which has two nice properties: it is directly interpretable as the ratio of children that survived the first
year to the number of children that died; and, of course, it increases with a better health status.
We have considered a third output measure, which we call Potential Years of Life Not Lost,
PYLNL. This variable was computed on the basis of the indicator Potential Years of Life Lost,
PYLL, reported by OECD (2005). This last variable, PYLL, equals the number of life years lost
due to all causes before the age of 70 and that could be, a priori, prevented. Therefore, and for
our subsequent DEA analysis, and similarly to the Infant Mortality Rate, a transformation had to
be done, in order to provide an increasing monotonic relation between the variable, number of
years not lost, and health status.
Our transformed variable is:
PYNLL=λ-PYLL, (3)
where λ=3 618 010 is an estimate of the number of potential years of life for a population under 70
years.^11
Therefore, our frontier model for health is based upon three output variables:
- the infant survival rate,
- and life expectancy,
- potential years of life not lost.
We compare physically measured inputs to outcomes. Quantitative inputs are the number of practising
physicians, practising nurses, acute care beds per thousand habitants and high-tech diagnostic medical
equipment, specifically magnetic resonance imagers (MRI).^12 Table 2 reports the relevant statistics for
the set of OECD countries.
Table 2 – Summary statistics of the input and output data
Mean
Standard
deviationMinimum MaximumLife expectancy (in years) 1/ 77.5
2.8
68.4
(TUR)81.5
(JAP)
Infant mortality rate (deaths per 1000
live births) 2/4.5
6.5
2.4
(ICE)36.3
(TUR)
Potential years of life lost (All causes- <70 year,/100 000) 2/
4083
981.2
2917
(JAP)7056
(HU)
Practising physicians, density per
1000 population 2/2.8
0.8
1.4
(TUR)4.4
(GRC)
Practising nurses, density per 1000
population 2/8.0
3.4
1.6
(KOR)14.7
(IRE)
Acute care beds, density per 1000
population 2/4.2
1.8
1.0
(MEX)9.1
(JAP)
MRI units, per million population 2/ 6.8
6.4
0.2
(MEX)32.3
(JAP)
Notes: 1/ Average for 2000 and 2003. 2/ Average for 2000-2003.
TUR – Turkey; JAP – Japan; ICE – Iceland; HU – Hungary; GCR – Greece; KOR – Korea; IRE – Ireland; MEX – Mexico.From Table 2 one notices that practising nurses per one thousand persons, in the period 2000–2003,
ranged from 1.6 in Korea to 14.7 in Ireland. For the same period there was also a high range of practising
physicians per one thousand persons, from 1.4–1.5 in Turkey and in Korea to 4.3–4.4 in Italy and in
(^11) See details in the Appendix.
(^12) A commonly used indicator of medical technology; see, for instance, Retzlaff-Roberts et al. (2004).