Last Thursday, Tyler Cowen posed an exam question for his macro class, consisting of a passage from a Michael Mandel column in Business Week, and the inquiry, “True, false, or uncertain?” The passage in question read as follows:

“Let’s do the calculations. Over the past 10 years, the U.S. has run up an accumulated goods and services trade deficit of roughly \$3 trillion. Sounds like a lot of money, doesn’t it?

Now let’s suppose those dollars had been used for good rather than evil. That is, rather than buying imported cars, toys, and handbags, thrifty Americans would have saved their money. It’s reasonable to believe that about half of that \$3 trillion would have gone into financing productive purchases here in the U.S.–new factories, power plants, office computers and the like–\$1.5 trillion worth.

So what would be the payoff from all that thriftiness? A reasonable rate of return on investment, after depreciation, is roughly 7%. So \$1.5 trillion in extra assets would have a return of about \$100 billion a year.

That \$100 billion is roughly 1% of an \$11 trillion economy. Over ten years, then, complete elimination of the trade deficit might–might–have added a tenth of a percentage point to growth.

That’s a good measure of the size of the virtues of savings–roughly a tenth of a percentage point on growth. That’s 0.1 percentage points.”

If the passage seems unclear, that’s because it is. As many complaints as there are about the mathematical formalism of economics, it provides a great deal of clarity– and I’ll leave it as an exercise to the reader to translate Mandel’s argument into mathematical form. Mandel’s an intelligent guy, but it seems that he’s put together an unusually muddled argument.James Hamilton tackled Tyler’s question using basic macroeconomic theory, and found that:

“If the U.S. were to increase annual investment spending by \$400 billion from the current \$1.9 trillion, that would represent about a 20% increase in s, implying eventually 10% higher real income per U.S. resident…

Is 10% more income per person a big deal? I would say that it is, though Mandel is certainly correct that, if we had some policy that could make even a modest change in the productivity growth rate, it could potentially have a much bigger effect over time. The problem is that I’m not sure what such a policy would be. Certainly insofar as productivity gains result from firms’ investments in new technology, the way to get those gains is through additional investment, which Pro-Growth Liberal logically sees as another reason why saving can indeed matter a great deal.”

In the process of finding a higher predicted growth rate due to savings, Hamilton corrects Mandel’s stranger assumptions, like the idea that only half of an increase in savings would go into financing productive purchases– does Mandel think that the other \$1.5 trillion would go into mattresses, or was he assuming that the other half would be used to invest overseas (implying an increase in exports), or was he just not thinking when he wrote that piece?

Yesterday, Mandel wrote a rebuttal, in which his thinking becomes even stranger. He accepts Hamilton’s calculations, but argues that,

“Hamilton says that a 20% increase in the savings rate would increase real income per person by 10%. Unfortunately, he doesn’t say how long that will take. Is it going to be 10 years, 20 years, or 30 years? It makes a difference. If it’s 30 years, then the increase in growth over that stretch is roughly 0.3 percentage points.”

His insistence on expressing increases in growth in percentage points rather than in percent should ring alarm bells, because it’s a rhetorical technique, not a logical argument. The average growth rate of the U.S. economy over the past 75 years has been between 3.5 and 3.6%. Thus, a 3.5 percentage point increase in average growth is equal to a 100% increase in the growth rate of the economy. A 0.3 percentage point increase is an 8.5% increase in the rate of growth. A 8.5% increase in the average rate of growth of the economy is nothing to scoff at.

More importantly, assuming that it would take 30 years for increases in the savings rate to raise the standard of living by 10% and calculating the additional growth rate over that 30 years is disingenuous. It relies on the assumption of a long time horizon for the benefits of saving to materialize, which is a significant assumption. More importantly, phrasing the argument in this way is a dodge– if a 20% increase in the savings rate could lead to a permanent increase in real income of 10%, over a lifetime that’s a pretty good deal.

Hamilton notes that finding a policy that could make “even a modest change in the productivity growth rate” would be an even better deal, but said that he doesn’t know what such a policy would be. This is polite, to say the least. Productivity growth is largely exogenous– investments in education and technology development are probably the only ways to affect it, and these are not sure bets by any means. This isn’t to say that they’re not investments worth making; however, the gains from these investments may not materialize for several decades if at all, and their magnitude is not predictable. Mandel ignores all this and pretends it’s a sure thing that would certainly be cheaper than increases in the savings rate:

“Hamilton says he doesn’t know a policy for increasing productivity growth. I’ve got a simple one–how about increasing government spending on basic research, especially in the area of energy technologies? Or is he assuming that current levels of government R&D spending are optimal?”

In addition to calling to mind H.L. Mencken’s declaration that, “For every problem, there is a solution that is simple, neat, and wrong”, this passage should raise some eyebrows. Mandel suggests that we spend more money on basic research. This is fine, even advisable, but how does he propose paying for it? We can either cut investment or cut consumption. A decrease in investment would offset an increase in research expenditure and thus be inefficent. I would actually be highly inefficient, as traditional investment is always required to take advantage of new technologies. To put it more intuitively, even if we developed a more efficient technique for making bobble-head dolls, we would need to buy new equipment to be able to use such a technique.

Thus, Mandel must either be trying to have a free lunch, or he is clearly advocating for a reduction in consumption to cover the added research expenditure. At the same time, though, he decries the fact that added savings would require a reduction in consumption:

“Moreover, he also doesn’t point that the real consumption per person is actually reduced by the amount of additional savings…

So here’s the situation. The pro-savings people are asking us to accept a sure decline in living standards today, in exchange for the possibility of a moderate increase in income somewhere off in the future.”

He pulls this same stunt, in which he recognizes a tradeoff in a plan he dislikes, but fails to acknowledge that it exists in his own, with the aforementioned tradeoff between research expenditure and increasing savings. He assumes that when Hamilton suggests cutting the budget deficit, that Hamilton would do so by reducing government spending, not by increasing taxes. Thus, cutting the budget deficit would mean decreasing research expenditure. This is true, if we accept his assumption of a constant tax rate. However, he doesn’t note the converse, which is that increasing research expenditure without increasing taxes would increase the budget deficit (and thus decrease investment, as noted before).

If we strip away the nonsense, Mandel has some good points (which makes the nonsense that much harder to bear). His observation that the savings rate ignores investments in education and research, while not unique, is a valuable one. Macroeconomic accounting would certainly be improved if expenditure on these things were grouped as a type of investment (ideally, separate from capital expenditure– the traditional notion of investment), rather than as consumption. The primary reason it is not is probably that while education spending is easy to quantify, spending on research and development is not. Research doesn’t only occur as a result of direct research spending by the government, it also occurs as a result of traditional investment creating demand for capital improvements combined with the suppliers’ desire to differentiate their products. Many of the productivity improvements that come from this process don’t come from research labs, but rather from engineers who create better ways of doing things in the daily course of designing new products. It’s unlikely that the amount of private spending on research and development is uniform, either within or across industries, meaning that constructing a reliable measure of this form of investment is probably very difficult.

Mandel’s point about the importance of education and research, if I may stretch it a bit, is probably strongest when we consider the topic of “pure” scientific research. This is the type of research that is most sensitive to public funding, as its products may have no apparent commercial application at the time, making private firms unlikely to invest in it. Many of these innovations have turned out to be extremely valuable in the long run– making public spending on pure science a wise investment. The benefits of this relative to savings, and whether such government-directed investment should compete in areas where commercial investment is likely, are questionable. Mandel argues here that “technology-based improvements in productivity can boost productivity growth and national wealth without requiring an increase in the national savings rate,” but he neglects to mention, as stressed before, both that there’s no way to simply spend one’s way towards technology-based improvements in productivity, and that some level of savings is necessary to realize these improvements.

To quote Hayek:

“It is because every individual knows so little and, in particular, because we rarely know which of us knows best that we trust the independent and competitive efforts of many to induce the emergence of what we shall want when we see it.

Humiliating to human pride as it may be, we must recognize that the advance and even the preservation of civilization are dependent upon a maximum of opportunity for accidents to happen. These accidents occur in the combination of knowledge and attitudes, skills and habits, acquired by individual men and also when qualified men are confronted with the particular circumstances which they are equipped to deal with. Our necessary ignorance of so much means that we have to deal largely with probabilities and chances.

Of course, it is true of social as of individual life that favorable accidents usually do not just happen. We must prepare for them.”

This should provide some guidance as to optimal policy. We do not know if or how much of a gain can be provided by government-directed research. We thus do not know if investment in research is a better idea than investment in capital improvements (and thus, indirect investment in private research). We do know that individuals who see better ways of doing things can benefit from developing such improvements, and that this can occur without the role of government. We also know that the benefits from increased savings are real and all but guaranteed. Finally, we know that pure science research is something that will not occur without government support.

Thus, we can conclude that addressing national savings through cutting the budget deficit, while not something the business crowd would like to consider, is probably a good long-run idea. It’s a variable that we can control to predictable, positive effect. Likewise, government investment in pure science is a good idea. However, government-sponsored research into applications of science is a bad one– it can be accomplished more efficiently by the private sector– however much the business community might like more subsidies.

A final note: in this link, where Mandel points out that “technology-based improvements in productivity can boost productivity growth and national wealth without requiring an increase in the national savings rate,” he’s merely stating a basic macroeconomic assumption about long-run growth. The rest of his argument, with the “lots of charts and graphs” he proudly mentions elsewhere, is painfully weak. He manages to ignore lags in productivity growth and ignore every other factor– he manages only to disprove the assertion that savings are the only input to productivity growth and have an immediate effect– an assertion nobody has (to my knowledge) ever made. Most macroeconomic indicators are heavily dependent on multiple factors, so the fact that no Phillips Curve appears when one graphs two indicators should never be a surprise. That’s why we use regression analysis– it controls for other factors and makes our analyses more meaningful.