Recipients of Supplemental Security Income and the Student Earned Income Exclusion

Introduction: Supplemental Security Income and the Student Earned Income Exclusion

The Supplemental Security Income (SSI) program provides monthly cash payments to persons who are aged, blind, or disabled and have income and resources below certain limits. SSI payments, roughly speaking, bring a recipient's total income up to at least a specified floor. This floor is the individual federal benefit rate (FBR), in the simplest case of an individual living alone in his or her own household.¹ The individual FBR is the maximum possible federal SSI payment to an eligible individual. If the recipient has other income, then depending on its type and amount, actual payments will typically be smaller. This article is based on data from 2004 and 2005; the individual FBR, which is adjusted each year for inflation, was $564 per month in 2004 and $579 per month in 2005.

Among the provisions of the SSI program are several financial supports and incentives for recipients to improve their prospects for employment and self-support. One of these—the Student Earned Income Exclusion (SEIE)—is the subject of this article. The SEIE applies automatically in months when an SSI recipient is under age 22, regularly attending school in grade 7 or above, and receiving earned income (almost always wages).² This article focuses on persons who received the SEIE in any month when they were due SSI payment during 2004 or 2005.³

Each month's federal SSI payment is typically calculated as the difference between the FBR and the recipient's countable income. If countable income exceeds the FBR, no SSI payment is due. Countable income consists of the recipient's earned and unearned income received in the appropriate month, reduced by certain exclusions such as the SEIE.

For SSI purposes, earned income consists of gross wages, net earnings from self-employment, sheltered workshop earnings, royalties, and honoraria—with wages being by far the most common. When SSI recipients meet the SEIE criteria (age, earnings, and student status), some or all of their earned income is excluded from their countable income. Thus, the SEIE can help an individual gain or maintain eligibility for cash SSI payments and is partly a work incentive and partly a financial support for education. For 2004 and 2005, respectively, the annual limits on the SEIE were $5,520 and $5,670; the monthly limits were $1,370 and $1,410.⁴

Since April 2005, the SEIE has applied to any working student in grade 7 or above and under age 22 whose income affects an SSI payment.⁵ Prior to April 2005, the SEIE was known as the Student Child Earned Income Exclusion and, under the more restrictive definition of "child," did not apply if the working student was a head of household or married. For SSI purposes, someone who lives alone and has no dependents can still be a head of household; the defining characteristics of a "head of household" are responsibility for day-to-day household decisions and absence of parental support.

For SSI purposes, a "student" may be regularly attending school (grades 7 through 12), college, university, or other training designed to prepare him or her for a paying job; this includes vocational or technical training and government antipoverty programs such as Job Corps.⁶ SSI recipients must report their income, and those in the SEIE age group must report changes in their student status. Because they do not have to take any action beyond these basic reporting requirements to receive the SEIE, we cannot, from the available data, distinguish those who deliberately take advantage of the SEIE from those who benefit from it inadvertently.

The SEIE can help an individual gain or maintain eligibility for cash SSI payments. If an SSI claimant has monthly earnings above $65 but below the monthly substantial gainful activity (SGA) level (which was $810 in 2004 and $830 in 2005), then the SEIE can, depending on the amount of countable unearned income, make the difference between establishment of initial eligibility and denial of the SSI claim on the basis of excess income.⁷

The SEIE will not help establish initial eligibility for SSI if the applicant's earnings are above the SGA level because receipt of Section 1619(a) payments—SSI payments received despite earnings that exceed SGA—requires a "prerequisite month" of receipt of regular SSI payment. However, once the "prerequisite month" is satisfied, the SEIE can help someone continue to receive cash SSI payments under Section 1619(a). Section 1619(a) payments are calculated in the same manner as regular SSI payments. Section 1619(a) is considered a work incentive because, in conjunction with the various exclusions for earned income (including the SEIE), it allows people who have already qualified for SSI to continue receiving payments even when their work activity reaches a level that would have resulted in denial of their original SSI claim.

The SEIE does not apply in the threshold test for Section 1619(b) status. Section 1619(b) enables SSI recipients to retain Medicaid eligibility despite having enough total income to reduce their SSI payments to zero; to qualify, they must be eligible for regular SSI payments but for their earnings, and their earnings must be below a certain threshold. Section 1619(b) is also considered a work incentive because it helps people who have received SSI to work without losing the health care benefits that normally accompany SSI eligibility.

For further discussion of the effect of the SEIE on an SSI recipient's income, see Appendix A.

About the Data

The Social Security Administration (SSA) has not previously published detailed statistics on the SEIE. The regular statistical publications covering the SSI program use cross-sectional (that is, single-point-in-time) data captured each December, and one might expect December SEIE recipients not to be representative of all SEIE recipients. First, one might expect students' earnings and hence their SEIE use to exhibit seasonality—to be higher in summer, for instance. Second, many of the highest earners might reach the calendar-year SEIE limit ($5,520 in 2004 or $5,670 in 2005—which is far less than twelve times the monthly limit of $1,370 or $1,410) and cease to receive SEIE prior to December each year.

For these reasons, monthly longitudinal data were used for this article. From a 10 percent sample of all SSI records, all individuals against whose income the SEIE applied during at least one month in 2004 or 2005 were selected. Data for 2 years were used in hopes of detecting any seasonal patterns in SEIE use. Although SEIE amounts can be posted to an SSI recipient's record even in months when no SSI payment is due, the selected group was further restricted to count a person as an "SSI recipient with SEIE" in a particular month only if he or she had SEIE applied against income earned in that month and was due an SSI payment for that month. For additional information on the sample selection, see Appendix B. For notes on sampling variability and tables showing standard errors, see Appendix C.

For brevity, this article often uses the term "SEIE recipient" to refer to an "SSI recipient with SEIE" as defined here. This article also uses the term "SEIE amount;" this term refers to an amount of money used in the SSI payment calculation, not an amount that is received directly.

Data for 2004 and 2005 were chosen despite the availability of more recent data because earnings, student status, and even disability status can be changed retroactively on the records of SSI recipients. Periodic "redeterminations" sometimes bring to light new information about an SSI recipient. So if the data originally entered for a given month were incorrect, the passage of 1 or 2 years would make discovery and correction more likely to have occurred.

SEIE Statistics

The following sections present statistics on demographic characteristics of SSI recipients with SEIE, measures of SEIE use, and seasonal patterns in SEIE use. All statistics presented in the tables and charts are population estimates. For instance, numbers of SEIE recipients and aggregate SEIE amounts are sample totals multiplied by 10.

SSI Recipients with SEIE

There were about 26,000 SSI recipients with SEIE in each of the years 2004 and 2005. The tables in this section describe some of their demographic characteristics as well as several simple measures of SEIE use.

Some tables give statistics spanning an entire calendar year; in these tables, a person's age is defined as the age used in determining December SEIE eligibility.⁸ "Numbers of SSI recipients aged 12–22" exclude all persons who, because of marital status or head of household status, would not have had SEIE amounts posted to their SSI records even had they been working students. The SEIE use rate is defined as the percentage of SSI recipients aged 12–22 who were SEIE recipients.

Table 1 shows that SEIE use started for a few persons prior to age 16, peaked—in terms of both number of recipients and use rate—around age 18 or 19 (at least for persons in the sample), and then fell off drastically well before the age-22 cutoff, possibly due to loss of student status upon completion of schooling. The majority of SEIE recipients in the sample were male, roughly in proportion with the gender distribution of SSI recipients in the relevant age bracket. Mental retardation was the most common diagnosis among SEIE recipients in the sample, followed by other mental disorders; together, all mental disorders accounted for nearly three-quarters of SEIE recipients' primary diagnoses, with nervous system disorders accounting for a large portion of the remainder. The nervous system disorders category includes, as a relatively small subset, the vast majority of persons who are eligible for SSI on the basis of blindness.

Differences across diagnosis groups in the estimated SEIE use rates may well derive, at least in part, from differences across age groups in the distribution of diagnoses. For example, SSI recipients with mental retardation outnumbered those with other mental disorders in the 18–21 age group, while the reverse was true for the 13–17 age group.⁹ This, in combination with the low SEIE use rates up to age 16 and the higher use rates at ages 17 through 20 or 21, could help account for the relatively low estimated SEIE use rates for persons with "other mental" disorders.

Table 1 shows that mental retardation was the most common diagnosis for SEIE recipients in the sample overall. Charts 1a and 1b and Table 2 show that mental retardation was also the most common diagnosis at each age from 17 or 18 to 22, across which ages it accounted for a fairly constant share of diagnoses. Other mental disorders, forming the second most common diagnosis group for SEIE recipients overall, were the most common diagnoses among those aged 16 and younger but trended downward as a percentage of diagnoses with increasing age. In contrast, the percentage of SEIE recipients in the sample with nervous system disorders mostly trended upward with age.

Tables 3a and 3b show that California, Illinois, New York, Pennsylvania, and Ohio were among the states with the most SEIE recipients in the sample. States with the highest SEIE use rates included Iowa, Kansas, Minnesota, Montana, Nebraska, New Hampshire, North Dakota, Ohio, South Dakota, Vermont, and Wisconsin. Geographic variations seen here in SEIE use rates are similar to geographic variations in the percentage of SSI recipients who worked¹⁰ and the percentage of SSI recipients who participated in Section 1619.¹¹

SEIE Use

Tables 4a and 4b show two measures of SEIE use: (1) the amount of income excluded per year under the SEIE and (2) the number of months per year with income excluded under the SEIE. Table 5 gives estimates of the number of people reaching the annual SEIE limit each month.

In most cases, SEIE recipients' earned income was much lower than the calendar-year SEIE limit. In fact, almost one-third of SEIE recipients used less than 10 percent of the annual limit, and approximately half used less than 20 percent. The earnings distribution continued to tail off steadily after this point, with only about 2 percent of SEIE recipients using between 80 percent and 90 percent of the annual limit. Earned income translates roughly into SEIE amounts, and so the two quantities have basically the same distribution. Whereas the earnings distribution tailed off steadily, however, the SEIE distribution had a second mode because of SEIE recipients with earnings equal to or greater than the SEIE annual limit. Of the 6–7 percent of SEIE recipients in Tables 4a and 4b using more than 90 percent of the annual limit, most reached the limit (as can be seen by comparison with Table 5). For a discussion of the limitations of using SEIE amounts to quantify the impact of the SEIE, see Appendix A.

For each year, SEIE use in any number of months between 1 and 6 was fairly common, with each number accounting for about 10–13 percent of SEIE recipients in the sample. SEIE use in all 12 months was also common, accounting for about 10 percent of SEIE recipients. Use in any number of months from 7 to 11 was much less common among sample members.

Table 5 shows that in each year, approximately 4–5 percent of SSI recipients with SEIE reached the annual limit. Some reached the limit as early as May, and a few reached the limit each month thereafter through the end of the year. (Because of the monthly limit on the SEIE, it is impossible to reach the annual limit prior to May.)¹²

Charts 2a and 2b and Table 6 show the estimated relationship between age and months of SEIE use per year. In the 12–15 age group in the sample, 1–3 months of SEIE use per calendar year was by far most common, followed by 4–6 months of SEIE use. This ranking held at each age up to and including age 18, with the proportion of SEIE recipients in the 1–3 month category trending down with increasing age and the proportion in the 4–6 month category trending up. The two proportions were approximately equal by age 19. The proportion of SEIE recipients in the 10–12 month category in the sample also generally trended upward with age, surpassing the proportion in the 7–9 month category at age 19 and approximately matching the proportions in the 1–3 month and 4–6 month categories at age 20. Thus, it appears that older SEIE recipients tended to have more months of SEIE use per calendar year than did younger SEIE recipients. However, at age 22, the increasing trend for the 10–12 month category and the declining trend for the 1–3 month category both reverse. This naturally results from the loss of eligibility for SEIE that occurs in the month after attainment of age 22.

Seasonality

There appeared to be seasonality both in monthly numbers of SSI recipients with SEIE and in monthly average and aggregate SEIE amounts. Contrary to intuitive notions about students, school vacations, and summer jobs, the number of SEIE recipients in the sample reached its annual trough around July. Aggregate, mean, and median SEIE amounts, in contrast, all peaked near July. Charts 3–6 plot the estimated monthly numbers of SSI recipients with SEIE and estimated monthly aggregate, mean, and median SEIE amounts; Table 7 presents the numeric values.

The number of SEIE recipients in December actually exceeded the number of participants in each of three other SSI work incentives—Plan for Achieving Self Support (PASS), Impairment Related Work Expenses (IRWE), and Blind Work Expenses (BWE)—even though none of these three incentives is, like the SEIE, age-limited.¹³

Increases and Decreases in the Number of SSI Recipients with SEIE

Chart 7 breaks down the monthly changes in the count of SSI recipients with SEIE according to the factors causing gain or loss of SEIE status. Anyone gaining or losing SEIE status from one month to the next is classified into one of five nonoverlapping categories, and Chart 7 displays, for each month, the net change attributable to each category. The categories correspond to changes in the following combinations of factors: (1) SSI eligibility alone; (2) earnings, alone or concurrently with SSI eligibility; (3) student status, alone or concurrently with earnings or SSI eligibility; (4) annual limit status, alone or concurrently with student status, earnings, or SSI eligibility; and (5) age status, alone or concurrently with any other factors.

The categories are hierarchical. Category assignment for a loss of SEIE, for instance, would proceed as follows: First, check whether age 22 was attained. If so, assign category 5 and stop. Second, check whether the annual limit was met. If so, assign category 4 and stop. Third, check whether school attendance ceased. If so, assign category 3 and stop. Fourth, check whether earnings ceased. If so, assign category 2 and stop. Fifth, the only remaining possibility is that SSI eligibility was suspended. Assign category 1.

For further information on the categories, see Appendix D.

Chart 7 suggests that relatively few SSI recipients remain eligible for the SEIE long enough to lose it upon attaining age 22; far more people lose SEIE eligibility upon leaving school prior to age 22.

Changes in student status appeared to drive the summer decrease in the count of SEIE recipients. For purposes of the SEIE, a person retains student status during school vacations provided he or she plans to (and does) return to school when classes resume; thus, most individuals should not lose their student status at the beginning of summer vacations only to regain it at the end. High school graduation, however, could account for numerous losses of student status (and hence of SEIE status) in June and July.¹⁴

The calendar-year limit on the SEIE also contributed to seasonality in the monthly numbers of SEIE recipients. In particular, some SEIE recipients reached the annual limit each month from June through December; then, in January, most of them regained SEIE status.

The bar segments in Chart 7, like the combinations of factors to which they correspond, are nonoverlapping. The first bar represents changes from January 2004 to February 2004; using 24 months' SEIE data, only 23 month-to-month changes could be calculated.

Table 8 shows the numeric values underlying Chart 7 and provides a more complete breakdown of the month-to-month changes in the count of SSI recipients with SEIE. It shows the number of gains, the number of losses, and the net change attributable to each category for each month. The table shows, for instance, that earnings were much more volatile than student status, in the sense that relatively small monthly net gains of SEIE status in the "earnings" category usually resulted from large numbers of mostly offsetting gains and losses.¹⁵

Summary

This article takes a preliminary descriptive look at SSI recipients with SEIE, attempting to answer the following questions: To what extent are SSI recipients using the SEIE? What are the characteristics of SEIE recipients? How intensively is the SEIE used by those who do use it? Which of the limitations on the SEIE—dollar maximums, age restrictions, and so on—are most often actually limiting? What seasonal patterns does SEIE receipt follow?

Regarding extent of SEIE use, there were about 26,000 SSI recipients with SEIE in each of the years 2004 and 2005; this represented about 3 percent of SSI recipients between the ages of 12 and 22 (Table 1). According to December counts (Table 7), the number of SEIE recipients exceeded the number of participants in PASS (Plan for Achieving Self Support), IRWE (Impairment Related Work Expenses), or BWE (Blind Work Expenses), even though none of the latter three provisions is age-limited (SSA 2005b, 2006). Working while attending school, at least among SSI recipients under age 22, is nearly tantamount to SEIE receipt; a person need not know about the SEIE to benefit from it, because the SEIE applies automatically when a student reports earned income—and income reporting is obligatory for SSI recipients. Nevertheless, even among SSI recipients who would presumably be high school students—those aged around 18 or 19 years—the SEIE use rate (and hence the proportion of working students on SSI) was under 8 percent each year (Table 1). A visual inspection of state-by-state SEIE use rates does suggest possible wide variation (Tables 3a and 3b), similar geographically to that in state-by-state rates of work and Section 1619 participation (SSA 2005b, 2006). Also, the estimated SEIE use rate appeared a bit higher for persons diagnosed with nervous system disorders or mental retardation and a bit lower for persons diagnosed with other mental disorders (Table 1); this could have derived in part from variations by age in the prevalence of different disability diagnoses. The SEIE could potentially help an SSI recipient stay in school by making tuition more affordable or by defraying other costs of continued school attendance. Indeed, about 4 percent of SSI recipients were still working students (and SEIE recipients) as they approached the age-22 SEIE cutoff (Table 1). The question of how much the SEIE affected such individuals' decision to work and continue attending school remains open.

What are the characteristics of SEIE recipients? SSI recipients with SEIE were, roughly like SSI recipients in the 12–22 age group overall, predominantly male (about 60 percent) and overwhelmingly diagnosed with mental disabilities (about 75 percent). They were mostly 16–21 years old, with the highest concentration near ages 18 and 19 (Table 1).

How intensively is the SEIE used by those SSI recipients who do use it? Many SEIE recipients had only a few hundred dollars of earned income per year subject to the SEIE (Tables 4a and 4b) and thus technically received SEIE even though other earned income exclusions were redundant. Almost one-third of SEIE recipients used less than 10 percent of the annual SEIE limit, and approximately half used less than 20 percent of the annual limit. Fewer and fewer SEIE recipients fell into each successive percentage-of-limit bracket, except for the highest bracket, which includes recipients with earnings equal to or greater than the SEIE limit; each year, about 4–5 percent of SSI recipients with SEIE reached the calendar-year SEIE limit (Table 5)—a few each month from May to December. The median annual SEIE amount was around $1,000, less than one-fifth of the limit (Tables 1, 3a, and 3b). About 70 percent of SSI recipients with SEIE received SEIE for 6 or fewer months; about 10 percent received SEIE continuously through the calendar year (Tables 4a and 4b).

Which of the limitations on the SEIE—dollar maximums, age restrictions, and so forth—are most often actually limiting? Most entries to the group of SEIE recipients occurred when an SSI recipient, already attending school, began working (Chart 7 and Table 8); most exits from the group of SEIE recipients occurred when an SEIE recipient ceased to attend school (almost always in June or July). The SEIE calendar-year limit did cause a smaller number of people to cycle out of the group of SEIE recipients and then back in the following January, and the proportion of SEIE recipients ceasing to qualify for SEIE because of the age constraint was similar to that affected by the annual limit—about 4–5 percent (Chart 7 and Table 8). This latter number excludes SSI recipients who did not actually receive SEIE in the month before reaching the age limit.

What seasonal patterns are evident? Apparently due to the large number of exits around what we might think of as the end of the spring school semester, the monthly number of SEIE recipients actually appeared to reach its annual trough in summer (Chart 3); aggregate SEIE amounts seemed to peak in the summer, however, as did average SEIE amounts, suggesting increased work activity during school vacations (Charts 4–6). Seasonal patterns observed in several charts in this article, particularly those involving exit and subsequent reentry caused by the SEIE annual limit (Chart 7), suggest that any future analyses of the SEIE should at least consider using full-year data rather than one monthly cross-section.

Appendix A: Effect of the SEIE on Total Income

How large is the financial effect of the SEIE? For SSI recipients with small amounts of earned income (up to $65 or even $85 per month, depending on unearned income), the SEIE is redundant with other income exclusions and thus has, arguably, no effect on its recipients' total income. For higher earners, it can have a great impact. For instance, in 2004, someone with no countable unearned income and monthly earned income equal to the monthly SEIE limit of $1,370 would typically receive no SSI payment if not eligible for the SEIE; with the SEIE, this person would receive the maximum monthly federal SSI payment of $564. A person with no countable unearned income and monthly earned income equal to one-twelfth of the annual SEIE limit, or $460, would receive an SSI payment of $376.50 without the SEIE or $564 with the SEIE, a difference of $187.50 per month. Depending on its type, unearned income in excess of $20 often reduces the federal SSI payment dollar for dollar, so typically the higher a person's unearned income, the more limited the potential impact of the SEIE.

Even people with the same total amounts of earned income, unearned income, and SEIE within a given calendar year theoretically could, simply due to the timing of the receipt of that income, receive substantially different SSI payments. This is a caveat for interpreting the amount of income excluded under SEIE as a measure of SEIE use, as it is not perfectly correlated with the monetary value of the SEIE to the recipient.

As an example, consider two SSI recipients who reach the annual limit near the middle of the year. Suppose one of them receives substantial unearned income in the months prior to reaching the annual limit and much less in subsequent months; this person will receive less total SSI during the year than the other, who has the same pattern of earnings and SEIE use but receives the bulk of the unearned income after reaching the annual limit rather than before. Table A-1 presents a hypothetical example, with values somewhat contrived so as to emphasize the disparity.

This example ignores certain technicalities related to deciding which month's countable income determines a given month's SSI payment amount, but if, for instance, we assume that neither person is due an SSI payment in December of the preceding year, then the scenario shown in the table is accurate except for a $100 understatement of the total calendar-year SSI amount for Person A.

Appendix B: Notes on Sample Selection and the Definition of "SEIE Recipients"

Several practical issues affected sample selection. The data selection necessarily excluded persons for whom explicit SEIE amounts were unavailable, most notably SEIE recipients who were ineligible for SSI (such as deemors and ineligible children—see note 5) and SEIE recipients who were members of eligible couples (that is, couples with both spouses eligible for SSI). Because of changes in the law that took effect in April 2005, eligible couples and deemors qualified for the SEIE only during the last 9 of the 24 months covered by the data; in this sense, their exclusion keeps the selection criteria for the data set more consistent over time. In some other cases, SEIE recipients may not have been identifiable as such from the available data, but such instances are probably rare. Of the 3,999 SEIE recipients originally selected, 9 were dropped because of difficulties parsing their records' data.

Even after everyone for whom complete SEIE data were available had been identified, definitional choices arose; the definition of "SEIE recipient" in this article is but one of several reasonable alternatives. Two principles guided its choice. The first principle was to focus on "cash SSI recipients"—disregarding, for example, SEIE amounts posted to the not-yet-terminated SSI record of someone who no longer met the SSI disability criteria. The second principle was to focus on people whose SSI eligibility or payment amount was actually affected by the SEIE.

These principles led to decisions to eliminate from the analysis any SEIE amounts posted during a long period of Section 1619(b) status or during a series of nonpayment months long enough that a new SSI application would be needed before SSI payments could resume. The decision to eliminate SEIE amounts posted during shorter periods of nonpayment months interspersed with months when SSI payment was due was more difficult: The two principles conflict here, as such SEIE amounts can interact with the calendar-year SEIE limit to affect subsequent SEIE receipt. However, elimination criteria involving nonpayment status or absence of SEIE "continuing through the end of the calendar year" would have serious drawbacks. Even though such criteria would perhaps be the most obvious way of keeping SEIE amounts that might affect subsequent ones while discarding others, they could bias the results by eliminating months occurring later in the calendar year more often than those occurring earlier. Consequently, all nonpayment months were eliminated, restricting the definition of "SEIE recipients" to those persons who were due an SSI payment in a month when the SEIE applied.

This definition yields a group that is mostly inclusive of, but somewhat larger than, the second principle's group of persons actually affected by the SEIE. In particular, SEIE amounts were counted for some months that would have been months of SSI eligibility even had the SEIE not applied; such SEIE amounts only sometimes increase the SSI payment amount as compared with the counterfactual situation involving no SEIE. Because of redundant exclusions (if earnings are $65 or less per month, then the "$65 plus half remainder" earned income exclusion will reduce a nonstudent's countable income as much as the SEIE would a student's), SEIE amounts associated with monthly earned income of $65 or less can never affect SSI eligibility or payment amount. Yet person-months with earned income under $65 were included in the analysis. Focusing on the group of "persons whose SSI eligibility or payment amount was affected by the SEIE" would have required hypothetical calculations of what SSI payment amounts would have been had the SEIE not been involved, and not all the data required for such calculations were obtained. Instead, the slightly more inclusive definition of the population of interest, given above, was chosen.

One final point deserves mention. Some states provide supplementary payments to SSI recipients, and it is possible for countable income to be too high for federal SSI payment in a particular month yet low enough for a state supplementary payment to be made. In this article, for states where SSA administers the supplementary payments, such months are counted as months of SSI receipt. This may make counts of SEIE recipients slightly higher than they would have been in the absence of federally-administered state supplementation; from another point of view, it creates some state-to-state variation in the maximum amount of income that a person can have and still be counted in this article as having received SSI and the SEIE.

Appendix C: Sampling Variability

The numbers presented in this article are subject to sampling variability; they are only estimates of numbers for the full population of SSI recipients with SEIE. Differences between the statistics for 2004 and those for 2005, if small relative to their standard errors, may have resulted from sampling variability rather than from actual differences in the full population of SEIE recipients. This also applies to differences between statistics (such as estimated mean SEIE amounts) across different groups of SEIE recipients.

The 10 percent sample file is the most complete source of longitudinal SEIE data readily available for statistical purposes. It is drawn from the Supplemental Security Record (SSR)—a database of all persons who have ever filed for SSI or were converted from state assistance payments to SSI in January 1974—based on the last two digits of SSI recipients' Social Security numbers (SSNs). Because any particular person's SSN is very nearly equally likely to end in any of the 100 possible pairs of digits 00 through 99, the 10 percent sample file can be regarded as a simple random sample.

Standard errors for median SEIE amounts were calculated by bootstrap. Standard errors for total numbers and percents of persons and for mean SEIE amounts were calculated according to the basic formulas for simple random samples or domains (subpopulations) thereof.¹⁶ Calculations were based on the original sample size of about 700,000 SSI recipients, not the much smaller intersection of that sample with the set of SEIE recipients. The sampling fraction for SSI recipients was assumed to be exactly 10 percent (which should be very close to true), and the formulas all involved a finite population correction. In cases where the SAS SURVEYMEANS procedure was used (for example, for standard errors of mean SEIE amounts), the Taylor series linearization formulas implemented by this procedure simplify to the basic simple random sample formulas. The statistics in Table 8 are differences between pairs of estimated population totals; the standard error estimates (see Table C-7) include an estimated covariance term.

Tables C-1a and C-1b provide standard errors for estimated total numbers of SSI recipients with SEIE. Tables C-1c and C-1d provide standard errors for estimated proportions of all SSI recipients with SEIE. This presentation format is possible because, given the sample size and sampling fraction (and for the proportions, also the total number of SSI recipients with SEIE in the sample), these standard errors depend only on the value of the statistic itself. Subsequent Appendix C tables correspond to specific tables found in the main article and give standard errors for quantities, such as estimated mean SEIE amounts, estimated proportions of subpopulations of SEIE recipients, and net changes in numbers of SSI recipients with SEIE, that are not amenable to the presentation format of Tables C-1a through C-1d. If a table from the main article does not have a corresponding Appendix C table, the reader may conclude that the standard errors in Tables C-1a through C-1d are applicable.

Appendix D: Notes on Chart 7 and Table 8 Categories

Chart 7 and Table 8 break down the monthly changes in the count of SSI recipients with SEIE according to the factors causing gain or loss of SEIE status. The analysis classifies persons gaining SEIE status only according to the last criteria to be met and persons losing SEIE only according to the first criteria they cease to meet. In other words, it classifies persons according to the factors that most proximately bring about the gain or loss of SEIE.

Although a gain or loss of SSI-with-SEIE status can result from a change in any 1 of 15 or more eligibility factor combinations, this analysis lumps these combinations of factors into just five categories both to ease visual interpretation and to keep standard errors in check.¹⁷ The following principles guided the creation of the categories:

1. Materiality. Combinations of factors that account for only a small number of gains or losses should be lumped together to the greatest extent reasonable. Losses of SEIE involving attainment of age 22 are all lumped together, no matter what other criteria concurrently cease to be met, partly for this reason. Similar reasoning applies to gains and losses involving the annual limit, since relatively few people reach the annual limit each month. Except when attainment of age 22 is involved, losses of SEIE due to any combination of factors involving the annual limit are all lumped together.
2. Permanence. If a change in one eligibility factor is more "permanent" than a change in others, then any combinations involving this relatively permanent factor should be lumped together. For example, attainment of age 22 causes permanent loss of SEIE, affording yet another reason for lumping into a single category all losses of SEIE involving attainment of age 22. The annual limit has a secondary degree of permanence, in that once someone reaches the annual limit, SEIE cannot resume until the next calendar year. This provides a second reason for lumping together all SEIE gains and losses that involve the annual limit but not attainment of age 22.
3. Seasonality. If seasonal patterns in one eligibility factor seem to drive seasonal patterns in the gains and losses of SEIE resulting from several combinations of factors, then these combinations should be isolated in their own category, separate from other combinations of factors that do not exhibit the same seasonal behavior. For example, concurrent changes in student status and earnings were put into the "student status" category because a visual inspection suggested that the seasonal pattern of the concurrent changes is more similar to that of student status than to that of earnings. The same reasoning was applied to concurrent changes in SSI eligibility and earnings or student status, which appeared to follow the latter two factors' seasonal patterns.
4. Causality. If a change in one eligibility factor causes a change in some combination of factors, then this combination can't be categorized separately from the causative factor. According to the SSI definition, student status is lost upon attainment of age 22; thus among persons turning 22, those who cease to attend school are, from the data used for this article, indistinguishable from those who continue to attend. This makes the lumping of concurrent age and student status changes into the "age" category the only viable option.

Five nonoverlapping categories result: (1) SSI eligibility alone; (2) earnings, alone or concurrently with SSI eligibility; (3) student status, alone or concurrently with earnings or SSI eligibility; (4) annual limit status, alone or concurrently with student status, earnings, or SSI eligibility; and (5) age status, alone or concurrently with any other factors.

A change in category (1), the "SSI eligibility" category, represents either a first month with SSI payment due on a newly filed SSI claim or a subsequent suspension or reinstatement of SSI payments. Persons who were already working and attending school and gained SEIE upon becoming newly eligible for SSI should fall into this category. An SEIE amount can be posted to an SSI record regardless of whether SSI payment is due for the month in question; however, this article focuses on just those person-months with SSI payment due as well as SEIE posted. Consequently, Chart 7 registers a loss in category (1) for each person whose SSI payments are suspended and a gain in category (1) for each person whose SSI payments are reinstated, provided they meet the earnings, student status, annual limit status, and age criteria for receipt of SEIE both before and after the suspension or reinstatement.

Changes in category (5), the "age" category, by definition involve attainment of age 22 and as such always result in loss of SEIE status. Changes in category (4), the "annual limit" category, between June and December necessarily result in loss of SEIE, while those in January necessarily result in gain of SEIE. Changes in category (4) cannot occur between February and May because the monthly limit makes reaching the annual limit prior to May impossible. Changes in category (2), the "earnings" category, refer to a gain of SEIE status due to commencement of positive earnings or a loss of SEIE due to cessation of earnings. Changes in categories (1), (2), or (3) (the "SSI eligibility," "earnings," and "student status" categories) can be gains or losses; for each of these categories, the chart shows the net change, that is, gains attributable to that category minus losses attributable. Gains in category (3), the "student status" category, could involve persons entering grade 7 (the lowest grade that confers student status for SSI purposes) or persons returning to school after a gap in attendance (other than a regular school vacation). If, prior to April 2005, someone lost or gained SEIE recipiency because of child status (that is, head of household or marital status), then the change would appear in category (3), the "student status" category. (The portion of student status changes attributable to child status, however, is negligible.)