PPH = Health System Employee* Health condition/Elderly/Smokers
= 1.179*1.012/0.927/1.172 = 1.098 (2)
Knowing that 1 is also the Italian average value for all the functionings (since they are
obtained multiplying and dividing indicators of commodities and conversion factors whose
average value is in turn 1), the value of PPH it is thus 9.8% above Italian average.
In our model every functioning is determined by different commodities: the final value of the
functioning is, as pointed out earlier (see 1.5), the weighted aggregation of the converted
commodities. Besides, we assume that the attribution of weights to each functioning is based on
the inverse function of the frequency of the indicators of the commodities in the Italian regions
(see equation (1), section 1.5). More specifically for each indicator we determine the frequency
(fi of equation (1)) of the observation below the national average (i.e. < 1). For example, PPH is
determined not only by the indicator “Health System Employee” as in the previous simplified
case, but also by the indicators “Environmental Quality” (referring to the commodity
environment), “Security” (referring to the commodity safety) and “Occupation” (referring to the
commodity employment), whose frequency of observations below the national average are
respectively 10, 12, 8, 8 (out of 20, the number of Italian regions). We can therefore calculate
the respective weights in equation (1). They are:
• 0.257 for “Health System Employee” (whose frequency < 1 is 10),
• 0.278 for “Environmental Quality” (whose frequency < 1 is 12),
• 0.232 both for “Security” and “Occupation” (whose frequencies < 1 are both 8).
Knowing from the model that the converted values of the four commodities (i.e. the
converted commodities) are:
• 1.018 for “Health System Employee”,
• 0.465 for “Environmental Quality”,
• 0.662 for “Security”,
• 1.936 for “Occupation”,
the value of PPH is:
PPH = 0.257*Converted Health System Employee + 0.278*Converted Environmental
Quality+ 0.232*Converted Security + 0.232*Converted Occupation
= 0.257*1.018+0.278*0.465+0.232*0.662+0.232*1.694
= 0.937 (3)
(or 6.7% below the national average)
Finally, to put dynamism into the system we must allow its elements (i.e. the indicators) to
change over time. Doing so, we can simulate the state of the system in subsequent time periods
and control the elements whose evolution we are interested in - the functionings. In this
tentative model the only variable elements are the commodities, which can have a positive or
negative growth rate. Moreover the latter could also change the system in subsequent time
periods via the positive or negative interactions with other commodities within the whole
system. For instance, the relation between the commodity referred to health and the one referred
to pollution is -0.01420: the growth of the indicator of pollution implies a greater reduction of the
indicator of health over time; the relation between occupation and safety is 0.02721 (the higher
the employment, the safer the society); the relation between occupation and training (a
commodity of the functioning Education and Training) is 0.24422.
20 Krzyzanowski , 2001.
21 Elaboration from Marselli-Vannini, 2000.
22 Laudisa, 2000.
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