Changes in the Terms of Trade and Canadas Productivity Performance

1
Changes in the Terms of Trade and Canadas
Productivity Performance

• 2008 World Congress on National Accounts and
  Economic Performance Measures for Nations, May
  12-17
• by W. Erwin Diewert, Department of Economics,
  University of British Columbia

2

• 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 1961-2006
  into contributions from 3 sources
• Productivity growth
• Growth in primary inputs
• Changes in real export and import prices.

3

• 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.

4
The Basic Framework

• Market sector GDP function
• gt(P,x) ? max y P?y (y,x) belongs to St
• Value of outputs equals value of inputs in period
  t
• gt(Pt,xt) Pt?yt Wt?xt yt is output xt
  is input
• Real income generated by market sector in period
  t is
• ?t ? Wt?xt/PCt wt?xt gt(pt, xt)
  Pt?yt/PCt pt?yt
• where PCt is consumption price
• This is the amount of consumption period t income
  can buy and this will be our suggested economic
  welfare measure.

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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?

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Productivity Growth

• Definition of a family of period t productivity
  growth factors
• ?(p,x,t) ? gt(p,x)/gt-1(p,x)
• Laspeyres type measure ?Lt ? ?(pt-1,xt-1,t) ?
  gt(pt-1,xt-1)/gt-1(pt-1,xt-1)
• Paasche type measure ?Pt ? ?(pt,xt,t) ?
  gt(pt,xt)/gt-1(pt,xt)
• Fisher type measure ?t ? ?Lt ?Pt1/2
• But how can we empirically implement the above
  theoretical definitions? It can be done by
  assuming a translog technology.

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Real Output Price Growth Factors

• Definition of a family of period t real output
  price growth factors
• ?(pt-1,pt,x,s) ? gs(pt,x)/gs(pt-1,x)
• Laspeyres type measure ?Lt ? ?(pt-1,pt,xt-1,t-1)
  
• 
  ? gt-1(pt,xt-1)/gt-1(pt-1,xt-1).
• Paasche type measure ?Pt ? ?(pt-1,pt,xt,t) ?
  gt(pt,xt)/gt(pt-1,xt).
• Fisher type measure ?t ? ?Lt ?Pt1/2
• Gives increase in real income due to changes in
  real output prices, including the real prices of
  X and M

8
Input Quantity Growth Factors

• Definition of a family of period t input quantity
  growth factors
• ?(xt-1,xt,p,s) ? gs(p,xt)/gs(p,xt-1)
• Laspeyres type measure ?Lt ? ?(xt-1,xt,pt-1,t-1)
  
• 
  ? gt-1(pt-1,xt)/gt-1(pt-1,xt-1).
• Paasche type measure ?Pt ? ?(xt-1,xt,pt,t) ?
  gt(pt,xt)/gt(pt,xt-1).
• Fisher type measure ?t ? ?Lt ?Pt1/2
• Gives the increase in real income due to input
  growth alone

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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 wt?xt/
  wt-1?xt-1 is the observable period t growth in
  real income and
• ln ?t ln PT(pt-1,pt,yt-1,yt) and ln ?t
  ln QT(wt-1,wt,xt-1,xt)
• where PT is the Törnqvist (real) output
  price index and QT is the Törnqvist input
  quantity index.
• We cumulate these observable relationships
• ?t/?t-1 ?t ?t ?t
• into the levels relationship ?t/?0 Tt
  At Bt

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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 CGI 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.

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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.

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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
  1961-2006, 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

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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).

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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).

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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.

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• 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

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Canadian Prices (PC ? PD)
18
Canadian After Tax Balancing Real Interest Rates
19

• 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, 1962-2006 using the
  traditional GDP approach

20
Canadian TFP Business Sector Growth Rates (Gross
Product) 1962-2006
21

• 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
  CGI 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

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Canadian Cumulated Real Income Growth Factors-
GDP Approach
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• The gross real income generated by the business
  sector grew 5.91 fold over the years 1961-2006.
• 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)

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• 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 0.997 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)

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Australian Cumulated Contribution Factors to Real
Income Growth GDP Approach
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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)

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Canadian TFP Growth Rates (Net Product Approach)
1962-2006
28
Canadian Cumulated Real Income Growth Factors-
NDP Approach
29

• The net real income generated by the Canadian
  business sector grew at an annual rate of 4.18
  percent on average over the period 1961-2006.
• 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.
  

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• 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).

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• 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

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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
1997-2006 below
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Australian Cumulated Contribution Factors NDP
Approach
34

• 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
  1995-2004.

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Australian Cumulated Contribution Factors to Real
Income Growth NDP Approach, 1995-2004
36
Canadian Business Sector Productivity Growth (Net
Framework) Summary 1961-2006

• 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, 1962-1973, TFP growth
  averaged a spectacular 3.09 per year.
• During the dismal years 1974-1991, TFP growth
  averaged only 0.23 per year.
• Over the period, 1992-1999, TFP growth has nicely
  recovered to average a very respectable 1.64 per
  year.
• Over the current 2000-2006 period, TFP growth has
  fallen to 0.34 (due to 2001 and 2003, which had
  drops of 1.3 and 4.3 respectively)

37
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
  1961-2006 is much larger than the comparable
  Statistics Canadas 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
  

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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.

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• 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.