Unbalanced Growth in Canada and the United States:
Demand and Supply Effects
Anik Dufour, Jianmin Tang and Weimin Wang
Micro-Economic Policy Analysis
Industry Canada
Drafted: Feb. 10, 05
Abstract
This paper examines industry contribution to aggregate output and productivity growth
in Canada and the United States, by distinguishing net demand effects from net supply
effects and using a framework consistent with the “utility-value concept” of real GDP. It
shows that during the period 1981-2000, the service sector accounted for 77 percent of
economic growth in Canada and almost all economic growth in the United States. The
increased importance of the service sector in the two countries is mainly driven by
increased demand for some services. In contrast, the contribution from the goods sector
was relatively small because the effect from positive supply shifts was offset by the
effect from the decline in output price in the sector. In addition, this paper shows that
despite its lower labour productivity growth the service sector was the largest contributor
to aggregate labour productivity growth in both countries. This happens because the
importance of the services sector, indicated by both higher output prices and increased
labour share, increased significantly at the expenses of the goods sector, driven by a
rapidly growing demand for some services. Finally, this paper shows that slow
productivity growth of the industries that contributed greatly to economic growth may be
explained by a rapidly growing demand for their outputs coupled with relatively stagnant
technological progress in those industries.
Note: This is a preliminary work for the Fourth Ottawa Productivity Workshop, February
17-18, 2005. It is subject to revision and should not be quoted without consultation with the
authors. The views expressed in this paper are our own and do not necessarily reflect those
of Industry Canada.
1
1. Introduction
In the past two decades, the importance of the service sector in Canada and the United
States, whether measured by output or employment, has increased considerably. For
example, the employment share of the service sector increased from 66.5 percent in 1981 to
73.0 percent in 2000 in Canada and from 67.2 percent to 76.3 percent in the United States.
This trend took place despite stronger productivity growth in the goods sector than in the
service sector.
The industrial structural change is not a new phenomenon and has been predicted by the
theory of unbalanced growth or the "cost disease model" (Baumol 1967). Under the
assumption that in the long run, wages in different sectors of the economy go up and down
together regardless of which sector is the most productive,1 the model predicts that the
importance of technologically non-progressive industries increases over time in terms of
relative output prices and employment and nominal output shares.
By extending the cost disease model, this paper studies the implications of unbalanced
growth to industry contributions to aggregate output and labour productivity growth.
Understanding the underlying factors behind fast economic and productivity growth is
important for economic policy development.
Many researchers and policy analysts have put effort in measuring industry contributions to
economic growth and aggregate labour productivity growth (e.g. Jorgenson and Stiroh 2000;
Jorgenson 2004; Faruqui 2003; Ho, Rao and Tang 2004). However, all these studies focus
mainly on the supply side and ignore the fact that the utility value of goods and services is
changing over time. This paper argues that industry contribution to economic growth should
be measured in such a way that reflects both supply and demand and that it should be
consistent with the “utility-value concept” of the real GDP based on the chain-Fisher index.
By the utility-value concept of real GDP, this paper means that the estimate of real GDP
should reflect the standard consumer theory of economics – the marginal utility of
consuming an extra unit of commodity or service being equal to the market price of the
commodity or the service. The chain-Fisher index, which has been adopted by the statistics
agencies in both Canada and the United States, has the important property. In measuring
real GDP, the index values a commodity or service more when its price increases and less
when its price drops.
Besides measuring industry contribution to economic and labour productivity growth, it is
also important to understand the sources of industry contributions. By developing a
framework being consistent with the utility-value concept of real GDP, this paper examines
the sources of industry contributions to economic growth and aggregate labour productivity
growth in Canada and the United States over the period 1981-2000. In particular, this paper
assesses whether net demand or net supply shifts dominated industry contributions of each
1
This appears to reflect the situation in Canada, where changes in relative wages do not reflect productivity
differentials, but the benefits of productivity gains are diffused across all workers (Baldwin, Durand and
Hosein 2001, p.32).
2
industry group during the sample period. It also examines whether the shifts were
associated with labour force movements from the more productive to the less productive
industry groups, or vice-versa. Furthermore, it determines the contribution of the demand
and supply shifts to the gaps in aggregate output and labour productivity growth between
Canada and the United States. Finally, it gives an economic interpretation of slow
productivity growth observed in some industry groups that experienced relatively strong
demand and contributed significantly to economic growth in the two countries.
This paper shows that during the period 1981-2000, the service sector accounted for 77
percent of economic growth in Canada and almost all economic growth in the United States.
The increased importance of the service sector in the two countries is mainly driven by
increased demand for some services. In contrast, the goods sector was mainly influenced by
positive output supply shifts. Despite its lower labour productivity growth the service sector
was the largest contributor to aggregate labour productivity growth in both countries. This
happens because the importance of the services sector, indicated by both higher output
prices and increased labour share, increased significantly at the expenses of the goods sector,
driven by a rapidly growing demand for some services. Finally, this paper shows that slow
or negative productivity growth of the industries that contributed greatly to economic
growth may be explained by a rapidly growing demand for their outputs coupled with
relatively stagnant technological progress in those industries.
The remaining paper has five sections. In section 2, we study industry contributions to
economic growth by presenting a methodology that is consistent with the utility-value
concept of real GDP. In section 3, we provide with an overview of the reasons why demand
for some services has been so strong in the last few decades. In this section, we also discuss
the effect of unbalanced demand and supply shifts on labour movement across sectors,
together with empirical evidences. In section 4, we examine industry contributions to
aggregate labour productivity growth, with a focus on the effects of demand and supply
shifts. In section 5, we provide an economic reason why an industry facing rapidly growing
demand for its output may maintain low or negative productivity growth. In section 6, we
wraps up with the main findings.
2. The Driving Force of Economic Growth: Demand or Supply?
Economic growth results from a few factors. At any stage of economic development, capital
accumulation and improvements in technology are two main factors that will bring higher
standards of living. At early stages of development, it is essential to build stable and
credible institutions. Once these foundations are in place, more rapid advances in
technology become the engine of growth.
2.1. An Overview of Growth Models
In the last half of a century, two important streams of thought on theories of economic
growth from the supply perspective have emerged2. The first evolves around the
neoclassical growth model (Solow 1956; Stiglitz and Uzawa 1969), introduced in the early
2
This section draws on the textbook of Dornbusch et al. (2001, pp. 53-72).
3
of 1960s. In this model, technological change is exogenous and is the key driver of long-run
growth. Over shorter periods, economic fluctuations are driven by changes in the savings
rate. When the amount of balances of savings differs from the investments required to
providing new workers with capital and to replacing old capital, changes in the savings rate
cause changes in capital per worker. Therefore, increases in the savings rate can raise the
standard of living (as measured by output per capita) over short periods, but the growth
potential is limited by production capacity. When savings are in equilibrium with
investments, output grows at a constant rate and output per capita reaches a steady value. In
the transitory period, an increase in the savings rate increases the steady-state level of
income per capita while an increase in population growth reduces it. But for steady state
levels and long-run growth to increase, an improvement in technology is needed. However,
the model does not explain how technological progress is achieved.
Around the early 1990s, the endogenous growth model (Lucas 1988; Romer 1986; Young
1993) was introduced to try to overcome the shortcomings of the neoclassical growth model.
The idea behind this theory is to explain economic growth with a model in which
technological progress results from economic choice. The theory emerged from attempts to
account for both the determinants of technological progress and the positive empirical
relationship between economic growth and savings rates. Therefore, the theory builds on
the neoclassical or Solow model and seeks to reach more realistic predictions. In this model,
the production function is a straight, upward-sloping line. The linear relationship between
capital and output implies a positive association between the savings rate and output growth.
To maintain the assumption of diminishing returns to capital for the firm – as established by
microeconomic principles – it assumes that capital also generates external benefits captured
by other firms in the form of increased productivity. That is, there are both private and
social returns to capital. If there is knowledge accumulation, for example, the benefits of
investments in research and other forms of knowledge tend to be partly captured by the
investing firm but also partly captured by other firms because methods and ideas are often
easy to copy.
In contrast to theories elaborated from the perspective of the production side, another stream
of thought argues that developments on the demand side of markets have also contributed to
economic growth3. Proponents of this approach emphasize the importance of interactive
changes in production and consumption. Theories under this approach focus on the role of
product variety, changes in preferences and innovations in consumer behaviour in the
process of economic growth. The increasing specialization of consumers in a growing
variety of products is seen as a driver of economic growth that prevents product satiation.
Consumer tastes is also perceived as shaping the way in which producers transform
technological opportunities into marketable products. Moreover, innovation may be as
important to the appreciation and consumption of new goods and services as it is to the
production side. In sum, this view claims that economic growth theory should focus as
much on consumption knowledge and other demand-side forces as on the traditional supplyside determinants (Witt 2001).
3
The Journal of Evolutionary Economics (vol. 11, 2001, pp. 1-164) presents a collection of papers that discuss
economic growth and demand side phenomena such as changes in products and services offered, changes in
consumer behaviour and changes in consumption patterns.
4
2.2. The Utility-Value Concept of Real GDP
Economic growth is typically estimated by growth in real GDP. As claimed in Nakamura
(2004), real GDP should reflect consumers’ value of goods and services. In the standard
consumer theory of economics, the marginal utility of consuming an extra unit of
commodity or service is equal to the market price of the commodity or the service. Hence,
changes in the prices of commodities and services reflect changes in marginal utilities of
consuming those commodities and services. Therefore, real GDP should reflect the “utilityvalue concept” and have a price effect. The real GDP based on the chained-Fisher index has
the property. It values a commodity or service more when its price increases and less when
its price drops since it uses average of the prices of each commodity or service for two
consecutive periods in constructing real GDP.
Statistical agencies in Canada and the United States have switched to the Fisher formula
from the Laspeyres formula when calculating real aggregates. The main reason for adopting
the Fisher formula is the “industry bias” associated with the Laspeyres formula in estimating
real GDP. The Laspeyres formula uses fixed base-year price weights to add up quantities.
Because of ignoring changes in industry output prices, it overestimates the importance of
industries with price declines and underestimates the importance of industries with price
increases. The industry bias is inconsistent with the standard consumer theory and has
become intolerably large due to dramatic declines in the prices of ICT goods and services. In
contrast, the chain Fisher formula provides a measure of output growth consistent with the
consumer theory. This paper will explore the important property of the Fisher formula to
determine each industry contribution to aggregate output growth.
2.3. Industry Contribution to Economic Growth
Under real GDP based on the chained-Fisher index, an industry contributes to aggregate
output growth through two channels: its own output growth and the rise of its real output
price. The rise in the industry’s real output price contributed to real output growth because
it raises the importance of the industry that produces the output in constructing real GDP.
For instance, when the price of a unit of service output rises relatively to the prices of a unit
of goods outputs, the weight assigned to that unit of service output in real GDP also
increases. Taking other parameters as constant, this will translate into a higher contribution
to aggregate output growth for that service industry.
This paper follows the top-down approach, which has been widely used in the literature4, to
study industry contributions to economic growth by decomposing aggregate output growth
into its industry components. We denote Y , Q and P as nominal GDP per capita, real GDP
per capita and the GDP price.5 Similarly, we denote yi , qi and pi as nominal value added
4
For instance, Faruqui (2003), Nordhaus (2002), Tang and Wang (2004), van Ark, Inklaar and McGuckin
(2002), and Wolff (2000).
5
To control for demand from population growth, this paper uses output per capita to present the demand for an
industry output of industry.
5
per capita, real value added per capita and the corresponding price index, respectively, for
industry i . Then we have
(1)
Y
Q 
P
y
i
P
i

i
pi qi
~
pi qi , with
P
i
p
~
pi  i ,
P
where ~p i can be called the real price of industry i as the price of the aggregate output, P , is
usually used to measure inflation. Equation (1) shows that the real aggregate output can be
expressed as a weighted sum of the quantities of its constituent industries. Real aggregate
output growth between year t and z, where t > z, becomes
Qt  Q z
1 


pit qit  ~
piz qiz 
  ~
Qz
Qz  i

1 


piz  qit  qiz    ~
pit  ~
piz   qiz   ~
pit  ~
piz   qit  qiz 
  ~
Qz  i

~
~
p  qiz  qit  qiz ~
p ~
p
p ~
p
q  qiz 
 .
   iz
 
 it ~ iz  it ~ iz  it
Qz
piz
piz
qiz 
i 
 qiz
g Q  z 
t
Alternatively, it can be written as
(2)
t
t
t
t
t
g Q z   wiz  g qi  z   wiz  g  ~
pi  z   wiz  g qi  z  g  ~
pi  z
i
i
i
where wiz is equal to yiz Yz , the nominal output share of industry i at the beginning of the
period, z.
The first summation term on the right hand side of equation (2) is the weighted sum of the
output growth of each industry, the second is the weighted sum of the growth in the price of
each industry’s output, and the third term is the weighted sum of the product of the output
growth and price growth for each industry. All three terms use the nominal output shares in
the beginning year of the period as the weights. The first two terms are called, in this paper,
the pure quantity effect and the pure price effect as they measure separately the contributions
of growth in quantities and growth in prices to real aggregate growth. The third term is the
interaction of the first two effects as measured by their cross-product. This effect occurs
because the change in relative price applies not only to the initial quantity but also to the
change in quantity. In other words, an increase in consumers’ utility value will also apply to
the change in quantity, and this contributes to output growth. As Equation (2) is additive,
the contribution of industry i to real aggregate growth can be written as
(3)
CPC i
t
z

t
t
t
t
 wiz  g qi  z  g  ~
pi  z  g qi  z  g  ~
pi  z

Equation (3) shows that each industry contributes to real aggregate growth through three
channels: the pure quantity effect, the pure price effect and the interaction term of the first
two, which is a second-order effect and is generally negligible.
6
The above decomposition technique has several desirable properties. First, it is consistent
with the “utility value concept” based on the standard consumer theory of economics. It
reflects the change in marginal utility of goods and services, which is captured by the
change in price. The pure price effect shows that besides contributing through a change in
real quantity, an industry also contributes positively (negatively) to the real GDP growth
when its real output price increases (decreases). Second, the decomposition is base-year
invariant because all variables used are either nominal shares or growth rates. Third, it is
valid for any long period as it is not necessary for year t and z to be adjacent. Fourth, it
allows us to pin down the sources (quantity effect or price effect) of each industry’s
contribution. And finally, the decomposition, based on an axiomatic approach, is consistent
with the one based on an economic approach. In other words, it can be derived algebraically
(to the first order approximation) from a producer behavioural equation, as shown in
Appendix A.
These prominent features are important for understanding economic growth. The first four
properties distinguish our decomposition technique from the traditional decomposition
technique used by Statistics Canada, the U.S. Bureau of Economic Analysis (BEA) and the
others researchers (Diewert 2002; Reinsdorf et al. 2002).6 Unlike the traditional
decomposition technique that suppresses the price effect using average prices, the proposed
technique in this paper isolates the price effect from the quantity effect to capture the rise or
fall of marginal utility of goods and services
Both demand and supply changes may influence an industry’s output (quantity and price) at
any given time. We assume an upward sloping supply curve and a downward sloping
demand curve. Then, an increase in demand (upward shift in the demand curve) for an
industry’s output will lead to an increase in both the quantity and price of the industry’s
output (Figure 1). And the opposite is true for a decrease in demand. Conversely, if the
supply curve of an industry shifts downward (the case shown in Figure 2) due to an
improvement in production efficiency, say, it will lead to an increase in output and a
decrease in price. And the opposite is true when the supply curve shifts upward due to a
decline in production efficiency.
Over a long period, an industry faces both demand and supply shifts. If the industry
experiences a positive demand shift and a positive supply shift during a given period, there
will necessarily be an increase in quantity, but the net effect on price will depend on the
strength of one shift against the other. If the demand shift is stronger, we will observe an
increase in price; if the supply shift is stronger, we will observe a decline in price.
Conversely, if the industry experiences a negative shift in both demand and supply, there
will be a decline in quantity but the net effect on price will again be uncertain. In the
remaining two possibilities, where the shifts are in opposite directions, the effect on price
can be determined but the effect on quantity is uncertain. The four possible net shifts are
shown in Table 1. Because it is difficult to distinguish between demand and supply shifts in
6
The traditional decomposition technique employs a Fisher formula. However, the Fisher formula is only
valid or additive for two consecutive periods. In addition, as price is averaged in the Fisher formula, quantity
effect and price effect cannot be separated (see Appendix B for details).
7
a given period and a given industry, this paper only addresses the net shift experienced by
each industry group.
We divide the total economy into eight industry groups: primary; manufacturing;
construction; trade and accommodations; transportation and communications; finance
intermediation; real estate and business services; and other services7. The division is
consistent with the international industry classification system, on which our data are based.
2.4. The Importance of Net Demand Shifts in Output Growth in 1981-2000
During the period of 1981-2000, all industries in Canada experienced either a net positive
supply or net positive demand shift, except for construction. Positive shifts are welfareimproving as shown in Figure 1. Four Canadian industry groups (primary, manufacturing,
trade and accommodation, and transportation and communications) underwent net positive
supply shifts, with positive growth in output per capita and a decline in price (Table 2).
Three Canadian industry groups (financial intermediation, real estate and business services,
and other services) underwent net positive demand shifts, with positive growth in output per
capita and an increase in price. Construction in Canada endured a negligible, negative
demand shift, with declines in output per capita and output price.
For Canada, GDP per capita grew 37 percent during the period of 1981-2000. In terms of
quantity growth (pure quantity effect), the single largest contribution to this growth came
from output growth in manufacturing (10 percentage points), followed by output growth in
real estate and business services (9 percentage points), and in trade and accommodation (7
percentage points). The price contributions were relatively small in magnitude and almost
offset each other among the industry groups. Taking into account both output and price
contributions, real estate and business services was the largest contributor (11 percentage
points), followed by 9 percent for manufacturing.
Similar trends took place in the United States, with one exception. Unlike in Canada,
construction in the U.S. underwent a positive demand shift; but in both countries the shifts
were small. For the United States, GDP per capita grew 50 percent during the period of
1981-2000. In terms of the quantity effect, the single largest contribution to U.S. output
growth came from pure growth in trade & accommodation (17 percentage points), followed
by manufacturing (11 percentage points) and real estate and business services (10
percentage points). However, when we combine the quantity and the price effects, real estate
and business services accounted one third of the aggregate GDP growth in the U.S. Other
services and trade & accommodation contributed 12 percentage points and 10 percentage
points, respectively. The manufacturing sector only contributed 2 percentage points.
There were some important differences between the shifts in Canada and in the United
States. The trade & accommodation group underwent a net supply shift in both countries,
but grew much faster in the United States. Its output per capita increased 96 percent in the
United States and 52 percent in Canada in the 1981-2000 period. Its output price declined
7
Real estate and business services also include renting. Other services include public administration,
education, health, and community services.
8
slightly faster in the United States. In terms of pure growth alone, this group explained
almost all the 14-percentage-points gap in aggregate output growth between Canada and the
United States. During the same period, the real output price in manufacturing declined
much faster in the United States (30 percent) than in Canada (virtually no change) (Table 3).
Because of this difference, the overall contribution to the aggregate GDP per capita growth
from this sector was 9 percentage points in Canada and only 2 percentage points in the
United States, although output growth in this industry was very similar in the two countries
(54 percent for the former and 50 percent for the latter).
Taken together, industry groups (primary, manufacturing, trade and accommodation, and
transportation and communications for both Canada and the United States) with a net supply
shift made a total contribution of 16 percentage points to aggregate GDP per capita growth
in Canada and 11 percentage points in the United States (Table 4). Except transportation
and communications, all these industries experienced a faster decline in output prices. As
result, Canada had an overall 9 percentage points advantage in terms of the pure price effect
on aggregate GDP per capita growth.
For industry groups with net positive demand shifts (mainly financial intermediation, real
estate and business services, and other services), total contribution in the United States (39
percentage points) was much larger than in Canada (23 percentage points). The major
difference was in the magnitude of the increase in industry output prices. During the period
of 1981-2000, the output price of financial intermediation increased 81 percent in the United
States compared to 23 percent in Canada (Table 4). Similarly, the output prices of real
estate and business services and of other services also increased faster in the United States
than in Canada. As a result, the United States had a 9 percentage points advantage in terms
of the pure price effect on aggregate GDP per capita growth (Table 4).
Under the assumption that the slopes of the demand and supply curves are similar in the two
countries, it is fair to conclude that the United States underwent larger shifts in both positive
demand and positive supply than Canada. And the difference in the growth of aggregate
output per capita between the two countries was mainly driven by stronger output growth in
trade and accommodation in the United States.
3. Increased Demand for Services and Employment Shifts Among Canadian
Industries
In this section, we give an overview the possible reasons of relatively strong demand for
some services, and provide empirical evidence that both demand and supply influence
employment shifts among Canadian industries.
3.1. Possible Reasons for Relatively Strong Demand for Some Services
The factors that have fuelled the demand for services can generally be divided into two
groups: factors related to final demand and factors related to intermediate demand. Final
demand factors broadly refer to determinants of household expenditure. The most common
discussed in the literature are rising income, and external forces such as the rise in women’s
9
labour force participation rate, the size of the welfare state, increased urbanisation, and
international trade (OECD, 2003; Messina, 2004).
There is some empirical evidence showing that demand for services is income elastic and
demand for goods is income inelastic. Many services are luxury goods with income
elasticity being greater than one. As real income per capita increases, demand for these
services grows more than proportionally. On the other hand, demand for services is price
inelastic.8 Therefore, although service prices increase much faster than goods prices as a
result of lagging labour productivity growth, the effect of rising living standards outweighs
the effect of rising relative prices, leading to an increased demand for services.
Changes in the composition of demand are another source of change in demand for services.
Female labour force participation, for example, is associated with increased demand for
services9. This either reflects changes in household tastes and income elasticities or the
substitution between external services and homework (Fuchs, 1980, p.20). Another factor
associated with increased demand for services is greater urbanisation. As cities grow in
size, the share of leisure services, for example, is likely to expand (Messina, 2004).10
Final demand for services is also influenced by the growth in international trade. One
reason is the important intermediary role played by services. Many services, such as
financial intermediation, transportation and distribution, are essential in facilitating
transactions between economic agents and in supporting the smooth functioning of the
economy. Increased globalisation has therefore resulted in a rise in exports of such services.
A second reason why service exports may increase is because of country specialisation in
human resources. Some services are typically more skill intensive relative to goods (in
terms of university education, for example). A country may accumulate human capital and
develop a comparative advantage, inducing an expansion in service exports.11
The growing interdependency between industries might also contribute to the increase in
producers’ demand for services that has occurred in past decades. This greater
interdependency is caused by two main factors. First, firms are outsourcing specialised
services while focusing on their core activities. This type of outsourcing is driven by
increased competitive pressure, the increased specialisation of services, and firms’ focus on
the area in which they have a competitive advantage. Second, firms are outsourcing services
8
OECD (2000, p.102) finds evidence that services are a luxury good. Möller (2000) examines 23 industries in
Germany, the United Kingdom and the United States from 1960 to the early 1990s (except data on U.K.
services, which start in 1973) and finds that the estimated income elasticities for the services industries
typically exceed one. The author also finds that demand for both services and goods tends to be price inelastic.
9
OECD (2000, footnote 10, p. 114) explains that as households have less time to devote to service tasks, the
increasing share of dual-earner households is linked to greater demand for market services, in particular social
and personal services.
10
Ibid. The empirical results show that a one percentage point increase in the share of population living in
urban areas is associated with an expansion of 0.32 percentage point in the service employment share.
11
ECB (2004) finds that after controlling for other factors, such as income per capita, trade specialisation has
little impact on cross-country differences of service employment shares. In contrast, institutional factors –
such as wage bargaining systems that compress wage structure and heavy administrative burdens that act as
barriers to new entrants – have a significant hampering effect on service employment share. To the extent that
those factors are important in Canada, this could have dampened the increase in demand.
10
to increase the efficiency of their production. In this case, firms are introducing services that
improve the organisation of their production (e.g. module production) or their mode of
supply (e.g. just-in-time delivery). In addition, outsourcing is also facilitated by digital
delivery and this mode of transferring information itself creates demand for business
services (OECD, 2004). Moreover, information and communication technologies and
changes in business organisation are driving the creation of new or higher quality services –
so-called dynamic services (references to other studies are included in OECD, 2000, p. 97).
So outsourcing itself is generating more demand for services.
3.2. Service Industry Groups with a Net Demand Shift in 1981-2000
Demand for output of all five services industry groups increased significantly in both
Canada and the United States during the period 1981-2000 (Table 2). Three of the five
services industry groups experienced a net demand shift. These industry groups were
financial intermediation; real estate and business services; and “other services”. Real estate
and business services recorded the largest increase in net demand, followed by financial
intermediation. Growth in output per capita for the real estate and business services industry
group was 65% in Canada and 68% in the U.S. over the twenty-year period. Similarly,
growth in output per capita for the financial intermediation industry group was 54% in
Canada and 52% in the U.S. The rise in overall income per capita partly contributed to the
rise in demand for these services. Messina (2004) finds that a significant amount of the
variation in the share of employment of financial & business services is explained by a
country’s GDP per capita.12
The business services producers were probably the largest contributor to output per capita
growth of the real estate and business services industry group. Business activities (including
accounting, other professional services, renting of machinery and equipment, computer
services, and R&D) outpaced real estate in terms of both real GDP and employment. In past
decades, intermediate demand for business services from local firms has increased rapidly.
Demand from abroad, including off-shoring activity, has also been strong. Of all
commercial services, computer and information services recorded the highest rate of growth
in trade among OECD countries in 1990-97. Computer services exports from the U.S. were
particularly strong over this period while Canada recorded healthy surpluses in both
computer and R&D services (OECD, 1999).13
The increase in net demand for “other services”, which include public administration, health
care, education, community, social and personal services, was more modest. This was partly
because the strength of some services was largely offset by the softness of others.
Moreover, services in this group are mostly suppliers to final users. Growth in services for
12
Messina (2004) notes that the relationship does not necessarily reflect a causal link. His model examines the
effect of a set of variables on employment shares in 27 OECD countries during 1970-1998. The results show
that a 2.6% increase in GDP per capita is associated with a 1% rise in the share of employment in financial and
business services.
13
OECD (1999, p. 12) identifies five strategic business services that are essential for business processes, firm
competitiveness and growth. These five services are: computer software and information processing, R&D
and technical testing, marketing, business organisation (including management consultancy and labour
recruitment) and human resource development.
11
final use in the past two decades did not match the rapid growth in producer services, which
was lifted by outsourcing activity. In both countries, output in public administration,
defence and social security contracted, but the contraction was more pronounced in the
United States. In contrast, the other sectors in the group expanded, and the growth was
somewhat more rapid in the United States. Demand for services such as recreational and
cultural services was solid, partly reflecting the growing influence of the urban culture as the
share of the population living in cities has grown in size14. The demand for health care
services was also strong and is set to accelerate as the population ages more rapidly. OECD
(2000) finds a positive and significant relationship between an ageing population and the
share of employment in health care services in OECD countries. This study also finds a
positive association between the share of employment in social services and both female
labour force participation and the size of the welfare state. However, the former relationship
should be interpreted with caution as it may reflect the existence of mutual causation
(OECD 2000).
3.3. Demand, Supply and Employment Shifts Toward Services
As shown in Table 3, employment has generally shifted toward producing services from
producing goods in both Canada and the United States. Employment share of services
industries increased from 66.5% in 1981 to 73.0% in 2000 in Canada and from 68.7% to
76.3% in the U.S. What factors are driving the shift in employment? This examines the
demand and supply factors. For an efficient economy, resources should flow freely from
one industry to another in response to changing demand and supply.
Messina (2004) examined employment shares of OECD countries in the last three decades
and found that the goods-services labour productivity differential partly explained changes
in employment share. But he also found that after controlling for the labour productivity
growth gap, GDP per capita remained highly significant, meaning that demand factors were
also a source of service employment expansion.
On the demand side, the leading explanation is that the demand for services has been driven
by rising income as well as increased intermediate demand and expansion of international
trade. As discussed earlier, demand for services is more income elastic than demand for
goods, and demand for goods and services is price inelastic. The substitution effect – which
predicts that consumers demand more goods than services as the price of goods declines
relatively that of services – has been more than offset by the income effect, resulting in an
expansion of the services sector relative to the goods sector. As a result, employment shifts
to the service sector.15
14
Messina (2004) examines the same four ISIC Divisions of services as in the present study and finds that a
7.7% increase in urbanisation (urban population share of the total population) results in a 1% rise in the share
of employment in “other services”. The urbanisation variable is also significant when transportation &
communication services employment is the independent variable, but the coefficient is four times as small.
15
Messina (2004) examines 27 OECD countries in the period 1970-1998. The study finds a positive
relationship between GDP per capita and the service employment share (p. 15). It also suggests that the rate of
expansion of the service employment share peaks when GDP reaches $19111 per capita and decelerates. This
suggests convergence in the share of service employment of OECD countries and is interpreted as a sign that
richer countries may have passed the saturation point in the expansion of the demand for services.
12
Supply-side factors have also been put forward to explain the expansion of services
employment. One view suggests that part of the change in industrial structure resulted from
the labour savings achieved through technological progress in the goods sector. Taking the
services sector as a whole as labour-intensive and the goods sector as capital-intensive, this
view argues that labour capacity released by the capital-intensive sector will tend to be
reallocated to the labour-intensive services sector. This is because technical progress in the
productive goods sector shifts the production possibility frontier up, causing income to
grow. So if demand for services and goods remains relatively balanced, the increase in
goods output is more than met by the productivity gains. The extra workers are hired by the
less productive services sector in order to meet the rise in demand for services products
(Figure 3). In other words, in the last few decades, the services sector has acted as a sponge
absorbing the greater abundance of labour (ten Raa and Schettkat, 2000)16.
In this paper, we undertake an econometrical analysis on the relationship of the labour
movement across Canadian industries with the shifts in supply and demand. We presume
that demand for an industry output is measured by real value added per capita, and that the
supply status of an industry is indicated by MFP. For the regression model, we specify that
the change in labour share of industry i at time t depends on the changes in demand and
supply of the industry, that is,17
(4)
n
m
j 0
k 0
 ln( LS i ,t )   i    j  ln( RVAi ,t  j )    k  ln( RMFPi ,t k )   i ,t ,
 i ,t ~ iid
where Fi ,t  Ft  Ft 1 for any variable F,
LS i is labour share of industry i in total economy,
RVAi is relative real value added of industry i, the ratio of industry real value added
to real GDP,
RMFPi is relative MFP of industry i, the ratio of industry MFP to the MFP for the
total economy,
n and m are the lagged years in which demand and supply, respectively, have effects
on the labour movement, and
 i is the error term.
16
In a two-sector model, technology-induced labour savings lead to a rise in the production possibility frontier
of the capital-intensive goods sector. As a result, employment shifts from goods sector to service sector. In a
closed economy, this shift occurs irrespective of the consumer utility function (ten Raa and Schettkat, 2000, p.
36-37). However, in an open economy, where firms allocate resources independently of domestic consumption
preferences, there is some empirical evidence showing that the growth in services employment is more
influenced by the labour supply. Erdem and Glyn (2000) examine the G-7 countries plus the Netherlands in
the 1913-1994 period and find that services employment growth is sensitive to the labour supply (measured by
the growth in the working age population), the initial share of agricultural employment and the initial rate of
employment in the agricultural sector. In contrast, employment growth in the goods sector is sensitive to the
growth in own capital stock (p. 49-53).
17
Similar results are obtained when absolute change is used instead of the log difference (which is essentially
growth).
13
The above model tests two hypotheses. It tests if demand stays constant, labour moves away
from industries with higher productivity growth towards industries with low productivity
growth. In addition, it tests if a positive demand increase for the output of an industry leads
to an expansion of the corresponding industry and the movement of labour to the industry.
We assume that a proportional increase in demand or efficiency for every industry has no
impact on labour movement across industry. So we use the relative concept for both
demand and supply. To capture the persistence of the impact of demand and supply on
labour movement, lagged variables are included in both regression models. The length of
the lag for each variable is determined by statistical fit.
The model is estimated using Canadian data from OECD STAN database. The database
provides us data on real and nominal value added, labour compensation, hours worked, and
non-residential capital stock by industry for the period of 1970-2000. It has 29 industries
on the basis of the International System of Industrial Classification (ISIC) Revision 3.
For the regression analysis, the labour share of an industry is the share in hours worked of
the industry in the Canadian economy. MFP is calculated as the residual of output net of
labour and capital contributions, using the growth accounting framework (Jorgenson, Gollop
and Fraumeni 1987; Jorgenson and Griliches 1995; Jorgenson 2001).
We first run the above regression to determine the length of lags for relative real value
added and relative MFP. The estimation shows that n=0 for relative real value added and
m=1 for relative MFP. This result indicates that the impact from a demand shift on labour
movement tends to be contemporary while the impact of a supply shift lasts two years.
As expected, the regression shows that a relatively strong positive demand shift for an
industry’s output increases the labour share of that industry (Table 5). On the other hand, a
relatively strong positive supply shift (a strong improvement in MFP) for an industry
reduces the labour share of that industry. The movement of labour force is more sensitive to
demand than to supply, as shown by the estimated elasticities. Also note that the
magnitudes of the estimated coefficients of current and one-year-lagged MFP are similar,
implying that labour adjustments in response to efficiency gain last two years, and the
adjustment in the second year is as important as in the first year.
These findings are consistent with the economic theory, which predicts that a firm with a
profit maximizing behaviour should employ labour to the point where the marginal product
value of labour equals the wage rate. This implies that labour will move away from
industries that have a relative decline in the marginal product value of labour to industries
that have a relative increase in the marginal product value of labour. An increase in demand
for an industry’s output raises the value of its product and, therefore, the marginal product
value of its labour18. On the other hand, an improvement in production efficiency lowers the
18
All else equal, the demand shift causes a movement along the production function. Therefore, a positive
(output increasing) demand shift will result in a decline in the marginal product of labour. Here, we assume
that the increase in the marginal value product of labour (MVPL) caused by the rise in price more than offsets
the decline in MVPL caused by the decline in the marginal product of labour.
14
price of its product under a competitive product market and thus reduces the marginal
product value of labour19. Therefore, labour moves to industries with a higher increase in
demand and away from those with a higher increase in productivity or a larger positive
supply shift.
Over the past two decades, the primary and manufacturing sectors have been losing labour
shares to financial intermediation and real estate and business services. The primary and
manufacturing sectors experienced a decline in output price due to relatively lower demand
for their output and larger improvements in productivity. In contrast, real estate and
business services and to a lesser extent financial intermediation experienced an increase in
output price due to higher demand for their output and smaller improvements in
productivity. These findings are consistent with the Baumol cost disease hypothesis that
predicts that resources will be absorbed predominantly by “stagnant” industries (Baumol
1967).
4. The Underlying Force of Aggregate Labour Productivity Growth: Demand or
Supply?
Demand and supply shifts influence the industrial structure in employment as well as output
prices. Do they have any implications for industry contribution to aggregate labour
productivity growth?
In this section, we use the aggregate labour productivity decomposition technique proposed
by Tang and Wang (2004) to examine industry contribution to aggregate labour productivity
growth. Like the decomposition technique for aggregate output growth proposed in this
paper, the decomposition technique for aggregate labour productivity by Tang and Wang is
also consistent with the standard of consumer theory, taking into account the price effect.
We examine if aggregate labour productivity growth was driven by demand or supply
effects. In addition, we determine the industry sources of the aggregate labour productivity
growth gap between Canada and the U.S.
According to Tang and Wang (2004), aggregate labour productivity growth over a period
ranging from years z to t can be decomposed into the sources of contribution of its industry
components:
(4)
g ( X ) tz   wiz g ( xi ) tz   wiz g (si ) tz   wiz g ( xi ) tz g (si ) tz ,
i
i
i
where wiz is equal to yiz Yz , the nominal output share of industry i at the beginning of the
period, z;
X and xi denote aggregate and industry i labour productivity, respectively; and
19
Here we assume that the decline in MVPL caused by the decline in price more than offsets the increase in
MVPL resulting from the rise in the marginal product of labour. Note that the negative impact of a positive
supply shift on labour shares will be larger for industries with output demand being income and price inelastic.
Those industries often are associated with more or less satiated product markets.
15
si  ~
pi li is the relative size of industry i, equal to the product of its labour input
share ( li  Li L ) and its relative output price ( ~p i ).
Thus, an industry’s contribution to aggregate labour productivity growth originates from two
sources. One is an improvement in the industry’s labour productivity and the other is an
increase in its relative size. The relative size, defined as the product of labour share and
relative output prices, captures the effects from a change in labour share as well as a change
in real output price of the industry.
The three terms from left to right are the pure productivity growth effect, the relative size
change effect and the interaction of the first two effects. The pure productivity growth
effect captures an industry’s contribution coming purely from the labour productivity
improvement of the industry. It is not affected by the change in the relative size of the
industry. Similarly, the relative size change effect reflects only the change in the relative
size of the industry. It is not affected by efficiency gains. The interaction term captures the
effect of the change in relative size on the change in productivity growth. For example, an
increase in labour share and/or relative price will apply not only to the initial labour
productivity level but also to the change in labour productivity.
Table 6 reports the results of decomposing the aggregate labour productivity growth in
Canada and the United States. In terms of the pure productivity growth effect, the
manufacturing sector was the largest contributor to the aggregate labour productivity growth
in both Canada and the United States. In contrast, the corresponding contribution from real
estate and business services was negative.
In term of the relative size change effect, it was real estate and business services that had the
largest contribution to the aggregate labour productivity growth in the two countries. In
contrast, the manufacturing and primary industry groups had the largest negative effect.
This is because that during this period, the importance of the manufacturing sector in the
two economies decreased while the importance of real estate and business services
increased, especially in the U.S.
The results show that in terms of total effect, which takes into account the pure labour
productivity growth effect and the effect from a change in relative size, the real estate and
business services industry group was the largest contributor to the aggregate labour
productivity growth in both Canada and the United States, followed by the manufacturing
sector for Canada and other services for the United States. It is interesting to note that the
total contribution of the manufacturing sector in the U.S. was negative, although it is small.
As discussed below, this is because its positive pure labour productivity effect was more
than offset by the negative effect from a decline in its relative size.
In terms of total contribution, industries with positive supply shifts contributed 12
percentage points to aggregate labour productivity growth in Canada and 3 percentage
points in the United States (Table 7). In contrast, industries with positive demand shift
contributed 19 percentage points in Canada and 28 percentage points in the United States.
Those two groups were responsible for almost all aggregate labour productivity growth in
16
the two countries. Moreover, the difference in positive demand shifts was mainly
responsible for the aggregate labour productivity growth gap between the two countries.
The decline in the importance of the manufacturing sector and the increase in the importance
of real estate and business services were fuelled by changes in both the shares of hours
worked and the output price (Table 4). For Canada, the share of hours worked in
manufacturing decreased from 19 percent in 1981 to 16 percent in 2000, and the
manufacturing output price was virtually unchanged. In contrast, the share of hours worked
in real estate and business services in Canada increased from 6 percent to 11 percent and the
output price for the group increased 8 percent over this period. The changes were more
pronounced in the United States. The share of hours worked in the U.S. manufacturing
sector decreased from 23 percent in 1981 to 16 percent in 2000 and the manufacturing
output price dropped 27 percent. In contract, the U.S. real estate and business service saw its
share of hours worked increase from 6 percent to 13 percent and its output price increase 23
percent.
The industry structure change could be explained by supply and demand shifts. The large
decline in the importance of the manufacturing sector in terms of relative size is because of a
strong and positive supply shift in this industry. This industry, with its relatively strong
improvement in productivity and decline in output price, required relatively less labour to
meet its demand. In contrast, real estate and business services, which experienced a strong
increase in demand and a rise in output price, had to employ relatively more labour to meet
the increase in demand due to its stagnant productivity growth.
5. A Economic Reason for Slow or Negative Labour Productivity Growth
One result that has emerged in many studies on productivity, which is somewhat puzzling, is
the negative productivity growth in an industry over a prolonged period. In this study, real
estate and business services reported large negative labour productivity growth in both
Canada (-16%) and the United States (-26%) during the 1981-2000 period.20 Interestingly,
this industry group also experienced a strong net positive demand shift.
Can strong and persistent growth in demand for an industry output explain negative
productivity growth over a given period? The simple answer is yes. We provide a detailed
economic rationale in the remaining section.
We start with an observation associated with the utility industry. A utility company often
owns several generators with different efficiency. High efficient generators are constantly
operated to meet the normal electricity demand, and low efficient ones are used only to meet
peak demand. As a result, productivity of the utility company will be lower during the peak
hours than during the non-peak hours.
For an industry with an increase in demand for its output, if technological progress in this
industry is relatively stagnant and if low efficient firms or units are added to meet the
20
In addition, other services and construction in the United States also recorded a small decline in labour
productivity, -2.3% and -1.9%, respectively.
17
increased demand, then the industry will register a negative productivity growth. As long as
the increase in demand is sufficiently strong, the increase in output price will more than
offset the decline in marginal product of labour and result in an increase in the value of
marginal product. A firm with profit maximizing behaviour will increase its output by
increasing its labour input until the value of marginal product of labour being equal to the
wage rate.21
Figure 4 illustrates a situation where an increase in demand for an industry output (from D 0
to D1 ) leads to an increase in employment in industry, which in turn pushes up the wage
rate. As a result, the supply curve shits from S 0 to S 1 . At the equilibrium, we observe that
the industry output increases from Q 0 to Q1 , the output price increases from P 0 to P 1 , the
employment increases from L0 to L1 , and the wage rate increases from P 0  MPL0 to
P1  MPL1 . Most importantly, the marginal product of labour decreases from MPL0 to
MPL1 . As a result, the average of labour productivity decreases, leading to negative labour
productivity growth.
Furthermore, output expansion to meet demand can bring on significant adjustment costs
and take time. This often relates to physical capital other than labour. For instance, the
electricity industry needs time to build an efficient generator, although it may has no
problem to recruit labour. If this is case, then we may observe that the industry will operate
under its production possibility frontier, which is often referred as x-inefficiency in the
literature. In other words, the supply curve will move from S 0 to S 1 , the production
possibility frontier (PPF) for labour will move down from PPFL0 to PPFL1 , and the
marginal product of labour curve also move toward the origin (Figure 5). Again, in this
case, we observe that the marginal product of labour decreases from MPL0 to MPL1 . As a
result, the average of labour productivity decreases, leading to negative labour productivity
growth. Unlike Figure 4, however, Figure 5 also implies a decline in multifactor
productivity growth because the industry operates under x-efficiency.
If this process is prolonged, it can result in a decline in labour productivity growth and MFP
growth over a long period of time. The industry group, real estate and business activities,
fits the profile. During the period 1981-2000, this industry experienced a strong demand for
its output (Table 2) and a significant increase in its output price (Table 3). At the same time,
we observe that this industry maintained both negative labour productivity and MFP growth
during the 1981-2000 period (Table 6 and Table 8).
21
The increased demand will have upward pressure on wage rate. Assuming unconstrained labour mobility
across sectors, wage rates will tend to grow at the same rate across the economy. This is consistent with the
assumption made by Baumol (1967) and the evidence for Canada. Baldwin, Durand and Hosein (2001) find
that changes in real wages are mostly determined by changes in prices. This supports the hypothesis that
nominal wages tend to grow at the same rate across industries. Note that this allows wage rates to differ across
industries depending on skills and other factors.
18
6. Conclusions
The services sector has become increasingly important in both Canada and the United States
in terms of output and employment. Over the period 1981-2000, the service sector
contributed substantially to economic growth in the two countries. In the United States, the
aggregate output growth per capita was almost entirely attributable to the services sector. In
Canada, the total contribution of the services sector to output growth was 77%. The driving
force of these gains was rapidly growing demand for some services.
Using a framework consistent with the “utility-value concept”, this paper shows that these
demand-driven industry groups (financial intermediation; real estate and business services;
and other services) were the main contributors to aggregate growth in output per capita in
both countries, with the largest contributor being real estate and business services industry
group. They contributed to economic growth through real output growth and increasing
output prices.
However, service industries are highly heterogeneous. With a behavior similar to the
manufacturing sector, some service industry groups underwent a net positive supply shift
and experience a decline in its output price during the 1981-2000 period. These supply
driven service industry groups are trade and accommodations; transportation and
communications. Together with primary and manufacturing, they contributed significantly
to economic growth in Canada and in the United States. But, their contributions were driven
by real output growth, which were offset somewhat by declines in their output prices. On its
own, the output growth in trade and accommodations, accounted for almost one third of the
aggregate output growth in the United States. It was more than two times farter than that in
Canada. As a result, the industry was the second largest contributor (after real estate and
business services) to the aggregate output growth gap between the two countries.
The unbalanced demand and supply shifts among industry groups were key drivers behind
the rise in the service share of employment. Demand forces attracted labour inputs while
supply forces released them. The real estate and business services industry group almost
fully absorbed the workers released from the goods sector over the period 1981-2000.
Because the increased labour share and to less extent, the increased output price, this
industry group was the largest contributor to aggregate labour productivity over the sample
period. In total, the demand-driven industries contributed to more than two-thirds of
aggregate labour productivity growth in Canada and 90 percent in the United States.
Interestingly, the manufacturing sector had a negative contribution to aggregate labour
growth in the United States because its faster labour productivity growth was more than
offset by its decline in its relative size. Its labour share decreased from 18.7 percent in 1981
to 15.5 percent in 2000, and at the same time, its output price decreased from 27.4 percent
over this period.
Paradoxically, the demand-driven industries contributed greatly to aggregate output and
labour productivity growth on average experienced lower productivity growth. For instance,
labour productivity and MFP in the real estate and business services industry group in
Canada declined 15.6 percent and 30.7 percent over the period 1981-2000. What explains
19
the phenomenon? This paper shows that as long as an increase in output price offsets a
decline in marginal product of labour, an industry facing increasing demand for its output
will expand its production to the point where the value of the marginal product of labour
equals the wage rate. The increased in employment will reduce the marginal product of
labour, resulting in negative labour productivity growth. If adjustment cost occurs during
the production expansion, the industry will operates under x-inefficiency, resulting negative
MFP growth.
20
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23
Appendix A
In this appendix, we derive a decomposition of industry contribution to aggregate output growth
using an economic approach, following the method proposed by Diewert (2002). First, equation
(1) can be rewritten as in the vector form, i.e.,
~q
(A1) Q  p
~ ) be the unit cost function, i.e.,
Let c(p
(A2)
~)  Minp
~  q, s.t.
c(p
q
f(q)  1
Hence we have
~  q  c (p
~ ) f (q ), t
(A3) p
t
t
t
t
Shephard’s Lemma implies
~ ) ~
c(p
pi
qi

(A4)
~)
~q
c (p
p
and Wold’s Identity implies
(A5)
~
f (q) qi
pi

~
~
c (p )
p q
Rewrite the real aggregate growth gives
~ q
~ ) f (q )
~ ) f (q )
Qt
p
c (p
c (p
t
t
t
1  ~ t
1  ~ t
1  ~t 
1
Qz
pz  qz
c(p z ) f (q z )
c(p z ) f (q z )
(A6)
~ )   f (q )   c(p
~ )   f (q ) 
 c (p
t
t
t
  ~  1  
 1   ~ t  1  
 1
 c(p z )   f (q z )   c(p z )   f (q z ) 
~ ) c(p
~ ) and f (q ) f (q ) can be interpret as the consumer’s “true” price index
The terms c(p
t
z
t
z
and “true” quantity index, respectively. The price change is
~)
~)
qi
~
pi
c(p
1
c(p
~
~
(A7)



p


p

  wi  g ( ~
pi )


i
i
~
~
~
~
~
c(p)
c(p)
p
p q
p
g Q  z 
t
i
i
i
i
i
Similarly, we have
(A8)
~
pi
q
f (q)
1
f (q)



q

 qi  i   wi  g (qi )


i
~
f (q)
f (q) i qi
qi
i p q
i
Substituting (A7) and (A8) into (A6) gives
24

t
t
t
t  
t 
g Q  z   wiz  g qi  z   wiz  g  ~
pi  z    wiz  g qi  z     wiz  g  ~
pi  z 
i
i
 i
  i

(A9)
Note that the only difference between equations (2) in the text and (A9) in this appendix is the
third term on the right hand side of both equations. Both these two terms are in second order and
would be disappear if linear approximation is used,22 which implies that the decomposition
technique of equation (2), based on an axiomatic approach, is a first order approximation to the
decomposition based on the economic approach in this appendix.
22
~ , q   c(p
~ ) f (q ) . The linear approximation to Q around Q is:
Given Qp
t
t
t
t
t
s
~ p
~   Q q  q  q   Q  q  p
~ p
~  p
~  q  q  ,
Qt  Q z  QzP  p
t
z
z
t
z
z
z
t
z
z
t
z
so real aggregate growth becomes:
g Q  z 
t
~ p
~  p
~  q  q 
 ~
q z  p
piz qiz
t
z
z
t
z

~

~
pz  qz
i pz  q z

~
p ~
p
q  qiz 
t
t
 it ~ iz  it
   wiz g qi  z  g  ~
pi  z
qiz 
i
 piz
25

Appendix B
The decomposition formula used by Statistics Canada and the BEA is
g (Q) t 1  FQItt 1  1
t
  p  p FPI q  q 

  p  p FPI q
  ~p  ~p q  q 

 ~p  ~p q
i ,t 1
t
t 1
i ,t
i ,t
i ,t 1
i
(B1)
j ,t 1
t
t 1
j ,t
j ,t 1
j
i ,t 1
i ,t
i ,t 1
i ,t
i
j ,t 1
j ,t
j ,t 1
j
Where FQItt 1  Qt Qt 1 denotes Fisher quantity index and FPI tt 1  Pt Pt 1 denotes Fisher price
index. Obviously equation (B1) is additive, so the corresponding contribution of component i to
real aggregate growth is
~pi,t 1  ~pi,t qi,t  qi,t 1 
t
(B2) CPC i t 1 
 ~p j ,t 1  ~p j ,t q j ,t 1
j
This equation (B1) decomposition is derived axiomatically. Through an economic approach,
Diewert (2002) and Reinsdorf et al. (2002) derived a decomposition of the Fisher index. Using
pi  pi P , the Diewert’s decomposition
the identity FPI tt -1 FQI tt -1  Yt Yt 1 and the definition ~
can be written as
g (Q) t 1  FQItt 1  1
i ~pi,t 1  ~pi,t  FQItt 1 qi,t  qi,t 1 

 ~p j ,t 1q j ,t 1   ~p j ,t q j ,t
t
(B3)
j
j
The corresponding contribution of a component to real aggregate growth then becomes
~
pi ,t 1  ~
pi ,t  FQItt 1 qi ,t  qi ,t 1 
t
(B4) CPCi t 1 
 ~p j ,t 1q j ,t 1   ~p j ,t q j ,t


j
j
Reinsdorf et al. (2002) claimed that the decompositions (B1) and (B3) are very close numerically
and concluded that the decomposition (B1) is a satisfactory decomposition.
The decompositions (B1) and (B3) have two main drawbacks. The additivity of the two
decompositions holds only for two consecutive periods. Official data on real aggregates in both
Canada and the U.S. for two non-consecutive periods are estimated from chained Fisher index,
so the growth rate between the two periods can be expressed as
26
g (Q) s  FQI ss 1  FQI ss 12    FQItt 12  FQItt 1  1
t
(B5)

t 1
FQI


1
 1,
s  t
s
~
  ~

 i pi , 1  pi , qi , 
 
  1.
~
~
  s    p j , 1  p j , q j , 1 
 j

t 1
It can be seen from equation (B5) that real aggregate growth between two non-consecutive
periods cannot be written as an additive form when the decomposition approach of equation (B1)
or (B3) is used. The reason is that both decompositions are derived based on the Fisher formula
itself. For these two decompositions to be additive for two non-consecutive periods, the Fisher
index connecting the two periods should be calculated directly, not by chaining. In addition, the
decompositions (B1) and (B3) evaluate the quantity change at (weighted) average prices of
current and previous periods. As a result, quantity effect and price effect cannot be separated.
27
Table 1: Net Shifts and the Change in Output and Price
Net shift
D (+): Net positive demand shift
D (-): Net negative demand shift
S (+): Net positive supply shift
S (-): Net negative supply shift
Observed change in output and price
Output
Price
+
+
+
+
Table 2: Aggregate Output Growth and Industry Contributions, 1981-2000
Contribution
Output per
capita growth*
Pure growth
Pure price
effect
effect
Canada
Interaction
Term
Total
Net
Shift
Primary
Manufacturing
Construction
Trade and
accommodations
Transportation and
communications
Financial
intermediation
Real estate and
business services
Other services
Total
0.196
0.535
-0.055
0.022
0.096
-0.004
-0.018
-0.002
-0.005
-0.004
-0.001
-0.000
0.000
0.094
-0.009
S (+)
S (+)
D (-)
0.518
0.070
-0.014
-0.007
0.049
S (+)
0.630
0.050
-0.022
-0.014
0.014
S (+)
0.535
0.028
0.012
0.006
0.046
D (+)
0.650
0.089
0.010
0.007
0.106
D (+)
0.099
0.374
0.023
0.373
0.048
0.009
0.005
-0.008
0.075
0.374
D (+)
NA
Primary
Manufacturing
Construction
Trade and
accommodations
Transportation and
communications
Financial
intermediation
Real estate and
business services
Other services
Total
0.175
0.500
0.360
0.013
0.105
0.015
-0.041
-0.058
0.009
-0.007
-0.029
0.003
-0.035
0.019
0.027
S (+)
S (+)
D (+)
0.958
0.167
-0.037
-0.035
0.095
S (+)
0.746
0.052
-0.013
-0.009
0.030
S (+)
0.523
0.024
0.038
0.020
0.082
D (+)
0.677
0.104
0.035
0.023
0.162
D (+)
0.134
0.031
0.078
0.010
0.119
0.498
0.511
0.011
-0.024
0.498
D (+)
NA
U.S.
* Output is value added for industry and GDP for the economy.
28
Table 3: Relative Size by Industry in Canada and the United States, 1981 and 2000
Industries
Employment Share
1981
Primary
Manufacturing
Construction
Trade and accommodations
Transportation and
communications
Financial intermediation
Real estate and business
services
Other services
Real Output Price
2000
Canada
1981
Relative Size
2000
1981
2000
0.074
0.187
0.074
0.236
0.049
0.155
0.066
0.241
1.000
1.000
1.000
1.000
0.838
0.990
0.936
0.897
0.074
0.187
0.074
0.236
0.041
0.154
0.062
0.236
0.068
0.067
1.000
0.718
0.068
0.048
0.058
0.062
1.000
1.232
0.575
0.077
0.058
0.106
1.000
1.075
0.575
0.114
0.247
0.254
1.000
1.210
0.247
0.307
U.S.
Primary
Manufacturing
Construction
Trade and accommodations
Transportation and
communications
Financial intermediation
Real estate and business
services
Other services
0.035
0.229
0.049
0.225
0.023
0.155
0.059
0.234
1.000
1.000
1.000
1.000
0.455
0.726
1.205
0.790
0.035
0.229
0.049
0.225
0.010
0.112
0.071
0.185
0.056
0.056
1.000
0.818
0.056
0.046
0.046
0.046
1.000
1.808
0.046
0.083
0.063
0.125
1.000
1.226
0.063
0.154
0.298
0.303
1.000
1.340
0.298
0.406
Table 4: Differences in Sources of the Aggregate GDP per Capita Growth: 1981-2000
S(+)
D(+)
D(-)
Total
Pure output growth
effect
Can
U.S. Diff.
0.24
0.34 -0.10
0.14
0.17 -0.04
-0.00 0.00 -0.00
0.37
0.51 -0.14
Pure price effect
Can
-0.06
0.07
-0.00
0.01
U.S.
-0.15
0.16
0.00
0.01
Diff.
0.09
-0.09
-0.00
-0.00
Interactive term
Can
-0.03
0.02
0.00
-0.01
U.S.
-0.08
0.06
0.00
-0.02
Diff.
0.05
-0.04
0.00
0.02
Total
Can
0.16
0.23
-0.01
0.37
U.S.
0.11
0.39
0.00
0.50
Diff.
0.05
-0.16
-0.01
-0.12
29
Table 5: Pool Estimation of the Impact of
Demand, Supply on Labour Movement in Canada, 1981-2000
(Heteroskedasticity-consistent estimates)
Change in relative output per capita
Change in relative MFP
Change in relative MFP (one year lag)
AR(1)
Industry Fixed effect
DW Statistics
Adjusted R 2
No of Observations
Estimation Estimation Estimation
(1)
(2)
(3)
0.3709
0.3493
(14.5)*
(12.7)*
-0.0689
-0.0432
(-6.10)
(-4.2)*
-0.0428
-0.0437
(-4.0)*
(-4.4)*
0.1509
0.1566
0.1035
(2.6)*
(2.8)*
(1.8)*
Yes
Yes
Yes
1.95
1.97
1.98
0.38
0.43
0.21
522
504
504
30
Table 6: Aggregate Labour Productivity Growth and Industry Contributions, 1981-2000
Industry
Labour
productivity
growth
Contribution
Pure
productivity
growth
Canada
Relative Interaction
size
term
Total
Net
shift
0.685
0.733
0.001
0.078
0.132
0.000
-0.050
-0.032
-0.013
-0.034
-0.023
0.000
-0.007
0.077
-0.013
S (+)
S (+)
D (-)
0.392
0.053
-0.011
-0.004
0.037
S (+)
0.556
0.044
-0.023
-0.013
0.008
S (+)
0.328
0.017
0.017
0.006
0.040
D (+)
-0.156
-0.022
0.133
-0.021
0.091
D (+)
Other services
0.003
0.001
0.056
0.000
0.056
D (+)
Total
0.289
0.303
0.077
-0.090
0.289
Primary
Manufacturing
Construction
Trade and
accommodations
Transportation and
communications
Financial
intermediation
Real estate and
business services
U.S.
Primary
Manufacturing
Construction
Trade,
accommodations
Transportation,
communications
Financial
intermediation
Real estate and
business services
Other services
Total
0.596
0.943
-0.019
0.045
0.198
-0.001
-0.053
-0.107
0.020
-0.032
-0.101
-0.000
-0.040
-0.010
0.018
S (+)
S (+)
D (+)
0.646
0.113
-0.031
-0.020
0.062
S (+)
0.536
0.037
-0.013
-0.007
0.017
S (+)
0.320
0.015
0.038
0.012
0.066
D (+)
-0.264
-0.041
0.222
-0.059
0.122
D (+)
-0.023
-0.005
0.083
-0.002
0.075
D (+)
0.311
0.361
0.158
-0.208
0.311
Table 7: Differences in Sources of the Aggregate Labour Productivity Growth: 1981-2000
S(+)
D(+)
D(-)
Total
Pure productivity
growth
Can
U.S. Diff.
0.31
0.39 -0.09
-0.00 -0.03
0.03
0.00
0.00
0.00
0.30
0.36 -0.06
Relative size
Can
-0.12
0.21
-0.01
0.08
U.S.
-0.20
0.36
0.00
0.16
Diff.
0.09
-0.16
-0.01
-0.08
Interactive term
Can
-0.07
-0.02
0.00
-0.09
U.S.
-0.16
-0.05
0.00
-0.21
Diff.
0.08
0.03
0.00
0.12
Total
Can
0.12
0.19
-0.01
0.29
U.S.
0.03
0.28
0.00
0.31
Diff.
0.09
-0.09
-0.01
-0.02
31
Table 8: Multifactor Productivity Growth by Industry in Canada, 1981-2000
Industry
MFP Growth
Primary
0.309
Manufacturing
0.430
Construction
-0.108
Trade and accommodations
0.202
Transportation and communications
0.348
Financial intermediation
-0.145
Real estate and business services
-0.307
Other services
-0.047
Total
0.155
Figure 1
Welfare Impact from a Downward-shift of
Output Supply Curve
P
Gain in consumer's
and producer's surplus
Figure 2
Welfare Impact from an Upward-shifting of
Output Demand Curve
P
S1
Gain in consumer's
and producer's surplus
S2
P1
P2
S
P2
P1
D
D2
D1
Y1 Y2
Y
Y1 Y2
Y
32
33
34