The Measurement of Output Instability in Western Canada By Kathleen Macaspac

The Measurement of Output Instability in Western Canada

∗

By

Kathleen Macaspac

ABSTRACT. This paper develops a series of volatility indicators for the Canadian provinces.

In contrast to previous studies, we find that the Western provinces exhibit greater stability than what has been generally perceived, owing to the absolute and relative improvement in their stability over time. Conversely, we find that Ontario, a province that is traditionally regarded as stable and more diversified economy with a strong manufacturing base, exhibits greater instability. Using the portfolio variance approach, this paper also examines the sources of aggregate output instability in Western Canada. Similar to past findings, we find that resource sectors contribute to output volatility in Western Canada. However, there is evidence that manufacturing and finance sectors have also become significant sources of output instability, which may be attributed to the impact of globalization and trade on volatility. Finally, this paper develops the contribution of changes in the industrial mix to output volatility (CIMV) index over time. Our results indicate that the reduction in the dependence on resource output production account for the decline in the change in output volatility for the most part of past decade. However, the recent trend in the index seems to indicate that the increasingly greater share of manufacturing, finance, and trade sectors in output may have been driving the steady increase in output volatility change.

Acknowledgement: I am sincerely grateful to my supervisor, Dr. Bev Dahlby, for the opportunity to do my thesis on such an interesting topic and for his invaluable guidance. I also wish to thank Dr. Denise Young and Dr. Mel McMillan for their valuable comments. I would like to thank my husband Jason for his love and support.

Correspondence: Kathleen Macaspac, Economics and Statistics, Alberta Finance and

Enterprise; E-mail: Kathleen.Macaspac@gov.ab.ca

; Tel No: (780) 427-7391

∗ This is a revised version of the author’s thesis paper submitted to the Faculty of Graduate Studies, University of

Alberta in September 2007. The views of this paper are those of the author and should not be attributed to the

Alberta Ministry of Finance and Enterprise.

1

I.

Introduction

Economic diversification has been a recurring theme in public policy debates due to its perceived role in promoting economic stability and security. In resource-dependent regions, it is generally believed that diversifying the economy would make the region less sensitive to the boom-and-bust cycle brought about by external volatilities. Economic diversification is also regarded as a means of securing long-term economic growth in the event of structural changes, such as the decline of the region’s resource base. On the other hand, some contend that diversification is a costly and unnecessary form of government intervention. It is often argued that economic agents can manage the adverse effects of economic volatility through adjustment mechanisms, such as inter-regional migration and consumption smoothing. It is also argued that the government can mitigate the undesirable impact of specialization through sound fiscal policies and the provision of social safety net to individuals. The perceived relationship between economic diversification and stability has been the rationale behind the development of volatility indicators as ‘performance measures’ for provinces, especially for Western Canada.

The objective of this paper is two-fold. First, this study develops an updated database of volatility measures based on several economic variables for all Canadian provinces. However, compared to previous studies that focused on employment or incomebased volatility indicators, this paper develops volatility measures using available data on output by industry. Second, the availability of data on output by industry allows us to examine the sources of output instability in the Western Canadian provinces, particularly the contribution of changes in the industrial structure to provincial output instability.

The paper is organized as follows. The next section discusses the empirical and theoretical issues surrounding the relationship between economic diversity and stability.

The third section provides a review of how instability has been defined and measured in the literature, with a focus on the portfolio variance approach. Building on the third section, the fourth section develops an updated database of volatility indicators based on several economic variables for all Canadian provinces, with a more detailed analysis for Western

Canada. Based on these volatility indicators, we assess the relative instability of Western

Canada compared to other provinces. Also, in the fourth section, we examine how changes in the industrial structure over time have had an impact on regional economic instability in the Western Canadian provinces by deriving an index of the contribution of changes in the

2

industrial mix to volatility. The fifth section gives a brief summary of the key findings of the paper and offers some concluding remarks.

II.

The Link Between Diversity and Stability

The widely-held belief that diversity promotes economic stability has been the basis for the promotion of economic diversification. This is based on the conventional argument that there exists an inherent trade-off between growth and stability. Based on the theory of comparative advantage, growth can be derived from specialization. However, specialization increases the vulnerability of a region to idiosyncratic

1 risk. Hence, economic diversification

is seen as a means of spreading out risk across sectors in the region, thereby leading to greater economic stability. In resource-abundant regions such as in Western Canada, resource-based specialization has been the cornerstone of economic growth and development but at the same time is also believed to be the main source of economic volatility.

In order to examine the link between diversity and stability, it would be useful to start off by looking at the relationship between specialization, growth, and instability in the context of a small, open economy. According to staple and export-based theories, exogenous demand plays a major role in regional economic growth, and this in turn is driven by its price or demand in the world market. An increase in the world price of, or demand for, a region’s primary export creates an incentive for its producers to boost production, thereby raising the sector’s demand for factor inputs. In a small open economy, the higher demand for the resource commodity causes labour and capital to move into the region. In addition, the expansion of the resource sector also generates direct and indirect linkage effects. Firstly, the growth of the resource sector increases the demand for its inputs (backward linkage) as well as a raises supply to local industries for which its product is an input (forward linkage). Secondly, the government experiences an increase in revenues from the resource sector arising from higher royalties and corporate income tax revenues. This, in turn, feeds through other sectors in the economy such as higher spending on infrastructure or education which creates another round of effects. Thirdly, higher employment in the region raises overall regional income and leads to further

1 Idiosyncratic (or non-systematic) risk is a terminology used in finance that refers to the risk that affects a particular asset or firm. This type of risk can be eliminated or reduced by portfolio diversification. This is in contrast to market (or systematic) risk which has to do with general market conditions that are common to all assets or firms (Bodie et al. 1995).

3

increases in aggregate demand through greater consumer spending and higher personal income tax revenues.

Although resource-based specialization acts as a stimulus to economic growth, it certainly has many drawbacks, as illustrated by the experience of Western Canada in the early 1990s and other underdeveloped economies (for instance Ghana and Nigeria). First, it is argued that the world price of primary products fluctuate considerably, making export earnings highly volatile and an unreliable source of growth for the regional economy (Gillis et al. 1996). The mechanism of inter-industry linkages can also be used to model the reverse impact of a contraction in the resource sector arising from highly volatile or declining prices. Furthermore, the impact of demand shocks on regional output also affects the price of factor inputs. In the case of a rapidly expanding resource sector, these supplyside effects can be highly unfavourable, a phenomenon coined by economists as the “Dutch

Disease”. For example, the rapid expansion of the resource sector bids up wages in the region in order to attract labour into the sector. The upward pressure on costs combined with slow short-run adjustment in the labour supply hurt other industries that have not experienced higher prices for their goods or services, thereby reducing their competitiveness.

Although export volatility and the adverse supply-side effects support the argument that resource-based specialization is in fact undesirable, the case for government intervention (in particular policy-induced diversification

2

) becomes more compelling if we look at the forms of market failure associated with specialization. This issue is not discussed extensively in the regional economics literature. For instance, Saint-Paul (1992) shows how financial markets can influence technological choice of firms and how the interaction between the two creates an externality where multiple equilibria exist. He develops a theoretical model in which there can be a “low” equilibrium where financial markets are underdeveloped and firms resort to less specialized or more flexible technologies which are less productive as a means of limiting risk. Since firms do not experience much risk, then there is no incentive to develop financial markets. There can also be a “high” equilibrium where financial markets are developed. In the latter case, the

2 In theory there is a distinction between market- and policy-induced diversification, although it is difficult to empirically isolate and quantify their contributions to structural changes in a region. An example of marketinduced diversification would be the reversal of Dutch Disease wherein the slowdown of the resource sector leads to a decline in factor costs, thereby making other sectors in the region become viable and attractive again (Mansell and Percy 1990). However, the belief is that macroeconomic stabilization and industrial policies implemented by the government play a decisive role in creating stability and stimulating diversification.

4

insurance market enables firms to diversify risk and at the same time employ riskier and more specialized, but highly productive, technologies. However, the high equilibrium is not necessarily preferred and depends on the cost of developing financial markets relative to the cost of diversified technologies. If the former is significantly larger than the latter, then individuals would be better off in the low equilibrium with lower productivity and less specialization.

Saint-Paul’s results are similar to those derived from a model of Acemoglu and

Zilibotti (1997), albeit under different assumptions including no fixed costs of financial markets. In their model, agents decide how much to save and invest in a safe asset with relatively low return. The rest is invested in imperfectly correlated investment projects

(called ‘open’ sectors) via purchasing shares. These investment projects yield higher expected returns but entail huge fixed costs and minimum size requirements which make them riskier relative to the safe asset. Due to these significant indivisibilities as well as the scarcity of capital at the early stages of development, only a few projects are undertaken, resulting in limited opportunity for risk spreading. This also makes output highly variable and economic progress slow. However, as the economy accumulates more capital, agents save more and undertake more projects, thereby improving diversification opportunities as well as productivity. Similar to Saint-Paul (1992), the ability of agents to diversify risk via shares creates an externality wherein the addition of a sector causes other existing projects to be more attractive relative to the safe asset because of the reduction in undiversified risk. This implies that in addition to buying new securities, agents are induced to buy more shares from the existing projects. Since agents do not internalize the effect of their actions on the diversification opportunities of others, too few projects are undertaken and the equilibrium is inefficient. They argue that government can restore this efficiency in the economy by subsidizing large projects which help to diversify the economy.

Although the supposition that diversification leads to greater stability is somewhat compelling, there have been numerous criticisms of this hypothesized relationship on both empirical and theoretical grounds. On the empirical front, there is inconclusive evidence on whether diversity promotes stability and growth. While there are several explanations offered by scholars to this empirical puzzle, the most prevalent is that most measures of diversity are theoretically or empirically flawed (See Kort 1981; Malizia and Ke 1993; Siegel et al. 1995a; and Wagner and Deller 1998). This lack of consensus among scholars on the most appropriate measure(s) of diversity is due to the fact that the concept is used in a

5

wide range of disciplines, such as industrial organization, regional economics, and finance.

Hence, the concept of diversity is developed within the different theoretical frameworks of each discipline, leading to different approaches to its measurement. Meanwhile, some suggest that other factors such as the use of small sample sizes, exclusion of control variables in the analysis, and flawed regression techniques account for the lack of empirical substantiation on this relationship

3

(Kort 1981; Smith and Gibson 1987; and Malizia and Ke

1993).

With regards to the theoretical issues, there has been a lot of discussion on the possibility of simultaneously pursuing economic stability and growth through diversification

(See Kort 1991; and Siegel et al. 1995a). Some have tried to reconcile this trade-off by placing the concepts of growth and stability into perspective. Wagner and Deller (1998, p.

542) claim that the “simultaneous pursuit of growth and stability is not contradictory when viewed in terms of the short-run and long-run”. In the short-run, regional planners develop policies aimed at promoting growth of industries where the region has comparative advantage. Over time, however, greater diversity in the economic structure is needed in order for the region to achieve stability. Wagner and Deller (1998, p. 542) thus view diversification as the “long-run envelope of the region’s short-run efforts in promoting growth”.

Parallel to this argument is the longstanding hypothesis that economies become more diversified as they become more developed. Studies that have examined the economic history of rich countries such as Canada have traced their development to resource–based specialization and this continues to hold true for developing economies

(Innis 1920). This historical trend would suggest that specialization is a precursor of diversification and long–run stability, and that diversification naturally evolves at different points in the development path. In addition, there is cross-country evidence that sectoral concentration follows a U-shaped pattern in relation to a nation’s income level (Imbs and

Wacziarg 2003)

4

. At first, economies diversify at early stages of development, but then start to specialize again at some later point in the development process. The turning point

3 See Dissart (2003) for a comprehensive summary of empirical studies done on regional economic instability and diversity

4 In the working version of their paper (Imbs and Wacziarg 2000), the authors propose a model predicting this non-monotonic relationship through the interaction between rising productivity levels and falling transport costs.

According to their model, an increase in the relative productivity of a country increases the range of commodities produced locally. On the other hand, demand externalities make it optimal for firms to cluster and localize, resulting in falling transport costs. These two forces compete along the development path and the outcome is based on which force dominates the other.

6

is such that for most OECD countries, higher income levels are associated with more specialization. However, such findings may not hold at the regional level given that external economies which induce industrial localization and specialization are stronger at the regional than country level.

III.

The Concept and Measurement of Stability and Diversification

A.

Economic Instability

Prior to our analysis, it is instructive to start off by formally defining economic stability.

Malizia and Ke (1993, p. 222) define [economic] stability as the “absence of variation in economic activity over time”. Hence, economic instability pertains to fluctuations in economic activity.

Although there is no consensus on the best measure of instability, there is at least some consistency in how it has been measured in the literature. Most studies employ a variance–based statistic wherein the main difference lies on the method employed to calculate the benchmark against which deviations are measured. This study employs the following measure of regional economic instability (REI) index

5 used by Postner and Wesa

(1985) and Mansell and Percy (1990):

REI

=

⎡

⎢

⎢

⎢

⎣ t

T ∑

=

1

( T

( e t

−

− e ˆ t

)

2

3 ) e

2

⎤

⎥

⎥

⎥

⎦

1 / 2

(1) where e t is the actual value of the economic variable of interest (e.g. output) in year t, ē is the mean over the selected period, T is the number of observation periods, and ê t

is the predicted value of the variable based on a non-linear (quadratic) time trend, defined by: e ˆ t

= β ˆ

0

+ β ˆ

1

( t )

+ β ˆ

2

( t

2

) (2)

5 This REI index was introduced by Conroy (1975) and used in U.S. studies on diversity and instability. The benchmark ê t

can be calculated using values based on linear, quadratic or log linear time trends. Others also employ moving average or historical values. See Mansell and Percy (1990) for other differences among various measures of economic instability.

7

By subtracting the approximated value of the trend from the actual (employment or output) series, we are isolating the trend component of instability

6 . This de-trending procedure has

been used in the literature especially when analyzing the relationship between economic instability and other variables using regression analysis. We then take the square root of the variance to generate a standard deviation–based measure of instability. Finally, the index is divided by the mean (of output or employment) in order to scale down the standard deviation to the size of the region, thereby allowing for inter-regional comparison. The REI index is defined as the (absolute) deviation of fluctuations in the variable (e.g., output or income) around the trend relative to its overall level. As mentioned earlier, the above index is a measure of volatility; i.e., a higher index implies greater instability, and vice versa.

Since the REI index employs squared deviations that attach proportionally greater weight to larger deviations, it serves only as an ordinal measure of instability.

As discussed in Section II, the conventional belief that resource-dependent economies are more unstable has its roots in both theory as well as the historical experience of some regional and underdeveloped economies. Mansell and Percy (1990) validate this empirically for Western Canada by calculating the REI index using data on population, GDP, and personal income over the period 1961–1985. They found that the

Western provinces were among the most unstable provinces in Canada with respect to these variables, with Alberta emerging as the most volatile province. They also found Alberta to exhibit the greatest employment variability among all provinces in Canada during the same period, to a degree that is considerably higher than Texas and Oklahoma, two U.S. states that have similar economic base. Much of the same picture emerges from the study of

Postner and Wesa (1985) using data on employment levels from 1970–1983. Their results show that the Western provinces (particularly Alberta) had greater employment instability compared to the Central provinces, particularly Ontario.

B.

The Portfolio Variance Approach

Diversity measures can be broadly classified into four classes

7

: Entropy or Equiproportional,

Type-of-Industry, Portfolio Variance, and the Input-Output Model. The first two are

6 In the economics literature, economic instability has four components: trend, cyclical, seasonal, and random.

Trend corresponds to movements that are relatively stable and depicts the general direction over a long period of time. Cyclical changes (or business cycle), on the other hand, are defined as alternating sequence of contraction and expansion in the economy and recur at certain intervals of variable length. The main difference between the trend and cycle is that the trend corresponds to a period which is longer than that of cycle. Seasonal fluctuations are repetitive and systematic movements in the economy and are tied to particular seasons. Random refers to variations in the economy attributable to random or unpredictable shocks.

7 See Wagner and Deller (1998), Wagner (2000), and Siegel et al (1995a) for a complete review and critique of diversity measures available in the literature .

8

traditional measures used in the regional economics literature and ascribe instability to either having an unequal distribution of economic activity (e.g. output) among sectors or specialization in inherently unstable sectors. One of the major limitations of these measures is that they are one-dimensional in their approach to measuring instability. More specifically, these measures only look at the instability of individual sectors (own–sector instability) without taking into account their relationship to other sectors in the region

(cross–sectoral instability). This shortcoming has led to the development of measures that take into account the importance of inter-industry relationships, one of which is the portfolio variance approach.

The portfolio method was originally developed in finance by Markowitz in the 1950s and later applied in the regional economics literature by Conroy (1975) and Brown and

Pheasant (1985). In finance, diversification is an attempt to reduce an investor’s exposure to overall risk. The risk associated with investing in a particular asset is measured in terms of the variance of its return. When applied to regional economic analysis, the portfolio variance approach treats the region’s industrial mix as analogous to an investor’s asset portfolio, while the volatility in output as akin to the risk associated with investing in a particular asset. So the variance in aggregate output, or the portfolio variance ( V ), is defined as:

V

=

N ∑ i

=

1 w i

2

V [ X i

]

+ i

=

1 j

N N ∑ ∑

=

1 , j

≠ i w i w j

Cov [ X i

, X j

] (3) where w i

is the share of sector i in total provincial GDP and is calculated by dividing the average GDP in sector i ( X i

) over the average of the total provincial GDP during the selected period. V[X i

] is the variance of GDP in sector i , COV[X i

,X j

] is the covariance of GDP between sector i and sector j , respectively, and N is the number of industries in the region.

Furthermore, V [X i

] and COV [X i

, Xj] are calculated as follows:

V [ X i

]

=

⎡

⎢

⎢

⎢

⎣ t

T ∑

=

1

( X i t

( T

−

−

3 )

X

ˆ i t

)

2

⎤

⎥

⎥

⎥

⎦

(4)

9

Cov [ X i

, X j

]

=

⎡

⎢

⎢

⎢

⎣ t

T ∑

=

1

( X it

−

X

ˆ it

)( X jt

( T

−

3 )

−

X

ˆ jt

)

⎤

⎥

⎥

⎥

⎦

(5) where X it is the actual GDP level in industry i at time t and X

ˆ is the predicted GDP level in it industry i at time t based on a non-linear (quadratic) time trend as in equation (2). Note that similar to the REI index, we measure output volatility in terms of the deviation of the actual level of output from its trend. As mentioned earlier, the portfolio variance approach allows us to decompose aggregate output instability into own–sectoral variance (captured by V[X i

]) and cross–sectoral variance (COV[X i

,X j

]), and would enable us to identify sources of output instability in the province.

However, in view of the wide disparity of output levels across provinces, we need to scale the sectoral variances and covariances by the level of sectoral output in order to allow for inter-provincial comparisons

8 . That is:

V [ X i

]

=

⎡

⎢

⎢

⎢

⎣ t

T ∑

=

1

( X i t

( T

−

−

3 ) X

X

ˆ i t i

2

)

2

⎤

⎥

⎥

⎥

⎦

Cov [ X i

, X j

]

=

⎡

⎢

⎢

⎢

⎣ t

T ∑

=

1

( X it

( T

−

X

ˆ it

)( X

−

3 ) X i

X jt j

−

X

ˆ jt

)

⎤

⎥

⎥

⎥

⎦

(4-A)

(5-A) where X is the mean GDP in sector i over the selected time period. i

There are several studies in Canada that have used the portfolio variance approach to measure the relative sectoral employment instability of the western provinces compared to other regions. Postner and Wesa (1985), for instance, used this to show the industrial disaggregation of the province–wide REI measures based on employment. They found a remarkable pattern of similarity across Western and Central provinces. In almost all

8 This method was used by Conroy (1974), Postner and Wesa (1985), and Mansell and Percy (1990) to compare variances in employment. In doing so, the portfolio variance V of aggregate GDP is just equivalent to the REI index. See Postner and Wesa for proof of decomposition identity of the REI index using the portfolio variance approach.

10

provinces, they found that the construction and primary sectors (which include forestry and mining) displayed the highest employment variability among the eight industries used in their analysis, while transportation, communication and utilities, trade, and finance as the least unstable sectors. Manufacturing, on the other hand, ranked somewhere in the middle of the instability rankings among industries. A disaggregation of the manufacturing sector also revealed some similarities across provinces, especially among Western provinces, including the relative instability of primary manufacturing sectors (such as wood, petroleum and coal products) compared to other manufacturing sub sectors.

In addition to own-sectoral instability, they also looked at cross-sectoral employment instability among provinces by using correlation coefficient matrices derived from the

(scaled and detrended) variance-covariance matrices

9 . The results showed that although

the correlation coefficients are positive and quite large (greater than 0.50), almost all of them were less than unity and for some industries were even close to zero. These results hold, generally speaking, within each province. Thus, each province experienced some degree of economic diversification with respect to sectoral employment fluctuations. In addition, they showed that in some provinces there are certain sectors that exhibited greater correlation with the remaining sectors. For example, Alberta’s mining sector displayed much higher correlation coefficients relative to other industries than in other provinces. Moreover, in most provinces, the manufacturing, services, finance, and trade sectors exhibit stronger correlation coefficients.

Chambers (1999) also employed the portfolio variance approach to study changes in employment volatility over time in Alberta, British Columbia, and Saskatchewan. In his study, he utilized quarterly percent changes in employment from 1976–1998 to calculate the three provinces’ employment variances for two sub-periods: the first period (Q1 of 1976 to Q4 of 1987) and the second period (Q1 of 1988 until Q2 of 1998). Similar to previous studies, he found the three provinces to be more unstable than the national average in the first period, with Alberta recording the highest level of employment instability. In the second period, however, Alberta experienced both a relative and absolute decline in employment variability, which placed the province as the least unstable in terms of employment. An industrial disaggregation of the province–wide variances also revealed that

9 The precise relationship between the matrix of correlation coefficients and the underlying matrix of (scaled) covariances is presented in Appendix A of Postner and Wesa (1985). The authors prefer to use correlation coefficients rather than covariances in their study to make the cross-sectoral relationships more apparent.

Nevertheless, using either of the two will lead to the same conclusions.

11

the relative stability of Alberta was due to the significant reduction in the variances of the majority of industries. In addition, Alberta’s manufacturing, construction, finance, and services sectors became more stable in the second period than in the other two western provinces.

Although the portfolio variance is a very useful indicator of which sectors in the region contribute to economic instability, there are several criticisms on its applicability in regional economic analysis. Unlike the equiproportional and type–of–industry measures, the portfolio method is a variance-based measure of diversity; i.e., a lower variance is believed to indicate a more diversified and more stable economy, and vice versa. Therefore, the portfolio variance approach should not be used to test the relationship between diversity and stability since the latter is also measured in terms of variance

10 . It is also argued that

there are fundamental differences between an individual’s financial portfolio and a regional economy. Unlike in a financial portfolio, the addition of a new sector often requires significantly large costs and its effects are often lagged (Seigel et al. 1995a). Moreover, the benefits of having a certain industry vary by region due to differences in comparative advantage (Sherwood-Call 1990). Finally, the portfolio variance approach does not capture the dynamics behind inter–industry relationships. More specifically, the covariance term only indicates the direction and degree in which two sectors move together, but offers no further insight on how these two industries may be linked (Wagner 2000).

Before concluding this section, it is important to also discuss the recent application of the portfolio variance framework into regional economic modeling as an alternative approach to studying diversification. Gilchrist and St. Louis (1991) pioneered the idea of integrating the concept of risk-return trade-off into Input-Output (I-O) models in Canada.

Using 1979 Input-Output tables for Saskatchewan, they assessed three alternative strategies for diversification. First, they developed a model of an open regional economy wherein the level of sectoral activity is assumed to be determined by the allocation of labour among sectors. Second, they assumed that the regional economy is subject to (sectorspecific) productivity and price shocks. Third, these shocks determine the expected level and variance of regional income via its effects on the value added output in the sector.

Hence, regional planners can improve a region’s welfare by reallocating labour among various sectors, on the assumption that welfare is increasing in expected regional income and decreasing in the variance of regional income. This redeployment of labour is what

10 This may explain why in studies that have examined different diversity measures, the portfolio variance emerged as the best diversity measure in explaining cross-sectional differences in instability.

12

they defined as diversification. They restricted their analysis to three forms of diversification strategies: (1) targeted sectoral development, wherein labour is drawn evenly from the remaining sectors in the economy and moved into the targeted sector; (2) reduced sectoral dependency, wherein diversification is aimed at releasing labour from an unstable sector (such as primary industries) to be absorbed by another (relatively more stable) sector; and (3) regional sufficiency, wherein labour is directed away from specialized export sectors and towards import competing industries.

The results were quite revealing. First, they developed an ‘efficiency frontier’ which showed the best possible combinations of the expected level and the variance of regional income (risk-return combinations) for Saskatchewan. Based on the sectoral labour allocation observed in 1979, they found Saskatchewan to be considerably below the frontier indicating that there is room for welfare improvement. Second, they found agriculture to be a relatively risky sector that yielded below average returns. This supports the recurring policy theme in Saskatchewan that moving away from agriculture is an effective diversification strategy. Third, they found most manufacturing sectors to be more stable but have lower returns while other resource-based industries (such as mining) offer higher returns at the expense of greater instability. This confirms the conventional wisdom that although expanding the manufacturing sector is stabilizing, Saskatchewan has tended to specialize in natural resources as these sectors yield higher per capita income. Finally, considering diversification in the direction of regional balance and self-sufficiency is not an appropriate strategy for Saskatchewan since they find trade to be significantly important to living standards.

C.

The Contribution of Changes in the Industrial Mix to Volatility

In addition to looking at inter-sectoral instability, the portfolio variance approach also provides a framework for analyzing how changes in the region’s economic structure can affect (i.e., increase or decrease) the aggregate regional variance. Re-writing equation (3), the variance in output of a province can be expressed as:

V

= i

N N ∑∑

=

1 j

=

1 w i w j

Cov [ X i

, X j

]

Note that Var[X i

] = Cov[X i

, X i

].

(3-B)

13

Any change in the variance due to changes in the province’s industrial mix can be approximated using a second order Taylor series approximation as:

Δ

V

= i n

∑

=

1

∂

V

∂ w i

Δ w i

+

1

2 i n

∑

=

1

∂ 2 V

∂ w i

2

(

Δ w i

)

2 (6) where:

∂

V

∂ w i

= j n ∑

=

1

2 w j

Cov [ X i

, X j

] and

∂ 2

V

∂ w i

2

=

2 Var [ X i

]

(7)

(8)

Therefore, we will define the CIMV (Contribution of Changes in Industrial Mix to Volatility) index as the approximate percentage change in the variance of output due to a change in the province’s industrial mix , or:

CIMV

=

Δ

V

100

V

=

V

1

⎡

⎢ i n n ∑∑

=

1 j

=

1

2 w j

Cov [ X i

, X j

]

Δ w i

+ i n ∑

=

1

Var [ X i

]

Δ w i

2

⎤

⎦

100 (9)

As noted earlier, the above index will enable us to examine the structural source of economic instability in the Canadian provinces, particularly in the Western provinces. More concretely, the CIMV index shows how changes in the industrial structure (i.e., the sectoral shares in provincial GDP) over time have contributed to the changes in regional output instability.

IV.

Empirical Analysis

A.

Western Canada’s Relative Instability

Using data on levels of population, employment, per–capita real GDP, per–capita real consumption, and per–capita real personal income, we calculate the REI index (equation 1) for all provinces for the period 1981–2006. These values are presented in Table 4.1 to

Table 4.5 in Appendix II.

Similar to the findings of Mansell and Percy (1990), our REI values for population for the four Western provinces are relatively higher than for other provinces, suggesting that interregional migration flows in these provinces are highly sensitive to changes in relative

14

economic conditions. On the other hand, the Western provinces (with the exception of

British Columbia) exhibit relative stability with respect to employment, particularly in comparison to Central provinces, which is somewhat similar to the results of Chambers

(1999).

In terms of Western Canada’s relative instability with respect to per-capita real GDP, consumption, and personal income, the results are quite surprising. Similar to employment, the Western provinces fared quite well compared to other provinces during the period under observation. In fact, three of the Western provinces are below the national average.

Moreover, it is surprising to find that Ontario exhibits greater variability than the Western provinces, considering that it has always been regarded as one of the most stable provinces in Canada. In fact, with the exception of population, Ontario is consistently at the higher end of the instability rankings, even surpassing the Western provinces with respect to GDP, consumption, and employment.

Given the results, two pertinent questions come into mind. First, how is it that the data consistently show the western provinces to be more stable than what has been generally perceived? Based on our results, it would seem that the commonly held belief that western provinces are among the most unstable regions in the country is not substantiated. Does this mean then that the western provinces have become relatively more stable over time? Second, why is it that Ontario, which is generally regarded as a more diversified and more stable province, has consistently exhibited greater instability than other provinces? To address the first question, we calculate the REI indices using the same variables for two time periods: 1962–1980

11 and 1981–2006. This will give us an

idea of how provincial instability might have evolved over time. The second issue is harder to investigate using an aggregated REI index and requires a closer examination of the sources of instability, which will be tackled later.

In order to examine how provincial instability has changed over time, we calculate the REI index using data on population, employment

12

, per-capita GDP, per-capita consumption, and per-capita income for the two periods. These values are presented in

11 The Western Canadian provinces have displayed exceptionally strong economic performance for almost two decades prior to the recession that took place in 1981. This recession raised concerns on the security and stability of economic growth in the Prairie region, which led to a renewed interest in diversification and stabilization policies

(Mansell and Percy 1990). Hence, this paper assumes that significant efforts have been made following the recession and has resulted in improved stability than the pre–1981 period.

12 Data on employment is available starting 1966. Hence, the REI values on employment for the first period are calculated over the period 1966–1980.

15

Tables 4.6 to 4.10 in Appendix II. In terms of population, we find that despite the absolute improvement in the REI values

13

in the second period, most Western provinces remain relatively unstable compared to other provinces. However, the results are different for employment, with most Western provinces seeing higher employment variability in the second period. Despite higher employment variability, most Western provinces experience an improvement in their relative rankings compared to the first period, particularly for

Saskatchewan and Alberta. This is also due to higher employment volatility in other provinces, both in absolute and relative terms. Most notable here is the higher employment variability displayed by Ontario in the last period.

Due to the limited data availability, we use nominal data instead to calculate the REI indices of per-capita GDP, per-capita consumption, and per-capita personal income for the two periods. For the period 1961–1980, the Western provinces (with the exception of

Manitoba) ranked as among the most unstable with respect to the three variables, while

Ontario exhibited relative stability. Our results are similar to those of Mansell and Percy

(1990) using data on nominal GDP and personal income for the period 1961–1985. As expected, factoring price changes into the calculation resulted in much higher REI values for all provinces (relative to using real GDP). Interestingly, though, there is no dramatic change in the instability rankings of most provinces (including three Western provinces) between using real and nominal data during the period 1981 to 2006. That is,

Saskatchewan and Manitoba continued to be among the most stable provinces in the country in terms of per-capita nominal GDP, while British Columbia remained close to the national average. The only outlier in the group is Alberta, which became significantly unstable once price volatilities are taken into account. This would suggest that energy price volatilities play a substantial role in Alberta’s aggregate output instability. This result also holds true when we look at the results for personal income. Meanwhile, the relative rankings of the four Western provinces did not change substantially if we look at the REI indices for consumption.

An inter-period comparison of the REI values for the three variables (i.e., comparing the values in the first two columns of the tables) confirms our earlier conjecture that the

Western provinces have become more stable. For all three variables of interest, all Western provinces showed a decline in REI values in the second period. For Manitoba and

Saskatchewan, this reduction in volatility resulted in an improvement in their relative

13 This may reflect the recent trend of international migration as a growing, steady source of population growth for the Western provinces.

16

position to other provinces, while for British Columbia and Alberta the instability ranking did not improve at all. Finally, our results also validate the conjecture raised earlier that

Ontario may have become more unstable over time. In contrast to Western provinces,

Ontario experienced an increase in REI values in the second period, particularly for nominal

GDP and personal income. This has resulted in a huge jump in Ontario’s instability ranking.

B.

Sources of Instability: The Portfolio Variance Analysis

We then calculate the variance and covariances for all provinces using data on real and nominal GDP by industry for the period 1984–2003. To make the discussion manageable for this paper, we shall present and discuss the results only for the four Western provinces and Ontario. The results from using real GDP are presented in Tables 4.11 through 4.16 in

Appendix II.

(1) Inter-Sectoral Comparison Within Provinces

A.

Real GDP

Our results confirm the widely–held belief that resource sectors are among the most volatile sectors in the Western provinces. Looking at the sectoral variances (the diagonal elements in the matrices), we notice that the resource sectors have among the highest variances in terms of real output. In Alberta, for example, the variance of output is 892.5 in the Oil and Gas (OAG) sector and 113.85 in the Support Activities for Mining (SAM) sector.

Meanwhile, in Manitoba and Saskatchewan the variance of output in Crop and Animal

Production (CAP) sector is 53.0 and 225.8, respectively. The significance of these results is further reinforced by the fact that these sectors account for a substantial portion of total output in these provinces. In Alberta, the OAG sector represents an average of about 18% of total provincial output for the period 1984–2003, while CAP accounts for about 6% and

10% of total output in Manitoba and Saskatchewan, respectively.

Manufacturing (MAN) and Finance (FIN) also exhibit high volatility in the four

Western provinces. This is a also particularly significant considering that these sectors represent a substantial portion of economic activity in the Western provinces–ranging from an average of 6% to 12% of total provincial output for Manufacturing and 16% to 22% for

Finance during the period 1984–2003. Other industries that are also highly volatile include

Construction (CON) and Wholesale Trade (WHL).

17

Now that we have identified the volatile sectors in the Western provinces, it would be interesting to see how these sectors may be linked (positively or negatively) to the remaining sectors. Taking a look at the covariances (off-diagonal elements in the matrices) reveals a few interesting results. First, the resource sectors which the Western provinces specialize in do not appear to have synchronized output fluctuations with most industries.

In the case of Alberta, OAG appears to have more industries with negative covariance (14 out of 21 industries) than with positive covariance, which would indicate that output fluctuations in these sectors move in opposite direction, thereby reducing overall output instability. The same can also be said for CAP in Manitoba and Saskatchewan. This is in contrast to British Columbia’s Forestry (FOR) sector which has more instances of positive

(than negative) covariance.

However, a closer inspection of the off–diagonal values leads us to conclude otherwise. In the case of Alberta, although OAG has many instances of negative covariance with other sectors, it has a very large, positive covariance with manufacturing

(in fact, the third largest). This is further reinforced by both sectors’ high volatility and significant shares in total provincial output. It may be the case that manufacturing’s weighted covariance is so large that its volatility may offset (or even exceed) those from industries with negative covariance. British Columbia’s Forestry sector also appears to have a very strong, positive linkage with manufacturing. This significant, positive linkage between the resource sectors and manufacturing reflects these provinces’ orientation towards resource–based manufacturing industries. For instance, in Alberta, about two– thirds of total manufacturing output consists of value–added resource products which include refined petroleum and chemical products, food and beverage, and forest products.

In British Columbia, four of the five biggest industries in the Manufacturing sector are also resource–based, which are wood, paper, food, and fabricated metals. In addition, almost all sectors in Alberta, Manitoba, and Saskatchewan are positively tied to Finance and

Construction, and given their relatively high volatility as well as their significantly large shares in total provincial output, fluctuations in these sectors tend to add to overall output instability. Furthermore, Manufacturing, Finance, and Construction also display very strong positive covariances with each other.

Finally, we turn our attention to Ontario, which has always been regarded as one of the most stable provinces in Canada. The results show that Ontario’s industrial source of instability is very similar to that of British Columbia. That is, Ontario exhibits the highest

18

output volatility in output in Manufacturing and Finance. These sectors account for a combined 40% of total provincial output for the period 1984–2003, which implies that these industries play a very significant role in Ontario’s output volatility. In addition, these two sectors display significantly large, and mostly positive, covariances with other sectors in the province.

B.

Nominal GDP

Now using nominal GDP, we again calculate the variance–covariance matrices for the

Western provinces and Ontario. The values are presented in Tables 4.17 to 4.21 in

Appendix II. Similar to using real output, we find the resource sectors to be the most volatile sectors in the Western provinces with respect to nominal output. The same can also be said for Manufacturing, Finance, and Construction. Moreover, the variances and covariances in the three energy industries (Oil and Gas, Mining, and Support Activities for

Mining) are substantially larger when using nominal GDP in all Western provinces. This further supports our earlier findings that energy price fluctuations drive much of the volatility in output production in these sectors over time. In addition, there are certain industries that became more volatile once price fluctuations are taken into account. This is shown by the higher variances (and in several instances, higher covariances) in terms of nominal output in sectors such as Healthcare (HC), Government (GOV), and Education

(EDU). These are in sharp contrast to agricultural industries (Crop and Animal Production,

Forestry, and Support Activities for Agriculture) whose variances and covariances are lower compared to those derived from real output. This would suggest that agricultural price fluctuations have less bearing on provincial output volatility. We find the opposite to be true in Ontario where resource price fluctuations do not drive much of the instability in the value of output in these sectors. However, there appears to be significant price volatilities in Manufacturing and Finance.

(2) Inter-Provincial Comparisons

As mentioned earlier, in order to allow for inter–provincial comparison, we scale the variances and covariances to the size of sectoral output (please refer to equations 4-A and

5-A). The scaled variance–covariance matrices for real and nominal output are presented in

Tables 4.22 to 4.31 in Appendix II. First, there appears to be some general pattern in output volatility in the resource sectors. For example, we find real output volatility in the agricultural industries (Crop and Animal, Forestry, and Support Activities) in Manitoba and

Saskatchewan to be higher compared to the same industries in other provinces. The same

19

can also be said for Saskatchewan and Alberta’s Oil and Gas sector. These results also hold true generally speaking when we look at the results derived from using nominal output.

Also notable is the relatively high output instability in the Government (GOV) and

Healthcare (HC) sectors in oil–rich Western provinces.

Finally, despite our earlier findings that Manufacturing is the main source of overall output volatility in Ontario, the relative instability of this sector is in fact much lower in

Ontario than in the Western provinces (both in real and nominal terms). Nevertheless, the results do show that Ontario’s output variability in most industries, particularly in major industries (i.e., in terms of output shares), are more or less on par with those of the western provinces. In fact, Ontario displays relative instability in both the volume and value of output in Finance, Construction, and Professional Services than most Western provinces.

C.

The CIMV Index

In addition to looking at the degree of own–sectoral and cross–sectoral instability, it is also interesting to see how changes in industrial structure over time have affected aggregate output instability in the western provinces. To this end, we derived the Contribution of

Changes in Industrial Mix to Volatility, or CIMV, Index (equation 9). Again, this represents the approximate percentage change in the variance of output due to a change in the province’s industrial mix. The base year for calculating the changes in the province’s sectoral output shares is 1984.

Before we proceed to the results, it would be useful to look at how sectoral output shares have changed over time. Figures 4.1 and 4.2 in Appendix II show the shares in total real GDP (in constant 1997 prices) for selected industries in the Western provinces and

Ontario for the period 1984 to 2003. The Western provinces appear to have reduced their dependency on resource sectors over time, particularly on those that they specialize in, as shown by the lower output shares in the out years. In Alberta, the output share of the Oil and Gas sector rose from 18.9% in 1984 to a peak of 20.3% in 1992, before making a steady decline to about 13% in 2003. British Columbia also saw falling output share in its

Forestry sector. Saskatchewan, on the other hand, experienced reduced output share on crop and animal production through most of the period, but higher emphasis on Oil and Gas production until 1998. In addition, most Western provinces exhibited increasingly greater output shares in Manufacturing and Finance during the period under observation. In

Alberta, for instance, the manufacturing sector’s output share rose steadily from about 7%

20

in 1984 to 11% in 2003. In British Columbia, on the other hand, the share of manufacturing output was on a steady decline through most of the 1990s, but picked up thereafter. Meanwhile, Ontario saw increasing output shares in Finance and Manufacturing through most of the period.

We calculate the CIMV Index for the Western provinces and Ontario using the variance–covariance matrices calculated earlier using real GDP. The CIMV values are presented in Table 4.32 and depicted in Figures 4.3 and 4.4 in Appendix II. The graph illustrates that for some Western provinces, there was an increase in output volatility during the 1990s. For instance, Alberta’s output volatility began to rise in the early 1990s.

Coincidentally, this period was accompanied by higher output share in the Oil and Gas sector in historical terms. British Columbia, on the other hand, experienced a decline in output volatility during this period. As mentioned earlier, this period saw a reduction in the output shares of Forestry as well as Manufacturing. Meanwhile, Saskatchewan also experienced an increase in output volatility during the 1990s, although unlike the rest of the

Western provinces, the volatility changes are fluctuating considerably. Similar to Alberta, this period is accompanied by increased shares in output in agriculture and oil and gas sectors. Our results do seem to suggest that there exists a strong positive relationship between resource-based specialization and changes in output volatility.

In the years following 1996, the changes in the industrial mix in the Western provinces had varying effects on the change in output volatility in each of the four provinces. For example, Alberta exhibited a decline in the CIMV index during this period which was also accompanied by a steady decrease in the output share of the oil and gas sector. Meanwhile, Manitoba continues to have an upward trend in the change in output volatility despite the gradual decrease in the share of crop and animal production in provincial output. However, as mentioned previously, this period is characterized by greater output shares in manufacturing and finance (even higher than the rest of the Western provinces). British Columbia, on the other hand, was not able to sustain its declining change in output volatility in the out years of the observation period.

The results are in stark contrast to Ontario. Prior to 1991, Ontario’s CIMV index has been declining and is lower than in most Western provinces. However, Ontario began an upward trend in output volatility which started in the 1990s, as depicted in Figure 4.4 in

Appendix II. This is in contrast to most Western provinces which experienced a decline in

21

output volatility during the latter part of the observation period. As noted earlier, Ontario saw a steady increase in manufacturing sector’s output share at the start of the 1990s. This led to Ontario gradually “catching up” and eventually surpassing the Western provinces, starting with British Columbia in 1992 and then followed by Alberta in 1995 and

Saskatchewan in 2000. By the year 2001, Ontario’s output volatility change is much higher than most of the Western provinces (with the exception of Manitoba).

V.

Conclusion

In this paper, we develop a database of volatility measures for Canadian provinces. In terms of our aggregate regional economic instability (REI) index, we find that compared to other provinces and the Canadian economy as a whole, the Western provinces exhibit greater stability than what has been generally perceived. The calculation of the REI index into time periods also shows that the Western provinces have become more stable over time, both in relative and absolute terms.

Next, we employ the portfolio variance model to examine the structural sources of regional output instability in Western Canada. In contrast to previous papers that used data on employment or income, we use data on real output by industry to calculate the variance– covariance matrices for the Western provinces and Ontario. Similar to past findings, we find that resource sectors play an important role in overall output instability in the Western provinces. However, we do not find output fluctuations in these sectors to be procyclical with most industries in general. Interestingly, contrary to past findings that used employment data, manufacturing and finance sectors emerged as among the most volatile industries in the Western region in terms of output with very strong (positive) linkages to almost all industries, including the resource sectors. Given their relative high output volatility and significantly large shares in total provincial output, fluctuations in these sectors tend to increase output instability in these jurisdictions. However, it is important to note that the manufacturing sector is comprised of various sub-sectors, so to some extent there is diversity within the sector. Nevertheless, the results suggest that the degree of volatility in these sectors may be much greater than what has been generally perceived, especially with the increasing importance of globalization and trade in these sectors.

Moreover, we derive and calculate the contribution of changes in the industrial mix to volatility (CIMV) index based on real output for the period 1984–2003. Our results suggest that there is a strong positive relationship between resource-based specialization and

22

changes in output volatility in Western Canada. However, the trend in the latter part of the observation period seems to indicate that the increasingly greater output share in manufacturing and finance sectors may have been driving the steady increase in output volatility change, particularly in Manitoba and British Columbia. Finally, this paper reveals that Ontario, a province that is traditionally regarded as more diversified with its manufacturing–based economy, exhibits greater output instability both relative to Western provinces and over time. In the portfolio variance analysis, we find that Ontario’s output instability can be traced largely to volatility in the manufacturing and finance sectors. Due to these sectors’ substantial linkages with other industries as well as their significance in the

Ontario economy, output fluctuations in these sectors tend to increase output instability.

The trend in the CIMV index also seems to support this finding.

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25

VII.

APPENDICES

A.

Appendix I: Definitions of Variables and Data Sources

• Population – Source: Statistics Canada (CANSIM, Table 051-0001).

• Nominal GDP – Gross Domestic Product in current prices. Source: Provincial

Economic Accounts, Statistics Canada (CANSIM, Table 384-0015 for 1961-1980 and

Table 384-0002 for 1981-2006).

• Nominal Consumption – Personal Expenditure on Goods and Services in current prices. Source: Provincial Economic Accounts, Statistics Canada (CANSIM, Table 384-

0015 for 1961-1980 and Table 384-0002 for 1981-2006).

• Personal Income – Personal income in current prices. Source: Provincial Economic

Accounts, Statistics Canada (CANSIM, Table 384-0035 for 1961-1980 and Table 384-

0013 for 1981-2006).

• Per-Capita – Calculated by dividing variable over population.

• Real GDP – Gross Domestic Product in chained 1997 prices. Source: Provincial

Economic Accounts, Statistics Canada (CANSIM, Table 384-0002).

• Real Consumption – Personal Expenditure on Goods and Services in chained 1997 prices. Source: Provincial Economic Accounts, Statistics Canada (CANSIM, Table 384-

0002).

• Real Personal Income – Calculated by dividing Personal Income over CPI times 100.

• CPI – Consumer Price Index, all-items using 2001 basket content. Base year:

1992=100. Source: Statistics Canada (CANSIM, Table 326-0002).

• Employment – number of persons who worked for pay or profit (full-time and parttime). Source: Statistics Canada (CANSIM, Labour Force Survey, Table 282-0008 for

1981-2006 and Provincial Economic Accounts, Table 384-0035 for 1966-1980).

• Real GDP by industry – Gross Domestic Product at basic prices, by North American

Industry Classification System (NAICS) in 1997 constant dollars. Source: Statistics

Canada (CANSIM, Table 379-0025).

• Nominal GDP by industry - Gross Domestic Product at basic prices, by North

American Industry Classification System (NAICS) in current dollars. Source:

Statistics Canada (CANSIM, Table 379-0025).

26

B.

Appendix II: Tables and Charts

TABLES

Table 4.1: REI Indices using Data on Population Levels:

All Provinces, 1981–2006

Province (ranked in ascending order) REI Index

Nova Scotia

New Brunswick

Canada

Prince Edward Island

Quebec

Manitoba*

Ontario

Alberta*

Saskatchewan*

Newfoundland

Yukon and NWT (incl. Nunavut)

British Columbia*

* Asterisk refers to western provinces. REI values here are multiplied by 10,000 for ease of presentation.

Table 4.2: REI Indices using Employment Levels:


Provinces (ranked in ascending order)

Alberta*

Saskatchewan*

Manitoba*


New Brunswick

Canada

Quebec

British Columbia*

Nova Scotia

REI Index

Ontario

Newfoundland


Table 4.3: REI Indices using Per-Capita Real GDP:


Province (ranked in ascending order) REI Index


Saskatchewan*

Alberta*

Manitoba*

New Brunswick

Quebec

Canada

British Columbia*

Nova Scotia

Ontario

Newfoundland



138

167

173

206

215

224

274

276

280

345

378

62

107

125

163

209

20

29

37

46

52

53

60

185

217

253

257

304

304

306

318

354

436

548

719

27

Table 4.4: REI Indices using Per-Capita Real Consumption:


Provinces (ranked in ascending order) REI Index

Saskatchewan*

Manitoba*

New Brunswick


Alberta*


Canada

Quebec

British Columbia*

Nova Scotia

Newfoundland

Ontario


Table 4.5: REI Indices using Per-Capita Real Personal Income:



New Brunswick

Quebec

Manitoba*

Saskatchewan*

Canada

Nova Scotia

Alberta*


Ontario

REI Index

British Columbia*


Newfoundland


Table 4.6: REI Indices using Population Levels: All Provinces

(ranking in parentheses)

Province (ranked in ascending order) 1961 –

1980

1981 –

2006

Nova Scotia

New Brunswick

Canada


Quebec

Manitoba*

Ontario

Alberta*

Saskatchewan*

(6) 68

(7) 79

(2) 38

(5) 68

(1) 32

(3) 65

(8) 80

(9) 114

(11) 191

(1) 20

(2) 29

(3) 37

(4) 46

(5) 52

(6) 53

(7) 60

(8) 62

(9) 107

Newfoundland


(4) 67

(12) 442

(10) 125

(11) 163

British Columbia* (10) 143 (12) 209


170

199

206

240

254

265

268

273

282

286

322

327

214

242

261

261

265

274

297

311

315

349

412

515

28

Table 4.7: REI Indices using Employment Levels: All Provinces


Alberta*

Saskatchewan*

Manitoba*


New Brunswick

Canada


Quebec

British Columbia*

Nova Scotia

Ontario

1966 –

1980

(6) 137

(9) 176

(4) 118

(11) 211

(7) 155

(2) 86

(5) 133

(3) 103

(8) 174

(1) 82

1981 –

2006

(1) 138

(2) 167

(3) 173

(4) 206

(5) 215

(6) 224

(7) 274

(8) 276

(9) 280

(10) 345

Newfoundland (10) 193 (11) 378


a Employment data by province only available since 1966.

Table 4.8: REI Indices using Per-Capita Nominal GDP: All Provinces

(rankings in parentheses)


Saskatchewan*

Manitoba*

New Brunswick

Quebec

Canada

British Columbia*

Ontario

Nova Scotia

Alberta*


Newfoundland

1980

1981 – 2006

(6) 524

(10) 963

(3) 422

(8) 685

(4) 450

(5) 453

(7) 537

(2) 342

(1) 339

(9) 890

(11) 1,017

(12) 1,885

(1) 299

(2) 349

(3) 356

(4) 369

(5) 370

(6) 374

(7) 398

(8) 448

(9) 519

(10) 569

(11) 974

(12)

20,876


Table 4.9: REI Indices using Per-Capita Nominal Consumption: All Provinces


1961 – 1980 1981 – 2006

Manitoba*

Saskatchewan*

British Columbia*

New Brunswick

Canada

Alberta*

Ontario

Quebec


Newfoundland


Nova Scotia

(4) 401

(10) 615

(9) 470

(5) 419

(6) 428

(11) 649

(2) 380

(8) 433

(3) 389

(7) 432

(12) 658

(1) 359

(1) 245

(2) 259

(3) 298

(4) 300

(5) 306

(6) 308

(7) 336

(8) 343

(9) 356

(10) 370

(11) 380

(12) 390


29

Table 4.10: REI Indices using Per-Capita Personal Income: All Provinces

(Sorted by 1961-2006 values in ascending order; ranking in parentheses)

Manitoba*

New Brunswick

1961 – 1980 1981 – 2006

(3) 386

(4) 396

(1) 288

(2) 293

Saskatchewan*

Quebec

Canada

Nova Scotia

British Columbia*


Ontario

Alberta*

Newfoundland

(11) 976

(7) 484

(5) 415

(2) 356

(6) 477

(9) 517

(1) 329

(10 ) 632

(8) 500

(3) 324

(4) 339

(5) 363

(6) 374

(7) 395

(8) 397

(9) 409

(10) 427

(11) 666

* Asterisk refers to western provinces. REI values here are multiplied by 10,000 for ease of presentation. Yukon and NWT (including Nunavut) not included as data on personal income only available starting 1977.

Table 4.11: Portfolio Variance using Nominal and Real Aggregate GDP:

All Provinces, 1984-2003 (Rankings in parentheses)

Provinces Nominal GDP Real GDP

Alberta*

British Columbia*

Canada

Manitoba*

New Brunswick

Newfoundland

Nova Scotia

Ontario


(10) 496

(1) 184

(5) 324

(3) 278

(4) 308

(11) 823

(8) 432

(9) 447

(2) 266

(4) 223

(1) 144

(8) 268

(3) 213

(5) 253

(11) 571

(7) 267

(10) 396

(2) 205

Quebec

Saskatchewan*

(7) 356

(6) 337


(9) 272

(6) 264

30

Table 4-12: Variance-Covariance Matrix for Manitoba:

Based on Real GDP, 1984-2003

CAP FOR SAA OAG UTL CON MAN WHL RET TRA INF FIN PRO EDU HC ART ACC OTH GOV

CAP

FOR

SAA

OAG

UTL

CON

MAN

WHL

RET

TRA

INF

FIN

PRO

ADM

EDU

HC

ART

ACC

OTH

52.98 -0.76 0.15 0.07

-0.69

-1.59

-9.87

-1.04

-0.76 0.13 0.02 -0.02

-0.26

0.15 0.02 0.03 -0.01

-0.24

0.28

0.14

0.37

-0.18

-0.11 0.23 0.16

0.04 0.05 -0.14

0.07 -0.02 -0.01 0.02

0.15

-0.01

-0.12

0.03 0.00 0.02

-0.69 -0.26 -0.24 0.15

4.54

-3.01

-0.26

-0.43 -1.22 1.46

-1.59 0.28 0.14 -0.01

-3.01

17.50

19.53

5.57 6.75 2.46

-9.87 0.37 -0.18 -0.12

-0.26

19.53

47.74

-1.04 -0.11 0.04 0.03

-0.43

5.57

8.80

-1.89 0.23 0.05 0.00

-1.22

-5.80 0.16 -0.14 0.02

1.46

6.75

2.46

9.88

11.30

8.80 9.88 11.30

6.00 3.36 2.24

3.36 4.20 2.56

2.24 2.56 4.90

-3.31 0.20 0.07 -0.07

-1.59

-3.52 0.14 -0.17 0.18

1.76

-2.05 0.11 0.08 -0.03

-1.75

0.63 0.06 0.10 -0.03

-1.55

-1.10 0.05 -0.01 0.05

0.06

1.44 0.14 0.18 -0.09

-2.72

-0.87 0.08 0.05 -0.03

-0.79

0.82 0.10 0.00 -0.04

0.00

-2.04 0.05 0.01 0.03

-0.04

4.20

4.17

2.33

1.83

1.37

2.02

1.61

1.33

3.48

5.75

5.10

2.48

0.56

1.75

0.25

2.69

3.23

6.24

1.30 2.02 0.88

2.15 2.46 1.76

1.66 1.63 0.73

0.98 0.93 -0.27

1.11 0.95 0.59

0.35 0.85 -0.76

0.76 1.14 0.77

0.46 1.10 0.71

1.44 1.80 1.29

0.88

1.65

0.46

0.92

0.56

0.24

0.98

0.68

0.52

0.97

-3.31

0.20

0.07

-0.07

-1.59

4.20

5.75

1.30

2.02

-3.52

-2.05

0.14

0.11

0.63

-1.10

0.06

0.05

1.44 -0.87 0.82 -2.04 2.77

-0.17

0.08

0.10

-0.01

0.18

-0.03

-0.03

0.05

-0.09 -0.03 -0.04 0.03

1.76

-1.75

-1.55

0.06

-2.72 -0.79 0.00 -0.04

4.17

2.33

5.10

2.48

2.15

1.66

2.46

1.63

1.43

0.40

-1.67

1.10

-0.06

0.75

1.23

0.18

1.30

0.41

1.83

1.37

0.56

1.75

0.98

1.11

0.93

0.95

1.76

0.73

-0.27

0.59

-0.76 0.77 0.71 1.29

0.46

0.92

0.56

0.24

7.57

0.24

-0.24

1.43

-1.67 -0.06 1.23 1.30

0.24

1.69

-0.24

0.94

0.94

0.86

0.40

0.25

0.25

0.68

0.90

-0.25

0.43

0.15

-0.25 0.15 0.18 0.59

2.02

0.58

0.58 -0.06 0.01 1.67

0.54

0.02

0.18

-0.06 0.36 1.08

0.18

0.59

0.01 0.43 0.50

0.50 0.54

1.34 0.04

GOV 2.77 0.14 0.20 -0.09

-2.58

1.73

-3.08

0.03 0.94 -2.13

0.87

-0.77

0.89

1.01

0.01

-- Variances and covariances are divided by 1,000 for ease of presentation.

Legend: CAP = Crop and Animal Production, FOR=Forestry and logging; SAA=Support activities for agriculture and forestry, OAG=Oil and Gas, UTL=Utilities, CON=Construction, MAN=Manufacturing,

WHL=Wholesale Trade, RET=Retail trade, TRA=Transportation (exclud. transit & ground passenger), INF=Information and cultural (exclud. Broadcasting & telecom), FIN=Finance, PRO=Professional, scientific and technical services, ADM=Administrative and support, EDU=Education, HC=Health care and social assistance, ART=Arts, entertainment and recreation, ACC=Accommodation and food services, OTH=Other services

(except public administration), GOV=Public Administration. * No MIN (Mining) and SAM (Support Activities for Mining and Oil & Gas) due to missing data *

Table 4-13: Variance-Covariance Matrix for Saskatchewan:


CAP FOR SAA OAG MIN UTL CON MAN WHL RET TRA FIN PRO ADM EDU HC ART ACC OTH GOV

CAP

FOR

SAA

OAG

MIN

UTL

CON

MAN

WHL

RET

TRA

FIN

PRO

ADM

EDU

HC

ART

ACC

OTH

225.83

1.07

1.07 0.99

0.34 0.11 1.50

0.99 0.11 0.07 0.71

-13.97

0.52

0.19

-0.25

0.38

0.11

-13.97 0.52 0.19 8.85

-0.25 0.38 0.11 7.37

2.38 1.08 0.68 6.34

8.95 0.91 0.51 8.59

-0.15 0.71 0.27 1.40

-6.52 0.33 0.07 5.32

7.37

6.14

1.99

2.18

3.04

3.24

0.60

2.99

5.01

6.34

1.99

1.93

0.93

19.65

12.71

1.84

2.27

0.32

1.85

2.38

1.08

0.68

8.59

11.66

2.18

3.04

0.93

12.71

5.65

6.09

1.35

8.95

0.91

0.51

1.84

13.97

5.99

5.00

3.83

-2.54

0.96 0.71

0.30 0.27

1.40 5.32

3.24 0.60

2.27 0.32

5.65 6.09

5.99 5.00

8.10

3.32

3.32

3.71

3.45 1.20

-6.52

0.33

0.07

16.66

2.99

1.85

1.35

3.83

3.45

1.20

4.14

-1.30 0.19 0.08 3.08

0.04 0.02 -0.01 0.37

7.37 -0.20 -0.15 -3.20

0.91

0.00

-2.04

3.51

0.60

0.13

-0.72

7.33

1.17

0.64

-1.97

-4.06

-4.23

-0.68

7.08

0.61

0.19

-1.41

-3.28

7.84 4.55

1.06 0.36

0.03 0.14

-0.49 -0.31

-5.48 -0.93

3.85

13.60

0.24

-0.02

1.41

0.44

-0.56

-4.43

-2.94

1.42

0.39

3.08

5.01

3.51

7.33

7.08

7.84

4.55

3.85

-1.81

-9.13

0.16 0.14 0.05 1.62

-3.07 0.20 0.04 3.15

-2.93 -0.20 0.00 -4.86

0.48

1.12

0.30

0.91

-0.91

-1.02

1.38

1.69

1.28

1.20

2.38

0.73 0.56

1.67 0.98

-0.44

-1.01

0.39

1.44

-1.21

1.15

2.82

-1.71

-1.30

0.19

0.04

7.37

2.46 0.16 -3.07 -2.93 4.73

0.02

-0.20

-0.82 0.14 0.20 -0.20

0.08

-0.01

-0.15

-0.06 0.05 0.04 0.00

0.37

-3.20

-16.06

0.91

0.00

-2.04

1.62 3.15 -4.86 -8.03 0.00

-4.06 0.48 1.12 -0.91

0.60

1.17

0.61

1.06

0.13

0.64

0.19

0.03

-0.72

-1.97

-1.41

-0.49

-4.23 0.30 0.91 -1.02

-0.68 1.38 1.69 1.28

-3.28 1.20 2.38 -0.44

-5.48 0.73 1.67 -1.01

0.36

0.14

-0.31

-0.93 0.56 0.98 0.04

0.24

-0.02

-0.56

-4.43 0.39 1.44 -1.21

1.41

0.44

-1.81

-9.13 1.15 2.82 -1.71

0.52

0.08

0.08

-0.40

-1.15 0.16 0.19 -0.24

0.14

-0.09

-0.39 0.08 0.11 -0.05

-0.40

-0.09

-1.15

-0.39

1.51

1.34

1.34 -0.23 -0.56 -0.01 0.79

11.36 -0.70 -2.42 2.65 3.62

0.16

0.19

0.08

0.11

-0.23

-0.56

-0.24

-0.05

-0.01

-0.70 0.16

-2.42 0.27

0.27 -0.15 -0.38

0.94

2.65 -0.15 -0.40

-0.40 -0.88

1.36 1.08

GOV 4.73 -0.33 -0.04 -8.03

-1.75

-1.36

-1.20

-1.46

-1.65 -1.12

-3.60

-0.64

-0.32

0.79

3.62 -0.38 -0.88 1.08 2.27



WHL=Wholesale Trade, RET=Retail trade, TRA=Transportation and warehousing (excl. postal services and transit & ground passenger), INF=Information and cultural industries, FIN=Finance, PRO=Professional, scientific and technical services, ADM=Administrative and support, EDU=Education, HC=Health care and social assistance, ART=Arts, entertainment and recreation, ACC=Accommodation and food services,

OTH=Other services (except public administration), GOV=Public Administration. * No SAM (Support Activities for Mining and Oil & Gas) and INF (Information and Cultural sector) due to missing data *

32

Table 4-14: Variance-Covariance Matrix for Alberta:


ADM

EDU

HC

ART

ACC

OTH

WHL

RET

TRA

INF

FIN

PRO

CAP

FOR

SAA

75.33

-0.41

FOR INF FIN PRO ADM EDU HC ART ACC OTH GOV

-0.41

0.38

-0.63 0.00 0.16

OAG 102.04 -5.27 -8.42 892.49 -15.78 85.39 20.16 -97.29 131.14 0.20 -41.20 -85.57

MIN 1.57 0.13 0.17 -15.78 3.28

SAM

UTL

CON

MAN

26.47 1.53 -2.13 85.39 -6.43 113.85 20.55 63.97

-3.90 -0.08 -0.25 20.16 -4.18 20.55 16.03

16.22 -1.02 0.83 -97.29 3.49 63.97 26.22 203.61 174.21 51.14 43.07 57.00 19.11 46.42 84.10 12.59 28.70 -34.09 -2.66 32.32 6.36

37.52 0.29 -3.03 131.14 -2.43 141.83 35.63 174.21 284.16 26.64 -7.64 110.59

-12.15 0.31 1.36 -119.37 2.63 14.25 3.05 51.14 26.64 65.64 20.85 -4.02

4.94 65.33 79.06 6.39 -1.49 -92.82 -3.38 33.29 -11.55

5.45 7.53 13.31 5.25 10.89 17.88 3.96 5.69 11.12 4.39

-7.25 0.17 1.19 -83.09 4.10 -14.73 3.53 43.07 -7.64 20.85 34.30 -6.05 7.67 6.03 17.32 5.39 17.17 11.66 0.72 5.88 6.39 5.24

27.52 -1.06 -1.82 151.52 0.90 43.30 10.75 57.00 110.59 -4.02 -6.05 63.03

-0.58 -0.13 0.46 -23.64 1.02 -4.24 1.48 19.11 4.94 5.45 7.67 1.62 3.61

-8.15 0.35 1.14 41.09

14.18 7.96 20.44 44.75

2.32 0.48 0.16 -20.18 0.29 2.30 1.81 12.59 6.39 5.25 5.39 -0.09 1.89 2.00 3.04 3.21

0.74 -0.18 0.96 -58.42 4.04 -14.07 -0.54 28.70 -1.49 10.89 17.17 0.16 5.43 -1.00 12.87 2.17 16.59

-29.71 0.91 1.97 -158.35 0.03 -34.88 0.88 -19.80 -25.24 0.54 4.72 58.47

-0.84 0.25 0.09 -5.73 0.00 0.45 -0.24 -2.66 -3.38 3.96 0.72 -2.75 -0.19 -1.87 -2.24 0.82 -0.84 2.32 1.08

-0.06 -0.08 12.38 5.74 32.32 33.29 5.69 5.88 12.71 3.02 11.03 13.01 2.57 2.38 -8.75 -0.38 7.04 0.41 -4.88

-8.09 0.03 0.65 -41.20 -0.52 -4.44 0.06 6.36 -11.55 11.12 6.39 -9.67 2.00 -0.98 -0.20 1.03 1.89 12.92 0.73 0.41 5.26 7.68

GOV -13.48 0.21 1.35 -85.57 -0.06 -23.91 -6.40 -15.16 -52.62 4.39 5.24 -28.71 2.01 -10.63 -11.24 -0.42 4.49 31.26 -0.06 -4.88 7.68 21.21


Legend: CAP = Crop and Animal Production, FOR=Forestry and logging; SAA=Support activities for agriculture and forestry, OAG=Oil and Gas, MIN=Mining, SAM=Support activities for mining and oil and gas,

UTL=Utilities, CON=Construction, MAN=Manufacturing, WHL=Wholesale Trade, RET=Retail trade, TRA=Transportation and warehousing (excl. postal services and transit & ground passenger), INF=Information and cultural industries (exclud. Broadcasting & telecom), FIN=Finance, PRO=Professional, scientific and technical services, ADM=Administrative and support, EDU=Education, HC=Health care and social assistance,

ART=Arts, entertainment and recreation, ACC=Accommodation and food services, OTH=Other services (except public administration), GOV=Public Administration.

33

Table 4-15: Variance-Covariance Matrix for British Columbia:


WHL

RET

TRA

INF

FIN

PRO

ADM

EDU

HC

ART

ACC

OTH

CAP

FOR

SAA

OAG

2.98

-4.11 87.91

MIN

SAM

UTL

-0.35 -0.06 2.47

-3.34 15.72 1.01 -1.08 16.10

CON 3.07 -12.73 0.96 -2.73 -15.33 5.33 -6.06 85.20 -127.16 21.50

MAN 13.61 44.71

0.52 21.08 1.92 -1.89 7.24 20.89

-4.07 43.06 0.88 0.94 16.87 2.39 0.23 -20.95 44.81 -17.61 13.59 47.96 1.77 -14.38 9.93 5.97 20.26 -16.02 2.93 13.15 12.17 -11.92

-26.44 3.79 -1.85 -1.74 -3.39 0.86 -1.93 1.29 -2.97

-358.62 9.07 -43.60 -14.38 341.69

-1.85

-47.14 23.15 -6.19 42.13 -8.29 25.37 -18.57 45.88

6.39

3.65 -12.27 1.71 -1.89 -9.65 0.24 -3.15 19.30 -26.78 8.35 -6.49 -16.02 -3.39 42.13 -15.41 2.38 -14.28

0.27

1.29

20.60 -0.15 -1.06 -8.45 10.37

1.33

3.05 -1.00

6.99 -7.58

GOV 2.14 -10.37 -1.07 1.42 -10.65 -1.14 -5.96 5.64 -22.61 3.66 -10.49 -11.92 -2.97 45.88 -10.57 -0.53 -11.70 10.37 -0.65 -1.00 -7.58 14.29





34

Table 4-16: Variance-Covariance Matrix for Ontario:


CAP

FOR

SAA

OAG

MIN

SAM

UTL

CON

MAN

WHL

RET

TRA

INF

FIN

PRO

ADM

EDU

44.0

-1.0

-1.0 -0.1 -0.2 -20.9 0.6 2.0 -160.5 314.2 -10.7 -0.3 32.8 -20.1 -159.8 0.8 -6.5 -23.6 -70.7 -15.6

7.6

8.0 -16.5 -57.6

0.0 1.9 0.0 -0.9 22.5 25.7 12.0 9.0 3.5 6.7 16.7 12.1 4.4 1.0 4.9 1.8 6.7 4.4 1.2

-0.2 -0.2 0.1 -0.4 -0.3 0.6 -4.9 -11.2 -3.2 -2.4 -1.2 -1.0 -4.3 -5.9 -0.7 0.8 2.5 0.1 -1.5 0.3 3.9

4.3 -18.7 422.2 143.1 171.0 103.0 31.7 98.4 287.3 174.6 74.8 12.3 74.8 32.3 90.7 51.4 20.1

0.0 3.2

-209.5 158.6 -92.6 -17.8 -13.4 -38.5 -80.1 -86.0 -36.2 -3.8 -24.4 -1.8 -74.6 -10.9 7.4

-160.5 113.8 22.5 -4.9 422.2 45.5 -209.5 5371.8 2908.6 2321.6 1524.3 511.3 1286.3 3471.1 2211.0 954.1 94.0 797.7 388.5 1139.6 621.3 89.2

314.2 288.9 25.7 -11.2 143.1 135.6 158.6 2908.6 16803.7 2652.0 2841.1 1686.9 1493.6 2522.7 3134.7 961.9 -431.5 -808.8 238.5 1831.2 693.4 -1381.4

844.3 341.6 624.6 1515.3 1164.4 455.1 11.1 248.5 168.9 604.7 296.4 -90.6

-0.3 66.2 9.0 -2.4 103.0 23.1 -17.8 784.5 321.9 474.9 1081.5 896.1 317.7 -22.5 85.5 106.5 484.7 230.1 -173.3

32.8 29.0 3.5 -1.2 31.7 17.1 -13.4 511.3 1686.9 341.6 321.9

-20.1 38.3 6.7 -1.0 98.4 15.5 -38.5

207.0 196.1 337.7 385.4 138.2 -53.0 -51.1 39.2 242.2 90.0 -141.1

359.8 881.3 624.8 256.8 6.6 141.5 96.0 347.2 181.3 -36.3

-159.8 92.6 16.7 -4.3 287.3 29.0 -80.1 3471.1 2522.7 1515.3 1081.5 337.7 881.3 2729.7 1579.4 604.3 120.2 553.4 256.9 756.7 460.5 64.3

0.8 72.7 12.1 -5.9 174.6 32.0 -86.0 2211.0 3134.7 1164.4 896.1 385.4 624.8 1579.4 1341.5 452.2 -15.1 155.2 153.0 661.4 291.3 -187.2

-6.5 23.8 4.4 -0.7 74.8 11.1 -36.2 954.1 961.9 455.1 317.7 138.2 256.8 604.3 452.2 199.6 0.6 106.5 70.3 255.5 124.5 -17.6

99.6

8.3

-22.9

18.1

83.3

HC

ART

ACC

OTH

8.0 36.0 6.7 -1.5 90.7 17.4 -74.6 395.1 167.6 -101.2

-10.9

256.9 35.8 80.4 52.5 28.1

108.2 24.3

GOV -57.6 -12.6 1.2 3.9 20.1 -17.0 7.4 89.2 -1381.4 -90.6 -17.6 83.3 293.6





35

Table 4-17: Variance-Covariance Matrix for Manitoba:

Based on Nominal GDP, 1984-2003


CAP

FOR

SAA

OAG

UTL

CON

MAN

WHL

RET

TRA

INF

FIN

PRO

ADM

EDU

HC

ART

ACC

OTH

29.72 -0.21 0.07 1.76

4.27

-0.04

-0.21 0.05

0.07 0.00

0.00 0.03

0.08

0.13

0.07

7.98

0.34

0.11 0.04 0.15

0.04

-0.28

-0.16

-1.11

-0.61 0.07 -0.20

1.76 0.03 0.04 0.38

0.15

-0.98

-0.11

-0.65 -0.44 -0.70

4.27 0.13 -0.28 0.15

11.64

-4.52

2.37

3.28 -4.51 0.67

-0.04 0.07 -0.16 -0.98

-4.52

11.24

10.93

5.11 6.79 4.92

7.98 0.34 -1.11 -0.11

2.37

10.93

41.83

13.55 1.89 8.42

1.70 0.11 -0.61 -0.65

3.28

5.11

13.55

7.93 1.75 3.93

-2.86 0.04 0.07 -0.44

-4.51

-1.60 0.15 -0.20 -0.70

0.67

6.79

4.92

1.89

8.42

1.75 7.33

3.93 2.31

2.31

4.09

-0.59 0.02 -0.11 -0.19

-0.28

-1.91 0.01 -0.23 -0.74

-1.31

-1.46 -0.01 -0.22 -0.34

0.03

-1.87 0.00 0.07 -0.22

-1.26

-3.28 -0.08 0.36 0.16

-5.21

-4.73 -0.07 0.61 0.26

-6.45

-1.18 0.04 0.04 -0.09

-0.63

0.29 0.08 0.07 0.18

1.26

3.37 -0.02 -0.26 -0.11

1.71

1.64

5.42

2.64

4.01

1.86

2.52

1.50

-1.79

1.41 0.98 0.92

3.60 3.64 2.27

2.41 1.68 0.92

0.20 2.25 0.37

0.77

-8.00

-3.42 3.86 -1.67

1.06

-14.60

-5.26 5.97 -2.49

1.00

0.60

1.60

0.35

0.73

5.55

0.25 1.31 0.44

0.15 1.35 0.41

2.86 -0.30 1.01

0.92

0.40

0.87

0.56

0.19

-0.19

-0.23

0.15

0.05

0.51

-0.59

0.02

-0.11

-0.19

-0.28

1.64

2.64

1.41

0.98

-1.91

-1.46

-1.87

-3.28

-4.73 -1.18 0.29 3.37

0.01

-0.23

-0.01

-0.22

0.00

-0.08

-0.07 0.04 0.08 -0.02

0.07

0.36

-0.74

-0.34

-0.22

0.16

0.26 -0.09 0.18 -0.11 0.25

-1.31

0.03

-1.26

-5.21

-6.45 -0.63 1.26 1.71

5.42

1.86

1.50

0.77

4.01

2.52

-1.79

-8.00

-14.60 0.35 0.73 5.55

3.60

2.41

3.64

1.68

2.27

0.87

0.92

0.56

0.20

2.25

-3.42

3.86

-5.26 0.25 0.15 2.86

0.37

-1.67

-2.49 0.44 0.41 1.01

0.19

-0.19

-0.23 0.15 0.05 0.51

1.22

0.42

4.73

1.79

1.79

1.22

1.49

0.60

0.42

-0.04

0.34

-0.08

0.57

0.38

0.05

-0.18

0.60

-0.04

-0.08 0.38 -0.18 0.65

1.09

1.57

1.57

2.61

0.53

0.35

5.24

7.88

0.66

0.69

13.41

1.02 0.46

1.58 0.35

0.35 -0.28 0.98

2.17 -0.26 2.02

0.77

0.65

-0.48

-1.92

-2.67 -0.28 -0.26 1.91 -1.13

GOV -2.81 0.04 0.13 0.25

-2.82

1.69

-3.15

-0.57 5.36 -0.54

0.31

1.35

0.93

1.90

4.90





36

Table 4-18: Variance-Covariance Matrix for Saskatchewan:


CAP FOR SAA OAG MIN UTL CON MAN WHL RET TRA FIN PRO ADM EDU HC ART ACC OTH GOV

CAP

FOR

SAA

OAG

MIN

UTL

CON

MAN

WHL

RET

TRA

FIN

PRO

ADM

197.07 1.81 2.19 27.69

-18.74

1.81 0.18 0.06 -1.61

0.99

2.19 0.06 0.15 0.88

-0.02

27.69 -1.61 0.88 234.60

-20.78

-18.74 0.99 -0.02 -20.78

22.94

-0.54 0.19 0.13 2.83

1.49

1.76 -0.05 -0.16 -4.14

17.08 0.68 -0.09 11.13

14.50 0.81 0.25 2.90

1.27 -0.06 0.19 -1.46

-11.79 -0.13 0.15 3.55

15.33 0.47 0.52 -3.93

2.66 0.13 -0.03 -3.67

3.96 -0.03 0.16 2.10

1.49

10.46

4.33

-3.21

-3.06

-1.62

2.12

-1.83

-0.54

1.27

-11.79

15.33

0.19

-0.05

0.68 0.81

-0.06

-0.13

0.13

-0.16

-0.09 0.25

0.19

0.15

0.47

2.66

3.96

2.77

0.13

-0.03

-0.16

0.52

-0.03

0.16

0.13

2.83

-4.14

11.13 2.90

-1.46

1.49

1.49

10.46 4.33

-3.21

3.55

-3.06

-3.93

-1.62

-3.67

2.12

2.10

-1.83

-0.14

-2.70

2.49

-0.96

-0.30 0.94

-0.97

-0.22

-0.96

-0.30

0.94

1.76

17.08 14.50

8.62

7.41

2.08

7.41 2.08

23.77

7.40

7.40

7.62

2.84

-0.32

-0.57

-1.62

-3.31

-0.49

-0.97

2.84

-0.32 -0.57

-0.22

-1.62

-3.31 -0.49

1.12

0.19

0.13

2.96

3.50 4.37

3.94

1.31

2.47

1.31

3.91

1.16

0.59

1.85 0.99

-0.65

-0.97

0.11

-1.18 0.08

0.36

0.15

1.12

2.96

3.50

4.37

0.19

0.59

0.13

-0.36

0.11

0.36

1.85

-1.18

-2.34

0.99

0.08

-1.16

2.47

-0.65

1.16

-0.97

0.36

0.15

0.98

0.23

7.98

0.03

1.07

0.61

0.03

0.52

-0.11

-0.24

1.07

-0.11

0.57

0.56

-10.57 -2.02 -1.16

-6.48 -0.29 0.31

1.12 -9.17

-0.85 -0.09 0.03 -0.04 -0.50

-0.05 0.02 0.02 -0.27 -0.23

-4.14 1.96 1.95 -3.74 -0.36

-5.63 -1.28 -0.13 1.91 -3.83

-2.51 -0.10 0.18 -0.46 -0.21

1.30 0.33 0.13 2.03 -0.56

-6.52 -0.53 0.50 3.44 -4.29

0.37 -3.32

3.93 0.83 0.26 -0.42 1.55

1.36 0.81 0.59 -1.61 1.23

-1.99 0.62 0.75 -0.48 -0.98

-1.21 -0.28 -0.13 0.54 -0.88

0.28 0.10 -0.01 -0.32 -0.26

EDU

HC

ART

ACC

2.77 -0.16 0.13 -0.14

-10.57 -0.85 -0.05 -4.14

-2.02 -0.09 0.02 1.96

-1.16 0.03 0.02 1.95

-2.70

-5.63

-1.28

-0.13

-0.36

-2.51

-0.10

0.18

0.36

1.30

0.33

0.13

-2.34 -1.16

-6.52 -6.48

-0.53 -0.29

0.50 0.31

0.98

3.93

0.83

0.26

0.23

1.36

-1.99

-1.21

0.81

0.59

0.61

-0.24

0.62

-0.28

0.56

0.28

0.10

0.95

2.04

0.23

0.75

-0.13

-0.01

-0.06

2.04 0.23 -0.06 -0.29 0.37

9.90

0.94

0.94 -0.32 -0.45 3.99

0.31

-0.32 0.17

0.17 -0.26 0.61

0.27 -0.15 0.03

OTH 1.12 -0.04 -0.27 -3.74

1.91

-0.46

2.03

3.44 0.37

-0.42

-1.61

-0.48

0.54

-0.32

-0.29

-0.45 -0.26 -0.15 1.35 -0.49

GOV -9.17 -0.50 -0.23 -0.36

-3.83

-0.21

-0.56

-4.29 -3.32

1.55

1.23

-0.98

-0.88

-0.26

0.37

3.99 0.61 0.03 -0.49 3.77





37

WHL

RET

TRA

INF

FIN

PRO

ADM

EDU

HC

ART

ACC

OTH

CAP

FOR

SAA

OAG

MIN

SAM

UTL

CON

MAN

Table 4-19: Variance-Covariance Matrix for Alberta:


CAP FOR SAA OAG MIN SAM UTL CON MAN WHL RET TRA INF FIN PRO ADM EDU HC ART ACC OTH GOV

62.3

1.8 0.7 0.2 34.6 0.1 2.0 -2.3 -2.0 15.3 -2.0 -1.3 0.3 -1.7 0.9 -2.0 0.8 -1.7 -1.1 0.3 -0.2 -1.6 -0.5

2.2 0.2 0.5

-42.9 32.5 -1.8 -8.7 -7.1 -15.3 11.8

29.6 0.0 -0.2 -1.3 -2.5 -0.5 -1.4 0.8 -1.6 -1.7 -0.2 -2.5 1.8 0.7 2.7 0.5 -0.4 -1.2 1.6

-15.2 322.6 32.1 250.7 1250.0 -23.5 -76.6 -150.8 -142.1 -37.8 -173.2 130.2 149.2 408.1 11.6 15.8 -20.2 217.1

-0.2 0.1 0.0 -15.2 1.0 2.4 2.1 -0.1 13.4 -0.1 -3.7 1.3 0.3 0.6 1.2 -1.0 -3.1 -4.8 -1.0 0.6 -0.9 -3.0

11.1 -14.0 10.5 -3.9 8.2 1.4

84.3 -42.9 25.8 31.4 31.8 8.7 58.9 35.5 6.2 20.9 38.7 2.8 3.1 24.3 -1.9

-44.7 61.9 83.8 14.2 14.7 55.7 45.7 9.9 52.6 74.7 12.2 16.0 38.4 31.8

32.5 15.3 -0.5 1250.0 13.4 114.2 -42.9 -44.7 932.2 47.3 -150.9

-15.1 -2.0 -1.4 -23.5 -0.1 11.1 25.8 61.9 47.3 63.9

-10.5 -1.3 0.8 -76.6 -3.7 -14.0 31.4 83.8 -150.9 24.6 93.5

34.3 -2.0 15.4 24.5 -19.1 -173.0 -237.9 -33.9 15.9 -41.3 -147.4

24.6 9.6 13.4 26.0 31.4 2.1 -3.4 -7.3 -1.0 7.4 13.9

-7.3 1.5 27.6 10.7 20.4 57.0 86.3 16.3 3.6 22.2 43.8

-1.8 0.3 -1.6 -150.8 1.3 10.5 31.8 14.2 34.3 9.6 -7.3 20.1

-8.7 -1.7 -1.7 -142.1 0.3 -3.9 8.7 14.7 -2.0 13.4 1.5 4.9 9.4

-7.1 0.9 -0.2 -37.8 0.6 24.9 58.9 55.7 15.4 26.0 27.6 17.2 0.9 54.9

31.4 10.7 12.0 13.9 28.2

-12.9 -1.7 0.7 149.2 -3.1 -20.6 20.9 52.6 -173.0 -3.4 57.0 -10.0 -2.1 7.3 -2.6 11.1 59.5 85.6 12.4 0.6 15.7 51.2

-11.0 -1.1 2.7 408.1 -4.8 -13.4 38.7 74.7 -237.9 -7.3 86.3 -19.3 -11.2 17.1 -11.3 24.3 85.6 21.6 -1.3 20.7 76.9

12.4 4.9

-4.7 -0.2 -0.4 15.8 0.6 2.3 3.1 3.6 1.7 2.8 4.3 6.4 -0.6 0.6 -1.3 -0.5 3.1 3.1 -0.2

-13.2 -1.6 -1.2 -20.2 -0.9 1.5 24.3 38.4 -41.3 13.9 22.2 1.9 6.3 11.0 13.3 0.1 15.7 20.7 2.8 3.1 12.6 9.2

GOV -10.4 -0.5 1.6 217.1 -3.0 -16.2 -1.9 31.8 -147.4 -13.8 43.8 -14.4 -7.4 5.1 -12.1 11.8 51.2 76.9 11.7 -0.2 9.2 51.4





38

Table 4-20: Variance-Covariance Matrix for British Columbia:



CAP 3.47

FOR -10.50

0.36 22.76 1.43 0.60 -6.13 2.80 23.70 3.93 4.77 3.52 1.58 0.99 -1.04 -2.70 2.42

140.93 0.48 -132.25 27.70 3.35 -6.37 -30.60 48.43 -13.87 -29.19 3.71 -5.50 32.26 -22.84 21.37 -0.46 -18.74 -6.91 13.81 -3.92

SAA

OAG 22.76 -132.25 6.51 336.86 -12.59 6.53 -21.26 78.90 160.41 41.18 56.11 23.90 3.57 18.11 -2.47 -5.43 45.24 3.25 4.53 -11.75 29.52

MIN

6.51 1.46 0.41 0.46 1.81 10.74 1.09 1.21 0.75 0.61 1.64 -0.31 1.28 -1.34 1.33

SAM

UTL

-5.95 8.88 1.28 4.64 3.23 0.58 0.11 2.16 0.19 1.95 -1.37 2.41

-59.46 130.88 -25.17 -17.91 -6.37 1.53 -47.85 5.04 -21.98 -8.72 -18.44 -4.40 -7.42 5.60 -17.27

CON -59.46 -270.43 66.16 45.43 -15.92 -8.66 173.45 9.02 34.89 46.94 78.69 -2.11 15.72 -12.27 76.48

MAN 23.70 48.43 10.74 160.41 127.69 1.28 130.88 -270.43 1,372.65 -27.33 -17.40 99.47 -22.54 -349.46 -9.22 -31.62 -111.60 -111.37 -8.50 -7.39 -2.99 -98.86

WHL 29.12 -5.13 -3.18 32.13 0.89 14.08 2.28 18.72 0.30 3.24 -6.22

RET -5.55 -0.72 2.41 4.44 9.12 -6.50 11.32 0.31 -0.05 -4.84

TRA 3.52 3.71 0.75 23.90 13.81 0.58 -6.37 -15.92 99.47 -5.13 -5.55 21.47 0.76 -27.95 3.53 -3.95 -8.75 -8.65 -1.16 -3.17 2.11 -8.68

INF -1.17 -5.50 7.89 -27.76 8.50 -9.01 -8.41 -11.93 -0.74 -7.77 7.64

FIN

PRO

ADM

-3.66 32.26 2.49 3.57 -41.00 9.37 -47.85 173.45 -349.46 32.13 2.41 -27.95 -27.76 283.58 -34.80 54.58 81.60 98.16 4.35 36.84 -31.70 93.98

-34.80 -11.55 -2.88 -2.87

EDU

HC

ART

ACC

OTH

-1.21 -0.46 0.61 -5.43 35.99

1.58 -18.74 1.64 45.24 -14.15 2.16 -18.44 78.69 -111.37 18.72 11.32 -8.65 35.56 52.97 0.73 13.97 -12.91 45.23

0.99 -6.91 -0.74 4.35 -3.96 1.20 -1.09 0.73 5.36 1.07 -0.81 3.47

-1.04 13.81 4.53 2.01 1.95 -7.42 15.72 -7.39 3.24 -0.05 -3.17 -6.34 12.45

-2.70 -3.92 -11.42 -10.45 -12.91 -0.81 -6.34 12.42 -14.00

GOV 2.42 -16.75 1.33 29.52 -12.42 2.41 -17.27 76.48 -98.86 19.43 11.47 -8.68 31.60 45.23 3.47 12.45 -14.00 44.89





39

Table 4-21: Variance-Covariance Matrix for Ontario:


WHL

RET

TRA

INF

FIN

PRO

ADM

EDU

HC

ART

ACC

OTH

CAP

FOR

SAA

OAG

MIN

SAM

UTL

CON

MAN

14.3

0.4

0.4 0.6 -0.2 26.0 0.6 -26.8 81.1 68.4 20.5 25.8 1.6 1.2 72.8 36.6 30.4 12.0 13.1 2.5 27.0 8.1 16.8

5.8 -2.7 0.3 8.4 0.8 -17.0 -13.1 283.5 28.9 -12.7 21.8 21.1 -13.0 26.2 -21.5 -52.0 -61.0 0.8 9.1 0.8 -52.3

0.6 -2.7 4.5 -0.2 4.3 -0.7 25.3 -11.6 -99.7 -32.1 10.9 -17.5 -29.0 -19.1 -26.7 30.2 38.9 51.0 -5.0 -4.6 -6.0 42.8

-0.2 0.3 -0.2 0.1

15.4 -87.8 953.1 1297.5 446.6 415.5 120.3 60.6 659.8 384.6 228.5 -56.7 96.6 46.3 185.4 91.9 96.7

0.6 0.8 -0.7 0.1 15.4 2.9

-26.8 -17.0 25.3 -2.7 -87.8 -6.4 529.6 -952.3 -1839.0 -482.7 -317.0 -233.5 -333.8 -877.9 -725.5 -8.8 278.0 210.1

81.1 -13.1 -11.6 3.1 953.1 35.3 -952.3 3349.7 2358.8 2772.0 639.1 732.1 4723.1 2457.0 1021.2

1.6 21.8 -17.5 1.8 120.3 8.5 -233.5 639.1 1807.5 440.1 227.0 215.9 214.3 430.3 389.5 -6.6 -308.0 -250.6 45.8 165.5 94.8 -247.9

1.2 21.1 -29.0 2.2 60.6 2.8 -333.8 732.1 1527.2 444.8 237.1 214.3 310.4 611.5 521.8 -97.2 -279.5 -242.0 65.5 194.0 148.5 -229.9

30.4 -21.5 30.2 -0.5 228.5 5.6 -8.8 28.6 223.3 554.4 -6.6 -97.2 698.1 247.1 439.2

85.8 1074.5 361.0 1119.5 816.1 889.8

68.4 283.5 -99.7 24.9 1297.5 82.3 -1839.0 3349.7 21,566.7 3234.3 1164.2 1807.5 1527.2 2057.0 3310.9 28.6 -3053.8 -2783.2 200.7 1468.6 493.5 -2597.9

72.8 -13.0 -19.1 5.1 659.8 30.3 -877.9 4723.1 2057.0 1693.5 2016.0 430.3 611.5 2148.3 698.1 121.7 885.7 300.1 851.7 666.4 742.9

12.0 -52.0 38.9 -2.5 -56.7 -20.9 278.0 85.8 -3053.8 -442.0 211.5 -308.0 -279.5 121.7 -246.9 269.1 745.2 872.2 -26.8 -57.4 23.9 815.2

13.1 -61.0 51.0 -1.4 96.6 -17.9 210.1 1074.5 -2783.2 -170.7 720.7 -250.6 -242.0 885.7 126.7 519.7 872.2 1,268.8 20.3 104.8 164.3 1133.5

2.5 0.8 -5.0 0.3 46.3 4.0 -77.9 361.0 200.7 152.7 136.0 45.8 65.5 300.1 162.4 27.0 -26.8 20.3 29.1 61.1 51.1 14.3

27.0 9.1 -4.6 2.1 185.4 2.4 -292.8 -57.4 104.8 61.1 292.9 178.6 89.0

8.1 0.8 -6.0 1.4 91.9 -2.0 -178.5 816.1 493.5 288.9 368.4 94.8 148.5 666.4 410.7 90.0 23.9 164.3 51.1 178.6 152.8 142.0

GOV 16.8 -52.3 42.8 -0.4 96.7 -16.5 229.3 889.8 -2597.9 -153.3 614.4 -247.9 -229.9 742.9 94.8 445.8 815.2 1133.5 14.3 89.0 142.0 1,072.1





40

Table 4-22: Variance-Covariance Matrix (Scaled to Mean) for Manitoba:



CAP

FOR

SAA

OAG

UTL

CON

MAN

WHL

RET

TRA

INF

FIN

PRO

ADM

EDU

HC

ART

ACC

OTH

28.01

-9.00

-9.00 1.80 0.56

33.50 6.30 -4.78

-0.55

-4.67

-0.88

3.50

-2.25

-0.50 -9.72

1.86

-1.22 2.59 1.86

13.10

1.80 6.30 8.09 -2.31

-4.57

1.84

-0.96

0.42 0.62 -1.72

5.05

0.56 -4.78 -2.31 2.74

1.94

-0.13

-0.45

0.20 0.00 0.19

-0.55 -4.67 -4.57 1.94

5.46

-2.51

-0.09

-0.31 -0.91 1.14

-0.88 3.50 1.84 -0.13

-2.51

10.14

4.66

-3.53

-7.06

2.80 3.51 1.33

12.92

-2.25 1.86 -0.96 -0.45

-0.09

-0.50 -1.22 0.42 0.20

-0.31

-0.94 2.59 0.62 0.00

-0.91

-3.00 1.86 -1.72 0.19

1.14

4.66

2.80

3.51

1.33

-9.72 13.10 5.05 -3.53

-7.06

12.92

-0.50 0.44 -0.56 0.43

0.38

0.62

-2.17 2.53 2.01 -0.51

-2.79

1.27 2.66 4.55 -0.91

-4.70

2.58

3.84

-0.53 0.50 -0.08 0.39

0.05

0.52 1.09 1.51 -0.56

-1.48

-2.41 5.08 3.13 -1.57

-3.30

0.86 2.41 -0.03 -0.64

0.00

-1.93 0.99 0.19 0.40

-0.06

0.69

0.76

4.68

1.46

3.44

4.69

1.82

2.11

2.52

7.28

0.31

1.13

0.48

0.37

0.04

3.22

1.46

2.54

1.82 2.11 2.52

2.62 1.52 1.05

1.52 1.96 1.25

1.05 1.25 2.49

1.59 1.62 0.76

1.79 1.75 -0.54

0.49 0.43 0.28

0.12 0.29 -0.27

1.92 2.96 2.09

0.44 1.09 0.73

1.24 1.60 1.20

7.28

3.46

5.58

2.54

3.46 5.58 2.54

26.90

0.28 0.33 0.25

0.37

5.38

6.23

0.65

1.98

10.38

3.04

5.06

-0.50

-2.17

0.44

2.53

1.27

-0.53

2.66

0.50

0.52 -2.41 0.86 -1.93 0.95

-0.56

2.01

4.55

-0.08

0.43

-0.51

-0.91

0.39

-0.56 -1.57 -0.64 0.40

0.38

-2.79

-4.70

0.05

-1.48 -3.30 0.00 -0.06

0.62

2.58

0.31

1.13

0.28

1.59

0.33

1.62

0.19

0.38

-0.16

0.80

-0.05

4.15

0.35

0.37

0.33

0.78

3.84

0.69

0.48

0.37

1.79

0.49

1.75

0.43

0.25

0.76

-0.54

0.28

-0.27 2.09 0.73 1.20

0.37

5.38

6.23

0.65

0.29

0.07

-0.13

0.19

-0.16 -0.05 0.35 0.33

0.07

3.57

-0.13

3.75

3.75

6.53

0.38

0.46

0.46

0.30

1.24

-0.08

4.50

0.39

-0.08 0.39 0.17 0.51

0.50

1.09

1.09 -0.04 0.01 0.39

7.79

0.07

0.17

-0.04 1.96 2.25

0.65

0.51

0.01 2.13 0.93

0.93 0.37

2.26 0.02

GOV 0.95 1.09 1.64 -0.49

-1.33

0.62

-0.46

0.01 0.30 -0.72

1.67

-0.07

0.61

1.31

0.00

-- Variances and covariances are multiplied by 1,000 for ease of presentation.




41

Table 4-23: Variance-Covariance Matrix (Scaled to Mean) for Saskatchewan:


CAP

FOR

SAA

OAG

MIN

UTL

CON

MAN

WHL

RET

TRA

FIN

PRO

ADM

EDU

HC

ART

ACC

41.70

5.70

5.70 6.23 -0.76

52.85 20.66 10.75

6.23 20.66 16.08 5.99

-0.76 10.75 5.99 18.28

-6.69 7.25 3.04 5.70

-0.15 6.68 2.19 6.03

0.68 8.97 6.67 2.44

2.42 7.09 4.70 3.13

-0.88 9.69 3.56 5.47

-0.05 7.32 3.28 0.67

-2.36 3.44 0.86 2.59

-0.31 4.39 1.44 2.40

-1.11 4.55 2.21 3.53

0.08 1.31 -0.64 0.92

2.21 -1.70 -1.59 -1.29

0.65 -6.26 -0.59 -5.71

0.47 11.38 5.42 6.30

-2.12 3.89 1.02 2.92

1.39

2.01

0.02

-1.58

-2.78

3.57

2.01

-6.69

7.25

3.04

5.70

7.62

3.14

1.62

2.13

2.93

0.55

2.81

-0.15 0.68

6.68 8.97

2.19 6.67

6.03 2.44

3.14 1.62

3.86 0.88

0.88 8.73

1.64 5.34

2.61 3.06

0.37 3.36

2.21 0.76

1.24 1.22

1.67 1.54

0.80 1.83

-0.71 -0.92

-3.68 -0.28

2.90 6.16

2.07 1.81

2.42 -0.05

7.09 9.69

7.32

4.70 3.28

3.13 0.67

2.13 0.55

1.64 2.61

0.37

5.34 3.06

3.36

5.56 3.07

2.61

3.07 2.23

2.61 2.54

2.04 0.84

1.11 0.94

0.76 1.70

0.60

0.52 0.11

0.50

-0.62 -0.28

-0.18

-1.27 -2.74

-0.47

5.10 3.98

3.13

2.41 1.31

-2.36

-0.31

-1.11

0.08

2.21

0.65 0.47 -2.12 -1.84 1.31

3.44

4.39

4.55

1.31

-1.70

-6.26 11.38 3.89 -3.67 -2.63

0.86

1.44

2.21

-0.64

-1.59

-0.59 5.42 1.02 0.03 -0.37

2.59

2.40

3.53

0.92

-1.29

-5.71 6.30 2.92 -4.10 -3.00

2.81

1.39

2.01

0.02

-1.58

-2.78 3.57 2.01 -1.48 -1.26

2.21

1.24

1.67

0.80

-0.71

-3.68 2.90 2.07 -2.11 -1.25

0.76

1.22

1.54

1.83

-0.92

-0.28 6.16 1.81 1.25 -0.52

2.04

1.11

0.76

0.52

-0.62

-1.27 5.10 2.41 -0.41 -0.59

2.36

1.58

1.70

0.11

-0.28

-2.74 3.98 2.17 -1.20 -0.86

0.84

0.94

0.60

0.50

-0.18

-0.47 3.13 1.31 0.05 -0.33

2.94

0.81

0.39

-0.06

-0.33

-2.30 2.20 1.95 -1.49 -0.61

0.81

0.84

0.69

0.47

-0.31

-1.40 1.92 1.13 -0.62 -0.58

0.39

0.69

2.03

0.67

-0.55

-1.40 2.08 0.59 -0.70 -0.81

-0.06

0.47

0.67

2.59

-0.27

-1.04 2.26 0.74 -0.29 -0.88

-0.33

-0.31

-0.55

-0.27

0.73

0.58 -1.06 -0.62 -0.01 0.36

-2.30

-1.40

-1.40

-1.04

0.58

4.30 -2.88 -2.39 2.38 1.44

2.20

1.92

2.08

2.26

-1.06

-2.88 7.35 2.91 -1.49 -1.63

1.95

1.13

0.59

0.74

-0.62

-2.39 2.91 2.44 -0.94 -0.91

OTH -1.84 -3.67 0.03 -4.10

-1.48

-2.11 1.25

-0.41 0.05

-1.49

-0.62

-0.70

-0.29

-0.01

2.38 -1.49 -0.94 2.91 1.02

GOV 1.31 -2.63 -0.37 -3.00

-1.26

-1.25 -0.52

-0.59 -0.33

-0.61

-0.58

-0.81

-0.88

0.36

1.44 -1.63 -0.91 1.02 0.94





42

Table 4-24: Variance-Covariance Matrix (Scaled to Mean) for Alberta:



CAP

FOR

SAA

OAG

MIN

SAM

UTL

CON

MAN

WHL

RET

TRA

INF

FIN

PRO

ADM

EDU

HC

ART

ACC

15.10 -0.93 -1.93 2.99

2.05

5.52

-0.72

1.12

2.00

-1.29 3.09

-0.93 9.88 -0.14 -1.76

1.99

3.64

-0.16

-0.80

0.17

0.37 -1.36

-1.93 -0.14 7.61 -3.78

3.36

-6.79

-0.71

0.87

-2.48

2.22 1.94

-3.13

2.99 -1.76 -3.78 3.83

-3.02

2.60

0.54

-0.98

1.02

-1.86 -1.30

2.49

2.05 1.99 3.36 -3.02

27.92

-8.73

-5.03

1.57

-0.84

1.83 2.85

0.66

5.52 3.64 -6.79 2.60

-8.73

24.65

3.94

4.58

7.85

1.58 -1.63

5.05

-0.72 -0.16 -0.71 0.54

-5.03

3.94

2.72

1.66

1.75

0.30 0.35

1.11

1.12 -0.80 0.87 -0.98

1.57

4.58

1.66

4.81

3.19

1.87 1.58

2.20

2.00 0.17 -2.48 1.02

-0.84

7.85

1.75

3.19

4.02

0.75 -0.22

3.30

-1.29 0.37 2.22 -1.86

1.83

1.58

0.30

1.87

0.75

3.71 1.18

-0.24

-0.77 0.20 1.94 -1.30

2.85

-1.63

0.35

1.58

-0.22

1.18 -0.36

3.09 -1.36 -3.13 2.49

0.66

5.05

1.11

2.20

3.30

-0.24 -0.36

3.96

-0.32 -0.84 3.92 -1.93

3.73

-2.46

0.76

3.67

0.73

1.62 2.28

0.51

-0.25 0.12 -0.54 0.07

0.02

0.88

0.25

0.49

0.53

0.12 0.10

0.42

1.84 -1.21 0.21 -0.01

2.66

2.91

1.09

3.74

2.72

0.91 2.52

0.69 1.63 0.75 -0.88

0.57

0.71

0.50

1.29

0.51

0.83 -0.02

0.08 -0.24 1.68 -0.97

3.00

-1.67

-0.06

1.12

-0.05

0.66 1.04

0.01

-3.00 1.05 3.05 -2.34

0.02

-3.66

-1.04

-1.18

-2.49

0.96 0.63

-3.04

-0.55 1.83 0.92 -0.55

0.01

0.31

-0.14

-0.60

-0.59

1.37 0.25

-1.00

-0.18 -0.13 -0.56 0.01

-0.10

2.40

0.98

2.07

1.65

0.56 0.58

1.33

-0.32

-0.25

1.84

0.69

0.08 -3.00 -0.55 -0.18 -1.73 -1.32

-0.84

0.12

-1.21

1.63

-0.24 1.05 1.83 -0.13 0.08 0.23

3.92

-0.54

0.21

0.75

1.68 3.05 0.92 -0.56 2.14 2.03

-1.93

0.07

-0.01

-0.88

-0.97 -2.34 -0.55 0.01 -1.29 -1.23

3.73

0.02

2.66

0.57

3.00 0.02 0.01 -0.10 -0.72 -0.04

-2.46

0.88

2.91

0.71

-1.67 -3.66 0.31 2.40 -0.99 -2.44

0.76

0.25

1.09

0.50

-0.06 -1.04 -0.14 0.98 0.01 -0.58

3.67

0.49

3.74

1.29

1.12 -1.18 -0.60 2.07 0.47 -0.51

0.73

0.53

2.72

0.51

-0.05 -2.49 -0.59 1.65 -0.66 -1.37

1.62

0.12

0.91

0.83

0.66 0.96 1.37 0.56 1.26 0.23

2.28

0.10

1.19

0.86

1.04 0.63 0.25 0.58 0.73 0.27

0.51

0.42

2.52

-0.02

0.01 -3.04 -1.00 1.33 -1.16 -1.58

5.61

0.10

2.87

1.58

1.73 0.25 -0.34 1.56 1.19 0.55

0.10

0.19

0.41

0.09

-0.02 -0.31 -0.19 0.31 -0.03 -0.16

2.87

0.41

3.74

0.59

0.95 -1.65 -0.94 1.56 -0.03 -0.71

1.58

0.09

0.59

1.43

0.37 0.08 0.79 0.71 0.33 -0.06

1.73

-0.02

0.95

0.37

1.08 0.27 -0.31 0.25 0.23 0.25

0.25

-0.31

-1.65

0.08

0.27 2.97 0.76 -0.82 1.39 1.54

-0.34

-0.19

-0.94

0.79

-0.31 0.76 2.30 -0.23 0.51 -0.02

1.56

0.31

1.56

0.71

0.25 -0.82 -0.23 1.22 0.08 -0.44

OTH -1.73 0.08 2.14 -1.29

-0.72

-0.99

0.01

0.47

-0.66

1.26 -1.16

1.19

-0.03

-0.03

0.33

0.23 1.39 0.51 0.08 1.20 0.80

GOV -1.32 0.23 2.03 -1.23

-0.04

-2.44

-0.58

-0.51

-1.37

0.23 -1.58

0.55

-0.16

-0.71

-0.06

0.25 1.54 -0.02 -0.44 0.80 1.02





43

Table 4-25: Variance-Covariance Matrix (Scaled to Mean) for British Columbia:


CAP

FOR

SAA

OAG

MIN

SAM

UTL

CON

MAN

WHL

RET

TRA

INF

FIN

PRO

ADM

EDU

HC

ART

2.92 -1.30 1.20 -0.36 -2.76

-1.30 8.97 2.39 -0.02 4.19

-1.39

3.80

1.20 2.39

-0.36 -0.02

-2.53 1.80

2.77 -0.95

5.59

-4.49

7.89

-1.39 3.80 35.74

0.59

4.71

-3.30

-0.25

-0.04

2.42

-2.87

0.57

0.48

5.30

1.93

0.17

1.33

-0.66

0.55

1.17 0.24

0.10

-0.83

-0.76

-0.73

1.24 0.04

1.23

2.85

0.22

0.37

3.63 0.75

0.39

-0.50

-0.52

-0.69 -0.64

-0.37

0.21

1.36

-2.31

0.76 -1.95

1.11

2.91

0.59

4.71

-3.30 -0.25

-0.04

2.42

1.77

-0.46

0.52 -0.21

0.09

0.02

-0.46

2.78

-1.99 0.90

-0.48

-0.78

0.52

-1.99

5.84 -0.39

0.84

0.80

-0.21

0.90

-0.39 -0.15

-0.84

0.09

-0.48

0.84 0.70

0.51

0.02

-0.78

0.80 0.51

2.05

0.51

-2.00

2.94 1.02

0.36

-0.47

0.78

-1.52 0.10

-0.39

-0.15

0.11

-0.38

0.61 -0.27

0.11

0.61

-0.60

1.23

-1.88 -0.18

0.14

0.74

0.43

-0.07

-0.73 -0.65

0.04

0.91

-0.20

0.52

-0.35 0.29

-0.18

-0.50

-0.23

-0.74

1.44 -0.37

0.42

0.60

-0.24

0.05

-0.88

0.00

-0.88 0.54 0.50 -0.17 -0.30 0.38

0.83

-0.27

0.75

1.37

0.33 -0.59 0.27 0.88 1.09 -0.60

1.66

-1.17

0.22

0.56

-0.87 0.55 1.32 0.05 -0.36 -0.41

-0.42

0.39

0.32

-0.13

0.44 -0.30 -0.80 -0.02 -0.03 0.27

2.56

-1.40

2.81

0.92

2.07 -1.20 1.15 0.51 2.42 -1.61

-2.87

0.57

0.48

5.30

1.93 0.17 1.33 2.92 1.16 -1.01

0.51

-0.47

0.11

-0.60

0.43 -0.20 -0.23 -0.41 0.22 -0.45

-2.00

0.78

-0.38

1.23

-0.07 0.52 -0.74 0.63 -0.41 0.18

2.94

-1.52

0.61

-1.88

-0.73 -0.35 1.44 -0.79 0.58 -0.35

-0.30

0.10

-0.27

-0.18

-0.65 0.29 -0.37 -0.46 -0.69 0.15

1.02

-0.39

0.11

0.14

0.04 -0.18 0.42 0.15 0.50 -0.35

0.36

-0.15

0.61

0.74

0.91 -0.50 0.60 0.86 1.08 -0.45

3.58

-1.29

1.12

-1.10

-0.38 -0.50 0.84 -0.61 0.55 -0.53

-1.29

0.81

-0.68

0.68

-0.07 0.31 -0.40 0.39 -0.39 0.40

1.12

-0.68

2.13

-0.28

0.77 -0.68 -0.07 0.04 0.95 -0.57

-1.10

0.68

-0.28

2.30

0.56 0.21 -0.02 1.25 0.17 -0.06

-0.38

-0.07

0.77

0.56

1.23 -0.46 -0.18 0.57 0.83 -0.46

-0.50

0.31

-0.68

0.21

-0.46 0.46 -0.02 -0.05 -0.54 0.28

0.84

-0.40

-0.07

-0.02

-0.18 -0.02 1.29 0.07 0.34 -0.12

ACC

OTH

2.92

1.16

-0.41

0.63

-0.79 0.15

0.86

0.22

-0.41

0.58 -0.69

0.50

1.08

-0.61

0.39

0.04

1.25

0.57 -0.05 0.07 1.23 0.41 -0.06

0.55

-0.39

0.95

0.17

0.83 -0.54 0.34 0.41 1.28 -0.59

GOV -1.01

-0.45

0.18

-0.35 -0.35

-0.45

-0.53

0.40

-0.57

-0.06

-0.46 0.28 -0.12 -0.06 -0.59 0.47





44

Table 4-26: Variance-Covariance Matrix (Scaled to Mean) for Ontario:


CAP

FOR

SAA

OAG

MIN

SAM

UTL

CON

MAN

WHL

RET

TRA

INF

FIN

PRO

ADM

EDU

HC

ART

4.73 -0.37 -0.11 -0.88

-0.37 9.38 3.71 -2.63

-0.11 3.71 5.43 0.78

-0.88 -2.63 0.78 20.86

-2.38 2.55 2.97 -1.89

0.98 11.21 0.71 -16.60

0.07 0.65 -0.40 0.87

-3.05 7.34 6.00 -3.79

1.52 4.73 1.74 -2.21

-0.20 4.45 3.08 -2.38

-0.01 4.55 2.56 -1.97

1.17 3.51 1.77 -1.76

-1.25 8.10 5.89 -2.53

-0.80 1.57 1.17 -0.87

0.02 6.26 4.30 -6.10

-0.31 3.91 2.97 -1.30

-0.46 -0.19 0.28 0.64

-1.20 0.41 1.16 1.76

-1.63 3.63 2.67 0.29

-2.38

0.98

2.55

11.21

2.97

0.71

-1.89

-16.60

5.25

7.00

7.00

71.94

-0.66

1.69

8.48

12.44

0.73

9.42

3.30

2.21

1.20

5.95

6.74

8.76

6.48

13.88

1.52

2.09

4.69

11.71

3.82

7.70

0.25

1.34

3.56

-2.08

-2.53

6.46

0.07

0.65

-0.40

0.87

-0.66

-3.05 -0.01

1.17

7.34 4.55

3.51

6.00 1.74 3.08

2.56

1.77

-3.79 -2.21 -2.38

-1.97

-1.76

8.48 0.73 3.30

2.21

1.20

-1.25

8.10

5.89

-0.80

1.57

1.17

0.02

6.26

4.30

-0.31

3.91

2.97

-0.46 -1.20 -1.63 0.35 -0.71 -1.05

-0.19 0.41 3.63 5.36 2.83 -0.78

0.28 1.16 2.67 4.11 2.64 0.30

-2.53

-0.87

-6.10

-1.30

0.64 1.76 0.29 -2.71 0.59 2.90

6.48

1.52

4.69

3.82

0.25 1.34 3.56 4.21 2.33 0.39

1.69

12.44 9.42 5.95

6.74

8.76

13.88

2.09

11.71

7.70

-2.08 -2.53 6.46 10.99 3.41 -4.44

1.54

-1.25 0.24 -0.53

-0.11

-0.15

-0.75

-0.13

-0.69

-0.55

-0.02 -0.13 -0.06 -1.03 -0.15 0.04

-1.25

18.09 2.49 7.51

5.48

3.23

14.20

3.07

9.95

8.18

0.32 2.40 7.16 8.86 4.72 0.29

0.24

2.49 2.18

2.59

2.71

4.19

0.57

3.58

2.09

-0.38 -0.62 1.12 3.61 1.34 -1.13

-0.53

2.18 2.91

2.08

6.62

1.29

5.03

3.75

0.04 0.72 2.99 4.52 2.16 -0.28

-0.11

-0.15

2.59 3.01

2.17

2.71 2.17

2.46

5.59

4.06

1.02

0.56

4.30

3.26

2.91

2.22

-0.08 0.27 2.09 4.02 1.87 -0.59

-0.34 -0.29 1.36 3.54 1.28 -0.85

-0.75

14.20 4.19 6.62

5.59

4.06

13.01

2.56

9.21

7.21

0.07 1.40 5.80 8.85 4.51 -0.38

-0.13

-0.69

-0.55

-0.02

-0.13

-0.06

3.07 0.57 1.29

1.02

0.56

9.95 3.58 5.03

4.30

3.26

8.18 2.09 3.75

2.91

2.22

0.32 -0.08

-0.34

2.40 0.27

-0.29

7.16 2.09

1.36

2.56

0.64

1.87

1.36

0.11 0.44 1.24 1.55 0.92 0.05

9.21

1.87

8.06

5.18

-0.07 0.62 3.77 6.87 2.96 -0.80

7.21

1.36

5.18

4.35

0.00 0.82 3.30 5.06 2.41 -0.14

0.07

0.11

-0.07

0.00

0.17 0.31 0.16 -0.18 0.14 0.27

1.40

0.44

0.62

0.82

0.31 1.01 1.23 0.43 0.76 0.75

5.80

1.24

3.77

3.30

0.16 1.23 3.61 3.42 2.18 0.49

ACC

OTH

0.35 5.36 4.11 -2.71

-0.71 2.83 2.64 0.59

4.21

10.99

2.33

3.41

-1.03

-0.15

3.61 4.02

3.54

1.34 1.87

1.28

8.85

1.55

6.87

5.06

-0.18 0.43 3.42 7.09 2.94 -0.75

4.51

0.92

2.96

2.41

0.14 0.76 2.18 2.94 1.86 0.18

GOV -1.05 -0.78 0.30 2.90

0.39

-4.44

0.04

-1.13 -0.59

-0.85

-0.38

0.05

-0.80

-0.14

0.27 0.75 0.49 -0.75 0.18 0.90





45

Table 4-27: Variance-Covariance Matrix (Scaled to Mean) for Manitoba:



CAP

FOR

SAA

OAG

UTL

CON

MAN

WHL

RET

TRA

INF

FIN

PRO

ADM

EDU

HC

ART

ACC

OTH

21.42 -4.70 1.04

-4.70 32.88 -0.24 7.84

3.68

1.04 -0.24 25.21 8.38

3.83

-5.19

-0.03

1.41

-2.21

2.24

2.98

-6.36

2.07 0.82 2.80

-7.47 0.78 -2.33

-3.25

3.14

-12.53

16.68 7.84 8.38 1.81

-8.87

-0.41

-5.15 -3.40 -5.28

-13.67

3.83 3.68 -5.19 1.81

12.99

-3.88

0.83

2.45 -3.30 0.48

-1.91

-0.03 1.41 -2.21 -8.87

-3.88

2.24 2.98 -6.36 -0.41

0.83

1.02 2.07 -7.47 -5.15

2.45

-1.68 0.82 0.78 -3.40

-3.30

-0.92 2.80 -2.33 -5.28

0.48

-3.25 3.14 -12.53 -13.67

-1.91

-0.34 0.06 -0.85 -1.75

-0.29

7.43

2.94

2.94

3.82

2.71

8.63

0.93

2.94

4.58

3.17

0.43

1.89

5.64

0.28

2.94 3.82 2.71

3.17 0.43 1.89

3.97

0.86

0.86 1.89

3.51

1.89 1.08

1.08

1.88

8.63

5.64

6.43

4.37

4.04

6.43 4.37 4.04

16.82

0.54 0.53 0.33

1.19

-2.16 -0.48 -6.74 -6.54

0.06

-4.55 0.00 3.67 -7.13

-3.79

-1.94 -1.46 4.34 1.25

-3.83

-2.06 -0.99 5.42 1.50

-3.50

-3.87 4.11 2.71 -4.07

-2.57

0.37 3.15 1.81 3.16

2.05

4.76 -0.97 -7.46 -2.01

3.01

2.63

1.45

3.49

-1.69

0.44

-1.84

-1.68 1.86 -0.79

0.44

-2.48

-1.91 2.12 -0.87

3.14

0.75

2.17

0.44

0.37

3.06

2.96 2.02 1.08

0.39 4.45 0.71

0.69 3.49 1.15

0.16 1.43 0.42

3.36 -0.34 1.14

6.26

3.58

-0.86

-0.78

3.63

0.54

5.45

-0.34

-2.16

-4.55

-1.94

-2.06 -3.87 0.37 4.76

0.06

-0.85

-0.48

-6.74

0.00

-1.46

-0.99 4.11 3.15 -0.97

3.67

4.34

-1.75

-6.54

-7.13

1.25

1.50 -4.07 3.16 -2.01 1.41

-0.29

0.06

-3.79

-3.83

-3.50 -2.57 2.05 3.01

0.93

2.63

3.49

0.44

0.28

1.45

-1.69

-1.84

-2.48 0.44 0.37 3.06

0.54

2.96

0.53

2.02

0.39

4.45

-1.68

1.86

-1.91 0.69 0.16 3.36

0.33

1.08

1.19

6.26

0.21

0.66

0.66

4.51

0.71

-0.79

-0.87 1.15 0.42 1.14

3.58

-0.86

-0.78 3.63 0.54 5.45

0.74

0.06

3.00

-0.05

-0.07 2.53 -0.47 1.87

0.74

3.00

0.06

-0.05

8.87

3.13

3.13

2.54

0.04

0.46

-0.07

2.53

0.02

-0.47

3.84

5.81

2.82

1.77

1.54

0.74

3.55

2.02 6.80

1.25 2.09

2.09 -1.78 1.93

5.15 -0.67 1.58

0.27

1.87

-2.29

-2.23

-2.29 -1.78 -0.67 5.28 -0.96

GOV -1.22 0.52 1.15 1.41

-1.51

0.70

-0.53

-0.21 1.89 -0.19

1.03

0.14

0.83

2.77

1.73

1.86

-- Variances and covariances are multiplied by 1,000 for presentation purposes.




46

Table 4-28: Variance-Covariance Matrix (Scaled to Mean) for Saskatchewan:


CAP

FOR

SAA

OAG

MIN

UTL

CON

MAN

WHL

RET

TRA

FIN

PRO

ADM

EDU

HC

ART

ACC

OTH

34.44 11.67 12.07 5.47

11.67 42.91 12.86 -11.70

12.07 12.86 25.34 5.48

5.47 -11.70 5.48 52.33

-9.59 18.60 -0.34 -12.01

-0.33 4.30 2.44 1.94

0.52 -0.58 -1.46 -1.37

4.85 7.08 -0.77 3.57

5.12 10.51 2.82 1.16

0.42 -0.79 1.95 -0.55

-3.59 -1.42 1.45 1.22

1.68 1.89 1.82 -0.49

2.47 4.29 -0.84 -3.86

6.88 -2.01 9.01 4.12

0.89 -1.95 1.36 -0.05

-2.86 -8.44 -0.44 -1.26

-4.81 -8.26 1.64 5.27

-0.84 0.81 0.54 1.59

0.95 -1.22 -7.23 -3.57

-9.59

18.60

-0.34

-12.01

34.38

2.64

1.28

8.70

4.49

-3.14

-2.73

-0.52

5.76

-9.31

-2.55

-4.46

-8.92

-0.28

4.73

-0.33 0.52

4.30 -0.58

2.44 -1.46

1.94 -1.37

2.64 1.28

5.25 -0.98

-0.98 4.24

-0.30 3.53

1.16 1.23

-1.12 1.59

-0.23 -0.83

0.43 0.55

0.60 0.92

0.81 0.33

-0.40 0.19

-2.36 0.59

-0.86 1.33

0.45 0.16

-1.35 2.87

4.85 5.12

0.42

7.08 -0.79

-0.77 2.82

1.95

3.57 1.16

-0.55

8.70 -3.14

-0.30 1.16

-1.12

3.53 1.23

1.59

10.98 4.26

-0.17

4.26 -0.39

-0.17 2.52

-1.64 0.76

0.63 0.52

2.80 1.85

-1.15

-3.34 0.28

1.20

-1.23 -0.76

0.61

-2.87 -3.55

2.03

-2.06 -1.41

3.78

0.58 0.36

4.73 -0.68

-3.59

1.68

2.47

6.88

0.89

-2.86 -4.81 -0.84 0.95 -2.63

-1.42

1.89

4.29

-2.01

-1.95

-8.44 -8.26 0.81 -1.22 -5.27

1.45

1.82

-0.84

9.01

1.36

-0.44 1.64 0.54 -7.23 -2.05

1.22

-0.49

-3.86

4.12

-0.05

-1.26 5.27 1.59 -3.57 -0.12

-2.73

-0.52

5.76

-9.31

-2.55

-4.46 -8.92 -0.28 4.73 -3.22

-0.23

0.43

0.60

0.81

-0.40

-2.36 -0.86 0.45 -1.35 -0.21

-0.83

0.55

0.92

0.33

0.19

0.59 1.33 0.16 2.87 -0.27

-1.64

0.63

2.80

-3.34

-1.23

-2.87 -2.06 0.58 4.73 -2.00

-0.30

0.97

1.85

0.28

-0.76

-3.55 -1.41 0.46 0.63 -1.93

0.76

0.52

-1.15

1.20

0.61

2.03 3.78 0.36 -0.68 0.85

2.08

0.22

-1.56

0.44

0.13

0.64 3.35 0.75 -2.37 0.61

0.22

0.55

0.02

1.17

0.12

-0.34 0.92 0.34 -0.25 -0.18

-1.56

0.02

2.56

-1.03

-0.41

-1.75 -3.56 -0.49 2.41 -1.34

0.44

1.17

-1.03

9.92

1.80

0.76 2.32 -0.09 -2.66 -0.74

0.13

0.12

-0.41

1.80

0.57

1.02 0.99 -0.08 -0.46 0.20

0.64

-0.34

-1.75

0.76

1.02

4.15 3.47 -0.35 -0.59 1.77

3.35

0.92

-3.56

2.32

0.99

3.47 10.21 1.70 -2.96 2.40

0.75

0.34

-0.49

-0.09

-0.08

-0.35 1.70 0.82 -0.52 0.03

-2.37

-0.25

2.41

-2.66

-0.46

-0.59 -2.96 -0.52 5.49 -0.68

GOV -2.63 -5.27 -2.05 -0.12

-3.22

-0.21 -0.27

-2.00 0.85

0.61

-0.18

-1.34

-0.74

0.20

1.77 2.40 0.03 -0.68 1.78





47

Table 4-29: Variance-Covariance Matrix (Scaled to Mean) for Alberta:



CAP

FOR

SAA

OAG

MIN

SAM

UTL

CON

MAN

WHL

RET

TRA

INF

FIN

PRO

ADM

EDU

HC

ART

9.65 4.03 5.94 0.90

4.03 22.94 8.95 10.55

-0.14

1.63

0.76

5.67

1.91

-5.27

-2.59

-1.76

1.58

10.84

-1.37

-2.64

-0.17

0.45

-6.32

-18.29

-0.20

0.37

-1.80

-3.42

3.06

3.06

-1.33 -1.02 -0.71 -0.83 -2.89 -0.94

-2.49 -1.48 2.75 -0.40 -5.08 -0.70

5.94 8.95 10.77

0.16

-0.79

-3.53

-2.65

-0.40

-2.13 1.32

-2.54

-21.86

-0.09

-5.07

7.97

1.27 4.28 4.91 -1.31 -4.65 2.51

0.90 10.55 10.77 49.17

-1.91

8.47

0.68

2.05

8.27

-0.29 -0.95

-1.87

-14.10

-0.15

-2.77

4.58

2.09 5.15 0.91 0.38 -0.60 2.67

-0.14 1.63 0.16 -1.91

5.69

2.74

1.99

-0.02

3.92

-0.07 -2.00

0.70

1.14

0.11

0.88

-1.57

-1.94 -2.65 -3.61 0.59 -1.20 -1.64

0.76 5.67 -0.79 8.47

2.74

15.54

5.74

1.76

6.95

1.26 -1.59

1.20

1.91 -5.27 -3.53 0.68

1.99

5.74

29.91

5.16

-2.12

2.37 2.91

2.94

-2.59 -1.76 -2.65 2.05

-0.02

1.76

5.16

3.99

-0.85

2.19 2.98

0.51

1.58 10.84 -0.40 8.27

3.92

6.95

-2.12

-0.85

14.31

1.35 -4.33

0.99

-1.37 -2.64 -2.13 -0.29

-0.96 -1.72 1.32 -0.95

-2.00

-1.59

2.91

2.98

-4.33

1.31 -0.39

-0.17 0.45 -2.54 -1.87

0.70

1.20

2.94

0.51

0.99

0.52 1.09

-6.32 -18.29 -21.86 -14.10

1.14

-3.57

6.46

4.18

-0.47

5.73 0.63

2.10

-0.20 0.37 -0.09 -0.15

0.11

0.89

1.72

0.62

0.14

0.44 0.29

-1.80 -3.42 -5.07 -2.77

0.88

1.20

4.25

2.10

0.91

2.17 0.83

3.06 3.06 7.97 4.58

-1.33 -2.49 1.27 2.09

-1.02 -1.48 4.28 5.15

-0.71 2.75 4.91 0.91

-0.07

-1.57

-1.94

-2.65

-3.61

1.26

0.45

-2.66

-1.56

-0.05

2.37

1.64

2.18

3.65

1.63

2.19

0.99

2.12

2.71

2.75

1.35

-1.55

-5.62

-6.97

-6.20

3.40 1.31

0.32 3.12

-0.20 3.46

-0.40 4.73

-0.35 5.58

0.52

-0.89

-0.61

-1.06

-0.77

-3.57

6.46

4.18

-0.47

5.73

0.44

2.17

0.32

-0.20 -0.40 -0.35 0.76 1.79 -0.73

0.63

0.47

0.74

3.12

3.46 4.73 5.58 0.37 2.86 2.33

2.10

0.29

0.83

-0.89

-0.61 -1.06 -0.77 0.18 0.25 -0.77

32.37

0.12

7.71

0.89

1.72

0.62

0.14

0.12

0.29

0.38

1.20

4.25

2.10

0.91

7.71

0.38

2.53

0.45

1.64

0.99

-1.55

-7.40

0.40

-1.19

-2.66 -1.56 -0.05 0.51 0.41 -1.83

2.18 3.65 1.63 0.55 5.41 -0.17

2.12 2.71 2.75 1.10 3.28 1.12

-5.62 -6.97 -6.20 0.89 -2.85 -4.20

-1.03 -4.91 -7.94 2.32 6.47 -3.16

0.14 0.29 0.56 0.14 0.45 0.09

-0.21 -0.80 -1.23 0.86 2.21 -0.83

-7.40

0.40

-1.19

5.22

1.91 3.78 4.84 -0.18 0.04 1.79

-1.03

0.14

-0.21

1.91

4.09 5.30 4.79 0.07 2.30 3.09

-4.91

0.29

-0.80

3.78

5.30 7.69 7.54 -0.13 2.72 4.18

-7.94

0.56

-1.23

4.84

4.79 7.54 -0.33 2.29 3.98

ACC

OTH

-0.83 -0.40 -1.31 0.38

0.59

0.51

0.55

1.10

0.89

0.76 0.37

0.18

-2.89 -5.08 -4.65 -0.60

-1.20

0.41

5.41

3.28

-2.85

1.79 2.86

0.25

2.32

0.14

0.86

-0.18

0.07 -0.13 -0.33 0.63 0.77 -0.02

6.47

0.45

2.21

0.04

2.30 2.72 2.29 0.77 3.92 1.18

GOV -0.94 -0.70 2.51 2.67

-1.64

-1.83

-0.17

1.12

-4.20

-0.73 -0.77

-3.16

0.09

-0.83

1.79

3.09 4.18 3.98 -0.02 1.18 2.72





48

Table 4-30: Variance-Covariance Matrix (Scaled to Mean) for British Columbia:


CAP

FOR

SAA

OAG

MIN

SAM

UTL

CON

MAN

WHL

RET

TRA

INF

FIN

PRO

ADM

EDU

HC

ART

2.89 -4.24 0.78 14.55 1.10

-4.24 27.63 0.50 -41.01 10.35

2.47

6.64

0.78 0.50 10.69 2.89

4.33

14.55 -41.01 165.22 -7.44

20.49

1.10 10.35 2.89 -7.44 31.77

12.57

-2.51

0.47

2.07 0.84

0.80

0.66

-1.27

-2.47

2.05 -1.44

-2.37

0.34

-1.43

-0.17

-0.09

0.28

-0.24 0.24 0.96 -0.32 -1.18 0.43

-3.28

0.74

-3.07

5.66

-0.04 -1.36 -3.26 2.06 -0.83 -1.45

0.49

0.77

2.41 0.52

0.36

-4.30

0.30

-0.40

2.07

0.31 0.63 -0.78 1.01 -1.51 0.61

-6.68

10.07

10.76 6.74

7.20

3.43

-13.80

0.13

3.85

-1.03

-0.83 5.21 2.42 1.07 -3.94 4.05

-5.76

-3.02

10.32 0.93

0.87

2.39

-1.12

-1.78

0.03

3.71

-3.08 -1.96 -1.61 0.57 1.08 -2.05

20.49 36.51

-11.94

7.24

0.55 4.85

2.65

0.53

-2.51 -1.27 -11.94

20.66

-4.86

5.62 -2.64

-1.47

-0.59

7.24

0.55

4.85

2.65

0.53

-4.86

5.62

7.47

-4.72

-4.72 2.82

12.60 -0.61

1.52

-0.31

-0.59

1.95

-8.81

2.16

-2.43

10.52

0.11 1.59 0.89 2.95 -2.94 2.11

0.93

-1.11

0.69

-5.89

-0.85 -1.36 -2.10 -1.12 1.20 -1.52

-2.12

1.63

0.50

3.80

1.86 2.36 -0.41 0.97 -1.07 2.73

-2.91

-1.73

-0.27

-1.81

-2.33 -1.75 -0.87 -0.24 -0.14 -1.85

-2.64

2.82

-0.61 1.25

-0.25

-1.00

0.39

0.06

1.97

0.12 0.72 0.07 0.26 -0.69 0.89

-1.47

1.52

-0.31 1.19

-0.21

-0.59

-0.59

1.95 -0.25

-0.21

0.90

-0.18

0.02

0.25

1.00

-0.26 0.34 0.06 0.00 -0.42 0.41

0.21

-0.30

0.22

-0.48

-0.39 -0.29 -0.25 -0.22 0.21 -0.35

0.93

-2.12

-2.91 -1.00

-0.18

0.21

14.30

-1.93

3.47

-7.25

-2.47 -2.64 -1.06 -3.53 4.92 -2.94 -8.81

2.16

-2.43

10.52

-1.11

0.69

-5.89

1.63

0.50

3.80

-1.73 0.39

-0.27 0.06

-1.81 1.97

0.02

0.25

1.00

-0.30

0.22

-0.48

-0.85

1.86

-2.33 0.12

-0.26

-0.39

-1.93

3.47

-7.25

-2.47

0.75

-0.54

1.68

0.92

-0.54

2.33

-2.10

-0.19

1.68

-2.10

7.63

1.63

0.92 0.83 0.24 0.64 -0.78 0.95

-0.19 -0.14 -1.28 -0.76 1.36 -0.45

1.63 1.89 0.76 2.41 -3.27 2.32

1.71 1.27 -0.25 0.80 -1.09 1.35 0.11

1.59

0.89

-1.36

-2.10

2.36

-0.41

-1.75 0.72

-0.87 0.07

0.34

0.06

-0.29

-0.25

-2.64

-1.06

0.83

0.24

-0.14

-1.28

1.89

0.76

1.27 1.43

-0.25 0.13

0.13 0.78 -1.01 1.46

6.07 0.38 -0.41 0.72

ACC

OTH

2.95

-2.94

-1.12

0.97

-0.24 0.00

-0.22

1.20

-1.07

-0.14 -0.42

0.21

-3.53

0.64

-0.76

2.41

0.80 0.78 0.38 1.32 -1.02 0.82

4.92

-0.78

1.36

-3.27

-1.09 -1.01 -0.41 -1.02 2.84 -1.31

GOV 2.11

-1.52

2.73

-1.85 0.41

-0.35

-2.94

0.95

-0.45

2.32

1.35 1.46 0.72 0.82 -1.31 1.72





49

Table 4-31: Variance-Covariance Matrix (Scaled to Mean) for Ontario:


CAP

FOR

SAA

OAG

MIN

SAM

UTL

CON

MAN

WHL

RET

TRA

INF

FIN

PRO

ADM

EDU

HC

ART

1.45

0.20

0.20 0.66 -0.97

14.48 -14.25 9.23

3.11

5.02

1.04

7.07

-1.08

-3.41

0.33 0.52

0.06

6.88 -1.26

4.02

0.11

9.22

0.38

-0.34

0.94

3.35

1.37

-4.81

0.25 0.23 0.32 1.28 0.40 0.32

-5.34 -5.35 0.48 2.14 0.21 -4.86

-2.52 -5.00 -6.38

2.23

-6.68

-26.13

-1.03

-7.04

13.99

8.27 9.24 -6.57 -2.23 -3.04 8.24 0.66 -14.25 48.06 -10.26

9.09

11.48

3.11 5.02 5.26 9.09

38.48

32.92

-12.70 32.92

93.53

-1.08 -3.41 10.47 -6.06

1.72 -1.38 -2.52 3.66

23.76

13.40

0.33 6.88 -5.00 6.79

5.26

-12.70

10.47

-4.15

7.44

-4.58

7.19

0.40 2.78 -6.38 3.47

10.15

10.03

-6.06

3.66 6.79 3.47

1.84

3.73

10.77

1.49

11.83

-1.34

-2.90 -1.37 2.15 5.62 3.93 -0.41

-4.15

23.76 7.44 10.15

9.76

5.24

-4.58

8.42

-7.98

-3.55

-3.69

13.40 7.19 10.03

-7.98 -3.55 -3.69

27.95 3.41 9.50

3.41 3.00

3.00

2.34

-2.50

11.54

1.12

3.54

5.63

-3.42

4.94

3.21

3.10

6.25

4.38

-11.58

13.39

6.43

7.42

4.07

2.85

-1.82

5.16

0.52

1.69

11.60

7.93

-7.36

13.14

4.07

5.21

12.08

4.53

-0.16

9.57

0.06

1.91

-1.38 2.00 6.89 10.32 5.34 2.12

-7.72 -5.65 9.16 2.06 -1.78 -5.52

2.27 1.46 -3.90 -5.48 -3.49 1.69

0.37 3.95 9.53 11.05 8.41 3.47

-3.03 -2.35 1.22 3.34 1.17 -2.33

-1.74 -0.57 3.68 4.01 2.71 -0.54

0.52 -1.26 2.23 1.84

0.06 4.02 -6.68 3.73

0.38 -0.34 -1.03 1.49

9.76

5.24

6.25

4.07

0.94 3.35 -7.04 11.60

2.34

5.63

-2.50

11.54 1.12 3.54

5.43

1.65

-3.42

4.94 3.21 3.10

1.65

2.91

4.09

6.85

2.08

0.82

5.22

3.64

4.90

-0.11

0.86 2.50 3.38 4.59 3.58 2.26

-2.32 -1.61 2.11 2.86 1.71 -1.69

4.38

-11.58

13.39 6.43 7.42

4.09

6.85

23.49

2.76

11.55

-3.77

-4.98 -3.68 7.15 7.92 6.33 -3.71

2.85

7.93

-1.82

-7.36

5.16 0.52 1.69

13.14 4.07 5.21

2.08

5.22

0.82

3.64

2.76

11.55

1.06

2.84

2.84

10.21

1.62

2.80

0.13 0.80 1.96 2.08 1.70 0.72

-1.29 0.56 5.19 7.05 5.12 0.45

1.37 -4.81 13.99 -1.34

12.08

0.25 -5.34 8.27 -2.90

-1.38

0.23 -5.35 9.24 -1.37

0.32 0.48 -6.57 2.15

2.00

6.89

4.53

-7.72

-5.65

9.16

-0.16

2.27

1.46

-3.90

9.57 0.06 1.91

4.90

-0.11

0.37 0.86

-2.32

3.95 2.50

-1.61

1.22 3.38

2.11

-3.77

1.62

2.80

8.73

2.46 4.05 1.51 3.78 1.97 3.69

-4.98

0.13

-1.29

2.46

3.13 3.12 -0.69 -0.55 0.24 3.10

-3.68

0.80

0.56

4.05

3.12 3.88 0.45 0.86 1.41 3.67

7.15

1.96

5.19

1.51

-0.69 0.45 4.59 3.60 3.14 0.33

ACC

OTH

1.28 2.14 -2.23 5.62

10.32

0.40 0.21 -3.04 3.93

5.34

2.06

-1.78

-5.48

11.05 3.34 4.01

4.59

2.86

-3.49

1.17 3.58

1.71

7.92

2.08

7.05

3.78

-0.55 0.86 3.60 6.46 4.11 0.77

6.33

1.70

5.12

1.97

0.24 1.41 3.14 4.11 3.67 1.29

GOV 0.32 -4.86 8.24 -0.41

2.12

-5.52

1.69

-2.33 2.26

-1.69

-3.71

0.72

0.45

3.69

3.10 3.67 0.33 0.77 1.29 3.68





50

Province

British Columbia 3.39

Table 4-32: CIMV Index (in percentage): 10 provinces, 1985-2003

Based on Variance-Covariance Matrix of Real GDP by Industry (base year: 1984)

2.41 12.27 13.28 8.16

New Brunswick

Nova Scotia


-3.96 -5.92 1.44

9.23 8.72 19.95 7.04

0.32

9.32

2.84

20.46

0.54

-0.76 -6.31 -4.73

1.93 1.75 -4.93 -7.14 -9.84 -11.32

51

CHARTS

Figure 4-1: Real Output Shares for Western Provinces: Selected Industries, 1984–2003

22.00%

OIL AND GAS

1991-1996: 19.4%

11.00%

20.00%

18.00%

16.00%

1984-1990: 17.6%

1991-1996: 8.0%

AB

SASK

10.00%

9.00%

1997-2003:

7.9%

8.00%

7.00%

14.00%

12.00%

1984-1990: 6.2%

1997-2003: 15.11%

10.00%

19

84

19

85

19

86

19

87

19

88

198

9

19

90

19

91

199

2

19

93

19

94

199

5

19

96

19

97

19

98

19

99

20

00

20

01

20

02

200

3

6.00%

5.00%

4.00%

MANUFACTURING

16.00% 16.00%

AGRICULTURE

16.00%

14.00%

12.00%

10.00%

8.00%

6.00%

4.00%

2.00% MANITOBA SASKATCHEWAN BC

0.00%

19

84

19

85

19

86

19

87

19

88

19

89

19

90

19

91

19

92

19

93

19

94

19

95

19

96

19

97

19

98

19

99

20

00

20

01

20

02

20

03

14.00%

12.00%

10.00%

8.00%

6.00%

4.00%

19

84

19

85

19

86

19

87

19

88

19

89

19

90

19

91

19

92

19

93

19

94

19

95

19

96

19

97

19

98

19

99

20

00

20

01

20

02

20

03

BC AB MANITOBA SASKATCHEWAN

Legend: AGRI=CAP+FOR+SAA where CAP=Crop and Animal Production.

14.00%

12.00%

10.00%

8.00%

6.00%

4.00%

FINANCE

22.00%

21.00%

20.00%

19.00%

18.00%

17.00%

16.00%

15.00%

19

84

19

85

19

86

19

87

19

88

19

89

19

90

19

91

19

92

19

93

19

94

19

95

19

96

19

97

19

98

19

99

20

00

20

01

20

02

20

03

MANITOBA SASKATCHEWAN BC AB

6.00%

5.00%

4.00%

3.00%

2.00%

1.00%

0.00%

26.00%

24.00%

22.00%

20.00%

18.00%

16.00%

14.00%

12.00%

52

Figure 4-2: Real Output Shares for Ontario: 1984–2003

MANUFACTURING FINANCE

25.00%

24.00%

23.00%

22.00%

21.00%

20.00%

19.00%

18.00%

19

84

19

85

198

6

19

87

19

88

19

89

19

90

19

91

19

92

19

93

199

4

19

95

19

96

19

97

19

98

19

99

20

00

20

01

200

2

20

03

10

5

-10

-15

Figure 4.3: CIMV Index (in percentage): Western Provinces, 1984-2003


Alberta

0

-5

198

5

198

6

19

87

19

88

19

89

199

0

199

1

199

2

19

93

19

94

19

95

199

6

199

7

19

98

19

99

20

00

200

1

200

2

200

3

British Columbia

20

15

10

5

-15

-20

-25

0

-5

19

85

-10

19

86

19

87

19

88

19

89

19

90

19

91

19

92

19

93

19

94

19

95

19

96

19

97

19

98

19

99

20

00

20

01

20

02

20

03

-30

Manitoba

40

35

30

25

20

15

10

5

0

19

85

198

6

198

7

19

88

198

9

199

0

199

1

19

92

199

3

19

94

199

5

19

96

199

7

19

98

199

9

20

00

200

1

20

02

200

3

Saskatchewan

60

50

40

30

20

10

0

-10

19

85

-20

19

86

19

87

198

8

19

89

199

0

19

91

199

2

19

93

199

4

19

95

19

96

19

97

19

98

19

99

20

00

20

01

20

02

20

03

-30

54

Figure 4.4: CIMV Index (in percentage): Ontario, 1984-2003


Ontario

30

25

20

15

10

5

0

-5

-10

19

85

19

86

19

87

19

88

19

89

19

90

19

91

19

92

19

93

19

94

19

95

19

96

19

97

19

98

19

99

20

00

20

01

20

02

20

03

-15

-20

55

The Measurement of Output Instability in Western Canada By Kathleen Macaspac

The Measurement of Output Instability in Western Canada

By

Kathleen Macaspac

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∑

Ontario

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The Measurement of Output Instability in Western Canada By Kathleen Macaspac

The Measurement of Output Instability in Western Canada

By

Kathleen Macaspac

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Ontario

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