European Tribune - Comments - Socratic Economics XI: Demographics

Socratic Economics XI: Demographics | 55 comments (55 topical, editorial, 0 hidden)

Re: Socratic Demographics: Birth Rates (none / 1)

Why don't you approximate the death rate by a logistic curve?

When the capital development of a country becomes a by-product of the activities of a casino, the job is likely to be ill-done. — John M. Keynes

by Migeru (migeru at eurotrib dot com) on Thu Jun 26th, 2008 at 10:10:08 AM EST

Re: Socratic Demographics: Birth Rates (none / 1)

Because of the ones that survive to 100 we expect a large fraction to die very soon. It's the probability of death for a person of age N, not the probability to die at age N. I use it to calculate the number of people at age N+1 for next year.

by someone (s0me1smail(a)gmail(d)com) on Thu Jun 26th, 2008 at 10:23:24 AM EST
[ Parent ]

Re: Socratic Demographics: Birth Rates (none / 0)

Still, if an exponential approximation with the midpoint at 100 years is a good approximation, is the cutoff at 105 years necessary?

When the capital development of a country becomes a by-product of the activities of a casino, the job is likely to be ill-done. — John M. Keynes

by Migeru (migeru at eurotrib dot com) on Thu Jun 26th, 2008 at 10:25:02 AM EST
[ Parent ]

Re: Socratic Demographics: Birth Rates (none / 1)

It would have to be tweaked, as the logistic function is mirror-symmetric about the midpoint, and we would not want the near-one value closer to 140 than 105. The function needs to rise rapidly to one over a few number of years after 100, is my intuition.

by someone (s0me1smail(a)gmail(d)com) on Thu Jun 26th, 2008 at 10:32:00 AM EST
[ Parent ]

Re: Socratic Demographics: Birth Rates (none / 0)

Hmm, notice you're talking about the death probability per year being larger than 1/2 already... Once you're a centenarian, does it really get that much worse at 105, 110, etc?

Your model doesn't allow people to live to 120 at all, which is worse than the alternative given the vanishingly small probability of survival year after year when the yearly one is under 1/2.

When the capital development of a country becomes a by-product of the activities of a casino, the job is likely to be ill-done. — John M. Keynes

by Migeru (migeru at eurotrib dot com) on Thu Jun 26th, 2008 at 10:36:17 AM EST
[ Parent ]

Re: Socratic Demographics: Birth Rates (4.00 / 2)

Does one or two very, very old people make much difference for aggregate statistics that lumps people 65+ together already?
I made the death rate slightly less for the calculation to maybe fudge out the cutoff age a bit. I.e., I moved the probability one death-age from 104 to 105, and slowed the curve a bit. Here are the two actual fits (exponential, and logistic):

I could redo the calculations with a higher cutoff and the logistic. (I want a cutoff to maintain finite vectors. But it could be 150, or more.)

by someone (s0me1smail(a)gmail(d)com) on Thu Jun 26th, 2008 at 10:59:49 AM EST
[ Parent ]

Re: Socratic Demographics: Birth Rates (none / 0)

Ack, I see what you are saying. Yeah, that would probably be better. However, in the data I obtained, which goes by one year, and then to 100+, one only see the rising exponential bit. So I extrapolated up, to a cutoff at 105 years so that I could have fixed size vectors.

by someone (s0me1smail(a)gmail(d)com) on Thu Jun 26th, 2008 at 10:27:51 AM EST
[ Parent ]

Socratic Economics XI: Demographics | 55 comments (55 topical, 0 editorial, 0 hidden)

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