quality adjustment: a review of some methods with examples from clothing presented by marc...
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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)
23-04-203 Statistics Canada • Statistique Canada
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.
23-04-204 Statistics Canada • Statistique Canada
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
23-04-205 Statistics Canada • Statistique Canada
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.
23-04-206 Statistics Canada • Statistique Canada
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.
23-04-207 Statistics Canada • Statistique Canada
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.”
23-04-208 Statistics Canada • Statistique Canada
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.
23-04-209 Statistics Canada • Statistique Canada
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.
23-04-2010 Statistics Canada • Statistique Canada
Quality adjustment methods
Implicit QA methods
• Direct price comparison
• Overlap
• Overall mean imputation
• Class mean imputation
• Linked-to-show-no-price-change
• Matched model
23-04-2011 Statistics Canada • Statistique Canada
Explicit QA methods
• Expert valuation
• Production costs
• Quantity adjustment
• Option cost
• Hedonics
Jevons price index formula
23-04-2012 Statistics Canada • Statistique Canada
It=
Pi,t
Pi,t−1
⎛
⎝⎜
⎞
⎠⎟
i=1
n
∏1n
×I t−1
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.
23-04-2014 Statistics Canada • Statistique Canada
1. Direct price comparison
23-04-2015 Statistics Canada • Statistique Canada
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.
23-04-2016 Statistics Canada • Statistique Canada
2. Overlap method
23-04-2017 Statistics Canada • Statistique Canada
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
23-04-2018 Statistics Canada • Statistique Canada
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)
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
23-04-2019 Statistics Canada • Statistique Canada
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.
23-04-2020 Statistics Canada • Statistique Canada
3. Overall mean imputation
23-04-2021 Statistics Canada • Statistique Canada
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 15.24 1.089 108.9
ITEM R (Replacement)
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.
23-04-2022 Statistics Canada • Statistique Canada
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.
23-04-2023 Statistics Canada • Statistique Canada
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.
23-04-2024 Statistics Canada • Statistique Canada
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,
23-04-2025 Statistics Canada • Statistique Canada
4. Class mean imputation
23-04-2026 Statistics Canada • Statistique Canada
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 15.56 1.111 111.1
ITEM R (Replacement)
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.
23-04-2027 Statistics Canada • Statistique Canada
5. Matched model
23-04-2028 Statistics Canada • Statistique Canada
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
ITEM R (Replacement)
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.
23-04-2029 Statistics Canada • Statistique Canada
23-04-2030 Statistics Canada • Statistique Canada
6. Link-to-show-no-price-change
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 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.
23-04-2031 Statistics Canada • Statistique Canada
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%
23-04-2032 Statistics Canada • Statistique Canada
Explicit quality adjustment methods
Direct adjustment methods
• Option price
• Production cost
• Expert judgement
• Hedonics More resource intensive compared to Implicit
methods.
23-04-2034 Statistics Canada • Statistique Canada
1. Direct adjustment
23-04-2035 Statistics Canada • Statistique Canada
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) 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.
23-04-2036 Statistics Canada • Statistique Canada
The model and parameter estimates
23-04-2037 Statistics Canada • Statistique Canada
P =b0 + bi Xi +ei∑
Hedonics: assumptions
Product characteristics must be quantifiable.
The collection of relevant product characteristics does not change.
23-04-2038 Statistics Canada • Statistique Canada
Hedonics: issues
Functional form Multicollinearity Sample size Coefficients need to be stable
23-04-2039 Statistics Canada • Statistique Canada
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.
23-04-2040 Statistics Canada • Statistique Canada
23-04-2041 Statistics Canada • Statistique Canada
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
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.
23-04-2043 Statistics Canada • Statistique Canada
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
23-04-2048 Statistics Canada • Statistique Canada
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
23-04-2049 Statistics Canada • Statistique Canada
Clothing: the Canadian practice
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.
23-04-2050 Statistics Canada • Statistique Canada
Clothing: the Canadian practice
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
23-04-2051 Statistics Canada • Statistique Canada
Clothing: the Canadian practice
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
23-04-2052 Statistics Canada • Statistique Canada
Back yoke
Long sleeves with single cuffs
No trim
Good workmanship
Safety stitch seams
Perma-press finish
6 pearlized buttons
Clothing: the Canadian practice
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
23-04-2053 Statistics Canada • Statistique Canada
Clothing: the Canadian practice
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
23-04-2054 Statistics Canada • Statistique Canada
Clothing: the Canadian practice
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.
23-04-2055 Statistics Canada • Statistique Canada
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.
23-04-2063 Statistics Canada • Statistique Canada
Clothing and hedonics (CDA)
23-04-2065 Statistics Canada • Statistique Canada
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.
Clothing and hedonics (CDA)
23-04-2066 Statistics Canada • Statistique Canada
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
23-04-2067 Statistics Canada • Statistique Canada
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