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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 728 
50-year period (°). It is the same for all 50 countries and it 
can be regarded as a primitive kind of fixed-plan policy under 
disregard of any kind of new information. 
The relative performance measure that will be used takes 
the form of a ratio: 
(6. I )strategy TS (6 I )perfect 
(6. I )naive -— (6 . I)perfect 
That is, we take the strategy value of the function (6.1) as a 
deviation from the value which this function takes in case the 
perfect approach is adopted and express this difference as a 
fraction of the similar difference for the naive approach. The 
ratio is zero when the strategy approach yields as good results 
as the perfect approach; it is one if the strategy approach is 
as good or as bad as the naive approach. We should obviously 
expect that the ratio is generally between o and 1, and this is 
indeed the case as we see from Table 4. 
TABLE 4. — 
Relative performance of the strategy approach. 
Standard deviation of the ¢’ s 
0.005 0.01 0.02 
Lower quartile . . . 
Median . . . . . . 
Upper quartile 
0.816 0.844 0.866 
0.896 0.911 0.916 
N 995 n 97% 0.976 
‘) In eq. (2.8) we approximated the logarithm of the ratio of 1—x, to 
t—x,_, by the ratio of —(x,—#,_1) to I—#,_1, which was approximated 
further to -b{(x.—x, ,)\ to ohtain a linear expression The latter approxi- 
71 Theil - pag. 22