Basically I don’t think you can understand this general phenomenon from within the confines of one single discipline. That is why the Lutz model is interesting since it combines some economics, some demography, and some social theory. I would definitely want to add-in evolutionary biology and evolutionary anthropology. Here are three papers to give you some idea of the extent of this. What we need IMHO is some integration of the following traditions:

Life History theory. Hillard Kaplan is a good example, here are a couple of papers:

Embodied Capital and the Evolutionary Economics Of the Human Lifespan

An Evolutionary and Ecological Analysis of Human Fertility, Mating Patterns and Parental Investment.

The sociological Life Course Theory. Here’s an illustrative paper:

Whose Lives? How History, Societies, and Institutions Define and Shape Life Courses by Karl Ulrich Mayer

The Economic Life Cycle Saving and Consumption Theory

Here’s a summary of the state of play on this from Princeton economist Angus Deaton:

“Franco Modigliani and the Life Cycle Theory of Consumption”

Well, I think there’s enough in all that to chew on :).

OK, I’ve been able to grab a bit of time to think about this. Firstly, I’m not saying that having pensions insurance doesn’t form part of the picture, what I don’t see is why it matters if the scheme is PAYGO or fully funded. If it is fully funded you should feel even more confident that you will have a pension, on this account, and therefore should reduce your fertility even more. Indeed, as I recall, you accept some version of rational expectations theory (which I am much more wary about), but if people were fully rational, or even pretty rational, wouldn’t they now see that these pension systems (both private and public) might one day crash, and hence have more children just in case?

Actually, fertility continues its steady decline.

Now Ronald Lee has some interesting material on all this. First an Article on “Age Structure and Dependency” written for the Encyclopedia of Population.

Then this article on intergenerational transfers again written for the Encyclopedia of Population.

This paper: Demographic Change, Welfare, and Intergenerational Transfers: A Global
Overview, is much more comprehensive and looks at the issue in historical perspective from hunter gatherers to the present day.

And if you really want some state-of-the-art theory you could do worse than this one:
Rethinking the evolutionary theory of aging: Transfers, not births, shape senescence in social species

Here’s the abstract:

The classic evolutionary theory of aging explains why mortality rises with age: as individuals grow older, less lifetime fertility remains, so continued survival contributes less to reproductive fitness. However, successful reproduction often involves intergenerational transfers as well as fertility. In the formal theory offered here, age-specific selective pressure on mortality depends on a weighted average of remaining fertility (the classic effect) and remaining intergenerational transfers to be made to others. For species at the optimal quantity–investment tradeoff for offspring, only the transfer effect shapes mortality, explaining postreproductive survival and why juvenile mortality declines with age. It also explains the evolution of lower fertility, longer life, and increased investments in offspring.

Yes, well I accept this in some sense. I take Ray’s point that this is a new situation, and that Lutz’s is a new theory, and as such I respect him for having come up with it. Of course arguments can be improved, I absolutely agree. I have some suggestions myself :).

“Short conclusion: Pay-as-you-go systems CAUSE low fertility rates.”

I’m afraid I don’t buy this. I think - in biological evolutionary terms - life expectancy and fertility are connected. I’m working on my ideas on this right now. At some stage I will post something.

The person who has done most original work in the line which interests you is Berkeley demographer Ronald Lee. I have to dash now but will put some more links later.

Basically, of cousre there is a link between pensions (whether Paygo or otherwise) and fertility decisions, but it is just one small part of the picture. More later.

Here’s what I mean by “PAYG makes people believe they need no children as a ‘pension insurance’”":

http://www.nber.org/papers/w11121
Social Security, Demographic Trends, and Economic Growth: Theory and Evidence from the International Experience. Isaac Ehrlich, Jinyoung Kim, NBER Working Paper No. 11121, February 2005

Short conclusion: Pay-as-you-go systems CAUSE low fertility rates.

There’s another purely economic mechanism that may cause low birth rate: monetary expansion. CPI baskets are mostly based upon prices of tradable goods. Since property prices are basically excluded from inflation calculations, home prices may rise beyond affordability of most young people. Hong Kong, for instance, has very basic PAYG system, but expensive housing. Birth rate is very low as a result of that. Go and have a family when a modest flat costs ten annual salaries or so!

Now combine PAYG and high property prices, and what you get: a strong contraceptive.

Where do you live? It is very hard for me to reconcile this with what I see around me. In the part of Europe I live in, the best schools are in the older parts of the cities.

We are seeing low birth rates in countries with free education.