03
Nov
2015
Reader Survey
There are no tricks here, I genuinely want to know: What do you teeming masses think Tyler, DeLong, and Krugman mean when they all refer to the “positive marginal product of capital” (in reference to possibly negative natural rates of interest)? For example, here’s DeLong, who in turn link to Tyler.
I’m going to write on this, but I want to know what you econ blog readers think they mean by that phrase.
A unit of additional capital invested will still yield a positive return, not a negative one? But that’s sorta vague.
E Harding so are you saying “positive marginal product of capital” means “the money-value of the increment in output associated with an extra unit of physical capital goods is greater than the money-value of the extra unit of physical capital goods” ? Or something else?
I would say “the money-value of the increment in output associated with an extra unit of physical capital goods which is greater than zero”.
That is: as long as you can buy a capital goods and make a profit from renting it out then the interest on lending money should also be positive.
Actually your “the money-value of the increment in output associated with an extra unit of physical capital goods is greater than the money-value of the extra unit of physical capital goods” is the correct definition that leads to “as long as you can buy a capital goods and make a profit from renting it out then the interest on lending money should also be positive”
That’s what i took Cowen to mean.
Transformer it’s ironic: Your first answer is what I think most people mean, but then you caught yourself and realized you need what I said in order to get a relation to interest.
Do you see what I mean? (This is the point I’m going to write about, which is why I say it’s ironic.)
Yeah, sure, sounds about right.
Dr. Murphy,
I’d go with “positive marginal product of capital” means the increment in real output associated with an extra unit of physical capital goods is greater than the real cost of the extra unit of physical capital goods.
How about “positive marginal product of capital” means the increment in consumption afforded by an extra unit of physical capital goods is greater than the forgone consumption necessary to acquire the extra unit of physical capital goods.
That’s good Capt. Notice though that that’s not dY/dK as others are saying matter of factly below.
Truth be told, can sign me up for the dY/dK camp Dr. Murphy. Eager to see what you have to say. I’m guessing it might have something to do with this: http://digamo.free.fr/arestis972.pdf chapter 4.
“In any case, this is an interesting case study of how weak or previously rebutted ideas can work their way back into economics.”
That about sums up the weak and previously rebutted mercantilist doctrines resurrected by Keynes in his general theory!
“What do you teeming masses think Tyler, DeLong, and Krugman mean when they all refer to the “positive marginal product of capital””?
Pretty sure they mean Keynes’ definition of the marginal efficiency of capital:
“…the rate of discount which would make the present value of the series of annuities given by the returns expected from the capital asset during its life just equal its supply price.” – General Theory, pg 135.
OK spell it out MF in terms that we all know. (I know what Keynes means by “supply price” etc. but spell it out.)
There are two ways of approaching this, one in money terms (which is quoted above, from Keynes) and the other in real terms (taking into account price deflation, which Cowen is doing).
Keynes’ treatment of returns in his marginal efficiency of capital deductions unfortunately switches back and forth between money terms and real terms. He equivocates between the two by starting with additional real incomes that results from more employment, and then claims out of this there is money hoarding out of the additional “incomes” which then requires so much additional investment that the rate of return drops to unacceptable levels, which then encourages investors to hoard money, reduce spending, and thus bring about growing unemployment once again.
It’s ridiculous but there you go.
Cowen is thinking that in an economy that is growing in real terms, there must be a positive real return on capital, and that the idea of the natural rate being negative makes no sense in this context.
Back to Keynes:
“If there is an increased investment in any given type of capital during any period of time, the marginal efficiency of that type of capital will diminish as the investment in it is increased, partly because the prospective yield will fall as the supply of that type of capital is increased, and partly because, as a rule, pressure on the facilities for producing that type of capital will cause its supply price to increase.… Thus for each type of capital we can build up a schedule, showing by how much investment in it will have to increase within the period, in order that its marginal efficiency should fall to any given figure. We can then aggregate these schedules for all the different types of capital, so as to provide a schedule relating the rate of aggregate investment to the corresponding marginal efficiency of capital in general which that rate of investment will establish. We shall call this the investment demand-schedule; or, alternatively, the schedule of the marginal efficiency of capital.” – General Theory, pg 136.
A lot is wrong in this passage (for example Keynes’ complete contradicting of the context in question, which is falling wage rates and prices of capital goods) but aside from that, what the bloggers you have listed likely have in mind for “positive marginal productivity of capital” is that we are not today in conditions where the real rate of return is negative. With a positive marginal productivity of capital, there must be a positive real “natural” discount rate. With a positive real discount rate, Cowen is asking, how in the world could the natural rate be negative?
DeLong is responding to Cowen by saying it is possible for there to be positive return on capital and very high unemployment which in DeLong’s more extreme devotion to Keynesianism than Cowen, can only be cured a massive increase in “demand” that is massive enough to offset the usual evil corporations investing in “financy type stuff” rather than workers producing widgets.
Then he rambles rather aimlessly and closes with saying the Fed starting with Greenspan is no longer worried about “demand” but rather with interest rates.
To sum up, they likely mean this: “If I invest in a machine that costs $10 million today, I will be able to earn some positive money income of say $1 million a year in sales, as my machine is used to produce a positive number of widgets.”
Keynes is talking about the price of a new piece of capital which I doubt they’re talking about. I assume they’re talking about dY/dK. Aside from that just being the definition of the term I think it’s also implied by his treatment of risk separately (so it’s not an expected rate of return on capital IOW, although it’s an important component of it).
Pretty much the same here: d F(K,L) / d K > 0.
OK Daniel and Toby, that’s what I think they all mean too. But I wanted to poll people before proceeding with that assumption.
(Hint: That doesn’t directly have anything to do with the real interest rate.)
It does if that particular piece of capital happens to be the very item on the margin which (in a hypothetical perfectly liquid capital market) is what all investors are considering whether to invest in or not.
And of course presuming that the curve of available investments is continuous and differentiable (that is to say, something exists on the margin at all possible investor preferences). Those conditions of perfect liquidity and continuous differentiability are admittedly somewhat idealized.
Yeah, and this is also ignoring risk factors and the difference between real return and the expectations of return, but let’s just suppose the investment community figure out a way to adjust for all that.
Tel, I said that dY/DK > 0 doesn’t directly have anything to do with r>0, and you said:
It does if that particular piece of capital happens to be the very item on the margin which (in a hypothetical perfectly liquid capital market) is what all investors are considering whether to invest in or not.
So please elaborate. Use an example, say.
Suppose (just examples) you have a bunch of potential projects to work on:
* a steel mill would offer a yield of 5% on investment,
* an oil refinery would offer 4%,
* a gold mine would offer 3.1%,
* a silver mine would offer 2.9%,
* a new federal highway would offer 2%.
Also suppose the investors all have a time preference such that they want 3% real return on their investments (pretend there’s no inflation or something). So the investor deciding whether to build the steel mill will be happy because she gets more than she was hoping for, so let’s build that steel mill… so on it goes and they build the oil refinery, and the gold mine.
However, once those things have been built, investors cannot just keep going back and building yet another steel mill expecting 5% return, because there’s already plenty of steel on the market. So all the good investments are used up now.
Investors thinking about building the silver mine will hem and haw a bit and think to themselves, “Hmmm, that silver mine only offers 2.9% but I would really want 3% so it doesn’t seem worth it”.
What happens is the job that sits on the margin is the one they are scratching their heads over whether to build or not, will be the one at the point where expectation of yield is equal (or very nearly equal) to the time preference of investors. That’s the marginal case.
It does require that you have sufficient spread of potential projects to choose from such that something does exist around that marginal region. However, usually in a large economy there will be a great many possible things you could do with the same money, so it isn’t a crazy presumption. I’m also ignoring risk here and presuming investors just adjust their expectation to correctly devalue risky ventures, in reality it’s more complex, but that’s the approximation.
Just to follow up on that, if the capital market is not really liquid you might not get capital flowing to each item in turn like the example above.
The federal highway might get built first because all this additional government department budget is available and if they don’t spend it this year they won’t get it next year.
Banks might be investing into mortgages mostly because Ginnie Mae is offering them mortgage insurance rather than because the return is really attractive.
I suspect there’s heaps of cases where you can find capital that doesn’t get allocated in a nice sequential manner from highest return to lowest return.
Tel, you’re saying if we assume a bunch of projects have positive financial rates of return, then we can conclude the interest rate is positive.
OK, but that’s not showing anything about physical capital goods.
If Tel assumes price inflation is zero, would not a positive financial return imply a positive real productivity of capital?
“OK, but that’s not showing anything about physical capital goods.”
Welcome to the Dark Side, my friend.
😀
Major.Freedom,
True, unless the projects he’s talking about are early recipients of new notes, before price inflation hits.
That same thing will happen for whatever investors preference might me. If investors are happy to keep handing out money right down to 0.001% return then all those prospects better than 0.001% will get funding.
The remaining prospects we can conclude must be a worse return than those investors are willing accept. So exactly where that threshold falls, depends on when the money stops coming. If you scroll up I did say:
Thus, it is conditional on where the operating margin happens to fall. My example picked a fairly arbitrary 3% not intending that to be set in stone or anything.
To the best of the investors’ ability to evaluate the return on investment, based on looking at those physical capital goods. I mean the rubber has to hit the road at some place… if we have a financial system completely decoupled from physical products there would be no way to make choices.
And yes I understand that investment decisions need to tie up a bunch of other factors beyond just the goods themselves such as prevailing prices, expected demand, competition, new technology, changes in material and labor costs, etc. I figured that spelling out those particulars would not add significantly to the main point.
Sure, if you have sufficient distortions in a system, all sorts of outcomes might happen. It’s very difficult to reason about that, because in the presence of largely arbitrary outside influence… it pretty much defeats any simplifying assumptions.
I think Cowen’s point is that it is incredibly unlikely that the natural (or Misesian “originary”) rate of interest is negative if the global economy is growing and investing in capital still yields productivity gains.
On the latter point, see my forthcoming comment below.
I’ve got a pretty good idea of what Tyler Cowan means, just be reading him:
Not quite at the Murphy level of crystal clear elucidation, but still fairly readable.
So “positive marginal product of capital” just means there is something useful you can do with your savings, so that you get some sort of real return.
Brad DeLong on the other hand; I read over several times without any great confidence of making sense of it. On a guess, I would say that although Cowan talks about whether the economy can put resources to productive use, maybe DeLong is talking about whether typical investor sentiment is expecting that the economy can put resources to productive use. That is to say, perhaps because of generally negative emotions we have a situation where although potentially something might be beneficial to invest in, nobody believes it, so nobody does it. This might be caused by (for example) extreme sovereign risk so people expect their profits to be confiscated.
From Henry Hazlitt, Failure of the ‘New Economics’ p169
What a clever guy!
Tel great find with that “rare” quotation. That’s perfect. (But I am still asking you about your claim about dY/dK etc.)
What I understand Cowen to mean is that investing in additional capital will still increase production by more than the money invested in capital. I.e., if I invest $X in capital today, that investment will yield $Y = ($X + a) in the value of what I product (all variables > 0 of course).
If economic growth is positive, then we expect the future to be better than the present.
If the marginal product of capital is positive, then we expect that capital investment today will pay off tomorrow.
Since both of those things imply a time-preference biased in favor of the future, then there would have to be something absolutely terrible happening to labor or technology to yield negative natural rates of interest. And since no one really thinks there are any such factors happening to labor or technology, then it’s almost certain that the natural rate of interest is positive.
That’s what I think Cowen means. DeLong seems to think that there are enough offsetting factors in low-risk investments and consumer sentiment that the natural rate of interest might still plausibly be negative. But that’s a hard sell to me.
The marginal product is a derivative. Saying it is positive is saying it is greater than zero. That implies you get more out than you put in, capital investment still pays.
Craw, but then that means Cowen is saying, “The natural rate is positive because interest rates are positive.” That doesn’t seem as deep as the way he wrote it.
I think I erred. I said get out more than you put in. All it means is putting more in gets more out, not that you get more out than you put in. If production rises 1 after I put 2 in, the derivative is positive. So my statement above is wrong. Agree?