Economics Data and Statistics Analysis Assignment

1

Economics 2550 Assignment 1 Retrieval and Analysis of Economic Data

Dmitry Kosarev 201200805

(N.B the last number of my student number is 5, so my assigned province is

Ontario)

2

Contents

Q13

Q2..16

Q3..20

Q4..26

Q5..30

Q6..32

Appendices..33

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Question 1

1.1 Unemployment rates in Canada and the 10 provinces between 2006-2012

Year Canada NL PEI NS NB QC ON MB SK AB BC

2006 6.3 14.7 11 7.9 8.7 8.1 6.3 4.3 4.7 3.4 4.8

2007 6.0 13.5 10.3 7.9 7.5 7.2 6.4 4.4 4.2 3.5 4.3

2008 6.1 13.2 10.8 7.7 8.5 7.2 6.5 4.2 4.1 3.6 4.6

2009 8.3 15.5 12.0 9.2 8.8 8.5 9.0 5.2 4.8 6.6 7.7

2010 8.0 14.4 11.2 9.3 9.3 8.0 8.7 5.4 5.2 6.5 7.6

2011 7.5 12.7 11.3 8.8 9.5 7.8 7.8 5.4 5.0 5.5 7.5

2012 7.3 12.5 11.3 9.0 10.2 7.8 7.8 5.3 4.7 4.6 6.7

0

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2006 2007 2008 2009 2010 2011 2012

Pe

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Year

Unemployment rates between 2006-12

Canada

NL

PEI

NS

NB

QC

ON

MB

SK

AB

BC

4

The table above as well as the table on which is based on gives an indication that provinces in the same

geographic area have similar unemployment rates. For instance the prairies, (Alberta, Manitoba and

Saskatchewan) have the lowest rates of unemployment amongst the provinces whilst the Atlantic provinces

(Newfoundland and Labrador, Nova Scotia, New Brunswick, Prince Edward Island) have some of the highest

with Newfoundland and Labrador having the highest by a significant margin. Ontario, British Columbia and

Quebec have unemployment rates similar to each other although only Ontario and Quebec are direct

geographical neighbors. This suggests that the provinces can be divided into these geographic groups for

closer analysis as they may share similar economic problems and fundamentals besides just unemployment.

However as British Columbias economy is based on primary industries just like Albertas, Saskatchewans

and Manitobas it is better to group BC with those provinces rather than Ontario or Quebec. Both Quebec

and Ontario have a similarly diversified economy with little focus on resource extraction and a much larger

reliance on manufacturing and service industries making it more sensible to group them together for

subsequent data analysis.

Overall across the period unemployment in Canada rose which is generally true for most provinces as result

of the economic downturn that started in 2008. Before then the rates were heading downwards slightly for

most provinces. Newfoundland and Labrador has proven the exception with its unemployment rate having

decreased in the time period specified. The significant fluctuations however may be pointing to the

economic instability that an economy reliant on its resource industries faces even as overall this reliance may

had a net positive effect on the unemployment rate in NLs case. This can also be argued about Alberta which

also had a significant shift in its unemployment rate, first a dramatic increase and then a steady decrease

almost back to the initial rate in 2006. In comparison Ontario, despite having a diversified economy with a

much smaller reliance on primary industries, has experienced a similar increase in unemployment rate

without the corresponding decrease in the latter years of the period observed.

Canada NL PEI NS NB QC ON MB SK AB BC

Average 5.6 10.2 8.5 6.7 7.1 5.9 6.0 4.0 3.6 3.8 5.2

Median 7.2 13.0 11.2 8.7 8.9 7.8 7.7 5.0 4.7 4.6 6.4

Standard deviation

2.4 4.6 4.1 3.1 3.3 2.8 2.5 1.7 1.6 1.3 1.9

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

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Provinces

Average, Median and Standard Deviation of the unemployment rates

Average

Median

Standard deviation

5

The above conclusions can be supported by the data in the table above. The Atlantic provinces clearly have

the highest average rates of unemployment in the time range. The data also supports the conclusion that ON

and QC have very similar unemployment rates with the Prairie provinces and BC having average

unemployment rates below the national average justifying their classification into one group for subsequent

analysis. However the standard deviation results are harder to explain. ON has twice the standard deviation

of QC, while AB and BC have four and five times respectively the standard deviation of SK. These

discrepancies suggest that even within the three geographic groups and despite seemingly similar data,

significant differences in the economic structure and problems between the provinces are present.

6

1.2 Inflation rates in Canada and across the provinces between 1981 and 2012

CPI Index Values 1981-2012


1981 49.5 53.1 52.7 50.8 50.9 50.2 48.2 49 49.5 49.8 51.8

1982 54.9 58.5 57.8 55.6 55.6 56 53.3 53.3 54 55.4 57.3

1983 58.1 62.4 60.7 59.1 59.3 59.1 56.6 56.8 57.4 58.3 60.4

1984 60.6 65.2 63.3 61.7 62.3 61.5 59.4 58.9 59.8 59.8 62.8

1985 63.0 67.9 65.6 64.5 65.2 64.2 61.8 61.4 62 61.6 64.8

1986 65.6 69.9 67 66.5 67.5 67.3 64.6 64.1 63.7 63.7 66.7

1987 68.5 71.9 69.4 68.8 69.4 70.2 67.8 66.8 66.8 66.3 68.7

1988 71.2 73.5 71.9 71.2 71.8 72.8 71 69.6 69.8 68.1 71.2

1989 74.8 76.2 74.6 74.4 75.2 75.9 75.1 72.9 72.9 70.9 74.4

1990 78.4 79.5 78.4 78.2 78.7 79.2 78.7 76.2 76 75 78.4

1991 82.8 84.4 84.3 82.9 83.8 85 82.4 80.1 80 79.4 82.6

1992 84.0 85.3 85 83.5 84.3 86.6 83.2 81.2 80.8 80.6 84.8

1993 85.6 86.7 86.6 84.5 85.4 87.7 84.7 83.4 83.3 81.4 87.8

1994 85.7 87.8 86.4 85.5 85.9 86.6 84.7 84.6 84.8 82.6 89.5

1995 87.6 89 87.8 86.6 87.2 88.1 86.8 86.9 86.4 84.5 91.6

1996 88.9 90.4 89.4 88.2 88.5 89.5 88.2 88.8 88.1 86.4 92.4

1997 90.4 92.3 90.5 90 90.1 90.8 89.8 90.6 89.2 88.1 93.1

1998 91.3 92.5 90.1 90.6 90.6 92.1 90.6 91.8 90.4 89.2 93.4

1999 92.9 93.8 91.2 92.1 92.1 93.5 92.4 93.6 92 91.4 94.4

2000 95.4 96.6 94.9 95.3 95.1 95.8 95.1 95.9 94.4 94.5 96.1

2001 97.8 97.7 97.4 97.1 96.8 98 98 98.5 97.2 96.7 97.7

2002 100 100 100 100 100 100 100 100 100 100 100

2003 102.8 102.9 103.5 103.4 103.4 102.5 102.7 101.8 102.3 104.4 102.2

2004 104.7 104.8 105.8 105.3 104.9 104.5 104.6 103.8 104.6 105.9 104.2

2005 107 107.6 109.1 108.2 107.4 106.9 106.9 106.6 106.9 108.1 106.3

2006 109.1 109.5 111.6 110.4 109.2 108.7 108.8 108.7 109.1 112.3 108.1

2007 111.5 111.1 113.6 112.5 111.3 110.4 110.8 110.9 112.2 117.9 110

2008 114.1 114.3 117.5 115.9 113.2 112.7 113.3 113.4 115.9 121.6 112.3

2009 114.4 114.6 117.3 115.7 113.5 113.4 113.7 114.1 117.1 121.5 112.3

2010 116.5 117.4 119.5 118.2 115.9 114.8 116.5 115 118.7 122.7 113.8

2011 119.9 121.4 123 122.7 120 118.3 120.1 118.4 122 125.7 116.5

2012 121.7 123.9 125.5 125.1 122 120.8 121.8 120.3 123.9 127.1 117.8

The above table shows the Consumer Price Index for all items which is an indicator of the changes in

consumer prices experienced by the target population and its variation between 1981 and 2012. This data

uses 2002 as the base year meaning that its CPI is assigned the base value of 100. Using the CPI it is

relatively easy to calculate the yearly inflation. The detailed equations, sample calculations are listed in

Appendix B. The tables and descriptive graphs of the inflation rate data are on the following page.

7

Year Inflation rate Canada

Inflation rate NL

Inflation rate PEI

Inflation rate NS

Inflation rate NB

Inflation rate QC

Inflation rate ON

Inflation rate MB

Inflation rate SK

Inflation rate AB

Inflation rate BC

1981 10.91 10.17 9.68 9.45 9.23 11.55 10.58 8.78 9.09 11.24 10.62

1982 5.83 6.67 5.02 6.29

6.65

5.54 6.19 6.57 6.30 5.23 5.41

1983 4.30 4.49 4.28 4.4 5.06 4.06 4.95 3.7 4.18 2.57 3.97

1984 3.96 4.14 3.63 4.54 4.65 4.39 4.04 4.24 3.68 3.01 3.18

1985 4.13 2.95 2.13 3.10 3.53 4.83 4.53 4.40 2.74 3.41 2.93

1986 4.42 2.86 3.58 3.46 2.81 4.31 4.95 4.21 4.87 4.08 3.00

1987 3.94 2.23 3.60 3.49 3.46 3.70 4.72 4.19 4.49 2.71 3.64

1988 5.06 3.67 3.76 4.49 4.74 4.26 5.77 4.74 4.44 4.11 4.49

1989 4.81 4.33 5.09 5.11 4.65 4.35 4.79 4.53 4.25 5.78 5.38

1990 5.61 6.16 7.53 6.01 6.48 7.32 4.70

5.20 5.26 5.87 5.36

1991 1.45 1.07 0.83 0.72 0.60 1.88 0.97 1.37 1.00 1.51 2.66

1992 1.90 1.64 1.88 1.20 1.30 1.27 1.80 2.71 3.09 0.99 3.54

1993 0.12 1.27 -0.23 1.18 0.59 -1.25 0.00 1.44 1.80 1.47 1.94

1994 2.22 1.37 1.62 1.29 1.51 1.73 2.48 2.72 1.89 2.30 2.35

1995 1.48 1.57 1.82 1.85 1.49 1.59 1.61 2.19 1.97 2.25 0.87

1996 1.69 2.10 1.23 2.04 1.81 1.45 1.81 2.03 1.25 1.97 0.76

1997 1.00 0.22 -0.44 0.67 0.55 1.43 0.89 1.32 1.35 1.25 0.32

1998 1.75 1.41 1.22 1.66 1.66 1.52 1.99 1.96 1.77 2.47 1.07

1999 2.69 2.99 4.06 3.47 3.26 2.46 2.92 2.46 2.61 3.39 1.80

2000 2.52 1.14 2.63 1.89 1.79 2.30 3.05 2.71 2.97 2.33 1.66

2001 2.25 2.35 2.67 2.99 3.31 2.04 2.04 1.52 2.88 3.41 2.35

2002 2.80 2.90 3.50 3.40 3.40 2.50 2.70 1.80 2.30 4.40 2.20

2003 1.85 1.85 2.22 1.84 1.45 1.95 1.85 1.96 2.25 1.44 1.96

2004 2.2 2.67 3.12 2.75 2.38 2.30 2.20 2.70 2.20 2.08 2.02

2005 1.96 1.77 2.29 2.03 1.68 1.68 1.78 1.97 2.06 3.89 1.69

2006 2.20 1.46 1.79 1.90 1.92 1.56 1.84 2.02 2.84 4.99 1.76

2007 2.33 2.88 3.43 3.02 1.71 2.08 2.26 2.25 3.3 3.14 2.09

2008 0.26 0.26 -0.17 -0.17 0.27 0.62 0.35 0.62 1.04 -0.08 0.00

2009 1.84 2.44 1.88 2.16 2.11 1.23 2.46 0.79 1.37 0.99 1.34

2010 2.92 3.41 2.93 3.81 3.54 3.05 3.09 2.96 2.78 2.44 2.37

2011 1.5 2.06 2.03 1.96 1.67 2.11 1.42 1.60 1.56 1.11 1.12

Average 2.96 2.79 2.86 2.97 2.88 2.90 3.06 2.95 3.02 3.09 2.70

Median 2.25 2.35 2.63 2.75 2.11 2.11 2.46 2.46 2.74 2.57 2.20 Standard Deviation 1.50 1.38 1.50 1.45 1.58 1.64 1.59 1.35 1.27 1.47 1.40

8

This shows that while the inflation rates of the Atlantic provinces in Canada generally follow Canadas as a

whole, occasionally there are serious divergences such as the period between 1985 and 1988. PEI stands out

in this regard since it shows considerable divergence from both Canadas and of other Atlantic provinces in

its inflation rate in multiple occasions such as 1986, 1991, 1998 and 2000. However all the provinces have

similar averages and standard deviations.

-1.5-1

-0.50

0.51

1.52

2.53

3.54

4.55

5.56

6.57

7.58

8.59

9.510

10.511

11.5

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Year

Inflation rate of Atlantic provinces and Canada Canada

NL

PEI

NS

NB

0

0.5

1

1.5

2

2.5

3

3.5

Canada NL PEI NS NB

Pe

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ge r

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Geographic area

Average

Median

Standard Deviation

9

Both inflation rates in QC and ON stay close to the national rate however when they diverge they are on

opposite sides of the national rate as displayed by 1991, 1994 and to a smaller extent by 2000-1 and 2006-

7. This can be explained by the fact that ON and QC are the two largest economies in Canada so they

moderate each others impact on the national inflation rate. The averages and standard deviations are

similar, close to both the national rates as well as to those of the Atlantic provinces.

-2

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Inflation rates of QC and ON compared to Canada

Canada

QC

ON

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3.5

Canada QC ON

Pe

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Geographic area

Average

Median

Standard Deviation

10

Again the provinces follow the national trend with some exceptions. An important one is AB in 1983, 1987,

2002 and 2005-6. This also applies to BC to a lesser extent in 2001. 1993 is an interesting data point as all

provinces in this group had a noticeable and similar divergence with the national rate. On average however

BC has the lowest inflation rate with a significant difference to other provinces and the national rate while SK

has the lowest deviation.

Overall the 3 preceding graphs show that the provinces with larger economies, such as ON, AB and QC often

have an inflation rate that is different to the national rate. Smaller Atlantic provinces also exhibit these

differentials. An interesting point to note is that these do not usually occur within the same year. However

on average all provinces have inflation rates and standard deviation rates that converge on the average

national rate. This shows that any provincial divergences are only temporary and do not have a significant

impact on the overall convergence.

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Year

Inflation rates of the prairie provinces and BC compared to Canada

Canada

AB

MB

BC

SK

0

0.5

1

1.5

2

2.5

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3.5

Canada MB SK AB BC

Pe

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Geographic area

Average

Median

Standard Deviation

11

1.3 Nominal GDP for Canada and the 10 provinces between 1981 and 2010

(dollars x 1,000,000)

The following table and graphs present the nominal GDP of Canada and the 10 provinces over time in their 3

groups as well as their share historically of Canadas total nominal GDP.


1982 379859 5609 1153 9186 7052 85218 138741 14053 15008 56803 45024

1983 411386 5988 1356 10364 8046 91832 154682 15106 15969 58397 47477

1984 449582 6373 1389 11437 8818 100292 172842 16998 17031 62282 49840

1985 485714 6647 1445 12393 9373 107391 189125 18536 17926 66785 53540

1986 512541 7244 1630 13403 10462 117156 208460 19260 17772 57961 56547

1987 558949 7763 1737 14432 11572 128438 230778 20385 18195 60070 62515

1988 613094 8467 1911 15294 12438 140845 256441 22016 18850 63936 69408

1989 657728 8995 2059 16306 13128 148431 278791 23370 19977 67377 75582

1990 679921 9219 2169 16993 13458 153330 282834 24193 21227 73257 79350

1991 685367 9587 2255 17650 13647 155156 283094 24029 21393 72892 81849

1992 700480 9549 2345 18094 14038 158362 286493 24434 21220 74936 87242

1993 727184 9771 2471 18343 14693 162229 293405 24590 22928 81179 94077

1994 770873 10264 2521 18667 15286 170478 311096 25958 24480 88041 100512

1995 810426 10652 2662 19296 16380 177331 329317 26966 26425 92036 105670

1996 836864 10417 2823 19512 16626 180526 338173 28434 28944 98634 108865

1997 882733 10533 2800 20368 16845 188424 359353 29751 29157 107048 114383

1998 914973 11176 2981 21401 17633 196258 377897 30972 29550 107439 115641

1999 982441 12184 3159 23059 19041 210809 409020 31966 30778 117080 120921

2000 1076577 13922 3366 24658 20085 224928 440759 34057 33828 144789 131333

2001 1108048 14179 3431 25909 20684 231624 453701 35157 33127 151274 133514

2002 1152905 16457 3701 27082 21169 241448 477763 36559 34343 150594 138193

2003 1213175 18119 3798 28851 22366 250752 493081 37451 36653 170113 145642

2004 1290906 19407 3983 29853 23672 262761 516106 39748 40796 189743 157675

2005 1373845 21960 4096 31199 24716 272049 537383 41681 43996 219810 169664

2006 1450405 26064 4315 31644 25847 282505 560576 45173 45604 238886 182251

2007 1529589 29249 4543 33031 27044 295928 583946 48920 50863 255787 192117

2008 1603418 30785 4687 34519 27499 304479 587055 51575 65649 288700 199441

2009 1528985 24762 4778 34774 27920 304861 581635 51518 57995 240697 191863

2010 1624608 28192 5010 36352 29448 319348 612494 54257 63557 263537 203147

12

As is evident from this graph the nominal GDP of the Atlantic provinces is miniscule compared to the total

nominal GDP of Canada. A more useful analysis would be the variation of each provinces share of the

national nominal GDP. This not only allows a comparison over time of what the importance of each

provinces economy to the national total, but also to see the relative economic growth, making it easy to see

provincial economic growth relative to the national rate of economic growth. If it is increasing, this means

that the province is growing faster than Canada overall, while a decrease shows a negative gap between

national and provincial growth rate.

0

200000

400000

600000

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1000000

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No

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DP

in m

iilio

ns

of

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Year

Nominal GDP of Canada and the Atlantic provinces

Canada

NL

NS

NB

PEI

0.00

0.50

1.00

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2.00

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3.00

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Individual provinces' proportion of national nominal GDP expressed as a percentage

NL Proportion

PEI Proportion

NS Proportion

NB Proportion

13

The above graph and the table to the left give a

clear picture. While NLs and NS nominal growth

rate fluctuated the most, PEI stayed almost

constant based on the standard deviation values.

Overall NS has the largest economy out of the 4

while PEI has the smallest. However NS share decreased while NLs increased. NBs and PEI retained a

constant share throughout the period.

This undoubtedly indicates that the both ONs and QCs economies make up an important part of total national

nominal GDP rate.

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x m

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Year

Nominal GDP of Canada, ON and QC

0.0

5.0

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45.0

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QC and ON percentage rate of national nominal GDP

QC Proportion

ON Proportion

NL PEI NS NB

Average 1.44 0.32 2.40 1.92

Median 1.39 0.31 2.38 1.93

Standard variation

0.14 0.010 0.12 0.082

14

The above graph and left table shows that both ON and QC contribute

significantly to the national nominal GDP with QCs share decreasing over

the given period while ONs rising and then falling with the starting and

ending shares almost equal with changes being gradual rather than sudden

as indicated by the standard deviation values which are small compared to

the mean.

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No

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x 1

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National nominal GDP, Canada, Prairie provinces + BC

Canada

MB

SK

AB

BC

QC ON

Average 21.4 40.0

Median 21.6 40.6

Standard variation

1.02 1.37

15

Overall this shows that even though previous data

has shown similarity between the provincial

economies in this group both BC and AB contribute a

significantly larger proportion to the national GDP.

This suggests that they are also much larger in size

compared to the other economies in this group.

However while BCs data has a small standard deviation, showing a stability in proportion and size, ABs data

indicates that its economy has undergone significant boom and bust cycles. The large standard deviation

value displays that the proportion AB contributes has fluctuated significantly over the time period of the

data, rising substantially when AB was experiencing a boom and also shrinking substantially when BC was

experiencing a bust. This may be related to the provinces significant dependence on the oil sands industry

and its cyclical economic nature.

0.0

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Year

Proportions of the prairie provinces + BC of the total nominal GDP

AB Proportion

BC Proportion

MB Proportion

SK Proportion

MB SK AB BC

Average 3.40 3.34 13.1 12.1

Median 3.37 3.20 13.1 12.2

Standard variation

0.189 0.273 1.91 0.523

16

Question 2

a) Real GDP data for Canada and Ontario

*All GDP data is to be multiplied by 1,000,000 dollars.

Year National CPI Canada nominal GDP Real GDP Ontario Nominal GDP Ontario Real GDP

1982 54.9 379859 691911 138741 252716

1983 58.1 411386 708065 154682 266234

1984 60.6 449582 741884 172842 285218

1985 63 485714 770975 189125 300198

1986 65.6 512541 781313 208460 317774

1987 68.5 558949 815984 230778 336902

1988 71.2 613094 861087 256441 360170

1989 74.8 657728 879316 278791 372715

1990 78.4 679921 867246 282834 360758

1991 82.8 685367 827738 283094 341901

1992 84 700480 833905 286493 341063

1993 85.6 727184 849514 293405 342763

1994 85.7 770873 899502 311096 363006

1995 87.6 810426 925144 329317 375933

1996 88.9 836864 941354 338173 380397

1997 90.4 882733 976475 359353 397514

1998 91.3 914973 1002161 377897 413907

1999 92.9 982441 1057525 409020 440280

2000 95.4 1076577 1128487 440759 462012

2001 97.8 1108048 1132973 453701 463907

2002 100 1152905 1152905 477763 477763

2003 102.8 1213175 1180131 493081 479651

2004 104.7 1290906 1232957 516106 492938

2005 107 1373845 1283967 537383 502227

2006 109.1 1450405 1329427 560576 513819

2007 111.5 1529589 1371829 583946 523718

2008 114.1 1603418 1405274 587055 514509

2009 114.4 1528985 1336525 581635 508422

2010 116.5 1624608 1394513 612494 525746

17

The data and graphs overall show that during 1982-1990 the rate of change of Ontario real GDP was very

similar to the national rate. After that, Ontarios real GDP became less responsive to the rate of change of

Canadas real GDP, rising and decreasing at a slower rate. This is shown by the slope of the curves, which is

steeper for Canada compared to Ontario. This trend becomes more pronounced after 2000 with the 2008

recession causing both economies to decrease and then rebound, with Ontarios however decreasing and

rebounding at a significantly smaller magnitude. A graph of the growth rate of Canada and Ontario over the

same time frame would show this more clearly.

0

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x 1

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Canada and Ontario Real GDP between 1982-2010

Canada Real GDP

Ontario Real GDP

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P x

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rs

Year

Real GDP of Canada and Ontario between 1982-2010

Canada Real GDP

Ontario Real GDP

18

b)

Year Rate of real GDP growth for Canada, %

Rate of real GDP growth for Ontario, %

1982 2.3 5.3

1983 4.8 7.1

1984 3.9 5.3

1985 1.3 5.9

1986 4.4 6.0

1987 5.5 6.9

1988 2.1 3.5

1989 -1.4 -3.2

1990 -4.6 -5.2

1991 0.7 -0.2

1992 1.9 0.5

1993 5.9 5.9

1994 2.9 3.6

1995 1.8 1.2

1996 3.7 4.5

1997 2.6 4.1

1998 5.5 6.4

1999 6.7 4.9

2000 0.4 0.4

2001 1.8 3.0

2002 2.4 0.4

2003 4.5 2.8

2004 4.1 1.9

2005 3.5 2.3

2006 3.2 1.9

2007 2.4 -1.8

2008 -4.9 -1.2

2009 4.3 3.4

Average 2.6 2.7

Median 2.8 3.2

Standard deviation

1.9 2.5

Q1 1.8 0.5

Q3 4.3 5.3

Min -4.9 -5.2

Max 6.7 7.1

19

The above graph delves deeper into the details of how the economic growth in Ontario diverged from the

economic growth of Canada. Between 1982 and 1990, Ontario either grew faster than Canada or contracted

at a larger rate. This trend was then ambiguous at best between 1991 and 2001 where first Canada

rebounded more strongly from the 1989-90 recession, followed by years of faster Ontario growth during

1996-98 and 2001. From 2001 Canada has unequivocally had larger absolute rates of change, both positive

between 2001 and 2007 and negative in 2008. However a look at the table above the graph shows that the

average rate of increase is almost identical between Canada and Ontario. However both the median and

standard deviation are larger for Ontario, suggesting that it has experienced more turbulence in its economic

growth.

This is also confirmed by the box-and-whisker plot. Although the range between the maximum and minimum

values is similar in magnitude, Canada has a smaller spread of values in its interquartile range than Ontario.

Even though its upper quartile is lower than Ontarios its lower quartile is higher also hinting at a more lower

but more stable and growth rate without such pronounced booms and busts like Ontario.

-15

-10

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Time

Rate of real GDP growth, Canada and ON, 1982-2009

Rate of real GDP growth forOntario, %

Rate of real GDP growth forCanada, %

-6

-4

-2

0

2

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8

10

Rate of real GDP growth for Canada Rate of real GDP growth for Ontario

Pe

rce

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ge r

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of

chan

ge o

f re

al G

DP

20

Question 3

3. To fit a line the method of least squares will be used.

For this question the equations will be listed here instead of the appendix as the question asks for the

equations specifically.

yt = a + bt

3.1.1 Canadas Real GDP for 1982-2009

Year Real GDP (Yi-Ybar) ti-tbar (ti-tbar)^2

(Yi-Ybar)(ti-tbar)

1982 691911 -307573.8 -13.5 182.25 4152246.11

1983 708065 -291419.8 -12.5 156.25 3642747.32

1984 741884 -257600.8 -11.5 132.25 2962409.04

1985 770975 -228509.8 -10.5 110.25 2399352.75

1986 781313 -218171.8 -9.5 90.25 2072631.96

1987 815984 -183500.8 -8.5 72.25 1559756.68

1988 861087 -138397.8 -7.5 56.25 1037983.39

1989 879316 -120168.8 -6.5 42.25 781097.11

1990 867246 -132238.8 -5.5 30.25 727313.32

1991 827738 -171746.8 -4.5 20.25 772860.54

1992 833905 -165579.8 -3.5 12.25 579529.25

1993 849514 603951.5 -2.5 6.25 -1509878.75

1994 899502 -99982.8 -1.5 2.25 149974.18

1995 925144 -74340.8 -0.5 0.25 37170.39

1996 941354 -58130.8 0.5 0.25 -29065.39

1997 976475 -23009.8 1.5 2.25 -34514.68

1998 1002161 2676.2 2.5 6.25 6690.54

1999 1057525 58040.2 3.5 12.25 203140.75

2000 1128487 129002.2 4.5 20.25 580509.96

2001 1132973 133488.2 5.5 30.25 734185.18

2002 1152905 153420.2 6.5 42.25 997231.39

2003 1180131 180646.2 7.5 56.25 1354846.61

2004 1232957 233472.2 8.5 72.25 1984513.82

2005 1283967 284482.2 9.5 90.25 2702581.04

2006 1329427 329942.2 10.5 110.25 3464393.25

2007 1371829 372344.2 11.5 132.25 4281958.46

2008 1405274 405789.2 12.5 156.25 5072365.18

2009 1336525 337040.2 13.5 182.25 4550042.89

21

Slope 25790

Intercept 625525

Y bar 999484.8

t-bar 13.5

Sum of (ti-tbar)^2 1827

Sum of (Yi-Ybar)(ti-tbar) 47118878

Graph of linear fit

y = 25790x + 625525

0

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DP

x 1

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Year

Linear fit of Canada's Real GDP

22

3.1.2 Ontarios real GDP for 1982-2009

Year Real GDP

(Yi-Ybar) ti-tbar (ti-tbar)^2

(Yi-Ybar)(ti-tbar)

1982 252716 -146870 -13.5 182.25 1982749

1983 266234 -133352 -12.5 156.25 1666904

1984 285218 -114368 -11.5 132.25 1315235

1985 300198 -99388.3 -10.5 110.25 1043577

1986 317774 -81812.3 -9.5 90.25 777216.9

1987 336902 -62684.3 -8.5 72.25 532816.6

1988 360170 -39416.3 -7.5 56.25 295622.3

1989 372715 -26871.3 -6.5 42.25 174663.5

1990 360758 -38828.3 -5.5 30.25 213555.7

1991 341901 -57685.3 -4.5 20.25 259583.9

1992 341063 -58523.3 -3.5 12.25 204831.6

1993 342763 -56823.3 -2.5 6.25 142058.3

1994 363006 -36580.3 -1.5 2.25 54870.45

1995 375933 -23653.3 -0.5 0.25 11826.65

1996 380397 -19189.3 0.5 0.25 -9594.65

1997 397514 -2072.3 1.5 2.25 -3108.45

1998 413907 14320.7 2.5 6.25 35801.75

1999 440280 40693.7 3.5 12.25 142428

2000 462012 62425.7 4.5 20.25 280915.7

2001 463907 64320.7 5.5 30.25 353763.9

2002 477763 78176.7 6.5 42.25 508148.6

2003 479651 80064.7 7.5 56.25 600485.3

2004 492938 93351.7 8.5 72.25 793489.5

2005 502227 102640.7 9.5 90.25 975086.7

2006 513819 114232.7 10.5 110.25 1199443

2007 523718 124131.7 11.5 132.25 1427515

2008 514509 114922.7 12.5 156.25 1436534

2009 508422 108835.7 13.5 182.25 1469282

Slope 9790

Intercept 257636

Y bar 399586

t-bar 13.5

Sum of (ti-tbar)^2 1827


23

Graph of linear fit for Ontarios rate of unemployment

Comparing the linear trends for the real GDP of Canada and Ontario yields some similarities. Both trend up

meaning that over the whole period real GDP has increased nationally and in Ontario. However the trend for

Canada has both a higher slope and intercept, showing that Canadas GDP increased at a higher rate and that

its starting real GDP at the beginning of the period (ie 1982) was higher than Ontarios.

y = 9789.7x + 257636

0

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Real GDP linear fit

24

3.2.1 Canadian unemployment rate for 2006-12

Year Rate % Time Yi-Ybar ti-tbar (ti-tbar)^2 (yi-ybar)*(ti-tbar)

2006 6.3 0 -0.8 -3.5 12.25 2.8

2007 6 1 -1.1 -2.5 6.25 2.75

2008 6.1 2 -1 -1.5 2.25 1.5

2009 8.3 3 1.2 -0.5 0.25 -0.6

2010 8 4 0.9 0.5 0.25 0.45

2011 7.5 5 0.4 1.5 2.25 0.6

2012 7.3 6 0.2 2.5 6.25 0.5

2012 7.3 7 0.2 3.5 12.25 0.7

Slope 0.2821

Intercept 5.9429

Y bar 7.07

t-bar 3

Sum of (ti-tbar)^2 29.75


Linear fit of Canadas rate of unemployment

y = 0.2821x + 5.9429

0

1

2

3

4

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6

7

8

9

2006 2007 2008 2009 2010 2011 2012

Rat

e o

f u

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mp

loym

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t %

Year

Rate of unemployment linear fit

25

3.2.2 Ontarios rate of unemployment

Year Rate % Time Yi-Ybar ti-tbar (ti-tbar)^2

(yi-ybar)*(ti-tbar)

2006 6.3 0 -0.8 -3.5 12.25 2.8

2007 6.4 1 -0.7 -2.5 6.25 1.75

2008 6.5 2 -0.6 -1.5 2.25 0.9

2009 9 3 1.9 -0.5 0.25 -0.95

2010 8.7 4 1.6 0.5 0.25 0.8

2011 7.8 5 0.7 1.5 2.25 1.05

2012 7.8 6 0.7 2.5 6.25 1.75

2012 7.8 7 0.7 3.5 12.25 2.45

Slope 0.3393

Intercept 6.1429

Y bar 7.5

t-bar 3

Sum of (ti-tbar)^2 29.75

Sum of (Yi-Ybar)(ti-tbar) 8.1

Linear fit of Ontarios rate of unemployment

Comparing the unemployment rate linear trends for Canada and Ontario yields some similarities. Both trend

upwards, showing that the rate of unemployment has increased overall over the period for both. Ontarios

has a higher slope meaning its rate has increased at a higher rate than the national rate and so is its intercept

signifying that Ontarios unemployment rate at the start of the period (ie 2006) was higher than the national

rate.

y = 0.3393x + 6.1429

0

2

4

6

8

10

2006 2007 2008 2009 2010 2011 2012

Un

em

plo

yme

nt,

%

Year

Linear fit of Ontario's rate of unemployment

26

Question 4

4.1.1 Output gaps for Canadas Real GDP

-8.00%

-6.00%

-4.00%

-2.00%

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

19

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09

Ou

tpu

t G

ap

Year

Canada Output Gap Year Yp Output

gap

1982 625525 10.61%

1983 651315.3 8.71%

1984 677105.6 9.57%

1985 702895.9 9.69%

1986 728686.2 7.22%

1987 754476.5 8.15%

1988 780266.8 10.36%

1989 806057.1 9.09%

1990 831847.4 4.26%

1991 857637.7 -3.49%

1992 883427.999 -5.61%

1993 909218.299 -6.57%

1994 935008.599 -3.80%

1995 960798.899 -3.71%

1996 986589.199 -4.59%

1997 1012379.5 -3.55%

1998 1038169.8 -3.47%

1999 1063960.1 -0.60%

2000 1089750.4 3.55%

2001 1115540.7 1.56%

2002 1141331 1.01%

2003 1167121.3 1.11%

2004 1192911.6 3.36%

2005 1218701.9 5.36%

2006 1244492.2 6.82%

2007 1270282.5 7.99%

2008 1296072.8 8.43%

2009 1321863.1 1.11%

27

4.1.2 Output gaps for Ontarios Real GDP

4.1.3 Conclusions

Comparing Ontarios and Canadas output gaps yields several resemblances . At the beginning of the period

in 1982, Ontario started at a slightly positive output gap while Canada had a significantly positive output.

However during 1982-1989 both had a positive output gap with Ontarios rising rapidly to a percentage

higher than Canadas while Canadas hovered around 10%, decreasing slightly and then bouncing back. At a

such a positive gap both Ontario and Canada are overusing their resources and capital, such as by making

their workers work overtime. This is often a sign of economic growth at a higher rate than the natural rate,

pointing at an economic boom. However at such a large output gap, domestic supply is unable to meet

demand and the number of imports tends to increase. Inflationary pressures are also likely to arise as

peoples incomes rise and so does their demand for goods. If businesses are unable to expand production

-10.00%

-5.00%

0.00%

5.00%

10.00%

15.00%

20.00%

19

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Ou

tpu

t G

ap

Year

Ontario Output Gap Year Yp Output

Gap

1982 257636 -1.91%

1983 267425.7 -0.45%

1984 277215.3 2.89%

1985 287005 4.60%

1986 296794.6 7.07%

1987 306584.3 9.89%

1988 316373.9 13.84%

1989 326163.6 14.27%

1990 335953.2 7.38%

1991 345742.9 -1.11%

1992 355532.6 -4.07%

1993 365322.2 -6.18%

1994 375111.9 -3.23%

1995 384901.5 -2.33%

1996 394691.2 -3.62%

1997 404480.8 -1.72%

1998 414270.5 -0.09%

1999 424060.1 3.82%

2000 433849.8 6.49%

2001 443639.5 4.57%

2002 453429.1 5.37%

2003 463218.8 3.55%

2004 473008.4 4.21%

2005 482798.1 4.02%

2006 492587.7 4.31%

2007 502377.4 4.25%

2008 512167 0.46%

2009 521956.7 -2.59%

28

sufficiently quickly, then more and more money will be chasing the same amount of goods, causing increases

in prices.

After 1989 this trend of positive output gaps was reversed dramatically. 1990 saw a significant decrease in

the percentage rate of the positive output gap for both Canada and Ontario with both halving in size. Ontario

experienced a negative output gap between 1991 and 1997, peaking at -6.30 in 1993. Canada saw a longer

period of negative output gaps, between 1991 and 1998, with a peak of -6.58 in 1993 as well. Both Canada

and Ontario saw a consistent increase in the negative output gap until 1993 with 1994-96 showing little

change. Ontario then rebounded to a real GDP almost equal to its potential GDP in 1998 while Canada

reached this point in 1999. What this shows this that during this period Canada experienced a period where

resources were underused. This suggests that there was decreasing demand which could be a sign of a

recession. Recessions occur when economic growth becomes negative or where Real GDP decreases over a

period of time. This seems to be the case for this period. Canada took one more year than Ontario to reach

the level of its potential real GDP, indicating that Ontario started to experience another economic boom one

year before many other provinces, even though Ontario experienced a downturn for the same amount of

time as Canada, ie around 1991-1993.

At the year 2000 both Canada and Ontario saw a spike in their output gap, with Ontarios being almost

double that of Canadas (6.50% vs 3.55%). However while Ontarios gap trended along the 5% mark between

2000 and 2007, Canadas dropped consistently between 2000-3 and then increased continuously until 2008.

This could reflect that Ontario emerged relatively unscathed from the dot-com bubble and its burst while

Canada as a whole was impacted more severely. Canada rebounded very strongly from this and between

2005-8 its positive output gap was higher than Ontarios. However while Ontarios and Canadas output gap

fell to almost zero, this took two years for Ontario, while Canadas plummeted rapidly from above 8%. This

shows that the 2008 recession impacted Ontario earlier than Canada but with a smaller impact, perhaps

reflecting the bust other provincial economies were experiencing, which is usually more pronounced in

resource dependent economies such as Albertas and NLs.

4.2.1 Unemployment gaps in Canada between 2006 and 2012.

-10.00%

-5.00%

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

2006 2007 2008 2009 2010 2011 2012

Un

em

plo

yme

nt

Gap

Year

Canada Unemployment Gap Year Ep Unemployment

Gap

2006 5.9 6.01%

2007 6.2 -3.61%

2008 6.5 -6.26%

2009 6.8 22.25%

2010 7.1 13.13%

2011 7.4 1.99%

2012 7.6 -4.39%

29

4.2.2 Unemployment gaps in Ontario between 2006 and 2012.

4.2.3 Conclusions

The unemployment gaps for both Ontario and Canada are remarkably similar. This could be explained by the

fact that Ontario contains approximately 40% of Canadas total population and so can be expect to

contribute around 40% of the total number of unemployed. This will impact the national unemployment rate

quite significantly . The overall shape of the graph is almost identical with some of the points being higher or

lower. Overall between 2006-8 the unemployment rate trends close to the natural trend. There is a massive

spike in 2009, where Ontario and Canada experienced unemployment 25.7% and 22.25% higher respectively

than the natural rate. This may be the result of large lay-offs in the wake of the 2008-9 recession. During

2010-12 the unemployment gap surged back towards the natural rate. Conclusions overall may not be as

reliable as the natural trend is derived from fewer data points unlike the Real GDP and output gap data.

-10.0%

-5.0%

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

2006 2007 2008 2009 2010 2011 2012U

ne

mp

loym

en

t G

ap

Year

Ontario Unemployment Gap Year Ep Unemployment

Gap

2006 6.14 2.6%

2007 6.48 -1.3%

2008 6.82 -4.7%

2009 7.16 25.7%

2010 7.50 16.0%

2011 7.84 -0.5%

2012 8.18 -4.6%

30

Question 5

5.1 Graph of Canadas unemployment rate and output gaps vs time

5.2 Graph of Ontarios unemployment rate and output gaps vs time

5.3 Conclusions

Both graphs somewhat similar shapes across the 4 years. Certain conclusions can be made although these

are without a high degree of confidence since only 4 coinciding data points for the unemployment rate and

output gap rate have been used. Ontarios graph shows that in the immediate pre-recession years, 2006 and

2007 both rates converged. 2008 saw a drastic decrease in the output gap while unemployment rate saw

minimal change. 2009 saw a similar change in the output gap as in the previous year while the

unemployment rate increased at a similar rate. Overall this makes it seem that inversely proportional

although not perfectly so. 2009 clearly shows this relationship while 2008 suggests that a change in the rate

of the output gap affects the unemployment rate but that a period of time is necessary for the

unemployment rate to change. This makes economic sense. A decrease in the output gap suggests that the

GDP growth is slowing or even decreasing. If it is truly decreasing then, fewer products will be made and

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

2006 2007 2008 2009

Pe

rce

nta

ge r

ate

Year

Canada Unemployemnt Rate and Output Gap 2006-2009

CanadaUnemployment rate

Canada Output Gap

-4.00

-2.00

0.00

2.00

4.00

6.00

8.00

10.00

2006 2007 2008 2009

Pe

rce

nta

ge r

ate

Year

Ontario Unemployemnt Rate and Output Gap 2006-2009

Ontariounemployment rate

Ontario output Gap

Year Canada unemployment rate

Canada Output Gap

2006 6.3% 4.31% 2007 6.0% 4.25% 2008 6.1% 0.46% 2009 8.3% -2.59%

Year Ontario unemployment rate

Ontario Output Gap

2006 6.30% 4.31%

2007 6.40% 4.25%

2008 6.50% 0.46%

2009 9.00% -2.59%

31

fewer resources such as labor are needed to produce them. Since labor is a factor of production that is the

easiest to reduce the use of in the short term, they would be the first factor of production of which the usage

would decrease. This would naturally lead to higher unemployment rates. Some time is needed to elapse for

firms to realize that there is less demand for their products and to decide to reduce their labor costs by

laying off workers. This also makes sense considering the context of the years used for the graphs. In 2008-

2009 there indeed was a decrease in GDP due to the global recession which led to a significant increase in

unemployment. The data from the Canada graph does not completely support these conclusions however it

does confirm the inverse relationship present. More data would be needed to confirm this relationship

however.

32

Question 6

Okuns Law states there is a relationship between output and unemployment gaps. As the unemployment

gap increases by 1% the output gap will increase by %.

Year Canada unemployment gap

Canada Output Gap

Year Ontario unemployment gap

Ontario Output Gap

2006 6.01% 6.82%

2006 2.60% 4.31%

2007 -3.61% 7.99%

2007 -1.30% 4.25%

2008 6.26% 8.43%

2008 -4.70% 0.46%

2009 22.25% 1.11%

2009 25.70% -2.59%

%Output gap = x %Cyclical unemployment where cyclical is unemployment above the natural rate of

unemployment. In other words cyclical unemployment is the unemployment gap.

where:

Y is actual output

Y* is potential output

u is actual unemployment

is the natural rate of unemployment

is a constant derived from regression to show the link between deviations from natural output and natural

unemployment.

The equation is in a linear structure with yi = % output gap and xi = unemployment gap. A simple linear

regression model has the form yi = 0 + ixi but the 0 is not readily apparent from Okuns Law.

Equation for Canada: Output gap = -30%(unemployment rate) + 8.4%

Equation for Ontario: Output gap = -17.5%(unemployment rate) + 2.6%

From the equations it is possible to see that Ontarios output rate is less sensitive to changes in

unemployment gaps and by extension to changes in unemployment than Canadas.

Sxx 1.42%

Sxy 0.22%

Sx 7.73%

Sy 6.09%

Slope -29.77%

Intercept 8.39%

Sxx 1.72%

Sxy -0.16%

Sx 5.58%

Sy 1.61%

Slope -17.50%

Intercept 2.58%

33

Appendices

Appendix A - CANSIM Series Labels

Table 109-5324 Unemployment rate, Canada, provinces and health regions (2013 boundaries), annual

(percent), 2006-2012

Table 384-0013 Selected economic indicators, provincial economic accounts, annual (dollars unless

otherwise noted), 1981-2010

Table 326-0021 Consumer Price Index (CPI), 2009 basket, annual (2002=100), 1981-2012

Appendix B Equations and Calculations

B.1 Inflation Calculation

A year is taken as the base year. It is represented by A while the immediately following year is B. The CPI

value from the second year or year B is subtracted from the CPI of the base year or A. This value is then

divided by the base year CPI value with the decimal then multiplied by 100 to give the percentage increase.

((B - A)/A)*100

Sample Calculation:

Year Canada CPI

1981 49.5

1982 54.9

Inflation rate for 1981: ((54.9-49.5)/49.5) * 100 = 10.91% It is 1981 since the CPI data reported is typically

reported for the start of every year, allowing the calculation of the inflation rate for the year that has just

ended.

B.2

Arithmetic Mean

Simply take the sum of all the values in a data series and then divide by the number of data points.

Sample calculation:

1/29(1.48+1.46+1.42+1.37+1.41+1.39+1.38+1.37+1.36+1.40+1.36+1.34+1.33+1.31+1.24+1.19+1.22+1.24+1.2

9+1.28+1.43+1.49+1.50+1.60+1.80++1.91+1.92+1.62+1.74) = 1.44

B.3 Standard Deviation

The standard deviation is found by taking the square root of the average of the squared differences

of the values from their average value.

34

Sample calculation will use data from sample calculation for arithmetic mean.

sqrt((1.48-1.44)2+(1.46-1.44)2+(1.421.37)2+.(1.92-1.44)2+(1.62-1.44)2+(1.74-1.44)2)/29) = 0.144

B.4 Calculating Real GDP using Nominal GDP and deflator (implicit price index)

Real GDP for a given year, in relation to a "base" year, is computed by multiplying the nominal GDP for a

given year by the ratio of the GDP price deflator in the base year to the GDP price deflator for the given year.

The GDP deflator is an economic metric that converts output measured at current prices into constant-dollar

GDP. This includes prices for business and government goods and services, as well as those purchased by

consumers. This calculation shows how much a change in the base year's GDP relies upon changes in the

price level. The GDP deflator used for this is the CPI index where 2002 prices are set to 100 which takes the

role of the base year.

Sample calculation

Real GDP: Nominal GDP * (100/60.4)

$379859 * (100/ 54.9) = $691911

B.5 Calculating Quartiles

First the data must be ordered from smallest value to largest.

Qn = n/100 * number of data points.

Q1 = 0.25 * 11 = 2.75 so use 3rd value in ordered array as Q1 which is -1.4.

Q3 = 0.75*11 = 8.25 so use 8th value in ordered array as Q3 which is 1.8.

B.6 Calculating the output gap

First the linear trend for a graph must be used to calculate the potential output or unemployment at a time.

The actual value at that time is then subtracted from that potential value to produce a difference that is

called an output gap.

Year Implicit price index

Nominal GDP (millions of dollars)

1982 54.9 379859

-4.9

-4.6

-1.4

0.4

0.7

1.3

1.8

1.8

1.9

2.1

2.3

35

Sample Calculation

Equation for potential:

Yp=1115573.89+33353.75t

At time =1 , Yp = 1115574 but the actual value is 1120146.

Output gap = ((1120146-1115574)/1115574) * 100 = 0.410%

B.7 Calculating correlation coefficients

sx = arithmetic mean of x

sy = arithmetic mean of y

sxx = Sum (xi2) / n where n = number of observations

sxy = sum(xi*yi) / n

b1 = the estimated slope

= (sxy-sxsy)/(sxx-(sx)^2)

Intercept = (sxxsy sxysx)/(sxx-(sx)^2)

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Economics Data and Statistics Analysis Assignment