5.4 Empirical methodology
5.4.2 Fixed effects instrumental variables estimation
To determine the causal effects of working shorter hours on health is diffi-cult because the work hours decision is endogenous to health which is un-observed. Individuals with worse health outcomes are more likely to reduce their work load or retire fully earlier. Estimating an OLS model of the form
Yi,t+k = βPRi,t+ f(ai,t) +Xitγ+νi,t, (5.2) where health outcomeYi,t+k for individualiin a future periodt+kdepends on part-time retirement status PRi,t, age function f(ai,t), the vector of the in-dividual’s characteristics Xit and an idiosyncratic error term νi,t, is biased if part-time retirement decision and health are correlated. Another source of bias is the individual specific unobservable factors which can be correlated with both the part-time work decision and health. I tackle these problems with fixed-effects instrumental variable analysis.
The individual fixed-effects estimates compare the full-time job and part-time job status at the individual level and relate the change in the status to the changes in the health outcomes at the individual level. This strategy elim-inates any unobserved time-invariant factors. To account for the unobserved heterogeneity and potentially endogenous decisions in the part-time retire-ment timing, I estimate within-two-stage least-squares and use the eligibility ages and the exogenous changes in these ages as an instrument for the part-time retirement decision8. That is, the estimating equation includes within transformation both in the first and the second stage9.
The first stage regression takes the form of a linear probability model:
PRi,t =γ1[ai =ei] +f(ai,t) +ρi+i,t, (5.3) where the part-time retirement, PRi,t, takes values 0/1 indicating whether individual has taken part-time pension or not, ei denotes the eligibility age
8The same kind of instrument is used for example by Bonsang et al. (2012), Kantarci and Kolodziej (2017), Lucifora and Vigani (2018) among others.
9In health and employment literature FE-IV estimation procedure has been used by Bon-sang et al. (2012), Frijters et al. (2014), (Ahn, 2016), Kantarci and Kolodziej (2017), Cygan-Rehm and Wunder (2018) and Lucifora and Vigani (2018)
for individual i and 1[ai = ei], the instrument, is an indicator function tak-ing value 1 if individual has reached the age of eligibility in the same year10. The γmeasures the discontinuity in the probability to retire at this age. The unobserved individual specific time-invariant variablesρiare abolished with within-transformation.
For the instrumental variable to work, it is required that the instrument is relevant for the actual part-time pension decision and satisfies the exclusion restriction. Figure 5.3 shows the discontinuous change in the probability to take up part-time pension with respect to years from the eligibility. About a third of part-time pensioners take up the part-time pension during the year they become eligible. Figure 5.A2 in appendix shows the retirement timing separately for groups where the lowest eligibility age differs due to the re-form taking place in 1998. While the rere-form made the programme more pop-ular and the largest spike is at the age 56, the older cohorts also retire around the year they become eligible. The identification is based on this disconti-nuity in the proportion of individuals reducing work load through part-time retirement right at the eligibility age conditional on a polynomial function of age.
While the specific eligibility ages have a direct effect on the decision to take part-time pension, it is less probable that they have a particular effect on the outcome variables except through the part-time retirement11. The re-verse causality, that the health would affect the instrument, would happen for example if the eligibility age is set to a certain age where health problems ac-cumulate. I have gone through the government’s proposition for the bill and the subsequent parliament discussion in order to see if these specific eligibil-ity ages were chosen because of population’s health conditions. This seems not to be the case.
The final estimation is based on the following second-stage fixed effects
10It is important to remember here that all individuals in the current sample take up part-time pension at some age. However, the timing differs and this instrumental variable research design is able to reveal the effects on the compliers who retire during the year becoming eligi-ble. These are the local average treatment effects.
11This is supported by the fact that I have looked at the trends in the health-related factors for the total population and the eligibility ages for part-time pension are not anomalous.
Figure 5.3 Take-up of first part-time pension spell since becoming eligible
0.1.2.3.4
Change in the part-time retirement probability
-3 -2 -1 0 1 2 3 4 5 6
years from the eligibility age
Notes: the estimates are based on a fixed effects model where years from the eligibility act as explanatory variables. The estimation is done for years 1995-2004 including the total part-time pensioners sample. The vertical lines represents 95% confidence intervals.
regression model
Yi,t+k = βPRi,t+f(ai,t) +μi+νi,t, (5.4) where μi denotes the unobserved time-invariant heterogeneity and captures all time-invariant characteristics that are associated with both the decision to reduce work hours and outcome variables. The coefficient β is the parame-ter of primary inparame-terest and represents the impact that reducing work hours through part-time pension has onYi,t+k. The identification of β is driven by changes in the outcome variables for individuals whose part-time retirement decision is affected by the eligibility age.
Figure 5.4 Difference in outcomes between the treatment and the control group, with controls.
-.05-.04-.03-.02-.010.01.02.03.04.05Difference (treatment-control)
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 Purchase of any drug, extensive margin
(a)Any drug purchases, extensive margin
-.05-.04-.03-.02-.010.01.02.03.04.05Difference (treatment-control)
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 Purchase of mental illness drug, extensive margin
(b)Mental illness drug purchases, extensive margin
-.5-.4-.3-.2-.10.1.2.3.4.5Difference (treatment-control)
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 Purchase of any drug, intensive margin
(c)Any drug purchases, intensive margin
-4-202468Difference (treatment-control)
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 Sickness absence days, over 10 days
(d)Sickness absences days, over 10 days
Notes: Coefficient for treatment group and 95% confidence intervals. Sickness absence days conditional on working. Standard errors are clustered at individual level.