Nobel Prize - Economics

Three Amigos

Eugene Fama - U. ChicagoLars Peter Hansen - U. ChicagoRobert Shiller - Yale

Financial Economics

American

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 Index22 Commodities 1967 = 100

Commodity Research Bureau - Foodstuffs Index1967 = 100

Commodity Research Bureau - Metals Index1967 = 100

Fall 2011 – Gold $1800/oz, wheat $330/tonne = 0.18 oz/tonne

Napoleanic Wars

WW I

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

( )

commodity j

sales of share % where

100

=

=

∗•= ∑

j

jjj

w

PwP

Simple average or weighted average ?• e.g. egg price index

Weights reflect relative importance (sales, volume)

Building an Index: Three Issues

2. Weighting prices Weighted or Geometric Average?

€

AG = Pjj=1

n

∏ ⎛

⎝ ⎜

⎞

⎠ ⎟

1/ n

AG = (1.10*1.20* 0.70)( )1/ 3= 0.97

Weighted average - index formed as a weighted sum of pricesGeometric - when price changes expressed as a product

E.g. stock price up 10%up 20%

Down 30%

How are you doing?

Building an Index: Three Issues

3. Choice of Base Year

yearbasetheinquantityQ

tperiodinquantityQ

Q

QindexQ

b

t

b

tt

where

100

==

•⎟⎟⎠

⎞⎜⎜⎝

⎛=−

Index reflects level

relative to the level some time in the past (Base year)to the level now

Base year is arbitrarye.g. index of agricultural output

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 IndicesTwo well known + popular indices

Current prices expressed relative to base year (base = 100)Prices weighted in relation to proportion of expenditureWeights are static

Laspeyres– Beginning year expenditure weights

Paasche– Ending year expenditure weights

Alternative Weights - Price Indices

€

Index i = w j • Pi j / P0 j( )j

∑ • 100

where i = current period; 0 = base period

j = commodity

w j = expenditure weight

) ( exp

) ( exp

periodbaseendituretotal

periodbasejonenditurew j =

Consumer Price Index

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

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)

CPI Canada 1996 BasketCANSIM I Series Number: P100001

10

30

50

70

90

110

130

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Statistics Canada: CANSIM II SERIES V735320 TABLE NUMBER: 3260001

CANSIM I Series Number: P100001

Stat Can., The DailySeptember 21, 2011

Nominal and Real (CPI deflated) Butter Prices in Ontario 1985 – 1997 (monthly data - 1986 base)

Source: Statistics Canada

1.50

1.70

1.90

2.10

2.30

2.50

2.70

2.90

1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996

$/dozen

Nominal Price

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

If CPI indicated 3%, while true inflation was 2%,

over 12 years inflate national budget by

Boskin Budget = $25,000

Consequences:

1 $ TRILLION

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 IndexMeasure impact of Increase in Pizza Price

BEER

PIZZA

U0

U1

I0I1

TCOLI = I1/I0

**

*

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

Pizza

MRS = MPP/MPB

Mechanics of Building the Index Number

Prices for each outlet collected

(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

“Elementary Level Index”

Combine m commodity indices into the final index using the Laspeyers Index

“Commodity Level Index”

€

(P11j, P12j, ..... P1kj)

€

(P1j, P2j, ..... Pnj)

€

(Pj) j =1 ... n

€

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 levelaggregating commodity prices into an index

substitution effects neglected

1.3 - between outletsdiscount operators with significant market share

discount share neglected

Elementary Level Bias

outlets across changes % price of variance= )(

rateinflation = i :

)()1()2/1(

ε

ε

VWhere

ViBE ⋅+⋅≈

Substitution (commodity) Bias Calculation is the same as elementary bias

Example:Diewert provides and example where he assumes that:

V(ε) = 0.005 i = 2 percent

total bias in the index of about 0.5 percentage points

Outlet Substitution Bias

s = market share of discountersd = percent discount

• For conservative assumptions, he estimates this bias at about 0.4 percentage points

€

BOS ≈ (1+ i) ⋅s ⋅d

2 Quality Bias

• Goods disappear, no longer sold, quality improved

• Disappearance about 20%/year

• Agencies “link in” improved product

€

BQ ≈ (1+ i) ⋅se

(1+ e)

⎡

⎣ ⎢ ⎤

⎦ ⎥

s = market share of new producte = 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

s = market share of new productd = decline in new good price

€

BN ≈ (1+ i) ⋅s ⋅d

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