24
communicated health. However, in order to derive the comparative statics it is more
convenient to use equation (4) directly by making use of the envelope property.
Differentiation of equation (4) with respect to
and
h
gives
2
3
( ( , )
( , , ))
( , , )
( , )
0.
2 ( ( , )
( , , ))
w
e
s
s
d
h
w
e
s
V h w V h w
V h w
h
h
h w
V h w V h w
(5)
This result is obtained since
( ( , )
( , , )) /
0
e
s
V h w V h w h
and
( , , ) /
0
s
V h w h
which is obtained directly from differentiating equations (2) and (3), and
( , )
( , , ) 0
e
s
V h w V h w
is implied by the preference assumption. The result states that
the more you suffer from bad health (holding wage constant) while working, the more
bad health you will communicate in order to avoid being sent back to work.
Turning to the effect of early interventions, differentiation of equation (4) with respect
to
and
T
gives
3
2
( , )
0
2 ( ( , )
( , , ))
T
e
e
d
e
e
s
h w
V h w V h w
(6)
This result also stems directly from differencing equations (2) and (3) and from the
preference assumption. Thus, for all individuals who prefer sickness absence before work
we get the result that treatment, which we assume is captured by a decrease in
T
, will
increase the level of bad health communicated to the SIA.
If individuals only differ in health status the moral hazard properties of the model are
not apparent – the probability of entering DB (exiting to work) is increasing (decreasing)
in the true level of bad health. But when also introducing wage heterogeneity the moral
hazard involved is made clearer. The comparative statics for wage are easily determined.
Consider instead the effects of changing the wage level while holding health status
constant. The structure of the model implies that
( , )
( , )
h
w
h w
h w
, which means
that increased pecuniary incentive to return to work mirrors the effect of better health.
22
The theoretical implication of having worse health is therefore the same as the effect of
having a lower wage. This means that an individual who communicates bad health could
be relatively healthy if he suffers from low pecuniary incentives to return to work. The
model could easily be extended to more subjective factors influencing the incentives to
22
In reality the Swedish sickness benefits can be characterized by
min( , )
b
w b
, where
denotes the replacement rate below the cap
b
. Our model with exogenous benefit level thus
corresponds to the case above the cap, which arguably overstates the average pecuniary incentive
to return to work due to a wage increase.
