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http://www.statcan.gc.ca/pub/75-001-x/2011004/charts-graphiques/11578/cg00l-eng.jpg

http://www.statcan.gc.ca/pub/75-001-x/2011004/charts-graphiques/11578/cg00m-eng.jpg

http://www.statcan.gc.ca/pub/75-001-x/2011004/article/11578-eng.htm#a7

Interesting thought experiment.

I judge your posts by the number of times I have to read them before I have the feeling (or illusion) of comprehension. This was a 2-read one.

My synopsis is:

The longer people expect to be retired the more they plan to save, and the more they plan to save the lower the rate of interest will be. In the extreme case (where people's savings is unrelated to the rate of interest?) there will be a direct and inverse correlation between r and R. Is that correct ?

Miami: good find. But interest rates are (mostly) set in world markets. It's world retirement lengths that will (mostly) matter.

TMF: Nearly. Your last line should be: in the average/simple(?) case, where the stock of saving is unrelated to the rate of interest, and the value of the stock of assets firms produce is inversely proportional to the rate of interest, in steady state, there will be an inverse proportional relationship between r and R/(R+L). If R/(R+L) doubles, r halves.

Got it, its R as a proportion of total years lived, not R in itself that drives the change in r.

If a substantial portion of retirement is provided through paygo taxes, much of the savings would be in the form of taxes but would not lower interest rates much, so raising taxes and benefits would raise interest rates.

Lord: correct. Not in the model, but could be added.

Retirement financed through PAYGO taxes is a lot like forced saving + government debt. It does raise the rate of interest, but that may be desirable if (r < g) and dynamic inefficiency applies.

anon: yep. But in my model, g=0 by assumption, and r > 0 because land exists, so r > g. (More generally, land will prevent the r < g dynamic inefficiency.)

Stylized facts, at least as I know them:
--Until 1950, reductions in mortality were largely reductions in infant mortality. After 1950, reductions in mortality were increases in longevity.
--Actuarial tables have historically increased longevity every decade they are produced, i.e., UP84 life expectancy at 65 is about 1 year larger than UP75.
--My guess is that life expectancy for adults hasn't increased enough to seriously impact interest rates. I do wonder if the social *expectation* of retiring early, especially by high wage earners, might have that effect.

Richard: thanks. Is that Canadian data? My guess is that the big change is coming from China, and similar places. When people are poor, they work until they die. When people are richer, they plan to stop working before they die, so they need to save. (There's also the effect of not being looked after by one's kids, and the effect of smaller families, but that's not formally in my "model".)

> I do wonder if the social *expectation* of retiring early, especially by high wage earners, might have that effect.

I'd start looking at senior poverty levels. In Canada, prior to OAS and full CPP eligibility, seniors were the most-poor age group. That indicates that while they may have *wished* to maintain a level-ish consumption path into retirement, they were unable to do so.

The modern phenomenon of not-poor seniors means that collectively they are now saving significantly more. Some of this savings trend may be from private savings (RRSP), but a substantial amount is "savings" from public funds. It looks something like the above-mentioned paygo pensions.

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