Changes in the Terms of Trade and Canada’s Productivity Performance 2008 World Congress on National Accounts and Economic Performance Measures for Nations, May by W. Erwin Diewert, Department of Economics, University of British Columbia

Introduction We adapt the Diewert and Morrison (1986), Kohli (1990), Diewert, Mizobuchi (2005) and Diewert and Lawrence methodology to decompose the growth in real income generated by the business section of the Canadian economy over the years into contributions from 3 sources: Productivity growth; Growth in primary inputs; Changes in real export and import prices.

Our results for Canada are very similar to the results obtained by Diewert and Lawrence (2006) for Australia. We consider both a traditional gross product as well as a net product productivity approach. Using the net product setup, the contribution of capital deepening to improving living standards is greatly diminished and the role of productivity improvements is greatly augmented. A disadvantage of our methodology is that industry contributions cannot be identified due to data limitations on the industrial allocation of X and M. We compare our results with comparable MFP results from Statistics Canada and find big differences.

The Basic Framework Market sector GDP function: g t (P,x)  max y {P  y : (y,x) belongs to S t } Value of outputs equals value of inputs in period t: g t (P t,x t ) = P t  y t = W t  x t ; y t is output; x t is input; Real income generated by market sector in period t is  t  W t  x t /P C t = w t  x t = g t (p t, x t ) = P t  y t /P C t = p t  y t where P C t is consumption price This is the amount of consumption period t income can buy and this will be our suggested economic welfare measure.

Identifying the Contributions The main determinants of growth in real income generated by the 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. We need a way of identifying the effect of each of these factors in isolation, i.e., what would have happened to real income if only each of these changes had occurred separately and all else remained the same?

Productivity Growth Definition of a family of period t productivity growth factors:  (p,x,t)  g t (p,x)/g t-1 (p,x) Laspeyres type measure:  L t   (p t-1,x t-1,t)  g t (p t-1,x t-1 )/g t-1 (p t-1,x t-1 ) Paasche type measure:  P t   (p t,x t,t)  g t (p t,x t )/g t-1 (p t,x t ) Fisher type measure:  t  [  L t  P t ] 1/2 But how can we empirically implement the above theoretical definitions? It can be done by assuming a translog technology.

Real Output Price Growth Factors Definition of a family of period t real output price growth factors:  (p t-1,p t,x,s)  g s (p t,x)/g s (p t-1,x) Laspeyres type measure:  L t   (p t-1,p t,x t-1,t-1)  g t-1 (p t,x t-1 )/g t-1 (p t-1,x t-1 ). Paasche type measure:  P t   (p t-1,p t,x t,t)  g t (p t,x t )/g t (p t-1,x t ). Fisher type measure:  t  [  L t  P t ] 1/2 Gives increase in real income due to changes in real output prices, including the real prices of X and M

Input Quantity Growth Factors Definition of a family of period t input quantity growth factors:  (x t-1,x t,p,s)  g s (p,x t )/g s (p,x t-1 ) Laspeyres type measure:  L t   (x t-1,x t,p t-1,t-1)  g t-1 (p t-1,x t )/g t-1 (p t-1,x t-1 ). Paasche type measure:  P t   (x t-1,x t,p t,t)  g t (p t,x t )/g t (p t,x t-1 ). Fisher type measure:  t  [  L t  P t ] 1/2 Gives the increase in real income due to input growth alone

Real Income Growth Decomposition The input growth and real output price contribution factors (to real income growth) can be broken down into separate effects that are defined in similar ways. With the assumption of a translog technology, we can get the following exact decomposition of real income growth into contribution factors:  t /  t-1   t =  t  t  t where  t = w t  x t / w t-1  x t-1 is the observable period t growth in real income and ln  t = ln P T (p t-1,p t,y t-1,y t ) and ln  t = ln Q T (w t-1,w t,x t-1,x t ); where P T is the Törnqvist (real) output price index and Q T is the Törnqvist input quantity index. We cumulate these observable relationships  t /  t-1 =  t  t  t into the “levels” relationship  t /  0 = T t A t B t

Terms of Trade Contribution Factors The effects of changes in the price of exports relative to the price of consumption and in the price of imports relative to the price of consumption show up as two of the three price effects in our model. The real export price effect adds to real income growth if the price of exports increases more rapidly than the price of consumption and The real import price effect which adds to real income growth if the price of imports falls compared to the price of consumption The third price effect in our model looks at the price of C+G+I relative to the price of C. This effect tends to be negative due to falling prices of I goods relative to C goods. Note that G here is not the usual G because government production is excluded.

The Real Net Income Approach Following Diewert, Mizobuchi and Nomura (2005) and Diewert and Lawrence (2006), in our net product approach, we take depreciation out of user cost and instead subtract it from gross investment. Now investment is converted to consumption equivalents only if it is positive after netting out depreciation; thus, we have moved from real GDP (GDP deflated by the consumption price index) to real NDP (NDP deflated by the consumption price index). The remaining user cost term is the reward for waiting or postponing consumption; thus, income is now labour income plus the net return to capital. In the net framework, the role of TFP growth is magnified and in the Canadian data, the role of capital deepening is diminished as we shall see.

Canadian Database Basic Approach: Use information on aggregate final demand expenditures, aggregate labour and capital input and then adjust these data to remove the outputs produced and the inputs used by the housing and general government sectors. Using published CANSIM II data covering the years , business sector data for 11 net outputs, 3 labour inputs (these are taken from the recently published Stat Can KLEMS data base), and 5 capital inputs. Net outputs are: Consumption (excluding all housing services) Government investment; Business sector investment in residential structures; Business sector investment in nonresidential structures;

Canadian Business Sector Net Outputs (cont) Business sector investment in machinery and equipment; Inventory change (some special adjustments were made here); Purchases of goods and services by the general government sector from the business sector less govt sales to the business sector Exports of goods; Exports of services; Imports of goods (minus sign) and Imports of services (minus sign).

Canadian Business Sector Labour Inputs The labour services of workers with some or completed post secondary certificate or diploma; The labour services of workers with a university degree or above; The labour services of workers with primary or secondary education These three types of labour input are taken directly from Statistics Canada recent KLEMS program; see Baldwin, Gu and Yan (2007).

Canadian Business Sector Capital Inputs The stock of machinery and equipment available to the business sector at the start of each year; The starting stock of business sector nonresidential structures; The stock of nonagricultural, nonresidential land used by the business sector; The stock of agricultural land used by the business sector and The starting stocks of inventories used by the business sector.

The above data were aggregated into: C domestic consumption excluding housing at producer prices D domestic final demand at producer prices X exports M imports L labour services K capital services In order to calculate productivity growth, we also need aggregate output Y and aggregate input Z

Canadian Prices (P C  P D )

Canadian After Tax Balancing Real Interest Rates

The sample before tax rate of return was 8.433% The sample after tax rate of return was a rather big 4.950% The next slide shows the year to year growth rates of Total Factor Productivity Growth of the Canadian Business Sector, using the traditional GDP approach

Canadian TFP Business Sector Growth Rates (Gross Product)

The next slide shows the cumulated contribution factors to the growth in real income of the Canadian business sector. AD is the contribution of changes in the price of C+G+I relative to the price of C AX and AM are the contributions of changes in the real prices of exports and imports (relative to the price of consumption) BK, BL and T are the contributions of labour, capital and productivity growth

Canadian Cumulated Real Income Growth Factors- GDP Approach

The gross real income generated by the business sector grew 5.91 fold over the years The main factors explaining this growth are: productivity increases (cumulative growth factor 1.64) growth of quality adjusted labour input (cumulative growth factor 2.04) growth of capital services (cum. growth factor 1.65) lower real import prices (cum. growth factor 1.13). Negative contributions from: declining real domestic output prices (cumulative growth factor 0.97) and declining real export prices (cumulative growth factor.98)

But the effects of changes in the prices of exports and imports are not always small. From 1998 to 2005, the cumulative real import price factor increased from to 1.126, a 13 percent increase, and this was the growth factor that had the second biggest impact (after quality adjusted labour growth) on real income growth over this period. (China effect!) Canada is quite similar to Australia. The following two Figures are taken from Diewert and Lawrence (2006)

Australian Cumulated Contribution Factors to Real Income Growth – GDP Approach

The Net Product Approach Real income is overstated using the gross product concept (although real income growth is not overstated as we shall see) However, the contributions of labour growth, capital growth and productivity growth are quite different in the net framework Methodology: take depreciation out of the list of primary inputs and treat it as a negative offset to gross investment. The depreciation part of user cost is treated as an intermediate input. What remains is the reward for waiting. (T.J. Rymes)

Canadian TFP Growth Rates (Net Product Approach)

Canadian Cumulated Real Income Growth Factors- NDP Approach

The net real income generated by the Canadian business sector grew at an annual rate of 4.18 percent on average over the period The corresponding average annual gross real income growth rate was 4.10 percent. Falling real domestic output prices averaged a tiny positive contribution to the growth in real net income of 0.06 percent per year. Falling real export prices also had a small negative contribution of  0.03 percent per year.

Positive average contributions to the growth of real net income were: Productivity improvements (1.26 percent per year compared to 1.14 percent in the gross income framework), Growth of labour input (1.85 percent per year compared to the previous gross income 1.60 percent), Growth of capital input (0.65 percent per year compared to the previous 1.11 percent) and Falls in real import prices (0.32 percent per year compared to the previous 0.28 percent).

Points to notice about the net vs gross: The role of productivity improvements is magnified in the net income framework The role of increases in labour input is also magnified The role of increases in capital input (capital deepening) is greatly diminished The role of falling real import prices is also magnified in the net income framework

Over short periods of time, the effects of changes in real import and export prices can be very substantial. See the results for Canada for below

Australian Cumulated Contribution Factors – NDP Approach

In both countries, the switch from GDP to NDP has similar effects: Real income growth is similar for the two approaches but The contribution of capital growth falls dramatically using the net approach and The contributions of labour and productivity growth greatly increase using the net approach. The effects of changes in international prices remains small for Australia over the entire period but in the recent decade, falling import prices have made a major contribution to the growth of real income in both countries. We show the Australian experience over the period

Australian Cumulated Contribution Factors to Real Income Growth – NDP Approach,

Canadian Business Sector Productivity Growth (Net Framework) Summary The average annual rate of TFP growth in the net income framework was a satisfactory 1.26% per year (and in the gross framework it was 1.14% per year) During the golden years, , TFP growth averaged a spectacular 3.09% per year. During the dismal years , TFP growth averaged only 0.23% per year. Over the period, , TFP growth has nicely recovered to average a very respectable 1.64% per year. Over the current period, TFP growth has fallen to 0.34% (due to 2001 and 2003, which had drops of 1.3% and 4.3% respectively)

But there are some Problems with the Canadian Data Our 1.14% average rate of (gross) TFP growth for the Canadian business sector over the years is much larger than the comparable Statistics Canada’s recent KLEMS program average Multifactor Productivity Growth over the same years of 0.43% per year. The difference appears to be due to differing treatments of capital services: the choice of the user cost formula matters and also our depreciation rates appear to be smaller than those used by the Statistics Canada KLEMS program

Conclusions The net output approach to productivity measurement seems to lead to a much smaller role for capital deepening as an explanation for improvements in the standard of living. The net real income methodology used here gives a much larger role for productivity improvements at least for Canada, Australia and Japan. There is a need for users of the national accounts to come to some agreement on the exact form of the user cost formula that should be used to measure capital services. Different formulae can give very different answers.

During the naughts, the real (net) income generated by the Canadian business sector grew at an average rate of 4.29 percent per year and declines in real import prices (the China effect) contributed 1.82 percentage points to this increase, which was greater than the effects of quality adjusted labour input growth (1.59 percentage points per year), increases in waiting services (0.70 percentage points per year). Thus for short periods of time, changes in the terms of trade can have a large effect on living standards. Our translog methodology adapted to measure real income growth is a useful addition to traditional growth accounting.