individual assignment5--321report
lizening
TheCPI.pdf
ECON 321 The Economic History of Canada
The CPI and How to Use It
OPTIONAL HANDOUT
Version 1
Recommended Reading
• Stand-Up Economics: Chapter 17, Section 17.2 [Very short]
• Stand-Up Microeconomics: http://standupeconomist.com/stand-up- economics-the-micro-textbook/ (Choose the version with calculus.)
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Optional Readings Part 1: Solved Problems
• California Department of Finance, “How to use CPI Data,” http://www.dof.ca.gov/Forecasting/Economics/Documents/How_to_Use_CPI_Data. pdf
• Gavin Thompson, “How to adjust for inflation,” www.parliament.uk/briefing- papers/SN04962.pdf
• Gerald Perrins and Diane Nilsen, “Math calculations to better utilize CPI data,” http://www.bls.gov/cpi/cpimathfs.pdf
• ILO, “An Introduction to Consumer Price Index Methodology,” http://www.ilo.org/public/english/bureau/stat/download/cpi/ch1.pdf (ADVANCED mathematical details of price index calculation. Overkill for this course, but presented for the curious.)
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Optional Readings Part 2: Canada’s CPI
• Statistics Canada, Your Guide to the Consumer Price Index, Catalogue No. 62-557- XPB. http://www5.statcan.gc.ca/olc-cel/olc.action?objId=62-557- X&objType=2&lang=en&limit=1 (A non-technical introduction to the CPI.)
• Inflation Calculator, Canada’s CPI Basket of Goods and Services, http://inflationcalculator.ca/cpi-basket/ (Shows what’s in the basket, and how basket weights have changed over time.)
• James Rossiter, “Measurement Bias in the Canadian Consumer Price Index,” Bank of Canada Working Paper 2005-39. http://www.bankofcanada.ca/wp- content/uploads/2010/02/wp05-39.pdf (Problems with the CPI, and how to deal with them.)
• Chiru, R. et al. (2015). Calculation of the Consumer Price Index. In The Consumer Price Index Reference Paper [Statistics Canada Item 62-553-X]. Retrieved from https://www150.statcan.gc.ca/n1/pub/62-553-x/2015001/chap/chap-6-eng.htm (Official details on CPI Calculation, from the definitive reference.)
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What is a price index? • Tracks the price of a basket of goods over time.
• (e.g. 1 can of pop + 1 cookie, or 1 bottle of cookie pop)
• Everything is compared to a base year.
• Let Ct = cost of the basket in year t
• Cbase = cost of the basket in the base year
• Index = Ct/Cbase x 100
• This shows how prices have changed since the base year.
• e.g. Index of 115 means prices are 115% of base year prices
• The CPI is a measure of the price level.
• Inflation measures the change in the price level.
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Using an index to calculate yearly inflation, f
• Let Pt = Price index for year t
• Inflation, f = the % increase in P from one year to the next
• The rate of inflation in 2016 (say) would then be (P2016 – P2015)/P2015 • f2016 = (P2016 – P2015)/P2015
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Some Common Indices • Consumer price index (CPI): goods bought by a representative household
• Producer price index (PPI): goods bought by a representative producer
• GDP Deflator: all goods and services produced within Canada in a given year.
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0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016
W e
ig h
ts (
% )
Year
Evolution of Canadian CPI Basket Weights (Broad Classes)
Food Shelter
Household Operations, Furnishings & Equipment Clothing and Footwear
Transportation Health and Personal Caare
Recreation, Education and Reading Alcoholic Beverages and tobacco Products
More details:
http://inflationcalculator.ca/cpi-basket/
These weights are shares of spending
(since $ are a convenient common unit).
How do these weights figure in?
• Canada (and many other countries) use a Laspeyres price index, which is a bit more complicated than our basic cookies & pop index.
• We need three components: • A price for each class j in year t, 𝑝𝑡𝑗 • A base year price for each class, 𝑝0𝑗 • A weight/share of base year spending by class, 𝑠0𝑗 (if the weights never change)
• Canada uses a modified Laspeyres index called a Lowe index, in which the shares are calculated using data from different years: quantities are from some weight reference year for which we have good quantity data, while prices are from the base year (price reference year). For details, see sections 6.23 to 6.35 on https://www150.statcan.gc.ca/n1/pub/62-553-x/2015001/chap/chap-6-eng.htm
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How do you calculate shares of spending? • The share of spending of Class j in year t is the % of the value of the basket that
year that was spent on Class j.
• Let 𝑞𝑡𝑗 be the quantity of Class j goods bought in Year t.
• Then total spending on Class j in Year t is 𝑝𝑡𝑗𝑞𝑡𝑗 (Price x Quantity)
• If there are n categories, total spending on ALL basket goods in year t is σ𝑖=1 𝑛 𝑝𝑡𝑖𝑞𝑡𝑖.
• The share of spending of Class j in year t is therefore
𝑠𝑡𝑗 = 𝑝𝑡𝑗𝑞𝑡𝑗
σ𝑖=1 𝑛 𝑝𝑡𝑖𝑞𝑡𝑖
• (Divide the amount spent on Class j, by the amount spent on all classes, in Year t.)
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𝒇 𝒙
Assembling the Laspeyres Price Index
• Suppose we are keeping our weights constant at base year (Year 0) levels.
• If there are n classes, then the Laspeyres price index for year t, Lt, is
𝐿𝑡 =
𝑖=1
𝑛 𝑝𝑡𝑖 𝑝0𝑖
𝑠0𝑖 × 100
• Keep in mind this is simpler than the CPI calculation actually used by Statistics Canada. For details, see https://www150.statcan.gc.ca/n1/pub/62-553- x/2015001/chap/chap-6-eng.htm
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𝒇 𝒙
Example: Apples and Oranges
• Using Year 0 as the base year, let’s calculate a Year 1 price index.
• For our Laspeyres Index, we only need Year 0 shares.
• Year 0 spending on apples: 1 $/apple x 10 apples = $10
• Year 0 spending on oranges: 3 $/orange x 8 oranges = $24
• Total Year 0 spending: $10 + $24 = $34
• s0apples = $10/$34 = 29%, s0oranges = $24/$34 = 71%
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Year 0 Price Year 1 Price Year 0 Quantity Year 1 Quantity
Apples $1 $2 10 9
Oranges $3 $4 8 7
Moving on…
𝐿1 = 𝑝1𝑎𝑝𝑝𝑙𝑒𝑠 𝑝0𝑎𝑝𝑝𝑙𝑒𝑠
𝑠0𝑎𝑝𝑝𝑙𝑒𝑠 + 𝑝1𝑜𝑟𝑎𝑛𝑔𝑒𝑠
𝑝0𝑜𝑟𝑎𝑛𝑔𝑒𝑠 𝑠0𝑜𝑟𝑎𝑛𝑔𝑒𝑠 × 100
𝐿1 = $2
$1 × 29% +
$4
$3 × 71% × 100 = 152.9 (rounded)
• Note that, by definition, the index is 100 in the base year.
• The choice of the base year depends on the application – your text uses the project’s ‘Year 0’, because that’s a very convenient choice for engineering economics applications.
• We could have just as easily used Year 1: in CPI indices, etc., the base year can be any year for which complete data is available.
• For example... Cake ingredients as a basket, 1925 as the base year:
12
13
15
20
25
30
35
40
45
50
55
60
1914 1919 1924 1929 1934 1939 1944 1949 1954 1959
Cost of Ingredients (Canadian cents) (Sources: DBS, The Canadian Cookbook 1925 & 1953)
Standard Cake Raisin Cake
14
50
75
100
125
150
175
1914 1919 1924 1929 1934 1939 1944 1949 1954 1959
In d
e x
(1 9
2 5
= 1
0 0
)
Year
Laspeyres Indices (1925 base) vs Official Canadian CPI
CPI(1925 base) Standard Cake Raisin Cake
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-30%
-20%
-10%
0%
10%
20%
30%
1914 1919 1924 1929 1934 1939 1944 1949 1954 1959
Year-on-Year Inflation, 3 Canadian Indices
CPI Standard Cake Raisin Cake
Year-on-Year Inflation = %
change in a price index from
one year to the next.
Problems with indices
• Substitution bias: Pizza’s more expensive? Switch to ramen. Problem: weights don’t reflect this. (This is one reason Canada re- calculates weights.)
• Increase in quality bias: a phone in 2002 is not the same as a phone in 2019
• New product bias: things that didn’t exist at the basket’s creation aren’t taken into account.
• Outlet bias: where should price be sampled? Thrifty’s or CostCo?
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=
2002 2019
??? =
Party trick: Price in any year
• Let 𝐶𝑡 = cost in year t
Cx CY
= CPIX CPIY
• When you hear ‘in 1995 dollars’ or some such, this is what they’re talking about.
• Intuition: If things are twice as expensive in Year X as in Year Y, the cost in Year X is twice the cost in Year Y.
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𝒇 𝒙
Where this might come in useful…
• Marty McFly uses a time machine to travel between 1955, 1985 and 2015.
• All of his destinations are in the United States.
• The US CPI was 26.8 in 1955, 107.6 in 1985 and 235.8 in 2015.
• The time machine is made out of a DeLorean DMC-12 car.
• In 1985, a DeLorean could be bought for $12,000
• In 2015, a DeLorean sold on average for for $54,000.
• Has the DeLorean become cheaper or more expensive with age?
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Originally, this example included highway construction costs...
…but where we’re going with this example, we don’t need roads.
P1985 = P2015 CPI1985 CPI2015
P1985 = $54,000 107.6
235.8 = $24,641.22
• In real terms, the DeLorean has doubled in price!
• Should Marty (and Doc) start a cross-time used car dealership?
• Sadly, over 30 years, that return only averages to about 2.5% a year…
• $24,641.22 = $12,000 × 1 + 0.24742 30
• Probably better to bring back a sports almanac…
What is the 1985 equivalent of $54,000 today?
19 http://www.kedificil.com/wp-content/uploads/2013/08/great-scott-doc-back-to-the-future-drawing.jpg
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300
350
400
450
500
550
600
650 C
a n
a d
ia n
C e
n ts
Price of Cake Ingredients (2017 $) (Sources: DBS, Statistics Canada, The Canadian Cookbook, Thrifty's)
Standard Cake Raisin Cake 2017 Standard 2017 Raisin
When I deflate using the
official CPI, note the LOW
cost during WWII, and the
HIGH cost in the late
1940s and early 1950s…
Inflation tracking for time travelers
• When going back in time from 1985 to 1955, Marty was surprised to find how cheap everything was.
• A 12-ounce bottle of Pepsi cost 10 cents in 1955, compared to 15 cents in 1985 (inferred from the cost of a 2-litre bottle).
• Let’s calculate average annual inflation between 1955 and 1985 using first the CPI, and then by using the price of 12 ounces of Pepsi.
• The two values will not be the same! There’s immediately clear reason why the price of Pepsi should track the CPI perfectly.
• Our two baskets (CPI basket, 12 ounces of Pepsi) are very different.
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Pepsi Ad, 1955
• Let P stand for the index used. After 30 years of inflation of f per year, something that cost $1 in 1955 would cost $1 x 1 + f 30 in 1985.
• Our index is 𝑃55 in 1955, and 𝑃85 in 1985.
𝑃55 1 + f 30 = 𝑃85
f = 𝑃85
𝑃55
1
30 − 1
f𝐶𝑃𝐼 = 107.6
26.8
1 30
− 1 = 4.7 %
f𝑃𝑒𝑝𝑠𝑖 = 0.15
0.10
1 30
− 1 = 1.4 % 22
1985 ad for Pepsi
What’s so bad about inflation?
• If all prices rise, including wages, why worry?
• First: some redistribution of income (winners and losers)
• If your income is ‘sticky’, you can lose out.
• (Important in many union negotiations)
• Menu costs: it costs money to send someone around with the price gun and/or print new menus
• Sometimes inflation can’t be accurately predicted.
• Unexpected(ly high) inflation helps borrowers and hurts lenders.
• Your turn: why?
• Unexpectedly low inflation helps lenders and hurts borrowers.
• Deflation is sticky, and brings its own problems… 23
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Inflation bad, deflation good? Not quite…
• In the 1990s (and after), Japan saw falling prices for just about everything.
• You’d think this would boost spending, since demand slopes downward.
• BUT people expected prices to fall.
• Lower sales, which led to lower prices
• A vicious self-fulfilling cycle of expectations.
• This trap is VERY difficult to get out of.
• Stable, small, positive inflation is what most central banks aim at
• (about 2% a year is a common target)
• It’s uncertain whether the Bank of Japan can create lasting inflation.
• (credibility, overcoming expectations)
(Source: http://www.japanreview.net/essays_can_the_bank_of_japan_create_inflation.htm )
Well worth reading, if a bit beyond the scope of this course. 25
