ANNOUNCEMENT #1 Third Quiz. 10% of Course Grade October 26th 30 MC questions. Lectures 6&7. Contingency Tables. Index Numbers. No make-ups. Don’t miss

ANNOUNCEMENT #1

Third Quiz. 10% of Course GradeOctober 26th

30 MC questions.Lectures 6&7.

Contingency Tables.Index Numbers.

No make-ups.Don’t miss it.

2013=100Index Numbers and Ratios

One of the most common types of quantitative tools, seen in many types of geographic data.

Examples are percentages, Consumer Price Index (CPI), stock indices such as TSX, NASDAQ, Location Quotients (LQ), Gini coefficients, demographic indces such as birth

and death rates, etc.

Just about any data can be converted to indices or ratios, and you can be very creative with building them.

Allows for comparison of datasets and/or growth rates between different datasets.

Index Numbers and Ratios

Consumer Price Index:Agency ‘Purchases’ a ‘shopping cart’ of goods and services,

then uses the cost of them as a base for measuring increases in prices of the same shopping cart at other times.

Stock Indices (TSX, NASDAQ, etc):Same as CPI – a ‘portfolio’ of stocks are valued at one point in

time, then re-valued and compared at other points in time.Big Mac Index:

Developed by The Economist magazine, this tongue in cheek but surprisingly accurate index compares the Purchasing

Power Parity of currencies in one nation to another – I.E. are they over-valued.

Ceridian-UCLA Pulse of Commerce Index:Monitors the purchase of diesel fuel by truckers using credit

and debit card swipes, as an indicator of the flow of raw materials, finished and semi finished products.

Index Numbers – Some Examples

1. Pick a selection of stocks (the Dow Industrials has 30, the TSX Composite has 100).

2. Add up their values, then either use that raw value or ‘weight’ by some measure or convert to a base 100 index.

3. Recalculate hourly, daily, weekly, etc and that’s that.4. Usually never ‘re-based’ (started again), hence TSX,

Dow, Hang Seng index numbers of 12,000+.

Stock indices can be based on value of the stocks or market capitalization or growth etc.

They measure general trend of the markets or specialized stocks such as the NASDAQ tech stocks.

How its done – stock indices

What the Dow(s) Jones looks like.

What the S&P(s) looks like.

Note the “dot.com” spike around 2000 as recorded by the NASDAQ. Also note that

S&P500 is more heavily weighted with tech stocks.

What it looks like plotted

The Big Mac Index1. Divide the price of a Big Mac in one country by the price in another (create the index number).

2. Compare that index number with the exchange rate between the two countries.

3. If it is lower then the currency of the first country is undervalued compared to the second; if it is

higher, then it is overvalued.

U.S.ArgentinaAustraliaBrazilU.K. (underpriced currency)Canada (overpriced currency)

Index created from truckers’ purchases of

diesel fuel; used as an indicator of

commerce and hence health of the

economy.

Grey line actual.Blue line MA3

(moving average period 3.

http://www.blytic.com/Player.aspx?key=c36b8092f2af42d4aec06e5d4525454c

Red line is Case-Schiller Composite Home Price Index.

Blue line is the Ceridian Pulse of Commerce MA3

index.

http://www.blytic.com/Player.aspx?key=c36b8092f2af42d4aec06e5d4525454c

Examples of Index Numbers Graphed.

U.K. consumer prices index.Note the relative increase in oil

and gas prices.

U.K. Value of construction index.Note the 2008 financial crisis.

How To Live With Percentages…

This is a test.Assume that you are asked to cut the price of a $100 dress by 25%, then raise the price by 25%.

How much would the dress now cost?

If you said $100, don’t go shopping for dresses.

If you said $93.75 you can probably make some money off the other person.

This is what it looks like:$100 – 25% = $75

$75 + 25% = $93.75

Moral: even calculating percentages can be tricky.

How To Lie With Percentages…

…Or How to Pick Your TruthConsider the following:

The city increases the your property tax rate from 3% to 5%. So by how much did it

increase?

The answer is: by how much would you like it to have increased?

This is not a trick question, but there is a trick to picking which truth makes your case sound

better – and the “other” person’s sound worse.

A Tale of Two Percent

If you are the city:“We only increased the property tax by 2%.”

(The absolute difference between 5% and 7%).

If you are the tax payer association:“The government increased our property tax by

67%!”(The percentage change between 5 and 7).

If you are a homeowner, which would you think is the most accurate interpretation because they are

both correct?

Have you heard this one?

Boss walks into your office and says:“I’m giving everyone in the company a 10% pay

raise!”

Your response is:

a. “Wow! Thanks! That’s an extra $8,000 a year! I’m so grateful!”

b. “What? You’re kidding right? Thanks a lot. I get $8K and you get $80K.”

Or this one?Toronto growth rate, 2006-2011 = 8.5%

Ho-hum.Stouffville growth rate, 2006-2011 = 100.5%

Holy Cow!Stouffville’s growth rate is almost 12 times that of

Toronto!

Stouffville growth rate, 2006-2011 = 12,475 people.Ho-hum.

Toronto growth rate, 2006-2011 = 400,433 people.Holy Cow!

Toronto’s growth rate is over 32 times that of Stouffville!

More Fun With NumbersHow much is 12%?(How much would you like it to be?)

Growth or Not And By How Much?The answer is not 12%.

First there is inflation/deflation.

Second, there is population change.

Third, there are issues about comparability of:the variables/units:apples or oranges?

litres or kilos?dollars or yen?

differences or magnitudes?time scales?

Fourth, there are components to a growth value.

Start with a Simple Question

Should you measure prosperity in income or wages?

Huh?

Has income increased? Yes, much more for more for rich people, but overall yes. All the trend lines are going up.

Highest

Lowest

Let’s try again.Has income increased? Yes for sure. Growth rates have all gone up, much more for more

for rich people for sure.

… But this time we’ll ask the question slightly differently:Has income increased if its measured with wages?

The subtlety here is that income measures what the household brings in regardless of the number of hours

needed to do so.

Wages measures how many hours you need to work to earn that income.

So your income can go up but if the number of hours needed to earn it goes up as well then how much better

off are you?

Once Again…

U.S. Male Hourly Wage 1979-2009

Apparently not much, if at all.Wages have not increased for lower income groups while

they have quite considerably for upper income groups.

19611965

19691973

19771981

19851989

19931997

20012005

2009$100.00

$1,000.00

$10,000.00

$100,000.00

GDP Per Capita $US Constant 2005

Canada High Income Low Income Middle Income World

Per C

apita

$U

S Co

nsta

nt 2

005

Global incomes have increased steadily, but …

Global inequality has increased much more, declining only since 2001.

Statistics is about extracting information from data.But you have to be able to get the right information.

Even simple data such as percentage change can hide nuances in the information it is apparently giving you.

When you calculate a 40% change between two periods of time, you cannot ever take it for granted that you

actually had a 40% growth rate.

Is the magnitude really 40%?What is hidden inside the value?

Can a large positive growth rate actually be a small negative one (strange but true)?

On Being Subtle and Sophisticated

An Illustration –The Canadian Economy

Look at the numbers - Two Questions:Is consumer spending growing faster than GDP?

Are consumer spending and GDP really growing at all?

Date GDP Consumer Spending2002 $1,152,905,000,000 $655,722,000,0002003 $1,213,175,000,000 $686,552,000,0002004 $1,290,906,000,000 $719,917,000,0002005 $1,373,845,000,000 $758,966,000,0002006 $1,450,405,000,000 $801,742,000,0002007 $1,529,589,000,000 $851,603,000,0002008 $1,603,418,000,000 $890,601,000,0002009 $1,528,985,000,000 $898,215,000,0002010 $1,624,608,000,000 $940,620,000,000

The Answer?Maybe, because

the values are increasing:

GDP grew by @41% and CS by

@43%.

But looks can be deceiving for

three reasons…

Growth rate: 40.9% Growth rate: 43.5%

Growth or Not And By How Much?

REASON #1Are the variables and/or units of measurement

comparable?

This asks whether you are talking about:

• Different things such as guns and butter.• Different magnitudes such as GDP$ or spending$.• Different measurement units such as annual or

quarterly, litres or kilos, totals or per capita.• Different base lines such as percentage points

difference or percentage change difference.

You fix it by indexing your data.


REASON #2:Removing the effect of inflation/deflation.

Inflation and deflation is caused when the costs and therefore subsequent prices of products increase or decrease, so any “growth/decline” is not caused by more/less consumption but by increased/decreased

price.

You fix it by converting current dollars to constant dollars using the consumer/producer price indices

and purchasing power parity.


REASON #3:Compensating for the effect of population change.

More people equals an increase in consumption and production and not an increase in individual spending

and production.

You fix it by using per capita rates.

Are the values comparable?(No. The magnitudes of values are much different – GDP is in

trillions and CS is in billions).

Fix it with a base 100 index number:

1. Make an arbitrary year’s real data value equal to 100.

2. Calculate every other year’s index number in relation to this base year

value (% change).

Now both sets of data values are directly comparable because they are relative to a single base value - 100.

Date

Current Dollar GDP

Index # 2002=100

Current Dollar

Consumer Spending Index #

2002=1002002 100.00 100.002003 105.23 104.702004 111.97 109.792005 119.16 115.752006 125.80 122.272007 132.67 129.872008 139.08 135.822009 132.62 136.982010 140.91 143.45

Removing the effects of inflation and population change

1. Collect the consumer price index (CPI) values.

2. Collect population data.

3. Use CPI to convert current to constant dollars for both variables.

4. Use population values to calculate per capita spending and GDP thus…

Consumer Price Index 2002 = 100

Canada Population

2002 100.0 31,373,0002003 102.8 31,676,0002004 104.7 32,048,0002005 107.0 32,359,0002006 109.1 32,723,0002007 111.5 33,115,0002008 114.1 33,506,0002009 114.4 33,894,000 2010 116.5 34,349,200

Removing the effect of inflation from GDP

Date GDP Current DollarsGDP Constant 2002

Dollars2002 $1,152,905,000,000.00 $1,152,905,000,000.002003 $1,213,175,000,000.00 $1,180,131,322,957.202004 $1,290,906,000,000.00 $1,232,957,020,057.312005 $1,373,845,000,000.00 $1,283,967,289,719.632006 $1,450,405,000,000.00 $1,329,427,131,072.412007 $1,529,589,000,000.00 $1,371,828,699,551.572008 $1,603,418,000,000.00 $1,405,274,320,771.252009 $1,528,985,000,000.00 $1,336,525,349,650.352010 $1,624,608,000,000.00 $1,394,513,304,721.03

Note that when removing inflation the constant dollar values are always lower than the current dollar values. When (rarely)

removing deflation they are always higher.

Base Year values are always the

same for current and

constant dollars.

That’s how you can tell

the base year.

Removing the effect of inflation from consumer spending

DateConsumer Spending

Current DollarsConsumer Spending

Constant 2002 Dollars2002 $655,722,000,000.00 $655,722,000,000.002003 $686,552,000,000.00 $667,852,140,077.822004 $719,917,000,000.00 $687,599,808,978.032005 $758,966,000,000.00 $709,314,018,691.592006 $801,742,000,000.00 $734,868,927,589.372007 $851,603,000,000.00 $763,769,506,726.462008 $890,601,000,000.00 $780,544,259,421.562009 $898,215,000,000.00 $785,152,972,027.972010 $940,620,000,000.00 $807,399,141,630.90

Base Year Values are always the same for

current and constant dollars.

That’s how you can tell

the base year.



Per Capita GDP Current Dollars

Per Capita Consumer Spending

Current Dollars

Per Capita GDP Constant 2002

Dollars

Per Capita Consumer Spending

Constant 2002 Dollars

2002 $36,748.32 $20,900.84 $36,748.32 $20,900.842003 $38,299.50 $21,674.20 $37,256.32 $21,083.852004 $40,280.39 $22,463.71 $38,472.20 $21,455.312005 $42,456.35 $23,454.56 $39,678.83 $21,920.152006 $44,323.72 $24,500.87 $40,626.69 $22,457.262007 $46,190.22 $25,716.53 $41,426.20 $23,064.162008 $47,854.65 $26,580.34 $41,940.98 $23,295.662009 $45,110.79 $26,500.71 $39,432.51 $23,164.952010 $47,296.82 $27,384.04 $40,598.13 $23,505.62

Compensating for the effect of population change

Base Year

Same

CURRENT DOLLARS CONSTANT DOLLARS



Correcting The Canadian Economy in Summary

What You SeeData uncorrected for…

Inflation… Use CPI to correct.

Population growth…Use population to correct.

What You GetData corrected for both…

Per capita values in constant dollars

2002 2003 2004 2005 2006 2007 2008 2009 2010100.0

105.0

110.0

115.0

120.0

125.0

130.0

135.0

Percapita GDP Current Percapita Consumer Spending Current

Per Capita GDP Constant Per Capita Consumer Spending Constant

Inde

x N

umbe

r (20

02=1

00)

Can You See The Difference?

So did the Canadian Economy ‘grow’ and if so by how much?

Growth Correction GDP Growth Rate

Consumer Spending

Growth Rate

No correction(current dollars) 40.9% 43.5%

Corrected for inflation only

(constant dollars)21.0% 23.1%

Corrected for population change only

(per capita rates)28.7% 31.0%

Corrected for both(Constant per capita) 10.5% 12.5%

Difference -30.4% -31.0%

So did the Canadian Economy ‘grow’ and if so by how much?

Growth Correction GDP Growth Rate

Consumer Spending

Growth Rate

No correction(current dollars) 40.9% 43.5%

Corrected for inflation only

(constant dollars)21.0% 23.1%

Corrected for population change only

(per capita rates)28.7% 31.0%

Corrected for both(Constant per capita) 10.5% 12.5%

Difference -30.4% -31.0%

An Illustration –The Canadian EconomyTwo Questions

1. Is consumer spending growing faster than GDP?2. Are consumer spending and GDP really growing at all?

Two Answers1. Can’t tell from these raw data.

2. Maybe, because the numbers are increasing.

But looks can be deceiving.

Date GDP Current DollarsConsumer Spending

Current Dollars2002 $1,152,905,000,000.00 $655,722,000,000.002003 $1,213,175,000,000.00 $686,552,000,000.002004 $1,290,906,000,000.00 $719,917,000,000.002005 $1,373,845,000,000.00 $758,966,000,000.002006 $1,450,405,000,000.00 $801,742,000,000.002007 $1,529,589,000,000.00 $851,603,000,000.002008 $1,603,418,000,000.00 $890,601,000,000.002009 $1,528,985,000,000.00 $898,215,000,000.002010 $1,624,608,000,000.00 $940,620,000,000.00

Raw Percent Change2002-1040.9%

Raw Percent Change2002-1043.5%

Real Percent Change2002-1010.5%

Real Percent Change2002-1012.5%

CALCULATING INDEX NUMBERS

Many types, most use base 100, some are used to further manipulate data (e.g.

constant dollars).

Easy to calculate – we’ll look at:

General base 100 indicesCPI and its use for…

Converting current to constant dollars

Simple Index NumbersVery simple to calculate by taking the base year

value, chosen arbitrarily, dividing it into each subsequent year’s value, then multiplying by 100.

Date GDP Index2002 $1,152,905,000,000 100.002003 $1,213,175,000,000 105.232004 $1,290,906,000,000 111.972005 $1,373,845,000,000 119.16

$1,213,175,000,000.00/$1,152,905,000,000 = 105.23$1,290,906,000,000.00/$1,152,905,000,000 = 111.97

NOTE THAT THIS IS JUST A PERCENTAGE CHANGE VALUE ADDED TO 100

The Consumer Price Index

• What is the CPI?– Basket of goods and services are “bought” and

their cost is set to equal an index number of 100.– The year the basket is “bought” is called the base

year, and it remains until a new base year is chosen.

– The same basket is “bought” the next year and its value is given an index # equal to 100 plus the percentage change from the previous year’s basket.

– This process is repeated each year (or other time period) until a new base year is chosen.

– The CPI is listed in a table and the base year is noted somewhere as, for example, 2002=100.

Therefore you do not calculate the CPI – you must look it up from Stats Canada

Examples of Price Indices• Data tables for Prices and price indexes – some SC examples:• Table 25.a Consumer Price Index• Table 25.b Average retail food prices• Table 25.1 Consumer Price Index, 1991 to 2010• Table 25.2 Consumer Price Index, All-items, by province and territory,

2005 to 2010• Table 25.3 Consumer Price Index, food, 2004 to 2010• Table 25.4 New Housing Price Index, by province, 2004 to 2010• Table 25.5 Raw Materials Price Index, 2004 to 2010• Table 25.6 Farm Product Price Index, 2004 to 2010• Table 25.7 Industrial Product Price Index, 1991 to 2010• Table 25.8 Machinery and Equipment Price Index, domestic and imported,

by industry, 2005 to 2010• Table 25.9 Composite Leading Index, March 2005 to March 2011• Table 25.10 Inter-city indexes of retail price differentials, by selected goods

and services, 2005 and 2009

The CPI – Example Tables

Table 25.a Consumer Price Index 2000 2010 2002=100All-items 95.4 116.5Food 93.3 123.1Shelter 95.6 123.3

Household operations, furnishings and equipment 96.7 108.8

Clothing and footwear 100.3 91.6Transportation 97.2 118.0Health and personal care 97.0 115.1

Recreation, education and reading 97.0 104.0

Alcoholic beverages and tobacco products 79.0 133.1

Core Consumer Price Index1 95.7 115.6

Note: Annual average indexes are obtained by averaging the indexes for the 12 months of the calendar year.

1. Bank of Canada definition.Source: Statistics Canada, CANSIM table 326-0021.

http://cansim2.statcan.gc.ca/cgi-win/cnsmcgi.exe?Lang=E&RootDir=CII/&ResultTemplate=CII/CII_pick&Array_Pick=1&ArrayId=326-0021


Farm Product Price Indices – Example Tables

Table 25.6 Farm Product Price Index, 2004 to 2010 2004 2005 2006 2007 2008 2009 2010 1997=100Canada 99.4 96.8 97.4 108.6 122.0 113.5 111.0Total crops 100.6 88.3 92.7 117.5 144.9 126.3 114.8Grains 94.1 76.5 84.3 133.3 168.3 128.5 102.5Oilseeds 95.2 74.5 72.2 97.5 133.5 116.5 113.1Specialty crops 102.5 85.2 80.2 120.6 185.9 158.6 137.9Fruit 108.7 117.4 124.6 124.4 126.3 112.5 118.3

Vegetables (excluding potatoes) 116.8 113.1 118.2 114.3 119.3 125.3 124.1

Potatoes 119.4 125.9 148.6 135.0 150.7 183.2 175.9

Total livestock and animal products 98.3 103.9 101.3 101.5 103.5 103.6 109.2

Cattle and calves 87.6 103.2 102.7 99.4 99.0 97.7 103.0

Hogs 89.7 83.0 72.3 68.3 67.3 67.5 80.4Poultry 97.9 96.4 93.2 102.2 115.0 116.6 111.8Eggs 105.6 97.3 98.7 100.8 107.9 103.4 109.0Dairy 119.9 128.0 130.3 137.2 139.9 142.4 143.3

Index numbers can increase (indicating inflation) or decrease

(indicating deflation).


The CPI and Purchasing Power Parity (PPP)

CPI only one part of cost of living – some places are just more expensive in which to live.

When values are corrected for the cost of living in different places the resulting data is labeled as PPP.

This means Purchasing Power Parity – that is, dollar values are corrected for the differences in the cost of

things like food, housing, taxes, gasoline, etc.

In this case the same basket of goods is valued in each place, compared, then indexed, and the resulting indexed values are used to inflate or deflate prices, incomes, GDP,

etc.

Inter City CPI PPP – Example Tables

Table 25.10 Inter-city indexes of retail price differentials, by selected goods and services, 2005 and 2009

St. John'sCharlotteto

wn & Summersid

eMontréal Toronto Winnipeg Edmonton Vancouve

r

2005 2009 2005 2009 2005 2009 2005 2009 2005 2009 2005 2009 2005 2009 combined city average=100

All-items 95 96 94 97 93 95 110 107 92 94 97 102 102 101

Food 103 105 100 103 97 102 101 99 98 101 101 100 106 105

Food purchased from stores 105 104 103 103 99 101 99 99 99 103 101 102 106 106

Meat, poultry and fish 101 103 108 102 103 99 97 99 93 96 99 103 106 108

Dairy products and eggs 105 102 99 93101 94 101 91 100 96 106 107 101 106

Indicates if a place is cheaper than (lower number) or more expensive than (higher number) the average (or other) places.

INTERPRETATION EXAMPLESToronto in 2009 was 107-100=7% more expensive than the average

city, while St.John’s was 94-100=6% cheaper.Toronto in 2009 was 107-94=13% more expensive to live in than

was Winnipeg.


Going to the Movies…

Top 5 highest grossing films of all time 2011:AvatarTitanic

The Dark KnightStar Wars Episode IV

Shrek 2

Top 5 highest grossing films of all time 2011 (adjusted for inflation):

Gone with the WindStar Wars Episode IVThe Sound of Music

E.T.The Ten Commandments

Current to Constant Dollar Conversion

To remove effect of inflation:

Constant $ = Current $/(CPI/100)

Example2001 CPI

102.8Current (2003) dollar GDP value

$1,213,175,000,000

Constant 2003 GDP$ = $1,213,175,000,000/(102.8/100)=$1,180,131,322,957.20

Basically, 2.8% of any “growth” between 2001 and 2003 is inflation.

More Complex Price Indices to Frighten YouWe won’t go into calculating price indices because they can become very complex, but the three most

commonly used are:

Carli Index, defined as the simple, or unweighted, arithmetic mean of the price relatives or price ratios

for the two periods, t0 and t1.

Dutot Index, which is defined as the ratio of the unweighted arithmetic mean prices.

Jevons index, defined as the unweighted geometric mean of the price relative or relatives, which is

identical to the ratio of the unweighted geometric mean prices.

RATIOSDefinition:

Basically, one number divided by another number.

Many Types – simple to complex:Per capita rates.

Many demographic stats such as birth and death rates.

Location Quotients (a ratio of ratios).

Gini coefficients (complex – an index number measuring inequalities).

Simple RatiosThe ‘Per’ Rates

Per Capita RatesIncorporates the effect of population growth.

Gives easy to compare values across time and space.Easy to calculate – divide variable of interest by the population, for

example:

Per Capita GDP in Constant 2002$ = GDP in Constant 2002$/Pop 2002

GDP in Constant 2002 $ = $1,152,905,000,000Population 2002 = 31,373,000

Per Capita GDP in Constant 2002 $ = $1,152,905,000,000/31,373,000 =$36,748.00

Demographic RatesIncorporates the effect of population size.

Gives comparable and understandable values.Easy to calculate – divide variable of interest (e.g. births) by the population and multiply by the base

value.

Base values vary according to the expected magnitude of the final ratio. For example, you generally try to get

a ratio between 1 and 100.

Birth, death, fertility, infant mortality rates are usually expressed as a value per 1,000 whereas disease incidence rates would be per 10,000 or 100,000

because the number of people with disease is much lower than the number of births, deaths, etc.

Demographic Rates – Some Examples:Birth rates:BR = # (births/population)*1,000BR = (381,382/34,108,800)*1,000 BR = 11.2 births per 1,000 population

Infant mortality rates:IM = (# deaths <= 1 year olds/population)*1,000IM = (160,311/34,108,800)*1,000IM = 4.7 infant deaths per 1,000 population

Morbidity (disease death) rates – all cancers:MR = (# cancer deaths/population)*100,000MR = (75,000/34,108,800)*100,000MR = 2.2 cancer deaths per 100,000 population

381,382/34,108,800=0.0112

Complex RatiosRatio of Ratios.

Components Approach.

Ratio of Ratios – An ExampleLocation Quotients

(LQ)

Ratio of Ratios: Location Quotients

A method of estimating whether a region has a surplus, deficit or the average employment in an industry, given

by:

Employment in industry i in region j Total employment in region j

Employment in industry I in the nation JTotal employment in the nation J

Also given as LQ = (Eij/Ej)/(EIJ/EJ)

Where i and j represent “industry” and “area” respectively, with lower case referring to the region in

question and upper case referring to, usually, the nation.

LQ =

Employment in industry i in region j Total employment in region j

Employment in industry I in the nation JTotal employment in the nation J

Ratio of Ratios: Location Quotients

You should be able to see that this is a ratio of ratios thus:

Ratio of regional employment in i to total

regional employment

Ratio of national employment in I to total

national employment

The resulting ratio is interpreted as follows:> 1.0: surplus to national average production= 1.0: equal to national average production< 1.0: deficit to national average production

Hispanics in region j Total population in region j

Hispanics in the nation JTotal population in the nation J

Ratio of Ratios: Location QuotientsShould be obvious that the relative concentrations of

many different variables can be calculated.

Ratio of Hispanics in region to total

population in region

Ratio of Hispanics in nation to total

population in nation

The resulting ratio is interpreted as follows:1.0: regional concentration of Hispanics

= 1.0: equal to national concentration of Hispanics< 1.0: regional scarcity of Hispanics

Using Location Quotients for Immigration Analysis

Components ApproachAn Example

Shift-Share Analysis

The components approach: Shift-Share Analysis

A fairly simple but powerful tool for analyzing components of growth.

Disaggregates a single overall growth rate in an industry into components of that growth rate, in

order to isolate:

- A region’s national growth component;- A region’s regional growth component;- A region’s industry growth component.

The reasons for doing this, by way of example…


If a region (say the GTA) shows a growth rate in electronics manufacture as 12% for a given time

period, the questions are:

What portion of the 12% can be attributed to the fact that the nation was perhaps growing/declining

anyway?

What portion of the 12% can be attributed to the fact that the GTA was perhaps growing/declining

anyway?

What should the electronics industry have been growing by, given the national growth rate in the

industry?

12% Total Growth

6% growth due to growth in the national

economy.

3% growth due to growth in the GTA

economy.

3% growth due to growth in the auto

industry.

GTA Growth in the Electronics Industry

A single growth value hides complexity.

The Basic Model:

Gij = Nij + Mij + Dij

where,

Gij = total growth in industry ì' at place `j'.Nij = national growth component in industry ì' at place `j'. Mij = industry growth component in industry ì' at place `j'.Dij = regional growth component in industry ì' at place `j‘.


12% Total Growth

6% growth due to growth in the national

economy.

3% growth due to growth in the GTA

economy.

3% growth due to growth in the auto

industry.

Shift Share Analysis - GTA Growth in the Auto Industry

A single growth value hides complexity.

Gij Nij

Mij

Dij


where,Nij = Eo * rMij = Eo * (ri - r)Dij = Eo * (rij - ri)

where,r, ri, rij, = (Et - Eo)/Eo

where,Eo = employment in ì' at `j' at start of periodEt = employment in ì' at `j' at end of periodr = national growth rate, all employmentri = national growth rate in ì'rij = growth rate in ì' at `j'

Note that you are removing the effect of national growth

from industry growth and industry growth from regional

industry growth.

And in case you were wondering what it all looks like together…

Gij = Nij+Mij+Dij

or

Nij = [Eo*(Etr-Eo)/Eo]Mij = [(Etri-Eori)-(Etr-Eo)/Eo)]

Dij = [(Etrij-Eoij)/Eoij)/(Etri-Eori)]

orGij = [[Eo*(Etr-Eo)/Eo]]+[[(Etri-Eori)-(Etr-Eo)/Eo)]]+[[(Etrij-Eoij)/Eoij)/(Etri-Eori)]]

(more or less)

And in case you were wondering…


Interpreting the results of a shift-share analysis is fairly straightforward:

The ‘r’ coefficients (r, ri, rij) are the growth factors – essentially percentage changes – for the

basic elements: Nij, Mij, and Dij.

The actual values that you get are the number of employees that should have been expected for

the basic elements: Nij, Mij, and Dij.

Using Mij and Dij you can get a good conceptual picture of a region…

NATIONAL INDUSTRY MIX COMPONENTMij

REGIONAL GROWTH

RATE COMPONENT

Dij

Growth Industry(+)

Declining Industry(-)

Growth Region

(+)

Good. Your region is growing in a

growth industry.

Poor. Your region is growing in a

declining industry.

Decline Region

(-)

Poor. Your region is declining in a growth industry.

Good. Your region is declining in a

declining industry.



Shift-Share Analysis Conclusion

The point of showing you all this stuff about Shift Share Analysis?

You can built some very involved and informative ratios without having to resort

to complex probability based statistical analysis.

BUT they will always be descriptive in nature.

Coefficients Approach – An ExampleGini Coefficient and Lorenz Curves

The coefficients approach: Gini Coefficients & Lorenz Curves

The Gini coefficient is a measure of the degree of inequality in a distribution.

Gives a number between 0 and 1 where 0 is complete equality and 1 is complete

inequality.

Sometimes numbers are multiplied by 100 to give coefficients between 0 and 100.

It is used most generally in describing income inequality in a population.

EXAMPLEA nation with a coefficient of 0 would mean

everyone had exactly the same income.

A nation with a Gini coefficient of 1 (or 100) would mean that one person had all the

income.

Sweden has coefficient of 23 whereas Namibia is 70.7, the USA is 45 and Canada is 31.

Global Gini is 40.


The Gini coefficient is used most widely for describing income inequalities and thus you will see it in World Bank, IMF, UN, WHO and many

other statistical agencies around the world.

THIS IS WHY YOU NEED TO KNOW WHAT IT IS.

You will likely never have to calculate one but you should know conceptually how it is done to

understand what it is saying. So here goes…


Nothing…You can read the rest of the Gini

slides for yourself.

No I won’t ask you to calculate a Gini coefficient.

Yes I likely will ask you what it means.

Higher social capital, higher income equality

Lower social capital, lower income equality

CURVES

Basically, any ratio or index can be graphed or mapped over time or space

to get a picture of your data.

Graphing data is not the domain of this course (though histograms etc are) so

I’m not going to go into it except to show you what you will find when you have to search for data on indexes and

ratios.

17th Century England

20th Century England

.

Note logged values for variables

The wealthier a nation, the lower the death rate.

Quantile AnalysisAnother Way to ‘Picture’ Data

There is another way to ‘picture your data that has nothing to do with pictures!

Quantile analysis takes the dataset and divides it up into 100ths and combinations thereof.

That is, it takes the total number of values in the dataset and makes it equal to 100 – in other words it calculates

your dataset as percentage shares.

The shares are typically combined into:Percentiles

DecilesQuintilesQuartiles

A percentile is one hundredth of the dataset.

Each value in the dataset, when ranked from lowest to highest, will fall into the first percentile, the second

percentile etc.

If you have 142 values, there will be 1.42 values in each percentile.


A decile represents an aggregation of percentiles into 10% increments.

The categories would be 10%, 20%, 30% etc up to 100% and your dataset would be shared

out into 10% chunks.

If you have 142 values, there will be 14.2 values in each percentile


A quintile represents an aggregation of percentiles into 20% increments.

The categories would be 20%, 40%, 60%, 80% and 100% and your dataset would be shared

out into 20% chunks.



A quartile represents an aggregation of percentiles into 25% increments.

The categories would be 25%, 50%, 75% and 100% and your dataset would be shared out

into 25% chunks.


See this more than the others.Very important for box plots.


Example: Calculating Quartiles for 100 Values

MEDIAN FOR ALL VALUES 0 TO 100 50

MEDIAN FOR VALUES BETWEEN 0 AND 50 25

MEDIAN FOR VALUES BETWEEN 51 AND 100 75

CALCULATED Q0 VALUE 0





Now go chill.

Documents

ANNOUNCEMENT #1 Third Quiz. 10% of Course Grade October 26th 30 MC questions. Lectures 6&7. Contingency Tables. Index Numbers. No make-ups. Don’t miss