1
Household Cost Indexes: Prototype Methods and
Results1
Robert S. Martin, Joshua Klick, William Johnson, Paul Liegey2
June 1, 2023
CONFERENCE PAPER/PRELIMINARY
Abstract
We estimate a family of price indexes known as Household Cost Indexes (HCI) using U.S.
data. HCIs aim to measure the average inflation experiences of households as they purchase
goods and services for consumption, and similar indexes are produced in the United Kingdom
and New Zealand. These differ from the Bureau of Labor Statistics’ headline Consumer Price
Index (CPI) products in two main respects. First, the upper-level aggregation of the HCIs weights
households equally, unlike most headline CPIs which implicitly give more weight to higher-
expenditure households. Second, the HCIs use the payments approach to value owner-occupied
housing services explicitly using household outlays. In contrast, the U.S. CPIs use rental
equivalence. The HCI for all urban consumers has an average 12-month change of 1.51% over
December 2011 to December 2021, compared to 1.86% for the CPI-U. The bulk of the
difference is due to the payments approach.
Key Words: Price index; inflation; democratic aggregation; payments approach
JEL Codes: C43, E31
1 We thank Anya Stockburger, Robert Cage, Thesia I. Garner, and many others at the Bureau of Labor Statistics for
helpful comments and guidance.
2 Division of Price and Index Number Research (Martin), Division of Consumer Price Indexes (Klick, Liegey), Division
of Price Statistical Methods (Johnson), Bureau of Labor Statistics, 2 Massachusetts Ave., NE, Washington, DC
20212, USA. Emails: [email protected], [email protected], [email protected], [email protected]
2
1. Introduction
This article estimates Household Cost Indexes (HCIs) using U.S. data. Similar price
indexes are already produced in the United Kingdom (Office for National Statistics, 2017) and
New Zealand (Statistics New Zealand, 2020). HCIs measure the change in cash outflows
required, on average, for households to access the goods and services they purchase at a
constant quality. Like the headline and subpopulation Consumer Price Indexes (CPIs) produced
by the Bureau of Labor Statistics (BLS), the HCIs aim to capture price change for consumer
goods and services. However, the HCIs differ in two important methodological respects from
the CPIs. First, the upper-level aggregation of the HCIs weights households equally, whereas the
CPI market baskets implicitly give higher weight to higher-expenditure households.3 Second,
the HCIs use the payments approach to value services from owner-occupied housing, using
outlays on mortgage interest, property taxes, and the full reported value of insurance,
appliances, maintenance and repairs (i.e., what the household pays and when they pay it). The
CPIs, in contrast, use an implicit measure of owner-occupied housing consumption called rental
equivalence, and all other goods and services are valued using acquisition prices and
expenditures (i.e., when the household acquired or took possession of the good). For HCIs in
principle, the payments approach should be applied more broadly, but this paper focuses only
on owner-occupied housing. We are ignoring household outlays for the purchase of vehicles
and other durable goods and instead are including the full acquisition expenditures for these
regardless of financing; including these in an HCI is left for a future study.
3 Households are still weighted by their sampling weight so that averages represent the population.
3
We compute an HCI for the urban U.S. population covering the period December 2011
to December 2021. The HCI is based on the Lowe (modified Laspeyres) formula using average
annual household weights with about a two-year lag. From December 2012 to December 2021,
we find an average twelve-month inflation rate of 1.51 percent for the HCI-U, compared to 1.86
for the CPI-U and 1.73 for the Chained CPI-U. We find that empirical differences between the
HCIs and CPIs are primarily due to the HCI’s use of the payments approach, which we estimate
subtracts 0.39 percentage points per year on average relative to an index that uses rental
equivalence. This difference reflects both a lower weight for owner-occupied housing in the HCI
as well as lower inflation in explicit housing costs when compared to owner’s equivalent rent. In
contrast, we estimate that equal household weighting increases the index only about 0.05
percentage points per year on average compared to an index which uses the standard
expenditure weighting, but otherwise uses the same methodology as the HCI.
CPIs are used in a wide variety of economic applications—as an overall macroeconomic
indicator, to deflate national accounts, to adjust marginal tax rates, and measure changes in the
cost-of-living representative of the entire economy. In such applications, measuring the change
in purchasing power of the average dollar of expenditure using an implicit consumption
concept like owner equivalent rent may be appropriate. In other cases, such comparing the
economic conditions of population subgroups, a measure tied to explicit outlays may be
attractive. One index cannot usually satisfy all needs, and in this sense the HCIs can provide
useful complimentary information about the average household inflation experience.
4
2. Literature Review
Current BLS CPI methodology is based on market-level expenditure weights and the
rental equivalence approach to owner-occupied housing (Bureau of Labor Statistics, 2020).
Household-weighted aggregation and the payments approach differ substantially from current
BLS CPI methodology, though neither is new to the price index literature. Astin and Leyland
(2015) propose using these methods to better capture the inflation experiences of households.
They argue such a measurement is more credible for indexing monetary values, while a
traditional CPI is superior for macroeconomic analysis and inflation targeting. Based in part on
their research, the Office of National Statistics developed a set of HCIs for the United Kingdom
(Office for National Statistics, 2017). Statistics New Zealand publishes a similar set of indexes
called the Household Living-Costs Price Indexes. Research on a similar set of indexes for the U.S.
began with Cage, et. al. (2018).
Household-weighted aggregation (also known as democratic aggregation) has been
considered at least since Prais (1958). The topic has been developed and reviewed in Pollak
(1989), National Research Council (2002), International Labor Organization (2004, Chapter 18),
Ley (2005), and Martin (2022), among others. Spending patterns differ across the distribution of
total expenditure. To the extent that these differences coincide with expenditure categories
that have higher or lower inflation than average, a household-weighted index will differ from a
traditional expenditure-weighted one. Equally weighted indexes have been studied with U.S.
data in Kokoski (2000) and Hobijn, et. al. (2009). The latter is notable for statistically matching
the interview and diary components of the Consumer Expenditure Survey (CE), and we follow
5
many aspects of its approach. Our paper also builds on work from Cage, et. al. (2018) and
Martin (2022), the latter of which finds that household-weighted aggregation adds about 0.08
percentage points per year to inflation measured by a Lowe-type CPI from December 2001 to
June 2021.
The payments approach to owner-occupied housing has been discussed at least since
the 1989 version of the International Labor Organization (ILO) CPI manual (as cited by
Goodhart, 2001), and much of our initial approach follows the 2004 version (International Labor
Organization, 2004, Chapter 10). The payments approach to owner-occupied housing focuses
on the month-to-month outlays by households rather than an upfront purchase price (the
acquisition approach) or the implicit consumption value (the use approach).4 In addition to the
HCIs for the United Kingdom and New Zealand, the payments approach is also used in the CPI
for Ireland (Central Statistics Office, 2016). Mortgage interest is also included in the housing
component of the CPI for Canada (Statistics Canada, 2019), and was a part of the U.S. CPI
housing component prior to 1983 (Gillingham and Lane, 1982). Diewert and Nakamura (2009)
contains a conceptual comparison of the payments approach against other methods like the
user cost approach and rental equivalence, while Garner and Verbrugge (2009) compare
methods empirically using the CE.
Astin and Leyland (2015) argue that the payments approach is superior for comparing
household inflation experiences and escalating payments. They make the case that because
rental equivalence is not tied to explicit outlays, an index which includes it as a large
4 Rental equivalence and user cost are both flavors of the use approach.
6
component may be less tethered to the actual price movements that affect household budgets.
For some subpopulations, there can be large differences between implicit rents and explicit
cash flows. For instance, in Cage et. al. (2018), the subpopulation of households which receives
at least 50% of its before-tax income from Social Security has higher relative expenditures on
shelter (35-39%) when measured using rental equivalence than the overall urban population
(32%), but lower relative expenditures when measured using payments (16-23%). This is
because these households are disproportionately likely to be owner-occupiers without
mortgages, meaning their explicit housing outlays are limited to items like property taxes,
insurance, and maintenance.
Astin and Leyland (2015), as well as ILO (2003) advocate such an index for escalation
purposes, but this position is not universally held. Diewert and Shimzu (2021) argue “it is not an
index that can measure household consumption of the services of durable goods because it
focuses on the immediate costs associated with the purchase of durable goods and ignores
possible future benefits of these purchases.” The payments approach has also been criticized in
Goodhart (2001), Poole, Ptacek, and Verbrugge (2005), and elsewhere on the basis that it
doesn’t reflect consumption in an economic sense. We agree that a flow-of-service method like
rental equivalence is more appropriate for a macro-focused CPI or a representative consumer’s
cost-of-living index (See, e.g., Diewert 1976). However, we study the HCIs as complementary
series intended to capture explicit outlays of households rather than the implicit consumption
prices (in an economic theoretic sense) reflected in a traditional CPI, though initially the
distinction is limited to owner-occupied housing. The objective of our paper is primarily to
compare owner-occupied housing and household aggregation methods.
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3. Methods and Data
Our methods for this paper are preliminary and based on utilizing existing BLS surveys or
publicly available data sources. Like the CPIs, the HCIs are constructed in two stages. First, basic
indexes are constructed for item-area strata (e.g., coffee in Washington, DC). These are then
aggregated using expenditure weights from the CE. As our initial version only applies the
payments approach to owner-occupied housing, the elementary indexes and underlying
household expenditures used in upper-level aggregation are largely the same. See Bureau of
Labor Statistics (2020) for more details. For housing, the owner equivalent rent elementary
indexes are replaced with indexes for property taxes, mortgage interest, and property
management services. In addition, we use the full reported value of household expenditures on
household appliances, maintenance and repair, and insurance when constructing upper-level
aggregation weights. Finally, we estimate equally weighted averages of household expenditure
shares based on matched CE Interview and Diary data and use these in the second-stage
aggregation.
3.A. Payments Approach Item Structure and Elementary Indexes
The payments approach for owner occupied housing reflects the housing-related cash
outflows of households. Compared to the CPI, the HCI item structure excludes owner’s
equivalent rent and includes three additional expenditure classes—property taxes, mortgage
interest, and other primary residence expenses. The payments approach also removes several
adjustments CPI makes to other category weights, which we discuss more later in this section.
Within property taxes and mortgage interest, we create new elementary item indexes
8
representing primary residences. These also serve as proxies for secondary residences. In the
CPI, the price index for owner’s equivalent rent of primary residences (numbered “01”) also
serves as the proxy for the unpriced item (numbered “09”) representing secondary residences.
A further item classification (see
9
Table 1 for details) for other primary residence expenses consists of ground rent,
parking, and property management services. This category comprises less than one half of one
percent of the overall index weight, and we provisionally measure its price change using the
producer price index for final demand property management services as a proxy. Finally, our
objective, where possible, is to limit expenditures to those pertaining to primary residences and
vacation homes and exclude investment properties.
The rest of this section details the construction of the property tax and mortgage
interest payment indexes. We follow what is (to our knowledge) international practice by
including the interest component of mortgage payments (excluding second mortgages or home
equity lines of credit) and excluding the portion that goes toward principal reduction (and by
this reasoning down payments and cash purchases). From the 2004 ILO manual, only the
interest portion is considered a pure cash outflow; the principal portion immediately shows up
on the household’s balance sheet as an increase in assets, so it may be considered more like an
investment with a potential future return (International Labor Organization 2004, Chapter 10).
This view is not universal (see Astin and Leyland, 2015). However, including mortgage principal
presents additional technical challenges.5
Also following international practice, the mortgage interest and property tax payments
indexes derive conceptually from two sources of potential change: a rate (an interest rate or an
effective property tax rate) and the base to which the rate is applied (the debt level or the
5 The most straightforward method to estimate the proportional impact of changing interest rates on mortgage
principal payments would involve plugging in aggregate (i.e., average) interest rates into a nonlinear function. In
the sense of measuring a change in average payments across households, the potential bias of such a plug-in
procedure from Jensen’s Inequality is unknown.
10
dwelling value). Changes in rates alone do not capture changes in purchasing power
(International Labor Organization 2004, Chapter 10). Some users could be concerned about
allowing the effects of home prices given these could be associated with (eventual) financial
returns to households. In our view, there is a tradeoff between representing the explicit outlays
of households and controlling for investment using economic theory. Indeed, as noted by
Poole, Ptacek, and Verbrugge (2005), adjusting housing payments to account for investment
results in the user cost approach, which is another implicit housing cost concept. Empirically,
Garner and Verbrugge (2009) show that user costs can differ greatly from explicit payments.6
Our initial strategy, following international practice, aims to exclude the investment aspect of
housing ownership by excluding mortgage principal. Appendix A shows the decision to
indirectly include home prices is significantly inflationary for the housing payments indexes and
suggests the decision to exclude mortgage principal is somewhat deflationary.
Finally, our preliminary results compute a single set of payments approach elementary
item indexes representing the U.S. urban population. We leave it to future research to extend
these methods to create elementary indexes by CPI geographic areas.
3.A.1. Mortgage Interest Payment Index
The mortgage interest payments index measures the proportional change in the interest
payment amount that would occur holding fixed the financing conditions—such as the loan
term and proportion of principal remaining. We aim to follow the recommendations in the
2004 ILO manual (Chapter 10), which is to use both a representative basket of interest rates
6 Garner and Verbrugge (2009) also find that user cost measures based on different underlying assumptions can
differ greatly from each other and from implicit rents.
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and a debt index, which holds “constant the age of the debt” between index periods
(International Labor Organization 2004, Chapter 10). Payments in each period are determined
by transactions occurring at many previous points in time, as mortgage loans are long-term
contracts. Consequently, our index is based on weighted averages of interest rates and house
prices corresponding to loans or debt of different ages. A fixed-basket approach has the
advantage of being feasible with aggregate interest rate and house price data, but the
disadvantage of not being micro-founded.7
Similar to Canada (Statistics Canada, 2019), we define the index as the product of a debt
index (which is influenced by home prices) and an interest rate index which compare payments
in the comparison period 𝑡 against the reference period 𝑠.8 The index is based on the model of
a thirty-year fixed rate mortgage, which dominates the U.S. market (about 75% of existing loans
as reported in the CE).9 It is written:
𝑃𝑀𝐼𝑃 = 𝑃𝐷𝑃𝑟 ,
(1)
where 𝑃𝐷 is the debt index and 𝑃𝑟 is the interest rate index. They are written
𝑃𝐷 =
∏ 𝐻
𝑡−𝑗
𝜓𝑏𝑗�̅�
𝑗=0
∏ 𝐻
𝑠−𝑗
𝜓𝑏𝑗�̅�
𝑗=0
(2)
and
7 We considered such a micro-founded approach which could, for example, average proportional changes in rates
actually paid by households between the reference and comparison periods without fixing the loan age. Such an
approach may be more appropriate for the U.S. market, which is dominated by 30-year fixed rate mortgages.
However, basing such an approach on CE interest rate microdata misses any variation which occurs when a
consumer unit moves from one house to another since consumer units are not followed.
8 While our debt index is similar to the housing component of Canada’s mortgage interest index, their interest rate
component is based on unit value-like averages using administrative banking data.
9 We ignore preferential treatment of mortgage interest in the tax code.
12
𝑃𝑟 =
∏ 𝑟
𝑡−𝑗
𝜑𝑏𝑗𝜃−1
𝑗=0
∏ 𝑟
𝑠−𝑗
𝜑𝑏𝑗𝜃−1
𝑗=0
. (3)
The indexes measure change from period 𝑠 to period 𝑡 by weighting past home prices (relative
to a common base) and interest rates according to the relative importance of loans or debt
initiated in those months to the index periods 𝑡 and 𝑠.10
In these expressions, 𝐻𝜏 is a home price index for month 𝜏, 𝑟𝜏 is an average interest rate
for month 𝜏, 𝜓𝑏𝑗 is the population-weighted proportion of mortgagor-month observations with
debt of age 𝑗 (measured as the number of months since the property was acquired), and 𝜑𝑏𝑗 is
the population-weighted proportion of mortgagor-month observations with current loans of
age 𝑗 (measured as the number of months since the first payment) during the reference period
𝑏. The 𝜓 and 𝜑 parameters differ due to refinances. We use the proportion of mortgagors
(rather than the proportion of debt, which is closer to what Statistics Canada uses) in keeping
with the equal-weighting objective of the HCI. The parameter 𝜃 equals 360 to reflect the
number of potential payments in a thirty-year loan, while �̅� is set higher to allow for acquisition
periods to be earlier on refinanced properties. While not well bounded in theory, we set �̅�
equal to 408 to accommodate the beginning of our house price indexes in January 1975. This
covers about 97.5% of observations in our sample. We evaluate adjacent months 𝑡 and 𝑠. We
set 𝑏 as the fourth quarterly lag of the quarter containing month 𝑡. This reflects a realistic
production constraint for using CE data to construct the weights while keeping them as current
as possible. We use CE microdata on mortgage expenses and keep those observations with 30-
10 While the product of two geometric means with identical weights could be written as one geometric mean,
writing the index as a product of two components makes for convenient discussion and analysis.
13
year fixed rate first mortgages on primary residences. We drop loan records that likely pertain
to non-housing expenditures (second mortgages and home equity lines of credit).
We use monthly averages of the weekly 30-year fixed mortgage rate averages from the
Freddie Mac Primary Mortgage Market Survey (PMMS), which are available only for the U.S.
market. We also use the Federal Housing Finance Agency’s (FHFA) All Transactions House Price
Index. This index is quarterly, and we interpolate monthly values using the natural spline in
SAS’s PROC EXPAND. The FHFA’s purchase only house price index is monthly and superior
conceptually for a debt index representing past home purchases. However, this series only goes
back to 1991, and would not be long enough to cover all loan ages in our sample.
3.A.2. Property Tax Payment Index
The property tax payment index measures the change in average property tax payments
for households. Our proposed method attempts to hold the aggregate quality of the housing
stock constant and uses annual data from the CE.11 Let 𝑋𝑠,𝑡 and 𝑉𝑠,𝑡 denote proportional growth
in population aggregates for property tax payments and owner-occupied housing unit values
between years 𝑠 and 𝑡, and let 𝐻𝑠,𝑡 be a constant-quality home price index between years 𝑠 and
𝑡. We use timeseries representing the entire U.S. and leave it for future research to extend the
method to geographic areas, which require more granular tax data than we currently have. We
compute the following:
𝑃𝑃𝑇𝑃 =
𝑋𝑠,𝑡
𝑉𝑠,𝑡
𝐻𝑠,𝑡. (4)
11 The CE asks homeowners the annual property taxes owed on their primary residence and adjusts these amounts
if the property is partly used as a business. The CE also asks the consumer unit to estimate the market value of
their primary residence. Investigating potentially more timely sources of property tax data is a task for future
research.
14
Our method is similar to that of Statistics Canada and the Office for National Statistics,
which compute unit value indexes, or ratios of average property tax payments, though they do
so for different geographic areas. Let 𝑁𝑠,𝑡 be the growth in the number of owner-occupied
housing units between 𝑠 and 𝑡. A similar approach we explored with CE data computes
𝑃𝑃𝑇𝑈𝑉 =
𝑋𝑠,𝑡
𝑁𝑠,𝑡
. (5)
where we use the number of owner-occupier consumer units to proxy for the number of
owner-occupied housing units.12 Equation (4) is equal to equation (5) divided by (𝑉𝑠,𝑡/𝑁𝑠,𝑡)/𝐻𝑠,𝑡
which is the growth in average home values deflated by the constant-quality home price index.
We interpret this ratio as a measure of change in dwelling quality which is relevant under the
assumption that the total housing market valuations 𝑉𝑠,𝑡 and the house price indexes 𝐻𝑠,𝑡
approximate changes in value and price as would be measured by tax assessors. We found that
the long-term trends of Eq. (4) and (5) were very similar. As in Canada and the U.K., we do not
attempt to control for potential differences in quality of municipal services.
Our preliminary efforts use annual property tax aggregates from the CE, as the survey
asks about annual tax obligations rather than monthly payments. The monthly expenditure
microdata include these figures divided by 12. We find that that using Equations (4) and (5) on
this average monthly data leads to substantial short-term sampling variation. For this reason,
we compute the property tax index at an annual frequency and interpolate monthly values
12 In the CE, consumer units are equivalent to households in the vast majority of cases but are defined by joint
economic decision making rather than residence or familiar relationships.
15
using a spline function. Statistics Canada and the Office for National Statistics, for instance,
update their property tax indexes once per year. The CE is not the ideal source for property tax
and housing value data, as data for a calendar year are released about nine months after that
year ends. For this reason, this paper’s analysis only covers through the end of 2021. Finding
timelier and larger samples using alternative data is an objective for future research.
3.B. Upper-level Aggregation
As in the CPI, we use CE data to derive upper-level aggregation weights, with some
important differences. As shown in
16
Table 1, the set of eligible elementary item strata now includes property taxes and mortgage
interest and excludes owner equivalent rent. The property tax and mortgage interest weight
are derived from the monthly expenditures on those items as collected by the CE. In addition,
we use the full reported values of expenditures on items like maintenance and repair,
homeowner’s insurance, appliances, and household furnishings. Under the rental equivalence
approach, these items are scaled down for owner-occupiers to reflect the likelihood of a renter
making the same purchase. Table 2 compares average housing-related relative importance
across consumer units in different subpopulations —by housing tenure, an indicator for being a
wage earner or clerical worker (as in the CPI-W), and an indicator for being elderly (age greater
than or equal to 62, as in the R-CPI-E)13—both under the payments approach and rental
equivalence. In general, housing payments make up a smaller share of overall spending under
the payments approach than under rental equivalence. For the urban population, for instance,
housing under the payments approach amounts to 34.3% of the market basket on average,
versus 42.9% on average under rental equivalence. Interestingly, patterns of spending across
some subpopulations differ by housing approach. For instance, under rental equivalence, the
average share going to housing among the elderly is relatively high at 46.8%. Under the
payments approach, however, the elderly have a high proportion going to insurance,
appliances, maintenance, and repairs (“other housing”), but relatively less going to mortgage
interest, resulting in a total housing weight of 34.1%, slightly less than the overall urban
population (34.3%).
13 Consumer units were classified according to their reported demographic in their last interview in the sample.
17
Table 1: Weights for Select Housing Items for the HCI Subsample in 2019
Payments
Rental
Equivalence
Code Description $ Bil. % RI* $ Bil. % RI*
HC01 Owner’s Equivalent Rent of Primary Residence NA NA 1,144.36 22.40
HC09 Unsampled Own. Equiv. Rent of Second. Res. NA NA 56.29 0.75
HD01 Tenants’ and Household Insurance 38.02 1.01 17.24 0.38
HH01 Floor Coverings 8.29 0.18 2.54 0.05
HK01 Major Appliances 17.05 0.39 2.38 0.06
HK09 Other Appliances 0.08 0.00 0.07 0.00
HM01 Tools, Hardware, and Supplies 17.23 0.43 11.67 0.26
HM09 Unsamp. Tools, Hardw., Outdoor Equip, Supp. 58.44 1.31 9.35 0.20
HP04 Repair of Household Items 46.52 0.83 4.14 0.08
HP09 Unsampled Household Operations 10.69 0.23 4.29 0.07
HR01 Property Tax of Primary Residence 199.70 4.51 NA NA
HR09 Property Tax of Secondary Residence 8.61 0.16 NA NA
HS01 Mortgage Interest of Primary Residence 211.64 4.26 NA NA
HS09 Mortgage Interest of Secondary Residence 4.55 0.08 NA NA
HT01 Other Owner Payments for Primary Residence 14.10 0.42 NA NA
HT09 Other Owner Payments for Secondary Res. 1.29 0.02 NA NA
* Average (equally weighted) relative importance across consumer units.
Table 2: Average Household Relative Importance for Housing by Subpopulation (percent)
Category Urban
Wage-
earner Elderly
Own. w/
Mortgage
Own. w/o
Mortgage Renter
Payments Approach
Rent 9.2 13.0 6.3 0.1 0.2 31.8
Property Tax 4.7 4.2 5.7 6.1 7.0 0.2
Mortgage Interest 4.3 5.2 2.7 10.2 0.2 0.1
Other Housing 16.0 14.8 19.4 16.9 22.0 8.8
Total Housing 34.3 37.2 34.1 33.2 29.5 40.9
Rental Equivalence Approach
Rent 9.2 13.0 6.3 0.1 0.2 31.7
Owner’s Equiv. Rent 23.1 20.9 29.4 31.1 33.9 0.8
Other Housing 10.6 10.4 11.1 10.9 12.0 8.7
Total Housing 42.9 44.3 46.8 42.1 46.1 41.2
Note: Cells show average December 2020 relative importance (2019 reference period weights price-updated to December
2020 values) across households meeting the HCI sample requirement. While expenditures cover a year, consumer units are
classified according by attribute from their last collection quarter.
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Our upper-level aggregation uses the Lowe formula, and same as the CPI (as of January
2023) the quantity weights pertain to annual expenditure reference periods which are updated
each year. The household-weighted aggregation starts from the CE Interview sample, as
consumer units contribute up to one year of data and the Interview comprises most eligible
expenditures. Eligible expenditures from the Diary survey are imputed to the Interview sample
using a matching procedure based on Hobijn, et. al. (2009), which is described further later in
this section and similar to that used in Martin (2022). The procedure matches eligible Diary
consumer units to an Interview consumer unit based on demographic characteristics that are
predictive of total expenditure. The second-stage aggregation is then based on the Lowe
formula with lagged expenditure weights.
𝑃𝐻𝐶𝐼 = ∑ ∑�̅�𝑎,𝑖,𝑣,𝑏𝑃𝑎,𝑖,𝑡,𝑣
𝑖∈ℐ𝑎∈𝒜
(6)
�̅�𝑎,𝑖{𝑣,𝑏} = (
𝐻𝑎,𝑏
𝐻𝑏
)𝐻𝑎,𝑏
−1 ∑ 𝜔ℎ
ℎ∈ℋ𝑎,𝑏
𝑠𝑖,𝑣,𝑏,ℎ
(7)
𝐻𝑎 = ∑ 𝜔ℎ
ℎ∈ℋ𝑎,𝑏
, 𝐻𝑏 = ∑ ∑ 𝜔ℎ
ℎ∈ℋ𝑎,𝑏𝑎∈𝒜
,
(8)
where 𝑎 indexes the geographic area, 𝑖 the item stratum, 𝑣 the index pivot month, 𝑏 the weight
reference period, and ℎ the consumer unit. The set of areas is 𝒜, the set of items ℐ, and the
set of consumer units in area 𝑎 during period 𝑏 is ℋ𝑎,𝑏. The elementary index between pivot
month 𝑣 and period 𝑡 for item 𝑖 in area 𝑎 is given by 𝑃𝑎,𝑖,𝑡,𝑣. The associated household-weighted
expenditure shares are 𝑠�̅�,𝑖,𝑣,𝑏. These are equally (with respect to the population) weighted
averages of individual consumer unit annual expenditure shares 𝑠𝑖,𝑣,𝑏,ℎ, with 𝜔ℎbeing
household ℎ’s sampling weight. The weight reference period 𝑏 is the calendar year two years
19
prior to the calendar year containing month 𝑡, and the expenditure shares 𝑠𝑖,𝑣,𝑏,ℎ are price-
updated to represent period 𝑣 values using the ratio of the elementary index in month 𝑣 to its
average over period 𝑏.
Consumer units participate in the CE for up to four collection quarters, providing up to
twelve months of expenditures. Because participation is on a rolling basis and there is unit
nonresponse and occasional attrition, the number of observations exactly lining up with a single
calendar year is relatively small, often only a few hundred. Therefore, for the HCI, we define a
“reference year” sample differently than does either the CE or CPI. We assign a consumer unit
to a reference year 𝑏 if its last month of expenditure occurred during year 𝑏. So that each ℎ’s
expenditure basket reflects a whole year, we include only observations which completed all
four quarterly interviews, even if some of their expenditures occurred in the prior calendar
year. For the 2019 reference year, for instance, (used for indexes in 2021), we include
consumer units with at least one month occurring in 2019, meaning we include some
observations whose sample tenure started as early February 2018. With the four-quarter
requirement, this amounts to a sample of 3,063 unique consumer units (12,252 collection
quarters) representing our 2019 reference year. In comparison, 11,740 unique consumer units
(comprising 22,957 collection quarters) in the CE have expenditures recorded for the calendar
year 2019.14 For index subgroup definitions, we use consumer unit characteristics from their
final collection quarter.
14 These sample sizes were calculated by counting the number of unique FAMID (or the consumer-unit specific
portion of the FAMID) for a given expenditure reference period.
20
As discussed in Martin (2022), including observations with periods less than one year
can distort household-weighted indexes due to greater variability in total expenditures and
lower average expenditure shares for less frequently purchased items. However, there is a
potential trade-off with the four-quarter requirement due to representativity. Table 3 shows
differences in the relative frequencies of a few consumer unit demographics. For the 2019
reference year, the HCI subsample has a greater proportion of owners and elderly than the full
sample of urban consumer units. At the same time, Table 2 shows there are differences in the
average expenditure shares on housing-related payments across these groups, suggesting
potential consequences for price indexes. For instance, the elderly spend relatively more on
property taxes than on mortgage interest, reflecting that they are disproportionately owners
without mortgages.
Table 3: Frequency of Consumer Unit Characteristics by Sample in 2019 (percent)
All Urban HCI Subsample
Owner with mortgage 37.3 41.4
Owner without mortgage 23.6 29.1
Renter 39.2 29.6
Wage earner 27.0 25.3
Elderly 30.8 37.7
Nevertheless, we find little evidence of a sample selection bias stemming from our HCI
eligibility criteria, at least over during sample period. Table 4 shows (comparing columns 2 and
3) the impact of using the CE subsample on major group-level weights is small relative to the
effect of using the payments approach or household aggregation. Additionally, we find
(Appendix C) that the sample selection impact on an expenditure-weighted version of the HCI-U
(corresponding to column 4 of Table 4) is minimal, about 0.01 percentage points per year.
21
Furthermore, our results show a CPI-like index calculated from these subsamples (with Diary
expenditures imputed as described in the next subsection), corresponding to column 3 of Table
4 closely matches the published CPI-U. These together imply our results are driven by the
payments approach and household-weighted aggregation, and not the reference period or CE
subsample. Our current method makes no adjustments to the CE sampling weights, which we
leave to future research. Such adjustments may be more important with more recent data than
our sample period, particularly with recent surges in mortgage interest rates.
There are a few other differences between our research indexes and official CPI
methods. Since the HCI is based on consumer unit-specific shares, which must be weakly
positive, we censor negative annual expenditures at zero.15 We also make some small item-
structure changes to simplify calculations using historical data. Finally, we omit weight-
smoothing procedures used in the CPI, including composite estimation for the item-area
weights, which are designed to lower their sampling variance across geographic areas. Our all
items, all areas CPI-U replications closely match the published indexes even without these
procedures, and our prototype procedure only estimates property tax and mortgage interest at
the national level. We leave it to future research to extend weight-smoothing procedures to the
HCIs.
Figure 1 below shows the December 2020 relative importance by major expenditure
group and select housing categories and compares them with the published shares for the CPI-
U. The HCI shares correspond to the 2019 weight reference year, while for the CPI they
15 This affects items RC01 “Sports Vehicles, Including Bicycles”, TA02 “Used Cars and Trucks”, and TA09
“Unsampled New and Used Motor Vehicles.” The CPI counts returns or sales as negative expenditures.
22
correspond to the 2017-18 reference period. Table 4 tracks the change in relative importance
by major group as different HCI elements are activated. The effects of the payments approach
and household-weighted aggregation on the relative weights are significant, but sometimes
have offsetting effects. For instance, the overall housing weight in the HCI is smaller than the
CPI, as property tax, mortgage interest, and the increase in other housing outlays amounts to
less than the decrease due to the exclusion of OER. By itself, this decrease in housing weight
increases the weight allocated to other categories, like medical and recreation. At the same
time, however, household-weighted aggregation shifts weight toward households with lower
total expenditures, further increasing the relative importance of rent and food while decreasing
that of transportation.
Figure 1: December 2020 Relative Importance for HCI-U and CPI-U
Panel a: HCI-U (2019 weights)
Panel b: CPI-U (2017-18 weights)
20.2%
9.2%
4.7%
4.3%
16.0%3.1%
14.2%
11.1%
6.6%
6.8%
3.8%
Food & Bev. Housing: Rent
Housing: Prop. Tax Housing: Mortgage
Housing: Other Apparel
Transportation Medical
Recreation Educ. & Comm.
Other
15.2%
7.9%
24.3%
10.3%
2.7%
15.2%
8.9%
5.8%
6.8%
3.2%
Food & Bev. Housing: Rent
Housing: OER Housing: Other
Apparel Transportation
Medical Recreation
Educ. & Comm. Other
23
Table 4: December 2020 Relative Importance for Different Index Types (percent)
Major Group CPI-U (2) (3) (4) HCI-U
Food and Beverages 15.16 15.68 15.60 17.96 20.16
Housing 42.39 41.84 42.13 33.34 34.26
Apparel 2.66 2.70 2.67 3.07 3.15
Transportation 15.16 15.43 14.60 16.80 14.23
Medical 8.87 8.79 9.18 10.58 11.09
Recreation 5.80 5.80 6.16 7.08 6.59
Education and Comm. 6.81 6.72 6.57 7.61 6.76
Other 3.16 3.04 3.09 3.56 3.76
Methods*
Reference Period 2017-18 2018-19 2019** 2019** 2019**
CE Sample Full Full 4-quarter 4-quarter 4-quarter
Aggregation Expenditure Expenditure Expenditure Expenditure Household
Owner Occ. Housing REQ*** REQ*** REQ*** Payments Payments
* Columns 2-5 also reflect other methodology changes and simplifications described in text.
** Under our sample eligibility criteria, this includes spending back to February 2018.
*** REQ = Rental Equivalence
3.B.1. Interview-Diary Matching Procedure
As mentioned, the basis of our household average expenditure weights is the CE
Interview sample, which covers about three-quarters of the expenditure basket as traditionally
sourced by the CPI. We implement a statistical matching procedure based on Hobijn et al.
(2009) to impute the remaining proportion which CPI sources from the Diary.16 Similar
observations from the Diary sample provide the remaining expenditure data for each Interview
consumer unit, according to a model of expenditures as a function of demographic
characteristics. The dependent variable is expenditures on items which HCI (and the CPI)
sources from the Diary, but for which the Interview either collects the same item or has more
16 Garner, et. al. (2022) and Martin (2022) also use matching processes based on Hobijn, et. al. (2009).
24
aggregate data.17 The model is a convenient way of combining many characteristics according
to which linear combination most strongly predicts expenditures. We then use the predicted
values to form measures of distance between an Interview recipient and its potential Diary
donors. For our main results, the only attribute guaranteed to match between donor and
recipient is quintile group membership based on the distribution of annual before-tax income.18
For our results on housing tenure subpopulations, we also guarantee this attribute matches.
The matching procedure is many-to-one, as we draw four donor Diaries for each Interview in
each month with replacement. The procedure is implemented separately by month so that
weekly Diary donors are evenly distributed temporally over the recipient Interview’s sample
tenure. Due to the sample selection criteria outlined earlier, for reference year 2019, for
example, that means we are running monthly regressions from February 2018 to December
2019. The stratification and model estimation are done on the full Interview sample, not just
the four-quarter subsample.
First, we stratify both Interview and Diary consumer unit samples for the reference
period by the sample quintiles of annual before-tax income. For each month 𝑡 and quintile
grouping 𝑞, we use the Interview sample to estimate the regression
𝑦ℎ𝑡 = 𝒙ℎ𝑡𝜷𝑞𝑡 + 𝑢ℎ𝑡,
(9)
17 From Martin (2022), Table A2, these amount to about 80% of Diary-sourced expenditures in 2019. Alternatively,
it might seem attractive to use the Diary sample to estimate Diary expenditures as a function of demographic
characteristics, as we intend to impute these expenditures for the Interview sample. However, we find that
characteristics explain relatively little variation in Diary expenditures, perhaps due to the short (week-long) recall
period.
18 The Diary samples are small enough that conditioning on multiple characteristics quickly leads to empty cells.
See Hobijn, et al. (2009) for more discussion.
25
where 𝑦ℎ𝑡 is logged expenditure of consumer unit h. The term 𝑢ℎ𝑡 is an error term, and 𝒙ℎ𝑡
include Census region, urban/rural, age, race, sex, and education of the reference person,
consumer unit size, the log of annual before-tax income (if positive), and an indicator for
whether income was negative.19 We use the least squares estimator weighted by the CE
sampling weight, finlwt21. Over the sample period, R-squared values for the quintile and
month-specific regressions averaged 0.17, while income quintile itself explained about 0.31 of
the variation in the dependent variable.
Let �̂�𝑞𝑡 be the slope estimate for quintile 𝑞 in month 𝑡. As household characteristics are
available and comparably defined in both surveys, we calculate predicted values �̂�ℎ𝑡 = 𝒙ℎ𝑡�̂�𝑞𝑡
for each Diary and Interview observation. For a given Interview observation ℎ and Diary
observation 𝑘, the distance metric is defined as
𝛿𝑡(ℎ, 𝑘) = |�̂�ℎ𝑡 − �̂�𝑘𝑡|.
(10)
Within each month and income quintile, we calculate 𝛿𝑡(ℎ, 𝑘) for all {ℎ, 𝑘} pairs. Then for each
Interview observation ℎ, we randomly select (with replacement) four 𝑘 from the twenty
smallest 𝛿𝑡(ℎ, 𝑘) out of all the Diary observations from the same month and income quintile.
The random component is intended to ensure a more even distribution of matches across Diary
observations. The detailed set of expenditures of the donor Diary is then assigned to the
recipient Interview. As one donor Diary is intended to represent one quarter of one month of
expenditure, but Diaries correspond to a one-week recall period, the donor Diary expenditures
19 These demographic variables technically pertain to the collection quarter or some other reference period, so we
implicitly assume they represent the associated reference months. For the matching regressions, we allow a
consumer unit’s attributes to vary by collection quarter.
26
are scaled by 13/12. This process is repeated for each Interview observation, for each month it
is in the sample.20 Since the Interview sample is much larger than the Diary on a per-month
basis, each Diary is matched with several Interviews. Further analysis of the matching
procedure is in Appendix B.
4. Results
We find the HCI-U follows similar patterns of acceleration and deceleration as the CPI-U,
but it has significantly lower average rates of growth during our sample period. The average 12-
month change in the HCI-U averages 1.51% versus 1.86% for the CPI-U, as shown in
Table 5.
20 In the CPI, diary expenditures are multiplied by 13 to account for the difference in recall periods between weekly
diaries and quarterly interviews. The scaling in our procedure is analogous in that an interview is matched with a
total of 12 diaries each quarter, and with the scaling these also represent 13 weeks.
27
Figure 2 plots the index levels, showing markedly different trends between the CPI-U
and HCI-U from 2012-2020. The two indexes increased at a similar rate in 2021, averaging 4.6-
4.7% year-over-year growth throughout the year.
Table 5 includes an index (U-EW-REQ) which uses expenditure weighting and the rental
equivalence approach but uses our CE subsample and processing methods. It also includes a
comparable series (U-EW-PAY) which instead uses the payments approach but uses
expenditure weighting as in the CPI. Comparisons of these indexes and the HCI-U show the
difference in trends and average growth reflects primarily the impact of the payments
approach. U-EW-PAY averages about 0.39 percentage points per year less than U-EW-REQ, and
in a single year (2016) averages 0.74 percentage points lower. In 2021, the impact of the
payments approach is to add 0.15 percentage points to the average 12-month percent change,
reflecting increasing home prices and interest rates. In 2022, we also expect this effect to be
positive and much larger in magnitude due to the large increase in mortgage interest rates. In
contrast, comparing HCI-U to U-EW-PAY shows the household-weighted aggregation adding
28
only slight amount to the overall average 12-month percent change (0.05%), but yearly average
differences are as high as 0.16 percentage points in 2017. In 2021, household-weighted
aggregation lowers HCI-U by 0.1 percentage points on average.
Figure 2: HCI-U and CPI-U Index Levels
Table 5: Average 12-month Percent Changes by Year, HCI and CPI
1
1.05
1.1
1.15
1.2
1.25
2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021
lowe-u (ew, req) lowe-u (ew, pay) cpi-u hci-u
29
Year HCI-U CPI-U
U-EW-
REQ
U-EW-
PAY
HCI-OM HCI-ONM HCI-RNT
2013 0.99% 1.47% 1.43% 0.86% 0.52% 1.22% 1.57%
2014 1.41% 1.62% 1.63% 1.27% 1.02% 1.65% 1.77%
2015 -0.44% 0.12% 0.15% -0.44% -0.88% -0.52% 0.27%
2016 0.56% 1.26% 1.24% 0.51% 0.10% 0.55% 1.19%
2017 1.76% 2.13% 2.13% 1.60% 1.41% 1.79% 2.24%
2018 2.36% 2.44% 2.42% 2.33% 2.32% 2.23% 2.52%
2019 1.39% 1.81% 1.81% 1.43% 1.30% 1.02% 1.80%
2020 0.93% 1.24% 1.21% 0.84% 0.65% 0.89% 1.31%
2021 4.62% 4.69% 4.58% 4.73% 4.54% 4.95% 4.44%
Average 1.51% 1.86% 1.84% 1.46% 1.22% 1.53% 1.90%
Notes: U signifies urban population. U-EW-REQ is a CPI-like replication using the HCI sample and simplified
expenditure processing methods, but expenditure-weighting and rental equivalence. Similarly, U-EW-PAY uses
expenditure-weighting, but the payments approach. “OM” is owners with a mortgage, “ONM” is owners
without a mortgage, and “RNT” is renters.
Figure 3 describes further how the actual outlays for owner-occupiers are associated
with lower inflation than would be implied by rental equivalence. Over the sample period, the
official index for owner’s equivalent rent increases 33.8% cumulatively, while our sub-aggregate
for owner’s payments (combining property tax, mortgage interest, and other owner payments)
increased only 11.5%. Within owner’s payments, the two major components, the trend in the
property tax index is similar to owner’s equivalent rent for most of the sample period.
However, the mortgage interest index trends flat, not yet picking up the sharp increases in
interest rates occurring in 2022 after our sample period ends.21 We also note that evolution of
the mortgage interest index is smoother than current average mortgage interest rates (from
21 Our analysis is constrained by sourcing property tax payments from the CE, which as of June 2023 are only
available through the first half of 2022. The average 12-month change for the mortgage interest index is 8.2% in
2022. Using the first half of 2022 property tax burden (X/V) as a crude forecast, we find an average change in the
owner’s payments index of 10.0% in 2022 (versus 5.7% for owner’s equivalent rent), and an average change in the
HCI-U of 8.7% (versus 8% for the CPI-U).
30
the Freddie Mac PMMS), because the index is averaging over 30 years of past mortgage rates in
order to reflect current payments.
Figure 3: Owner’s Equivalent Rent vs. Owner’s Payments
Finally, we further illustrate the treatment of owned housing outlays by estimating HCI’s
for three subpopulations, owners with a mortgage (OM), owners without a mortgage (ONM),
and renters (RNT). We define these using the housing tenure value reported by the consumer
unit in their final interview. The final three columns of
0
1
2
3
4
5
6
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021
Owner's Equiv. Rent (HC) Owner's Payments (HR, HS, HT)
Property Tax (HR) Mortgage Interest (HS)
Other Owner Payments (HT) 30-yr fix. rate (r. axis, %, PMMS)
31
Table 5 show the average 12-month percent changes, while Figure 4 plots the index levels. HCI-
RNT has average inflation of 1.9% and is closest to the CPI-U. While there may be overall weight
differences between the urban population and the subpopulation of renters, the evolution of
owner’s equivalent rent is close enough to the evolution of actual rent that this result is not
surprising. In contrast, the HCI inflation for owners is significantly lower, averaging 1.53% per
year for those without a mortgage and 1.22% per year for those with a mortgage. As with the
urban indexes, the relative rankings are not the same year to year. For instance, owners
without mortgages had the highest average inflation in 2021, 4.95%, versus 4.54% for owners
with a mortgage and 4.44% for renters.
Figure 4: HCIs for Housing Tenure Subpopulations
4.A. Alternative Treatments of Owner Payments for Housing
As discussed in Section 3.A, we follow international practice in excluding mortgage
principal and basing mortgage interest and property tax index changes on two sources: a
1
1.05
1.1
1.15
1.2
1.25
2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021
hci-om hci-onm hci-rnt
32
change in a rate (the interest rate or the effective property tax rate), and the change in a
monetary base (the debt level and the housing value). The appendix, including Figure 5 and
Figure 6, explore the sensitivity of the indexes to these decisions. Including mortgage principal
would raise the owner’s payments subindex (combining mortgage interest, property tax, and
other payments as in Figure 3) by 0.8 percentage points per year. Combined with the associated
weight increase to mortgages, this would result in an all-items HCI-U that is higher by 0.10
percentage points per year. The effect of home prices would be more substantial, lowering the
owner’s payments index by 4.0 percentage points per year and the all-items HCI-U by 0.38
percentage points per year.
5. Conclusions and Future Research
Our results show the HCI differs substantially from the CPI because it uses the payments
approach for owner occupied housing, and slightly because it weights households equally in its
upper-level aggregation. The payments approach tracks the actual outlays of homeowners,
which over our sample period of 2012 to 2021 have escalated at a lower trend than (imputed)
owner’s equivalent rent, resulting in lower inflation as measured by the HCI than as measured
by the CPI. We do not argue that the payments approach is superior from the standpoint of
measuring the cost-of-living as an economic theoretic concept or for use in monetary policy.
Rather, by reflecting the explicit outlays of owners, we show the HCI offers a measurement of
the household inflation experience which is empirically different than the CPI.
Future research could focus on many areas. Our measures of price change for mortgage
and property tax payments use only national-level data. A natural next step would be to extend
33
these to subnational geographic areas, if relevant and feasible. Further down the road,
exploring mortgage microdata of the sort described by Bhutta, et. al. (2020) could be
informative on different experiences of subpopulations, to the extent that long enough
histories can be obtained to account for the long lives of mortgage loans. More timely and
granular property tax data would also improve the HCI. In addition, in principle, the payments
approach could be extended to any durable good where payment occurs over a long
timeframe, with automobiles in particular being a high priority. Martin (2022) suggests treating
automobiles under an approach consistent with the target of the index (payments, in our case)
is critical if higher-frequency household weights are to be taken seriously, such as for a monthly
weighted superlative like the C-CPI-U. Custom sampling weights should also be created to
account for demographic differences for the four-quarter sample of consumer units used for
the HCIs, but further analysis may also be warranted related to weight frequency and
subsample selection. With the payments approach weighting of automobiles, for instance,
perhaps infrequent purchase issue discussed in Martin (2022) is less salient. Finally, the impact
household-weighted aggregation on the all-items index’s sampling variation or the potential of
weight-smoothing techniques have yet to be explored.
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36
Appendix
A. Alternative Mortgage Interest and Property Tax Indexes
The mortgage payments index which includes mortgage principal replaces the interest
rate component, Eq. (3), with the following representing change in full mortgage payments
between months 𝑠 and 𝑡:
𝑃𝑓 =
∏ [𝑓(𝑟𝑡−𝑗, 𝜃 − 𝑗)]
𝜑𝑏𝑗𝜃−1
𝑗=0
∏ [𝑟𝑠−𝑗 , 𝜃 − 𝑗)]
𝜑𝑏𝑗𝜃−1
𝑗=0
.
(11)
where 𝑓(𝑟, 𝜔) = 𝑟𝑅𝜔 (𝑅𝜔 − 1)⁄ , 𝜔 > 1, where 𝑅 = 1 + 𝑟. The function 𝑓 represents the
fixed mortgage payment as a proportion of the current debt amount. In this expression, the
interest rate 𝑟 is the annualized rate divided by 12 so that it corresponds to one month. Note,
when estimated using aggregate data, even if 𝑟𝑡−𝑗 equals an average interest rate across
households with loans of age 𝑗, the amount 𝑓(𝑟𝑡−𝑗, 𝜃 − 𝑗) cannot be interpreted as an average
mortgage payment ratio across households due to Jensen’s inequality. The relationship
between 𝑓(𝑟𝑡−𝑗, 𝜃 − 𝑗) and a true household average is unknown (at least to the authors) but
using such an average in a price index would require microdata tracking individual mortgagors
across loan changes including refinances (which we can observe in the CE) and new loans
(which we often do not observe due to address-based sampling). The mortgage payment
indexes without home prices remove the debt index component, Eq. (2), while the property tax
index without home prices is just the effective tax rate component, 𝑋𝑠,𝑡 𝑉𝑠,𝑡⁄ from Eq. (4).
37
Figure 5 plots the different Owner’s Payment subindexes (combining mortgage interest,
property taxes, etc., as in Figure 3) and compares them again against owner’s equivalent rent.
Adding mortgage principal increases the owner’s payments index by about 0.8 percentage
points per year when home prices are included, and about 1 percentage point per year when
home prices are excluded. Given the strong upward trend of home prices over the past several
decades, removing their lowers the payments index by 4.0 percentage points per year when
mortgage principal is excluded and by 6.6 percentage points per year when mortgage principal
is included, resulting in downward trends. Figure 6 tracks these payments indexes changes on
the all-items HCI-U, accounting for changes in both the elementary indexes and the aggregation
weights. The overall effect of mortgage principal is modest, adding 0.10 or 0.03 percentage
points per year depending on whether house prices are included. Home prices themselves have
a larger impact on the all-items index, decreasing it by either 0.38 or 0.45 percentage points per
year depending on whether mortgage principal is included.
Figure 5: Alternative Versions of Owner’s Payments
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021
Owner's Equiv. Rent (HC) Paym. (HR, HS, HT)
Paym. (with principal) Paym. (no home prices)
Paym. (with principal, no home prices)
38
Figure 6: HCI-U Under Alternative Versions of Owner’s Payments
B. Interview-Diary Matching Details
We base our household-averaged weights on the CE Interview sample but use a
statistical matching procedure to assign sets of weekly Diary expenditures to each Interview
consumer unit. Our procedure is similar in spirit to that of Hobijn, et. al. (2009), though that
paper models expenditure change (implied by a consumer-unit specific price index) rather than
expenditure levels. Modeling expenditure changes is attractive given the ultimate use of the
matched dataset for price indexes, but Martin (2022) finds demographics explain much less of
the variation in expenditure changes. We limit the dependent variable to categories collected in
both the Interview and the Diary to ensure that the correlations picked up by the model are
relevant to the expenditures we ultimately wish to impute. Over the sample period, R-squared
values for the quintile and month-specific regressions averaged 0.17, while income quintile
itself explained about 0.31 of the variation in the dependent variable. Figure 7 below plots the
average regression R-squared for each quintile, where the averaging is over the 23 months used
1
1.05
1.1
1.15
1.2
1.25
2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021
cpi-u hci-u
hci-u (with principal) hci-u (no home prices)
hci-u (with principal, no home prices)
39
for each reference period. The figure shows that average R-squared for the income quintiles are
fairly stable over time, averaging about 0.23 for the 1st quintile, 0.17 for the second quintile,
0.13 for the third quintile, 0.11 for the fourth quintile, and 0.15 for the fifth quintile. The fits
(conditional on income quintile) are not particularly strong, which motivates matching an actual
diary’s expenditure set to an interview consumer unit rather than using regression fitted values.
Figure 7: Average R-Squared by Reference Period and Income Quintile
The rest of this section presents figures comparing the imputed weekly diary
expenditures to the actual. Figure 8 shows average imputed weekly expenditures for the
reference period track the actual averages well over time, always falling within 1% of the true
averages. Figure 9 compares average weekly Diary expenditures over time by major group. For
food and beverages, which is by far the largest category sourced from the Diary, the imputed
averages fall within 1% of the actual averages, and they fall within 10% for all other categories.
Figure 10 compares the deciles of weekly imputed Diary expenditures to those of the actual
0
0.05
0.1
0.15
0.2
0.25
2010 2011 2012 2010 2013 2014 2015 2016 2010 2017 2018 2019
IQ1 IQ2 IQ3 IQ4 IQ5
40
Diary expenditures for the 2019 reference period (results are similar for other periods). The two
marginal distributions line up well—the imputed deciles are within a few dollars of the actual
deciles.
Figure 8: Actual and Imputed Average Weekly Diary Expenditures by Reference Period
220
230
240
250
260
270
280
290
300
310
2010 2011 2012 2013 2014 2015 2016 2017 2018 2019
actual imputed
41
Figure 9: Average Weekly Diary Expenditures by Reference Period and Major Group
Panel a: Food and Beverages
Panel b: Housing
Panel c: Apparel
Panel d: Transportation
Panel e: Medical
Panel f: Recreation
Panel g: Education and Communication
Panel h: Other
0
50
100
150
200
actual imputed
0
10
20
30
40
actual imputed
0
10
20
30
40
actual imputed
0
5
10
15
20
25
30
actual imputed
0
2
4
6
8
actual imputed
0
10
20
30
40
actual imputed
0
1
2
3
4
actual imputed
0
5
10
15
actual imputed
42
Figure 10: Deciles of Actual and Imputed Weekly Diary Expenditures for 2019 Reference Year
In terms of joint distributions, the matching procedure also does a good job at
replicating average diary expenditures by several demographic characteristics, as shown in
Figure 11 for 2019. Not surprisingly, because income quintile is conditioned on, the procedure
replicates average expenditures by income quintile quite well. The procedure also does well
replicating average differences by housing tenure, age categories, Census region, presence of
children, and education categories, even though these characteristics are not explicitly
conditioned on in the matching process. In these cases, the match quality is being driven by the
correlation between these characteristics and income, as well as the extent to which similarity
in these characteristics across surveys is predictive of expenditures, and so leading to lower
distance between similarly attributed observations.
0
100
200
300
400
500
600
700
1 2 3 4 5 6 7 8 9
actual imputed
43
Figure 11: Average Weekly Diary Expenditures by Attribute, 2019 Reference Period
Panel a: Income Quintile
Panel b: Housing Tenure
Panel c: Age
Panel d: Presence of Children
Panel e: Census Region
Panel f: Education
0
100
200
300
400
500
600
1 2 3 4 5
actual imputed
0
100
200
300
400
Own w/
Mort.
Own w/o
Mort.
Renter No cash
rent
Student
actual imputed
0
50
100
150
200
250
300
350
<=61 >61
actual imputed
0
100
200
300
400
No kids Kids
actual imputed
260
270
280
290
300
310
320
330
NE MW S W
actual imputed
0
100
200
300
400
< H.S. H.S. & Some
Coll.
>= Bachelors
actual imputed
44
C. All-items Indexes Using Different CE subsamples
Figure 12: Twelve-month inflation of CPI and indexes using payments approach by subsample
As a check of our sample requirement that consumer units contributing to the HCI have
four quarters of data in the CE survey, we compare all-items indexes (all using the payments
approach) with this eligibility requirement against all-items indexes without. For this
comparison, we examine expenditure-weighted aggregates across households, as equally
weighted aggregates can be sensitive to weight frequency and overall dispersion in total
expenditures (Ley, 2005; Martin, 2022). We consider both the full CE sample for the reference
year, as well as for the full CE sample for the biennial period ending in the reference year, as
our HCI subsample also includes four-quarter households who entered the CE in the year prior
to the reference year. Figure 12 plots the twelve-month percent changes of these indexes as
well as the CPI-U for reference. Over this period, average inflation of the CPI-U is 1.86% per
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
D
ec
-1
2
M
ay
-1
3
O
ct
-1
3
M
ar
-1
4
A
u
g-
1
4
Ja
n
-1
5
Ju
n
-1
5
N
o
v-
1
5
A
p
r-
1
6
Se
p
-1
6
Fe
b
-1
7
Ju
l-
1
7
D
ec
-1
7
M
ay
-1
8
O
ct
-1
8
M
ar
-1
9
A
u
g-
1
9
Ja
n
-2
0
Ju
n
-2
0
N
o
v-
2
0
A
p
r-
2
1
Se
p
-2
1
lowe-u (ew, pay, 4Q) lowe-u (ew, pay, full-be)
lowe-u (ew, pay, full-a) cpi-u
45
year. The payments approach index using the four-quarter sample averaged 1.46%, while the
indexes using the full annual and biennial samples averaged 1.47% and 1.46%, respectively.
Figure 13: Twelve-month inflation of HCI and indexes using payments approach by subsample
Figure 13 repeats the analysis in Figure 12, but compares the HCI-U and comparable
household-weighted indexes using the full annual or biennial CE samples. The HCI-U averaged
1.51% year-over-year, while the index using the full annual and full biennial samples averaged
1.50% and 1.51%, respectively, though larger differences occurred in 2021. Here, index
differences could reflect sample selection effects, but also likely reflect the mixed frequencies
of household weights underlying the full-sample indexes, as some consumer units have only a
few months or quarters of expenditure due to normal sample rotations and unit nonresponse.
Higher frequency expenditure shares tend to give less weight to less frequently purchased
items and more weight to more frequently purchased items (Martin, 2022). We do not want to
capture this latter effect because, in the case of the HCI’s, it is an artifact of using CPI weights
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
D
ec
-1
2
M
ay
-1
3
O
ct
-1
3
M
ar
-1
4
A
u
g-
1
4
Ja
n
-1
5
Ju
n
-1
5
N
o
v-
1
5
A
p
r-
1
6
Se
p
-1
6
Fe
b
-1
7
Ju
l-
1
7
D
ec
-1
7
M
ay
-1
8
O
ct
-1
8
M
ar
-1
9
A
u
g-
1
9
Ja
n
-2
0
Ju
n
-2
0
N
o
v-
2
0
A
p
r-
2
1
Se
p
-2
1
hci-u lowe-u (hw, pay, full-be) lowe-u (hw, pay, full-a)
46
for automobiles, which are measured by full purchase price at the time of acquisition, rather
than ongoing monthly payments. In 2021, when HCI-U (over the four-quarter sample) has
slightly higher inflation than the two full sample indexes. In 2021, vehicle price inflation was
high relative to the average inflation across all items, and the comparison in the figure is
consistent with the full-sample indexes giving too little weight to vehicles. A payments
approach for vehicles should mitigate this effect in the full samples.
