Matthew Yglesias does it again.

I think very highly of Matthew Yglesias, but I don't want this blog to consist entirely of comments on his blog. Also it is odd that so many of those comments are critical, since I think very highly of Matthew Yglesias.

I strongly advise him to avoid using quantitative terms when making qualitative arguments. In the post below, I note that he blithely asserts that a proposal which involves investing 60% of one's wealth in stock is just like social security. He is refering to a post which refers to an intertemporal budget constraint. Rates of return can't be ignored or brushed over when making or discussing such calculations. The post to which the post to which Yglesias linked included a calcuation, with various numbers, one of which is not at all relevant to social secutrity.

Now he's done it again. He considers a world without social security in which people are prudent and forward looking and save for retirement. He goes on

This will lead to a decline in the rate of economic growth, and therefore to the expected return on investment. Either workers will need to start increasing their savings rate, or else they’ll need to accept lower living standards when retired. In other words, they’ll face the exact same choice we currently face in the form of higher taxes or lower benefits.

Yglesias just asserted that all reductions in living standards are exactly the same. Read the quoted passage. That assumption is definitely made. The fact that different negative numbers might not be exactly the same is not considered.

Now I think the word "exact" is redundant and the claim would be false with "the same change," but why add the word "exact" to casual reflection without calculation ?
The statement would be correct if "the exact same" were replaced by "a similar".

I can quantify the changes and do so fairly easily if I only look at very long run effects and make standard assumptions about consumption/savings decisions.
I assume that prudent savers act according to the life cycle permanent income hypothesis -- this is almost redundant as I am assuming rationality and time consistency. I assume infinitely lived households the number of members of which grows over time. I assume that the total appetite of a household is proportional to the number of people in it. I am following David Romer's Advanced Macroeconomics (and anticipating the lecture I am supposed to give tomorrow). All the assumptions are there and are standard.

What is the effect of a reduction in the rate of growth of labor supply on the rate of growth of the wage bill and on the real rate of return on savings ? Note Yglesias says they are exactly identically the same. There are complicated dynamics for a while, but the model converges to a balanced growth path. I will discuss the long run effect (comparing balanced growth paths) of a permanent decline in the rate of growth of labor supply (presumably due to a decline in the rate of growth of population). This is the rate of return people can get on their contributions ot the social security system. In the long run, It's decline converges to the decline in the rate of growth of labor supply.

How about the real interest rate ? Well in the new balanced growth path it is exactly identically the same as it was before. As time goes on it goes back to the original real interest rate. There is a temporary decline in the real interest rate, but it gradually comes back up.

The effects are not exactly the same at all.

This conclusion really depends on the exact assumptions about consumption saving decisions which I did not explain (they are in the book).

I think this mathematical exercize was pointless. I typed it here exactly because of the word "exact."