Comment on “Comment on ‘Asset Returns and Economic Growth ‘ by Baker, Delong and Krugman by N.Gregory Mankiw” by Robert Waldmann

Mankiw’s comment is well written and is the right length. No surprise at all given the commenter. It is also very polite and quite favorable by the standards of Brookings Panel comments. I very much liked one point “The natural response to this theoretical ambiguity is to muster evidence, either from timeseries data or from the international cross-section, about the actual effect of population growth.” [footnote: I would add that, in the impossible case that economic theory were not ambiguous, it would still be necessary to look at the data to see if the theory corresponds to reality. When I say “impossible“ I do mean to say that the core assumptions of economic theory can not possibly have either testable predictions or policy implications so the implications of economic theory always depend on particular assumptions which no one finds plausible.]

Mankiw’s particular points are much less interesting largely because they do not, in general, amount to criticisms. It is difficult to write an interesting comment on a paper which makes a point which is obvious, but which policy makers have chosen to deny.

Mankiw’s first semi-criticism is that Baker Delong and Krugman (BDK) start with the Gordon formula which calculates returns from the dividend yield and the growth rate of dividends by assuming that they are constant. This approach has been criticized by people who claim that dividend payout policies might change. Mankiw notes that this criticism of the BDK argument is clearly invalid, since it is made without rejecting the assumptions of the Modligliani Miller model in which payout policy does not matter at all to investors. Oddly, he presents this as a mild criticism of BDK, because, he seems to say, according to Modigliani and Miller, dividends to not matter. If so, papers which purport to demonstrate that the stock market isn’t efficient by analysing stock prices and dividends would be totally silly and proof that their authors do not understand basic finance. Obviously, Mankiw does not really mean to say that dividends do not matter but rather that different streams of dividends consistent with the same stream of operating profits give the same returns to investors who buy optimal portfolios of debt and equity. In the end he concludes that the analysis is convincing, since BDK perform exactly the calculation which he proposes.

Mankiw then considers the open economy analysis in BDK. Here I must say that I am totally puzzled both by Makiw’s analysis. BDK argue that if profits earned by US based corporations are to grow much faster than profits earned in the US, US based corporations will have to invest much more abroad than foreigners invest in the US. They note that there is no sign of this happening and it is extremely implausible that it would happen on the massive scale required. They implicitly assume that investment by different agents earn roughly similar returns.

Mankiw argues that even if investment flows balance, US firms might earn more and more profits abroad if foreigners invest more and more in the US. In the simplest possible standard model rational investment and efficient financial markets would imply that all investments pay the same expected returns, so the difference between profits earned in the US and profits earned by US based firms would not be affected. Mankiw must be thinking of some other model. I can think of two.

First possible foreigners are irrational so they invest in the US where returns are low rather than in other countries where the returns are high. Thus US firms and their shareholders could benefit by exploiting the errors of foreigners. I am sure that this is not what Mankiw has in mind.

Second, US firms might have access to superior technology, organisation or managerial human capital than is available abroad. This would mean that they earn higher returns than foreign based firms (whether the profits are earned in the US or abroad). The word available is important. It is not enough that some foreign firms be inefficient. This must be what Mankiw has in mind.

In particular he, and Baker, consider the possibility that US based firms will invest directly abroad and that foreigners will buy their shares financing this investment. This is supposed to imply higher returns to current shareholders than would otherwise be possible. This is very odd. In the simplest model of the firm, all investors including new investors earn the marginal product of capital leaving nothing left for others. In less simple models entrenched managers somehow divert cash to themselves. I know of no model in which current shareholders gain some of the marginal product of new investment at the expence of the new investors who finance it.

Of course I can think of one. Current shareholders elect xenophobic managers and change the rules so they can not be removed. The xenophobes offer discounts on goods sold in the US to shareholders. This benefits US based shareholders but not foreign investors. Or maybe the xenophobes can predict exchange rate fluctuations and time dividends for periods in which the dollar is undervalued. I think these are about the most plausible such models and note that, when I said it was always possible to come up with a model to make any prediction, I didn’t say that all such models pass the laugh test.

I will assume that all shareholders of a firm must earn the same returns. If so, even if a firm can earn supernormal returns, selling shares to new investors who would otherwise have to accept a lower return current shareholders will not benefit. The assumption implies that the returns to technology will be shared proportionally to share ownership, so the part corresponding to investment financed by foreigners will go to the foreigners. Now consider if the firm does not issue new shares and foreigners buy from current investors. Imagine two steps. First the firm sells new shares to foreigners and invests overseas. So far no gain to current investors. Second the firm buys back shares from US based investors. Mankiw assuumes that share buybacks are essentially equivalent to increased dividends and according to Modigliani, Miller and Mankiw can make only a small difference to current shareholders.

Another way to look at it is that the problem according to BDK is that, given a low GDP growth rate, the capital ratio in the US will increase implying lower returns on capital. For this to cease to be true in an open economy it is necessary for the US private sector to run a capital account deficit (current account surplus) to get rid of the capital. Otherwise one would have to assume that firms are investing in the US earning a low return and abroad eaning a high return. That is US firms would have to be irrational (and Mankiw is certainly not assuming that).

This brings us to the growth models which BDK use to argue that slow growth implies an increase in the ratio of capital to effective labor (labor corrected for labor augmenting technological progress). In the Ramsey Cass Koopmans model, the standard but extreme assumption of perfect intergenerational altruism implies that dencreased population growth causes saving to dencrease enough to keep the capital labor ration the same as it would have been. BDK note that anything less than perfect altruism implies that, in this model as in others, decreased population growth implies a higher steady state capital labor ratio and a lower return on capital. Mankiw does not argue that perfect altruism is plausible. Rather he considers the fact that an extreme assumption implies zero effect while all others imply the same sign means that the effect is ambiguous. I certainly agree with him that this is an emprical question which should be addressed with data, but that is more because, like BDK, I don’t trust the models than because I consider a limiting case of zero to mean that the theory is ambiguous.

Mankiw’s case would be much stronger if he presented an example in which decreased population growth implies an increased return on capital. This is always possible, but I find this difficult. If people in the US cared more about those who will live in the USA in 2500 than about themselves (including all of the offspring of imigrants) then there were be more than perfect intergenerational altruism so the effect of population growth on saving would outweigh the effect on labor supply. Aside from that, right now I can only think of models in which for the same capital stock, the marginal product of capital is lower if the population is higher. This can happen if there is another key factor of producion in limited supply (land say or maybe energy) and increased population reduces the supply for firms (that is increases the rent they must pay on unimproved land or the price of energy). It is really hard to make such a model consistent with a stable return to capital, and, of course, impossible to reconcile it with available data. These models don’t pass the rotflmao test.

Mankiw is not at all thrilled by the BDK model of the equity premium. Neither, for that matter, are BDK. They describe it as “the simplest crudest and most extremely ad-hoc model of the equity premium.” I skipped that section of the paper. I just read it and I have to say that I agree with BDK and Mankiw. I think it is included because the paper is a not so veiled critique of Bush’s secret welfare reform plan and the plan can be defended by claiming that the equity premium is not justified by risk. BDK mainly note that, if they believed the equity premium is overlarge and likely to remain so, they would advocate having the social security administration invest directly, as proposed by Clinton and Reagan.

Finally Mankiw argues that he supports personal accounts for reasons other than estimates of the return on investment including personal accounts Here I agre, that is, I oppose personal accounts and would even if share prices dropped so much that the return on equity became very high. In that case I would go with Clinton and Reagan. Brad DeLong, however, disagrees.