Changes in the Terms of Trade
and the Productivity
Performance of Canada and
the Netherlands
by W. Erwin Diewert, Department of
Economics, University of British Columbia
Presented at the
Workshop on Index Number Theory
Tinbergen Institute at the University of
Amsterdam, October 9, 2008
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 and the (entire)
Dutch economy over the years 1960-2007 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 results for the Netherlands are quite different
from the Canadian and Australian results in that
changes in the terms of trade are not an important
explanatory factor in explaining the growth of real
income generated by the Dutch economy.
• However, switching from a gross product approach
to a net product approach does change the relative
importance of the explanatory factors for the growth
of real income in the Netherlands.
• Dutch real income growth over the sample period
has been very good as we shall see.
• Note: since we could not obtain adequate data for
the nonmarket sector of the Dutch economy, our
theory is somewhat off for the Netherlands.
The Basic Framework
• Market sector GDP function:
gt(P,x) max y {Py : (y,x) belongs to St}
• Value of outputs equals value of inputs in period t:
gt(Pt,xt) = Ptyt = Wtxt ; yt is output; xt is input;
• Real income generated by market sector in period t is
t Wtxt/PCt = wtxt = gt(pt, xt) = Ptyt/PCt = ptyt
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.
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) 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 Pt]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:
(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 Pt]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:
(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 Pt]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 = wtxt/ wt-1xt-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
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 for Canada
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 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 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;
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
The Dutch Data
• Basically, we used the data on the Netherlands that
can be downloaded on the OECD data website:
OECD.STAT.
• The national accounts data there only go back to 1969
but the data for the 1960’s are available in earlier
OECD publications.
• There are some problems with constructing measures
of labour input and capital inputs and so our results
are not completely reliable!
• It would be good if the CBS would construct a nice set
of official productivity accounts so that researchers
would not always have to start from scratch.
• The EUKLEMS data base is a start in the right
direction but it does not go back to the 1960s.
Canadian Prices (PC PD)
12
10 PC
PD
8 PX
PM
6
PL
4 PK
PY
2
PZ
0
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46
Canadian data:
Year t PC PD PX PM PL PK PY PZ
1961 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
2006 5.9 5.7 5.8 4.6 10.2 10.4 6.3 10.4
Year t QC QD QX QM QL QK QY QZ
1961 ___ 28.5 7.3 -8.2 19.2 8.5 27.7 27.7
2006 ___164.6 89.1 -107.0 56.9 36.6 152.6 92.7
Dutch data:
Year t PC PD PX PM PL PK PY PZ
1960 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
2007 4.8 5.7 2.5 2.4 16.6 4.1 5.8 10.6
Year t QC QD QX QM QL QK QY QZ
1960 __ 19.4 10.2 -10.1 12.1 7.3 19.5 19.5
2007 __ 78.5 166.2 -156.3 18.8 44.3 85.1 46.6
Dutch Prices
18
16
14
PC
12
PD
10 PX
8 PM
PL
6
PK
4
2
0
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46
Canadian After Tax Balancing Real
Interest Rates
r
0.1
0.08
0.06
r
0.04
0.02
0
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46
Dutch Balancing Real Interest Rates
R
0.09
0.08
0.07
0.06
0.05
R
0.04
0.03
0.02
0.01
0
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46
• The sample before tax rate of return in Canada was
8.433%
• The sample after tax rate of return in Canada was a
rather big 4.95% and in the Netherlands it was an
also big 4.58%
• The land and inventory stocks problem
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; the average rate of growth was
1.14% (compared to the Statistics Canada 0.43%).
The following slide shows (gross approach) TFP
growth for the entire Dutch economy, 1961-2007.
The Dutch average annual rate of growth is 1.30%.
Canadian TFP Business Sector Growth
Rates (Gross Product) 1962-2006
Prod
1.08
1.06
1.04
1.02
1
Prod
0.98
0.96
0.94
0.92
0.9
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43
Dutch annual rates of TFP growth (gross
product approach); entire economy
Annual DutchTFP growth (gross)
1.06
1.04
1.02
1
0.98
0.96
0.94
0.92
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46
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
2.5
2
1.5
1
0.5
0
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46
Tt ADt AXt AMt BLt BKt
• 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)
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!)
• But why is there no China effect for Holland and
Belgium?
Canada is quite similar to Australia. The following
Figure is taken from Diewert and Lawrence (2006)
Australian Cumulated Contribution
Factors to Real Income Growth – GDP
Approach
2.0
Productivity
1.8
Labour
Input
1.6
1.4 Capital
Input
1.2
Terms of
Trade
1.0
Domestic Output
0.8 Price
0.6
1960
1962
1964
1966
1968
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
Dutch Cumulated Real Income Growth
Factors- GDP Approach
2
1.8
1.6
T
1.4
AD
1.2
AX
1 AM
0.8 BL
BK
0.6
Real TofT
0.4
0.2
0
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46
• Note that Dutch real (gross) income grew 5.3 fold
over the 48 year (3.65% average annual growth)
• The overall growth factor for productivity is 1.83
• The growth factor for domestic real price growth is
1.20
• The growth factor for export prices is 0.69
• The growth factor for import prices is 1.47 but this
just cancels off the fall in export price effects
• The growth factor for labour is 1.32
• The growth factor for gross capital services is 1.81
• The growth factor for export and import prices
combined is 1.01 which is negligible
• Thus growth of TFP. capital services, and labour
services explain most of the real income growth
• When we divide real income by the population aged
15 to 65, per capita Dutch (gross) real income
increased 3.36 fold over the 48 years. Impressive!
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) 1962-2006
Prod grth
1.08
1.06
1.04
1.02
1
Prod grth
0.98
0.96
0.94
0.92
0.9
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43
Canadian Cumulated Real Income
Growth Factors- NDP Approach
2.5
2
1.5
1
0.5
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45
Tt ADt AXt AMt BLt BKt
• 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.
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 1997-2006 below
1.2
1.15
1.1
1.05
1
0.95
0.9
0.85
1 2 3 4 5 6 7 8 9
T AD AX AM BL BK
Australian Cumulated Contribution
Factors – NDP Approach
2.2
Productivity
2.0
1.8
Labour
1.6
Input
1.4
Capital
Input
1.2
Terms of Trade
1.0
Domestic Output Price
0.8
1960
1962
1964
1966
1968
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
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.
Australian Cumulated Contribution
Factors to Real Income Growth – NDP
Approach, 1995-2004
1.3
Productivity
1.2
Labour Input
1.1
Terms of Trade
Capital Input
1.0
Domestic Output Price
0.9
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
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)
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 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
Dutch TFP Growth Rates (Net Product
Approach) 1961-2007
TFP growth (Net Product)
1.15
1.1
1.05
1
0.95
0.9
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47
Dutch Cumulated Real Income Growth
Factors- NDP Approach
2.5
2 Tech
AD
1.5 AX
AM
1 BL
BK
0.5 TofT
0
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46
Summary of Dutch Real Income Growth using
the Net Output and Waiting Services Approach
• Dutch real income grew 5.14 fold over the 1960-2007 period;
3.59% per year. (Per capita real net income increased 3.16 fold
compared to 3.26 fold in the gross income framework). Very
impressive!
• TFP growth factor = 1.99
• Growth factor for real domestic prices = 1.24
• Growth in real export prices = 0.64
• Growth (really falls) in real import prices = 1.58
• Growth in real labour input = 1.40
• Growth in waiting services = 1.47
• The combined growth factor for changes in real export and
import prices = 1.013 (negligible).
• 5.14 = 1.99x1.24x0.64x1.58x1.40x1.47
• The contribution of capital services growth falls in the net
setup (from 1.81 to 1.47) while others rise
Conclusions
• The net output approach to productivity
measurement seems to lead to a much smaller role
for capital deepening (but not so much for the
Netherlands) 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 (at least Kohli, Morrison and
Diewert think so!)