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## February 01, 2005

### Paul Krugman on Social Security Returns

He writes:

The New York Times > Opinion > Op-Ed Columnist: Many Unhappy Returns: The fight over Social Security is, above all, about what kind of society we want to have. But it's also about numbers. And the numbers the privatizers use just don't add up. Let me inflict some of those numbers on you. Sorry, but this is important.

Schemes for Social Security privatization, like the one described in the 2004 Economic Report of the President, invariably assume that investing in stocks will yield a high annual rate of return, 6.5 or 7 percent after inflation, for at least the next 75 years. Without that assumption, these schemes can't deliver on their promises. Yet a rate of return that high is mathematically impossible unless the economy grows much faster than anyone is now expecting.

To explain why, I need to talk about stock returns. The yield on a stock comes from two components: cash that the company pays out in the form of dividends and stock buybacks, and capital gains. Right now, if dividends and buybacks were the whole story, the rate of return on stocks would be only 3 percent. To get a 6.5 percent rate of return, you need capital gains: if dividends yield 3 percent, stock prices have to rise 3.5 percent per year after inflation. That doesn't sound too unreasonable if you're thinking only a few years ahead.

But privatizers need that high rate of return for 75 years or more. And the economic assumptions underlying most projections for Social Security make that impossible. The Social Security projections that say the trust fund will be exhausted by 2042 assume that economic growth will slow as baby boomers leave the work force. The actuaries predict that economic growth, which averaged 3.4 percent per year over the last 75 years, will average only 1.9 percent over the next 75 years. In the long run, profits grow at the same rate as the economy. So to get that 6.5 percent rate of return, stock prices would have to keep rising faster than profits, decade after decade.

The price-earnings ratio - the value of a company's stock, divided by its profits - is widely used to assess whether a stock is overvalued or undervalued. Historically, that ratio averaged about 14. Today it's about 20. Where would it have to go to yield a 6.5 percent rate of return? I asked Dean Baker, of the Center for Economic and Policy Research, to help me out with that calculation (there are some technical details I won't get into). Here's what we found: by 2050, the price-earnings ratio would have to rise to about 70. By 2060, it would have to be more than 100...

**UPDATE:** Paul Krugman writes:

...here are the "technical details" for today's column.

1. Rate of return: the CPI consistently rises a bit faster than the GDP deflator, because tech-intensive goods with falling relative prices are a higher share of investment spending than of consumer spending. So a 6.5 percent real rate of return in terms of the CPI is 6.8 percent in terms of the GDP deflator, which is the number I used.

2. The dividend yield falls as the price-earnings ratio rises. The calculation assumes that 60 percent of profits are used for dividends and buybacks. That's a 3 percent dividend yield at a PE of 20, but only 1.5 percent at a PE of 40.

3. I assumed thar profit growth exactly matches GDP growth, and used SSA projections from the 2004 Trustees' Report: annual from 2004 to 2010, then their growth rates from 2010 to 2015 and 2015 to 2080.

This calculation gives one major hostage to the other side: it ignores the fact that a significant fraction of aggregate profits in 2050 will be earned by companies not now in the indexes, so profit growth for existing companies will actually be smaller than GDP growth.

Basically, what I did today was invert Dean Baker's test: instead of trying to find a rate of return consistent with growth, I asked what the rate of return assumed by privatizers implies; the point is that saying "the PE must go to 100 to give the return they say" is, I hope, more comprehensible to readers than trying to explain the Gordon model of returns ....

Posted by DeLong at February 1, 2005 07:40 AM