22
5
Theoretical Framework
The purpose of this theoretical section is to show that the empirical patterns we have
found may be explained by a simple dynamic model. The basic ideas of the model are the
following: (i) we assume that the caseworkers only observe the health signaled by the
individuals and not their true health, (ii) conditional on health, wage and benefits, a sick-
absent individual chooses a health-signal that maximizes the value of being on sickness
benefits, taking into account that the transition rates to work and DB are determined by
the signal, (iii) signaling bad health is, however, not without effort. The effort of signaling
bad health is assumed to be lower when the working capacity is being assessed by the
caseworker.
17
5.1
The model
We consider a large number of forward-looking and infinitely lived individuals. All
individuals start in the sick absent state (
s
). They may exit sickness absence and i) go
back to work (
e
), or ii) enter the disability insurance system (
d
). These last two states
are both considered as absorbing.
18
The individuals differ in health status,
(0, )
h
. A
higher value of
h
indicates worse health. The instantaneous utility of working is
w h
,
where
w
is the wage. The health status is arguably of main importance for the
instantaneous utility of working.
19
Health is unobserved by the caseworker. A sick absent individual communicates a
health status (
) to the caseworker at the SIA.
(0, )
is a continuous individual
choice variable where a high value of
means a strong signal of health problems.
Communicating bad health is associated with instantaneous effort given by
T
, where
sub-index
T
takes value one if an individual has been given priority to interventions (e.g.,
Sassam) and zero if not. We assume
1
0
, i.e. that the effort of communicating bad
health is lower if one belongs to the prioritized group.
17
It may seem natural to assume a positive causal link between early interventions and health.
However, since this is not consistent with our empirical results we for simplicity take health status
as given and focus on the communication between the sick absent individual and their caseworker.
18
The assumption that DB is an absorbing state corresponds well with the fact that very few
individuals reenter the workforce after entering the disability insurance system. However, that
employment is absorbing is arguably unrealistic. The assumption is made in order to keep the
model analytically tractable. A reasonable conjecture is that a more rigorous treatment would
change the quantitative, but not qualitative, results of the model.
19
For our purpose there is no gain in including disutility of bad health in either SB or DB. The key
assumption is that an individual suffers more from bad health while working compared to not
working. Engström and Holmlund (2007) specify a model with a similar assumption.
