Examining U.S. inflation across households grouped by equivalized income

This article extends our previous research on producing price indexes for households in different income groups.¹ For this earlier research, we defined income groups solely on the basis of household income. In this article, we define income groups by using equivalized household income (income that accounts for household size).² In addition, we introduce smoothing techniques to improve expenditure-weight coverage and use a weighted ranking to classify households into quintile groups. As we did in our previous work, we use integrated data from the two independent surveys composing the Consumer Expenditure Surveys (CE)—the Diary Survey and the Interview Survey—to form expenditure shares at the basic-index level for each cohort. Our earlier research divided households into four groups, and this article divides households into five groups. As before, to estimate inflation by cohort, we aggregate price changes for the urban population by using cohort-specific weights calculated from expenditure weights. In addition, we define two new research measures of inflation: a CPI based on a Lowe formula, referred to as the R-CPI-I, and a Chained CPI (C-CPI) based on a Törnqvist formula, referred to as the R-C-CPI-I.³ Household inflation rates defined by both index methods are presented and compared by income quintile.

As a standard practice within the income-inequality literature, researchers equivalize income before ranking households for distributional analysis.⁴ For this article, we equivalize household income by dividing it by the square root of household size. This procedure is needed because an annual household income of, say, $80,000 implies a different level of resources for a four-person household than it does for a single-person household. In this example, the equivalized income for the four-person household would be $40,000, because the equivalence adjustment is 2. In terms of ranking income cohorts, the four-person household with an equivalized income of $40,000 would be ranked lower than the single-person household with an income of $80,000. Because using equivalized instead of unequivalized income has a minor impact on the R-CPI-I and R-C-CPI-I annualized inflation rates for the 2006–23 (R-CPI-I) and 2006–22 (R-C-CPI-I) periods (see appendix A), the remainder of this article uses equivalized income, unless otherwise noted.

In our previous research, the period of analysis ended in 2018. For this article, we extend the period to 2023 for the R-CPI-I. The inflation picture for the urban population changed substantially between 2018 and 2023. For context, the 12-month percent change in the all-items CPI-U was 1.9 percent in December 2018, but it accelerated sharply after mid-2021, peaking at 9.1 percent in June 2022.⁵ Despite this change in inflation since our last study, the gap between the inflation rates for the highest and lowest income groups did not change. The average annual inflation rate from 2006 to 2023 was the fastest for the lowest income quintile and the slowest for the highest income quintile. The inflation gap between the two quintiles was 0.28 percentage point per year.

The present article also extends the period of analysis for the R-C-CPI-I, moving its ending year from 2018 to 2022. The R-C-CPI-I more closely approximates a conditional cost-of-living index (an index for which environmental factors, such as crime or climate change, are held constant) and uses a Törnqvist formula and monthly weight shares, which are available with a lag. The 12-month percent change for the all-items R-C-CPI-I peaked in June 2022, at 8.7 percent. Over the period of analysis, the gap between the R-C-CPI-I inflation rates for the lowest and highest income households was 0.42 percentage point per year, higher than the gap measured with the R-CPI-I. The results for the R-CPI-I and the R-C-CPI-I indicate inflation gaps similar to those found in our previous analysis.

Background

BLS publishes CPIs for subgroups of a target urban population. The CPI for Urban Wage Earners and Clerical Workers (CPI-W) became a subgroup index in 1978, when BLS adopted an urban-population target and began calculating the CPI-U. In 1988, BLS introduced a research index measuring price change for Americans 62 years of age and older, the R-CPI-E. BLS research on inflation rates for low-income consumers began in the 1990s.⁶ Prior research on this topic is briefly summarized in a BLS working paper we published in March 2021.⁷

Interest in income-based inflation measures continues to grow. In June 2021, an interagency technical working group convened by the Office of Management and Budget issued a report recommending that BLS produce a new consumer price measure for use in the calculation of the U.S. official poverty thresholds.⁸ The group recommended that BLS produce a C-CPI for low-income households. In April 2022, The National Academies of Sciences, Engineering, and Medicine issued a report recommending the development of price indexes by income group.⁹

Determining how to produce an index for cohort groups poses a challenge for BLS. For example, in our March 2021 working paper, we outlined many caveats and limitations associated with using current BLS methodology to produce price indexes for cohorts not based on income (specifically, the CPI-W and the R-CPI-E). Briefly put, these caveats and limitations suggest that constructing indexes by using the same areas, stores or rental units, items, and prices sampled for the urban population does not necessarily capture cohort-specific differences (based on age, occupation, or income) that may affect the inflation experiences of specific groups. Other researchers have shown that consumer price indexes for both a target population and population subgroups underestimate the gap between the inflation rates experienced by the highest and lowest income households.¹⁰ These researchers use different data sources and definitions of income groups, and their results are limited to a subset of item categories. However, their results suggest that household heterogeneity at lower levels of index aggregation is an important issue. Because the results presented in this article do not account for this heterogeneity, the caveats and limitations identified in our March 2021 working paper also apply here.

Income-cohort definition

To define income groups, we use CE data collected from 2004 to 2021 for the R-CPI-I and CE data collected from 2004 to 2022 for the R-C-CPI-I.¹¹ We use final before-tax income, imputing income values of less than $1.00 (including negative values) to a minimum value of $1.00. Imputation occurs for less than 0.5 percent of responses to the Interview Survey and the Diary Survey.¹²

We define income groups in terms of household income and size. This approach allows us to produce quintiles of equivalized household income. As noted earlier, equivalized income is household income divided by the square root of household size, or the number of “equivalent adults” in a household. Because household size and composition vary across survey respondents, equivalized income allows comparisons across households and is a better measure of household economies of scale.¹³

Further, we divide the population of urban households into five equal groups (quintiles) on the basis of the ranking of those households’ equivalized income. In this procedure, household population weights are assigned to each equivalized income, with weights being relatively equal across quintiles. In our previous analysis, we grouped households into quartiles by ranking them according to their unequivalized income, without applying population weights; this grouping resulted in the same number of unweighted households in each quartile.¹⁴ Although quartiles have a larger sample of households and more closely represent the number of households in the population of urban wage earners (see table 1), improvements to smoothing described later in this section enable us to use a quintile definition of income.

We use a household-weighted ranking procedure to distribute households equally across quintiles, an approach comparable to that used in the CE.¹⁵ However, unlike the CE ranking, which uses unequivalized income, our ranking is based on equivalized income. In addition, in the CE, the weighted-income variable used for ranking is processed for the total rather than urban population. Differences between the urban and rural populations across CE quintiles (the rural population’s proportion in the total population is higher for lower quintiles) motivate the CPI program to calculate a weighted-income distribution for which weights are distributed relatively equally for the CPI-eligible urban population.¹⁶ Household weighting does not substantively change our R-CPI-I and R-C-CPI-I results at the all-items U.S.-city-average level.

To show the impact of creating quintile groups based on equivalized household income, chart 1 presents median values of equivalized income, by quintile, for all three CPI population groups (urban population, wage earners, and Americans 62 years of age and older). Not surprisingly, the median equivalized income for the third quintile is close to that for the urban population.

Besides improving the income-cohort definition, this article improves the calculation of expenditure shares with smoothing techniques used in the production of published CPIs. Survey data collected in the CE are subject to sampling error. To mitigate the impact of this error, BLS uses smoothing techniques across geography in the calculation of expenditure shares. By smoothing these shares at the item-area level, BLS reduces the survey data’s expenditure-weight variance across geography. Smoothed (composite-estimated) annual expenditure weights are derived by combining local-area annual weights and the weights of more stable and broader levels of geography (self-representing regions and nonself-representing regions). Each weight takes a value between 0 and 1 and is based on minimizing the mean-squared error.¹⁷ In contrast to smoothed annual weights, smoothed (ratio-allocated) monthly weights are derived from a 12-month moving average of the share each area contributes to total spending on an item. The 12-month moving-average ratio is then multiplied by the reference-month expenditure at the item-area level.¹⁸ The impact of smoothing by quintile on expenditure-weight cell coverage is described later in the article (see table 4 for the R-CPI-I and table 7 for the R-C-CPI-I).

Income-cohort demographic characteristics

To understand who is represented by each income quintile, we also examine the distribution of households by several demographic variables. This examination is necessary because a household’s expenditure shares are affected not only by its income but also by its demographic composition (which influences spending preferences). Using CE-collected demographic data, table 2 presents the percent distribution of households by demographic characteristics (household size and number of children) and across income quintiles based on equivalized and unequivalized income.

As shown in table 2, equivalizing income by household size results in a more consistent demographic distribution of households (in terms of household size, including number of children) across income quintiles. In the case without accounting for household size, more single-person households and households without children are included in the lowest income quintile, and fewer such households are included in the highest income quintile. By contrast, using equivalized household income to create quintile groups results in more households with children being included in the lowest income quintile and fewer such households being included in the highest income quintile. These patterns are consistent across income quintiles.

The data presented in table 2 confirm that household groupings based on equivalized and unequivalized income produce different household distributions. Differences in expenditure patterns across households grouped by unequivalized income more likely reflect differences in household composition. By contrast, differences in expenditure patterns across households grouped by equivalized income (differences presented in the next section) more likely reflect meaningful differences in household purchasing power and preferences.

As shown in table 3, households across income quintiles have different rates of homeownership, working status, and educational attainment. Households in the lowest quintile of equivalized income are more likely to rent their home and not work for pay than are higher income households. Among households with retired members, 64 percent report incomes that fall in the first and second quintiles. Among retired homeowners in the lowest income quintile, 67 percent do not have a mortgage. Higher income households are more likely to own their home with an outstanding mortgage, and they are more likely to hold an associate’s degree or higher.

Data inputs

The inputs to price-index calculation are weights and prices. This section discusses weight quality to demonstrate the feasibility of defining income quintiles (as opposed to income quartiles), presents weight differences across income quintiles, and offers an analysis of the underlying price data used to calculate indexes.

Quality of weights defined by equivalized-income quintile

Expenditure-weight coverage refers to the proportion of missing item-area cells used to weight basic indexes for aggregate-index calculation. When price change occurs, constructing aggregate indexes requires an accurate weighting of basic indexes. A basic index is an index for one of 243 item strata (categories of goods and services purchased by consumers) in one of 32 index areas (geographic areas dividing the urban portion of the United States). The combinations of item strata and index areas are referred to as item-area combinations, or basic cells. In measuring coverage, we define item-area basic cells with less than $1.00 as missing. We use basic-cell coverage as a data-quality metric, but we understand that, in some cases, missing data may be an accurate reflection of spending. For example, because some areas of the country lack infrastructure for the supply of natural gas, spending for the basic cells corresponding to those areas is truly zero. Smoothing procedures populate each basic cell with expenditures, making it suitable for use in index estimation.

Basic indexes can be divided into sampled and nonsampled series. The weights of nonsampled series are subject to infrequent reporting of expenditures, and their price movement is imputed by using an aggregate-priced series. Because important differences exist in the coverage of sampled and nonsampled items, the results for these categories are presented separately.¹⁹ An additional adjustment is made for health insurance, which is partially excluded from basic-cell-coverage analysis.²⁰

Table 4 presents statistics on the expenditure-weight coverage for reference year 2021. For the urban population, the overall proportion of missing expenditure item-area basic cells in the production of expenditure weights is 4 percent. For sampled items, however, the missing rate is only 1 percent. Smoothing reduces the basic-cell proportion of sampled items missing. For the wage-earner population (not shown in the table), this proportion is 7 percent, but smoothing reduces it to 1 percent. For the first (lowest) and fifth (highest) quintiles of equivalized income, the proportions based on collected data are, respectively, 14 and 5 percent, with both figures being reduced to nearly 0 percent after smoothing. Therefore, smoothing has a larger impact on the lowest income quintile (relative to the other quintiles) and improves the weighting coverage for index estimation.

Income-quintile spending weights (average spending)

In producing price indexes, we use spending weights to calculate average price change.²¹ Although the spending weights for the urban population reflect average spending, they may not reflect the spending of an individual household or a group of households. Spending weights vary across the distribution of equivalized income. Generally, households in the lowest quintile of income allocate a larger share of their spending to essential goods and services.²² By contrast, households in the highest quintile of income allocate a larger share of their spending to recreational and leisure goods and services. In chart 2, we show a snapshot of spending-share differences across quintiles for 2021, focusing on goods and services categories with the largest differences. (From these data, we construct cost-weight relative importances for December 2022; these relative importances, shown in appendix B, represent implicit expenditure shares we use to calculate indexes for 2023.) For context, the all-items income-quintile expenditure weight within the urban population is distributed as follows: 11.4 percent for the first quintile, 15.2 percent for the second quintile, 18.0 percent for the third quintile, 22.2 percent for the fourth quintile, and 33.2 percent for the fifth quintile.

Price analysis

BLS calculates price indexes for different populations by applying spending weights to the same set of underlying basic price indexes. For example, when price changes are averaged across all items, the price change for rent has a greater impact on the overall price change for households in the lowest income quintile than on the price change for households in the highest income quintile. This difference occurs because the weight for rent is higher for the lowest than highest income households. If all individual-item prices changed at the same rate (or remained unchanged), inflation rates would not differ across subpopulation groups. In this section, we present item categories that help explain overall index differences.

Chart 3 compares the urban index relatives at the expenditure-class level (2023 average of 1-month price changes) with differences between the spending shares of households in the lowest and highest income quintiles for selected components of the CPI. The index relative is de-meaned, which means that the average of the all-items index relative (0.3 percent) is subtracted from each observation to center the data around 0 on the y-axis. The y-axis shows if an expenditure-class relative is greater or smaller than the average all-items relative. For example, for motor vehicle insurance, the average 1-month relative is 1.6 percent (1.3 percent when de-meaned). The x-axis shows spending-share differences (between the lowest and highest income quintiles) based on 2021 spending shares. For example, for rent of primary residence, the first-quintile budget share is more than 10.9 percentage points greater than the fifth-quintile budget share. As another example, for owners’ equivalent rent of residences, the first-quintile budget share is 7.4 percentage points smaller than the fifth-quintile budget share. Results in the upper right and lower left quadrants of the chart increase the inflation gap between the first and fifth quintiles.

Price indexes by income quintile

In this section, we present price indexes by income quintile. Generally, we find that households in the lowest quintile experience higher inflation rates than do households in the highest quintile. In addition, inflation for the overall urban population is about the same as that for households in the fourth quintile. Below, we present these (and additional) index results, including analyses for periods that deviate from the overall trend.

Overall CPI results

Chart 4 shows R-CPI-I annualized inflation rates (compound average annual rates of change) by income quintile for the 2006–23 period. (See appendix C for average 12-month percent changes by year.) As seen in the chart, households in the lowest income quintile experienced higher inflation rates—0.28 percentage point higher, on average—than did households in the highest quintile. Cumulatively, over the period’s 18 years, the inflation gap between the lowest and highest income households was 7.70 percentage points.

Variation in inflation gap over time

Chart 5 shows the difference between the R-CPI-I inflation rates for the lowest and highest income households over the 2007–23 period. The gap in inflation rates peaked in August 2008, when the lowest income households experienced inflation rates 1.38 percentage points higher than the rates of the highest income households, and troughed in February 2016, when the highest income households experienced inflation rates 0.31 percentage point higher than the rates of the lowest income households.

Variation in inflation gap by item category

As noted previously, when aggregated across all items in the CPI market basket, inflation rates over the study period were higher for lower income households than for higher income households. This section identifies which item categories drove this difference, presenting inflation rates by eight major CPI groups defined by BLS.²³ The next section decomposes the contribution of each major group to the overall inflation gap between the lowest and highest income households.

Chart 6 shows R-CPI-I inflation rates for each major group over the 2006–23 period, along with the inflation gap between the lowest and highest income households. Compared with households in the highest income quantile, households in the lowest quintile experienced higher inflation rates for the categories of other goods and services, housing, and transportation. The reverse was true for apparel, medical care, education and communication, and food and beverages. In absolute terms, the inflation gap was the smallest for recreation and the largest for other goods and services.

To interpret these results, recall that our methodology adjusts spending shares on item categories (e.g., women’s dresses, men’s pants, and children’s clothing) to reflect the shopping behavior of households in each income quintile. Price change at the major-group level reflects different averages of price change across different item categories. For example, over the period of analysis, households in the highest quantile of equivalized income faced higher apparel inflation than did households in the lowest quintile, because they spent a larger share on item categories whose prices were rising faster than average (or a smaller share on item categories whose prices were falling or rising slower than average). These results do not reflect any potential differences in shopping behavior below the item-strata level.

Items explaining the inflation gap

The previous section showed the variability in the inflation gap below the all-items level. To understand how different components of the market basket contribute to the all-items inflation gap, we need measures that incorporate relative weights across item categories. These measures are called effects and contributions.²⁴ Effects are expressed as decimals and reflect individual items’ effects on the all-items price change. Contributions are component-item effects scaled as a percentage (0–100 percent).

These contributions and effects can be extended to explain inflation rates for income groups. Table 5 displays the top three and bottom three inflation-contributing items for all urban households and households in the first (lowest) and fifth (highest) income quintiles. For example, among all item strata in 2023, owners’ equivalent rent was the largest contributor to overall inflation for households in the urban population (42.5 percent), the lowest income quintile (33.0 percent), and the highest income quintile (45.5 percent). If owners’ equivalent rent had not changed in 2023, the all-items price change would have been 1.8 percentage points lower for the urban population, 1.5 percentage points lower for the lowest income quintile, and 1.8 percentage points lower for the highest income quintile. The second and third ranked items differ across households. In 2023, rent was the second-largest contributor to inflation for urban households overall and for households in the lowest quintile, and motor vehicle insurance was the second-largest contributor for households in the highest quintile.²⁵ Gasoline, the bottom-ranked item, had small negative effects and small contributions relative to the items with the largest positive effects.

Given that owners’ equivalent rent is a major contributor to inflation for all index populations, it is important to uncover what explains the inflation gap between the lowest and highest income quintiles. To answer this question, we redefine the contribution and effect measures in order to identify the item categories that contribute the most to widening (positive effect) and narrowing (negative effect) the inflation gap.²⁶

Chart 7 shows the percent contributions (positive and negative) of different item categories to the inflation gap in 2023. In that year, the year-over-year change in the inflation gap was 0.6 percentage point. Rent of primary residence, motor vehicle insurance, and commercial health insurance had the largest positive contributions, with households in the lowest income quintile spending more of their budget shares on these categories relative to households in the highest income quintile. Owners’ equivalent rent of primary residence and new vehicles had the largest negative contributions, with households in the highest income quintile spending more of their budget shares on these categories relative to households in the lowest income quintile.

Differences across income quintiles

Although we observe inflation-rate differences between households in the lowest and highest income quintiles (see chart 5), it is important to examine whether these (and other) differences are statistically significant. Table 6 summarizes differences in inflation rates between income groups from 2006 to 2023 (204 months), organizing the results in two panels: one comparing the urban population with each of the five quintiles (left panel) and another comparing the first quintile with the other four quintiles (right panel). As shown in the table’s left panel, the first quintile exhibits the largest positive mean difference when compared with the urban population. The fourth quintile is the only quintile with a mean inflation rate that is not significantly different from that of the urban population. The absolute-value summary in table 6 shows that the sum of absolute differences for the first quintile is 41.60 percentage points, with a mean of 0.20 percentage point and a root-mean-square error of 0.17 percentage point. The results presented in the table’s left panel indicate that all differences, except those for the fourth quintile, are statistically significant at the 0.001 level. The sum in the absolute-value summary for the fourth quintile is about half the sums for the other quintiles, indicating that the fourth quintile is most comparable to the urban population.

Comparing the first quintile with the other quintiles (right panel of table 6) indicates that the growth-rate differences are statistically significant for all quintiles, with the difference between the first and fifth quintiles being the largest. In terms of an absolute-value summary, the sums shown for the second through fifth quintiles are at least 22.07 percentage points, with a mean of at least 0.11 percentage point and a root-mean-square error of at least 0.12 percentage point. In a regression holding the month of observation constant, the differences across quintiles are jointly significant at the 0.005 level.

Results for the Chained CPI

So far, we have presented inflation rates based on price indexes calculated with a Lowe formula (the formula used to calculate the headline CPI-U) and spending shares that are periodically updated. Relative to a cost-of-living index, these indexes usually have an upward bias because consumers tend to shift their spending shares in response to relative price change. To address this issue, this section presents inflation rates, by income quantile, with the use of a different measure of consumer inflation—the R-C-CPI-I. This index, calculated with a Törnqvist formula and spending shares updated monthly, more closely approximates a cost-of-living index.²⁷

Using CE data, we calculate monthly spending shares by income quintile. (Recall that spending shares are needed for the 243 item strata and 32 index areas, for a total of 7,776 indexes.) Table 7 shows the coverage for these monthly spending shares.²⁸ Given that each month represents one-twelfth of the annual reference period, the proportion of basic item-area cells with no expenditure information is higher for monthly (table 7) than annual (table 4) spending shares. For the urban population, the overall proportion of cells missing is 21 percent prior to smoothing and 4 percent after smoothing. For sampled items, however, the missing rate based on collected data is only 16 percent, dropping to 1 percent after smoothing. Also for sampled items, the proportions for the lowest and highest income quantiles are, respectively, 54 and 37 percent prior to smoothing and 14 and 4 percent after smoothing. Therefore, smoothing has a larger impact on the data for the lowest income quintile and improves the weighting coverage for R-C-CPI-I estimation.

Chart 8 shows R-C-CPI-I measures calculated with a Törnqvist formula and monthly spending shares (as 2-month moving averages) for the period from 2006 to 2022.²⁹ (Average 12-month percent changes by year are displayed in appendix C.) The results presented in the chart are similar to our Lowe-index results, indicating that households in the lowest income quintile tend to experience higher inflation rates than households in the highest income quintile. Over the period of analysis, the lowest income households faced annual inflation rates that were, on average, 0.41 percentage point higher than those of the highest income households. Cumulatively, over the period’s 17 years, the inflation gap was 10.24 percentage points.

Summary of upper-level substitution bias

For each income group, the Törnqvist formula generally yields a lower measure of price change than does the Lowe formula, a difference referred to as upper-level substitution bias. Table 8a shows this bias over the 2006–22 period. As seen in the table, while the R-C-CPI-I (Törnqvist index) rises more slowly than the R-CPI-I (Lowe index) for all income groups, the difference between the rates of change for the two indexes is the smallest for households in the lowest income quintile. Indeed, the upper-level substitution bias for households in the lowest income quintile is less than half that for all urban households. The substitution bias for households in the highest income quintile is similar to that for all urban households.

Table 8b presents an alternative measure of substitution bias. Here, instead of measuring substitution bias, we estimate a substitution measure. Specifically, we calculate indexes with a constant-elasticity-of-substitution formula, which uses a parameter as a direct measure of consumer substitution. We tested a range of consumer-substitution parameter values (from 0 to 1), comparing the results with the R-C-CPI-I.³⁰ Table 8b shows how the optimal consumer-substitution parameter varies by income quintile. For 2 of the 5 years presented in the table, the optimal consumer substitution for households in the lowest income quintile is lower than that for urban households. This alternative measure highlights that substitution due to price change varies by year for the urban population and across income quintiles.

Conclusion

BLS produces different consumer-inflation measures that may be used to assess the health of the U.S. economy. This article adds to these measures by presenting price indexes for households grouped by income quintile. The article builds on our previous research by defining income groups in terms of equivalized income and extending the period of analysis to 2023 for the R-CPI-I and to 2022 for the R-C-CPI-I. Consistent with our results for earlier periods, we find that households in the lowest income quintile generally faced higher inflation rates than did households in the highest income quintile, with the average inflation gap between the two groups remaining unchanged despite overall inflation recently increasing above historical norms. From 2006 to 2023, the cumulative inflation gap, measured with the R-CPI-I, was 7.67 percentage points, averaging 0.28 percentage point per year. Measured with the R-C-CPI-I, which more closely approximates changes in the cost of living, the cumulative gap over the 2006–22 period was 10.24 percentage points, averaging 0.42 percentage point per year. The long-term inflation gap between the lowest and highest income households is unaffected by whether quintiles are defined in terms of equivalized or unequivalized income (however, short-term differences in the inflation gap exist).

The inflation gap results from differences in spending shares across households and from price changes for the items accounting for the biggest differences. Compared with households in the highest income quintile, households in the lowest quintile allocate larger spending shares for rent, gasoline, and electricity. Because prices for these items rose faster than average in 2022, the spending-share differences associated with them resulted in higher inflation measures for households in the lowest income quintile. In 2023, rent increases explained over 25 percent of the inflation gap. Prices for new vehicles and owners’ equivalent rent also rose faster than average in 2022. Because the highest income households dedicated larger spending shares to these items, they faced higher inflation rates for them, an effect that moderated the inflation gap.

We see several promising areas for future research. Two such areas include investigating the use of equivalized-income quintiles in analyses of subgroup price indexes and consumer substitution and, similarly, evaluating the potential impact of income imputation on those quintiles. Perhaps more importantly, we recognize the importance of capturing price-change differences at lower levels of index aggregation, by income quintile. Constructed as reweighted aggregations, the income-quintile indexes presented in this article are baseline measures of inflation that inform data users about the inflation experiences of income subgroups within the urban population. Household scanner data (price data gathered from retail checkout scanners) covering the CPI market basket are sparse and currently represent a small portion of that basket. For example, the lack of scanner data for rent presents ongoing research challenges. As other researchers have demonstrated, considerable heterogeneity in prices paid and unique items purchased may affect the overall measure of inflation.³¹ Although previous research has found little difference in rent inflation by income group,³² we are interested in exploring this finding further, along with the impact of rent subsidies and rent controls, which more strongly affect households in the lowest income quintile.

Another promising area for future research is considering geography in CPI weighting by income. Initially, we considered defining income quintiles by geography, whereby CE respondents would be classified into income quintiles within a city (referred to as primary sampling unit in the CPI). Ultimately, we concluded that representing all households across a single, nationally defined income distribution would be preferred for constructing a national-level index. This approach is methodologically consistent with U.S. Bureau of Economic Analysis (BEA) and BEA–BLS products for, respectively, distribution of personal income and distribution of personal consumption expenditures.³³ An area stratification of the income distribution would have a minimal impact on national-level indexes and would change the overall definition and purpose of the products. A limitation of this method is that it makes the construction of subnational indexes infeasible because index weights are not equivalent across quintiles. We will continue our research on considering geography in weighting CPIs by income.

Lastly, although we define quintiles in terms of before-tax income, we recognize that household groupings based on other measures may be better suited for certain uses. For example, defining quintiles by out-of-pocket spending may reclassify some households into different quintiles (e.g., some households in the lowest quintile of before-tax income would be reclassified into the highest quintile of out-of-pocket spending). Furthermore, there could be measures of wealth that are more useful for categorizing households.

Appendix A: Inflation-rate comparisons based on equivalized and unequivalized income

Appendix B: Cost-weight relative importances

Appendix C: R-CPI-I and R-C-CPI-I inflation rates