# New Evidence on Earnings and Benefit Claims Following Changes in the Retirement Earnings Test in 2000

by Jae G. Song and Joyce Manchester
ORES Working Paper No. 107 (released June 2006)

The authors are with the Division of Economic Research, Office of Research, Evaluation, and Statistics, Office of Policy, Social Security Administration.

Acknowledgments: The authors are grateful to Ed DeMarco for his support. We received helpful comments from Mark Duggan, Leora Friedberg, Steve Goss, Tim Kelly, Bert Kestenbaum, Wojciech Kopczuk, Emmanuel Saez, David Stapleton, David Weaver, participants at the NBER Summer Institute 2005 and Tax Economists Forum, and other Office of Policy staff members. The authors thank Bill Kearns, Henry Ezell, Pat Cole, and Nancy O'Hara for their help.

Working papers in this series are preliminary materials circulated for review and comment. The findings and conclusions expressed in them are the authors' and do not necessarily represent the views of the Social Security Administration.

## Summary

This paper evaluates responses to the removal of the retirement earnings test in 2000 for persons at the full retirement age and older. We examine annual earnings and retirement benefit claims from Social Security administrative data that cover the 4 years before and after the change. Three findings emerge from the study.

First, the effect on earnings of removing the earnings test is uneven over the distribution of individuals' earnings. Quantile regression methods show that although the effect on earnings in the lower percentiles is not statistically significant, the effect on earnings in the higher (50th to 80th) percentiles is large and significant. Such a finding indicates that effects of the removal are limited to earnings levels above the test threshold. The largest increases in earnings are found at the 70th percentile for persons who have attained ages 65–69 (where earnings increase between $180 and$1,670) and at the 60th percentile for those turning 65 (where earnings increase between $1,500 and$2,800).

Second, there is no clear evidence of the effect of the test's removal on the labor force participation rate among individuals reaching age 65, whereas work participation among individuals who have attained ages 65–69 increased between 1 and 2 percentage points after the removal. Further analysis indicates that the increase in work participation is mostly attributable to retaining older workers rather than inducing older persons to return to the workforce. The effect appears to increase over the postremoval period, suggesting that the removal has long-lasting effects on work participation due to the state-dependent nature of labor force participation and labor market rigidities.

Third, following the removal of the earnings test, applications for benefits accelerated by 2 to 5 percentage points among individuals aged 65–69 and by 3 to 7 percentage points among those reaching age 65. Results show relatively constant effects for the same age cohorts for different years, indicating that the long-term effects can be estimated from reactions immediately after the test's removal or from reactions among persons who just attained the full retirement age.

## Introduction

The retirement earnings test, which has been part of the Social Security Old-Age and Survivors Insurance (OASI) program since its inception in 1935, has been gradually modified by exempting certain age groups, increasing allowable earnings, and decreasing withholding rates. A rationale for modifications is to encourage older people to work so that their earnings can supplement their Social Security benefits as people live longer and healthier lives. The most recent major modification occurred in April 2000, when Congress enacted the Senior Citizens Freedom to Work Act of 2000, which removed the earnings test for individuals at the full retirement age (FRA), age 65 and over.1 The 2000 removal of the test is one of the most substantial changes in recent years because it affects both the most recent cohorts of persons who have reached the FRA and a wider range of ages than had other modifications.

Although the earnings test compensates individuals for postponing benefit entitlement by increasing their future benefit streams through the delayed retirement credit and automatic benefit recomputation, many people do not view those adjustments as actuarially fair. That is, many people view the earnings test as a tax on earnings above the test threshold, causing both a reduction in work effort (for example, hours of work, earnings, and work participation) of old-age beneficiaries and a delay in applications for Social Security retirement (old-age) benefits. This tax aspect of the earnings test causes kinks in the budget constraint in a static labor supply model (Burtless and Moffitt 1985, Friedberg 2000).2 In the static model, removing the earnings test causes a decline in the marginal tax rate for those who earn above the threshold.

A number of studies have analyzed how incentives generated by Social Security program rules have affected work participation and benefit claims. Those studies relied primarily on cross-sectional variations in benefit amounts as identification information (see Krueger and Meyer (2002) for an overview and survey). In response to the identification problem caused by the fact that all workers face an identical benefit schedule in the Social Security system, the earnings test has drawn attention from economists who seek to investigate the disincentive effect that Social Security program rules have on labor supply. Three recent studies—Friedberg (2000), Gruber and Orszag (2003), and Loughran and Haider (2005)—used the experimental approach by noting that modifications of the earnings test in the United States affected some groups but not others.3 Although Friedberg's results indicated a small but significant effect of the earnings test on the labor supply of older workers, Gruber and Orszag indicated that the earnings test had no robust influence on labor supply and appeared to accelerate benefit receipt among eligible individuals. Results reported in Haider and Loughran indicated that the earnings test has a substantial impact on hours worked and benefits claimed for men. Disney and Tanner (2002) and Baker and Benjamin (1999) examined the elimination of a similar earnings test in the United Kingdom and Canada. Disney and Tanner reported that the elimination of the earnings test increased hours worked by men in the United Kingdom by about 4 hours per week. Baker and Benjamin found a shift from part-time to full-time work among Canadian men aged 65–69.

Unlike other studies, this study focuses on the most significant single change in the history of the U.S. earnings test.4 It provides comprehensive empirical evidence on the effects of removing the earnings test for persons aged 65–69 by using a large and accurate Social Security Administration (SSA) administrative data set that covers the period from 4 years before to 4 years following the removal (1996–2003). By including 4 years of data after the removal, we are able to investigate reactions not only immediately following the removal but also for several years after. This extended period can help us understand dynamic responses to changes in the relative price of labor among older workers, some of whom face substantial constraints on reentering the labor force because of deteriorating health and outdated skills. Further, by using quantile regression methods, we can examine the uneven impact of the earnings test removal across the distribution of earnings. That uneven impact, predicted by the kinked budget constraint in the presence of the earnings test, represents a key problem with using reduced-form analysis of the earnings test.

## Earnings Test Rules and Theoretical Prediction

The retirement earnings test operates in a relatively simple manner. Social Security benefits are reduced if earnings exceed the threshold amounts, but the reduction in benefits is at least partially offset in the future through the delayed retirement credit and benefit recomputation.5 Thus, the earnings test has both "tax" and "transfer" features.

The tax feature of the earnings test includes both threshold amounts and withholding rates. The threshold amount varies by the year in which the test applies and by the ages of the beneficiaries. Before the 2000 removal of the earnings test, the thresholds for persons aged 65–69 as of 1996, 1997, 1998, and 1999 were $12,500,$13,500, $14,500, and$15,500; for those aged 62–64 they were $8,280,$8,640, $9,120, and$9,600, respectively. The benefit withholding rate was $1 for each$3 of earnings above the earnings test threshold for individuals aged 65–69 and $1 for each$2 for those aged 62–64.

The transfer feature of the earnings test, often overlooked because of the focus on the tax feature, compensates for the withholding of benefits by increasing the primary beneficiary's future benefit stream. Two aspects of the Social Security rules compensate individuals who are subject to the earnings test: the delayed retirement credit and benefit recomputation. Future benefits for individuals who have not received benefits because of the earnings test (or for any other reason) are increased for each month in which no benefits are paid. This increase is 1/4 of 1 percent for each month, plus 1/24 of 1 percent for each even numbered year, from 1990 through 2008, in which workers are at the FRA or older. Thus, for those who turned 65 in 2000–2001, the delayed retirement credit is 1/2 of 1 percent for each incremental month, or 6 percent per year.6 A benefit recomputation rule may apply to persons who become entitled to benefits but who subsequently have substantial covered earnings. The recomputation can increase benefits when earnings in the additional years are higher than the lowest earnings used in the current computation.7

The earnings test does not apply to individuals who are entitled to benefits because of disability or who are living outside the United States and their work is not covered by Social Security.8 When earnings exceed the test's threshold, the total family benefit is reduced accordingly, including all benefits (other than Disability Insurance) payable to anyone in the family entitled to benefits on the primary earner's earnings record. For purposes of the earnings test, an individual's earnings for the entire taxable year are counted, even if the individual has not been entitled for the entire year.9 In addition, self-employment earnings are counted for the year in which they are received, regardless of when they are earned. Countable income for the earnings test includes wages from covered employment, cash payments for agricultural or domestic work, cash tips, deferred compensation, and pay for work not covered by Social Security if the work is done in the United States.

After the earnings test removal in 2000, beneficiaries remain subject to an earnings test until they reach the FRA. Social Security benefits of persons aged 62–FRA* (that is, the FRA minus 1 month) at year-end are reduced by $1 for every$2 earned beyond the threshold, which was $11,520 in 2003. Those who reach the FRA during the year are subject to a more moderate test. Benefits are reduced$1 for every $3 earned beyond the threshold, which was$30,720 in 2003.10 Thus, the removal of the earnings test in 2000 not only eliminated the test for those who had attained ages 65–69 (more precisely, FRA to 69), but it also considerably relaxed the test for those turning 65 (FRA).11

The direction and magnitude of the effects of eliminating the earnings test depend on several factors, such as the benefit withholding rate, test threshold, delayed retirement credit, cost-of-living adjustment, individuals' time preference, and mortality. Economic theory on the effects of the earnings test on labor supply is fairly straightforward and can be found in numerous studies.12 A general consensus from those studies is that a delayed retirement credit that was actuarially fair would offset the effects of the earnings test. Yet they question whether the relevant population is aware of the transfer aspect of the earnings test. It is relatively straightforward to show that a static budget constraint contains kinks under the earnings test when the transfer aspect of the earnings test is ignored (or unfair) or when the discount rate is high. In those situations, eliminating the test would yield results equivalent to reducing marginal tax rates. In the case of the earnings test, however, effects of reducing the marginal tax rate depend on individuals' earnings levels and benefit entitlement status. In the presence of the earnings test, we expect to see negative income effects above the upper threshold where all benefits are withheld, both negative income effects and positive substitution effects between the upper and lower threshold, and no effects below the lower threshold. We also expect that removing the test would affect decisions about benefit claims as well as work participation and earnings. Moreover, evaluating the mean effect alone might miss the true effect of the test's removal (Heckman, Smith, and Clements 1997; Song 2003/2004; Bitler, Gelbach, and Hoynes 2003).

## Data and Identification Strategy

### Data

This study uses data from an extract of the Social Security Administration's 1 percent (active) sample, commonly known as the Continuous Work History Sample (CWHS) active file.13 The 1 percent samples are selected on the basis of certain serial digits of the Social Security number (SSN) and are generally considered to be random samples. Once a person is selected, he or she stays in the active sample for life. For selected SSNs, information on annual earnings (both capped and uncapped), OASDI (Old-Age, Survivors, and Disability Insurance) benefit entitlements, and death records, if any, are obtained from several SSA administrative files. The sources for the CWHS include the Numident, the Master Earnings File (MEF), and the Master Beneficiary Record (MBR). The Numident is a numerically ordered master file of assigned SSNs that contains birth and death dates, place of birth, race, and sex. The MEF contains annual FICA summary earnings from 1937 to the present. It also contains annual detailed earnings, Medicare taxable compensation, and total compensation from 1978 to the present for the U.S. population. The earnings records are taken directly from W-2 forms. A MEF record is created when the corresponding Numident record is created. The MBR file contains data related to the administration of the OASDI program, such as application and entitlement dates, benefit amounts, payment status, type of benefits, and demographic information. An MBR record is established when an individual applies for benefits and the application is processed.14

The 1 percent extract of SSA administrative records provides several advantages over other data used for studying the effects of the earnings test. First, the 1 percent extract contains accurate annual earnings records that are not plagued by the self-reporting problems that are common in survey-based records. Since the earnings test is based on earnings amounts rather than on labor hours, accurate earnings data are crucial for analyzing responses around the test threshold. We use Medicare taxable earnings because deferred earnings are taxed for Medicare purposes and counted for purposes of the earnings test.15 Second, SSA data contain the exact date of entitlement for old-age benefits. For the earnings test, individuals' earnings for an entire taxable year are counted even if the individuals were not entitled to benefits for the entire year.16 Hence, whether or not an individual becomes entitled to retirement benefits during a given year is critical information. Third, the 1 percent sample contains a large number of observations that represent the general population. Some disadvantages exist as well, however. We have no information on hours of work or other covariates that are crucial in labor supply models, such as wages, other income, health status, education, and family characteristics. Hence it is not possible to use the data to estimate a structural model of labor supply.

In this study, we focus on the labor supply or earnings of primary workers who are fully insured, not survivors or dependents. Primary-worker beneficiaries are the largest group among Old-Age and Survivors Insurance beneficiaries; they constituted approximately 75 percent of total OASI beneficiaries in 2002 (Social Security Administration 2003). Further, while earnings of primary-worker beneficiaries that exceed the test threshold cause reductions in total family benefits, including benefits to spouses and children, excess earnings of a survivor or a dependent beneficiary reduce only the worker's monthly benefits. Moreover, a worker must be fully insured before retirement benefits can be paid to the worker or to his or her family. Thus, we subset our sample to include individuals who have accumulated enough quarters of coverage to be fully insured between the year they turn age 21 and the year they reach 62.17 Our analytical samples exclude Social Security Disability Insurance (DI) beneficiaries, old-age beneficiaries converted from DI benefits, and those who are not fully insured under Social Security.

### Defining Treatment and Control Groups

The main features of the 2000 change in the earnings test are (1) the complete elimination of the earnings test for individuals who have attained the FRA as of December 31 of the year before the relevant year and (2) a modified earnings test with significantly increased test threshold amounts for those who reach the FRA during the relevant year.18 Hence we consider two separate treatment groups: those who turn 65 during the year and those who have attained ages 65–69 by January 1 of a particular year. As control groups, we consider those both older and younger than the treatment groups: individuals turning 62–64 and those who have attained ages 70–72.19 During the study period, those who had attained ages 70–72 faced no earnings test, while those turning 62–64 faced the same test rules, except that the threshold amounts were gradually increased. As a result, there are two treatment groups and two control groups in each calendar year from 1996 through 2003:

• Group 1—the younger control group, who turn ages 62–64;
• Group 2—the younger treatment group, who turn age 65;
• Group 3—the older treatment group, who have attained ages 65–69;
• Group 4—the older control group, who have attained ages 70–72.

The "treatment" in this study depends on both time and age because earnings test rules are specific to age as well as to calendar year. Thus, we cannot take full advantage of the longitudinal format of the SSA administrative data in defining treatment and control groups. Instead, we arrange the data such that each yearly cross section covers the age range 62–72, as shown in Table 1. The dependent variables of our study—earnings and labor force participation as well as benefit claims—are functions of the passage of time (aging); different age groups have their own time trends arising from interactions of group- and time-specific effects on the outcome variables. Thus, by defining control groups to include exactly the same age range in each year, our control groups can isolate both age- and year-specific effects. By including both older and younger age groups as control groups, we expect to learn more about the dynamics of labor supply in response to the removal of the earnings test.20

Table 1. Sample size, by birth year and calendar years before and after the removal of the retirement earnings test
Birth year Before removal After removal Group
1996 1997 1998 1999 2000 2001 2002 2003
1923 12,219
1924 13,325 12,919
1925 13,151 12,796 12,395
1926 13,552 13,196 12,820 12,437
1927 14,184 13,849 13,465 13,083 12,668
1928 14,431 14,091 13,750 13,393 13,018 12,619
1929 14,435 14,130 13,841 13,522 13,154 12,762 12,373
1930 15,228 14,970 14,681 14,350 14,010 13,651 13,255 12,826 Group 4
1931 14,419 14,221 13,988 13,760 13,506 13,235 12,929 12,609
1932 14,414 14,258 14,102 13,920 13,702 13,443 13,174 12,913
1933 14,324 14,187 14,036 13,881 13,697 13,484 13,268 13,045 Group 3
1934 14,804 14,675 14,530 14,367 14,169 13,961 13,748 13,521
1935 15,289 15,161 15,014 14,853 14,685 14,493 14,297
1936 15,529 15,383 15,240 15,071 14,897 14,707
1937 15,933 15,798 15,648 15,493 15,329
1938   16,786 16,662 16,515 16,370 Group 2
1939     16,763 16,653 16,511 Group 1
1940     17,811 17,671
1941     18,418
All birth years 168,486 168,581 168,298 169,043 170,601 171,984 174,609 178,217
SOURCE: Authors' tabulations using the 1 percent extract of the Social Security Administration's Master Earnings File and Master Beneficiary Record.
NOTE: Group 1 is the younger control group, who turn ages 62–64; Group 2 is the younger treatment group, who turn age 65; Group 3 is the older treatment group, who have attained ages 65–69; and Group 4 is the older control group, who have attained ages 70–72.

Our study period covers 4 years before and 4 years following the removal of the earnings test (that is, from 1996 through 2003) for the following reasons. First, data through 2003 were the latest available at the time of the analysis. Second, by including a multiple-year period before the removal of the earnings test, we are able to test whether the outcome measures for the treatment and control groups are comparable during the preremoval period. The fundamental identification assumption in this kind of model is that the mean (or other measure) change in outcome in the absence of the treatment is the same for both the treated and the nontreated groups. We test this assumption by asking whether or not the coefficients of the treatment dummies (the treatment-group dummies interacted with calendar years) for 1996 through 1999 equal zero. Third, by including multiple years following the test's removal, we are able to examine responses in work participation and annual earnings for several years after the removal as well as immediately after the removal. One would expect that immediate responses to the removal of the earnings test might differ from longer-term responses because of the difficulty and cost in changing one's hours of work or returning to the labor market after a period of absence.

Sample sizes by calendar years vary from 168,486 to 178,217, depending on the reference year (Table 1). The age range of the sample in each year is exactly the same over the reference period. Observations consist of persons who are fully insured as of age 62 and are not receiving Disability Insurance benefits. Once selected, those persons remain in our analytical sample until they reach age 72 unless death occurs. Thus, sample attrition is caused entirely by deaths. The race and sex variables show that approximately 88 percent are white and 54 percent are male.

## Descriptive Analyses on Work and Retirement Among Workers Aged 62–72

From 1996 through 2003, the data show movements in work participation and benefit entitlement of the treatment groups relative to the control groups (Table 2). If our control groups are valid, we expect to see parallel movements in outcome variables of the treatment and control groups during the pre-2000 period. Work participation rates during the preremoval period among those in the age groups 62–64, 65, 65–69, and 70–72 are approximately 52 percent to 55 percent, 40 percent to 44 percent, 26 percent to 29 percent, and 16 percent to 18 percent, respectively. At the beginning of each reference year, old-age benefit entitlement rates during the preremoval period for the four groups are approximately 21 percent, 63 percent to 65 percent, 88 percent to 89 percent, and 91 percent to 92 percent, respectively.

Table 2. Work participation and benefit entitlement status, by age group
Status 1996 1997 1998 1999 2000 2001 2002 2003
Number Percent Number Percent Number Percent Number Percent Number Percent Number Percent Number Percent Number Percent
Group 1, turning ages 62–64
Total sample
All 43,542 100.00 44,151 100.00 45,220 100.00 46,330 100.00 47,824 100.00 49,073 100.00 50,979 100.00 52,600 100.00
Working 22,784 52.33 23,588 53.43 24,412 53.98 25,324 54.66 26,623 55.67 27,348 55.73 28,235 55.39 29,128 55.38
Beneficiaries already entitled on January 1
All 9,258 21.26 9,331 21.13 9,421 20.83 9,745 21.03 10,058 21.03 9,766 19.90 10,040 19.69 9,988 18.99
Working 4,649 10.68 4,689 10.62 4,842 10.71 4,852 10.47 5,194 10.86 5,221 10.64 5,042 9.89 5,037 9.58
Beneficiaries becoming entitled during year
All 14,768 33.92 14,596 33.06 14,880 32.91 14,952 32.27 15,226 31.84 15,719 32.03 15,703 30.80 15,601 29.66
Working 4,810 11.05 4,880 11.05 4,948 10.94 5,217 11.26 5,295 11.07 5,148 10.49 5,200 10.20 5,098 9.69
Group 2, turning age 65
Total sample
All 14,419 100.00 14,258 100.00 14,036 100.00 14,367 100.00 14,853 100.00 15,071 100.00 15,493 100.00 16,370 100.00
Working 5,843 40.52 5,988 42.00 6,026 42.93 6,253 43.52 6,661 44.85 6,795 45.09 6,992 45.13 7,327 44.76
Beneficiaries already entitled on January 1
All 9,352 64.86 9,172 64.33 8,807 62.75 9,070 63.13 9,219 62.07 9,295 61.67 9,520 61.45 9,877 60.34
Working 2,631 18.25 2,773 19.45 2,634 18.77 2,834 19.73 2,892 19.47 2,952 19.59 3,008 19.42 2,954 18.05
Beneficiaries becoming entitled during year
All 2,989 20.73 2,977 20.88 3,076 21.92 3,179 22.13 4,113 27.69 4,159 27.60 4,244 27.39 4,099 25.04
Working 2,167 15.03 2,189 15.35 2,252 16.04 2,307 16.06 3,122 21.02 3,161 20.97 3,235 20.88 3,071 18.76
Group 3, have attained ages 65–69
Total sample
All 71,830 100.00 71,261 100.00 70,362 100.00 69,433 100.00 69,084 100.00 68,808 100.00 69,580 100.00 70,899 100.00
Working 18,890 26.30 19,432 27.27 19,926 28.32 20,290 29.22 21,221 30.72 21,628 31.43 22,163 31.85 22,752 32.09
Beneficiaries already entitled on January 1
All 63,680 88.65 63,070 88.51 62,033 88.16 61,051 87.93 60,772 87.97 62,143 90.31 62,907 90.41 64,058 90.35
Working 16,021 22.30 16,466 23.11 16,904 24.02 17,133 24.68 18,032 26.10 19,630 28.53 20,144 28.95 20,626 29.09
Beneficiaries becoming entitled during year
All 810 1.13 776 1.09 838 1.19 1,005 1.45 1,838 2.66 475 0.69 395 0.57 588 0.83
Working 548 0.76 549 0.77 599 0.85 717 1.03 1,399 2.03 272 0.40 228 0.33 331 0.47
Group 4, have attained ages 70–72
Total sample
All 38,695 100.00 38,911 100.00 38,680 100.00 38,913 100.00 38,840 100.00 39,032 100.00 38,557 100.00 38,348 100.00
Working 6,109 15.79 6,401 16.45 6,643 17.17 6,847 17.60 7,328 18.87 7,366 18.87 7,509 19.48 7,502 19.56
Beneficiaries already entitled on January 1
All 35,308 91.25 35,685 91.71 35,542 91.89 35,777 91.94 35,745 92.03 35,804 91.73 35,420 91.86 35,216 91.83
Working 5,574 14.40 5,926 15.23 6,181 15.98 6,382 16.40 6,850 17.64 6,850 17.55 7,018 18.20 7,036 18.35
Beneficiaries becoming entitled during year
All 240 0.62 90 0.23 50 0.13 40 0.10 48 0.12 33 0.08 46 0.12 49 0.13
Working 74 0.19 36 0.09 25 0.06 22 0.06 29 0.07 17 0.04 25 0.06 23 0.06
SOURCE: Authors' tabulations using the 1 percent extract of the Social Security Administration's Master Earnings File and Master Beneficiary Record.
NOTE: The sample universe comprises persons who are fully insured in the year they turn age 62 and are not receiving Disability Insurance benefits.

The percentage of beneficiaries who became entitled in 1999 and 2000 increased from 22 percent to 28 percent for the younger treatment group (those who were turning 65). Over the same period, the percentage nearly doubled for the older treatment group (those who had attained ages 65–69). During the postremoval period, benefit entitlement rates increased slightly for the two older age groups, but they decreased slightly for the two younger age groups. Work participation rates increased slightly over the study period to the following levels: 55 percent to 56 percent, 45 percent, 31 percent to 32 percent, and 19 percent to 20 percent, respectively. Benefit entitlement rates among those aged 64 or younger tended to fall slightly over the study period, but rates for those aged 65 or older tended to increase slightly over time.

Although the descriptive results show no clear evidence of effects of the earnings test removal on work participation rates, they suggest that benefit entitlement rates for persons turning 65 are somewhat higher after the removal. The magnitude of the increase does not appear to be large, perhaps because most individuals have already become entitled to old-age benefits before they reach age 65.

The large sample size and the longitudinal format of our data allow us to construct transition matrices so that we can follow persons of a particular age from one year to the next. For each age 65 through 69 as of the end of year t1, Chart 1 presents joint probabilities of transitions from "not working" in year t1 to "working" in year t2 from 1996 through 2003. Similarly, Chart 2 presents age-specific probabilities of transitions from "not entitled" to "entitled." Results show that the probability of transition from "not working" to "working" increased noticeably between 1999 and 2000 but then stabilized at a lower level for ages 65–69. The probabilities of transition from "not-entitled" to "entitled" for those aged 65–66 more than doubled between 1999 and 2000, then stabilized at a lower level after 2000. The numbers suggest that the 2000 removal of the earnings test had a clear impact on work and benefit claims among older workers.

Chart 1.
Transition from not working to working, by age at the end of t1
SOURCE: Authors' tabulations using the 1 percent extract of the Social Security Administration's Master Earnings File and Master Beneficiary Record.
Chart 2.
Transition from not entitled to entitled, by age at the end of t1
SOURCE: Authors' tabulations using the 1 percent extract of the Social Security Administrations Master Earnings File and Master Beneficiary Record.

In an effort to more closely examine the effects on earnings at different points along the distribution, we look at nominal earnings at the 40ththrough 80th percentiles for those who work over the study period, by age group (Table 3). Results show gradual increases in the earnings of working individuals over the study period, measured either by the simple mean over the entire sample or at each decile of the earnings distribution. The gradual increases in earnings at the various deciles appear to accelerate slightly in 2000 for both treatment groups, which could indicate that earnings of the treatment groups are affected by the earnings test removal.21

Table 3. Nominal earnings, by age group and earnings percentile, 1996–2003 (in dollars unless otherwise indicated)
Earnings percentile 1996 1997 1998 1999 2000 2001 2002 2003
Group 1, turning ages 62–64
All
Number in group 43,542 44,151 45,220 46,330 47,824 49,073 50,979 52,600
Mean earnings 14,596 15,715 17,196 17,207 18,173 19,094 19,825 20,263
Working
Number in group 22,784 23,588 24,412 25,324 26,623 27,348 28,235 29,128
Mean earnings 27,893 29,414 31,853 31,480 32,644 34,262 35,795 36,591
40th percentile 10,866 11,578 12,444 13,096 13,571 14,885 15,642 16,476
50th percentile 16,471 17,214 18,282 19,063 19,679 21,002 21,825 22,936
60th percentile 22,366 23,381 24,583 25,300 25,934 27,418 28,337 29,789
70th percentile 28,893 30,177 31,502 32,504 33,488 35,169 36,350 38,083
80th percentile 38,453 40,167 41,765 43,146 44,942 46,360 48,000 50,094
Group 2, turning age 65
All
Number in group 14,419 14,258 14,036 14,367 14,853 15,071 15,493 16,370
Mean earnings 10,707 10,134 11,046 13,028 12,426 12,973 13,509 14,849
Working
Number in group 5,843 5,988 6,026 6,253 6,661 6,795 6,992 7,327
Mean earnings 26,421 24,130 25,728 29,932 27,707 28,773 29,935 33,175
40th percentile 7,800 8,174 9,000 9,138 10,263 10,850 11,618 12,285
50th percentile 10,562 11,196 12,479 12,313 14,609 15,300 16,606 17,200
60th percentile 14,494 15,149 16,972 16,214 19,931 21,330 22,747 23,894
70th percentile 22,185 23,008 24,651 23,918 27,825 28,564 30,200 31,986
80th percentile 32,206 33,065 35,825 35,247 38,596 39,082 41,564 44,174
Group 3, have attained ages 65–69
All
Number in group 71,830 71,261 70,362 69,433 69,084 68,808 69,580 70,899
Mean earnings 4,843 5,543 5,785 5,869 6,741 7,480 7,602 8,223
Working
Number in group 18,890 19,432 19,926 20,290 21,221 21,628 22,163 22,752
Mean earnings 18,418 20,326 20,427 20,084 21,946 23,798 23,866 25,625
40th percentile 5,754 5,888 6,264 6,639 6,984 7,875 8,304 8,787
50th percentile 7,884 8,207 8,586 9,111 9,600 10,791 11,497 12,250
60th percentile 10,400 10,912 11,359 11,997 12,750 14,468 15,508 16,737
70th percentile 12,766 13,551 14,437 15,394 17,000 19,602 21,337 23,120
80th percentile 21,549 22,208 22,632 23,652 25,354 28,824 30,882 33,023
Group 4, have attained ages 70–72
All
Number in group 38,695 38,911 38,680 38,913 38,840 39,032 38,557 38,348
Mean earnings 2,376 2,657 3,029 3,107 3,275 3,288 3,394 3,658
Working
Number in group 6,109 6,401 6,643 6,847 7,328 7,366 7,509 7,502
Mean earnings 15,049 16,149 17,638 17,657 17,356 17,421 17,426 18,700
40th percentile 4,348 4,784 4,945 5,180 5,083 5,685 5,678 6,181
50th percentile 6,341 6,632 7,008 7,193 7,259 7,934 8,064 8,757
60th percentile 8,795 9,114 9,522 9,722 9,850 10,617 10,968 11,641
70th percentile 11,566 12,000 12,364 13,000 13,278 14,400 14,597 15,717
80th percentile 16,546 16,900 17,517 18,200 18,332 20,182 20,774 22,431
SOURCE: Authors' tabulations using the 1 percent extract of the Social Security Administration's Master Earnings File and Master Beneficiary Record.

Numbers on upward earnings mobility by age indicate that the percentage of individuals with increased earnings over a 2-year span is strictly greater in later years than in earlier years (Chart 3). Between 1999 and 2000, the probabilities of observing increased earnings for workers aged 65–69 rose by approximately 2 percentage points relative to earlier years, for all ages 65–69. Individuals with increased earnings can be decomposed into (1) those whose earnings rose from zero to a positive amount and (2) those who had positive earnings followed by even larger earnings. The first component of earnings mobility is equivalent to transitions in work participation from "not working" to "working." The lower panel of Chart 3 shows the second component of earnings mobility. Results indicate that most of the increases in earnings between 1999 and 2000 are attributable to higher earnings among those who were already working. This result is more powerful than results based on pooled cross-sectional data because it comes from comparing earnings of the same individual over 2 consecutive years.22

Chart 3.
Probability of an increase in earnings if earnings at t1 are greater than or equal to zero or greater than zero, by age at t1
Earnings at t1 greater than or equal to zero
Earnings at t1 greater than zero
SOURCE: Authors' tabulations using the 1 percent extract of the Social Security Administration's Master Earnings File and Master Beneficiary Record
NOTE: Earnings are in current dollars.

Clustering just below the earnings test threshold provides simple evidence of labor supply reactions to the earnings test (Friedberg 2000). Thus, we show the distribution of earnings in $1,000 intervals relative to the threshold for all four groups during the preremoval and postremoval period (Chart 4). Results show clustering just below the threshold for those turning 62–64 in both periods because the earnings test is in effect for them. For those turning 65 and those who have attained ages 65–69, we observe clustering in the preremoval period but not in the postremoval period. Those who have attained ages 70–72 show no clustering in either period. The clustering results indicate that the kink in the static budget constraint created by the earnings test affects the labor supply behavior of some individuals. Chart 4. Distribution of old-age beneficiaries with earnings in$1,000 intervals relative to the earnings test threshold for treatment and control groups, before and after removal
SOURCE: Authors' tabulations using the 1 percent extract of the Social Security Administration's Master Earnings File and Master Beneficiary Record.
a. Threshold values for Group 1 for 1996–1999 are $8,280,$8,640, $9,120, and$9,600; for 2000–2003 they are $10,080,$10,680, $11,280, and$11,520. Threshold values for Group 2 for 1996–1999 are $8,280,$8,640, $9,120, and$9,600; for 2000–2003 they are $17,000,$25,000, $30,000, and$30,720.
b. For illustrative purposes, we assume the thresholds of Group 4 to be the same as those for Group 3 in 1996–1999 ($12,500,$13,500, $14,500, and$15,500), and the thresholds for both groups to be $16,500,$17,500, $18,500, and$19,500 for 2000–2003.

## Regression Analysis

In this section, we present two sets of reduced-form regression estimates. We estimate the effects on work participation and benefit entitlement using a Probit specification and the effects on the earnings distribution using ordinary least squares (OLS), truncated, and percentile regressions. The regression estimates are based on the difference-in-difference model

$y i ⁢ t j = a + g ⁢ Δ t + h ⁢ Δ j + β ⁢ Δ t j + c ′ ⁢ X i + e i ⁢ t j ,$

where X is a vector of the individual's characteristics; Δs are dummy variables; index j = 1 for the treatment groups (those turning 65 and those who have attained ages 65–69; index j = 0 for the control groups (those turning 62–64 and those who have attained ages 70–72); and time index t = 1996, 1997, …, 2003.23 Thus, effects of the earnings test removal are identified by the βs that are the coefficients on the year-specific, posttreatment dummies. Since effects immediately after the removal may differ from later effects, we include yearly treatment dummies rather than just one treatment dummy to cover the whole postremoval period. The dependent variable (y) is either benefit entitlement status, work participation status, or observed annual earnings.

Choosing the specification for evaluating effects on benefit entitlement and work participation is straightforward because observed outcomes are binary, discrete variables. We use a Probit specification for both binary outcome variables. Choosing the earnings specification is more difficult. Because the earnings of a large fraction of the samples are zero, we need to account for the difference between the censored zero observations and the continuous nonzero observations in estimating the effects on earnings.24 Although the Tobit (Type I) regression method is a simple and popular way to account for the difference, it is problematic in our context because earnings cannot take on negative values (Hausman and Wise 1977, Maddala 2001). Here we use the truncated regression method to examine average effects over individuals with earnings.25 Neither truncated regression nor OLS-based estimates are appropriate to capture the uneven impact over the distribution that is predicted by theory. Thus, we use quantile regression methods, where we limit the sample to working individuals (nonzero earners).

The difference-in-difference model presented above relies on two critical assumptions: (1) no contemporaneous shock other than the 2000 earnings test removal has affected the dependent variable of the treatment groups relative to the control groups, and (2) any change in the dependent variable in the absence of the treatment is the same for all groups. Thus, we offer a simple specification test to see whether the estimate of β is zero in the absence of changes in the earnings test. If β identifies the effects of the earnings test removal, coefficients of the pretreatment (false treatment) dummies (Δj1997, Δj1998, and Δj1999) would each equal zero. To show that our model captures the causal effect, we present estimates from the model, including year-specific, pre- and posttreatment dummies; a second specification includes year-specific, posttreatment dummies (true treatment dummies).26

### Estimated Effects on Benefit Entitlement

We report estimated effects of the earnings test removal on benefit claims from two separate regressions, one for each treatment group (individuals who have attained ages 65–69 and those who are turning 65) (Table 4). Model I includes the full set of interaction dummies from 1997 through 2003 for purposes of the specification test, and Model II includes interaction dummies for the postremoval period. We consider Model II to be our base model, and marginal effects on the base model are also included in the table. To show how estimates vary by the choice of control group, we report separate estimates from models that include only the younger control group (Model III) or only the older control group (Model IV).

Table 4. Probit estimates of effects on benefit entitlement
Variable Model I Model II Marginal effects Model III Model IV
Estimate Standard
error
Estimate Standard
error
Estimate Standard
error
Estimate Standard
error
Estimate Standard
error
Effects on those who have attained ages 65–69
Treatment dummy, 1997 0.0076 0.0116 . . . . . . . . . . . . . . . . . . . . . . . .
Treatment dummy, 1998 0.0029 0.0116 . . . . . . . . . . . . . . . . . . . . . . . .
Treatment dummy, 1999 0.0120 0.0116 . . . . . . . . . . . . . . . . . . . . . . . .
Treatment dummy, 2000 0.0936 0.0117 0.0880 0.0093 0.0219 0.0023 0.0986 0.0099 0.0656 0.0133
Treatment dummy, 2001 0.1396 0.0118 0.1340 0.0093 0.0333 0.0023 0.1449 0.0099 0.1109 0.0132
Treatment dummy, 2002 0.1610 0.0117 0.1553 0.0093 0.0386 0.0023 0.1787 0.0098 0.0951 0.0133
Treatment dummy, 2003 0.2076 0.0117 0.2020 0.0092 0.0502 0.0023 0.2368 0.0097 0.1070 0.0133
N 1,250,952 1,250,952 940,976 871,233
Log of likelihood -518,157.04 -518,157.66 -436,402.95 -247,676.07
Effects on those turning age 65
Treatment dummy, 1997 0.0036 0.0197 . . . . . . . . . . . . . . . . . . . . . . . .
Treatment dummy, 1998 -0.0173 0.0197 . . . . . . . . . . . . . . . . . . . . . . . .
Treatment dummy, 1999 0.0189 0.0196 . . . . . . . . . . . . . . . . . . . . . . . .
Treatment dummy, 2000 0.2485 0.0204 0.2471 0.0165 0.0748 0.0050 0.2571 0.0167 0.2312 0.0192
Treatment dummy, 2001 0.2438 0.0202 0.2424 0.0162 0.0734 0.0049 0.2528 0.0164 0.2240 0.0189
Treatment dummy, 2002 0.2449 0.0199 0.2435 0.0159 0.0737 0.0048 0.2656 0.0161 0.1897 0.0187
Treatment dummy, 2003 0.1090 0.0191 0.1077 0.0147 0.0326 0.0045 0.1444 0.0150 0.0060 0.0177
N 808,562 808,562 498,586 428,843
Log of likelihood -391,760.93 -391,762.66 -307,996.83 -124,504.34
SOURCE: Authors' estimates.
NOTES: The dependent variable is old-age benefit entitlement status (1, entitled; 0, not entitled).
Other covariates included in the regression are a constant, male, race (white), age group dummies (62–64 and 70–72), and calendar-year dummies from 1996 through 2002.
Model I includes the two control groups and false treatment dummies; Model II, the control groups and only true treatment dummies; Model III, the younger control group (62–64) and true treatment dummies; and Model IV, the older control group (70–72) and true treatment dummies. Model II is the base model.
. . . = not applicable.

Results from our base model (II) show that estimated coefficients of β for all 4 years are large and statistically significant, which suggests that the earnings test removal in 2000 has increased benefit entitlements for both treatment groups. The effects tend to increase over the 4 years for the older treatment group, but they are relatively stable for the younger treatment group. Estimated marginal effects indicate that the benefit entitlement rate for the older treatment group increased approximately 2 to 5 percentage points after the test's removal.27 It also increased approximately 3 to 7 percentage points for the younger group.

Results from Model I show that estimated coefficients of the false treatment dummies are all small and not statistically significant, indicating that in the absence of the treatment the changes in benefit entitlement rates are similar for all groups. From Models I and II, we can easily calculate the likelihood test statistics for testing the model specification. The likelihood test statistic of the model is 1.24 (3 d.f.) for individuals who have attained ages 65–69 and 3.46 (3 d.f.) for those who are turning 65. Thus, we cannot reject the null hypothesis of β1997β1998β1999 = 0 at the 5 percent significance level, indicating that estimates from our base model do capture the effect of the earnings test removal.

Although the base model (II) is preferable to the models that include only the younger control group (III) or only the older control group (IV), Models III and IV provide additional insights into the reliability of estimates from the base model and response dynamics. Some economists argue that eliminating the earnings test for individuals who have attained ages 65–69 could have spillover effects on benefit-claiming behavior for those younger than 65 (Vroman 1985, Packard 1990, Gruber and Orszag 2003).28 If such spillover exists, using those who are turning 62–64 as the only control group might cause us to overestimate the effect. Likewise, using those who have attained ages 70–72 as the only control group might cause the effect to be underestimated, because any causal effect on the benefit entitlement of those who have attained ages 65–69 will eventually affect the benefit entitlement of those who have attained ages 70–72. The magnitude of the underestimation is likely to increase over time, because all observations in the current treatment group will eventually enter the control group (those who have attained ages 70–72). Results from Models III and IV are consistent with these speculations. The estimated effects from Model III are all larger than those from Model IV. Estimates from Model III can be considered to be upper-bound estimates, and those from Model IV can be considered to be lower-bound estimates.29

### Estimated Effects on Work Participation

In Table 5, we present estimated effects on work participation from four models for each treatment group, as we did in estimating effects on benefit entitlement. Results from Model II (base model) show that the estimated coefficients for all four treatment dummies are statistically significant for those who have attained ages 65–69 but not for those turning 65. Estimated marginal effects indicate that the work participation rate among individuals who have attained ages 65–69 has increased by 0.8 to 2 percentage points following the earnings test removal in 2000. Results further show that those effects increased over the study period.

Table 5. Probit estimates of effects on work participation
Variable Model I Model II Marginal Effects Model III Model IV
Estimate Standard
error
Estimate Standard
error
Estimate Standard
error
Estimate Standard
error
Estimate Standard
error
Effects on those who have attained ages 65–69
Treatment dummy, 1997 0.0029 0.0097 . . . . . . . . . . . . . . . . . . . . . . . .
Treatment dummy, 1998 0.0149 0.0097 . . . . . . . . . . . . . . . . . . . . . . . .
Treatment dummy, 1999 0.0246 0.0097 . . . . . . . . . . . . . . . . . . . . . . . .
Treatment dummy, 2000 0.0332 0.0097 0.0225 0.0076 0.0082 0.0027 0.0335 0.0086 0.0046 0.0100
Treatment dummy, 2001 0.0521 0.0096 0.0414 0.0075 0.0150 0.0027 0.0520 0.0085 0.0241 0.0100
Treatment dummy, 2002 0.0610 0.0096 0.0504 0.0075 0.0183 0.0027 0.0724 0.0084 0.0130 0.0099
Treatment dummy, 2003 0.0669 0.0095 0.0562 0.0074 0.0204 0.0027 0.0793 0.0083 0.0162 0.0099
N 1,250,952 1,250,952 940,976 871,233
Log of likelihood -746,984.89 -746,988.99 -601,411.83 -485,697.76
Effects on those turning age 65
Treatment dummy, 1997 0.0110 0.0164 . . . . . . . . . . . . . . . . . . . . . . . .
Treatment dummy, 1998 0.0142 0.0164 . . . . . . . . . . . . . . . . . . . . . . . .
Treatment dummy, 1999 0.0129 0.0163 . . . . . . . . . . . . . . . . . . . . . . . .
Treatment dummy, 2000 0.0108 0.0161 0.0013 0.0127 0.0005 0.0048 0.0125 0.0133 -0.0168 0.0142
Treatment dummy, 2001 0.0162 0.0161 0.0067 0.0126 0.0025 0.0048 0.0174 0.0132 -0.0108 0.0142
Treatment dummy, 2002 0.0155 0.0160 0.0059 0.0125 0.0023 0.0047 0.0281 0.0130 -0.0316 0.0141
Treatment dummy, 2003 0.0054 0.0158 -0.0041 0.0122 -0.0015 0.0046 0.0192 0.0128 -0.0443 0.0139
N 808,562 808,562 498,586 428,843
Log of likelihood -488,129.76 -488,130.23 -342,543.26 -226,842.87
SOURCE: Authors' estimates.
NOTES: The dependent variable is work participation status (1, working (earnings > 0); 0, not working (earnings = 0)).
Other covariates included in the regression are a constant, male, race (white), age group dummies (62–64 and 70–72), and calendar-year dummies from 1996 through 2002.
Model I includes the two control groups and false treatment dummies; Model II, the control groups and only true treatment dummies; Model III, the younger control group (62–64) and true treatment dummies; and Model IV, the older control group (70–72) and true treatment dummies. Model II is the base model.
. . . = not applicable.

Likelihood test statistics for Model II against Model I are 8.2 (3 d.f.) for individuals who have attained ages 65–69 and 0.94 (3 d.f.) for those turning 65. Hence we only marginally reject the null hypothesis of β1997β1998β1999 = 0 at a 5 percent significance level for those who have attained ages 65–69. That is, estimates of βs for those aged 65–69 may be capturing effects other than the pure causal effect. Estimates from Model I show a gradual increase in the magnitude of estimates for interaction dummies over our study period, suggesting that a group-specific time trend, independent of the earnings test removal, may contaminate the estimates. If this gradually increasing time trend is not controlled in the model, we could overestimate the true effects of the test's removal. However, we expect the bias to be small.

Finding a gradual increase in the effect of removing the earnings test on work participation is not surprising, for several reasons. Returning to the labor market may require a difficult and costly job search for those aged 65–69. Thus, estimated effects immediately following the removal are probably biased downward. However, additional years of job search may not significantly affect the work participation of those older workers, because their declining health and outdated skill levels constrain their labor market choices. If this is true, then an increase in work participation over time can result from the gradual increase in the number of older workers remaining in the labor market, not from older workers returning to the labor market. The gradual increase in work participation may have affected the work participation of those aged 70–72 as well. If work participation in this older group is affected with a lag by the 2000 removal of the earnings test, estimated effects using those aged 70–72 as the only control group may underestimate the true causal effects. One can also speculate on a spillover effect to a younger age group. If labor market rigidities limit entry into and exit out of the labor force, we expect to see a positive spillover effect on those turning 62–64. However, estimates from Model III contradict this speculation, because the estimates are larger than those from the base model. It seems plausible that the difference in estimates from Models III and IV is not caused by spillover effects but rather by time trends specific to the different age groups.

### Estimated Effects on Earnings

We estimate the reduced form, difference-in-difference equation using the following specifications: truncated regression, OLS over samples with nonzero earnings, and quantile regressions over samples with nonzero earnings. Estimates from the truncated regression specification of the difference-in-difference model show that estimated coefficients of effects for individuals who have attained ages 65–69 are large and statistically significant in the base model (Model II). Since the dependent variable is the logarithm of earnings, coefficients of treatment dummies indicate the percentage change in earnings after the 2000 removal. Earnings increase approximately 4 percent to 10 percent per year among working individuals (Table 6). Effects in 2000 appear to be much smaller than effects in 2001–2003. The result for persons who have attained ages 65–69 seems plausible because the law was enacted in April 2000 and older people needed time to respond. Effects on earnings for individuals turning 65 are also found here; estimates for 2000–2003 are 6.5 percent, 5.3 percent, 6.4 percent, and 7.5 percent, respectively.

Table 6. Truncated regression estimates of effects on earnings
Variable Model I Model II Model III Model IV
Estimate Standard error Estimate Standard error Estimate Standard error Estimate Standard error
Effects on those who have attained ages 65–69
Treatment dummy, 1997 -0.0143 0.0220 . . . . . . . . . . . . . . . . . .
Treatment dummy, 1998 -0.0128 0.0219 . . . . . . . . . . . . . . . . . .
Treatment dummy, 1999 -0.0102 0.0217 . . . . . . . . . . . . . . . . . .
Treatment dummy, 2000 0.0357 0.0215 0.0452 0.0166 0.0411 0.0172 0.0582 0.0272
Treatment dummy, 2001 0.0701 0.0214 0.0795 0.0164 0.0856 0.0170 0.0567 0.0271
Treatment dummy, 2002 0.0964 0.0213 0.1058 0.0163 0.1066 0.0168 0.1032 0.0269
Treatment dummy, 2003 0.0957 0.0211 0.1051 0.0161 0.1171 0.0167 0.0595 0.0268
N 429,449 429,445 373,744 222,007
Log of likelihood -831,459.00 -831,459.30 -718,322.60 -442,343.90
Effects on those turning age 65
Treatment dummy, 1997 0.0384 0.0329 . . . . . . . . . . . . . . . . . .
Treatment dummy, 1998 0.0495 0.0328 . . . . . . . . . . . . . . . . . .
Treatment dummy, 1999 0.0286 0.0325 . . . . . . . . . . . . . . . . . .
Treatment dummy, 2000 0.0946 0.0320 0.0652 0.0247 0.0602 0.0246 0.0804 0.0335
Treatment dummy, 2001 0.0819 0.0319 0.0525 0.0245 0.0581 0.0243 0.0303 0.0334
Treatment dummy, 2002 0.0938 0.0317 0.0644 0.0242 0.0652 0.0241 0.0611 0.0331
Treatment dummy, 2003 0.1040 0.0314 0.0746 0.0238 0.0867 0.0237 0.0278 0.0328
N 315,032 808,562 259,327 107,590
Log of likelihood -601,195.80 -601,197.00 -487,526.20 -212,979.60
SOURCE: Authors' estimates.
NOTES: The dependent variable is the logarithm of earnings.
Other covariates included in the regression are a constant, male, race (white), age group dummies (62–64 and 70–72), and calendar-year dummies from 1996 through 2002.
Model I includes the two control groups and false treatment dummies; Model II, the control groups and only true treatment dummies; Model III, the younger control group (62–64) and true treatment dummies; and Model IV, the older control group (70–72) and true treatment dummies. Model II is the base model.
. . . = not applicable.

Estimates of false treatment dummies (Model I) for those who have attained ages 65–69 are not only statistically insignificant but also small in magnitude. It is particularly notable that the magnitude of the estimates jumps from 1999 to 2000. The likelihood ratio test statistics indicate that our specification of the model appropriately captures the effect of removing the earnings test for both experimental groups. The likelihood ratio statistic is 0.6 (3 d.f.) for those who have attained ages 65–69 and 2.4 (3 d.f.) for those reaching 65. Such results indicate that we cannot reject the null hypothesis β1997β1998β1999 = 0 at a 5 percent significance level in both models.30 Estimated effects from either Model III or Model IV are comparable with those from the base model.

We next estimate the models using nominal earnings (in thousands of dollars) as the dependent variable using both OLS and quantile regression methods to capture the change in actual earnings (Table 7).31 Estimates based on OLS are small and not significant at the 10 percent level, indicating that the mean earnings of persons who have attained ages 65–69 were not affected by the earnings test removal (see Gruber and Orszag 2003). Although results based on OLS regression show no significant effect on mean earnings, results based on quantile regression show that the removal has increased earnings for individuals who have attained ages 65–69 at the 60th conditional percentile of the earnings distribution in 2000, 60th to 70th percentiles in 2001, and 60th to 80th percentiles in 2002 and 2003 by statistically significant amounts, indicating that the effects are uneven across the earnings distribution (Table 7, top panel).32 At the 60th percentile, earnings in 2001, 2002, and 2003 are increased by $734 (5.8 percent),$1,066 (8.5 percent), and $1,138 (9.0 percent), respectively. At the 70th percentile, earnings in 2000, 2001, 2002, and 2003 are increased by$180 (1.1 percent), $966 (5.9 percent),$1,460 (9.0 percent), and $1,670 (10.4 percent), respectively. Earnings at the 80th percentile in 2001–2003 also increase by similar amounts. Interestingly, our estimated effects in years immediately following the removal of the test (1–2 years) are comparable with the estimate (5.3 percent) reported in Friedberg (2000), where an entirely different empirical approach was taken. Table 7. Regression estimates of effects on earnings (earnings in thousands of dollars) Variable Quantile regression Ordinary least squares 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 Effects on those who have attained ages 65–69 (N = 429,449) Constant 1.2611 (0.0511) 3.7817 (0.1118) 6.5156 (0.1019) 8.7451 (0.1564) 10.4437 (0.1523) 12.5956 (0.1986) 16.0643 (0.2661) 22.1667 (0.3703) 35.3851 (0.5893) 11.5920 (0.7176) Treatment dummy, 2000 0.0226 (0.0529) -0.1162 (0.0852) -0.4192 (0.1049) -0.1956 (0.1704) -0.0847 (0.1622) 0.4013 (0.2163) 0.1802 (0.2863) -0.1921 (0.4263) -1.4246 (0.8158) 0.0291 (0.8684) Treatment dummy, 2001 -0.0819 (0.0474) -0.3305 (0.1051) -0.3824 (0.0991) -0.2646 (0.1694) 0.1469 (0.1687) 0.7335 (0.2161) 0.9565 (0.3102) 1.2221 (0.4273) -0.5214 (0.6319) 0.5189 (0.8616) Treatment dummy, 2002 -0.0135 (0.0545) -0.2453 (0.1013) -0.4848 (0.1039) -0.3165 (0.1507) 0.1112 (0.2053) 1.0662 (0.2809) 1.4596 (0.2971) 1.4536 (0.4973) -0.6260 (0.7177) -0.7408 (0.8528) Treatment dummy, 2003 -0.1236 (0.0384) -0.3394 (0.1223) -0.6633 (0.1141) -0.5580 (0.2203) 0.0609 (0.1657) 1.1379 (0.2566) 1.6702 (0.2864) 1.5430 (0.4734) -0.6693 (0.8642) 0.0322 (0.8444) R-square 0.0053 0.0131 0.0194 0.0239 0.0372 0.0517 0.0581 0.0609 0.0672 0.0149 Effects on those turning age 65 (N = 315,032) Constant 1.8091 (0.0718) 4.9622 (0.1252) 8.3903 (0.1297) 10.7848 (0.1776) 12.5908 (0.1718) 16.4331 (0.2936) 21.9045 (0.3609) 30.3644 (0.4686) 43.1540 (0.7872) 16.8818 (0.9468) Treatment dummy, 2000 0.0547 (0.1045) 0.2140 (0.2020) 0.1771 (0.2092) 0.8382 (0.2543) 1.5987 (0.4175) 1.6765 (0.4982) 1.5675 (0.5302) 1.2879 (0.6200) 1.1383 (0.8661) -1.2780 (1.4282) Treatment dummy, 2001 0.1682 (0.0979) 0.1408 (0.2141) -0.0576 (0.2366) 0.3256 (0.3364) 1.5221 (0.3633) 1.7235 (0.4453) 1.4488 (0.5336) 0.3402 (0.6856) -0.1752 (1.2814) -1.3841 (1.4169) Treatment dummy, 2002 0.0372 (0.0865) 0.1992 (0.2363) 0.1845 (0.2226) 0.5874 (0.3308) 2.3427 (0.2967) 2.5045 (0.3754) 1.9187 (0.5043) 0.5939 (0.7411) 0.3488 (1.4093) -1.3584 (1.4012) Treatment dummy, 2003 0.1207 (0.1185) 0.2729 (0.2080) 0.2287 (0.1878) 0.6025 (0.2295) 2.1035 (0.3859) 2.3703 (0.5114) 2.8352 (0.5456) 0.9764 (0.9951) 1.1521 (1.4436) 0.9228 (1.3781) R-square 0.0150 0.0121 0.0178 0.0229 0.0363 0.0468 0.0533 0.0598 0.0686 0.0146 SOURCE: Authors' estimates. NOTES: The dependent variable is annual earnings in thousands of dollars. The sample includes observations with nonzero earnings. Numbers in parentheses are standard errors. Standard errors are calculated by bootstrap resampling with 40 repetitions. Other covariates used in this regression are constant, male, race (white), age group dummies (62–64 and 70–72), and calendar-year dummies from 1996 through 2002. Our quantile regression results indicate that the effects on earnings are concentrated around the 60th to 80th conditional percentiles of the earnings distribution. Thus, it is worthwhile to find out how these conditional percentile values are related to the earnings test threshold. Since our regression controls for sex (male) and race (white) in addition to group and year dummies, estimates of the intercept terms represent percentile values for nonwhite females at ages 65–69. Our regression estimates indicate that earnings at the 60th to 80th percentiles in 1999 for nonwhite females aged 65–69 are$8,863, $11,336, and$15,444, respectively.33 Corresponding earnings percentiles for white males aged 65–69 are $14,961,$21,901, and $34,874, respectively. Accordingly, the earnings test threshold in 1999 ($15,500) is just around the 80th percentile for nonwhite females aged 65–69 and between the 60th and 70th percentile for white males aged 65–69.34 These results indicate that the removal of the earnings test has affected the earnings distribution just below the test threshold and up, as predicted by economic theory.

Again, the estimates using OLS show no effects on earnings for persons turning age 65. However, results based on quantile regressions indicate that the test's removal affects the 40th to 80th conditional percentiles of earnings in 2000, the 50th to 70th percentiles in 2001 and 2002, and the 40th to 70th percentiles in 2003. More specifically, at the 50th percentile, earnings in 2000, 2001, 2002, and 2003 increased by $1,599 (12.7 percent),$1,522 (12.1 percent), $2,343 (18.6 percent), and$2,104 (16.7 percent), respectively. At the 60th percentile, earnings in 2000–2003 increased by $1,677 (10.2 percent),$1,724 (10.5 percent), $2,505 (15.2 percent), and$2,370 (14.4 percent), respectively. It is notable that estimated effects are larger for persons who are turning age 65 than for those who have attained ages 65–69. This result is not surprising, because the younger age group has not only better health and skills but also more choices in the labor market.

Earnings at the 50th, 60th, and 70th percentiles in 1999 for nonwhite females turning age 65 are $9,624,$12,631, and $17,197, respectively. Corresponding earnings for white males turning age 65 are$15,640, $22,420, and$31,958, respectively.35 The earnings test thresholds for those attaining age 65 in 1999–2003 were $9,600,$17,000, $25,000,$30,000, and $30,720, respectively. Thus, those percentiles where the effects are significant correspond to the earnings test threshold for those attaining age 65. To summarize, a conventional mean-based evaluation fails to detect the effect of the earnings test removal on earnings. A significant effect on a relatively small fraction of the sample could be overlooked if we were to focus on mean effects only (Heckman, Smith, and Clements 1997). But by analyzing the effects over different percentiles of the earnings distribution, this study finds statistically significant effects of the test's removal in a way that is exactly predicted by economic theory. In both treatment groups, we found small and sometimes negative estimates for the 90th percentile, suggesting the presence of income effects. However, examining the income effect using quantile regression on earnings alone seems inappropriate because the upper threshold, where all benefits are withheld, depends on (family) benefit amounts and not just the primary worker's earnings. Even at the 90th percentile, earnings of those who have very high benefit amounts would be affected not only by the income effect but also by the substitution effect. Thus, estimated effects on high earnings quantiles would imprecisely measure the income effect. The income effects could be precisely measured by responses in earnings among those who earn above the upper threshold. Thus, our small and statistically insignificant effects at the 90th percentile are not surprising.36 Lastly, we estimate quantile regressions by including interaction dummies for 1997–2003 and plot point estimates of those effects by year and percentile (Chart 5).37 The chart shows (1) how the earnings distributions of the treatment groups have evolved since 1996 after controlling for both time and group effects and (2) that the earnings distributions of the treatment groups during the postremoval period have not changed significantly from those of 1996, thereby lending support to the specification of our model. For persons who have attained ages 65–69, earnings at the 60th to 80th percentiles of the distributions during the postremoval period clearly contrast with earnings of the preremoval period. Similarly, earnings at the 50th to 70th percentiles of the distributions for persons turning 65 are clearly affected by the test's removal. More important, estimates for the false treatment dummies (1997–1999) are located near the horizontal line that indicates an estimate of zero. If our estimates captured effects caused by factors other than the earnings test removal, we would not expect to see the observed pattern of changes in the earnings distributions of the treatment groups. Chart 5. Estimates of the effects on earnings, by percentile and year Have attained ages 65–69 Turning age 65 SOURCE: Authors' estimates. NOTE: The dependent variable is annual earnings in thousands of dollars. The samples include observations with nonzero earnings. Other covariates used in this regression are a constant, male, race (white), age group dummies (62–64 and 70–72), and calendar-year dummies from 1997 through 2002. ## Ideas for Future Research The results shown in this paper apply specifically to a change in the retirement earnings test, but the response to changes in thresholds may generalize to other policies. For example, the amount that Disability Insurance beneficiaries can earn without losing benefits, known as the substantial gainful activity (SGA) limit, increased from$500 per month during the 1990s to $700 per month in July 1999. On January 1, 2001, the SGA limit became$740 per month and was indexed to average wage growth. We might expect to find increased earnings among persons close to the threshold after the increase in the SGA, just as we found increased earnings among persons close to the earnings test threshold for whom the earnings test was relaxed or eliminated.

We have several ideas for future research. First, we would like to explore the work activities and claiming behavior of women in response to the removal of the earnings test separately from that of men. Second, the behavior of high-income beneficiaries in response to the removal of the earnings test might be worth further exploration. Those workers received a windfall when the earnings test was eliminated, but it appears from our results that they did not change their earnings or the timing of benefit claims much, perhaps because of reasons we discussed earlier in the paper. Such a result could also be caused by small sample sizes in the top end of the earnings distribution of high-income workers, or it might be the result of some as yet unexplored factors. Third, policymakers are interested in the net programmatic cost or gain to the Social Security system that arises from three sources: the loss of revenue following the elimination of the earnings test, higher payroll taxes coming from older workers who earn more, and accelerated benefit claims. Estimating both an annual cost and a long-term cost would be informative. Fourth, we would like to expand our analyses of spillover effects among persons who are younger than the FRA.

## Notes

1. The FRA has been 65 for those who reach 62 in 1999 or earlier, and it gradually increases to 67 for beneficiaries who reach age 62 in 2022 or later. The law was enacted April 7, 2000, but the elimination of the earnings test for beneficiaries was effective for taxable years ending after December 31, 1999. Earnings tests for individuals aged 75 or older, 72–74, and 70–71 were eliminated in 1950, 1954, and 1983, respectively (Social Security Administration, Annual Statistical Supplement to the Social Security Bulletin, 2003 (2004)).

2. See the Senate debate on the 2000 elimination of the earnings test (http://www.socialsecurity.gov/history/senateret.html). The observation that people bunch at the kink and respond to changes in the earnings test rules has been considered to be a basis for supporting that view (Friedberg 2000).

3. Friedberg investigated three changes in earnings test rules in 1978, 1983, and 1990. Effects reported in Gruber and Orszag (2000) for 1973–1998 and in Haider and Loughran (2005) for 1975–2003 are identified by all changes, including gradual increases in the test threshold in each year. See Leonesio (1990) for reviews of and references to early studies on the earnings test.

4. Song (2003/2004) examined the 2000 earnings test removal using the Social Security Administration's administrative data matched with the Survey of Income and Program Participation (SIPP). Although the study used innovative data sources, his analysis focused on the initial impact of the removal of the test by covering only the first year following the removal.

5. The benefit recomputation after initial entitlement is not directly associated with the earnings test. However, the benefit recomputation is relevant if eliminating the earnings test affects earnings and if the new earnings are substantially higher than the lowest earnings in the current benefit computation.

6. Note that for persons claiming early benefits, monthly benefits are reduced from the full benefit amount at the rate of 5/9 of 1 percent per month for the first 36 months and 5/12 of 1 percent for any additional months. The delayed retirement credit for those who reach age 65 in 2005–2006 is 2/3 of 1 percent for each incremental month (or 8 percent per year).

7. Work by a person entitled to dependent benefits would not increase his or her benefit.

8. The foreign work test can be applied for persons under the FRA who reside outside the United States. See Social Security Administration 2001.

9. Monthly benefits are reduced by the amount of excess earnings beginning with the first month of the year in which the individual is entitled to benefits. In the first year that an individual is entitled to monthly benefits, benefits will not be reduced because of the retirement earnings test for any month that is a nonservice month, regardless of the amount of annual earnings for the year. A nonservice month is a month in which a person's earnings from employment do not exceed 1/12 of the annual exempt amount and he or she does not perform substantial services in self-employment. For persons reaching the FRA, only earnings before the month of attaining the FRA are counted for purposes of the test.

10. See Social Security Administration, Annual Statistical Supplement to the Social Security Bulletin, 2003 (2004, 240–241) for a brief history of changes in the retirement earnings test.

11. The removal eliminated the test beginning with the month a beneficiary reaches the FRA. Note that the FRA gradually increases beginning with individuals born in 1938 or later. Since those who were born in 1938 reach the FRA in 2003, most of them (those born in March or later because the FRA is 65 and 2 months for the 1938 cohort) are subject to the 62–64 earnings test through 2002 and the modified earnings test in 2003.

12. Some examples are Blinder, Gordon, and Wise (1980), Burkhauser and Turner (1981), Reimers and Honig (1983), Vroman (1985), Burtless and Moffitt (1985), Gustman and Steinmeier (1985, 1991), and Packard (1990).

13. There are two versions of the CWHS: an active file and an inactive file. The active file includes individuals with earnings from any employment, whether from covered or noncovered work.

14. For further discussions on the MEF, MBR, and other SSA administrative files, see Panis and others (2000).

15. Further, since 1994, Medicare has taxed all covered wage and self-employment income, including deferred compensation, without limit.

16. For those who are attaining the FRA, earnings up to the month before reaching the FRA are counted for purposes of the earnings test.

17. Workers born before 1929 need less than 40 quarters of coverage to be fully insured (see Social Security Administration 2001).

18. For the sample used in this paper, the FRA is 65 except for those born in 1938 or later. The 1938 birth cohort reaches the FRA in 2003 if born in October or earlier, or in 2004 if born in November or December. Thus, defining the control and treatment groups on the basis of age appears to be inconsistent with the rules in 2003. However, the FRA was 65 during the preremoval period considered in this paper. To maintain consistency throughout the study period, we maintain the definition of the control and treatment groups partitioned by age for the rest of this paper. We would expect to detect any anomalies arising from the FRA change by including year-by-year dummies in the analysis rather than one posttreatment dummy.

19. For example, those who were born in 1936 through 1938 are turning 62–64 in 2000, and those who were born in 1927 through 1929 have attained ages 70–72 as of December 31, 1999. Those who were born in 1935 are turning 65 in 2000, and those who were born in 1930 through 1934 have attained ages 65–69 as of December 31, 1999. In 2000, therefore, the modified earnings test applies for those who were born in 1935, but the test no longer applies to those who were born in 1930 through 1934.

20. We also expect that including both control groups improves the efficiency of our estimate. Meyer (1995, 157) suggested that "the more similar the comparison group is to the treatment group the better" and that "for a given degree of similarity with the treatment group, greater differences across comparison groups are desirable…."

21. It is tempting to look at earnings of beneficiaries because the earnings test is applicable only to OASI beneficiaries. Since the pool of beneficiaries after the 2000 removal includes new entrants who are induced to claim benefits, results that examine work and earnings of beneficiaries before and after the earnings test removal are seriously flawed (Moffitt 1992). Perhaps we could examine work and earnings of beneficiaries who had become entitled before turning 65. However, if benefit entitlement status for those who have not reached age 65 has been affected by the removal, those results are also flawed. Similarly, results that examine benefit entitlements by current work status or earnings levels are flawed as well.

22. One can argue that the stock market crash after September 11, 2001, may have caused some older workers to work more hours. The argument could be relevant in our analyses if ratios of stocks to financial assets among those aged 65–69 are significantly different from those of the control groups. However, we find no such evidence in tabulations of Poterba (2004) using the Survey of Consumer Finances.

23. Hence Δ1996 = 1 if t = 1996 and 0 otherwise; Δj = 1 if j = 1 and 0 otherwise; and Δj2000 = 1 if t = 2000 and j = 1, and 0 otherwise.

24. Although the OLS approach can be useful in measuring the mean effect over the whole sample, it fails to distinguish between censored and noncensored values of earnings. Further, when the dependent variable is censored, OLS estimates over all samples tend to be biased toward zero (Amemiya 1985).

25. Results based on the Tobit model can be provided on request. We acknowledge that the truncated regression method is also problematic because we are ignoring information in the independent variables for those zero earners. An appropriate approach would be a general Tobit (Type II) that accounts for the two-step process for the labor supply decision that generates observed zero and nonzero earnings (Amemiya 1985). However, one needs to model the work decision separately from the decision about work hours (or earnings). Further, two conditions must hold: (1) the covariance term of the equation for work participation and the equation for earnings level must be zero; (2) at least one variable in the earnings equation cannot be included in the work participation equation (Maddala 1983). It is not feasible for us to use the general Tobit specification because the SSA administrative data contain limited information on individuals' characteristics. Therefore, caution is necessary in interpreting truncated regression results and using the estimate for other purposes.

26. Here Δj1996 is the omitted interaction dummy. See Angrist and Krueger (1999) for further discussion on the specification test for the difference-in-difference model.

27. The estimated increase in benefit claims of 2.2 percentage points in 2000 following the test's removal is not surprising and appears to be consistent with the result reported in Song (2003/2004). The estimated magnitude of 2 to 5 percentage points may not seem large, but it indicates a substantially large impact on benefit claims among those who had not yet become beneficiaries by age 65. Only 10 percent of those who had attained ages 65–69 had not yet claimed old-age benefits before 2000.

28. An individual aged 62–64 who wants to claim benefits may decide to continue working until reaching age 65 rather than to reduce work (or to retire). Similarly, an individual aged 62–64 who works above the earnings test threshold may decide not to claim benefits until reaching age 65. Both types of spillover are likely to occur because of labor market rigidities. Because of older workers' declining health and outdated skill levels, reentry into the labor market would be quite limited for them.

29. Obviously, the presence of such dynamics could undermine the accuracy of our estimates. Since the dynamics work in opposite directions for the older and younger control groups, we attempt to neutralize potential bias by including both control groups in our base model.

30. As was true for the estimates for benefit claims and work participation, we found similar results if one or the other of the control groups was used.

31. We also estimated effects on earnings from a semi-log specification of the difference-in-difference percentile regression over samples with nonzero earnings. Those estimates can be interpreted as the percentage change in earnings at specific points along the earnings distribution after the test was removed. We do not include these results in the paper, but they can be provided on request. In this paper, we report results based on a model with nominal earnings (in thousands of dollars) as the dependent variable because the primary interest of the paper is the location on the earnings distribution where significant effects are observable.

32. Because the rule was changed in April 2000 and effective retroactively from January 2000, relatively small effects in 2000 are not surprising. See Buchinsky (1998) for the interpretation of quantile regression estimates.

33. Note that we estimated the model by including year dummies from 1996 through 2002. When the 1999 year dummy is omitted instead of the 2003 year dummy, the estimated intercept terms for the 60th to 80th percentile regression would be the estimate of the intercept terms plus the estimates of the 1999 year dummy, that is $8,863 (= 12,596 − 3,733),$11,336 (= 16,064 − 4,728), and $15,444 (= 22,167 − 6,723). 34. Note that 88 percent of persons in our sample are white and 54 percent are male. 35. The earnings test thresholds in 2000–2003 for persons reaching 65 were$17,000, $25,000,$30,000, and $30,720, respectively. Earnings at the 70th percentile in 2000–2003 were$27,825, $28,564,$30,200, and \$31,986, respectively. (See Table 3 for other percentile values.)

36. We are currently undertaking a follow-up study to investigate the income effect using a different empirical framework.

37. Results for logged earnings can be provided on request.

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