Abstract
Retirement is an important event in the life of an individual. The decision to retire or exit from full-time employment may be motivated by several factors, including health. This paper explores the effect of both subjective and relatively more objective physical and mental health conditions on the probability of exit from full-time employment. Using longitudinal data on older Americans from ten waves of the Health and Retirement Study (1992–2010), eight health indices are created from a wide range of health measures by principal component analysis. The effect of these health indices on the time until exit from full-time employment is empirically examined in a proportional hazard model. Single and competing risk specifications are estimated that allow for multiple spells of full-time employment and control for unobserved heterogeneity. The main results suggest that better self-reported health decreases the likelihood of exit from full- time employment, while poor physical health (functional limitations factor) increases the likelihood of exit from full-time employment via complete retirement and disability. For mental health, I find that depression increases the likelihood of exit via complete retirement, part-time work and unemployment while cognitive disorders lead to an increase in likelihood of exit via the disability exit route. Hence, physical and mental health problems are both impediments to continued work. These results have implications for public policies targeted towards retaining older workers within the labor market.
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Notes
However, such investments might come at an “unanticipated cost” of extending the individual’s lifespan, so that the government may end up paying more in social security over all. Boskin et al. (1987); Coile et al. (2002) and Gruber and Wise (2005) explore this area, which is beyond the focus of this paper.
Since each wave is two years apart.
Twenty eight different health measures have been used in PCA.
The HRS (Health and Retirement Study) is sponsored by the National Institute on Aging (grant number NIA U01AG009740) and is conducted by the University of Michigan. More information is available at: http://hrsonline.isr.umich.edu/
Since I am focusing here on initial employment spells, any subsequent transitions back to full-time work are ignored. This implies I am considering retirement to be an absorbing state.
In the HRS, individuals who report working 35 or more hours per week are considered full-time and those working less are considered part-time. This includes the hours and weeks worked in both the main and second job. The key HRS variable of interest here is the labor force participation variable (LFPV). If the respondent reports working full- time then their LFPV is set to that status. If he/she is working part-time and also reports retirement LFPV is set to partly retired. If there is no such reporting of retirement, then the variable is set to working part-time. If the respondent is neither working nor looking for work but there is reporting of retirement, then his LFPV is set to retired (completely retired). If retirement is not mentioned and a disabled employment status is given, then it is set to disabled. Otherwise, it is set to “not in the labor force.” If the respondent is not working but is looking for a full-time work, labor force participation is set to unemployed. If he/she is looking for a part-time job and mentions retirement, then it is set to partly retired. Finally, individuals looking for a part-time job and not reporting retirement, have LFPV set to unemployed.
The available HRS data allows me to follow the individuals through nine transitions: 1992–94, 1994–96, 1996–98, 1998–00, 2000–02, 2002–04, 2004–06, 2006–08, and 2008–10. The 4128 individuals who were at least 50 years old and worked full-time in 1992 are followed over the next 18 years (1992–2010). Between 1992 and 1994, 20 individuals leave the sample due to attrition (death or other reason), so 4108 individuals are “at risk” of retirement (exit) during 1994–1996. Among them 349 individuals already exit via complete retirement route by 1994. Another 148, 209, 70 and 67 individuals exit via partial retirement, part-time work, unemployment and disability/not in labor force routes respectively. Of the 3265 individuals who remain full-time employed in the sample in 1994, 27 are lost due to attrition, so only 3238 remain at the risk of retirement. Among them 372 individuals already exit via complete retirement route by 1996. Another 173, 20, 87 and 76 individuals exit via partial retirement, part-time work, unemployment and disability/not in labor force routes respectively. Similar pattern is observed between each two year time period. Finally, among the 4128 individuals only 142 remain full-time employed through all 18 years while the rest exited via one of the five routes or attrite.
This is reported in Appendix, Table 8.
The associated baseline hazard rates are reported in Appendix Table 9.
Factors having eigen-values greater than 1 are retained. These eight factors are the “principal components” of the health of individuals in the sample. In other words, they represent perceived health status of individuals in the sample in the best possible objective way. From twenty eight diverse health outcome variables. Eight factors with Eigen value greater than 1 are generated using Principal Component Factor Analysis which is used to create the health indices used as explanatory variable in the hazard model.
Refer to Appendix Table 11 to see the factor loadings (i.e. which measures load heavily in each factor).
I have also estimated the following other parametric models Gompertz (proportional hazard model), Log normal, Log logistic and Gamma (Accelerated Failure Time models) for all specifications (not reported) and found the time ratios (similar to hazard ratios). In the generalized gamma model, the Wald test for κ =1 provides support for adopting the Weibull distribution.
Expected subjective probability of living until age 85.
Individuals with the same observed characteristics are not identical. The notion of unobserved heterogeneity amounts to observations being conditionally different (heterogeneous) in terms of their hazards in ways that are unaccounted for in the standard hazard model. In other words, some observations are more “frail” than others.
The drawback of such fixed effects model is that it does not differentiate between full-time employment spells of different duration.
In both panels, B and C chronic conditions lead to a statistically significant increase in probability of complete retirement. However, from the estimates in panel B it is only possible to say whether the presence of multiple chronic conditions (dichotomous) affect the probability of complete retirement. However, panel C has a more objective measure of chronic illness because Factor 1 includes information on the count of chronic conditions based on medical diagnosis as well as information on intake of prescriptions drugs specific for treating those chronic conditions. Similarly, in Panel B it is possible to state that presence of psychological disorder (dichotomous) raises the probability of complete retirement. While in Panel C, factor 5 indicates a high score on CESD scale (depression), having work-related stress and medically diagnosed psychological disorder for which the individual also takes prescription medication, increases the probability of complete retirement. Therefore, the panel C health factors are clearly more objective than the panel B standard health measures.
Here Absolute Effect = Hazard Ratio * Average Exit Probability via that route. Average Exit Probability = No. of Exits / (No. of Spells * Average Spell Length).
The initial exit model with frailty is presented in Appendix Table 12.
Cox-Proportional Hazard Model for multiple exits is reported in Appendix Table 13.
These results are reported in Appendix Table 14.
I define a reduction in overall self-reported health by flagging anyone that went from excellent to poor self-reported health between waves. Similarly, I defined a reductions in health associated with ADL difficulties and chronic conditions by flagging anyone that went from reporting a 0 to a 5 between waves. Finally, anyone with an onset of a memory-related disease was flagged.
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Appendices
Appendix 1
Latent Health Stock
The HRS has a variety of health measures. These include a subjective general measure of individual’s self-reported health and relatively more objective measures of health based such as functional limitations (ADL difficulty), medical diagnosis of chronic illnesses, body mass index and health care utilization which are reported in Table 1. Although self-reported health has been widely used in several studies based on survey data, it may be plagued with problems that lead to bias. As discussed earlier in the paper the problems pertaining to self-reported health are first, self-reported measures of health are based on subjective judgments and there is no reason to believe that these judgments are comparable across individuals. Second, since poor health may represent a legitimate reason for a person of working age to be outside the labor force, respondents who are not working may cite health problems as a way to rationalize behavior (the “justification hypothesis”). The alternative to using self-reported health could be substituting it by relatively more objective measures of health.Footnote 26 But these measures may also be self-reported or assessed by the interviewer such that they are not superior indicators of an individual’s health (Bound 1991). In order to mitigate the problems associated with self-reported measure of individual health, I have defined a latent health stock variable. Following Bound (1991) and implemented in Bound et al. (1998), a model of self-reported health as a function of relatively more objective measures of health (reported in Table 1) is estimated to create a latent health stock.Footnote 27 Then the predicted value for the latent health stock is used as a regressor in hazard analysis.
I adopted the approach of Rice et al. (2010) and used an ordered probit model to estimate self-reported health, where the ordered measure of self-reported health (1 = poor, 2 = fair, 3 = good or very good and 4 = excellent) is regressed on 16 relatively more objective physical and mental health explanatory variables and healthcare utilization. The predicted value of the outcome from this estimation is the latent health stock variable which is used as a regressor in proportional hazard model in the main body of the paper. Accordingly, a lower level of health status is given by a smaller value of the latent health stock while a higher level of health status is given by a larger value of the latent health stock. Table 15 presents the marginal effects of the objective health measures for the four different responses (cut points) for self-reported health in an ordered probit model. All objective measures have a statistically significant impact on an individual’s self-report of health but each measure weighs differently across the four response categories. In Table 15, column (1) positive marginal effects imply incidence of functional limitations, chronic conditions, depression, higher BMI, more nights spent at hospital, more doctor office visits and higher out of pocket medical expenditure will increase the probability with which an individual is predicted to be in the lowest health category (poor). Similarly, in column (4) the negative marginal effects signify incidence of functional limitations, chronic conditions, depression, higher BMI, more nights spent at hospital, more doctor office visits and higher out of pocket medical expenditure will increase the probability with which an individual is predicted to be in the highest health category (excellent). The same holds true for the marginal effects in the other columns. An increase in latent health stock implies a change from prediction of poor health to better health.
Principal Component Analysis (PCA).
Principal components analysis is a method for detecting a small number of uncorrelated variables, called “principal components”, from a large dataset. The objective of principal components analysis is to explain the maximum amount of variance with the minimum number of principal components. PCA analyzes a dataset representing observations described by several variables, which are, in general, inter-correlated. Its goal is to extract the important information from the data and to express this information as a set of new orthogonal variables called principal components. The primary goal of principal component analysis is data reduction and addressing multicollinearity. It is a non-parametric technique which has an underlying weakness- data reduction due to PCA leads to loss of information. The association between the components and the original variables is called the component’s eigenvalue. In multivariate analysis, the correlation between the component and the original variables is called the component loadings (factor loadings) which are analogous to correlation coefficients, squaring them give the amount of explained variation. Therefore the component loadings tell us how much of the variation in a variable is explained by the component.
In this paper, the main purpose of using principal component analysis is to lend more objectivity to health measures. According to the theory of health production function, an individual’s health is a durable good which depends on several factors, some of which may be influenced by an individual. Hence health status of an individual does not solely depend on incidence of physical and mental diseases but on factors like utilization of healthcare inputs, lifestyle behavioral practices, job characteristics, genetic elements etc. Accordingly, I use twenty-eight interrelated variables that are likely to influence the health status of an individual. These variables are reported in Appendix Table 11. In addition to the standard physical and mental health measures (which includes ADL difficulties, other mobility difficulties, chronic illnesses, depression and cognitive problems), I have included information on memory related diseases (Dementia and Alzheimer), healthcare utilization (hospital stay, nursing home stay, doctor office visits and out of pocket medical expenditure), lifestyle factors (smoking, drinking behavior, exercising), job related characteristics (stress, physical effort at work) and genetic information (proxied by average age of parents). From variables, PCA yields 28 factors or principal components. Out of these 28 extracted components only eight with Eigen value greater than 1 are retained (reported in Appendix Table 10). This is known as the “Kaiser-Gutman” Rule. The sum of all Eigen values is equal to number of included variables. In Table 10, ‘Difference’ column shows the difference in two consecutive Eigen values. ‘Proportion’ represents the relative weight of each factor in the total variance. For example Factor 1 (Chronic Condition Factor) explains 13% of the total variance. ‘Cumulative Proportion Explained’ shows the amount of variance explained by n + (n-1) factors. For example Factor 1 (Chronic Conditions Factor) and Factor 2 (Functional Limitations) explain 22% of total variance. Similarly the eight chosen factors together explain 54% of the total variance. Table 11 shows the pattern matrix which gives a clearer picture of the relevance of each variable in a factor. Factor loadings are the weights and correlations between each variable and the factor. The higher the load the more relevant is the variable in defining the factor’s dimensionality. A positive sign indicates a positive relation between the variable and the factor and a negative value indicates an inverse impact on the factor. Uniqueness is the variance that is ‘unique’ to the variable and not shared with other variables. Each factor is named keeping in mind the variables that load heavily in them. As illustrated in Appendix Table 11, number of chronic conditions load most heavily in Factor 1. Number of ADL difficulties and Mobility Difficulties define Factor 2, but the former has higher loading or correlation with the factor. Hence ADL difficulties are more important that mobility difficulties. Similarly, nights spent at hospital and nursing home define Factor 3, incidence of memory related diseases (Dementia and Alzheimer) and total cognition score defines Factor 4. The heaviest factor loadings for each factor are shaded in grey in Appendix Table 11.
These factors are orthogonal to each other which means they are not correlated to each other. Based on factor loadings I have labeled the factors as Factor 1: Has chronic conditions, Factor 2: Has functional limitation, Factor 3: Hospital stay, Factor 4: Has cognitive functioning problems, Factor 5: Has depression, Factor 6: Lack of physical exercise, Factor 7: Has cancer, and Factor 8: Has lifestyle behavioral problems. Principal components are used because several variables together rather than alone define an interpretable concept. The predicted value of the factors are then used in hazard analysis. Without using PCA it would not be possible to disentangle the causal effect of the health measures since they are highly interrelated. Although uncorrelated factors created through PCA are valuable for empirical model in the paper, there are limitations like loss of information due to aggregation and difficulty in interpretation of regressions coefficients.
Appendix 2
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Roy, S.B. Effect of Health on Retirement of Older Americans: a Competing Risks Study. J Labor Res 39, 56–98 (2018). https://doi.org/10.1007/s12122-017-9255-6
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DOI: https://doi.org/10.1007/s12122-017-9255-6
Keywords
- Health indices
- Principal component analysis
- Retirement
- Competing risks
- Proportional hazard
- Unobserved heterogeneity