Transcript 311 orientation - McGill University

Nobel Prize - Economics
Three Amigos
Financial Economics
American
Eugene Fama - U. Chicago
Lars Peter Hansen - U. Chicago
Robert Shiller - Yale
Case-Shiller Housing Index
Chap 3 - Index Numbers
Statistics Canada - “The Daily” - Online
Index Numbers - Outline
• Constructing an Index - 3 Issues
• Price Relatives – an example
• Weighting Schemes
– Simple average - Geometric average
– Laspeyres index
– Paasche index
• Consumer Price Index
• Diewert article – other issues in building the CPI
Commodity Research Bureau - Spot Index
22 Commodities 1967 = 100
Commodity Research Bureau - Foodstuffs Index
1967 = 100
Commodity Research Bureau - Metals Index
1967 = 100
Napoleanic Wars
WW I
Fall 2011 – Gold $1800/oz, wheat $330/tonne = 0.18 oz/tonne
Building an Index: Three Issues to Consider
1.
Which commodities to include?
Fundamental conflict (cost – benefit)
–
–
–
–
Reflect population of interest
Data availability
Proxy data - high correlation
Price level or price changes?
Building an Index: Three Issues
2. Weighting prices
Simple average or weighted average ?
• e.g. egg price index
Weights reflect relative importance (sales, volume)
P   w j  Pj 100
j
where w j  % share of sales
j  commodit y
Building an Index: Three Issues
2. Weighting prices
Weighted or Geometric Average?
Weighted average - index formed as a weighted sum of prices
Geometric - when price changes expressed as a product
E.g. stock price up 10%
up 20%
Down 30%
How are you doing?
 n 1/ n
AG  Pj 
j 1 
AG  (1.10*1.20* 0.70)
1/ 3
 0.97
Building an Index: Three Issues
3. Choice of Base Year
Index reflects level
relative
to the level some time in the past (Base year)
to the level now
Base year is arbitrary
e.g. index of agricultural output
 Qt 
Q  indext     100
 Qb 
where Qt  quantityin period t
Qb  quantityin the base year
Example: Price Relatives
• Objective:
– build indices to measure proportional price variation during a trading day
– For each commodity, + for the group
• 3 commodities (wheat, corn, beans) - $/bu
• Data: high & low prices and volume of trade for September 15, 2003
Alternative Weights - Price Indices
Two well known + popular indices
Laspeyres
– Beginning year expenditure weights
Paasche
– Ending year expenditure weights
Current prices expressed relative to base year (base = 100)
Prices weighted in relation to proportion of expenditure
Weights are static
Alternative Weights - Price Indices


Indexi   w j  Pi j / P0 j  100
j
where i  current period; 0 = base period
j  commodity
w j = expendit ure weight

expenditure on j (base period)
wj 
total expenditure (base period)
Consumer Price Index
Uses of CPI
– compare changes in real wages and income
– adjust expenditure data for price changes
=> estimate changes in quantities
http://www.statcan.gc.ca/cgi-bin/imdb/p2SV.pl?Function=getSurvey&SDDS=2301&lang=en&db=imdb&adm=8&dis=2
(2013 active)
Laspeyres index
– calculated each month
– national sample of retail prices (600 goods)
Weights - past (base period) expenditure shares (fixed)
Weights reflect expenditure patterns of national sample of households
CPI Canada 1996 Basket
CANSIM I Series Number: P100001
130
110
90
70
50
30
10
1950
1955
1960
1965
1970
1975
Statistics Canada: CANSIM II SERIES V735320
CANSIM I Series Number: P100001
1980
1985
1990
TABLE NUMBER: 3260001
1995
2000
2005
Stat Can., The Daily
September 21, 2011
Nominal and Real (CPI deflated) Butter Prices in Ontario
1985 – 1997 (monthly data - 1986 base)
Source: Statistics Canada
$/dozen
2.90
Nominal Price
2.70
2.50
2.30
2.10
1.90
1.70
1.50
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
Erwin Diewert:
Index Number Issues JEP (1988)
Objective:
•
Problems related to measuring price changes, based on the Laspeyers index
•
Differences between Laspeyres & other cost of living indexes
1995 Boskin Commission
Mandate from US Senate
CPI overestimated price changes by 1.1% per year
Consequences:
If CPI indicated 3%, while true inflation was 2%,
over 12 years
inflate national budget by
1 $ TRILLION
Boskin Budget = $25,000
Some History: Cost of Living (COL) Index
• individual or society
• A. Konus (1939) - True Cost of Living Index
– (individual or family)
• min cost to achieve U0 (base period) relative to
subsequent period - given a price increase
• R. Pollak (1981) generalized the concept to a social cost of
living index – society as a whole
• concept the same, practically very difficult
• Not the same as Laspeyres or Paache indices
True Cost of Living Index
Measure impact of Increase in Pizza Price
U0
BEER
U1
TCOLI = I1/I0
*
*
*
I1
I0
PIZZA
Laspeyres Index
used to construct the CPI
over estimates impact of rising prices on welfare
product substitutions
Paache Index
under-estimates the impact of price changes
Diewert (1983)
Pollak-Konus true COL index somewhere in between
not observable
Alternative to Konus-Pollack
•
•
Some average of LI + PI
Diewert argues for Irving Fisher’s (1922) Index
geometric mean of LI & PI vs arithmetic mean
satisfies many desirable properties
superlative index
–
–
–
–
index increases if prices increase?
lays somewhere between the LI and the PI
if all prices increase by 10%, index increases by 10% (CRTS)
it is exact when preferences are homothetic
Homothetic Preferences
BEER
MRS = MPP/MPB
MRS
Pizza
Mechanics of Building the Index Number
Prices for each outlet collected
(P11j, P12j, ..... P1kj )
(k prices gathered for commodity j
for outlet 1 for example)

Calculate Unit value price for each outlet
- k prices combined for each outlet i
- n outlet prices for commodity j
Combine n outlet prices to create and
index for commodity j, using the
Laspeyers Index or other method
(P1j, P2j, ..... Pnj )

(Pj )
j  1 ... n
“Elementary Level Index”
Combine m commodity indices into the
final index using the Laspeyers Index

“Commodity Level Index”

LI = f(P1, P2, ..... Pm )
Biases - use of the LI for the CPI
1 Substitution Biases –relative to Fisher Index
1.1 - elementary index level
aggregating prices across outlets using LI
substitution effects neglected
1.2 - commodity level
aggregating commodity prices into an index
substitution effects neglected
1.3 - between outlets
discount operators with significant market share
discount share neglected
Elementary Level Bias
B E  (1 / 2)  (1  i) V ( )
Where : i = inflationrate
V ( ) = varianceof price% changes across outlets
Substitution (commodity) Bias
Calculation is the same as elementary bias
Example:
Diewert provides and example where he assumes that:
V() = 0.005
i = 2 percent
total bias in the index of about 0.5 percentage points

Outlet Substitution Bias
BOS  (1 i)  s  d
s = market share of discounters
d = percent discount
• For conservative assumptions, he estimates this bias at
about 0.4 percentage points
2 Quality Bias
• Goods disappear, no longer sold, quality improved
• Disappearance about 20%/year
• Agencies “link in” improved product
BQ
 se 
 (1 i)  

(1 e)
s = market share of new product
e = percent increase in efficiency of improved product


3 New Goods Bias
how to deal with new goods?
“linked in” after some time
initial high price that falls later – not captured
BN  (1 i)  s  d
s = market share of new product
d = decline in new good price
WHAT TO DO ?
• Use of new index formula's
• Scanner data - construct better indices at the elementary level
• Hedonic methods (regression) to adjust for quality changes
– value of product attributes
• New goods bias - introduce these goods more quickly