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ANNOUNCEMENT #1 Second Quiz. 12.5% of Course Grade October 23 rd 8:10 until 8:50am

ANNOUNCEMENT #1 Second Quiz. 12.5% of Course Grade October 23 rd 8:10 until 8:50am 40 MC questions. Lectures 4, 5, 6, 7. Central Tendency. Dispersion. Contingency Tables. Index Numbers. No make-ups. Don’t miss it. ANNOUNCEMENT #2 NO LAB TOMORROW I’LL BE IN MY OFFICE IF YOU NEED ME.

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ANNOUNCEMENT #1 Second Quiz. 12.5% of Course Grade October 23 rd 8:10 until 8:50am

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  1. ANNOUNCEMENT #1 Second Quiz. 12.5% of Course Grade October 23rd 8:10 until 8:50am 40 MC questions. Lectures 4, 5, 6, 7. Central Tendency. Dispersion. Contingency Tables. Index Numbers. No make-ups. Don’t miss it.

  2. ANNOUNCEMENT #2 NO LAB TOMORROW I’LL BE IN MY OFFICE IF YOU NEED ME.

  3. 2013=100 Index Numbers and Ratios

  4. Index Numbers and Ratios One of the most common types of quantitative tools, seen in many types of geographic data. Examples are Consumer Price Index, stock indices such as TSX, NASDAQ, Location Quotients, Gini coefficients, demographic analyses 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.

  5. Index Numbers– Some Examples 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.

  6. How its done – stock indices 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.

  7. What the Dow(s) Jones looks like.

  8. What the S&P(s) looks like.

  9. What it looks like plotted Note the “dot.com” spike around 2000 as recorded by the NASDAQ. Also note that S&P500 is more heavily weighted with tech stocks.

  10. The Big Mac Index 1. 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. Argentina Australia Brazil U.K. (underpriced currency) Canada (overpriced currency)

  11. Grey line actual. Blue line MA3 (moving average period 3. Index created from truckers’ purchases of diesel fuel; used as an indicator of commerce and hence health of the economy.

  12. 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

  13. 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.

  14. Playing with Numbers. How much is 12%?

  15. 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.

  16. On Being Subtle and Sophisticated Statistics is about extracting information from data. But you have 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 take it for granted that you 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?

  17. 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? The Answer? Maybe, because the values are increasing: GDP grew by @40% and CS by @43%. But looks can be deceivingfor three reasons… Growth rate: 43.5% Growth rate: 40.9%

  18. Growth or Not And By How Much? • REASON #1 • Are 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$ and spending $ • Different measurement units such as annual or quarterly, litres or kilos • You fix it by indexing your data.

  19. Growth or Not And By How Much? REASON #2: Removing the effect of inflation/deflation. Inflation and deflation is caused when the costs and subsequent prices of products increase or decrease, so “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 price index and purchasing power parity.

  20. Growth or Not And By How Much? REASON #3: Compensating for the effect of population change. More people equals an increase in consumption and production and not an increase in individualspending and production. You fix it by using per capita rates.

  21. 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.

  22. 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…

  23. Removing the effect of inflation from GDP Base Year values are always the same for current and constant dollars. That’s how you can tell the base year. Note that when removing inflationthe constant dollar values are always lower than the current dollar values.

  24. Removing the effect of inflation from consumer spending Base Year Values are always the same for current and constant dollars. That’s how you can tell the base year. Note that when removing inflationthe constant dollar values are always lower than the current dollar values.

  25. Compensating for the effect of population change CURRENT DOLLARS CONSTANT DOLLARS Base Year Same Note that when removing inflationthe constant dollar values are always lower than the current dollar values.

  26. Correcting The Canadian Economy in Summary What You See (data uncorrected for…) Inflation… Use price indexes to correct Population growth… Use population to correct What You Get (data corrected for both…) Per capita values in constant dollars

  27. What You See – The Current Dollars

  28. Can You See The Difference?

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

  30. An Illustration –The Canadian Economy Two Questions 1. Is consumer spending growing faster than GDP? 2. Are consumer spending and GDP really growing at all? Two Answers 1. Can’t tell from these raw data. 2. Maybe, because the numbers are increasing. But looks can be deceiving. Raw Percent Change 2002-10 40.9% Raw Percent Change 2002-10 43.5% Real Percent Change 2002-10 12.5% Real Percent Change 2002-10 10.5%

  31. 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 indices CPI and its use for… Converting current to constant dollars

  32. Simple Index Numbers Very simple to calculate by taking the base year value, chosen arbitrarily, dividing it into each subsequent year’s value, then multiplying by 100. $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

  33. 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

  34. 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

  35. The CPI – Example Tables

  36. Farm Product Price Indices – Example Tables Index numbers can increase (indicating inflation) or decrease (indicating deflation).

  37. 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.

  38. Inter City CPI PPP – Example Tables Indicates if a place is cheaper than (lower number) or more expensive than (higher number) the average (or other) places. INTERPRETATION EXAMPLES Toronto in 2009 was 107-100=7% more expensive than the average city. Toronto in 2009 was 107-94=13% more expensive to live in than was Winnipeg.

  39. Current to Constant Dollar Conversion To remove effect of inflation: Constant $ = Current $/(CPI/100) Example 2001 CPI 102.8 Current (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

  40. More Complex Price Indices to Frighten You We 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, 0 and t. Dutot Index, which is defined as the ratio of the unweightedarithmetic mean prices. Jevons index, defined as the unweightedgeometric mean of the price relative or relatives, which is identical to the ratio of the unweighted geometric mean prices.

  41. RATIOS Definition: 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).

  42. Simple RatiosThe ‘Per’ Rates

  43. Per Capita: Incorporates 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 $ = $1,152,905,000,000 Population 2002 = 31,373,000 Per Capita GDP in Constant 2002 $ = $1,152,905,000,000/31,373,000 = $36,748.00

  44. Demographic Rates Incorporates 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.

  45. 381,382/34,108,800=0.0112 Demographic Rates – Some Examples: Birth rates: BR = # (births/population)*1,000 BR = (381,382/34,108,800)*1,000 BR = 11.2 births per 1,000 population Infant mortality rates: IM = (# deaths <= 1 year olds/population)*1,000 IM = (160,311/34,108,800)*1,000 IM = 4.7 infant deaths per 1,000 population Morbidity (disease death) rates– all cancers: MR = (# cancer deaths/population)*100,000 MR = (75,000/34,108,800)*100,000 MR = 2.2 cancer deaths per 100,000 population

  46. Complex RatiosRatio of Ratios.Components Approach.

  47. Ratio of Ratios – An ExampleLocation Quotients(LQ)

  48. 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 J Total 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 =

  49. 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 Employment in industry i in region j Total employment in region j Employment in industry I in the nation J Total employment in the nation J 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

  50. Ratio of Ratios: Location Quotients Should be obvious that the relative concentrations of many different variables can be calculated. Ratio of Hispanics in region to total population in region Hispanicsin region j Total population in region j Hispanicsin the nation J Total population in the nation J 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

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