Nobel Prize - Economics Three Amigos Eugene Fama - U. Chicago Lars Peter Hansen - U. Chicago Robert 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 Index 22 Commodities 1967 = 100

Commodity Research Bureau - Foodstuffs Index 1967 = 100

Commodity Research Bureau - Metals Index 1967 = 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 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? 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?

Building an Index: Three Issues 3. Choice of Base Year Index reflects level relativeto the level some time in the past (Base year) to the level now Base year is arbitrary e.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 Indices Two well known + popular indices Current prices expressed relative to base year (base = 100) Prices weighted in relation to proportion of expenditure Weights are static Laspeyres –Beginning year expenditure weights Paasche –Ending year expenditure weights

Alternative Weights - Price Indices

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 (2013 active)

Statistics Canada: CANSIM II SERIES V TABLE NUMBER: CANSIM I Series Number: P100001

Stat Can., The Daily September 21, 2011

Nominal and Real (CPI deflated) Butter Prices in Ontario 1985 – 1997 (monthly data base) Source: Statistics Canada $/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 U 0 (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 BEER PIZZA U0U0 U1U1 I0I0 I1I1 TCOLI = I 1 /I 0 * * *

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 = MP P /MP B

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 ”

Biases - use of the LI for the CPI 1 Substitution Biases –relative to Fisher Index elementary index level aggregating prices across outlets using LI substitution effects neglected commodity level aggregating commodity prices into an index substitution effects neglected between outlets discount operators with significant market share discount share neglected

Elementary Level Bias Substitution (commodity) Bias Calculation is the same as elementary bias Example: Diewert provides and example where he assumes that: V(  ) = i = 2 percent total bias in the index of about 0.5 percentage points

Outlet Substitution Bias 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 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 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