Social Security Disability Insurance: Applications, Awards, and Lifetime Income Flows

by Brent Kreider
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Social Security Disability Insurance: Applications, Awards, and Lifetime Income Flows
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Brent Kreider
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1999
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Journal of Labor Economics
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17
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4
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Abstract:

 

Social Security Disability Insurance: 
Applications, Awards, and Lifetime 
Income Flows 

Brent Kreider, University of Virginia

This article provides new evidence about the impact of Social Secu- rity Disability Insurance on male labor force participation decisions based on estimates from a structural model of applications, awards, and state-contingent lifetime income flows. The lifetime framework makes it possible to consider long-term opportunity costs associated with early labor force withdrawal and the disincentive to applications resulting from the statutory waiting period before benefits may be received. Estimation techniques account for the self-selected nature of the pool of applicants when predicting the individual-specific probability of acceptance and the opportunity costs of applying.

I. Introduction

The Social Security Act was amended in 1956 to provide cash benefits to former workers who could demonstrate, through medical screening, their inability to continue gainful employment. When the Social Security Disability Insurance (SSDI) program was introduced, "disability" was

I thank Robert Haveman, Charles Manski, Robert Moffitt, Ed Olsen, John Pepper, Stuart Rosenthal, John Rust, Jonathan Skinner, Steven Stern, and Alex Tabarrok for providing helpful comments on earlier versions of this article. I am especially indebted to Barbara Wolfe, Arthur Goldberger, and Hidehiko Ichimura for their expert assistance. Seminar participants at Johns Hopkins University, the University of Wisconsin-Madison, Mathematica, McMaster Uni- versity, the University of Virginia, and Virginia Tech also provided useful com- ments. Fidel Perez and Hua Fang provided valuable research assistance. Generous financial support was received from the National Institute of Mental Health (grant 5 T32 MH1).

[Journal of Labor Economics, 1999, vol. 17, no. 4, pt. 11 
O 1999 by The University of Chicago. All rights reserved. 
0734-306X/1999/1704-0006$02.50 

regarded mainly as a clinical concept. As the size and cost of SSDI expanded rapidly during the 1960s and 1970s, researchers began to con- sider disability more broadly as a behavioral phenomenon based in part on economic, psychological, and social factors.'

This study provides new evidence about the effects of SSDI on male labor force participation decisions based on estimates from a structural model of applications, awards, and lifetime state-contingent income flows. The model is used to measure the impacts of three policy instru- ments: the individual-specific disability benefit level, the individual-spe- cific probability of being accepted into the program, and the statutory waiting period before benefits may be received. Although the relationship between labor supply and disability benefit levels has been widely stud- ied, there has been very little research about the effects of other important disability policy instruments on work behavior. Halpern and Hausman (1986), Parsons (1991b), and Gruber and Kubik (1997) are among the few previous studies that examine the effect of denials on disability applica- tions or labor force participation.2 The current study is apparently the first to explicitly model the effect of the statutory waiting period on applications.

Much academic and public interest in the SSDI program has stemmed from a time-series observation first highlighted by Parsons (1980): the rapid decline in labor force participation of older men in recent decades has been closely paralleled by an increase in SSDI beneficiaries. From 1960 to 1980, the labor force participation rate fell from 95.7% to 91.2% for men aged 45-54 and from 86.8% to 72.1% for men aged 55-64 (Bound 1989). The corresponding percentage of men on the SSDI rolls grew from 0.8% to 4.2% for the younger group and from 3.5% to 11.3% for the older group.

There is considerable controversy about the effects of SSDI benefit levels on work behavior. Parsons (1980) and Slade (1984) attribute nearly

'In 1967 SSDI benefits were being received by 2.1 million recipients, which more than doubled to 4.8 million by 1979. The annual direct cost of providing these transfers increased sixfold over this period (Halpern and Hausman 1986). Although the number of beneficiaries declined to 4.1 million by 1990, the number of applications and awards began to rise rapidly once again during the 1990s. The SSDI program expanded from 4.3 million to 6.2 million beneficiaries between 1990 and 1997 (an average annual rise of 6%), with a parallel increase in direct annual payments from $32 billion to $46 billion in 1997 dollars (Social Security Administration, Office of Research, Evaluation, and Statistics 1997). Nagi (1965) is usually credited with being the first to provide a conceptual framework for studying the behavioral aspects of work-related medical impairments.

Marvel (1982) also examines the effects of denial rates on SSDI applications, but his results are difficult to interpret because of a data error that was corrected in Parsons (1991b).

all of the decline in labor force participation to growth in the generosity of federal disability benefits. Leonard (1979) also finds large effects of the disability system on nonparticipation. Haveman and Wolfe (1984b), Haveman, Wolfe, and Warlick (1984), Bound (1989), and Haveman, de Jong, and Wolfe (1991), however, find much smaller impacts. Other factors that may be related to the decline in work effort of older men include the increased contribution of spousal earnings to household income, decreased stigma associated with early retirement, and more generous Social Security retirement benefits obtainable at earlier ages (Haveman and Wolfe 1984b). The proportion of individuals with work- related impairments may have also risen over time.3 Bound (1989), who bases his inferences on observed work patterns of rejected SSDI appli- cants, argues that growth in the federal disability system can be largely attributed to increased knowledge about the SSDI program and to reduc- tions in the number of beneficiaries in other cash-assistance programs targeted to the disabled (such as Aid to the Permanently and Totally Disabled). Bound and Burkhauser (in press) provide a comprehensive survey of the disability-related literature for the United States and abroad (see also Danzon 1993).

Halpern and Hausman (1986) develop the only previous econometric model of an individual's application decision, the true choice faced by workers, in attempts to disentangle the application process (supply of beneficiaries) from the eligibility process (demand for beneficiaries). Their model accounts for the kinked nature of a potential applicant's budget constraint implied by an SSDI restriction on a beneficiary's allowable labor earnings. Apart from the econometric difficulties associated with kinked budget constraints, however, other researchers have avoided that approach in this literature because an SSDI beneficiary's complex true budget constraint may depend on a myriad of other sources of nonlabor income emphasized by Haveman and Wolfe (1984a) and ig- nored in the Halpern-Hausman appr~ach.~

Disability insurance benefi- ciaries may be eligible for Supplemental Security Income (SSI) or other means-tested income support (such as food stamps and general assis- tance), and they may receive income from private sources such as relatives or a private insurance policy. Burkhauser and Wittenburg (1996) report that about 15% of male SSDI beneficiaries also receive SSI payments and another 15% receive other means-tested cash transfers; about 4% receive

As medical technology improves, individuals who previously would have died from their health conditions might now be able to continue to live with functional limitations.

Heckman (1983) and Moffitt (1990) discuss a special type of errors-invariables bias that results from misspecification of the true budget constraint in such analyses.

both SSI and other cash transfer^.^ There does not appear to be any paper in the literature that attempts to formally model the interrelations among the various sources of potential income support available to the di~abled.~ This is not surprising given the decentralization of the U.S. welfare system in which state programs vary dramatically in their eligibility requirements and benefit amounts. Following the general approach in the papers by Haveman and Wolfe, this article attempts to at least account for total expected income when predicting income flows in various states of nature (SSDI beneficiary, nonapplicant, rejected applicant, and waiting period).

Like the other previous literature, Halpern and Hausman do not consider the role of potential foregone future labor earnings on applica- tions, nor do they account for self-selection into the applicant pool. Also, their findings pertain only to the population of men under the age of 50. Since most SSDI applicants are older than 50, there are no published structural SSDI application estimates for the most relevant population of potential applicants. In addition, Halpern and Hausman treat a given percentage change in disability benefits as an equivalent percentage change in a beneficiary's total income. Since other sources of income are often available to this population, they may overestimate the sensitivity of applications to changes in SSDI benefits.

The model in this article places a worker's application decision in a lifetime framework while accounting for important selection issues ig- nored in the previous literature. Apotential applicant to SSDI must consider both immediate and long-term consequences of labor force withdrawal. The expected opportunity cost of foregone labor earnings depends not only on current earnings but also on the anticipated path of future earnings. Impaired workers who expect earnings to grow over time despite a work limitation can be expected to make different labor market choices than workers who expect earnings to rapidly decline. Moreover, as part of its screening process the Social Security Administration (SSA) requires that applicants "demonstrate" their inability to work by remain- ing virtually detached from the labor force for at least 5 months before

There is little interaction between SSDI and the state workers' compensation programs. Workers' compensation targets short-term benefits toward partially disabled workers recently injured on the job, whereas SSDI is targeted toward the long-term severely disabled population, most of whose health conditions are not the result of an injury. Workers' compensation and SSDI are simultaneously received by less than 1% of the population of males with disabilities (Burkhauser and Wittenburg 1996). Social Security Disability Insurance benefits are reduced for recipients whose total benefits from other transfer programs exceed 80% of average earnings before the onset of disability.

'Benitez-Silva et al. (in press) discuss interactions between the disability and old-age components of the Social Security system.

eligibility is determined. This feature of the adjudication process repre- sents an important indirect cost of applying for workers with residual work capacity- especially those without savings at the onset of the work limitation. As discussed below, this waiting period can extend well be- yond a year in practice. Estimates in this article suggest that the waiting period represents a substantial disincentive to applications, consistent with Parsons's (1991b) conclusion that delays in the award process, including ~otential appeals, serve as an effective self-screening device. It is less clear whether such self-screening is target-efficient, though Gruber and Kubik (1997) provide evidence that these incentive effects are stron- ger for more able individuals.'

The simultaneous framework in this article makes it possible to obtain consistent predictions of a worker's probability of being granted benefits and his opportunity costs of withdrawing from the labor force. Most previous studies do not model the government's award decision at all (e.g., Parsons 1980; and Haveman, de Jong, and Wolfe 1991). As empha- sized by Halpern and Hausman, however, a worker's probability of successful application is a crucial variable in an application model since the chances of being accepted vary widely across potential applicants, and the rejection rate has often exceeded 50%. The award decision, made at the state level subject to federal guidelines, necessarily has a subjective component because the extent of disability is not easy to quantify.8

Although Halpern and Hausman predict the probability of successful

7As noted by Parsons and by Gruber and Kubik, self-screening through delayed eligibility determination can be perverse. For example, the more disabled may be discouraged from applying (or from appealing an initial denial) if they have less savings or restricted access to capital markets, or if they have higher time discount rates.

The Social Security Administration defines disability as "the inability to engage in any substantial gainful activity by reason of any medically determinable physical or mental impairment which can be expected to result in death or can be expected to last for a continuous period of not less than one year." If the applicant has sufficiently low labor market earnings (currently less than $500 a month), satisfies a substantial work history criterion (which typically requires 40 quarters of covered work for older workers, some in recent years), and has a severe medical condition expected to last at least 12 months or result in death, then benefits are automatically awarded if it is determined that the impairment "meets" or "equals" a condition listed in the Social Security Administration regulations. If the impair- ment is not found in the published list, and it is determined that the applicant cannot continue employment in his previous occupation, then nonmedical factors are considered. At this point, the burden of proof switches to the government to demonstrate that the applicant can engage in substantial gainful activity elsewhere in the economy, considering the applicant's type of impairment, age, education level, and work experience. A beneficiary with labor income above the ceiling is considered working on a trial basis and may be terminated from the program. Only about 10% of SSDI enrollees recover and leave the program before age 65,

application for each member of the sample, their predictions do not account for self-selection of applicants into the applicant pool. Nor do their estimates account for selection when predicting state-contingent income flows. For the probability of acceptance, the issue is that research- ers observe the award decision only for the subsample of individuals who actually applied for benefits; we do not know what the award decision would have been for a nonapplicant had he chosen to apply. Halpern and Hausman estimated a probit model of awards over the subsample of applicants and then generated fitted values of the conditional probability of acceptance for each member of the sample based on the estimated coefficients and observed individual attributes. The SSA's assessment of an individual's capacity to work, however, depends largely on informa- tion that is unobserved in the data, such as the severity of an individual's health condition and his qualifications for various types of jobs. It is likely that applicants tend to be more disabled (and to otherwise have restricted labor market opportunities) than observationally identical workers who choose not to apply to the program, thus making it simul- taneously more likely that they will apply for benefits and more likely that they would be awarded benefits conditional on applying.

Similarly, it is important to account for self-selection when predicting a applicant's opportunity costs of labor force withdrawal. Fore- gone labor earnings can represent the largest costs of program participa- tion for impaired individuals who retain some work capacity. Again, nonapplicants likely have favorable job opportunities compared with observationally identical individuals who choose to apply for disability benefits. This article finds substantial biases in the estimated impact of policy changes on applications when failing to account for self-selection in predicting the probability of successful application or the long-term opportunity costs of applying.

Identification of the relevant policy effects with available data remains an important issue in this research. Because it is often difficult to justify identifying exclusion restrictions in structural models, and it is impossible to prove their validity, it may often be desirable to estimate reduced-form models of individual behavior. A concern with reduced-form estimation, however, is that inferences are subject to the well-known Lucas critique: the parameters of interest may not be invariant to changes in the policy being measured. As a more practical issue in the present context, it does not seem ~ossible to construct an appropriate reduced-form model that identifies the effect of changes in SSDI policy instruments (e.g., generos- ity, leniency, and the waiting period) on application behavior. Since there

however, at which time benefits are automatically converted into normal Social Security retirement benefits (Hennessy and Dykacz 1989).

are no U.S. experimental data available for assessing SSDI policy changes, and SSDI is one of the largest and most expensive transfer programs in the United States, it seems worthwhile to estimate structural parameters to obtain point estimates of these effect^.^ This article provides a formal econometric discussion of the identification problem in the context of structural disability application models, a discussion largely absent in the previous disability literature. Extensive sensitivity analysis was also con- ducted to ensure that the main policy simulation conclusions are robust to reasonable changes in specification.

The next section provides a description of the data, followed by the development of the applications and awards model in Section III. Iden- tification and specification are discussed in Section IV. Section V then discusses the empirical results, including results from policy simulations. Concluding comments are provided in Section VI.

11. Data

The data used in this study come from the 1978 Survey of Disability and Work (SDW), the most recent comprehensive survey of the working and nonworking disabled adult population that includes information pertaining specifically to SSDI applications. Nearly 10,000 civilian non- institutionalized adults between the ages of 21 and 64responded to a variety of questions related to labor force participation, health conditions, work limitations, income by source, demographic characteristics, and participation in government programs. Importantly, the SDW asked re- spondents whether they ever applied for SSDI benefits, not merely whether they were currently receiving such benefits.'' Applicants were

'Using difference-in-difference and other estimators, Gruber (1996) estimates a sizeable Canadian labor force participation response to an increase in benefit levels. Provinces other than Quebec raised their benefit levels by 36% in 1987, while benefits in Quebec remained the same. In an important paper discussed below, Bound (1989) uses a nonstructural approach to provide an upper bound estimate for the effects of the SSDI program on labor force participation rates. That paper conducts a mental experiment not addressed in this article: "What would we observe if there were no Social Security Disability program?" Bound's basic point is that rejected SSDI applicants have low labor force participation rates, and the labor force participation rate of beneficiaries (who are presumably at least as disabled as rejected applicants) might be expected to be still lower even in the absence of the program. This approach, however, does not provide point estimates of the effects of various policy changes on behavior, and it requires its own set of assumptions that have been criticized by Parsons (1991~). Parsons believes that the Bound techniaue understates the im~act of SSDI on work. Among other objections, Parsons suggests that rejected applicants who could work might remain out of the labor force in anticipation of filing a new claim and that the application process itself is detrimental to future labor market success.

lo The recent Health and Retirement Study (HRS) does not distinguish between

also asked the year they applied for benefits and the year they filed an appeal (if ever), though successful applicants were not asked the year they were awarded benefits. A shortcoming of the SDW is that the application and awards information is self-reported, so the responses are subject to recall error and other forms of reporting bias. Measurcment error in applications could potentially affect the consistency of the estimates, especially if the errors are nonrandom-for example, if reporting errors vary systematically with disability level.

Although the data are cross-sectional, information was gathered about employment history and the development of health problems, and lon- gitudinal social security earnings records were subsequently matched to 98% of the respondents. I matched year- and region-specific unemploy- ment rate information to these data to capture varying general macroeco- nomic conditions across time and region using information from various issues of Employment and Earnings (U.S. Bureau of Labor Statistics, various years). Several studies have found that the number of disability applications rises during economic downturns. For example, Stapleton et al. (1995) find that each percentage point increase in the unemployment rate between 1988 and 1992 led to a 4% increase in SSDI applications (see also Leonard [1989], pp. 69-70).

The SDW is composed of two separate panels, both of which are used in this study. The first panel, comprising about 60% of the respondents, is a random sample selected from the 1976 cohort of the Health Interview Survey (HIS76). Respondents from the HIS76 were reinterviewed in 1978 for the SDW. The second panel, obtained from SSA records, consists of an additional sample of SSDI applicants. Within the Social Security panel, beneficiaries were oversampled relative to denied applicants. Manski- Lerman (1977) weighting methods are employed in the maximum likeli- hood estimations to account for the oversampling of SSDI applicants and beneficiaries.

The sample in this study consists of 2,703 men aged 40-62 considered "at risk" of applying for SSDI benefits between 1970 and 1977, the time frame considered in this study. The vast majority of the applicants in the sample (more than 96%) applied during these years." Of these respon-

SSDI and SSI applications. Several national surveys ask respondents whether they are enrolled in SSDI, but apart from the 1972 Survey of Disabled and Nondisabled Adults, I am not aware of any other large-scale comprehensive survey like the SDW that asks respondents specifically about applications to SSDI. Riphahn and Kreider (1998) use the HRS data to estimate the effects of federal disability policy on applications to either SSDI or SSI and focus on behavioral differences between men and women.

"Respondents considered at risk of applying between 1970 and 1977 are those who had some type of health condition or limitation and were not already

dents, 1,986 applied for benefits, and 1,744 of these applicants were accepted into the program. Using sample weights to return the observa- tions back to the population,13% of the respondents applied to the program, 58% of whom were ultimately accepted (after possible appeals). These numbers are roughly in line with SSDI program data published by the Department of Health and Human services during the relevant time period.

111. A Model of Applications and Awards

A worker is assumed to make a rational decision whether to apply to the SSDI program based on labor force attachment and expected state- contingent lifetime income flows. This application choice depends in part on the expected potential SSDI benefit level, the subjective probability of being found eligible for benefits, and the expected length of the waiting period before such benefits would be received. Although SSDI applica- tions and applications for other types of benefits are not jointly modeled, individuals are assumed to form unbiased expectations about total income flows in various states of nature (i.e., SSDI beneficiary, rejected applicant, waiting period, and nonapplicant) based on the experiences of similar individuals currently in those states.

Worker i is assumed to decide whether to apply for SSDI benefits at the beginning of period 0, with each period having a length of 1 year. Time is measured continuously from this period until the worker's normal retirement date, denoted T,, taken to be at age 65." For applicants, period

participating in the SSDI program by 1970. Very few beneficiaries lose eligibility before reaching the age of 65. The full sample includes 9,859 respondents. Of these, 300 individuals were excluded from the sample used in this study because they were members of both the HIS76 and SSA sample frames; appropriate use of the sample weights provided in the data when using the combined frames requires that such respondents be excluded from the analysis. Next, 4,329 women were excluded from the sample, along with 2,142 men who were not between the ages of 40 and 62. Men older than 62 were excluded to minimize complications associated with interactions between the SSDI program and the early retirement Social Security program. Of the remaining 3,088 respondents, 312 were excluded because they reported no health condition or functional limitation. Next, 11 individuals were excluded because it was unknown whether they applied for benefits. An additional eight respondents were excluded because information about schooling was missing. Finally, 56 respondents who were already enrolled in the program by 1970 were excluded, thus reaching the final sample size of 2,703. Twenty-two rejected applicants who applied before 1970 were considered at risk of applying again during the sample period. They were relabeled as nonapplicants in this study since they did not do so.

l2 Although a simulation that alters the expected normal retirement age by a few years (e.g., to age 62) leads to a nonnegligible change in the proportion of applications, such a change in the assumed normal retirement age before estima-

O is measured as the year the application was filed. Nonapplicants are randomly assigned an "application year" between 1970 and 1977 to represent period O such that the sample proportion of applicants in a given year reflects the true population proportion.'3 The application decision is assumed to be made only once since there is no information in the SDW about multiple applications. Most workers who eventually qualified for benefits after being initially rejected did so through the appeals process and not through reapplication (Bound 1991~). Unfortunately, given other complexities in the model it did not appear feasible to explicitly model the timing of an appli~ation.'~

A worker must be almost completely detached from the work force for at least 5 months before benefits may be received. Evidence from Bound (1991a) suggests that the initial application process took an average of about 8.5 months at the time of the 1978 survey. Based on this evidence, T = 0.7 years is taken to be the expected waiting time for each member of the sample. The waiting period can be longer for rejected applicants who choose to enter the multistage appeals process, but I assume that potential applicants ignore the possibility of an extended waiting period due to a subsequent appeal.15

tion (which does not constitute a simulation but instead leads to small changes in the coefficient estimates themselves) does not have a sizable effect on the policy simulations involving changes in benefits or the probability of successful appli- cation.

13 Halpern and Hausman (1986) assigned the year of their survey as the decision date for nonapplicants. Random assignment of this date for nonapplicants was chosen here so as to avoid "stacking the deck." For example, if the unemployment rate happened to be relatively high in the survey year and that year was chosen as the observation date for nonapplicants, then parameter estimates might spuriously suggest that workers are more likely to leave the labor force when the unemploy- ment rate is low.

l4 Burkhauser et al. (1992) use a hazard model to estimate the length of time individuals wait following the onset of an impairment to apply for disability benefits. They find that the speed at which impaired workers apply for benefits can be influenced by policy instruments.

15 Rejected applicants may petition the state agency for a reconsideration. If this fails, an appeal can be made to an administrative law judge and then to the Appeals Council. As a last resort, a rejected applicant may file a civil action in a U.S. district court. The SDW does not provide information sufficient to calculate actual waiting periods, and there do not appear to be published statistics (e.g., by the Social Security Administration) that would allow potential applicants to more precisely predict their waiting times based on personal characteristics. I never- theless experimented with allowing for heterogeneity in expected waiting times using information about the timing of applications and awards for a sample of SSDI beneficiaries in the HRS. Adding heterogeneity to T based on the experi- ences of those beneficiaries had virtually no effect on the results in this article. Unfortunately, this selected HRS sample was not representative of all SSDI

Respondents are categorized as beneficiaries (B), rejected applicants (R), or workers who did not apply for benefits (N).A tree diagram of the basic components of the applications model is provided in figure I. An individual's propensity to apply to SSDI is specified as

where Uj,is the ith individual's discounted utility in state j and Piis the worker's subjective probability of being accepted into the program if applying. Preferences are approximated in quasi-linear form as

where Y is income, H is labor hours, and v represents other factors affecting utility that may vary across the applicant and nonapplicant states. The coefficient on income in the nonapplicant and rejected appli- cant states are constrained to be the same, although the coefficient on income may differ between the beneficiary and working states to allow for the possibility that marginal utility from a dollar of transfer income is different than marginal utility from other income sources (e.g., due to possible stigma associated with government transfers). Following several earlier studies, beneficiaries attain maximum leisure time with H = 0, while workers expect to supply a fixed number of labor hours H = H.16 There is thus no labor supply effect operating through the wage rate in this model. This seems to be a reasonable approach given evidence from labor supply studies that labor hours supplied by prime-age men are quite inelastic." Applicants are assumed not to work during the waiting period.

applicants because it did not include rejected applicants; it is not possible in the HRS to distinguish rejected SSDI applicants from rejected SSI applicants (who do not face a statutory waiting period). For the sample of SSDI beneficiaries, per- sonal characteristics such as age, education, race, disability level, white collar, and region had almost no explanatory power in predicting the waiting period.

16 See, e.g., Haveman and Wolfe (1984b), Marvel (1982), and Haveman, de Jong, and Wolfe (1991).

17 Surveying the labor supply literature, Pencavel (1986) concludes that the

"vast proportion of that work- both based on the static model and that based on the life-cycle model-indicates that the elasticities of (male) hours of work with respect to wages are very small" (p. 94.) Based on the static model, his best guess of the uncompensated wage elasticity for prime-age men in the United States is -.lo (p. 82). Killingsworth (1983, p. 185) reports that most uncompensated wage elasticity estimates for U.S. men fall between -20 and .14, a range that narrows to -.03 and .14 when restricting attention to studies producing positive compen- sated wage elasticity estimates.

Obtbl; (waiting period) 0 b t b r income: I;(t) = y,! exp(tg,,) income: &(t) =yo, LFP: Hj(t)= H LFP: Hi(t)= 0

r<t<l; z<t<I; income: y(t) = y,, income: r(1)= yR,exp(tg,,)

LFP: H,(t)= 0 LFP: H,(t)= i?

t =time

r =waiting period date

T = normal retirement date

yo= expected income during the waiting period if applying for SSDI benefits

y, = expected income if receiving SSDI benefits

y, =expected initial income if not applying

y, = expected initial income if applying and rejected

g, =expected income growth if not applying

g, =expected income growth following waiting period if applying and rejected

K = labor hours if working

FIG. 1.-Tree diagram of income and labor force participation

Preferences for nonwork are allowed to vary across the population of potential applicants according to

where X, consists of personal characteristics such as education and disability level, and E~ represents unobserved influences on tastes for nonwork.

Let yN represent expected initial income in period O if remaining in the workforce. A worker assumes that income will grow or decline at a constant rate following the application decision until age 65:

where the anticipated gowth rate gN varies depending on personal characteristics. This parameterization of income growth is adopted from Willis and Rosen (1979) who study the returns to college education. Their infinite horizon parameterization, however, is replaced by a finite horizon approach that recognizes that workers may apply for transfers within a few years of normal retirement age. Earnings growth is calculated for workers remaining in the workforce using the matched longitudinal Social Security earnings records and information about other family income. This growth measure is taken to be unobserved for beneficiaries since there are no data on what they would have earned had they remained in the labor force.''

A nonapplicant's discounted utility is then given by

I 1 1 1

where Sl = ;-;exp(-rT), S2 = 7-;(; 1 + T)exp(-rT), Z = HX~,

IS Real net income growth if not applying is calculated as g,; = ln[(E,,,

+ O,)l(E,,, + 0,)]/6 -0.07, where E,,; is average earnings from 1970 to 1972, E,,, is average earnings from 1976 to 1978, and Oiis other income reported at the time of the survey. The constant term adjusts for inflation from 1971 to 1977. It is assumed that the real growth rate of other income is zero given the data limitation that such income is reported for only 1 year. The actual growth values used in this study are based on predicted earnings values generated from a Tobit regression with a varying upper limit point since Social Security earnings data are censored above at maximum taxable income amounts (maximum reported earn- ings are censored at different values for different years). This procedure is taken from Bound (1989, n. 17). The explanatory variables are age, age2, age3, and a set of year dummies.

and r is the subjective time discount rate which is set to 0.07 for the empirical analysis." Similarly, income for an SSDl beneficiary is given by

0 5 t 5 T YBZ(t)= yoz,

YB~,T < t 5 T,,

where yo is expected income during the waiting period. The associated discounted utility is

1 I 1

with S, = ;-;exp(-r~) and S, = ;exp(-r~) -exp(-rT).

Expected beneficiary income is equal to the sum of the individual's family SSDI benefit level and other expected family income as an SSDI beneficiary. The statutory disability benefit level is equal to the individ- ual's Primary Insurance Amount (PIA), the same amount he would receive if old enough to be eligible for normal Social Security retirement benefits. The PIA value is increasing in the worker's average indexed monthly earnings since age 21. In 1996, the average monthly family benefit amount, including benefits paid to dependent children and spouses, was about $900 (Social Security Administration, Office of Re- search, Evaluation, and Statistics, 1997). Since SSDI benefits are indexed to inflation and the fraction of a beneficiary's income obtained through work is usually zero or negligible, the expected net real growth rate of income as a beneficiary is assumed to be zero.

A rejected applicant receives income in period t given by

0 5 5 T yRL(t)= ( Yoi,yRietgR2,T < t 5 T,,

where y~ is a rejected applicant's expected initial income following the waiting period, and g~ is a rejected applicant's expected growth rate of income following the waiting period. A rejected applicant's discounted utility is then given by

I' Empirical estimates are fairly insensitive to the choice of r for values between

0.01 and 0.10. Since disabled individuals may have higher than average time discount rates, I also experimented with values of r as high as 0.30. The simulated application responsiveness to a 10% cut in benefits is about 15% lower when r = 0.30 than when r = 0.07.

where S, = ;(;11 + ~)exp(-YT)-:(: + T)exp(-YT).

To prevent a difficult estimation problem from becoming unmanage- able, a worker is assumed to approximate that initial income and growth as a rejected applicant would be proportional to these values as a nonap- plicant: yRi = SyyNi, and gR, = 6,gNi. This approach avoids a severe multicollinearity problem in the application equation and substantially reduces the number of parameters that must be estimated." This assump- tion is somewhat weaker than a common alternative assumption made explicitly by Marvel (1982) and implicitly by Parsons (1980), Haveman and Wolfe (1984b), and Haveman, de Jong, and Wolfe (1991) that ex- pected income if rejected is equal to expected income if not applying. The current framework allows for the possibility postulated by Halpern and Hausman (1986) that rejected applicants are financially penalized by prospective employers.21

Combining the previous equations, the application equation is given by

The first term measures the value of discounted expected nonlabor in- come if applying, which includes the value of income during the waiting period plus the value of beneficiary income after the waiting period, accounting for the probability of acceptance into the program. The second term measures the discounted expected monetary opportunity costs of applying, which includes forgone nonapplicant earnings less the value of income earned following a potential rejection. The third term measures the discounted value of detachment from the labor force, at-

''The correlation coefficient between predicted income if remaining in the labor force and predicted income as a rejected applicant exceeds 0.80.

21 Halpern and Hausman predict labor income by estimating a single income equation over the subsample of nonbeneficiaries and controlling for whether the worker is arejected applicant. A problem with that approach is that they treat the outcome of being a rejected applicant as exogenous.

tained by beneficiaries and by rejected applicants during the waiting period.22 For compactness, the applications equation will be rewritten as

A := A,, + P,A,i -(10)

where A, = yBS,ln yo + yN[S4(ln 6, + In yN) + S56ggN-Slln yN -S2g~1+ SJP,, and A2 = yBS41n yB -yN[S4(ln 6, + In yN)

+ S56,g,l + S4ZPL. Although A:$ is unobserved, an indicator A is available for whether the

worker applied to SSDI. It is assumed that the worker applies for dis- ability benefits if and only if A::. is positive:

1, A;>O

A= { 0, otherwise.

Since many applicants are rejected, it is important to specify the deter- minants of the award decision. Let the government's unobserved propen- sity to accept an individual's application for benefits be denoted G". The process by which workers form expectations about G':. is assumed to be given by

where XG is a set of observed individual characteristics relevant to the award decision and EG captures unobserved influences. Although G'qs unobserved for all members of the sample, an indicator G is available to distinguish accepted applicants from rejected applicants. Let the award decision be favorable if and only if the government's propensity to grant benefits is positive:

1, Gq>O Gz={ 0, otherwise.

This award decision is observed only for the subsample of applicants. Using equations (12) and (13), the application equation can be rewritten as

22 For purposes of this model, rejected applicants are not considered detached from the labor force even though they may not work, at least initially, following a failed application.

where A,, = XGiPGand 0is the cumulative distribution function (c.d.f.) of EG.

The potential applicant's calculated family PIA value is a function of past earnings and may thus be correlated with current work preferences. The model includes a separate equation for the determination of benefi- ciary income, with unobserved determinants of benefits allowed to be correlated with unobserved determinants of applications.23 The model also includes separate equations for expected income during the waiting period, expected income if not applying for benefits, and expected income growth if not applying for benefits:

Expected income and growth if not applying are observed only for the subsample of nonapplicants (A = 0). The disturbances in these equations may be correlated with each other and with the disturbances in the application and award equations.24 Expected income as a beneficiary is observed only for the subsample of respondents for whom A =1 and G = 1. One version of the model drops this equation and treats beneficiary income as observed for all respondents based on direct PIA calculations. As discussed below, this alternative approach avoids an identification issue but introduces an endogeneity problem if prior earnings are corre- lated with current tastes for leisure. Expected income during the waiting period is observed only for recent applicants for whom the award deci- sion had not yet been determined at the time of the survey.

The model to be estimated consists of equations (11)-(18). Efficient

23 Similar to a strategy by Gordon and Blinder (1980) and Haveman and Wolfe (1984b), with this approach I generate a predicted value of the family benefit level (plus other family income) for each member of the sample to use in place of the actual PIA. It makes little difference in the simulated results whether actual or predicted benefit levels are used in the estimation.

24 For example, unobserved influences on current earnings may also have an effect on growth. Growth may be flatter when initial earnings are high if luck is involved in securing a high-wage job or if the employer has incomplete knowl- edge about the worker's productivity when setting wages. Alternately, the oppo- site tendency might hold if wages are set based in part on indicators of ability not observed in the data.

simultaneous estimation of the entire system of equations was not feasi- ble, so I follow Halpern and Hausman (1986) and generate income predictions that are treated as true values in the estimation of applications and awards. These predictions are generated using methods analogous to those provided by Heckman (1976) and Lee (1982), allowing for selection into both the applicant and beneficiary pools (see apps. A and B). For estimation purposes, I assume that the disturbances are joint normally distributed conditional on the explanatory variables and that they are independent across workers.25 The covariance matrix is assumed fixed but unrestricted.

The log-likelihood for applications and awards derived from equations (11)-(14) is given by

where p is the correlation between the application and award distur- bances. The choice-based weights are given by F;I = q(j)/q(j), j = 6,R, N,where q(j) is the fraction of the population in state j and q(j) is the corresponding fraction for the regime-based sample.26 Details about the gradient of this likelihood function are provided in appendixC.

IV. Identification and Specification

Following an identification argument implicit in Halpern and Hausman (1986), all of the coefficient parameters in this model can technically be identified (up to scale for applications and awards), without exclusions, based on the structure implied by von Neumann-Morgenstern expected utility theory.27 In particular, the coefficients in the application equation are identified if the probability of acceptance into SSDI is not constant across observed individual attributes in the data. A formal identification

25 Like FIalpern and Hausman (1986), I assume that heteroskedasticity is sufficiently minor that the disturbances can be treated as identically distributed across resuondents.

26 The asymptotic covariance matrix for thc coefficient estimates is given by mr, where r is the negative inverse of the Hessian of the weighted log- likelihood, and R is the summed outer products of the first derivatives of the wei hted log-likelihood.

2kHdpern and Hausman do not discuss identification in their paper.

argument, which does not require exclusion restrictions, is provided in appendix A. Although this argument relies on nonlinearity in functional form, nonlinearity based on expected utility theory may be considered less arbitrary than ad hoc nonlinearities in some models. Identification can alternately be attained if appropriate exclusion restrictions are avail- able. Without the structure implied by expected utility theory, and ig- noring the other structure in equation (10) implied by the identification of the application coefficients requires that measures rele- vant to the award decision and income flows do not directly affect applications.

In the absence of exclusions, identification of the coefficients in the income equations relies on the strong joint normal distributional assump- tion or on nonlinearity in the selection equation(s). For an income equation in which selection is based only on the application decision (and not the award decision), identification is aided by a variable that affects the probability of applying but not expected income. Based on the expected utility framework, however, we have the natural exclusion P that affects the probability of applying but not income, and there is wide variation in P across observed individual attributes. For the beneficiary income equation in which selection is based on both the application and award decisions, identification is aided by a variable affecting the prob- ability of applying that does not directly affect beneficiary income (such as P) and a variable affecting the award decision that does not affect beneficiary income. In one version of the model, beneficiary income is assumed to be observed for all respondents based on direct calculations of their PIAs. In this case there is no issue of identification, although a potential endogeneity issue is introduced since tastes for work may be correlated with prior income levels. As discussed in Section V, however, I find no evidence of selection for beneficiary income, and there is only a minor difference in the policy simulation results between the two ap- proaches.

Specific exclusion restrictions to aid with identification are discussed below. Some specifications utilize information from other data sources to supplement the variables available in the SDW. Since identification through exclusions can never be proved, extra care was taken to check the sensitivity of the results to alternative specifications.

The core set of variables included in each of the regression equations includes age, an indicator for race, years of schooling, indicators for high school and college graduation, marital status at the onset of the work

28 Other nonlinearities in the application equation also technically aid in iden- tification (e.g., those resulting from modeling the waiting period), but these other nonlinearities are not considered in the formal argument.

limitation, 10 occupation indicators, the unemployment rate (which varies across region and application year), and a disability index. Nonworking individuals are matched to their former occ~~ations.~'

The disability index is constructed using detailed information about health conditions and work limitation following a procedure in Kreider (in press) and is designed to be purged of self-reporting bias related to the work deci- siom30 Definitions of variables are provided in table 1, with descriptive statistics presented in table 2.

As shown in table 3, the application equation includes additional measures related to application costs and labor force attachment. First, the existence of net savings at the onset of disability is expected to have a positive influence on applying to SSDI since the often lengthy waiting period can represent a strong barrier to applying for workers without savings. A likelihood ratio test for overidentification did not reject the hypothesis that net savings has no effect on expected income. Similar tests were conducted before imposing the other restrictions discussed below to take care that relevant exogenous measures are not excluded from any of the structural specifications.

Also included in the application equation is a time- and region-varying measure of local physician density, constructed using information from the Statistical Abstract of the United States (various years). A high con- centration of physicians in an area may reduce the average monetary and time costs of obtaining sufficient medical documentation of a severe long-term disability. Regarding attitudes toward work, respondents were

29 To preserve degrees of freedom for the specification of expected income

during the waiting period, I combined the occupation measures into four broad categories defined by Gordon and Blinder (1980) in their study of the early retirement decision.

30 In that article, "true disability" and labor force participation are simulta- neously determined, with true disability specified as a function of observable and unobservable health and socioeconomic characteristics that combine to determine work capacity. Many researchers are concerned that self-reports of work limita- tion may be influenced by work status or participation in a disability program. In particular, nonworkers may systematically overreport the extent to which a health condition limits their abilitv to work (e.e.. Door health mav be considered a

\ O'l

socially justifiable reason for early labor force withdrawal). Some researchers have thus turned to "objective" indicators of disability (e.g., subsequent mortality, body mass indices, ability to lift various objects or climb stairs) in place of self-reported work limitation. As emphasized by Bound (1991b), however, these objective indicators may be poor proxies for work capacity, and this may also lead to biased inferences about the effects of policy on work behavior. Using an approach that offers a compromise between accepting systematic reporting bias and simply discarding all useful direct self-reports of work limitation, the meth- odology in Kreider (in press) treats self-reports from nonworkers as unreliable while exploiting the limitation responses from workers.

Table 1 Variable Definitions

Variable

Physician density

Married at onset Professional Manager Sales Clerical Craftsmen Operatives Transport operatives Laborers Services Not classified White collar l;+

White collar 2 Skilled blue collar

Unskilled blue collar Work. became

boring Job out of mind Savings at onset Family size

k!:a:rbility index

Family income

Years of schooling High school

graduate College graduate Earnings risk

Union War veteran

Mining Rural

~ ~

-

Black New England Middle Atlantic East North Central West North Central South Atlantic East South Central West South Central Mountain Pacific Local leniency

Unem~lovment rate

Definition

Active nonfederal physicians per 100,000 population, varies across location and "application year" (Statistical Abstract of the United States, various ears)

1 if married at the onset of tle limitation; 0 otherwise

1 if professional or technical occupation; 0 otherwise

1 if manager (except farm); 0 otherwise

1 if sales occupation; 0otherwise

1 if clerical occupation; 0 otherwise

1 if craftsman; 0 otherwise

1 if operative other than transport; 0 otherwise

1 if transport o erative; 0 otherwise

1 if laborer (in$uding farm); 0 otherwise

1 if services occupation (including household); 0 otherwise

1 if occupation unknown/unclassified; 0 otherwise

1 if rofessional, technical worker, nonfarm manager, afministrator; o otherwise

1 if sales, clerical; 0 otherwise

1 if craftsman, operative, private household, services; 0 otherwise 1 if laborer, farm manager; 0 otherwise 1 if respondent became bored at work (currendmost recent job)

1 if able to "put work out of mind" at the end of the day

1 if respondent had net savings at onset of the limitation

Number of family members in the household

Respondent's age Continuous work limitation measure described in n. 30 (see Kreider, in press)

Household income from all sources, including labor earnings and all transfers Number of years of schooling 1if high school graduate; 0 otherwise

1 if college raduate; 0 otherwise

Constructedmeasure of uncertainty about potential future labor earnings described in n. 32 (see Kreider 1998) 1 if a member of a labor union in current/last job; 0 otherwise1 if the res ondent participated in the military during World War 11, %e Korean War, or the Vietnam War; 0 otherwise 1 if mining industry; 0 otherwise 1 if rural residence; 0 otherwise 1 if black race; 0 otherwise 1 if New England region residence; 0 otherwise 1 if Middle Atlantic re ion residence; 0 otherwise I if East North ~entra! region residence; 0 otherwise 1 if West North Central region residence; 0 otherwise 1 if South Atlantic region residence; 0 otherwise 1 if East South Central region residence; 0 otherwise 1 if West South Central region residence; 0 otherwise 1 if Mountain region residence; 0 otherwise 1 if Pacific region residence; 0 otherwise

SSDI acceptance rate in the respondent's region during the 3 years preceding the respondent's "application date" Unem~lovment rate. varies across region and "a~ulication date"

'&As classified by Gordon and Blinder (1980).

asked whether they were able to put their current or last job out of their mind at the end of the day. Workers having difficulties sleeping or "winding down" after work may be more inclined to withdraw from the labor force before usual retirement age. Similarly, respondents who felt that work had become boring (conditional on income and occupation) are presumably more likely to search for alternatives to work.31 Additional determinants of applications include family size, membership in a union, and a measure of earnings risk. The earnings risk measure is constructed using techniques discussed in Kreider (1998). That paper shows that for most risk-averse workers, the likelihood of applying for public transfers rises with the degree of uncertainty about future labor earnings, and it estimates that the application rate for SSDI is about 15% higher than it would be in the absence of earnings risk.32 These last three variables are also included in the income regressions but not the award equation since none of these measures should affect eligibility. A claims administrator is not likely to even be aware of a labor union ass~ciation.~~

A measure of local leniency, defined as the SSDI acceptance rate in the respondent's region over the 3 years before his application decision, is included as an additional predictor of a worker's probability of being awarded benefits. Marvel (1982) finds considerable variation in award standards across regional SSA offices. This measure is irrelevant to ex- pected income and the application decision, conditioning on the predicted probability of being accepted, P, since it provides no additional informa- tion. A second additional measure included in the award equation follows a strategy by Marvel, who identifies applications by including in his awards specification the proportion of a state's workers in the mining industry. Marvel notes that disabilities associated with mining are rela- tively difficult to evaluate in the SSDI awards process, leading to a high

31 Since these labor force attachment indicators may be endogenous, they were excluded in some of the estimations used in the robustness checks (discussed at the end of Section V). Results from McCallum (1972) and Wickens (1972) suggest, however, that asymptotic bias introduced from omitting a relevant factor from an equation often dominates the bias associated with its possible endogeneity.

32 In that article. the loneitudinal Social Securitv earnines records from the

0 "

SDW are used to construct a measure of a potential applicant's uncertainty about labor earnings as a labor force participant. An observed measure of earnings volatility for workers is calculated as the variance of detrended labor earnings over the 5-year period following the SSDI application date. Earnings risk as a rejected SSDI applicant and as a nonapplicant are then predicted for each member of the sample based on observed attributes such as age and occupation. The estimation ~rocedure accounts for ~ossible selection bias (e.e.. SSDI a~vlicants mav have

\ 0' I I

applied in part because they tended to face more uncertainty about potential labor earnings). In this article, the estimated sensitivity of applications to the benefit level declines by nearly 10% after controlling for earnings risk in the estimation. 33 Based on discussions with several SSA officials about variable specification.

Table 2
Descriptive Statistics (Weighted)
All Respondents (N = 2,703) SSDI Beneficiaries(N= 1,744) Rejected Applicants(N= 242) Nonapplicants(N = 717)
Mean SD Mean SD Mean SD Mean SD
Applied to SSDI      
Granted benefits      
Unemployment rate      
Family income ($1,000)      
AgeBlack      
Work became boring      
Disability      
Earnings risk      
Years of schooling      
High school graduate      
College graduate      
Physician density      
Job out of mind      
Married at onset      
Professionals      
Managers      
Sales      
Clerical      

Craftsmen Operatives Transport operatives Laborers Services Nonclassified occup. White collar 1 White collar 2 Skilled blue collar Unskilled blue collar Savings at onset Family size Union Local leniency Mining industry Rural residence War veteran East North Central East South Central Middle Atlantic Mountain New England Pacific South Atlantic West North Central West South Central

Table 3 Variable Specification, Base Model

Apply Grant Income

P (award probability) Age

Disability index Years of schooling High school graduate College graduate Married at onset of disabilitv Unemployment rate Blaclr Occupation (10 categories) Job became boring Job out of mind at night Physician density Net savings at onset of disability Family size Union current/previous Earnings uncertainty Local leniency Mining industry Age2 Rural Region Veteran

rejection rate high among miners.34 Following Marvel, an indicator for past work in the mining industry is expected to have a negative influence on acceptances with no independent effect on applications. The mining indicator was also included in the income regressions in some of the robustness checks, but it never had close to a significant effect.

Additional measures included in the income specification but not the participation equations follow several earlier studies. Following Halpern and Hausrnan (1986) and others, this set includes age squared to allow for a concave earnings profile and indicators for geographic region.35 Veteran status is also included in this set following Haveman, de Jong, and Wolfe (1991); eligibility for veterans' benefits does not preclude eligibility for SSDI or vice versa. In contrast to previous studies, I include in the application equation a large number of occupation categories, along with the measure of the local unemployment rate to account for regional variations in macroeconomic conditions. It appears that none of the

34 According to Marvel (1982, p. 401), "A principal reason for the establishment of a separate black-lung disability program for coal miners appears to have been to grant the miners a more generous standard for disability benefits than that allowed under the ordinary DI determination process."

35 Lee (1978) and Haveman and Wolfe (19846) among others also include age squared in this set.

studies in this literature includes region variables in the participation equation.

As discussed at the end of Section V, the qualitative findings in this study are robust to reasonable changes in specification. As part of the robustness checks, I estimate alternative specifications based on exclusion restrictions found in the most cited previous studies in this literature. The Halpern-Hausman study, for example, employs the following sets of exogenous exclusions:

X: = {family size}, 
X; = {family size, savings, "other" nonlabor income}, 
X$ = {rural, age squared, assets, "other" nonlabor income, geographic 

region), 
X$ = 0,and 
xA, = {geographic region, rural, age squared}, 

where X! denotes the set of measures included in equation j but not in equation k, with A = apply, G = grant, and Y = income. Anderson and Burkhauser (1985) and Haveman and Wolfe (198417) attempt to identify their labor force participation equations by including various education spline measures in X$(where participation represents the work decision instead of an application decision in their case). Aarts and De Jong (1992) include education interacted with age in this set.

For additional exclusions in the robustness specifications, I estimated an application equation that included variables that proxy for the degree of employer tolerance toward a disability. In particular, information is available about whether a respondent's employer was willing to make changes in the workplace to accommodate his work limitation. For the award equation, I constructed a measure of local political climate follow- ing the spirit of Marvel (1982), who formed an indicator of a state's "liberalness" using AFL-CIO voting records. In this analysis, I included in the eligibility equation an indicator for whether the respondent lived in a region in which cost-of-living adjusted Medicaid benefits were more generous than average.

V. Results

Parameter estimates are presented in tables 4 and 5. Estimates for the income regressions in table 4 are consistent with prior expectations. The estimated coefficients on the selection terms for income and !growth if not applying are both positive and significant, suggesting that nonapplicants had a comparative advantage in the labor market relative to applicants, controlling for observed characteristics. There is no evidence of selection effects for the other income equations. Since this study focuses on the

Table 4
Income and Income Growth
Work
ln(1ncome)
Dependent Variable Coefficient   SE
Constant      
AgeAge2      
Black      
Disability index      
Years of schooling      
High school graduate      
College graduate      
Married at onset      
Professional, technical?      
Managers, administrators      
Sales      
Clerical      
Operatives, except transport      
Transport operatives      
Laborers      
Services      
Unclassified occupation      
Unemployment rate      
Family size      
Union      
Rural      
Northeast3      
West      
South      
War veteran      
White collar 1s      
White collar 2      
Skilled blue collar      
A,      
AAC,      
AAGZ      
A      
Adjusted RZ      
N      

:'Estimated over only 702 respondents because income data were inco~nplctc for 15 nonapplicants.
? O~nittcd category is craftsmen. 
i O~nittcd category is North Central. 
SOmitted categories arc unskilled blue collar and unclassified. 

determinants of applications and awards, the other coefficients for these equations are not discussed here to save space.

In table 5, expected income as a beneficiary has a positive and signifi- cant effect on applications (at better than the 10% level) while expected income if not applying has a negative impact. Disability level has the anticipated positive influence on applications. Years of schooling has a negative impact; stigma associated with program participation may be higher among the more educated, though stigma associated with partic-

Work Beneficiary Waiting Period
Income Growth ln(1ncome) In(1ncome)
Coefficient SE Coefficient SE Coefficient SE

ipation in a social insurance program like SSDI may be lower than that associated with welfare programs like AFDC.~~

The estimated diploma effects were insignificant. Respondents with positive net savings at the onset of disability are found more likely to apply, presumably in part because the statutory waiting period represents a weaker barrier to ap-

36 See Warlick (1982) for a discussion of this literature.

Table 5
Applications and Awards
Apply   Grant
Dependent Variable Coefficient SE Coefficient SE
,)(-7Labor income Beneficiary income (yo)        
Constant        
AgeBlack        
Disability index        
Years of schooling        
Hi h school graduate        
cof1ege graduate        
Married at onset        
Professional, technical''        
Managers, administrators        
Sales        
Clerical        
Operatives except        
transportation        
Transport operatives        
Laborers        
Services        
Unclassified occupation        
Unemployment rate        
Job became boring        
Job out of mind at home        
Physician density        
Earnings risk        
Savings at onset        
Family size        
Union        
Local leniency        
Mining industry        
6,        
6, P        
LL        
N        
:'Omitted categoryis craftsmen.        

plications for workers with net assets. As expected, both the unemploy- ment rate and level of earnings risk have positive estimated impacts on the probability of applying. Also as anticipated, respondents able to put work out of their mind at the end of the day are found significantly less likely to apply, while those who felt that work had become boring had a significantly higher probability of applying. The estimated positive effect of physician density on applications is insignificant using a two-sided test, though the impact is significant at the 10% level using a one-sided test. Family size has a negative estimated influence on the probability of applying.

Turning to the eligibility equation, the probability of being granted benefits if applying is found to be positively related to age, disability level, the recent regional acceptance rate (local leniency), and being married at the onset of the limitation. The screening process for older workers may be less stringent since such workers would be eligible for disability benefits only a few years before their benefits would automatically be converted to normal retirement transfers. Former mining workers were significantly less likely to be accepted into the program controlling for other factors, as suggested by Marvel (1982). Neither race nor the edu- cation measures has a significant effect on awards after controlling for occupation.

The estimate of p is positive and significant, consistent with a hypoth- esis that applicants tended to have more severe health conditions or otherwise had limited job opportunities compared with observationally identical nonapplicants. Single-equation probit estimates for applications and awards that do not account for selection bias were also obtained (not shown). For this case, I first estimated equations (12) and (13) as a probit model of SSDI awards over only the subsample of applicants. The coef- ficient estimates were then used to generate predictions of the probability of successful application P for both applicants and nonapplicants. I next generated predictions for the income and growth measures without ac- counting for selection. Using these values, the application model given by equations (11) and (14) was then estimated using probit techniques. As discussed below, results from the policy simulations based on the simul- taneous estimation are substantially different from those based on esti- mates that assum: away such selection bias.

The estimates 6y = 0.64 and 6g = 0.052, which together measure the expected discounted income loss associated with being a rejected appli- cant compared with not applying, seem reasonable but are imprecisely e~timated.~'To check the sensitivity of the results to different values for these parameters, I reestimated the model for cases in which 6ywas fixed at either 0.25 or 1.0 and 6, was fixed at either O or 1.0. The sensitivity of the simulation results, presented below, was within the range described at the end of this section for the sensitivity results regarding variable spec- ification.

The proportion of respondents in the weighted sample who applied for benefits is 0.130. To simulate the effects of changes in the generosity and leniency of the disability program on applications, each worker's expected family SSDI benefit level and/or predicted probability of accep-

37 Using a different approach mentioned in n. 21, Halpern and Hausman estimated that the average worker could anticipate a 50% loss in labor income if he applied to SSDI and was rejected.

tauce into the program is altered up or down by 10%. A change in the benefit level is assumed to have no influence on income available from other sources. Using the original set of coefficient estimates, a new proportion of applicants is predicted after the hypothetical policy change and compared with the original proportion.

Simulation results are presented in table 6. In frame A, applications are predicted to fall by 7.1% following a 10% decline in the probability of successful application, more than three times the responsiveness predicted by Halpern and Hausman (1986). Recall that Halpern and Hausman restrict their sample to men under the age of 50, and they do not account for the self-selected nature of the pool of applicants when predicting a worker's probability of successful application. These two factors together account for about four-fifths of the difference in our results for changes in leniency. The selection bias correction by itself accounts for about three-fifths of this difference. Allowing for income growth and the wait- ing period in the model makes little contribution to the difference in my results regarding leniency. Parsons (1991b) estimated that a 10% increase in the initial denial rate induces about a 4% decline in applications, a smaller response than the 7% decline predicted in this article. Gruber and Rubik (1997) do not model applications distinctly from work nonpar- ticipation, but they estimate that a 10% average increase in denial rates during the late 1970s was responsible for about a 3%decline in nonpar- ticipation.

Regarding program generosity, I find that decreasing the benefit level by 10% induces an 8.6% decline in applications, about three-fourths the effect predicted by Halpern and Hausman. There seem to be two primary reasons this article finds smaller responses to changes in benefits. The first is the added treatment of time. When time is eliminated from the model (i.e., the model considers only current income and not future income flows or the waiting period), a simulated 10% reduction in the family PIA lcvel leads to a decline in applications about 1.3 times as large as that simulated using the base model.

The other important difference involves the measurement of benefi- ciary income. Halpern and Hausman treat a 10% change in the benefit level as an equivalent change in income available to a beneficiary. Since this article includes predicted nondisability income in the measure of total income available to a beneficiary, a 10% change in the benefit level

-

corresponds to a change in total income that is less than 10%. When both time and other potential sources of income for beneficiaries are eliminated in the model, a simulated 10% reduction in the family PIA level leads to a decline in applications about 1.5 times as large as that simulated using the base model. Thus, the estimated application responses to changes in benefits are even greater in this study than in the Halpern and Hausman v,

A. Simulated Changes in Program Generosity and Leniency C.

Predicted Proportion Applying for SSDI Benefits

g

Probability of Acceptance Probability of Acceptance zDecreased by 10% Base Probability of Acceptance Increased by 10%

-

-.

u"

Absolute % Absolute YO Absolute % HProbability Change Change Probability Change Change Probability Change Change $

b;

Benefits decreased by 10% ,109 -.021 -16.4 ,119 -.011 -8.6 ,126 -.004 -3.1

R

Base benefit level ,121 -,009 -7.1 ,130 . . . .I38 +.008 +6.3 ro Benefits increased by 10% ,131 +.001 +.8 ,139 +..669 +7.0 .I44 +.014 +10.9

B. Waiting Period

Predicted Proportion Applying for SSDI Benefits 

Probability Absolute Change 
% Change

Base case Eliminate waiting period

C. Benefit Reduction Simulations, Selected Subsamples

Predicted Proportion Applying for SSDI Benefits

Base 10% Decline in Benefit Level Difference

Full sample (N = 2,703)

Disability: Low disability (N = 462) High disability? (N = 459)

Education: High school graduate (N = 1,098) .076 ,071 (-,005) Nongraduate (N = 1,605) ,207 ,193 (-,014)

Predicted ln(income,): High income? (N = 366) ,024 .022 (-,002) m Low income' (N = 376) ,272 ,251 (-,021) ;;;

'' At least 1 SD below the mean. 
t At least 1 SD above the mean. 

study when ignoring time and non-SSDI sources of beneficiary income.

As discussed earlier, the SSDI benefit component of total expected beneficiary income was calculated two different ways to check robust- ness. The simulation results presented above were based on predicted benefit levels accounting for the double selection into the application and award pools. The alternative method calculated the family benefit com- ponent directly using prior earnings records. The simulated application responsiveness to changes in benefits is slightly larger using the latter approach. In that case, applications were predicted to fall by 9% following a 10% reduction in benefits, compared with the 8.6% predicted decline using the former method.

While accounting for self-selection has a substantial impact on the results for changes in program leniency, it has a relatively small impact on the results for generosity. In this case, the consequences of failing to account for selection bias with respect to expected income and with respect to the probability of being ganted benefits tend to cancel each other. Heuristically, the potential applicant is concerned with a measure of expected benefits, which depends on both the benefit level and the probability of receiving the benefits. Failing to account for selection bias in the income equations leads to an overestimate of the effect of the benefit level on applications, but failing to account for selection bias in the eligibility equation leads to an underestimate of the sensitivity of appli- cations to the benefit level.

The waiting period appears to create a substantial disincentive to applications. Recall that applicants with residual work capacity following the onset of a health condition forego labor earnings for at least 5 months before benefits may be received. When the waiting time T is set to zero in the model, the predicted proportion of workers applying for benefits rises from 0.130 to 0.142, a 9.2% increase. This simulated effect is roughly comparable to that of increasing the benefit amount by 10%.

Frame B presents benefit simulation results for various subsamples of individuals: those with disability at least one standard deviation above or below the mean, high school graduates and nongraduates, and individuals with predicted labor income at least one standard deviation above or below the mean. As expected, workers with a high level of disability, nongraduates, and those with low predicted labor earnings are all more likely to apply for disability benefits. These groups are also the most responsive to changes in benefits levels, suggesting that the reduction in labor supply induced by the expansion of the disability system is primar- ily associated with groups with lowest labor market productivity.

Haveman and Wolfe (198417) find the smallest impact of the effects of the federal disability system on labor force participation among com- monly cited studies. While the labor force participation rate decreased by 4.5 (12) percentage points for males aged 45-54 (55-64) from 1968 to 1978, they estimate that only about 1.8 percentage points can be attrib- uted to the increase in benefits per recipient (43% in real dollars) over this period. Other researchers, such as Parsons (1980) and Slade (1984), have found much larger impacts. Leonard (1989) provides a critique of these and other studies.

I find that a 10% decline in the benefit level induces about a 1.1 percentage point decline in the proportion of applications among men aged 40-62, the same age group considered by Haveman and Wolfe. This corresponds to about a 0.11 percentage point change in applications for each 1% increase in the expected benefit level. This relationship is ap- proximately linear over the indicated range. Multiplying each worker's predicted change in probability of applying by his predicted probability of acceptance, each 1% increase in the expected benefit level is found to result in about a 0.059 percentage point increase in the number of bene- ficiaries.

Bound (1989) contends that no more than half the SSDI beneficiaries would be working if the program did not exist. He finds that fewer than 50% of all rejected applicants return to the labor force within several years. Assuming that the health status of beneficiaries is no better than that of rejected applicants, he proposes that 0.5 serve as an upper bound for the probability that a beneficiary would be working if the disability program were unavailable. In my data, and consistent with Bound's results, 51% of the rejected applicants had returned to work by the time the survey was taken.38 Using this upper bound and assuming that rejected applicants are as likely to work as if they had never applied, each 1% increase in benefits is predicted to induce a 0.030 percentage point decrease in labor force participation. Based on the 43% increase in real benefits from 1968 to 1978, I find the increased generosity of the disabil- ity program to be responsible for no more than about 1.3 percentage points of the decline in male labor force participation over this period. This estimate is even lower than the 1.8 percentage points predicted by Haveman and Wolfe. As with prior studies, it is difficult to have confi- dence that these estimates are reliable for large policy changes over time. These estimates overstate labor force responsiveness, however, to the extent that beneficiaries have less work capacity than rejected applicants.

In 1993, 3.73 million disabled workers received an average monthly payment of $642; in addition, 273,000 dependent spouses received an average monthly payment of $156, and 1.26 million dependent children received an average monthly payment of $173. Based on these numbers,

38 The average time between a rejected applicant's application date and the survey date was about 4.5 years.

the average family benefit per disabled recipient was $712 per month. The simulations suggest that a 10% reduction in the benefit level would lead to about a 4.3% decline in primary beneficiaries. The estimated direct cost savings associated with a 10% reduction in benefits is therefore $368 million per month, or $4.4 billion per year. The average worker's prob- ability of being accepted would need to decline by about 12% (7 per- centage points) to lead to the same estimated cost savings.

As discussed earlier, I examined the sensitivity of the simulation results by predicting application responses to changes in benefits using different specifications with respect to exclusions and control variables. One alter- native specification used measures in the Halpern and Hausman (1986) specifications to the extent possible given our different data sets. Another used the core set of measures in this study along with the Halpern- Hausman sets of additional identifying variables provided in Section IV. Other specifications used combinations of the restrictions discussed at the end of that section. The simulations using the preferred specification indicate that applications decline by about 8.6% following a 10% decline in the statutory family benefit level. Estimates from the specification that yielded the largest application response found about a 10.1% following the policy change, while the lowest estimate was a 7.8% decline in applications.39 In general, the simulation results were fairly insensitive to the choice of exclusion restrictions, and the qualitative findings in this study are robust to reasonable changes in specification.

VI. Conclusion

Estimates of the relationship between SSDI benefit levels and work decisions in the literature vary widely. This study finds significant work disincentive effects associated with the disability program. The results, however, suggest that the expansion in real SSDI benefit levels over the last several decades made a fairly modest contribution to the decline in male labor force participation rates. I estimate that the increase in real SSDI benefit levels between 1968 and 1978 was responsible for only about one-third of the decline in male labor force participation rates during that period.

Halpern and Hausman (1986) provide the only previous structural model of applications to the program. Compared with their results, policy simulations conducted in this study suggest less responsiveness to changes in benefit levels but substantially greater responses to changes in program leniency. The findings attest to the importance of considering the path of

39 The sensitivity of the simulations regarding program leniency is comparable, with slightly wider bounds.

expected future income flows in the application decision and of account- ing for self-selection of workers into the applicant pool.

Simulations in this article suggest that a 10% reduction in monthly benefits to all beneficiaries would reduce annual direct program outlays by about $4.4 billion a year, with about one-fourth of this cost savings attributable to fewer applications and awards. The same estimated cost savings would be achieved by reducing each worker's anticipated prob- ability of being accepted into the program by about 12%, or 7 percentage points. This article appears to be the first to estimate the magnitude of the barrier to SSDI applications resulting from the statutory waiting period. The estimates suggest that eliminating the waiting period would have about the same impact on applications as a 10% rise in the benefit level for all accepted applicants, a finding consistent with Parsons' (1991b) con- clusion that time delays in the disability awards process induce substantial self-screening.

Appendix A

Formal Identification Argument

To make the identification issue explicit, the application and award components of the model are written as

and

where X includes all the variables in the model (including XL, XG, Xy, etc.). Normalizing the variances of and EG to one since they cannot be identified, the probability of applying to SSDI and the probability of being accepted are given by

and

respectively, where F is the standard bivariate normal c.d.f. and p is the correlation coefficient between and E,. From equation (A3), we have

Substituting equation (A5) into equation (A4) then yields

Since F( . , -, -) is monotonic in the second argument, we can invert this f~~nction

for each p, holding constant the value of the first argument in equation (A6):

Thus,

and assuming E(XXr) is invertible,

Substituting equation (A9) into equation (A6), we have a nonlinear equation in p:

Pc = F[@-'(PA), X'E (XX')-'E{xF-'[@-'(P,), P, p]), p]. (A10)

By minimizing the distance between the left-hand side and the right-hand side of (A10) over p, we can identify p and hence PG from equation (A9).

Given identification of P,, thc coefficients in the application equation are identified up to scale as long as the probability of acceptance into SSDI, P = @(XPG), is not constant across X. To see this, multiply equation (A5) by the vector [XPX]' and take expectations to obtain

XX'

(A11)

Invertibility of the first matrix can be shown by pre- and postmultiplying this matrix by (a', b') and (a', b')', respectively, yielding E[(Xa

+ Pxb2)] = E[X(a + Pb)12. Thus, a sufficient condition for invert- ibility is that E[X(a + Pb)'] > O for any vectors a and b such that (a', b') is not a zero vector. Suppose there exists a'hnd b'such that X(a'+ Pb'" is a degenerate random variable at zero; that is, X(a" + Pb:?) = O almost surely. For invertible E(XX1), this implies a'$ + Pb'" = Oalmost surely, or a'$ = -Pb': almost surely. This is not possible if P varies with X with positive probability because the left-hand side variance is zero while the right-hand side variance is positive. Therefore, if E(XX1) is invertible and P is not constant across X, then the matrix is invertible and the coefficients in the application equation are identified.40 Without the structure implied by expected utility theory, and ignoring the other structure in equation (10) implied by the discounted utility model, iden- tification of the application coefficients would require that a measure relevant to PG(X) and a measure relevant to income flows does not affect PA(X). Specific exclusion restrictions to aid with identification are dis- cussed in the main text.

To examine identification of the income equation coefficients, consider the general specification

where we only observe Y for a particular subsample in the data due to selection. Conditional on observing Y'", we have either

depending on whether selection is on A only or on both A and G, where v, has mean zero conditional on the relevant subsample. The particular form for the function g is provided by Heckman (1976), and the partic- ular form for h is provided in appendix B.

Following Robinson (1988) and Ahn and Powell (1993), P can be identified in the first case for an arbitrary unknown smooth function g if

is nonsingular, observing from equation (A13) that

Similarly, we can identify P in the second case for an unknown smooth function h if

is nonsingular. Thus, we can apply least-squares techniques over the relevant subsample to obtain consistent estimates, assuming the nonsin- gularity condition holds. To satisfy the nonsingularity condition, the vector X must not be jointly degenerate, which would be the case if

40 Note that 6 is identified in eq. (10) because y, and y,ln 6, are identified, and Gg is identified because y, and y,ln Gg are identified.

PA(X) = PA(Xd) for some nonzero vector d.41 Thus, without an exclu- sion restriction, identification depends on the nonlinearity in the selection equation. Based on the expected utility framework, however, we have the natural exclusion P that enters PA but not the income equation, and there is wide variation in P across observed individual attributes.

For equation (A14) where selection is based on both A and G, identification is aided by a variable affecting PA(X) that does not directly affect beneficiary income, such as P,and a variable affecting PG(X) that does not affect beneficiary income. As noted in the main text, beneficiary income is assumed to be observed for all respondents in one version of the model based on direct calculations of their PIAs. Then there is no identification issue, though there is an endogeneity issue if work prefer- ences are correlated with prior income levels.

Appendix B

Derivation of Equation (A14)

Let the disturbances in the application, award, and relevant income equation be given by vq, VG, and E, respectively. Since (vA, VG, E) is trivariate normally distributed with zero means, E(&IvA, v G) = bZvA

+ b2vG, where (bl, b,)' = v-l[crAE, aGEI1

and V is the variance matrix of (vA, vG)' By the law of iterated expectations,

The relevant conditional expectations are obtained using Johnson and Kotz (1974, p. 113):

411n that case, E{(X -E[X(P,(X)])(X -E[XIP,(X)])')d = E{[X -E(XIX'~)][X-E(XIX1d)]'Jd= E{[X-E(XIX1d)][X'd-E(X1dlX'd)]') = 0, so the matrix is singular.

and

Note that since bl, b.,, and uAGare identified, we can also identify the correlations CAE = bl + uAGb2and uGE= b2 f uAGbl.

Appendix C Likelihood Gradient

Denotingf the standard bivariate normal density function and defining

A? = A1 + @(A3)A2,

the gradient for the likelihood function is computed using and

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