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

Alternative Data and Hedonic 

Price Indexes in the U.S. 

Consumer Price Index: 

A Review of Recent Research

Craig Brown

Senior Economist | Bureau of Labor Statistics | Consumer Price Index

Jeremy Smucker

Economist | Bureau of Labor Statistics | Consumer Price Index

FCSM Conference

October 26, 2022
2 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Hedonic Imputation 
3 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

CPI’s Matched-Model Methodology

Survey data is used 

to select a sample 

of goods that fall 

within an item 

definition

Once goods are 

selected, price 

relatives are 

calculated by 

comparing the 

previous period price 

to the current period

If a selected good is 

no longer available, it 

is replaced by a 

different good within 

the same item 

definition. Quality 

Adjusted Relatives are 

calculated between 

new and old goods

Price relatives from 

both continuing goods 

and substitutions are 

aggregated to form an 

index for a specific 

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

CPI Methodology - Problems

New Goods Problem

Occurs if the prices of new 

goods are not used in the 

construction of a price index 

and those prices are 

systematically lower/higher, 

on a quality-adjusted basis, 

than the prices of old items.

Entering & Exiting Goods

Goods in their first and last 

months of pricing show 

unique price movement. CPI’s 

6-month initiation cycle 

procedures mean we are not 

capturing the price behavior 

of entering goods

Product Life Cycle Effects

Many products decrease in 

price over their lifecycle. If a 

product ages, drops in price, 

and then rotates out of the 

sample without being 

replaced, the index may drop 

while average price in the 

sample increases 
5 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Hedonic Imputation

Hedonic Imputation is a price index methodology that compares predicted prices for

products in the current and previous period.

Prices are predicted using hedonic regressions where price or log(price) is used as a

dependent variable, and the product characteristics are the independent variables.

Matched Model

Collected 202201 

price: 399.99

Collected 202202 

price: 349.99

Observation Relative = 0.875 

Hedonic Imputation

Observation Relative = 0.956 

Predicted 202201 

price: 381.88

Predicted 202202 

price: 365.08
6 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Problems Solved by Hedonic Imputation

 A quality adjusted index with no individual item replacement decisions

 Hedonic Imputation is not beholden to an item’s product lifecycle like matched model

 Little analyst or data collection intervention, minimal respondent burden

 If we have a universe, we don’t have to sample

 Hedonic Imputation imputes prices for entering or exiting goods, unlike current CPI procedures

 Hedonic Imputation innovations (Erickson & Pakes 2011) make it possible to control for 

unobserved characteristics
7 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Model Selection
8 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Classical Statistical Approach vs. Machine 

Learning Approach

Aspect Statistical Machine

Modeling Rigid – A particular model is 

specified after thorough data 

analysis

Flexible – Few, if any 

assumptions made on 

underlying distribution

Inference Explaining and understanding is 

the focus; Considers confidence 

intervals and parameter estimates

Prediction or classification is 

usually the focus

Variable Selection/ 

Model Fitting

Relies on a battery of model 

misspecification and goodness of 

fit tests

Variable selection and 

overfitting models can be 

problematic
9 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Model Selection Process

 Stepwise selection procedure that uses the F 

statistic to gauge improvement in model fit 

 K-fold Cross Validation predicted residual sum 

of squares statistic terminates the process

Results in more parsimonious models

Prevents overfitting the models

Reduces prediction error
10 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Estimate Model on each Fold

1. Partition the data into K 

subsets (folds)

2. Estimate model for each K 

iteration with training 

data

3. Compute predicted RSS 

on validation folds for 

each K iteration

4. Sum of five predicted RSS 

is estimate of prediction 

error
11 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Estimate Model on Full Data Set

5. Estimate model on full data 

set using selection criteria

6. Compute RSS for model 

with each “best candidate” 

variable added/removed

7. If model RSS score is 

greater than the “trained” 

model RSS score, selection 

process terminates
12 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Corp14
13 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Corp14 Data

 API collected data from a 

consumer electronics retail store

 Prices collected 3 times per month 

 94 Unique Specification Variables

 3rd party household survey data 

used to weight observations
14 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

CORP14 - Hedonic Model 

 Selected independent variables in the 

televisions model remained very 

consistent during the time period that we 

have CORP14 data (Oct 2020 – Jun 2022). 

 Technology change for the item is 

minimal within the short time period we 

have data for. 

 While relevant independent variables 

were constant across time periods, the 

impact of each independent variable on 

log(price) varied over time
15 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

CORP14 - Televisions Model 

 Newer technology (8k, 

OLED, HDMI 2.1 ports) 

become cheaper to 

produce over the time 

period

 4k resolution (now by far 

the highest selling 

resolution) and refresh 

rate were more stable

 But the effects of each 

individual coefficient don’t 

tell the whole story...

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Impact on log(price)

Month

Independent Variables Impact on log(price) over time

_120Hz _4K__2160p_ _8K__4320p_ Number_of_HDMI_Inputs OLED_Dummy

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Impact on log(prie)

Month

Independent Variables Impact on log(price) over time

_120Hz _4K__2160p_ _8K__4320p_

Number_of_HDMI_Inputs OLED_Dummy Intercept
16 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Index Results - Televisions

90

95

100

105

110

115

202010 202101 202104 202107 202110 202201 202204

CPI Production Hedonic Imputation - Corp14
17 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Wireless Telephone Service
18 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Wireless Telephone Services Data

 Prices and Characteristics

Data purchased from a 3rd party vendor

Collected via web-scraping and non-automated methods

Detailed information about offer prices and service plan features 

 Weights

Data purchased from a 3rd party vendor 

Calculate expenditure shares for plans to weight the regression and 

aggregate relatives

Adjust the plan shares by carrier national market shares
19 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Results Summary

 Service Plans by Availability and Month

Average 171 plans per month

6.5% entering, 6.5% exiting, 87% continuing

 Weighted Regression Models by Month

Dependent variable is the log(plan price)

Average of 8 independent variables per model

Average R-squared value of 0.88
20 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Index Results – Wireless Telephone Services

85

90

95

100

105

201812 201906 201912 202006 202012 202106 202112

Official CPI Hedonic Imputation (ML) Hedonic Imputation (Analyst)
21 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Summary

 Research hedonic imputation indexes deviate from official CPI in 

important ways

 Model selection methodology may lead to high variances if 

model specifications change frequently

 Looking to extend methodology to residential telecom services 

and other electronic devices
22 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Thank you

brown.craig@bls.gov smucker.jeremiah@bls.gov