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In anticipation of Michael Kinsley's new & improved proof that Social Security privatization can't work.

Michael Kinsley reports being impressed by the blogosphere's response to his previous claim to have presented "mathematical proof" that privately owned accounts in Social Security can't work. But he alerts us that a new and improved proof is coming...

"I won't bore you with my mathematical proof that Social Security privatization can't work. Not quite true: I will bore you with it, but not until next week... [though] I'll be hard-put, next week, even to summarize my own argument, let alone discuss those of others, in the space available to a columnist."

Yet I don't think space will be the issue. For if the new proof tries to support the same claim as the old one -- that new private investments in Social Security will "bid down" returns to stocks, so it will be mathematically impossible to get the higher returns from stocks that privatization schemes rely on -- then no matter how long it runs it will have the same fundamental problems as the old one.

To recap, here's the gist of the Kinsley argument to date:

My contention: Social Security privatization ... is mathematically certain to fail. Discussion is pointless.

To "work," privatization must generate more money for retirees than current arrangements....

Greater economic growth requires either more capital to invest, or smarter investment of the same amount of capital. Privatization will not lead to either of these.

If nothing else in the federal budget changes, every dollar deflected from the federal treasury into private social security accounts must be replaced by a dollar that the government raises in private markets. So the total pool of capital available for private investment remains the same....

If the economy doesn't produce more than it otherwise would, the Social Security privatization bonus must come from other investors in the form of a lower return.

The money newly available for private investment will bid up the price of (and thus lower the return on) stocks, while the government will need to raise the interest on bonds in order to attract replacement money... [emphasis added]

And thus the return on stocks will fall, that on government bonds will rise, and the higher return on stocks relative to that on bonds that is needed to make privatization schemes work will disappear. As he said: "Q.E.D."

Ah, but for this claim to prove itself as true it must first jump two hurdles...

1) One can't talk "mathematical proof" without considering actual quantities and scale.

Privatization proposals talk about investing the likes of $2 trillion in private accounts over a decade or so. Call that $200 billion a year. And that amount would not be entirely invested in stocks any more than the full balances of all IRAs and 401(k)s are. But for argument's sake let's assume a new full $200 billion is invested in stocks through privatized Social Security accounts each year.

The market capitalization of the New York Stock Exchange is $12 trillion. (I've looked it up since last mentioning the subject). But that's just one stock exchange. The capitalization of the world's major stock exchanges combined exceeds $33 trillion (if anything in this world is globalized the financial markets are, and return isn't going to plunge in one without doing so in others -- and, of course, diversified private investment accounts can invest anywhere). Moreover, their capitalization is growing at a long-term average rate of about 4%, over a trillion dollars a year.

Now, $200 billion equals less than 0.6% -- six tenths of one percent -- of total stock market capitalization (and that percentage will decline as time passes).

So hurdle-to-jump #1 is:

How is it plausible that increasing demand for stocks by all of six tenths of one percent will produce an historic change in the pricing and yields of stocks? For that matter, how will it produce one big enough for anyone to even notice?

2) The economy is not static, no matter what one assumes.

For argument's sake again, let us assume that some measurable increase in the price of stocks does occur to measurably reduce the yield on them, due to the increase in demand for them arising from new private Social Security accounts.

But we can't stop there! How will businesses react to that?

Well, since they now can sell shares for more -- for a higher price, while paying lower dividend yields on them -- they will sell more shares. This is just the law of supply and demand: increase in price brings an increased quantity of product to market. If you increase the amount that companies can get for selling stock shares, they will be happy to print and sell more.

Lower yields on stock shares make it less expensive for companies to issue new stock to finance new productive investment -- just exactly like lower yields on bonds make it less expensive to issue new bonds for the same purpose.

Thus, with higher stock prices and lower yields on them, productive investments that were uneconomic for firms previously become profitable, and so will be financed with new stock issuances. Real economic investment increases.

This is exactly the benefit of increased savings that Kinsley assumes isn't supposed to exist when he makes the assumption: "If the economy doesn't produce more than it otherwise would". Yet with rising stock prices and declining stock yields it is unavoidable that investment increases! Real investment and the real productive economy grow faster.

Hey, this is exactly why economists of all political stripes are constantly saying the US savings rate is too low -- because they want to produce this effect to spur the productive economy!

Moreover, of course, this very increase in the supply of stock shares due to increased demand for them will offset much of that increase in demand for them. And this in turn will act as a countervailing force to check and prevent any dramatic increase in the price of, and decline in the yield on, stocks. This is why the term "equilibrium" is important in economics.

So hurdle-to-jump #2 is:

How does Kinsley propose to enforce his assumed "steady state economy", where these feedback equilibrium effects don't occur, as his model specifies?

We can only wait and see how his new & improved proof meets these challenges.

And, hey, we can only hope that private Social Security accounts will have a significant enough effect on stock prices and total investment to have these effects!

For the record, Kinsley's full earlier column and this little corner of the blogsphere's rather longer comments on it -- including a couple of other points that Kinsley doesn't consider but which seem relevant around here -- are a few posts back.

But the above seems like it will remain the gist of things, unless he changes what he is trying to prove.