Appendix - Sensitivity and Robustness
A.1 Disabled individuals: past labor income and self-reported work status
People on DI are mechanically transferred from disability pension to retirement pension at age 805 months. We need to make sure that the positive physical health effects found in the main analysis are not driven by these individuals. Initially, there is no reason to believe that there should be a health effect for people on DI, as they were not working before retirement, and should therefore have no change in circumstances. However, as the physical health measure contains elements of self-assessed health, it is possible that someone who is disabled may need to justify their disability status, consciously or subconsciously, by under-reporting health. In this case, health prior to retirement may be under-reported. Post retirement, when they are no longer in a situation where poor health is defining their labor market status, they might feel healthier, or they no longer have the need to report poor health. Provided this is a plausible scenario; We need to rule out that the results found in Section 5 are driven by justification bias.
The first two rows of Table 8 displays the results on two sub-samples of the survey data (labeled “Working” and “Income”), each aimed at running the analysis only on the sub-sample that was recorded as working until the statutory retirement age. The working sub-samples are defined in Section 4.2. Finding coefficients of the same sign and magnitude, especially for the rule based on self-assessed work status, ensures us that these effects are not driven by the disability justification hypothesis. The estimations based on the income-rule yields large and insignificant coefficients, both a consequence of the small sample sizes. Yet, the direction of the effects is similar to what was found in the main analysis.
For the outcomes from the administrative data, we should expect that individuals who retire formally at 67 but without any actual change in circumstances should water down the effects, as the health measures from this data source are not subject justification bias. We can therefore expect that this assessment can uncover significant effect, not detected in the gross sample. The first rows of Tables 9 and 10 present the estimations restricted to “workers” for acute hospitalizations and mortality, respectively. Here, we find no significant results for any of the sub-groups. The significant result on hospitalizations found for men with low education in the main analysis is no longer present.
A.2 Robustness checks and validity of the regression discontinuity design
Below we assess the sensitivity of the results for different bandwidth selections; we check for discontinuities in the forcing variable, age, at the cutoff; we test for discontinuities in other outcomes that should not have been affected by the threshold; and, we check for discontinuities in the outcomes of interest at points in the age distribution where there should be no discontinuities. This robustness assessment follows the suggestions in Imbens and Lemieux (2008) closely.
A.2.1 Bandwidth selection
The worry in an RD application is that using a bandwidth that is too wide, allows for other things than the intervention of interest to drive differences in outcomes for those right above compared to those right below the threshold. In Table 8 we display the results using bandwidths of 7 and 15 months for physical health. Using a bandwidth of 7 months does not alter the results, whereas increasing the bandwidths to 15 months somewhat reduces the effects. This is not surprising given the downward slope of the health trajectory across age and the upward shift in this trajectory at the retirement eligibility threshold.
The results for hospitalizations and mortality are displayed in Tables 9 and 10. For acute hospital admissions, we find that increasing the bandwidth to 15 months yields significant, negative effects. The effects are still small ranging from 0.7 to 1 percentage points. As the incidence is 14%, this entails a 5–7% reduction in the likelihood of acute hospitalization. Increasing the bandwidth increases the likelihood of factors, other than retirement, affecting acute hospital admissions. Another explanation can be that it takes some time for retirement to take effect on health issues such as stroke and acute heart conditions, thus including more post-retirement months increase the likelihood of finding significant effects. As in the main analysis, we find no effects of retirement on mortality at any of these bandwidths.
A.2.2 Continuity of the forcing variable
Vital to any RD application is the individual’s incapability of manipulating the forcing variable. In this case, the forcing variable is age (reported by public registers), which individuals cannot manipulate in any way. It could, however, be the case that retired individuals are more likely to respond to the survey due to the reduced opportunity cost of time. Figure 4 shows two histograms of age in months assessing potential bunching at the threshold. There is no evidence of any discontinuity in the forcing variable at the threshold. We also performed a more formal test proposed by Cattaneo et al. (2016). This implies testing the null of the continuous density of the forcing variable at the threshold using a local polynomial density estimator. The p-value under this test is 0.3251. For the population level data, this holds by construction, as people cannot manipulate their age and as all individuals in the population are represented in the data.
A.2.3 Placebo tests
The placebo tests entail testing for discontinuities in the three health outcomes at points in the age distribution where there should be no discontinuities. A common practice is to conduct placebo tests at the median age of the two sub-samples below and above the actual cut-off. In this case, the median age below the threshold is age 62. However, some individuals can retire at this age, thus making is an unsuited placebo threshold. Consequently, we use age 61 for the lower placebo. For the upper placebo, we use age 73. No discontinuities or significant effects were found at these placebo thresholds for physical health (Table 8). For acute hospital admissions (Table 9), we find significant effects for both the upper and lower placebo. For the lower placebo, this could be due to some occupations having special age-limits for retirement at 61. However, we find no explanations for why the upper placebo yields significant, and even positive effects. This finding reduces the credibility of the effects found in the main analysis for this outcome. The placebo results for mortality is presented in Table 10. There are no significant effects and the coefficients are close to zero for all sub-group at both placebo thresholds.
A.2.4 Discontinuity in Other Outcomes
Finally, we look for discontinuities in an outcome that should not be affected by retirement, at least not in the short-term. Here, we assess the likelihood of living with a partner or spouse (NorLAG) or being married (administrative data). The regression results shown in Tables 8 and 11 confirm that there are no retirement effect on these outcomes.