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

 

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 (50^th to 80^th) 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 70^th percentile for persons who have attained ages 65–69 (where earnings increase between $180 and $1,670) and at the 60^th 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.

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.

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 40^ththrough 80^th 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

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

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 (Δ^j₁₉₉₇, Δ^j₁₉₉₈, and Δ^j₁₉₉₉) 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).

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 β₁₉₉₇ = β₁₉₉₈ = β₁₉₉₉ = 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.

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 β₁₉₉₇ = β₁₉₉₈ = β₁₉₉₉ = 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.

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 β₁₉₉₇ = β₁₉₉₈ = β₁₉₉₉ = 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 60^th conditional percentile of the earnings distribution in 2000, 60^th to 70^th percentiles in 2001, and 60^th to 80^th 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 60^th 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 70^th 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 80^th 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.