Stress inducing or relieving? Retirement s causal effect on health

Transcription

1 Stress inducing or relieving? Retirement s causal effect on health Peter Eibich 1 This Version: June 27, 2013 Abstract This paper estimates the causal effect of retirement on health using Regression Discontinuity Design and instrumental variables. Age serves as an assignment variable for the RDD estimation and eligibility for a state pension is used as an instrument for retirement. Self-reported health status and the physical and mental summary score of the SF12 measure are used as dependent variables. The results show an increase in subjective health and mental health. There is evidence for effect heterogeneity with respect to gender, education and job satisfaction. Keywords: retirement, health, regression discontinuity design, instrumental variables, pension eligibility JEL codes: I12, J14, J26 1 DIW Berlin, Mohrenstrasse 58, Berlin and University of Hamburg, Germany, peibich@diw.de, Phone: +49-(30) , Fax: +49-(30)

2 1 Introduction The relationship between retirement and health is the subject of intensive discussion in the years leading up to Many researchers study the influence of health and health shocks on the retirement decision (e.g. Bound et al., 1999; Hagan et al., 2008). On the one hand, the demographic change in developed countries is expected to result in a larger share of elderly people. This has led to public concerns about the sustainability of state pension funds. On the other hand, health and vitality of the elderly have greatly increased during the last decades of the 20 th century. Therefore, policy makers in several European countries have agreed upon reforms that increase the official retirement age. However, the effects of retirement on health are largely ignored. This paper estimates the causal effect of retirement on health using Regression Discontinuity Design and Instrumental Variables. There are several possible ways through which retiring might affect health. The opportunity costs of a healthy lifestyle (e.g. physical exercise, healthy diet) are lower for retirees than for employees. Furthermore, retirement might reduce the amount of stress and physical strain that an individual experiences from work. Hence, retirement might have a positive effect on health. On the other hand, retirees might be less physically active and their social network and social support might decrease as a result of the transition. Moreover, individuals who are very satisfied with their work might experience stress as a result of being forced to retire. In this instance health could decrease as a result of retirement. The direction of the effect has implications for both policies affecting the official retirement age and the labor supply of elderly people. If retiring decreases health, an increase of the retirement age preserves the health of elderly employees. In contrast, if retirement has a positive effect on health, then an increase in the retirement age would lead to poorer health and increased health care spending, which could partially offset the savings of the state pension funds. Previous studies on the causal effect of retirement on health are inconclusive. Several studies report a significant increase in subjective health after retirement (e.g. Johnston and Lee, 2009, Neuman, 2008, Coe and Lindeboom, 2008), whereas Coe and Zamarro (2011) also find significant and positive effects on objective health measures. In contrast, Behncke (2012) and Dave et al. (2006) report significant negative effects on both objective and subjective health measures. The inconclusive and seemingly contradictory evidence might stem from two different sources: endogeneity and effect heterogeneity. Since health status influences the decision of whether or not an individual retires, researchers need to address the reverse-causality of retirement status. The studies 2

3 mentioned above use a range of identification strategies, e.g. Instrumental Variables (Charles, 2002; Neuman, 2008; Coe and Lindeboom, 2008; Coe and Zamarro, 2011), Regression Discontinuity Design (Johnston and Lee, 2009), Propensity Score Matching (Behncke, 2012) and Fixed-Effects models (Dave et al., 2006). A negative effect of retirement on health might indicate that endogeneity has not been entirely resolved. Another possibility are heterogeneous effects. Due to different job characteristics and socio-demographic background, some individuals might experience a healthpreserving effect upon retirement, whereas others experience no effect or a health-limiting effect. There is little research on heterogenous effects in this area, with the exception of Coe and Lindeboom (2008) who report that better-educated individuals experience fewer limitations in Activities of Daily Life. This paper uses two different identification strategies to address the endogeneity of retirement: Regression Discontinuity Design (RDD) and Instrumental variables (IV). The RDD approach exploits that the probability of being retired increases rapidly at the ages of 60 and 65. These thresholds can be explained by the institutional setting in Germany. Discontinuities in the age-health profile corresponding to these age thresholds are interpreted as a causal effect of retirement. The IV strategy uses eligibility for a state pension plan as an instrument for retirement. Since state pensions are the main source of income during retirement in Germany, there is a high correlation between eligibility for a state pension and retirement status. Furthermore, I use the institutional setting in Germany to identify exogenous variation in eligibility. There are five different state pension plans in Germany, all of which have different eligibility criteria and age thresholds. In addition, two reforms in 2000 and 2007 gradually increased the age thresholds for all state pension plans. Hence, there exists variation in eligibility between pension plans and within pension plans that is not correlated with health. I estimate the causal effect of retirement on health using representative survey data from Germany, where the aforementioned studies concentrate mostly on England and the US. Furthermore, I investigate heterogeneous effects by stratifying the sample along several relevant characteristics, most notably gender, education and job satisfaction. In addition, I account for unobserved heterogeneity by allowing for individual fixed effects. Lastly, I investigate changes in health-related behavior, which might potentially explain changes in health itself. The results show that retirement has a significant and positive effect on both subjective health and mental health. The negative effect on physical health is not significant for the whole sample. There is also evidence for effect heterogeneity for physical health men and lower educated individuals expe- 3

4 rience a large decrease in physical health. However, this effect is offset for the large majority of individuals having at least vocational training. In contrast, the effects on subjective health and mental health are mostly homogenous. All in all, retirement seems to relieve individuals from work-related stress. This implies that an increase in the retirement age could result in more mental-health problems in later life. Since mental-health problems are one of the main reasons for health-related retirement in some occupations, policy makers should address the problem of work-related stress in order to increase labor force participation among the elderly. The rest of the paper is structured as follows: Section 2 gives a short overview of studies on the relationship between retirement, health and mortality. Section 3 describes the institutional setting in Germany and the dataset. The identification strategies and the corresponding econometric models are explained in section 4. Section 5 states and discusses the results. Section 6 concludes. 2 Review of the literature While there is a large literature on health and retirement, most studies focus on the effect of health on retirement. In these studies, health is regarded as a factor that influences whether an individual continues working or decides to retire. For example, Bound et al. (1999) and Hagan et al. (2008) suggest that not the level of health but declines in health increase the probability to retire. McGarry (2004) reports that health has a larger effect on labor supply than financial incentives, and that unexpected changes in health affect the expected retirement age. She concludes that some retirees might experience financial strains since they were forced into retirement by negative health shocks Beginning in the 1970s several studies in the fields of Gerontology and Health Economics have addressed the question whether retirement has an impact on health. For example, Ekerdt et al. (1983a) analyze changes in physical health and compare male retirees to peers who continue to work. Their results show no significant effect of retirement on physical health. Ekerdt et al. (1983b) investigate whether retirement improves health. They compare men who retrospectively claimed that retirement had a positive effect on their health to men who report no effect using longitudinal data on selfreported health. Their results do not confirm the claims. Mein et al. (2003) analyze the effects of retirement on physical and mental health of civil servants in England. While their effects on physical health are not significant, they report an improvement in mental health upon retirement. 4

5 The authors of these studies are aware of the problem posed by reverse causality. They address it by excluding individuals who retired due to illness or disability or by controlling for baseline health. Nevertheless, their results cannot be interpreted as causal effects. Controlling for baseline health might mitigate the problems caused by initial differences in health or negative trends prior to retirement. However, health shocks that occur prior to retirement would be attributed to the change in retirement status in these specifications; hence the results could be biased. There are a few, recent studies that employ different identification strategies to allow for a causal interpretation of the results. Charles (2002) examines the effect of retirement on psychological wellbeing. He exploits discontinuities in retirement incentives and mandatory retirement rules as instruments to address endogeneity. His results indicate that individuals with low levels of well-being and those who experience negative changes in well-being are more likely to retire. However, if reverse causality is accounted for, the effect of retirement on well-being is positive and significant. Coe and Lindeboom (2008) use early retirement windows offered by employers as an instrument. They report an improvement in self-rated health in the short-run and no significant effects in the long-run. Coe and Zamarro (2011) investigate the effects across several European countries using country-specific early and full retirement ages as instruments for retirement status. They report that retirement has a long-lasting positive effect on measures of general health. Neuman (2008) investigates the effects on both subjective and objective measures of health. He uses age brackets and spouse age as instruments and finds that there is a significant improvement in subjective health upon retirement. However, the effects on objective health measures are mostly insignificant. Johnston and Lee (2009) use a Regression Discontinuity Design and arrive at similar conclusions, namely that there is significant and positive effect on subjective health whereas objective health is not affected by retirement. While the findings of these studies are in line with evidence from earlier, non-causal studies, there are also contrary findings. For example, Dave et al. use data from the Health and Retirement Study. They estimate fixed effects models to account for individual heterogeneity and restrict their sample to individuals without health problems prior to retirement. They report large and significant decreases in both physical and mental health, which are caused by changes in lifestyle. Behncke (2011) uses two different identification strategies nonparametric propensity score matching and instrumental variables. She state pension age conditional on gender as an instrument. Her results indicate that retiring significantly increases the risk to be diagnosed with a severe cardiovascular disease or cancer. Moreover, she reports a decline in self-reported health. 5

6 In addition to these studies analyzing general measures of health, there are a few studies that focus on more specific outcomes, i.e. mortality and cognitive functioning. While the literature treats cognitive functioning as a dimension of human capital different from health (Mazzonna and Peracchi, 2012), it is clearly related to it. For example, Alzheimer disease and dementia are characterized by a decline in cognitive functioning. Coe and Zamarro (2011) also investigate the effect of retirement on cognitive functioning, but report no significant effects. In contrast, Rohwedder and Willis (2010), Mazzonna and Peracchi (2012) and Bonsang et al. (2013) all report a significant decline in cognitive functioning for retirees. Both Rohwedder and Willis and Bonsang et al. argue that the effect on cognitive functioning is not instantaneous but occurs within the first few years after retirement. However, Coe and Zamarro estimate a short-term effect, which might explain why their findings are not significant. Lastly, mortality is probably the most extreme health outcome. Again, the evidence from the few studies analyzing the effect of retirement on mortality is mixed. While Kuhn et al. (2010) report a significant increase in mortality among early retirees in Austria, Hernaes et al. (2013) find no significant effect for an early retirement program in Norway. Bingley and Pedersen (2011) even report a reduction in mortality among early retirees in Denmark. All three studies rely on institutional changes, which introduce variation in eligibility for early retirement. 3 Institutional setting and data 3.1 The state pension system in Germany Old-age provisions in Germany consist of three elements state pensions, employer-based pensions and private pension insurance schemes. Although policy makers introduced several reforms since aimed at increasing the share of private pension schemes, the state pension scheme is still the single most important source of old-age provisions. According to the FEDERAL MINISTRY OF LA- BOUR AND SOCIAL AFFAIRS (2012) 64 per cent of the gross household income of retirees comes on average from state pensions paid by the GERMAN STATUTORY PENSION INSURANCE SCHEME. Employer-based pensions and private pension schemes amount to less than 20 per cent of the house- 2 The Riester- Rente (Riester pension) was introduced in 2001, and the Rürup-Rente (Rürup pension) was introduced in

7 hold income. Moreover, 63 per cent of all retirees rely on state pensions as their only source of income. Eligibility for state pensions depends on the number of contribution years. Contribution times are accumulated either by paying an insurance premium, or through recognition of non-income periods, e.g. periods of unemployment, maternity leave or education. Not insured in the state pension system are regular soldiers, judges, civil servants, employees with an income less than 400 Euros per month, retirees and self-employed in certain occupations. 3 The amount of the pension paid then depends on the number of contribution years, the amassed compensation credits 4 and several adjustment factors. The nominal pension level states the ratio of benchmark pension to average income. 5 It can be interpreted as the share of the last income that an (average) employee would receive upon retirement. In 2011 it is reported as 46 per cent gross and 50 per cent net. The GERMAN STATUTORY PENSION INSURANCE SCHEME offers 6 different pension plans (GERMAN STATUTORY PENSION INSURANCE SCHEME, 2012). These pension plans are targeted towards different segments of the population, hence the eligibility criteria differ. The standard old-age pension requires only five contribution years. A policy change introduced in 2007 raised the age threshold stepwise from age 65 up to age 67 (see Table 1). Individuals born before 1947 can still retire at age 65. For individuals born between 1947 and 1959 retirement age is increased by one month per birth cohort. For the birth cohorts between 1959 and 1963 retirement age is raised by two months per year. For individuals born from 1964 on the official retirement age is 67. The pension for long-term insured is intended for individuals with at least 35 years of contribution. The age thresholds are the same as for the old-age pension, including the policy change. Unlike the old-age pension however, the pension for long-term insured allows for early retirement. If the eligibility criterion is met, individuals can choose to retire from the age of 63 onwards (albeit with deductions from their pension of up to 14.4 per cent). However, individuals born after 1947 and before 1955 have a possibility to retire between the age of 62 and 63 if they signed an agreement on partial retirement with their employer before January 1, Self-employed craftsmen, artists, publicists, and self-employed in educational, nursing or naval professions are mandatory insured in the GERMAN STATUTORY PENSION INSURANCE SCHEME. 4 These are calculated based on gross income up to a contribution threshold. 5 The benchmark pension is the amount a retiree would receive if she had 45 contribution years and earned average income in all years. 7

8 The pension for especially long-term insured is available for individuals with at least 45 contribution years. Non-income periods are not recognized for this pension plan. The age threshold is 65, and there is no possibility of early retirement. Since this pension plan was only introduced in 2012, it will not be included in the empirical analysis. The pension for women is available to women born before It also requires 15 contribution years, and 10 years after the age of 40 during which insurance premiums were paid. The official retirement age for this pension plan is 65, however eligible women can retire early at the age of 60 (with deductions of 18 per cent of their pension). The pension due to unemployment or partial retirement is intended for individuals who are currently unemployed and have been in unemployment for at least 52 weeks beyond the age of 58 and 6 months. Alternatively, individuals have to be in partial retirement for at least 24 months. Eligibility for this pension plan also requires 15 contribution years, and individuals should have paid social security contributions for 8 out of last 10 years. The official retirement age in this pension plan is 65. However, individuals can retire early, depending on their birth cohort. Individuals born before 1946 can retire at age 60. For the birth cohorts from January 1946 to November 1948 the early retirement age increases in monthly steps. Individuals born between December 1948 and December 1951 can retire early at age 63. This pension plan is not available for individuals born from 1952 onwards. Finally, the pension for severely disabled people is targeted at individuals with a degree of disability that exceeds 50 per cent. In addition, individuals with incapacity to work are eligible if they are born before This pension plan requires 35 contribution years (including recognition of nonincome periods). The official retirement age is 63 for individuals born before 1952 and is raised stepwise for individuals born between 1952 and Individuals born after 1964 can retire officially at age 65. Early retirement age is 60 for individuals born before 1952 and 62 for individuals born after However, in this analysis I disregard this pension plan, since disabled individuals differ in several aspects from non-disabled persons and hence might experience a different transition into retirement. Table 1 below provides a short overview over all pension plans and the respective policy changes. Although the changes are only introduced gradually, they prove effective: between 2000 and 2011 the mean retirement age increased from 62.3 to 63.5 (GERMAN STATUTORY PENSION IN- SURANCE SCHEME, 2012). 8

9 (Table 1: Overview over the German state pensions) 3.2 Data The data for this analysis comes from the German Socio-Economic Panel Study (SOEP). The SOEP is a representative panel study of private households in Germany. Starting in 1984, individuals are surveyed annually. The study expanded to include residents of former East Germany in All respondents answer about 150 questions on a range of topics, e.g. on labor market participation, education, family status, attitudes and perceptions, as well as health and health behavior. Moreover, the head of the household fills in a household questionnaire. Since 2000 the study interviews more than 20,000 individuals across more than 10,000 households. For further details, see Wagner, Frick and Schupp (2007). The SOEP includes several measures of individual health. The standard 5-categorical Self-Assessed Health (SAH) and the 11-categorical health satisfaction measure are surveyed annually since In addition, since 2002, the continuous quasi-objective SF12 measure and the objective grip strength measure are included in every second year. Information on health behavior is available since 2006 in every second year Dependent variables For the empirical analysis I use both the SAH measure as well as the SF12 measure. For the SAH, respondents are asked how they would describe their current health status on a 5-point scale. The answers range from bad and poor to satisfactory, good and very good. For the analysis, I dichotomize the variable. The outcome good health is defined as 1 for the best three categories and 0 for the worst two categories. 6 For this outcome the sample consists of 70,748 person-year observations over the period from 1994 to The SF12 consists of two measures for physical health (pcs) and mental health (mcs). For these measures, respondents answer 12 questions that relate to different dimensions of health, e.g. vitality, bodily pain, or emotional functioning. These questions are then aggregated into 8 subscales, and a specific algorithm generates the two dimensions physical and mental health. In the standard SOEP version, both measures take on continuous values between 0 and 100, with a mean of 50 and a 6 I deviate from the definition in the literature ( 1 for the worst two categories) to achieve consistency in the sign across the three different health measures. 9

10 standard deviation of 10. A detailed description of the algorithm is given by Andersen et al. (2007). For these two outcomes the sample encompasses 31,737 person-year observations for five years between 2002 and In all models, individuals younger than 50 and older than 80 are excluded from the analysis, since these observations are too far away from the retirement transition and hence should not influence the results Definition of retirement and eligibility Before analyzing the effect of retirement, it is necessary to define the treatment. There are several definitions used in the literature. In general, retirement implies that an individual exits the labor market. This encompasses also individuals who are technically unemployed, but are not actively searching for a job. On the other hand, some retirees might exit their main occupation, but continue to work in another occupation, for example to generate additional income, meet other people or engage in meaningful work. In this paper I use self-reported retirement status as the treatment variable. I assume that the transition into retirement (and hence the treatment effect) occurs if an individual recognizes herself as retired. If a respondent does not work, but does not report herself as retired, it could imply that she is actively looking for work, or pursuing voluntary work. Hence, I would expect that the effects of the transition into retirement have not occurred. Eligibility for a state pension is constructed from the survey data and not measured directly. 7 Hence, there might be a measurement error. However, it is implausible that the measurement error is systematically linked to health. Thus, it should not bias my results. Respondents of the survey are asked for their employment history. I assume that the number of contribution years is the sum of the experience in full-time and part-time work as well as unemployment. 8 Moreover, the year and month of birth of every respondent is used to choose the appropriate age threshold for the respective birth cohort. I use the longitudinal dimension of the data to check when an individual has entered partial retirement and how long she has been in unemployment or partial retirement during the previous two years. However, it is not possible to check for how many years an individual has paid social security during the last 10 years (pension due to unemployment or partial retirement) or after the age of 40 (pension for women), respectively. While the panel dimension enables measuring changes for individuals over time, the sample size would become too small due to panel attrition. Eligibility for 7 Linking data from the survey to data from the GERMAN STATUTORY PENSION INSURANCE SCHEME is not permitted under German law. 8 Periods of registered unemployment are recognized as non-income periods. 10

11 each pension plan is calculated separately using the age thresholds for early retirement (if applicable). The final instrument is then constructed as a binary variable which is 1 if an individual is eligible for any pension plan and 0 otherwise. The econometric models also include additional control variables, e.g. gender, marital status, household income and education. Education is measured by two dummy variables for individuals who completed vocational training, and individuals who obtained a university degree, respectively. Table 2 below provides summary statistics for all variables. (Table 2: Summary Stats) The first column provides the mean and standard deviation (in italics) for all variables, whereas columns 3 and 5 provide the summary statistics for the control group (non-retirees) and the treatment group (retirees), respectively. Columns 4 and 6 provide the corresponding sample sizes. Lastly, column 7 and 8 provide the difference in means and the t-statistic. Table 2 shows there are significant differences between retirees and non-retirees. For example, retirees are less likely to report their health status as good, and they have on average a lower physical health score. However, retirees have on average better mental health. Nevertheless, these differences cannot be interpreted as causal effects of retirement. Table 2 also highlights that there are significant differences in important control variables, e.g. income, marital status, and perhaps most important, age. The treatment group is on average 13 years older than the control group. Thus, the differences in health might be due to the usual changes in health with increasing age. 4 Econometric models 4.1 Endogeneity Apart from the need to distinguish the effect of retirement on health from the effect of aging, it is also necessary to resolve the endogeneity problem of retirement status. The literature identifies two sources of endogeneity omitted variable bias (OVB) and reverse causality. Omitted variable bias might be induced through differences in unobserved individual characteristics, which influence both health and the retirement decision. For example, the genetic makeup might influence both health and the preference for retirement. Another example could be subjective life expectancy. A lower subjective life expectancy might be related to health problem, and at the same time influence the 11

12 decision when to retire. In order to control for unobserved, time-invariant individual heterogeneity, all models are estimated as Fixed-effects panel data models. Reverse causality poses the more severe problem. As mentioned earlier, several studies have shown that health affects the retirement decision. Moreover, unexpected health shocks have a larger impact than a steady decline in health. This means that comparisons even within individuals - of preretirement health to post-retirement health cannot be causally interpreted. A (negative) change could occur in two different scenarios: On the one hand, a negative health shock could have occurred after the last observation prior to retirement and retirement itself. In this case, the health shock might have forced the individual into retirement; hence it should be interpreted as the causal effect of health on retirement. On the other hand, the change could have occurred between the transition into retirement and the first interview after retiring. In this case, it can be interpreted as the effect of retirement on health. A simple regression analysis cannot disentangle these two effects. In order to allow for a causal interpretation of the analysis, I use two different identification strategies: Regression Discontinuity Design (RDD) and Instrumental Variables (IV). 4.2 Regression discontinuity design The RDD approach exploits institutional rules by which the treatment is assigned. It requires an assignment variable that (partly) determines whether individuals or treated or not. Individuals above a certain threshold receive the treatment, whereas individuals just below the threshold are not treated. Then, a discontinuity in the outcome variable at the threshold of the assignment variable can be interpreted as a causal effect of the treatment under some mild assumptions. These assumptions require, for example, that the assignment cannot be precisely manipulated near the threshold, i.e. individuals cannot select into or out-of treatment (Lee and Lemieux, 2010). This paper uses age as an assignment for retirement. While in Germany individuals are not forced into retirement 9, the statutory pension schemes provide strong incentives to retire at certain ages, i.e. there are thresholds for early and full retirement, and individuals are not eligible for any individuals 9 Working contracts or collective agreements may contain stipulations that an individual has to retire at the official retirement age. 12

13 retiring before the early retirement age have to accept deductions from their pensions. 10 However, this implies that treatment is not completely determined by age, instead the probability to retire increases rapidly at the thresholds for early and full retirement. This implies that the analysis is based on a fuzzy regression discontinuity design. Formally, the estimand of the treatment effect τ can be written as: τ = lim x c E[Y X=x] lim x c E[Y X=x] lim x c E[D X=x] lim x c E[D X=x], (4.2.1) where D i is a dummy variable indicating the treatment status, and c is the value of the discontinuity in X.. Hence, the treatment effect is estimated in a two-stage model: First, the effect of the assignment variable on the treatment is estimated by comparing individuals just above and just below the threshold c. In the second stage, the endogenous treatment variable is instrumented by the predicted values of the first stage. The estimated treatment effect is a Local Average Treatment Effect (LATE), i.e. the effect on the compliers affected by the instrument. In this case, the estimated effect should be interpreted as the effect on individuals retiring once they exceed the specified age threshold, which is used as a discontinuity. Figure 1 shows the share of retirees at every age between 50 and 80 in the dataset. (Figure 1: Probability of retirement) Although there are already a few retirees before the age of 60, the probability of being in retirement increases rapidly between 60 and 65. While less than 20 per cent are retired before the age of 60, more than 80 per cent are retired after the age of 65. Figure 2 shows the increment in the share of retirees by age. While the probability to retire is quite high for each year between 60 and 65, the spikes at age 60 and age 65 stand out. Given that the lowest threshold for early retirement is at age 60 (see Table 1) and the threshold for official retirement is 65 for most individuals, this result should be expected from the institutional setting. (Figure 2: Probability to retire) In the analysis I focus on the discontinuity at age 60, since it is the first possibility to receive a state pension. As a robustness check, I also investigate the discontinuity at age 65. However, since ap- 10 There are also incentives to postpone retirement, i.e. if an individual continues to work beyond the official retirement age she receives a premium for every month of eligibility. 13

14 proximately 75 per cent of all individuals have already retired by age 64, the remaining population is probably different with respect to unobservable characteristics. The compliers for the discontinuity at age 60 are individuals who retire as soon as they are eligible for state pensions, although they have to accept deductions. In contrast, the compliers at age 65 are individuals who comply with the official retirement age, i.e. they retire relatively late, and probably passed opportunities to retire earlier. Therefore, I would expect to find a different effect for this population than for the compliers at age 60. The assumption that the assignment variable cannot be precisely controlled near the threshold is met in this case, since individuals cannot manipulate their age. I also check for discontinuities in predetermined variables at age 60. If there would be a discontinuity in another, predetermined variable, this would cast doubt on the identification strategy, since the results could be driven by an unobserved confounder. Figure 3 below shows the probability of being married and cohabiting by age. Clearly, marital status should not be affected by retirement. The dots indicate local averages over bins of width 0.1. The lines are fitted by local polynomial smoothing. While the percentage of married individuals decreases with age, there is no discontinuity at age 60. (Figure 3: Marriage by age) (Figure 4: Income by age) Figure 4 shows a similar plot for income. Here, in contrast to marital status there seems to be a small discontinuity at age 60. However, this does not question the validity of the RD design, since I would expect from the institutional setting that income decreases as an effect of retirement. Therefore, the health effect that can be attributed to the change in income is part of the overall effect of retirement, since the change in income is also caused by retirement. Nevertheless, I include income as a control variable to isolate the income effect from the overall effect. The estimand in eq. (4.2.1) is estimated using both parametric and nonparametric methods. In the parametric case, a two-stage model of the following form is estimated: D it = γ 0 + γ 1 Age it + γ 2 Age 2 it + γ 3 Age 3 it + π it (1 + γ 1 Age it + γ 2 Age 2 it + γ 3 Age 3 it ) + z it θ + μ i + ε it Y it = β 0 + β 1 Age it + β 2 Age 2 it + β 3 Age 3 it + D ıt + z it θ + α i + δ t + ν it. (4.2.2) 14

15 Here, π it is a binary variable that is 1 if individual i in year t is at the right-hand side of the discontinuity at age 60, and 0 if she is on the left-hand side. D it is the treatment dummy and D ıt denotes the predicted values from the first stage. μ i and δ t are individual-fixed effects, z it denotes a vector of control variables and δ t a set of month- and year-fixed effects. ε it and ν it are the idiosyncratic errors for the first and second stage respectively. The first stage allows for different functions of age on the left- and right-hand side of the discontinuity. In the main specifications I restrict γ 1, γ 2, γ 3 to zero, i.e. I assume that for retirement status the age function is the same on both sides of the discontinuity. However, I estimate both variants as a robustness check. The parametric model has the disadvantage that observations on one side of the discontinuity have the same influence on the estimator, regardless of their distance to the discontinuity. In a nonparametric model observations are weighted so that observations close to the cutoff have a higher weight than observations far away from the cutoff. The estimand in eq. (4.2.1) is also estimated using local linear regression. In this case, the expectations in (4.2.1) are estimated by fitting a regression functions to observations located within a bin of width h on both sides of the cutoff. The local linear regression can be written as min αl :β l Y i α l β l (X i c) 2 i:c h<x i <c for the left side of the discontinuity, and min αr :β r Y i α r β r (X i c) 2 i:c<x i <c+h (4.2.3) for the right-hand side of the discontinuity. The denominator in (4.2.1) is estimated through similar regressions (Imbens and Lemieux, 2008). A crucial point is the choice of the bandwidth h. On the one hand, a small h implies a low bias; however the variance may become too high for a precise estimation due to the lower number of observations (Lee and Lemieux, 2010). In this paper estimation of (4.2.3) is carried out using the Stata module rd by Nichols (2011). The chosen bandwidth equals the estimated optimal bandwidth given by Imbens and Kalyanaraman (2009), which minimizes the Mean Squared Error (MSE) for sharp RDD designs. Multiples of the estimated optimal bandwidth are used to ensure robustness of the results. 15

16 4.3 Instrumental variables The second identification strategy relies on instrumental variables. I use eligibility for a state pension as an instrument for retirement status. In order to allow for a causal interpretation of the IV model, the instrument must fulfill two conditions validity and relevance. Validity requires that the instrument is not correlated with the error term of the model. Since the main concern in this analysis is reverse causality driven by unobserved health shocks, eligibility of a state pension should not be associated with shocks in health. This appears plausible, since on the one hand eligibility is not determined by health status. As mentioned above, the pensions for severely disabled people are excluded from the analysis. Pensions for unemployment or partial retirement require a certain time spent in unemployment or partial retirement for eligibility. Therefore, even if a decline in health causes job loss or partial retirement, this does not immediately lead to eligibility for a state pension. Moreover, the number of contribution years should not be related to health, since non-income periods are recognized as well, e.g. periods of child rearing or unemployment. Lastly, I exploit exogenous variation induced by policy changes. These policy changes lead to variation in eligibility based on birth cohort, hence it should not be correlated with health during old age. The second assumption of the IV model requires that the instrument is strongly correlated with the endogenous regressor. Since state pensions are the single most important source of income for retirees, I would expect that eligibility for a state pension has a large impact on the decision when to retire. However, I also report the F-statistic and the estimate of the instrument in the first stage for all models. The IV model is then estimated using a two-stage least squares variant of the within estimator, i.e. the model can be expressed as: D it = γ 0 + γ 1 Age it + γ 2 Age 2 it + γ 3 Age 3 it + τ it + z it θ + μ i + ε it Y it = β 0 + β 1 Age it + β 2 Age 2 it + β 3 Age 3 it + D ıt + z it θ + α i + δ t + ν it, where τ it denotes eligibility for a state pension. Table 3 shows the eligibility for all four pension plans included in the analysis by age. Clearly, no one is eligible before the age of 60, and at age 65 all individuals in the sample are eligible for the old-age 16

17 pension. There is considerable variation due to differences between pension plans. All in all, around 50 per cent of the sample becomes eligible at age 60 and 80 per cent at age 63. (Table 3: Eligibility by age) 5 Results 5.1 Results from regression discontinuity design First, I investigate the outcome variables graphically in order to detect possible discontinuities. As mentioned earlier, this paper focuses on the discontinuity at age 60, although there also might be an effect for age 65. Figure 5 below shows the health-age profile for all three outcomes. As before, the dots mark local averages over intervals of width 0.1, while the red and green lines are fitted on the original data by local polynomial smoothing. According to the graph, physical health decreases almost linearly with age. Subjective health also decreases with age, however it appears to be stable until age 65, and then decreases linearly. The relationship between mental health and age is nonlinear. The mental health summary score increases with age until approximately 70, and then decreases slightly. From the graphical inspection it remains unclear whether there is a discontinuity at age 60 or not. While the fitted lines indicate a gap for physical and mental health, this discontinuity is rather small. Especially for physical health it seems that this is rather caused by the fitting of two separate lines than by an actual discontinuity. The discontinuity for mental health is larger than for the other two outcomes, thus the effect on mental health is likely to be more pronounced. As for subjective health, the difference between the two regression lines is minimal, so there appears to be no effect on the probability of reporting a good health status. (Figure 5: Health-age profiles for subjective, physical and mental health) I estimate both parametric and nonparametric models as described in section 4.2. The nonparametric models are estimated using multiple bandwidths. The default bandwidth equals the estimated optimal bandwidth for a sharp RD design provided by Imbens and Kalyanaraman (2009). As Nichols (2011) notes, the optimal bandwidth in a fuzzy RD design tends to be larger than in the sharp 17

18 design 11, but in some cases the additional bias (from a larger bandwidth) might dominate the increase in variance. In these cases, the optimal bandwidth would in fact be smaller. Since there is no clear guidance on this, I also report results for half and twice of the optimal bandwidth. For the parametric models, robustness checks are performed by decreasing the number of years used on both sides of the discontinuity (i.e. the parametric bandwidth ) to 5 and 2 years, respectively, while including a more parsimonious age trend in the model. (Table 4: Estimates in the RD design) Table 4 above shows the result for all three health outcomes. First, the effect of retirement on subjective health is positive and significant in almost all specifications. Both the nonparametric and the parametric model with the smallest bandwidth exhibit no significant effect; however in these models the number of observations is probably too low to detect an effect. Overall, retiring at age 60 seems to increase the probability to report a good health status by between 8 and 26 per cent. For physical health there is no significant effect. The nonparametric models result in a positive point estimate, whereas the parametric models exhibit a negative effect. Nevertheless, in both cases the effect seems to be rather small and very imprecisely estimated. Lastly, for mental health the nonparametric models find no significant effect. In contrast, the preferred parametric specification (model 4) displays a large and significant increase in mental health upon retirement. The significance vanishes in the robustness checks. Nevertheless, the sign remains positive and the effect is sizable in all parametric specifications. Although an increase in mental health would be plausible given the significant effect on subjective health, further evidence - provided by the IV strategy - is needed to draw a conclusion. In order to gain additional insights on the mechanism, I estimate the effect separate effects by gender, education and work satisfaction (not shown here, results are available upon request). However, there appears to be almost no effect heterogeneity. In the nonparametric models, women experience a larger increase in subjective health, and in the parametric models individuals with an above average work satisfaction experience a larger increase in subjective health and mental health. However, the results from the nonparametric models contradict the latter finding. 5.2 Results from instrumental variables estimation 11 The increase in variance stems from the fact that the jump in the probability of the treatment (the denominator in eq. (4.2.1)) has to be estimated as well. 18

19 First, Figure 6 below presents graphical evidence on the effect of retirement on health. The health measures are plotted against the years to retirement. The year of retirement is highlighted by the vertical red line. As in Figure 5, the dots represent local averages and the red and green lines show a nonparametric fit. The graphs closely resemble the results in Figure 5 there are small gaps for physical health and mental health, whereas subjective health seems to be unaffected. Only the increase in mental health appears sizable. However, Figure 6 does not account for reverse causality, i.e. negative health shocks causing individuals to retire. This would likely induce a negative bias, hence the estimated effects might be larger than the changes shown in the graph. (Figure 6: Health by years to retirement) Table 5 shows the estimated effects on subjective health. Each of the seven columns represent a different specification the first two columns show the local average treatment effect estimated without and with controls for marital status, education and household income. Columns 3 to 6 add interaction effects for male gender, retirement age, education and work satisfaction. Column 7 shows the result from a model which allows both for an instantaneous treatment effect (captured by a dummy variable) and a linear trend. In order to assess the relevance of the instrument, the F- statistic of the first stage is reported. (Table 5: Estimates from Instrumental Variables subjective health) First, the F-statistic in all models is high and well above the value of 10, which is usually used as a rule-of-thumb to detect weak instruments. Furthermore, the results show that the effect of retirement on subjective health is positive but insignificant in all models but the first. There, retiring increases the probability to report a good health status by approx. 5 per cent. The interaction effects imply that there is a positive effect for individuals with at least vocational training, and for individuals with above average work satisfaction. While the findings of a positive effect are in line with the results from the RD design, the effect estimated in the RD design is higher and significant in most cases. Taking the graphical evidence as well as the estimates from both strategies into account, I conclude that there is a small increase in subjective health upon retirement. Table 6 shows the results for physical health. As in the RD design, the treatment effect is not significant in most models. However, the effect is consistently negative and rather large, compared to the results from RD. In addition, there are a number of highly significant interaction effects. First, there 19

20 seems to be a negative effect for male individuals. Perhaps work is of higher importance for males as a source of social support and physical exercise than for females. In addition, there are negative effects for individuals who retire relatively early, and for lower educated individuals. In model 5, the overall treatment effect refers to individual within the omitted base category for education, i.e. individuals without an educational degree. This large and negative effect is offset for individuals with at least vocational training. One possible explanation for this would be that higher educated individuals continue an active lifestyle. In contrast, lower educated individuals are more likely to work in physically strenuous occupations, and might therefore use the increase in leisure time to rest. Surprisingly, column 7 shows that while the instantaneous treatment effect is negative but insignificant, there is a small and significant positive trend in physical health. This could be interpreted as a recovery process during retirement. However, given the steady decline of physical health with age, it merely implies a slower decline of physical health during retirement. The general finding of no significant effect is in line with both the graphical evidence and the estimates from RD design. Nevertheless, the interaction effects imply the presence of sizeable effect heterogeneity. (Table 6: Estimates from Instrumental Variables subjective health) The results for mental health are displayed in Table 7. The overall treatment effect is positive and highly significant in almost all models. Interestingly, in contrast to physical health there appears to be neither effect heterogeneity nor a significant trend. In line with the graphical evidence, the results imply an instantaneous increase in mental health upon retirement. The size of the effect is around 2 points (i.e. 0.2 standard deviations), which is rather large compared to other explanatory variables. While almost all models in the RD design show a positive effect on model health, this effect is only significant in the preferred parametric specification. However, given that the effect is positive and significant in all IV models, I conclude that there is a significant increase in mental health upon retirement. (Table 7: Estimates from Instrumental Variables subjective health) In order to check the robustness of the results, I redefine the instrument using only a subset of the four pension plans. The results are robust to the exclusion of the pension due to unemployment or partial retirement. If both the pension for women and the pension due to unemployment or partial retirement are excluded, the significance and magnitude of some effects change, nevertheless the sign remains in line with the reported specifications. 20

21 6 Conclusion This paper estimates the causal effect of retirement on individual health using regression discontinuity design and instrumental variables as identification strategies. In the RD design, I exploit a jump in the probability to retire at age 60. The instrumental variables strategy uses eligibility for a state pension as an instrument for retirement. Taking into account four pension plans with different eligibility criteria and age thresholds, the effect is identified using variation between pension plans and exogenous variation induced by policy changes within pension plans. The results indicate that retirement slightly increases the probability to report a good health status. Closely connected to this, individuals experience a sizeable increase in mental health, which equates to 0.2 standard deviations. However, there appears to be no significant effect on physical health. This indicates that retirement might mainly act as a relief from work-related stress, which increases both subjective health and mental health. This interpretation is supported by the finding that for subjective and mental health only the immediate, short-term effect matters. In contrast, there is no significant short-term effect for physical health, but a small but significant positive trend after retirement. I also investigate effect heterogeneity. There are no significant differences across subpopulations for subjective health and mental health. In contrast, the effect on physical health is negative and significant for men and lower educated individuals. Whether this is due to different job characteristics, or caused by different lifestyles during retirement remains unclear. If researchers could identify the mechanism through which retirement affects mental health and well-being, policy makers could use this knowledge to design labor market policies in order to increase mental health among elderly workers. Considering both the rise in mental health problems and the increasing retirement age, it becomes more and more important to ensure good mental health in old age. An interesting starting point is provided by Lemola and Richter (2012), who report that the increase in sleep satisfaction in old age coincides with retirement. On the other hand, it remains unclear why specific subgroups experience a decrease in physical health upon retirement. Clearly, more research on the relationship between retirement and health behavior would prove fruitful. 21

22 References Behncke, S., Does retirement trigger ill health?, Health Economics, 21, Bingley, P. and Pedersen, P.J., Does early retirement keep you healthy and extend your life? Unpublished. Available online via Bonsang, E., Adam, S. and Perelman, S., Does retirement affect cognitive functioning? Journal of Health Economics, 31, Bound, J., Schoenbaum, M., Stinebrickner, T. and Waidmann, T., The dynamic effects of health on the labor force transitions of older workers, Labour Economics, 6, Charles, K., Is retirement depressing?: Labor force inactivity and psychological well-being in later life. NBER Working Paper Coe, N.B. and Lindeboom, M., Does Retirement Kill You? Evidence from Early Retirement Windows, IZA Discussion Paper Coe, N.B. and Zamarro, G., Retirement effects on health in Europe, Journal of Health Economics, 30, Dave, D., Rashad, I. and Spasojevic, J., The effects of retirement on physical and mental health outcomes, NBER Working Paper Ekerdt, D.J., Baden, L., Bossé, R. and Dibbs, E., 1983a. The effect of retirement on physical health. American Journal of Public Health, 73(7), Ekerdt, D.J., Bosse, R. and LoCastro, J.S., 1983b. Claims that retirement improves health. Journal of Gerontology, 38(2), FEDERAL MINISTRY OF LABOR AND SOCIAL AFFAIRS, Report on old-age assurance Available online via Gesetze/alterssicherungsbericht_2012.pdf? blob=publicationfile GERMAN STATUTORY PENSION INSURANCE SCHEME, Pension insurance in numbers. Available online via /cae/servlet/contentblob/238692/publicationfile/50368/rv_in_zahlen_2012.pdf GERMAN STATUTORY PENSION INSURANCE SCHEME, The right penion insurance for you. Available online via /cae/servlet/contentblob/258148/publicationfile/57746/die_richtige_altersrente_fuer_sie. pdf 22

23 Hagan, R., Jones, A. M. and Rice, N., Health Shocks and the Hazard Rate of Early Retirement in the ECHP, Swiss Journal of Economics and Statistics, 144, Hernaes, E., Markussen, S., Pigott, J. and Vestad, O.L., Does retirement age impact mortality? Journal of Health Economics, 32, Imbens, G.W. and Kalyanaraman, K., Optimal Bandwidth Choice for the Regression Discontinuity Estimator, NBER Working Paper Imbens, G.W. and Lemieux, T., Regression Discontinuity Design: A guide to practice. Journal of Econometrics, 142(2), Johnston, D. and Lee, W.-S.,2009. Retiring to the good life? The short-term effects of retirement on health, Economic Letters, 103, Kuhn, A., Wuellrich, J.P. and Zweimuller, J., Fatal attraction? Access to early retirement and mortality. IZA Discussion Paper Lee, D.S. and Lemieux, T., Regression Discontinuity Design in Economics. Journal of Economic Literature, 48, Mazzonna, F. and Peracchi, F., Ageing, cognitive abilities and retirement. European Economic Review, 56, Mein, J., Martikainen, P., Hemingway, H., Stansfeld, S. and Marmot, M., Is retirement good or bad for mental and physical health functioning? Whitehall II longitudinal study of civil servants. Journal of Epidemiology and Community Health, 57, Neuman, K.,2008. Quit Your Job and Get Healthier? The Effect of Retirement on Health, Journal of Labor Research, 29, Nichols, A.,2011. rd 2.0: Revised Stata module for regression discontinuity estimation. Available online at last accessed on March 27, Rohwedder, S. and Willis, R.J., Mental Retirement. Journal of Economic Perspectives, 24(1), Wagner, G. G., Frick, J. R., and Schupp, J., The German Socio-Economic Panel study (SOEP) - evolution, scope and enhancements. Schmollers Jahrbuch, 127(1),

24 Tables Table 1: Overview over the German state pensions Retirement age Name Contribution years Additional eligibility criteria Pre-reform Post-reform Year of the reform Early Official Early Official Old-age pension Pension for long-term insured Pension for especially long-term insured a) female Pension for women 15 b) born before 1952 c) 10 years of social security contributions after the age of a) born before 1952 Pension due to unemployment or partial retirement 15 b) currently unemployed or in partial retirement c) 52 weeks of unemployment after the age of 58.5 or 24 months of partial retirement d) social security contributions in 8 out of the last 10 years Pension for severely disabled people 35 degree of disability exceeds 50% Source: German Statutory Pension Insurance Scheme, Notes: Column 8 gives the first year in which individuals are affected by the reform instead of the year the reform was enacted. 24

25 4 provide the mean and the number of cases for the control group. Column 3 and 4 provide the summary statistics and number of cases for Table 2: Summary Statistics Variable Overall Not retired N 1 Retired N 2 Difference t good health *** physical health *** mental health *** age *** male gender marital status *** household income 1, , , *** , , , university degree *** no degree *** work satisfaction *** employee *** full-time experience *** part-time experience *** unemployment experience *** Source: SOEP v28, own calculations. Notes: Column 1 gives the overall mean and standard deviation (in italics) of the variable. Column 3 and the treatment group. Column 5 gives the estimated difference in mean and Column 6 the corresponding t-statistic. Significance is as follows: * = 0.1, ** = 0.05, *** =

26 Age Old-age pension Table 3: Eligibility by age Pension Pension Pension due to for longterm in- for women partial retirement unemployment or sured Eligibility overall Sources: SOEP v28, own calculations. Notes: Columns 1-6 give the share of individuals in the sample who are estimated to be eligible for the specified pension plan. Elgibility is estimated based on the criteria stated in Table 2. Table 4: Estimates from Regression Discontinuity design nonparametric parametric Specification subjective health * *** ** *** physical health mental health *** Bandwidth 100% 50% 200% Age bracket Age trend cubic quadratic linear Control Variables x x x Individual Fixed Effects x x x Sources: SOEP v28, own calculations. Notes: Columns 1-3 give the estimates obtained from local linear regression, Columns 4-6 state estimates obtained via instrumental variables fixed-effects regression. Standard errors are given in italics. Control variables include gender, education, marital status and household income. Significance is coded as follows: * = 0.1, ** = 0.05, *** =

27 Table 5: Estimates from IV regression - subjective health Specification retired ** Years spent in retirement Interaction: male gender Interaction: age Interaction: age Interaction: vocational training ** Interaction: university degree *** Interaction: work satisfaction *** F-test First Stage continued on next page 27

28 Table 5 continued Age bracket Age trend Cubic Cubic Cubic Cubic Cubic Cubic Cubic Controls no yes yes yes yes yes yes Individual Fixed Effects yes yes yes yes yes yes yes Month & Year Fixed Effects yes yes yes yes yes yes yes R² N Source: SOEP v28, own calculations. Notes: Standard errors are given in italics. Control variables include gender, education, marital status and household income. Significance is coded as follows: * = 0.1, ** = 0.05, *** =

29 Table 6: Estimates from IV regression - physical health Specification retired ** Years spent in retirement ** Interaction: male gender * ** ** * Interaction: age ** Interaction: age Interaction: vocational training ** - - Interaction: university degree ** - - Interaction: work satisfaction F-test First Stage continued on next page 29

30 Table 6 continued Age bracket Age trend Cubic Cubic Cubic Cubic Cubic Cubic Cubic Controls no yes yes yes yes yes yes Individual Fixed Effects yes yes yes yes yes yes yes Month & Year Fixed Effects yes yes yes yes yes yes yes R² N Source: SOEP v28, own calculations. Notes: Standard errors are given in italics. Control variables include gender, education, marital status and household income. Significance is coded as follows: * = 0.1, ** = 0.05, *** =

31 Table 7: Estimates from IV regression - physical health Specification retired *** ** ** ** ** ** Years spent in retirement Interaction: male gender Interaction: age Interaction: age Interaction: vocational training Interaction: university degree Interaction: work satisfaction * - F-test First Stage continued on next page 31

32 Table 7 continued Age bracket Age trend Cubic Cubic Cubic Cubic Cubic Cubic Cubic Controls no yes yes yes yes yes yes Individual Fixed Effects yes yes yes yes yes yes yes Month & Year Fixed Effects yes yes yes yes yes yes yes R² N Source: SOEP v28, own calculations. Notes: Standard errors are given in italics. Control variables include gender, education, marital status and household income. Significance is coded as follows: * = 0.1, ** = 0.05, *** =

33 Figures Figure 1: Probability of retirement by age Notes: Figure 1 shows the share of retirees by age, calculated as the mean of the treatment dummy for each year of age. 33

34 Figure 2: Probability to retire by age Notes: Figure 2 shows the probability to retire by age, calculated as the increment of Figure 1 for each year of age. 34

35 Figure 3: Probability of marriage by age Notes: Figure 3 shows the probability to be married and cohabiting for each year of age. The dots indicate local averages calculated over intervals of width 0.1. The red and green lines are fitted via local polynomial regression for all individuals under age 60 and above 60, respectively. The vertical red line indicates the discontinuity at age

36 Figure 4: Household income by age Notes: Figure 4 shows equivalized household income for each year of age. The dots indicate local averages calculated over intervals of width 0.1. The red and green lines are fitted via local polynomial regression for all individuals under age 60 and above 60, respectively. The vertical red line indicates the discontinuity at age

37 Figure 5: Health-age profile for subjective, physical and mental health Notes: Figure 5 shows the health-age profile for subjective, physical and mental health. The dots indicate local averages calculated over intervals of width 0.1. The red and green lines are fitted via local polynomial regression for all individuals under age 60 and above 60, respectively. The vertical red line indicates the discontinuity at age

38 Figure 6: Health by years to retirement Notes: Figure 6 shows subjective, physical and mental health by years to retirement. The dots indicate local averages calculated over intervals of width 0.5. The red and green lines are fitted via local polynomial regression for the non-retirees and retirees, respectively. The vertical red line indicates the year of retirement. 38