Quality adjustment: a review of some methods with examples from clothing Presented by Marc Prud’Homme Chief of Research on Consumer Prices Prepared for

Quality adjustment: a review of some methods with examples

from clothing

Presented by Marc Prud’Homme

Chief of Research on Consumer Prices

Prepared for the ILO/UNECE

workshop series

May 2010

23-04-202 Statistics Canada • Statistique Canada

Outline

Introduction Some theory Methods of quality adjustment

• Quality adjustment techniques

• Evaluations

• Recommended quality adjustment methods

Clothing• Overview

• The Canadian Experience

• Hedonic model for clothing

Final thoughts

Introduction The measurement of price change is complicated by the

appearance of new products and the disappearance of old products.

Existing products also change. • Price levels are affected

• Price changes are affected

Improper treatment = BIAS Quality bias occurs when the price change is not accurately

separated from the quality change. Boskin = 0.60 / 1.10 (percent points per annum)


The theory

CPI: A consumer price index measures a price change for a constant market basket of goods and services from one period to the next.

A temporal price index (e.g., CPI) should be an estimate of “pure” price change.

Matched sampling is used to “hit” this target.


The theory Matched sample: a sample in which the items selected for analysis share

all properties (characteristics) except that under investigation (price). MS holds constant the quality of the products that have been selected for

the index. To keep quality changes from influencing the price index, specifications of

the articles to be priced are of crucial importance. In practice, a matched sample is a “dream” and the reality is a “nightmare”.

• Products disappear

• Products change


The theory

If the disappearance is expected to be short lived then there is no major issue.

If not then a different approach must be used which often consist of replacing the items with a substitute.

If the substitute is of the same quality as the one to be replaced the price of the substitute can be used instead of the old one.


The theory

If there is a difference in quality between the old and the new item then an adjustment is needed.

The next section presents an overview of various quality adjustment methods.


The theory (guiding principles)

Quality is a pervasive concept. Quality adjustment is more an ART than a

science. Hulten (1997): “from a strictly theoretical

standpoint, no natural economic concept of quality exists.”


The theory (guiding principles)

DO NOT assume automatically…

• … That all price change is a reflection of the change in quality.

• … That products with different qualities are essentially equivalent.


Quality adjustment methods

Explicit (or direct) quality adjustment methods directly estimate the value of the quality difference between the old and new product and adjusts one of the prices accordingly.

Implicit (or indirect) quality adjustment methods estimate the pure price change component of the price difference between the old and new products based on the price changes observed for similar products.


Quality adjustment methods

Implicit QA methods

• Direct price comparison

• Overlap

• Overall mean imputation

• Class mean imputation

• Linked-to-show-no-price-change

• Matched model


Explicit QA methods

• Expert valuation

• Production costs

• Quantity adjustment

• Option cost

• Hedonics

Jevons price index formula


It=

Pi,t

Pi,t−1

⎛

⎝⎜

⎞

⎠⎟

i=1

n

∏1n

×I t−1

IMPLICIT QUALITY ADJUSTMENT METHODS


Direct price comparison

A simple approach where the price of the new product in the current period is directly compared with the price of the old product from the previous period.

Assumes no quality difference and the products are perfectly comparable.


1. Direct price comparison


PERIODPrice index

period 1

Price in period 1

Price in period 2

Price relativePeriod 2

Price index

period 2

ITEM X 100 15 16 1.067 106.7

ITEM Y 100 22.5 25 1.111 111.1

ITEM Z 100 14 N/A N/A N/A

ITEM R (Replacement)

18 1.286 128.6

All 100 16.78 19.31 1.151 115.1

Direct price comparison: evaluation

In the absence of any information on the new product, it can be the only choice.

Used when the quality difference are subtle or not valued by consumers.


2. Overlap method


When the old item and the replacement exist simultaneously on the market.

The price change from period t - 1to t is measured using the price of the old item.

The price change from period t to t + 1 is measured using the price of the replacement item.

Assumption: The price difference between the old and new products reflect the value of the quality difference.

2. Overlap method


PERIODPrice index

period 1

Price in period 1

Price in period 2


Price index

period 2

ITEM X 100 15 16 1.067 106.7

ITEM Y 100 22.5 25 1.111 111.1



16 18 1.125 112.5

All 10017.54

19.31 1.101 110.116.78

Overlap method: evaluation Simple and easy to implement. Acceptable if it is believed that the price ratio reflects the quality

ratio. This is a reasonable assumption

• If your are pricing the same item but in a different store.

• Reasonable assumption in competitive markets. Absence of necessary data Few quantities available (end-of-cycle) Perverse results depending on current marketing strategies


Overall mean imputation

When the price of the missing item is not known, an estimate of the price for the missing item is made.

An overlap price is imputed for the old item in the current period by taking the price changes between the previous and current periods of items in the same group.

The replacement’s price changes come into the index only in period 3.

Also called the Imputed price change-implicit quality adjustment method or bridged overlap.


3. Overall mean imputation


PERIODPrice index

period 1

Price in period 1

Price in period 2


Price index

period 2

ITEM X 100 15 16 1.067 106.7

ITEM Y 100 22.5 25 1.111 111.1

ITEM Z 100 14 15.24 1.089 108.9


n/a n/a 18 n/a n/a

All 100 16.78 18.27 1.089 108.9

Overall mean imputation: evaluation The method assumes that the pure price change from the replaced

item to the replacement item is the same for the composite of all items in the group.

This may or may not be true depending on the marketing environment at the time of the imputation.

The price change for the item replacement in the sample is imputed from the “pure” price changes of the other items for which their quality did not change.

An implicit quality adjustment is made.


Overall mean imputation: evaluation

The effect is as follows:• If quality is improving then the IP-IQ method misses some price

change because it inappropriately counts some price change as quality change.

• If prices are rising, it over adjusts for quality change and vice versa.

• The direction of the bias depends on the direction of the price change than the direction of the quality change.


Overall mean imputation: evaluation

The method should be used when the prices of the items in sample (the market) react in sync.

Should not be used when the prices of the products fluctuate as a result of market conditions.


Class mean imputation

Same approach as the Overall mean imputation but the price movement for the missing item is imputed from items in the sample of comparable quality.

Same conclusions as the IP-IQ method,


4. Class mean imputation


PERIODPrice index

period 1

Price in period 1

Price in period 2


Price index

period 2

ITEM X 100 15 16 1.067 106.7

ITEM Y 100 22.5 25 1.111 111.1

ITEM Z 100 14 15.56 1.111 111.1


n/a n/a 18 n/a n/a

All 100 16.78 18.39 1.096 109.6

Matched model (monthly chaining)

Index is calculated only from the sample of matching items from period to period.

When a replacement is chosen in period t, it is not used in the calculation of the index.

No attempt is made to adjust for any quality difference. Only the matched items that were in the sample in t – 1

AND t are used. Generates same result as the IP-IQ method.


5. Matched model


PERIOD

Price index period

1

Price in

period 1

Price in

period 2

Price relativePeriod

2

Price index

period 2

Price in period 3

Price relativePeriod

3

Price index

period 3

ITEM X 100 15 16 1.067 106.7 17 1.063 113.3

ITEM Y 100 22.5 25 1.111 111.1 27 136.1 120.0

ITEM Z 100 14 N/A 1.089 136.1 N/A N/A N/A


18 N/A 136.1 20 1.111 121.0

All 100 16.78 18.39 1.089 108.9 20.9 1.084 118.0

Link-to-show-no-price-change

With the “link-to-show-no-price-change” it is assumed that any price difference from the old model and the new item is explained by their quality disparity.



6. Link-to-show-no-price-change

PERIODPrice index

period 1

Price in period 1

Price in period 2


Price index

period 2

ITEM X 100 15 16 1.067 106.7

ITEM Y 100 22 25 1.111 111.1

ITEM Z 100 14 n/a n/a n/a

ITEM R (Replacement) 18 18 1.000 100.0

All 10016.78

19.31 1.058 105.818.25

LSNPC: evaluation

The method implies no inflation by assuming that all price change between the old and the new model is the result of quality differences.

The index is biased downward when prices are rising and vice versa.

Method which makes it difficult to isolate the pure price change.

EEC forbids its use.


Results compared

Method Price change Quality change

Direct comparison 28.6% 0%

Overlap method/matched model 12.5% 16.1%

Overall mean imputation 8.9% 19.7%

Class mean imputation 9.6% 19.0%

Link with no price change 0% 28.6%


EXPLICIT QUALITY ADJUSTMENT METHODS


Explicit quality adjustment methods

Direct adjustment methods

• Option price

• Production cost

• Expert judgement

• Hedonics More resource intensive compared to Implicit

methods.


1. Direct adjustment


PERIODPrice index

period 1

Price in period 1

Price in period 2


Price index

period 2

ITEM X 100 15 16 1.067 106.7

ITEM Y 100 22.5 25 1.111 111.1


ITEM R (Replacement) 17 18 1.059 105.9

All 100 16.78 19.31 1.079 107.9

Value of the quality difference

is $3

Value of the quality difference

is $3

Hedonics

Hedonic price index is any price index, which uses information from a hedonic regression. Hedonic regressions describe how a product’s price could be explained by the product's features (or characteristics).

Hedonics have proven to be very useful when applied to information and communication products (e.g. personal computers), because they can help overcome such problems (or challenges) such as new goods and rapid quality change.


The model and parameter estimates


P =b0 + bi Xi +ei∑

Hedonics: assumptions

Product characteristics must be quantifiable.

The collection of relevant product characteristics does not change.


Hedonics: issues

Functional form Multicollinearity Sample size Coefficients need to be stable


Hedonics: possible approaches

• Estimate the equation and use the coefficients as the “shadow” (or implicit) price of the characteristics.

• Estimate the hedonic equation in the base period and use it to estimate the price of the product in the comparison period. The difference in price is explained by quality change.



Has the quality changed?Has the quality changed?

Can the quality difference be explicitly quantified?

Yes

NoContinue to use

matched samplingContinue to use

matched sampling

YesUse direct adjustment

Manually assess

Manually assess

Production costs

Production costs

Expert panelsExpert panels

Option costsOption costs

HedonicsHedonics

No price difference is due to quality

Use direct comparisonUse direct

comparison

Overlap methodOverlap method

No

All price difference is due to quality

Are the old item and the new items available simultaneously?

Are the old item and the new items available simultaneously?

YesNo Linked with no price

changeLinked with no price

change

Overall class mean

imputation

Overall class mean

imputation

Is a replacement available?

Yes

Replacement available

No replacement available

Carry Forward

Carry Forward

Clothing: the Canadian practice


Before moving on…

• Each and every instance of commodity substitution is unique and must be carefully considered to ensure that the aim of measuring pure price change is respected, as far as practicable.

• Which method is used to make the quality assessment must also be considered on a case by case basis.

• Different approaches generate different results.


Clothing


Monthly clothing indexes. Jan 2001 to Sept 2009


Monthly clothing indexes. Jan 2001 to Sept 2009



Clothing: the issues

The apparel component of the CPI was chosen as the subject of the research described in this article due in part to the difficulty of correctly measuring price change for apparel items and the labor-intensive nature of the microlevel review of price and characteristic data associated with apparel.

Brown and Stockburger, 2007


Clothing: the issues

The seasonal nature of apparel The large number of item replacements The need on maintaining a constant-quality

price index Result: resource intensive exercise



Direct approach Field agents collect the prices and the features of the

apparel item on a Quality Price Change Report (QPCR). The analysts at the head office then decide if the

substitute is comparable or not to the replaced item. They also make the quality valuation. Examples of a QPCR for clothing at Statistics Canada. It starts with the item specification.



Item Specification Description• Item Name : Women's Shirt 2

• Desirable Quantity and Unit of Measure : 1 UT

• When to Price : Monthly

• Amendment Notice Number : 802

• Amendment Notice Date : 20020106



Item Description:• Shirt

• Misses size range or S, M, L

• Broadcloth, polyester/cotton or polyester/rayon (viscose) fibre

• Thread count approx. 128 x 72 per 2.5 cm2

• Solid colours including fashion colours

• Folded over buttoned front


Back yoke

Long sleeves with single cuffs

No trim

Good workmanship

Safety stitch seams

Perma-press finish

6 pearlized buttons


Acceptable Added value features:• 100% cotton broadcloth

• 100% rayon (viscose)

• One breast pocket

• Button-down collar

• Front placket

• Printed fabric

• Yarn dyed woven check or striped fabric

• Moderate amount of trim such as ruffles, piping, etc

• Double stitched collar

• Packaged



Acceptable Decreased value feature:• Up to 10% lower thread count and 8-10 stitches per 2.5 cm

• No back yoke

• Short sleeves

• Roll up sleeves

• 5 plastic buttons

• One piece collar

• One colour only



Acceptable Deviations:• Oxford cloth, Polyester/cotton, Polyester/rayon (viscose) fibre with a thread

count of approx. 84 x 50 per 2.5 cm2 with the same styling features may be selected at equal value

• A dress blouse of 100% polyester in solid colours

• With moderate lace trim and/or pleating

• Front buttons (may have placket and/or ties)

• May be priced but upon selection, specifics must be indicated

• If, because of a certain characteristic (e.g. fibre content), it is not possible to find an item that exactly meets the specification, if that particular characteristic is mentioned on the checklist, it will be allowed as an acceptable deviation.















Clothing and hedonics (Liegey 1993) To calculate the quality adjusted price… Assume a woman’s coat without lining contained 20% wool and

80% polyester (base variable) was no longer available for pricing. The replacement now has lining and contains a 40% wool and

60% polyester mix, ceteris paribus. The value of the lining and the 20% additional wool would be

added to the price of the old item. Constant quality prices are compared. Polyester is the base, so nothing needs to be done here.


Clothing and hedonics (CDA)




If this model were to be used in quality adjustment we would assess a unit change in the percentage of cotton fibre resulting from substitution at 49 cents.

However, if the brand changed upon substitution from a store brand or a miscellaneous brand to a national/regional brand the quality difference would be assessed at $7.11.

The outlet variables included in this model would not be used in quality adjustment directly, but are present in the model simply to improve its specification.



If this model were to be used in quality adjustment we would assess a unit change in the percentage of cotton fibre resulting from substitution at 49 cents.

However, if the brand changed upon substitution from a store brand or a miscellaneous brand to a national/regional brand the quality difference would be assessed at $7.11.

The outlet variables included in this model would not be used in quality adjustment directly, but are present in the model simply to improve its specification.

Final thoughts about clothing

The issue of fashion Should sale prices be used? Dutch approach: seasonal baskets Hedonics


The end


Documents

Quality adjustment: a review of some methods with examples from clothing Presented by Marc Prud’Homme Chief of Research on Consumer Prices Prepared for