Part I Chapter 1

What Are We Trying to Estimate?

Turnout, work time, food insecurity, and poverty: telling a changed target from a changed estimator or an assumption about who did not answer.

DataATUS · CPS Voting · CPS Food Security · CPS ASEC

Which turnout number goes in the table?

You are writing the descriptive table that opens a paper on participation, and you need one number for turnout in 2020. The Census Bureau's report on the November 2020 election put it at 66.8% of citizen adults. You open the same Current Population Survey file, keep citizens 18 and older who answered the voting question, apply the supplement weight, and get 79.2%. Same rows, same weight column, and about 12 percentage points apart. Either can go in the table, a footnote can defend either, and the referee who asks "did you use the weights?" will not catch the difference between them. Before you inspect the weight column, inspect the denominator: the two numbers describe two different populations, and only one of them is the one your paper is about.

This chapter's four examples each yield more than one defensible-looking number, and the numbers disagree for different reasons. Some comparisons change the target: the population a number describes and the unit it counts. Some keep the target and change the estimator. Some change what is assumed about the people who gave no answer, and one changes the definition of the quantity itself. Not every plausible number is a different estimand, and the work of the chapter is telling the kinds apart, because the fix for each is different.

Comparison	What changes	Kind of change
Turnout: Census convention or respondents only	Who stays in the denominator	An assumption about the people who did not answer
Turnout among respondents, weighted or unweighted	How each respondent counts	The estimator
Work time: all days, weekdays, employed people, days with work	Which days are averaged	The target
Work time over all days, weighted or unweighted	How each diary counts	The estimator
Food insecurity among households, people, or children	The unit counted	The target
Poverty: official measure or Supplemental Poverty Measure	What counts as resources and needs	The definition of the quantity

What was turnout in 2020?

Every November after a federal election, the CPS asks whether each adult citizen in its sample voted. Three careful analysts working from the 2020 file get three answers. The first counts every citizen adult that the survey weight counts and treats anyone who did not answer the voting question as a nonvoter: 66.8%. The second keeps only the people who answered: 79.2%. The third does the same without weights: 79.6%. All three look like "the share who voted."

Predict first

One of the three is the figure the Census Bureau publishes. Which one, and what separates the other two from it?

The Census Bureau publishes the first. Weighting is not what separates it from the second: dropping the weights moves the respondents-only answer by 0.4 percentage points, while the first two answers are about 12 points apart. The difference is the denominator. In 2020, 15.7% of weighted citizen adults gave no answer to the voting question. The Census convention keeps them in the denominator and counts them as nonvoters. The respondents-only estimate drops them, and it can be read two ways. Read literally, it is a descriptive rate for a narrower group, citizen adults who answered, which is rarely the population anyone set out to study. Read as turnout among all citizen adults, it assumes that the people who did not answer voted at the same rate as those who did. The Census convention assumes instead that they did not vote. Both are assumptions about people the survey did not hear from. Official vote totals put 2020 turnout at about two-thirds of eligible citizens, much closer to the first answer (McDonald 2020), though that external benchmark has a denominator problem of its own: someone has to estimate who was eligible.

Is the racial turnout gap eight points or four?

A level is rarely the number a paper is about. The paper is about a gap, and the denominator choice does not cancel out of a gap. Consider the question a political scientist actually brings to this file: how large was the turnout difference between non-Hispanic White and non-Hispanic Black citizens in 2020? Under the Census convention, 70.9% of White citizen adults and 62.8% of Black citizen adults voted, a gap of 8.1 percentage points. Among respondents only, the rates are 82.4% and 78.5%, a gap of 3.9 points. The same file supports a paper about an eight-point gap and a paper about a four-point gap, and both authors used the weights.

Predict first

The two conventions differ only in what they do with people who gave no answer. For the gap to halve, nonresponse must differ between the two groups. Which group has the higher nonresponse to the voting question, and does the Census convention or the respondents-only convention make that group's turnout look lower?

The mechanism is nonresponse that is not evenly spread. In 2020, 20.0% of weighted Black citizen adults gave no answer to the voting question, against 13.9% of White citizen adults. The Census convention counts every one of them as a nonvoter, which lowers the Black rate by more than the White rate. The respondents-only convention assumes each group's nonrespondents voted like its respondents, which erases most of the difference in nonresponse and, with it, half of the gap. Neither convention observed a single one of these people voting. The choice between them is an assumption about nonrespondents, and in a gap it is an assumption about how that nonresponse differs by group. Figure 1.1 shows that the pattern holds in 2016 and 2024 as well; in each election the gap under the Census convention is larger, and the nonresponse difference is the reason.The Census Bureau's Table 2 for 2020 publishes the voting rate and the no-response share for White alone non-Hispanic citizens and for Black alone citizens, a group that includes Hispanic Black citizens. The file reproduces the White figures to the decimal and the Black figures to within that definitional difference; each fact carries the published value as an external benchmark.

The Black–White turnout gap under two denominators

Non-Hispanic White and non-Hispanic Black citizens 18 and older, CPS November supplements

Table for the 2016, 2020, and 2024 elections showing White and Black turnout under the Census convention and among respondents only, the gap under each, and the share of each group with no answer to the voting question. The gap is about twice as large under the Census convention because nonresponse is higher among Black citizens.
Election	White, everyone counted	Black, everyone counted	Gap (pts)	White, respondents only	Black, respondents only	Gap (pts)	White, no answer	Black, no answer
2016	65.3%	59.6%	5.7	75.2%	72.2%	3.0	13.1%	17.5%
2020	70.9%	62.8%	8.1	82.4%	78.5%	3.9	13.9%	20.0%
2024	70.5%	60.1%	10.4	80.6%	72.9%	7.7	12.6%	17.6%

Figure 1.1.In each of three elections the Black–White turnout gap is roughly twice as large under the Census convention as among respondents only, because a larger share of Black citizens gave no answer to the voting question.Note: Weights-only extract: point estimates only. Gaps are White minus Black in percentage points, computed from unrounded rates. race_eth5 groups: Hispanic of any race is a separate group, so 'White' and 'Black' are single-race non-Hispanic.Source: IPUMS CPS November Voting and Registration Supplements, 2016, 2020, 2024 (analysis/cps/cps_voter.parquet)

A paper that reports a turnout gap needs to say which convention it used and why. The Census convention is the one whose levels match the published tables, and its assumption, that nonrespondents did not vote, is the one the producer chose. If the paper's argument depends on the gap, the honest version reports both and says what the nonresponse difference implies.

Five populations

The turnout disagreement is a disagreement about which population the estimate describes. Survey methodology separates five populations, and keeps each apart from what one survey happens to realize.

Population	What it is	In the 2020 turnout example
Target	The population the question is about	U.S. citizens 18 and older, November 2020
Frame	What the sample can be drawn from	The civilian population in housing units and other noninstitutional quarters; people in prisons, nursing homes, and on active military duty are outside it
Sampled	The part of the frame with a positive chance of selection	Essentially the whole frame. The households actually selected for November 2020 are the sample, a realization rather than a population
Respondent	Those in the sampled population who would respond if selected	People who would complete the basic CPS interview and answer the voting question. Those who did so in November 2020 are the observed respondents
Analytic	Who remains after the analyst's restrictions and missing-data rules, with their weights	Census convention: every citizen adult with a positive supplement weight. Respondents only: those who answered

The frame is already narrower than the target, so the published rate describes citizen adults outside institutions and the military. The weights carry the sample back toward that population one step at a time. The CPS weight adjusts for households that did not complete the basic interview and calibrates the result to population totals. It does not adjust for people who skipped the voting questions: for every citizen adult it counts from 2008 to 2024, the supplement weight equals the basic monthly weight. What the nonrespondents contribute is left to a convention, and the two conventions choose differently. The analytic population is where that choice lives, and it is the one population on the list that you, not the producer, define.

A category change, not a change in voters

Starting with November 2022, "No Response" is no longer a category of the voting variable in the IPUMS files (Flood et al. 2025). In the 2022 and 2024 files, citizen adults who skipped the supplement carry the code "Not in universe," the label that elsewhere means a question did not apply. They keep a positive supplement weight: 8,597 citizen adults in 2022 and 7,398 in 2024. The survey still counts them. A recode that trusts the label drops them from the denominator, and turnout becomes 59.5% for 2022 and 73.4% for 2024, about 7 and 8 percentage points above the published rates. Counting everyone the weight counts, with these records as nonvoters, gives 52.2% and 65.3%, the published rates to the decimal (Figure 1.2).

The voters did not change. The weighted share without an answer was 16.5% in 2022 and 14.1% in 2024, inside the range of 12.8% to 17.7% seen from 2008 to 2020. The weight encodes a decision about who counts. The recode overrode that decision without anyone making it.The book's own analysis store carried this recode for 2022 and 2024 until it was corrected. The error is easy to make and invisible in the code.

What was turnout? Five answers per election

Citizens 18 and older, CPS November supplements

Table of reported turnout by election, 2008 to 2024, under the Census convention, a recode that drops 'not in universe', respondents only (weighted), and respondents only (unweighted), next to the Census Bureau's published rate and the share who did not answer. The Census convention reproduces every published rate; the recode departs from it only in 2022 and 2024.
Election	Census published	Everyone the weight counts	Drop 'not in universe'	Respondents only	Respondents, unweighted	Did not answer
2008	63.6%	63.6%	63.6%	73.8%	74.3%	13.8%
2010	45.5%	45.5%	45.5%	54.2%	56.1%	16.0%
2012	61.8%	61.8%	61.8%	70.9%	72.0%	12.8%
2014	41.9%	41.9%	41.9%	49.8%	51.9%	15.8%
2016	61.4%	61.4%	61.4%	71.9%	72.5%	14.6%
2018	53.4%	53.4%	53.4%	64.9%	65.4%	17.7%
2020	66.8%	66.8%	66.8%	79.2%	79.6%	15.7%
2022	52.2%	52.2%	59.5%	62.5%	63.7%	16.5%
2024	65.3%	65.3%	73.4%	76.1%	76.7%	14.1%

Figure 1.2.The Census convention reproduces every published turnout rate from 2008 to 2024. Dropping nonrespondents raises turnout in every year; a recode that trusts the 'not in universe' label departs from the published rate only after the 2022 category change.Note: Weights-only extract: point estimates only. Published rates: Census Bureau. From 2022 supplement nonrespondents are coded 'Not in universe' but keep a positive weight.Source: IPUMS CPS November Voting and Registration Supplements, 2008-2024 (analysis/cps/cps_voter.parquet; raw VOTED codes from parquet/cps/cps_voter.parquet)

Analysis Ledger

What was turnout? (CPS November 2020)

Target population: U.S. citizens 18 and older in the civilian noninstitutional population, not in the armed forces, November 2020
Estimand: Share of that population who voted in the November 2020 election, as reported in the CPS
Estimator: Census convention: sum(w_i v_i) / sum(w_i) over every citizen adult with a positive supplement weight, where v_i = 1 for a reported vote and 0 otherwise, so supplement nonrespondents count as nonvoters. w = VOSUPPWT.
Explicit weights: VOSUPPWT, identical on every record to WTFINL, the basic CPS final weight: base weight, household noninterview adjustment, and calibration to population controls. It carries no adjustment for supplement nonresponse.
Implicit weights: None beyond w. The convention imputes 'did not vote' to the 15.7% (weighted) who did not answer; the respondents-only alternative instead gives them zero weight, which assumes they vote like respondents.
Source of randomness: Sampling of housing units, household response to the CPS, and person response to the supplement.
Variance estimator: Not computed: the extract carries no replicate weights or design variables (weights-only tier); an SE from VOSUPPWT alone would not be design-based.
Assumptions: Supplement nonrespondents did not vote; respondents report their own voting accurately. Both are assumptions, not data.
Numbers reported: 66.8%
79.2%
15.7%
8.1percentage points
3.9percentage points

How much do Americans work?

A labor economist wants a number for hours worked per day, and the Bureau of Labor Statistics' release on the 2023 American Time Use Survey (ATUS) offers two. On an average day, people 15 and older spent 3.56 hours working. On the days they worked, employed people worked 8.27 hours (BLS 2024). A reader who quotes the first concludes that Americans barely work; a reader who quotes the second concludes that the eight-hour day is intact. Both numbers come from the same 8,548 diaries, in which one person per sampled household accounts for every minute of a single designated day, and from the same weight. The outcome is the same in each: minutes spent working and in work-related activities, including travel for work, as BLS classifies them. Between the two published figures sit at least four more that are just as defensible, and the file will produce any of them without complaint.

Predict first

Before opening the switcher, make two directional guesses. Is the average over weekdays above or below the average over all days? And which raises the average more: restricting to employed people, or restricting to days that included some work?

How much do Americans work? Six defensible answers

How much do Americans work?

All person-days, unweighted

155.4

Unit: person-day
Weight: none
Records (n): 8,548

Same target as the next option, wrong estimator: weekend diaries are 48.9% of the sample but 28.8% of weighted days.

Weights-only extract: point estimates only; no intervals.

What is held fixed. The data and the indicator are the same for every option. Only the unit of analysis and the weight change, so each option answers a different question: these are different estimands, not competing estimates of one.

Six answers to one question

ATUS 2023: minutes per day of working and work-related activities

Table of six estimates of daily work time from ATUS 2023: 155.4 minutes unweighted, 213.8 weighted over all person-days, 272.0 on weekdays, 325.8 for employed people, 487.5 on days with any work, and 496.4 for employed people on days they worked, with the population of days, weight, and number of diaries for each.
Answer	Population of days	Conditions on	Weight	Diaries	Minutes per day	Hours per day
All person-days, unweighted	All person-days (each diary counted once)	nothing	none	8,548	155.4 min	2.59
All person-days	All person-days	nothing	WT06	8,548	213.8 min	3.56
Weekdays only	Monday–Friday person-days	the day of the week	WT06	4,366	272.0 min	4.53
Employed people	Person-days of employed people	employment status	WT06	4,976	325.8 min	5.43
Days with any work	Person-days that include some work	the outcome itself	WT06	2,897	487.5 min	8.13
Employed people, on days they worked	Work days of employed people	employment and the outcome	WT06	2,804	496.4 min	8.27

Figure 1.3.One file gives six answers. The first two rows share a target and differ in the estimator; each later row averages over a different population of days.Note: Weights-only extract: point estimates only. The first two rows share a target; each later row changes the population of days.Source: IPUMS ATUS 2023 (analysis/atus/atus_respondent.parquet)

The answers run from 155.4 to 496.4 minutes a day (Figure 1.3). The second row is the published all-days figure, 213.8 minutes, and the last row is the published figure for employed people on days they worked. The same file reproduces two more published figures: some work happens on 43.9% of person-days, and on those days it averages 487.5 minutes, or 8.13 hours (BLS 2024). Restricting to weekdays gives 272.0 minutes, and to employed people 325.8. So the weekday average sits above the all-days average, since weekends pull the all-days mean down, and restricting to days with some work raises the average far more than restricting to employed people, whose days still include weekends and days off.

Five are correct answers to five different questions. The sixth, the unweighted mean, is a wrong answer to the second question.

Estimand, estimator, estimate

Definition

Three objects

An estimand is the population quantity a question asks for, here a mean over a specified population of days. An estimator is the rule that turns sample records into a number. An estimate is the number that rule produces from this sample.

Predict first

The unweighted and weighted all-days means use the same diaries. Which of the three objects differs between them? Which differs between the weighted all-days mean and the weighted weekday mean?

Write $U$ for a population of days and $y_j$ for the minutes of work on day $j$ . The estimand is a property of the population; the estimator is a rule applied to the sample $s$ :

\theta_U = \frac{1}{N_U}\sum_{j \in U} y_j , \qquad \hat\theta_U = \frac{\sum_{i \in s} w_i\,\delta_i\,y_i}{\sum_{i \in s} w_i\,\delta_i} .

Here $N_U$ is the number of days in $U$ , $w_i$ is the survey weight on diary $i$ , and $\delta_i = 1$ when diary $i$ falls in $U$ . Rows two through six of the table above use the same estimator. Only $\delta$ changes, because only the population changes. Weekdays, employed people, days with work, and employed people's work days are four choices of $U$ beyond the full population, so they are four more estimands. They do not compete with one another or with the published figure. A paper that reports any of them has answered a real question, provided it says which one.

The first two rows differ in another way. They share an estimand, the mean over all person-days, and use different estimators. The unweighted mean sets every $w_i = 1$ , a claim that each diary stands for the same number of days. ATUS does not sample that way: weekend days are 48.9% of the diaries but 28.8% of the weighted person-days, and the weights also adjust for who responds. Chapter 2 takes the weight apart. The unweighted mean does not answer a different question. It answers this one badly.

What the weight counts

Every weight has a unit, and the unit belongs to the estimand. The ATUS weight counts person-days. The 2023 weights sum to 99.0 billion person-days, 365 for each of about 271.3 million people aged 15 and older.Dividing by 365 treats everyone as present all year. People turning 15, dying, or migrating make the quotient an average population. A weighted mean of ATUS diaries is an average over person-days. "Americans work 3.56 hours a day" means the average person-day contains that much work, which is a different claim from how long a typical worker works. The employed-people rows are still averages over days, the days that belong to employed people. The days-worked rows average over days on which work happened, a population defined by the outcome itself.

The puzzle has no answer until the question names its population and its unit. A labor economist studying time on the job wants one of the last two rows; a researcher asking how Americans spend their days wants the second. That choice comes before any estimation, and the weight has to be read in the same unit.

In code: one estimator, five filters

The structure of the calculation makes the point. The estimator line never changes; only the filter does.

python

import duckdb
 
MEAN = "SUM(WT06 * BLS_WORK) FILTER (WHERE {u}) / SUM(WT06) FILTER (WHERE {u})"
universes = {
    "all_days": "TRUE",
    "weekdays": "DAY BETWEEN 2 AND 6",            # DAY: 1 = Sunday ... 7 = Saturday
    "employed": "emp3 = 'Employed'",
    "days_worked": "BLS_WORK > 0",
    "employed_days_worked": "emp3 = 'Employed' AND BLS_WORK > 0",
}
means = ", ".join(f"{MEAN.format(u=u)} AS {name}" for name, u in universes.items())
duckdb.sql(f"""
    SELECT AVG(BLS_WORK) AS unweighted, {means}
    FROM 'analysis/atus/atus_respondent.parquet'
    WHERE YEAR = 2023
""").show()

Analysis Ledger

How much do Americans work? All person-days (ATUS 2023)

Target population: All 2023 person-days of the U.S. civilian noninstitutional population aged 15 and older
Estimand: Mean minutes per person-day of working and work-related activities (BLS major category; includes work-related travel), all 2023 person-days, U.S. civilian noninstitutional population aged 15 and older
Estimator: Weighted mean sum(w_i y_i) / sum(w_i) over all 2023 diaries, w = WT06
Explicit weights: WT06, the ATUS final weight. Each diary counts for the number of person-days it represents: the 2023 weights sum to 99.0 billion person-days, about 365 for each of 271.3 million people. BLS constructs it so that weekday and weekend diaries add up to the weekday and weekend person-days in each quarter, for the population and selected subgroups.
Implicit weights: None beyond WT06.
Source of randomness: Sampling (ATUS draws households from those completing the CPS, one person aged 15+ per household, and assigns the diary day) and response.
Variance estimator: Not computed. The store carries no ATUS replicate weights (BLS publishes them as RWT06), so an SE from WT06 alone would leave out the design, and its error could run in either direction.
Assumptions: The designated diary day represents that person's days of its type; WT06's calibration population matches the target; BLS_WORK classifies activities as BLS does.
Numbers reported: 213.8minutes per day
3.56hours per day
99.0 billionperson-days

Which weight goes with which unit

Your file has two weight columns, one for households and one for persons, and the outcome is a household characteristic copied onto every person record. Which weight? The U.S. Department of Agriculture's report on food security in 2023 says that 13.55% of households were food insecure (Rabbitt et al. 2024). Summaries of the same report say that 47.4 million people lived in those households, and that nearly one child in five did. All three statements rest on the CPS Food Security Supplement, fielded each December, and on one classification: a household is food insecure when its answers show difficulty affording enough food during the previous year. The classification belongs to the household. The file copies it onto every person in the household and supplies both a household weight and a person weight, and each weight answers a different question.

Predict first

Households with children are more often food insecure than households without them. Will the share of people living in food-insecure households be above or below the share of households, and will the share of children be above or below the share of people?

One indicator, three units, four weights

Food insecurity, CPS December 2023 Food Security Supplement

Unweighted
Weighted

Show data

Group	Estimate for	Estimate	n
Households	Households, unweighted	12.47%	30,824
Households	Households, FSSUPPWTH	13.55%	30,824
Households	Households, FSHWTSCALE	13.55%	30,824
Households	Households, HWTFINL	13.51%	30,824
People	People, FSSUPPWT	14.33%	72,169
People	Children, FSSUPPWT	19.18%	14,805

Figure 1.4.The same household classification gives a larger share of people than of households, and a larger share of children than of people. The choice among three household weights barely matters.Note: Weights-only extract: point estimates only, no intervals. Reference line: USDA ERS (ERR-337).Source: IPUMS CPS, December 2023 Food Security Supplement (analysis/cps/cps_foodsec.parquet)

Weighted by the household supplement weight, 13.55% of households were food insecure in 2023, which matches USDA's published rate. The food security scale weight gives 13.55%; in 2023 it equals the supplement weight on every household record. The basic monthly household weight, built for the monthly labor force survey rather than the supplement, gives 13.51%. The unweighted share of the 30,824 interviewed households is 12.47%. Among legitimate household weights, the choice barely registers.

Changing the unit does register (Figure 1.4). Weighted by the person weight, 14.33% of people, 47.4 million in all, lived in food-insecure households, as did 19.18% of children and 12.97% of adults. The shift works through an implicit weight. Counting people instead of households counts each household once per member, and counting children counts it once per child.Reweighting the household rate by household size alone gives 14.19%, and by number of children 18.94%. Person weights are calibrated on their own, so the match is close rather than exact. Households with children were more often food insecure than households without them, 17.90% against 11.91%, so each step toward counting children raises the rate. Food insecurity is a larger problem measured in children than measured in households, and both statements are true.

USDA also publishes a child-specific measure, which asks whether the children themselves, and not only the household, were food insecure. By that definition 9.9% of children lived in a household where at least one child was food insecure (Rabbitt et al. 2024). Unit, weight, and definition each move the answer. The supplement carries no design variables or replicate weights, so these are point estimates without intervals; the lesson here is about targets, not uncertainty.

Set beside the ledger for the household rate, the ledger below changes the fields that concern the unit: the target population and the estimand now count children, the explicit weight is the person weight, and the implicit weights count each household once per child. The household classification, the source of randomness, and the missing variance estimate stay the same.

Analysis Ledger

Children in food-insecure households, 2023 (CPS December Food Security Supplement)

Target population: Children under 18 in the U.S. civilian noninstitutional population, December 2023
Estimand: Share of children living in households classified food insecure over the previous 12 months
Estimator: sum(w_i y_h(i)) / sum(w_i) over children in households with a status, w = FSSUPPWT; y_h(i) is the status of child i's household
Explicit weights: FSSUPPWT, the supplement person weight: each child counts for the children he or she represents.
Implicit weights: Relative to the household rate, each household enters in proportion to the number of children in it; households without children drop out.
Source of randomness: Sampling of housing units, household response to the CPS, and response to the supplement.
Variance estimator: Not computed: the extract carries no replicate weights or design variables (weights-only tier).
Assumptions: A household's classification applies to every child in it. USDA's child-referenced measure, whether the children themselves were food insecure, is a different estimand.
Numbers reported: 19.18%
14.33%
13.55%

When the estimand is a definition

Is child poverty 5 percent or 15 percent? In September 2022 the Census Bureau reported that child poverty in 2021 had fallen to 5.2%, the lowest rate on record, and in the same release that it stood at 15.3% (Creamer et al. 2022). The first figure fed a national argument about whether the expanded Child Tax Credit should be made permanent. The second was the official poverty measure, which had barely moved. Both are computed from the Annual Social and Economic Supplement (ASEC) to the CPS, with the same person weight, for the same children. A researcher who needs a child poverty rate for a regression's dependent variable, or for the first row of a table, has to pick one, and no choice of weight or denominator reconciles them.

The official measure compares a family's pre-tax cash income with thresholds first set in the 1960s and raised each year with consumer prices. The Supplemental Poverty Measure (SPM) counts tax credits and noncash benefits as resources, subtracts taxes and necessary spending such as medical and work expenses, and sets thresholds from current spending on basic needs, adjusted for local housing costs (Shrider and Bijou 2025). They are two estimands, and the choice between them is a choice of definition.

Predict first

The SPM adds refundable tax credits and benefits to resources and subtracts medical spending. For which age group should the SPM rate fall furthest below the official rate, and for which might it rise above it?

Two definitions of poverty, opposite verdicts by age

Share in poverty by income year, CPS ASEC 2020-2025, with 95% replicate intervals

Children, Official
Children, SPM
65 and older, Official
65 and older, SPM

Show data

Series	Income year	Share in poverty	95% CI
Children, Official	2019	14.4%	13.8%–15.0%
Children, Official	2020	16.0%	15.3%–16.7%
Children, Official	2021	15.3%	14.6%–16.0%
Children, Official	2022	15.0%	14.3%–15.7%
Children, Official	2023	15.3%	14.5%–16.0%
Children, Official	2024	14.3%	13.6%–15.0%
Children, SPM	2019	12.4%	11.8%–13.0%
Children, SPM	2020	9.7%	9.1%–10.2%
Children, SPM	2021	5.2%	4.8%–5.6%
Children, SPM	2022	12.4%	11.8%–13.0%
Children, SPM	2023	13.8%	13.1%–14.5%
Children, SPM	2024	13.3%	12.7%–14.0%
65 and older, Official	2019	8.9%	8.4%–9.3%
65 and older, Official	2020	8.9%	8.4%–9.5%
65 and older, Official	2021	10.3%	9.8%–10.8%
65 and older, Official	2022	10.2%	9.7%–10.7%
65 and older, Official	2023	9.7%	9.2%–10.2%
65 and older, Official	2024	9.9%	9.5%–10.4%
65 and older, SPM	2019	12.7%	12.1%–13.3%
65 and older, SPM	2020	9.5%	8.9%–10.0%
65 and older, SPM	2021	10.7%	10.1%–11.2%
65 and older, SPM	2022	14.2%	13.6%–14.8%
65 and older, SPM	2023	14.1%	13.5%–14.7%
65 and older, SPM	2024	15.0%	14.3%–15.6%

Figure 1.5.The two definitions disagree in opposite directions by age. Child poverty was far lower under the SPM in 2021; for people 65 and older the SPM rate is the higher of the two in every year shown, by a wide margin from 2022 on.Note: Income year = survey year minus 1. The official measure uses IPUMS POVERTY; IPUMS also offers OFFPOV, which this extract lacks. The SPM lines break between 2019 and 2020: Census revised the SPM methodology from the 2019 estimates onward, and the 2019 point here is SPMPOV as first released, which matches the unrevised published rate. Estimates from 2020 on use 2020 Census-based population controls.Source: IPUMS CPS ASEC 2020-2025 (analysis/cps/cps_asec/part_2020_2025.parquet); 95% intervals from 160 SDR replicate weights, df = 159

In 2021 the official measure put 15.3% (95% CI 14.6%–16.0%) of children in poverty and the SPM put 5.2% (95% CI 4.8%–5.6%) there, a gap of 10.1 (95% CI 9.5–10.7) percentage points (Figure 1.5). The Census Bureau attributes most of that year's SPM decline for children to the stimulus payments and the expanded, fully refundable Child Tax Credit, which count as resources under the SPM and not under the official measure (Creamer et al. 2022). SPM child poverty had been 9.7% in 2020; after the expansion lapsed it was 12.4% in 2022.

For older Americans the ordering reverses: 10.3% official against 10.7% SPM in 2021, and 9.9% against 15.0% in 2024, a gap of 5.0 (95% CI 4.6–5.5) percentage points. In the Census Bureau's accounting, subtracting out-of-pocket medical expenses raises the SPM rate for people 65 and older by more than it does for children (Creamer et al. 2022). Across all ages the SPM rate was below the official rate in 2021, 7.8% against 11.6%, and above it in every later year. Same survey, same weight, same people, and differences of opposite sign by age. A paper on poverty among the old and a paper on poverty among the young can each pick the definition that makes its problem look larger, which is a reason to state the definition in the same sentence as the number.

The ASEC is the one source in this chapter with replicate weights, so its intervals are design-based. Each uses the 160 successive-difference replicate weights, $\widehat{\Var}(\hat\theta) = \tfrac{4}{160}\sum_{r=1}^{160}(\hat\theta_r - \hat\theta)^2$ , with 159 degrees of freedom. The interval for a gap comes from the replicate estimates of the gap itself, so it accounts for both measures being computed on the same children. Chapter 3 and Lab 3 develop the machinery.

Replication check against the Census Bureau's published rates

Two qualifications apply to these rates. Official poverty here is IPUMS's POVERTY variable, not its OFFPOV variable, and the SPM rates use the ASEC person weight rather than the SPM weight IPUMS recommends, which this extract lacks. Checked against the Census Bureau's published rates for all people, children, and people 65 and older in 2019–2024, the official rates reproduce 18 of 18, and the SPM rates reproduce 12 of 18 and are never more than 0.13 percentage points away.

Replication check against Census published poverty rates

CPS ASEC 2020-2025 (income years 2019-2024)

Table comparing this chapter's official and SPM poverty rates for all people, children, and people 65 and older, 2019 to 2024, with 95% replicate intervals, against the Census Bureau's published rates, and whether they agree to one decimal.
Measure	Group	Income year	This chapter	95% interval	Census published	Agrees
Official	All people	2019	10.5%	10.2%–10.8%	10.5%	yes
Official	All people	2020	11.5%	11.1%–11.8%	11.5%	yes
Official	All people	2021	11.6%	11.2%–11.9%	11.6%	yes
Official	All people	2022	11.5%	11.1%–11.9%	11.5%	yes
Official	All people	2023	11.1%	10.8%–11.4%	11.1%	yes
Official	All people	2024	10.6%	10.3%–10.9%	10.6%	yes
Official	Children under 18	2019	14.4%	13.8%–15.0%	14.4%	yes
Official	Children under 18	2020	16.0%	15.3%–16.7%	16.0%	yes
Official	Children under 18	2021	15.3%	14.6%–16.0%	15.3%	yes
Official	Children under 18	2022	15.0%	14.3%–15.7%	15.0%	yes
Official	Children under 18	2023	15.3%	14.5%–16.0%	15.3%	yes
Official	Children under 18	2024	14.3%	13.6%–15.0%	14.3%	yes
Official	People 65 and older	2019	8.9%	8.4%–9.3%	8.9%	yes
Official	People 65 and older	2020	8.9%	8.4%–9.5%	8.9%	yes
Official	People 65 and older	2021	10.3%	9.8%–10.8%	10.3%	yes
Official	People 65 and older	2022	10.2%	9.7%–10.7%	10.2%	yes
Official	People 65 and older	2023	9.7%	9.2%–10.2%	9.7%	yes
Official	People 65 and older	2024	9.9%	9.5%–10.4%	9.9%	yes
SPM	All people	2019	11.7%	11.4%–12.1%	11.7%	yes
SPM	All people	2020	9.2%	8.9%–9.4%	9.2%	yes
SPM	All people	2021	7.8%	7.5%–8.0%	7.8%	yes
SPM	All people	2022	12.4%	12.0%–12.7%	12.4%	yes
SPM	All people	2023	12.9%	12.6%–13.3%	12.9%	yes
SPM	All people	2024	12.9%	12.6%–13.3%	12.9%	yes
SPM	Children under 18	2019	12.4%	11.8%–13.0%	12.5%	no
SPM	Children under 18	2020	9.7%	9.1%–10.2%	9.7%	yes
SPM	Children under 18	2021	5.2%	4.8%–5.6%	5.2%	yes
SPM	Children under 18	2022	12.4%	11.8%–13.0%	12.4%	yes
SPM	Children under 18	2023	13.8%	13.1%–14.5%	13.7%	no
SPM	Children under 18	2024	13.3%	12.7%–14.0%	13.4%	no
SPM	People 65 and older	2019	12.7%	12.1%–13.3%	12.8%	no
SPM	People 65 and older	2020	9.5%	8.9%–10.0%	9.5%	yes
SPM	People 65 and older	2021	10.7%	10.1%–11.2%	10.7%	yes
SPM	People 65 and older	2022	14.2%	13.6%–14.8%	14.1%	no
SPM	People 65 and older	2023	14.1%	13.5%–14.7%	14.2%	no
SPM	People 65 and older	2024	15.0%	14.3%–15.6%	15.0%	yes

Note: 'Agrees' means equal after rounding to one decimal. Published values marked blank were not verified in this pass.Source: This chapter's build; published rates from Census Bureau, Poverty in the United States: 2021 (P60-277), 2022 (P60-280), and 2024 (P60-287), Tables A-1, A-3, B-2, and B-3

Analysis Ledger

Child poverty in 2021 under two definitions (CPS ASEC 2022)

Target population: Children under 18 in the civilian noninstitutional population (ASEC universe), calendar year 2021
Estimand: Two estimands: the share of children in families whose pre-tax money income is below the official threshold, and the share in SPM units whose resources after taxes, transfers, and necessary expenses are below the SPM threshold
Estimator: sum(w_i y_i) / sum(w_i) over children in each measure's universe, w = ASECWT
Explicit weights: ASECWT, the ASEC person weight.
Implicit weights: None beyond w. The universes differ slightly: the official measure excludes unrelated children under 15 (296 records in 2022); the SPM includes them.
Source of randomness: Sampling of housing units, household response, and ASEC supplement response.
Variance estimator: Successive difference replication with the 160 person replicate weights: Var = (4/160) sum_r (theta_r - theta)^2, df = 159, centred on the full-sample estimate. svy 0.28 with method='replication' and variance_center='estimate', checked against a hand computation and R survey 4.5.
Assumptions: IPUMS POVERTY reproduces the official measure (IPUMS also offers OFFPOV, which this extract lacks); SPMPOV weighted by ASECWT reproduces Census SPM rates (the SPM weight is not in the extract); reported income and benefits are accurate enough for both measures.
Numbers reported: 15.3%
5.2%
10.1percentage points

An oversample by design

Box

Provenance: the PSID's low-income oversample

The Panel Study of Income Dynamics began in 1968 by combining a national probability sample with a large supplementary sample of low-income families, drawn on purpose to study poverty. A poverty rate computed from the pooled file without weights describes that pooled sample, in which poor families are overrepresented by design. It does not describe the country. Solon, Haider, and Wooldridge use this case to motivate the first reason to weight: when the goal is a population descriptive statistic and units were sampled with unequal probabilities, the weights are what point the estimator at the population quantity (Solon, Haider, and Wooldridge 2015). The ATUS weekend oversample is the same situation in a current survey. The box describes the case; it does not reproduce the PSID numbers.

Note

A new case

A survey records a household characteristic, say whether the home is overcrowded, and copies it onto every person record, alongside a household weight and a person weight. An analyst reports the person-weighted share. What has changed relative to the household rate, and when will the two differ?

One answer

The unit has changed, and with it the estimand. A person-weighted share of a household characteristic counts each household once per member, so it describes people living in such households, not households. The classification is unchanged; the implicit weight on each household is now its size. The two rates differ whenever the characteristic is more or less common in larger households, as food insecurity is more common in households with children. For a household rate, use the household weight on one record per household.

What we learned about the question

How much Americans work depends on whose days are averaged: 213.8 minutes per person-day across the population, 496.4 minutes on the days employed people work. Turnout in 2020 was 66.8% of citizen adults under the Census convention and 79.2% of those who answered, and the Black–White turnout gap was 8.1 points under the first convention and 3.9 under the second. Food insecurity reached 13.55% of households and 19.18% of children. Child poverty in 2021 was 15.3% or 5.2%, depending on the definition.

What the method changed

The method changed the denominator: all citizens or only those who answered, all days or some of them. It changed the represented unit: person-days rather than people in the time diaries, and households, people, or children in the food security supplement. And it paired each weight with its unit. In the turnout example, weighting moved the answer by 0.4 percentage points; the choice of denominator moved it by about 12, and halved a group gap.

What this analysis does not establish

The ATUS, voting, and food security estimates come from extracts with weights but no design information, so this chapter attaches no uncertainty to them and tests none of their contrasts, including the racial turnout gap under either convention. Nothing here shows which turnout convention is closer to the truth: both rest on an assumption about people who did not answer, and self-reports can overstate voting, possibly by different amounts in different groups. The official–SPM gap is a difference between two definitions. It is not an estimate of what the Child Tax Credit did to poverty, and the Census Bureau's attribution is an accounting of resources, not a causal estimate. Whether the weights themselves are right is the subject of Chapter 2.