at the start of each year; • Q29, The starting stock of business sector non-residential structures; • Q30,The starting stocks of inventories used by the business sector; • Q31, The stock of agricultural land use by the business sector and • Q32, The stock of non-agricultural, non-residential land used by the business sector. As explained in Chapter 2, user cost prices for the last six primary 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. Details of the construction are given in Chapter 2 where the price and quantity series constructed from the 23 net outputs and 9 primary inputs are also shown. In this section, we will aggregate the above net outputs and primary inputs into D, domestic output, equal to an aggregate of the first eight net outputs; X, exports equal to an aggregate of the eight types of exports of goods and services; M , imports equal to an aggregate of the seven types of imports of goods and services; L, labour services equal to an aggregate of the three types of labour services; K, capital services equal to an aggregate of the six types of capital services. Once these aggregates have been constructed, we further aggregate the three net outputs D + X − M into real gross domestic product Y and aggregate the two inputs K and L into domestic input Z and finally construct a conventional measure of productivity Y/Z. 6These three types of labour services input data are taken directly from Statistics Canada KLEMS program; see Baldwin, Gu and Yan (2007) for description. 8 Chapter 1. Productivity Performance of Canada The aggregations were done using chained Törnqvist price indexes,7 and the resulting prices and quantities are shown in Tables 1.1 and 1.2. Table 1.1: Prices of Canadian Business Sector Output and Input Aggregates Year P tC P t D P t X P t M P t L P t K P t Y P t Z 1961 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1962 1.00538 1.00538 1.02992 1.05787 1.03625 1.01691 0.99683 1.03034 1963 1.02055 1.02264 1.04054 1.09648 1.06604 1.15494 1.00691 1.09305 1964 1.02437 1.02959 1.05692 1.10526 1.11049 1.23317 1.01577 1.14776 1965 1.03690 1.05092 1.07980 1.10214 1.18272 1.25857 1.04400 1.20580 1966 1.07553 1.08861 1.12451 1.11930 1.25929 1.34193 1.08930 1.28444 1967 1.11050 1.12289 1.15421 1.14426 1.33342 1.23578 1.12505 1.30269 1968 1.15168 1.15976 1.20119 1.16726 1.41620 1.30595 1.16924 1.38147 1969 1.18980 1.19995 1.23088 1.19648 1.52197 1.34691 1.20982 1.46616 1970 1.22208 1.23858 1.26710 1.21965 1.61278 1.40223 1.25289 1.54532 1971 1.24828 1.28233 1.28552 1.24798 1.72528 1.39719 1.29339 1.61828 1972 1.29847 1.34008 1.33325 1.27498 1.86392 1.49709 1.35869 1.74411 1973 1.38744 1.44587 1.51489 1.35954 2.03837 2.06511 1.49788 2.05198 1974 1.58382 1.65206 1.91283 1.64641 2.35044 2.47332 1.73334 2.39718 1975 1.82198 1.87090 2.16694 1.89029 2.70332 2.21008 1.95274 2.53719 1976 1.90726 1.97372 2.29702 1.92853 3.10646 2.39955 2.09001 2.86510 1977 2.03175 2.09967 2.50231 2.17241 3.38889 2.74058 2.19373 3.17107 1978 2.19264 2.26119 2.73837 2.41667 3.53495 3.09969 2.34654 3.39783 1979 2.40645 2.48060 3.20786 2.73027 3.78520 3.80986 2.60728 3.82051 1980 2.69497 2.75772 3.73464 2.97957 4.11781 3.97428 2.97313 4.09308 1981 2.95335 3.03059 3.99821 3.26618 4.59295 4.05499 3.23724 4.42379 1982 3.22860 3.28484 4.08926 3.43918 5.02021 3.61928 3.46983 4.51822 Continued on Next Page. . . 7More specifically, the chained Divisia option in Shazam was used to do the aggrega- tions. 9 Chapter 1. Productivity Performance of Canada Table 1.1 – Continued Year P tC P t D P t X P t M P t L P t K P t Y P t Z 1983 3.46323 3.46344 4.15051 3.42324 5.22085 4.44415 3.68247 4.97537 1984 3.61506 3.60128 4.29656 3.58225 5.48101 4.94318 3.81283 5.33580 1985 3.72257 3.71138 4.38071 3.67711 5.75670 5.17976 3.91833 5.59935 1986 3.80422 3.80294 4.37060 3.74437 5.90250 5.08340 3.98140 5.65108 1987 3.89726 3.90844 4.45792 3.69150 6.11054 5.74526 4.14995 6.03889 1988 4.00205 4.01307 4.47080 3.60108 6.51242 5.76285 4.30933 6.29679 1989 4.11690 4.12618 4.56005 3.59364 6.78864 5.58998 4.47092 6.40227 1990 4.35206 4.28654 4.52868 3.64367 7.04667 5.31935 4.60964 6.45499 1991 4.59099 4.42296 4.37107 3.57992 7.34245 4.50786 4.72731 6.30363 1992 4.65258 4.47108 4.49573 3.72567 7.48023 4.98747 4.75269 6.58795 1993 4.74252 4.55596 4.69389 3.92460 7.45961 5.15125 4.82121 6.64462 1994 4.77089 4.62372 4.97322 4.16089 7.41314 6.03823 4.89058 6.98418 1995 4.79147 4.65787 5.29132 4.27688 7.53622 6.56286 5.02353 7.27300 1996 4.88952 4.71581 5.32097 4.22185 7.63205 6.99768 5.13502 7.50733 1997 4.96547 4.77523 5.32718 4.23677 7.91076 7.00934 5.19090 7.68381 1998 5.03224 4.84195 5.31558 4.37960 8.13918 6.93415 5.15347 7.79482 1999 5.12045 4.91274 5.37870 4.36044 8.33890 7.36196 5.27960 8.08916 2000 5.25425 5.02564 5.71039 4.44227 8.74780 8.33839 5.54730 8.73198 2001 5.40970 5.14618 5.80311 4.58416 8.97770 8.04237 5.62691 8.75403 2002 5.47743 5.22044 5.68895 4.61494 9.09489 8.53655 5.61217 9.02599 2003 5.61543 5.29558 5.64768 4.31493 9.26253 8.32732 5.87497 9.04388 2004 5.69551 5.37836 5.78629 4.20643 9.48779 9.25929 6.12630 9.55745 2005 5.81654 5.49862 5.95274 4.15511 9.84265 9.80219 6.39760 9.99376 2006 5.92386 5.63197 5.97000 4.12736 10.29074 9.81133 6.58063 10.27222 2007 6.02712 5.75706 6.02590 4.02177 10.66121 10.14050 5 6.84476 10.63228 10 Chapter 1. Productivity Performance of Canada Table 1.2: Quantities of Canadian Business Sector Output and Input Aggregates, TFP Levels and TFP Growth Rates Year t QtD Q t X Q t M Q t L Q t K Q t Y Q t Z T t τt 1961 28752 6867 −7897 19202 8520 27722 27722 1.00000 − 1962 30578 7195 −8033 20042 8739 29750 28782 1.03361 1.03361 1963 32261 7832 −8031 20574 9007 32113 29582 1.08555 1.05024 1964 34602 9105 −8989 21446 9324 34766 30768 1.12995 1.04090 1965 37904 9418 −10180 22416 9751 37149 32164 1.15499 1.02216 1966 40831 10696 −11579 23550 10328 39949 33880 1.17914 1.02091 1967 41117 11827 −12306 24056 11057 40656 35112 1.15790 0.98198 1968 42835 12910 −13527 24158 11627 42246 35756 1.18152 1.02040 1969 46062 13802 −15377 24718 12059 44521 36737 1.21189 1.02571 1970 46017 15211 −15293 24798 12569 45988 37285 1.23341 1.01776 1971 48326 15929 −16480 25333 13007 47844 38238 1.25120 1.01442 1972 52098 17257 −18892 26101 13416 50590 39410 1.28367 1.02595 1973 59241 19008 −21754 27591 13866 56663 41362 1.36992 1.06719 1974 65163 18347 −23977 28558 14615 59579 43080 1.38298 1.00953 1975 63453 16951 −23228 28530 15571 57119 43961 1.29930 0.93949 1976 67488 18390 −24774 28499 16309 61084 44559 1.37086 1.05508 1977 70950 19678 −24836 28805 17018 65759 45492 1.44552 1.05446 1978 73085 21544 −26197 30018 17690 68588 47367 1.44801 1.00173 1979 78467 22467 −28092 31737 18344 72879 49736 1.46532 1.01195 1980 77309 22548 −28715 32833 19285 71254 51757 1.37669 0.93951 1981 80810 23012 −30716 33723 20148 73083 53480 1.36653 0.99262 1982 70930 22882 −25710 32059 21330 68632 52707 1.30214 0.95288 1983 75524 24326 −28444 32283 21742 72008 53296 1.35109 1.03759 1984 80477 28444 −33270 33497 22102 76807 54884 1.39943 1.03578 1985 85491 29938 −35548 34871 22585 81087 56743 1.42902 1.02114 1986 88667 31456 −37965 36384 23167 83519 58843 1.41937 0.99325 1987 94688 32933 −39889 38166 23747 89072 61210 1.45517 1.02522 Continued on Next Page. . . 11 Chapter 1. Productivity Performance of Canada Table 1.2 – Continued Year t QtD Q t X Q t M Q t L Q t K Q t Y Q t Z T t τt 1988 101144 35371 −45163 39912 24550 93146 63746 1.46120 1.00414 1989 104645 35434 −47820 40981 25638 94280 65839 1.43198 0.98000 1990 102201 37556 −48551 41030 26721 93557 66811 1.40032 0.97789 1991 96067 38167 −49281 39707 27455 87853 65884 1.33345 0.95224 1992 98558 40921 −51473 39311 27831 91077 65705 1.38615 1.03952 1993 98528 45382 −55461 40184 28050 92144 66858 1.37821 0.99427 1994 103227 51076 −60606 41745 28099 97970 68602 1.42809 1.03619 1995 105681 55452 −64385 42958 28426 101581 70163 1.44779 1.01380 1996 108585 58646 −67340 44212 28923 105126 71906 1.46199 1.00981 1997 116675 63457 −77378 45636 29440 109300 73839 1.48025 1.01249 1998 120947 69086 −81755 47078 30519 115417 76307 1.51254 1.02182 1999 124963 76337 −88261 48781 31631 121154 79074 1.53216 1.01297 2000 132088 83350 −95661 50512 32736 128862 81864 1.57409 1.02737 2001 132099 80654 −90649 51183 33919 130142 83653 1.55574 0.98834 2002 140327 81599 −92347 52290 34561 137310 85376 1.60829 1.03377 2003 142198 79268 −96341 53129 35172 133617 86799 1.53939 0.95716 2004 150705 83281 −104558 55049 35675 139173 89210 1.56007 1.01343 2005 158450 84730 −112492 55875 36549 141962 90878 1.56211 1.00131 2006 165871 85022 −117772 56905 37720 145225 93035 1.56098 0.99928 2007 173734 86002 −124556 58347 38998 148654 95699 1.55335 0.99511 12 Chapter 1. Productivity Performance of Canada Note that we have also listed the price of our household consumption aggregate, P tC , in Table 1.1, which will play a role in the subsequent sections. The productivity level in year t of the Canadian business sector, T t, can be defined as the aggregate year t output, QtY divided by the aggregate year t input, QtZ , 8 T t ≡ Q t Y QtZ t = 1961, . . . , 2007 (1.1) Productivity growth for year t, τ t, is defined as the productivity level in year t, T t, divided by the productivity level from the previous year, τ t ≡ T t T t−1 t = 1962, . . . , 2007 (1.2) Table 1.2 lists the quantities that match up to the prices in Table 1.1 and it also lists productivity levels and growth rates. The average rate of total factor productivity (TFP) growth over the 46 years (1962-2007) is 1.01% per year,9 which is much higher than the 0.5 to 0.7% per year range that Diewert and Lawrence (2000) found over the period 1962-1996. The present 1.01% average rate of TFP growth can also be compared with Statistics Canada’s recent KLEMS program average Multifactor Productivity Growth over the same years of 0.38% per year,10 which is a rather substantial difference.11 8This is known as Multifactor Productivity or Total Factor Productivity. 9This rate of TFP growth is reasonably close to the average rate of productivity growth of 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 of 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). 10See CANSIM II series V41712881, Canada, Multifactor Productivity, Business Sector, Table 3830021, Multifactor Productivity, Value Added, Capital Input and Labour Input in the Aggregate Business Sector and Major Sub-Sectors. Comparing levels of TFP with the starting level being 1 in 1961, our TFP ended up at 1.553 in 2007 whereas KLEMS Multifactor Productivity ended up at 1.184 in 2007. This is a very substantial difference. 11Our measures of business sector output and capital input were different from the KLEMS measures because we excluded rental housing from our measure of capital ser- vices, whereas the KLEMS measures included rental housing in their output and capital input measures. Our measures of labour input were identical and it turned out that the 13 Chapter 1. Productivity Performance of Canada During the golden years of 1962-1973, Canada’s TFP growth averaged about 2.68% per year; over the dismal years of 1974-1991, the average TFP growth was essentially 0 (−0.086 per year); TFP growth nicely recovered during 1992-1999 to an average of 1.76% per year. Finally, from 2000-2007, the average TFP growth fell to only 0.20% per year. There were two years of poor productivity growth, 2001 and 2003, where drops of 1.17% and 4.28% occurred. After some increases in productivity growth in 2004 and 2005, slight drops in productivity growth again occurred in 2006 and 2007. If the two poor-performing years are excluded, the productivity growth during this period is on average 1.4% per year. Productivity growth does not necessarily represent the whole story behind the growth in living standards. If the prices of Canadian exports increases more rapidly than the prices of Canadian imports, then the real income gen- erated by the business sector increases. This terms of trade effect is not taken into account in the conventional productivity growth computation. Thus in the following section, we implement the translog real income methodology explained in Subsections 1.8.2-1.8.5 and this approach will enable us to assess the contribution to Canadian living standards of improvements in Canada’s terms of trade. 1.3 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 non-technical terms. The business sector faces exogenous domestic and in- ternational prices for the net outputs it produces: domestic outputs, exports and (minus) imports. It also utilises inputs of labour and capital in order to produce its outputs. The value of outputs produced by the business sector average rate of growth of our business sector value added measure was very close to the corresponding KLEMS average growth rate. The capital services growth rates differed substantially. 14 Chapter 1. Productivity Performance of Canada less the value of imports used (value added) must eventually flow back to the labour and capital primary inputs that were used to produce the value added. This is the gross income generated by the business sector. In order to turn this into real income ρt, we divide the gross income in year t by the price of consumption in year t, P tC . 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 of domestic output, export, import, labour and capital services (P tD, P t X , P t M , P t L and P t K) by the price of consump- tion, P tC , to form the corresponding real output and input prices facing the Canadian business sector in each year. Our measures of gross real income generated by the business sector, ρt and the corresponding real output and input prices are shown in Table 1.3. 15 Chapter 1. Productivity Performance of Canada Table 1.3: Gross Real Income Generated by the Canadian Business Sector and Real Output and Input Prices Year t ρt PtD Pt C PtX Pt C PtM Pt C PtL Pt C PtK Pt C 1961 27722 1.00000 1.00000 1.00000 1.00000 1.00000 1962 29497 1.00000 1.02441 1.05221 1.03070 1.01147 1963 31684 1.00205 1.01959 1.07440 1.04457 1.13169 1964 34474 1.00509 1.03178 1.07897 1.08407 1.20383 1965 37404 1.01352 1.04137 1.06292 1.14063 1.21379 1966 40460 1.01216 1.04554 1.04070 1.17085 1.24769 1967 41188 1.01115 1.03936 1.03040 1.20074 1.11281 1968 42890 1.00701 1.04299 1.01353 1.22968 1.13395 1969 45270 1.00853 1.03453 1.00561 1.27918 1.13205 1970 47147 1.01350 1.03684 0.99801 1.31970 1.14742 1971 49573 1.02727 1.02983 0.99976 1.38213 1.11929 1972 52936 1.03205 1.02679 0.98191 1.43547 1.15296 1973 61173 1.04211 1.09186 0.97989 1.46916 1.48843 1974 65204 1.04308 1.20773 1.03952 1.48403 1.56162 1975 61218 1.02685 1.18933 1.03749 1.48373 1.21301 1976 66937 1.03485 1.20436 1.01115 1.62875 1.25811 1977 71002 1.03343 1.23160 1.06923 1.66796 1.34888 1978 73403 1.03126 1.24889 1.10217 1.61219 1.41368 1979 78961 1.03081 1.33303 1.13456 1.57294 1.58319 1980 78608 1.02328 1.38578 1.10560 1.52796 1.47470 1981 80108 1.02615 1.35379 1.10592 1.55517 1.37301 1982 73760 1.01742 1.26657 1.06522 1.55492 1.12101 1983 76566 1.00006 1.19845 0.98845 1.50751 1.28324 1984 81009 0.99619 1.18852 0.99092 1.51616 1.36739 1985 85351 0.99699 1.17680 0.98779 1.54643 1.39145 1986 87409 0.99966 1.14888 0.98427 1.55157 1.33625 1987 94847 1.00287 1.14386 0.94720 1.56791 1.47418 Continued on Next Page. . . 16 Chapter 1. Productivity Performance of Canada Table 1.3 – Continued Year t ρt PtD Pt C PtX Pt C PtM Pt C PtL Pt C PtK Pt C 1988 100298 1.00275 1.11713 0.89981 1.62727 1.43997 1989 102387 1.00225 1.10764 0.87290 1.64897 1.35781 1990 99095 0.98495 1.04058 0.83723 1.61916 1.22226 1991 90462 0.96340 0.95210 0.77977 1.59932 0.98189 1992 93036 0.96099 0.96629 0.80078 1.60776 1.07198 1993 93673 0.96066 0.98975 0.82753 1.57292 1.08618 1994 100428 0.96915 1.04241 0.87214 1.55383 1.26564 1995 106501 0.97212 1.10432 0.89260 1.57284 1.36970 1996 110404 0.96447 1.08824 0.86345 1.56090 1.43116 1997 114262 0.96169 1.07285 0.85325 1.59315 1.41162 1998 118198 0.96219 1.05630 0.87031 1.61741 1.37794 1999 124920 0.95943 1.05044 0.85157 1.62855 1.43776 2000 136049 0.95649 1.08681 0.84546 1.66490 1.58698 2001 135368 0.95129 1.07272 0.84740 1.65956 1.48666 2002 140688 0.95308 1.03862 0.84254 1.66043 1.55850 2003 139793 0.94304 1.00574 0.76841 1.64948 1.48294 2004 149700 0.94432 1.01594 0.73855 1.66584 1.62572 2005 156144 0.94534 1.02342 0.71436 1.69218 1.68523 2006 161326 0.95073 1.00779 0.69673 1.73717 1.65624 2007 168821 0.95519 0.99980 0.66728 1.76887 1.68249 17 Chapter 1. Productivity Performance of Canada The results show that the gross real income generated by the Canadian business sector has grown from $27,722 million dollars worth of 1961 con- sumption bundles in 1961 to $168,821 in 2007, a 6.09 fold increase. The real price of domestic output has fallen to 0.9552 times the starting level (due to the fact that machinery and equipment prices have risen less rapidly than the prices of consumption) and the real price of exports has fallen slightly to 0.9998 times of the starting level while the real price of imports has fallen substantially to 0.6673 times the starting level. The quality adjusted real wage of business sector workers have risen to 1.77 times their initial 1961 levels. The real price of capital services has risen 1.68 fold, this reflects rapidly rising prices of agricultural land and non-agricultural business land as well as upward trends in machinery and equipment depreciation rates and in real rates of return. The details are discussed in Chapter 2.12 There are six quantitative factors that can be used to explain the real income ρt generated by the business sector in year t: 1. The price of domestic production (an aggregate of C + I +G) relative to the price of consumption in year t, P t D P tC ; 2. The price of exports relative to the price of consumption in year t, P t X P tC ; 3. The price of imports relative to the price of consumption in year t, P tM P tC ; 4. The quantity of labour used by the business sector in year t, QtL; 5. The quantity of capital used by the business sector in year t, QtK and 6. The level of technology of the business sector in year t. 12The volatility of the real price of capital services reflects the fact that we have used balancing real rates of return in our user costs and these real rates are subject to a considerable amount of measurement error. One would expect the aggregate real price of capital services to decline, reflecting the decline in the real price of machinery and equipment, but this decline is offset by a large increase in the real price of land services. 18 Chapter 1. Productivity Performance of Canada The formal model outlined in Section 1.8, 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 αtD, α t X , α t M , β t L, β t K and τ t that describe the effects of changes in the six quantitative factors listed above going from year t− 1 to t. The following equation which decomposes the year to year growth in real income generated by the business sector, ρ t ρt−1 , into a product of six year to year explanatory contribution factors:13 ρt ρt−1 = τ tαtDα t Xα t Mβ t Lβ t K t = 1962, 1963, . . . , 2007. (1.3) Thus if αtD 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 αtD measures the contribution of rising real domestic output prices to the growth in real income. Similarly, if αtX is greater than one, this means Canadian export prices grew faster than the price of consumption going from year t − 1 to t and αtX measures the contribution of rising real export prices to the growth in real income generated by the Canadian business sector. However, if αtM is larger than one, this means the Canadian import prices did not increase as quickly as the price of consumption going from year t−1 to t and αtM measures the contribution of falling real import prices to the growth in real income generated by the Canadian business sector. If βtL is larger than one, then the labour input in the business sector increased going from year t− 1 to t and βtL measures the contribution of the increase in labour input to the growth in real income generated by the Canadian business sector. Similarly for βtK , if it is greater than one, then the business sector capital service input increased going from year t − 1 to t and βtK measures the contribution of the increase in capital input to the growth in real income generated by the business sector. Finally, if τ t is larger than one, then the efficiency of the Canadian business sector increased from year t−1 13See Equations (1.50), (1.59) and (1.64) in Section 1.8 in order to derive this equation. All of the variables in Equation (1.3) can be identified using data in Chapter 2. 19 Chapter 1. Productivity Performance of Canada to t and τ t measures the contribution of the efficiency increase to the growth in real income generated by the Canadian business sector.14 The year to year contribution factors and the averages of them are listed in Table 1.4. The periodic averages of the year to year growth in real income show that the gross real income generated by the Canadian business sector over the entire sample period grew at 4.10 percent per year over the 47 years (1961-2007). The biggest contributor to this growth was the growth of quality adjusted labour input at 1.60 percentage points per year. Next was capital services input, which contributed on average 1.13 percentage points per year, followed by TFP growth (1.01 percentage points per year) and declines in real import prices (0.43 percentage points per year). Declines in real domestic output prices and real export prices give rise to negative average contribution factors, −0.09 and −0.03 percentage points per year respectively. The last column in Table 1.4 gives the product of the real export and real import price contribution factors, αtXM , which is defined as, αtXM ≡ αtXαtM (1.4) Roughly speaking, αtXM is the terms of trade contribution factor, it gives the contribution to real income growth of the combined effects of real changes in the international prices faced by the Canadian business sector.15 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 0.38 percentage points per year to real income growth over the entire sam- 14The productivity growth rates, τ t, computed here do not completely agree with the ones computed in the last section. The discrepancy arises because the input aggregates in calculating τ t here is a direct Törnqvist quantity index whereas an implicit quantity index is used in the earlier computation. 15Ulrich Kohli has pointed out that this is a slight abuse of terminology. Strictly speak- ing, the terms of trade is the price of exports over the price of imports and hence involves only two prices. Our definition of αtXM 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. 20 Chapter 1. Productivity Performance of Canada ple period.16 However, for shorter periods, the effects of changing real in- ternational prices can be far more important in explaining changes in the real income generated by the market sector of the economy. If the atten- tion is restricted to the recent years (2000-2007), it can be seen that the improvements in Canadian terms of trade become larger than the average contribution of capital deepening. During this period, the average annual growth in the real income generated by the Canadian business sector was 3.88% per year, which can be explained by the following factors: decreases in the real price of imports (1.63 percentage points), increases in quality adjusted labour input (1.40 percentage points), increases in capital services input (1.01 percentage points) and improvements in TFP (0.20 percentage points). There were also small negative contributors to market sector real income growth during the naughts: decreases in the real price of domesti- cally produced goods and services (−0.05 percentage points) and decreases in real prices of exports (−0.34 percentage points). 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 pe- riod. Overall, the joint effects of changes in real export and import prices contributed about 1.28 percentage points per year on average to the growth of market sector real income during this period, which was larger than the capital deepening contribution of 1.01 percentage points per year.17 16Thus the contribution of falling real import prices outweighs the effects of the falling export prices. 17These 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. 21 Chapter 1. Productivity Performance of Canada Table 1.4: Business Sector Year to Year Growth in Real In- come and Year to Year Contribution Factors Year t ρ t ρt−1 τ t αtD α t X α t M β t L β t K α t XM 1962 1.06402 1.03361 1.00000 1.00602 0.98556 1.03028 1.00773 0.99150 1963 1.07414 1.05024 1.00210 0.99882 0.99418 1.01820 1.00943 0.99301 1964 1.08806 1.04090 1.00308 1.00312 0.99883 1.02848 1.01127 1.00194 1965 1.08499 1.02216 1.00854 1.00248 1.00428 1.03048 1.01448 1.00677 1966 1.08172 1.02091 0.99862 1.00108 1.00622 1.03428 1.01841 1.00730 1967 1.01799 0.98199 0.99899 0.99830 1.00302 1.01478 1.02126 1.00131 1968 1.04133 1.02040 0.99587 1.00107 1.00519 1.00296 1.01535 1.00627 1969 1.05548 1.02571 1.00153 0.99744 1.00259 1.01608 1.01117 1.00003 1970 1.04146 1.01776 1.00497 1.00073 1.00253 1.00223 1.01266 1.00326 1971 1.05145 1.01443 1.01352 0.99775 0.99943 1.01508 1.01033 0.99717 1972 1.06785 1.02595 1.00468 0.99901 1.00617 1.02134 1.00911 1.00518 1973 1.15561 1.06713 1.00988 1.02092 1.00072 1.03876 1.01043 1.02166 1974 1.06589 1.00953 1.00096 1.03484 0.97865 1.02287 1.01826 1.01275 1975 0.93887 0.93953 0.98361 0.99488 1.00076 0.99933 1.02109 0.99563 1976 1.09342 1.05508 1.00821 1.00415 1.00992 0.99926 1.01435 1.01412 1977 1.06072 1.05446 0.99858 1.00755 0.97932 1.00735 1.01349 0.98671 1978 1.03382 1.00172 0.99784 1.00495 0.98842 1.02793 1.01294 0.99331 1979 1.07573 1.01194 0.99955 1.02461 0.98852 1.03661 1.01293 1.01285 1980 0.99553 0.93951 0.99259 1.01519 1.01049 1.02181 1.01843 1.02584 1981 1.01907 0.99262 1.00286 0.99086 0.99988 1.01743 1.01559 0.99074 1982 0.92076 0.95289 0.99143 0.97430 1.01502 0.96690 1.01927 0.98894 1983 1.03805 1.03756 0.98324 0.97884 1.02800 1.00458 1.00660 1.00625 1984 1.05802 1.03578 0.99618 0.99668 0.99903 1.02358 1.00609 0.99572 1985 1.05360 1.02114 1.00080 0.99590 1.00130 1.02563 1.00803 0.99719 1986 1.02411 0.99325 1.00270 0.99013 1.00150 1.02750 1.00923 0.99162 1987 1.08509 1.02522 1.00323 0.99823 1.01598 1.03099 1.00898 1.01417 1988 1.05747 1.00414 0.99988 0.99069 1.02084 1.02900 1.01207 1.01133 Continued on Next Page. . . 22 Chapter 1. Productivity Performance of Canada Table 1.4 – Continued Year t ρ t ρt−1 τ t αtD α t X α t M β t L β t K α t XM 1989 1.02083 0.98000 0.99949 0.99669 1.01242 1.01743 1.01513 1.00907 1990 0.96784 0.97789 0.98239 0.97601 1.01721 1.00080 1.01395 0.99280 1991 0.91289 0.95226 0.97770 0.96525 1.03013 0.97776 1.00854 0.99433 1992 1.02845 1.03952 0.99745 1.00613 0.98853 0.99310 1.00421 0.99460 1993 1.00684 0.99427 0.99965 1.01091 0.98478 1.01498 1.00253 0.99552 1994 1.07211 1.03618 1.00887 1.02652 0.97368 1.02550 1.00059 0.99949 1995 1.06047 1.01379 1.00300 1.03239 0.98772 1.01850 1.00418 1.01971 1996 1.03665 1.00981 0.99248 0.99158 1.01786 1.01829 1.00644 1.00929 1997 1.03495 1.01249 0.99721 0.99167 1.00659 1.02019 1.00656 0.99820 1998 1.03444 1.02182 1.00051 0.99062 0.98839 1.02012 1.01304 0.97912 1999 1.05687 1.01297 0.99722 0.99650 1.01318 1.02301 1.01296 1.00963 2000 1.08909 1.02737 0.99710 1.02251 1.00432 1.02211 1.01289 1.02693 2001 0.99499 0.98834 0.99495 0.99152 0.99867 1.00825 1.01348 0.99021 2002 1.03930 1.03377 1.00177 0.98014 1.00323 1.01340 1.00711 0.98331 2003 0.99364 0.95716 0.98994 0.98132 1.05112 1.00995 1.00664 1.03148 2004 1.07087 1.01343 1.00129 1.00574 1.02093 1.02224 1.00542 1.02679 2005 1.04305 1.00131 1.00104 1.00412 1.01731 1.00912 1.00950 1.02150 2006 1.03319 0.99928 1.00552 0.99168 1.01286 1.01119 1.01240 1.00443 2007 1.04646 0.99511 1.00461 0.99587 1.02185 1.01543 1.01301 1.01763 Averages 1962-2007 1.04100 1.01010 0.99904 0.99969 1.00430 1.01600 1.01130 1.00380 1962-1973 1.06870 1.02680 1.00350 1.00220 1.00070 1.02110 1.01260 1.00290 1974-1991 1.02340 0.99914 0.99562 0.99665 1.00540 1.01320 1.01310 1.00190 1992-1999 1.04130 1.01760 0.99955 1.00580 0.99509 1.01670 1.00630 1.00070 2000-2007 1.03880 1.00200 0.99953 0.99661 1.01630 1.01400 1.01010 1.01280 23 Chapter 1. Productivity Performance of Canada Figure 1.1 shows the contribution of the combined effects of real changes in export and import prices (αtXM − 1) and the changes in real income ([ρt/ρt−1]− 1) in 1962-2007. As shown in the figure, the movements of the two series start out quite differently, but are very similar from 1994 onward. In fact, as we mention earlier, during the years 2000-2007, much of the changes in real income can be explained by the combined changes in the international prices, largely coming from the decreases in import prices. Figure 1.1: Real Income Change and Terms of Trade Contribution 1962-2007 (Gross Output Approach) -10 -5 0 5 10 15 20 1 9 6 2 1 9 6 4 1 9 6 6 1 9 6 8 1 9 7 0 1 9 7 2 1 9 7 4 1 9 7 6 1 9 7 8 1 9 8 0 1 9 8 2 1 9 8 4 1 9 8 6 1 9 8 8 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4 2 0 0 6 Year P e rc e n ta g e  p o in ts Real income TOT 24 Chapter 1. Productivity Performance of Canada The various growth factors for the four subperiods, as listed in Table 1.4 are: • The 12 golden years for the Canadian economy, 1962-1973, when the real income generated by the business grew by 6.87% per year and TFP growth was a stellar 2.68% per year; • The 18 dismal years for the Canadian economy, 1974-1991, charac- terised by stagflation, oil shocks and rapidly increasing tax rates when the real income generated by the business sector grew by 2.34% per year and TFP growth was essentially zero; • The 8 years after the recession of 1991, 1992-1999, when real income growth recovered to 4.13% per year and TFP growth recovered to 1.76% per year and • The 8 years in this century, 2000-2007, when TFP growth dropped to 0.20% per year but real income growth was strong at 3.88% due to the very strong contribution made by falling real import prices during this period, which contributed on average 1.63% per year to real income growth. The annual changes presented in Table 1.4 can be converted into levels using Equations (1.54) with extensions to multiple inputs and outputs. Let T t, AtD, A t X , A t M , B t L, B t K and A t XM be the cumulated products of the annual link factors τ t, αtD, α t X , α t M , β t L, β t K and α t XM respectively. Using these definitions and cumulating Equation (1.3) 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: ρt ρ1961 = T tAtDA t XA t MB t LB t K ; t = 1962, 1963, . . . , 2007. (1.5) The cumulated variables that appear in Equation (1.5) are presented in Table 1.5 along with the cumulated terms of trade contribution factor, AtXM 25 Chapter 1. Productivity Performance of Canada defined to be the product of the two cumulated international price factors, AtX and A t M . Table 1.5 shows that the gross real income generated by the business sec- tor grew 6.09 fold over the years 1961-2007. The main factors explaining this growth are growth of quality adjusted labour input (with cumulative growth factor 2.06), productivity increases (with cumulative growth factor 1.55), growth of capital services (with cumulative growth factor 1.67) and lower import prices (with cumulative growth factor 1.21). There were neg- ative contributions from declining real domestic output prices (with cumu- lative growth factor 0.96) and declining real export prices (with cumulative growth factor 0.98). The real prices of Canadian raw material exports have increased dramatically in recent years, but these increases do not show up in the AtX column of Table 1.5, i.e. the overall real price of Canadian exports have remained relatively constant in the recent years. This apparent con- tradiction can be explained by the falling real prices for Canadian exports of manufactured goods. As already noted above, in the same period, the effects of the falling real import prices have been substantial. 26 Chapter 1. Productivity Performance of Canada Table 1.5: Business Sector Cumulated Growth in Real In- come and Cumulated Contribution Factors Year t ρ t ρ1961 T t AtD A t X A t M B t L B t K A t XM 1961 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1962 1.06402 1.03361 1.00000 1.00602 0.98556 1.03028 1.00773 0.99150 1963 1.14291 1.08554 1.00210 1.00483 0.97983 1.04903 1.01723 0.98456 1964 1.24355 1.12994 1.00519 1.00796 0.97868 1.07891 1.02869 0.98648 1965 1.34925 1.15498 1.01378 1.01046 0.98288 1.11179 1.04359 0.99316 1966 1.45950 1.17913 1.01238 1.01155 0.98899 1.14991 1.06280 1.00042 1967 1.48576 1.15790 1.01136 1.00983 0.99197 1.16691 1.08540 1.00172 1968 1.54716 1.18151 1.00719 1.01091 0.99713 1.17037 1.10206 1.00800 1969 1.63300 1.21189 1.00873 1.00832 0.99971 1.18918 1.11437 1.00803 1970 1.70070 1.23340 1.01374 1.00905 1.00224 1.19184 1.12848 1.01131 1971 1.78820 1.25120 1.02745 1.00678 1.00167 1.20981 1.14014 1.00845 1972 1.90953 1.28367 1.03226 1.00578 1.00785 1.23563 1.15052 1.01367 1973 2.20668 1.36984 1.04246 1.02683 1.00857 1.28352 1.16252 1.03563 1974 2.35207 1.38289 1.04346 1.06260 0.98704 1.31287 1.18375 1.04883 1975 2.20829 1.29927 1.02636 1.05716 0.98778 1.31200 1.20871 1.04425 1976 2.41459 1.37083 1.03478 1.06155 0.99759 1.31103 1.22605 1.05899 1977 2.56120 1.44548 1.03331 1.06956 0.97696 1.32066 1.24259 1.04492 1978 2.64781 1.44798 1.03108 1.07485 0.96565 1.35754 1.25867 1.03793 1979 2.84833 1.46527 1.03062 1.10130 0.95457 1.40724 1.27495 1.05127 1980 2.83559 1.37664 1.02298 1.11803 0.96458 1.43794 1.29844 1.07844 1981 2.88968 1.36648 1.02590 1.10781 0.96447 1.46300 1.31869 1.06845 1982 2.66070 1.30211 1.01711 1.07935 0.97896 1.41457 1.34410 1.05663 1983 2.76193 1.35101 1.00006 1.05651 1.00637 1.42105 1.35297 1.06324 1984 2.92218 1.39934 0.99624 1.05300 1.00540 1.45455 1.36120 1.05869 1985 3.07883 1.42893 0.99704 1.04868 1.00671 1.49183 1.37214 1.05571 1986 3.15306 1.41928 0.99972 1.03833 1.00822 1.53286 1.38481 1.04686 1987 3.42136 1.45508 1.00295 1.03649 1.02432 1.58036 1.39724 1.06170 Continued on Next Page. . . 27 Chapter 1. Productivity Performance of Canada Table 1.5 – Continued Year t ρ t ρ1961 T t AtD A t X A t M B t L B t K A t XM 1988 3.61799 1.46111 1.00284 1.02684 1.04567 1.62620 1.41411 1.07373 1989 3.69336 1.43190 1.00233 1.02344 1.05865 1.65455 1.43550 1.08347 1990 3.57459 1.40024 0.98467 0.99889 1.07687 1.65588 1.45553 1.07567 1991 3.26319 1.33340 0.96272 0.96417 1.10931 1.61905 1.46796 1.06957 1992 3.35604 1.38609 0.96026 0.97009 1.09659 1.60787 1.47414 1.06379 1993 3.37900 1.37814 0.95993 0.98067 1.07990 1.63196 1.47788 1.05903 1994 3.62268 1.42800 0.96844 1.00667 1.05148 1.67357 1.47875 1.05849 1995 3.84175 1.44770 0.97135 1.03928 1.03856 1.70452 1.48493 1.07936 1996 3.98254 1.46190 0.96404 1.03053 1.05711 1.73569 1.49449 1.08938 1997 4.12172 1.48016 0.96135 1.02195 1.06407 1.77074 1.50430 1.08743 1998 4.26368 1.51245 0.96184 1.01236 1.05172 1.80636 1.52391 1.06472 1999 4.50616 1.53206 0.95917 1.00882 1.06558 1.84792 1.54366 1.07497 2000 4.90761 1.57400 0.95639 1.03152 1.07018 1.88878 1.56356 1.10392 2001 4.88304 1.55565 0.95156 1.02278 1.06876 1.90437 1.58464 1.09311 2002 5.07494 1.60819 0.95324 1.00247 1.07221 1.92989 1.59591 1.07486 2003 5.04267 1.53930 0.94365 0.98374 1.12702 1.94909 1.60651 1.10869 2004 5.40004 1.55997 0.94487 0.98939 1.15061 1.99244 1.61521 1.13840 2005 5.63249 1.56201 0.94585 0.99346 1.17052 2.01060 1.63056 1.16287 2006 5.81943 1.56088 0.95107 0.98519 1.18558 2.03310 1.65078 1.16802 2007 6.08978 1.55325 0.95545 0.98112 1.21149 2.06447 1.67226 1.18862 28 Chapter 1. Productivity Performance of Canada As discussed in Subsection 1.8.6, the concept of income used in this section is biased upwards. The problem is that depreciation payments are part of the user cost of capital for each asset but depreciation does not provide households with any sustainable purchasing power. Hence, the measure of real income, ρt that is used in this section is overstated. In the following section, we implement the net real income model that is described in more detail in Subsection 1.8.6. 1.4 Explaining Real Income Growth Generated by the Canadian Business Sector: the Net Output Approach The overstatement of income problem that is implicit in the gross output approach used in the previous section can readily be remedied: all we need to do is take the user cost formula for an asset that has investment price P tI in year t and decompose it into two parts: • One part that represents depreciation and foreseen obsolescence, δP tIKt, and • The remaining part that is the reward for postponing consumption, rtP tIK t. The depreciation part δP tIK t will be removed from the user cost and treated as an intermediate input as an offset to gross investment. The user costs in the previous section took the form of: U t = (rt + δt + τ tB)P t I (1.6) where rt is the period t balancing real rate of interest, δt is a geometric depreciation rate for period t, τ tB is an appropriate business taxation rate on the asset (including property taxes if applicable) and P tI is the period t investment price for the asset. However, in the net output approach to the 29 Chapter 1. Productivity Performance of Canada measurement of income,18 we split up each (gross product) user cost times the beginning of the period stock Kt into the depreciation component δP tIK t and the remaining term (rt + τ tB)P t IK t and we regard the second term as a genuine income component but we treat the first term as an intermediate input cost for the business sector and as an offset to gross investment made by the business sector during the year under consideration. Thus in this section, the new aggregate for domestic output will aggregate C+ I +G like before, but the depreciation series for business structures, ICT and non-ICT machinery and equipment as negative outputs of the business sector. The ICT and non-ICT machinery and equipment and non-residential structures user costs are also changed because now the depreciation terms are omitted. The new investment aggregate I is a net investment aggregate (gross invest- ment components were indexed with a positive sign in the aggregate and depreciation components were indexed with a negative sign in the aggre- gate) and the new capital services aggregate is now a “reward for waiting” capital services aggregate.19 By including these changes, the aggregate data series would have changed. The new net product prices, quantities and real income series (counterparts to Tables 1.1 to 1.3) are shown in Tables 1.6 to 1.8.20 18See Diewert (2006a) for a more detailed discussion of the net output approach to income measurement. 19This approach seems to be broadly consistent with an approach advocated by Rymes (1968, 1983), who stressed the role of waiting services: “Second, one can consider the ’waiting’ or ’abstinence’ associated with the net returns to capital as the non-labour pri- mary input.” T.K. Rymes (1968, p.362). Denison (1974) also advocated a net output approach to productivity measurement. 20The TFP growth rate τ t in Tables 1.7 and 1.9 differ slightly because when calculating τ t in Table 1.9, the input aggregate is a direct Törnqvist quantity index whereas in Table 1.7, the input aggregate is an implicit quantity index; i.e. the value of inputs was deflated by the Törnqvist input price index. Both the direct and implicit Törnqvist indexes are superlative and hence will generally approximate each other very closely; see Diewert (1978). 30 Chapter 1. Productivity Performance of Canada Table 1.6: Prices of Canadian Business Sector Net Output and Input Aggregates Year P tC P t D P t X P t M P t L P t K P t Y P t Z 1961 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1962 1.00538 1.00477 1.02992 1.05787 1.03625 1.01517 0.99506 1.03177 1963 1.02055 1.01951 1.04054 1.09648 1.06604 1.21066 1.00167 1.09654 1964 1.02437 1.02570 1.05692 1.10526 1.11049 1.32368 1.01000 1.15544 1965 1.03690 1.04437 1.07980 1.10214 1.18272 1.32976 1.03635 1.21382 1966 1.07553 1.08188 1.12451 1.11930 1.25929 1.43384 1.08239 1.29617 1967 1.11050 1.11723 1.15421 1.14426 1.33342 1.23143 1.11942 1.31158 1968 1.15168 1.15726 1.20119 1.16726 1.41620 1.33236 1.16779 1.39834 1969 1.18980 1.19642 1.23088 1.19648 1.52197 1.35774 1.20736 1.48633 1970 1.22208 1.23208 1.26710 1.21965 1.61278 1.39712 1.24801 1.56563 1971 1.24828 1.27432 1.28552 1.24798 1.72528 1.33648 1.28652 1.63857 1972 1.29847 1.33283 1.33325 1.27498 1.86392 1.45722 1.35367 1.77330 1973 1.38744 1.44088 1.51489 1.35954 2.03837 2.36282 1.49982 2.11395 1974 1.58382 1.64631 1.91283 1.64641 2.35044 2.88611 1.73846 2.47391 1975 1.82198 1.86583 2.16694 1.89029 2.70332 2.22381 1.95864 2.59155 1976 1.90726 1.96938 2.29702 1.92853 3.10646 2.45812 2.10208 2.95469 1977 2.03175 2.09474 2.50231 2.17241 3.38889 2.93446 2.20157 3.28528 1978 2.19264 2.25525 2.73837 2.41667 3.53495 3.40699 2.35179 3.51206 1979 2.40645 2.47513 3.20786 2.73027 3.78520 4.47127 2.61939 3.96092 1980 2.69497 2.75871 3.73464 2.97957 4.11781 4.51719 3.00661 4.22499 1981 2.95335 3.03348 3.99821 3.26618 4.59295 4.37549 3.27072 4.55078 1982 3.22860 3.29615 4.08926 3.43918 5.02021 3.31517 3.50723 4.60204 1983 3.46323 3.51354 4.15051 3.42324 5.22085 4.86150 3.76691 5.15888 1984 3.61506 3.65788 4.29656 3.58225 5.48101 5.66773 3.90201 5.56258 1985 3.72257 3.76949 4.38071 3.67711 5.75670 5.97348 4.00777 5.84765 1986 3.80422 3.86708 4.37060 3.74437 5.90250 5.68664 4.07122 5.88540 1987 3.89726 3.98569 4.45792 3.69150 6.11054 6.89128 4.26595 6.34107 Continued on Next Page. . . 31 Chapter 1. Productivity Performance of Canada Table 1.6 – Continued Year P tC P t D P t X P t M P t L P t K P t Y P t Z 1988 4.00205 4.09782 4.47080 3.60108 6.51242 6.81320 4.44386 6.62912 1989 4.11690 4.21841 4.56005 3.59364 6.78864 6.34569 4.62309 6.72753 1990 4.35206 4.39764 4.52868 3.64367 7.04667 5.68557 4.77719 6.76258 1991 4.59099 4.59362 4.37107 3.57992 7.34245 4.19549 4.95539 6.60905 1992 4.65258 4.64682 4.49573 3.72567 7.48023 5.09947 4.98029 6.94680 1993 4.74252 4.73209 4.69389 3.92460 7.45961 5.28267 5.04452 6.97845 1994 4.77089 4.78795 4.97322 4.16089 7.41314 6.90899 5.10110 7.35256 1995 4.79147 4.81456 5.29132 4.27688 7.53622 7.86053 5.24941 7.68006 1996 4.88952 4.87348 5.32097 4.22185 7.63205 8.64495 5.37425 7.94364 1997 4.96547 4.93146 5.32718 4.23677 7.91076 8.52931 5.42748 8.13030 1998 5.03224 4.99337 5.31558 4.37960 8.13918 8.19333 5.36027 8.22664 1999 5.12045 5.08140 5.37870 4.36044 8.33890 9.06262 5.51701 8.58639 2000 5.25425 5.20795 5.71039 4.44227 8.74780 11.02286 5.83458 9.36276 2001 5.40970 5.34378 5.80311 4.58416 8.97770 10.23916 5.91943 9.35715 2002 5.47743 5.42904 5.68895 4.61494 9.09489 11.21972 5.89394 9.67799 2003 5.61543 5.56047 5.64768 4.31493 9.26253 10.98273 6.26151 9.75266 2004 5.69551 5.66394 5.78629 4.20643 9.48779 12.99255 6.57696 10.39319 2005 5.81654 5.80418 5.95274 4.15511 9.84265 14.07954 6.90744 10.91980 2006 5.92386 5.95701 5.97000 4.12736 10.29074 13.95161 7.12388 11.23987 2007 6.02712 6.10280 6.02590 4.02177 10.66121 14.56298 7.44707 11.66971 32 Chapter 1. Productivity Performance of Canada Table 1.7: Quantities of Canadian Business Sector Net Out- put and Input Aggregates, TFP Levels and TFP Growth Rates Year t QtD Q t X Q t M Q t L Q t K Q t Y Q t Z T t τt 1961 25452 6867 −7897 19202 5220 24422 24422 1.00000 0.00000 1962 27156 7195 −8033 20042 5348 26328 25391 1.03690 1.03690 1963 28698 7832 −8031 20574 5509 28554 26083 1.09471 1.05576 1964 30880 9105 −8989 21446 5701 31052 27143 1.14400 1.04503 1965 33935 9418 −10180 22416 5925 33184 28332 1.17124 1.02381 1966 36532 10696 −11579 23550 6230 35653 29773 1.19750 1.02242 1967 36362 11827 −12306 24056 6592 35906 30646 1.17166 0.97842 1968 37696 12910 −13527 24158 6852 37114 30995 1.19743 1.02199 1969 40646 13802 −15377 24718 7070 39110 31769 1.23106 1.02808 1970 40280 15211 −15293 24798 7342 40264 32096 1.25450 1.01904 1971 42286 15929 −16480 25333 7549 41816 32831 1.27365 1.01526 1972 45763 17257 −18892 26101 7730 44262 33788 1.30999 1.02854 1973 52582 19008 −21754 27591 7933 49995 35471 1.40947 1.07594 1974 58017 18347 −23977 28558 8319 52422 36838 1.42305 1.00963 1975 55709 16951 −23228 28530 8833 49405 37340 1.32313 0.92979 1976 59148 18390 −24774 28499 9121 52781 37551 1.40561 1.06233 1977 62034 19678 −24836 28805 9410 56883 38119 1.49224 1.06164 1978 63659 21544 −26197 30018 9728 59212 39650 1.49336 1.00075 1979 68536 22467 −28092 31737 10037 62995 41659 1.51215 1.01259 1980 66718 22548 −28715 32833 10516 60768 43244 1.40523 0.92929 1981 69487 23012 −30716 33723 10875 61904 44491 1.39137 0.99013 1982 58666 22882 −25710 32059 11336 56604 43138 1.31216 0.94307 1983 62713 24326 −28444 32283 11395 59449 43409 1.36953 1.04372 1984 67214 28444 −33270 33497 11520 63785 44743 1.42557 1.04092 1985 71770 29938 −35548 34871 11757 67611 46338 1.45908 1.02351 1986 74416 31456 −37965 36384 12018 69537 48102 1.44561 0.99077 Continued on Next Page. . . 33 Chapter 1. Productivity Performance of Canada Table 1.7 – Continued Year t QtD Q t X Q t M Q t L Q t K Q t Y Q t Z T t τt 1987 79795 32933 −39889 38166 12246 74450 50086 1.48644 1.02824 1988 85403 35371 −45163 39912 12556 77740 52113 1.49175 1.00357 1989 87899 35434 −47820 40981 12974 77984 53590 1.45520 0.97550 1990 84568 37556 −48551 41030 13358 76421 53985 1.41560 0.97278 1991 77953 38167 −49281 39707 13573 70326 52730 1.33371 0.94215 1992 79864 40921 −51473 39311 13581 72949 52299 1.39486 1.04585 1993 79507 45382 −55461 40184 13599 73662 53248 1.38337 0.99177 1994 83827 51076 −60606 41745 13567 79042 54838 1.44137 1.04192 1995 85817 55452 −64385 42958 13673 82146 56148 1.46303 1.01503 1996 88197 58646 −67340 44212 13898 85143 57603 1.47809 1.01029 1997 95522 63457 −77378 45636 14100 88674 59196 1.49799 1.01346 1998 98627 69086 −81755 47078 14461 93588 60980 1.53474 1.02454 1999 101444 76337 −88261 48781 14834 98099 63031 1.55635 1.01408 2000 107179 83350 −95661 50512 15180 104411 65066 1.60470 1.03107 2001 106033 80654 −90649 51183 15588 104590 66165 1.58075 0.98507 2002 113127 81599 −92347 52290 15743 110657 67391 1.64202 1.03876 2003 114374 79268 −96341 53129 16011 106675 68489 1.55756 0.94856 2004 121796 83281 −104558 55049 16135 111286 70423 1.58024 1.01457 2005 128251 84730 −112492 55875 16435 113118 71554 1.58088 1.00040 2006 134178 85022 −117772 56905 16858 115217 73025 1.57777 0.99804 2007 140386 86002 −124556 58347 17304 117368 74899 1.56702 0.99318 34 Chapter 1. Productivity Performance of Canada Comparing Table 1.6 with Table 1.1, we see that the 2007 price of domestic absorption, PD has increased to 6.10 from the gross approach level of 5.76. This is because net investment is considerably smaller than gross investment and so the relatively low inflation prices of ICT and non-ICT machinery and equipment get much smaller weights in net domestic absorption compared to their weights in gross domestic absorption. The other striking difference between the results of the two approaches is that the price of waiting services, P tK , in Table 1.6 grew 14.56 fold over the sample period whereas the price of traditional capital services, P tK , in Table 1.1 grew only 10.14 fold. The difference in growth rate can be explained by the fact that the prices of ICT, machinery and equipment services get much lower weights in the calculation of capital services aggregate for Table 1.6 than in the calculation for Table 1.1 because the corresponding user cost for the net concept of capital services now excludes the very large depreciation terms in the net user cost. Thus the prices of agricultural land and business non-agricultural land get much higher weights in the net user cost compared to the gross concept user cost.21 However, even though the land components now get a much higher weight in waiting services compared to machinery and equipment, the overall price increase in input prices has only increased to 11.67 fold (compared to the gross output model 10.63 fold increase in input prices) over the sample period due to the fact that the importance of capital services dramatically shrinks relative to labour services in the net output framework. Thus the level of business sector TFP using the net approach increased 1.57 fold over the period 1961-2007 and the average rate of net TFP growth was 1.04 percent per year. Recall that using the gross approach, the level of business sector TFP increased 1.55 fold over the period 1961-2007 and the average rate of gross product TFP growth was 1.01 percent per year. There- fore switching to the more appropriate net approach does not substantially increase Canadian business sector TFP growth on average. Table 1.9 shows 21From Table 2.13, we estimate the price of agricultural land increased 19.26 fold and the price of business non-agricultural land increased 52.46 fold over the period 1961-2007. For comparison purposes, the price of residential land increased 88.93 fold over this period. 35 Chapter 1. Productivity Performance of Canada the breakdown of the net TFP growth and the averages over subperiods. Figures 1.2 and 1.3 show the levels of productivity and the rates of pro- ductivity growth using the two approaches. Throughout the sample period, the level of productivity calculated using the net output approach is con- stantly higher than the one using the gross output approach. However, the difference between the rates of productivity growth is not as clear. Figure 1.2: Level of Total Factor Productivity in Canada 1961-2007 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1 9 6 1 1 9 6 3 1 9 6 5 1 9 6 7 1 9 6 9 1 9 7 1 1 9 7 3 1 9 7 5 1 9 7 7 1 9 7 9 1 9 8 1 1 9 8 3 1 9 8 5 1 9 8 7 1 9 8 9 1 9 9 1 1 9 9 3 1 9 9 5 1 9 9 7 1 9 9 9 2 0 0 1 2 0 0 3 2 0 0 5 2 0 0 7 Year gross output net output 36 Chapter 1. Productivity Performance of Canada Figure 1.3: Rate of Productivity Growth in Canada 1962-2007 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1 9 6 2 1 9 6 4 1 9 6 6 1 9 6 8 1 9 7 0 1 9 7 2 1 9 7 4 1 9 7 6 1 9 7 8 1 9 8 0 1 9 8 2 1 9 8 4 1 9 8 6 1 9 8 8 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4 2 0 0 6 Year gross output net output 37 Chapter 1. Productivity Performance of Canada The net counterpart to Table 1.3 is Table 1.8; ρt now represents the net real income generated by the Canadian business sector in year t. Table 1.8: Net Real Income Generated by the Canadian Busi- ness Sector and Real Output and Input Prices Year t ρt PtD Pt C PtX Pt C PtM Pt C PtL Pt C PtK Pt C 1961 24422 1.00000 1.00000 1.00000 1.00000 1.00000 1962 26058 0.99939 1.02441 1.05221 1.03070 1.00974 1963 28025 0.99899 1.01959 1.07440 1.04457 1.18628 1964 30616 1.00130 1.03178 1.07897 1.08407 1.29219 1965 33166 1.00720 1.04137 1.06292 1.14063 1.28244 1966 35880 1.00591 1.04554 1.04070 1.17085 1.33315 1967 36195 1.00606 1.03936 1.03040 1.20074 1.10890 1968 37633 1.00484 1.04299 1.01353 1.22968 1.15688 1969 39687 1.00556 1.03453 1.00561 1.27918 1.14115 1970 41119 1.00818 1.03684 0.99801 1.31970 1.14323 1971 43096 1.02086 1.02983 0.99976 1.38213 1.07066 1972 46143 1.02647 1.02679 0.98191 1.43547 1.12226 1973 54045 1.03851 1.09186 0.97989 1.46916 1.70300 1974 57540 1.03945 1.20773 1.03952 1.48403 1.82225 1975 53111 1.02407 1.18933 1.03749 1.48373 1.22055 1981 58173 1.03257 1.20436 1.01115 1.62875 1.28882 1977 61637 1.03101 1.23160 1.06923 1.66796 1.44430 1978 63509 1.02855 1.24889 1.10217 1.61219 1.55383 1979 68569 1.02854 1.33303 1.13456 1.57294 1.85804 1980 67795 1.02365 1.38578 1.10560 1.52796 1.67616 1981 68556 1.02713 1.35379 1.10592 1.55517 1.48153 1982 61489 1.02092 1.26657 1.06522 1.55492 1.02681 1983 64662 1.01453 1.19845 0.98845 1.50751 1.40375 1984 68848 1.01184 1.18852 0.99092 1.51616 1.56781 Continued on Next Page. . . 38 Chapter 1. Productivity Performance of Canada Table 1.8 – Continued Year t ρt PtD Pt C PtX Pt C PtM Pt C PtL Pt C PtK Pt C 1985 72791 1.01260 1.17680 0.98779 1.54643 1.60467 1986 74417 1.01652 1.14888 0.98427 1.55157 1.49482 1987 81494 1.02269 1.14386 0.94720 1.56791 1.76824 1988 86322 1.02393 1.11713 0.89981 1.62727 1.70243 1989 87573 1.02466 1.10764 0.87290 1.64897 1.54138 1990 83886 1.01047 1.04058 0.83723 1.61916 1.30641 1991 75908 1.00057 0.95210 0.77977 1.59932 0.91385 1992 78088 0.99876 0.96629 0.80078 1.60776 1.09605 1993 78353 0.99780 0.98975 0.82753 1.57292 1.11390 1994 84512 1.00358 1.04241 0.87214 1.55383 1.44816 1995 89997 1.00482 1.10432 0.89260 1.57284 1.64053 1996 93584 0.99672 1.08824 0.86345 1.56090 1.76806 1997 96925 0.99315 1.07285 0.85325 1.59315 1.71772 1998 99689 0.99228 1.05630 0.87031 1.61741 1.62817 1999 105696 0.99237 1.05044 0.85157 1.62855 1.76989 2000 115943 0.99119 1.08681 0.84546 1.66490 2.09789 2001 114445 0.98781 1.07272 0.84740 1.65956 1.89274 2002 119071 0.99117 1.03862 0.84254 1.66043 2.04835 2003 118949 0.99021 1.00574 0.76841 1.64948 1.95581 2004 128508 0.99446 1.01594 0.73855 1.66584 2.28119 2005 134333 0.99788 1.02342 0.71436 1.69218 2.42060 2006 138557 1.00560 1.00779 0.69673 1.73717 2.35515 2007 145019 1.01256 0.99980 0.66728 1.76887 2.41624 39 Chapter 1. Productivity Performance of Canada Table 1.9: Business Sector Year to Year Growth in Net Real Income and Net Year to Year Contribution Factors Year t ρ t ρt−1 τ t αtD α t X α t M β t L β t K α t XM 1962 1.06695 1.03690 0.99936 1.00682 0.98365 1.03439 1.00509 0.99037 1963 1.07552 1.05573 0.99958 0.99866 0.99342 1.02062 1.00654 0.99209 1964 1.09244 1.04503 1.00235 1.00352 0.99868 1.03219 1.00817 1.00219 1965 1.08330 1.02381 1.00602 1.00279 1.00483 1.03441 1.00908 1.00764 1966 1.08183 1.02242 0.99868 1.00121 1.00702 1.03875 1.01165 1.00824 1967 1.00877 0.97846 1.00016 0.99807 1.00342 1.01676 1.01232 1.00148 1968 1.03974 1.02199 0.99878 1.00122 1.00592 1.00337 1.00799 1.00714 1969 1.05457 1.02808 1.00073 0.99708 1.00296 1.01835 1.00651 1.00003 1970 1.03608 1.01904 1.00263 1.00083 1.00289 1.00256 1.00771 1.00372 1971 1.04810 1.01527 1.01250 0.99741 0.99934 1.01734 1.00547 0.99676 1972 1.07070 1.02854 1.00555 0.99887 1.00709 1.02456 1.00446 1.00595 1973 1.17124 1.07552 1.01191 1.02388 1.00082 1.04429 1.00568 1.02472 1974 1.06467 1.00963 1.00093 1.03955 0.97585 1.02594 1.01228 1.01445 1975 0.92302 0.93008 0.98430 0.99415 1.00087 0.99924 1.01408 0.99501 1981 1.09531 1.06233 1.00882 1.00478 1.01144 0.99915 1.00651 1.01627 1977 1.05956 1.06162 0.99842 1.00869 0.97623 1.00846 1.00663 0.98472 1978 1.03037 1.00074 0.99754 1.00571 0.98666 1.03229 1.00764 0.99229 1979 1.07966 1.01254 0.99999 1.02844 0.98677 1.04236 1.00801 1.01484 1980 0.98872 0.92929 0.99516 1.01757 1.01214 1.02525 1.01249 1.02992 1981 1.01123 0.99015 1.00348 0.98937 0.99986 1.02031 1.00834 0.98923 1982 0.89691 0.94322 0.99391 0.96965 1.01780 0.96092 1.00885 0.98690 1983 1.05161 1.04339 0.99387 0.97483 1.03347 1.00546 1.00113 1.00745 1984 1.06473 1.04092 0.99739 0.99609 0.99886 1.02789 1.00279 0.99495 1985 1.05728 1.02351 1.00075 0.99518 1.00152 1.03017 1.00531 0.99670 1986 1.02234 0.99078 1.00390 0.98843 1.00176 1.03236 1.00552 0.99017 1987 1.09509 1.02822 1.00612 0.99793 1.01871 1.03633 1.00477 1.01659 1988 1.05925 1.00358 1.00122 0.98918 1.02427 1.03381 1.00644 1.01319 Continued on Next Page. . . 40 Chapter 1. Productivity Performance of Canada Table 1.9 – Continued Year t ρ t ρt−1 τ t αtD α t X α t M β t L β t K α t XM 1989 1.01449 0.97551 1.00072 0.99614 1.01449 1.02035 1.00782 1.01058 1990 0.95790 0.97280 0.98583 0.97186 1.02025 1.00094 1.00640 0.99155 1991 0.90490 0.94235 0.98998 0.95890 1.03585 0.97366 1.00297 0.99327 1992 1.02871 1.04579 0.99815 1.00731 0.98635 0.99178 1.00010 0.99356 1993 1.00340 0.99177 0.99902 1.01303 0.98186 1.01790 1.00025 0.99466 1994 1.07861 1.04182 1.00581 1.03168 0.96871 1.03047 0.99950 0.99940 1995 1.06490 1.01503 1.00121 1.03853 0.98545 1.02197 1.00188 1.02342 1996 1.03985 1.01029 0.99235 0.99006 1.02114 1.02164 1.00419 1.01099 1997 1.03570 1.01346 0.99657 0.99019 1.00777 1.02386 1.00370 0.99788 1998 1.02852 1.02454 0.99914 0.98892 0.98629 1.02383 1.00616 0.97536 1999 1.06026 1.01408 1.00009 0.99586 1.01562 1.02730 1.00618 1.01141 2000 1.09695 1.03105 0.99888 1.02656 1.00509 1.02609 1.00605 1.03178 2001 0.98708 0.98508 0.99688 0.99002 0.99844 1.00973 1.00708 0.98847 2002 1.04043 1.03876 1.00315 0.97657 1.00382 1.01586 1.00263 0.98029 2003 0.99897 0.94856 0.99909 0.97802 1.06051 1.01173 1.00451 1.03720 2004 1.08037 1.01455 1.00406 1.00672 1.02453 1.02607 1.00212 1.03142 2005 1.04532 1.00040 1.00326 1.00479 1.02017 1.01062 1.00538 1.02506 2006 1.03145 0.99804 1.00745 0.99032 1.01498 1.01303 1.00744 1.00516 2007 1.04664 0.99318 1.00676 0.99519 1.02549 1.01799 1.00754 1.02056 Averages 1962-2007 1.04070 1.01040 1.00030 0.99958 1.00510 1.01850 1.00620 1.00450 1962-1973 1.06910 1.02920 1.00320 1.00250 1.00080 1.02400 1.00760 1.00340 1974-1991 1.02090 0.99781 0.99791 0.99591 1.00650 1.01530 1.00710 1.00210 1992-1999 1.04250 1.01960 0.99904 1.00690 0.99415 1.01980 1.00270 1.00080 2000-2007 1.04090 1.00120 1.00240 0.99602 1.01910 1.01640 1.00530 1.01500 41 Chapter 1. Productivity Performance of Canada Note that from Tables 1.8, the starting level of net real income in 1961, $24,422 million, is less than the corresponding starting value of gross real income in 1961 from Tables 1.3, which was $27,722 million (see Figure 1.4). This makes sense since we now subtract depreciation from the previous estimates of gross income. Net real income generated by the Canadian business sector grew 5.94 fold over the period 1961-2007 which is 2.5 percent less than the 6.09 fold growth of gross real income. The real price of waiting capital services grew 2.42 fold, which is more rapid than the previous 1.68 fold increase in the real price of gross capital services. This difference is due to the fact that depreciation gave the prices of ICT and other machinery and equipment (which decreases in real terms) a larger role in the price of gross capital services but when depreciation is regarded as an intermediate input, the price of land (which increases in real terms) gets a much larger weight in the price of waiting capital services. The same translog contributions methodology explained in Section 1.8 can be applied to the net output model used in this section. Thus Equation (1.3) in the last section is applicable to our new measure of real income generated by the Canadian business sector and Table 1.9 shows the net income gen- erated (counterpart to Table 1.4). The contribution of the combined effects of real changes in international prices (αtXM − 1) and the changes in real income ([ρt/ρt−1]−1) in 1962-2007 using the net approach are also depicted in Figure 1.5. 42 Chapter 1. Productivity Performance of Canada Figure 1.4: Real Income Generated by the Business Sector in Canada 1961- 2007 0 20000 40000 60000 80000 100000 120000 140000 160000 180000 1 9 6 1 1 9 6 3 1 9 6 5 1 9 6 7 1 9 6 9 1 9 7 1 1 9 7 3 1 9 7 5 1 9 7 7 1 9 7 9 1 9 8 1 1 9 8 3 1 9 8 5 1 9 8 7 1 9 8 9 1 9 9 1 1 9 9 3 1 9 9 5 1 9 9 7 1 9 9 9 2 0 0 1 2 0 0 3 2 0 0 5 2 0 0 7 Year M il li o n  D o ll a rs Gross Net 43 Chapter 1. Productivity Performance of Canada Figure 1.5: Real Income Change and Terms of Trade Contribution 1962-2007 (Net Output Approach) -15 -10 -5 0 5 10 15 20 1 9 6 2 1 9 6 4 1 9 6 6 1 9 6 8 1 9 7 0 1 9 7 2 1 9 7 4 1 9 8 1 1 9 7 8 1 9 8 0 1 9 8 2 1 9 8 4 1 9 8 6 1 9 8 8 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4 2 0 0 6 Year Real income TOT 44 Chapter 1. Productivity Performance of Canada The net real income generated by the Canadian business sector grew at an annual rate of 4.07 percent on average over the 47 year period (1961- 2007), which is slightly less than the gross real income growth rate of 4.10 percent. Real domestic output prices averaged a tiny positive contribution to the growth in real net income of 0.03 per year and falling real export prices made a tiny negative contribution of −0.04 per year. Positive average contributions to the growth of real net income were due to productivity im- provements (1.04 per year compared to 1.01 in the gross output framework), growth of labour input (1.85 per year compared to the previous gross income 1.60), growth of capital input (0.62 per year compared to the previous 1.13) and falls in real import prices (0.51 per year compared to the previous 0.43). Comparing these average contribution growth rates in the gross and net real income frameworks leads to the following observations: • The role of productivity improvements is magnified in the net output framework compared to the gross output framework;22 • The role of increases in labour input is also magnified in the net output framework; • The role of increases in capital input (capital deepening) is greatly diminished in the net income framework and • The role of falling real import prices is also magnified in the net output framework. During the naughts, the average contribution factor for changes in real export and import prices together was 1.28 percentage points per year in 22This phenomenon is reasonably well known and is explained in Schreyer (2001): as the input denominator in a total factor productivity measure shrinks (by treating inputs as negative outputs and placing them in the net output numerator), the resulting measure of TFP will increase. This magnification effect shows up most clearly during periods of large productivity growth; i.e. during the period 1962-1973, the average net TFP growth was 2.92% per year compared to the average gross rate of 2.68% and during the period 1992-1999, the average net TFP growth rate was 1.96% per year compared to the average gross rate of 1.76%. 45 Chapter 1. Productivity Performance of Canada the gross framework and 1.50 percentage points per year in the net frame- work. The corresponding contribution factor for capital growth during the naughts was 1.01 percentage points in the gross framework and 0.53 per- centage points in the net framework. Looking at the contribution of falling import prices alone in the net output framework, during the entire sample period, falling import prices contributed about 0.51 percentage points per year to real income growth whereas the effects of net capital accumulation contributed about 0.62 percentage points per year. During the years of the present decade, falling import prices contributed a very large 1.91 percent- age points per year to real income growth whereas the effects of net capital accumulation contributed only 0.53 percentage points per year and TFP im- provements contributed only 0.12 percentage points per year. Thus for short periods, changes in the real export or import prices that a country faces can have substantially larger effects on living standards than the effects of net capital accumulation or improvements in TFP. The average annual rate of TFP growth in the net output framework was a satisfactory 1.04 percentage points per year. As usual, there are considerable variations in the average over different periods. During the golden years, 1962-1973, TFP growth averaged a spectacular 2.92 percentage points per year. During the dismal years, 1974-1991, TFP growth actually averaged −0.22 percentage points per year. The TFP growth recovered during 1992- 1999 to average a respectable 1.96 percentage points per year. However, during the years 2000-2007, net TFP growth fell to 0.12 percentage points per year, and the decline can be explained all by two poor performance years (2001 and 2003). When these two years are excluded, the TFP growth averaged 1.27 percentage points. The year to year growth presented in Table 1.9 can be cumulated and the decomposition given by Equation (1.5) in the last section is applied to the new net data. The cumulated variables are shown in Table 1.10. 46 Chapter 1. Productivity Performance of Canada The net real income generated by the business sector grew 5.94 fold over the years 1961-2007. The main factors explaining this growth are growth of labour input (cumulative growth factor factor 2.31), productivity increases (cumulative growth factor 1.57), growth of waiting capital services (cumula- tive growth factor 1.33), lower real import prices (cumulative factor 1.25)23 and higher real domestic output prices (cumulative growth factor 1.01). There was a small negative contribution from declining real export prices (cumulative growth factor 0.97). 23Note that most of this growth took place over the years 2001-2007. 47 Chapter 1. Productivity Performance of Canada Table 1.10: Business Sector Cumulated Growth in Net Real Income and Cumulated Contribution Factors Year t ρ t ρ1961 T t AtD A t X A t M B t L B t K A t XM 1961 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1962 1.06695 1.03690 0.99936 1.00682 0.98365 1.03439 1.00509 0.99037 1963 1.14753 1.09468 0.99895 1.00548 0.97718 1.05572 1.01166 0.98254 1964 1.25360 1.14397 1.00130 1.00902 0.97589 1.08970 1.01993 0.98469 1965 1.35802 1.17121 1.00732 1.01184 0.98060 1.12720 1.02920 0.99221 1966 1.46915 1.19747 1.00599 1.01306 0.98749 1.17088 1.04118 1.00039 1967 1.48203 1.17168 1.00615 1.01111 0.99086 1.19050 1.05401 1.00187 1968 1.54093 1.19745 1.00492 1.01234 0.99672 1.19452 1.06243 1.00902 1969 1.62502 1.23108 1.00565 1.00939 0.99967 1.21644 1.06935 1.00906 1970 1.68365 1.25452 1.00830 1.01022 1.00256 1.21955 1.07760 1.01281 1971 1.76462 1.27368 1.02091 1.00761 1.00190 1.24070 1.08349 1.00953 1972 1.88938 1.31002 1.02657 1.00647 1.00901 1.27116 1.08832 1.01553 1973 2.21292 1.40896 1.03879 1.03050 1.00983 1.32747 1.09450 1.04063 1974 2.35603 1.42253 1.03975 1.07126 0.98545 1.36190 1.10794 1.05567 1975 2.17468 1.32306 1.02343 1.06499 0.98630 1.36086 1.12354 1.05040 1976 2.38194 1.40553 1.03246 1.07008 0.99758 1.35971 1.13085 1.06749 1977 2.52380 1.49215 1.03083 1.07939 0.97387 1.37121 1.13835 1.05118 1978 2.60045 1.49325 1.02829 1.08555 0.96087 1.41549 1.14704 1.04308 1979 2.80761 1.51198 1.02828 1.11643 0.94816 1.47544 1.15623 1.05856 1980 2.77594 1.40507 1.02330 1.13605 0.95967 1.51269 1.17067 1.09023 1981 2.80710 1.39124 1.02686 1.12397 0.95954 1.54342 1.18044 1.07849 1982 2.51771 1.31225 1.02061 1.08985 0.97661 1.48310 1.19088 1.06436 1983 2.64765 1.36919 1.01435 1.06242 1.00930 1.49120 1.19222 1.07230 1984 2.81903 1.42521 1.01171 1.05826 1.00815 1.53279 1.19555 1.06689 1985 2.98050 1.45871 1.01246 1.05316 1.00969 1.57904 1.20190 1.06336 1986 3.04707 1.44526 1.01641 1.04097 1.01146 1.63013 1.20853 1.05291 1987 3.33683 1.48605 1.02263 1.03882 1.03038 1.68935 1.21430 1.07038 Continued on Next Page. . . 48 Chapter 1. Productivity Performance of Canada Table 1.10 – Continued Year t ρ t ρ1961 T t AtD A t X A t M B t L B t K A t XM 1988 3.53455 1.49137 1.02388 1.02758 1.05539 1.74646 1.22212 1.08450 1989 3.58575 1.45484 1.02462 1.02362 1.07068 1.78199 1.23167 1.09597 1990 3.43478 1.41527 1.01011 0.99481 1.09237 1.78368 1.23956 1.08670 1991 3.10813 1.33368 0.99998 0.95392 1.13153 1.73670 1.24324 1.07939 1992 3.19738 1.39475 0.99813 0.96090 1.11609 1.72243 1.24336 1.07244 1993 3.20824 1.38326 0.99715 0.97342 1.09584 1.75326 1.24367 1.06672 1994 3.46043 1.44111 1.00295 1.00426 1.06155 1.80668 1.24305 1.06607 1995 3.68503 1.46276 1.00416 1.04295 1.04611 1.84638 1.24539 1.09104 1996 3.83187 1.47781 0.99648 1.03258 1.06822 1.88633 1.25061 1.10302 1997 3.96868 1.49771 0.99306 1.02245 1.07652 1.93133 1.25523 1.10069 1998 4.08186 1.53446 0.99220 1.01112 1.06176 1.97735 1.26297 1.07356 1999 4.32783 1.55606 0.99229 1.00693 1.07835 2.03132 1.27078 1.08582 2000 4.74740 1.60437 0.99119 1.03367 1.08383 2.08432 1.27846 1.12032 2001 4.68605 1.58043 0.98809 1.02335 1.08214 2.10460 1.28752 1.10741 2002 4.87549 1.64169 0.99121 0.99937 1.08627 2.13798 1.29090 1.08559 2003 4.87047 1.55724 0.99030 0.97741 1.15200 2.16307 1.29673 1.12597 2004 5.26189 1.57990 0.99433 0.98398 1.18026 2.21947 1.29948 1.16135 2005 5.50038 1.58054 0.99756 0.98870 1.20406 2.24303 1.30647 1.19045 2006 5.67335 1.57743 1.00500 0.97913 1.22210 2.27225 1.31619 1.19659 2007 5.93796 1.56668 1.01179 0.97442 1.25325 2.31313 1.32611 1.22119 49 Chapter 1. Productivity Performance of Canada 1.5 Productivity Performance Comparison with Other Countries Canada’s official productivity growth rate of 0.70 percent per year (1962- 2008) had led to worries of low productivity performance comparing to fel- low industrial countries and stimulated many discussions on how to close the wide “productivity gap” between Canada and the U.S. According to Statistics Canada official estimates, between 1961 and 2008 (shown in Table 1.11), productivity in Canada rose 2.0% a year on average, while productiv- ity grew 2.3% on average in the United States. This comparison shows that the average labour productivity growth in Canada has been satisfactory as compared to the United States in the last four decades. However, when the focus is restricted to the present decade, the productivity growth rate is estimated to be only 0.7% per year in Canada while the United States grew 2.6% per year. Statistics Canada decomposed the labour productiv- ity growth into three components: capital deepening, labour composition change and multifactor productivity growth. The results of their decompo- sition shows that contributions of the first two components are similar in the two countries, and the slow growth in productivity in Canada post-2000 was entirely contributed by the slow growth in multifactor productivity. In the previous section, we had shown that it is possible to estimate well using the “top down” approach and our estimates seem reasonable. Our TFP (multifactor) growth by the net approach is 1.04% (1961-2007) while the official estimate is 0.38% (1961-2007). The large difference between our estimate and the official estimate suggests that there may be possibility of miscalculation in the official estimates. Now if this is truly the case, then the so called “productivity gap” between Canada and the U.S. should in fact be narrower than we had initially thought. How does Canada compare with other developed countries? Base on the same net output approach used in this chapter, Diewert, Mizobuchi and Nomura (2005) had estimated the productivity performances in Japan (1956- 50 Chapter 1. Productivity Performance of Canada Table 1.11: Average Productivity Growth in Canada and the United States, 1961-2008 1961-2008 2000-2008 percent per yeara Canada Output per hour worked 2.0 0.7 Contribution of capital deepening 1.3 1.1 Contribution of labour compensation 0.4 0.3 Multifactor productivity growth 0.3 −0.6 United States Output per hour worked 2.3 2.6 Contribution of capital deepening 0.8 1.0 Contribution of labour compensation 0.2 0.2 Multifactor productivity growth 1.2 1.4 a Source: The Canadian Productivity Review, 15-206-X no.025, Statistics Canada 2003) and Diewert and Lawrence (2006) for Australia (1961-2004). Table 1.12 summarises the estimated results of Canada, Japan and Australia in the same subperiods. Overall, the average real income growth rates of all three countries are very close, all of which had an estimated rate of approximately 4.00 percent. In all subperiods, Canada had been similar to Australia in terms of real income growth rate. Japan, on the other hand, had a substantial decline in real income growth since 1992. However, Canada is the lowest in the three countries for TFP growth. In the subperiod 1962-1973, Canada had a higher TFP growth rate than Australia. But the situation had reversed since; Australia had outperformed Canada in all the remaining subperiods. Japan had experienced low growth in TFP in 1992-1999 but had somewhat recovered in 2000 onward. Thus, the three countries have similar average real income growth but very different TFP growth. The average TFP growth in Canada had been reasonable compared to other countries, and certainly not as poor as official estimates had shown. 51 Chapter 1. Productivity Performance of Canada Table 1.12: Real Income and TFP Growth of Canada, Japan and Australia Average Growth Rate (%) 1962- 1962-1973 1974-1991 1992-1999 2000- ρt ρt−1 Canada 4.07 6.91 2.09 4.25 4.09 Japan 3.94 8.79 3.21 0.02 0.47 Australia 3.78 5.66 2.52 3.52 4.26 τ t Canada 1.04 2.92 0.00 1.96 0.12 Japan 2.86 6.08 2.33 0.13 1.03 Australia 1.86 2.62 1.12 2.80 1.16 Recall that we had shown earlier that Canada had benefited most from increases in labour and capital inputs, and productivity improvement. The contribution of terms of trade improvements was also significant and pos- itive for all subperiods. However, this is not the case in Australia and Japan. Diewert and Lawrence (2006) showed that terms of trade improve- ment was transitory in Australia: in 1974-1991 and 1992-1999, the contribu- tions of terms of trade were negative. Similar results were found in Japan by Diewert, Mizobuchi and Nomura (2005). This transitory property of terms of trade contributions had caused the overall effect of international prices changes to be much smaller as compared to what was found in Canada. The comparison between these countries shows that Canada had generated similar real income growth rates as other developed countries through the additional benefit of terms of trade improvement over short period of time. However, it is still lagging behind in the TFP improvements. Higher TFP growth is important for income growth to be sustainable. Thus, the worries of the Canadian government are not totally unfounded, policies to encourage technology advancement are needed in the long term. In the following section, we will use our disaggregated data on exports and imports and our net output methodology to determine the effects of 52 Chapter 1. Productivity Performance of Canada changing disaggregated real export and import prices on the growth of real income generated by the production sector. 1.6 The Effects of Changing Real Export and Import Prices on Real Income Growth We generate real price series for eight export sectors and seven import sectors using value and quantity series from disaggregated trade data. De- tails describing the actual construction of these price indexes are shown in Chapter 2. The export commodity classes are as follows, • X1, Exports of agricultural and fish products; • X2, Exports of energy products; • X3, Exports of forest products; • X4, Exports of industrial goods and materials (excluding energy and forest product exports); • X5, Exports of machinery and equipment (excluding automotive prod- ucts); • X6, Exports of automotive products; • X7, Exports of other consumer goods (excluding automotive prod- ucts); • X8, Exports of services; and the import commodity classes are, • M1, Imports of agricultural and fish products; • M2, Imports of energy products; • M3, Imports of industrial goods and materials (including imports of forest products but excluding imports of energy products); 53 Chapter 1. Productivity Performance of Canada • M4, Imports of machinery and equipment (excluding automotive prod- ucts); • M5, Imports of automotive products; • M6, Imports of other consumer goods and • M7, Imports of services. The values, prices and quantities of Canadian export that we constructed are depicted in Figures 1.6-1.8; and the values, prices and quantities of Cana- dian imports are shown in Figures 1.9-1.11. As can be seen in Figure 1.6, the export values of forest products, agricultural products and other con- sumer goods remained rather steady over the sample period. The services sector had grown a lot during 1980s and 1990s in its value of export but the growth seemed to have stopped since. On the other hand, industrial goods and materials (excluding energy and forest products), machinery and equip- ments, energy products and automotive products all had increased quite a great deal. For the export prices, most of the sectors had steady growth throughout the sample period as shown in Figure 1.7. The only exception is the energy sector which experienced huge price increase in the recent years. The export quantities depicted in Figure 1.8 show that machinery and equipment had been the fastest growing in export quantity component. Automotive products and industrial goods were also impressive in terms of growth. The other sectors had been rather slow in growth or stagnant through out the sample period. As can be seen in Figure 1.9, the most rapid growing value of imports was machinery and equipment but the growth leveled off during the last ten years. Imports of industrial goods and materials, services imports and auto- motive imports all grew at similarly moderate rate, while imports of other consumer goods, energy products and agricultural products all experienced little growth only. As energy prices are determined internationally, the price of energy imports grew most as in the case of exports. Prices of other im- ports as shown in Figure 1.10 show they grew much slower and at similar 54 Chapter 1. Productivity Performance of Canada rate. For import quantities (shown in Figure 1.11), machinery and equip- ment grew the fastest, this reflects Statistics Canada had quality adjusted the prices of information and computer technological devices. The rest of the import sectors seemed to be growing only moderately and at similar rate in quantity. Comparing Figures 1.7 and 1.10, it can be seen that the export prices increase more rapidly than the import prices, and this leads to the improvement in Canadian terms of trade and in living standards. Figure 1.6: Canadian Export Values 1961-2007 0 20000 40000 60000 80000 100000 120000 1 9 6 1 1 9 6 3 1 9 6 5 1 9 6 7 1 9 6 9 1 9 7 1 1 9 7 3 1 9 7 5 1 9 7 7 1 9 7 9 1 9 8 1 1 9 8 3 1 9 8 5 1 9 8 7 1 9 8 9 1 9 9 1 1 9 9 3 1 9 9 5 1 9 9 7 1 9 9 9 2 0 0 1 2 0 0 3 2 0 0 5 2 0 0 7 Year M il li o n s  o f d o ll a rs VX1 VX2 VX3 VX4 VX5 VX6 VX7 VX8 55 Chapter 1. Productivity Performance of Canada Figure 1.7: Canadian Export Prices 1961-2007 0 5 10 15 20 25 1 9 6 1 1 9 6 3 1 9 6 5 1 9 6 7 1 9 6 9 1 9 7 1 1 9 7 3 1 9 7 5 1 9 7 7 1 9 7 9 1 9 8 1 1 9 8 3 1 9 8 5 1 9 8 7 1 9 8 9 1 9 9 1 1 9 9 3 1 9 9 5 1 9 9 7 1 9 9 9 2 0 0 1 2 0 0 3 2 0 0 5 2 0 0 7 Year PX1 PX2 PX3 PX4 PX5 PX6 PX7 PX8 56 Chapter 1. Productivity Performance of Canada Figure 1.8: Canadian Export Quantities 1961-2007 0 5000 10000 15000 20000 25000 30000 35000 40000 1 9 6 1 1 9 6 3 1 9 6 5 1 9 6 7 1 9 6 9 1 9 7 1 1 9 7 3 1 9 7 5 1 9 7 7 1 9 7 9 1 9 8 1 1 9 8 3 1 9 8 5 1 9 8 7 1 9 8 9 1 9 9 1 1 9 9 3 1 9 9 5 1 9 9 7 1 9 9 9 2 0 0 1 2 0 0 3 2 0 0 5 2 0 0 7 Year M il li o n s  o f 1 9 6 1  d o ll a rs QX1 QX2 QX3 QX4 QX5 QX6 QX7 QX8 57 Chapter 1. Productivity Performance of Canada Figure 1.9: Canadian Import Values 1961-2007 0 20000 40000 60000 80000 100000 120000 140000 1 9 6 1 1 9 6 3 1 9 6 5 1 9 6 7 1 9 6 9 1 9 7 1 1 9 7 3 1 9 7 5 1 9 7 7 1 9 7 9 1 9 8 1 1 9 8 3 1 9 8 5 1 9 8 7 1 9 8 9 1 9 9 1 1 9 9 3 1 9 9 5 1 9 9 7 1 9 9 9 2 0 0 1 2 0 0 3 2 0 0 5 2 0 0 7 Year M il li o n  o f d o ll a rs VM1 VM2 VM3 VM4 VM5 VM6 VM7 58 Chapter 1. Productivity Performance of Canada Figure 1.10: Canadian Import Prices 1961-2007 0 5 10 15 20 25 30 35 1 9 6 1 1 9 6 3 1 9 6 5 1 9 6 7 1 9 6 9 1 9 7 1 1 9 7 3 1 9 7 5 1 9 7 7 1 9 7 9 1 9 8 1 1 9 8 3 1 9 8 5 1 9 8 7 1 9 8 9 1 9 9 1 1 9 9 3 1 9 9 5 1 9 9 7 1 9 9 9 2 0 0 1 2 0 0 3 2 0 0 5 2 0 0 7 Year VP1 VP2 VP3 VP4 VP5 VP6 VP7 59 Chapter 1. Productivity Performance of Canada Figure 1.11: Canadian Import Quantities 1961-2007 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 1 9 6 1 1 9 6 3 1 9 6 5 1 9 6 7 1 9 6 9 1 9 7 1 1 9 7 3 1 9 7 5 1 9 7 7 1 9 7 9 1 9 8 1 1 9 8 3 1 9 8 5 1 9 8 7 1 9 8 9 1 9 9 1 1 9 9 3 1 9 9 5 1 9 9 7 1 9 9 9 2 0 0 1 2 0 0 3 2 0 0 5 2 0 0 7 Year M il li o n s  o f 1 9 6 1  d o ll a rs VQ1 VQ2 VQ3 VQ4 VQ5 VQ6 VQ7 60 Chapter 1. Productivity Performance of Canada The methodology explained in Section 1.8 can be used to work out the contribution of each change in the real export price for our eight classes of exports to the business sector real income growth. Table 1.13 can be viewed as a decomposition of the aggregate export contribution factor αtX which appeared in Table 1.4 of the previous section into eight commodity specific factors, αtX1 to α t X8, which multiply together to yield the overall export contribution factor αtX . αtX = α t X1α t X2α t X3α t X4α t X5α t X6α t X7α t X8 (1.7) The arithmetic averages of the contribution factors for the years 1962-2007 are listed in the last row of Table 1.13. The average contribution factors for the eight classes of exports are as follows. The increases in real energy products export prices had contributed an average of 0.16 percentage points to real income growth. Real export price increases in materials, services and forest products had contributed on average 0.04, 0.03 and 0.01 percent- age points respectively. The big negative contributors were machinery and equipment and autos which by their increases in export prices contributed −0.14 and −0.11 percentage points on average. Both agricultural products and other consumer goods had minor negative contributions (−0.02 and −0.006 percentage points). Overall the cumulative effects of real export price changes were not large. 61 Chapter 1. Productivity Performance of Canada Table 1.13: Year to Year Export Contribution Factors Using the Gross Output Approach Year t αtX1 α t X2 α t X3 α t X4 α t X5 α t X6 α t X7 α t X8 1961 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1962 1.00246 0.99979 1.00175 1.00105 1.00047 1.00001 0.99998 1.00050 1963 0.99909 1.00013 0.99984 0.99946 0.99993 1.00000 0.99999 1.00038 1964 1.00024 0.99981 1.00077 1.00085 1.00029 1.00003 1.00005 1.00108 1965 1.00005 1.00009 1.00025 1.00082 1.00027 0.99990 0.99999 1.00110 1966 1.00105 0.99965 0.99910 1.00106 0.99995 0.99962 0.99995 1.00069 1967 0.99912 0.99892 0.99937 0.99955 1.00024 0.99947 0.99995 1.00169 1968 0.99842 1.00004 0.99947 1.00204 1.00080 0.99926 0.99996 1.00108 1969 0.99775 1.00020 1.00063 0.99980 0.99970 0.99862 1.00003 1.00070 1970 0.99799 0.99978 0.99837 1.00243 1.00121 0.99960 0.99985 1.00150 1971 1.00017 1.00058 1.00064 0.99524 0.99947 1.00035 0.99997 1.00133 1972 1.00062 0.99975 1.00186 0.99786 0.99977 0.99863 0.99993 1.00059 1973 1.01170 1.00227 1.00621 1.00512 0.99895 0.99633 0.99997 1.00025 1974 1.01167 1.01381 1.00379 1.00950 0.99948 0.99661 0.99995 0.99960 1975 0.99357 1.00875 1.00085 0.99584 0.99932 0.99734 0.99982 0.99942 1976 0.99550 1.00655 0.99938 1.00068 0.99921 1.00080 1.00007 1.00193 1977 0.99542 1.00491 1.00152 1.00382 0.99996 1.00128 0.99998 1.00067 1978 1.00112 1.00101 1.00138 1.00165 0.99880 1.00162 0.99994 0.99942 1979 1.00390 1.00475 1.00535 1.01165 0.99911 1.00036 0.99984 0.99948 1980 1.00059 1.01020 0.99756 1.01039 0.99739 0.99936 1.00002 0.99968 1981 0.99965 0.99911 0.99821 0.99362 0.99822 1.00063 1.00008 1.00132 1982 0.99470 0.99797 0.99410 0.98862 0.99867 0.99986 0.99987 1.00027 1983 0.99600 0.99596 0.99645 0.99553 0.99710 0.99767 0.99988 1.00007 1984 0.99986 0.99692 1.00309 0.99859 0.99680 1.00148 0.99992 1.00005 1985 0.99878 0.99680 0.99926 0.99713 0.99824 1.00461 1.00007 1.00103 1986 0.99854 0.98521 1.00399 1.00146 1.00474 0.99414 1.00048 1.00147 1987 0.99813 0.99830 1.00334 1.00036 0.99942 0.99806 1.00009 1.00053 Continued on Next Page. . . 62 Chapter 1. Productivity Performance of Canada Table 1.13 – Continued Year t αtX1 α t X2 α t X3 α t X4 α t X5 α t X6 α t X7 α t X8 1988 1.00074 0.99338 1.00021 1.00308 0.99894 0.99445 1.00004 0.99985 1989 1.00108 1.00160 1.00074 0.99741 0.99889 0.99644 1.00017 1.00036 1990 0.99633 1.00251 0.99411 0.99146 0.99753 0.99582 0.99965 0.99836 1991 0.99523 0.99360 0.99252 0.99124 0.99535 0.99815 0.99975 0.99890 1992 1.00301 1.00080 1.00079 0.99933 0.99883 1.00391 0.99988 0.99959 1993 1.00162 1.00137 1.00417 0.99950 0.99939 1.00426 0.99997 1.00061 1994 1.00218 0.99856 1.00769 1.00981 1.00161 1.00497 1.00029 1.00116 1995 1.00412 0.99903 1.01136 1.01013 1.00106 1.00404 1.00031 1.00199 1996 1.00197 1.00840 0.99328 0.99105 0.99645 1.00045 0.99995 1.00012 1997 0.99693 1.00055 0.99879 0.99775 0.99595 1.00104 0.99984 1.00081 1998 0.99868 0.99053 1.00139 0.99571 0.99862 1.00535 1.00003 1.00032 1999 0.99868 1.00929 0.99979 0.99644 0.99571 0.99687 0.99991 0.99985 2000 0.99949 1.02921 0.99874 1.00405 0.99534 0.99595 0.99967 1.00076 2001 1.00108 0.99990 0.99941 0.99601 0.99679 1.00079 0.99974 0.99778 2002 0.99956 0.98790 0.99586 0.99798 0.99896 0.99959 0.99985 1.00029 2003 0.99818 1.01374 0.99544 0.99746 0.99209 0.98638 0.99949 0.99862 2004 0.99897 1.00663 1.00271 1.00759 0.99623 0.99343 0.99976 1.00050 2005 0.99670 1.01989 0.99665 1.00302 0.99619 0.99198 0.99970 1.00026 2006 0.99901 0.99604 0.99714 1.00937 0.99629 0.99433 0.99978 0.99976 2007 1.00169 0.99898 0.99747 1.00571 0.99727 0.99492 0.99971 1.00013 Average 0.99981 1.00160 1.00010 1.00040 0.99859 0.99889 0.99994 1.00030 63 Chapter 1. Productivity Performance of Canada As in the case of export prices, the import price cumulative contribution factor, αtM from Table 1.4 can be decomposed as a multiplicative contribu- tion factors of the seven sectors as follows, αtM = α t M1α t M2α t M3α t M4α t M5α t M6α t M7 (1.8) Table 1.14 lists the decomposition of the aggregate import contribution fac- tor from 1961 to 2007 constructed using the gross output approach. We calculate the arithmetic averages of these series to find the individual con- tribution factor of each import sector over the sample period. The biggest contribution was by the lower machinery and equipment real import prices which contributed 0.42 percentage points to the real income growth in the business sector. The lower real import prices in autos, other consumer goods, material and forest products and agricultural products also provided small contributions to the real income growth (0.05, 0.05, 0.04 and 0.02 percent- age points respectively). However, the higher real energy products import prices had a negative contribution of −0.11 percentage points. Real services import prices also had −0.05 percentage points contribution. Overall, the cumulative effects of real import price changes using the gross output ap- proach were rather large but most of the effects can be explained by the large contribution of lower machinery and equipment real import prices. 64 Chapter 1. Productivity Performance of Canada Table 1.14: Year to Year Import Contribution Factors Using the Gross Output Approach Year t αtM1 α t M2 α t M3 α t M4 α t M5 α t M6 α t M7 1961 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1962 0.99874 0.99961 0.99670 0.99415 0.99894 0.99981 0.99754 1963 0.99376 1.00056 0.99909 1.00100 0.99996 1.00035 0.99948 1964 1.00066 1.00014 0.99901 1.00027 0.99953 0.99988 0.99934 1965 1.00535 0.99987 0.99962 0.99936 1.00083 1.00036 0.99889 1966 1.00137 1.00013 1.00229 1.00074 1.00077 1.00055 1.00035 1967 1.00143 1.00134 1.00032 1.00008 1.00020 1.00037 0.99926 1968 1.00014 0.99971 1.00310 1.00207 1.00021 1.00061 0.99935 1969 1.00060 1.00103 1.00046 1.00118 1.00054 1.00038 0.99839 1970 0.99914 1.00024 1.00083 1.00175 1.00102 1.00052 0.99903 1971 0.99983 0.99895 1.00293 0.99961 0.99933 1.00039 0.99839 1972 0.99925 0.99947 1.00294 1.00253 1.00108 1.00014 1.00075 1973 0.99638 0.99828 0.99795 1.00345 1.00322 1.00104 1.00042 1974 0.99773 0.97757 0.99099 1.00353 1.00350 1.00143 1.00348 1975 1.00262 0.99610 1.00285 0.99800 0.99926 1.00095 1.00098 1976 1.00315 1.00033 1.00209 1.00360 0.99988 0.99990 1.00093 1977 0.99634 0.99794 0.99672 0.99895 0.99575 0.99803 0.99541 1978 0.99914 0.99912 0.99549 1.00532 0.99538 0.99812 0.99583 1979 0.99941 0.99529 0.99284 1.00335 0.99939 0.99986 0.99835 1980 1.00068 0.98932 0.99713 1.02330 1.00048 0.99939 1.00024 1981 1.00000 0.99625 1.00065 1.01201 0.99413 0.99851 0.99842 1982 1.00303 1.00359 1.00474 1.00039 1.00076 1.00142 1.00102 1983 1.00245 1.00362 1.00491 1.01029 1.00281 1.00233 1.00131 1984 0.99957 1.00058 1.00070 1.00194 0.99914 0.99895 0.99815 1985 1.00136 0.99998 1.00327 1.00153 0.99795 0.99986 0.99737 1986 0.99894 1.00798 0.99979 1.00109 0.99793 0.99820 0.99758 1987 1.00113 0.99970 1.00175 1.00762 1.00328 1.00074 1.00166 Continued on Next Page. . . 65 Chapter 1. Productivity Performance of Canada Table 1.14 – Continued Year t αtM1 α t M2 α t M3 α t M4 α t M5 α t M6 α t M7 1988 1.00021 1.00303 0.99992 1.00726 1.00483 1.00124 1.00421 1989 1.00090 0.99950 1.00203 1.00592 1.00120 1.00092 1.00190 1990 1.00120 0.99742 1.00494 1.00733 1.00273 1.00159 1.00189 1991 1.00138 1.00371 1.00632 1.00840 1.00454 1.00210 1.00332 1992 1.00034 1.00025 0.99958 0.99776 0.99624 0.99815 0.99616 1993 1.00038 1.00079 0.99927 0.99694 0.99632 0.99799 0.99302 1994 0.99816 1.00010 0.99494 0.99505 0.99449 0.99722 0.99344 1995 0.99853 0.99957 0.99249 1.00373 0.99720 0.99875 0.99740 1996 1.00087 0.99777 1.00560 1.01056 1.00119 1.00137 1.00040 1997 0.99962 1.00043 1.00162 1.00582 1.00034 1.00057 0.99819 1998 1.00056 1.00344 0.99860 0.99798 0.99625 0.99712 0.99442 1999 1.00139 0.99781 1.00394 1.00745 1.00194 1.00104 0.99956 2000 1.00077 0.99235 0.99897 1.00809 1.00286 1.00123 0.99998 2001 0.99976 1.00165 0.99912 1.00127 1.00032 0.99895 0.99762 2002 0.99993 0.99961 1.00220 1.00182 1.00012 1.00052 0.99902 2003 1.00174 0.99824 1.00786 1.01891 1.00875 1.00741 1.00725 2004 1.00109 0.99661 0.99805 1.01224 1.00458 1.00520 1.00304 2005 1.00114 0.99293 1.00044 1.01076 1.00552 1.00355 1.00289 2006 1.00116 0.99622 0.99800 1.00870 1.00420 1.00347 1.00111 2007 0.99972 0.99996 1.00341 1.00795 1.00516 1.00359 1.00190 Average 1.00020 0.99887 1.00040 1.00420 1.00050 1.00050 0.99954 66 Chapter 1. Productivity Performance of Canada The decomposition of the aggregate export contribution factor αtX in Ta- ble 1.9 (net output approach) is listed in Table 1.15. The increases in real energy products export prices had contributed an average of 0.18 percent- age points to real income growth. Real export price increases in materials, services and forest products had contributed 0.04, 0.04 and 0.01 percent- age points respectively to the growth. Machinery and equipment and autos both contributed negatively, −0.17 and −0.13 percentage points, to the real income growth. Agricultural products and other consumer goods had minor negative contributions (−0.02 and −0.007 percentage points). Again, over- all the cumulative effects of real export price changes, αtX , were not large, but it can be seen that the net output approach has magnified the results obtained from the gross output approach. 67 Chapter 1. Productivity Performance of Canada Table 1.15: Year to Year Export Contribution Factors Using the Net Output Approach Year t αtX1 α t X2 α t X3 α t X4 α t X5 α t X6 α t X7 α t X8 1961 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1962 1.00279 0.99976 1.00198 1.00119 1.00053 1.00001 0.99998 1.00056 1963 0.99897 1.00014 0.99982 0.99939 0.99992 1.00000 0.99998 1.00043 1964 1.00027 0.99979 1.00087 1.00096 1.00032 1.00003 1.00005 1.00122 1965 1.00006 1.00010 1.00028 1.00093 1.00031 0.99989 0.99998 1.00124 1966 1.00119 0.99960 0.99899 1.00120 0.99994 0.99957 0.99994 1.00078 1967 0.99900 0.99878 0.99929 0.99949 1.00028 0.99940 0.99994 1.00191 1968 0.99820 1.00005 0.99939 1.00233 1.00091 0.99916 0.99995 1.00123 1969 0.99744 1.00023 1.00072 0.99977 0.99966 0.99843 1.00003 1.00080 1970 0.99770 0.99975 0.99814 1.00278 1.00139 0.99954 0.99983 1.00172 1971 1.00020 1.00067 1.00074 0.99453 0.99939 1.00040 0.99996 1.00153 1972 1.00072 0.99971 1.00214 0.99755 0.99974 0.99842 0.99993 1.00068 1973 1.01333 1.00258 1.00708 1.00584 0.99881 0.99581 0.99997 1.00029 1974 1.01322 1.01566 1.00429 1.01077 0.99941 0.99617 0.99994 0.99954 1975 0.99265 1.01001 1.00097 0.99525 0.99922 0.99696 0.99979 0.99934 1976 0.99481 1.00755 0.99928 1.00078 0.99909 1.00093 1.00008 1.00222 1977 0.99473 1.00566 1.00175 1.00440 0.99995 1.00148 0.99998 1.00077 1978 1.00129 1.00116 1.00160 1.00190 0.99862 1.00187 0.99993 0.99933 1979 1.00450 1.00548 1.00617 1.01346 0.99898 1.00042 0.99981 0.99940 1980 1.00069 1.01179 0.99718 1.01202 0.99699 0.99926 1.00003 0.99963 1981 0.99959 0.99896 0.99792 0.99258 0.99793 1.00073 1.00009 1.00154 1982 0.99373 0.99760 0.99302 0.98655 0.99842 0.99984 0.99985 1.00032 1983 0.99523 0.99518 0.99578 0.99467 0.99654 0.99722 0.99985 1.00008 1984 0.99984 0.99636 1.00365 0.99833 0.99623 1.00174 0.99990 1.00005 1985 0.99857 0.99624 0.99913 0.99663 0.99793 1.00542 1.00008 1.00121 1986 0.99829 0.98267 1.00468 1.00171 1.00557 0.99313 1.00056 1.00172 1987 0.99782 0.99802 1.00391 1.00042 0.99932 0.99774 1.00010 1.00062 Continued on Next Page. . . 68 Chapter 1. Productivity Performance of Canada Table 1.15 – Continued Year t αtX1 α t X2 α t X3 α t X4 α t X5 α t X6 α t X7 α t X8 1988 1.00086 0.99231 1.00024 1.00358 0.99877 0.99355 1.00005 0.99983 1989 1.00126 1.00187 1.00086 0.99698 0.99871 0.99586 1.00020 1.00041 1990 0.99568 1.00295 0.99309 0.98997 0.99710 0.99509 0.99959 0.99808 1991 0.99434 0.99241 0.99113 0.98961 0.99449 0.99781 0.99971 0.99869 1992 1.00359 1.00095 1.00094 0.99920 0.99860 1.00466 0.99986 0.99951 1993 1.00193 1.00163 1.00497 0.99940 0.99927 1.00509 0.99996 1.00073 1994 1.00260 0.99828 1.00917 1.01170 1.00192 1.00593 1.00035 1.00138 1995 1.00489 0.99885 1.01349 1.01202 1.00125 1.00479 1.00037 1.00236 1996 1.00232 1.00993 0.99206 0.98943 0.99581 1.00054 0.99994 1.00015 1997 0.99638 1.00064 0.99857 0.99735 0.99522 1.00123 0.99981 1.00095 1998 0.99844 0.98881 1.00164 0.99493 0.99837 1.00633 1.00003 1.00038 1999 0.99843 1.01101 0.99976 0.99579 0.99493 0.99629 0.99989 0.99983 2000 0.99940 1.03446 0.99851 1.00477 0.99451 0.99523 0.99961 1.00090 2001 1.00128 0.99988 0.99931 0.99531 0.99622 1.00093 0.99970 0.99738 2002 0.99948 0.98571 0.99511 0.99761 0.99878 0.99952 0.99982 1.00034 2003 0.99785 1.01620 0.99463 0.99701 0.99068 0.98397 0.99940 0.99837 2004 0.99880 1.00776 1.00317 1.00888 0.99559 0.99231 0.99972 1.00058 2005 0.99616 1.02318 0.99610 1.00351 0.99557 0.99067 0.99965 1.00030 2006 0.99885 0.99539 0.99668 1.01090 0.99568 0.99340 0.99974 0.99972 2007 1.00197 0.99881 0.99706 1.00665 0.99682 0.99409 0.99967 1.00015 Average 0.99977 1.00180 1.00010 1.00040 0.99834 0.99871 0.99993 1.00040 69 Chapter 1. Productivity Performance of Canada The decomposition of the aggregate import contribution factor αtM in Ta- ble 1.9 is shown in Table 1.16. The lower machinery and equipment real import prices contributed 0.49 percentage points to the real income growth. The lower real import prices in autos, other consumer goods, material and forest products and agricultural products contributed minor to the real in- come growth (0.06, 0.06, 0.05 and 0.03 percentage points respectively). The higher real energy products import prices had a −0.13 percentage points contribution whereas the higher real services import prices had a −0.06 per- centage points contribution. Overall, the cumulative effects of real import price changes, αtM using the net output approach were quite large (0.51 per- centage points) but again mostly can be explained by the large contribution of lower machinery and equipment prices. As in the case of export prices, the net output approach has magnified the results of the gross output approach. 70 Chapter 1. Productivity Performance of Canada Table 1.16: Year to Year Import Contribution Factors Using the Net Output Approach Year t αtM1 α t M2 α t M3 α t M4 α t M5 α t M6 α t M7 1961 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1962 0.99858 0.99956 0.99626 0.99337 0.99879 0.99978 0.99722 1963 0.99295 1.00063 0.99897 1.00113 0.99996 1.00040 0.99941 1964 1.00075 1.00016 0.99888 1.00030 0.99947 0.99986 0.99925 1965 1.00604 0.99986 0.99958 0.99928 1.00094 1.00040 0.99875 1966 1.00154 1.00014 1.00259 1.00083 1.00087 1.00062 1.00039 1967 1.00162 1.00152 1.00036 1.00009 1.00023 1.00042 0.99916 1968 1.00016 0.99967 1.00353 1.00236 1.00024 1.00069 0.99926 1969 1.00068 1.00118 1.00053 1.00135 1.00061 1.00043 0.99817 1970 0.99902 1.00027 1.00095 1.00200 1.00116 1.00060 0.99889 1971 0.99980 0.99880 1.00337 0.99956 0.99923 1.00045 0.99815 1972 0.99913 0.99939 1.00338 1.00291 1.00124 1.00016 1.00086 1973 0.99587 0.99804 0.99767 1.00393 1.00367 1.00119 1.00048 1974 0.99743 0.97463 0.98980 1.00400 1.00397 1.00162 1.00394 1975 1.00300 0.99554 1.00325 0.99771 0.99916 1.00109 1.00112 1976 1.00363 1.00038 1.00241 1.00414 0.99987 0.99988 1.00108 1977 0.99578 0.99763 0.99622 0.99880 0.99511 0.99773 0.99472 1978 0.99900 0.99898 0.99479 1.00614 0.99467 0.99783 0.99519 1979 0.99932 0.99457 0.99174 1.00386 0.99929 0.99983 0.99810 1980 1.00078 0.98766 0.99669 1.02697 1.00055 0.99930 1.00028 1981 1.00000 0.99563 1.00075 1.01400 0.99317 0.99826 0.99816 1982 1.00359 1.00424 1.00560 1.00046 1.00090 1.00169 1.00121 1983 1.00292 1.00432 1.00586 1.01228 1.00334 1.00278 1.00156 1984 0.99950 1.00068 1.00083 1.00230 0.99899 0.99876 0.99782 1985 1.00159 0.99997 1.00384 1.00180 0.99760 0.99984 0.99691 1986 0.99876 1.00937 0.99975 1.00128 0.99757 0.99789 0.99716 1987 1.00132 0.99965 1.00205 1.00892 1.00383 1.00087 1.00194 Continued on Next Page. . . 71 Chapter 1. Productivity Performance of Canada Table 1.16 – Continued Year t αtM1 α t M2 α t M3 α t M4 α t M5 α t M6 α t M7 1988 1.00024 1.00353 0.99990 1.00844 1.00562 1.00144 1.00490 1989 1.00104 0.99942 1.00236 1.00690 1.00140 1.00107 1.00222 1990 1.00141 0.99697 1.00581 1.00862 1.00320 1.00187 1.00222 1991 1.00163 1.00441 1.00750 1.00998 1.00539 1.00249 1.00394 1992 1.00041 1.00030 0.99949 0.99733 0.99553 0.99780 0.99542 1993 1.00045 1.00094 0.99913 0.99635 0.99561 0.99761 0.99168 1994 0.99780 1.00012 0.99398 0.99410 0.99343 0.99668 0.99219 1995 0.99826 0.99949 0.99110 1.00443 0.99668 0.99852 0.99691 1996 1.00103 0.99736 1.00662 1.01249 1.00140 1.00162 1.00048 1997 0.99955 1.00051 1.00191 1.00686 1.00040 1.00068 0.99787 1998 1.00067 1.00407 0.99834 0.99761 0.99557 0.99660 0.99341 1999 1.00165 0.99741 1.00466 1.00883 1.00229 1.00124 0.99948 2000 1.00091 0.99101 0.99879 1.00954 1.00338 1.00145 0.99997 2001 0.99972 1.00195 0.99896 1.00149 1.00038 0.99876 0.99719 2002 0.99992 0.99954 1.00260 1.00215 1.00014 1.00062 0.99884 2003 1.00205 0.99792 1.00927 1.02232 1.01032 1.00874 1.00854 2004 1.00128 0.99604 0.99772 1.01434 1.00536 1.00609 1.00356 2005 1.00133 0.99177 1.00051 1.01253 1.00643 1.00413 1.00336 2006 1.00135 0.99560 0.99768 1.01012 1.00489 1.00403 1.00129 2007 0.99968 0.99995 1.00397 1.00927 1.00600 1.00418 1.00221 Average 1.00030 0.99871 1.00040 1.00490 1.00060 1.00060 0.99945 72 Chapter 1. Productivity Performance of Canada The detailed breakdown of the average contributions by changes in export and import sectoral prices shows that the real income growth generated by the business sector has benefited from lower machinery and equipment im- port prices. The negative effects of higher real import prices in energy and services on real income growth were offset by the large positive contribution by machinery and equipment. Other real import prices had only minor con- tributions. Although the cumulative effects of the real export price changes had been quite small, the cumulative effects of the real import price changes had been large and so the overall improvement in terms of trade 1961-2007 was relatively large. Note that the results obtained using the net output ap- proach were slightly bigger than the results obtained using the gross output approach. 1.7 Conclusion Statistics Canada has substantially revised their published KLEMS database and we use these revised data in our analysis. We have included data from 2007 and revised our estimations for other years. Furthermore, Statistics Canada made available to the authors some unpublished data from their KLEMS database on land, inventories and ICT capital which improved our earlier estimates and narrowed the differences of our estimates of TFP growth in Canada and the official Statistics Canada estimates. By incorpo- rating these data, the precision of our analytical results was highly enhanced. We also provide a more detailed breakdown of exports and imports in the present paper so that the effects of changes in real export and import prices by commodity category on real income can be determined. There are six major conclusions that we can draw from the results. First, using new detailed data, we have shown that the productivity per- formance of the business sector of the Canadian economy has been reason- ably satisfactory over the past 47 years. In particular, traditional gross income TFP growth averaged 1.01 percent per year over the period 1962- 73 Chapter 1. Productivity Performance of Canada 200724 and when the net output framework was used, TFP growth averaged 1.04 percent per year. However, there was a long period (1974-1991) where the productivity performance of the Canadian business sector was decidedly unsatisfactory. We also compared Canada’s productivity performance with those of Australia and Japan. The three countries had very similar overall average real income growth. However, the estimated Canadian TFP growth rate is relatively lower than Australia and much lower than Japan. Thus the overall welfare in Canada is comparatively good on an international level, but there is still need to encourage productivity improvement. Second, we have shown that the role of explanatory factors for growth in the real income generated by the business sector of the Canadian econ- omy changes substantially when we shift from the standard gross product growth accounting framework to a theoretically more appropriate net prod- uct growth accounting framework. In general, the main positive drivers of real income growth (growth in labour input, TFP growth and declining real import prices) are magnified but the effects of capital services input growth are greatly diminished when we switch to the net output framework as com- pared to the gross output framework.25 An important implication of this result is that improvements in TFP probably become the most important factor for explaining improvements in per capita living standards in the long run and the favourable effects of capital deepening are not as big as they appear to be in the traditional gross income growth accounting methodology. Third, we have shown that the “top down” approach performs well when estimating the productivity functions using the final demand deliveries. Thus, the large difference between the estimates from this approach and the official KLEMS estimates using the “bottom up” approach indicates there is a need to review the calculation of the official estimates. More 24The corresponding Statistics Canada average Multifactor Productivity growth rate over 1962-2006 was only 0.43 percent per year. 25Diewert, Mizobuchi and Nomura (2005) and Diewert and Lawrence (2006) found sim- ilar results for Japan and Australia using a similar net output framework. 74 Chapter 1. Productivity Performance of Canada importantly, this unveils the possibility that the wide ”productivity gap” between Canada and the U.S. may not have been as severe as portrayed. Fourth, the results presented here show that over short periods of time, changes in the external price environment facing an economy can have sub- stantial effects on living standards. Thus during the years of the present decade, the real net income generated by the Canadian business sector grew at an average rate of 4.07 percent per year and declines in real import prices (the China effect) contributed 1.91 percentage points to this increase, which was greater than the effects of quality adjusted labour input growth (1.64 percentage points per year), increases in waiting services (0.53 percentage points per year).26 Fifth, in the decomposition of year to year real income growth, we found that changes in export and import prices can have substantial effects on real income growth. By applying detailed trade statistics, we constructed export and import price indexes for the 15 commodity classes to calculate their individual contribution to the real income growth. We found that the increases in real energy products export prices and the lower real import prices of machinery and equipment (except auto) had contributed most to real income growth. The lower export prices in machinery and equipment and autos, and higher real energy products import prices contributed neg- atively to the real income growth. Overall, the cumulative effects of real import price changes were much larger than the cumulative effects of real export price changes. Finally, the study uncovered many data problems which should be ad- dressed in future work on Canadian productivity performance. A discussion of the data problems is presented in Chapter 2. More generally, it is evident that statistical agencies are able to provide reasonably accurate data on the prices and quantities of the outputs produced and intermediate inputs used 26The Canadian experience with improvement in the terms of trade during the past decade is similar to the Australian experience; see Diewert and Lawrence (2006). 75 Chapter 1. Productivity Performance of Canada by the various industries in the economy. This is in large part due to the fact that the System of National Accounts 1993 used by most statistical agencies has developed an adequate methodology for the treatment of gross outputs and intermediate inputs. However, the corresponding methodology for the treatment of primary inputs was not well developed.27 In particular, the treatment of capital services was absent the System of National Accounts 1993 and will only be introduced in the next international version of the Sys- tem of National Accounts. This absence of a standard methodology for the treatment of capital services means that national statistical agencies have not been able to deliver a generally accepted treatment of capital services in their productivity accounts. Thus detailed data on capital stocks and flows by industry is either not available from national statistical agencies or is not provided due to the lack of information on capital inputs. Given the importance of accurate information on productivity growth, it is im- portant that international agencies provide guidance on acceptable methods for measuring primary input prices and volumes and that national statisti- cal agencies provide more details on how they construct their estimates of primary inputs in their productivity accounts. National departments that have an interest in better productivity measurement (e.g., central banks, department of finance and industry departments) should support initiatives that will improve the measurement of primary input growth. 1.8 Explaining Real Income Growth with The Translog Approach 1.8.1 Introduction This section will present in details the theoretical frameworks that are used in the main text. Subsection 1.8.2 looks at the production theory framework that is mainly drawn from Diewert and Morrison (1986). Sub- 27The System of National Accounts 1993 (SNA) has a good chapter on wage indexes but does not provide a standard methodology for the treatment of self-employment labour input. The recent preliminary manual on the measurement of capital by Schreyer (2007) fills in an important methodological gap in the existing SNA. 76 Chapter 1. Productivity Performance of Canada section 1.8.3 explains the Translog GDP function approach. Subsection 1.8.4 shows how to decompose aggregate contribution factor due to changes in all market sector primary inputs into separate effects. Then in Subsection 1.8.5, we explain the deflated NDP Translog approach. Finally, Subsection 1.8.6 introduces how sectoral contributions to real income growth are calculated. 1.8.2 The Production Theory Framework In this subsection, we present the production theory framework which will be used in the main text of the paper.28 The main reference is Diewert and Morrison (1986)29 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 behaviour 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 behaviour. 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.30 28With the exception of the last subsection of this section, the material is drawn from Diewert (2005b), Diewert, Mizobuchi and Nomura (2005) and Diewert and Lawrence (2006). 29The theory also draws on Samuelson (1953), Diewert (1974; 133-141)(1980)(1983;1077- 1100), Fox and Kohli (1998), Kohli (1978)(1990)(1991)(2003)(2004a)(2004b)(2006)(2008), Morrison and Diewert (1990), Samuelson (1953) and Sato (1976). 30The 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. 77 Chapter 1. Productivity Performance of Canada Initially, we assume that the market sector of the economy produces quan- tities of M (net) outputs31, y ≡ [y1, . . . , yM ], which are sold at the positive producer prices P ≡ [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 utilised by the market sector of the economy; denote this period t produc- tion possibilities set by St. We assume that St is a closed convex cone that exhibits a free disposal property.32 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,33 gt(P, x) ≡ max y {P · y : (y, x) belongs to St}; t = 0, 1, 2 . . . (1.9) Thus market sector GDP depends on t (which represents the period t tech- nology set St), on the vector of output prices P that the market sector faces 31If 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 “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. 32For more explanation for the meaning of these properties, see Diewert (1973)(1974; 134) or Woodland(1982) or Kohli (1978)(1991). The assumption that St is a cone means that the technology is subject to constant returns to scale. This is an important as- sumption 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 inter- national trade literature (see Kohli (1978)(1991), Woodland (1982) and Feenstra (2004; 76)). It was introduced into the economics literature by Samuelson (1953). Alternative terms for this function include: (i) the gross profit function; see Gorman (1968); (ii) the restricted profit function; see Lau (1976) and McFadden(1978); and (iii) the variable profit function; see Diewert (1973)(1974). 33The 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 (1973)(1974; 136). Notation: P · y ≡∑Mm=1 Pmym. 78 Chapter 1. Productivity Performance of Canada and on x, the vector of primary inputs that is available to the market sector. If P t 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 (P t, xt), then the period t vector of market sector outputs yt will be equal to the vector of first order partial derivatives of gt(P t, xt) with respect to the components of P ; i.e., we will have the following equations for each period t:34 yt = ∇P gt(P t, xt); t = 0, 1, 2, . . . (1.10) Thus the period t market sector supply vector yt can be obtained by dif- ferentiating the period t market sector GDP function with respect to the components of the period t output price vector P t. If the GDP function is differentiable with respect to the components of x at the point (P t, xt), then the period t vector of input prices W t will be equal to the vector of first order partial derivatives of gt(P t, xt) with respect to the components of x; i.e., we will have the following equations for each period t:35 W t = ∇xgt(P t, xt); t = 0, 1, 2, . . . (1.11) Thus the period t market sector input prices W t 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: 34These relationships are due to Hotelling (1932; 594). Note that ∇P gt(P t, xt) ≡[ ∂gt(P t,xt) ∂P1 , ..., ∂g t(P t,xt) ∂PM ] . 35These relationships are due to Samuelson (1953) and Diewert (1974; 140). Note that ∇xgt(P t, xt) ≡ [ ∂gt(P t,xt) ∂x1 , ..., ∂g t(P t,xt) ∂xN ] . 79 Chapter 1. Productivity Performance of Canada gt(P t, xt) = P t · yt = W t · xt; t = 0, 1, 2, . . . (1.12) 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 Equation (1.12), we have gt(P t, xt) = P t · yt = W t · xt. As an approximate welfare measure that can be associated with market sector production,36 we will choose to measure the real income generated by the market sector in period t, rt, in terms of the number of consumption bundles that the nominal income could purchase in period t; i.e., define ρt as follows, ρt ≡ W t · xt P tC t = 0, 1, 2, . . . = wt · xt = pt · yt = gt(pt, xt) (1.13) where P tC > 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 con- sumption expenditures price index; i.e., we have the following definitions:37 36Since some of the primary inputs used by the market sector can be owned by for- eigners, 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. 37Our approach is similar to the approach advocated by Kohli (2004b; 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 80 Chapter 1. Productivity Performance of Canada pt ≡ P t P tC ; wt ≡ W t P tC ; t = 0, 1, 2, . . . (1.14) The first and last equality in (1.13) 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(P t, xt). Thus the growth in real income over time can be explained by three main factors: τ (Technical Progress or TFP 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 (1.10) and (1.11) hold using the deflated prices p and w:38 yt = ∇pgt(pt, xt); t = 0, 1, 2, . . . (1.15) wt = ∇xgt(pt, xt); t = 0, 1, 2, . . . (1.16) Now we are ready to define a family of period t productivity growth factors or technical progress shift factors τ(p, x, t):39 τ(p, x, t) ≡ g t(p, x) gt−1(p, x) ; t = 1, 2, . . . (1.17) Thus τ(p, x, t) measures the proportional change in the real income pro- duced by the market sector at the reference real output prices p and reference sector GDP, whereas Kohli deflates all of GDP (probably due to data limitations). Our treatment of the balance of trade surplus or deficit is also different. 38If 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). 39This measure of technical progress is due to Diewert and Morrison(1986; 662). A special case of it was defined earlier by Diewert (1983; 1063). 81 Chapter 1. Productivity Performance of Canada input quantities used by the market sector x where the numerator in Equa- tion (1.17) uses the period t technology and the denominator 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. Note that we are using the chain system to measure the shift in technology. It is natural to choose special reference vectors for the measure of techni- cal progress defined by Equation (1.17): a Laspeyres type measure τ tL that chooses the period t− 1 reference vectors pt−1 and xt−1 and a Paasche type measure τ tP that chooses the period t reference vectors p t and xt: τ tL ≡ τ(pt−1, xt−1, t) = gt(pt−1, xt−1) gt−1(pt−1, xt−1) ; t = 1, 2, . . . (1.18) τ tP ≡ τ(pt, xt, t) = gt(pt, xt) gt−1(pt, xt) ; t = 1, 2, . . . (1.19) 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 index number theory40 (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.41 Thus we define the geometric mean of (1.18) and (1.19) as follows,42 τ t ≡ [τ tLτ tP ] 12 t = 1, 2, . . . (1.20) 40See Fisher (1922; 64). 41See 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. 42The theoretical productivity change indexes defined by (1.19)-(1.20) were first defined by Diewert and Morrison (1986; 662-663) in the nominal GDP context. See Diewert (1993) for properties of symmetric means. 82 Chapter 1. Productivity Performance of Canada At this point, it is not clear how we will obtain empirical estimates for the theoretical productivity growth indexes defined by (1.18)-(1.20). One obvi- ous 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 (1.15) and (1.16) and use econometric techniques to estimate the unknown parameters in the assumed functional form. How- ever, econometric techniques are generally not completely straightforward: different econometricians will make different stochastic specifications and will choose different functional forms.43 Moreover, as the number of out- puts and inputs grows, it will be impossible to estimate a flexible functional form. Thus we will suggest methods for implementing measures like (1.20) in this section 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):44 α(pt−1, pt, x, s) ≡ g s(pt, x) gs(pt−1, x) ; s = 1, 2, . . . (1.21) 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. Thus each choice 43“The estimation of GDP functions such as (19) can be controversial, however, since it raises issues such as estimation technique and stochastic specification. ... We therefore prefer to opt for a more straightforward index number approach.” Kohli (2004a; 344). 44This 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), Diew- ert (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 (1.21) is analogous to the Konüs (1924) true cost of living index which is a ratio of cost functions, say C(u,p t) C(u,pt−1) where u is a reference utility level: g s replaces C and the reference utility level u is replaced by the vector of reference variables x. 83 Chapter 1. Productivity Performance of Canada 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 (1.21): a Laspeyres type measure αtL that chooses the period t−1 reference technology and reference input vector xt−1 and a Paasche type measure αtP that chooses the period t reference technology and reference input vector xt: αtL ≡ α(pt−1, pt, xt−1, t−1) = gt−1(pt, xt−1) gt−1(pt−1, xt−1) ; t = 1, 2, . . . (1.22) αtP ≡ α(pt−1, pt, xt, t) = gt(pt, xt) gt(pt−1, xt) ; t = 1, 2, . . . (1.23) 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:45 αt ≡ [αtLαtP ] 12 ; t = 1, 2, . . . (1.24) 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):46 β(xt−1, xt, p, s) ≡ g s(p, xt) gs(p, xt−1) ; s = 1, 2, . . . (1.25) 45The indexes defined by (1.21)-(1.24) were defined by Diewert and Morrison (1986; 664) in the nominal GDP function context. 46This 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). 84 Chapter 1. Productivity Performance of Canada 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 quan- tities 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. Thus each choice of the reference technology s and the ref- erence 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. Again, it is natural to choose special reference vectors for the measures defined by (1.25): a Laspeyres type measure βtL that chooses the period t − 1 reference technology and reference real output price vector pt−1 and a Paasche type measure βtP that chooses the period t reference technology and reference real output price vector pt: βtL ≡ β(xt−1, xt, pt−1, t−1) = gt−1(pt−1, xt) gt−1(pt−1, xt−1) ; t = 1, 2, . . . (1.26) βtP ≡ β(xt−1, xt, pt, t) = gt(pt, xt) gt(pt, xt−1) ; t = 1, 2, . . . (1.27) 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:47 βt ≡ [βtLβtP ] 1 2 t = 1, 2, . . . (1.28) Recall that market sector real income for period t was defined by (1.13) as ρt equal to nominal period t factor payments W t · xt deflated by the household consumption price deflator P tC . It is convenient to define γ t as the period t chain rate of growth factor for real income: 47The theoretical indexes defined by (1.25)-(1.28) were defined in Diewert and Morrison (1986; 665) in the nominal GDP context. 85 Chapter 1. Productivity Performance of Canada γt ≡ ρ t ρt−1 ; t = 1, 2, . . . (1.29) It turns out that the definitions for γt and the technology, output price and input quantity growth factors τ(p, x, t), α(pt−1, pt, x, s), β(xt−1, xt, p, s) defined by (1.17), (1.21) and (1.25) respectively satisfy some interesting identities, which we will now develop. We have: γt ≡ ρ t ρt−1 t = 0, 1, 2, ... = gt(pt, xt) gt−1(pt−1, xt−1) using definitions (1.12) and (1.13) = [ gt(pt, xt) gt−1(pt, xt) ] [ gt−1(pt, xt) gt−1(pt−1, xt) ] [ gt−1(pt−1, xt) gt−1(pt−1, xt−1) ] = τ tPα(p t−1, pt, xt, t− 1)βtL using definitions (1.19), (1.21) and (1.26) (1.30) In a similar fashion, we can establish the following companion identity: γt ≡ τ tLα(pt−1, pt, xt−1, t)βtP ; using definitions (1.18), (1.21) and (1.27) (1.31) Thus multiplying (1.30) and (1.31) together and taking positive square roots of both sides of the resulting identity and using definitions (1.20) and (1.28), we obtain the following identity: γt ≡ τ t[α(pt−1, pt, xt, t− 1)α(pt−1, pt, xt−1, t)] 12βt; t = 1, 2, . . . (1.32) 86 Chapter 1. Productivity Performance of Canada We can derive the following alternative decomposition for γt into growth factors in a similar way: γt ≡ τ tαt[β(xt−1, xt, pt, t− 1)β(xt−1, xt, pt−1, t)] 12 ; t = 1, 2, . . . (1.33) It is quite likely that the real output price growth factor [α(pt−1, pt, xt, t− 1)α(pt−1, pt, xt−1, t)]1/2 is fairly close to αt defined by (1.24) and it is quite likely that the input growth factor [β(xt−1, xt, pt, t−1)β(xt−1, xt, pt−1, t)]1/2 is quite close to βt defined by (1.28); i.e., we have the following approximate equalities: [α(pt−1, pt, xt, t− 1)α(pt−1, pt, xt−1, t)] 12 ≈ αt; t = 1, 2, . . . (1.34) [β(xt−1, xt, pt, t− 1)β(xt−1, xt, pt−1, t)] 12 ≈ βt; t = 1, 2, . . . (1.35) Substituting (1.34) and (1.35) into (1.32) and (1.33) respectively leads to the following approximate decomposition for the growth of real income into explanatory factors: γt ≈ τ tαtβt; t = 1, 2, . . . (1.36) where τ t is a technology growth factor, αt is a growth in real output prices factor and βt is a growth in primary inputs factor. Rather than look at explanatory factors for the growth in real market sector income, it is sometimes convenient to express the level of real income in period t in terms of an index of the technology level or of TFP in period t, T t, of the level of real output prices in period t, At, and of the level of 87 Chapter 1. Productivity Performance of Canada primary input quantities in period t, Bt.48 Thus we use the growth factors τ t, αt and βt as follows to define the levels T t, At and Bt: T 0 ≡ 1; T t ≡ T t−1τ t; t = 1, 2, . . . (1.37) A0 ≡ 1; At ≡ At−1αt; t = 1, 2, . . . (1.38) B0 ≡ 1; Bt ≡ Bt−1βt; t = 1, 2, . . . (1.39) Using the approximate equalities (1.36) for the chain links that appear in (1.37)-(1.39), we can establish the following approximate relationship for the level of real income in period t, ρt, and the period t levels for technology, real output prices and input quantities: ρt ρ0 ≈ T tAtBt; t = 0, 1, 2, . . . (1.40) In the following subsection, we note a set of assumptions on the technology sets that will ensure that the approximate real income growth decomposi- tions (1.36) and (1.40) hold as exact equalities. 1.8.3 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:49 ln gt(p, x) ≡ at0 + M∑ m=1 atm ln p t m 48This 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 (1991)(2003)(2004a)(2004b) and Fox and Kohli (1998). 49This 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. 88 Chapter 1. Productivity Performance of Canada + 1 2 M∑ m=1 M∑ k=1 amk ln ptm ln p t k + N∑ n=1 btn lnx t n + 1 2 N∑ n=1 N∑ j=1 bnj lnxtn lnx t j + M∑ m=1 M∑ n=1 cmn ln ptm lnx t n; t = 0, 1, 2, . . . (1.41) Note that the coefficients for the quadratic terms are assumed to be con- stant over time. The coefficients must satisfy the following restrictions in order for gt to satisfy the linear homogeneity properties that we have as- sumed in Subsection 1.8.2:50 M∑ m=1 atm = 1 for t = 0, 1, 2, . . . (1.42) N∑ n=1 btn = 1 for t = 0, 1, 2, . . . (1.43) amk = akm for all k,m (1.44) bnj = bjn for all n, j (1.45) M∑ k=1 amk = 0 for m = 1, . . . ,M (1.46) N∑ j=1 bnj = 0 for n = 1, . . . , N (1.47) 50There 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. 89 Chapter 1. Productivity Performance of Canada N∑ n=1 cmn = 0 for m = 1, . . . ,M (1.48) M∑ m=1 cmn = 0 for n = 1, . . . , N (1.49) Recall the approximate decomposition of real income growth going from period t− 1 to t given by (1.36), γt ≈ τ tαtβt. Diewert and Morrison (1986; 663) showed that51 if gt−1 and gt are defined by (1.41)-(1.49) above and there is competitive profit maximizing behaviour on the part of all market sector producers for all periods t, then (1.36) holds as an exact equality; i.e., we have γt = τ tαtβt t = 1, 2, . . . (1.50) In addition, Diewert and Morrison (1986; 663-665) showed that τ t, αt and βt could be calculated using empirically observable price and quantity data for periods t− 1 and t as follows, lnαt = M∑ m=1 1 2 [( pt−1m yt−1m pt−1 · yt−1 ) + ( ptmy t m pt · yt )] ln ( ptm pt−1m ) = lnPT (pt−1, pt, yt−1, yt) (1.51) lnβt = N∑ n=1 1 2 [( wt−1n xt−1n wt−1 · xt−1 ) + ( wtnx t n wt · xt )] ln ( xtn xt−1n ) = lnQT (wt−1, wt, xt−1, xt) (1.52) 51Diewert 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) = g t(P, x)/PC and the linear homogeneity property of gt(P, x) in P . 90 Chapter 1. Productivity Performance of Canada τ t = γt αtβt (1.53) where PT (pt−1, pt, yt−1, yt) is the Törnqvist (Törnqvist (1936) and Törnqvist and Törnqvist (1937)) output price index and QT (wt−1, wt, xt−1, xt) is the Törnqvist input quantity index. Since Equations (1.50) now hold as exact identities under our present assumptions, Equations (1.40), the cumulated counterparts to Equations (1.36), will also hold as exact decompositions; i.e., under our present as- sumptions, we have ρt ρ0 = T tAtBt t = 1, 2, . . . (1.54) We will implement the real income decompositions (1.50) and (1.54) in Sec- tions 1.3 and 1.4. 1.8.4 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 some- times 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 subsection, we show how this can be done, making the same assumptions on the technology that were made in the previous subsection. 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 (1.22) and (1.23) in 91 Chapter 1. Productivity Performance of Canada Subsection 1.8.2 for changes in all (deflated) output prices are the following Laspeyres type measure αtLm that chooses the period t − 1 reference tech- nology 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 αtPm that chooses the period t reference technology and refer- ence input vector xt and holds constant other output prices at their period t levels: αtLm ≡ gt−1(pt−11 , . . . , p t−1 m−1, p t m, p t−1 m+1, . . . , p t−1 M , x t−1) gt−1(pt−1, xt−1) ; m = 1, . . . ,M ; t = 1, 2, . . . (1.55) αtPm ≡ gt(pt, xt) gt(pt1, . . . , p t m−1, p t−1 m , ptm+1, . . . , p t M , x t) ; m = 1, . . . ,M ; t = 1, 2, . . . (1.56) 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:52 αtm ≡ [αtLmαtPm] 1 2 ; m = 1, . . . ,M ; t = 1, 2, . . . (1.57) Under the assumption that the deflated GDP functions gt(p, x) have the translog functional forms as defined by (1.41)-(1.49) in the previous subsec- tion, the arguments of Diewert and Morrison (1986; 666) can be adapted to give us the following result: 52The indexes defined by (1.55)-(1.57) were defined by Diewert and Morrison (1986; 666) in the nominal GDP function context. 92 Chapter 1. Productivity Performance of Canada lnαtm = 1 2 [( pt−1m yt−1m pt−1 · yt−1 ) + ( ptmy t m pt · yt )] ln ( ptm pt−1m ) ; m = 1, . . . ,M ; t = 1, 2, . . . (1.58) Note that lnαtm is equal to the m th term in the summation of the terms on the right hand side of (1.51). 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: αt = αt1α t 2 . . . α t M ; t = 1, 2, . . . (1.59) 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: 1. Domestic sales (C + I + G); 2. Exports (X) and 3. Imports (M). Commodities 1 and 2 are outputs, so y1 and y2 will be positive but com- modity 3 is an input into the market sector, so 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 contribution terms defined by (1.58) for m = 2 (where ytm > 0) and for m = 3 (where y t m < 0). 93 Chapter 1. Productivity Performance of Canada As mentioned above, it is also useful to have a decomposition of the aggre- gate 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 quan- tity, say xn, going from period t − 1 to t. Counterparts to the theoretical Laspeyres and Paasche type quantity indexes defined by (1.26) and (1.27) above for changes in input n are the following Laspeyres type measure βtLn 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 βtPn 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: βtLn ≡ gt−1(pt−1, xt−11 , . . . , x t−1 n−1, x t n, x t−1 n+1, . . . , x t−1 N ) gt−1(pt−1, xt−1) ; n = 1, . . . , N ; t = 1, 2, . . . (1.60) βtPn ≡ gt(pt, xt) gt(pt, xt1, . . . , x t n−1, x t−1 n , xtn+1, . . . , p t N ) ; n = 1, . . . , N ; t = 1, 2, . . . (1.61) 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:53 βtn ≡ [βtLnβtPn] 1 2 ; n = 1, . . . , N ; t = 1, 2, . . . (1.62) 53The indexes defined by (1.60)-(1.62) were defined by Diewert and Morrison (1986; 667) in the nominal GDP function context. 94 Chapter 1. Productivity Performance of Canada Under the assumption that the deflated GDP functions gt(p, x) have the translog functional forms as defined by (1.41)-(1.49) in the previous subsec- tion, the arguments of Diewert and Morrison (1986; 667) can be adapted to give us the following result: lnβtn = 1 2 [( wt−1n xt−1n wt−1 · xt−1 ) + ( wtnx t n wt · xt )] ln ( xtn xt−1n ) ; n = 1, . . . , N ; t = 1, 2, . . . (1.63) Note that lnβtn is equal to the n th term in the summation of the terms on the right hand side of (1.52). 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: βt = βt1β t 2 . . . β t N ; t = 1, 2 . . . (1.64) 1.8.5 The Deflated NDP Translog Approach There is a severe flaw with all of the analysis presented in the previous subsections. The problem is that depreciation payments are part of the user cost of capital for each asset but depreciation does not provide households with any sustainable purchasing power. Hence our real income measure defined by (1.13) is overstated. To see why GDP overstates income, consider the model of production that is described by the following quotations: “We must look at the production process during a period of time, with a beginning and an end. It starts, at the commencement of the Period, with an Initial Capital Stock; to this there is applied a Flow Input of labour, and from it there emerges a Flow Output called Consumption; then there is a Closing Stock of Capital left 95 Chapter 1. Productivity Performance of Canada over at the end. If Inputs are the things that are put in, the Outputs are the things that are got out, and the production of the Period is considered in isolation, then the Initial Capital Stock is an Input. A Stock Input to the Flow Input of labour; and further (what is less well recognized in the tradition, but is equally clear when we are strict with translation), the Closing Capital Stock is an Output, a Stock Output to match the Flow Output of Consumption Goods. Both input and output have stock and flow components; capital appears both as input and as output” John R. Hicks (1961; 23). “The business firm can be viewed as a receptacle into which factors of production, or inputs, flow and out of which outputs flow...The total of the inputs with which the firm can work within the time period specified includes those inherited from the pre- vious period and those acquired during the current period. The total of the outputs of the business firm in the same period in- cludes the amounts of outputs currently sold and the amounts of inputs which are bequeathed to the firm in its succeeding period of activity.” Edgar O. Edwards and Philip W. Bell (1961; 71-72). Hicks and Edwards and Bell obviously had the same model of production in mind: in each accounting period, the business unit combines the capital stocks and goods in process that it has inherited from the previous period with “flow” inputs purchased in the current period (such as labour, materi- als, services and additional durable inputs) to produce current period “flow” outputs as well as end of the period depreciated capital stock components which are regarded as outputs from the perspective of the current period (but will be regarded as inputs from the perspective of the next period).54 54For more on this model of production and additional references to the literature, see the Appendices in Diewert (1977)(1980). The usual user cost of capital can be derived from this framework if depreciation is independent of use. 96 Chapter 1. Productivity Performance of Canada All of the “flow” inputs that are purchased during the period and all of the “flow” outputs that are sold during the period are the inputs and outputs that appear in the usual definition of cash flow. These are the flow inputs and outputs that are very familiar to national income accountants. But this is not the end of the story: the firm inherits an endowment of assets at the beginning of the production period and at the end of the period, the firm will have the net profit or loss that has occurred due to its sales of outputs and its purchases of inputs during the period. As well, it will have a stock of assets that it can use when it starts production in the following period. Just focusing on the flow transactions that occur within the production period will not give a complete picture of the firm’s productive activities. Hence, to get a complete picture of the firm’s production activities over the course of a period, it is necessary to add the value of the closing stock of assets less the beginning of the period stock of assets to the cash flow that accrued to the firm from its sales and purchases of market goods and services during the accounting period. We illustrate the above theory by considering a very simple two output, two input model of the market sector. One of the outputs is output in period t, Y t and the other output is an investment good, It. One of the inputs is the flow of non-capital primary input Xt and the other input is Kt, capital services. Suppose that the average prices during period t of a unit of Y t, Xt and It are P tY , P t X and P t I respectively. Suppose further that the interest rate prevailing at the beginning of period t is rt. The value of the beginning of period t capital stock is assumed to be P tI , the investment price for period t. In order to induce households to let the business sector use the initial stock of capital, firms have to pay households interest equal to rtP tIK t. Then neglecting balance sheet items, the market sector’s period t cash flow is:55 CF t ≡ P tY Y t + P tIIt − P tXXt − rtP tIKt (1.65) 55For equity financed firms, we need to include an imputed return for equity capital. 97 Chapter 1. Productivity Performance of Canada Kt is interpreted as the firm’s beginning of period t stock of capital it has at its disposal and its end of period stock of capital is defined to be Kt+1. These capital stocks are valued at the balance sheet prices prevailing at the beginning and end of period t, P tI and P t+1 I respectively. The market sector period t pure profit is defined as its cash flow plus the value of its end of period t capital stock less the value of its beginning of period t capital stock: Πt ≡ CF t + P t+1I Kt+1 − P tIKt (1.66) Now the end of period depreciated stock of capital is related to the be- ginning of the period stock by the following equation: Kt+1 = (1− δ)Kt (1.67) where 0 < δ < 1 denotes the depreciation rate. Now substitute (1.65) and (1.67) into the definition of pure profits (1.66) and we obtain the following expression: Πt ≡ P tY Y t + P tIIt − P tXXt − rtP tIKt +P t+1I (1− δ)Kt − P tIKt = P tY Y t + P tII t − P tXXt −{rtP tI + δP t+1I − (P t+1I − P tI )}Kt (1.68) The expression that precedes the capital stock Kt, {rtP tI+δP t+1I −(P t+1I − P tI )}, can be recognized as the user cost of capital ;56 it is the gross rental price that must be paid to a capitalist in order to induce him or her to loan the services of a unit of the capital stock to the production sector. 56See Christensen and Jorgenson (1969) for a derivation in continuous time and Diewert (1980; 471) for a derivation in discrete time. 98 Chapter 1. Productivity Performance of Canada Some simplifications for (1.68) occur if we make two additional assump- tions: • Assume that producers and households expect price level stability so that the end of the period price for a new unit of capital P t+1I is expected to be equal to the beginning of the period price for a new unit of capital P tI ; in this case, we can interpret r t as the period t real interest rate;57 • Assume that pure profits are zero so that Πt equals zero. Substituting these two assumptions into Equation (1.68) leads to the fol- lowing expression: Πt = P tY Y t + P tII t − P tXXt − {rtP tI + δP tI}Kt = 0 (1.69) Equation (1.69) can be rearranged to yield the following value of output equals value of input equation: P tY Y t + P tII t = P tXX t + {rtP tI + δP tI}Kt (1.70) Equation (1.70) is essentially the closed economy counterpart to the (gross) value of outputs equals (gross) value of primary inputs equation (1.12), P t · yt = W t · xt, that we have been using thus far in this section. We now come to the point of this rather long digression: the (gross) payments to pri- mary inputs that is defined by the right hand side of (1.70) is not income, in the sense of Hicks.58 The owner of a unit of capital cannot spend the entire period t gross rental income {rtP tI + δP tI} on consumption during period t because the depreciation portion of the rental, δP tI , is required in order to keep his or her capital intact. Thus the owner of a new unit of capital at 57This assumption can be relaxed somewhat and we can still end up with much the same model; see Diewert (2006a). 58We will use Hicks’ third concept of income here: “Income No. 3 must be defined as the maximum amount of money which the individual can spend this week, and still be able to expect to spend this week, and still be able to expect to spend the same amount in real terms in each ensuing week.” J.R. Hicks (1946; 174). 99 Chapter 1. Productivity Performance of Canada the beginning of period t loans the unit to the market sector and gets the gross return {rtP tI + δP tI} at the end of the period plus the depreciated unit of the initial capital stock, which is worth only (1− δ)P tI . Thus δP tI of this gross return must be set aside in order to restore the lender of the capital services to his or her original wealth position at the beginning of period t. This means that period t Hicksian market sector income is not the value of payments to primary inputs, P tXX t + {rtP tI + δP tI}Kt; instead it is the value of payments to labour P tXX t plus the reward for waiting, rtP tIK t. Us- ing this definition of market sector (net) Hicksian income, we can rearrange Equation (1.70) as follows: Hicksian market sector income ≡ P tXXt + rtP tIKt = P tY Y t + P tII t − δP tIKt = Value of consumption + value of gross investment − value of depreciation (1.71) Thus in this Hicksian net income framework, our new output concept is equal to our old output concept less the value of depreciation. We take the price of depreciation to be the corresponding investment price P tI and the quantity of depreciation is taken to be the depreciation rate times the beginning of the period stock, δKt. Hence the overstatement of income problem that is implicit in the ap- proaches used in previous subsections can readily be remedied: all we need to do is to take the user cost formula for an asset and decompose it into two parts: • One part that represents depreciation and foreseen obsolescence, δP tIKt, and • The remaining part that is the reward for postponing consumption, rtP tIK t. 100 Chapter 1. Productivity Performance of Canada In our empirical work, our user costs in the gross output approach took the following form: ut = (rt + δt + τ t)P tI (1.72) where rt is the balancing period t real rate of interest, δt is a geometric depreciation rate for period t, τ t is an average capital taxation rate on the asset and P tI is the period t investment price for the asset. However, when we used the net output approach, we split up each (gross product) user cost times the beginning of the period stock Kt into the depreciation component δtP tIK t and the remaining term (rt + τ t)P tIK t and we regarded the second term as a genuine income component but the first term was treated as an intermediate input cost for the market sector and was an offset to gross in- vestment made by the market sector during the period under consideration. In the paper, when the net approach was used, the investment aggregate I was a net investment aggregate (gross investment components were indexed with a positive sign in the aggregate and depreciation components were in- dexed with a negative sign in the aggregate). The capital services aggregate in the net approach was a “reward for waiting” capital services aggregate rather than the gross return aggregate that was used in the gross output approach.59 1.8.6 Sectoral Contributions to Real Income Growth The above theory applied to the market sector as a whole. However, it is of considerable interest to determine which separate industries contributed the most to the overall growth of real income generated by the market sector of the economy. Hence, in this subsection, we outline how this can be done if industry data on outputs, inputs and the corresponding prices 59This approach seems to be broadly consistent with an approach advocated by Rymes (1968) (1983), who stressed the role of waiting services: “Second, one can consider the ‘waiting’ or ‘abstinence’ associated with the net returns to capital as the non-labour pri- mary input.” T.K. Rymes (1968; 362). Denison (1974) also advocated a net output ap- proach to productivity measurement. 101 Chapter 1. Productivity Performance of Canada are available.60 However, at the outset, it should be noted that in general, we will not be able to single out the effects of changes in real international prices as we were able to do when the entire business sector is treated as a single industry.61 We assume that there are I industries in the market sector of the economy. As in Subsection 1.8.2, we assume that there is a common list of M (net) outputs which each industry produces or uses as intermediate inputs. The net output vector for industry i in period t is yit ≡ [yit1 , . . . , yitM ], which are sold at the positive producer prices for industry i in period t, P it ≡ [P it1 , . . . , P it M ], for i = 1, . . . , I. There is also a common list of N primary inputs used by each industry. In period t, we assume that industry i uses non-negative quantities of N primary inputs, xit ≡ [xit1 , . . . , xitN ] which are purchased at the positive primary input prices W it ≡ [W it1 , . . . ,W itN ] for i = 1, . . . , I. In each period t, we assume that there is a feasible set of net output vectors yi that can be produced by industry i if the vector of primary inputs xi is utilised by that industry; denote this period t production possibilities set by Sit. We assume that Sit is a closed convex cone that exhibits a free disposal property. We shall take the net product point of view developed in the previous subsection for each industry in what follows. 60In Canada, such data are available from the Input-Output and Productivity Divisions of Statistics Canada. However, these data for the past five years are not available at present. 61The problem is not methodological; it is a data problem. In order to determine the effects of changing real import and export prices on the real income generated by an industry, we require information on the value and price of exports produced by the in- dustry and on the value and price of imports used by the industry. However, the System of National Accounts 1993 does not set up the production accounts so that the exports produced and imports used by an industry are recorded in the recommended system of production accounts. In theory, this problem can be remedied simply by distinguishing industry outputs as being either exported or delivered to domestic users and by distin- guishing industry inputs as being either imports or supplied by a domestic producer; see Diewert (2007b)(2007c) for the details of the resulting modified industry accounts. In practice, it will be extremely difficult to collect the required information. For further discussion of these issues, see Section 2.1 in Chapter 2. 102 Chapter 1. Productivity Performance of Canada Given a vector of industry i net output prices P it and a vector of available primary inputs xit for that industry, we define the industry i period t net product function, git(P it, xit), as follows, git(P it, xit) ≡ max y {P it · y : (y, xit) belongs to Sit} = P ityit; i = 1, . . . , I; t = 0, 1, 2, . . . (1.73) Since we have assumed constant returns to scale for each industry, it is natural to assume that the income generated by industry i in period t, W it ·xit, is equal to the corresponding value of net product, P it · yit; i.e., we have: P it · yit = W it · xit i = 1, . . . , I; t = 0, 1, 2, . . . (1.74) Define the period t, industry i real input and output price vectors, wit and pit respectively, as follows, wit ≡ W it P tC ; pit ≡ P it P tC ; i = 1, . . . , I; t = 0, 1, 2, . . . (1.75) As in Subsection 1.8.2, we can define the real income generated by industry i in period t, ρit, as the nominal income generated by industry i in period t, W it · xit, divided by the consumption price deflator for period t, P tC . Using (1.73)-(1.75), we have: ρit ≡ W it · xit P tC i = 1, . . . , I; t = 0, 1, 2, . . . = wit · xit 103 Chapter 1. Productivity Performance of Canada = P it · yit P tC = pit · yit = git(pit, xit) (1.76) where the last equality follows using (1.73)-(1.75) and the linear homogeneity of git(P it, xit) in P it. We now rework the theoretical analysis presented in Subsections 1.8.2- 1.8.4, except we apply it at the industry level instead of the economy-wide market sector level. Thus define γit as the period t chain link rate of growth factor for the real income generated by industry i: γit ≡ ρ it ρit−1 ; i = 1, . . . , I; t = 1, 2, . . . (1.77) Now assume that the industry i, period t (deflated) GDP function, git(p, x), has a translog functional form analogous to that defined above by (1.41)- (1.49). Repeat the analysis at the national level that led up to Equation (1.50), except now apply it at the industry level. We can derive the following industry counterparts to the national equation (1.50): pit · yit pit−1 · yit−1 = ρit ρit−1 = γit = τ itαitβit; i = 1, . . . , I; t = 0, 1, 2, . . . (1.78) where the period t, industry i chain link technical progress growth rate τ it, output price growth rate αit and input quantity growth rate βit can be cal- culated using the period t and t − 1 price and quantity data for industry i as follows, for i = 1, . . . , I; t = 0, 1, 2, . . .: lnαit ≡ M∑ m=1 1 2 [( pit−1m yit−1m pit−1 · yit−1 ) + ( pitmy it m pit · yit )] ln ( pitm pit−1m ) 104 Chapter 1. Productivity Performance of Canada = lnPT (pit−1, pit, yit−1, yit) (1.79) lnβit ≡ N∑ n=1 1 2 [( wit−1n xit−1n wit−1 · xit−1 ) + ( witnx it n wit · xit )] ln ( xitn xit−1m ) = lnQT (wit−1, wit, xit−1, xit) (1.80) τ it ≡ γ it αitβit (1.81) where PT (pit−1, pit, yit−1, yit) is the period t, industry i Törnqvist output price index and QT (wit−1, wit, xit−1, xit) is the period t, industry i Törnqvist input quantity index. Recall that in Subsection 1.8.3, we defined cumulated counterparts to the chain link Equations (1.50). We can do the same type of operation for the industry data. Thus define the industry i level of total factor productivity in period t relative to period 0 as T it, the industry i level of real output prices in period t relative to period 0 as Ait and the industry i level of primary input in period t relative to period 0 as Bit. These industry levels can be defined in terms of the corresponding industry chain link factors, τ it, αit and βit as follows, T i0 ≡ 1; T it ≡ T it−1τ it; t = 1, 2, . . . (1.82) Ai0 ≡ 1; Ait ≡ Ait−1αit; t = 1, 2, . . . (1.83) Bi0 ≡ 1; Bit ≡ Bit−1βit; t = 1, 2, . . . (1.84) 105 Chapter 1. Productivity Performance of Canada Since Equations (1.78) hold as exact identities under our present assump- tions, the following cumulated counterparts to these equations will also hold as exact decompositions: pit · yit pi0 · yi0 = ρit ρi0 = T itAitBit; i = 1, . . . , I; t = 1, 2, . . . (1.85) Thus three factors contribute to the period t level of real income generated by industry i relative to the period 0 level: the level of period t total factor productivity of industry i in period t (relative to period 0), T it, the growth in real output prices for industry i going from period 0 to t, Ait, and the growth in primary inputs utilised by industry i going from period 0 to t, Bit. The nominal value of market sector output in period t is the corresponding sum of industry nominal values, ∑I i=1 P it · yit, which can be converted into the period t real income generated by the market sector, ρt, by dividing this sum by the period t consumption price deflator, P tC : ρt ≡ I∑ i=1 P it · yit P tC = I∑ i=1 pit · yit = I∑ i=1 ρit; t = 0, 1, . . . (1.86) where the last equality follows using (1.76). Define industry i’s share of market sector nominal (or real) net output in period 0 as, s0i ≡ ρi0 ρ0 ; i = 1, . . . , I (1.87) Using the above definitions, we can decompose the growth in market sector real income, going from period 0 to t, as follows, 106 Chapter 1. Productivity Performance of Canada ρt/ρ0 = [∑I i=1 ρ it ] ρ0 using (1.86) = I∑ i=1 [ ρit ρi0 ] [ ρi0 ρ0 ] = I∑ i=1 s0i [ ρit ρi0 ] using (1.87) = I∑ i=1 s0iT itAitBit using (1.85) (1.88) Equation (1.88) shows the factors that determine the evolution of market sector real income growth over time. There are four sets of factors at work: • The industrial structure of net product in the base period; i.e., the base period industry shares of market sector net output, s0i ; • The total factor productivity performance of industry i cumulated from the base period to the current period; i.e., the industry produc- tivity factors, T it; • The growth in industry output prices (deflated by the price of the consumption aggregate) going from period 0 to t; i.e., the industry real output price factors, Ait and • The growth in primary inputs utilised by industry i going from period 0 to t; i.e., the industry primary input growth factors, Bit. Note that if an industry i experiences growth in its (net) output prices relative to the price of consumption, then the corresponding real output price factor Ait will be greater than one and this effect will contribute to overall real income growth. Traditional Total Factor Productivity decompositions does not include this type of factor; i.e., the traditional analysis ignores 107 Chapter 1. Productivity Performance of Canada favourable (or unfavourable) output price effects.62 62Improvements in the country’s terms of trade are also ignored by the traditional methodology. This does not mean that the traditional emphasis on pure efficiency im- provements is “wrong”; it just does not answer the question that we are focusing on, which is: what is the rate of growth in consumption equivalents that the market sector of the economy is generating? 108 Chapter 2 Business Sector Data on Outputs and Inputs for Canada 1961-2007 2.1 Introduction The basic approach to measuring productivity growth is to use recently released information on business sector outputs and inputs from Statistics Canada’s KLEMS database along with information on aggregate final de- mand expenditures in order to construct “top down” measures of the pro- ductivity performance of the Canadian business sector.63 We also make extensive use of Statistics Canada’s National Balance Sheet estimates for information on various capital inputs used by the business sector. Thus 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 indus- trial sectors and aggregates up sectoral productivity growth rates in order to obtain national business sector estimates.64 With reliable data, the two approaches should give very similar answers.65 Unfortunately, data on in- 63The database used in Chapter 1.8 was constructed in October, 2008. 64The “bottom up” approach is used by the Statistics Canada KLEMS program; see Baldwin, Wu and Yan (2007) for an overview and Baldwin and Gu (2007) for additional information on the construction of the Statistics Canada KLEMS capital services aggre- gates. 65In 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 Diewert (2006b)(2007c). 109 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 dustry inputs and outputs are not likely to be as reliable as the corresponding national data for a variety of reasons66 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 existing 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 subtrac- tions) 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.67 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. 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. The study in Chapter 1 is an extension of these previous studies but there are some differences: • Statistics Canada has provided new data on national expenditure ag- gregates back to 1961 using annual chained index numbers and so it is 66For a detailed discussion of these reasons, see Diewert (2001). 67It 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. 110 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 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 has 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 measure- ment program. In particular, we will use the KLEMS estimates of labour input, which are 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 ad- ministration industry. In this study, we adopt the Statistics Canada definition of the non-business sector (except that we add to it the res- idential rental housing industry) and include the general government sector and the publicly funded defence, hospital and education sectors in the non-business sector.68 Since output in the non-business sector is measured by input, the use of the broader definition of the govern- ment 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 has 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 is very useful in making adjustments to output prices for indirect tax effects.69 68The non-business sector consists of the following industries: (1) Government fund- ing 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. 69In 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 behaviour on the part of producers, since producers do not derive any benefit from indirect taxes that fall 111 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 There had been a substantial revision of the Statistics Canada data used in Diewert (2008), therefore we use in this paper more recent published Statistics Canada data70 as well as some unpublished disaggregated capital data made available to us from the Statistics Canada KLEMS database. Note that the business 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.71 The main conceptual changes in our present database from the data tabled in Diewert (2008) are as follows: • The trade data were disaggregated; • Machinery and equipment investment in Diewert (2008) has been dis- aggregated into ICT machinery and equipment and non-ICT machin- ery and equipment;72 • 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 non-residential structures, ICT machin- ery and equipment and non-ICT machinery and equipment were re- estimated using balance sheet and KLEMS program information along with revised investment information. on their outputs and thus these taxes should be removed. 70These data were obtained in October 2008. 71Our reason for excluding the services of rental housing from our business sector ag- gregate 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 exactly the same as that used by the Statistics Canada KLEMS program so only our output measure and capital services input measures differ from the corresponding KLEMS estimates. 72Our thanks to Wulong Gu for making the disaggregated data available to us. 112 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 In Section 2.2, we will list the basic final demand expenditure series that were used. Section 2.3 simply lists the three published business sector mea- sures of quality adjusted labour input for the Canadian business sector that are available on CANSIM as part of the Statistics Canada KLEMS program. Section 2.4 studies the problems associated with forming estimates for cap- ital inputs. Section 2.5 forms 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 subsections in order to calculate user costs for five classes of capital input: machinery and equipment, non-residential struc- tures, agricultural land, non-agricultural and non-residential business land and inventories. Section 2.6 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. 2.2 Estimates of Canadian Final Demand Expenditures Much of the information tabled in this section is updated information that can be found in the Canadian Economic Observer, Statistics Canada (2007), Table 1: Gross Domestic Product (GDP) by Income and Expendi- ture (millions of dollars and in chained 2002 dollars). The October 2008 version of these data were used, using the Statistics Canada online data service CANSIM II, which were listed as quarterly data. If the quarterly data were seasonally adjusted, then the data for a year were summed and divided by four 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 II series V498087 and V1992044 respectively. Dividing the current dollar series VCT by the 113 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 constant dollar series QCT gives us an implicit price series PCT for 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 pro- ductivity 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 mea- sure 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 compo- nents.73 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 inputs into the business sector.74 Information on current dollar expenditures on imputed rents and paid rents (this is the series VPR in Table 2.1) for the years 1961-2007 is available from CANSIM II series V498532 and V498533 respectively. The corresponding information on chained 1997 constant dollar expenditures on imputed rents and paid rents (QPR) is available from CANSIM II series V1992078 and V1992079 only for the years 1981-2006.75 We divide VPR by QPR in order to form 73The 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, Gu and Yan (2007; 43). 74This means our productivity estimates will be biased downward slightly since the inputs that are used in the rental housing market are included in our estimates but the corresponding outputs are not included. 75We did construct the corresponding expenditure based price series for imputed rents for the period 1981-2006 and compared this price index with the corresponding industry 114 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 a price index for paid rents, PPR. We could follow the same strategy to form a price index for imputed rents for the years 1981-2007.76 However, an alternative series on the imputed value of OOH services for the years 1961-2004 is available from the industry accounts. This series is CANSIM II series V3859926, Business Sector: Owner Occupied Dwellings, from Table 370023: Gross Domestic Product (GDP) at Basic Prices in Current Dollars, System of National Accounts, Benchmark Values, by North American In- dustry Classification System (NAICS) and is listed as VIMR in Table 2.1.77 The final demand value series for imputed rents (not listed) is about 13% higher than its industry counterpart, VIMR. We use the industry series for imputed rents rather than the final demand series because we want our business sector value added to closely approximate the Statistics Canada KLEMS program business sector value added, except that our aggregate will not include paid residential rents.78 based price index for imputed rents described below for the years 1981-2004 and found that the movements were similar. We used the expenditure based price index for the years 2004-2007 to extend the industry based price index from 2004 to 2007. 76We explain below how this industry based value series for imputed rents was extended from 2004 to 2007. 77We explain below how this industry based value series for imputed rents was extended from 2004 to 2007. 78The KLEMS business sector value added aggregate excludes imputed rents whereas our business sector value added aggregate will exclude both imputed and paid rents. Our treatment of inventory change is also different. 115 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.1: Housing Value, Quantity and Price Series for Im- puted and Paid Rents Year t V tIMR Q t IMR V t PR Q t PR P t IMR P t PR 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 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 Continued on Next Page. . . 116 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.1 – Continued Year t V tIMR Q t IMR V t PR Q t PR P t IMR P t PR 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 87614 6482 34133 2487 13.51648 13.72279 2005 91546 6730 35435 2560 13.60266 13.83987 2006 96714 6985 37137 2638 13.84590 14.07851 2007 103152 7246 39262 2714 14.23568 14.46634 117 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 We now describe how we estimated a price index for the paid rents series for the years 1961-1981 and how we formed a price index for the industry value added series for the imputed rents for OOH for the years 1961-2007. An old series for the industry value added generated by OOH, CANSIM II series V334072, Canada: Current Prices; Business Sector; Owner Occupied Dwellings, from Table 3790001, Gross Domestic Product (GDP) at Factor Cost, System of National Accounts Benchmark Values, by Industry, is avail- able for the years 1961-1997. The corresponding series in constant 1992 dollars is available for the years 1961-2000 as CANSIM II Series V328857 in Table 3790004. We use these two series to form a price index for im- puted rent for the years 1961-1997, P tIMR in Table 2.1. A constant dollar industry series for the services of OOH for the years 1997-2007 can be ob- tained from CANSIM II Series V14183160, Canada; Seasonally Adjusted at Annual Rates; Chained 1997 Dollars; Owner Occupied Dwellings in Ta- ble 3790018, Gross Domestic Product (GDP) at Basic Prices by NAICS.79 Dividing V tIMR by this constant dollar series will give us a price index for imputed rents running from 1997 to 2007 and we link this series to the earlier P tIMR series that ran from 1961 to 1997. We then normalized the price series to equal 1 in 1961 and formed the quantity series QtIMR as V t IMR divided by P tIMR. V t IMR, Q t IMR and P t IMR are listed in Table 2.1. Recall that we have a value series for paid rents, V tPR, that covers the years 1961-2007 but the corresponding price index series, P tPR, covers only the years 1981-2007. We extend P tPR back to 1961 using the movements in P t IMR. The resulting price series is normalized to equal 1 in 1961 and a quantity series for paid rents, QtPR, is obtained by dividing V t PR by P t PR. These three series are also listed in Table 2.1.80 79Somewhat mysteriously, this constant dollar series extends all the way to 2007 whereas the corresponding current dollar series ends at 2004. As noted above, we extended the industry price index for imputed rents from 2004 to 2007 using the movements in the corresponding expenditure based price index for imputed rents over the years 2004-2007. Given this extended price index plus the industry based constant dollar series for imputed rents, the industry based value series for imputed rents was extended to 2007. 80The units for all value and quantity series are millions of current dollars for the V series and millions of 1961 dollars for the Q series. 118 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Recall the price and quantity series for a consumption aggregate (which includes all rents, paid and imputed), PCT and QCT , along with the two price and quantity series for imputed and paid rents in Table 2.1. 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 on the quantities) and rents (negative sign on the 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 V tIT , CANSIM II series V1997473, for the years 1961-2007. 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 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 price and quantity of consumption series, P tC and Q t C , are listed in Tables 2.2 and 2.3. 81 81We renormalize all price and quantity series so that the normalized price is 1 in 1961. The units for quantity and value series are in millions of current and 1961 dollars respectively. 119 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.2: Prices Indexes for Business Sector Outputs: Con- sumption and Investment Year P tC P t IG P t IR P t ICT P t IME P t INR P t II 1961 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1962 1.00538 1.00855 1.00504 0.99939 1.01477 1.00592 1.00240 1963 1.02055 1.03939 1.02769 0.99650 1.06598 1.03251 1.01346 1964 1.02437 1.06231 1.07312 1.00502 1.06773 1.06158 1.03169 1965 1.03690 1.13926 1.13368 1.02393 1.10198 1.12281 1.05486 1966 1.07553 1.21007 1.20765 1.02944 1.12251 1.19323 1.07231 1967 1.11050 1.23160 1.28518 1.07473 1.12792 1.24188 1.08449 1968 1.15168 1.23844 1.31431 1.10902 1.13973 1.25227 1.10971 1969 1.18980 1.28464 1.38118 1.14444 1.17197 1.32495 1.13490 1970 1.22208 1.33877 1.42615 1.19472 1.23029 1.39058 1.15046 1971 1.24828 1.40873 1.53179 1.22722 1.27216 1.46812 1.20264 1972 1.29847 1.48528 1.67349 1.26956 1.30444 1.55098 1.31611 1973 1.38744 1.64838 1.97123 1.30782 1.34535 1.71873 1.42683 1974 1.58382 2.01078 2.36134 1.35698 1.51430 2.03419 1.54691 1975 1.82198 2.23421 2.56072 1.45867 1.73112 2.27337 1.65112 1976 1.90726 2.34499 2.76853 1.45190 1.82918 2.40093 1.77007 1977 2.03175 2.48990 2.87768 1.44467 1.98862 2.52980 1.92666 1978 2.19264 2.66206 3.04069 1.40748 2.19453 2.71145 2.13561 1979 2.40645 2.88522 3.28046 1.38366 2.44348 2.96312 2.34120 1980 2.69497 3.19858 3.55455 1.21888 2.69736 3.32520 2.55883 1981 2.95335 3.68313 3.99273 1.12880 2.98813 3.68676 2.75849 1982 3.22860 3.92658 4.08226 1.16812 3.19883 3.96113 2.91040 1983 3.46323 4.01498 4.25350 1.02222 3.26756 3.93090 3.04428 1984 3.61506 4.17063 4.41785 0.96342 3.40812 4.08142 3.12590 1985 3.72257 4.20827 4.55564 0.89167 3.57237 4.21351 3.15838 1986 3.80422 4.20267 4.90827 0.82129 3.70845 4.27520 3.20668 1987 3.89726 4.22375 5.40819 0.75277 3.69804 4.47320 3.26271 Continued on Next Page. . . 120 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.2 – Continued Year P tC P t IG P t IR P t ICT P t IME P t INR P t II 1988 4.00205 4.33769 5.78293 0.71401 3.69075 4.72840 3.31521 1989 4.11690 4.43728 6.13195 0.64691 3.79390 4.92520 3.36284 1990 4.35206 4.53066 6.11231 0.61403 3.87130 5.08853 3.36458 1991 4.59099 4.31837 6.32257 0.54586 3.74170 5.00311 3.51938 1992 4.65258 4.31896 6.39710 0.51043 3.88288 4.97541 3.52557 1993 4.74252 4.34342 6.58445 0.50164 4.04523 5.03758 3.70024 1994 4.77089 4.42033 6.76485 0.48119 4.24754 5.20497 3.83041 1995 4.79147 4.51572 6.76717 0.44755 4.44740 5.27332 3.91857 1996 4.88952 4.53812 6.75581 0.41150 4.57050 5.43035 3.78206 1997 4.96547 4.57906 6.87512 0.39399 4.69221 5.56694 3.80677 1998 5.03224 4.59706 6.95993 0.36919 4.90374 5.71450 3.86651 1999 5.12045 4.57201 7.13210 0.33873 4.94358 5.82995 3.95640 2000 5.25425 4.68967 7.29782 0.32384 5.01831 6.02775 4.04039 2001 5.40970 4.68012 7.48766 0.31733 5.17017 6.07934 4.10861 2002 5.47743 4.72977 7.81242 0.30560 5.25354 6.18175 3.87128 2003 5.61543 4.72659 8.21290 0.27567 4.94953 6.30506 3.91048 2004 5.69551 4.79882 8.71618 0.24913 4.85253 6.70389 3.95736 2005 5.81654 4.91308 9.11452 0.23077 4.79667 7.12403 4.02157 2006 5.92386 5.09878 9.78750 0.21439 4.71044 7.64020 4.14724 2007 6.02712 5.28795 10.49192 0.20857 4.58255 8.04719 4.15442 121 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.3: Quantity Indexes for Business Sector Outputs: Consumption and Investment Year t QtC Q t IG Q t IR Q t ICT Q t IME Q t INR Q t II 1961 20265 1887 2211 312 1925 2618 1 1962 21331 2094 2271 358 2067 2545 560 1963 22290 2101 2354 399 2199 2637 936 1964 23529 2141 2715 412 2744 3050 532 1965 24974 2426 2825 472 3257 3320 1228 1966 26240 2668 2699 580 3899 3802 1313 1967 27228 2718 2754 617 3866 3613 454 1968 28525 2758 3132 592 3537 3593 619 1969 29923 2700 3551 673 3817 3592 1580 1970 30450 2645 3254 677 3868 3946 180 1971 32321 2985 3728 744 3924 4089 −232 1972 34891 2938 4066 806 4338 4074 148 1973 37676 2781 4371 932 5336 4396 2542 1974 39789 2845 4464 1167 5925 4675 4839 1975 41468 2962 4386 1310 6089 5286 −334 1976 43911 2855 5172 1568 6219 5168 250 1977 45480 2916 5242 1647 6057 5479 1319 1978 47255 2875 5291 1895 6202 5626 1300 1979 48694 2803 5251 2225 6988 6337 3691 1980 49521 2869 4977 3074 7165 7055 167 1981 49914 2967 5279 4423 8211 7620 891 1982 48210 3095 4340 4205 6867 6929 −4603 1983 49567 2991 5079 5184 6414 6361 −1049 1984 51955 3124 5131 6297 6397 6288 1744 1985 54842 3497 5578 7438 6909 6590 1467 1986 56973 3485 6267 8984 7454 6210 1029 1987 59433 3621 7190 12586 8084 6454 1701 Continued on Next Page. . . 122 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.3 – Continued Year t QtC Q t IG Q t IR Q t ICT Q t IME Q t INR Q t II 1988 61835 3789 7340 14111 9704 7110 2078 1989 63760 4184 7640 17019 10096 7345 1406 1990 64001 4463 6835 18392 9331 7346 −583 1991 62103 4692 5824 19836 8856 7075 −3899 1992 62821 4621 6238 24332 7995 5960 −551 1993 63783 4560 6024 26001 7449 5993 −878 1994 65822 4894 6271 30044 8001 6533 709 1995 67161 4740 5340 33319 8373 6574 3164 1996 68967 4536 5852 39474 8500 6696 2417 1997 72495 4390 6330 49575 10434 7881 1780 1998 74536 4361 6106 60330 10647 7906 2329 1999 77521 5039 6324 72466 11106 8101 1249 2000 80901 5229 6656 85220 11270 8266 2915 2001 82720 5830 7363 84440 10798 8712 −1856 2002 85721 6044 8403 83843 10625 8195 3367 2003 88311 6370 8854 90145 11417 8651 −1722 2004 91157 6773 9519 105113 12185 9257 1058 2005 94522 7521 9845 115589 13473 10184 1981 2006 98708 8021 10061 130883 14066 11093 1104 2007 103366 8644 10363 140217 15069 11047 1757 123 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 We turn our attention to the investment components of final demand. Current dollar government gross fixed capital formation is available as CAN- SIM II series V498093 for the years 1961-2007. 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, P tIG and Q t IG, which are listed in Tables 2.2 and 2.3. 82 The current and constant chained dollar series for the years 1961-2006 for residential structures investment can be obtained as CANSIM II series V498096 and V1992053 respectively, the current and constant chained dollar series for non-residential structures investment can be obtained as CANSIM II series V498098 and V1992053 respectively and the resulting price and quantity series are denoted by P tIR, P t INR, Q t IR and Q t INR and are listed in Tables 2.2 and 2.3. Statistics Canada provided us with unpublished series on the price and value of ICT and non-ICT machinery and equipment in- vestments for the years 1961-2006. The resulting price and quantity series for ICT investment and non-ICT machinery and equipment are denoted by P tICT , Q t ICT , P t IME and Q t IME respectively, 83 as listed in Tables 2.2 and 2.3. These tables also include the price and quantity of inventory change, P tII and QtII change but the description of how they were constructed is deferred until we discuss how we formed estimates of the beginning of the year stocks of inventories. 82The 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. 83We used the rates of increase in the price and quantity of all investment in machinery and equipment going from 2006 to 2007 from the published Statistics Canada expenditure accounts (see the current and constant chained dollar series for machinery and equipment investment, CANSIM II series V498099 and V1992056 respectively) to extend the ICT and non-ICT machinery and equipment price and quantity series to 2007. When we aggregated up the two unpublished ICT and other machinery and equipment investment series using chained Fisher indexes and compared the resulting aggregate KLEMS based machinery and equipment investment series with the corresponding national accounts based series, we found that the value series were very close but the KLEMS based price series grew 2.32 fold over the years 1961-2006 whereas the national accounts based price series grew 2.60 fold, which is 12% higher. We chose to use the KLEMS based data series for investment in machinery and equipment. 124 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 All of the outputs described above 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 non-business sector and it also purchases smaller amounts of goods and services from the non-business sector. We now describe how we formed price and quantity estimates for the net sales of the business sector to the non-business sector. For the years 1961-2007 from the National Income and Expenditure Ac- counts, CANSIM II series V498092; 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 current dollars. From the same table and for the same years, CANSIM II series V1992049; Government Current Ex- penditure 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 govern- ment sector expenditures, P tG and Q t G, which are listed in Table 2.4. 125 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.4: Business Sector, Non-business Sector, Government Final Demand and KLEMS Business Sector Price and Quan- tity Aggregates Year t QtB Q t N Q t G Q t BKLEMS P t B P t N P t G P t BKLEMS 1961 33097 5204 6624 30805 1.00000 1.00000 1.00000 1.00000 1962 35338 5480 6928 33059 1.00919 1.03863 1.02916 1.00509 1963 37217 5713 7164 35013 1.02992 1.08205 1.05990 1.01881 1964 39810 5952 7542 37567 1.04877 1.14227 1.09761 1.03600 1965 42658 6120 7883 40122 1.07554 1.21527 1.15160 1.06938 1966 45529 6409 8581 42827 1.12248 1.34490 1.24333 1.11745 1967 46616 6870 9334 43728 1.16053 1.45671 1.32836 1.15516 1968 49335 7263 9944 46133 1.19304 1.54780 1.41575 1.18948 1969 51965 7585 10376 48537 1.23452 1.71317 1.53846 1.23074 1970 52968 7962 11287 49889 1.29437 1.84146 1.64279 1.27609 1971 55844 8255 11631 51843 1.33615 1.95964 1.75921 1.33535 1972 59086 8549 11995 54998 1.40300 2.12810 1.89268 1.40260 1973 63467 8887 12559 59206 1.54872 2.31234 2.04912 1.55366 1974 65346 9295 13357 61310 1.79635 2.65779 2.33927 1.79872 1975 65545 9790 14251 62061 2.03754 3.05325 2.65962 2.01795 1976 70082 10097 14525 66118 2.17572 3.45337 2.99471 2.15434 1977 72425 10348 15205 68823 2.32657 3.73913 3.24567 2.27212 1978 74875 10644 15473 71979 2.51505 3.96850 3.45708 2.42047 1979 77878 10805 15635 75134 2.80145 4.29236 3.77635 2.69350 1980 79169 11138 16169 76938 3.12982 4.66836 4.14895 2.98837 1981 81847 11496 16441 80244 3.40152 5.22919 4.64970 3.21385 1982 78970 11693 16767 77088 3.65996 5.83630 5.18504 3.44460 1983 81077 11952 17045 79192 3.89493 6.12278 5.48059 3.65571 1984 86041 12198 17222 84752 4.03944 6.37296 5.69544 3.76522 1985 90944 12471 17959 89260 4.13895 6.57967 5.90593 3.87314 1986 93580 12708 18283 91514 4.19906 6.81314 6.09362 3.92907 Continued on Next Page. . . 126 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.4 – Continued Year t QtB Q t N Q t G Q t BKLEMS P t B P t N P t G P t BKLEMS 1987 97824 12840 18525 96022 4.38354 7.17180 6.36273 4.08969 1988 102723 13057 19370 100981 4.58086 7.53056 6.60377 4.26785 1989 105427 13224 19903 103685 4.75619 8.03351 6.95695 4.41096 1990 106128 13541 20605 103235 4.85194 8.60166 7.34874 4.52286 1991 104194 13849 21208 99027 4.90597 9.01919 7.64969 4.63908 1992 105171 14045 21414 99628 4.92162 9.36188 7.88200 4.64471 1993 108151 14150 21422 102483 4.97722 9.50865 7.98997 4.69377 1994 113766 14218 21156 108795 5.08269 9.55910 8.11082 4.75837 1995 117124 14279 21034 112401 5.23638 9.61980 8.19895 4.89045 1996 119744 14025 20786 114956 5.33957 9.72826 8.23447 4.99301 1997 125797 13787 20579 121417 5.40168 9.95401 8.34626 5.04144 1998 131475 13890 21240 127127 5.37429 10.07510 8.44225 5.00882 1999 139515 14320 21687 135542 5.47529 10.18237 8.57899 5.10349 2000 147808 14614 22356 144108 5.71191 10.65177 8.94989 5.34163 2001 149733 14926 23229 146512 5.80825 10.88586 9.11375 5.41622 2002 153895 15241 23802 150269 5.82601 11.29659 9.42889 5.42824 2003 156933 15608 24551 153124 6.02555 11.73665 9.71085 5.62745 2004 162130 15921 25044 158534 6.23215 11.96951 9.87845 5.82088 2005 167081 16154 25429 163342 6.45631 12.39824 10.23229 6.04364 2006 171718 16519 26385 168301 6.65413 12.80917 10.57143 6.21454 2007 175972 16945 27359 172358 6.89723 13.13041 10.83655 6.44335 127 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 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 Divi- sion 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 V tB in year t. Statistics Canada also produces a companion non-business sector value added aggregate (at factor cost) which we will denote by V tN in year t. If the value of indirect taxes less subsidies on products for year t, V tIT , 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: V tB + V t N + V t IT = V t GDP (2.1) We will now describe how we formed estimates for V tB and V t N 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 V tB series (title is Canada: Business Sector Industries) for the years 1961-2004 from CANSIM II Series V3860037. From the same Table 3790024, we can obtain the V tN series (title is Canada: Non-Business Sector Industries) for the years 1961-2004 from CANSIM II Series V3860040. We can obtain price indexes P tB, P t N and quantity indexes Q t B, Q t N for V t B and V t N 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 non-business sector value added at basic prices in current dollars and in constant 1992 dollars. Using CANSIM Table 3790020, we can find estimates for QtB (Series V14182646) and for QtN (Series V14182651) in chained 1997 dollars for the years 1997- 128 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 2007. Hence using these series in conjunction with our earlier value series V tB and V tN which run from 1961 to 2004, we can obtain price series for business and non-business sector value added at basic prices for the years 1997-2004. These price series can be linked to our earlier price series P tB and P t N which extended to 1997 so that the resulting price series will run from 1961 to 2004. However, we still do not have price or value series for the B and N sectors for 2004-2007, although we do have quantity series for these years. We extended the price series P tN from 2004 using an implicit price index for government goods and services, which was constructed using CANSIM Table 3800002, series V498092 in current dollars and series V1992049 for chained 2002 dollars. It turns out that the total of V tB and V t N is available in another CANSIM II 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 P tB and the value of business sector output V t B for the years 2004-2007. The business and non-business sector price and quantity series, P tB, P t N and Q t B, Q t N for real value added at basic prices are listed in Table 2.4. It is also of some interest to compare the price and quantity of the above Industry Division business sector prices and quantities P tB and Q t B with the corresponding business sector prices and quantities P tBKLEMS and QtBKLEMS that originate with the Statistics Canada productivity program. 84 These series are also listed in Table 2.4. The source for QtBKLEMS for the years 1961-2007 is CANSIM II series V41712932: Canada, Real Gross Do- mestic Product (GDP), Business Sector from Table 3830021: Multifactor Productivity, Value Added, Capital Input and Labour Input in the Aggre- gate Business Sector and Major Sub-sectors by the North American Indus- try Classification (NAICS). The corresponding nominal value added series V tBKLEMS is available in the same table for the years 1961-2004 as CANSIM 84Recall that the Productivity Program business sector value added aggregate V tKLEMS should be equal to the Industry Division value added aggregate V tB less the value of imputed rents from the Industry Division, V tIMR. 129 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 II series V41713153: Canada: Gross Domestic Product (GDP), Business Sector. The values V tBKLEMS for the missing years 2005-2007 can be ob- tained by adding the value of imputed rents, V tIMR, to the Industry Division value added for the Business Sector, V tB. Finally, P t BKLEMS can be obtained by dividing V tBKLEMS by Q t BKLEMS . As usual, we normalized the resulting price and quantity series so that P tBKLEMS equals 1 when t equals 1961. The resulting P tBKLEMS and Q t BKLEMS are listed in Table 2.4. Recall the GDP identity defined by (2.1), which expressed the nominal value of GPD, V tGDP , at final demand prices as being equal to the value added of the Industry Division business sector value added at basic prices, V tB, plus non-business sector value added, V t N , plus the value of indirect taxes less subsidies on products, V tIT . 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 investment plus government expenditures on goods and services plus exports less imports: V tGDP = V t CT + V t I + V t G + V t X − V tM (2.2) We define a new consumption aggregate at basic prices V tCN as the value of consumption at final demand prices, V tCT , less indirect taxes less subsidies on products, V tIT : V tCN ≡ V tCT − V tIT (2.3) Now equate the two expressions for the value of GDP given by (2.1) and (2.2) and use the resulting equation to express business sector value added V tB in terms of final demand components and the value of non-business sector value added V tN . Making use of (2.3), the resulting equation is the following one:85 85The identity (2.4) 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 (2.3) to adjust 130 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 V tB = V t CN + V t I + V t X − V tM + (V tG − V tN ) (2.4) Conceptually, the aggregate V tG − V tN should be equal to the sales of the business sector of goods and services to the non-business sector less the purchases of intermediate inputs of the business sector from the non-business sector. Put another way, the business sector’s net sales of goods and services should equal its net deliveries to final demand sectors (V tC +V t I +V t X −V tM ) plus its net deliveries to the non-business sector (V tG − V tN ). 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 V tR be equal to the sum of imputed residential rent V tIMR and paid residential rent V t PR (see Table 2.1 for these series). Conceptually, if we subtract rents V tR from V t CN , we should get V tC , the consumption aggregate whose price and quantity is listed in Tables 2.2 and 2.3. Thus subtracting V tR from both sides of (2.4) leads to the following identity: V tB − V tR = V tC + V tI + V tX − V tM + (V tG − V tN ) (2.5) Thus our business sector value added aggregate can be formed using either the left or right hand sides of the identity (2.5). We will use the right hand side of (2.5) 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 (2.5) be calculated? Obviously, each cell in the supply and use tables that correspond to the value aggregate on the left hand side of (2.5) could be aggregated up using a chained superlative index final demand consumption prices for indirect tax wedges, we used a corresponding slight modification of the identity (2.4). 131 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 number formula provided that an appropriate price deflator were available for each cell.86 On the other hand, the value cells that are components on the right hand side of (2.5) that correspond to final demand compo- nents (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 (2006b)(2007b)(2007c). 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 de- mand component approaches are perfectly consistent.87 In addition, if two stage aggregation procedures are used and a superlative index number for- mula is used at each stage of aggregation, then the theoretical and empirical results in Diewert (1978) show that the commonly used single stage superla- tive indexes will approximate their two or more stage counterparts to a high degree of approximation if the chain principle is used.88 Using the above results, we will construct our measure of business sec- tor real value added by aggregating up the value components on the right hand side of (2.5). Rather than work with both V tG and V t N as final demand components, we will aggregate over these two components to form the value aggregate V tGN equal to (V t G − V tN ), and conceptually, this value aggregate should be equal to the net deliveries of goods and services of our business sector to the non-business sector less the purchases of intermediate inputs by our business sector from the non-business sector. The year t price and quantity aggregates, P tGN and Q t GN , that correspond to these value aggre- gates V tGN are calculated using chained Fisher indexes with Q t N getting a negative weight in the index number formula. P tGN and Q t GN are listed in 86Quantities in the Make matrix would have a positive sign while quantities in the Use matrix would have a negative sign. 87See Diewert (2006b)(2007b) and the numerical examples in Diewert (2007c) in par- ticular. 88The 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. 132 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.5. 133 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.5: Price Indexes for Business Sector Outputs: Net Sales to the Non-business Sector Year t P tGN Q t GN 1961 1.00000 1420 1962 0.99388 1447 1963 0.97566 1446 1964 0.92683 1596 1965 0.91239 1798 1966 0.88328 2320 1967 0.89087 2684 1968 0.96139 2950 1969 0.96769 3068 1970 1.00582 3858 1971 1.10291 3885 1972 1.14412 3942 1973 1.22092 4247 1974 1.35752 4819 1975 1.48446 5397 1976 1.64265 5254 1977 1.78697 5963 1978 1.92861 5833 1979 2.18540 5796 1980 2.48896 6062 1981 2.79431 5845 1982 3.10614 6019 1983 3.37412 5998 1984 3.48567 5838 1985 3.67204 6539 1986 3.74218 6635 1987 3.79747 6789 Continued on Next Page. . . 134 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.5 – Continued Year t P tGN Q t GN 1988 3.78607 7814 1989 3.82606 8423 1990 3.86395 9043 1991 3.92576 9508 1992 3.94383 9458 1993 3.96988 9223 1994 4.17941 8537 1995 4.29853 8165 1996 4.20205 8263 1997 4.10280 8414 1998 4.13974 9511 1999 4.29033 9380 2000 4.43225 10022 2001 4.45850 11040 2002 4.56662 11443 2003 4.56905 12088 2004 4.60878 12331 2005 4.77387 12551 2006 4.93210 13651 2007 5.05578 14632 135 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 We now turn our attention to the export and import components of final demand. Current dollar exports of goods are available as CANSIM II series V498104 for the years 1961-2007. The corresponding chained 2002 dollar series is CANSIM II series V1992061 and we use these two series 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 II series V498105 for the years 1961-2007. The corresponding chained 2002 dollar series is CANSIM II series V1992062 and we use these two series to form price and quantity series for the exports of services, P t16 and Q t 16, which are listed in Tables 2.6 and 2.7. 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 seven classes for the years 1971-2007: • Q9, Exports of agricultural and fish products; • Q10, Exports of energy products; • Q11, Exports of forest products; • Q12, Exports of industrial goods and materials (excluding energy and forest product exports); • Q13, Exports of machinery and equipment (excluding automotive prod- ucts); • Q14, Exports of automotive products and • Q15, Exports of other consumer goods (excluding automotive prod- ucts). 136 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 The CANSIM series numbers for the first seven 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 1997 chained dollars) can be found for the years 1981-2007 in CANSIM Table 3800012 and the series numbers are V1992162- V1992168. We used these series to form chained price and quantity series for these seven export categories for the years 1981-2007. 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 1971.89 There remains the problem of obtaining price series for the above 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 com- modity sections, current values, we can obtain value series covering exports for the years 1946-1975 for the following five 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 five 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 five classes of exports that cover the years 1961-1971. Unfortunately, these price indexes are of the fixed base 89There 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. 137 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 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 five series back to 1961. The above operations give us five disaggregated export price and quantity series for the period 1961-1971 but we have seven classes of exports of goods for the years 1971-2007. 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, P t9 and Q t 9, 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 six 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, P t10 and Q t 10, for energy at the year 1971. In order to create aggregate Forestry exports for the years 1961-1971, we aggregated data for seven classes of forest product exports using the M level of aggregation: Lumber and timber, Veneer and plywood, Other wood fab- 138 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 ricated 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, P t11 and Q t 11, for forest product exports at the year 1971. We aggregated the input output data for two classes of automotive prod- uct exports using the M level of aggregation: Motor vehicles and Motor ve- hicle 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, P t14 and Q t 14, for automotive product exports at the year 1971. In order to create an aggregate for Exports of other consumer goods (ex- cluding automotive products) for the years 1961-1971, we aggregated data for eight classes of consumer goods type exports using the M level of ag- gregation: Leather and leather products, Other textile products, Hosiery and knitted wear, clothing and accessories, appliances and receivers (house- holds), 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, P t15 and Q t 15, for exports of other consumer goods at the year 1971. We generated price and quantity series over the years 1961-1971 for Ex- ports of industrial goods and materials (excluding energy and forest product exports), P t12 and Q t 12, as a chained Fisher aggregate of our price and quan- tity series for Crude materials (inedible) (G419) and Fabricated materials (inedible) (G421) less our series for exports of energy products P t10 and Q t 10) and exports of forest products (P t11 and Q t 11). 90 The resulting export price 90All 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. 139 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 and quantity series for the years 1961-1971 are linked to our earlier series for P t12 and Q t 12 at the year 1971. Finally, we generated price and quantity series over the years 1961-1971 for Exports of machinery and equipment (excluding automotive products), P t13 and Q t 13, 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 P t14 and Q t 14) and less exports of other consumer goods (P t15 and Q t 15). 91 The resulting export price and quantity series for the years 1961-1971 are linked to our earlier series for P t13 and Q t 13 at the year 1971. There is one additional adjustment which affects the price of energy ex- ports. During the years 1974-1985, Canada imposed an export tax on its energy exports, which is included in the price of exports. However, produc- ers 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 se- ries V499746 from the National Income and Expenditure Accounts. After making this adjustment, the resulting price and quantity series are P t10 and Qt10, which are listed in Tables 2.6 and 2.7 along with the other price and quantity series for the eight classes of exports. 91All 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. 140 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.6: Price Indexes for Eight Commodity Classes of Exports, 1961-2007 Year t P t9 P t 10 P t 11 P t 12 P t 13 P t 14 P t 15 P t 16 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 0.99880 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 1.21130 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 1.34434 1.61655 1.49521 1.46833 1.18656 1.25988 1.79018 1974 2.47603 2.37211 1.97968 1.94140 1.65047 1.27902 1.42184 2.02338 1975 2.44172 3.47049 2.31660 2.10541 1.86186 1.40313 1.56638 2.29526 1976 2.27544 4.36340 2.39386 2.22651 1.90587 1.48840 1.66746 2.51896 1977 2.13627 5.37242 2.62455 2.50906 2.02758 1.61582 1.76846 2.72893 1978 2.37658 5.96944 2.90165 2.77108 2.11566 1.78223 1.88273 2.90258 1979 2.88982 7.40098 3.47704 3.53655 2.27395 1.96622 2.00068 3.14587 1980 3.28365 10.39436 3.73797 4.45064 2.41362 2.17714 2.24946 3.49696 1981 3.56932 11.17124 3.96546 4.55036 2.55522 2.41373 2.49659 3.94719 1982 3.46707 11.69844 3.85284 4.31903 2.72280 2.63304 2.66992 4.34103 1983 3.39310 11.53824 3.83642 4.35230 2.75291 2.73815 2.80369 4.66353 1984 3.53005 11.27486 4.26336 4.45480 2.69323 2.90539 2.88654 4.87299 1985 3.51503 10.86479 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 Continued on Next Page. . . 141 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.6 – Continued Year t P t9 P t 10 P t 11 P t 12 P t 13 P t 14 P t 15 P t 16 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 4.14794 23.46718 6.44732 6.11917 2.87531 3.46196 4.51188 8.29947 2006 4.09923 22.90367 6.08392 6.87211 2.82144 3.31328 4.54101 8.42538 2007 4.38863 23.04150 5.71715 7.39951 2.78882 3.16568 4.54902 8.58781 142 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.7: Quantity Indexes for Eight Commodity Classes of Exports, 1961-2007 Year t Qt9 Q t 10 Q t 11 Q t 12 Q t 13 Q t 14 Q t 15 Q t 16 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 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 Continued on Next Page. . . 143 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.7 – Continued Year t Qt9 Q t 10 Q t 11 Q t 12 Q t 13 Q t 14 Q t 15 Q t 16 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 7256.1 3705.8 5653.2 13721.1 32346.3 25417.7 3800.7 8284.5 2006 7613.6 3789.4 5478.7 13664.5 33058.2 24838.7 3922.2 8185.4 2007 7831.6 3977.5 5118.7 14111.7 33500.8 24419.5 4118.9 8042.4 144 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 We now turn our attention to imports. Current dollar information on imports of services can be found as CANSIM II series V498108 for the years 1961-2007 and the corresponding constant 2002 chained dollar series is CANSIM II series V1992065. We use these two series to form price and quantity series for the imports of services, P t23 and Q t 23, which are listed in Tables 2.8 and 2.9. Note that since imported goods and services are inputs into the business sector, when we form a value added aggregate, a minus sign is appended to any quantity series pertaining to imports. As was the case for our treatment of exports, the starting point for ob- taining 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 seven classes of imported good that was used for exports for the years 1971-2007. However, imports of forest products was small throughout the sample period and so this import component was ag- gregated with imports of industrial goods and materials (excluding forest and energy imports).92 Thus we used CANSIM Table 38000012 in order to generate prices and quantities for the following six classes of imports for the years 1971-2007:93 • Q17, Imports of agricultural and fish products; • Q18, Imports of energy products; • Q19, Imports of industrial goods and materials (including imports of forest products but excluding imports of energy products); • Q20, Imports of machinery and equipment (excluding automotive prod- ucts); • Q21, Imports of automotive products and • Q22, Imports of other consumer goods. 92Chained Fisher indexes were used in order to do the aggregation. 93As in the case of export indexes, we used chained indexes whenever they were available. 145 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 There remains the problem of obtaining price series for the above six classes of imports to cover the years 1961-1971. From Leacy (1983), Series G429-442: Foreign trade, imports, excluding coin and bullion, by main com- modity 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 five 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 five 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 five 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 five 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 use the 1948 based indexes to further extend these 5 series back to 1961. The above operations gave us five disaggregated export price and quantity series for the period 1961-1971 but we have six classes of imports of goods for the years 1971-2007. We generated Fisher chained price and quantity indexes for imports of Live animals and for exports of Food, feed, beverages 146 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 and tobacco for the years 1961-1971 and linked these series to our earlier series, P t17 and Q t 17, imports of agricultural and fish products. As was the case for extending our export series back to the 1960s, we need some ad- ditional series so that we can match the import series for the 1960s to the series that cover the post 1971 period. We will create separate import se- ries 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 parallel 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.94 The series on customs import duties is CANSIM II 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 2.8 and 2.9. 94This is only a very rough approximation to the truth. 147 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.8: Price Indexes for Seven Commodity Classes of Imports, 1961-2007 Year t P t17 P t 18 P t 19 P t 20 P t 21 P t 22 P t 23 1961 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1962 1.04883 1.02856 1.05578 1.09816 1.05195 1.01253 1.05228 1963 1.30508 1.00981 1.08637 1.09743 1.06958 1.01429 1.07921 1964 1.28197 1.00471 1.10651 1.09682 1.09414 1.02308 1.09777 1965 1.06938 1.02524 1.12598 1.12082 1.07648 1.02077 1.13619 1966 1.05080 1.05430 1.13068 1.15070 1.09270 1.03586 1.17024 1967 1.02344 0.98958 1.16189 1.18684 1.12302 1.05402 1.22610 1968 1.05513 1.04752 1.14800 1.19862 1.16016 1.06806 1.28761 1969 1.06398 1.00624 1.17757 1.21963 1.18860 1.08873 1.36902 1970 1.13052 1.01555 1.19414 1.22480 1.20108 1.09806 1.42900 1971 1.16283 1.11732 1.16445 1.25747 1.24031 1.10649 1.49900 1972 1.24651 1.20329 1.15700 1.26668 1.26989 1.14591 1.53952 1973 1.52015 1.43514 1.27659 1.29789 1.29640 1.18635 1.63282 1974 1.87300 4.22172 1.65984 1.42128 1.40659 1.29665 1.75102 1975 1.97450 5.43394 1.83511 1.67222 1.63529 1.44968 1.98130 1976 1.85375 5.63358 1.85932 1.67883 1.71458 1.52194 2.04366 1977 2.24663 6.42113 2.09118 1.81185 1.93225 1.71419 2.34119 1978 2.49806 7.14772 2.42204 1.83462 2.20965 1.95044 2.69834 1979 2.79922 9.22856 2.93293 1.94108 2.44387 2.14927 3.04229 1980 3.05858 14.04487 3.40659 1.71574 2.71841 2.44883 3.39335 1981 3.35205 16.89476 3.70305 1.67637 3.26363 2.79785 3.81611 1982 3.27980 16.65354 3.79588 1.82550 3.52543 2.94081 4.10352 1983 3.19245 15.35401 3.78529 1.74893 3.62370 2.95617 4.30819 1984 3.39093 15.57686 3.91220 1.78888 3.82410 3.17305 4.63802 1985 3.29961 16.05971 3.85316 1.81429 4.02632 3.27951 4.98855 1986 3.52718 10.45556 3.94881 1.83440 4.20229 3.51229 5.29276 1987 3.44257 10.91648 3.94832 1.74520 4.15738 3.53064 5.28864 Continued on Next Page. . . 148 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.8 – Continued Year t P t17 P t 18 P t 19 P t 20 P t 21 P t 22 P t 23 1988 3.50154 9.09050 4.05930 1.67407 4.03524 3.50861 5.09254 1989 3.45272 9.69611 4.06260 1.63403 4.08857 3.52386 5.09401 1990 3.45595 11.94481 4.01098 1.61746 4.16440 3.57930 5.24914 1991 3.43419 10.19284 3.86391 1.58265 4.12731 3.59254 5.31731 1992 3.43112 10.16216 3.93946 1.63533 4.39452 3.79083 5.63381 1993 3.44632 9.84044 4.05394 1.70897 4.68083 4.02323 6.19826 1994 3.70890 9.83576 4.32449 1.78245 4.99133 4.27046 6.68231 1995 3.92677 10.17736 4.70222 1.74664 5.15679 4.39186 6.90224 1996 3.88275 11.94335 4.52874 1.66405 5.19805 4.36419 7.01253 1997 3.99625 11.84732 4.52516 1.62932 5.26105 4.38392 7.26074 1998 3.97357 9.76539 4.64624 1.67064 5.51748 4.66991 7.80221 1999 3.85703 11.43514 4.55850 1.62996 5.52100 4.67035 7.97505 2000 3.84946 16.95310 4.72363 1.59815 5.52428 4.69368 8.18543 2001 3.99707 16.32263 4.90529 1.63313 5.67016 4.91888 8.64576 2002 4.05634 16.80830 4.85791 1.63385 5.73431 4.93873 8.84642 2003 3.91718 18.58307 4.58281 1.46138 5.39577 4.49645 8.39644 2004 3.81803 21.35868 4.74735 1.34910 5.21353 4.18264 8.24087 2005 3.72978 27.03564 4.82559 1.26664 5.00314 4.01666 8.14870 2006 3.62982 30.53146 5.01981 1.20443 4.84982 3.84873 8.19437 2007 3.73318 31.10128 4.92307 1.14851 4.63116 3.67501 8.15599 149 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.9: Quantity Indexes for Seven Commodity Classes of Imports, 1961-2007 Year t Qt17 Q t 18 Q t 19 Q t 20 Q t 21 Q t 22 Q t 23 1961 824.1 478.0 1850.2 1840.7 615.1 754.0 1535.0 1962 840.3 480.7 1926.5 1797.9 699.1 811.6 1479.6 1963 786.0 541.8 1952.1 1788.1 707.1 799.6 1466.8 1964 810.8 547.7 2235.8 2092.0 857.4 842.2 1618.7 1965 934.5 583.4 2482.1 2400.7 1157.2 948.7 1692.5 1966 1026.7 592.8 2666.5 2826.7 1573.4 1066.8 1850.0 1967 1086.6 638.9 2528.6 3077.0 1963.9 1109.3 1934.6 1968 1127.9 685.5 2726.8 3135.8 2649.7 1240.3 2013.8 1969 1290.9 737.9 3052.2 3522.5 3030.9 1461.0 2336.7 1970 1279.6 766.3 3041.7 3548.7 2758.7 1459.4 2471.7 1971 1293.5 817.1 3359.3 3712.9 3249.2 1650.7 2476.3 1972 1424.2 895.9 3855.8 4450.5 3819.2 2010.7 2585.9 1973 1625.4 928.1 4182.5 5370.1 4619.0 2325.5 2888.3 1974 1674.4 788.6 4742.9 6357.6 4931.1 2642.7 3277.5 1975 1675.3 766.1 4071.1 6031.1 4954.5 2583.3 3550.2 1976 1940.0 719.6 4177.8 6189.4 5417.1 2998.7 3971.3 1977 1846.2 654.2 4160.4 6312.2 5864.7 2943.3 3883.1 1978 1872.6 625.7 4499.4 7651.1 5918.6 2988.3 3824.2 1979 1855.1 624.7 5082.4 9325.4 6096.9 3148.4 3637.1 1980 1921.5 598.8 4917.6 12269.7 4900.3 3016.1 3760.0 1981 1994.6 573.7 5163.8 15342.7 4799.6 3113.5 3860.0 1982 1914.8 404.5 4146.0 11976.5 4128.6 2890.3 3594.5 1983 1985.9 336.2 4779.6 13552.5 5142.3 3228.1 3689.7 1984 2169.3 393.7 5469.4 16671.9 6668.0 3613.1 3774.9 1985 2190.2 395.2 6052.7 17490.1 7684.4 3557.1 3904.9 1986 2287.9 486.3 6369.6 19038.1 7845.2 3806.2 4267.7 1987 2388.1 541.7 6424.7 21231.5 7844.3 3991.8 4536.3 Continued on Next Page. . . 150 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.9 – Continued Year t Qt17 Q t 18 Q t 19 Q t 20 Q t 21 Q t 22 Q t 23 1988 2381.6 569.4 7298.0 26838.5 8225.8 4266.7 5184.6 1989 2625.7 641.6 7645.9 29100.6 7812.7 4681.5 5792.5 1990 2779.6 686.3 7577.4 29167.1 7319.2 4868.6 6405.6 1991 2871.4 650.4 7342.9 29676.0 7501.5 5065.0 6664.1 1992 3100.3 637.4 7950.1 31183.3 7664.1 5459.7 6738.8 1993 3437.0 708.1 8947.7 33412.5 8533.4 5711.6 6865.2 1994 3617.1 707.6 10111.7 39325.5 9583.4 5854.9 6755.0 1995 3597.8 711.1 10694.6 45780.5 9712.7 6144.3 6763.0 1996 3839.3 804.2 11268.5 48400.6 9832.0 6242.8 7110.7 1997 4101.5 897.0 13177.8 58701.8 11561.6 7109.8 7374.5 1998 4531.5 884.1 14104.5 63169.9 12105.0 7726.6 7366.6 1999 4760.9 936.4 14810.3 69069.7 13753.7 8239.7 7683.6 2000 4998.2 1053.1 15872.4 79742.9 14016.8 8861.7 8114.0 2001 5301.6 1087.2 15123.8 71310.1 12799.3 9072.2 7954.1 2002 5594.2 985.7 15449.5 67567.7 14207.5 9805.4 8090.6 2003 5735.7 1066.2 15563.8 70541.0 14176.3 10757.9 8830.5 2004 5842.3 1160.3 16838.7 80434.0 14839.8 11893.8 9363.0 2005 6159.0 1245.4 17648.1 91268.2 15667.0 12840.8 9823.2 2006 6731.2 1134.1 18076.1 99174.3 16464.5 14081.0 10104.3 2007 7118.8 1175.8 18659.2 105849.0 17274.7 15541.1 10697.4 151 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 We now turn our attention to forming estimates of business sector labour input. 2.3 Business Sector Labour Input Estimates Quality adjusted measures of the quantity of three types of labour for the years 1961-2007 are available from the Statistics Canada KLEMS produc- tivity program; see CANSIM Table 3830021 which has the title: Multifactor Productivity, Value Added, Capital Input and Labour Input in the Aggre- gate Business Sector and Major Sub-Sectors, by the North American In- dustry Classification System (NAICS). The three series are V41713000 (the title is Canada: Labour Input of Workers with Primary or Secondary Ed- ucation; Business Sector), V41713017 (Labour Input of workers with Some or Completed Post-Secondary Certificate or Diploma; Business Sector) and V41713034 (Labour Input of Workers with University Degree or Above, Business Sector). The corresponding value of labour input or labour com- pensation series are found in the same table and their CANSIM series num- bers are V41713187, V41713204 and V41713221 respectively. These value series however only cover the years 1961-2004.95 These KLEMS labour se- ries allowed us to construct the three business sector labour input series QtL1, Q t L2 and Q t L3 for the years 1961-2007 (see Table 2.10 for a listing of these data) and the corresponding wage index series P tL1, P t L2 and P t L3 for the years 1961-2003 (see Table 2.10). 95This is very puzzling: the quantity series run from 1961 to 2007 but the corresponding value series stops at 2004. 152 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.10: Price and Quantity Indexes for Three Types of Business Sector Labour Year t P tL1 P t L2 P t L3 Q t L1 Q t L2 Q t L3 1961 1.00000 1.00000 1.00000 17122 710 1370 1962 1.02980 1.18632 1.01126 17345 1216 1448 1963 1.05959 1.21347 1.04509 17259 1723 1487 1964 1.10555 1.24560 1.09234 17482 2230 1566 1965 1.18267 1.29309 1.15814 17774 2762 1657 1966 1.26544 1.33357 1.24479 18152 3345 1788 1967 1.34988 1.36529 1.31145 18066 3852 1853 1968 1.44254 1.40528 1.40547 17740 4282 1853 1969 1.55946 1.46444 1.53399 17740 4789 1918 1970 1.66484 1.50846 1.62547 17379 5195 1983 1971 1.77957 1.67298 1.59351 17190 5777 2166 1972 1.93443 1.81847 1.60097 17190 6411 2336 1973 2.13905 1.97009 1.63324 17705 7247 2505 1974 2.49530 2.23902 1.78277 17826 7931 2740 1975 2.90404 2.52097 1.99402 17328 8362 2870 1976 3.39630 2.82284 2.16028 16916 8793 2897 1977 3.75369 3.03206 2.22664 16675 9300 3066 1978 3.90502 3.15557 2.39954 16967 10110 3314 1979 4.17384 3.37618 2.61573 17482 11149 3640 1980 4.51590 3.71514 2.83118 17654 11960 3901 1981 5.00927 4.09363 3.43078 17843 12492 4188 1982 5.50893 4.47191 3.61769 16761 11985 4149 1983 5.58062 4.79842 3.92881 16727 12188 4254 1984 5.95405 4.90205 4.14250 17053 12771 4697 1985 6.20453 5.19867 4.38987 17499 13455 5062 1986 6.33749 5.30440 4.65051 17946 14241 5480 1987 6.64512 5.43184 4.69809 18530 15153 5911 Continued on Next Page. . . 153 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.10 – Continued Year t P tL1 P t L2 P t L3 Q t L1 Q t L2 Q t L3 1988 7.12085 5.79003 4.88684 19045 16040 6432 1989 7.26900 5.96671 5.70897 19268 16648 6798 1990 7.26005 6.49660 5.97755 18908 16927 7007 1991 7.42364 6.73848 6.66739 17843 16547 7137 1992 7.57474 6.90164 6.68101 17242 16471 7450 1993 7.69212 6.83616 6.46124 16864 17079 8246 1994 7.69473 6.84046 6.22327 16795 18371 8768 1995 7.81823 7.01644 6.20187 16692 19537 9055 1996 7.93652 6.96834 6.54102 16812 20322 9538 1997 8.12992 7.18146 7.03193 16332 21918 10073 1998 8.34882 7.36378 7.31313 16383 22679 10856 1999 8.51971 7.52497 7.58425 16984 23414 11325 2000 8.92053 7.90809 7.95222 17311 24199 12082 2001 9.06503 8.10605 8.30514 16967 24706 12695 2002 9.14718 8.18965 8.50473 17173 25339 13048 2003 9.33522 8.37832 8.56340 16778 26226 13517 2004 9.56758 8.56262 8.80245 17156 27113 14313 2005 9.92027 8.90341 9.10008 17122 27062 15292 2006 10.37190 9.30873 9.51436 17396 27189 15983 2007 10.74529 9.64385 9.85688 17242 28101 16818 154 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 The Statistics Canada productivity program aggregate labour input mea- sure 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 aggre- gate labour input measure is constructed by aggregating hours at work data for each of 56 types of workers classified by their edu- cational 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 composi- tion of workers.” John R. Baldwin, Wulong Gu and Beiling Yan 2007; 37. Baldwin, Gu and Yan (2007; 26) describe their more disaggregated mea- sures of labour input as follows: “Labour input for MFPmeasures reflects the compositional shifts of workers by education, experience and class of workers (paid versus self-employed). The growth of labour input (labour ser- vices) 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 QtL1, Q t L2 and Q t L3 is a Fisher quantity aggregate over the other characteris- tics, 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 oc- curred during the 1990s. In the past, it had been assumed that 155 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 the self employed essentially earned incomes similar to the em- ployed. 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 as- sumes that the hourly earning of self-employed workers is pro- portional to that of paid workers with the same level of educa- tion and 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.” Overall, we believe that Statistics Canada has done an excellent job in con- structing their new measures of labour input and we will use these measures in the present study.96 The effect of using the Statistics Canada measures of quality adjusted labour input is to increase the growth of labour input by about 37% over the sample period compared to using hours worked as the measure of labour input.97 Basically, there was a big shift in labour inputs from less skilled and less educated workers to more educated workers over this period which served to greatly increase quality adjusted labour input compared to unweighted hours worked by all types of labour. As noted above, the KLEMS estimates of real labour input for the three types of labour run from 1961-2007 but the corresponding value series stop 96The labour input that is used in the residential rental of housing industry should be deducted from our measure of labour input (since we exclude all residential housing outputs from our definition of the business sector while the KLEMS program business sector excludes only the services of Owner Occupied Housing). However, the KLEMS database that is available in CANSIM does not include information on the three types of labour input that is used in the residential housing rental industry so we were not able to deduct these labour inputs from total business sector labour input. Thus our productivity estimates will have a tiny downward bias due to this factor. 97Estimates of total hours worked in the KLEMS business sector for the years 1961-2007 are available from CANSIM II series V41712966, (Canada, Hours Worked, Business Sector) in Table 3830021 (Multifactor Productivity, Value Added, Capital Input and Labour Input in the Aggregate Business Sector and Major Sub-Sectors, by North American Industry Classification System (NAICS)). 156 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 at 2004. Hence we need to estimate either wages or values for the three types of labour for the years 2004-2007. In order to accomplish this task, we formed our own estimates of the total value of labour input over the years 1961-2007. Estimates of wages, salaries and supplementary labour income for the business sector are available from CANSIM II series V498167 for the years 1961-2007. However, this measure of business sector payments for labour services neglects the labour input of the self-employed (and unpaid family workers); i.e., it includes only the gross wages of employees. The value of the labour services rendered by the self employed are part of the gross operating surplus of the household sector, which includes also the returns to the capital and land used by the self employed. An upper bound to the value of self employed labour services is the sum of unincorporated business net income which is available for 1961-2007 as CANSIM II series V498170. We assumed that two thirds of unincorporated net income is a return to labour and one third is the return to capital. We added this imputed labour income of the self employed to the labour income of employees in the business sector and compared this measure of total business sector labour compensation to the corresponding total labour compensation from the KLEMS database98 and found that these two series were very close until about 1995 and then they gradually diverged to end up about 4% apart in 2003. We used the rates of growth of our imperfect measure of business sector labour income growth to extend the official KLEMS business sector labour compensation series from 2004 to 2007. We then divided this extended measure of total labour compensation by the KLEMS business sector measure of aggregate labour input99 in order to obtain an implicit wage rate for aggregate business sector labour for the years 2004-2007. We used the movements in this implicit wage rate to extend the KLEMS wage indexes P tL1, P t L2 and P t L3 from 2004 to 2007; see Table 2.10 for the results of these manipulations. 98See the CANSIM II series V41713170, Canada, Labour Compensation, Business Sec- tor, in Table 3830021, Multifactor Productivity, Value Added, Capital Input and Labour Input in the Aggregate Business Sector and Major Sub-Sectors, by NAICS. 99See the CANSIM II series V41712949 with the title Canada, Labour Input, Business Sector. 157 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 We now turn our attention to the problems associated with the estimation of beginning of the year capital stocks for the business sector. 2.4 Business Sector Capital Stock Estimates Our general strategy in this section will be to use estimates from the Na- tional Balance Sheets to obtain estimates of inventory and land stocks used by the business sector (see Statistics Canada (1997)). This balance sheet in- formation is also used to calibrate estimates of depreciation for reproducible capital stocks used by the business sector. For the years 1962-2008, beginning of the year estimates of various na- tional wealth components can be obtained from the CANSIM II database. National totals for the value of various assets can be obtained from CANSIM Table 3780004 (National Balance Sheet Accounts, by Sectors) for residential structures (see series V34675), non-residential structures (V34676), machin- ery and equipment (V34677), inventories (V34679) and land (V34680). The same table has the corresponding asset values for the persons and unin- corporated business sector; for residential structures (see series V33464), non-residential structures (V33465), machinery and equipment (V33466), inventories (V33468) and land (V33469). Table 3780004 also has the cor- responding asset values for corporations and government business enter- prises; for residential structures (see series V31693), non-residential struc- tures (V31694), machinery and equipment (V31695), inventories (V31696) and land (V31697). Finally, Table 3780004 has the corresponding asset val- ues for the government sector; for residential structures (see series V32575), non-residential structures (V32576), machinery and equipment (V32577), inventories (V32578) and land (V32579). We subtracted the government sector value of non-residential structures, machinery and equipment and inventories from the corresponding total economy asset values in order to obtain business sector estimates of the value of beginning of the year t busi- ness sector non-residential structure stocks V KtNR, business machinery and equipment stocks, V KtME , and business inventory stocks V K t BI ; see Table 158 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 2.11 for a listing of these business sector stock values. Although residen- tial structures are not part of our domain of definition for business sector output, it will prove useful to have some information on the value of residen- tial structures and residential land for comparison purposes. Thus the total value of residential structures from the national balance sheets for Canada, V KtRS , is also listed in Table 2.11. We ended up not using the balance sheet information on the value of business sector machinery and equipment. Instead, we used the investment series on ICT machinery and equipment, P tIICT and Q t IICT , and on non-ICT machinery and equipment, P tIME and Q t IME , listed in Tables 2.2 and 2.3 that were provided to us by Statistics Canada from their KLEMS database. Statistics Canada also provided us with the companion business sector price and quantity series for the beginning of the year capital stocks for ICT and non-ICT machinery and equipment. This allowed us to compare the two price series for ICT. The KLEMS ICT investment price decreased from 1 in 1961 to 0.214 in 2006 whereas the KLEMS ICT capital stock price decreased from 1 in 1961 to 0.462 in 2006, which is a considerable difference.100 If there were no asset heterogeneity in the class of ICT investments (which there cer- tainly is), then using the geometric model of depreciation (which is used by the KLEMS program), we would expect these two price series to be very close to each other. The KLEMS non-ICT machinery and equipment invest- ment price increased from 1 in 1961 to 4.71 in 2006 whereas the KLEMS non-ICT capital stock price increased from 1 in 1961 to 5.23 in 2006, which again indicates some asset heterogeneity, but the divergence between these two series is not nearly as large as the divergence in the two ICT investment and capital stock price series. The question now arises: which of these two price series should we use for a geometric model of depreciation? 100There are even bigger differences in the rates of growth of the KLEMS ICT capital stocks versus the corresponding KLEMS measures of ICT services growth: the ICT stock grew 110 fold over the period 1961-2006 while the flow of ICT services grew 591 fold over the same period. This seems implausible. 159 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Using the geometric or declining balance depreciation model of depreci- ation, the starting capital stock of a generic asset in period t + 1, QKt+1, is equal to one minus the depreciation rate in period t, δt, times the previ- ous period’s starting stock, QKt, plus the new investment in the previous period, QtI ; i.e., we have: QKt+1 = (1− δt)QKt + QtI (2.6) Given information on beginning of the year capital stocks and investment during each year, the above equation can be solved for a balancing depreci- ation rate, δt, that reconciles the investment information with the balance sheet information: δt = [QKt −QKt+1 + QtI ]/QKt (2.7) Using the Statistics Canada KLEMS database for ICT investment and capital, we tried deflating the value data by either the ICT investment price deflator or the ICT capital stock price deflator. Using the latter deflator, the implied ICT depreciation rate trended up from 0.238 in 1961 to 0.837 in 2005. These depreciation rates seem to be too large. However, when we implemented Equation (2.7) using the ICT investment price deflator, the implied ICT depreciation rate trended up from 0.239 in 1961 to 0.329 in 2005. These depreciation rates seem to be very reasonable so we decided to use the ICT investment price deflator as the price of both ICT investments and capital stocks. Since the implied depreciation rates for ICT capital using Equation (2.7) had a pronounced upward trend, we regressed these rates on a constant and a time trend. The estimated constant was 0.19909 with a standard error of 0.01644 and the estimated trend parameter was 0.00263 with a standard error of 0.0006437 so that both estimated param- eters were significant. Thus we decided to assume a starting depreciation rate of 0.200 in 1961 and we increased this depreciation rate by 0.00263 each subsequent year. We then used Equation (2.6) above along with the Statistics Canada 1961 value of the ICT capital stock as our starting value 160 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 for the 1961 quantity of ICT capital in order to generate a new series for the business sector beginning of the year ICT capital stock, QKtICT (see Table 2.12). An entirely analogous procedure was used to generate a new series for the business sector beginning of the year non-ICT machinery and equipment capital stock, QKtME . Again, we used the KLEMS investment price deflator for non-ICT machinery and equipment, P tIME listed above in Table 2.2 as the deflator for the value of the non-ICT machinery and equipment capital stocks and the associated values of investments from the KLEMS database and we calculated the implied depreciation rates using Equation (2.7). The resulting implied depreciation rates had a small up- ward trend, starting at 0.160 in 1961 and ending up at 0.175 in 2005. Since this implied depreciation rates for ICT capital had an upward trend, we regressed these rates on a constant and a time trend. The estimated con- stant was 0.15034 with a standard error of 0.005459 and the estimated trend parameter was 0.00067351 with a standard error of 0.0002137 so that both estimated parameters were significant. Thus we decided to assume a starting depreciation rate of 0.150 in 1961 and we increased this depreciation rate by 0.00067 each subsequent year. We then used Equation (2.6) along with the Statistics Canada KLEMS program 1961 value of the non-ICT machinery and equipment capital stock as our starting value for the 1961 quantity of non-ICT machinery and equipment capital in order to generate a new series for the business sector beginning of the year ICT capital stock, QKtME (see Table 2.12).101 101We used the rate of price inflation in Machinery and Equipment investment (using national accounts data) over the years 2006-2007 in order to extend P tIICT and P t IME to 2007. 161 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.11: Beginning of Year Asset Values for Residential Structures and Land and Six Business Sector Capital Stocks Year t V KtICT V K t ME V K t NR V K t BI V K t AL V K t BL V K t RL V K t RS 1961 1236 11994 27850 13594 5954 6376 10680 28710 1962 1297 12291 29388 13698 6203 6820 11423 29923 1963 1384 13161 31414 14292 6573 7281 12083 31707 1964 1506 13526 33599 15398 7303 7840 12548 34310 1965 1633 14853 37288 16224 8156 8537 13682 37875 1966 1778 16465 41694 17884 9132 9621 14974 42144 1967 2079 18394 46012 19588 10281 10971 16365 46525 1968 2361 20118 48638 20303 11298 12138 17719 49296 1969 2575 21618 53654 21462 11476 13161 19830 54058 1970 2892 23849 58457 23742 11534 14717 22130 58649 1971 3129 25718 64343 24275 11709 16421 24498 65459 1972 3440 27339 70782 25097 12542 18614 28056 74892 1973 3777 29576 81305 27660 15088 21533 32837 92703 1974 4266 36087 100032 33614 19533 26117 40030 116929 1975 5202 44936 116373 43928 24583 32759 47559 133160 1976 5841 51020 128858 46336 28876 38954 53411 150350 1977 6670 58919 141312 50117 33354 43763 59187 164910 1978 7226 67818 157802 57091 39666 49318 66442 183222 1979 7968 78428 179306 66060 49189 55774 73636 207120 1980 7976 91337 210699 81062 62176 64557 83608 234113 1981 8990 106059 245999 89024 70108 75224 101065 272325 1982 12096 121176 278898 98428 70197 86636 118825 288844 1983 12154 125826 287481 90451 68838 93532 117239 307383 1984 13465 131389 306422 91417 65974 96021 127037 328929 1985 14798 137700 323505 99318 62107 101438 139331 348994 1986 16116 144732 336131 104983 57733 105796 142788 388346 1987 17570 147727 357496 109889 54270 113337 165711 444678 Continued on Next Page. . . 162 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.11 – Continued Year t V KtICT V K t ME V K t NR V K t BI V K t AL V K t BL V K t RL V K t RS 1988 21135 152490 384524 117358 53316 122547 195773 498048 1989 23038 167116 409950 126135 56789 134213 223325 551991 1990 26275 180720 433558 132675 61388 145366 262598 574912 1991 26883 179871 435196 130781 63028 155133 258677 614114 1992 28186 189167 439422 123077 61853 159092 287087 633754 1993 32035 195633 445261 121352 62227 162090 307046 667294 1994 34428 201705 460244 124117 64707 169691 330460 698905 1995 36200 210289 468982 131198 69745 179044 352720 713616 1996 37274 216893 485422 146615 75539 185095 343616 719997 1997 40724 223783 500321 150648 81546 193888 352946 743640 1998 45118 244159 522564 158409 86376 202313 374636 766757 1999 49415 255591 541413 169901 89497 211188 394371 797843 2000 56416 269491 568533 178794 92140 221506 425256 829875 2001 65453 286828 582195 194366 95020 234213 452800 867239 2002 69434 296458 602645 190023 97613 243534 502343 926184 2003 66302 282138 621034 192080 99905 254448 573841 1003732 2004 63616 282551 669186 187291 102197 270107 633362 1099801 2005 64580 287617 723667 193723 104627 293163 733545 1190816 2006 65678 295028 795080 204832 107323 313706 834713 1323948 2007 70684 299576 862641 215812 111010 334379 949764 1468026 163 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Determining the value of business sector land is difficult. The problem is that the household sector owns a considerable amount of land that is used for business purposes; i.e., unincorporated persons own farm land and rental business properties 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 and we are trying to exclude these inputs from our measure of business sector input. We will make some rough approximations in an attempt to solve these difficulties. We first find estimates for the price and quantity of agricultural land, P tAL and QKtAL. Estimates of the area of agricultural land are available for the Census years 1981, 1986, 1991, 1996, 2001 and 2006 from CANSIM II series V32166910 and we interpolated the quantity of land in use in agriculture between these years using constant rates of growth (geometric interpolation). From Leacy (1983), series M-23, Area of Land in Farm Holdings, Census Data in thousands of acres, we can obtain estimates of the area of farm land for 1961 and 1971. After converting from acres to hectares, these data can be appended to the previous data and again geometric interpolation between the various census years can be used to complete our estimates for QKtAL; see Table 2.12 for a listing.102 CANSIM Table 20020 (Balance Sheet of the Agricultural Sector at December 31) has asset value data for the end of the year for 1981-2007, which is beginning of the year values for the years 1982- 2008. The two series that are of interest to us from this table are V157698 (the value of farm real estate) and V157699 (the value of farm land), which we denote by V KtAL for year t. Thus for the years 1982-2008, the price of agricultural land, the price of agricultural land, P tAL can be obtained by dividing V KtAL by QK t AL. For the years 1961-1980, we link P t AL to CANSIM series V381831 (the title is Canada, Value per Acre) in Table 20003, Value per Acre of Farm Land and Buildings. This last series runs from 1961 to 2008 and we found that it was quite close to P tAL for the overlap years 1981- 2008. With estimates for the price and quantity of agricultural land for the 102As usual, the listed data are normalised so that the corresponding price is unity in 1961. 164 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 years 1961-1980, we can form estimates for the corresponding values, V KtAL; see Table 2.11. The price and quantity of agricultural land, P tAL and QK t AL, are listed in Tables 2.13 and 2.14. We assumed that agricultural land is an input into our business sector. We also assumed that the value of residential land, V KtRL, is equal to the total value of household and unincorporated business land less the value of agricultural land. Finally, we assumed that the value of non-agricultural business land is equal to equal to the value of corporate enterprise land, V KtBL; see Table 2.11. We also assumed that the quantity of residential land QKtRL and the quan- tity of business non-agricultural land QKtBL are constant over the sample period and hence the corresponding price series P tRL and P t BL are propor- tional to the corresponding value series V KtRL and V K t BL for the years 1962-2007. We extended these two price series back to 1961 using the move- ment from 1961 to 1962 in another land price series; namely series S319 in Leacy (1983): Average Land Cost per Dwelling Unit, NHA, Single De- tached. These land price series, P tRL and P t BL are listed in Table 2.13 and the corresponding quantity series, QKtRL and QK t BL are listed in Table 2.14. 103 From Table 2.2, we have price deflators for non-residential structures for year t, P tINR, and we use these deflators to divide V K t NR by P t INR in order to obtain preliminary beginning of the year capital stock quantity series QKtME and QKtNR. 104 Recall that a series for the annual quantity of investment in 103The Statistics Canada KLEMS program made available to us their aggregate price and quantity series for land used in the business sector. These series cover our agricultural land and our nonagricultural and nonresidential land series and also cover the part of residential land that applies to rental housing. The KLEMS capital stock of land grew 2.01 fold over the period 1961-2006 and the corresponding price series grew 18.7 fold. On the other hand, our estimate of the growth in the quantity of agricultural land and nonresidential and nonagricultural business land is essentially zero, with corresponding 18.6 fold and 48.5 fold increases in the price of these two business land components. We estimate even higher growth rates in the price of residential land but more research in this area is needed. 104The use of these prices (which are average prices over the year) for stock deflation purposes is not quite appropriate because conceptually, we should be using the prices that 165 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 non-residential structures, QtINR, is available from Table 2.3. Now we will apply Equation (2.7) again and generate a series of geometric depreciation rates δtNR for the non-residential stock of structures for the years 1962- 2006. The mean of these depreciation rates turned out to be 0.0616 with a standard deviation of 0.03253, so there was a considerable amount of variability in these rates. There appeared to be a slight upward trend in these depreciation rates so we regressed them on a time trend. The estimated constant was 0.045439 with a standard error of 0.009565 and the estimated trend parameter was 0.0007034 with a standard error of 0.0003621. Thus we decided to assume a starting depreciation rate of 0.045 in 1961 and we increased this depreciation rate by 0.0007 each subsequent year. We then used Equation (2.6) along with the Statistics Canada balance sheet value of the stock of non-residential structures in 1962 as our starting value in order to generate a new series for the business sector beginning of the year non-residential capital stock, QKtNR (see Table 2.14). From Table 2.2, we have price deflators for residential structures for year t, P tIR, and we use these deflators to divide V K t RS by P t IR in order to ob- tain preliminary beginning of the year capital stock quantity series, QKtRS . Recall that a series for the annual quantity of investment in residential struc- tures, QtIR, is available from Table 2.3. Now we are in a position to apply Equation (2.7) again and generate a series of geometric depreciation rates δtRS for the residential structures capital stock for the years 1962-2006. The mean of these depreciation rates turned out to be 0.040239 with a standard deviation of 0.01795. There appeared to be no trends in these depreciation rates so we decided to assume a constant geometric depreciation rate of 0.04 for each year. We then used Equation (2.6) along with the Statistics Canada balance sheet value of the stock of residential structures in 1962 as our starting value in order to generate a new series for the business sector beginning of the year residential capital stock, QKtRS (see Table 2.14). prevail for these stock components at the beginning of the year rather than the average prices in the year which follows. However, for our purposes, the errors made here will not be material. 166 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 The smoothed geometric depreciation rates δtICT , δ t ME , δ t NR and δ t RS are listed in Table 2.12. Table 2.12: Smoothed Geometric Depreciation Rates for ICT, Non-ICT Machinery and Equipment, Non-residential Struc- tures and Residential Structures Capital Stocks Implied by the Balance Sheets and Investment Flow Data Year t δtICT δ t ME δ t NR δ t RS 1961 0.20000 0.15000 0.0450 0.04 1962 0.20263 0.15067 0.0457 0.04 1963 0.20526 0.15134 0.0464 0.04 1964 0.20789 0.15201 0.0471 0.04 1965 0.21052 0.15268 0.0478 0.04 1966 0.21315 0.15335 0.0485 0.04 1967 0.21578 0.15402 0.0492 0.04 1968 0.21841 0.15469 0.0499 0.04 1969 0.22104 0.15536 0.0506 0.04 1970 0.22367 0.15603 0.0513 0.04 1971 0.22630 0.15670 0.0500 0.04 1972 0.22893 0.15737 0.0527 0.04 1973 0.23156 0.15804 0.0534 0.04 1974 0.23419 0.15871 0.0541 0.04 1975 0.23682 0.15938 0.0548 0.04 1976 0.23945 0.16005 0.0555 0.04 1977 0.24208 0.16072 0.0562 0.04 1978 0.24471 0.16139 0.0569 0.04 1979 0.24734 0.16206 0.0576 0.04 1980 0.24997 0.16273 0.0583 0.04 1981 0.25260 0.16340 0.0590 0.04 1982 0.25523 0.16407 0.0597 0.04 1983 0.25786 0.16474 0.0604 0.04 Continued on Next Page. . . 167 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.12 – Continued Year t δtICT δ t ME δ t NR δ t RS 1984 0.26049 0.16541 0.0611 0.04 1985 0.26312 0.16608 0.0618 0.04 1986 0.26575 0.16675 0.0625 0.04 1987 0.26838 0.16742 0.0632 0.04 1988 0.27101 0.16809 0.0639 0.04 1989 0.27364 0.16876 0.0646 0.04 1990 0.27627 0.16943 0.0653 0.04 1991 0.27890 0.17010 0.0660 0.04 1992 0.28153 0.17077 0.0667 0.04 1993 0.28416 0.17144 0.0674 0.04 1994 0.28679 0.17211 0.0681 0.04 1995 0.28942 0.17278 0.0688 0.04 1996 0.29205 0.17345 0.0695 0.04 1997 0.29468 0.17412 0.0702 0.04 1998 0.29731 0.17479 0.0709 0.04 1999 0.29994 0.17546 0.0716 0.04 2000 0.30257 0.17613 0.0723 0.04 2001 0.30520 0.17680 0.0730 0.04 2002 0.30783 0.17747 0.0737 0.04 2003 0.31046 0.17814 0.0744 0.04 2004 0.31309 0.17881 0.0751 0.04 2005 0.31572 0.17948 0.0758 0.04 2006 0.31835 0.18015 0.0765 0.04 2007 0.32098 0.18082 0.0772 0.04 168 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.13: Prices for Residential Structures and Land and Six Business Sector Capital Stocks Year t PKtICT PK t ME PK t NR PK t BI P t AL P t BL P t RL P t RS 1961 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1962 0.99939 1.01477 1.00592 1.00758 1.04000 1.06956 1.06956 1.00504 1963 0.99650 1.06598 1.03251 1.01000 1.10000 1.14186 1.13138 1.02769 1964 1.00502 1.06773 1.06158 1.02114 1.22000 1.22953 1.17489 1.07312 1965 1.02393 1.10198 1.12281 1.03951 1.36000 1.33883 1.28108 1.13368 1966 1.02944 1.12251 1.19323 1.06286 1.52000 1.50884 1.40204 1.20765 1967 1.07473 1.12792 1.24188 1.08044 1.72000 1.72055 1.53236 1.28518 1968 1.10902 1.13973 1.25227 1.09271 1.90000 1.90357 1.65913 1.31431 1969 1.14444 1.17197 1.32495 1.11812 1.94000 2.06400 1.85677 1.38118 1970 1.19472 1.23029 1.39058 1.14350 1.96000 2.30803 2.07210 1.42615 1971 1.22722 1.27216 1.46812 1.15918 2.00000 2.57526 2.29387 1.53179 1972 1.26956 1.30444 1.55098 1.21176 2.16000 2.91918 2.62704 1.67349 1973 1.30782 1.34535 1.71873 1.32609 2.62000 3.37696 3.07471 1.97123 1974 1.35698 1.51430 2.03419 1.43765 3.42000 4.09586 3.74822 2.36134 1975 1.45867 1.73112 2.27337 1.55864 4.34000 5.13750 4.45312 2.56072 1976 1.45190 1.82918 2.40093 1.66364 5.14000 6.10905 5.00114 2.76853 1977 1.44467 1.98862 2.52980 1.78349 5.92000 6.86323 5.54193 2.87768 1978 1.40748 2.19453 2.71145 1.94126 7.02000 7.73441 6.22122 3.04069 1979 1.38366 2.44348 2.96312 2.15180 8.68000 8.74688 6.89491 3.28046 1980 1.21888 2.69736 3.32520 2.35895 10.94000 10.12430 7.82863 3.55455 1981 1.12880 2.98813 3.68676 2.57823 12.30000 11.79717 9.46319 3.99273 1982 1.16812 3.19883 3.96113 2.77940 12.28000 13.58689 11.12613 4.08226 1983 1.02222 3.26756 3.93090 2.93246 12.00746 14.66837 10.97760 4.25350 1984 0.96342 3.40812 4.08142 3.06736 11.47452 15.05871 11.89508 4.41785 1985 0.89167 3.57237 4.21351 3.14959 10.77083 15.90824 13.04615 4.55564 1986 0.82129 3.70845 4.27520 3.18232 9.98330 16.59100 13.36985 4.90827 1987 0.75277 3.69804 4.47320 3.23099 9.38642 17.77433 15.51626 5.40819 Continued on Next Page. . . 169 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.13 – Continued Year t PKtICT PK t ME PK t NR PK t BI P t AL P t BL P t RL P t RS 1988 0.71401 3.69075 4.72840 3.28744 9.22342 19.21871 18.33108 5.78293 1989 0.64691 3.79390 4.92520 3.34034 9.82631 21.04826 20.91090 6.13195 1990 0.61403 3.87130 5.08853 3.38833 10.62426 22.79735 24.58825 6.11231 1991 0.54586 3.74170 5.00311 3.39008 10.91042 24.32908 24.22111 6.32257 1992 0.51043 3.88288 4.97541 3.54606 10.69755 24.94996 26.88125 6.39710 1993 0.50164 4.04523 5.03758 3.55229 10.75269 25.42013 28.75011 6.58445 1994 0.48119 4.24754 5.20497 3.72829 11.17139 26.61217 30.94243 6.76485 1995 0.44755 4.44740 5.27332 3.85944 12.03048 28.07898 33.02674 6.76717 1996 0.41150 4.57050 5.43035 3.94827 13.01832 29.02794 32.17431 6.75581 1997 0.39399 4.69221 5.56694 3.81073 14.07653 30.40692 33.04791 6.87512 1998 0.36919 4.90374 5.71450 3.83563 14.93456 31.72819 35.07889 6.95993 1999 0.33873 4.94358 5.82995 3.89582 15.49944 33.12003 36.92678 7.13210 2000 0.32384 5.01831 6.02775 3.98639 15.98327 34.73818 39.81866 7.29782 2001 0.31733 5.17017 6.07934 4.07102 16.50975 36.73098 42.39774 7.48766 2002 0.30560 5.25354 6.18175 4.13975 16.95600 38.19277 47.03668 7.81242 2003 0.27567 4.94953 6.30506 3.90062 17.34990 39.90438 53.73129 8.21290 2004 0.24913 4.85253 6.70389 3.94012 17.74345 42.36014 59.30452 8.71618 2005 0.23077 4.79667 7.12403 3.98736 18.16070 45.97595 68.68515 9.11452 2006 0.21439 4.71044 7.64020 4.05205 18.62402 49.19765 78.15794 9.78750 2007 0.20857 4.58255 8.04719 4.17868 19.25890 52.43974 88.93074 10.49192 170 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.14: Quantities of Residential Structures and Land and Six Business Sector Capital Stocks Year t QKtICT QK t ME QK t NR QK t BI QK t AL QK t BL QK t RL QK t RS 1961 1236 11994 27850 13594 5954 6376 10680 28710 1962 1298 12112 29215 13595 5965 6376 10680 29773 1963 1389 12346 30425 14150 5976 6376 10680 30853 1964 1499 12668 31650 15079 5986 6376 10680 31972 1965 1595 13478 33210 15607 5997 6376 10680 33409 1966 1727 14668 34942 16826 6008 6376 10680 34898 1967 1934 16308 37050 18130 5977 6376 10680 36201 1968 2129 17651 38840 18580 5946 6376 10680 37507 1969 2250 18446 40495 19195 5915 6376 10680 39139 1970 2420 19385 42038 20763 5885 6376 10680 41124 1971 2550 20216 43827 20942 5854 6376 10680 42733 1972 2710 20958 45637 20711 5806 6376 10680 44752 1973 2888 21984 47305 20858 5759 6376 10680 47028 1974 3144 23831 49175 23381 5711 6376 10680 49518 1975 3566 25958 51190 28184 5664 6376 10680 52001 1976 4023 27892 53670 27852 5618 6376 10680 54307 1977 4617 29628 55859 28101 5634 6376 10680 57307 1978 5134 30903 58198 29409 5650 6376 10680 60257 1979 5759 32097 60513 30700 5667 6376 10680 63137 1980 6544 33862 63364 34364 5683 6376 10680 65863 1981 7965 35493 66725 34529 5700 6376 10680 68205 1982 10355 37881 70409 35413 5716 6376 10680 70756 1983 11890 38508 73134 30845 5733 6376 10680 72266 1984 13976 38552 75077 29803 5750 6376 10680 74455 1985 16596 38546 76778 31534 5766 6376 10680 76607 1986 19623 39028 78623 32989 5783 6376 10680 79121 1987 23340 39947 79920 34011 5782 6376 10680 82223 Continued on Next Page. . . 171 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.14 – Continued Year t QKtICT QK t ME QK t NR QK t BI QK t AL QK t BL QK t RL QK t RS 1988 29601 41317 81322 35699 5781 6376 10680 86124 1989 35612 44049 83235 37761 5779 6376 10680 90019 1990 42792 46682 85203 39156 5778 6376 10680 94058 1991 49249 48072 86985 38578 5777 6376 10680 97130 1992 55220 48718 88319 34708 5782 6376 10680 99069 1993 63861 48362 88388 34162 5787 6376 10680 101344 1994 71547 47487 88424 33291 5792 6376 10680 103314 1995 80884 47284 88935 33994 5797 6376 10680 105453 1996 90581 47455 89391 37134 5803 6376 10680 106574 1997 103363 47692 89874 39533 5793 6376 10680 108164 1998 122207 49790 91445 41299 5784 6376 10680 110167 1999 145882 51702 92868 43611 5774 6376 10680 111867 2000 174209 53702 94319 44851 5765 6376 10680 113715 2001 206260 55477 95766 47744 5755 6376 10680 115823 2002 227207 56430 97488 45902 5757 6376 10680 118553 2003 240511 57003 98498 49243 5758 6376 10680 122214 2004 255354 58228 99821 47534 5760 6376 10680 126179 2005 279847 59962 101581 48584 5761 6376 10680 130651 2006 306347 62633 104065 50550 5763 6376 10680 135269 2007 338899 65373 107198 51646 5764 6376 10680 139920 172 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 End of the year current market value starting stocks of inventories for the entire economy and for the government sector are available from the National Balance Sheet Accounts; see CANSIM series V34679 and V32578 (Table 3780004) for the years 1961-2007. Subtracting the government in- ventory stocks from the total inventory stocks will give us estimates for the value of the business sector beginning of the year inventory stocks for the years 1962-2008, V KtBI . We can subtract the value of inventory change for 1961 (see CANSIM II series V498100; Table 3800002; Canada, Current Prices, Business Investment in Inventories) from the starting stock of inven- tories in 1962 in order to extend the value of inventory stock series back to 1961. Diewert (2002), drawing on Diewert and Lawrence (2000), used older national balance sheet information to construct current and constant dollar estimates of beginning of the year stocks of inventories for the years 1962-1999. These series may be used to construct a price of inventory series P tBI for the years 1962-1999. We extended this price series to the years 1961 and 2000-2005 by using the Industrial Product Price Index for Canada and for All Commodities, CANSIM II series V1574377, table 3290039. The inventory value series V KtBI can be divided by the inventory stock price series P tBI , in order to obtain a real beginning of the year business sector stock of inventories, QKtBI . The resulting price and quantity series (after normalization so that the price is unity in 1961) are listed in Table 2.13 for P tBI and Table 2.14 for QK t BI . 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 II series V498100 estimates the cur- rent 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 ob- tain an alternative SNA based estimated value of inventory change, which ended up at $91,315 million at the start of 2007. However, using the balance sheet estimates for the beginning of 2008 value of business inventories, we 173 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 obtained the estimate $215,812 million, which is 2.35 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 im- plies an increasing need for inventories. In any case, we will take the balance sheet estimates of inventory stocks as the “truth”.105 Recalling Tables 2.2 and 2.3, a preliminary price series for inventory change P tII in year t is set equal to P t+1 BI listed in Table 2.13. 106 A pre- liminary series for the quantity of inventory change in year t listed, QtII , is set equal to the stock at the beginning of year t + 1, QKt+1BI , less the stock at the beginning of year t, QKtBI . These preliminary series, P t II and Q t II are then re-normalized so that P tII equals unity in 1961 and these re-normalized series are the series which appear in Tables 2.2 and 2.3. 2.5 Primary Input Tax Rates, Balancing Real Rates of Return and User Costs Non-residential 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 con- structing user costs of capital for business non-residential structures and business land. Information on property taxes for the years 1961-2007 is available from Statistics Canada; see CANSIM II series V499942, Table 105This 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. 106Diewert (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. 174 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 3800035 (Real Property Taxes of Local Governments) and CANSIM II se- ries V499841, Table 3800033 (Real Property Taxes of Provincial Govern- ments). We approximate the asset base on which these taxes fall as the total beginning of the year national value of land, residential structures and non-residential structures. Data on these values are available for the years 1962-2008 from the National Balance Sheets and these data are described at the beginning of Section 2.4. 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 τ tP in Table 2.15 107 and it will be used in the construction of the user costs of business sector land and non-residential structures.108 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 provided 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 II series V1992216, Table 3800001) less local government and provincial gov- ernment property taxes; • Total government taxes on income from corporations and government business enterprises (CANSIM II series V499131, Table 3800007 ) and • Total government taxes on income from non-residents (CANSIM II series V499132, Table 3800007). The sum of the above three sources of general business taxes that fall on capital stock components was divided by the corresponding sum of the beginning of the year value of assets for our six types of business sector asset; 107The tax rate for 1961 was set equal to the corresponding rate for 1962. 108This is a very rough approximation to the actual property tax rates on business sector land and non-residential 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. 175 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 i.e., the above sum of taxes for year t was divided by PKtICT×QKtICT (year t starting value of ICT machinery and equipment) plus PKtME×QKtME (year t starting value of non-ICT machinery and equipment) plus PKtNR×QKtNR (year t starting value of non-residential structures) plus PKtBL×QKtBL (year t starting value of business sector land) plus PKtAL×QKtAL (year t starting value of agricultural land) plus P tBI ×QKtBI (year t value of starting stocks of inventories) and the resulting year t general business tax rate is denoted as τ tB, which is listed in Table 2.15. Using the property tax rates τ tP , the general business tax rates τ t B, the ICT machinery and equipment depreciation rate δtICT , the non-ICT machinery and equipment depreciation rates δtME and the non-residential structures depreciation rates δtNR, the user costs of ICT and non-ICT machinery and equipment, non-residential structures, business land, agricultural land and inventories, U tICT , U t ME , U t NR, U t BL, U t AL and U t BI respectively, can be de- fined as follows,109 U tICT ≡ [rt + τ tB + δtICT ]PKtICT (2.8) U tME ≡ [rt + τ tB + δtME ]PKtME (2.9) U tNR ≡ [rt + τ tB + τ tP + δtNR]PKtNR (2.10) U tBI ≡ [rt + τ tB]PKtBI (2.11) U tAL ≡ [rt + τ tB + τ tP ]PKtAL (2.12) U tBL ≡ [rt + τ tB + τ tP ]PKtBL (2.13) 109For additional material on user costs and many historical references, see Jorgenson (1989)(1996a) (1996b)and Diewert (2005a)(2006a) . 176 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 where rt is suitable real rate of return 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;110 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 (2.8)-(2.13) 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: P tCQ t C + P t IGQ t IG + P t IRQ t IR + P t INRQ t INR + P t IMEQ t IME +P tIIQ t II + P t GNQ t GN + P t XGQ t XG + P t XSQ t XS + P t MGQ t MG + P t MSQ t MS = P tL1Q t L1 + P t L2Q t L2 + P t L3Q t L3 + [r t + τ tB + δ t ICT ]PK t ICTQK t ICT +[rt + τ tB + δ t ME ]PK t MEQK t ME 110For most purposes, it is probably preferable to use an exogenous real rate of return in the user costs (2.8)-(2.13) since the resulting prices will probably approximate market rental prices better. For discussion of this topic, see Diewert (2006a). However, in our study of productivity growth, there was little difference in the empirical results if the sample average real rate of return (4.827%) was used in place of the balancing real rate; i.e., in the gross output model, average TFP growth changed from 1.01% to1.25% per year and in the net output model, average TFP growth changed from 1.04% to 1.25% per year. This is similar to results obtained by Diewert and Lawrence (2005)(2006) for Australia. Their first study used the sample average balancing real rate for Australia whereas their second study used the year by year balancing real rates of return. However, Baldwin and Gu (2007; 27) found substantial differences for the Canadian business sector in their TFP growth rates for the period 1961-1981 where their estimated average TFP growth rates increased from the 0.90 to 1.01% per year range using balancing or endogenous interest rates to the 1.18 to 1.26% range using an exogenous interest rate. The differences that Baldwin and Gu (2007; 28) found for the 1981-2001 period were not nearly as large: an increase from the 0.30-0.38% range to the 0.32-0.43% range. Baldwin and Gu (2007; 18) mention that they used a constant real rate of interest equal to 5.1 % in their exogenous interest rate models, which is very close to the 4.827 % real rate that we used in our exogenous real rate computations. 177 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 +[rt + τ tB + τ t P + δ t NR]PK t NRQK t NR + [r t + τ tB + τ t P ]PK t BLQK t BL +[rt + τ tB + τ t P ]PK t ALQK t AL + [r t + τ tB]PK t BIQK t BI (2.14) where the various price and quantity series are defined in the tables of this Chapter.111 The resulting series of balancing real rates of return is listed in Table 2.15. Once rt has been determined, then the six series of user costs defined by (2.8)-(2.13) can also be calculated; these series are also listed in Table 2.15. Note that rt is a real after tax 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. 111P tXG and Q t XG are chained Fisher aggregates of our seven classes of exports of goods, P tXS and Q t XS are the price and quantity of exports of services, P t MG and Q t MG are chained Fisher aggregates of our six classes of imports of goods and P tMS and Q t MS are the price and quantity of imports of services. 178 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.15: Business Sector Tax Rates, Balancing Real Rates of Return and User Costs Year t τtP τ t B r t UtICT U t ME U t NR U t BI U t AL U t BL 1961 0.01528 0.03225 0.03650 0.26875 0.21875 0.12903 0.06875 0.08403 0.08403 1962 0.01528 0.03281 0.03578 0.27106 0.22250 0.13034 0.06912 0.08723 0.08971 1963 0.01525 0.03318 0.04750 0.28494 0.24733 0.14696 0.08149 0.10552 0.10954 1964 0.01534 0.03468 0.05119 0.29524 0.25400 0.15745 0.08769 0.12348 0.12445 1965 0.01536 0.03353 0.04779 0.29882 0.25786 0.16222 0.08453 0.13148 0.12944 1966 0.01533 0.03249 0.05042 0.30478 0.26520 0.17510 0.08812 0.14933 0.14823 1967 0.01524 0.03054 0.03555 0.30294 0.24827 0.16210 0.07141 0.13989 0.13993 1968 0.01590 0.03299 0.03652 0.31930 0.25552 0.16944 0.07595 0.16227 0.16258 1969 0.01624 0.03428 0.03291 0.32986 0.26082 0.17758 0.07513 0.16185 0.17220 1970 0.01607 0.03153 0.03428 0.34584 0.27292 0.18519 0.07525 0.16047 0.18897 1971 0.01554 0.03206 0.02737 0.35065 0.27495 0.18640 0.06889 0.14993 0.19306 1972 0.01506 0.03382 0.02783 0.36891 0.28570 0.20072 0.07471 0.16570 0.22394 1973 0.01380 0.03757 0.05809 0.42794 0.34131 0.27990 0.12685 0.28677 0.36963 1974 0.01255 0.04094 0.06004 0.45483 0.39326 0.34100 0.14518 0.38829 0.46503 1975 0.01217 0.03639 0.02907 0.44093 0.38922 0.30106 0.10203 0.33691 0.39882 1976 0.01283 0.03314 0.03320 0.44398 0.41412 0.32335 0.11038 0.40696 0.48369 1977 0.01333 0.03120 0.04273 0.45653 0.46663 0.36292 0.13185 0.51658 0.59888 1978 0.01317 0.03105 0.04783 0.45546 0.52730 0.40389 0.15314 0.64625 0.71202 1979 0.01205 0.03217 0.06274 0.47357 0.62792 0.48763 0.20424 0.92848 0.93563 1980 0.01198 0.03248 0.05146 0.40699 0.66535 0.51280 0.19800 1.04933 0.97109 1981 0.01207 0.03143 0.04056 0.36639 0.70337 0.52742 0.18560 1.03391 0.99164 1982 0.01218 0.02773 0.02063 0.35463 0.67952 0.47628 0.13440 0.74340 0.82251 1983 0.01273 0.02880 0.04443 0.33845 0.77758 0.57532 0.21474 1.03215 1.26088 1984 0.01254 0.03198 0.05234 0.33220 0.85111 0.64470 0.25864 1.11142 1.45859 1985 0.01260 0.03173 0.05501 0.31196 0.90318 0.67898 0.27321 1.07001 1.58038 1986 0.01276 0.03070 0.05025 0.28474 0.91858 0.66783 0.25761 0.93553 1.55481 1987 0.01262 0.03305 0.06412 0.27517 0.97846 0.77381 0.31395 1.03052 1.95141 Continued on Next Page. . . 179 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Table 2.15 – Continued Year t τtP τ t B r t UtICT U t ME U t NR U t BI U t AL U t BL 1988 0.01253 0.03318 0.05905 0.25936 0.96079 0.79750 0.30321 0.96627 2.01340 1989 0.01267 0.03323 0.04822 0.22971 0.94929 0.78175 0.27209 0.92490 1.98116 1990 0.01303 0.03249 0.03650 0.21200 0.92299 0.74964 0.23376 0.87139 1.86982 1991 0.01360 0.03066 0.01785 0.17872 0.81795 0.64092 0.16443 0.67758 1.51093 1992 0.01418 0.03054 0.02931 0.17425 0.89545 0.70016 0.21221 0.79188 1.84691 1993 0.01418 0.03271 0.02850 0.17325 0.94110 0.71929 0.21742 0.81059 1.91629 1994 0.01392 0.03528 0.04441 0.17635 1.06954 0.84170 0.29711 1.04577 2.49121 1995 0.01369 0.03729 0.05185 0.16943 1.16489 0.90509 0.34405 1.23716 2.88751 1996 0.01371 0.04085 0.05500 0.15962 1.23083 0.97235 0.37844 1.42627 3.18027 1997 0.01366 0.04436 0.04773 0.15238 1.24910 0.97949 0.35092 1.48857 3.21548 1998 0.01386 0.04021 0.04498 0.14121 1.27485 0.97115 0.32674 1.47920 3.14252 1999 0.01395 0.04567 0.04749 0.13315 1.32792 1.04185 0.36292 1.66008 3.54736 2000 0.01320 0.05092 0.06134 0.13434 1.44719 1.19200 0.44748 2.00514 4.35800 2001 0.01296 0.04095 0.06042 0.12901 1.43815 1.13880 0.41265 1.88744 4.19919 2002 0.01255 0.03963 0.07025 0.12765 1.50961 1.21244 0.45488 2.07595 4.67601 2003 0.01239 0.04193 0.06610 0.11536 1.41639 1.22833 0.42137 2.08922 4.80516 2004 0.01212 0.04536 0.07973 0.10916 1.47468 1.42330 0.49287 2.43457 5.81222 2005 0.01167 0.04517 0.08577 0.10307 1.48894 1.55589 0.52207 2.58973 6.55621 2006 0.01110 0.04621 0.07823 0.09493 1.43474 1.62001 0.50423 2.52426 6.66814 2007 0.01065 0.04605 0.07965 0.09316 1.40462 1.71843 0.52524 2.62584 7.14985 Average 0.01351 0.03569 0.04827 0.26874 0.78978 0.64956 0.23351 0.95212 1.91810 180 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Note that the sample average of the balancing after tax real rates of return rt was a rather large 4.827% per year.112 The average property tax rate τ tP was 1.351% while the average business tax rate on assets was 3.569%. Thus the before business tax real rate of return averaged 8.396%. Thus it appears that governments are taking about 42.5% of the before tax return to capital assets on average.113 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. The volatility in the above real rates of return is a source of concern since it is likely that a considerable proportion of the volatility is caused by various measurement errors. The volatility in the real rates of return also causes volatility in the user costs and possible volatility in productivity growth rates. However, we repeated our productivity calculations using a constant after tax real rate of return (equal to the sample average real rate of 4.827%) and found no material difference in our productivity growth rates. Hence the volatility in the productivity growth rates is mainly due to volatility in our output measures. 112The corresponding balancing real rate of return for Australia averaged around 3 per- cent; see Diewert and Lawrence (2006). Normally, after tax real rates of return are in the 1 to 3 percent rate whereas our average rate is close to 5 percent. This suggests that our estimates of the value of output are too high or that the value of labour input are 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 for this chapter, we calculated a business sector nominal and real value of business sector output and we also calculated the corresponding business sector nominal and real capital stock inputs where the real measures were calculated using chained Fisher indexes. We found that the nominal business sector capital output ratio fell from 2.417 in 1961 to 1.861 in 2007 while the real capital output ratio fell from 2.417 in 1961 to 1.538 in 2007. These falls in the capital output ratio seem unlikely. See Diewert and Fox (2001) for a discussion of output mismeasurement problems. 113This 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. See Diewert and Lawrence (2002) for a methodology for estimating the deadweight losses due to capital taxation. 181 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 2.6 Sources of Error There are many problems with the data constructed in this paper. 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 asso- ciated 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 non-business sector is rather indirect and subject to some error.114 • 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 the Statistics Canada KLEMS program estimates for quality adjusted labour and there may be some amount of error in these estimates. In particular, it is very difficult to account for the hours of work and labour compensation for the self-employed. • It proved to be difficult to reconcile balance sheet information with investment information. Our treatment of investment and capital ser- vices was highly aggregated and hence contains some aggregation er- rors. We also relied heavily on the Statistics Canada Balance Sheet estimates and these estimates are highly aggregated; in particular, there is not enough detail on the allocation of land. Moreover, the Balance Sheet stocks appear to give asset values that are too small.115 114In particular, we did not have access to chained price indexes for the non-business sector for the years prior to 1997 and this will lead to some aggregation errors. 115Evidence of this possible undercounting of asset values in the Balance Sheet accounts 182 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 • Our treatment of property 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. The next international version of the System of National Accounts (SNA) will recognize capital services in the production accounts. This will be a big step forward since it will allow 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. The revised SNA also needs to consider the following problems: • 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 in- ternational 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. are the declining capital output ratios that are implied by our data. Moreover, the assessed value of real property (land and structures) in British Columbia for 2007 was just over one trillion dollars. If we add up the value of land and structures in the National Balance Sheets for the beginning of 2007, we get a value of about 4 trillion dollars. If we multiply the British Columbia value by a factor of 8, it seems that the national value of real property should be equal to about 8 trillion instead of the 4 trillion in the accounts. 183 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 • The treatment of inventory change in the present SNA seems inade- quate for the needs of productivity accounts. Inventory change should be integrated with the balance sheet accounts and the user cost ac- counts. • The investment accounts need to be integrated with the corresponding balance sheet accounts, both in nominal and real terms. • 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.116 • 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 ad- dressed. The introduction of capital services into the SNA will provide challenges for statistical agencies. However, as national statistical agencies make pro- ductivity accounts a part of their regular production of the national ac- counts, there will be benefits to the statistical system as a whole since a natural output of the new system of accounts will be balancing real rates of return by sector or industry. These balancing real rates of return will provide a check on the accuracy of the sectoral data: if the rates are erratic or very large or very small, this can indicate measurement error in the sec- toral data and hence will give the statistical agency an early indication of problems with the data. 116There are some difficult conceptual and practical problems involved in separating structure value from land value; see Diewert (2007a) for a discussion of some of these problems. 184 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 Statistics Canada already has an extensive productivity program. It is to be hoped that as the program evolves in the future, the data will be presented to the public in some detail and hopefully, at some level of aggregation, revised series will be made available back to 1961.117 2.7 Recommendations for the Statistics Canada Productivity Program There are substantial difficulties in accessing data on the prices and quan- tities of primary inputs used by the business and non-business sectors from CANSIM. Also it is evident that the coverage of primary input usage by in- dustry by Statistics Canada is not nearly as extensive as the corresponding coverage of gross outputs and intermediate inputs. With the next revision of the System of National Accounts recommending a decomposition of gross op- erating profits into price and quantity components, it seems time for Statis- tics Canada to devote more effort into improving measurement with respect to primary inputs used by industries in the Canadian economy. Without accurate information on the flow of labour and capital services by industry, governments and businesses will not be able to plan ahead for Canada’s future. It is important to know past trends in TFP growth by industry so that future trends can be anticipated and so that budgetary planning can be carried out on a more rational basis. Hopefully, other national departments interested in Canadian productivity growth (the Bank of Canada, the De- partment of Finance and Industry Canada to name a few) will support an initiative that will put more resources into the hands of Statistics Canada so that they can provide better information on productivity growth. Important priorities for improving Statistics Canada’s productivity pro- gram include the following ones: 117It is important to have data back to the early 1960’s since the 1950’s and 1960’s were decades of very high productivity growth. Hence if we want to explain the productivity slowdown that took place in the 1970’s, it is important to have comparable data for the 1960’s. 185 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 • The National Balance Sheet accounts need to be fully integrated with the productivity program; i.e., Statistics Canada collects information on 30 classes of assets with some degree of industry breakdown but publishes only a crude four type of asset by households, corporations and governments breakdown. The household sector needs to be split into a self employed business component and a “consumer of goods and services” component and the corporate sector should be decomposed into industries with price and quantity information for the 30 classes of asset made available by quarter and by industry. • The National Balance Sheet information on the value of land, resi- dential structures and non-residential structures needs to be greatly expanded so that more information on the price and quantity of real property by industry is made available.118 The problems associated with finding adequate constant quality price indexes for residential and non-residential structures are formidable119 but given the impor- tance of real property in the Canadian economy, it is necessary to put additional resources into this area of economic measurement. • The KLEMS program has developed very useful price and quantity information on 56 types of labour used by the Canadian business sec- tor but has only made a highly aggregated form of this information (the information on three types of labour service used in this study) available on CANSIM II. However, this information is extremely use- ful to the general community. If it is felt that the disaggregated in- formation is not reliable enough to be released in this form, then it should be aggregated up and released at some level of detail that is more detailed than the present three price and quantity series that are available on CANSIM II. Furthermore, corresponding information on disaggregated labour input by type of worker should also be provided 118We have some concerns that the National Balance Sheets are perhaps missing some growth in the value of real assets. Indirect evidence that points in this direction includes declining capital output ratios for the Canadian business sector. Part of the problem may be the very high depreciation rates that are being used by the KLEMS program. 119For a review of these problems, see Diewert (2007a). 186 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 for the non-business sector.120 • More information on the incidence of taxes needs to be provided in the Input-Output accounts; i.e., we need to know exactly in which cell of the Input-Output accounts various indirect and direct taxes are applied.121 Not only is this information required to reconcile final demand indexes with production accounts indexes, it is also required in order to evaluate the efficiency of our tax system.122 • The estimations in Chapter 1 has shown that over short periods of time, changes in the real price of exports and imports can have sub- stantial effects on living standards. The methodology used in the paper is applied only to the aggregate business sector. In Section 1.8 of Chapter 1, we showed how the methodology can be extended to the industry level but in order to implement this methodology to show the effects of changes in the terms of trade by industry, it will be nec- essary to expand existing Input-Output tables to include information on exports produced and imports used by industry.123 Government departments who have an interest in productivity measurement by in- dustry will have to consider whether it would be worthwhile extending the production accounts in this direction. These extended accounts would enable researchers to study issues related to outsourcing and globalization in a more scientific manner. • Baldwin and Gu (2007; 15-22) have a nice discussion about many of 120Statistics Canada has been a pioneer in developing and publishing very detailed in- formation on the prices and quantities of outputs produced and intermediate inputs used by industry back to 1961 in its input output tables. What we are asking here is that these tables be extended to also cover the 56 types of labour input and 30 types of capital input that are being used in the Statistics Canada KLEMS program. Note that extending the Input-Output tables to cover primary input allocations will also involve extensions to the corresponding final demand accounts, which in the case of inputs, will be corresponding household and government supplies of labour and capital. 121Recall that we were forced to make guesses about the incidence of various consumption, import, property and capital taxes in order to reconcile final demand prices with producer prices. For additional material on how to accomplish this reconciliation, see Diewert (2006b)(2007b). 122See Diewert (2001; 97-98) for an elaboration of this point. 123Diewert (2007b)(2007c) explains these expanded production accounts in more detail. 187 Chapter 2. Business Sector Data on Outputs and Inputs for Canada 1961-2007 the unresolved issues in constructing an appropriate user cost formula in order to price capital services and note that an unambiguous “best practice” measure has not yet emerged. Given this state of affairs, we recommend that Statistics Canada provides not only the actual user costs by asset and year that they used in the KLEMS program but that they provide supplementary information on the various ingredients (interest rates, property taxes, business taxes, asset price appreciation terms and asset prices) that go into the making of the user costs so that researchers can construct their own preferred versions of user costs. Eventually, a view will form on what the “best practice” user cost is but we are not at this point yet and hence it is essential that Statistics Canada provides analysts with information on the various components of user costs. 188 Chapter 3 Does Lobbying Affect Antidumping Case Determinations in Canada? 3.1 Introduction A large number of petitions against dumping124 were filed globally in the last decade125 indicating that many countries are involved either as plaintiffs or defendants in antidumping litigation. Canada is no exception. In fact, Canada is a seasoned user of antidumping legislation. According to the World Trade Organisation (WTO), Canada ranks 6th among its 45 reporting members in the total number of antidumping initiations from 1995 to 2007.126 GATT Article 6 of the WTO stated that all countries are allowed to introduce their own antidumping legislation. Thus, a domestic firm that believes it is victimised by dumping can file an antidumping petition with its government. In Canada, antidumping cases are determined according to the antidumping legislation mandate which states that factors such as prices and market share cannot be used in the injury determination. Most importantly, the determinations are supposed to be immune from political pressure. This suggests that there should be no need for firms to apply 124Dumping means an export good is being sold below the cost of its production or below the price it is normally charged in the country of production. 125According to the World Trade Organization Antidumping Gateway, there were over 2,800 antidumping initiation filed by member countries between 1998 to 2008. 126Statistics taken from the World Trade Organisation Antidumping Gateway. 189 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? political influence after they file antidumping petition. In fact, however, Canadian firms have often lobbied antidumping agencies after they filed petitions. This indicates that Canadian antidumping legislation mandate may not be as apolitical as it was designed to be. This paper examines antidumping cases in Canada from 1996 to 2003, focussing on the relationship between the outcomes of the cases and various economic and political factors, in order to determine whether the mandate is independent of political influences. Using the Canadian Lobbyists Regis- tration data, we construct a new political variable to test for the effect of the political influence on Canadian antidumping cases determinations. We find that antidumping case determinations in Canada are not independent of political influence. This paper contributes to the literature in two ways. First, while sev- eral previous studies have found evidence that political influence affects antidumping cases in the United States, this is the first paper to study the role of lobbying in affecting antidumping cases in Canada. Finger et al. (1982) is the pioneer of empirical studies in antidumping and found some evidence that political pressure was able to influence U.S. antidump- ing cases.127 Leipziger and Shin (1991), Hansen and Park (1994), Hansen and Prusa (1997), Bown, Hoekman and Ozden (2003), Drope and Hansen (2004), Francois and Niels (2004), and Evans and Sherlund (2006) also found evidence of non-economic influences on U.S. antidumping case determina- tions. In particular, Hansen and Park (1994), Hansen and Prusa (1997), and Drope and Hansen (2004) found that political factors are significant in affecting the decisions made by the antidumping agencies in the U.S. These studies used a large variety of political variables ranging from indus- 127Most subsequent empirical studies shifted the focus towards economic determinants and their influences on antidumping cases, such as Herander and Schwartz (1984), Feinberg (1989), Coughlin et al. (1989), Leidy (1997), Prusa and Skeath (2001), Knetter and Prusa (2003) and Feinberg (2005). These studies found that microeconomic variables such as industry capacity utilisation rate, wage to value-added ratio and unionisation coverage; and macroeconomic variables such as inflation, real exchange rate and real GDP growth are significant in influencing the decision of filings. 190 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? try concentration to number of political party representatives to political contributions by industry to represent political pressures.128 However, a problem with these variables is that it is hard to tell if the political pressure is truly targeted to influence antidumping cases.129 Second, unlike previous empirical studies that have had to rely on proxies to construct political pressures, this paper is able to utilise a new set of data on Canadian lobbyists. The details of the Canadian Lobbyists Registration data make it possible to identify the lobbyists who lobbied antidumping legislation agency, thus making the political variable constructed in this paper more appropriate than those previously used. The rest of the paper is organised as follows: Section 3.2 introduces the background of antidumping legislation, petition filing process and lobbyists registration in Canada. Section 3.3 includes the empirical analysis with de- tails on data choices and methodology, and the discussion of results. Finally, in Section 3.4, there is a brief conclusion of the empirical analysis. 3.2 Antidumping and Lobbying Dumping is said to occur if the exporter charges a price that is lower than either the price at which it is sold in the exporter country or the cost of production. Dumping can lead to consequences such as reduced domestic prices, reduced sales, reduced market share or reduced profit, all of which can injure the domestic producers. Domestic producers who believed they are victimised can file antidumping petitions with the government agency 128There is also a small theoretical literature that investigates the role of political influ- ence in antidumping cases. For example, Anderson (1994) developed a two-stage game which allows the firm to make a decision on filing in the first stage and then consider whether to lobby the antidumping agency for a specific outcome in the second stage. Gasmi et al. (2004) also examined a model in which a domestic firm can choose to lobby an agency that administers international antidumping legislation in order to influence a determination. 129Nelson (2006) pointed out that empirical works in antidumping have very little con- nection with the theoretical development due to reasons like this. 191 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? responsible for antidumping cases. Upon the receipt of a petition, the agency will start an investigation and can levy antidumping duties if injury from dumping is found. In Canada, the Special Import Measures Act (SIMA) that went into ef- fect on December 1, 1984, states that industries producing the same goods as imports and suspect the imports are dumped, may file complaints with the Canada Border Services Agency (CBSA). Suspected cases are usually filed by the industry or by a representative firm that believes it has been victimised. At least 25% of the Canadian production of that industry must support the complaint, and the proportion of support must also be larger than the opposition. A complaint must include information on the domes- tic goods, the imports, the domestic industry and the conditions in the Canadian market. The complaint must also include evidence of injury. If satisfied that the complaint is properly documented, CSBA will launch an investigation to determine whether the named imports are dumped by the named countries. CSBA is also responsible for determining the amount of antidumping duties to be imposed.130 Another antidumping agency that works independently from the CBSA is the Canadian International Trade Tribunal (CITT). The tribunal consists of nine full time members appointed by the government. Their responsibili- ties include conducting inquiries into whether dumped imports have caused injury to domestic producers and hearing appeals of cases determined by CSBA. It also conducts antidumping injury inquiry through public hear- ings and is responsible for the final decision on injury after the inquiries. The SIMA restricts the factors that can be included in the determination of injury to include only domestic production values, market prices, market share of the complaining firms, profits, employment level, capital utilisation and investment expenditure. 130See CBSA website for details of antidumping cases investigation procedure. 192 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? Upon preliminary affirmative ruling, a temporary duty will be imposed by Canada Border Service Agency. In the case where a final injury decision is issued in favour of the Canadian industry, an antidumping duty will be implemented on imports from the named countries that were dumped.131 Exporters named in the investigation can alternatively, before full investi- gation is instigated, choose to work on an undertaking that commits them to change their pricing practices that are causing harm to the Canadian in- dustry. Any proceedings or rulings of the cases are published in the Canada Gazette. Over 150 complaints had been filed with the Tribunal and were given rulings since the introduction of the Special Import Measures Act in 1984. For the past two decades, about two-third of the antidumping cases filed in Canada eventually led to injury findings and only a few of the cases resulted in a price undertaking. Table 3.1 shows a summary of the antidumping cases filed from 1990 to 2006 and Table 3.2 shows the country classifications of the named countries from 1990 to 2004.132 There were a total of 87 complaints that named 74 countries during this period.133 Most of the antidumping complaints in Canada were initiated by four industries: steel products, textiles, food products and chemical products. The most named trade partners were the U.S. followed by China and Taiwan. European countries like the United Kingdom and Germany were named regularly but less frequently. However, the U.S. and France were the only countries that ever accepted undertaking during this period. 131This is different from the U.S. where duties begin at the stage before ruling. 132Classification is from International Monetary Fund Economic Outlook 2007. Bown, Hoekman and Ozden (2003) reported that in the U.S., developing countries are often named and they believed this is partly because those countries have limited resources to retaliate, are unable to raise the already high protection further and are unfamiliar with litigation procedure for appeal. However, in Canada, advance economies have been named slightly more often than developing countries have been named. 133Author’s own recoding, details described in the Section 3.3. 193 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? Table 3.1: Antidumping Cases in Canada 1990-2006 Country Times Namedb Injury Found Undertaking Accepted United States 56 29 8 China 24 15 0 India 11 8 0 Taiwan 14 7 0 Germany 13 8 0 United Kingdom 11 8 0 France 12 8 1 Other Countries 175 122 0 Total 316 205 9 b Each case may consist of multiple named countries and multiple NAICS6 industries, the combination of one country and one industry is considered as one count. 194 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? Table 3.2: Antidumping Cases in Canada by the Named Country’s Economic Status 1990-2004 Initiation Year Advanced Economiesc Developing Countries 1990 6 9 1991 12 0 1992 39 17 1993 18 6 1994 3 0 1995 36 1 1996 3 7 1997 8 5 1998 5 6 1999 11 18 2000 8 16 2001 9 16 2002 1 4 2003 7 15 2004 6 5 Total 172 125 c Classification comes from International Monetary Fund’s World Economic Outlook 2007. Canada’s antidumping legislation process is quite different from that in the United States. First, no ex-ante duties are collected, and the named countries are allowed to raise export prices and accept undertaking before any final decisions are made. Second, named countries with dumping mar- gins less than a threshold set by CBSA are excluded from injury determi- nation.134 Thus, not all named countries will have duties imposed if the determination is affirmative. However, once an affirmative decision is made, Canada tends to impose a heavier duty to eliminate the dumping margin. 134U.S. calculates its dumping margin using a practice called “zeroing” which eliminates any negative dumping margins and includes all named countries, thus possibly overesti- mating the margin. 195 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? Figure 3.1: Antidumping Cases in Canada by the Named Countries 1990- 2006 56 24 11 14 13 11 12 175 29 15 8 7 8 8 8 122 8 0 0 0 0 0 1 0 0 20 40 60 80 100 120 140 160 180 200 US China           India           Taiwan          Germany        UK France          Other Named Injury found Undertaking accepted 196 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? In Canada, the Lobbyists Registration Act became effective in 1995 and required all lobbyists to register with Industry Canada. They must also list which company they represent, what purpose they have and what actions they plan to take. Actions usually include meetings with legislators and attending committee meetings where the politicians who have the power to influence policies attend. Table 3.3 shows the number of active lobbyist registrations in Canada from 1996 to 2005, and it can be seen that the total number of active lobbyists that registered with Industry Canada has doubled since 1996. Unlike direct political contributions, there is no restriction on lobbying expenditure. Thus, industries can spend as much on lobbying as they prefer to reach their goals and may hire as many lobbyists as they wish to represent them. Table 3.3: Active Lobbyist Registrations in Canada 1996-2005 Year Consultant In-house (Corporate) In-house (Organisation)d 1996-1997 1774 380 295 1997-1998 2012 367 327 1998-1999 2060 352 362 1999-2000 2401 336 382 2000-2001 2682 300 363 2001-2002 3003 234 357 2002-2003 3095 296 316 2003-2004 3287 298 330 2004-2005 3417 192 271 d Data from Office of Registrar of Lobbyists, recorded as of March 31st in the year In Canada, firms and industries that petition for antidumping are ob- served hiring lobbyists to lobby CITT for their cases. Table 3.4 shows the percentage of Canadian lobbyists between 1996-2003 who had indicated they planned to lobby the CITT. 18.7% of all lobbyists on average showed inten- tion to lobby the CITT. The percentage in manufacturing is higher, with 197 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? 23.8% of all lobbyists on average planned to lobby the CITT.135 Table 3.4: Percentage of Lobbyists that Lobbied Canadian International Trade Tribunal 1996-2003 Year Lobbies CITT Lobbies CITT & Foreigne All 1996 15.5% 0.3% 1997 17.5% 0.2% 1998 18.1% 0.3% 1999 20.2% 0.7% 2000 20.5% 0.9% 2001 19.0% 0.9% 2002 18.8% 1.0% 2003 19.8% 1.1% Manufacturing Only 1996 18.9% 0.6% 1997 21.4% 0.5% 1998 22.4% 0.8% 1999 26.3% 2.2% 2000 26.4% 2.7% 2001 24.5% 2.3% 2002 24.6% 2.7% 2003 25.5% 3.3% e Author’s own recoding, each registration is counted as one lobbyist, raw data from Public Registry of Lobbyists, Industry Canada 135Blonigen and Prusa (2003) suggested that directly unproductive profit-seeking activity like lobbying is more explicit in administered protection like antidumping duties than in traditional protection like tariffs. 198 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? 3.3 Empirical Analysis In this section, we analyse the factors influencing antidumping case deter- minations in Canada during 1996-2003. The economic and political determi- nants that can affect an affirmative determination are drawn from previous empirical analyses of antidumping case determinations. A key assumption underlying our work is that firms only file based on their likelihood of success in getting an affirmative decision.136 We assume that the relation between affirmative determinations and the independent variables can be described by ni = F (pi, ci, ei, di) (3.1) where ni is the dependent variable representing number of antidumping cases by industry i that are determined affirmative, pi represents the political vari- ables, ci represents the determinants CITT uses for injury determination, ei represents the additional economic determinants and di represents dumping indicators. The dependent variable is constructed as the number of antidumping pe- titions that were determined affirmative. Data on petitions are taken from the Historical Listing of Antidumping Cases in the Canada Border Services Agency website. Cases that had been filed, investigated and ruled on in Canada are listed in the data base with the Harmonised System (HS) 10 digits product code of dumped products, the initiation dates of the investiga- tion, the specific accusation (dumping or subsidised), the countries named, the disposition, the dumping margins and the final rulings. To construct this variable at industry level, each HS 10 digits product is matched with its corresponding North America Industry Classification System 6 digits code (NAICS6) using a concordance provided by Statistics Canada. Each peti- tion may have more than one exporting country named and more than one 136This assumption means industries self-select into filing antidumping petitions given the expected likelihood of success in affirmative decision. 199 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? product identified as dumped. In the construction of the dependent vari- able, each named country in each complaint is to be treated as an individual petition. For example, the complaint initiated on March 1, 1996 named two products, HS codes 4823.51.00.00 and 4820.10.00.00; and named two coun- tries, Indonesia and Brazil. The equivalent NAICS6 industry codes for these products are respectively, 323119 and 323116. Therefore, the number of pe- titions would be two for each of the two industries. By the same logic, and excluding complaints that were terminated before decision or complaints filed by non-manufacturing industries, there were 163 petitions filed by 50 industries, among which 127 cases were determined affirmative or had un- dergone price undertakings. Hansen and Prusa (1997) suggested that cases that were settled (went through price undertakings) should also be included because political pressure plays heavily in explaining these cases. 3.3.1 Economic and Political Determinants According to the CITT mandate, all determinations of injury must be made purely based on evidence that the imports are dumped. Reasons that are unrelated to the discrepancy of import prices relative to prices in the exporter countries should not be considered.137 Profits, capacity utilisation138 and capital investment139 are included in the analysis as industry-specific CITT economic injury determinants. In- stead of the total number of employees, the annual growth rate in employ- ment is used for analysis, as it is a better indication of industry injury than the total employment. Average labour earnings growth and output growth 137Industry specifics such as profits, employment, capacity utilisation and investment can be considered for determinations of injury as they are indirectly affected by imports dumped. However, changes in domestic demand, technology, export performance of Cana- dian firms, volume and prices of non-dumped imports, trade restrictiveness and perfor- mance of firms should not be included. 138A capital utilisation rate that is less than 100 percent would indicate the industry has excess capacity available to increase production for replacing any displaced imports. 139Capital investment data are only readily available in subcategories of NAICS, thus requires re-weighing by the industry’s proportion in total output of the subgroup to de- termine an approximate amount of capital investments. 200 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? are also included as additional economic determinants. Industry export intensity is used to proxy the economic interdependence described by Finger et al. (1982). Export intensity is calculated as the ratio of domestic exports to manufacturing shipments. Therefore, a high export intensity indicates an industry is highly dependent on exports and will probably experience less injury in case of dumping. Knetter and Prusa (2003) and Feinberg (2005) both found that macroe- conomic indicators such as currency depreciation can be influential in an- tidumping cases. Thus a year dummy each for 1997 and 2001 is included to indicate a depreciation in Canadian dollar relative to the year before. The former is the year of Asian financial crisis and the latter is the year terrorists attacked the U.S. Both years saw overall deterioration in world economy and weakened Canadian dollars. 140 The “interest group” theory assumes that interest groups influence politi- cians for desirable policy outcome. The channel of influence is not specific. It can be contributions, lobbying or some other type of political influence. In earlier empirical studies, political influence was often represented by vari- ables that are not exactly political in nature. However, as suggested by Baldwin (1989), better measures are needed to illustrate the extent of polit- ical pressures exerted by economies than indirect measures such as industry concentration ratio or sales growth. To address this, in this analysis, a political variable is constructed using the Canadian Lobbyists Registration database from 1996 to 2003. The Lobbyists Registration database discloses details of all active lobbyists including what particular concerns the lobby- ists have and which government agencies they plan to lobby. Thus for this analysis, lobbyists who have listed their lobbying concerns as “Special Im- port Measures Act (SIMA)”, “antidumping regime” or those who planned 140Knetter and Prusa (2003) also showed that real GDP growth increase antidumping cases in Canada but real GDP growth of the Canadian economy has been very steady over the sample period. It would be obsolete to include as macroeconomic determinant. 201 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? to lobby CITT are selected. Out of the 163 antidumping cases initiated in the sample period, about one-quarter of them had lobbyists that lob- bied CITT or had SIMA concern. Each of these lobbying firms is manually matched with its NAICS6 industry code by searching through the Canadian Companies Capability Database.141 Drope and Hansen (2004) suggest that lobbyists data should be comple- mented by political contributions data to identify how much industries spent in seeking protection. Therefore, a second political variable formed by the amount of lagged political contributions is included in the analysis. The total amount of political contributions by each industry is matched with the corresponding NAICS6 code as in the case of the lobbyists data.142 Political contributions may not directly influence the antidumping case determina- tions as they differed from direct lobbying in nature. However, recent lit- erature, like Austen-Smith (1995) has suggested that political contributions and lobbying are complementary, i.e. the hard-money contributions are used as access fee for future lobbying. All values of the political contributions are transformed into logarithms for easier interpretation. As CITT mandate is assumed to be independent of political pressure, therefore, any political determinants should not be significant in determination. In other words, if the antidumping legislation is correctly implemented, the effects of both lobbying and contributions variables should be zero. Many previous empirical studies (such as Finger et al. (1982) and Hansen and Prusa (1997)) included variables that reflected the collective action hy- pothesis (Olson (1965)). The hypothesis says a more concentrated industry is able to organise more easily, and that organised industries fare better in 141If a firm is not found in the Canadian Companies Capability database, other online sources such as Lexis-Nexis Academic and Manta will be searched. If the industry code is still unfound after these sources are exhausted, information listed on the company websites will be checked and an appropriate code will then be assigned. 142Political contributions data are taken from Election Canada website. However, unlike the lobbyists data, political contributions by businesses and trade unions cannot be iden- tified by what the donations were for, since each contribution will only be associated with the donor’s name and the intended party. 202 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? obtaining affirmative determinations than the non-organised ones. While these studies did not find strong support on the collective action theory, an industry concentration ratio is included in this analysis to test the col- lective action hypothesis in Canadian antidumping case determinations. A Herfindahl-Hirschman index would be the best indicator of concentration of an industry as it is weighted by the market share. However, due to limited availability of data, we use a four-firm industry concentration instead. In addition to the CITT economic injury determinants and other economic determinants and political determinants, import price growths and import penetration ratios are included as dumping indicators. Import unit value, calculated by dividing the total import value with total import volume, is used as a proxy for import prices.143 Import penetration ratio is calcu- lated as the imports of goods as a ratio to the domestic consumption, i.e. how much of domestic demand is satisfied by imports. 144 Industries that have high import penetration ratio are hypothesized to be able to obtain protections more easily than those that have low import penetration. Bown, Hoekman and Ozden (2003) showed that developing countries were named more frequently than developed countries in antidumping petitions in the U.S. However, as shown in Table 3.2, developing countries are not named more often than the advanced economies in Canadian antidumping cases. The economic natures of the named countries are therefore irrelevant in Canada. A possible reason is that Canada trades mostly with the U.S. and European countries, and less so with developing countries. There is a possibility of endogeneity issue that needs to be addressed be- fore moving on to our main analysis. If increased lobbying can generate more affirmative determinations in antidumping cases, then it is possible that in- creased affirmative determinations encourage more lobbying in the future. 143Import values and volumes are reported in HS code, these are recoded into NAICS6 using the Statistics Canada concordance. 144Domestic consumption equals the sum of domestic output and imports less exports. 203 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? We examine this possibility as follows. Assume that the number of lobby- ists hired to represent an industry can be loosely taken as the amount of lobbying effort exerted by an industry and that the lobbying expenditure by an industry is positively correlated to the number of lobbyists representing the industry. Thus, an increased number of lobbyists hired would indicate a larger amount of effort. We show in the following analysis that lobbying efforts are influenced by industry-specific characteristics by regressing the number of lobbyists hired by each industry on three types of characteristics. We also include two variables to account for the influence of past affirmative determination in antidumping cases, a variable that represents the cumula- tive number of affirmative determinations and a dummy that indicates there was ever an affirmative determination. There are three types of industry-specific characteristics: political factors, market-related factors and production-related factors. The political factors include variables that represent whether there is counter-lobbying in the in- dustry, whether there is previous experience in lobbying and whether the industry had contributed politically before. They are included to examine how these political involvements affect the industry lobbying efforts. The market-related factors are the import elasticities the industry faces, the im- port penetration ratio the industry experiences, the amount the industry sells to the government, the amount of subsidy the industry receives from government and the number of complaints the industry files with government agencies. They are included to examine how the market environment affects the amount of lobbying efforts. Finally, the production-related factors are the industry concentration, the amount of industry output and value-added, the number of employees and establishments in the industry, the amount of capital investment of the industry, the capital-labour ratio, the cost of en- ergy and R&D expenses and the industry’s export propensity. These are included to examine the effects of industry production characteristics on lobbying efforts. 204 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? Note that there are some industries that have never lobbied, which yields some zeros in the data for the number of lobbyists. To deal with overdis- persion caused by the excessive zeros, unobserved heterogeneity and serial dependence, a random effects negative binomial regression is used to reduce the possibility of biased estimates. The results of the regression of lobbying efforts are presented in Table 3.5. 205 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? Table 3.5: Regression of Lobbying Efforts Models 1 2 3 4 Independent Variablesf Cumulate affirmative 0.025 1.680 0.025 1.636 (0.005) (0.525) (0.005) (0.506) Ever affirmative −0.059 −1.525 0.099 −1.830 (0.080) (0.543) (0.072) (0.526) Lagged counter-lobbying 0.073 0.070 (0.052) (0.069) Experience in lobbying 0.036 0.035 (0.006) (0.013) Lagged contribution 0.056 0.055 (0.016) (0.022) Import elasticities 0.502 1.603 (1.224) (1.019) Import penetration 0.356† 0.511 (0.190) (0.331) Sales to government 0.215 0.116 (0.049) (0.054) Government subsidy 0.003 0.020 (0.026) (0.027) Complaints 0.012 0.007 (0.010) (0.009) Industry concentration −0.006 0.001 (0.002) (0.003) Output 0.466† 0.404 (0.250) (0.284) Employees 0.002 −0.009 (0.005) (0.008) Establishments 0.051 −0.073 (0.041) (0.070) Capital investment 0.034 0.005 (0.160) (0.199) Capital labour ratio −0.001 −0.004 (0.004) (0.006) Cost of energy 0.001 −0.000 (0.000) (0.001) Value-added −0.090 0.006 (0.102) (0.117) Export propensity −0.075 −0.004 (0.120) (0.342) R&D expenses 0.051 0.061 (0.042) (0.060) Concentration*export propensity 0.004 −0.004 (0.002) (0.005) Log-likelihood ratio −2452.628 −1461.565 −3242.040 −1091.282 Number of observations n=1310 n=761 n=2055 n=500 f Standard errors are in parentheses, ,  and † represent the significance levels of 1%, 5% and 10%. 206 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? The first three specifications are regressions of the number of lobbyists on each of the three sets of characteristics plus the two variables accounting for past affirmative determinations. The results show that the cumulative number of affirmative determinations is always significant and positive, while the dummy that indicates if there was ever an affirmative determination is not. Note that in each specification, a few additional variables are signifi- cant, such as lobbying experience and lagged contributions in the political factors; import penetration ratio and sales to government in the market- related factors; and industry concentration ratio, industry output and cost of energy in the production-related factors. The final specification includes all three sets of factors and an interaction term of industry concentration and export propensity. The interaction term is used to capture the resultant effect of the opposing effects of industry concentration and export propensity. The two variables that represent in- fluences of past affirmative determinations are significant but with opposite effects. The cumulative number of affirmative determinations increases the lobbying effort. However, if there was ever an affirmative determination, the industry will lower the number of lobbyists they hire. It will be difficult to say whether the opposing effects will net out. But as both factors are sig- nificant, endogeneity between affirmative determination and lobbying seems to exist. We will take this into account in the empirical work below. Almost all other factors, except for the political factors, become insignif- icant when regressed together. Both the lobbying experience and political contributions increase lobbying effort. Thus, industries that are experienced in lobbying and have contributed will exert more effort. The existence of counter-lobbyists does not seem to have significant effect on lobbying effort. The only other significant factor is the sales to government. Overall, the above results show that in Canada, the amount of lobbying efforts exerted by the industries is highly motivated by the previous success in obtaining determinations and what previous political involvements they had. Lastly, the overdispersion test results show that the choice of negative binomial 207 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? regression is appropriate in all of the specifications. Next we describe the econometric model used for analysing the historical cases. 3.3.2 Econometric Analysis A negative binomial model that can utilise the count data nature is used to study the effect of the determinants on the number of occurrences of an event (affirmative determinations). The model assumes the mean and the variance are unequal (as opposed to equal mean and variance in Poisson regression) which can be used to overcome the problem of overdispersion that is common in count data. Moreover, data in trade and political economics typically have large variations and excess zeroes.145 The structure of a negative binomial is in the form of yi ∼ Poisson(μi∗) (3.2) μi∗ = exp(xiβ + ui) (3.3) eui ∼ gamma ( 1 α , 1 α ) (3.4) where ui represents an omitted variable such that eui follows a gamma dis- tribution, α is the overdispersion parameter. Another advantage of using a negative binomial model is that it allows for unobserved heterogeneity between events through ui. A likelihood ratio test will be performed to justify the use of negative binomial regression. If the null hypothesis of non-unity dispersion factor cannot be rejected, then the model reduces to a simple Poisson. 145Examples of excess zeroes in this analysis would be there are some industries that have never filed for antidumping, which creates a skew in the distribution. The mean and variance would undoubtedly be unequal. 208 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? The data for all cases initiated from 1996 to 2003 are pooled for analysis and all variable values are deflated to 1997 constant dollars using industrial product price index. There are a total of 127 affirmative determinations out of 163 cases among 258 manufacturing industries. The countervailing cases contributed to less than 1% of all cases, and thus will be excluded from the analysis. Although lobbying is often done at firm level, most antidumping cases are raised at industry level. Analyses are therefore performed at in- dustry level. Furthermore, the lack of detailed data for characteristics at firm level made it difficult to carry out analyses at firm level. Table 3.6 shows the averages of the determinants and their expected signs as regression coefficients in the negative binomial analysis. Table 3.6: Expected Signs of Determinants Determinant Averageg Expected Sign Lobbyist 1.3 + Political contributions (dollars) 9317 + Industry concentration ratio 52.6 + Profit (bil. dollars) -1.4 − Employment growth -3.1% − Capacity utilisation rate 82.9 − Capital investments (bil. dollars) 12.1 + Growth in average earnings 1.9% − Output growth 4.7% − Import price change 6.6% − Import penetration ratio 0.5 + Export intensity 47% − g Several industries do not have information on import prices. We tried several specifications of the model and the estimation results are shown in Tables 3.7 and 3.8. The first three specifications each regresses on a different set of variables that represents the political variables, the CITT economic injury determinants and the additional economic determinants. 209 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? The fourth specification regresses on all determinants with an addition vari- able, the interaction between industry concentration and export intensity. In order to account for possible endogeneity between lobbying and affirma- tive determinations, we include an independent variable that is equal to the lagged percentage of affirmative cases in terms of all successful antidumping petitions in the fifth to eighth specifications which are repeats of the first four specifications. 210 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? Table 3.7: Negative Binomial Regression on Antidumping Case Determina- tions Models 1 2 3 4 Independent Variables h Lobbyist 0.050 0.053 (0.018) (0.019) Industry concentration ratio 0.001 −0.003 (0.007 ) (0.012) Lagged contributions 0.249 0.247 (0.116) (0.118) Profit (bil. dollars) 0.093 0.003 (0.155) (0.023) Employment growth 0.018 0.028† (0.012) (0.015) Capacity utilisation rate 0.032 0.031 (0.033) (0.038) Capital investments 0.001 −0.006 (0.010) (0.010) Growth in average earnings −0.014 −0.026 (0.020) (0.019) Output growth −0.002 0.008 (0.011) (0.015) Import price change −0.002 −0.002 (0.005) (0.005) Lagged import penetration 0.003 0.004 (0.031) (0.033) Export intensity −0.009† −0.010 (0.005) (0.015) Concentration*Intensity 0.000 (0.001) Year dummy No No No Yes Log-likelihood −147.534 −186.800 −179.736 −136.456 Number of observations n=1465 n=2048 n=1857 n=1307 h Standard errors are in parentheses, ,  and † represent the significance levels of 1%, 5% and 10%. 211 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? Table 3.8: Negative Binomial Regression on Antidumping Case Determina- tions (Cont’d) Models 5 6 7 8 Independent Variables i % of affirmative cases 0.855 1.908 1.747 0.675 (0.904 ) (0.667) (0.667) (0.941) Lobbyist 0.047 0.048 (0.019) (0.019) Industry concentration ratio 0.008 0.002 (0.010 ) (0.013) Lagged contributions 0.255 0.274 (0.126) (0.124) Profit (bil. dollars) 0.084 0.004 (0.155) (0.024) Employment growth 0.020 0.028 (0.013) (0.016) Capacity utilisation rate 0.060† 0.057 (0.034) (0.040) Capital investments 0.001 −0.001 (0.010) (0.010) Growth in average earnings −0.017 -0.026 (0.019) (0.020) Output growth −0.005 0.003 (0.012) (0.015) Import price change Lagged import penetration 0.005 0.005 (0.030) (0.031) Export intensity −0.010 −0.008 (0.006) (0.016) Concentration*Intensity −0.000 (0.000) Year dummy No No No Yes Log-likelihood −127.527 −162.330 −163.517 −121.992 Number of observations n=1274 n=1794 n=1750 n=1233 i Standard errors are in parentheses, ,  and † represent the significance levels of 1%, 5% and 10%. 212 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? The result from the first specification shows that the number of affirma- tive determinations increases when the industries that filed the petition also hired lobbyists to lobby CITT and when they had contributed monetarily before. Thus, political involvement is positively associated with adminis- tered protection in Canada. Both lobbyists and lagged contributions are significant though the industry concentration does not seem to influence administered protection. The next two specifications show some surprising results. Of all the economic determinants, only export intensity is found to be significant and of expected sign. This is surprising because the economi- cal determinants are the only determinants that are supposed to be used in determinations. The results indicate that being economically independent (as suggested in Finger et al. (1982)) can lower the number of affirmative determinations. The fourth specification includes all determinants as re- gressors. Both lobbyists and lagged contributions continue to be significant. Employment growth is the only economic determinant that turns out to be significant except that the sign is not as expected. Thus, if we ignore the endogeneity between affirmative determinations and lobbying, increased amount of political involvements of industries increases the number of affirmative determinations. The insignificance of economic determinants is quite unanticipated, especially the ones used by CITT. How- ever, this is similar to what Hansen and Prusa (1997) found: that is, in- creasing economic injury may not improve the chance of protection. The growth in employment is expected to have a negative effect on determina- tion because if dumping injures an industry, one would expect a decline in employment to follow. The estimation result shows otherwise. A possible explanation is that growth in employment represents increase in the size of an industry that needs protection. If that is the case, the results of the positive relation can be justified and can be interpreted as the size effect overpowering the economic effect. Widely accepted dumping indicators like import price change and lagged import penetration are not significant even though they are of expected 213 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? signs. There is a possibility that on average, import prices did not fluctuate a lot in the sample period even though import prices for some commodities such as machinery had decreased quite significantly. Similarly, the average import penetration ratio is only 0.5, showing that the Canadian economy overall does not face a high import penetration. The lack of significance in economic determinants also shows that antidumping cases may not be deter- mined based on the proof of unfair trade practices by the foreign exporters (such as lower import prices), but rather on other determinants. The year dummies do not seem to have any effect, which can be easily explained by the fact that Canadian economy remained rather steady in the sample pe- riod. Therefore, the economic setbacks in 1997 and 2001 were not sufficient to affect antidumping case determinations in Canada. Overall, when ignoring the endogeneity issue, the empirical results indi- cate that antidumping case determinations may have been influenced by factors other than those stated in the CITT mandate. The next four specifications take into account the endogeneity between af- firmative determinations and lobbying (note that in the seventh and eighth specifications, import price growth is removed to maintain the concavity assumption). We find that, when the number of affirmative determinations is regressed on the lagged percentage of affirmative determinations and the political variables, only the number of lobbyists and lagged contributions are significant. However, when the regression is carried out on economic determinants, the lagged percentage of affirmative determinations became significant. This shows that if cases are determined only on economic de- terminants, the affirmative rate of past antidumping cases can influence the number of future affirmative determinations. In the eighth specification, when all regressors are included, the lagged percentage of affirmative determinations returns to being insignificant. Both the number of lobbyists and lagged contributions are significant while other economic determinants are not. Thus, the result here does not support there 214 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? is an endogeneity between lobbying and determinations. Political involve- ment is much more important in terms of affecting determinations. The results from the last four specifications are intriguing because they indicate that if the mandate is truly apolitical, the determinations of an- tidumping cases is influenced by the rate of affirmative determination in the past. Yet when firms are lobbying to the CITT, the influence is switched to the political strategies. Summarising the results of all specifications, we have evidence that political factors have influences on the number of affirmative case determinations in Canada. One question that remains is whether lobbying leads to industries obtain- ing affirmative determinations or whether it also leads to more antidumping petitions. We tried the same analysis on the number of successful antidump- ing petitions. A successful petition is one that had been filed, investigated and determined but not necessarily affirmative. The results are shown in Table 3.9. 215 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? Table 3.9: Negative Binomial Regression on Antidumping Petitions Models 1 2 3 4 Independent Variables j Lobbyist 0.064† 0.072 (0.037) (0.039) Industry concentration ratio 0.025 0.009 (0.009 ) (0.021) Lagged contributions 0.419 0.361 (0.136) (0.152) Profit (bil. dollars) 0.009 0.005 (0.072) (0.029) Employment growth 0.001 0.077 (0.000) (0.030) Capacity utilisation rate 0.133 0.042 (0.043) (0.049) Capital investments 0.001 0.001 (0.010) (0.010) Growth in average earnings −0.026 −0.075† (0.033) (0.042) Output growth −0.043† 0.029 (0.023) (0.030) Import price change −0.035 −0.018 (0.025) (0.015) Lagged import penetration 0.354 0.006 (0.618) (0.075) Export intensity −0.022 0.001 (0.014) (0.022) Concentration*Intensity −0.000 (0.000) Year dummy No No No Yes Log-likelihood −203.244 −256.832 −247.607 −185.678 Number of observations n=1465 n=2048 n=1857 n=1307 j Standard errors are in parentheses, ,  and † represent the significance levels of 1%, 5% and 10%. 216 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? Comparing the results in Table 3.7 and Table 3.9, it can be seen that the estimates are quite close. The determinants that are significant in Table 3.7 are also significant in Table 3.9. There are a few exceptions such as in- dustry concentration ratio is significant in the first specification, the growth in output is significant in the third specification, and the growth in average earnings is significant and of expected sign in the fourth specification. There are two possible explanations to why the results are similar. First, it is pos- sibly an indication that the number of successful petitions and the number of affirmative determinations are driven by similar determinants. Thus if political involvements like lobbying promotes affirmative determinations, it also promotes the successful petitions. Second, the affirmative determina- tion rate is moderately high relative to the number of successful petitions. In fact, the percentage of affirmative determinations relative to successful petitions is almost 70% over the sample period. Nonetheless, both analyses provide evidence that in Canada, antidumping cases are not independent of political influences. 3.4 Concluding Remarks Using the Canadian Lobbyists Registration data and the historical an- tidumping cases in Canada, this paper attempts to determine to what extent the economic and political factors are affecting administered protection. In the above empirical analyses, the number of CITT lobbyists is always significant and positive. Economic determinants on the other hand do not affect determinations as much. Similar studies on U.S. antidumping case de- terminations found rather different results. Economic determinants are often found equally important as political determinants, if not more so. The differ- ence is most probably driven by the fact that Canada and the U.S. are very different in terms of their economic structures and antidumping legislations. First, Canada is very export dependent compared to the U.S. This means Canadian industries may be more economically independent in the Finger et al. sense and thus may endure lower amount of injuries in case of dumping. 217 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? Second, Canada’s antidumping legislation is very straightforward, using a prospective system that publishes “undumped” prices that are sufficient to eliminate the need to pay dumping duties. Therefore, importers can simply follow these guidelines in setting prices. By contrast, the U.S. antidumping legislation is very complicated. It applies a retrospective system that col- lects an ex-ante dumping duties. Adjustments in duties such as collecting more from the importers or refunding them only occur in regular reviews after determination. Some of the U.S. practices may lead to importers being fined more (the zeroing practice in calculation of margin) and industries fil- ing more antidumping petitions than needed (motivated by incentive such as the Bryd Amendment). The U.S. Department of Commerce also uses many different rules in its reviews than the original investigation, many of which are rules that could result easier in affirmative determinations. Furthermore, importers are allowed to lower their home prices instead of raising the U.S. import prices to avoid dumping duties which does not relieve any dumping injuries that domestic industries experience. The complexity in the U.S. antidumping legislation made it possible for industries to manipulate their levels of injury for affirmative determinations. In other words, Canada’s simple antidumping legislation made manipulation of injuries almost impos- sible. These two important differences combined increases the importance of using political strategies to influence determination. Another finding from the empirical analyses is that the determinants that are significant in influencing affirmative determinations are also significant in influencing successful petitions. This suggests political strategies such as lobbying the CITT affect both stages of antidumping cases. Lack of appropriate data has made it difficult to empirically analyse the relation of political strategies with policy outcomes. This paper, like many of its predecessors, reflects the same difficulty. Although the Lobbyists Reg- istration data has provided a suitable set of detailed data to construct a political variable, an ideal political variable should be constructed using lobbying expenditure. Fortunately, one can still isolate the lobbyists who are interested in influencing particular outcomes in order to conduct more 218 Chapter 3. Does Lobbying Affect Antidumping Case Determinations in Canada? focussed studies. In this case, only lobbyists who lobbied CITT were selected to study whether the antidumping case determinations are independent of influences other than those allowed as stated in the mandate. Nonetheless, use of the Lobbyists Registration data allows the study of political strate- gies to go beyond the traditional use of industry concentration or political contributions. For the economic determinants, there are also many situa- tions where less detailed measures must be used. The measure of capital investments is one of the determinants CITT is allowed to consider regarding injury and has been shown to be an influential determinant in previous stud- ies. However, capital investment data by industry are often not released due to information protection. In this case, this variable has to be constructed by weighing the aggregate level of capital investments using industry out- put, which greatly reduces its accuracy. Other variables such as the industry concentration ratio and the capacity utilisation rate are also only available at NAICS 3 digit level instead of the NAICS 6 digit level needed for the analysis. Furthermore, much of the data transformation requires applica- tions of concordance or manual matching, either of which could translate into sources of error. Another weakness of our analysis is that only a short time series of data is available. The antidumping cases that were initiated during this period amount to only a small portion of the total number of antidumping cases in Canada. If data were available for a longer time series, the estimates would be more reliable. Further research may need to consider problems such as identifying individual firms’ intents to lobby CITT (whether it is for or against protection) and whether the firms that lobby are also the pe- titioners of the cases. Other considerations may include incorporating the institutional structure of the agencies responsible for antidumping investiga- tion and injury determination, and developing ways to quantify the benefits and costs associated with antidumping cases. 219 Bibliography [1] Aggarwal, Aradhna (2004) ‘Macro Economic Determinants of An- tidumping: A Comparative Analysis of Developed and Developing Countries.’ World Development 32(6), 1043–1057 [2] Alterman, W., W.E. Diewert, and R.C. Feenstra (1999) ‘International Trade Price Indexes and Seasonal Commodities.’ Technical Report, Washington, US Department of Labor, Bureau of Labor Statistics [3] Andere, Eduardo (1992) ‘The Political Economy of Protectionism: An- tidumping in the Mexican-U.S. Trade Relationship.’ PhD dissertation, Boston College [4] Anderson, James E. (1994) ‘Strategic Lobbying and Antidumping.’ Working Papers in Economics 269, Boston College [5] Anderson, Simon P., Nicholas Schmitt, and Jacques-Francois Thisse (1995) ‘Who Benefits from Antidumping Legislation?’ Journal of In- ternational Economics 3-4, 321–337 [6] Archibald, R.B. (1977) ‘On the Theory of Industrial Price Measure- ment: Output Price Indexes.’ Annals of Economic and Social Measure- ment 6, 57–72 [7] Baldwin, J.R., and W. Gu (2007) ‘Multifactor Productivity in Canada: An Evaluation of Alternative Methods of Estimating Capital Services.’ Research Paper, The Canadian Productivity Review Catalogue No. 15- 206-XIE-No. 009, Ottawa: Statistics Canada 220 Bibliography [8] (2009) ‘Productivity Performance in Canada 1961-2008 An Update on Long Term Trend.’ Research Paper, The Canadian Productivity Review Catalogue No. 15-206-X-No. 205, Ottawa: Statistics Canada [9] Baldwin, J.R., W. Gu, and B. Yan (2007) ‘User Guide for Statistics Canada’s Annual Multifactor Productivity Program.’ Research Paper, The Canadian Productivity Review Catalogue No. 15-206-XIE-No. 014, Ottawa: Statistics Canada [10] Baldwin, R.E. (1989) ‘The Political Economy of Trade Policy.’ Journal of Economic Perspectives 3(4), 119–135 [11] Baldwin, R.E., and J.W. Steagall (1994) ‘An Analysis of ITC Decisions in Antidumping, Countervailing Duty and Safeguard Cases.’ Review of World Economics (Weltwirtschaftliches Archiv) 130(2), 290308 [12] Balk, B.M. (1998) Industrial Price, Quantity and Productivity Indices (Boston: Kluwer Academic Publishers) [13] Blonigen, Bruce A. (2006) ‘Working the System: Firm Learning and the Antidumping Process.’ European Journal of Political Economy 22(3), 715–731 [14] Blonigen, Bruce, and Thomas Prusa (2003) ‘The Cost of Antidumping: the Devil is in the Details.’ The Journal of Policy Reform 6(4), 233–245 [15] Bown, Chad P. (2007) ‘Canada’s Antidumping and Safeguard Poli- cies: Overt and Subtle Forms of Discrimination.’ The World Economy 30(9), 1457–1476 [16] Bown, Chad P., Bernard Hoekman, and Caglar Ozden (2003) ‘The Pattern of U.S. Antidumping: The Path From Initial Filing to WTO Dispute Settlement.’ World Trade Review 2(3), 349–371 [17] Christensen, L.R., and D.W. Jorgenson (1969) ‘The Measurement of U.S. Real Capital Input, 1929-1967.’ Review of Income and Wealth 15, 293–320 221 Bibliography [18] Christensen, L.R., D.W. Jorgenson, and L.J. Lau (1971) ‘Conjugate Duality and the Transcendental Logarithmic Production Function.’ Econometrica 39, 255–256 [19] Coughlin, Cletus C., Joseph V. Terza, and Noor Aini Khalifah (1989) ‘The Determinants of Escape Clause Petitions.’ The Review of Eco- nomics and Statistics 71(2), 341–347 [20] Denison, Edward F. (1974) ‘Accounting for United States Economic Growth 1929-1969.’ Technical Report, Washington, D.C.: The Brook- ings Institution [21] Diewert, W.E. (1973) ‘Functional Forms for Profit and Transformation Functions.’ Journal of Economic Theory 6, 284–316 [22] (1974) ‘Application of Duality Theory.’ vol. II (Amsterdam: North Holland) pp. 106–171 [23] (1977) ‘Walras’ Theory of Capital Formation and the Existence of a Temporary Equilibrium.’ (Reidel Publishing Company) pp. 73–126 [24] (1978) ‘Superlative Index Numbers and Consistency in Aggrega- tion.’ Econometrica 46, 883–900 [25] (1980) ‘Aggregate Problems in the Measurement of Capital.’ (Chicago: The University of Chicago Press) pp. 433–528 [26] (1993) ‘Symmetric Means and Choice Under Uncertainty.’ vol. Contributions to Economic Analysis 217 (Amsterdam: North-Holland) pp. 355–433 [27] (1997) ‘Commentary on Mathew D Shapiro and David W. Wilcox, “Alternative Strategies for Aggregating Price in the CPI”.’ The Federal Reserve Bank of St. Louis Review 79:3, 127–137 [28] (2001) ‘Which (Old) Ideas on Productivity Measurement are Ready to Use?’ vol. 63 of NBER Studies in Income and Wealth (Chicago: University of Chicago Press) pp. 85–101 222 Bibliography [29] (2002) ‘Productivity Trends and Determinants in Canada.’ (Cal- gary: University of Calgary Press) pp. 31–57 [30] (2005a) ‘Issues in the Measurement of Capital Services, Deprecia- tion, Asset Price Changes and Interest Rates.’ vol. 65 of NBER Studies in Income and Wealth (Chicago: University of Chicago Press) pp. 479– 542 [31] (2005b) ‘On Measuring Inventory Change in Current and Con- stant Dollar.’ Discussion Paper 05-12, Department of Economics, The University of British Columbia, Vancouver, Canada [32] (2005c) ‘Welfare, Productivity and Changes in the Terms of Trade.’ Presented at the Bureau of Economic Analysis, Washington D.C., November 17 [33] (2006a) ‘Comment on Aggregation Issues in Integrating and Accel- erating the BEA’s Accounts: Improved Methods for Calculating GDP by Industry.’ vol. 66 of NBER Studies in Income and Wealth (Chicago: University of Chicago Press) pp. 287–307 [34] (2006b) ‘The Measurement of Income.’ Chapter 7 as Tutorial Pre- sented at the University Autonoma of Barcelona, Spain, September 21-22,2005 [35] (2007a) ‘Price Indices Using an Artificial Data Set.’ Draft of Chap- ter 19 of the Export Import Price Manual, IMF, Washington D.C. [36] (2007b) ‘The Economic Approach.’ Draft of Chapter 17 of the Export Import Price Manual, IMF, Washington D.C. [37] (2007c) ‘The Paris OECD-IMF Workshop on Real Estate Price Indexes: Conclusions and Future Directions.’ Discussion Paper 07-01, Department of Economics, The University of British Columbia, Van- couver, Canada 223 Bibliography [38] (2008) ‘Changes in the Terms of Trade and Canada’s Productivity Performance.’ Discussion Paper 08-05, Department of Economics, The University of British Columbia, Vancouver, Canada [39] Diewert, W.E., and A.M. Smith (1994) ‘Productivity Measurement for a Distribution Firm.’ The Journal of Productivity Analysis 5, 335–347 [40] Diewert, W.E., and D. Lawrence (2000) ‘Progress in Measuring the Price and Quantity of Capital.’ Essays in Honor of Dale W. Jorgenson (Cambridge: The MIT Press) pp. 273–326 [41] (2002) ‘The Deadweight Costs of Capital Taxation in Australia.’ (Boston: Kluwer Academic Publishers) pp. 103–167 [42] (2005) ‘Estimating Aggregate Productivity Growth for Australia: The Role of Information and Communications Technology.’ Occasional Economic Paper, Canberra: Department of Communications, Informa- tion Technology and the Arts, Australian Government [43] (2006) ‘Measuring the Contributions of Productivity and Terms of Trade to Australia’s Economic Welfare.’ Report by Meyrick and Associates to the Productivity Commission, Canberra, Australia [44] Diewert, W.E., and K.J. Fox (2001) ‘The Productivity Paradox and Mismeasurement of Economic Activity.’ (London: MacMillan Press) pp. 175–197 [45] Diewert, W.E., H. Mizobuchi, and K. Nomura (2005) ‘On Measuring Japan’s Productivity, 1995-2003.’ Discussion Paper 05-22, Department of Economics, The University of British Columbia, Vancouver, Canada [46] Drope, Jeffrey M., and Wendy L. Hansen (2004) ‘Purchasing Protec- tion? The Effect of Political Spending on U.S. Trade Policy.’ Political Research Quarterly 57(1), 27–37 [47] Edwards, E.O., and P.W. Bell (1961) The Theory and Measurement of Business Income (Berkeley, CA: University of California Press) 224 Bibliography [48] Eurostat, International Monetary Fund, Organisation for Economic Co- operation, United Nations Development, and World Bank (1993) ‘Sys- tem of National Accounts 1993 .’ Technical Report, Luxembourg, New York, Paris, Washington D.C. [49] Evans, Carolyn L., and Shane M. Sherlund (2006) ‘Are Antidumping For Sale?’ International Finance Discussion Paper 888, Board of Gov- ernors of the Federal Reserve System [50] Feenstra, R.C. (2004) Advanced International Trade: Theory and Evi- dence (Princeton, NJ: Princeton University Press) [51] Feinberg, Robert M. (1989) ‘Exchange Rates and Unfair Trade.’ The Review of Economics and Statistics 71(4), 704–707 [52] (2005) ‘U.S. Antidumping Enforcement and Macroeconomic Indi- cators Revisited: Do Petitioners Learn?’ Review of World Economics (Weltwirtschaftliches Archiv) 141(4), 612–622 [53] Feinberg, Robert M., and Barry T. Hirsch (1989) ‘Industry Rent Seek- ing and the Filing of Unfair Trade Complaints.’ International Journal of Industrial Organization 7(4), 325–340 [54] Fisher, F.M., and K. Shell (1972) The Pure Theory of the National Output Deflator [55] Fisher, I. (1922) The Making of Index Numbers (Boston: Houghton- Mifflin) [56] Francois, Joseph, and Gunnar Niels (2004) ‘Political Influence in a New Antidumping Regime: Evidence from Mexico.’ Discussion Papers 4297, CEPR [57] Gasmi, Farid, Eric Malin, and François Tandé (2004) ‘Lobbying in An- tidumping.’ IDEI Working Papers 320, Institut d’Économie Industrielle (IDEI) 225 Bibliography [58] Gorman, W.M. (1968) ‘Measuring the Quantities of Fixed Factors.’ (Chicago: Aldine Press) pp. 141–172 [59] Hansen, Wendy L., and Kee Ok Park (1995) ‘Nation-state and Plural- istic Decision Making in Trade Policy: the Case of the International Trade Administration.’ International Studies Quarterly 39, 181211 [60] Hansen, Wendy L., and Thomas J. Prusa (1997) ‘The Economics and Politics of Trade Policy: An Empirical Analysis of ITC Decision Mak- ing.’ Review of International Economics 5(2), 230–245 [61] Herander, M.G., and J.B. Schwartz (1984) ‘An Empirical Test of the Impact of the Threat of US Trade Policy: The Case of Antidumping Duties.’ Southern Economic Journal 51(1), 59–79 [62] Hicks, J.R. (1946) Value and Capital, second edition ed. (Oxford: The Clarendon Press) [63] (1961) ‘The measurement of Capital in Relation to the Measure- ment of Other Economic Aggregates.’ (London: Macmillan) pp. 18–31 [64] Hill, R.J. (2006) ‘Superlative Indexes: Not All of Them are Super.’ Journal of Econometrics 130, 25–43 [65] Hotelling, H. (1931) ‘Edgeworth’s Taxation Paradox and the Nature of Demand and Supply Functions.’ Journal of Political Economy 40, 577– 616 [66] Irwin, Douglas A. ‘The Rise of U.S. Antidumping Activity in Historical Perspective.’ Technical Report, International Monetary Fund [67] Jorgenson, D.W. (1989) ‘Capital as a Factor of Production.’ (Cam- bridge, MA: The MIT Press) pp. 1–35 [68] (1996a) ‘Empirical Studies of Depreciation.’ Economic Inquiry 34, 24–42 [69] (1996b) Investment: Volume 2; Tax Policy and the Cost of Capital (Cambridge, MA: The MIT Press) 226 Bibliography [70] Jorgenson, D.W., and Z. Griliches (1967) ‘The Explanation of Produc- tivity Change.’ The Review of Economic Studies 34, 249–283 [71] (1972) ‘Issues in Growth Accounting: A Reply to Edward F. Deni- son.’ Survey of Current Business 52:4, Part II, 65–94 [72] Knetter, Michael M., and Thomas J. Prusa (2003) ‘Macroeconomic Fac- tors and Antidumping Filings: Evidence from Four Countries.’ Journal of International Economics 61, 1–18 [73] Kohli, U. (1978) ‘A Gross National Product Function and the Derived Demand for Imports and Supply of Exports.’ Canadian Journal of Eco- nomics 11, 167–182 [74] (1990) ‘Growth Accounting in the Open Economy: Parametric and Nonparametric Estimates.’ Journal of Economic and Social Mea- surement 16, 125–136 [75] (1991) Technology, Duality and Foreign Trade: The GNP Function Approach to Modeling Imports and Exports (Ann Arbor: MI: University of Michigan Press) [76] (2003) ‘Growth Accounting in the Open Economy: International Comparisons.’ International Review of Economics and Finance 12, 417– 435 [77] (2004a) ‘An Implicit Törnqvist Index of Real GDP.’ Journal of Productivity Analysis 21, 337–353 [78] (2004b) ‘Real GDP, Real Domestic Income and Terms of Trade Changes.’ Journal of International Economics 62, 83–106 [79] Konüs, A.A. (1939) ‘The Problem of the True Index of the Cost of Living.’ Econometrica 7, 10–29. Translated from 1924 original [80] Lau, L. (1976) ‘A Characterization of the Normalized Restricted Profit Function.’ Journal of Economic Theory 12:1, 131–163 227 Bibliography [81] Leacy, F.H., ed. (1983) Historical Statistics of Canada, second edition ed. (Ottawa: Canada: Statistics Canada) [82] Leidy, M.P. (1997) ‘Macroeconomic Conditions and Pressures for Pro- tection under Antidumping and Countervailing Duty Laws: Empirical Evidence from the United States.’ Staff Papers 44, International Mon- etary Fund. p. 132144 [83] Leipziger, Danny M., and Hyun Ja Shin (1991) ‘The Demand for Pro- tection: A Look at Antidumping Cases.’ Open Economies Review 2, 27– 38 [84] Mah, Jai S. (2000) ‘Antidumping Decisions and Macroeconomic Vari- ables in the USA.’ Applied Economics 32, 1701–1709 [85] McFadden, D. (1978) ‘Cost, Revenue and Profit Functions.’ vol. 1 (Am- sterdam: North-Holland) pp. 3–109 [86] Moore, Michael O. (1992) ‘Rules or Politics?: An Empirical Analysis of ITC Anti-dumping Decisions.’ Economic Enquiry 30(3), 449–466 [87] Morrison, C.J., and W.E. Diewert (1990) ‘Productivity Growth and Changes in the Terms of Trade in Japan and the United States.’ (Chicago: University of Chicago Press) pp. 201–227 [88] Moyer, B.C., M.B. Reinsdorf, and R.E. Yuskavage ‘Aggregation Issues in Integrating and Accelerating the BEA’s Accounts: Improved Meth- ods for Calculating GDP by Industry.’ vol. 66 of NBER Studies in Income and Wealth (Chicago: University of Chicago Press) [89] Nelson, Douglas ‘The Political Economy of Antidumping: A Survey.’ European Journal of Political Economy [90] Niels, Gunnar (2000) ‘What is Antidumping Policy Really About?’ Journal of Economic Surveys 14(4), 467–492 [91] OECD (1972) ‘Labour Force Statistics.’ Technical Report, Paris: OECD 228 Bibliography [92] (1993) ‘Labour Force Statistics.’ Technical Report, Paris: OECD [93] Prusa, Thomas J. (2001) ‘On the Spread and Impact of Anti-dumping.’ Canadian Journal of Economics 34(3), 591–611 [94] Prusa, Thomas J., and Susan Skeath (2001) ‘The Economic and Strate- gic Motives for Antidumping Filings.’ Working Paper 8424, NBER [95] Rymes, T.K. (1968) ‘Professor Read and the Measurement of Total Factor Productivity.’ Canadian Journal of Economics 1, 359–367 [96] (1983) ‘More on the Measurement of Total Factor Productivity.’ The Review of Income and Wealth 29, 297–316 [97] Samuelson, P.A. (1953) ‘Prices of Factors and Goods in General Equi- librium.’ Review of Economic Studies 21, 1–20 [98] Samuelson, P.A., and S Swamy (1974) ‘Invariant Economic Index Num- bers and Canonical Duality: Survey and Synthesis.’ American Eco- nomic Review 64, 566–593 [99] Sato, K. (1976) ‘The Meaning and Measurement of the Real Value Added Index.’ Review of Economics and Statistics 58, 434–442 [100] Schreyer, P. (2001) OECD Productivity Manual: A Guide to the Mea- surement of Industry-Level and Aggregate Productivity Growth OECD (Paris) [101] (2007) Measuring Capital: Revised Manual OECD Statistics Di- rectorate (Paris:OECD). Paper presented at the Meeting of the Work- ing Party on National Accounts [102] Secretariat, WTO (2007) ‘Semi-Annual Report of Antidumping Ac- tions.’ Technical Report, World Trade Organization [103] Solow, R.M. (1957) ‘Technical Change and the Aggregate Production Function.’ Review of Economics and Statistics 39, 312–320 229 Bibliography [104] Statistics Canada (1987) The Input-Output Structure of the Canadian Economy 1961-1981 Ottawa:Statistics Canada [105] (1997) National Balance Sheet Accounts; Annual Estimates 1996 Ottawa:Statistics Canada [106] (2007) Canadian Economic Observer, Historical Statistical Sup- plement 2006/07 Ottawa:Statistics Canada [107] Törnqvist, L. (1936) ‘The Bank of Finland’s Consumption Price In- dex.’ Bank of Finland Monthly Bulletin 10, 1–8 [108] Törnqvist, L., and E. Törnqvist (1937) ‘Vilket är förhällandet mellan finska markens och svenska kronans köpkraft?’ Ekonomiska Samfundets Tidskrift 39, 1–39. Reprinted as p. 121-160 in Collected Scientific Pa- pers of Leo Törnqvist, Helsinki: The Research Institute of the Finnish Economy, 1981 [109] Woodland, A.D. (1982) International Trade and Resource Allocation (Amsterdam: North-Holland) [110] Wooldrige, Jeffrey M. (2002) Econometric Analysis of Cross Section and Panel Data (Cambridge, MA: The MIT Press) [111] Zanardi, Maurizio (2005) ‘Antidumping: A Problem in International Trade.’ European Journal of Political Economy 22(3), 591–617 230

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