25
return to work, such as social work norms and other subjective rewards of being in work
compared to sick leave (and DB). Heterogeneity in any other dimension related to work
incentives will cause moral hazard, provided that the social objective is only to insure
against bad health chocks.
5.3
A Numerical Example
By choosing specific model parameters we can give a numerical illustration of the flows,
month by month, and facilitate qualitative comparisons between model and data. The
results from this numerical example are displayed in Figures 4 and 5.
We normalize the wage to unity and let the health measure be uniformly distributed
between zero and 1.5, that is,
1
w
and
~ (0,1.5)
h U
. The sickness benefit is set to
0.5. The monthly baseline outflow rates are given by
0.01
d
and
0.1
e
. We
capture the effect of being (randomly) prioritized to early interventions with a decrease in
T
from its baseline level,
0
0.2
(control), to
1
0.15
(treatment). We let the size
of the treatment and control group be normalized to 1. We think of these groups as very
large and abstract from aggregate uncertainty. Finally, we set the monthly subjective
discount rate to
0.01
.
Figure 4 graphs the relative risk, or odds ratios, for the treated compared to controls
in each state for each month from December 2007 to January 2008. From this figure we
can clearly see the locking-in effect of the intervention. The treated have initially a higher
risk of being sick in February. The relative risk is approximately 2 percent higher for the
treated compared to the controls. Thereafter the relative odds are decreasing. The
pattern of the relative risk of SB is explained by the relative sizes of the total exit rate
from SB. In the beginning, when average health is relatively high, the control’s exit rate is
higher due to high exit back to work. Later on, however, when average health is low, the
treated exit relatively fast due to higher exit rate to DB. The pattern of the relative risk of
being in DB is due to a direct treatment effect and dynamic selection. At the beginning
the treated exit is faster to DB since their cost of communicating bad health is lower.
However, as time passes the number of individuals with bad health will be higher in the
control group, which explains the downward sloping odds ratio for DB.
The general result of an increased risk of around 20 percent for the treated of taking DB
is in line with the empirical results. However, the time pattern, with an almost immediate
higher likelihood of receiving DB, is not what we find in the data. This result stems from
the simplifying assumption that an individual who communicates bad health (i.e., high
)
will immediately get a higher probability to enter into DB. In real life the decision to
receive DB takes some time. For example, in our data no individual receives DB during
the second month (see Table 3).
