Promising Abstract, Disappointing Paper

I haven't read the paper, but a much more likely variable, which is highly correlated with urbanization, is simply the level of real per capita GDP. It is certainly a stylized fact, that with the exception of a few communist countries, poor countries simply do not have social security systems, whereas all high income countries do in some form or other, although some have partially privatized ones.

It is quite possible that the urban/rural balance, or perhaps separately simply the number of children per family, might be a stronger variable in explaining what is going on than real per capita income. But the latter is unquestionably highly correlated, and would be consistent with the general patter of "Wagner's Law," that higher income countries tend to have a larger government share (something you guys do not probably want to talk about much), although the latter is probably at least partly due to "Baumol's cost of services disease."

It was highly amusing to see this pop up in my RSS reader: "Arnold Kling Promising Abstract, Disappointing Paper".

Somehow, it wasn't as funny once I deciphered it. But I did laugh out loud at the "disturbing scenes of mathematical masturbation".

So your chain of causation runs:

Cities => smaller families => need for larger network for inter-generational risk-sharing?

Too simple, I think. Other factors:

The incomes of farmers on their own land are partly labor income, partly capital. Old people can implicitly enjoy capital income after their labor incomes diminish.

Farm work is diverse, mixing a "design" aspect (the old farmer knows how it's done from years of experience) with the physical labor. Old people can specialize in the know-how side and tell younger people what to do, and still be useful. Factory work is "dumb" and regimented: you do it, or not. This makes old people more clearly parasitic.

The opportunity cost of looking after one's parents is higher in the city, where entertainment is abundant.

Young people can be independent more easily in the city, where one can live by one's labor alone, than in rural areas, where one also needs land.

Maybe the authors made some of these points (in mathematical garb)?

I think Nathan has a major element that needs to be incorporated into the analysis and that is the ownership of capital.

As a uncle explained to me when I was a youth in Ky,
the farmer works all his life essentially to provide his living and sells his farm to provide for his retirement. Alternatively, he gives it to one child who takes on the responsibility of taking care of grandma and grandpa.

But in the modern industrial society the worker (farmer) does not own the means of production
so he does not have the assets to support his retirement. Note, that in this traditional economy there is no need for large personal savings to finance retirement.

I would think this explains much more of the demand for social security in modern societies
then any other factor.

I have not read the paper, but I hope that the term "mathematical masturbation" is in response to poor modeling, or even misuse of math, and not due to the writer's "mathematical ineptness."