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Nick,

you're completely missing the point.

In a world with money you hoard that because the storage cost of money in a savings account is pretty close to zero. After all, the bank doesn't even physically store the notes. Furthermore, without expected inflation money looks like an even better investment than can beans. Money has a lower storage cost, less depreciation and can be more easily turned into consumption when the time comes.

The problem is that money, a non-produced good, has a superior risk-return profile to the canned beans.

Nobody ever said that in a world without money the negative full employment interest rate would cause a recession.

Also, Nick says "But if you expect the relative price of beans to fall, you must expect the relative price of some other goods to rise."

Well, sticky prices is also a problem. With fully flexible prices the negative interest rate would also not cause a recesssion. Prices today would fall relative to prices tomorrow and this would set up the expected inflation that delivered the negative real rate and maintained full employment.

Notice as well, in the world with sticky prices, money and no expected inflation, while it may be that the real rate is negative on the full employment consumption path, the real rate you ACTUALLY OBSERVE IN THE ECONOMY is not negative. People still want to satisfy their euler equation so consumption today falls relative to expected consumption tomorrow until the new consumption path is consistent with a non-negative real rate. That's why we get a lack of demand.

The basic condition has nothing to with money per se, however the fall in consumption comes about when combining this basic condition with a world that has money and sticky prices and not enough expected inflation.

Notice also, I said "fall in consumption". I did not say recession. The real question is why doesn't investment demand go sky high with a negative real interest rate. I've already explained in several places that this is due to the precence of a risk premium that keeps the required return on real investment above zero (and above the required return to holding money as an investment good).

But you can have negative nominal interest rates on a savings account. It's currency where it's technically harder to have negative interest rates.

Why is storing beans risky, if I know I will want to consume beans next year? They are safer than money, if inflation is uncertain. By buying beans now and storing them, I am satisfying my demand for future beans. A "real" Arrow-Debreu future good, if you like.

I am saying that there cannot be a negative full employment real rate of interest, under plausible assumptions about storage costs and relative prices, so even in a world with money we can't empirically get an absolute liquidity trap.

Or rather, I am questioning the empirical plausibility of a negative full employment real interest rate and absolute liquidity trap, in a world where beans etc., exist.

Does this mean you've decided to ignore my question on your "Scott Sumner's plan for monetary policy" post about whether Scott's plan would really "elimnate the liquidity trap"?

This post does not answer it.

I wasn't talking about a world without money. (And all my other posts, on excess demand for money being the proximate cause of a general glut, show I agree that you can't have a general glut in a world without money, regardless of the natural rate.)

This post was not intended to answer your question on Scott, Adam. I'm not ignoring it. But it is a hard question. If I can think of some sort of intelligent answer I will post it.

How do you know what real interest rates are?

This is a serious question - people may have expectations about future inflation, but that comes with a degree of uncertainty. People KNOW what the nominal rate of interest is. That is a significant difference.

reason, we don't.

However, the theoretical argument is worth having because it has real policy implications. You don't know what supply and demand curves look like either, other than perhaps at the single point where they intersect.

Nick,

I understood that we weren't talking about a world without money, my comments never assumed that you were.

Nick,

I think your theory ignores depreciation (although you could consider it a storage cost). Buying a can of beans today is worthless if I want to consume it in 10 years and it goes bad before then. Also, some goods cannot be purchased well in advance (airplane tickets and golfing green fees are two that come to mind).

Also, if we all rushed out to do our consumption today because of a negative natural interest rate, wouldn't that drive prices up really high and exhaust supply in the short run? It seems to me some of us would be willing to wait a while for supply to replenish and then purchase items at a lower price if that were the case.

Can't seem to post multiple paragraphs, will try again later.

Nick: "By buying beans now and storing them, I am satisfying my demand for future beans."

But is future beans what I'm demanding or is it future consumption in general, my entire consumption basket? Since beans are storable if I have an excess demand for future beans then yes, this can be satisfied by supplying more beans today.

Now, same question for money.

Is future money what I'm demanding or is it future consumption in general. Since money is storable if I have an excess demand for future money then yes, thic can be satisfied by supplying more money today.

Here’s some home spun musing on a topic that seems insane to begin with. There's a fair chance that 100 per cent of the following is wrong:

Is there a difference in the implication of negative real rates for consumer goods and investment goods?

I’m not sure why one would focus only on “The demand to store newly-produced goods as part of investment demand.” Why not focus on the other part of investment demand?

Hoarding consumer goods is limited by storage costs and/or by durability.

But the world would also be less capital intensive - a world that instantaneously produces demanded output on a “just in time” basis and without investment requirement.

There is a distinction between hoarding food financed by consumer borrowing, and real investment financed by borrowing.

There is not one real rate, negative or positive. A constellation of real rates is defined according to risk premiums.

If the real risk free rate is negative, and the real risky rate is less negative, then the risk premium is positive. Example is a bank with negative real rates on deposits that are more negative than negative real rates on loans. The risk premium for the expected real return on equity is still positive.

The most negative real rate by definition should be the real risk free rate.

The least negative, or the most positive, should be the riskiest expected return; e.g. junk bonds, or high risk equity.

Consumer borrowing rates are one type of real rate. Consumers can arbitrage the real interest rate on borrowing if it less than expected inflation plus the cost of storage. Presumably this is true whether the real rate is positive or negative. If storage is 5 per cent, deflation is 2 per cent, and the cost of borrowing is minus 3 per cent, the consumer breaks even. Presumably consumer rates adjust to preclude arbitrage in equilibrium.

For investment purposes, negative real rates seem consistent with a less capital intensive world. Economic investment is not the same thing as hoarding of newly produced goods. The latter is a consumer inventory or arbitrage function. But if investors earn a negative real rate of return on economic investment, they have the incentive to consume now instead of invest. In equilibrium, this implies that capital goods would constitute a smaller proportion of total output. The economy would become “lighter”. Because the natural requirement for capital investment is lower, real rates are lower.

Therefore, under negative real rates, the equilibrium for consumer borrowing is an arbitrage free condition. The equilibrium for investment is an economy with less capital intensity.

Perhaps consumption is bounded in a similar way to interest rates. Positive real rates move the consumer to a lower bound on consumption. Negative real rates move him/her to an upper bound.

Seems the idea of negative real rates in equilibrium is nonsensical. If real rates are negative, people will attempt to borrow to arbitrage time preference in consumption. But if such arbitrage is possible, you get a contradiction between the assumption of negative real rates in equilibrium and the assumption for inflation. Similarly, if there is zero real investment, there is no requirement for borrowing, and real rates go negative in equilibrium.

JKH: "If real rates are negative, people will attempt to borrow to arbitrage time preference in consumption. " No. Suppose your consumption today was 100 (units of the consumption basket) and tomorrow your consumption was 5. Futhermore, suppose you need 10 units of consumption to live. Suppose the real interest rate was -50%. Would you borrow 10, consume a total of 110 today and zero tomorrow? Or, would you consume 90 today, saving 10? Saving 10 gives you 5 more tomorrow so your total tomorrow is 10 and you live. Even at -50% real return you are willing to save.

my point is simply that aggregate desire to save depends on how much consumption is available tomorrow. If it is likely, or feared, that consumption will be relatively scarce tomorrow then you might save at zero or negative rates of return.

I guess my post meant that I'm not sure I know what is meant by negative real interest rates at equilibrium, since it means that the nominal interest rate is below inflationary expectations - this belies the question - whose inflationary expectations? If expectations diverge and there is considerable uncertainty about future inflation, couldn't it be possible that with a heterogenous population your thought experiment has aggregation errors. And given uncertainty of course, arbitrage is not possible, speculation is. So risk aversion becomes an important parameter.

Adam P,

I said:

"Negative real rates move him/her to an upper bound."

I think you just identified the upper bound.

but reason, even though my example was extreme but surely it shows that there are times when an individual might save at a negative rate of return. If that's true of one then why not of all?

In real life sometimes people actually do hoard canned beans.

JKH, yes you're right. I didn't read the whole comment, just took the last statement out of context. Sorry. I don't really agree with the upper lower bound characterization though. I think you just equalize the ratio of marginal utilities with the relative prices.

Adam P,

You wrote:

"it is likely, or feared, that consumption will be relatively scarce tomorrow then you might save at zero or negative rates of return"

Doesn't "might save" imply an upper bound on today's consumption?

Couldn't such an upper bound be consistent with "you just equalize the ratio of marginal utilities with the relative prices"?

It would just imply some ratio going asymptotic to some line, but I can't visualize the right one.

Maybe there's a numerical example of how this works?

My view is that it is technically possible for real rates to be slightly negative, but nevertheless that Nick's theory might well be "true enough" to have some very practical implications. In my research on the Great Depression I came across two competing views of the real interest rate. One view said that the deflation of 1929-32 was partially anticipated, and hence ex ante real rates were pretty high. Another group said that the deflation was basically unanticipated, and thus that ex ante real rates were pretty low. I don't have an ax to grind here, if anything my "monetary" approach to the Great Depression might have tilted me toward high real rates. But I came to the conclusion that real rates were pretty low, because the deflation was mostly unanticipated. Here was my reasoning: The goods that are easiest to arbitrage (commodities) are traded in auction-style markets, and their prices follow something close to a random walk. Other sticky prices may respond with a lag, and hence be somewhat predictable, but they will be difficult to arbitrage. In my model if there is a monetary policy that reduces the future inflation rate sharply, then commodity prices should fall precipitously, and other prices should respond with a lag. I think that is roughly what happened last fall. Now let's turn this around to Nick's expected inflation scenario. Could the expected inflation rate ever exceed the nominal interest rate? This should be easy to check. Do commodity futures prices (as a class) ever show expected changes that exceed the nominal interest rate on equally risky investments. If I understand Nick correctly, he is saying no. My hunch is that he is right.

reason: what Adam P said. Yes, it is hard to observe people's expectations of inflation, and there may be different expectations for different people and different goods. But this is more of a theoretical point.

Some people have argued that in certain circumstances the real rate of interest would need to be negative in order for demand for goods to equal the "full-employment" supply of goods. In other words, the natural (real) rate of interest is negative. In other words, the IS curve crosses the x axis and hits full-employment at a negative real interest rate. In other words, since nominal interest rates cannot go negative, we could only have full employment equilibrium at positive expected inflation. And maybe that is the problem today, and is causing the current recession. (And I'm one of those "some people", in that I have at least thought it might be possible.)

Now, there certainly is a theoretical possibility this could happen. I (or Adam) could easily come up with an example of a world where goods were not storable, and where people thought they would be poorer in the future, where the equilibrium real rate of interest in a non-monetary economy would be negative.

But I am now arguing that maybe it is not empirically plausible that we live in such a world.

There are some goods that can be stored at very low cost. Even if the expected average rate of inflation were zero, some goods will be expected to rise in price (and others fall). All we need is one good for which the expected rate of relative price increase exceeds the storage cost, and the demand for that good would be indefinitely large, so that aggregate demand would be bigger than full-employment aggregate supply, even if nominal interest rates were zero, and average expected inflation were zero.

Adam says we need to consider risk, when deciding whether to buy goods to store or hold currency instead. He's right. If storing goods were risky and storing currency were were safe, we would need the safe real interest rate to be negative, to cover the risk premium, before we would store goods (leaving aside relative price changes and storage costs).

But I would argue that storing beans can actually be less risky than storing money. If I know I will want to eat beans next year, beans are a safer investment than money, because if I store money I am uncertain about how many cans of beans that money will buy. Safety is defined in terms of utility, and future consumption, not in terms of money. (Think of the Consumption-based Capital Asset Pricing Model). The safest form of pension plan is to buy now all the goods I will want to consume when I retire, then I don't face any risk of changes in the price of those goods.

That ignores the risk of theft, of course. But the risk of my cash getting stolen is higher than the risk of my beans getting stolen, I would argue. Thieves accept a massive discount to fence goods and turn them into cash.

Now, what about a risk premium in lending money? If the safe real interest rate is zero, but I can only borrow to invest in stored goods at a potive real rate, to reflect the risk I might not repay the loan, I might not buy beans for storage.

But for every borrower there's a lender. If the potential lender thinks loans are risky (and they are), he won't lend money at a zero rate, so I can't borrow it at a zero rate. But that doesn't matter. The potential lender won't lend, and he won't store cash. He will invest in beans himself. In other words, we don't need riskless capital markets for this to work. Savers invest directly in stored goods.

JKH: The distinction between "consumption" and "investment" keeps changing. Theoretically, buying beans and storing them is investment. Buying beans and eating them now is consumption. (But Stats Can doesn't define them this way, because they don't have enough bean counters to go round every house). (Sorry!). But it doesn't really matter how we divide purchases of newly-produced goods between consumption and investment in this case; it's only the sum of the two that matters, and whether that aggregate demand is as big as aggregate supply.

In general I agree with your point, that investment by firms at a zero real rate might be indefinitely large too, not just investment by households in buying beans. But I concentrated on households in my example. Why? Because some households are savers, and hold net positive stocks of savings. They don't have to borrow from the market and pay a risk-premium to invest in beans. They just borrow from themselves. This is less likely to be true for firms.

If by "arbitrage" you mean Buying beans now, and selling them later (including selling them to yourself, to eat), I agree. We can think of negative real rates ans creating unbounded arbitrage demand for goods.

Adam: I know I addressed some of your points (like the risk premium). I might have missed some. I will post and collect my thoughts.

Scott: just saw your comment.

This is too long already.

Nick

I agree with some of the other posts that you missed the point about negative real interest rates although you actually got it too, in a way.

The expected real interest rate is the expected nominal rate minus the expected rate of inflation. If the nominal rate is zero, that's as low as it can go but if you can somehow make people expect inflation, you have created a negative expected real interest rate.

You're right that that would make people want to buy more beans. They expect the price to go up, so buy now if you have the money. But that's the whole point. You've just stimulated spending by dropping the real interest rate, just as you would have if you dropped the nominal interest rate in normal times, when that option is available.

Scott: You say that most goods that are easy to arbitrage tend to be traded in auction markets and so have flexible prices. If you mean "arbitrage" literally, I think you are right. Buy now and sell later works best when the goods are fungible commodities, so can easily be traded on auction markets.

But storing goods for your own later use is like arbitraging with yourself. You buy beans now, and "sell" it back to yourself in the future at a "price" equal to your future opportunity cost. So it would work even if there were no resale market, or very high transactions costs in resale.

This means that the goods we might want to buy and store might not be "commodities" and might have sticky prices.

Paul: Yes, I should probably have prefaced the whole thing by saying: "Is it possible that the economy could get into an absolute liquidity trap because the real natural rate went negative, or is it only possible if monetary policy mistakes cause expected inflation to go negative?" I would then argue the latter.

A world with a declining population can have a negative real rate of interest. More people would attempt to save for their retirement while there will be fewer to produce then. There would be less need for capital investment and existing investment would be consumed over time. Over long periods of time, nothing would store value because there would be fewer needing them in the future. All storable goods would lose value compared to perishables, and attempting to sell stored goods to purchase perishables would only diminish their relative value faster. The best one could do to try to find what would lose the least value such as inputs to the production of perishable goods, but only the lowest cost producer as falling demand would remove marginal production out of use.

I think Keynes has already addressed this problem in chapter 17 in “General Theory.”
http://www.marxists.org/reference/subject/economics/keynes/general-theory/ch17.htm

In his example economy of house, wheat, and money in this chapter, the following equation consists in equilibrium:
a1 + q1 = a2 - c2 = l3
where a1 is expected percentage appreciation (or depreciation) of houses, a2 is that of wheat, c2 is carrying cost of wheat, l3 is liquidity premium of money. Here he assumes yield on money is negligible; i.e. nominal interest rate is zero.

In this equation, it is possible that some weighted average of a1 and a2 (= overall inflation rate) exceeds l3. That is, real interest rate in equilibrium could be negative. And as l3 is unobservable, we cannot know from data if this is really happening.

Nick,

a simple example of how a natural real rate that's negative might happen is posted here: http://canucksanonymous.blogspot.com/2009/05/purpose-of-this-post-is-to-explain-what.html

Just to follow up on this comment:

Nick: "By buying beans now and storing them, I am satisfying my demand for future beans."

But is future beans what I'm demanding or is it future consumption in general, my entire consumption basket? Since beans are storable if I have an excess demand for future beans then yes, this can be satisfied by supplying more beans today.

But if what I really want is more of my whole consumption basket (and assuming beans are a very small part of that) then storing beans only satisfies my demand for savings if I can sell them later.

Now, for the sake of argument let's assume that I can sell my beans later, as can everyone else. If we all hord beans today and try to sell them tomorrow their value will fall tomorrow and since we all know this we infer a lower real return from bean storage and are discouraged from the practice (thus avoiding high demand for beans today). However, if their is a central bean repository that is committed to maintaining the price of beans and is expected to reduce their supply next period then we may well end up hoarding beans.

Same for money, if the central bank is committed to support the value of currency then it may be hoarded but if the promise to reduce the future value of currency (inflation) then we are discouraged from hoarding it. But it is the expected future value that matters, not how much they supply today.

Finally, on your last point of whether it is a micro economic problem if their is an excess demand for canned beans due to their use as an investment good. If demand for beans suddenly exceeds our capacity to produce beans and their price is sticky then what that is is an adverse productivity shock, very much a macro event. Futhermore it is an endogneous productivity shock that can be avoided simply by promising future inflation, that is by lowering the real rate of interest.

Lord,
like your post.
himaginary,
you forgot to explain what q1 is (the rate of growth of the stock of housing?)
Nick
I was going to post a reply to your post but then I read the post above -
what Adam P just said.

Lord,
though in fact, you must admit the story with a declining population is more complicated - real wages should rise, so superior goods should appreciate.

>you forgot to explain what q1 is (the rate of growth of the stock of housing?)

Sorry. Let me cite the explanation of Keynes here:

Let us, for purposes of illustration, assume that on houses the yield is q1 and the carrying cost and liquidity-premium negligible; that on wheat the carrying cost is c2 and the yield and liquidity-premium negligible; and that on money the liquidity-premium is l3 and the yield and carrying cost negligible. That is to say, q1 is the house-rate of interest, -c2 the wheat-rate of interest, and l3 the money-rate of interest.

Nick: "But if you expect the relative price of beans to fall, you must expect the relative price of some other goods to rise. So store one of those other goods instead."

And if I think the prices of all storable goods will fall and the prices of all non-storables to rise?

Yep, if only (say) 1% of the goods you consume are storeable, this extra demand for goods today might not be enough. Depends how long the low real interest rate period would last. If you live 100 years, and only 1% of the goods you consume are storeable, you could double your expenditure for 1 year by buying a lifetimes supply of beans this year. Enough to prevent an absolute liquidity trap for one year.

But it's gotta be more than 1%.

Off canoeing. See you guys Tuesday.

Have a good time.

But you missed the point(of my 6:04 and 2:58), it's not about percentage of storables in consumption, it's about expected real returns.

hey Adam,

Just subscribed to your blog, but Canucks Anonymous doesn't seem to allow anonymous commenting:(

Nice first post. I'm really looking forward to having another great blog to read

bob, thanks.

Anonymous commenting now enabled.

It is a case of can rather than will as technological innovation can cause increased demand for the new while diminishing demand for the old providing a source for growth and a reason for positive real rates again. The most storable goods are commonly the most durable as well so the amount one would store would be limited by future need, while the most perishable would be limited by shelf life. Land, whether productive farmland or urban area would depreciate among the least if it were already at price equilibrium depending on the storage costs of taxation. Superior goods would suffer less but would not necessarily appreciate if total demand were falling. Storable goods would probably reach saturation relatively quickly since they are also hedges against inflation and would not necessarily ever be under inventoried.

Beyond that afforded by a positive real return elsewhere, that is.

I don't think anyone has yet made explicit this story:

Real interest rate = marginal product of capital less depreciation

To the extent that there's an overhang of essentially useless capital, then the MPK could well be less than the depreciation rate.

It's always worthwhile, when posing a theoretical argument, to ask yourself whether it's in fact theoretical. This one ISN'T theoretical. We've been there. Large numbers of Germans faced this sort of question before and during WWII due at first to inflation, then because of banking restrictions under the Nazis, and later with the looming certainty of defeat in war.

They didn't store beans. Beans get stolen. Mattresses aren't a "secret" hiding place any more. So what's compact (so easily hidden), imperishable (you can bury it), likely to hold its value, and not heavily regulated (unlike gold or gems)? Remarkably, back then, the answer turned out to be "optical lenses." These were hoarded in large numbers. Archaeologists thousands of years from now will be finding them in farmer's fields (if there are still farmers, then.)

But this practice DID represent a negative rate of interest, because a lens, while valuable, isn't highly liquid. Worse, individual citizens have to buy retail and sell wholesale. Even so, they were an excellent investment, in fending off later hunger. So, wise Germans did in fact accept a negative rate of interest, gladly. Unwise ones got a high theoretical rate of interest in a bank account (but by law could not withdraw the vast majority of their money, which subsequently vanished with defeat) had their property seized, or in the end looted by Russians who were quite excited by the prospect of beans.

You can still argue that the imperturbability of rule of law, better banking standards, or, or, or will fend off the possibility. But the common acceptance of a negative rate of interest is more than a possibility. It's an historical fact.

Summarizing so far, negative equilibrium real interest rate can occur from external negative shock, such as negative shock in population growth (as Lord described), or that in productivity (as Adam P described in his blog), or war (as Russell Johnston exemplified). Maybe the point Prof. Gordon noted could also be categorized into the example of external shock, because necessity of such large depreciation compared to MPK must come from technological/innovational shock, or boom-bust shock.

FYI:
Paul Krugman once asserted that negative equilibrium real interest rate in Japan comes from decline in population. (Many Japanese economists were skeptical of his assertion, though.)
http://www.pkarchive.org/others/interview.htm
"After all, one core problem the Japanese have is a prospective shortage of Japanese.
...
There is an answer, which basically is that money has to be very, very cheap, both to discourage people from saving and to encourage other people to invest. But between the demography and the banking problem and so on, the interest rate that they would need to keep demand up turns out to be negative."

He also showed a simple land-economy model in which population decline leads to negative equilibrium real interest rate.
http://web.mit.edu/krugman/www/bpea_jp.pdf
"Now suppose that demographers project that the next generation will be smaller than the current one, so that the labor force and hence (given elastic demand for labor) the real price of land will decline. Then even though land has a positive marginal product, the expected return from investing in it can in principle be negative."

Stephen,

regarding your point about the marginal product of capital being too low due to an overhang from a preceding investment boom I just did a quick post about that

http://canucksanonymous.blogspot.com/2009/05/why-do-liquidity-traps-tend-to-follow.html

Nick, hope you had a good trip! To welcome you back it occurs to me that there is another place where your agrument here goes wrong. You say about storable consumption goods, "At negative real interest rates, why wait? Why not buy them now?" Well yes, that's what we want. But, as I pointed out in my commment May, 14 2:00am, the whole problem is that while the NATURAL real rate is negative, the ACTUAL real rate in the economy is not. The actual real rate in the economy is around zero and that, of course, is the problem. If the fed promises inflation THEN we'd have a negative real rate, people would behave as you suggest and AD would rise.

Thanks Adam! Yes, I'm baaaack! It was a good canoe trip. But the weather was not good. Fine the first day. Rained all the next day. Temperature dipped below 0 one night, and then we had snow flurries. Paddled back to the base a day early in a blizzard, fortunately with following wind and waves.

I have never dumped out of a canoe yet, except once when I was very new to canoeing and tried to heel the canoe (like I had seen proper Canadians do) while sitting solo in the rear seat (big mistake), and a few times deliberately, seeing if I could re-enter from the water. But it would be really bad news to dump in those conditions. Forget drowning (I always wear PDF); it's the hypothermia that's lethal. It was a bit scary.

My brain is still a bit frozen. Even slower than normal. But let me try to wrap this thread up.

If the sum of expected inflation plus the real natural rate gets less than 0%, then we have a problem.

So if you (Adam) think expected inflation is about 0% today, and the natural rate is (say) -1%, then we have a problem. But I would tend to blame monetary policy mistakes, for letting expected inflation fall below the 2% target (the Fed perhaps doesn't have an explicit target, but does seem to have an implicit one).

If all consumption goods were costlessly storable, then the natural rate could not be negative (agreed?). (A costless storage technology is like a perfectly elastic infinite demand for investment at a 0% MPK, with zero depreciation). If none were storable, then it could go negative (under some conditions) (I agree, as I always have).

The real world is somewhere in between those two extreme cases. We have multiple goods, with different expected rates of inflation, and different storage costs. The simplest one-good macro model can't handle these cases.

If there were a small, and short duration, excess of desired savings over investment (excluding storage) at 0% real interest rate, and at full employment, then I would argue that storage could make up the difference. There are enough goods that are storeable, at very low costs, or with relative prices expected to increase, for storage to create a big enough demand for goods.

But if there were a large, and expected long duration, excess of desired savings over investment (excluding storage) at 0% real interest, and full employment, then storage opportunities would not be enough to make up the difference.

I visualise an IS curve something like this:

It slopes down, then at 0% real (or close) it goes horizontal (or near), as demand for storage kicks in. Then when storage opportunities get exhausted (savers are already storing everything than can be stored for their own future consumption), it starts sloping down again, into the negative interest rate region.

A fully worked out model would have to work out what happens to relative prices when people store. If there were perfect substitutibility between goods in production, then storage would not affect relative prices. If there were zero technical change in storable goods, but technical improvement in non-storables, then the relative price of storables would be expected to rise. Those assumptions are best if you want to make the case that storage prevents a negative natural rate. Make the opposite assumptions, and it's harder to make the case for storage.

Brain still slow. That's not as clear as I wanted it to be.

himaginary: It's interesting you bring up Paul Krugman's land example.

When I was writing this post, I wrote a whole section that I subsequently deleted. It went like this:

In high school economics I learned that the real interest rate could never go negative. The teacher's example (this was in England, and before environmentalism) was that at 0% real interest it would pay to bulldoze the Rocky Mountains and convert it into productive farmland. The NPV of the land rents, stretching into the infinite future, discounted at 0%, would be infinite, and enough to pay for any number of bulldozers.

I deleted it because I realised this example could only prove that the real interest rate cannot be permanently 0% (plus, it was a digression). As PK notes; this example doesn't stop a temporary negative real interest rate.

We are completely in agreement until here:"There are enough goods that are storeable, at very low costs, or with relative prices expected to increase, for storage to create a big enough demand for goods."
The problem here is that expected future prices are endogenous, large demand for storing these goods reduces their future price, the price that will prevail when it's time to sell them and consume again. Thus they don't end up delivering the basically zero real return, they deliver a much lower real return. Money has a central bank that most poeple believe will defend its value. Thus money is expected to deliver the higher real return and thus money is what gets hoarded.

Adam:

Assume all goods are produced under constant returns to labour: qi=ai.li.
Assume that labour is freely mobile between goods.

In this case, relative prices as fixed by the ratios of the coefficients ai/aj (as long as savers don't sell enough that production of the stored goods would go negative).

Also, assume that the ai grow at different exogenous rates over time. Some goods will have zero growth in a. Others will have high growth in a. Pick a good to store that has zero (or low) growth in a. The actual real rate of interest for that good would be negative even when the average actual real rate of interest were zero.

Sure, these are special assumptions.

I take your point that the more beans people store, the lower will be the expected rate of inflation on beans. But it does not make storage totally irrelevant. It would only make storage totally irrelevant if there were zero substitutibility in production.

But these are all differences of degree. Storage can help prevent the natural rate of interest becoming negative. We live somewhere between the two extremes of all goods costlessly storable and infinite costs of storage. Between perfect substitutibility in production (and consumption) and zero substitutibility.

>If all consumption goods were costlessly storable, then the natural rate could not be negative (agreed?).

I think what Krugman showed in his simple land-economy model is that it could be negative even in that case, though the effect of such kind of external shock (i.e. decline in population) may not be what you(Nick) want to discuss here.


And as for storable goods and non-storable goods, I think Keynes already discussed them in Chapter 17 of General Theory, as I noted in my previous comment. In his model, houses correspond to storable goods, and wheat corresponds to non-storable goods (in his notation, natural rate of houses is q1, and natural rate of wheat is -c2).
As Adam noted, large demand for storing houses reduces their future price, so a1 (expected price change of houses) becomes negative. In partial equilibrium between houses and wheat, a1+q1 equals -c2.
The problem is, again as Adam noted, money kicks in here. Natural rate of money is always positive (l3 in Keynes’ notation), so demands pour into money infinitely. To accomplish equilibrium between houses and wheat and money, the following equation must consist:
a1 + q1 = a2 - c2 = l3
So we need positive a2 (expected price change of wheat), and a1 need to become higher accordingly (whether a1 needs to be positive or negative depends on whether q1 is smaller than l3 or not). In other words, we need inflation to reach equilibrium.

And as for Nick@12:28PM, I think you're somewhat mixing relative price change and natural rate of each goods. In Keynes, they are distinguished as shown above.

himaginary: but I think land is different from consumer goods like beans.

If you buy land now, you get a future flow of beans (grown on the land). The price of land and the price of beans are not the same.
If you buy beans now, you get to consume beans at one point in the future.

When we say "the real rate of interest is 0%", someone could always reply "which real rate of interest?". There are as many different real rates of interest as there are price indices. If relative prices don't change, it doesn't matter, and we get the same real rate of interest regardless.

This was behind Pierro Sraffa's critique of the natural rate theory (and Keynes may have been responding to it). Each good has its own natural rate, since its relative price may change, so it's own expected rate of inflation may differ.

In general, I don't think Sraffa's critique works, because whichever price index we use, we just need to make sure we apply the same price index, and hence the same definition of inflation, to the natural rate and the actual rate. It's the difference between the actual rate and the natural rate that matters, so subtracting the same number from each won't affect anything.

If the central bank is targeting 2% CPI inflation (like Canada), then it makes sense to define the real interest rate accordingly. A 2% CPI inflation target should give the real natural rate (defined also on CPI inflation) leeway to go as low as minus 2% before we hit the zero nominal bound. At minus 2% real, storage starts to look like an attractive portfolio choice.

Nick,
Targets are not always acchievable.

Nick, agreed that perfect substitutibility in production combined with some storables allows the transfer of consumption from now to later. However, you need relative prices and wages to change today to cause the factors of produciton to all get moved into making storables today. Presumably sticky prices in aggregate comes from sticky prices at the single good level so you really are talking about a fundamentally different model. If you take away both nominal frictions (sticky prices/wages) and real frictions (imperfect substiutibility of factors) then of course there's no recession! I do, however, feel a real vs nominal frictions post might be in order.

>but I think land is different from consumer goods like beans.

Exactly. The point Krugman made was that even return on capital with a positive marginal product could be negative. Corollary: return on consumer goods (whose MPK is 0%) could well be negative.


>It's the difference between the actual rate and the natural rate that matters

Agreed. And the question is, in liquidity trap, what brings about that difference. In other words, what hinders the realization of equilibrium: a1 + q1 = a2 - c2 = l3
Culprit #1: l3 (liquidity-premium of money) is too large
...We still haven't found the way to decrease or diminish it.
Culprit #2: a1 and a2 (inflation) are too small
... As reason and Adam noted, price stickiness hinders the realization of inflation we need. And as you can see from the above equation, to attain equilibrium, the price of goods with lower natural rate (i.e. less storable goods) must decline more in order to have higher expected inflation. Difference in natural rate leads to relative price change (and to different expected inflation), not vice versa.


>At minus 2% real, storage starts to look like an attractive portfolio choice.

This attractiveness may help to reach equilibrium, by way of the logic I noted above. That is, because of this attractiveness, the price of more storable goods (i.e. with higher natural rate) declines less (or even rises), and expected inflation of those goods becomes smaller (or even negative).

Liquidity-trap disequilibrium occurs when money is too attractive. However, if a1+q1 is larger than l3, it could be that storable goods are too attractive. Then, and only then, demands pour into storable goods as you described. But that phenomenon could also happen when nominal interest rate is larger than zero. And haven’t we just experienced that phenomenon recently?

Nick:

Think of an economy without currency. All money is deposits. Monetary policy keeps inflation zero. The real interest rate is the nominal interest rate. There is no zero nominal bound.

Think about negative nominal and real interest rates. No inflation. Relative prices can change.

So, negative nominal and real interest rates are possible. Producing consumer goods now and storing them and selling them in the future is an investment project.

Nominal interest rates not keeping up with expected inflation so that people store goods as inflation hedges--well, OK. But I think that the cashless payments system with price level stability and negative nominal and real interest rates is the best way to get a pure "take" on what happens.

Bill: good to see you commenting here!

Yes, the cashless economy might be a good way to think about this question. Or a pure barter economy. And storing consumer goods is investment.

But if all produced goods could be costlessly stored, I take it you agree that real interest rates could not go negative? The only question is: are there enough cheaply storable goods whose relative prices would be expected to rise for other reasons without storage, to satisfy the excess demand for savings, of a magnitude that might empirically occur?

You can earn a positive carry by “investing in inflation”, when real rates are negative and the nominal (borrowing) rate is less than the inflation rate.

Can you also earn a positive carry by “investing in deflation”, when real rates are positive and the nominal (borrowing) rate is less than the real rate?

Is this problem symmetric or asymmetric? Why?

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