Comments and Discussion

N. Gregory Mankiw: This paper by Baker, DeLong, and Krugman is really three papers in one. The first paper is a straightforward review of how population growth affects the return to capital in standard models of economic growth. The second paper is a discussion of what return one should expect for the stock market in the coming decades, given current measures of valuation. The third paper offers some ruminations about the equity premium.

What links the three papers is their motivation. President Bush has called for reform of the Social Security system. According to the Social Security actuaries, the system faces large unfunded liabilities. That conclusion, however, is based on a projection that includes much slower labor force growth (and thus economic growth) than the United States has experienced historically. This raises the question of what rate-of-return projections should be assumed as the nation considers possible reforms.

When evaluating reform proposals, the Social Security Administration uses a projected real annual return on equities of 6.5 percent (which, given the trustees' assumption about the risk-free rate, implies an equity premium of 3.5 percent). Paul Krugman has written elsewhere that "a rate of return that high is mathematically impossible unless the economy grows much faster than anyone is now expecting."¹ This three-in-one paper began as an attempt to justify that assertion. I will discuss each of the three papers in turn, before addressing the policy motivation.

Population and Growth Theory.

The first paper in this paper reviews several standard neoclassical growth models. The aim is to see what these models predict for the relationship between population growth and the rate of return to capital.

The Solow growth model gives a clear answer to this question: slower population growth lowers the rate of return. Because the saving rate is fixed, slower population growth raises the steady-state capital-labor ratio, which in turn means a lower marginal product of capital. The Diamond model gives a similar answer, at least for the functional forms assumed here.

The Ramsey model, however, leads to a very different conclusion. In that model the saving rate adjusts so that the rate of return is invariant to the population growth rate. This adjustment of the saving rate is economically intuitive: if there are going to be fewer people in the future, we need to save less for the future.

This conclusion is the essence of the analysis presented in a 1990 Brookings Paper called "An Aging Society: Opportunity or Challenge?" written by David Cutler, James Poterba, Louise Sheiner, and Lawrence Summers.² They used a standard Ramsey model to argue that, "the optimal policy response to recent and anticipated demographic changes is almost certainly a reduction rather than an increase in the national saving rate." I should note that national saving is currently low by historical standards, but I will not suggest that this is necessarily the "optimal policy response" that Cutler and his coauthors were proposing.

Realizing that the Ramsey model does not support the main contention of the paper, Baker, DeLong, and Krugman propose a new but unpersuasive generalization of it. The authors claim that the standard Ramsey model is one of "perfect familial altruism." That is not how I would describe it. Even the standard Ramsey model includes discounting, so that my utility is weighted more heavily than that of my children and grandchildren. What the proposed generalization does is make the effective discount rate for future utility depend on the population growth rate. When population growth slows, the effective discount rate falls, and this fall in the discount rate blunts the decline in the saving rate that occurs in the standard Ramsey model.

Is this generalization appealing? Not to me. As the parent of three children, I can attest that one of the things parents do when child N is born is to assure the N - 1 children that they will be loved just as much. The generalization of the Ramsey model proposed here is, in essence, a denial of this claim.

In the end it is clear that the tools of modern growth...