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RESEARCH ARTICLE |
a Department of Sociology and Gerontology Program, Purdue University, West Lafayette, Indiana
Jessica A. Kelley-Moore, Purdue University, 1365 Stone Hall, West Lafayette, IN 47907-1365 E-mail: kelleyj{at}sri.soc.purdue.edu.
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Abstract |
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 TOP Abstract Functional Limitations and...MethodsResultsDiscussionReferences |
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Methods. With 2 waves of a national probability sample of adults aged 60 years and older, this research used structural equation models to estimate the influence of these 2 mechanisms.
Results. Results indicated that functional limitations were associated with less frequent religious service attendance at the same wave, largely because of the barrier mechanism; no support was found for the benefit mechanism. Neither mechanism was significant over time.
Discussion. Findings suggest that there is a temporal and salient decline in social activities such as religious service attendance when lower body functional limitations are highest. However, long-term engagement in religious service attendance is not predicted by baseline functional limitations, indicating that there are not long-term declines in attendance because of higher levels of functional limitations.
THE role that religion plays in health, long neglected in scholarly research, has drawn considerable attention in the past decade. A good portion of the research has revealed a positive relationship between religion and health among older people, but the precise mechanisms that explain this relationship remain to be clarified.
Participation in a religious group has been shown to have health benefits. For instance, older adults who attend regularly tend to have better health (Idler and Kasl 1992
, Idler and Kasl 1997b). However, some scholars have argued that experiencing serious health problems can actually be a barrier to religious participation (Ainlay, Singleton, and Swigert 1992; Barusch 1999). Thus, adults with greater physical limitations may be unable or less willing to attend religious services, leaving the more healthy adults in the religious group. As Levin and Vanderpool 1987(p. 593) observed: "Correlations between health and religious attendance may, in reality, represent correlations between health and functional health (i.e., the capability to get out of bed and go to services)."
There may be two processes at work: the benefit mechanism and the barrier mechanism. Persons who are active in religious groups may receive health benefits through that participation, which is considered the benefit mechanism. However, functional limitations may be a barrier to frequent or even regular activity within the religious group. It is possible that both processes occur simultaneously. Participation in religious groups may spur better functional health, but this may only occur for those who are healthy enough to participate in the first place. Most empirical research to date has focused only on the benefit mechanism and has been derived from a cross-sectional research design.
Our purpose in the present research was to consider the link between religious service attendance and functional limitations by systematically examining whether both benefit and barrier mechanisms are at work—and if so, which is stronger. We used longitudinal data from a national probability community sample to examine the competing influences of functional limitations and religious service attendance among older adults. We used structural equation models to test simultaneously the effects of religious service attendance as a benefit mechanism and functional limitations as a barrier mechanism across time.
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Functional Limitations and Religious Attendance |
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TOPAbstractFunctional Limitations and...MethodsResultsDiscussionReferences |
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; Chatters 2000; Hummer, Rogers, Nam, and Ellison 1999; Idler 1987; Krause 1998; Levin 1996; Levin and Chatters 1998; Levin and Vanderpool 1991; Oman and Reed 1998; Strawbridge, Shema, Cohen, and Kaplan 2001; Witter, Strock, Okun, and Haring 1985), especially older persons (Idler and Kasl 1997a, Idler and Kasl 1997b). Participation in a religious group can have health benefits including lower risk of mortality (Strawbridge, Cohen, Shema, and Kaplan 1997), less depression (Koenig et al. 1997), and better overall mental health (Levin and Chatters 1998).
Most of the research on the effect of religious participation on physical health has focused on subjective health (Ainlay et al. 1992; Drevenstedt 1998; Ferraro and Albrecht-Jensen 1991). The relationship between religious service attendance and subjective health has been well documented in both cross-sectional and longitudinal analyses (Ellison 1991; Idler 1987; Idler and Kasl 1997a). Persons who regularly attend religious services are more likely to rate their health better.
A much smaller body of research on religion and physical health has demonstrated that religious service attendance influences functional limitations, with attendance providing a protective effect (Idler and Kasl 1997b). Using the New Haven sample of the multiwave Established Populations for Epidemiologic Studies of the Elderly, Idler and Kasl examined the effect of religious service attendance on functional disability over time. The effect may be temporary for those experiencing health decline, but religious service attendance and functional disability are negatively correlated. This means that those who attend religious services more frequently tend to have fewer functional limitations. This study used a sample of a single community, however, and no attention was given to the simultaneous effect of physical function on service attendance.
In considering this negative association between functional limitations and religious service attendance, the literature suggests two separate mechanisms for the relationship. The first is the benefit mechanism, described by Idler 1987 and Idler and Kasl 1992, Idler and Kasl 1997b. They and others have argued that the experience of religious participation, manifested in fellowship, ritual, and ideology, is beneficial to health, thereby decreasing the risk of functional limitations (Levin 1996).
The exact reasons why religion positively affects physical health have been systematically studied and, despite differences in samples and measurement, have produced strong and consistent results (Chatters 2000; Levin 1996; Strawbridge et al. 2001). Activity within a religious group may provide social support from other group members, which has been demonstrated to buffer the effect of stressors on health, including functional limitations (Newsom and Schulz 1996; Strawbridge et al. 2001). In addition, religious ideology may offer positive coping mechanisms, which would help provide meaning for existing pain (Kotarba 1983). Research has shown that individuals who use positive religious coping tend to have better health or are better able to control pain from chronic conditions (Keefe et al. 2001; Koenig, Pargament, and Nielsen 1998). Finally, some religious groups have proscriptive behavior norms, including abstention from alcohol, tobacco, caffeine, and meat. Active, committed members may be more likely to follow these norms as a demonstration of their faith, simultaneously avoiding many potentially disabling health problems such as heart disease, stroke, and diabetes (Levin and Vanderpool 1987; Strawbridge et al. 2001).
For the benefit mechanism, the causal ordering places service attendance before functional limitations, positing that religion has a salutary effect on health. This interpretation has been offered repeatedly, but some have argued that conclusions about the salutary effects of religious attendance on health may be overstated because the second mechanism has not been considered (Levin and Vanderpool 1987).
The second mechanism posits that functional limitations hinder participation in religious social life; disabled persons may have a difficult time getting to and sitting through religious services. Functional limitations may not hamper participation in meditative and mystical dimensions of religiosity, but especially for older people, functional limitations may make attendance at religious services a difficult experience (e.g., rituals requiring kneeling or standing for long periods of time, inability to dress oneself to go to services). Whether functional limitations impede social participation in religious activities has been studied by several researchers, but only cross-sectionally (Ainlay et al. 1992; Barusch 1999). However, they found that higher levels of functional limitations were associated with lower religious participation.
Persons with moderate to severe levels of functional limitations may face a variety of obstacles such as stairs, manual doors, or standard-sized parking spaces, which may be physical barriers to social engagement. Even before arriving at the place of worship, functional limitations may prevent an older adult from buttoning a shirt or brushing hair. Older adults often experience an increase in functional limitations because of chronic illness. Even among older adults who believe they do not have a disability, 21% can be classified as disabled according to activities of daily living measurements—and another 40% have mild or moderate disability (Langlois et al. 1996). Often these persons who believe they do not have a disability attribute their limited mobility and inability to perform daily functions to "old age" or "getting older" (Williamson and Fried 1996).
Nevertheless, older adults tend to have stronger religious beliefs and higher levels of participation in religious activities compared with younger adults (Moberg 1997). At a time when functional limitations may be steadily limiting mobility, there are still markedly higher rates of public and private religious behaviors among older adults, even those with severe functional limitations (Idler 1987). However, other research has demonstrated that attendance at religious services wanes as functional limitations increase (Barusch 1999).
Although both the physical barrier and the health benefit mechanisms have been examined in previous research, we are unaware of any study that considered the two mechanisms simultaneously with longitudinal data. Thus, our purpose in this research was to examine the two mechanisms simultaneously by addressing two overarching research questions. First, do functional limitations curb attendance at religious services for older adults? Second, if both the benefit and the barrier mechanisms are at work, which is the stronger of the two? Although religious service attendance is only a single indicator of overall religiosity, it was the primary outcome in this analysis because it captures the physical act of going to a religious service. Private religious behaviors and beliefs may not vary among older adults by health status, but functional limitations could create a barrier to active social engagement at the place of worship (Hays et al. 1998). On the basis of previous literature, we expected that the health benefits received from religious service attendance would outweigh the negative effect of functional limitations on attendance.
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Methods |
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. The original sample was 3,617 adults aged 18 and older, with an oversample of African Americans and persons aged 60 years and older. In this study we used a subsample of adults who were aged 60 years and older and were not institutionalized or living in group quarters (N = 1,617). The baseline data were collected in 1986 and the respondents were followed up in 1989 (N = 1,282), referred to as Wave 1 (W1) and Wave 2 (W2), respectively. These data were ideal for this analysis because they provided a nationally representative sample of adults aged 60 and older who were followed up almost 3 years later. The survey also included repeated measures of both religious service attendance and functional limitations. Both waves of the ACL occurred before the 1990 Americans with Disabilities Act, which required facilities to be accessible for those who have physical limitations. Religious organizations were among the many institutions targeted for their facilities that were disability "unfriendly." The results from this study are still applicable in that religious rituals with repeated standing and kneeling may not have changed, even if the physical plant did. Thus, even though group members may be sympathetic to older adults who have difficulty or cannot perform the activity or ritual, older individuals may still feel social embarrassment or stigma.
Measures
Religious service attendance, measured at both waves, was one of the endogenous variables in the analysis. It was measured by the question, "How often do you usually attend religious services?" The six response categories at each wave were scored "never" (1), "less than once a month" (2), "once a month" (3), "2–3 times a month" (4), "once a week" (5), and "more than once a week" (6).
We included binary variables indicating religious preference in the analysis to control for differences in religious service attendance norms (these were not available at the follow-up survey). Respondents were asked at baseline, "What is your religious preference?" Five response categories were available: Protestant, Catholic, Jewish, Other, or None. Immediately following, respondents were asked to identify their specific religious group within the broad category. From these responses, we created several binary variables to highlight specific religious preferences, including Jewish, conservative Protestant, Catholic, Southern Baptist, other Protestant, and no religious preference. Preliminary analyses of these variables on both functional limitations and religious service attendance revealed that only two religious preferences were significant: conservative Protestant and no religious preference. Conservative Protestants (27% of total sample) including Fundamentalist denominations (e.g., Church of God, Pentecostal, Assembly of God, and Church of Christ) and Southern Baptists, generally had higher rates of attendance. No religious preference (7% of total sample) was for all those who responded "none" when asked to specify a religion.
Three other religion indicators were used: religious belief salience, how often the respondent read religious materials, and how often the respondent watched or listened to religious programming. For belief salience, respondents were asked, "In general, how important are religious or spiritual beliefs in your day-to-day life?" Four response categories were used: "very important" (4), "fairly important" (3), "not too important" (2), and "not at all important" (1). For the other two religion variables, the possible answer choices ranged from "never" (1) to "more than once a week" (6).
Attendance at religious services was measured with one item at each wave; functional limitations, the other endogenous variable in the analysis, was a latent variable with four indicators at each wave. The first indicator was self-rated activity limitation: "How much are your daily activities limited in any way by your health or health-related problems?" Five categories followed ranging from "not at all" (1) to "a great deal" (5). The second indicator of functional limitations was a dichotomous self-report of whether the respondent was restricted to a bed or chair all day (all others were zero). The final two indicators were the amount of difficulty the respondent had walking blocks and the amount of difficulty the respondent had climbing stairs. The categories ranged from "none" (1) to "cannot do" (5).
Baseline morbidity was included as an exogenous variable. It was a sum of 10 possible health conditions, asked of each respondent: "We would like to know if you have experienced any of the following health problems during the last 12 months. Have you had (specific condition)?" The conditions were arthritis, stroke, foot problems, heart attack or trouble, incontinence, diabetes, lung problems, hypertension, broken bones, and cancer.
Three indicators of social integration were included as exogenous variables. Research has indicated that social networks have positive effects on the availability of resources for those with disabilities (Idler and Kasl 1997a). Therefore, those who are active in the community or live with another person may engage in social groups differently than those who are less integrated.
The first social integration variable was whether the respondent received help from another person or agency to get around the community. Although it is not explicitly stated in the question, this may include rides to religious services. It was a binary variable, coded 1 for "yes" and 0 for "no." Second, frequency of attendance at voluntary association meetings was measured with the question: "How often do you attend meetings or programs of groups, clubs, or organizations that you belong to?" Answer categories ranged from "never" (1) to "more than once a week" (6). Third, respondents who lived alone were identified with a binary variable.
Depression was included as a control variable in the analysis because persons who have functional limitations may be more likely to be depressed than nondisabled persons, and depression may also be associated with more negative ratings of physical limitations (Ainlay et al. 1992; Frerichs, Aneshensel, Yokopenic, and Clark 1982; Idler and Kasl 1992; Turner and Noh 1988). Depression was measured with the Center for Epidemiologic Studies–Depression (CES-D) short scale of 11 items (Radloff 1977).
Additional variables were included in the analysis as covariates. Age was measured in years (60–97). Education ranged from "0–8 years" (1) to "17 years or more" (6). Total family income was measured with 10 categories ranging from "less than $5,000" (1) to "more than $80,000" (10). (Respondents were asked to point to the letter beside the correct income range.) Two status characteristics were measured with dummy variables: Black and female, each coded 1 for "yes" and 0 for "no."
Table 1 provides a list of all variables used in the analysis with the coding, means, and standard deviations of the sample. Endogenous indicators are listed first, followed by the covariates or exogenous indicators. A number of additional variables were tested in preliminary analyses based on ordinary least squares but were deleted from further analyses because they were not significantly related to either functional limitations or religious service attendance. These variables included being married, living in a southern region, and living in a rural region.
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). Generalized least squares were used as the estimation procedure because the endogenous variables were not normally distributed (Bentler and Bonett 1980; Schumacker and Lomax 1996). Estimates were based on an asymptotic covariance matrix generated from polychoric and polyserial correlations calculated in Prelis 2.30 (Joreskog and Sorbom 1993; Schumacker and Lomax 1996).
The hypothesized model in this research was a nonrecursive model testing both the barrier and the benefit mechanisms. Fig. 1 is a simplified illustration of the proposed structural relationships among the endogenous variables. The model consisted of two endogenous variables at each wave: functional limitations and religious service attendance. It tested the simultaneous effects of functional limitations and attendance on each other at baseline while concurrently testing the lagged effects of baseline functional limitations and attendance on the endogenous variables at W2. No causal relationship was specified between attendance and functional limitations at W2; however, the errors between the two endogenous variables (
) were allowed to correlate. We first tested this simple model without the covariates to avoid interpretational confounding (Burt 1976). Finally, the entire model was tested, including all of the covariates listed in Table 1 .
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). Paths across time were measured for both functional limitations and attendance. In preliminary analyses we modeled men and women separately. Because there were no significant differences in either the barrier or the benefit mechanisms, in further analyses we proceeded with the total sample. |
Results |
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TOPAbstractFunctional Limitations and...MethodsResultsDiscussionReferences |
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2 (133, N = 1,282) = 137.62. Other measures of goodness of fit indicated a satisfactory model fit: root mean square error of approximation was .00 and adjusted goodness of fit index was .98. In addition, the normed fit index was above the .90 threshold, and the comparative fit index was 1.00 (Bentler and Bonett 1980; Kelloway 1998). Thus, the results from Model 1 are presented in the following section. None of the alternative specifications provided a better fit than Model 1.
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y) are presented in Table 1 . The y value for each of the indicators was greater than .80, and we placed equality constraints on the functional limitations indicators across time to ensure consistent measurement for change analysis (Hayduk 1987). We estimated elements of the off-diagonal of the theta-epsilon in previous models to correlate the measurement errors among the variables measured at both waves. Only one correlation was significant: between activity limitations at baseline and at W2.
Parameter estimates for Model 1 are presented in Table 3 . Because the hypothesized baseline relationship between functional limitations and attendance was nonrecursive, each of the baseline endogenous variables required at least one instrumental variable (Bollen 1996).
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The second equation in Table 3 shows that stronger religious beliefs, reading religious materials, and watching or listening to religious media were associated with higher frequency of attendance at religious services. Those who volunteered frequently were also more likely to attend religious services. In other words, those who engaged in religious and social activities were also likely to attend the services of a religious group.
At baseline, the path from functional limitations to attendance was negative and significant (p < .01). As specified in the barrier mechanism, this meant that those who had higher functional limitations were less likely to attend religious services. Comparing the standardized slopes (not shown) for the two mechanisms at baseline, functional limitations had a stronger influence on attendance (-.19) than attendance had on functional limitations (.10). This provided clearer evidence in support of the barrier mechanism.
The third equation in Table 3 was for functional limitations at W2. Results showed that those who were older and had higher morbidity were more likely to be disabled. Persons with more functional impairment at W1 were very likely to have higher impairment at W2. The lagged effect of W1 attendance on W2 functional limitations was nonsignificant.
Finally, the fourth column in Table 3 shows the equation for religious service attendance at W2. Just as for attendance at W1, reading religious materials and volunteering frequently were associated with higher religious service attendance. Those who attended frequently at baseline were more likely to attend frequently at W2.
Although the barrier mechanism was observed for the baseline equation, it did not hold across time. Functional limitations at W1 did not significantly affect religious service attendance at W2 (although the slope was in the anticipated direction and close to significance). The correlated error () between functional limitations and attendance at W2 was also nonsignificant, indicating that there was little residual variation in the two constructs once their association at baseline and their W1 values were considered. The overall model provided support only for functional limitations as a barrier mechanism; no support was found for the religious service attendance as a benefit mechanism among respondents of ACL.
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Discussion |
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, Idler and Kasl 1997b). The second mechanism views functional limitations as a barrier to effective social engagement, including attendance at religious services. This process identifies the influence of functional limitations on the experience of religion, especially religious activity (Ainlay et al. 1992; Levin and Vanderpool 1987). Whereas much of the previous research used ordinary least squares on cross-sectional data to investigate one or the other of these mechanisms, this is the first study of which we are aware to use longitudinal data to test both mechanisms. An advantage of this analysis is that both the benefit and the barrier mechanisms were tested simultaneously with structural equation models.
Tests of several recursive and nonrecursive models do not offer support for the benefit mechanism. Even when attendance significantly affects functional limitations, the relationship is weak and positive rather than negative. Those who attend services frequently are more likely to have slightly higher functional limitations. Although some may argue that religious service attendance is deleterious to functional ability, we think that the more reasonable interpretation is that of a convergence of persons with physical limitations—perhaps permanent ones—to religious settings. Moreover, this effect is uncovered only when the nonrecursive model is specified.
The conclusion is that many people with modest forms of functional limitations continue to attend religious services. Older adults, who are more likely to be disabled than younger adults, tend to be more religiously active and attend religious services more frequently (Moberg 1997). Religion may be providing inspiration and meaning to those with less severe forms of functional limitations.
In considering the lack of support for the benefit mechanism in this study, it is important to recall that these models do not measure whether religious service attendance affects subjective health. It is entirely possible that going to religious services and activities has many health benefits including lower depression and better subjective health—but that attendance has no effect on whether a respondent can walk up a flight of stairs. In addition, one of the four indicators of functional limitations in this study is whether the respondent is confined to a bed or chair all day. Respondents whose health has deteriorated to the point that they are no longer able to get out of bed are most likely not going to be attending services. The significant barrier mechanism may be capturing this effect.
A second possibility for why the benefit mechanism is not supported is the uniqueness of the ACL sample. The survey manifests a fairly high level of religiosity. For instance, the modal response for religious belief salience was "very important," and the modal response for frequency of service attendance was "once a week." Idler and Kasl 1997a, Idler and Kasl 1997b data are from New Haven, CT, an area with a generally lower level of religious participation. Although we tested for southern and rural residence in preliminary models, one wonders if differences in sampling may account for our inability to replicate their findings.
No significant differences by gender or race are found in these models. These findings are unexpected in light of the empirically consistent health differences and religious service attendance norms. White adults and men are less likely to attend religious services or be privately religious (Levin, Taylor, and Chatters 1994). Women are more likely to be disabled than men. In addition, there is a consistent health differential between Whites and African Americans, including physical function (Guralnik, Land, Blazer, Fillenbaum, and Branch 1993). Drevenstedt 1998 found that religious service attendance significantly predicted self-rated health for all Whites, as well as Black and Latino women, but it was not a significant predictor for Black and Latino men. The author concluded that if the sample sizes for Black and Latino adults had been comparable to the White sample, some of the relationships might have been significant. ACL has an oversample of African Americans, providing the necessary statistical power for the analyses in this study. The lack of significant differences may indicate that the impact of functional limitations on religious service attendance is a universal experience of managing pain and physical limitations regardless of gender or race. Future studies should examine the barrier and benefit mechanisms with multidimensional measures of religiosity, especially public practice, to determine if the relationship holds.
Although we find no support for the health benefit mechanism, the physical barrier mechanism is consistently significant. The barrier mechanism is significant in both recursive and nonrecursive models of cross-sectional relations, but there is no longitudinal barrier effect. In other words, much of the effect of functional limitations on religious service attendance is immediate, reflecting the temporal salience of pain or incapacity on social engagement. This is consistent with previous research on functional limitations, which has argued that social withdrawal happens almost simultaneously with the functional limitations experienced (Barusch 1999).
Several features of the measure of functional limitations constructed from the ACL should be considered in interpreting results supporting the barrier mechanism. First, the ACL measures include both objective and subjective elements. Decisions about whether to attend religious services or engage in any social activity are based on the respondent's perceived level of ability rather than actual level. The measure of functional limitations used here combines the objective and subjective responses to capture both functional ability and perceptions of function.
Second, the measure of functional limitations focuses on mobility or lower body function (whether the respondent is in a bed or chair all day, the level of difficulty walking blocks, and the level of difficulty climbing stairs). The experience of physical limitations varies from person to person on the basis of the type of health condition and how much help is needed to maneuver. In addition, persons with lower body functional limitations tend to be much less mobile than persons with exclusively upper body limitations (Clark, Mungai, Stump, and Wolinsky 1997; Ferrucci et al. 1998). The measurement model developed from the ACL targets those who have trouble walking, driving, or sitting for long periods of time—all of which are often needed for full participation in a religious group. This is a claim for data strength when some may argue that it is a weakness. The negative relationship between functional limitations and religious service attendance, at baseline and over time, demonstrates how those with lower body limitations may be more likely to disengage from social activities because of pain, incapacity, or the awkwardness associated with reduced mobility. At the same time, it is possible that the measures available in ACL make it more difficult to uncover the benefit mechanism. Perhaps the benefit effect found in other studies is a result of physical function measures that combine upper and lower body disability. Many researchers have used scales originally developed by Katz, Ford, Moskowitz, Jackson, and Jaffee 1963, Rosow and Breslau 1966, and Nagi 1965 that were designed to encompass both upper and lower body mobility (Ainlay et al. 1992; Idler 1987; Idler and Kasl 1992, Idler and Kasl 1997a, Idler and Kasl 1997b). Unfortunately, ACL does not have measures of upper body function. Future research should examine the relationship between religious service attendance and domain-specific functional limitations.
Another limitation of the present study is the limited religion variables available in the ACL. The demonstration of a negative relationship between functional limitations and attendance reflects the level of social engagement in the religious group. This outcome is of primary interest because it captures the physical act of getting to the religious service. We make no inferences about the private religious behaviors of persons who have functional limitations. Physical health problems may not necessarily act as a barrier to prayer or personal faith. Respondents were never asked about their frequency of prayer and were only asked about consuming religious media (watching/listening to religious programs, reading religious materials) at W1. Religious service attendance was the only religious behavior measure asked about again at W2. Other religious practices could be substituted for declining attendance, but we cannot test these effects with ACL.
The literature offering support for the benefit mechanism has a preponderance of studies that rely on more subjective health measures such as self-rated health or well-being (Ainlay et al. 1992; Ferraro and Albrecht-Jensen 1991). In addition, there clearly are some studies that support the benefit thesis on other outcomes such as morbidity and mortality (Hummer et al. 1999; Idler and Kasl 1997a, Idler and Kasl 1997b; Oman and Reed 1998; Strawbridge et al. 1997). Although the benefit thesis may apply to certain types of functional limitations, there is no evidence in the ACL survey that it exists once one considers both mechanisms simultaneously. Without entertaining the possibility of a barrier process, it is possible that one may overestimate the benefit mechanism.
Persons with disabilities may find it difficult to participate in social settings, including religious groups, that are not conducive to their needs. Repeated standing and sitting, and sometimes kneeling, during a religious service can be much more difficult for those who have physical limitations. The findings from this research demonstrate that functional limitations are associated with lower levels of religious service attendance and offer no support for the hypothesis that attendance reduces functional limitations. Religious service attendance may benefit various dimensions of health, but such benefits can only accrue if the person is functionally capable of attending. The present research shows the importance of the barrier mechanism and the utility of simultaneously considering both the barrier and benefit mechanisms.
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Acknowledgments |
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Received for publication September 11, 2000. Accepted for publication May 15, 2001.
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