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Latent Work Disability and Reporting Bias.


A measure of "true" disability is constructed as a continuous index of unobserved work limitation using information from the Health and Retirement Study. Estimates from a simultaneous model of work participation, disability, and income flows suggest that nonworkers tend to substantially overreport limitation, with overreporting most prevalent among nonworking women, high school dropouts, nonwhites, and former blue collar workers. Former white collar workers are found unlikely to overreport limitation. Use of a "biased" disability measure in the model leads to an upward-biased estimate of the effect of limitation on nonwork and to a downward-biased estimate of the effect of income.

I. Introduction

Work capacity is an important determinant of labor force behavior, including decisions about when to retire and about whether to apply for disability-related public transfers. [1] Biased survey responses to questions about work limitations, however, may seriously compromise researchers' efforts to accurately measure disability or its role in determining labor force participation decisions. The appropriate use of health measures in participation models has particular relevance for policy since biases in such measures may spill over into inferences about the effects of economic factors, such as program benefit levels, on labor force attachment. Estimates of the sensitivity of work behavior to changes in the design of the Social Security program, for example, may depend on the measure of health used in the analysis.

It is often desirable to have available a summary measure of work limitation (disability), especially given the potentially high computational costs of employing numerous health measures in econometric labor supply models. One purpose of this study is to provide researchers a simple method for constructing a disability index purged of reporting bias related to the work outcome. [2] Another purpose is to measure the degrees to which various types of respondents may overreport disability. Finally, the analysis examines empirically the extent to which overreporting affects inferences about the roles of disability and financial factors on participation outcomes.

Most studies that have included a disability measure to help explain work decisions have employed individuals' self-evaluations of work limitations. [3] A number of writers, however, have expressed concern that self-reports of work limitations may be influenced by work preferences or labor market success (see, for example, Zabalza, Pissarides, and Barton 1980; Myers 1982; Parsons 1982; Chirikos and Nestel 1984; Bazzoli 1985; Bound 1991; Bound, Schoenbaum, and Waidmann 1995; Bound and Burkhauser, forthcoming). Much of the literature suggests that we should be especially skeptical about nonworkers' responses to questions about disability since certain incentives may lead them to systematically overreport the extent to which a health condition limits work capacity. Health-related work limitation may be one of the few socially acceptable reasons for men younger than normal retirement age to be out of the labor force. [4] Moreover, work limitation is fundamentally tied to eligibility for certain types of public t ransfers to the nonworking, such as Social Security Disability Insurance (SSDI) benefits.

Some studies, including Nagi (1979), Stern (1989), and Dwyer and Mitchell (1998) have concluded that such self-reports are reliable. [5] Taking all self-reports of work limitation as accurate, Benitez-Silva et al. (1998) define a respondent in the HRS as "truly disabled" if and only if the respondent classifies himself as unable to work due to a health condition. They then use this classification for coding Type I and Type II errors in the federal adjudication process for disability benefits. Bound and Burkhauser (forthcoming), however, criticize this definition based on the likelihood that "those who apply for SSDI and especially those who are awarded benefits tend to exaggerate the extent of their work limitations (relative to those who do not apply)" (p. 15). In other recent work, O'Donnell (1998) develops a work participation and limitation model that allows for the possibility that a health condition completely precludes the possibility of work instead of merely altering expected income flows and tastes for leisure. Based on his estimates, he rejects the hypothesis that self-reported work capacity is reliable. Kerkhofs and Lindeboom (1995) conclude that reporting errors depend systematically on labor market status.

The appropriateness of various types of health indicators in behavioral models has been described by Anderson and Burkhauser (1984) as "the major unsettled issue in the empirical literature on the labor supply of older workers." Although little has been resolved, Bound (1991) and Bound et al. (1995) have since provided careful analyses of the main issues related to the endogeneity of health measures. They distinguish between two types of biases associated with self-reports of work limitation. First, they show that if nonworkers are more likely to identify themselves as work-limited, conditioning on actual disability, then the estimated effect of work limitation on labor force withdrawal will tend to be upward-biased under plausible assumptions. The influences of other factors may be partially masked, so the effects of financial measures, for example, may tend to be underestimated. An errors-in-variables bias is likely to work in the opposite direction; the estimated impact of disability on nonwork will tend to be downward-biased to the extent that work limitation is imperfectly measured.

Many researchers have decided to completely discard self-reports of work limitation in favor of more "objective" measures of health status, such as sick hours in a year (Burkhauser 1979) or subsequent mortality experience (Parsons 1980, 1982; Anderson and Burkhauser 1985). A number of data sets, including the Health and Retirement Study (HRS) used in this research, also contain information about respondents' abilities to successfully engage in various activities such as jogging, climbing stairs, or lifting objects. [6]

Unfortunately, these more objective responses may have little relation to the question at issue: how effectively can the respondent actually work? Few workers are required to jog a mile or climb stairs to adequately perform their prescribed tasks. Moreover, nonworkers may exaggerate specific functional limitations for the same reasons they might exaggerate their difficulties in working. Haveman and Wolfe (1984) criticize the use of mortality indices used by Parsons as "weak and arbitrary" proxies for disability status. Back ailments, for example, often contribute to disability but seldom lead to death. [7] The usefulness of "sick hours" as a proxy for work capability is suspect as well. Because objective proxies for disability may not be good measures of work capacity, errors-in-variables biases associated with these proxies may outweigh biases associated with self-reported limitation measures.

Bound (1991) concludes that "even a moderate amount of measurement error in such proxies can easily lead to the conclusion that the self-reported measure will give a more accurate picture of the impact of health and financial incentives on labor supply" and further suggests that "the search for 'objective' or exogenous indicators may have been a bit misplaced." He further notes that while the possibility of using more objective measures to instrument the self-reported measures has "much appeal," this approach does not in itself solve the problem of endogenous self-reports of limitation. [8] As discussed below, while this study uses health conditions to instrument disability, it does so in a framework that accounts for reporting bias of limitation associated with the work outcome. [9]

Self-reported measures of work limitation presumably provide valuable information about work capacity that should not be completely discarded. Consistent with this view, Stem (1989) uses self-reported work limitation in an analysis of the effect of disability on work behavior, explicitly accounting for the potential endogeneity of reported limitation. His approach, which uses data from the 1979 cohort of the Health Interview Survey (HIS79) and the 1978 Survey of Disability and Work (SDW), treats health conditions as exogenous instruments in a simultaneous model of work limitation and labor force participation. Stern models reported disability as a function of "true" disability and the respondent's propensity to work. The idea is that individuals who attach lowest value to work exaggerate disability the most.

Although Stern's analysis is useful for assessing the endogeneity of self-reported limitation, his approach (discussed in Section III) places a high degree of structure on the form of misreporting by nonworkers. In particular, overreporting in his model is linearly related to the value of work and cannot depend directly on other attributes like education or occupation. Furthermore, he does not model the effects of income flows on the work decision, so he could not assess the extent to which biased limitation reports lead to biased inferences about the role of financial factors on participation. [10] Additionally, the 1970s data used in his study may not closely reflect currently existing relationships between health status and work limitation.

Consistent with Stern's approach, this analysis treats an individual's level of true disability as an unobserved phenomenon related to physician-diagnosed health conditions and socioeconomic factors that may influence the degree to which such health conditions affect work capacity. However, the model does not impose structure on the relationship between nonworkers' misreported and true disability. Instead, potential reporting bias is treated as a censored sample problem. Responses to questions about work limitation are taken to be reliable on average for workers but of unknown quality for nonworkers. This assumption that workers' limitation responses are accurate on average constitutes a form of "outside information" imposed on the model in the context of Bound's (1991) identification discussion. [11]

With this approach, a particular nonworker may or may not overreport disability, and the degree of overreporting may depend on factors other than the desire to work. To the extent that Stem's imposed structure is correct, however, a primary advantage of his approach is that he exploits limitation data on both workers and nonworkers. An issue in both approaches is that judgements about limitations may not be completely comparable, even among similar individuals (for example, if they have difficulty interpreting the limitation questions or have differing perspectives about where critical thresholds lie in defining various degrees of limitation).

Following Stem (1989), Bound et al. (1995), Dwyer and Mitchell (1998), and O'Donnell (1998) among others, this study uses physician-diagnosed health conditions as instruments in a work limitation specification. Questions about specific conditions are often considered more concrete and less subjective than questions about work capacity. Appealing to historical and other evidence about reporting patterns, Bound et al. (1995) suggest that it may be reasonable to treat self-reports of chronic health conditions as exogenous. [12]

Nevertheless, there are still reasons to be skeptical about the reliability of reported conditions. Individuals wishing to withdraw from the labor market, perhaps to apply for disability benefits, may be more likely to see a doctor and have a preexisting health condition diagnosed. Similarly, labor force participants are more likely to have health insurance which may in turn lead to more contacts with health practitioners. Moreover, the specific conditions could be endogenous if they are correlated with past participation (which is correlated with current participation). [13] Finally, the work decision may itself affect health status; for example, stress or unfavorable working conditions among workers or inactivity among nonworkers may lead to a deterioration in health (Sickles and Taubman 1986; Stem 1989). Pointing out difficulties in interpreting Butler et al.'s (1987) exogeneity test results for an arthritis measure, however, Bound et al. (1995) find it "hard to imagine how one could directly test" for th e endogeneity of the health measures in the Health Retirement Study. For want of obviously superior indicators, specific conditions (and in some cases specific activity limitations) will be used as instruments in this analysis.

The next section discusses the data used to generate the disability index, followed by the development of the work and limitation model in Section III. A disability index can be easily constructed by others using coefficient estimates presented in Section IV combined with demographic information available in many widely used data sets. Use of this measure requires information about the existence of health conditions, but it does not require information about work status or about limitation itself. Section V assesses the degrees to which various groups of nonworkers may overreport limitation. It also examines how reporting bias may affect inferences about the roles of disability and income on participation decisions. Concluding comments are provided in Section VI.

II. Data

The data used in this study come from the first wave of the Health and Retirement Study, which consists of a national sample of individuals born between 1931 and 1941 and their spouses or partners. In total, 12,652 adults submitted to detailed questioning about their labor force experience, health conditions, work limitations, participation in government transfer programs, sources of income and wealth, family structure, and other personal characteristics. This analysis consists of 5,205 men and 5,623 women between the ages of 50 and 64. [14] Extensive information on specific physician-diagnosed diseases and conditions, along with information on self-reported limitations, makes the HRS ideally suited to this study. [15]

Of the 5,205 men in this analysis, 4,041 (78 percent) are labeled "workers," defined as those who identify themselves as currently working, temporarily laid off, unemployed but looking for work, or on temporary sick or other leave. The corresponding number of female workers is 3,451 (61 percent). Unemployed workers searching for work are classified in the work group in part to best follow standard definitions of labor force participation and in part so that the work/nonwork distinction hinges on whether the respondent has substantial labor force attachment. [16]

To construct an indicator of work disability, workers and nonworkers are categorized into three groups based on their responses to questions about health limitations related to work and nonwork activities. Let the ordered variable L = 0 indicate that the respondent reports not being limited in any major activity by a health condition, let L = 1 indicate that the individual reports that a health condition limits some type of nonwork activity (such as the ability to do work in or around the house) but not paid work, and let L = 2 indicate that the individual reports that a health condition limits the kind or amount of paid work that can be performed. [17] This measure is intended to be an ordered indicator of work limitation but not necessarily an ordered indicator of health status or general limitation. Respondents for whom L = 1 claim not to be limited in their ability to perform paid work, but they are presumably closer to the threshold of being work-limited than respondents who claim to have no limitation at all.

For comparison purposes, a binary work limitation measure [L.sup.b] is also constructed for this study. This indicator is set equal to 1 if L = 2 and is set equal to 0 otherwise--that it, it distinguishes between those claiming a work limitation and those not claiming a work limitation, while ignoring information about limitations related only to nonwork activities. The trichotomous L indicator is employed in the primary analysis because it provides more information about work limitation than its binary counterpart and may thus provide greater efficiency in the parameter estimates.

As shown in Table 1, nonworkers were slightly less likely than workers to report a general limitation that affects an activity such as housework or yard work but not paid work (4.0 percent of male nonworkers and 6.6 percent of female nonworkers compared with 8.2 percent of male workers and 9.7 percent of female workers). At 61.3 percent compared with 10.7 percent, however, male nonworkers were nearly six times more likely than their working counterparts to report that a health condition limits their ability to perform paid work. Female nonworkers were nearly four times as likely as female workers to report that a health problem specifically limits paid work. Although nonworkers undoubtedly tend to be more disabled than workers, the large differences in these responses between workers and nonworkers may raise suspicions that nonworkers tend to have lower thresholds for reporting that a particular health problem limits paid work.

III. A Model of Disability and Work

The model consists of a work limitation equation, a work participation equation, and income equations associated with the work and nonwork options. Labor force participation depends on limitation and expected income flows, and income flows depend on limitation. For simplicity, individual preferences over income and labor force participation are approximated in quasi-linear form as

(1) [[U.sup.*].sub.i] = [gamma] ln [[Y.sup.*].sub.i] + [[zeta].sub.i] [W.sub.i],

where [Y.sup.*] represents income and W is an indicator for work status equal to 1 if the individual participates in the labor force and equal to 0 otherwise. The coefficient on income [gamma] is constrained to be constant across individuals, but [[zeta].sub.i] is allowed to vary across personal characteristics and job attributes according to

(2) [[zeta].sub.i] = [alpha][[L.sup.*].sub.i] + [Z.sub.i][delta] - [[epsilon].sub.wi],

where [L.sup.*] [epsilon] (-[infinity], [infinity] is an unobserved continuous measure of "true" limitation discussed below, Z is a set of observed characteristics affecting tastes for work, and [[epsilon].sub.w] captures other unobserved determinants of labor force preferences. An individual's propensity to work is then defined as the utility difference between working and not working:

(3) [[W.sup.*].sub.i] = [gamma](ln [[Y.sup.*].sub.wi] - ln [[Y.sup.*]]) + [alpha][[L.sup.*].sub.i] + [Z.sub.i][delta] - [[epsilon].sub.wi],

denoting [[Y.sup.*].sub.w] expected income if working and [[Y.sup.*].sub.n] expected income if not working. An individual is assumed to participate in the labor force if and only if [W.sup.*] [greater than] 0. [18]

Unobserved work limitation is specified as

(4) [[L.sup.*].sub.i] = [X.sub.Li][[beta].sub.L] - [[epsilon].sub.Li],

where [X.sub.L] is a set of observed measures that affect limitation including specific health conditions, behavioral indicators (such as smoking and heavy drinking), type of occupation, and demographic characteristics. The disturbance [[eqsilon].sub.L] captures unobserved influences on limitation such as the severity of a health condition, unobserved job requirements, and personal motivation. [19] Definitions of the variables used in this study and descriptive statistics are provided in Tables 2 and 3, respectively.

Although work limitation is unobserved, discrete indicators are available. Accurate responses to questions regarding limitations are assumed to follow the sorting rule:

(5) [L.sub.i] = { 0 if [[L.sup.*].sub.i] [less than or equal to] 0

1 if 0 [less than] [[L.sup.*].sub.i] [less than or equal to] [micro],

2 if [[L.sup.*].sub.i] [greater than] [micro]

where [micro] an unknown threshold parameter to be estimated (the first threshold is normalized to zero without loss of generality). The rule for the dichotomous analog is that [L.sup.b] = 1 if [L.sup.*] [greater than] 0 and [L.sub.b] = 0 otherwise.

The income values are censored; income if working is observed only for the subsample of workers, while income if not working is observed only for the subsample of nonworkers. These values are specified in reduced-form as

(6) ln [[Y.sup.*]] = [X.sub.yi][[beta].sub.1] + [[epsilon].sub.1i]

(7) ln [[Y.sup.*].sub.0i] = [X.sub.yi][[beta].sub.0] + [[epsilon].sub.0i],

where [X.sub.y] represents observed factors affecting expected income, including all the limitation determinants in [X.sub.L]. The disturbances are allowed to be correlated with each other and with the disturbances in the work and limitation equations. Substituting Equations 6 and 7 into Equation 3, the value of work can be rewritten as

(8) [[W.sup.*].sub.i] = [alpha]([X.sub.Li][[beta].sub.L]) - [gamma][X.sub.Yi]([[beta].sub.1] - [[beta].sub.0]) + [Z.sub.i][delta] - [v.sub.i],

with v = [[epsilon].sub.w] + [alpha][[epsilon].sub.L] - [gamma]([[epsilon].sub.1] - [[epsilon].sub.0]).

Equation 4 governs the true limitation process for workers and nonworkers alike, but I suppose that nonworkers will not necessarily follow the rule given by Equation 5--they may respond that they are work-limited even if [L.sup.*] [less than or equal to] [micro]. Although some workers may also provide inaccurate representations of their work limitations as noted by Myers (1982) and Stern (1989), workers do not systematically face the incentives emphasized in the literature to misrepresent work capacity to a survey-taker. Econometrically, the limitation indicator L is taken to be observed reliably only for the subsample of respondents who were working at the time the limitation questions were asked. Reported limitation is thus given by:

(9) [L.sub.Ri] = {[L.sub.i] if [W.sub.i] = 1

missing if [W.sub.i] = 0

The dependent limit variable in Equation 4 is thus further "limited" in that we observe only a categorical indicator instead of true continuous disability, and even this categorical indicator is unobserved for nonworkers. [20] With this approach, consistent coefficient estimates can be obtained for both the work and limitation equations regardless of whether nonworkers overreport disability. Estimates will be inefficient if nonworkers in fact offer reliable self-reports and this information is not exploited, but much of the literature, and results in this study, suggest that they do not.

Equations 4-9 comprise the model to be estimated. It is important to allow the disturbances in these equations to be correlated since the subsample of workers is self-selected based in part on unobserved attributes, and unobserved influences on work limitation are likely to also affect the participation decision. Clearly, even if many nonworkers overreport their work limitation, they may still be more limited than observationally identical individuals who have remained in the labor force. For example, labor force participation is likely correlated with unobserved severity of the health conditions.

Conditional on the explanatory variables, ([[epsilon].sub.L], v, [[epsilon].sub.1], [[epsilon].sub.0]) is assumed to have a joint normal distribution with covariance matrix


and to be independent across respondents. Given the presence of a constant term in Equations 4 and 6-8, it can be assumed without loss of generality that these disturbances have zero conditional means. The variances of [[eplison].sub.L] and v have been normalized to one since they cannot be identified.

Estimating the parameters in the limitation equation using single-equation techniques (such as ordered probit) over the subsample of workers would lead to an inconsistent estimate of [[beta].sub.L] if [[rho].sub.Lv] is nonzero. Consistent estimates can nevertheless be obtained by estimating limitation and work simultaneously, accounting for self-selection in the labor market and for the censored nature of the limitation indicator. Equation 8 can be written in reduced form as

(10) [[W.sup.*].sub.i] = [X.sub.i][pi] - [v.sub.i],

where X includes all the measures in [X.sub.L], Z, and [X.sub.y]. Equations 4, 5, 9, and 10, along with the distributional assumptions, constitute an ordered probit model with sample election. When the limitation dependent variable is dichotomous, this model is bivariate probit with sample selection.

To instead obtain consistent estimates of the structural coefficients in the model (which are necessary to assess the impact of work limitation and income flows on participation), the parameters in Equations 4-9 are estimated by maximum likelihood. The appropriate likelihood function is derived as:

L = [[[pi].sub.W=1].sub.L=2] [[omega].sub.12] [[[pi].sub.W=1].sub.L=1] [[omega].sub.11] [[[pi].sub.W=1].sub.L=0] [[omega].sub.10] [[pi].sub.W=0] [[Omega].sub.0]

with the [omega] terms provided in Appendix 1. After obtaining a consistent estimate for [[beta].sub.L], either from the reduced form or structural estimation, a "true" index of disability can be constructed for all respondents as the fitted values for the dependent [L.sup.*] variable.

Identification of the participation equation requires that [X.sub.L] in the limitation equation and [X.sub.y] in the income equations contain at least one measure not directly relevant to participation. Given sample separation (an indicator for work status is available) and the distributional assumptions, the income coefficients [[beta].sub.l] and [[beta].sub.0] are identified without further restrictions. All the coefficients in the work limitation equation are identified given the normalization that the variance of [[epsilon].sub.L] is one. [21] To further aid identification, however, an age spline measure at age 61 and a regional unemployment rate measure are included only in the participation equation. The age spline measure captures the discontinuity associated with the availability of early Social Security retirement benefits at age 62; there is no obvious reason why disability would be discontinuous at this age. It also seems reasonable to exclude the unemployment rate measure from the limitation equa tion. [22]

Indicators for body mass, smoking, and heavy drinking (described in the next section) included as determinants of limitation are excluded from the participation equation. Following Stem (1989), the specific health conditions are also excluded from this equation. In contrast to that study, however, a measure of pain associated the conditions is available and is included in both the limitation and participation equations. Region variables in the income specifications are excluded from the participation equation following a number of labor force participation studies (for example, Halpern and Hausman 1986). The unemployment rate measure, however, captures regional differences in employment opportunities. The correlation coefficients [[rho].sub.L0] and [[rho].sub.10] are not identified.

To compare the approach in this article with Stem's (1989) approach, we can write the propensity to report disability as

(11) [[L.sup.*].sub.R] = [L.sup.*] + [[omega].sub.R],

where [[epsilon].sub.R] is a reporting error. Given the distributional assumptions in the model, if [[epsilon].sub.R] were uncorrelated with [L.sup.*], then after substituting in the values of [L.sup.*] from Equation 4 it would be possible to generate consistent predictions of [[L.sup.*].sub.R] (as fitted values [X.sub.L][[beta].sub.L] to serve as consistent predictions for true disability. The concern, however, is that [[epsilon].sub.R] is correlated with [L.sup.*] (or with the observed determinants of true limitation, [X.sub.L]). This would be the case, for example, if nonworkers systematically have more serious health problems than workers and also systematically overreport disability relative to workers.

Stem assumes that the reporting error in Equation 11 can be written as

(12) [[epsilon].sub.R] = [phi][W.sup.*] + [[epsilon].sub.0],

with [phi] expected to be negative and [[epsilon].sub.0] assumed to be orthogonal to [L.sup.*] and [W.sup.*]. Then reported limitation is equal to true limitation on average plus a value that varies inversely with the propensity to work:

(13) [[L.sup.*].sub.R] = [L.sup.*] + [phi][W.sup.*] + [[epsilon].sub.0].

Consistent predictions of [[L.sup.*].sub.R], uncorrelated with [[epsilon].sub.0], can then be obtained after consistently predicting the values of [W.sup.*] (somewhat similar to an inverse Mill's ratio correction). This specification, however, implicitly and implausibly requires the degree of overreporting to be a monotonic function of true disability. In particular, assuming [alpha] and [phi] are negative, those with the most debilitating health conditions are specified to exaggerate their inability to work the most since the value of work declines with true disability and overreporting declines with the value of work. It also does not seem realistic to assume that all nonworkers exaggerate disability at all, let alone by an amount determined solely by the value of working. This structure also implies that workers systematically underreport work limitation. Although it is possible that some workers underreport work limitations, there is no apparent reason to believe that the degree of this underreporting wou ld be systematic and monotonically increasing in the worker's ability to perform required tasks on the job. The present framework does not place any restrictions on the form of overreporting by nonworkers; instead, [L.sup.*] and [[epsilon].sub.R] are assumed to be uncorrelated for workers without specifying the structure of potential overreporting of limitation by nonworkers.

IV. Estimation results

Parameter estimates for the reduced-form model are presented in Table 4, by gender, using the ordinal measure of work limitation as the dependent limitation variable. [23] The specific health conditions are ranked in the order in which they influence limitation based on the magnitudes of the estimated coefficients. The largest impact for men comes from having poor sight, [24] followed by heart problems, cancer, having had a stroke, problems with legs or feet, lung problems (other than asthma), back problems, and diabetes. The conditions having the least impact on limitation (in order of ascending impact) are poor hearing, kidney problems, stomach or ulcer problems, hypertension, asthma, arthritis/rheumatism, and emotional/psychological conditions. All of the conditions have a significantly positive individual effect on limitation (at the 10 percent level) except poor hearing and kidney problems. As seen in the right-hand side of Table 4, the pattern of the relative impacts of conditions on limitation are dif ferent for women. Heart problems have the largest effect for this group, followed by back problems, emotional/psychological problems, arthritis/rheumatism, and stroke. Surprisingly, the estimated effects of poor sight and cancer are not statistically significant. Similar to the men, the smallest effects on work limitation come from stomach or ulcer problems, hypertension, diabetes, kidney problems, and poor hearing. For both men and women, most of these conditions have a significant negative influence on the work decision. Interactions between the number of reported conditions and years of schooling or white collar status do not have significant impacts on limitation. [25] An index of a respondent's usual degree of pain has a highly significant impact on work limitation and participation for both men and women.

Most of the other variables included in the limit equations have the anticipated signs but are not individually significant at the 10 percent level (though many are nearly significant, and various natural tests of joint significance cannot be rejected). Information on respondents' height and weight in the HRS allow the construction of a body mass index (BMI). Fahey, Insel, and Roth (1997) define ideal body mass as 20-25 kilograms per meter squared and label the 25-30 range as "grade 1 obesity," the 30-40 range as "grade 2 obesity," and the 40+ range as "grade 3 obesity." Each of the coefficients on indicators for BMI values outside the ideal range are positive for both men and women (collapsing the 30-40 and 40 + ranges into one), although the only individually significant effect is for women with values exceeding 30. The potential for reverse causality exists, however, since body mass may be high or low in part due to a health problem. For both men and women, having low body mass significantly increases the probability of not participating in the labor force. [26]

Also included in the specifications are variables intended to capture the effects of personal behavior on work limitation. Drinking more than two alcoholic drinks per day or being a smoker (defined as smoking more than 100 cigarettes during the respondent's lifetime) were also included in the specification, but the positive coefficients on these measures are insignificant for both men and women. Light exercise (defined as exercising once or twice a week) and heavy exercise (three or more times per week) both have negative estimated effects on work limitation, though their impact is jointly significant only for men. The potential for endogeneity again exists since limitation can affect the desire and ability to regularly exercise. For men, current or previous exposure to health hazards (such as toxic chemicals) in a job lasting more than a year contributes positively to work limitation. Nonwhite females are found significantly less likely to be work-limited conditional on the set of health conditions and othe r measures. [27]

The estimated correlation coefficient between limitation and work is negative for both men and women as expected, indicating that unobserved factors influencing disability level are negatively correlated with the probability of working. Although these correlation coefficients are not significant, the fairly large magnitude for men (-0.43) suggests that estimating the limitation equation as ordered probit over the subsample of workers without controlling for selection could substantially bias the coefficient estimates.

An index of "true" work limitation L can be constructed (separately for men and women) as the fitted values X[[beta].sub.L] using the coefficient estimates from the limitation equation. Section V will compare this index to an analogous measure, L, constructed using estimates (not shown) based on a model that includes the limitation self-reports from both the workers and nonworkers in the estimation. This alternative index does not account for possible overreporting of limitation by nonworkers, and as such will be referred to as a "biased" measure for ease of exposition. [28]

For comparison purposes, estimates for alternative reduced fonn models are shown in Appendix 2. In Table A1, the model is reestimated with the ordered L dependent variable replaced with the binary indicator Lb (defined in Section II). The pattern of coefficients for men is similar for these two measures, though the magnitudes of the conditions coefficients decline and several of the estimated effects become insignificant. In contrast, there is a substantial re-ranking of the impacts of specific conditions on limitation for women. For example, poor sight now makes the largest contribution to work limitation (previously eighth) and poor hearing moves up to second from eleventh.

Table A2 provides results for the same model when 17 specific activity limitations are also included as determinants of work limitation. [29] For men, activity limitations having a significantly positive impact on work limitation include difficulty in climbing stairs, jogging a mile, lifting ten pounds, pulling/pushing large objects, and reaching or raising arms above the shoulders. [30] The list is similar for women: difficulty jogging a mile, lifting ten pounds, pulling/pushing large objects, and stooping or kneeling. The ranking of the impacts of specific conditions on work limitation remains fairly robust for men when the activity limitations are included. Among other differences for women, the impact of arthritis on work limitation rises from eighth to second (compared with Table Al), the effect of poor sight falls from first to eleventh, and the effect of having a stroke falls from third to eighth. [31]

V. Comparison of the Disability Measures

Because disability is inherently unobservable, formally demonstrating the superiority of one disability measure over another in a participation model does not seem possible. Although providing a specification test to determine which type of disability measure most successfully helps predict participation decisions would be straightforward, the results of such a test would not be useful. Measures corrupted by exaggerated self-reports of limitation by nonworkers might make the largest contributions to the likelihood function because the self-reports are endogenous to the work decision. Suppose, for example, that nearly all nonworkers report that they are disabled regardless of whether they are work-limited or not. A disability measure based on such responses would be a strong predictor of work status because regressing labor force participation on this measure would be almost tantamount to regressing work status on nonwork status.

We can nevertheless compare the disability measures and consider various implications of using a biased measure when predicting participation outcomes. For the ordered work limitation case, let [P.sub.i] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [phi]([L.sub.i] - [micro]) denote the probability across individuals. Similarly, let P' denote the analogous average predicted probability based on the biased limitation measure L[minutes] discussed in the previous section. [32]

Table 5 presents evidence about the degree of overreporting of work limitation among nonworkers by examining differences between P and P'. The proportion of male nonworkers predicted to be work-limited based on the true disability measure is 0.314, a proportion that rises to 0.340 based on the biased measure. This difference represents 2.8 standard deviations, which is marginally significant at the ten percent level. The difference is considerably higher for women at 6.2 standard deviations, marginally significant at the 1 percent level. For both men and women, overreporting of disability is found to be most prevalent among nonworking high school dropouts, nonwhites, and those who worked in blue collar occupations. Former white collar workers are predicted to slightly underreport work limitation, but the difference is not significant for either men or women. Age has little effect on overreporting in the sample range of 50 to 64. Least squares estimates of the determinants of overreporting among nonwo rkers are presented in Table 6, where the dependent variable is P[munites] - P. The pattern of coefficients is the same for men and women, with estimated overreporting positively associated with being younger, less educated, nonwhite, unmarried, and with former work in a blue collar occupation (the last effect being insignificant for women).

Table 7 presents overreporting estimates for alternative models. Numbers in the top rows for ordered limitation are taken directly from Table 5. The next two sets of estimates are based on results from the same model estimated over only either high school graduates or nongraduates, with findings consistent with earlier results regarding schooling differences. Next, results are provided when the bivariate work limitation measure Lb is used in place of the ordered measure in the estimation. For this case, the index L is constructed using the coefficient estimates in Table Al; the variant of the model used to generate the biased index L' is simply the common bivariate probit model. [33] There is little difference compared with the top row for women, but the estimated degree of overreporting among men rises substantially. Adding the activity limitations to the bivariate specification in the next row has little effect on the estimated magnitude of overreporting for men, but the effect rises substantially for wome n. [34]

Two issues of estimation bias have drawn particular attention in the literature. First, biased disability measures lead to biased inferences about the effect of limitation on labor force participation. Second, such biases may spill over into inferences about the effects of financial variables on participation. The estimated impact of a change in available public transfers on work behavior, for example, may be biased if a limitation measure corrupted by reporting bias is employed in the estimation.

The implications of using a biased disability measure in the work specification are investigated after estimating the structural parameters of the model. Estimation results are provided in Table 8. For both men and women, the estimated effects of the health conditions on limitation are quite similar to their respective reduced form counterparts in Table 4. In particular, the magnitudes and rankings of the specific conditions impacts on limitation are about the same in the two cases. As expected, work limitation has a negative and significant effect on participation for both men and women, and the expected percentage income gain associated with working has a significantly positive effect. [35]

Inferences about the roles of income and disability on participation are examined in Table 9 based on simulated changes in the expected income and disability levels. For the base case in Model A, each respondent's predicted probability of not working was recalculated using the coefficient estimates in Table 8 after increasing the income replacement rate (ratio of predicted income if not working to predicted income if working) by 10 percent. The predicted proportion of male nonworkers rises 3.62 percent (from .224) following the income change. In a similar simulation, the predicted proportion of male nonworkers rises by 64.4 percent when each respondent's predicted disability value is increased by one standard deviation. Simulated female responses to changes in income were similar, though women were only about half as responsive to changes in the disability level. Analogous simulations for Model B were based on the alternative set of 'biased' coefficients, which included all respondents' limitation self-repor ts in the estimation. In this case, the predicted proportion of nonworking men rises only 2.76 percent following the income change (23.9 percent less than the change in Model A), and it rises 75.4 percent following the change disability index (17.2 percent more than in Model A). Results for women are comparable. Findings for comparisons based on the binary [L.sup.b] dependent limitation measures were similar to those in Table 9, with somewhat larger differences between Model A and Model B for this group. Results were also similar when activity limitations were included in the specification.

These findings are consistent with (if not as pronounced as) Gordon and Blinder's (1980) warning that the impact of their self-reported disability measure on early retirement was too huge to be believed. The results also support Anderson and Burkhauser's (1984) and Bound's (1991) conclusions that the effects of financial factors on labor force participation will likely be understated when relying on a typical self-reported limitation measure. [36] The finding that overreporting has a substantial impact on the measured effect of limitation on work contrasts with a conclusion in Stern (1989). Because participation does not depend on income in Stern's model, it is not possible to compare results regarding financial incentives.

In estimating the effects of policy on labor force participation, it might be wondered whether using no disability measure is preferable to using a biased one. For Model C in Table 9, no disability index is used in the estimation. In this case, a simulated 10 percent rise in the replacement rate leads to only about a 1.8 percent increase in nonparticipation, about half the change predicted in Model A. The result is again similar for women, although the percentage difference compared with Model A is smaller. For both men and women, the estimated downward bias associated with using no disability measure is about twice that associated with using the biased measure. Although there is no econometric reason that using a poor proxy for disability should be preferred to excluding the measure altogether, it appears in this study that relying on the biased measure is preferable to using none at all. [37] A contrasting result was found in Kreider (forthcoming) when the analysis in this article was tailored to applicati ons for federal disability benefits. In that study, inferences about the sensitivity of applications to changes in eligibility standards were found to be more accurate when omitting disability as a control measure than when relying on a biased index. [38]

VI. Conclusion

Accurate predictions of the determinants of labor force behavior require accurate measures of work disability. Due to skepticism about the reliability of self-reported work limitation, especially for nonworkers, many researchers have turned to more "objective" health indicators to proxy for disability. However, although "disability" is related to "poor health" and "functional limitation," the terms are not synonymous. Depending on an array of social, occupational, and other individual-specific factors, workers in poor health can often work effectively on the job, and individuals in good overall health may still have substantial difficulties performing their work-related tasks. Similarly, individuals with activity limitations (such as difficulties in climbing stairs) may remain perfectly capable of continuing in their jobs. Bound (1991) finds that inferences in labor supply models using objective health indicators may be more misleading than in those using self-reported measures of work limitation.

The premise of this analysis is that self-reports of work limitation provide valuable information about work capacity that should not be completely dismissed. In a compromise between simply accepting bias from self-reports and completely discarding all useful information in such reports, this study treated reporting bias as a censored sample problem in which responses were assumed to be reliable on average for workers but of unknown quality for nonworkers. Using physician-diagnosed health conditions as instruments in this framework, consistent estimates could be obtained regardless of whether nonworkers overreport disability. The constructed continuous index of "true" disability also provides more information about work capacity than a discrete indicator of work limitation. Although the approach cannot address many important issues related to the appropriateness of various types of health measures, it does address one of the most important ones: the perception among many researchers that nonparticipants in t he labor force systematically exaggerate work limitation.

Empirical findings indicate substantial overreporting of work limitation by nonworkers, especially among women, nonwhites, high school dropouts, and former blue collar workers. Former white collar workers, in contrast, do not appear to over-report disability as a group. Simulations lend support to conjectures in the literature that reporting bias leads to upward-biased estimates of the effect of disability on labor force withdrawal and to downward-biased estimates of the influence of financial incentives. Although tempered by a divergent finding in Kreider (forthcoming) for the particular case of disability applications, results in this study also suggest that using a typical "biased" disability measure is preferable to using none at all when making inferences about the effects of public policy on work behavior.

Appendix 1

Likelihood Function

Let g denote a trivariate normal probability density function (p.d.f.), h a bivariate normal p.d.f., [phi] the standard normal p.d.f., [phi] the standard normal c.d.f., and [theta] the standard bivariate normal c.d.f. Then the terms in the likelihood function provided in the text are given by

[[omega].sub.12] = [[[integral of].sup.A].sub.-[infinity]] [[[integral of].sup.[X.sub.L][[beta].sub.L] - [micro]].sub.-[infinity]] g(v, [[epsilon].sub.L], [[epsilon].sub.1])d[[epsilon].sub.L]dv


[[omega].sub.11] = [[[integral of].sup.A].sub.-[infinity]] [[[integral of].sup.[X.sub.L][[beta].sub.L]].sub.[X.sub.L][[beta].sub.L]-[micro]] g(v, [[epsilon].sub.L], [[epsilon].sub.1])d[[epsilon].sub.L]dv




where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] = [alpha]([X.sub.L][[beta].sub.L]) + [gamma][X.sub.y]([[beta].sub.1] - [[beta].sub.0]) + Z[delta] and [[rho].sub.Lv] = ([[rho].sub.Lv] - [[rho].sub.v1][[rho].sub.Ll])/[[(1 - [[[rho].sup.2].sub.v1])(1 - [[[rho].sup.2].sub.Ll])].sup.1/2] is the correlation between v and [[epsilon].sub.L] given [[epsilon].sub.1] (see Johnson and Kotz 1974, 86-87).
                                Appendix 2
       Reduced Form Estimates for Bivariate Work Limitation and Work
                Men (N = 5,205)
                     Limit                  Work
                                Standard              Standard
                  Coefficient    Error   Coefficient   Error
Sight         1       0.774     (0.196)       -0.585  (0.120)   1
Heart         2       0.567     (0.116)       -0.395  (0.0697)  4
Cancer        4       0.485     (0.176)       -0.315  (0.128)  15
Stroke        3       0.489     (0.277)       -0.818  (0.113)   3
Legs/feet     8       0.327     (0.0990)      -0.247  (0.0651)  5
Long          6       0.411     (0.166)       -0.491  (0.0851) 14
Back          7       0.350     (0.0890)      -0.164  (0.0617)  7
Diabetes      5       0.429     (0.140)       -0.387  (0.0804) 11
Emotional     9       0.327     (0.168)       -0.509  (0.0842)  6
Arthritis    10       0.174     (0.0919)      -0.0247 (0.0626)  8
Asthma       14       0.0412    (0.146)       -0.184  (0.102)  10
Hypertension 12       0.120     (0.120)        0.230  (0.167)   9
Stomach      11       0.142     (0.111)       -0.0640 (0.0830) 13
Kidney       13       0.0848    (0.151)       -0.289  (0.0828) 12
Hearing      15      -0.0780    (0.157)       -0.0453 (0.110)   2
             Women (N = 5,623)
                  Limit                    Work
                               Standard              Standard
             Coefficient        Error   Coefficient   Error
Sight              0.416       (0.216)       -0.260  (0.107)
Heart              0.332       (0.164)       -0.208  (0.0718)
Cancer             0.0692      (0.251)       -0.261  (0.0909)
Stroke             0.369       (0.323)       -0.443  (0.129)
Legs/feet          0.306       (0.137)       -0.141  (0.0573)
Long               0.127       (0.172)       -0.144  (0.0795)
Back               0.300       (0.141)       -0.150  (0.0571)
Diabetes           0.164       (0.242)       -0.357  (0.0772)
Emotional          0.302       (0.267)       -0.472  (0.0640)
Arthritis          0.284       (0.134)       -0.133  (0.0562)
Asthma             0.166       (0.191)       -0.187  (0.0867)
Hypertension       0.230       (0.167)       -0.220  (0.0631)
Stomach            0.159       (0.138)       -0.0834 (0.0741)
Kidney             0.159       (0.179)       -0.236  (0.0666)
Hearing            0.405       (0.325)       -0.145  (0.167)
Pain index                                         0.438    (0.0653) -0.351
#conditions * schooling                            0.438    (0.0062)  0.0057
#conditons * white collar                         -0.00737  (0.0544)  0.0432
BMI [less than] 20                                 0.283    (0.252)  -0.481
25 [less than or equal] 30 BMI [less than] 30      0.0603   (0.0747) -0.241
BMI [less than or equal] 30                        0.0228   (0.0891)  0.0472
Drinks [greater than] 2                           -0.0636   (0.105)   0.0383
Smoker                                             0.0534   (0.0720) -0.0519
Light exercise                                    -0.0637   (0.0708) -0.108
Heavy exercise                                    -0.150    (0.0995)  0.0191
Constant                                          -2.44    (10.7)    -4.09
Age                                                0.0159   (0.387)   0.262
Age squared                                       -6.48e-5  (0.0036) -0.0028
Schooling                                         -0.0348   (0.146)   0.150
Schooling * age                                    0.00056  (0.0027) -0.0028
Nonwhite                                           0.0160   (0.138)  -0.310
Married                                           -0.0477   (0.0877)  0.122
White collar                                      -0.126    (0.140)   0.0287
Job hazards                                        0.178    (0.0733)  0.0757
Kids at home                                       0.176    (0.171)   0.0337
Northeast [a]                                      0.0482   (0.0933)  0.101
West                                               0.146    (0.0943) -0.0289
South                                             -0.0403   (0.0776)  0.0364
Age spline 61                                                        -0.136
Unemployment rate                                                    -0.0737
p                                                 -0.387    (0.474)
LL                                            -3,261
Pain index                                    (0.0383)      0.324    (0.0841)
#conditions * schooling                       (0.0033)     -0.00023  (0.0087)
#conditons * white collar                     (0.0332)     -0.0176   (0.0563)
BMI [less than] 20                            (0.174)       0.130    (0.214)
25 [less than or equal] 30 BMI [less than] 30 (0.0544)      0.0075   (0.0891)
BMI [less than or equal] 30                   (0.0652)      0.151    (0.0939)
Drinks [greater than] 2                       (0.0732)      0.120    (0.283)
Smoker                                        (0.0518)      0.0406   (0.0723)
Light exercise                                (0.0468)      0.0400   (0.0817)
Heavy exercise                                (0.0642)      0.0363   (0.122)
Constant                                      (8.0415)     -1.54    (11.0)
Age                                           (0.285)      -0.0473   (0.386)
Age squared                                   (0.0025)      0.00073  (0.0035)
Schooling                                     (0.0992)      0.392    (0.182)
Schooling * age                               (0.0017)     -0.00080  (0.0032)
Nonwhite                                      (0.0641)     -0.246    (0.108)
Married                                       (0.0633)      0.119    (0.226)
White collar                                  (0.0825)     -0.226    (0.246)
Job hazards                                   (0.0458)      0.0016   (0.242)
Kids at home                                  (0.130)      -0.0854   (0.0732)
Northeast [a]                                 (0.0804)     -0.169    (0.113)
West                                          (0.0742)      0.290    (0.120)
South                                         (0.0582)     -0.0306   (0.0908)
Age spline 61                                 (0.0577)
Unemployment rate                             (0.0270)
p                                                          -0.126    (0.786)
LL                                                     -4,072
Pain index                                    -0.194  (0.0288)
#conditions * schooling                        0.0056 (0.0034)
#conditons * white collar                      0.0137 (0.0286)
BMI [less than] 20                            -0.240  (0.0853)
25 [less than or equal] 30 BMI [less than] 30  0.0518 (0.0457)
BMI [less than or equal] 30                    0.0227 (0.0515)
Drinks [greater than] 2                       -0.275  (0.127)
Smoker                                        -0.0108 (0.0377)
Light exercise                                -0.0902 (0.0386)
Heavy exercise                                -0.103  (0.0605)
Constant                                      -6.61   (5.81)
Age                                            0.287  (0.205)
Age squared                                   -0.0028 (0.0018)
Schooling                                      0.162  (0.0958)
Schooling * age                               -0.0022 (0.0017)
Nonwhite                                       0.0630 (0.0539)
Married                                       -0.481  (0.0453)
White collar                                   0.420  (0.0791)
Job hazards                                    0.502  (0.0512)
Kids at home                                  -0.0112 (0.0392)
Northeast [a]                                  0.136  (0.0665)
West                                          -0.0864 (0.0636)
South                                          0.0045 (0.0487)
Age spline 61                                 -0.112  (0.0938)
Unemployment rate                             -0.0408 (0.0225)
(a.)Omitted region is Midwest.
          Reduced Form Estimates for Dichotomous Work Limitation and
                      Work, with Activity Limitations
                       Men (N = 5,205)
                            Limit                   Work
                                       Standard              Standard
                         Coefficient    Error    Coefficient  Error
Sight                1      0.683       (0.206)    -0.328    (0.136)  11
Heart                3      0.379       (0.117)    -0.183    (0.0759)  1
Cancer               2      0.443       (0.190)    -0.148    (0.134)  14
Stroke              11      0.0814      (0.239)    -0.481    (0.128)   8
Legs/feet            8      0.175       (0.0968)   -0.00275  (0.0716)  4
Lung                 6      0.199       (0.160)    -0.252    (0.0911) 15
Hack                 5      0.265       (0.0956)   -0.0118   (0.0661)  5
Diabetes             4      0.296       (0.141)    -0.198    (0.0876) 13
Emotional            7      0.195       (0.161)    -0.396    (0.0915)  6
Arthritis            9      0.129       (0.0992)    0.124    (0.0678)  2
Asthma              12     -0.0346      (0.148)    -0.0485   (0.110)   7
Hypertension        13     -0.0358      (0.119)    -0.0986   (0.0772)  9
Stomach             10      0.100       (0.119)     0.0642   (0.0913) 10
Kidney              14     -0.0535      (0.140)    -0.137    (0.0909) 12
Hearing             15     -0.225       (0.164)     0.229    (0.127)   3
Walk across room            0.236       (0.983)    -0.252    (0.421)
Bathe without help          3.71       (87.6)      -0.0967   (0.365)
Get in/out of bed          -1.07        (1.28)      0.215    (0.278)
Walk a block               -0.168       (0.605)    -0.313    (0.194)
Walk several blocks        -0.0647      (0.173)    -0.0917   (0.111)
Use calculator             -0.178       (0.114)    -0.115    (0.0748)
Climb stairs                0.695       (0.333)    -0.202    (0.150)
Several flights             0.227       (0.150)    -0.384    (0.0868)
Getup from chair            0.196       (0.229)     0.0232   (0.155)
Jog a mile                  0.365       (0.0772)   -0.186    (0.0532)
                                Women (N 5,623)
                       Limit                       Work
                                Standard                    Standard
                    Coefficient  Error          Coefficient  Error
Sight                  0.0847   (0.207)           -0.0729   (0.114)
Heart                  0.210    (0.160)           -0.116    (0.0766)
Cancer                -0.120    (0.240)           -0.205    (0.0948)
Stroke                 0.144    (0.290)           -0.234    (0.145)
Legs/feet              0.166    (0.144)           -0.0419   (0.0603)
Lung                  -0.124    (0.175)           -0.0489   (0.0841)
Hack                   0.149    (0.142)           -0.0952   (0.0601)
Diabetes               0.0319   (0.207)           -0.278    (0.0805)
Emotional              0.146    (0.200)           -0.395    (0.0680)
Arthritis              0.173    (0.146)           -0.104    (0.0592)
Asthma                 0.149    (0.188)           -0.126    (0.0919)
Hypertension           0.113    (0.159)           -0.172    (0.0663)
Stomach                0.103    (0.154)           -0.0228   (0.0771)
Kidney                 0.0598   (0.163)           -0.183    (0.0700)
Hearing                0.173    (0.334)           -0.100    (0.177)
Walk across room      -1.14     (0.760)           -0.461    (0.432)
Bathe without help    -0.465    (0.829)           -0.292    (0.323)
Get in/out of bed      0.0544   (0.635)           -0.536    (0.265)
Walk a block           0.228    (0.299)           -0.217    (0.155)
Walk several blocks    0.284    (0.182)           -0.0868   (0.0921)
Use calculator         0.114    (0.165)           -0.309    (0.0631)
Climb stairs          -0.0836   (0.234)           -0.183    (0.113)
Several flights        0.188    (0.117)           -0.115    (0.0625)
Getup from chair      -0.0253   (0.191)            0.107    (0.112)
Jog a mile             0.267    (0.0899)          -0.0551   (0.0420)
Lift 10 pounds                                     1.02    (0.238)  -0.364
Use a map                                         -0.0521  (0.157)  -0.0189
Pick up dime                                       0.105   (0.430)  -0.0628
Pull/push                                          0.441   (0.249)  -0.631
Raise arms                                         0.582   (0.238)  -0.0865
Sit two hours                                     -0.148   (0.171)  -0.109
Stoop/kneel                                        0.253   (0.164)  -0.358
Pain index                                         0.335   (0.0583) -0.176
[#cond.sup.*] schooling                            0.00738 (0.0060) -0.00238
[#cond.sup.*] white collar                         0.00712 (0.0572)  0.0367
BMI [less than] 20                                 0.138   (0.251)  -0.153
25 [less than or equal to] BMI [less than] 30      0.0791  (0.0810) -0.0319
BMI [greater than or equal to] 30                 -0.0177  (0.0972)  0.0678
Drinks [greater than] 2                           -0.0452  (0.112)   0.0346
Smoker                                            -0.0071  (0.0766) -0.0397
Light exercise                                    -0.0123  (0.0769) -0.201
Heavy exercise                                    -0.125   (0.109)  -0.0150
Constant                                          -1.65    (10.9)   -5.50
Age                                               -0.0141  (0.393)   0.333
Age squared                                        0.00017 (0.0036) -0.0035
Schooling                                          0.0406  (0.166)   0.0809
[Schooling.sup.*] age                             -0.00092 (0.0030) -0.00156
Nonwhite                                          -0.0204  (0.122)  -0.271
Married                                           -0.0259  (0.0939)  0.151
White collar                                      -0.138   (0.149)   0.0154
Joh hazards                                        0.206   (0.0671)  0.0375
Kids at home                                       0.132   (0.180)   0.123
Northeast [a]                                      0.0368  (0.100)   0.146
West                                               0.162   (0.102)  -0.0162
South                                             -0.0797  (0.0841)  0.0765
Age spline 61                                                       -0.137
Unemployment rate                                                   -0.0811
PLW                                               -0.0608  (0.496)
LL                                            -3,015
Lift 10 pounds                                (0.130)        0.447   (0.171)
Use a map                                     (0.111)       -0.190   (0.129)
Pick up dime                                  (0.289)        0.0830  (0.429)
Pull/push                                     (0.130)        0.581   (0.168)
Raise arms                                    (0.179)        0.251   (0.327)
Sit two hours                                 (0.105)       -0.0711  (0.161)
Stoop/kneel                                   (0.0962)       0.315   (0.113)
Pain index                                    (0.0450)       0.170   (0.0602)
[#cond.sup.*] schooling                       (0.00357)      0.0034  (0.0090)
[#cond.sup.*] white collar                    (0.0337)       0.0101  (0.0599)
BMI [less than] 20                            (0.221)        0.0322  (0.195)
25 [less than or equal to] BMI [less than] 30 (0.0564)      -0.0117  (0.0960)
BMI [greater than or equal to] 30             (0.0682)       0.0452  (0.101)
Drinks [greater than] 2                       (0.0766)       0.230   (0.277)
Smoker                                        (0.0549)       0.0274  (0.0785)
Light exercise                                (0.0493)       0.0792  (0.0881)
Heavy exercise                                (0.0669)       0.0819  (0.127)
Constant                                      (8.57)        -1.13    (11.4)
Age                                           (0.303)       -0.0634  (0.401)
Age squared                                   (0.0027)       0.00079 (0.0036)
Schooling                                     (0.109)        0.0755  (0.206)
[Schooling.sup.*] age                         (0.00187)     -0.0014  (0.0037)
Nonwhite                                      (0.0683)      -0.254   (0.134)
Married                                       (0.0659)       0.0700  (0.166)
White collar                                  (0.0834)      -0.202   (0.218)
Joh hazards                                   (0.0486)       0.112   (0.149)
Kids at home                                  (0.138)       -0.0525  (0.0785)
Northeast [a]                                 (0.0840)      -0.137   (0.124)
West                                          (0.0779)       0.275   (0.129)
South                                         (0.0613)      -0.0632  (0.0953)
Age spline 61                                 (0.0608)
Unemployment rate                             (0.0290)
PLW                                                          0.166   (0.531)
LL                                                      -3,896
Lift 10 pounds                                -0.271  (0.0770)
Use a map                                     -0.114  (0.0572)
Pick up dime                                  -0.346  (0.306)
Pull/push                                     -0.228  (0.0809)
Raise arms                                    -0.119  (0.160)
Sit two hours                                 -0.0140 (0.0876)
Stoop/kneel                                   -0.0361 (0.0733)
Pain index                                    -0.0864 (0.0316)
[#cond.sup.*] schooling                        0.0032 (0.0036)
[#cond.sup.*] white collar                     0.0084 (0.0304)
BMI [less than] 20                            -0.178  (0.0895)
25 [less than or equal to] BMI [less than] 30  0.0492 (0.0465)
BMI [greater than or equal to] 30              0.0390 (0.0532)
Drinks [greater than] 2                       -0.271  (0.130)
Smoker                                        -0.0069 (0.0386)
Light exercise                                -0.132  (0.0397)
Heavy exercise                                -0.114  (0.0617)
Constant                                      -5.67   (5.93)
Age                                            0.259  (0.209)
Age squared                                   -0.0025 (0.0019)
Schooling                                      0.165  (0.0978)
[Schooling.sup.*] age                         -0.0025 (0.0017)
Nonwhite                                       0.133  (0.0553)
Married                                       -0.539  (0.0472)
White collar                                   0.428  (0.0803)
Joh hazards                                    0.487  (0.0528)
Kids at home                                  -0.0128 (0.0401)
Northeast [a]                                  0.146  (0.0683)
West                                          -0.0812 (0.0654)
South                                          0.0239 (0.0498)
Age spline 61                                 -0.129  (0.0928)
Unemployment rate                             -0.0448 (0.0227)
(a.)Omitted region is Midwest.

The author is an assistant professor of economics at the University of Virginia. He thanks John Bound, Arthur Goldberger, Bill Johnson, Robert Moffitt, Ed Olsen, John Pepper, David Salkever, Steven Stern, Barbara Wolfe, two anonymous referees, and seminar participants at Johns Hopkins University, the University of Virginia, and the University of Wisconsin for helpful comments on earlier drafts of this article. Fidel Perez and Xin Li provided valuable research assistance, and generous financial support was received from the National Institute of Mental Health. The data used in this article can be obtained beginning June 2000 through May 2003 from the author at the following address: Department of Economics, University of Virginia, Charlottesville, VA 22903.

[Submitted August 1996; accepted March 1999]

(1.) Inclusion of a disability measure in a labor force participation specification can considerably improve predictive performance (see, for example, Sickles and Taubman 1986).

(2.) The purpose is not, however, to construct a measure of general health status or functional limitation. The constructed work disability index is more appropriate as a predictor of labor market outcomes (such as early retirement) than of, say, life expectancy, utilization of medical services, or admission into a nursing home. See Berg (1973) and Nagi (1979) for detailed discussion on relationships between general health, impairment, and work disability.

(3.) In studies of a worker's decision to withdraw from the workforce, Boskin and Hurd (1978), Slade (1984), Hanoch and Honig (1983), and Berkovec and Stem (1991) each measure disability as the individual's response to a question of the form "Do you have a health condition that limits the kind or amount of work you can do?" Gordon and Blinder (1980) include three health indicators in their participation equation: whether the individual reported a short-term health problem that limits ability to work, whether the individual reported a long-term health problem that limits ability to work, and whether the individual reported leaving his or her last job for health reasons.

(4.) In an analysis of a worker's retirement decision, Gordon and Blinder (1980) conclude that their estimated effect of "left last job for health reasons" on early retirement is "too huge to be believed."

(5.) Using a Hausman-Wu test of exogeneity, the latter authors cannot reject the hypothesis that OLS and instrumental variables estimated effects of self-reported limitation on work participation are the same. Their participation measure, however, is "expected date of future retirement" instead of actual retirement date, so they cannot test the hypothesis that former workers do not rationalize their nonwork status.

(6.) See Spector (1990) or Weiner et al. (1990) for discussion about functional disability scales and activity limitations. Limitations in activities are used, for example, in Chirikos and Nestel (1981).

(7.) Colvez and Blanchet (1981) find inverse relationships between mortality and the incidence of many types of health impairments over the time frame they consider, lending credence to the view that the timing of subsequent mortality is an inappropriate measure of limitation. One hypothesis is that improvements in medical technology have increased the longevity of individuals with health impairments, thus increasing the proportion of living individuals with such impairments.

(8.) In fact, he found that instrumenting self-reported health with mortality experience exacerbated the effects of reporting bias in his participation model.

(9.) Results in this study using instrumented work limitation without accounting for reporting bias are consistent with Bound's findings.

(10.) Stern recognizes that an identification problem precludes the possibility of allowing overreporting in his model to depend on any observed determinants of either work participation or true disability status. As noted by Bound (1991), one implication is that it is not possible to use Stern's approach to consistently estimate the effect of financial incentives on participation if self-reports of limitation are directly sensitive to those incentives. Also, reduced-form estimates in his study cannot be used to construct an unbiased disability index; an index can only be constructed using structural estimates that rely on identifying exclusion restrictions.

(11.) In contrast, Stem's (1989) outside information assumption is that misreporting of disability is linearly related to an individual's propensity to work.

(12.) For example, they note that the proportion of working-aged men reporting work limitations increased rapidly during the 1970s, a period in which the availability and generosity of federal disability benefits expanded substantially. Self-reports of work limitations for men aged 65 or older remained stable. During this same period, self-reported prevalence rates for health conditions rose at approximately the same rate for both age groups, suggesting that changes in such prevalence rates were not primarily attributable to changes in reporting incentives.

(13.) I thank an anonymous referee for these last two observations.

(14.) From the original 12,652 respondents, 530 men and 66 women were excluded from the sample used in this study because they were older than 64. Another 132 men and 1,096 women were dropped because they were younger than 50.

(15.) See Wallace and Herzog (1995) for a comprehensive overview of the health indicators available in the HRS. Because one purpose of this study is to provide a method for readers to construct a disability index using their own data, it focuses on health measures available in many widely used data sets.

(16.) Reclassifying 211 men looking for work (4 percent) and 157 women looking for work (3 percent) as nonworkers bad virtually no effect on the results in this analysis.

(17.) This variable is crested using three questions in the HRS: (a) "Do you have any impairment or health problem that limits the kind or amount of paid work you can do?"; (b) "Does any impairment or health problem limit the kind or amount of work you can do around the house?"; and (c) "Are you limited in any way in activities because of an impairment or problem?" The ordered limit variable is set equal to 2 if the answer to question (a) is "yes," it is set equal to 1 if the answer to (a) is "no" but the answer to either (b) or (c) is "yes," and it is set equal to 0 otherwise.

(18.) This work participation condition can alternately be motivated by assuming that an individual works if and only if his expected percentage income gain associated with working, approximated by In [[Y.sup.*].sub.w] - In [[Y.sup.*].sub.n], exceeds a reservation wage which depends on work limitation and other individual attributes. See, for example, Lee (1978) and Bound (1991).

(19.) It is not possible to model work limitation as a function of binary participation status in this simultaneous framework because a logical consistency problem arises: the probabilities of working and not working do not sum to unity unless the coefficient on work is restricted to be zero. Using generalized method of moments techniques in a somewhat different framework, however, Haveman et al. (1994) find that hours of work has a negligible and insignificant effect on health. Stem (1989) allows limitation to depend on the work outcome itself, but he restricts the coefficient on work status to be zero using the justification that his estimated effect of participation on reported disability is zero (his footnote 11). However, this justification seems incorrect because his finding that the effect of participation on reported disability ([[sigma].sub.d] + [[sigma].sub.r], in his article) is not significantly different from zero does not imply that the effect of actual work on the latent value of work ([[sigma] .sub.p][[sigma].sub.r] in his article in his equation 5a after correcting a typo) is not significantly different from zero as required for logical consistency.

(20.) Although it might be desirable to treat a nonworker's response of "no limitation" as accurate instead of missing, an identification problem precludes the possibility of treating some responses as observed and others as missing for a particular subsample of respondents.

(21.) Since this normalization is arbitrary, the constructed disability index differentiates individuals' disability levels in relative but not absolute terms; multiplying each respondent's computed disability level by the same constant does not affect the relative scale.

(22.) Noting that identification is problematic in these types of models, Stern (1989) relies on excluding marital status from his limitation equation.

(23.) Because this study does not focus on the determinants of income, estimates for the income specifications are not shown to save space. The set of estimates for these equations seemed reasonable and unremarkable.

(24.) Only two people in the sample are blind. Both identify themselves as having a work limitation.

(25.) To minimize the potential for endogeneity, occupation is classified based on the last job held prior to the Onset of disability for those claiming a work limitation.

(26.) Gruber and Kubik (1997) rely exclusively on such anthropometric body mass indicators to control for disability in their study of the effects of denial rates on applications for federal disability benefits.

(27.) Self-reported prevalence rates of physician-diagnosed conditions are higher among nonwhite females than white females in these data for arthritis, asthma, feet/leg problems, poor hearing, heart problems, kidney problems, poor sight, stomach disorders, and especially diabetes, stroke, and hypertension. Prevalence rates are lower for back problems, cancer, emotional/psychological problems, and lung problems. For men, prevalence rates are higher among nonwhites for asthma, cancer, feet/leg problems, kidney problems, stomach disorders, and especially diabetes, stroke, poor sight, and hypertension. Prevalence rates are lower among male nonwhites for arthritis, back problems, emotional/psychological problems, poor hearing, heart problems, and especially lung problems. Both male and female nonwhites reports greater number of health conditions and more usual pain than whites.

(28.) Econometrically, Equation 9 is changed to LR = L for each member of the sample (for practical purposes this equation is discarded).

(29.) These indicators are not included in the version of the model that uses the ordinal L indicator as the dependent variable since that dependent variable would be definitionally related to these activity limitation measures.

(30.) Limitations in ability to eat or dress were not included in the specification because there were too few cases observed in the data.

(31.) The model was also estimated using a third variant of the dependent limitation variable, which was set equal to 1 for respondents who claim any kind of limitation (work-related or otherwise) and set equal to 0 otherwise. For men, results from that model were quite similar to those using the ordered dependent variable. In particular, the ranking of the specific condition impacts on limitation were mostly unchanged compared with the ordered case and the coefficients had similar magnitudes. Results for women were also similar, though less so than for men. The greatest differences for women were that the impact of stroke on limitation increased from fifth to first and the impact of poor sight dropped from eighth to twelfth.

(32.) For comparison purposes, a constant was subtracted from L[minutes] before calculating its associated probabilities such that the mean predicted probability of being limited for workers is equated for the two indices. Without this normalization, part of the difference between P and P[minutes] would be due simply to a constant difference in the distributions, and the inferred degree of overreporting among nonworkers would be exaggerated. When using the index in a regression, however, shifting the mean of the index does not affect any parameter estimates except the constant term.

(33.) This biased measure is similar to Bound's (1991) instrumented measure of work limitation, except that Bound uses subsequent mortality to instrument disability instead of the specific health conditions used here (see footnote 8).

(34.) Results for the case that activity limitations but not specific conditions are included (not shown) are similar, with somewhat smaller overreporting found for the male sample.

(35.) The model restricts the ratio of the impact of each health condition on participation to its impact on limitation to be equal to a common value [alpha] (I thank an anonymous referee for pointing this out). I tested these joint proportionality restrictions using a Wald test based on results from the reduced form estimation presented in Table 4. For men, the test statistic was 12.3, with a marginal significance level of 0.58. The test statistic for women was 14.8, which is marginally significant at the 0.39 level. Thus, the imposed restrictions cannot be rejected at common significance levels. (When the model is estimated over men and women together, however, the joint restrictions can be rejected at better than the 5 percent significance level, perhaps providing evidence that men and women should not be pooled together in these estimations.)

(36.) Using disability measures constructed from estimates in this study, results in Kreider (1999) suggest that the estimated sensitivity of applications for SSDI benefits is understated by about 15 percent when relying on a biased limitation measure.

(37.) This finding is consistent with conclusions in McCallum (1972) and Wickens (1972) that the use of a proxy in a regression, even when it is badly measured, may be preferable to excluding it because the omitted variable bias often exceeds the measurement error bias.

(38.) The estimated responsiveness of applications to changes in the probability of being accepted into the program was found to he about 1.2 times too large when using no disability measure, but it was found to be underestimated by an even greater magnitude when using the biased measure. The sensitivity of applications to changes in expected applicant income was found to be underestimated by about one-fifth when using the biased index, which was less than the estimated bias when using no disability measure.


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                    Work Status and Reported Limitation
                Workers   Nonworkers
              (N = 4,041)  (N 1,164)
        2     431 (10.7%) 713 (61.3%)
Limit   1     332  (8.2%)  47  (4.0%)
        0   3,278 (81.1%) 404 (34.7%)
                Workers    Nonworkers
              (N = 3,451)   (N 2,172)
        2     324  (9.4%)   875 (35.4%)
Limit   1     336  (9.7%)   162 (6.6%)
        0   2,791 (80.9%) 1,135 (45.9%)
Note: Limit = 2 if reported work limitation.
Limit = 1 is some limitation, but does not affect ability to work.
limit = 0 if nolimitation.
                         Definitions of Variables
Age                        Respondent's age at the time of the
                           survey interview
Age spline 61              Max {O, age-61 1 (number of years
                           older than 61)
Nonwhite                   1 if nonwhite race (0 otherwise)
Education                    Years of schooling
Job hazards                1 if ever exposed to dangerous
                             chemicals or other hazards
                             at work for more than one year
Kids at home               1 if kids in the household
Married                    1 if married at time of survey
Unemployment rate            Unemployment rate in respondent's
                             region (disaggregated
                             to nine regions)
Midwest                    1 if respondent resides in the Midwest
Northeast                  1 if respondent resides in the
South                      1 if respondent resides in the South
West                       1 if respondent resides in the West
Work                       1 if currently working, unemployed and
                             looking for work,
                             or on temporary (sick or other)
White collar               1 if professional or managerial
                             occupation (before onset of
                             disability if reporting a work
Drinks [greater than] 2    1 if respondent consumes more than two
                             alcoholic drinks
                             per day
Smoker                     1 if respondent has smoked more than
                             100 cigarettes in
                             life time
Light exercise             1 if the respondent exercises 1-2
                             times per week
Heavy exercise             1 if the respondent exercises at least
                             three times per week
BMI [less than] 20         1 if body mass index [a] [less than]
                             20 kilograms /[meters.sup.2]
25 [less than or equal to]   if body mass index between 25 and 30
BMI [less than] 30           [meters.sup.2]
BMI [greater than or       1 if body mass index exceeds 30
equal to] 30
Arthritis                  1 if arthritis/rheumatism condition
Asthma                     1 if asthma condition
Back                       1 if back condition
Cancer                     1 if treated for cancer in the last
Diabetes                   1 if current diabetic
Emotional                  1 if emotional, nervous, or
                             psychological condition
Legs/feet                  1 if problem with legs or feet
Hearing                    1 if fair or worse hearing
Heart                      1 if heart condition
Hypertension               1 if hypertension
Kidney                     1 if kidney condition
Lung                       1 if lung condition
Sight                      1 if fair or worse sight
Stomach                    1 if stomach or ulcer condition
Stroke                     1 if had a stroke
Number of conditions Number of specific health conditions
                       reported by respondent
Pain index           Normalized measure of usual pain such that "none"=0.29,
                     "mild" = 0.92, "moderate" = 1.35, and "severe" = 2.1. [b]
Walk across room     1 if walking across a room is very difficult/can't do
Bathe without help   1 if baffling or showering without
                       help is very difficult/ can't do
Get in/out of bed    1 if getting in and out of bed is very difficult/can't do
Walk a block         1 if walking a block is very difficult/can't do
Walk several blocks  1 if walking several blocks is very difficult/can't do
Use calculator       1 if using a calculator to help balance a
                       checkbook is very difficult/can't do
Climb stairs         1 if climbing a flight of stairs without
                       resting is very difficult/can't do
Several flights      1 if climbing several flights of stairs
                       without resting is very difficult/can't do
Get up from chair    1 if getting up from a chair after sitting
                       for long periods is very difficult/can't do
Jog a mile           1 if jogging a mile is very difficult/can't do
Lift 10 pounds       1 if lifting or carrying more than 10 pounds, like a
                       bag of groceries, is very difficult/can't do
Use map              1 if using a map to figure out how to get around in a
                       strange place is very difficult/can't do
Pick up dime         1 if picking up a dime from a
                       table is very difficult/can't do
Pull/push            1 if pulling or pushing large objects like a living
                       room chair is very difficult/can't do
Raise arms           1 if reaching or extending arms above
                       shoulders is very difficult/can't do
Sit two hours        1 if very difficult/can't do
                     1 if stooping, kneeling, or crouching
Stoop/kneel            is very difficult/can't do

(a.)Fahey et al. (1997) define ideal body mass range to be 20-25 kilograms/[meters.sup.2]

(b.)This normalization follows a procedure in Bound et al. (1995, P.S259) that rescales the {0, 1, 2, 3} responses to the standard normal distribution based on the fraction of respondents reporting each value.
                       Means and Standard Deviations
                                             Workers (N = 4,041)
                                             Mean                Deviation
Age                                          56.0                3.56
Age spline 61                                 0.129              0.512
Nonwhite                                      0.131              0.337
Education                                    12.4                3.35
Job hazards                                   0.413              0.492
Kids at home                                  0.0255             0.158
Married                                       0.844              0.363
Unemployment rate                             7.04               1.01
Northeast                                     0.174              0.380
South                                         0.417              0.493
West                                          0.160              0.367
White collar                                  0.306              0.461
Drinks [greater than]2                        0.0928             0.290
Smoker                                        0.732              0.443
Light exercise                                0.556              0.497
Heavy exercise                                0.162              0.368
BMI [less than]20                             0.0109             0.104
25 [less than or equal to]BMI [less than] 30  0.485              0.500
BMI [greater than equal to] 30                0.232              0.422
Arthritis                                     0.289              0.453
Asthma                                        0.0433             0.204
Back                                          0.301              0.459
                                             (N = 1,164)
                                             Mean        Deviation
Age                                          58.3        3.82
Age spline 61                                 0.477      0.928
Nonwhite                                      0.210      0.408
Education                                    11.4        3.61
Job hazards                                   0.458      0.498
Kids at home                                  0.0284     0.166
Married                                       0.808      0.394
Unemployment rate                             7.15       0.914
Northeast                                     0.171      0.377
South                                         0.429      0.495
West                                          0.169      0.375
White collar                                  0.214      0.410
Drinks [greater than]2                        0.0997     0.300
Smoker                                        0.784      0.412
Light exercise                                0.543      0.498
Heavy exercise                                0.116      0.320
BMI [less than]20                             0.0335     0.180
25 [less than or equal to]BMI [less than] 30  0.474      0.500
BMI [greater than equal to] 30                0.246      0.43 1
Arthritis                                     0.441      0.497
Asthma                                        0.0842     0.278
Back                                          0.448      0.497
                                             Workers (N = 3,451)
                                             Mean                Deviation
Age                                          55.3                3.34
Age spline 61                                 0.0191             0.164
Nonwhite                                      0.186              0.389
Education                                    12.4                2.78
Job hazards                                   0.216              0.411
Kids at home                                  0.387              0.487
Married                                       0.663              0.473
Unemployment rate                             7.10               1.02
Northeast                                     0.204              0.403
South                                         0.402              0.490
West                                          0.148              0.355
White collar                                  0.274              0.446
Drinks [greater than]2                        0.0159             0.125
Smoker                                        0.536              0.499
Light exercise                                0.499              0.500
Heavy exercise                                0.108              0.311
BMI [less than]20                             0.0417             0.200
25 [less than or equal to]BMI [less than] 30  0.354              0.478
BMI [greater than equal to] 30                0.261              0.439
Arthritis                                     0.392              0.488
Asthma                                        0.0571             0.232
Back                                          0.308              0.462
                                             (N = 2,472)
                                             Mean        Deviation
Age                                          56.3        3.53
Age spline 61                                 0.0635     0.351
Nonwhite                                      0.175      0.380
Education                                    11.1        3.24
Job hazards                                   0.131      0.337
Kids at home                                  0.378      0.485
Married                                       0.767      0.423
Unemployment rate                             7.11       0.938
Northeast                                     0.163      0.369
South                                         0.440      0.497
West                                          0.167      0.373
White collar                                  0.114      0.318
Drinks [greater than]2                        0.0230     0.150
Smoker                                        0.544      0.498
Light exercise                                0.489      0.500
Heavy exercise                                0.0976     0.297
BMI [less than]20                             0.0599     0.237
25 [less than or equal to]BMI [less than] 30  0.344      0.475
BMI [greater than equal to] 30                0.299      0.458
Arthritis                                     0.524      0.500
Asthma                                        0.0875     0.283
Back                                          0.431      0.495
Cancer               0.019   0.137  0.0455 0.209  0.0432   0.203  0.0585
Diabetes             0.0634  0.244  0.164  0.371  0.0591   0.236  0.124
Emotional            0.0539  0.226  0.162  0.368  0.0904   0.287  0.219
Legs/feet            0.257   0.437  0.481  0.500  0.344    0.475  0.485
Hearing              0.0312  0.174  0.0610 0.239  0.00957  0.0973 0.0212
Heart                0.121   0.326  0.284  0.451  0.0811   0.273  0.157
Hypertension         0.113   0.317  0.227  0.419  0.135    0.342  0.207
Kidney               0.0616  0.240  0.169  0.375  0.0916   0.288  0.181
Lung                 0.0544  0.227  0.158  0.365  0.0655   0.247  0.116
Sight                0.0156  0.124  0.0773 0.267  0.0200   0.140  0.0576
Stomach              0.0822  0.275  0.137  0.344  0.0753   0.264  0.131
Stroke               0.0178  0.132  0.102  0.303  0.0136   0.116  0.0410
Number of condi-
  tions              1.64    1.55   3.04   2.26   1.79     1.63   2.84
Pain index          -0.0899  0.525  0.327  0.845 -0.00156  0.632  0.319
Walk across room     0.00099 0.0314 0.0301 0.171  0.000869 0.0295 0.0216
Bathe without help   0.00099 0.0314 0.0395 0.195  0.00116  0.0340 0.0281
Get in/out of bed    0.00223 0.0471 0.0361 0.187  0.00203  0.0450 0.0235
Walk a block         0.00594 0.0769 0.107  0.309  0.0104   0.102  0.0695
Walk several blocks  0.0314  0.174  0.228  0.420  0.0411   0.199  0.153
Use calculator       0.114   0.318  0.252  0.434  0.0823   0.275  0.220
Climb stairs         0.0604  0.238  0.359  0.480  0.0203   0.141  0.114
Several flights      0.0106  0.103  0.154  0.361  0.118    0.323  0.300
Get up from chair    0.0144  0.119  0.113  0.317  0.0220   0.147  0.0797
Jog a mile           0.356   0.479  0.666  0.472  0.507    0.500  0.652
Lift 10 pounds       0.0139  0.117  0.195  0.396  0.0522   0.222  0.202
Use map              0.0418  0.200  0.125  0.330  0.119    0.324  0.250
Pick up dime         0.00272 0.052  0.0369 0.189  0.00261  0.051  0.0175
Pull/push            0.0146  0.120  0.223  0.417  0.0484   0.215  0.190
Raise arms           0.00693 0.083  0.0747 0.263  0.00724  0.0848 0.05 16
Sit two hours        0.0396  0.195  0.124  0.329  0.0438   0.205  0.0971
Stoop/kneel          0.0339  0.181  0.260  0.439  0.0782   0.269  0.217
Cancer              0.235
Diabetes            0.329
Emotional           0.413
Legs/feet           0.500
Hearing             0.144
Heart               0.364
Hypertension        0.405
Kidney              0.385
Lung                0.320
Sight               0.233
Stomach             0.338
Stroke              0.198
Number of condi-
tions               2.28
Pain index          0.861
Walk across room    0.145
Bathe without help  0.165
Get in/out of bed   0.151
Walk a block        0.254
Walk several blocks 0.360
Use calculator      0.414
Climb stairs        0.318
Several flights     0.458
Get up from chair   0.271
Jog a mile          0.476
Lift 10 pounds      0.402
Use map             0.433
Pick up dime        0.131
Pull/push           0.393
Raise arms          0.221
Sit two hours       0.296
Stoop/kneel         0.413
        Reduced Form Estimates for Ordered Work Limitation and Work
                           Men (N = 5,205)
                           Limit (ordered)             Work
                                           Standard             Standard
                             Coefficient    Error   Coefficient  Error
Sight                    1      0.864      (0.160)    -0.573    (0.120)   8
Heart                    2      0.745      (0.0867)   -0.392    (0.0700)  1
Cancer                   3      0.598      (0.155)    -0.281    (0.129)   9
Stroke                   4      0.590      (0.218)    -0.821    (0.113)   5
Legs/feet                5      0.531      (0.0761)   -0.244    (0.0652)  6
Lung                     6      0.526      (0.124)    -0.476    (0.0851) 10
Back                     7      0.480      (0.0731)   -0.158    (0.0618)  2
Diabetes                 8      0.460      (0.115)    -0.370    (0.0805) 13
Emotional                9      0.382      (0.131)    -0.503    (0.0845)  3
Arthritis               10      0.326      (0.0776)   -0.0180   (0.0628)  4
Asthma                  11      0.289      (0.112)    -0.182    (0.103)   7
Hypertension            12      0.205      (0.0943)   -0.232    (0.0720) 14
Stomach                 13      0.183      (0.0940)   -0.0587   (0.0832) 15
Kidney                  14      0.176      (0.117)    -0.287    (0.0832) 12
Hearing                 15      0.0556     (0.136)    -0.0216   (0.110)  11
Pain index                      0.481      (0.0495)   -0.356    (0.0382)
Number of                      -0.0051     (0.0048)    0.0046   (0.0032)
 conditions * schooling
                        Women (N = 5,623)
                         Limit (ordered)              Work
                                          Standard             Standard
                           Coefficient     Error   Coefficient  Error
Sight                         0.227       (0.173)    -0.274    (0.107)
Heart                         0.377       (0.128)    -0.215    (0.0710)
Cancer                        0.213       (0.179)    -0.273    (0.0905)
Stroke                        0.331       (0.275)    -0.467    (0.127)
Legs/feet                     0.315       (0.105)    -0.147    (0.0565)
Lung                          0.174       (0.135)    -0.149    (0.0793)
Back                          0.359       (0.106)    -0.158    (0.0564)
Diabetes                      0.122       (0.176)    -0.360    (0.0769)
Emotional                     0.339       (0.181)    -0.475    (0.0635)
Arthritis                     0.339       (0.102)    -0.139    (0.0556)
Asthma                        0.282       (0.141)    -0.200    (0.0861)
Hypertension                  0.116       (0.128)    -0.230    (0.0624)
Stomach                      0.0319       (0.115)    -0.0904   (0.0739)
Kidney                        0.153       (0.131)    -0.242    (0.0661)
Hearing                       0.163       (0.292)    -0.155    (0.166)
Pain index                    0.417       (0.0569)   -0.194    (0.0288)
Number of                    0.0011       (0.0069)    0.0057   (0.0033)
 conditions * schooling
Number of                                         -0.0110  (0.0443)   0.0495
 conditions * white collar
BMI [less than] 20                                 0.236   (0.225)   -0.464
25 [less than or equal to] BMI [less than] 30      0.0761  (0.0605)  -0.0255
BMI [greater than or equal to] 30                  0.118   (0.0736)   0.0445
Drinks [greater than] 2                            0.0086  (0.0871)   0.0356
Smoker                                             0.0781  (0.0582)  -0.0536
Light exercise                                    -0.0750  (0.0584)  -0.108
Heavy exercise                                    -0.110   (0.0771)   0.0179
Age                                               -0.0386  (0.315)    0.502
Age squared                                        0.00046 (0.0029)  -0.0049
Schooling                                         -0.0019  (0.118)    0.153
Schooling * age                                    0.00076 (0.0021)  -0.0028
Nonwhite                                           0.0160  (0.112)   -0.314
Married                                           -0.0125  (0.0742)   0.127
White collar                                      -0.0128  (0.106)    0.0162
Job hazards                                        0.184   (0.0598)   0.0749
Kids at home                                       0.125   (0.144)    0.0399
Northeast [a]                                      0.0169  (0.0765)   0.105
West                                               0.103   (0.0791)  -0.0239
South                                             -0.0461  (0.0637)   0.0379
Constant                                          -1.32    (8.78)   -10.7
Age spline 61                                                        -0.0958
Unemployment rate                                                    -0.0756
[micro]                                            0.444   (0.0451)
[rho]                                             -0.426   (0.368)
LL                                            -4,194
Number of                                     (0.0333)     -0.0327  (0.0434)
 conditions * white collar
BMI [less than] 20                            (0.1738)      0.163   (0.164)
25 [less than or equal to] BMI [less than] 30 (0.0544)      0.0604  (0.0688)
BMI [greater than or equal to] 30             (0.0652)      0.198   (0.0733)
Drinks [greater than] 2                       (0.0732)      0.0360  (0.209)
Smoker                                        (0.0518)      0.0472  (0.0556)
Light exercise                                (0.0468)     -0.0171  (0.0610)
Heavy exercise                                (0.0643)     -0.0232  (0.0968)
Age                                           (0.284)       0.138   (0.340)
Age squared                                   (0.0025)     -0.0010  (0.0031)
Schooling                                     (0.0995)      0.0518  (0.149)
Schooling * age                               (0.0017)     -0.00070 (0.0026)
Nonwhite                                      (0.0640)     -0.257   (0.0823)
Married                                       (0.0633)      0.0709  (0.142)
White collar                                  (0.159)       0.0084  (0.0825)
Job hazards                                   (0.0459)     -0.0066  (0.153)
Kids at home                                  (0.130)      -0.0639  (0.0569)
Northeast [a]                                 (0.0804)     -0.0732  (0.0853)
West                                          (0.0741)      0.204   (0.0912)
South                                         (0.0581)     -0.0430  (0.0700)
Constant                                      (8.03)       -6.31    (9.70)
Age spline 61                                 (0.0573)
Unemployment rate                             (0.0270)
[micro]                                                     0.554   (0.0332)
[rho]                                                      -0.118   (0.512)
LL                                                     -4,972
Number of                                      0.0134 (0.0285)
 conditions * white collar
BMI [less than] 20                            -0.252  (0.0852)
25 [less than or equal to] BMI [less than] 30  0.0504 (0.0457)
BMI [greater than or equal to] 30              0.0201 (0.0515)
Drinks [greater than] 2                       -0.273  (0.127)
Smoker                                        -0.0107 (0.0376)
Light exercise                                -0.0919 (0.0386)
Heavy exercise                                -0.101  (0.0605)
Age                                            0.642  (0.205)
Age squared                                   -0.0060 (0.0018)
Schooling                                      0.208  (0.0950)
Schooling * age                               -0.0030 (0.0017)
Nonwhite                                       0.0652 (0.0539)
Married                                       -0.480  (0.0453)
White collar                                   0.428  (0.0790)
Job hazards                                    0.505  (0.0512)
Kids at home                                  -0.0081 (0.0392)
Northeast [a]                                  0.134  (0.0665)
West                                          -0.0891 (0.0636)
South                                          0.0039 (0.0487)
Constant                                      -16.6   (5.80)
Age spline 61                                 -0.0479 (0.0927)
Unemployment rate                             -0.0412 (0.0224)
(a.)Omitted region is Midwest.
              Overreporting of Work Limitation--Ordered Model
                                                                in Standard
                                         P("True") P'("Biased") Deviations
Entire sample                              0.153      0.159        +1.9
  Workers                                  0.107      0.107
  Nonworkers                               0.314      0.340        +2.8
    Married                                0.302      0.320        +1.8
    Unmarried                              0.369      0.424        +2.6
    Schooling [less than] 12               0.404      0.459        +3.5
    Schooling [less than or equal to] 12   0.262      0.270        +0.7
    Older than 55                          0.296      0.316        +2.0
    55 or younger                          0.367      0.406        +2.2
    Nonwhite                               0.363      0.423        +3.0
    White                                  0.302      0.317        +1.6
    Blue collar                            0.342      0.378        +3.5
    White collar                           0.214      0.199        -0.9
Entire sample                              0.132      0.143        +4.7
  Workers                                  0.094      0.094
  Nonworkers                               0.193      0.221        +6.2
    Married                                0.169      0.183        +2.8
    Unmarried                              0.271      0.349        +7.1
    Schooling [less than] 12               0.239      0.304        +8.1
    Schooling [less than or equal to] 12   0.163      0.168        +1.0
    Older than 55                          0.200      0.230        +4.7
    55 or younger                          0.182      0.210        +4.0
    Nonwhite                               0.221      0.320        +8.3
    White                                  0.187      0.200        +2.7
    Blue collar                            0.198      0.231        +6.7
    White collar                           0.153      0.145        -0.6
Entire sample                                0.214
  Nonworkers                                 0.099
    Married                                  0.200
    Unmarried                                0.117
    Schooling [less than] 12                 0.052
    Schooling [less than or equal to] 12     0.369
    Older than 55                            0.181
    55 or younger                            0.164
    Nonwhite                                 0.085
    White                                    0.234
    Blue collar                              0.055
    White collar                             0.654
Entire sample                                0.044
  Nonworkers                                 0.010
    Married                                  0.144
    Unmarried                                0.004
    Schooling [less than] 12                 0.001
    Schooling [less than or equal to] 12     0.349
    Older than 55                            0.036
    55 or younger                            0.066
    Nonwhite                                 0.001
    White                                    0.147
    Blue collar                              0.006
    White collar                             0.591
     Least Squares Estimates of the Determinants of Overreporting Among
                         Nonworkers (Ordered model)
                          Dependent Variable:
                          "Overreporting" (P' - P)
                                                   Standard   Significance
                          Coefficient               Error     (Two-Sided)
Age                       -0.00135                 (0.000491)    0.006
Schooling                 -0.00555                 (0.000553)    0.000
Nonwhite                   0.0268                  (0.00470)     0.000
Married                   -0.0247                  (0.00478)     0.000
White collar              -0.0211                  (0.00496)     0.000
Constant                   0.186                   (0.0293)      0.000
Adjusted [R.sup.2] 0.22
(N = 1,164)
Age                       -0.00128                 (0.000445)    0.004
Schooling                 -0.00847                 (0.000520)    0.000
Nonwhite                   0.0683                  (0.00427)     0.000
Married                   -0.0383                  (0.00388)     0.000
White collar              -0.00579                 (0.00526)     0.278
Constant                   0.213                   (0.0262)      0.000
Adjusted [R.sup.2] = 0.29
(N = 2,172)
       Overreporting of Limitation by Nonworkers for Various Models
                                        Difference Between "True"
                                          and "Biased" Measures
                                         in Standard Deviations
Ordered Work Limitation
  Men                                             +2.8
  Women                                           +6.2
Ordered work limitation, model
   estimated over only high school
   graduates [a]
  Men                                             +0.4
  Women                                           +4.0
Ordered work limitation, model
   estimated over only nongraduates [b]
  Men                                             +2.3
  Female                                          +4.7
Bivariate work limitation without
   activity limitations
  Men                                             +3.7
  Women                                           +6.5
Bivariate work limitation with
   activity limitations and specific
  Men                                             +3.8
  Women                                           +9.8
Ordered Work Limitation
  Men                                      0.099
  Women                                    0.010
Ordered work limitation, model
   estimated over only high school
   graduates [a]
  Men                                      0.426
  Women                                    0.066
Ordered work limitation, model
   estimated over only nongraduates [b]
  Men                                      0.147
  Female                                   0.036
Bivariate work limitation without
   activity limitations
  Men                                      0.049
  Women                                    0.011
Bivariate work limitation with
   activity limitations and specific
  Men                                      0.022
  Women                                    0.000
(a.)Model estimated separately over 3,708 male graduates
and 3,966 female graduates.
(b.)Model estimated separately over 1,497 male
nongraduatesand 1,657 female nongraduates.
         Structural Estimates for Ordered Work Limitation and Work
                               Men (N = 5,205)
                               Limit (ordered)               Work
                               Coefficient       Error    Coefficient
Limit [*]                                                   -0.542
In [Y.sub.w] -- In [Y.sub.N]                                 0.334
Age spline 61                                               -0.164
Unemployment rate                                           -0.0603
Constant                        -5.26           (8.76)     -12.8
Pain index                       0.423          (0.0625)    -0.0491
Age                              0.0745         (0.414)      0.502
Age squared                     -0.00060        (0.00377)   -0.0048
Schooling                        0.00771        (0.145)      0.153
Schooling [*] age                0.00063        (0.00234)   -0.0024
Nonwhite                        -0.0169         (0.156)     -0.334
Married                         -0.00422        (0.0804)     0.216
White collar                    -0.0171         (0.0952)     0.0436
Job hazards                      0.197          (0.0601)     0.162
Kids at home                     0.136          (0.152)      0.114
Sight                        1   0.845          (0.173)
Heart                        2   0.720          (0.0990)
Cancer                       3   0.612          (0.166)
Stroke                       7   0.434          (0.177)
                                        Women (N = 5,623)
                                        Limit (ordered)
                             Standard                     Standard
                              Error     Coefficient        Error
Limit [*]                    (0.0416)
In [Y.sub.w] -- In [Y.sub.N] (0.182)
Age spline 61                (0.0901)
Unemployment rate            (0.0237)
Constant                     (9.23)        9.82           (8.04)
Pain index                   (0.0502)      0.373          (0.0651)
Age                          (0.297)       0.291          (0.286)
Age squared                  (0.0027)     -0.00240        (0.00252)
Schooling                    (0.114)       0.0662         (0.146)
Schooling [*] age            (0.0037)     -0.00078        (0.0026)
Nonwhite                     (0.100)      -0.239          (0.0842)
Married                      (0.0736)     -0.0242         (0.0908)
White collar                 (0.0555)      0.0764         (0.116)
Job hazards                  (0.0735)      0.0943         (0.0959)
Kids at home                 (0.134)      -0.0618         (0.0552)
Sight                                 8    0.166          (0.169)
Heart                                 1    0.310          (0.131)
Cancer                                9    0.161          (0.154)
Stroke                                5    0.258          (0.228)
                             Coefficient Error
Limit [*]                      -0.433    (0.0501)
In [Y.sub.w] -- In [Y.sub.N]    0.553    (0.201)
Age spline 61                  -0.260    (0.146)
Unemployment rate              -0.0367   (0.0202)
Constant                      -18.7      (6.20)
Pain index                     -0.0195   (0.0342)
Age                             0.649    (0.222)
Age squared                    -0.0058   (0.0020)
Schooling                       0.221    (0.0941)
Schooling [*] age              -0.0037   (0.0022)
Nonwhite                       -0.120    (0.0585)
Married                        -0.268    (0.0733)
White collar                    0.387    (0.0615)
Job hazards                     0.489    (0.0566)
Kids at home                    0.0328   (0.0429)
Legs/feet                                      4      0.576  (0.0935)
Lung                                           6      0.472  (0.124)
Back                                           5      0.416  (0.0843)
Diabetes                                       8      0.403  (0.111)
Emotional                                     10      0.285  (0.110)
Arthritis                                      9      0.345  (0.0855)
Asthma                                        11      0.267  (0.132)
Hypertension                                  13      0.163  (0.0960)
Stomach                                       12      0.192  (0.102)
Kidney                                        14      0.121  (0.107)
Hearing                                       15      0.0459 (0.152)
Number of cond [*] schooling                         -0.0042 (0.0049)
Number of cond [*] white collar                      -0.0021 (0.0453)
BMI [less than] 20                                    0.149  (0.210)
25 [less than or equal to] BMI [less than] 30         0.0793 (0.0616)
BMI [greater than or equal to] 30                     0.132  (0.0714)
Drinks [greater than] 2                               0.0176 (0.0900)
Smoker                                                0.0734 (0.0543)
Light exercise                                       -0.102  (0.0523)
Heavy exercise                                       -0.120  (0.0842)
Northeast                                             0.0231 (0.0901)
West                                                  0.0981 (0.0833)
South                                                -0.0475 (0.0635)
[micro]                                               0.466  (0.0369)
[[rho].sub.LW]                                       -0.322  (0.392)
[[rho].sub.LI]                                       -0.179  (0.220)
[[rho].sub.WI]                                                        -0.212
[[rho].sub.WO]                                                         0.327
LL                                               -4,241
Legs/feet                                              4      0.267  (0.118)
Lung                                                  10      0.139  (0.118)
Back                                                   2      0.303  (0.107)
Diabetes                                              14      0.0640 (0.137)
Emotional                                              6      0.251  (0.129)
Arthritis                                              3      0.277  (0.112)
Asthma                                                 7      0.215  (0.135)
Hypertension                                          13      0.0701 (0.104)
Stomach                                               15      0.0062 (0.102)
Kidney                                                12      0.114  (0.101)
Hearing                                               11      0.119  (0.274)
Number of cond [*] schooling                                  0.0026 (0.0062)
Number of cond [*] white collar                              -0.0222 (0.0427)
BMI [less than] 20                                            0.131  (0.147)
25 [less than or equal to] BMI [less than] 30                 0.0592 (0.0667)
BMI [greater than or equal to] 30                             0.187  (0.0732)
Drinks [greater than] 2                                       0.0122 (0.192)
Smoker                                                        0.0442 (0.0547)
Light exercise                                               -0.0195 (0.0546)
Heavy exercise                                               -0.0311 (0.0893)
Northeast                                                    -0.0651 (0.0823)
West                                                          0.176  (0.0861)
South                                                        -0.0413 (0.0689)
[micro]                                                       0.0550 (0.0388)
[[rho].sub.LW]                                                0.104  (0.290)
[[rho].sub.LI]                                                0.247  (0.202)
[[rho].sub.WI]                                (0.372)
[[rho].sub.WO]                                (0.298)
LL                                                       -5,019
Number of cond [*] schooling
Number of cond [*] white collar
BMI [less than] 20

25 [less than or equal to] BMI [less than] 30
BMI [greater than or equal to] 30
Drinks [greater than] 2
Light exercise
Heavy exercise
[[rho].sub.WI]                                -0.194 (0.313)
[[rho].sub.WO]                                 0.401 (0.343)
  Comparison of Disability Indices in the Participation Equation--Ordered
                                                                Model C
                                       Model A   Model B     No Disability
                                       "True"   "Biased"        Measure
  Base proportion of nonworkers          0.224     0.224          0.224
  Percentage change following 10 per-    3.62      2.76           1.78
   cent increase in income replace              (-23.9%) [a]   (-50.9%)
   ment rate
  Percentage change following one       64.4      75.4
   standard deviation increase in lim-         (+ 17.2%)
  Base proportion of nonworkers          0.386     0.386          0.386
  Percentage change following 10 per-    4.41      3.54           2.80
   cent increase in income replace-             (-19.7%)       (-36.5%)
   ment rate
  Percentage change following one       29.5      36.9
   standard deviation increase in lim-                         (+24.9%)

Notes: Model A: "True" limitation index used in participation equation.

Model B: "Biased" limitation used in participation equation (includes limitation responses of nonworkers.

Model C: No limitation index used in participation equation.

(a.)Numbers in parentheses represent percentage changes compared with Model A.
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Author:Kreider, Brent
Publication:Journal of Human Resources
Date:Sep 22, 1999
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