The late shift: How retirement affects civic participation and well-being - Appendix A

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The late shift: How retirement affects civic participation and well-being

van den Bogaard, L.B.D.

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2016

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Citation for published version (APA):

van den Bogaard, L. B. D. (2016). The late shift: How retirement affects civic participation and

well-being.

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APPENDIX A: Additional robustness checks for chapter four

In this Appendix I present the results of several additional analyses and provide some guiding text. These additional analyses were performed to ensure the robustness of the results presented in chapter four and serve mainly to deal with the problem of endogeneity, or possible self-selection into retirement. Certain people in the data may be more likely to experience the retirement transition, and this raises the question whether the ‘effect’ of retirement is truly caused by retirement, or merely associated with it via a non-included variable. While it remains difficult to firmly establish causal relations with observational data, there are several ways to test the causal mechanism more stringently. I provide two: a fixed-effect specification of the models in which the dependent variable is the change in self-rated health (SRH) rather than SRH at t₂ controlled for SRH at t₁; and multiple propensity score matching analyses.

First, I present the results of a number of analyses in which I adopted the change score method rather than the conditional change method (Allison, 1990, 1994), which basically leads to a more strict test of the hypotheses. Such a fixed-effects approach might seem preferable in a general sense, but as Allison has noted, when modelling the change in a variable between to waves (Y₂ – Y₁), it is basically futile to include the Y₁ values (used to compute the change score) as regressors, since you end up with a model that is mathematically similar to the conditional change approach (Allison, 1990, 1994). Simplified, the conditional change model in the chapter looks like:

[1]

While for the change score method, the model is defined by:

[2]

Testing the interaction of retirement with pre-retirement SRH, as I do in the chapter 4, means introducing the Y₁ variable in formula [2] on both sides of the equal sign:

[3]

In essence, [3] and [1] are equivalent, since the Y₁ to the left of the equal sign may be transposed to the right-hand side. As a basic goal of this chapter is to investigate whether the effect of retirement differs along lines of pre-retirement SRH, the change-score approach is thus unfeasible as an overall technique. However, as a robustness check of the basic retirement effect, I tested the models in chapter four without SRH at t₁ as a regressor, and with the change in SRH as the dependent variable.

First, Appendix table A1 provides the basic information on the change score variable. Appendix table A2 is in essence a replication of table 4.3 from chapter four, using the approach described above. It is an ordered logit model (as in chapter four) with the change score variable as

[1]

[2]

[3]

[2]

[3]

APPENDIX A

A

dependent. The main effect of retirement is found again in all models, as well as the interaction with psychological work stress, which even achieves a lower p-value. Appendix table A3 also shows the results of analyses modelling the change in SRH, but now using a linear approach rather than the ordinal logit one. This was done to get a more tangible idea of the ‘treatment effect’ of retirement, which is 0.19 in all models. Overall, these tables show that also with a fixed-effects approach, the results reported in chapter four are found.

Appendix table A4 shows the results of propensity score matching. Matching is a technique in which cases that received a treatment (in this case, retirement) are compared to cases that did not receive a treatment (kept working), but are otherwise similar. This way, it is possible to get a less biased estimate of the ‘treatment effect’. In this case, I use a difference-in-difference approach as the dependent variable is again the change in SRH. Different specific techniques can be used to generate the control group, or the cases similar to the ‘treatment’ group (for an overview, see Austin (2011)). I have applied several of these techniques. First, the table shows the difference in health change (without any controls) between those who retired and those who kept working, which is 1.47. A t-test shows this difference to be statistically significant. Next, the results from Appendix table A3 are presented, which can be interpreted as the estimated effect of retirement, controlled for all variables in the model. As noted earlier, this effect is significant, but the goal is to test the robustness of this finding. This is done in the rest of the table, which shows the estimated average treatment effects for the treated (ATET) from four analyses. First, the radius approach was applied, in which the treated are compared to control cases that are similar within a certain radius, or caliper. This caliper can be set at any level between 0 and 1. I have performed two such analyses with different, standard caliper values, namely 0.05 and 0.1. In both cases, a significant ATET value is produced (0.159 and 0.163, respectively). This result is similar with the Kernel approach, but the final stratification approach does not yield a significant ATET value.

Overall, the results of the robustness checks described above appear to provide ample reason to have confidence in the results chapter four. Models with the fixed-effects specification generated results similar too, or even more pronounced than, the models with the conditional change approach. Different propensity score matching techniques also provided broad confirmation of the results found earlier. To reiterate, establishing causality beyond doubt will remain difficult with the type of data employed in this study, but I feel that the robustness checks above significantly add to the credibility of the chapter.

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Appendix table A1. Descriptive statistics and background information on SRH change score variable Variable Mean Standard deviation Description

Change in self-rated health -0.03 0.77 Based on questions in both waves: How

is your health, in general? 0 = very bad, 4

= very good. Computed as SRHt1 – SRHt2.

Range: -3 to 4. N = 1455

APPENDIX A

A

Appendix table A2. Ordered logistic regression of change in self-rated health (fixed-effects approach) on retirement and other variables (standard errors)

Model 1 Model 2 Model 3 Model 4 Retired 0.47*** _0.47*** _0.48*** _0.48***

(0.13) (0.13) (0.13) (0.13) Retired × Physical stress 0.23* _0.14

(0.10) (0.11) Retired × Psychological stress 0.31** _0.26*

(0.10) (0.11) Physical stress 0.17** _0.17** _{0.01 0.03} (0.06) (0.06) (0.08) (0.08) Psychological stress 0.05 -0.07 0.04 -0.03 (0.06) (0.08) (0.06) (0.08) Middle educationa _{-0.04 -0.05 -0.05 -0.05} (0.14) (0.14) (0.14) (0.14) High educationa _{-0.03 -0.03 -0.04 -0.04} (0.14) (0.14) (0.14) (0.14) Female 0.15 0.15 0.15 0.15 (0.13) (0.13) (0.13) (0.13) Non-working partnerb _{-0.15 -0.12 -0.15 -0.14} (0.16) (0.16) (0.16) (0.16) Working partnerb _{-0.18 -0.16 -0.19 -0.18} (0.19) (0.19) (0.19) (0.19) Child(ren) in household -0.21+ _-0.20+ _-0.21+ _-0.21+ (0.12) (0.12) (0.12) (0.12) Income 0.21** _0.20** _0.22*** _0.21** (0.06) (0.06) (0.06) (0.06) Age -0.08 -0.08 -0.08 -0.08 (0.06) (0.06) (0.06) (0.06) Cut 1: Constant -5.65*** _-5.64*** _-5.67*** _-5.65*** (0.49) (0.49) (0.49) (0.49) Cut 2: Constant -3.65*** _-3.64*** _-3.67*** _-3.66*** (0.25) (0.25) (0.25) (0.25) Cut 3: Constant -1.21*** _-1.20*** _-1.22*** _-1.21*** (0.20) (0.20) (0.20) (0.20) Cut 4: Constant 1.52*** _1.55*** _1.53*** _1.54*** (0.20) (0.20) (0.20) (0.20) Cut 5: Constant 3.80*** _3.82*** _3.81*** _3.82*** (0.25) (0.25) (0.25) (0.25) Cut 6: Constant 6.02*** _6.05*** _6.04*** _6.05*** (0.53) (0.53) (0.53) (0.54) Cut 7: Constant 7.41*** _7.44*** _7.43*** _7.44*** (1.02) (1.02) (1.02) (1.02) Pseudo R2 _{0.013 0.014 0.016 0.016} -2 Log Likelihood -1635 -1633 -1631 -1630 N of observations 1455 1455 1455 1455 Levels of significance: + _{p < 0.10,} * _{p < 0.05,} ** _{p < 0.01,} *** _{p < 0.001.} a _{Reference: low education}

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Appendix table A3. – Ordinary least squares regression of change in self-rated health (fixed-effects approach) on retirement and other variables (standard errors)

Model 1 Model 2 Model 3 Model 4 Retired 0.19*** _0.19*** _0.19*** _0.19***

(0.05) (0.05) (0.05) (0.05) Retired × Physical stress 0.10* _0.07

(0.04) (0.04) Retired × Psychological stress 0.13*** _0.11**

(0.04) (0.04) Physical stress 0.07*** _0.07*** _{0.00 0.01} (0.02) (0.02) (0.03) (0.03) Psychological stress 0.03 -0.03 0.03 -0.01 (0.02) (0.03) (0.02) (0.03) Middle educationa _{-0.01 -0.02 -0.02 -0.02} (0.05) (0.05) (0.05) (0.05) High educationa _{-0.00 -0.00 -0.01 -0.01} (0.05) (0.05) (0.05) (0.05) Female 0.05 0.05 0.05 0.05 (0.05) (0.05) (0.05) (0.05) Non-working partnerb _{-0.07 -0.06 -0.07 -0.07} (0.06) (0.06) (0.06) (0.06) Working partnerb _{-0.09 -0.08 -0.10 -0.09} (0.07) (0.07) (0.07) (0.07) Child(ren) in household -0.08+ _-0.08+ _-0.08+ _-0.08+ (0.05) (0.05) (0.05) (0.05) Income 0.09*** _0.08*** _0.09*** _0.09*** (0.02) (0.02) (0.02) (0.02) Age -0.03 -0.03 -0.03 -0.03 (0.02) (0.02) (0.02) (0.02) Constant -0.05 -0.06 -0.05 -0.05 (0.08) (0.08) (0.08) (0.08) R2 _{0.034 0.039 0.042 0.043} Observations 1455 1455 1455 1455 Levels of significance: + _{p < 0.10,} * _{p < 0.05,} ** _{p < 0.01,} *** _{p < 0.001.}

a _{Reference: low education} b _{Reference: no partner}

APPENDIX A

A

Appendix table A4. Summary of robustness tests for effect of retirement on self-rated health123

Estimation method Difference / treatment effect t-statistic p-value

T-test 0.147 3.61 0.000 Regression with controls 0.191 3.89 0.000 ATET radius (caliper: 0.05) 0.159 3.65 0.000 ATET radius (caliper: 0.10) 0.163 3.23 0.001 ATET kernel 0.161 2.15 0.032 ATET stratification 0.100 1.06 0.289

1 _{The dependent variable is the change in health between waves 1 and 2, automatically leading to a}

difference-in-difference model for the ATET estimation;

2 _{All ATET estimates result of 1000 replications with bootstrapped standard errors;} 3 _{No nearest neighbor method applied because it yields too few comparable untreated cases}