>> >e iSadly, I didn't mean anything so clever. Among finance/econ geeks,
E is
>>
>> also the "expectation" operator. So E(0) in this context is
"Expectation
>> at time 0". Brad said that life expectancy at birth was the least worst
>> measure. I objected that E(0) wasn't equal to E(0)(E(10)) "expectation
at
>> time 0 of expectation at time 10". Usually, this would be equal to E(0)
-
>> after all, there's something funny about expecting your expectation to
>> change, which is where the reference to "law of iterated expectations"
came
>> in. But when you're talking about life expectancies, you can expect
that
>> if you survive until ten, then your expectation of your lifespan will
>> change markedly. I suggested that you should be comparing expectancies
on
>> the basis of life expectancy at the most common age for people to die,
>> which, frankly, sounds a lot less silly when you use five-shilling words
>> like "modal"
>I am still confused.
My fault entirely
>1) What's the difference between E(10) and E(0)(E(10))? Don't they both
>represent "how long people who make it to age 10 are expected to live"?
Yes, that's right, albeit that they're conditional on different information sets. But, if we're assuming an unbiased expectation, they should always be the same number. E(0) and E(0)(E(10)) can be significantly different, though. (I should be using a conditional expectation operator here, and saying E(0)(E(10|alive)), but am following the "when in a hole" principle.)
>2) If 1) is true, then E(0) can never be equal to E(0)(E(10)), unless
noone
>dies before age 10, right?
Well... yes, basically. More exactly, unless nobody was expected to die before age 10.
>3) Wouldn't the modal age of death be tremendously dependent on the
interval
>you choose to distribute deaths? If you do it by month, then you'll get
that
>the modal "month" of death is the one after birth. If you do it by decade,
>then you'd probably get the 80s (I am just guessing here). If so, then
>choosing E(modal age of death) doesn't make much sense, does it?
[cough] ... I was thinking about doing it by year, and you're always going to get these sorts of problems when you do anything statistically, so you're free to pick your grouping to give you the most useful number. I would guess that doing it by decade would give you a sort of bimodal function -- 70s/80s for developed societies, 0-10 for countries with high infant mortality. Maybe I should have said "median", or something. I was just trying to pick an age which, for any society, would cut out the effect of infant mortality on life expectation. Maybe just picking a figure like E(10) would be better, but I was wondering whether the period of high risk was different in some societies from others. God I wish a proper economist would drop in and say "actually Amartya Sen solved this problem in 1972".
dd
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