1 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

in the BLS Price Programs

Quality Adjustment

Steven Sawyer, Producer Price Program

Aric Schneider, International Price Program

Ryann Watkins, Consumer Price Program

Data Users’ Conference

April 21, 2021
2 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

International Price Program

Quality Adjustment

Overview

Aric Schneider
3 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Introduction

1. Overview – Why and What is Quality Adjustment

2. When does BLS Quality adjust

3. How we Adjust

4. Questions
4 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Why and what is quality adjustment
5 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

When to quality adjust

 Old and new products are comparable

 Explicit quality adjustment

 Cost-based

 Hedonic quality adjustment

 Change in size/quantity

 Old and new products are not comparable

 New product previous price

 Price imputation
6 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

When to quality adjust (cont.)

CPI PPI MXPI

Old/new products 

comparable

Direct Comparison Direct comparison Direct Comparison

Explicit quality 

adjustment

Cost-Based

Hedonics

Cost-Based

Hedonics

Cost-Based

Hedonics for computers

Change size/quantity Quantity Adjustment Ratio method Link Adjustment

New product 

previous price

*new products previous price 

not used 

Overlap method Discontinue and Replace

Price imputation Class mean imputation and 

cell relative imputation

Link to cell relative Discontinue and Replace
7 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Consumer Price Program

Quality Adjustment

for Consumer Prices

Ryann Watkins
8 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Consumer Price Index (CPI) quality adjustment

 The quality adjustment (QA) method is 1 of 3 methods 

used when handling replacement items

 3 methods used:

Directly use price change

Impute price change

Adjust for quality changes

– Occurs at the item level, not index level
9 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Consumer Price Index (CPI) quality adjustment: Why?

 Why do we use quality adjustments in the CPI?

Items in the market basket sometime leave the marketplace and 

need to be replaced

Often, replacement items have quality differences and cannot be 

compared directly to the unavailable item 

This is where QAs come in!

– QAs make it possible to compare different items across time periods
10 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Consumer Price Index (CPI) quality adjustment: When

 When do quality changes happen in the CPI?

Quality changes in replacement items are most likely to occur during:

Seasonal Changes 

(Mostly apparel items) Upgrades to Existing 

Items (model year 

changes for new vehicles)

Innovation and 

Technological Changes

***Note: technological changes and upgrades are not mutually exclusive
11 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

CPI quality adjustment: by the numbers

Item Group 

Total 

Items

Items 

with a 

Price 

# 

Replacement 

Items

%

Replacement 

Items

% Direct 

Comparison

% Quality 

Adjusted

% Noncomparable

APPAREL 181028 93797 8408 9% 39.0% 23.5% 37.5%

FOOD 393277 264313 4608 1.7% 19.6% 15.8% 64.3%

HOUSEHOLD 56170 36385 1202 3.3% 31.0% 13.1% 55.8%

SERVICES 249083 155790 6794 4.4% 23.9% 36.5% 39.4%

TRANSPORTATION 214144 166159 10011 6% 51.7% 11% 37.2%

Total 1093702 716444 31023

Average 4.3% 33.0% 20.0% 47.0%

Number of CPI replacement items in 2020 
12 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

CPI item checklists

 How do we know when the replacement item has a quality difference?

“Item checklist”

 Each item has a checklist that capture all its important characteristics

 Data collectors use checklists to choose replacement items

 Analysts review the characteristic changes to determine if there’s been 

quality changes
13 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

CPI item checklist example: computers

Category 

Characteristic
14 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

QA methods used in CPI

 Hedonic based QA method

 Uses statistical regression models to estimate the values of specific 

characteristics

 Data used to build models come from CPI sample or alternative data 

sources

 Examples: apparel items, televisions, cell phones

 Cost based QA method

 Exact monetary values are assigned to specific characteristics 

 Values are obtained from manufacturers, alternative data sources, 

website information, etc.

 Example of items: new vehicles, computers
15 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Hedonic based QA

Purpose: Hedonic QAs remove the difference in quality between replacement items and 

unavailable items allowing us to show a better estimate of price change

Data: Item’s CPI sample or alternative data source

Requirements: Sample ≥ 100 observations and has sufficient variation 

Regression Equation (semi-log function): 

Log(Price)= a + β1x1 + β2x2+ +.... βnxn + ɛ
16 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Hedonic model example: women’s dresses 

Variable

Category

Independent

Variable (Xn)

Parameter

Estimate (βn)

Variable 

Category

Independent 

Variable (Xn)

Parameter

Estimate (βn)

Fiber Spandex -0.00894 Size Misses, Petites, Plus base

Silk 0.00480 Juniors -0.37011

Wool 0.00356

Nylon 0.00169 Lining No lining -0.10506

Poly, Rayon, Cotton base Full/partial lining base

Type Bridal 1.23375 Length Below knee 0.05881

Formal 0.20270 Knee and above base

Casual base Sleeve 

length

Long sleeve 0.12287

Brand Cat. Exclusive 1.13463 Short sleeve, sleeveless base

Boutique 0.89729 Closure Zipper base

High end national 0.63105 Button -0.07697

National base None -0.17508

Special line private -0.15400 Features Sequin, bead, 

rhinestone

0.11495

Private label -0.28324 Jacket 0.09642

Misc -0.26275 None base
17 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Hedonic based QA example: women’s dresses

Type of Quality

Change Old Item Replacement Item

Fiber 100% Polyester 60% Nylon 40% 

Polyester

Type of Dress Casual dress Formal dress

Lining No lining Lining

Closure No closure Zipper closure

Price $125 $250
18 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Hedonic based QA example: calculation for women’s dresses

1. Calculate the adjusted price of the old item, which will be used 

to calculate the price change used in the index

Price old item* ee(Σ rrrrrrrrrrrrrrrrrrrrrr ee ee ee− Σ oo oo ee ee ee) = Price adjusted old item

$125 old item* ee((0.101+0.203)−(−0.105−0.175)) = $224.15adjusted old item
19 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Hedonic based QA example: calculation for women’s dresses (cont.)

2. Calculate the price change of the adjusted old price and the 

replacement item’s price:

[(Price replacement ̶ Price adjusted old item)/ Price adjusted old item]∗100= Adjusted Price Change

[($250 ̶ $224.15)/ $224.15] ∗100 = 12%  Adjusted price change used in index

NOTE: QA, in this case, is more accurate than directly comparing prices:

[($250 ̶ $125)/ $125] ∗100 = 100% Price change without QA (not used in index)
20 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Cost based QA 

Purpose: Cost based adjustments also remove the difference in quality between replacement and 

unavailable items 

Difference from hedonic QA: Cost based adjustments use actual dollar values, not estimated dollar 

values from a regression model

Data: Price & characteristic data provided by manufacturers, alternative data sources, and/or online 

info

Requirements: Prices associated with specific characteristics are available
21 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Cost based QA example: new vehicles

Type of Quality

Change

2020 Model

(MSRP $33,550)

2021 Model

(MSRP $34,750)

ReportedValue 

of 

Characteristic

Interior Not standard Smartphone 

integration

$50

Transmission 6 speed 

transmission

9 speed 

transmission

$399

Remote/

keyless entry

No Yes (Auto 

Start/Stop)

$459
22 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Cost based QA example: calculation for new vehicles

1. Calculate the adjusted price of the old item, which will be used to calculate 

the price change used in the index

Price old item+ New Characteristics– Old Characteristics= Price adjusted old item 

$33,550+ ($50+$399+$459)– 0= $34,458adjusted old item
23 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Cost based QA example: calculation for new vehicles (cont.)

2. Calculate the price change of the adjusted old price and the replacement 

item’s price

[(Price replacement ̶ Price adjusted old item)/ Price adjusted old item]∗100= Adjusted Price Change

[($34,750-$34,458)/$34,458]∗100 = 0.85%Adjusted price change used in index

NOTE: QA, in this case, is more accurate than directly comparing prices:

[($34,750 ̶ $33550)/ $33550] ∗100 = 3.6% Price change without QA (not used in index)
24 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Producer Price Program

Quality Adjustment

for Producer Prices

Steven Sawyer
25 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Why the PPI quality adjusts

 Continual innovation and improvements across the U.S. 

economy means products change on a regular basis

 All of this change makes quality adjustment crucial to the PPI, a 

matched-model price index
26 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Common changes to goods

 Upgraded parts

 Different materials

 Different physical properties

 Software
27 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Common changes to services

 Time

 Location

 Speed

 Activity

 Software
28 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Base prices and price relatives

 Price change is measured as the change in the ratio of the net 

price (NP) to the base price (BP), known as the long-term 

relative (LTR)

ΔPrice = Δ

NNNN

BB

= ΔLTR

 Quality adjustment involves changing the BP

 Product’s price can change because of a change in NP, BP or 

both
29 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Explicit quality adjustment

 Used when a PPI Industry Analyst (IA) can obtain the change in 

production cost (typically from the respondent) associated 

with the change in the product

 Change in production cost also is called the value of quality 

adjustment (VQA)
30 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Explicit quality adjustment formula

 BBBBNN NN= BBBBOO �

NNNNNNNNww

NNNNNNNN −VVVVVV

 Denominator of the fraction, NN NN NN − VVVVVV, represents 

the estimated net price of the old product in the month the 

substitution is made effective
31 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Explicit Quality Adjustment Example

 Price of a new model car is $14,000 and the price of the 

previous year’s version is $13,500 

o $200 of that increase is due to the extra product cost and 

normal margin associated with the addition of governmentmandated safety equipment 

o Pure price change is only $300 
32 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Explicit Quality Adjustment Example (cont.)

 Assume BBBBOO = 13,200

 BBBBNN NN= 13,200 �

14,000

14,000−200

= 13,391.3043

 Estimated price old model car in current period is 13,800

 LLLLLLOO =

13,500

13,200

= 1.0227

 LLLLLLNN NN =

14,000

13,391.3043

= 1.0455

 ∆ PPPPPP =

1.0455−1.0227

1.0227

= 0.0223
33 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

PPI hedonic models

 Microprocessors

Desktop

Notebook

Server

 Computers (jointly developed with IPP)

Desktop

Notebook

Server

 Broadband high speed Internet service
34 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Computer hedonic QA example

CCCCCCCCCCCCCCCC pppp = aa + bb11CCCCCC ss ss +

bb22CCCCCC + bb33MM MM + bb44SS SS + bb55OO/SS

Variable Quantity Coefficient (a or b) Marked up cost

Intercept - 100 100

CPU speed 3.2 50 160

CPU cores 4 22 88

Memory 4 20 80

Storage 750 0.14 105

Operating system 1 100 100

Computer price - - 633
35 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Broadband hedonic QA example

log(Broadband price) = a + 0.45log(Download speed) + 0.1(Business) + 

0.61(Company A) 

VVVVVV = yy0[(

xx1

xx0

)bb1 − 1]

= 40[(

75

50)0.45 − 1]

= 8.0066

Old New

Price 40 45

Download

speed

50 75
36 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Time dummy hedonic models

ll = αα00 + ∆DD +11 + ββ22ll (XX22) + ⋯ + ββkkll ( XXkk)

 Typically in log-log form

 Same form as hedonic quality adjustment model, but with a time dummy (DD(tt+1))

 Dataset is typically a two time period unbalanced panel (pooled cross-section)
37 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Time dummy hedonic models (cont.)

 Time dummy coefficient (Δ) gives an estimate of quality adjusted price 

change between time periods

Price is directly adjusted

Base price does not change

 Currently used in PPI Integrated microcircuits index
38 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Time dummy hedonic model example

log(CPU price) = a + -0.02Dt+1 + 0.09log(CPU speed) + 0.52log(CPU cores) + 

0.76log(Cache) + 0.21log(Threads) 

Price change = ee∆ − 1

= ee−0.02 − 1

= -0.0198

= -1.98% 
39 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Microprocessors matched-model vs. time 

dummy hedonic index

O

Official PPI 

Index

Time Dummy 

Hedonic Index
40 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Ratio method

 Useful when the ratio of the old and new price are expected to be equal 

to the ratio of two values such as a quantity or size

One associated with old product

Another associated with new product

BBBBNN NN = BBBBOO �

VVNN NN

VVOO

where

VVNN NN = value corresponding to the new product 

VVOO = value corresponding to the old product
41 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Ratio method example

 A ready-mix concrete company used to report prices by cubic yard and 

now reports by truckload

Mixer contains 8.5 cubic yards

Price increased from $100/cubic yard to $850/truckload

 If the old base price is $95, then 

BBBBNN NN= $95 �

8.5

1

= $807.5000
42 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Overlap method

 VQA not available

 Net prices for both the old product and the new product are available 

for previous time period 

 Ratio of the two net prices can be used to calculate a new base price:

BBBBNN NN= BBBBOO � NNNNNNNN pppppppppppppp∗

NNNNOOOO pppppppppppppp∗

*in previous time period
43 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Overlap method (cont.)

 Method captures price changes between previous and current 

period

Input price changes

Demand changes

Other market changes
44 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Overlap method example

 Tire company discontinues a passenger car tire

No direct replacement available

 Respondent provides a tire from another product line that has been in 

production for a few months

Previous month’s price for the old tire is $105 

Previous month’s price for the new tire is $103

Current month’s price for new tire is $107 

 If the old base price is $101, then

BBBBNN NN = $101 �

$103

$105

= $99.0762
45 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Overlap example price change

 LLLLLLOO =

105

101

= 1.0396

 LLLLLLNN NN =

107

99.0762

= 1.0800

 ∆ PPPPPP =

1.0800−1.0396

1.0396

= 0.0389
46 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Link to cell relative

 Used with a non-comparable substitute

No VQA available

No overlap price available

 Method imputes a price change for the product 

Price change (the “cell relative”) equals the average price change for 

all products in the product’s lowest level index (“cell”) which actually 

have good (non-imputed) prices
47 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Link to cell relative formula

BBBBNN NN= BBBBOO �

NN NN NN

eeee NN

where est NP represents the estimated net price (aka, cell relative) for the old product in the month that 

the substitution is made effective
48 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Link to cell relative example

 Steel foundry provides a substitute casting

 Respondent cannot provide a VQA for the new casting and 

there is no overlap pricing

 New casting price is $29.30, old casting price is $28.90, old 

base price is $26.70 and cell relative price is $33.50

BBBBNN NN= $26.70 �

$29.30

$33.50

= $23.5636
49 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Link to cell relative example price change

 LLLLLLOO =

28.9

26.7

= 1.0824

 LLLLLLNN NN =

29.3

23.5636

= 1.2434

 ∆ PPPPPP =

1.2434−1.0824

1.0824

= 0.1487
50 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

International Price Program

Quality Adjustment

for Import and Export Prices

Aric Schneider
51 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Import and Export Price Index (MXPI) quality 

adjustment

 MXPI – Primarily explicit cost-based QA, quantity/size 

adjustments and new item replacements 

 Hedonic modeling for computers and soon microprocessors

 MXPI uses a “link price” method to QA
52 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

How we capture this information
53 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Quality adjustment - MXPI
54 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

How we capture this information: cost associated with change
55 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

How we capture this information: incomplete items
56 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

How we capture this information: replace items
57 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

MXPI explicit quality adjustment

Price Ratio = LL

−1

= LPSTR

 Link Price (LP) used in place of New Price

 IIIIII II VVVVVVVV = LLLLLL −1 � LL LLLLLL
58 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Explicit cost-based quality adjustment MXPI

 Using the same scenario for an explicit QA 

that Steve demonstrated:

202101 202102 202103

Pre-link Price $13,500.00 $13,500.00 $14,000.00

Percent 

Change

0.0% 3.7%

Link Price $13,800.00

Percent 

Change

2.22%
59 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Quantity/size quality adjustment

 Again using the same example that Steve showed us using the 

PPI Ratio Method:

202101 202102 202103

Pre-link Price $100.00 $100.00 $850.00

Percent 

Change

0.0% 0.0%

Link Price $100.00

Percent 

Change

0.0%
60 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

New item replacement MXPI

 New Item Replacements are introduced as a New Series vs. a 

continuation

 MXPI uses similar “link to cell relative” concept as the PPI

 MXPI again uses a similar “overlap” concept as PPI
61 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Steve Sawyer, Senior Economist 

Producer Price Program 

sawyer.steven@bls.gov

Aric Schneider, Branch Chief 

International Price Program 

schneider.aric@bls.gov

Ryann Watkins, Economist 

Consumer Price Program

watkins.ryann@bls.gov

Contact information