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Very interesting post, Nick, as always. Not totally off topic, but I recently made an introductory video on nominal GDP path targeting that I originally linked to on Scott Sumner's blog. If you have a bit of time to kill, have a look and let me know what you think:


In retrospect I should've framed the section on liquidity traps a bit differently, but understand that my target audience is folks on the fence about market monetarism.

It's a WCI classic! Logical reasoning, artful exposition, a model that holds together perfectly ... until you try to use it as a description of the real world. Sort of like one of those gorgeous modernist chairs that looks great in the living room, just don't try to sit in it.

I invite you to perform the following exercise. Let GDP be your expectation for GDP 25 years from now, or whatever you think is the relevant horizon. Now ask, is E(GDP) < GDP? I feel confident saying the answer is No. (Productivity in Canada is growing a lot faster than the workforce is shrinking, and that's leaving aside the possibility of increased immigration, etc.) So g is positive. Now, is the natural rate of interest lower than the growth rate of GDP? Again, I feel confident that your answer is No. In which case i > 0. But suppose you allow that maybe i < g? You're still out of luck, because as we've discussed here previously, that means the government can Ponzi-finance itself indefinitely. No need to tax the young to pay the borrowing back, so no intergenerational transfer in that case either.

Conclusion: If desired private savings only equal desired private investment at a negative interest rate, then the government can and should borrow enough to bring the interest rate up to zero (or whatever the practical minimum is). because, given that overall growth is still positive, there's only two ways this situation could arise. Either private investors are applying a discount rate higher than the natural rate of interest, in which case debt-financed public investment has a positive present value; or the natural rate of interest is below the growth rate, in which case the Ponzi finance option is available, a free lunch which the government should eat.

(Oops, in the second paragraph that should be "Let E(GDP) be your expectation..."

Steve is really on to something about the non-equilibrium nature of the Great Moderation and how this will require ever larger central bank interventions however it does so and you have another reason for the deficiency of interest rate targeting. I would put it in intragenerational terms. Increased transfers due to an increased elderly population induce the wealthy to flee real assets and seek money as the next generation will not be able to pay much for them so only if we can deter this through increased inflation will we be able to stem the demand for money, though I doubt this would even lead to much inflation other than in real asset values. The money drop would just be a more effective and neutral means of doing so.

I love Steve's post. The constant decline of interest rates from c. 1980 to 2008 always bugged me. It has to have an explanation. It also incorporates credit standards as a mechanism aside from the interest rate, which I regard as key.

When interest rates cratered in 2008 I thought "Gee, for probably the only time in my life I can accurately predict where nominal interest rates are going to go: up." See constant Globe & Mail exhortations to lock in your mortgage at 5-year rates as this is a once-in-a-life time (or very long time) opportunity.

Sounds like a great argument for allowing more young foreign bakers into the country...

JW: if r less than g *permanently*, because of (say) permanent population growth, then yes the economy is dynamically inefficient, and needs a bubble/ponzi/bigger debt free lunch. There's always more young people who want to buy the old people's bonds. But that's not the same as Frances' example, where there's a temporary baby boom.

I'm grading midterms, so can't spend much time on comments. Sorry.

Edit. Warning: don't use the "less than" sign in comments. Weird things happen, as I just rediscovered.

Public service announcement: the less-than and greater-than signs can be used by writing out their HTML entities in the comment field, viz. &lt; (<) and &gt; (>) respectively.

Maybe I'm missing the point of this post but why would interest rate be negative in this situation ? I'm not sure I understand why in this situation "there just aren't enough profitable investment projects to match desired saving even at a zero real rate of interest"

Even if total aggregate production were declining with the size of the workforce then I see no reason why price spreads would not adjust to maintain profitability and still make it worth while for businesses to borrow at a positive rate. Prices would be rising if the money supply stayed the same, so there would be an inflation premium on interest rates anyway.

If this is true then rather than burying goods in the ground would not the aging population be better off investing in the stocks and bonds of businesses ?

This would mean that when they stopped working and start consuming their capital then the structure of productive would have to change to reflect the
additional need for food and consumer goods. Profit spreads would have to increase to reflect this change in time preference and this would be reflected in downward pressure on real wages (though these might increase anyway due to the increase in demand for labor as the workforce shrinks).

In a free market I believe it would be this rather than taxes and government inspired inter-generational transfers that would solve this problem.

Rob: "If this is true then rather than burying goods in the ground would not the aging population be better off investing in the stocks and bonds of businesses ?"

What would those businesses invest the proceeds in? If those businesses invest in burying goods in the ground, it's no different.It's only when those businesses that find other real investment projects, where labour today, makes goods that can be consumed in 20 years, that this works. Robots would be good.

As long as the baby boomers consume less and save more when they are working then these savings would automatically lead to increased investment in capital goods and to higher productivity and a greater capacity to produce consumer goods in the future when they stop working (and saving). In addition, as you suggest, forward-looking capitalist who understand the trend could also invest in things that would exploit the changing demographics - like robotic baking machines, more capital-intensive farms (and possibly even storage systems).

If people are free to plan for the future then changing demographics should not create any unsolvable problems for the free market.

Rob: take the extreme case. Suppose there is only one person in the next generation? How productive do you think the capital would be, with only one worker and all those machines? Burying canned food might be a lot more productive form of investment.

And remember: free markets can't push us outside the (intertemporal) production possibility frontier. When they work perfectly, they can get us to the best point on the PPF. Sometimes the PPF we face is a nasty one. Neither free markets, nor government, can solve that one.

Right, since you've raised such a Hayekian point, might I point you to Roger Garrison's Time and Money which lays out the relationship of the PPF to the temporal production structure of the economy and the loanable funds market in three linked diagrams on one page?

As Roger would have it, we can expand, or try to expand, the PPF by investing. That is what Rob is describing. But that assumes that investment cannot fail, which is false. Given our present knowledge and technical ability, can we expand the PPF sufficiently? Maybe yes, maybe no. It depends. We have to try.

It is possible, but perverse, that our investments in additional capacity actually reduce capacity because of the inputs they require. We need a breakthrough and we don't have one.

That is, regardless of money, additional capacity will require additional inputs that must be taken from existing production. There is no net expansion.

Good point, under some (presumably unlikely) circumstances then productive capacity may not be able to sustain the population and stocks of consumer goods and food would be needed to survive.

I believe that as an economy approached this situation that market signals (futures markets for foods etc) would indicate to capitalists (and individuals) that the most profitable capital goods to produce would move away from being machines , factories etc , and become future consumer goods to be manufactured and stored. These goods could then sell for a premium or be consumed by the owner in the future.

In this case I do not see how inter-generational transfers are relevant. If not enough stuff is being produced , and there are not enough stores of stuff to draw on, then here is a problem that only prior market-driven or state planning could solve. Would NGDP-targetting help in any way with this scenario ?

And to complete the thought: I think that if (and when) producing consumer goods for storage becomes a profitable form of investment then banks could still earn a non-negative rate of interest lending to business in this line.

it seems to me you are empirically challenged here. The worst hit economy is the US and the least hit (until now) the German economy. But the demographics are the other way around.

And if it was baby boomers savings that were driving the low natural rate of interest (rather than an overvalued exchange rate as I think), wouldn't the US be running a trade surplus.


compare with


Don't you think you are setting yourself as a target for OWS?

All joking aside, I was bit upset you didn't reply to my comment - but I guess this is your reply. In general, I guess that we have to agree to disagree. On the policy side (I'm definitely on Steve's side). Except that I think we should have ALREADY been doing the helicopter drop and it should be a massive automatic stabiliser.

f r less than g *permanently*, because of (say) permanent population growth, then yes the economy is dynamically inefficient, and needs a bubble/ponzi/bigger debt free lunch. There's always more young people who want to buy the old people's bonds. But that's not the same as Frances' example, where there's a temporary baby boom.

Well, one would have to work through the math to see if it's the same or not. It's not obvious. It seems to me that if interest rates are negative over any finite period, then the government can increase its net worth, and hence reduce the present value of the future tax burden, by borrowing more for that period. Why do you think borrowing in this situation would increase the future tax burden?

But anyway, that was an aside, about the unlikely case of r less than g. You think that r is generally greater than g. So if demographic changes haven't reduced g below zero, what makes you think they've reduced r below zero? Why does slower population growth not only reduce the natural rate of interest, but reduce it relative to the growth rate?

More broadly, suppose that we have a baby boom (which isn't actually that big relative to normal population growth, but whatever) such that for to periods t1 and t2, there is an unusually low ratio of desired consumption to income in t1 and an unusually high ratio in t2. Frances says that there is nothing to be done, people who want to consume in period t2 are just going to get less. But that's not what economics says. Economics says that we should produce a greater quantity of long-lived assets in period t1, when desired consumption is lower. This will raise output in t2 and later periods. This is why we think, in general, that countries with higher savings rates have higher levels of growth. You've introduced here, in an ad hoc and completely unexplained way, the assumption that the marginal product of capital has fallen to zero or below, so that there is no way for increased savings to boost growth. Do you really believe this?

Anyway, even if it were true, your and Frances conclusion *still* wouldn't follow, because even if there is no private investment than can be profitably made at t1, public spending can still be shifted from t2 to t1. In the baby boom situation, the logical conclusion is that any government spending with a reasonable degree of intertemporal substitutibility should be moved forward from t2. So right now we should be building/repairing lots more roads, schools, bridges, water mains, etc. than usual.

"Stop whining" reflects a certain temperament or political commitment. It's not economics.

One can argue we have done the best we can by building so many homes which are as long lived as it gets. We just have to liquidate the debt acquired along the way.

Sometimes the PPF we face is a nasty one.

Not here on planet Earth, tho, at least not based on demographics in Canada.

Statistics Canada projects that the share of the Canadian population between 20 and 64 will fall from 63 percent to 55 percent over the next 25 years. (Overall population growth will slow by only a trivial amount -- from 1.1 to 0.95 percent annually.) In recent decades, real Canadian GDP growth has been about 3 percent, meaning it doubles over 25 years. So demographic changes only reduce growth by about 10 percent. Even if you believe that labor productivity will be slower in the future (rather than faster as economics says should result from slower labor force growth), demographic effects are just not that big. Even GDP growth of 1.5 percent -- half the historic norm -- gets you 45 percent growth over 25 years, dwarfing the ten percent fall in the labor force. There's no remotely plausible way to get from actual demographic trends to a negative natural interest rate, or any shortage of real resources to provide an adequate standard of living to both workers and retirees, now or in the future.

The problem is not the PPF. The problem is finance and the distribution of income, not technology and demographics. The only reason to say "you cannot solve this problem" is if you don't want to solve it.

One can argue we have done the best we can by building so many homes

Sure ... if by argue you mean assert.

Here in the US the housing stock is actually well below trend at this point -- the shortfall over the bust considerably exceeds the excess construction during the bubble. I wouldn't be surprised if the same is true for Canada.

More broadly, I think people are tossing around the idea of negative natural rate of interest (nnri) without thinking through its full implications.

Let's say you think there is a nnri between periods t1 and t2. That is equivalent to saying that there are no capital goods produced in t2 such that the return from t1 to t2 would exceed its carrying cost over the same period. Is this a realistic description of any existing economy?

Imagine all the long-lived goods that will be produced next year --- all the houses, office buildings, roads, cars, machinery, software, etc. Now suppose I offer you the use of any of those goods you like for the next year, at no charge whatsoever. All you have to do is make good any using-up or wearing-out that happens during the year you have it. All the income you can get out of it is yours to keep. The claim that there is a nnri is equivalent to saying that there is not a single good to be produced next year, for which any actor in the economy would find that offer worth taking. No house or office that can be rented for more than the cost of its upkeep, no machinery that produces output worth more than its operating costs, etc. It's an extraordinary claim that would require extraordinary evidence to support it; no such evidence has been offered.

JW: any good that is costlessly storeable will have an own real rate of interest that cannot be negative. But if other goods are not costlessly storeable, then it depends on the technology, and if there will be enough workers in future to specialise in producing those goods.

Take the simplest possible example: wheat (costlessly storeable) and haircuts (produced by labour only, with zero technical change). If there are few future workers, the relative price of haircuts in terms of wheat will rise. If the boomers are storing wheat, the real rate of interest measured against the price of wheat will be 0%. But the real interest rate measured against a basket of wheat and haircuts will be negative.

(Actually it's even stronger than that. For the natural rate of interest to be negative at t1, there must be no good that generates income at least equal to its carrying costs between t1 and *any* future period. So for Frances' story to work, it's not enough that's impossible to store bread to eat when you retire in 20 years. It must be impossible to store anything at all.)

if other goods are not costlessly storeable, then it depends on the technology, and if there will be enough workers in future to specialise in producing those goods.

But that only matters if production of all goods whose return exceeds their carrying costs has already been shifted forward to the initial period. In other words, the natural rate of interest between two periods cannot be lower than the lowest own-rate of interest of those goods produced in both periods.

So I agree that the fact that houses - let's say - produce output in excess of their storage costs over some period, does not in itself prove that the natural rate of interest cannot be negative. But that fact, plus an expectation that houses will be produced at later dates within the relevant period, does prove it. Right?

You're right, JW Mason. Nobody wants to discuss income distribution, which is intertwined with ability to get a good job (using your full skill set based on education and experience. No university grads in call centres or flipping burgers).

ISTM Market Monetarists don't want to go anywhere near that question because it brings up taxes, redistribution and "socialism" right away.

Speaking of politics, the C.D. Howe Institute, which Nick is associated with, just brought out a recommendation that RRSP contribution limits be eliminated. The limit is 18% of income or $22,000. Few get caught but this.

As far as an income-related policy recommendation goes, it was out to lunch. Nonsense, absolute nonsense.

JW: interesting. I had to think about that one. If you had a linear PPF between houses and haircuts in each period, and if houses were still being produced in the future, then I think you would be right. Because that linear PPF pins down the relative price of houses and haircuts (as long as both goods are being produced in both periods). So if the own rate of interest on houses were non-negative, so would the own rate of interest on haircuts. But if that future PPF were non-linear, the transfer of future resources away from houses towards haircuts would require an increase in the relative price of haircuts. So the own rate of interest on haircuts would be negative. So the consumption-weighted average own rate of interest would also be negative.

JW: "Here in the US the housing stock is actually well below trend at this point -- the shortfall over the bust considerably exceeds the excess construction during the bubble. I wouldn't be surprised if the same is true for Canada."

This is just a BTW. It's *very* different (so far) in Canada compared to the US. There was only a small drop in house prices in Canada a couple of years back, then it recovered and kept on increasing (on average across the country). Construction did not collapse like in the US. Some Canadians (including me) worry that prices are getting a bit high and we have a bubble here, at least in some parts of the country. There was no (real) bust.

Here's our version of Case Shiller: http://www.housepriceindex.ca/

BTW guys: It's possible some of you are missing the point of this post. Maybe I wasn't clear enough.

Steve Waldman asks how NGDP targeting would work in a world where the natural rate of interest was driven down below zero. He also gave a story as to why he thought the natural rate could be driven down below zero. I would have argued with his story, but that seemed pointless to me. Because it is theoretically possible to have a negative natural rate of interest, even if Steve's story doesn't work. So I would be ducking his question. So I gave my own story, borrowing from Frances, of how the natural rate could be negative, and then said how NGDP targeting would have to work in that context.

If you don't think the natural rate of interest can in fact be negative, OK. Then I don't have to worry about how NGDP targeting would handle such a case. But I think it is theoretically possible. Empirically likely? Maybe not. But it *could* happen.

And the problem with Steve's story, by the way, is that even if you grant all his assumptions, you still have to face the question I've posed here: if the borrowers borrow up to the hilt, and can't borrow any more, why can't the savers just invest, or store goods?

reason: empirically, I don't know how much of the natural rate can be explained by demographics over the last few decades. My hunch is that global demographics are unprecedented. In the past, most people either died young, or worked till they died. Very few people were retired, or expected to be retired for very long. And my hunch is that global demographics are a biggie, and are a lot to do with what has been happening to real interest rates over time. I might be wrong. But it is theoretically possible. And it's theoretically possible for demographics to create a negative natural rate. That's all I needed for this post.

Germany has other countries to lend to. And China lends to the US. One big global capital market with perfect capital mobility might be too strong. Especially since some goods are non-traded, and political and economic risk varies a lot. It's not obvious to me how demograhics in one country and global demographics fit together to give a pattern of interest rates across countries.

"All joking aside, I was bit upset you didn't reply to my comment - but I guess this is your reply."

I'm a bit lost. I have had a lot of different conversations going on all over the blogosphere. My ADD is an occupational disease. I'm not sure which comment you mean. I can't keep up with everything. But I'm sorry you are upset.

if that future PPF were non-linear, the transfer of future resources away from houses towards haircuts would require an increase in the relative price of haircuts. So the own rate of interest on haircuts would be negative. So the consumption-weighted average own rate of interest would also be negative.

You're right, and I was wrong. We can't rule out a negative natural rate of interest as easily as I thought. Well, that's the good thing about these debates -- one learns from one's mistakes.

I still don't think it's a useful description of real world economies, though. But since it seems you don't think so either, you were just using it to frame a what-if question, I won't continue arguing the point.

It's *very* different (so far) in Canada compared to the US.

Interesting. The OECD has a construction index. I should have looked at that before speculating. And sure enough, Canada looks very different from the US in terms of construction volume as well as prices. Construction here is down by two thirds from the peak; for you guys, it's not down at all.

From an Austrian perspective as the natural rate of interest is based on time preference it can never be negative. One would always prefer 10 apples now to 10 later, other things being equal. I would argue that comparing goods now compared to a future where productive capacity is greatly reduced is not comparing the same good. Given knowledge of the future scarcity it may be a valid choice based on time preference to choose 7 apples in the future over 10 now - they are in effect different goods. Assuming time preference stays constant over time then the (inflation-adjusted) prices of apples and the factors needed to produce apples will adjust to keep the rate of interest on apple production constant and positive even as the cost of apple production rises and the output of apples declines. At some point as the workforce shrinks the best way (in terms of resource usage) of producing "future apples" will be to store "current apples" (by freezing them ?) for later sale and consumption.

My conclusion: The real money rate of interest will always be positive in equilibrium as if it dropped to zero their would be no incentive to produce anything for the market. The "own" rate of interest is not a valid measure when present goods cannot be compared with future goods because of future scarcity (like the famous "ice in summer" v "ice in winter" example).

Rob: you have misunderstood the Austrian perspective. Yes, according to the Austrian approach, the (natural) rate of interest is a subjective phenomenon. And maybe (or maybe not) there is *pure* time preference, in the sense of preferring 10 apples today to 10 apples in future. But you have forgotten that equally important part of the Austrian perspective. You have forgotten the *at the margin* bit.

Suppose you expect (I originally wrote "know", then remembered how totally un-Austrian that would be :) ) that your tree will produce 12 apples this year and 8 apples next year. *At the margin* you will (very probably) prefer one *extra* apple next year to one extra apple this year. The rate of interest is the *marginal* rate of time preference.

OK, I am assuming you cannot store apples at zero cost. If you could, and if you are storing some apples, that means your marginal rate of time preference must be zero.

You are right about it being "expectations" that is driving his decisions rather than "knowledge" and I agree that the "at the margin" bit is key.

I think however it was implicit in my post. Based on expectations about current and future productive capacity an individual will choose the combination of present and future goods that will equalize his utility at the margin. It is important to note that that the calculation of future utility will factor in his rate of time preference,

For example: Assuming he could store apples at zero cost and he has 20 apples and he decides to consume 11 and save 9 apples. The discounted marginal utility of his 9th apple in the future equals that of his 11th in the present. He is choosing to store apples but has a positive time preference. I'm not sure about the concept of "marginal rate of time preference" and how that fits in. It is his pure time preference and his discounted "marginal utility" that is driving the decision.

Rob: OK. Draw an indifference curve between present and future consumption. Pure time preference (aka time preference proper) is the slope of that indifference curve where it crosses the 45 degree line. Marginal rate of time preference is the slope of that indifference curve at the actual point, which may be off the 45 degree line.

Roughly, marginal time preference = pure time preference plus the ratio of the marginal utilities.

I think a similar use of time preference and marginal utility that drives the money rate of interest. It is the rate where the demand for money (from individuals whose time preference will lead them to equalize their marginal utility for present and future goods by borrowing money at that rate) with the supply of money (from individuals whose time preference will lead them to equalize their marginal utility for present and future goods by lending money at that rate).

Thanks for the clarification. As long as one accepts the validity of indifference curves then the concept of marginal time preference makes sense and is useful. I still don't get how the interest rate would end up being set to this though rather than the rate of interest derived from pure time preference (as described by the Austrians). Is there a simple explanation?

Not sure if you are still monitoring this but I thought it through some more and now think;

- You are correct, in a world of falling productive capacity then you can in theory get negative natural rate of interest. The incentive to invest then comes from the greater real loss made from holding cash combined with the necessity of planning for the future.

- The negative rate of interest will be the market signal that will encourage greater investment in capital that increases productivity , and for businesses and individuals to save physical goods for the future since if wastage and storage costs were less than the negative rate of interest this becomes the most "profitable" strategy.

- The negative interest rate would be reflected in a rate of inflation being greater than a positive nominal interest rate. It would be very bad if the government tried to set a zero or low inflation target. This would make holding cash the best option and destroy investment.

Rob. Yep. Still following. Don't always have time to respond.

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